'ORPL D BANK TECHNiCAL PAPER NUMBER 45 WTP- 45 The International Road Roughness Experiment Establishing Correlation and a Calibration Standard for Measurements Michael W. Sayers, Thomas D. Gillespie, and Cesar A. V. Queiroz i FILE COPY i--,0---t0 WORLD BANK TEC11NICAL PAPERS No. 1. Increasing Agricultural Productivity No. 2. A Model for the Development of a Self-Help Water Supply Program No. 3. Ventilated Improved Pit Iatrines: Recent Developments in Zimbabwe No. 4. The African Trypanosomiases: Methods and Concepts of Control and Eradication in Relation to Development (No. 5.) Structural Changes in World Industry: A Quantitative Analysis of Recent Developmei No. 6. Laboratory Evaluation of Hand-Operated Water Pumps for Use in Developing Countries No. 7. Notes on the Design and Operation of Waste Stabilization Ponds in Warm Climates of Developing Countries No. 8. Institution Building for Traffic Management (No. 9.) 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Queiroz A collaborative study undertaken by The University of Michigan Transportation Research Institute GEIPOT-Empresa Brasileira de Planejamento de Transportes, Brazil IPR/DNER-Instituto de Pesquisas Rodoviarias, Brazil Laboratoire Central des Ponts et Chaussees, France Centre de Recherches Routieres, Belgium Transport and Road Research Laboratory, United Kingdom The World Bank The World Bank Washington, D.C., U.S.A. Copyright (© 1986 The International Bank for Reconstruction and Development/THE WORLD BANK 1818 H Street, N.W Washington, D.C. 20433, U.S.A. All rights reserved Manufactured in the United States of America First printing January 1986 This is a document published informally by the World Bank. In order that the informnation contained in it can be presented with the least possible delay, the typescript has not been prepared in accordance with the procedures appropriate to formal printed texts, and the World Bank accepts no responsibility for errors. The publication is supplied at a token charge to defray part of the cost of manufacture and distribution. The World Bank does not accept responsibility for the views expressed herein, which are those of the author(s) and should not be attributed to the World Bank or to its affiliated organizations. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of materiaL and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates concerning the legal status of any country, territory, city, area, or of its authorities, or concerning the delimitation of its boundaries or national affiliation. The most recent World Bank publications are described in the annual spring and fall lists; the continuing research program is described in the annual Abstracts of Current Studies. The latest edition of each is available free of charge from the Publications Sales Unit, Department T, The World Bank, 1838 H Street, N.W, Washington, D.C. 20433, U.S.A., or from the European Office of the Bank, 66 avenue d'Iena, 75116 Paris, France. Michael W Sayers is assistant research scientist and Thomas D. Gillespie is research scientist at the Transportation Research Institute of the University of Michigan in Ann Arbor. Cesar A. V. Queiroz is assistant director of the Brazilian Road Research Institute (IPR/DNER) in Rio de Janeiro. Library of Congress Cataloging-in-Publication Data Sayers, M. W. (Michael W.) International road roughness experiment. (World Bank technical paper, ISSN 0253-7494 ; no. 45) Bibliography: p. Contents: v. 1. Main report -- v. 2. Data and analysis. 1. Roads--Riding qualities--Measurement. 2. Surface roughness--Measurement. I. Gillespie, T. D. (Thomas D.) II. Queiroz, Cgsar V. III. Title. IV. Series. TE153.157 1986. 625.8'028'7 85-22748 ISBN 0-8213-0589-1 ABSTRACT Road roughness is gaining increasing importance as an indicator of road condition, both in terms of road pavement performance, and as a major determinant of road user costs. This need to measure roughness has brough a plethora of instruments on the market, covering the range from rather simple devices to quite complicated systems. The difficulty is the correlation and transferability of measures from various instruments and the calibration to a common scale, a situation that is exacerbated through a large number of factors that cause variations between readings of similar instruments, and even for the same instrument at different times and under different conditions. This need to correlate and calibrate led to the International Road Roughness Experiment (IRRE) in Brazil in 1982. The IRRE covered two categories of instruments - profilometers, which measure the logitudinal elevation profile of the road and converts this into a roughness index - and response-type road roughness measuring systems (RTRRMS's), which integrate readings of the device into an instrument- specific numeric. The analyses demonstrated a good correlation between the RTRRMS'. and between the RTRM's and profilometer records, and showed that they could all be calibrated to a single roughness scale without compromising their accuracy. Thus, all the instruments tested will give outputs which are sufficiently accurate and reproducible for comparative evaluation, but will need to be correlated to some given standard to ensure transferability and consistency over time. A large array of possible Standard Indices were evaluated, some based purely on the geometric charateristics of the road profile, some based on simulation of the road profile - vehicle interaction, and some based on spectral analysis of the roughness recorder output. These analyses, which also include measurement travelling speed, are described in the text, and elaborated in the Appendices, with ample tabulations and diagrams to illustrate the correlations. A practical manual emanating from the IRRE is contained in a companion volume in this Series, entitled Guidelines for Conducting and Calibrating Road Roughness Ileasurements (World Bank Technical Paper Number 46). Appendices contain full documentation of the data collected and the analyses performed. iii ACKNOWILEDGEMENTS The International Road Roughness Experiment (IRRE) reported here was sponsored by a number of institutions: the Brazilian Transportation Planning Agency (GEIPOT), the World Bank (IBRD), the Brazilian Road Research Institute (IPR/DNER), the French Bridge and Pavement Laboratory (LCPC), the British Transport and Road Research Laboratory (TRRL), and the Belgian Road Research Center (CRR). The Australian Road Research Board (ARRB) and the Federal University of Rio de Janeiro (COPPE/UFRJ) provided roughness measuring equipment. The University of Michigan Transportation Research Institute (UMTRI) provided personnel and computer support through contract with the World Bank. Appendix H, included in this volume, was prepared by S. W. Abaynayaka and L. Parsley of TRRL. Appendices E and G were prepared jointly by UMTRI, IPR/DNER, CRR, and LCPC. Appendix K was prepared by W. D. 0. Paterson of the World Bank. Many individuals contributed towards the completion of the IRRE and the subsequent analyses reported here, and it would be impossible to mention here all of their names. However the participation of the following people was invaluable for the success of this work: S. W. Abaynayaka, H. Hide and G. Morosiuk formed the research team from TRRL; M. Boulet, A. Viano and F. Marc formed the reesearch team from LCPC; J. Reichert and M. B. Gorski formed the research team from CRR; M. I. Machado (GEIPOT) supervised the subjective rating study and aided in the data entry; I. L. Martins (GEIPOT), Z. M. S. Mello (IRP/DNER) and H. Orellana (GEIPOT) aided in the data entry and analysis; L. G. Campos (GEIPOT) was responsible for selection of test sites, and together with 0. Viegas (IPR/DNER) provided day-to-day supervision and control of the IRRE; M. Paiva (GEIPOT) repaired and calibrated the GMR Profilometer, and worked together with S. H. Buller (GEIPOT) to provide technical support during the IRRE. Aid in the planning of the IRRE was provided by an expert working group that included W. R. Hudson, R. Haas, V. Anderson, R. S. Millard, and W. Phang. Help was also provided by A. Visser. Finally, grateful acknowledgement is extended to C. G. Harral (World Bank), who conceived the idea of the IRRE and arranged for the participation of the different agencies worldwide; to P. E. Fossberg, who supervised subsequent phases of the work by the World Bank; and to W. D. 0. Paterson, who participated during the planning and execution of the field work and had an active role in the subsequent evaluation. iv TABLE OF CONTENTS CHAPTER 1 INTRODUCTION ......................................................... I Background.a c k gr.o u...n.d. ..... ... e 1 Objcies...... e c...t i..v es .... o ........... 4 Report Organization...*..*. .. .. .*. .. 7 CHAPTER 2 EXPERIMENT .............. o. .. .oo. . ........... . . .......... 9 Subjective Rating Studies ...... .... c . ... cc. .ee... 18 Design of Experiment ... c..... ...... . ........ ... o.. 18 Testing Procedures ................................ .......... ...... a a 21 CHAPTER 3 ANALYSIS AND FINDINGS ...... ..................... ......... e 25 Overview.ooo ...... ,.......... 25 Spectral Analyses of the Road Profile ...... ................... ....... 27 Computation of Profile-Based Numerics.....o..#...o.... ............. 30 Comparison of Profile Measurement and Analysis Methods............ 41 Correlations Among Profile-Based Numerics ............ .......... .... 47 Correlation of RTRRMS Numerics..*.***.* ... o... ........ . 51 Correlation of Profile-Based Numerics with RTRRMS Numerics. .......... 57 Calibration Requirements ...... ... ...... .......... ......... .,. 65 Comparison of Subjective Ratings with Roughness Measures. ........0. 68 CHAPTER 4 SELECTION OF AN INTERNATIONAL ROUGHNESS INDEX ................ 71 Criteria for the International Roughness Index (IRI)................ 71 Definition of the IRI ........... *..**..O .......c.............o...... 73 Selection of a Calibration Reference..o ........................... 80 Classification of Measurement Methods. ............... ... .... .....o 85 Demonstration of the IRI. ...... ...................... .. ......... .. 93 Conversion of the IRI from QI and BI...... ................................ . , 96 CHAPTER 5 SUMMARY AND CONCLUSIONS ........... ... .... ... ........ . s .. . 99 REFERENCES .... . .c...... , c 105 v APPENDIX A DESCRIPTION OF THE EQUIPMENT ................................ 1o9 Response-Type Road Roughness Measuring Systems (RTRRMSs) ...... . ... 109 The APL Dynamic Profilometer.o...... ................ 115 Static Profile Measurements .... .. .. ...... ... ..... 118 APPENDIX B DATA FROM THE RTRRMSs. ............... ....... ............121 Summary of Measurements......*...*.** ..... .......121 Discussion.*#*.* *............ *. ........... .......................... . 122 Tables ............ ....... ......... ........o..o... 124 APPENDIX C CORRELATIONS BETWEEN RTRRMS MEASURES ............ ..$165 Purpose of the Comparisons....*............ ...... ........ ........ .... 165 Correlations With Objctv Rge.se.............. 166 Tables.Q ............ALYS........ .......... .........................oo... 2170 Figures lopen of t Ruhe .................... 184 MtPPEN DIX D SUBJECTIVE RATINGS ...........................207 Experiment of .Q ..in th oIR.e ... ................. 193 Da ta Normalization o..o..#.. ....................... ..... ....... .e..193 Example Correlations With Objective Roughness Ileasures ..... .*................................ 196 APPENDIX E QI ANALYSIS ............... .................. .................. 203 Development of the QI Roughness Scale..* ......... ............ .... 204 Mathematical Definitions of the QI Scales S...ot..........io...... . 207 Measurement of QI in the IRRE ............................223 Calibration of RTRRMSs ...... ................................... . 231 APPENDIX F QUARTER-CA R SIMULATION E................................... 249 Development and History** ..... .*................. 4 Mathematical Definitoon of th e Quarter-Car Si mulation ............... 251 Computational Details. .... .#. .... ..*. ... . ............................. 262 Measurement of RQCS Numerics in the IRRE ...... ................................... 273 Calibration of RTRRMS ..o.... s...*................... ........ .... oo... 294 APPENDIX G APL ANALYSES USED IN EUROPE ................................................ 317 Description of the APL Summary Numerics ............................... . ............. 318 Findings from the IRRE.... ............ .... ......................... 323 Example APL Profiles ......... .................... . .............. ..... . 346 Conc1usionso..e.&.o..o. ....... ....................... a-* ........... 353 vi APPENDIX H TRRL PROPOSALS FOR ROAD ROUGHNESS CALIBRATION AND STANDARDIZATION ....................... ............... o.*.......357 Introduction.. . ............. ***. . .. . *** **.357 TRRL Beam Profile Analysis................................ .357 Interpretation and Discussion of Results ........................... .363 A Standard International Roughness Index*..*.......... ........ *..... . . 367 Proposed Method of Calibrating and Standardizing of RTRRMSs.........369 Validation Study in St. Lucia ...... ... ..eo.... .371 Tablesosooo .................................. .0.................374 Figures ............ o.... o... ...... ........ o.*.... *..o*.................402 APPENDIX I SPECTRAL CONTENT OF ROAD PROFILES ........................... 405 Power Spectral Density (PSD) Functions ................. .405 Spectral Contents of Road Profiles ................................. *.407 Sensitivity of Simple Variance to Measurement Methods ...... .......411 Summary of the PSD Data from the IRRE............ ..**e*......412 Comparison of the Different Measurement Methods .....................413 Charts of PSD Functions-* ... ... ........................ ... .e*.416 APPENDIX J ADDITIONAL ANALYSES WITH THE MOVING AVERAGE ................. 429 Mathematical Definition of the Moving Average ........... 429 Bandwidth of the Moving Average.*...... .... ... ............ ..... 431 Effect of Sample Interval............ .......................0432 Comparison of Dynamic and Static Measures of CP ..................... 435 APPENDIX K SUBJECTlVE ESTIMATION OF ROUGHNESS BY SCALE DESCRIPTOR METHOD. ........................ ............................ . 443 Experimentoo .... ...- - ..... ....-v443 Data Analysis..o..ot..o...*.o.. L oo..,o,oo..,,*,444 vii LIST OF ABBREVIATIONS AND ACRONYMS Note: English equivalents are given when abbreviations refer to non-English expressions. ARRB - Australian Road Research Board APL - Longitudinal Profile Analyzer ARS - Average Rectified Slope ARV - Average Rectified Velocity BI - Bump Integrator BPR - Bureau of Public Roads CA - Asphaltic Concrete CAPL25 - APL Coefficient (of roughness over 25 m) COPPE/UFRJ - Federal University of Rio de Janeiro CP - Coefficient of Smoothness CRR - Road Research Center, Belgium GEIPOT - Brazilian Transportation Planning Agency GMR - General Motors Research GR - Gravel HCS - Half-car Simulation BRD - The World Bank IPR/DNER - Road Research Institute, Brazil IRRE - International Road Roughness Experiment IRI - International Roughness Index LCPC - Central Bridge and Pavement Laboratory, France NCHRP - National Cooperative Highway Research Program, United States PSD - Power Spectral Density QCS - Quarter-car Simulation QI - Quarter-car Index (originally) RARS - Reference Average Rectified Slope RARV - Reference Average Rectified Velocity RBI - Refererice BI Trailer Index ROCS - Reference Quarter-car Simulation RMS - Root-mean-square RMSD - RMS Deviation (from a linear regression line) RMSE - RMS Elevation RMSVA - RMS Vertical Acceleration RTRRMS - Response-type Road Roughness Measuring System SR - Subjective Rating TE - Earth Surface TRRL - Transport and Road Research Laboratory, Great Britain TS - Surface Treatment UMTRI - University of Michigan Transportation Research Institute viii SUMMARY The International Road Roughness Experiment (IRRE) was proposed to find, the best practices appropriate for the many types of roughness measuring equipment now in use. At the same time, the IRRE was planned to provide a means for comparing roughness data obtained by different procedures and instruments. This research was needed because different methods used for characterizing road roughness are generally not equivalent. In some cases, the measures are neither consistent nor stable with time. Thus, utilization of roughness data can be difficult, particularly when considering roughness data obtained by more than one method. Ideally, a standard roughness index could be used to eliminate most of these problems. The IRRE was held in Brasilia, Brazil in 1982, and was conducted by research teams from Brazil, England, France, the United States, and Belgium. Forty-nine (49) test sites were measured using a variety of test equipment and measurement conditions. The sites included a full roughness range of asphaltic concrete, surface treatment, gravel, and earth roads. The equipment included two categories. In the first--profilometric methods--the longitudinal elevation profile of the road is measured and then analyzed to obtain one or more roughness indices. Both manual quasi-static methods and high-speed profilometers were used in the IRRE. In the second category--Response-Type Road Roughness Measuring Systems (RTRRMSs)--a vehicle is instrumented with a roadmeter device. The roadmeter produces a roughness reading as the result of the vehicle motions that occur while traversing the road. Seven RTRRMSs participated in the experiment, including five that consisted of roadmeters installed in ordinary passenger cars, and two that are self-contained roadmeter/trailer units. Each RTRRMS made repeated measures on all of the sites at several speeds. Analyses of the collected data showed that all of the RTRRMSs give highly correlated measures when they are operated at the same test speed, and that all could be calibrated to a single roughness scale without compromising their accuracy. Analyses of the profile data demonstrated that the different profilometric methods can yield some--but not all--of the common roughness indices when the appropriate analysis is applied to the measured profile. Several of the profile-based roughness indices showed excellent correlation with the measures from the RTRRMSs. Thus, a single index is proposed, called the International Roughness Index (IRI). The IRI is measurable by all of the roughness measuring equipment included in the IRRE, and is also compatible with nearly all equipment used worldwide. The IRI is based on the roadmeter measure, called by its technical name of average rectified slope (ARS), or more typically by the units used (m/km, in/mi, etc.). For technical and practical reasons, a standard speed of 80 km/h (50 mph) is proposed. The calibration reference is a mathematical model of a RTRRMS, that provides a reference ARS (RARS) index computed from a measured profile. This index, designated RARS , is identical to the calibration reference described earlier in NCH#? Report No. 228. It was selected over several other profile based numerics that were also considered because: 1) it most closely matches the concept of a reference RTRRMS, 2) it results in the best RTRRMS accuracy, and 3) it is compatible with more profilometric methods than any of the other indices. A separate document contains practical guidelines for measuring the IRI with various instruments (see reference 35). ix CHAPTER 1 INTRODUCTION Background The "roughness" of a road is defined In this report as "the variation in surface elevation that induces vibrations In traversing vehicles," and historically has been long recognized as an important measure of road performance. By causing vehicle vibrations, roughness has a direct influence on vehicle wear, ride comfort, and safety [1, 2, 3, 41. In turn, the dynamic wheel loads produced are implicated as causative factors in roadway deterioration [5]. The effect of roughness on road safety is also being recognized. As a consequence, the characterization and measurement of road roughness is a major concern of highway engineers worldwide. As the highway networks in developed countries near completion, the maintenance of acceptable quality at minimum cost gains priority. In sophisticated management systems, roughness measurements are an Important factor in making decisions toward spending limited budgets for maintenance and improvements. Analysis of roughness can aid in the diagnosis of roadway deterioration and the design of appropriate maintenance. In developed countries, ride comfort has been emphasized because it is the manifestation of roughness most evident to the public. In less developed countries, the same concerns face administrators from the very beginning; constrained by limited resources, they must choose between quantity and quality in the development of public road systems. Optimizing road transport efficiency involves trade-offs between user costs and road costs. User costs are strongly related to road roughness and are typically many times greater than road construction and maintenance costs. Hence, studies of the important relationship between roughness and vehicle operating costs (fuel, oil, tires, maintenance parts and labor, vehicle depreciation) have been or are being undertaken in Kenya [21, India [6], Brazil [7, 8], and other locations. Other user costs are less direct but are also a consequence 1 of roughness. These include transport speed limitations, accidents, and cargo damage. A persistent problem in these studies is characterizing the roughness of a road in a universal, consistent, and relevant manner. The popular methods now in use are based on either profile measurement or measurement of vehicle response to roughness. When profile is measured, the continuous representation of the road can be inspected to identify local defects, or processed to yield roughness numerics adapted to specific applications. Direct comparison of profiles obtained by different methods is not always possible, since profiles measured with high-speed dynamic profilometers generally do not include the underlying slope of the road, nor variations that occur over very long wavelengths. On the other hand, static measurements obtained with manual methods such as rod and level do include the long wavelengths, but are not practical for covering long distances, due to the required effort. (Note that wavelength limitations of profilometers usually do not limit their utility, since long wavelengths are of no consequence for most applications, including measurement of all of the roughness indices described in this report.) The second type of measurement is obtained using a vehicle instrumented to produce a numeric proportional to the vehicle response to road roughness, when the road is traversed at a constant speed. These systems have acquired the name response-type road roughness measuring systems (RTRRMSs), and have been developed from a practical approach to the problem, often without a thorough technical understanding of exactly how the measures relate either to road profile geometry or vehicle response. As a result, the relationship between different RTRRMS measurements is sometimes uncertain, as is also the relevance to ride comfort or road-user costs. Nonetheless, most of the currently popular RTRRMS Instrumentation systems share a commonality in configuration and operation, and are in such widespread use that they can be expected to play a large role in measurement methodology in the near future. Early high-speed profilometers were costly, complex, difficult to maintain, and required knowledgeable users to operate them and make good use 2 of the measurements. This is one of the reasons why the more simple RTRRMSs have been so popular. More recent designs have resulted in profilometers that are less complicated, less expensive, and can be used over a wider range of conditions. Future trends In profilometry are likely to yield lower costs and greater operating simplicity, making these instruments more comparable with RTRRMSs for routine use. Already they have advantages in terms of improved accuracy and relatively simple calibration procedures that make them more cost-effective overall than RTRRMSs for some uses. But for the present time, RTRRMS use can be expected to continue, and even grow, as more agencies begin monitoring roughness for the first time, purchasing roadmeter instruments for mounting in vehicles for use as "entry-level" roughness measurement systems. The users of RTRRMSs recognize that the roughness numeric obtained from one of these systems is the result of many factors, two of which are road roughness and test speed. Other factors, that affect the responsiveness of the vehicle to road excitation at Its travelling speed, can be difficult to control. While great effort Is spent limiting the variability of these other factors, there is growing recognition that some variation will still persist between RTRRMSs, and that even the most carefully maintained systems should be independently calibrated occasionally. One method for calibrating a RTRRMS is by the use of control sections to perform a "calibration by correlation." The calibration is performed by running the RTRRMS over a number of "control" road sections that have known values of roughness, obtained through concurrent measurement by a reference method. The measures obtained from the RTRRMS, together with the reference roughness numerics, are used to determine a regression equation that is used to convert future RTRRMS measures to estimates of what the reference measure would have been. These estimates are the "calibrated" roughness measures. Variations of this approach has been developed since 1970 by several agencies [7, 27, 40]. More recently, comprehensive research on the topic, funded by the National Cooperative Highway Research Program (NCHRP), has indicated that the "calibration by correlation" approach is in fact the only calibration approach that will be valid for any roughness level or surface type [9]. 3 The key to this approach Is the ability to assign reference roughness levels to the control sections. This requires the ability to accurately measure the longitudinal profiles of the control sections in the wheeltracks traversed by the RTRRMS. It also requires a method for reducing the information in a profile to a single roughness measure for the correlation. Although RTRRMS use is popular, there has been no consensus as to how a RTRRMS should be operated, nor agreement as to what reference measure should be used in its calibration by correlation. In response to this need, the World Bank proposed that roughness measurement devices representative of those in use be assembled at a common site for an International Road Roughness Experiment (IRRE). The purpose was to determine correlations among the instruments and encourage the development and adaptation of an International Roughness Index (IRI) to facilitate the exchange of roughness-related information. The IRRE was held in Brasilia, Brazil, during May and June of 1982. Research teams participated from the Brazilian Transportation Planning Agency (GEIPOT), the Brazilian Road Research Institute (IPR/DNER), the British Transport and Road Research Laboratory (TRRL), the French Bridge and Pavement Laboratory (LCPC), and The University of Michigan Transportation Research Institute (UMTRI--formerly the Highway Safety Research Institute, HSRI). In addition, the Belgian Road Research Center (CRR) participated in the analyses of the data after the experiment. The IRRE included the participation of a variety of equipment: seven RTRRMSs (four types), two high-speed dynamic profilometers (only the data from one were processed, however), and two methods for statically measuring profile. Four road surface types were included: asphaltic concrete, surface treatment, gravel, and earth. At the finish of the experiment, all of the sections were subjectively evaluated for roughness by a panel of raters. Objectives Main Objective: Define an International Roughness Index (IRI). The meaningful exchange of road roughness data and findings related to road 4 roughness is presently difficult, and can usually be accomplished only with the use of regression equations that are imprecise and often valid only under limited conditions. By selecting a single standard roughness measurement to which all measurements are scaled, information can be compared directly. In order for the IRI to eliminate these problems, it must be: * Stable with time * Transportable (measurable with equipment available in most countries, including developing countries with less technical support) * Valid (reproducible with various types of equipment from-all over the world, on all types of road surfaces without bias) * Relevant (indicative of road condition as it affects user cost, ride quality, and safety) Although not strictly necessary, it is preferable that the IRI also be: * Simple and convenient * Well known (i.e., already in use by some agencies.) In order to qualify for these criteria, the IRI must be compatible with the RTRRMSs now in use, and must be defined by profile geometry (to be stable with time). In order to define such an IRI, a number of more immediate sub- objectives first had to be met: Sub-Objective #1: Establish valid calibration procedures for popular measurement practices. Obtaining a roughness measure that is stable with time has often proven difficult. The IRRE allows the evaluation of alternate calibration methods for many of the combinations of equipment and procedure that were included. Thus, the reproducibility of the measures obtained using 5 specific methods can be determined, and practitioners can rationally select a method that is best for local conditions. Sub-Objective #2: Establish the correlation between different RTRRMSs. Measures from two different RTRRMSs can be made somewhat "equivalent" (and therefore reproducible) through calibration. The IRRE was designed to help determine the degree of reproducibility that is possible, and the ranges of roughness, surface type, and operating speeds over which that reproducibility can be obtained. Sub-Objective #3: Establish measurement requirements for profile-based roughness measures. One of the problems in transferring methods worldwide is that certain equipment may be feasible in one country but not another, for technical, political, or economic reasons. For example, the rod and level survey method is a labor-intensive method that is well suited to countries with low labor costs, whereas certain profilometers may require technical support that is not available in less developed countries. In the past, specific analysis methods have been associated with particular profile measurement methods, and some of the analysis methods depend, in part, on the specifics of the measurement method. The various measures of profile obtained in the IRRE can be processed identically and the results compared to determine whether certain profile analyses are compatible with different profilometric methods. Sub-Objective 14: Establish correlations between profile-based numerics and RTRRMS numerics. Although there is a general agreement among users of RTRRMSs that the RTRRMS must be calibrated by correlation against a reference, a number of potential references have been proposed. The accuracy of the calibrated RTRRMS measure is limited by the degree of correlation between the RTRRMS and the reference; hence, the conditions for obtaining the best correlations must be investigated in order to specify both an appropriate reference numeric and the appropriate operation of the RTRRMS to best match that reference. Sub-Objective #5: Perform and document auxiliary analyses of the profile data. A wealth of profile information was obtained in the IRRE which can be 6 processed to yield many detailed descriptions of the road that are not necessarily compatible with the simple numerics that can be obtained with RTRRMSs. These include waveband analyses used in Europe, Power Spectral Density (PSD) functions, and plots of profiles to show heterogeneities. These analyses are essential to understand some of the relationships observed between RTRRMS numerics, and the results are also a valuable resource for linking summary numerics obtained in the IRRE to potential future applications. Report Organization This report documents the experiment, the data obtained, and a number of analyses applied to that data. The findings are then applied to recommend an IRI. Many of the descriptions are technical and detailed, and most of the data, needed for verification and further analyses, will not be of interest to the average reader. Therefore, this main report is limited to an overview of the IRRE (Chapter 2), an overview of the analyses and relevant findings (Chapter 3), and the rationale for selecting the IRI and a description of the IRI (Chapter 4). (Chapter 5 contains a summary and concluding remarks, while references are included in Chapter 6.) The bulk of the technical information is sorted and presented in Appendices A - K, contained in Volume II. 7 CHAPTER 2 EXPERIMENT This chapter describes the physical aspects of the International Road Roughness Experiment (IRRE). It summarizes the methods used to acquire roughness data, the ranges of road and operating conditions covered in the IRRE, and the testing procedure. Participants The experiment included the participation of eleven pieces of equipment, which are separated into three categories in this report: response-type road roughness measurement systems (RTRRMSs), static profile measurement, and dynamic profile measurement (profilometers). Appendix A provides a technical discussion for each piece of equipment and offers much greater detail than the following overview. RTRRMSs. All of the RTRRMSs that participated in the IRRE consist of a vehicle equipped with special instrumentation. Although different designs are employed, all of the instruments are theoretically measuring the same type of vehicle response: an accumulation of the relative movement of the suspension between axle and body. The measurements obtained with these instruments are in the form of discrete counts, where one count corresponds to a certain amount of cumulative deflection of the vehicle suspension. When the host vehicle is a passenger car, the instrument is mounted on the body, directly above the center of the rear axle. Alternatively, some are mounted on the frame of a single-wheeled trailer to one side of the wheel, directly above the axle. Four types of RTRRMSs (seven total) participated in the IRRE: 1. Opala-Haysmeter Systems. Three RTRRMSs were provided and operated by the Brazilian Transportation and Planning Agency 9 (GEIPOT). These consisted of Chevrolet Opala passenger cars equipped with Maysmeters, manufactured by the Rainhart Co. of Austin, Texas [10] as modified by the researchers of the international project, "Research on the Interrelationships Between Costs of Highway Construction, Maintenance and Utilization" (PICR). The modifications were made to eliminate the strip-chart recorder normally used to read roughness measurements, replacing it with an electronic counter with a digital display [7]. The modified meters produce a display for every 80 meters of road travel, which is shown until the next 80 m is reached. The meter can also be adjusted to display every 320 m. 2. A Caravan station wagon with two roadmeters. A Bump Integrator (BI) unit, produced and operated by the British Transport and Road Research Laboratory (TRRL) [11], and a NAASRA Roughness Meter, provided by the Australian Road Research Board (ARRB) [121, were both installed in a single Chevrolet Caravan. The Caravan is made in Brazil and comes from the same automotive family as the Opala used for the Maysmeter systems. Both meters were installed and operated by the TRRL team, and all measures made with the NAASRA and BI units were made simultaneously. 3. Bump Integrator Trailer. The BI Trailer, produced and operated by TRRL, is a single-wheeled trailer equipped with a BI unit (see Figure la) [11]. It is based on the old BPR Roughometer design [13], but has undergone a great deal of development by TRRL to achieve better standardization and more ruggedness. 4. Soiltest BPR Roughometer. A Road Roughness Indicator, made by Soiltest, Inc. of Evanston, Illinois is owned by the Federal University of Rio de Janeiro (COPPE/UFRJ) and was operated by personnel from the Brazilian Road Research 10 a. Bump Integrator Trailer b. BPR Roughometer made by Soiltest, Tnc. Figure 1. Two RTRRMSs based on the BPR Roughometer design. 11 Institute (IPR/DNER). The trailer is built to the specifications of the BPR Roughometer (see Figure 1.b) [13]. Normal measurement speed for the two trailers is 32 km/h (20 mph). A standard speed does not exist for car-based systems, although 80 km/h (50 mph) is the speed often recommended and used. Standard speeds in the vehicle operating cost part of the PICR project were 80 (96% of the paved roads), 50 (94% of the unpaved roads), and 20 km/h [141. Standard test speeds for the NAASRA Meter as used in Australia with a different vehicle are 50 and 80 km/h. Static Profile Measurement. Two static methods were used to obtain the longitudinal elevation profile of each wheeltrack over a test section. Each method uses a fixed horizontal reference as a datum line. Measures are then made of the distance between this datum and the ground at specific locations that are at fixed Intervals. One method is the traditional rod and level survey, shown in Figure 2. A surveyor's level provides the datum, while datum-to-ground measures are made with a marked rod. Using a measurement interval of 500 mm, a trained crew of three can survey both wheeltracks of two 320 m test sections in an eight-hour working day (about 2500 elevation points for three man-days). The rod and level survey method was included in the IRRE because previous study in Brazil demonstrated that a relevant roughness index can be determined from analysis of rod and level profile [8]. The second method used in the experiment is based on an experimental instrument that was in development by TRRL, the "TRRL Beam," shown in Figure 3. The horizontal datum is provided by an aluminum beam nominally three meters in length. The ground-to-datum measures are made with an instrumented assembly that contacts the ground through a small pneumatic tire and can slide along the beam on precision rollers. To operate the device, the Beam is levelled by an adjustment at one end, and the sliding assembly is moved from one end of the beam to the other. The moving assembly contains a microcomputer that digitizes the measures at pre-set 12 Figure 2. Measurement of longitudinal profile by the rod and level method. 13 _^ik 40 t0r Figure 3. Measurement of longitudinal profile with the TRRL Beam. 14 intervals of 100 mm and prints them on paper tape. A trained crew of two or more was able to survey two wheeltracks of a 320 m test section in one day (about 6400 elevation points for two man-days). Subsequent development of the TRRL Beam has included automatic processing of the profile, including the computation and printing of a roughness numeric. With the improved version, a 320 m wheelpath can be surveyed in one hour, resulting in more than 25000 elevation measures for two man-days of effort. Dynamic Profile Measurement (Profilometers). The two vehicle-based profilometer systems that participated are each designed to measure longitudinal profile over a selected wavenumber range (wavenumber = 1/wavelength). In both cases, an inertial datum is used that is not fixed, but is dynamic, providing a reference valid only for frequencies above a certain limit. The name "profilometer" is sometimes controversial, as opinions differ as to what qualifies an instrument as a profilometer. In this report, a system is considered to be a profilometer If it produces a signal that can be processed directly to yield the correct value of a profile- based roughness numeric. "Processed directly" means that the numeric is computed directly from the profilometer signal based on the mathematical definition of the numeric, as opposed to a "calibration by correlaton" that must be derived empirically using regression methods. It is expected that most profilometric instruments qualify as "profilometers" for some applications but not others. The first type of profilometer, made by the French Bridge and Pavement Laboratory (LCPC), is called the Longitudinal Profile Analyzer (APL) Trailer and shown in Figure 4. This instrument has a design that isolates its response solely to profile inputs. Movements of the towing vehicle, applied at the towing hitch-point, do not elicit any measurement. The datum consists of a horizontal pendulum that has an inertial mass, a spring, and a magnetic damper. The response of the pendulum is designed to provide a correct datum for frequencies above 0.5 Hz. The trailer wheel also acts as a follower wheel, and has a response that allows measurement with fidelity 15 a. APL Trailer b. Inertial reference of the APL Trailer. Figure 4. The APL Profilometer. 16 for frequencies up to 20 Hz [15, 16, 171. The waveband (range of wavenumbers, wavenumber = 1/wavelength) measured by the APL Trailer is determined by its measurement speed, as its true response is always over the frequency range of 0.5 - 20 Hz. The APL Trailer is nearly always used by LCPC in conjunction with one of two standard analyses, called the APL 25 analysis and the APL 72 analysis [15, 17, 18]. These analyses require that the trailer be towed at specific speeds (21.6 km/h for t;he APL 25 and 72 km/h for the APL 72), and that the test sections be of certain length (integer multiples of 25 m for the APL 25, and multiples of 200 m for the APL 72). In Belgium, APL signals are analyzed to yield a type of numeric called coefficient of evenness (CP), based on a moving average, and computed for sections of 100 m [19, 201. All of these analyses are described in more detail in Appendix G. A second dynamic profilometer also participated in the experiment, but the results have not been analyzed. This was a General Motors Research (GMR) type of Profilometer (also called a Surface Dynamics Profilometer), manufactured by K. J. Law, Inc. of Farmington, Michigan. The GMR-type Profilometer uses an accelerometer to provide the reference dat.um, while the datum-to-ground measure is made by a follower wheel instrumented with a potentiometer [21, 22]. This particular GMR-type Profilometer was used Ln the early portion of the PICR project [7, 8], but had not been in use for several years before the IRRE and as a result, considerable effort was spent preparing it for the IRRE. Due to an almost endless series of problems--mostly related to the vehicle portion of the profilometer--it was able to obtain data on little more than half of the sections. Due to a number of factors discovered by the Brazilian engineers in preparation for the IRRE, the on- board data analysis equipment was not valid for the conditions covered in the IRRE [23]. It was also found that the measures made during the PICR project were not valid profile-based numerics (see Appendix E). To avoid repeating past mistakes, processing of the data had to be done afterwards in the same manner as used for the APL system. 17 As other sources of profile data became available from the TRRL Beam and the APL Trailer, the measures from this profilometer assumed less importance, and the signal processing was never completed. Most of the GMR-type profilometers now in operation do not employ mechanical follower wheels, but instead use non-contacting displacement sensors. Thus, the data from this particular instrument (with a mechanical follower wheel) are not nearly as relevant to present-day practice as they were during the planning of the IRRE. Subjective Rating Studies After the completion of the experiment (for the RTRRMSs), all test sections were evaluated by a panel rating process, documented in Appendix D. In this study, a panel of 18 persons was driven over the sections and asked to provide a rating ranging from 0 to 5. All panel members were driven in Chevrolet Opalas at 80 km/h over the paved sections, and 50 km/h over the unpaved sections. A second study, of a much more limited scope, was also conducted to determine whether descriptions and photographs of representative roads could be used to "calibrate" raters so that ratings assigned are comparable to an objective roughness scale. Results are presented in Appendix K. Design of Experiment Forty-nine (49) test sites were selected in the area around Brasilia. Thirteen of these were asphaltic concrete sections; twelve were sections with surface treatment; twelve were gravel roads; and the remaining twelve were earth roads. All of the candidate sections had been rated with an Opala-Maysmeter RTRRMS, to ensure that the selected sections demonstrated a uniformly spread range of roughness. Generally, six levels of roughness were sought for each surface type, with two sections having each level of roughness as measured by the RTRRMS. Most sections were fairly homogeneous over their lengths, and all were on tangent roads. 18 Site Length. Each section was 320 meters long. This length was selected based on the following considerations: * RTRRMSs are limited in precision, resulting in random error if the sections are too short. Standard test lengths in use throughout the world range from 0.16 km (0.1 mile) to over 3 km. * The Maysmeters used in Brazil can only be used on sections with lengths that are integer multiples of 80 m (0.05 mile): the readout frequency. * The process of measuring profile by the rod and level method is slow and tedious. Given the number of sections, the available time, and the available manpower for the survey crews, sections much longer than 320 m were not possible if all wheeltrack profiles were to be measured. * Some of the necessary combinations of roughness, surface type, homogeneity, geometry, traffic density, and geographic location were difficult to find. The difficulty was increased with test length. * All sections had to have the same length for equal significance in the planned analyses. The major disadvantage of the 320 m test length was its incompatibility with the APL 72 requirement of a multiple of 200 m length. This incompatibility was not known by the Brazilian team at the time of site selection, and could not be corrected with the available equipment. For the normal APL 72 measurements used by LCPC, the values of Index (I), energy (W), and equivalent displacement (Y) were calculated for a 200 m length completely contained within the 320 m test site. The APL 72 measurements routinely used by CRR were obtained as the average of three 100 m subsections contained within the site. For the APL 25 measurements, the average value of the 12 or 13 individual CAPL 25 coefficients (each 19 measured over 25 m) was reported. The test sites were generally homogeneous over their length, yet it should be understood when comparing results that some of the APL numerics presented later were not computed over the entire site length. Test speed. Measurements were made with the RTRRMSs at four speeds when possible: 20, 32, 50, and 80 km/h. The 32 km/h speed is standard for the BPR Roughometer and the Bump Integrator from TRRL. The 80 km/h speed (50 mph) is the most common measurement speed for RTRRMSs on highways and is recommended by several roadmeter manufacturers. The other speeds of 20 and 50 were used as standard speeds in the PICR project. The APL trailer was operated at its standard speeds of 21.6 and 72 km/h. The roughness went to sufficiently high levels that high-speed measurements were not expected to be within the allowable range for any of the equipment on the roughest unpaved sections. The operators of the instruments were given the option of declining to make any measurements that thev felt would either be invalid or damaging to the equipment. Initially, all of the RTRRMSs were operated at all four speeds. After the first week of testing, the operators of the BPR roughometer limited testing to 50 km/h and less, because the equipment kept breaking at the highest speed. The BI Trailer and Caravan system (with two installed roadmeters) were both able to operate at 80 km/h without damage, but the operators (the research team from TRRL) declined to make measurements with these systems at 80 km/h after the first week on the grounds that the speed was unsafe for some of the sites, and also that they felt the speed was not relevant to developing country environments. As a result, only the three Opala-Maysmeter systems were run at 80 km/h on all of the surface types. Repeatability. Several measurements were made with the RTRRMSs to demonstrate repeatability and allow' averaging to reduce some of the random error that occurs with RTRRMS measurement over short lengths. The RTRRMSs that were based on passenger cars made five measurements at each speed when possible, while the trailer-based systems made three runs in each wheeltrack (six per site). 20 Because the tests conducted at different speeds all covered a standard distance, longer times were needed to cover the 320 m distance at the lower speeds. Therefore, some random effects related to time (rather than distance) were subjected to greater averaging at the lower speeds. An experimental design in which both speed and site length were varied would have required a great deal more time and effort to conduct, and was not possible. Sequence. The sequence of tests was scheduled with several goals in mind. From a statistical point of view, it is helpful to randomize the sequence of each variable (roughness, surface type, speed, instrument). On the other hand, any measurements that risk damage to the instruments should be scheduled last when all of the low-risk measurements have been completed. Transit time to and from the sections is minimized by schedul' all measures in one day for sections that are near each other. The actual testing sequence used was a compromise of the above considerations. All of the paved sections were tested before the unpaved sections, in an order dictated according to geographical convenience. The paved sections were not measured in any particular order in terms of their roughness. The smooth and moderate unpaved sections were measured according to geographical convenience, while the very roughest were measured last. Because of the logistics involved when a number of RTRRMSs are making measures on the same section, all repeats were made at one test speed before continuing to the next speed. The sequence of test speeds was randomized for each section when possible. However, some of the test sites were adjacent sections of road which were both tested in one pass of the RTRRMS; the same speed sequence was necessarily used for these tests. Testing Procedure The experiment took place over a period of one month, beginning on May 24 and ending on June 18, 1982. All of the vehicles underwent a speed calibration on the first day, based on a precision transducer on the APL Trailer, which was in turn checked by stopwatch. During the following 21 month, about 1 - 1/2 weeks were unscheduled, allowing make-up runs for the equipment that had experienced problems. The research teams from GEIPOT, TRRL, and LCPC operated their equipment, while the vehicles were driven by employees of GEIPOT. The tests were performed in caravan fashion, with all of the measures being made by the RTRRMSs at one speed before beginning the next speed. The testing was supervised by two test site controllers, who kept track of the progress of each system. Occasional spot checks were made of the test speed with stopwatches, to confirm that the test speeds were being maintained by the drivers. The APL Trailer, which operated at different speeds, did not follow the caravan, but made its measurements as needed on the same sites as the others. The test sites were all located within a 50 km radius of the garage at GEIPOT used for storage and repair of equipment. The drive from the garage to the test sites served as a warm-up, to allow the shock absorber and tire temperatures to stabilize. The test sites on unpaved roads were located such that the last 10 minutes of driving to the sites was over unpaved roads; therefore, the RTRRMSs were never operated "cold" on any surface type. An exception to this was the Soiltest BPR Roughometer, which was towed only on the actual test sites, to minimize the damage to that system that seemed to occur on a daily basis. The static measures of profile were much slower than those of the RTRRMSs, and were made on different days. Measurements with the rod and level were made on all of the paved sections before the experiment, and repeated for many of the sections during the experiment. When testing proceeded to the unpaved sections, the rod and level measures were made immediately (two days or less) before the RTRRMS tests. The TRRL Beam did not arrive until the end of the experiment. Measures made with the Beam were made after the RTRRMS testing, on sites selected by the TRRL team to cover the full range of surface types and roughness conditions. Ten sites were completely profiled by the Beam. An additional eight wheeltracks were profiled on sections that displayed 22 nearly identical roughness levels on the right and left wheeltracks (as measured by the BI Trailer). Repeat runs with the BI Trailer on the sections that were profiled were used to confirm that the roads had not changed between the RTRRMS measures and the beam measures. (The IRRE took place during the dry season, and as usual, there was no rain during the months of June, July, and August. The unpaved roads used for test sites normally saw little traffic. Marks were made to define the test wheeltrack with paint on the paved roads, lime on the earth roads, and with colored ribbon nailed to the surface of the gravel roads. Even at the end of July, the markers were still intact.) 23 CHAPTER 3 ANALYSIS AND FINDINGS Overview The data obtained from the IRRE are possibly the most comprehensive ever obtained in the field of road roughness measurement. Each RTRRMS produced five or six repeat roughness measurements for each of the 49 test sections for each of the three or four measurement speeds. Every wheeltrack profile was measured by the rod and level survey method at least once, and typically twice for the paved roads, yielding 641 elevation measurements for every one of the 140 profiles (70 two-track sites) obtained. LCPC provided profiles as measured with the APL trailer in the APL 25 configuration for 97 of the 98 wheeltracks (1281 numbers per wheeltrack) and 73 profiles obtained in the APL 72 configuration (6401 numbers per wheeltrack). The experimental Beam from TRRL was used on 28 wheeltracks, providing 3201 measures for each. In addition, all 49 sections were rated subjectively by 18 panel members, and also by four persons rating the surfaces by a "calibrated description" method. A number of computer systems were employed in parallel to prepare the data for analysis during and immediately after the IRRE. The rod and level survey measures were copied by typists into the IBM 370 computer system at GEIPOT. The RTRRMS data, the subjective ratings, and the elevation readings from the TRRL Beam were all typed into an Apple II+ microcomputer, using special entry and checking programs written specifically for the project. The analog signals produced by the APL 72 system were digitized for plotting with a system based on a European ITT microcomputer, compatible with the Apple II+. Programs were prepared to store the APL data on the floppy diskettes used by the Apple. APL 25 profiles were digitized during measurement and stored on cassettes, and later played back into the LCPC microcomputer for copying onto Apple diskettes. In the months immediately following the IRRE, most of the analyses described in this report were performed in Brazil. The APL numerics routinely 25 used by LCPC were computed by the LCPC team during the IRRE and distributed to the participants then, along with samples of profile and roughness heterogeneities (as described in Appendix G). The RTRRMS measures were entered, checked, and rescaled to the same units of average rectified slope (ARS): m/km (scaling conversions are reported in Appendix A). The profiles were all processed on the GEIPOT IBM computer and two Apple computers to obtain the quarter-car and Ql numerics (described in Appendices E and F). A number of fundamental correlation analyses were performed using the Apples, and presented in a preliminary version of this report dated December 1982 that was distributed to the participants. Following this activity, analyses were performed by TRRL in Great Britain (Appendix H), by LCPC in France, and by CRR in Belgium. (Results from the LCPC and CRR analyses are reported in Appendices E, G, and J.) A meeting of the IRRE participants was held in Washington D.C. in July 1983, in which the findings to-date were presented and discussed, with the goal of obtaining a consensus towards defining an International Roughness Index (IRI). A number of issues were resolved, but several areas emerged where further analysis was needed, and therefore, selected analyses were performed at UMTRI to help fill in the gaps. The analyses are covered in detail in Appendices C - J, and are therefore merely summarized in this chapter, so that the findings can be more clearly presented. The remainder of this chapter begins with the findings about the profile measurement methods and the wavenumber (spectral) contents of the roads, since these findings help to explain some of the other results. The chapter then proceeds by summarizing the profile analyses that were used in the IRRE, and the measurement requirements needed for those analyses. The agreement that is possible between RTRRMS measures is then shown, in order to place in perspective the correlations between RTRRMS measures and the profile- based numerics that follow. Finally, the subjective ratings are compared to the objective roughness measures to indicate which measures are more related to the public judgment of road roughness. (Results of the "calibration by description" experiment were analyzed even more recently and are reported in Appendix K.) 26 Spectral Analyses of the Road Profile Nearly all of the correlations and comparisons of roughness numerics that follow are influenced, in part, by the spectral content of the road profiles. Therefore, the power spectral density (PSD) function of every profile obtained in the IRRE was computed, and most are presented in Appendix I. The PSD functions obtained by the different profile measurement methods show that the rod and level, the TRRL Beam, the APL 25 system, and the APL 72 system can all be considered valid methods for measuring profile amplitude over their design wavebands. More specifically, * The TRRL Beam measurements had the highest quality. They were performed statically and thus were known to: 1) apply to the precise wheeltrack position marked on the road, and 2) include the longest wavelengths and the mean slope of the wheeltrack. The 100 mm sample interval provided the widest waveband of any of the profile measurements. * The rod and level measurements were equivalent to those of the Beam, but did not include the shortest wavelengths because a larger sample interval of 500 mm was used. Due to that sample interval (which was the smallest that could be used to include all 98 wheeltracks, given time and manpower constraints), the profile measures were not valid for some of the analyses considered. * The APL Trailer bandwidth, measured in the laboratory to cover the temporal frequency range of 0.5 - 20 Hz, was confirmed by the PSD functions. PSD functions from the APL 72 system matched the static measures for wavenumbers (wavenumber = 1/wavelength) between 0.025 and 1.0 cycle/m (wavelengths of 1 - 40 m), and PSD functions from the APL 25 matched the static measures over the wavenumber range: 0.08 - 1 cycle/m. (The sample interval for the APL 25 limited the upper wavenumber 27 response, rather than the trailer dynamics.) While the agreement appears excellent for some of the wheeltracks, in other cases the APL PSDs differ from the statically measured ones, reflecting the additional testing variables (starting position and lateral wheeltrack location) introduced when profiles are measured at high speed. The PSD functions alone (shown in Appendix I) are not adequate to determine the accuracy of each profilometric method for the measurement of specific roughness indices. The more direct validation for a particular application is made by applying the actual analysis to the different profiles, and determining whether the differences in the resulting numerics are acceptable. These comparisons are made later for a number of profile-based summary numerics. In addition to comparing the profile measurement methods, the PSD functions in Appendix I very clearly show the differences in the four surface types included in the IRRE. Figure 5 presents normalized aggregate PSD functions obtained by graphically overlaying the PSD functions corresponding to each surface type. The PSD amplitudes were all normalized by one of the roughness statistics, so that the plots show the relative distribution of the roughness over wavenumber when the amplitude scale factor is removed. Figure 5 shows that the different surface types have characteristically different "signatures," reflecting their distributions of roughness over wavenumber, and that: * The asphaltic concrete (CA) sites have proportionately the least roughness at high wavenumbers. * The surface treatment (TS) and gravel (GR) sites show a minimum at wavenumbers near 0.1 (10 m wavelengths), with more roughness at lower wavenumbers and also at higher wavenumbers. * The earth sites generally show the highest concentration at high wavenumbers. 28 tn~~~~~~~~~~~~~~~~~~I . N E X * **,.N E l 0 *----- ,Co D * 0 ............. 'C,% >' ' ........... - ~ ~ ~ L O '.- .- ..-- - .--.- . : :-:-:-. .......~~~~~~.......... = , ,-,N E * .0 1 ., . X a; , . ~* 5-I0a _ ,; ~~~~~...... ...; > b ~~~~~~~~~~~~~~~. . . . . . . . . . . . . t3. . .. : : ; . 4a ........... .... ......:.j_ E ...' .~~~~~~ - 3 ..-.:3 0L 0 . . . . 0'y * 0~~~~~~~~~~0 C* ...... O.- ~ ~.0) OSd 9dolS PaZilDWJON 0Sd adoiS psziiDLU4ON bo . . . . . . ................ ~~~~~~~~~~~~~~~~~~~~~~~~~~co . . . . . . ............ .............. ~ ~ U E ~~~bti Q).Q ~~~~~~0-O~~~~~~~~~~~~ _4 b 5-i .... .. ... .. 0 Lf I) .. . . > o....k OL~~~~~~~ L 2. 9 * Several of the sites include corrugations, and these sites also appear as "outliers" in correlation plots ("outliers" are data points that do not fall within the scatter range exhibited by the rest of the data). This is because the site has a corrugation that causes one measuring system (or analysis method) to "tune in" and respond highly, while other systems respond more conventionally. Several of the surface treatment had 2.0 m corrugations (wavenumber = 0.5), as shown in Figure 5b. These "signatures" are also evident from the waveband analyses used in Europe by LCPC and CRR. (Appendix G.) Computation of Profile-Based Numerics The measured profiles were processed to obtain eight types of simple summary statistics. Note that most of the names of roughness numerics used in this report are more explicit than is common in other reports. This is necessary to clearly distinguish the many measures under discussion. (Most of the following numerics are called "roughness" by users.) Whenever possible, simple metric units are used to facilitate comparisons. (For example, all slope measures are reported as "m/km," and can be readily converted to other units used, such as mm/km and inches/mi.) 1. Reference Quarter-Car Simulation (RQCS). The concept of using a reference RTRRMS has shortcomings when applied to a mechanical vehicle-based system, which can be overcome by defining the reference as a mathematical description of such a system. The mathematical description (model) is used to process direct profile measurements to obtain the summary ARS-type of roughness numeric. The mathematical model needs to be standardized by a choice of parameter values that describe the simulated vehicle, namely: sprung mass, unsprung mass, suspension spring rate, tire spring rate, and suspension linear damping rate. The model also includes a baselength parameter for a moving average, corresponding to the finite contact area between a pneumatic tire and the road. When the model is used with a single wheeltrack (one 30 wheel), it has been called a quarter-car. The model parameter values used in this project were selected in earlier work for maximum agreement with RTRRMSs that have stiff shock absorbers, because the use of stiff shock absorbers reduces many of the sensitivities of RTRRMSs to factors other than roughness and test speed [9]. To distinguish the QCS implied by this set of parameter values, it is called the reference QCS (RQCS). The measured profile is used as an input to the RQCS, and the simulated motions of the suspension are accumulated mathematically, simulating an ideal roadmeter. The roughness numeric thus obtained with the RQCS is called reference average rectified slope (RARS), and can be reported with the same units of ARS used for a RTRRMS (m/km, mm/km, in/mile). Since the RARS numeric varies with simulation speed, the simulation speed is usually noted as a subscript: e. g., RARS means the simulation speed so was 50 km/h. The RQCS can be implemented any number of ways. Regardless of the method, four variables that describe the simulated vehicle must be computed. For analog profile measurements, an electronic analog of the mechanical model has been used in the past [7, 9, 22, 24]. (Different parameter values were used.) For digital measures, several methods have also been used. One of these is called the state transition method and has the form: zl = s11 * Z1 + s12 Z2 + s12 Z3 + S14 Z4 + p Y Z2 = s21 * Z1 + S22 * Z2 + S23 * Z3' + S24 * Z4 + P2 * y' Z3 =3l 3 1 + S32 Z2 + S33 *Z3 + S34 *Z4 + P3 *yi Z4 =S41 1Z + s42 Z2 + S43 Z3 + S44 Z4 + P4 Y (1) where Z ... Z4 are the four vehicle variables (velocities and accelerations of the sprung and unsprung masses) at the present position along the road x, and Z1' ... Z4' are the values at the previous position: x - dx (where dx is the interval between elevation measures). The coefficients S11 ... S44 and P, ... P4 are constants that can be obtained from tables corresponding to the proper combination of simulation speed and measurement 31 interval dx. Y', the input, is the average profile slope over a distance of 0.25 m, computed for the interval between x-dx and x. The RARS numeric has several interpretations, with the most direct being that RARS is the average slope of the profile, seen through the RQCS "filter." Hence, it can be visualized as a profile attribute. A perfectly smooth profile (no variation in slope) has an RARS value of zero. RARS is linearly proportional to the profile amplitude, such that the units of RARS are determined by the scaling of the profile elevation. A second interpretation is that of a reference RTRRMS, where RARS is similar to the ARS measure obtained with a mechanical RTRRMS. When the same units are used for RARS and the ARS measure from a RTRRMS, the practitioner can see whether the RTRRMS is more or less responsive than the reference. (A third interpretation exists when the roughness is expressed as an RARV numeric, in which case the RARV is the average vertical velocity "seen" by a vehicle traversing the road at the simulation speed.) A more complete description of the RQCS and the RARS numeric is provided in Appendix F. 2. Half-Car Simulation (HCS). A half-car is simulated simply by averaging the left- and right-hand wheeltracks, point by point, before processing with a QCS. The numeric obtained with a HCS is not the same as computing two QCS numerics and averaging the RARS values. This is because some of the variations in the two profiles will cancel when averaged for a HCS, whereas they contribute fully to the QCS numerics. The QCS is a closer simulation of a single-track RTRRMS such as the BPR Roughometer or BI Trailer, while the HCS more closely replicates a two-track RTRRMS. For realistic road inputs, the numerics computed using a HCS will always be lower than when computed from two independent QCSs. 3. QI r* The Qlr numeric was developed by Brazilian researchers during the PICR project as a means for using rod and level profiles to calibrate RTRRMSs [8]. It replaces a numeric obtained from a particular piece of hardware (that numeric, QI, was an abbreviation of Quarter Car Index). In concept, QI is identical to the RARS statistic. However, due to hardware 32 problems described in Appendix E, the original QCS definition cannot be used to reproduce the QI roughness scale, and Ql is therefore effectively defined by the more recent QIr numeric. The Qlr numeric that replaced the electronic QCS is independently defined strictly by profile geometry, and has been suggested as a standard roughness scale for calibrating RTRRMSs. QIr is based on the RMSVA summary statistic (hence the subscript "r"). RMSVA is an abbreviation for root-mean- square (RMS) vertical acceleration [25], even though the computation procedure that has been used results in a numeric that has no relationship whatsoever with vertical acceleration. Rather, RMSVA is equivalent to the RMS deviation at the midpoint of a rolling straightedge of length 2*b, as shown in Appendix E (RMS mid-chord deviation). (Since RMSVA varies with b, the baselength should be subscripted.) Mathematically, RMSVAb is the RMS value of the variable VAb, which is defined as: VA (x) = [ Y(x-b) + Y(x+b) - 2 * Y(x) * b2 (2) b where Y(x) is the profile elevation at position x. To obtain the QI numeric, the profile is processed to yield two RMSVA values for baselengths of 1.0 and 2.5 m, which are then combined as: QIr = -8.54 + 6.17* RMSVA1 0 + 19.38 * RMSVA2.5 (3) The above equation assumes that elevation is measured in mm and that b (1.0, 2.5) is measured in m, resulting in RMSVA numerics with the units: 1/m * 10 3 Although the RMSVA "filters" are linear, when the two RMS values are combined in Eq. 3, the resulting QIr numeric cannot be defined by a linear transform. Thus, care must be taken to convert the profile to the proper units before applying Eq. 3. Note also that a perfectly smooth profile would have a QIr rating of -8.54. The QIr numeric has been used in recent years as a RTRRMS calibration reference in Brazil, Bolivia [26], and South Africa [27]. A very similar 33 numeric called MO, that is also a weighted sum of two RMSVA measures, is used as a calibration reference in Texas [28]. Appendix E provides more information about the Qlr numeric, and also the other QI numerics (QI and QI ). 4. CAPL 25. This numeric is obtained by towing the APL Trailer at 21.6 km/h, and calculating the average absolute value of the signal produced by the trailer. The average is taken over sections of road that are 25 m long; hence the name APL 25 Coefficient (CAPL 25). CAPL 25 can be scaled to any convenient unit of displacement, such as mm. A perfect road has a CAPL 25 value of 0, and the coefficient increases linearly with profile amplitude. Due to the simple nature of the computation, the CAPL 25 is defined in part by the response properties of the APL Trailer, and it is shown in Appendix G that suitable filtering of the APL 72 signal can produce a "simulated" APL 25 signal. However, given the objectives of this report (which emphasize compatibility with RTRRMSs), further efforts were not made to characterize the APL Trailer response sufficiently to compute the CAPL 25 coefficients from other types of profile (APL 72, rod and level). The CAPL 25 numeric was developed to check quality of road layers during construction, and to isolate short sections that might require further work before proceeding with the next phase in the construction [15, 19]. Compared with some of the other roughness numerics, it is not the best calibration standard for RTRRMSs, and RTRRMSs in general cannot be used for the applications for which the APL 25 measure was designed. Examples of the use of the CAPL 25 coefficients are presented in Appendix G, along with a more complete description of the measurement methodology. 5. LCPC APL 72 Waveband Analysis. LCPC has developed this analysis method to summarize the present condition of roads [17, 18, 191. The method is based on the recording of a road profile at a speed of 72 km/h (20 m/sec). At this speed, the APL Trailer transduces profile wavelengths from 1 - 40 m. The APL signal is played back into three electronic band-pass filters, each of which isolates a specific waveband from the profile. The filtered signals are 34 squared and integrated to obtain mean-square "energy" values (W) calculated over a road length of 200 m. The mean-square values can be used to compute the "equivalent amplitude" (Y) of a sine wave within the waveband, which is reported with units: mm. However, more typically, the "energy" values (W) are used to assign a rating to the road. The rating index (I) goes from 1 (the worst) to 10 (the best), and was designed to cover the range of road quality seen in France. The result is that each 200 m section of road is described by three indices, corresponding to the relative road quality for short, medium, and long wavelengths. In normal operation, the profiles of the right and left wheeltracks are measured simultaneously with two APL Trailers. During the IRRE, the wheeltracks were analyzed separately and roughness measures were reported for each wheeltrack. The indices (I) obtained in the IRRE on the unpaved roads often had a value of 1 (the worst), indicating that the roughness range covered in the IRRE goes far beyond the range considered typical in France. The (W) and (Y) numerics are more descriptive for the IRRE data, since they can increase with roughness to any level. A perfect road yields (W) and (Y) values of zero (for all three wavebands). The energy (W) numeric is proportional to the square of profile input amplitude, while the equivalent displacement (Y) is linearly proportional to input amplitude. The response properties of the APL Trailer should play no role in determining the numerics for the three wavebands, because in all three cases, the frequency response of the APL Trailer is broader than that of the filters. Thus, the same analysis could potentially be applied to signals obtained from other profilometric methods. However, since the filters are electronic, digital equivalents would need to be developed for use with profiles that exist only in numerical form, such as those obtained using rod and level. Since the CP analysis used by the Belgian CRR (described below) is used for the same purpose as the LCPC analyses, but is numerical rather than electronic, the CP numerics were tested for measurement with rod and level. Further details concerning the APL 72 analysis are presented in Appendix G, along with the (W), (Y), and (I) values obtained for the test sections in the IRRE. 35 6. CP (Moving Average). A moving average analysis of profile has been used by TRRL and CRR [19, 20] to obtain roughness numerics from profile measurements. The characterization of the measured profile used by CRR is called CP, and is obtained by evaluating the variation of the surface profile relative to a reference line obtained by smoothing the same profile using a moving average. The CP analysis acts as a filter, attenuating long wavelengths. For its application, the APL signal is digitized, triggering on a pulse train issued from the measuring wheel of the APL. The sample interval of 1/3 m is such that all of the information contained within the bandwidth of the APL Trailer is retained. (Information theory requires a sampling frequency at least equal to twice the higher cut-off frequency of the APL measuring device.) After the recorded profile is sampled and converted to a set of numerical values, those values are, in turn, smoothed using a moving average over an arbitrary baselength. The mean absolute value of the difference between the original profile and the smoothed one has been defined as the coefficient of evenness (CP: "coefficient de planeite"). The CP unit has the dimensions: 1 CP = 105 m (= 104 mm2/km) Since the mean value is divided by two, one mm of the mean absolute value is equal to 50 CP units. It should be noted that the process of summation involving a moving average has a value dependent on the baselength used. Thus, the CP value must be associated with the baselength, e.g. CP2.5 implies that the baselength for the moving average was 2.5 m. For a given baselength, the roughness level increases as the CP increases, with a CP of zero indicating a profile with no variation. The APL 72 profiles obtained in the IRRE were processed at CRR, using the routine processing methods to obtain three CP numerics for baselengths of 2.5, 10, and 40 m for every 100 m of profile. Although the analyses differ 36 from those used by LCPC, the CP numerics for these three baselengths correspond closely with the LCPC numerics (W), (Y), and (I) for short wavelengths (2.5), medium wavelengths (10), and long wavelengths (40). Appendix G describes the CP analysis in more detail, and presents the CP numerics obtained from the APL 72 signals by CRR. A moving average analysis was also performed by TRRL, using a variety of baselengths and sample intervals. These results are presented in Appendix H. Appendix J presents additional information about the properties of the moving average filter, and includes numerics computed from APL 72, Beam, and rod and level profiles. 7. RMS Vertical Elevation (RMSVE). This numeric was tested by TRRL, and corresponds approximately to the area between a longitudinal profile and a datum line, over a specified baselength. The area is computed according to Simpson's rule. RMSVE values were computed from the TRRL Beam profiles using baselengths ranging from 0.4 - 10 m, and sample intervals ranging from 100 mm to 1.0 m, in steps of 100 mm. The study using RMSVE was primarily for determining sensitivities to baselength and sample interval, and suggested that a statistic called RMSD, described next, might be a better numeric for the objectives of the IRRE. Details of the RMSVE analysis and a listing of the results are provided in Appendix H. 8. RMS Deviation (RMSD). From the results obtained using the Moving Average and the RMSVE numerics, a statistic called RMSD suggested itself. RMSD is computed over a baselength b by determining the linear regression line Y = A + B * x where Y is profile elevation, x is longitudinal distance, and A and B are the regression coefficients. RMSD is the RMS deviation of the original profile elevation, relative to the regression line. TRRL considered various combinations of baselength and sample interval, which both affect the RMSD numeric, and found that a baselength of 1.8 m together with a sample interval of 300 mm gave the best correlation with several of the RTRRMSs when they were operated at 32 km/h. Unlike the other numerics, sample interval is standardized for the RMSD numeric, therefore both baselength and sample interval are subscripted, e.g. RMSD1.8,300. 37 The RMSD1.8,300 analysis was applied using both a moving baselength, and also by dividing the profile into separate segments, equal in length to the baselength (1.8 m), which were processed independently (discrete baselengths). When the moving baselength was used, a RMSD 8,300 value was computed for every profile point (except for the beginning and end sections). Results were nearly identical. The second approach is very well suited to the TRRL Beam, since it means that a single RMSD numeric can be obtained for each setup of the Beam, and that consecutive Beam profiles do not have to be linked for computational purposes. In order to present the RMSD1.8,300 numeric in the ARS units familiar to users of RTRRMSs, the displacement RMSD1.8,300 measures are rescaled according to a regression equation derived from the IRRE data. The BI Trailer, as it existed during the IRRE, is taken as the reference measure of road roughness that is estimated from RMSD1.8,300 The regression equation is: RBI32 = 472 + 1437 * M.MSD1*8 300 + 225 * (RMSD1 8 23002 (4) The name RBI32r indicates that the numeric represents the measure of a Reference Bump Integrator, at a speed of 32 km/h, as defined by RMSD (the small "r" in the subscript.) The units recommended by TRRL are "mm/km," which correspond to ARS/2. (When ARS has units of m/km as used in this report, then "mm/km" = ARS m/km x 500.) The RMSD1*8 300 numeric is approximately linear with profile amplitude; however, the scaling applied by Eq. 4 defines a roughness scale that varies nonlinearly with profile amplitude. Note that a perfect road would have a roughness of 472 "mm/km." Appendix H contains the details of the RMSDb,d analyses applied, the RMSDb ,dx numerics obtained, and the correlations observed with several of the RTRRMSs. The appendix also includes the results and findings from a second experiment, independent of the IRRE, which was performed in 1983 in St. Lucia. Comparison and Summary of Analysis Methods. Each of the above eight types of roughness numerics computed from profile is designed to isolate a particular waveband of interest from the original longitudinal profile. The 38 LCPC APL 72 analyses do this directly with standard electronic band-pass filters, while all of the others "filter" the profile signal by subtracting the rapidly changing original profile from a slowly changing datum line. (The RQCS analysis uses a rapidly changing datum line rather than the original profile.) The RMSVA "filters," used in the QI analysis, define the datum line as a rolling straightedge that contacts the profile at two points on either side of the present position, to provide a mid-chord deviation. The CP (moving average) analyses use the average of the profile over a certain baselength as the datum. The RMSVE and RMSD analyses also have a datum determined at any position along the profile by a baselength. For these analyses, the selection of a baselength determines the degree to which the datum follows the profile closely: a longer baselength implies that the datum follows the profile less, resulting in larger deviations and thus higher roughness measures. The datum for the CAPL 25 "filter" is the mechanical pendulum used in the APL Trailer, and in this case, the properties of the datum are determined by the towing speed of the trailer, rather than a geometric length. For the RQCS and HCS "filters," the simulated axle position is the rapidly changing component, while the simulated body position is the datum. In this case, the selection of simulation speed determines how closely the datum follows the profile contours. (Unlike the other analyses, the RQCS and HCS do not compute the difference between the original profile and a datum, but use two datum lines that are computed--one changing rapidly and one changing slowly with profile. Both are influenced similarly by the choice of simulation speed.) Because each analysis is influenced by at least one choice of parameter value (baselength or speed), specific standard values have been determined for each type of analysis. Figure 6 compares the sensitivity of four of the analyses to wavenumber (wavenumber = 1/wavelength) for a slope input. Because the spectral contents of the four types of roads were shown in Figure 5 as slope inputs, these response curves can be interpreted as a "weighting" that is applied to the inputs shown in Figure 5. Since the slope input is fairly uniform over 39 0-~~~~~~~~~~~~~-~~ ~ 5 .1 2 5 9 CA, c E 9 sTs CDC Wavenumber - cycle/m Wavenumber- cycle/m U.) 0LC)RAS,0 . l 2c5.1 2 5 2 5 2. 2 R 1 2 5 Wavenumber - cycle/rn Wavenumber - cycle/rn a.C25d.RARSMSb Qapoimae Figure 6. Sensitivity to wavenumber of four profile analyses. 40 wavenumber, the plots shown in Figure 6 illustrate approximately the contributions of different wavenumbers to the numerics obtained with the different analyses. The plots shown in Figure 6 serve as a technical basis for determining the bandwidth needed in a profile measurement to obtain the "true" value of the associated numeric. They also help in interpreting some of the correlation results presented later. (Due to the fact that different units are used for each roughness index, the "weightings" shown also have different units, meaning that comparisons between analyses must be relative rather than absolute.) All of the above analyses can be affected by the choice of sample interval. In each case, the analysis will converge when sufficiently small sample intervals are used to the limit reached when dx--> 0. Most of the analyses are intended to be used for sample intervals that are sufficiently small to eliminate the effect of variations in sample interval. For example, nearly the same values of RARS80 are obtained for any value of dx less than 700 mm. In contrast, the RMSD analysis is recommended by TRRL along with the "standard" sample interval of dx = 300 mm. For this interval, the RMSD18 analysis has not yet converged, with the result that use of a different sample interval will result in a different RMSD1.8 value (e.g., RMSD1.8,300 # RMSD1.8,200). Standardizing dx has two implications: first, error due to a poor choice of dx is eliminated; second, the options available for measuring profile become limited. (In the IRRE, the RMSD1.8,300 analysis could not be applied to the rod and level data, nor to the APL 25 data because of incompatibility in the sample interval.) Comparison of Profile Measurement and Analysis Methods For a roughness measure to be transportable, it must be measurable by different profilometric methods. Accordingly, the profilometric methods used in the IRRE were evaluated as to their suitability for measuring the various profile-based numerics. The main advantage of a profile-based numeric is that 41 it can be measured directly, without the need for a new correlation experiment every time a new piece of equipment is acquired or a new type of road condition is encountered. Therefore, correlations obtained between numerics computed from different profile measures are not always of interest here. Rather, the level of agreement is quantified simply by the absolute differences in the numerics obtained from the different profilometric methods. In some cases, the effects of other variables were also studied. These include: * Sample interval. What is the maximum sample interval allowed before the measures are biased or have unacceptable random error? * Waveband requirements. What range of wavelengths must be included in the profile measurement to accurately obtain the numeric? * Precision. How precisely must profile elevation be measured to obtain an acceptable reading for each numeric? The RARS (RQCS), QI (RMSVA), and CP (moving average) analyses were applied to profiles obtained by different methods, and the results are summarized here. RARS. This method of profile analysis had been used mainly with GMR- type profilometers in the United States, Brazil, and elsewhere prior to the IRRE. (The name RARS implies a specific set of vehicle parameter values, defined in an NCHRP project [9]. Similar analyses, using different vehicle parameter values, have a long history of use in the United States and elsewhere, and involve other profilometric methods.) For that application, the simulation speed is generally 80 km/h, and rough roads are not measured. As part of the research included in the IRRE, the procedures for computing RARS were refined and simplified, and the measurement requirements for valid computation of RARS were quantified. The findings are presented in Appendix F, and include the following: 42 * Sample interval. For simulation speeds of 50 km/h and higher, the sample interval can be as large as 500 mm without introducing bias. As sample interval decreases, slightly better accuracy is obtained, and the chances of error due to missing significant profile features in the measurement are reduced. For sample intervals less than 250 mm, little effect is observed. Figure 7a shows a sample of the repeatability obtained using two static profile measurement methods, which also involved different sample intervals (100 mm for the TRRL Beam and 500 mm for the rod and level). The effect of sample interval decreases with simulation speed, with RARS80 being the least sensitive to sample interval for the speeds considered. * Waveband of measurement. The waveband required for the RARS80 numeric is shown in Figure 6, while the wavebands needed for other simulation speeds are shown in Fig. F.2 in Appendix F. The RARS numeric can be computed directly from the APt signal, using the same procedure as used for the static measurements. It is essential that the towing speed of the APL Trailer be chosen to approximately match the simulation speed of the RQCS, although some difference is allowable because the APL Trailers has a wider bandwidth than the RQCS "filter." For a simulated speed of 20 km/h, the APL 25 signals could be used, while for the higher speeds of 32, 50, and 80 km/h, the APL 72 signals could be used. Figure 7b compares the measures of RARS80 obtained statically (averages of the numerics obtained with rod and level and TRRL Beam) and with the APL 72 profile signal. Although there is more scatter than when two static measures are compared, bias error is negligible. * Precision of measurement. A study was performed using the profiles measured with the TRRL Beam. The profiles, measured with a precision of 1.0 mm, were rounded off on the computer to determine the effect of less precise measurement. It was found that the precision needed was directly proportional to RARS80, with less precision needed on rougher roads. For negligible 43 0C U > RMS Diff. = 0.5 m/km / EC) (0.4 n/km for R&1)I -oSg fro TRLBa AS0fonS StcMsu o E o 0- s 0~~~~~~~~~~~~~~~ co LO ^< O. Co, ,, ,4 RM,S Diff. 0.8 /km 0 15 20 02 4 6 8150 12 RARS8Q from TRRL Beam RARS8Q from Static Measures a. Two static measures of RARSao b. Static and dynamic measures of RARS C~~~~~~4 /~~~~~4 CN N~~~ AL <0~~~~~~~~~ EP- 0 i r~~~~~~~~~~~~ ~~x 0 50 100 150 200 0 50 100 150 200 Qir from Static Measures CP2.5 from TRRL Beam c. Static and dynamic measures of QIr d. Static and dynamic measures of CP?_5 Figure 7. Comparison of roughness measures from different profilometric methods. 44 error, a precision of 0.5 mm should probably have been used on the three smoothest sites; a precision of 1.0 mm is recommended for all but the roughest paved roads; a precision of 2.0 mm is adequate for the roughest paved roads and all of the unpaved roads; and a precision of 5.0 mm is adequate for the rougher unpaved roads. QI r. The QIr numeric had been used only with the rod and level method prior to the IRRE. In its development, the RMSVA numerics were compared for rod and level and a GMR-type profilometer, and found to differ; hence, QIr was recommended only for the static measurement methods. All of the profile measurements were processed to yield QIr numerics, and certain measurement requirements were also investigated. The findings are reported in detail in Appendix E, and include the follouing: * Sample interval. The RMSVA numeric requires that the sample interval divide evenly into the baselength. Because QIr uses baselengths of 1.0 and 2.5 m, any sample interval that divides evenly into 500 mm can be used for the computation, such as 500, 250, 100, 50 mm. For other intervals, such as 300 mm, these RMSVA numerics cannot be computed directly. Comparisons of Q0r obtained from repeated rod and level profile measures and with the TRRL Beam showed the same degree of agreement as with the RARS numerics, shown in Figure 7a. * Waveband of measurement. The waveband required for QI is shown approximately in Figure 6 (an exact wavenumber sensitivity curve does not exist for non-sinusoidal inputs). The plot shows that the Qlr response resembles that of a quarter-car, as was intended in its derivation. Although most of the QIr numeric derives from wavenumbers between .1 and .7 cycle/m (wavelengths from 1.4 - 10 m), the numeric also includes the effects of wavenumbers lying outside of that range. When the Qlr analysis is applied to the APL 25 and APL 72 profiles, the numerics obtained are too low, because the signal from the APL Trailer does not include all of the 45 wavenumbers that the static profiles contain. Figure 7c shows that for the APL 72, the effect is noticeable mainly on unpaved roads, where the significant presence of high wavenumbers (wavelengths shorter than 1 m) is included in the statically measured profiles but not the APL 72 signal. Measures of Qlr with the APL 25 show much greater error. Although the QIr numerics computed directly from APL profiles are biased, there is excellent correlation. LCPC has derived alternate regression equations for estimating QI r using the APL measures of RMSVA obtained in the IRRE. These data, presented in Appendix E, show that the APL Trailer can be used to estimate Qlr, and also demonstrate the methods that may be needed in adopting the QIr analysis to new types of profile measuring equipment and/or road types. (Because the wavenumber content of the APL profile signal is the result of both the APL and the road surface type, the relations developed are not necessarily valid for road types not included in the IRRE.) * Precision of measurement. The study of required profile precision that was described above for the RARS computation was also performed for the QIr computation, with nearly identical results. The precision needed for valid measurement of QIr is proportional to the magnitude of QIr, and is almost exactly the same as the precision ineeded for the RARS computation. CP (Moving Average). The CP numerics used by CRR are obtained with a moving average. All of the analyses applied by TRRL (moving average, RMSVE, and RMSD) are also related to a moving average. Analyses of the mathematical properties of the moving average, and comparisons of numerics computed from the APL 72 and statically measured profiles resulted in the findings reported in Appendix J, which include the following: * Sample interval. A true moving average is closely approximated if the baselength includes many profile points. But when only a few points are included in the average, then the analysis is 46 no longer a true moving average, and the sample interval influences the results. This is demonstrated both theoretically (Appendix J) and experimentally (Appendix H). The CP10 numeric can be obtained without bias using intervals up to at least 500 mm, although it was found that CP2.5 requires a shorter interval. Figure 7d shows the agreement between the CP2.5 numeric computed from APL 72 and TRRL Beam profiles. (Values computed from rod and level, with a sample interval of 500 mm, were biased low.) Comparisons for intervals of 333 mm, 100 mm, and 50 mm showed close agreement. * Waveband of Measurement. The wavenumber sensitivity plots shown in figure 6 correspond to the CP2.5 numeric. For longer baselengths, the plots have the same shape, but would be shifted to the left in proportion to the ratio of baselengths. For example, the plot shown for a baselength of 2.5 m has a peak at 0.4 cycle/m (2.5 m wavelength). For a baselength of 10 m, the peak would occur at 0.1 cycle/m (10 m wavelength). Numerics obtained from the APL 72 and the static profile measurements were in agreement for baselengths of 2.5 and 10 m (The comparisons of CP10 included some outliers, which were explained on the basis of differences in wheeltrack properties observed in Appendix 1.) For a baselength of 40 m, the APL 72 numerics were lower, because the moving average analysis is influenced by long wavelengths not transduced by the APL Trailer at 72 km/h, but which appear in statically obtained profiles. To obtain a better match between the CP 2.5 numerics obtained for APL and rod and level, the analysis for rod and level would need to account for the long wavelength response attenuation properties of the APL Trailer. Correlations Among Profile-Based Numerics It was noticed that several of the profile-based numerics were highly correlated, as might be expected since they include wavebands that overlap., 47 Although the data presented in the appendices could be used to derive empirical relationships between all of the profile-based numerics, this was not done as part of the IRRE analyses. The rationale is that anyone making profile measurements in the future can usually compute these numerics directly, and should be encouraged to do so because direct computation is more accurate than indirect estimation. Should an approximate "conversion" between two of the profile-based roughness scales be needed to consider existing data bases, the data in the appendices can of course be used to derive regression equations for the surface types of interest. Nonetheless, there are several cases in which correlations between different profile-based numerics are relevant to the objectives of the IRRE, because most of the profile-based numerics could not be measured by every profile measurement method represented in the IRRE. Consider some of the profile-based numerics proposed as calibration references for RTRRMSs: QIr cannot be measured directly with the APL trailer; RBI32r (based on the RMSD1.8,300 statistic) requires a sample interval of exactly 300 mm; and the half-car simulation requires the measurement of both profiles, and further requires that the two profiles be properly synchronized. On the other hand, the RARS numerics can be measured by all of the methods. Therefore, it is helpful to know how the above numerics are related to RARS. Half-car Simulation (HCS). The closest agreement between any two profile-based numerics was between the ARS as computed with a Half-Car Simulation (HCS) and the RARS numeric, computed with the RQCS. These two analyses differ only in the order in which the two wheeltracks are combined. (In the HCS, the profiles are averaged and then filtered; in the RQCS, the profiles are processed separately and the RARS numerics are averaged.) For the roads included in the IRRE, the HCS numeric for any site was approximately 0.76 times the average of the two RQCS numerics. This relationship should not be assumed to be universally valid for arbitrary road inputs, however. For example, if one wheeltrack is perfectly smooth (RARS=O), then the HCS numeric must equal the average of the two QCS numerics. (The ratio would be 1.0 instead of 0.76.) Since the two analyses gave what were essentially redundant measures in the more realistic conditions of the IRRE, differing by a scale 48 factor of 0.76, only the the RQCS numerics are shown in this report. (HCS numerics are presented in Appendix F.) 01 . CRR and LCPC have shown that the Q0r numeric is strongly correlated with the CP2 5 numeric routinely used by CRR. An even stronger correlation was noted between QIr and RARS80. These relations are shown in Figure 8. Note that the relationship between QIr and RARS80 is very good, differing only for one of the earth sites. (When only the paved road data are plotted on a more detailed scale, differences can also seen for a few of the surface treatment sites.) For all practical purposes, RARS80 can be viewed as an improved computation method for obtaining QI, since it is in fact a true Quarter-car Index rather than an estimate of one. The main functional differences between QIr and RARS80 are: 1) RARS80 agrees better with measures from RTRRMSs on surface treatment sites, and 2) RARS80 can be measured with a wider range of instruments. Since the QI roughness scale used in the PICR project rescaled RTRRMS measures made at 80 km/h, the close relationship to RARS80 indicates that RTRRM.S measures calibrated against RARS80 should be compatible with QI . An approximate "conversion" equation between QIr and RARS80 is provided in the next chapter. RSD 1.8300and RBI 32r* The RMSD 1.8300 numeric is very well suited to the TRRL Beam because the numeric can be computed independently from each consecutive set-up. However, this is not an advantage for continuous profilometric methods, and many methods will not be convenient for the 300 mm sample interval required by RMSD 1.8,300* For example, the rod and level profiles measured in the IRRE cannot be processed to yield the RMSD1.8,300 numeric because a different sample interval was used. Other RMSDb,dx numerics might also be evaluated that might be more universally applicable (for example, using RMSD for a sample interval sufficiently short that the analysis has converged and is no longer influenced by variations in sample interval); however, this was not done during the study. 49 8' x CA CP (2.5) = 14.0 1.06 'Q * *TS S A E + GR 160 J + +It T0 + o CP2.5 0 Q 80 I4, RAR80_ =IOERNS Diff. - 14 CP cs / QC7S a " ,3 RAR5.6- tO 4 ECQIr3 ~~~~40- 0 S~E a .5S unis/kM r7L:,9g O~~~ r_ -Ez M hk ri .9 1 1 1 I - 1 -i | --I 0 ) 5 10 15 20 40 80 120 160 RARSsO - m/km a. Ql and RARS80 b. QIr and CP2.5 04~~~~~~ .E X ' . NC1 4 E~ E ~ ~ ~ ~ E E A E 0 0 2 4 6 0 5 10 15 20 2 RS - ++ x 4-- +xC (BI Trail)TS < ~~~~~~~~~~0 . U1. - ~~~~~~+ GR + xTE 0 _ _ _ _ _ _ _ _ _ _ _ _ ~~0 _ _ __ _ __ _ _ 0 2 4 6 0 5 ~~~ ~~~ ~~~~~~~~~~~~~10 15 2 25 RMSD mm RARS50 - r/km c. RMSD and RARS 5o d. RARS50 and the TRRL reference "mm/kmv' (131 Trailer) FiS,&&t.# S.EaftPle correlations between profile-based roughness numerics 50 Figure 8c shows that the RMSD 8,300 and RARS50 numerics are highly correlated. The CP2.5, RARS32, and RARS80 numerics are also highly correlated. Given that the RMSD 8,300 numerics are converted to RBI32 according to Eq. 4, the correlation between RARS50 and RMSD 8,300 is of less interest than the correlation between RARS50 and the measures obtained from the BI Trailer (RBI32), which defined the reference roughness measure in the derivation of Eq. 4 in Appendix H. Figure 8d shows that indeed, the RAIS .0 and RBI32 numerics are also highly correlated. The correlation betwmS the BI trailer measures (at 32 km/h) and RARS50 (as calculated using all 98 wheeltracks from the IRRE) is actually better than the correlation with RMSD1.8,300 (calculated using the 28 wheeltracks measured with the TRRL leam). The correlation is also better with RARS32 (using the 28 wheeltracks measured with the TRRL Beam) than with RMSD 18,300- Other correlation plots between RBI32 and profile-based numerics are shown in the appendices. A plot for the BI Trailer and CP2.5 is shewR in Appendix G, and plots of RBI32 vs. the quarter-car numerics RARS32 and IARS80 are shown in Appendix F. An approximate "conversion" equation betwe*n RI 32 and RARS 8 is provided in the next chapter. Correlation of RTRRMS Numerics Regardless of the choice of a reference calibration standard, measures obtained with a RTRRMS are limited to the quality of the original ARS measure. Day-to-day changes in the properties of a RTRRMS, errors in using the instruments, and the normal random error of measurement cannot be rs&ueod simply by rescaling the ARS measures according to a calibration equatie. These factors cause variations in use that reduce the repeatability of the RTRRMS. The variations can be reduced through careful maintenance to centrol the variables that influence the measurement [91, and by standardi±a4 measurement procedures, such as those used in the PICR project [71. Assuming that good practices are used to ensure that day-to-day meaoures made with.a RTRRMS are repeatable, the final "calibrated" RT1RHS measures may 51 still have only limited equivalence if the different RTRRMSs are producing raw measures that are largely unrelated. No transformation will make the measures compatible if different systems rank the same set of roads in dissimilar order by roughness. A calibration can eliminate average differences that occur over an aggregate of conditions, but cannot ensure that a specific measure obtained by one calibrated RTRRMS is reproducible with another. Since the equivalence between measures based on independently calibrated RTRRMSs is necessarily "second best" to a direct side-by-side correlation of the RTRRMSs, the data collected in the IRRE can be examined to determine the degree of reproducibility that is possible between different RTRRMSs. Appendix B contains all of the data from the RTRRMSs, and also presents the summary results obtained by averaging repeat runs. Appendix C reports the results of a correlation exercise, in which the measures of each RTRRMS were regressed against those of every other, for each of the 40 possible combinations of speed and surface type that exist when both instruments are operated at all four of the test speeds. The major findings of these Appendices are presented below. Repeatability. The repeatability error is neither constant for all roughness levels, nor proportional to roughness, but something in between. By and large, the repeatability of the instruments in the IRRE was better than 5% (standard deviation of repeated ARS measurements divided by the mean value), and a repeatability of 3% is fairly typical. The measurement speed did not seem to be a factor, indicating that repeatability for a particular RTRRMS is only a function of section length. Although the effect of site length cannot be shown from the IRRE data, random signal theory indicates that random error can be reduced by either repeated measurements (ensemble averaging) or by using longer sites (averaging over length) for profiles that qualify as statistically stationary. (A profile can be considered stationary if it has a relatively uniform roughness over the entire length.) In either case, the error in the mean measurement is inversely proportional to the square root of the total length. Thus, the repeatability should be improved by using longer sections. For sites that are four times longer than those used in the IRRE, the random error should be reduced by half. 52 Choice of roadmeter. One of the RTRRMS vehicles was equipped with two roadmeters: a BI unit and a NAASRA unit. When the readings (in counts) were scaled to the same units of ARS (m/km), the measures were virtually interchangeable. (The BI numerics were higher by a constant but very small amount, which is an effect caused by two meters having different amounts of hysteresis.) For all practical purposes, the readings obtained from the Bl and NAASRA units are redundant measures of the ARS of the Caravan vehicle. Because different roadmeters use different units for their displays (inches, mm, counts), and also because the manufacturers recommend different measurement practices, there is often a tendency to assume that the same brand of roadmeter instrument must be used in all vehicles for good agreement. Yet the theoretical understanding and the experimental evidence obtained in recent years show that the choice of roadmeter instrument is not of primary importance. Instead, the critical factor is the methodology adopted to obtain and analyze the roughness data. It has even been shown (prior to the IRRE) that PCA meters can be used to measure ARS by eliminating the complicated PCA data reduction process [9]. Correlation for different RTRBMS speeds. In every case, the best correlations between two RTRRMSs are obtained when the instruments are operated at the same test speed, even when the test speed is not "standard" for one of the instruments. For example, the BI trailer is normally operated at 32 km/h, while the Opala-Maysmeter system is typically operated at 80 km/h. Figure 9 shows the agreement between the ARS measures obtained when both are operated at the same speed and at different speeds. The solid lines are quadratic regression curves, calculated separately for each surface type. When operated at the same speeds (Figs. 9a, 9b, and 9c), there is very little scatter about the regression lines, and the ARS measures from one RTRRMS could be "converted" to those of the other, with good reproducibility. Also, the four regression lines are very similar, indicating that a single relationship holds for the different surface types. In contrast, there is more scatter when different test speeds are used by the different devices (Fig. 9d), and separate underlying relationships appear (as shown by the regression lines) for the individual surface types. The reason for this is that the waveband "seen" by the RTRRMS is a function of the speed, as shown in Fig. F.2 in Appendix F. 53 O 5 CA C m CA _ * TS I.. eTS GR + £ GR + TE + T+ E ° E RI' m Asphaltic Concrete o x CA a, * Surface Treatment o TS A Gravel + A A GR + Earth +xT L Go /f< L AA I.-a,xTEl o AJ 0~~~~~~~~~~~0 0 5 lO 15 20 0 5l 15 BI Trailer @ 50, Beam B Trailer 0 50, Beam a. Brazil and TRRL Equipment b. TRRL, France Ta L wO m Asphaltic Concrete mx CA a Surface Treat,ment * TS / *Gravel +*GR* + Earth o ' +xTE AA7 + O ~~m /+ A *5 00 5.- 11 0511 z~~~~~~~~ 9 p~~~~~~F 0 5 10 15 0 5 10 15 NAASRA 0 50, APL 0 72 Bl Trailer 0 32, Beam c. Brazil, Australia, France d. TRRL, France Figure 13. Examples of the agreement that is obtained using alternate measures of the IRI. 94 sites were regressed against the ARS50 measures of the NAASRA meter, and the resulting equation was used to re-scale all 49 measures. This calibration does not include any gravel test sites. The figure shows the levels of agreement that can be realistically expected when comparing measurements from very different RTRRMSs that have been calibrated using very different profile measurement methods. In all four of the plots, the agreement is sufficient to exchange roughness information in general terms: over a range of 2 to 20 m/km, reproducibility within I m/km is typical. Figure 13a illustrates the good agreement obtained when RTRRMS calibrations include all four surface types, and similar speeds are used by the different RTRRMSs. In comparing Figures 13b and 13d, the effect of the RTRRMS speed can be seen. Note that the data points for the surface treatment and some of the earth sites (TS and TE) tend to lie under the line of equality, whereas the points for the other two surface types tend to lie above the line. This bias due to surface type can be expected when the RTRRMS speed differs from the 80 km/h speed selected as standard. The biases increase with the difference in speed: greater bias is seen in Figure 13d for the lower RTRRMS speed of 32 km/h. The greatest errors in the four examples are seen in Figure 13c, for two reasons. First, the Opala-Maysmeter measures include the "outlier" surface treatment sites that had corrugations. (The calibrated MM #2 measure for one of those sites is 80% higher than the calibrated measure from the NAASRA.) This illustrates once again that the "tuning effect" of a RTRRMS cannot be compensated using an aggregate calibration equation. Instead, it should be reduced mechanically, by installing stiffer shock absorbers. Figure 13c also shows measures based on an incomplete calibration. The gravel roads were not measured in both wheeltracks with the APL 72, and are therefore not included in the calibration of the NAASRA. When the calibration equation is 95 applied to the NAASRA measures on the gravel roads, the estimates of IRI are too low. Even with these sources of error, the agreement is sufficient for most applications involving roughness data from different sources. Note that the agreement is quite good for the majority of the sites, which were represented in the calibrations. Conversion to the IRI from QI and BI Hopefully, future problems in comparing roughness measures from different sources will be reduced by the application of the findings of the IRRE. In the simplest of cases, roughness measures will be made using the IRI directly. Even if a different index is used, comparisons are simplified when higher quality data are obtained through the use of improved practices. Yet there is still the problem of relating to past measurements of road roughness. specifically, relationships between road roughness and user-cost have been developed using roughness measures from BI Trailers, operated at 32 km/h, and also from other RTRRMS measures calibrated to the QIr scale. The IRI is proposed, in part, because there have been problems associated with the QI and BI Trailer measures, which limit their accuracy and transportability. Nonetheless, the IRRE provides a unique opportunity to compare these roughness scales, and to derive approximate conversions between them. Table 3 presents four equations that are suggested to convert back and forth between IRI, the BI Trailer "mm/km," and QIr. They are derived from the IRRE data, and thus reflect the surface types and roughness amplitudes covered. Therefore, they may or may not be appropriate to other conditions. Note that the two equations in each pair are reversible. That is, they are algebraically equivalent. They were obtained by simplifying more complex least-square regression equations, and thus reflect a trade-off of accuracy to obtain the convenience of reversible conversions between the roughness scales. 96 Table 3. Approximate Conversions between IRI, BI, and QI Conversion Equation RMS Error Percent Error 1-track (2-track) 1-track (2-track) QIr 14 * IRI - 10 7.7 (6.4) 10% ( 8%) IRI (Qor + 10) / 14 0.55 (.46) 9% ( 8%) RBI 630 * (IRI) 1.12 804 (680) 17% (14%) 32 0.8 IRI 0.0032 * (RBI32) 0.88 (.75) 15% (12%) Units: IRI: m/km RBI32: mm/km QIr_: counts/km Errors for 1-track are based on measures for 98 wheeltracks; errors for 2-tracks are based on 49 lanes. 97 CHAPTER 5 SUMMARY AND CONCLUSIONS The International Road Roughness Experiment (IRRE) brought together representative equipment and methodologies used throughout the world to characterize road roughness, resulting in a substantial data base that includes profile measurements, measures from response-type road roughness measuring systems (RTRRMSs), and subjective panel ratings. The data show the degree of correlation between different summary roughness numerics, and link the simple average rectified slope (ARS) measures from RTRRMSs to more extensive profile-based analyses. It also shows the similarities and differences in a profile as measured statically and by a profilometer, and indicates which analyses of profile are compatible with the different measurement methods. The IRRE constitutes a major step forward in facilitating the exchange of roughness data worldwide. 1) It has demonstrated that the roughness measures from diverse types of RTRRMSs are, in fact, compatible and can be compared when appropriate controls on their calibration and operation are observed. 2) It has demonstrated the link between RTRRMS measures and profile-based analyses, clearly defining the degree of equivalence with various profile measurement methods and various profile analysis methods. 3) It has provided a basis for rationally choosing an IRI to serve as a standard scale on which roughness properties of roadways may be quantified and communicated. 99 Findings from the IRRE that are of particular significance are presented under topical headings below. Profile measurement. The completely manual rod and level method and the partly automated TRRL Beam gave results that were nearly interchangeable, other than the differences due to the selected sample interval. Although the profile signals obtained with the APL Trailer appear to have little in common when compared graphically with the statically measured profiles, spectral analyses and some of the roughness numerics validate the APL Trailer as a profilometer over its design frequency bandwidth of 0.5 - 20 Hz. The two static measurement methods were validated over the entire roughness range covered in the IRRE, while the APL was able to cover all but the roughest sites at 72 km/h, and was able to measure all sites at a lower speed of 21.6 km/h. Although the APL Trailer is validated as a profilometer, the repeatability is not as good as with the static measures for the 320 m site length used in the IRRE. RTRRMSs. There were four roadmeter designs represented in the IRRE, and all appeared to produce the ARS measure with approximate equivalence. Side- by-side comparisons with two roadmeters installed in the same vehicle gave measures that were nearly redundant. Only one of the roadmeters was an unmodified commercial instrument (the roadmeter in the BPR Roughometer), and it was the most fragile and least reliable. The others, developed or modified by TRRL, ARRB, and GEIPOT for their own use, were able to operate over the entire range of test conditions and produce valid measurements. All experienced some degree of trouble though, indicating that practitioners must be ever alert to the condition of the instrumentation. There were also four types of vehicles used in the RTRRMSs, and the choice of vehicle was shown to be relatively unimportant except for ruggedness. The conclusion regarding equipment is that both the vehicle and roadmeter should be chosen on the basis of robustness and convenience. When calibrated to a valid reference, cosmetic differences (whether the roadmeter is a Maysmeter, BI unit, or NAASRA meter; whether the vehicle is a sedan, 100 station wagon, or a towed trailer) are negligible. (Naturally, earlier findings regarding the maintenance of the vehicle and roadmeter still apply: the test vehicle must be maintained more carefully than a routine transportation vehicle to ensure that its response properties remain as constant as possible.) The good agreement between measurements from two RTRRMSs holds true only when they are operated at the same speed. When operated at different speeds, the relationships are influenced by surface type and roughness level, and degraded correlations are obtained. It should be noted that the relationships between the Brazilian Maysmeters and the BI Trailer observed in the IRRE are only valid for that point in time, although other data available from the PICR project may be used to relate measurements backward in time. The same is not true for the NAASRA meter which was installed in the Caravan station wagon for the experiment. Because of vehicle differences, the data acquired in the IRRE cannot be validly related to measurements in Australia by the ARRB. The IRI. In order to define an IRI that can be measured with a RTRRMS, it is necessary to standardize the RTRRMS measurement procedure, and to find a profile-based numeric that is suitable for most profilometry techniques and which has maximum correlation with the RTRRMS measures. The conclusion of the participants in the IRRE was that the IRI should reflect a single standard speed (rather than a traffic speed concept such as ARV). Based on both technical and practical considerations, it is clear that a choice of 80 km/h would be most appropriate for the greatest number of RTRRMS users. For profilometer users, the choice is not at all critical, since the only implication is that different data reduction methods should be used in conjunction with different RTRRMS speeds. Therefore, the speed selected for the IRI is 80 km/h. (This differs from the 50 km/h speed recommended in an earlier draft of this report, and in several related technical papers that have recently been published.) A number of profile-based numerics were considered to provide a time- stable definition of the IRI. Of these, the RARS80 numeric, developed 101 earlier in an NCHRP project as a reference quarter-car simulation, was the most closely linked to the concept of a RTRRMS operated at 80 km/h. This numeric was also the most highly correlated with the RTRRMs measures, and thus offers the greatest accuracy for users of RTRRMSs. The RARS80 numeric was one of only two profile-based numerics that could be measured with all of the profile measurement methods represented in the IRRE. (The other was RARS50, computed from the same reference quarter-car simulation but using a different simulation speed.) Thus, the IRI is defined as RARS80: the numeric obtained from the reference RTRRMS simulation for a speed of 80 km/h. Guidelines for measuring RARS80, the proposed IRI, are available [35]. They describe the procedures for planning and operating programs for monitoring road roughness using the RARS80 scale with several types of equipment, including RTRRMSs calibrated against rod and level. Other profile analyses. A number of other analyses are described and applied to the profiles measured in the IRRE. The power spectral density (PSD) function was computed and plotted for every measured profile, and Appendix I presents about 300 of these plots. This information provides a very detailed look at the roughness properties of both wheeltracks of every site in the IRRE. The plots show the actual differences between the surface types covered in the IRRE, and should be useful for many future applications in which details of road roughness are needed to test hypotheses and candidate analyses. In addition to the PSD functions, the IRRE roads are characterized using the analyses applied by LCPC and CRR in Europe. Both agencies use waveband analyses (the APL 72 energy (W), equivalent amplitude (Y), Index (I), and coefficient of evenness (CP) that also indicate the spectral content of the road, but using simpler numerics that are more suited for survey purposes than PSD functions. A simple numeric used for evaluating road quality during construction, the CAPL 25 numeric, was also provided for all of the IRRE sites, and several examples were shown illustrating how the CAPL 25 describes the heterogeneity of a road along its length. 102 Several profiles are also shown to demonstrate the diagnostic information that can be obtained using characterization methods more sophisticated than is possible with a RTRRMS-type of summary measure. Other summary numerics that are presently used were also studied, and shown to be highly correlated with both the RTRRMS ARS measures and the profile-based RARS numerics. These include 1) QIr, computed as the weighted sum of two RMSVA numerics and developed in Brazil for the rod and level profilometric method, 2) the APL 72 short wave energy (W), normally measured electronically in France using the APL 72 system, 3) CP2.5, computed digitally in Belgium from the APL 72 signal using a moving average, and 4) RMSDD1.8300, developed by TRRL for use with the Beam. The data from the IRRE have been used to demonstrate the correlation among these numerics, and can be used to tie into past measures made with these numerics. Conversion equations were derived for converting old data based on the Brazil QI scale and the TRRL BI Trailer. They are suggested for use when derivation of more accurate relationships (reflecting local road characteristics) is not possible. Concluding remarks. The major questions that motivated the IRRE have been answered, and procedures have been demonstrated that allow the standardized measurement of roughness with a wide variety of equipment. Since the representation of equipment was by no means complete, equipment and methods that were not included should also be validated for use in measuring the IRI and other roughness indices. Other high-speed profilometers are in use, and newer designs are in development. Faced with the obvious problems of poor time-stability that can be seen with RTRRMSs, the acquisition of a profilometer or other instrument that is stable with time may at first appear to solve all of the problems. However, profilometers will not generally be suited for all profile analyses. Therefore, the validity of profilometers should be demonstrated experimentally for every analysis used (including IRI) by direct comparison with rod and level. 103 The influence of site length on accuracy was not investigated in the IRRE. Generally, variations due to random effects (e.g., the lateral positioning of the instrument in the travelled lane) can be reduced by selecting longer standard lengths. Test lengths other than 320 m, of course, can be used when measuring IRI (or any of the roughness numerics described in this report), although lengths shorter than 160 m should be avoided due to repeatability problems with RTRRMSs. When site lengths other than 320 m are used, the accuracy of the measurements (as characterized by reproducibility) should be determined when possible. In addition to the four surface types included in the IRRE, the RARS80 numeric has also been demonstrated to be valid for PCC roads [93. Care should be taken when performing calibrations to avoid surfaces with corrugations that could result in vehicle tuning. If measures are to be made on roads with unusual properties (corrugations, brick, etc.) then extra care should be taken to ensure valid measurements. If a profilometer is used, the measured profile should include all of the relevant pavement irregularities. If a RTRRMS is used, the vehicle should be de-tuned by installing stiff shock absorbers. Naturally, the procedures developed as a result of the IRRE [351 should be refined as necessary. It is recognized that the proposed IRI is a numeric that summarizes the roughness spectrum in a single number which is appropriate to vehicle calibration, but which is not the most appropriate for other applications, especially when profile measurement is performed. Other measures may serve as better indices of various qualities of pavement condition, or specific components of vehicle cost. As profilometric methods become more common, specialized analyses tailored to those applications may be considered candidates for future standardization. The various numerics used by CRR and LCPC from the APL dynamic profilometer already show this philosophy. 104 REFERENCES 1. Brickman, A.D., Park, W.H., and Wambold, J.C. "Road Roughness Effects on Vehicle Performance." Pennsylvania Transportation and Traffic Safety Center, Rept. No. TTSC-2707, 1972. 2. Abaynayaka, S.W., Hide, H., Morosiuk, G., and Robinson, R. "Tables for Estimating Vehicle Operating Costs on Rural Roads in Developing Countries." Transport and Road Research Laboratory, Rept. No. 723, 1976. 3. Van Dusen, B.D. "Analytical Techniques for Designing Ride Quality into Automotive Vehicles." SAE Paper No. 670021, January 1967. 4. Gillespie, T.D. and Sayers, M. W. "The Role of Road Roughness in Vehicle Ride." Paper presented at Session 60 of the Transportation Research Board Meeting, Washington, D.C., January 1981. 5. Sweatman, P.F. "A Study oE Dynamic Wheel Forces in Axle Group Suspensions of Heavy Vehicles." Special Rept. No. 27, Australian Road Research Board, June 1983. 6. "Road User Cost Study in India." Reports published quarterly, Central Road Research Institute, New Delhi, India. 7. Visser, A. and Queiroz, C.V. "Roughness Measurement Systems." Working Document #10, Research on the Interrelationships between Costs of Highway Construction, Maintenance, and Utilization, Empresa Brasileira de Planejamente de Transportes (GEIPOT), Brazil, July 1979. 8. Queiroz, C.V. "A Procedure for Obtaining a Stable Roughness Scale from Rod and Level Profiles." Working Document #22, Research on the Interrelationships between Costs of Highway Construction, Maintenance, and Utilization, Empresa Brasileria de Planejamente de Transportes (GEIPOT), Brasilia, July 1979. 9. Gillespie, T.D., Sayers, M. W., and Segel, L. "Calibration of Response-Type Road Roughness Measuring Systems." NCHRP Rept. No. 228, December 1980. 10. Mays Ride Meter Booklet. 3rd Ed., Rainhart Co., Austin, Texas, 1973. 11. Jordan, P.G. and Young, J.C. "Developments in the Calibration and Use of the Bump-Integrator for Ride Assessment." TRRL Supplementary Rept. 604, Transportation and Road Research Laboratory, 1980. 12. Gray, W.J. "A Review of Australian Experience with Road Roughness as Measured by the NAASRA Roughness Meter." Presented at the Symposium on Road Roughness at the 1981 TRB Annual Meeting. 13. Buchanan, J.A. and Catudal, A.L. "Standardizable Equipment for Evaluating Road Surface Roughness." Public Roads , February 1941. 105 14. Paterson, W.D.O. "Interim Report Reviewing Data Collection and Analysis in the Brazil PICR Project." Transportation Dept., World Bank, December 1981. 15. "Measurement of the Evenness of Pavement Courses Using the APL 25 Dynamic Longitudinal Profile Analyzer." Preliminary Draft Procedure, Laboratoire Central des Ponts et Chaussees, Division des Structures et Characteristiques de Chaussees. 16. Belgium Report Question II. Road Construction and Maintenance - XVII World Road Congress, PIARC, Sydney, 1983. 17. Lucas, J. and Viano, A. "Systematic Measurement of Evenness on the Road Network: High Output Longitudinal Profile Analyser." French Bridge and Pavement Laboratories, Rept. No. 101, France, June 1979. 18. "Analyseur de Profil en Long - APL 72." Bulletin 1 B AC 76, Materiels des Laboratories des Ponts et Chaussees. 19. Reichert, J. and Romain, J.E. "Road Evenness Measurement and Analysis in Permanent International Association of Road Congresses Countries." Presentation at the 60th Annual TRB Meeting, Washington, D.C., January 1981. 20. Gorski, M.B. "Etude de l'uni longitudinal des revetements routiers." Rept. CR 15/81, Centre de Recherches Routieres, Belgium, 1981. 21. Spangler, E.B. and Kelly, W.J. "GMR Road Profilometer, a Method for Measuring Road Profile." Research Publication GMR-452, General Motors Corp., Warren, Mich., December 1964. 22. Darlington, J.R. "Evaluation and Application Study of the General Motors Corporation Rapid Travel Profilometer." Research Rept. No. R-731, Michigan Dept. of State Hwys., October 1970. 23. Private Discussions, Mr. Michael Sayers and Mr. Marcio Paiva, June/July 1982, Brasilia, Brazil. 24. Burchett, J.L., et al. "Surface Dynamics Profilometer and Quarter-Car Simulator: Description, Evaluation, and Adaptation." Research Rept. No. 465, Kentucky Dept. of Transportation, 1977. 25. McKenzie, D. and Srinarawat, M. "Root Mean Square Vertical Acceleration (RMSVA) as a Basis for Mays Meter Calibration." Brazil Project Technical Memo BR-23, Center for Transportation Research, The University of Texas at Austin, February 1978. 26. Butler, B.C. "Report on RMSVA in Bolivia." July 1982. 27. Visser, A.T. "A Correlation Study of Roughness Measurements with an Index Obtained from a Road Profile Measured with Rod and Level." National Institute for Transport and Road Research, CSIR, South Africa, Tech. Rept. RC/2/82, March 1982. 106 28. McKenzie, D.W. and Hudson, W.R. "Road Profile Evaluation for Compatible Pavement Evaluation." Presentation at the 61st Annual TRB Meeting, Washington, D.C., January 1982. 29. Sayers, M. W. and Gillespie, T.D. "A Better Method for Measuring Pavement Roughness with Road Meters." Transportation Research Record 836, 1981, pp. 35-41. 30. Little, L.J. "A New Method of Calibrating NAASRA Roughness Meters." Australian Road Research Board, Internal Rept. AIR 354-1, 1980. 31. Carey, W.N., Jr. and Irick, P.E. "The Pavement Serviceability-Performance Concept." HRB Bulletin 250, 1960, pp. 40-58. 32. Rasmussen, R.E. "Validation of Mathematical Models for Vehicle Dynamics Studies." GMR Rept. 434, General Motors Research Laboratories, October 1964. 33. Clark, S.K. (ed.). Mechanics of Pneumatic Tires. DOT HS 805 952, August 1981. 34. Sayers, M.W., and Gillespie, T.D., "Dynamic Pavement/Wheel Loading for Trucks with Tandem Suspensions." Proceedings, 8th IAVSD Meeting, Cambridge, Mass., 1983 35. Sayers, M.W., Gillespie, T.D. and Paterson, W.D.O. Guidelines for Conducting and Calibrating Road Roughness Measurements. World Bank Technical Paper No. 46. Washington, D.C., 1986. 36. Mathematical Handbook for Scientists and Engineers. 2nd Ed., G.A. Korn and T.M. Korn, Eds., McGraw-Hill Book Co., New York, 1968. 37. Schultz, D.G. and Melsa, J.L. State Functions and Linear Control Systems. McGraw-Hill Book Co., New York, 1967. 38. "Effect of Road Profile Measurement Resolution on Dynamic Response of Quarter-Car Simulations." Unpublished studies from the NCHRP Project 1-18, The Univ. of Michigan, 1979. 39. Bendat, J.S. and Piersol, A.G. Engineering Applications of Correlation and Spectral Analysis. John Wiley & Sons, New York, 1980. 40. Walker, R.S. and Hudson, W.R. "A Correlation Study of the Mays Road-Meter with the Surface Dynamics Profilometer." Research Report 156-1, Center for Highway Research, University of Texas, Austin, February 1973. 107 APPENDIX A DESCRIPTION OF THE EQUIPMENT This appendix describes the various instruments that were used in the International Road Roughness Experiment (IRRE) to obtain measures of road roughness. In addition to detailing their design and normal usage, operational problems that occurred in the IRRE are noted. In all, there were seven Response-Type Road Roughness Measuring Systems (RTRRMSs), one APL dynamic profilometer (operated in two different modes), and two methods for statically measuring longitudinal profile. A GMR-type profilometer was also used, but it experienced a number of problems that prevented immediate data processing. (Rather than the instrumentation, the problems were mainly related to the age of the USA-made vehicle and the fact that it is not normally sold or serviced in Brazil.) The availability of other profile measurements reduced the importance of this data with respect to the objectives of the IRRE, and the signals were not processed. Texture depth measurements were made on the paved road sections by the sand patch method. The texture measures were found to be uncorrelated to any of the roughness measures, and are not included in this report. RESPONSE-TYPE ROAD ROUGHNESS MEASURING SYSTEMS (RTRRMSs) A RTRRMS consists of a vehicle instrumented with a roadmeter, which transduces and accumulates the suspension motion of the vehicle. The measure obtained from the roadmeter is generally a number of counts, where each count corresponds to a certain amount of suspension displacement. When the measure is normalized by the distance travelled during a test, the resulting measure has units of slope. Since the accumulation performed by the roadmeter is equivalent to a rectification of the suspension stroking speed, the measure obtained is proportional to the Average Rectified Velocity (ARV) of the 109 axle-body motion. When reported as a slope, it is called Average Rectified Slope (ARS). The ARV and ARS measures are influenced by the speed of the vehicle, and therefore the RTRRMS speed is included in this report as a subscript, e.g., ARS50 would be the measure obtained at 50 km/h. Four types of RTRRMSs participated in the IRRE, and are described below. The descriptions focus on the distinguishing features of each system; a more complete technical description of RTRRMS operation can be found in Reference [9]. (Note--numbers in brackets indicate references in the main text.) Opala-Maysmeter Systems Three of the RTRRMSs consisted of Chevrolet Opala passenger cars, made in Brazil, equipped with Maysmeters that are manufactured by the Rainhart Company in the USA [101. The Opala-Maysmeter systems, owned and operated by GEIPOT, had been used in the ICR project (Research on the Interrelationships Between Costs of Highway Construction, Maintenance and Utilization) [71. As delivered by Rainhart, the Maysmeter consists of two units: a transducer that is mounted in the rear of the vehicle; and a strip-chart recorder, normally placed in the front seat of the vehicle, which produces a paper plot whose length at the end of a test is the raw roughness numeric for that test. The units of the roughness measure are, therefore, those of length. The recorder employs two stepper motors, and is designed to advance the paper in proportion to accumulated axle deflection. For low roughness levels, the stepper motors perform as intended. However, the motors are not capable of responding accurately for high roughness levels that were covered in the ICR. Accordingly, the strip-chart units were replaced with electronic counters and digital displays [7]. Each electronic pulse that would normally be sent to the stepper motor instead increments an electronic counter. The Brazilian units are therefore capable of accurately measuring deflection for roughness levels much higher than would be possible with unmodified units. (Laboratory measurements made at The University of Michigan showed that the the stepper motors cannot track stroking speeds in excess of 800 mm/sec [71.) The transducer is based on an optical system, and produces counts when the deflection crosses thresholds, in effect, quantizing the suspension 110 deflection. In addition to the quantization, the units are affected by hysteresis, caused by spaces between windows in the film used by the optical sensor. Measurements of similar units have shown quantization levels of 2.54 mm and hysteresis levels of 0.75 mm [9]. In normal operation, the roughness measures are reported as "counts/km," and calibration equations are used to convert to the QI* roughness scale used in Brazil and described in Appendix E. The Brazilian meters were designed to produce one count for deflection quantities of 5.08 mm; however, it was found that one of the units (designated MM #3) required 10.16 mm of deflection to produce a count. The reason for this discrepancy was not found. Normal operating speeds used by GEIPOT since the ICR project are 80, 50, and 20 km/h. During the IRRE, the results of MM #3 were suspected of being invalid because they were much lower than the readings from the other two systems. Also, near the end of the IRRE, one of the mechanical connections loosened, causing a part of the transducer to fall off. The low readings were later explained by the different deflection/count calibration, and even though the failure of the roadmeter led to early speculation that the data would not be usable, the measures collected with MM #3 compare closely with measures obtained from the other two Opala-Maysmeter systems. The readings from MM #1 were also suspect. Calibrations were performed by the Brazilian team for all three Opala-Maysmeter Systems, before and after the experiment, over a series of control sections of road. The measures obtained with Maysmeter #1 differed by about 10% before and after the experiment, indicating that something was wrong. A quick examination of the instrument after the discrepancy was found did not reveal the cause. Since this type of variation is a normal characteristic of RTRRMSs, the results are considered representative and valid. The Opala-Maysmeter system designated MM #2 operated without any failures during the IRRE, and is usually used as the example Opala-Maysmeter system in plots and limited analyses. 111 Caravan Car-Based Systeus A Caravan station wagon, made in Brazil, was instrumented with two independent roadmeters: a BI unit and a NAASRA meter. All measures taken by the two roadmeters were made simultaneously, and were operated by the TRRL research team. Although neither the BI nor the NAASRA meters are normally used with this particular passenger car, the data obtained allow comparison of the meters, and provide what should be redundant measures. BI Roadmeter. The Bump Integrator (BI) is an instrument manufactured by TRRL that mounts between the axle and body of a vehicle and produces counts that are proportional to suspension motion [11]. The unit consists of a body-mounted transducer containing a pulley on a shaft, which is spring-loaded to maintain a cable in tension that connects the body and axle of the vehicle. Hence, the pulley rotates proportionately to the suspension motion. A mechanical clutch is used to transmit rotation in one direction only to a pulse generator component. The overall effect is that the instrument follows the suspension deflection in one direction, while remaining unresponsive to movement in the other direction, thereby accumulating the displacement. When the accumulated movement reaches 25.4 mm (1.0 inch), a pulse is sent to an electronic counter. Therefore, each count corresponds to one inch of deflection in one direction, or 50.8 mm when considering both directions. ARS numerics reported for the BI roadmeter in this report are based on the scale factor of 50.8 mm/count. Normally, TRRL reports the measures using a scale factor of 25.4 mm/count, resulting in numerics that would have 1/2 the amplitude of the ARS measures repored here. Unlike the Maysmeter, the BI transducer has no design hysteresis or quantization. (The quantization involved in producing the discrete counts occurs in the display, rather than the transducer.) In practice, however, the transducer has limitations due to its mechanical properties. Very small vibrations were seen to produce no response, due to small amounts of free play (hysteresis) in various parts of the system (bearings, linkages, etc.). During the experiment, the BI suffered a broken spring, which was replaced. As soon as the measurements were finished, this particular BI was 112 installed in the BI trailer, to replace a more troublesome BI roadmeter. NAASRA Roadmeter. The NAASRA meter is a mechanical instrument that operates on the same principles as the BI. One count produced by the NAASRA meter corresponds to an accumulated deflection in one direction of 15.2 mm, or a total accumulated deflection in both directions of 30.4 mm. ARS numerics presented in this report are based on the scale factor of 30.4 mm/count. This meter also demonstrated a small amount of mechanical hysteresis (free play), which was not measured. The NAASRA meter was operated by members of the the TRRL research team. Although they had little experience with the device, it was simple to use, and only suffered one problem with a broken wire that was easily repaired. The Bump Integrator Trailer The BI Trailer, also called the towed fifth wheel, is basically a BPR Roughometer that has undergone a great deal of development by TRRL. It consists of a single-wheeled trailer with a leaf spring suspension and special shock absorbers and is shown in Figure 1 in the main report. The shock absorbers are claimed to have damping properties that are fairly insensitive to time and operating conditions. All BI Trailers are constructed to be nearly identical. Because most of the vehicle properties that influence the roughness measure are controlled, measures from a BI Trailer have been reported without any further corrections or calibration, usually in units of mm/km, corresponding to the accumulated suspension movement in one direction. The ARS measures reported in this document assume a scaling of 50.8 mm/count, and are twice the value of the "mm/km" numeric normally reported by TRRL, since ARS is based on the accumulated motion in both directions. The BI trailer is designed to be unresponsive to movements of the towing hitch induced by the towing vehicle through the careful placement of the percussion center of the trailer frame. Nevertheless, the trailer used in the IRRE did produce measurements in the garage when the towing vehicle was 113 bounced, indicating that dynamic properties of the towing vehicle can influence the roughness measures. The mechanical properties of the trailer are checked periodically using simple bounce tests [111, although even when the bounce tests are within tolerances, changes in the response properties have been observed [7]. A BI roadmeter is attached on one side of the trailer to measure the movement of the axle relative to the trailer frame. The normal towing speed of the trailer is 32 km/h. The tow hitch for the trailer was fabricated in Brasilia for the experiment, and a number of problems were experienced until the hitch attachment was properly strengthened and aligned. Other problems existed in the BI unit attached to the trailer. A spring broke and was repaired; the clutch failed and needed to be stripped, cleaned, and reassembled; and the unit produced extraneous counts on occasions. As a result, all of the tests on the paved sections were repeated after the other instruments had finished. During the entire experiment, many of the measurements made by the BI Trailer were "make-ups," made on week-ends, during lunch, etc. The measurements made last were accomplished with the use of the BI Transducer that had been in the Caravan. BPR Roughometer The BPR Roughometer that participated in the IRRE, shown in Figure 1 in the main report, is a single-wheeled trailer built to the specifications published in 1940 by the Bureau of Public Roads [13] by Soiltest, Inc., as the Road Roughness Indicator Model CT444. This trailer is equipped with a magnetic sensor that produces a pulse for a deflection of 0.002 inch in either direction. Because the original BPR mechanical transducer measured deflection in only one direction, the display is scaled to show one half of the accumulated deflection, in inches. Although the actual transducer is not mechanical, a cable connection with a tension spring is employed, with the potential for vibration problems at high roughness levels. One gear involved in the linkage often slipped on its shaft, resulting in a loss of counts. 114 The normal measurement speed for a BPR Roughometer is 32 km/h (20 mph). During the experiment, the BPR trailer experienced breakdowns and failures almost on a daily basis. Support pins for the shock absorbers were broken frequently. On two occasions, studs for universal joints in the shock absorber connections were lost and replacements had to be fabricated in a local machine shop. All too frequently, screws that held a critical gear to the main shaft in the transducer loosened, allowing slippage and therefore reduced roughness measures. At the beginning of the experiment, the trailer was towed to and from the test sites. After the first two weeks, it was carried in the truck that served as the towing vehicle, and unloaded at the test sites to minimize its exposure to road vibrations and damage. Also, the operators learned the limits of the instrument, and declined to subject it to the more demanding conditions near the end of the experiment. THE APL DYNAMIC PROFILOMETER The APL Trailer The Longitudinal Profile Analyser (APL) Trailer, shown in Figure 2 in the report, is an instrument developed by the French Bridge and Pavement Laboratory (LCPC) to obtain a signal proportional to profile over the frequency range 0.5 - 20 Hz [15, 17, 18]. The trailer consists of three mechanical elements: a frame that acts as a sprung mass, a follower wheel, and a horizontal pendulum. The trailer frame and the suspension serve only to keep the follower wheel on the road by reducing bouncing and oscillations. Compared to a passenger car, the suspension is soft and exhibits high damping. The observed resonance of the sprung mass is well below 1 Hz, and the damping is close to critical. Unlike the BI Trailer and BPR Roughometer, the APL Trailer does not include a roadmeter, and does not measure the deflection between the axle and frame. Instead, a LVDT displacement transducer is located between the trailing arm that supports the follower wheel and the horizontal pendulum. The horizontal pendulum consists of an arm with weights at each end, supported 115 in the center by a Bendix-type pivot with crossed blades. One of the weights can be repositioned, allowing adjustment of the rotational moment of inertia. The pendulum is centered by a coil spring, while damping is provided magnetically. Together, the pendulum, spring, and damper constitute a mechanical system that is tuned in the laboratory to provide a unity gain for input frequencies over 0.5 Hz. (Lower input frequencies result in an attenuated response.) The displacement that is measured is designed to replicate the wavenumber content of the longitudinal road profile over the wave number range that corresponds to the frequency range of 0.5 - 20 Hz at the measurement speed. The upper limit is imposed by the dynamic response of the follower-wheel assembly, which will attenuate any inputs at frequencies above 20 Hz. Rather than following changes in road elevation at high frequencies, the follower wheel will absorb the changes through deflections of the compliant tire. This device contrasts with a conventional passenger car design, in which the unsprung mass (axle and wheels) will over-respond at the resonance frequency of the unsprung mass. This behavior is avoided with the APL Trailer because the suspension is designed to provide much more damping. The lower limit of the trailer response at 0.5 Hz is imposed by the dynamic properties of the horizontal pendulum. The trailer is certified at manufacture by placing a dynamic shaker under the follower wheel and measuring the ratio of the output signal amplitude to the input amplitude for sinusoidal inputs. The locations of the shock absorber and coil spring in the suspension are adjusted to optimize the response. The shaker is also placed under the towing hitch, to assure that the trailer is acceptably unresponsive to these movements. The trailer used in the IRRE was demonstrated to be completely unaffected by movements of the towing vehicle. With the vehicle stationary in the garage and the instrumentation functioning, bouncing motions of the towing vehicle did not cause any signal to appear. This contrasts with similar checks of the other two trailers (BPR and BI), which showed that these two systems were not decoupled, but did in fact respond to movements of the hitch. The distance travelled and the towing speed are measured from a signal generated with the use of a toothed disk attached to the follower wheel. 116 The instrumentation that is used to record data varies with the configuration of the APL trailer (APL 25 and APL 72), described below. APL 25 System When operated for the APL 25 analysis, the trailer was towed at 21.6 km/h (6.0 m/s), and the transducer signal was digitized with a resolution of 1.0 mm at 250 mm intervals (as detected by the distance pulse signal). The samples were summed over an interval of 25 m to yield the CAPL 25 roughness statistic during measurement. (The CAPL 25 analysis is discussed in more detail in Appendix G.) The digitized signal, and also the CAPL 25 numerics, were stored in digital form on a tape cassette. Later, in the laboratory, the cassette was played back into a microcomputer (a European version of the Apple II+, made by ITT) for plotting of either the raw signal, or the CAPL 25 coefficients as functions of the distance travelled, using a digital X-Y recorder (examples are presented in Appendix G). The computer also created copies of the cassette data files on flexible diskettes, to facilitate further analyses. Copies of these diskettes were used for the alternate analyses described in Appendix E and F, performed after the completion of the experiment. APL 72 System During testing in the APL 72 configuration, the signals were recorded on an analog FM tape recorder. Back in the laboratory, the tapes were played back, with the profile signal going into a bank of three electonic processors. (Six processors are used when two APL Trailers are towed together over both travelled wheeltracks.) Each processor passes the signal through an electronic bandpass filter, then squares and integrates the signal over a travelled distance of 200 m. The resulting three numerics (per wheeltrack) are the APL 72 coefficients, described in more detail in Appendix G. The tapes were also played into a microcomputer (a European equivalent to the Apple II+ made by ITT) through an 8-bit (resolution = 0.35 mm) digitizer, sampling at 50 mm intervals for plotting purposes. Normally, the digitized 117 data were plotted but not stored in digital form, since the routine analyses performed in Europe by LCPC use the analog signal. During the IRRE, a program was written on the microcomputer to edit and store these data on diskette, for the alternate processing of APL 72 signals described in Appendices E, F, and J. After returning to France, the tapes were re-processed by LCPC to obtain complementary numerics and to validate the results provided by the LCPC team in Brazil. The analog tapes were loaned to the Belgian Road Research Center (CRR) for analyses there. At CRR, the analog signals were digitized at 1/3 m intervals, using equipment that processed 100 m sections. These digitized signals were used to prepare the CP numeric reported in Appendix G. ST&TIC PROFILE MEASUREMENTS Rod and Level Survey The longitudinal profile of each wheeltrack was measured directly with the conventional rod and level method. In this measurement, a crew of three persons was used, as shown in Figure 3 in the report. A surveying level is used to establish a horizontal reference, and is operated by one of the crew members. One of the wheelpaths of the test site is marked and a surveyor's tape is placed on it to provide a simple distance reference. A second crew member holds the rod, marked in mm, on the tape at the appropriate distance. Sighting through the level, the first crew member calls out the reading from the rod (which is the difference in elevation between the level and the road surface where the rod is placed) to the third crew member, who writes the figure on a special coding. When possible, a fourth crew member was included. The members would rotate positions to reduce fatigue. In this experiment, elevations were measured at 500 mm intervals. It normally took about 3 - 1/2 hours for a trained crew to complete both wheeltracks of one of the 320 m long test sections. All of the paved test sections were surveyed before the start of the experiment. During the experiment, many of the sections were re-surveyed. The second half of the experiment, covering unpaved sections, was scheduled 118 such that all of the sections were surveyed before being measured by the other equipment. In all cases, the survey was performed no more that two days before the other equipment was run. At the end of the experiment, six wheelpaths were surveyed with a 100 mm interval. At various times throughout the project, there were from one to three crews operating simultaneously. The field forms were checked back in the offices at GEIPOT, and submitted to keypunchers who entered the data into the GEIPOT computer system. There, the profile was computed, and checked for obvious errors. Further details about the procedures used are given in Reference [81. All of the rod and level profiles were put on an IBM 9-track tape, and taken to UMTRI, where they were copied onto floppy diskettes for distribution to the other participants. The TRRL Beam The TRRL Beam is an experimental device developed by TRRL to measure longitudinal profile, with less effort than is needed with the rod and level surveying approach. A beam, 3 meters long, is supported at each end by a tripod with adjustable height, as shown in Figure 4 in the report. The beam acts as a track and guide for an instrumented sliding fixture, that contacts the ground via a 250 mm follower wheel. The sliding fixture contains a transducer that detects its position along the length of the beam, and a second transducer that detects the vertical position of the follower relative to the beam. The signals from these two transducers are fed to a microcomputer that digitizes the vertical position signal (resolution = 1.0 mm) at constant intervals. The Beam is operated by placing each tripod on the endpoints of the three-meter section of track to be measured. One or both of the tripods are adjusted to level the beam. The sliding unit is moved to the "begin" end of the beam, and the instrumentation is activated. Then the sliding unit is moved to the "finish" end of the beam, at a normal walking pace, such that no bouncing of the follower wheel occurs. Then, the entire Beam assembly is picked up and relocated, such that the new "start" position of the first 119 tripod coincides with the old "finish" position of the second tripod. The Beam is again levelled, and the process is repeated. At the time that the experiment began, the Beam was still being tested and programmed in the UK. The Beam did not arrive in Brasilia until the experiment was nearly finished for the other equipment; therefore, the profile measures made with the Beam were not within the same I - 2 day time frame as the other measures. In all, 28 wheeltracks were profiled with the Beam, at the rate of about two per day. The microcomputer used in the Beam was programmed to calculate two roughness measures and to store the profile at 100 mm intervals. Only the profile measures (relative to the Beam reference for each set-up) were validated by the TRRL team, and submitted as valid data. These measures were available only as paper printouts, and had to be typed into a computer system by hand for analysis. A program was written in Brasilia to allow rapid entry of the data into an Apple II+ computer, and the data for all 28 sections were entered in Brasilia by members of the GEIPOT staff. (Due to time limitations, some of the profiles were entered by the TRRL team in the UK using the same computer program, so that they could begin their analyses immediately.) With practice, it took slightly under two hours to enter all 3,200 data points for one wheeltrack. Once in the computer, another program was used to convert each set of 30 relative measurements corresponding to one Beam set-up to a continuous profile and check for errors. 120 APPENDIX B DATA FROM THE RTRRMSs This appendix presents all of the average rectified slope (ARS) measures that were gathered by response-type road roughness measuring systems (RTRRMSs) during the International Road Roughness Experiment (IRRE). Sum-ary of Neasurements All of the roadmeters used in the IRRE produce measurements that are equivalent, being the accumulation of suspension deflection of the host vehicle. Each instrument reports the measure in "counts," however, rather than a standard unit. To facilitate simple comparisons, all of the results have been converted to the same units, namely, "slope x 1000." The "slope" represents the accumulated suspension deflection (in both directions) divided by the distance travelled. This measure is dimensionally equivalent to the "Inches/Mile," "mm/km," and "counts/km" that are used by different agencies throughout the world, with the scaling differences clearly defined by the units. The factor of 1000 corresponds to the metric ratios: "m/km" and "mm/m." This particular scaling was selected for convenience in preparing tables and figures for this report: slope (m/m) values were too small, and slope x 1,000,000 (mm/km) figures were too large for fitting onto the tables and plot axes. Tables B.1 - B.28 present the results for the RTRRMSs. The paved sections were divided into categories of asphaltic concrete and surface treatment types. The unpaved sections were split into groups with gravel and earth surfaces. These four surface types are abbreviated (based on their spelling in Portuguese) as CA, TS, GR, and TE, respectively. During testing, the car-based systems generally made five consecutive measurements for each section. These measures are listed as "RUN 1," "RUN 2," etc. The "B" listed under TRACK indicates that the vehicle travelled both the right- and left-hand tracks simultaneously during each run, and that the RTRRMS was a "two-track" type. The two single-track trailer instruments usually made three repeats in 121 each of the two wheel-tracks. The track is indicated by an "R" or "L," for right or left. The mean and standard deviation of the test results are listed under MEAN and SIGMA, while the relative error, defined by SIGMA/MEAN is listed under S/M. Although the testing procedure was intended to allow each vehicle to "warm up" prior to testing, the possibility exists that the shock absorbers or pneumatic tires had not reached steady-state temperature, and were changing during testing. To examine this possibility, a regression was performed between the measures and the run number for each test condition (site and speed). The slope of the regression equation, with units "slope x 1000/run," is reported under TREND, while the correlation coefficient is reported under R. These two columns allow one to determine, at a glance, whether or not the measures were consistently increasing or decreasing during testing for any condition. Tables B.29 - B.32 summarize the results of all seven instruments, by presenting only the mean values. The data from the trailers are combined to yield the average of the two wheeltrack measures for each site, for comparison with the two-track RTRRMS measurements. Discussion Tables B.1 - B.28 indicate that, by and large, the repeatability of the instruments is better than 5% (S/M), with a repeatability of around 3% being typical for this test length of 320 m. Relative measurement error is larger on the smoothest sections, although in absolute units, the errors are still smaller than the errors on the rougher sections. In most cases, trends were very small, leading to the conclusion that the warm-up procedures used in the testing were adequate. However, there was concern that the warm-up was insufficient for the roughest surfaces, which show high R values. Some repeat tests were made with one of the Maysmeter systems on the roughest sections (GR11, GR12, TE05, and TE06) after the IRRE was complete, to ensure that steady-state conditions had been achieved. In each case, 12 or more consecutive measures were made. These results indicated that an absolute steady state was difficult to obtain, but that the results obtained earlier were representative. In practice, a true steady state may not exist for the 122 extremely rough sections because the rough sections of the road are quite short. The best practice here is to use heavy-duty shock absorbers, selected for maximum damping and minimum sensitivity to temperature. Tables B.29 - B.36 offer a direct comparison of the different RTRRMSs. A larger number for one system in comparison with another means that there was more response, either by the vehicle or by the meter. In most cases, the results of all five of the car-based systems are similar. As should be expected, the measures from the BI and the NAASRA meter, which were both mounted in the same vehicle, were usually redundant. These data are analyzed in Appendix C, in terms of correlation. 123 Table B.1. Summary of Results from Miays Meter #1 on the Asphaltic Concrete Roads. INTERNATIONPL ROAD ROU&HNESS EXPERIMENT - BRASILIA - JUNE 1982 MAYS METER #1 SITE SPEED TRACK ROU6HNESS HEASURENENT (SLOPE X 1000) QK/0) NEAN RUN I RUN 2 RN 3 RO 4 RN 5 SIGM SIN TREND R CAOI 20 B 2.54 2.57 2.4 2.54 2.6 2.6 .09 .034 .027 .497 32 B 3.13 3.33 3.17 3.13 3.16 2.84 .18 .057 -.1 -.886 50 B 3.92 3.83 3.75 3.97 3.98 4.1 .14 .035 .078 .99 so B 4.29 4.19 4.25 4.29 4.25 4.44 .1 .022 .051 .843 CMA2 20 B 3.26 3.19 3.27 3.33 3.17 3.32 .07 .022 .016 .348 32 B 3.79 3.86 3.73 3.73 3.76 3.83 .06 .015 -3E-03 -.087 50 B 4.32 4.16 4.35 4.3 4.37 4.41 .1 .023 .052 .852 80 B 4.5 4.35 4.43 4.57 4.48 4.67 .12 .028 .068 .872 CA03 20 B 6.01 5.97 6.03 6 6.1 5.97 .05 9E-03 6E-03 .189 32 B 6.12 6.05 6.19 6.08 6.13 6.18 .06 .01 .019 .495 50 B 5.7 5.62 5.76 5.84 5.72 5.56 .11 .02 -.017 -.244 80 a 6.18 6.16 6.18 6.08 6.27 6.19 .07 .011 .016 .368 CAo4 20 B 5.34 5.21 5.29 5.37 5.45 5.4 .09 .018 .054 .905 32 B 5.86 5.84 5.86 5.86 5.87 5.89 .02 3E-03 .011 .971 50 a 5.98 5.78 5.91 6.03 6.13 6.05 .14 .023 .076 .878 80 B 5.55 5.37 5.51 5.62 5.68 5.56 .12 .022 .056 .728 CA85 20 B 7.47 7.38 7.48 7.490 7.46 7.56 .06 BE-03 .033 .838 32 3 7.27 7.25 7.19 7.41 7.33 7.16 . 1 .014 -5E-03 -.072 50 b 6.98 6.91 7.06 6.95 7.05 6.92 .07 .01 2E-03 .034 80 B 6.5 6.29 6.51 6.59 6.48 6.64 .13 .021 .067 .784 CA06 20 B 7.77 7.7 7.78 7.84 7.72 7.79 .06 8E-03 .013 .342 32 B 7.5 7.4 7.46 7.59 7.45 7.6 .09 .012 .04 .685 50 B 7.43 7.33 7.35 7.46 7.48 7.52 .08 .011 .051 .965 80 B 7.53 7.43 7.48 7.59 7.68 7.46 .11 .014 .027 .404 CA07 20 B 2.1 2.17 2.08 2.1 2.05 .05 .026 -.037 -.872 32 B 2.11 2.17 2.08 2.1 2.03 2.16 .06 .028 -8E-03 -.214 50 B 2.62 2.71 2.6 2.62 2.57 2.57 .06 .022 -.032 -.854 9O B 3 3.1 3.03 2.98 2.97 2.92 .07 .022 -.041 -.983 CAO8 20 B 2 1.94 2.02 2 2.06 .05 .026 .037 .099 32 B 1.75 1.73 1.67 1.75 1.78 1.84 .06 .037 .033 .822 50 B 2.31 2.3 2.4 2.25 2.27 2.3 .06 .024 -.013 -.362 80 B 2.89 3.06 2.86 2.79 2.83 2.89 .11 .037 -.038 -.571 CAO9 20 B 3.6 3.62 3.49 3.65 3.56 3.67 .07 .02 .016 .347 32 B 3.47 3.35 3.49 3.46 3.51 3.52 .07 .02 .037 .828 50 B 3.79 3.86 3.79 3.76 3.84 3.68 .07 .018 -.03 -.684 g0 B 4.25 4.35 4.27 4.18 4.21 4.24 .07 .016 -.029 -.675 CAlO 20 B 2.81 2.71 2.81 2.86 2.87 .07 .025 .052 .947 32 B 2.98 2.89 2.94 3 3.05 3.03 .07 .022 .04 .94 50 B 3.44 3.4 3.4 3.49 3.44 3.44 .04 .012 .014 .567 80 B 3.72 3.59 3.73 3.64 3.75 3.92 .13 .034 .068 .841 CAII 20 B 6.43 6.37 6.4 6.51 6.4 6.48 .06 9E-03 .022 .581 32 B 6.72 6.78 6.73 6.65 6.76 6.7 .05 8E-03 -.013 -.394 50 B 5.7 5.72 5.59 5.73 5.65 5.81 .08 .015 .025 .478 80 B 5.95 5.84 5.95 6.03 5.91 6 .08 .013 .027 .563 CA12 20 B 1.23 1.32 1.24 1.16 1.25 1.16 .07 .055 -.03 -.704 32 B 1.32 1.29 1.48 1.37 1.19 1.27 .11 .082 -.032 -.464 50 B 1.26 1.17 1.37 1.35 1.29 1.13 .11 .084 -.017 -.261 80 B 1.96 2 1.87 2.06 1.9 1.97 .08 .039 -3E-03 -.066 CA13 20 B 1.16 1.19 1.14 1.19 1.08 1.19 .05 .042 -6E-03 -.205 32 B 1.14 1.1 1.24 1.17 1.08 1.13 .06 .056 -.01 -.234 50 B 1.36 1.44 1.33 1.33 1.4 1.29 .06 .046 -.025 -.647 80 B 2.09 1.92 2.21 2.06 2.22 2.03 .13 .06 .024 .298 124 Table B.2. Summary of Results from Mays Meter #1 on the Surface Treatment Roads. INTERNPJTIONAL ROAiD ROU&HNESS EXPERIMENT - BRASILIA - JUNE 1982 MAYS METER #1 SITE SPEED TRACK ROUGHNESS MEASUREMENT (SLOPE X 1000) (KIH) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA SlN TREND R TSO1 20 B 7.47 7.56 7.51 7.46 7.38 7.43 .07 9E-03 -.038 -.887 32 B 5.72 5.72 5.65 5.64 5.75 5.86 .09 .016 .038 .678 50 B 5.21 5.25 5.19 5.14 5.29 5.18 .06 .011 -6E-03 -.171 80 B 6.14 6.18 6.21 6.1 6.08 6.16 .05 9E-03 -.016 -.466 TS02 20 B 9.39 9.45 9.35 9.38 9.48 9.29 .08 8E-03 -.019 -.397 32 B 7.44 7.46 7.6 7.43 7.38 7.33 .1 .014 -.048 -.735 50 B 5.62 5.57 5.64 5.43 5.7 5.75 .12 .022 .041 .528 80 B 4.92 4.92 5.02 4.84 4.89 4.92 .06 .013 -.013 -.314 TS03 20 0 8.73 8.79 8.72 8.72 8.64 8.79 .07 8E-03 -BE-03 -.189 32 B 7.68 7.6 7.68 7.72 7.640 7.75 .06 8E-03 .024 .65 50 3 6.9 6.89 6.89 6.95 6.89 6.86 .03 5E-03 -6E-03 -.289 80 B 5.9 5.84 5.89 5.86 5.97 5.92 .05 9E-03 .024 .739 TS04 20 B 8.17 8.22 8.1 8.25 8.19 8.1 .07 9E-03 -.016 -.343 32 B 7.85 8.08 7.91 7.79 7.640 7.84 .16 .021 -.075 -.728 50 B 6.33 6.16 6.21 6.35 6.48 6.48 .15 .023 .09 .966 80 B 7.890 7.79 7.94 7.87 7.95 7.91 .06 BE-03 .024 .599 TS05 20 B 9.47 9.37 9.41 9.51 9.49 9.59 .09 9E-03 .052 .957 32 B 8.53 8.43 8.56 8.59 8.57 8.49 .07 8E-03 .014 .343 50 B 7.05 6.92 7.05 6.98 7 7.3 .15 .021 .071 .766 80 B 9.58 9.4 9.54 9.68 9.6 9.65 .11 .012 .057 .799 TS06 20 B 4.69 4.81 4.67 4.71 4.64 4.6 .08 .017 -.044 -.873 32 B 3.84 3.84 3.84 3.84 3.83 3.84 .01 2E-03 -2E-03 -.354 50 B 3.48 3.54 3.57 3.4 3.48 3.4 .08 .023 -.038 -.751 80 8 3.22 3.41 3.32 3.03 3.22 3.11 .15 .048 -.07 -.721 TS07 20 B 3.9 4.05 3.89 3.83 3.89 3.86 .09 .022 -.038 -.702 32 B 3.72 3.75 3.91 3.73 3.64 3.59 .12 .033 -.059 -.76 50 B 3.41 3.44 3.4 3.4 3.32 3.48 .06 .018 -2E-03 -.042 80 B 3.14 3.17 3 3.17 3.1 3.25 .1 .031 .025 .418 TS08 20 B 5.36 5.51 5.32 5.4 5.24 5.35 .1 .019 -.04 -.627 32 B 4.51 4.81 4.48 4.44 4.51 4.32 .18 .04 -.095 -.828 50 B 3.38 3.4 3.25 3.37 3.38 3.51 .09 .027 .035 .61 80 B 3.74 3.62 3.81 3.78 3.67 3.81 .09 .024 .024 .427 TS09 20 B 5.6 5.65 5.72 5.62 5.48 5.56 .09 .016 -.043 -.743 32 B 5.25 5.41 5.3 5.11 5.19 5.21 .12 .022 -.052 -.715 50 B 5.05 4.92 4.92 4.71 4.78 5.92 .49 .098 .186 .594 80 B 3.93 3.91 4.03 3.89 3.94 3.87 .06 .016 -.016 -.398 TSIO 20 B 5.85 5.79 5.89 5.79 6 5.75 .1 .017 2E-03 .025 32 B 5.15 4.94 5.24 5.19 5.24 5.14 .13 .024 .041 .521 50 B 4.66 4.7 4.76 4.62 4.57 4.65 .07 .016 -.029 -.617 80 B 4 3.95 3.98 4.13 3.91 4.03 .08 .021 8E-03 .148 TSII 20 B 3.71 3.76 3.71 3.79 3.68 3.6 .07 .02 -.035 -.747 32 B 3.11 2.89 3.1 3.22 3.11 3.25 .14 .046 .075 .822 50 B 2.34 2.32 2.41 2.29 2.3 2.37 .05 .022 -2E-03 -.048 80 B 2.82 2.78 2.86 2.75 2.79 2.92 .07 .025 .022 .504 TS12 20 B 3.67 3.65 3.59 3.67 3.71 3.75 .06 .017 .032 .822 32 B 3.15 3.1 3.17 3.24 3.14 3.11 .06 .018 0 0 50 B 2.43 2.44 2.37 2.37 2.35 2.64 .12 .049 .037 .483 80 B 2.79 2.7 2.83 2.76 2.79 2.87 .07 .024 .032 .762 125 Table B.3. Summary of Results from Mays Meter #1 on the Gravel Roads. INTERNATIONAL ROAD ROiJHNE S;S EXPERIMENT - BRASILIA - JUNE 1982 MAYS METER#1 SITE SPEED TRACK ROUGHNESS MEASUREMENT (SLOPE X 1000) (K7H) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA S/N TREND R BRO 20 B 3.81 3.95 3.75 3.86 3.78 3.73 .09 .024 -.041 -.706 32 B 3.68 3.7 3.67 3.68 3.75 3.62 .05 .013 -8E-03 -.271 50 B 2.8 2.76 2.91 2.87 2.83 2.64 .11 .038 -.033 -.493 80 B 3.28 3.41 3.33 3.16 3.19 3.3 .1 .032 -.037 -.553 BRO2 20 B 4.12 4.08 4.14 4.05 4.19 4.14 .06 .014 .017 .486 32 B 3.9 3.89 3.95 3.84 3.78 4.03 .1 .025 .011 .179 50 B 3.25 3.24 3.32 3.35 3.21 3.16 .08 .024 -.027 -.543 80 B 3.17 3.16 3.27 3.21 3.14 3.1 .07 .021 -.025 -.605 6R03 20 B 10.23 10.29 10.21 10.18 10.26 10.22 .04 4E-03 -8E-03 -.293 32 9 8.7 8.65 8.81 8.64 8.73 8.68 .07 8E-03 -2E-03 -.036 50 B 7.490 7.48 7.51 7.45 7.54 7.490 .04 5E-03 6E-03 .283 go B 6.58 6.48 6.62 6.490 6.54 6.75 .11 .017 .046 .657 6RN4 20 B 8.14 8.11 8.19 8.25 .8.08 8.08 .08 9E-03 -.017 -.359 32 B 7.25 7.27 7.16 7.3 7.32 7.21 .07 9E-03 3E-03 .075 50 B 6.45 6.41 6.54 6.52 6.43 6.32 .09 .014 -.03 -.527 80 B 5.73 5.76 5.68 5.75 5.79 5.65 .06 .01 -.011 -.299 BRO5 20 B 13.4 12.64 13.51 13.64 13.49 13.73 .44 .033 .217 .784 32 B 12.71 12.73 12.62 12.54 12.7 12.95 .16 .012 .052 .533 50 B 11.15 11.53 11.06 10.94 11.26 10.95 .25 .022 -.095 -.611 80 B 10.79 10.65 10.94 10.76 10.78 10.83 .1 .01 .019 .29 8806 20 B 12.34 12.45 12.32 12.41 12.37 12.18 .11 9E-03 -.049 -.736 32 B 11.12 11.13 11.06 11.26 10.94 11.19 .12 .011 0 0 50 B 10.13 10.18 9.99 10.32 10.19 10 .14 .014 -.014 -.161 80 B 9.25 8.72 9.54 9.33 9.4 9.27 .32 .034 .097 .484 6R07 20 B 8.52 9.08 8.43 8.46 8.29 8.32 .32 .038 -.167 -.813 32 B 7.640 7.75 7.6 7.60 7.38 7.78 .16 .021 -.016 -.158 50 B 6.79 6.97 6.68 6.64 6.75 6.92 .15 .022 -3E-03 -.034 80 B 5.91 5.95 5.84 5.7 5.86 6.21 .19 .032 .052 .44 BROS 20 B 5.76 5.95 5.73 5.86 5.65 5.6 .14 .025 -.078 -.849 32 B 4.89 5.59 4.95 4.95 4.89 4.06 .54 .111 -.311 -.907 50 B 4.28 4.27 4.27 4.19 4.32 4.37 .06 .015 .024 .58 80 B 4.04 3.94 3.92 3.97 4.22 4.13 .13 .033 .068 .811 6RQ9 20 B 12.27 12.05 12.3 12.4 12.29 12.3 .13 .011 .049 .598 32 B 10.88 10.91 10.65 10.92 11.03 10.91 .14 .013 .038 .43 50 B 9.53 9.26 9.64 9.91 9.21 9.67 .3 .031 .04 .212 80 B 9.19 8.97 10.14 8.94 9.21 8.72 .56 .061 -.144 -.409 GRIO 20 B 9.48 9.46 9.76 9.43 9.27 9.46 .18 .019 -.049 -.437 32 B 8.58 9.59 8.6 8.72 8.57 8.4 .11 .013 -.041 -.572 50 B 7.57 7.48 7.J5 7.51 7.59 7.62 .07 .01 .022 .475 80 B 8.36 8.3 8.16 8.35 8.43 8.54 .14 .017 .075 .829 BRI} 20 8 21.73 21.61 21.75 21.84 21.88 21.57 .14 6E-03 6E-03 .074 32 B 26.92 27.05 26.81 26.94 27.13 26.69 .18 7E-03 -.041 -.365 50 B 18.57 18.11 18.32 18.73 18.89 18.81 .34 .018 .197 .919 6R12 20 B 24.3 23.83 23.65 23.84 24.92 25.26 .73 .03 .413 .09 32 B 19.15- 17.99 18.13 18.24 18.1 18.27 .12 6E-03 .054 .742 50 B 17.01 16.81 16.53 17.05 17.18 17.46 .36 .021 .195 .867 126 Table B.4. Summary of Results from Mays Meter #1 on the Earth Roads. INTERNigTIONAL ROAD RUGHHN3ESS EXPERIhJENT - BRSZL1/ - JUNE 19f2 MAYS METER #1 SITE SPEED TRACK ROUGHNESS MEASUREHENT (SLOPE X 1000) (KIH) HEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA S/N TREND R TEOI 20 8 6.67 6.54 6.67 6.56 6.73 6.84 .13 .019 .067 .84 32 8 5.26 5.19 5.14 5.16 5.24 5.57 .18 .034 .086 .763 50 B 4.39 4.38 4.35 4.33 4.46 4.43 .05 .012 .021 .611 80 9 4.19 4.29 4.21 4.21 4.08 .09 .02 -.062 -.936 TE02 20 B 6.44 6.6 6.4 6.3 6.35 6.56 .13 .02 -.014 -.172 32 B 5.09 4.87 5.24 5.18 5.1 5.06 .14 .027 .024 .272 50 8 4.07 4.06 3.92 3.98 4.19 4.21 .13 .031 .056 .701 80 8 3.98 3.95 4.06 3.91 4.02 .07 .018 3E-03 .059 TE03 20 8 12.6 12.41 12.86 12.46 12.73 12.54 .19 .015 .013 .107 32 B 11.11 11.18 11.02 11.13 11.08 11.14 .06 6E-03 0 0 50 3 8.3 8.19 8.19 8.38 8.41 8.33 .11 .013 .051 .763 80 B 7.02 6.91 6.91 7.05 7.08 7.14 .11 .015 .065 .961 TE04 20 8 13.05 13.02 12.67 13.14 13.16 13.24 .23 .017 .094 .656 32 B 11.24 11.24 11.35 11.11 11.18 11.32 I 9E-03 -2E-03 -.025 50 B 8.6 8.59 8.46 8.64 8.73 8.57 .1 .011 .024 .383 80 B 6.76 6.64 6.73 6.83 6.76 6.86 .09 .013 .048 .866 TE05 20 Q 19.09 19.02 19.05 19.13 19.18 19.07 .06 3E-03 .022 .548 32 a 15.79 14.16 16.13 16.26 16.22 16.18 .91 .058 .413 .716 50 B 14.75 14.6 14.78 14.7 14.76 14.89 .11 7E-03 .056 .834 TE07 20 B 4.03 3.91 4.06 3.89 4.13 4.16 .13 .031 .057 .722 32 B 5.11 5.05 5.14 5.18 5.05 5.11 .06 .011 3E-03 .088 50 B 5.31 5.35 5.22 5.37 5.45 5.16 .12 .022 -.016 -.218 80 B 3.5 4.33 3.33 3.24 3.32 3.27 .47 .134 -.214 -.724 TEOB 20 B 4.85 4.83 4.91 5.03 4.75 4.76 .12 .024 -.029 -.385 32 B 5.77 5.6 5.78 5.79 5.86 5.83 .1 .017 .052 .838 50 B 5.56 5.64 5.68 5.62 5.54 5.32 .14 .026 -.078 -.952 80 3 3.91 4.16 3.97 3.73 3.81 3.86 .17 .043 -.076 -.725 TE09 20 B 12.41 12.43 12.29 12.51 12.27 12.54 .12 .01 .021 .263 32 B 10.92 10.97 10.8 10.92 10.99 10.91 .07 7E-03 6E-03 .134 50 B 8.84 8.83 8.73 8.83 8.87 8.92 .07 BE-03 .033 .746 80 B 5.06 5.6 5.46 5.14 3.79 5.3 .73 .144 -.227 -.492 TEIO 20 B 17.77 17.91 18.03 17.84 17.76 17.2? .29 .016 -.151 -.835 32 E 14.4 14.65 14.26 14.02 14.49 14.59 .26 .018 .011 .067 50 B 12.23 12.29 12.13 12.21 12.32 12.19 .08 6E-03 0 0 80 8 7.68 7.78 7.68 7.62 7.54 7.76 .1 .013 -.017 -.277 TEII 20 9 19.6 19.59 19.68 19.56 19.67 19.49 .08 4E-03 -.021 -.413 32 P 16.6 16.68 16.51 16.48 16.67 16.64 .09 6E-03 6E-03 .106 50 B 11.34 11.35 11.21 11.4 11.41 11.33 .08 7E-03 .017 .339 80 B 10.9 10.95 10.86 10.92 10.83 10.95 .O 5E-03 -3E-03 -.087 TE12 20 B 15.92 15.81 16 15.87 16.08 15.84 .11 7E-03 .014 .197 32 B 14.12 14.16 13.64 14.18 14.29 14.34 .28 .02 .1 .565 50 B 9.99 10.02 10.16 9.84 9.95 9.99 .11 .011 -.027 -.372 80 B 9.16 9.37 9.05 9.06 9.24 9.1 .14 .015 -.035 -.405 127 Table B.5. Summary of Results from Mays Meter #2 on the Asphaltic Concrete Roads. INTERNATIONAqL ROiAD ROUGHNESS EAPERIMENT - BRASILIA - JUNE 1932 MAYS METER #2 SITE SPEED TRACK ROUGHNESS NEASUREMENT (SLOPE X 1000) (K/H) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA SIN TREND R CAOI 20 0 2.56 2.71 2.37 2.19 2.73 2.79 .27 .104 .052 .312 32 8 3.68 4.06 3.43 3.64 3.41 3.86 .20 .076 -.043 -.241 50 2 5.03 4.84 5.11 5.06 5 5.13 .12 .023 .046 .629 so B 4.91 4.43 4.83 5.08 5.13 5.11 .3 .061 .167 .885 CA02 20 8 3.8 3.84 3.91 3.4 3.97 3.91 .23 .061 .019 .13 32 B 4.53 5.1 4.3 4.4 4.29 4.56 .34 .074 -.11 -.516 50 B 5.11 5 5.14 5.03 5.16 5.1S .06 .016 .04 .75 80 B 5.16 4.76 5.21 5.24 5.24 5.33 .23 .044 .117 .825 CA03 20 B 6.57 6.4 6.73 6.89 6.46 6.38 .23 .034 -.03 -.211 32 1 7.37 7.18 7.45 7.27 7.27 7.68 .2 .027 .084 .662 50 B 7.45 7.37 7.33 7.51 7.57 7.490 .1 .014 .049 .772 80 B 7.78 7.19 7.56 7.91 8.14 8.08 .4 .051 .237 .939 CA04 20 B 5.95 6.21 5.97 5.62 5.94 & .21 .035 -.044 -.333 32 B 6.91 6.59 6.91 6.65 7.03 7.35 .31 .045 .165 .848 50 B 7.11 6.81 7.11 7.18 7.240 7.22 .18 .025 .095 .857 80 B 6.32 5.87 6.29 6.38 6.67 6.4 .29 .045 .143 .785 CA05 20 0 7.75 7.67 7.67 7.56 7.94 7.91 .17 .021 .075 .71 32 8 8.32 8.67 8.27 8.08 8.3 8.25 .22 .026 -.079 -.583 50 B 5.21 4.83 5.14 5.45 5.35 5.3 .24 .047 .116 .756 80 B 7.68 7.16 7.72 7.75 7.92 7.87 .31 .04 .164 .847 CA06 20 B 8.79 8.97 8.54 8.62 8.95 8.87 .2 .023 .022 .177 32 B 9.26 9.6 9.06 9.03 9.48 9.13 .26 .028 -.054 -.327 50 B 8.72 8.59 8.79 8.76 8.72 8.75 .08 9E-03 .024 .472 80 B 9.32 8.81 9.11 9.56 9.64 9.51 .35 .038 .192 .864 CA07 20 B 2.16 2.57 2.16 2 2.1 1.95 .25 .114 -.13 -.837 32 B 2.36 2.41 2.19 2.35 2.56 2.27 .14 .059 8E-03 .09 50 B 2.72 2.75 2.71 2.79 2.64 2.71 .06 .021 -.014 -.39 80 I 2.85 2.71 2.94 2.87 2.83 2.89 .08 .03 .024 .446 CAM 20 B 1.78 1.89 1.83 1.59 1.76 1.84 .12 .066 -.016 -.214 32 B 1.71 1.52 1.57 1.73 1.83 1.9 .16 .095 .102 .989 50 B 2.31 2.32 2.3 2.3 2.3 2.3 .01 3E-03 -3E-03 -.707 80 B 2.87 2.78 2.71 2.89 2.97 2.98 .12 .041 .067 .893 CA09 20 B 3.65 3.95 3.52 3.6 3.68 3.51 .18 .049 -.073 -.639 32 1 3.78 3.75 3.81 3.86 3.75 3.71 .06 .015 -.013 -.348 50 B 3.98 4 3.92 3.97 4.02 3.98 .04 9E-03 6E-03 .275 80 B 4.29 4.18 4.11 4.41 4.29 4.48 .15 .036 .078 .798 CAIO 20 B 2.91 2.92 2.92 2.86 2.89 2.98 .05 .016 .01 .32 32 B 3.48 3.57 3.38 3.59 3.51 3.35 .11 .031 -.032 -.46 50 B 3.88 3.87 3.81 3.86 3.91 3.97 .06 .015 .029 .766 80 B 3.95 3.86 3.91 3.86 3.98 4.13 .11 .029 .062 .861 CAII 20 B 6.66 6.59 6.67 6.73 6.490 6.84 .13 .02 .033 .395 32 B 7.03 6.89 6.87 7.21 7.18 7 .16 .022 .052 .531 50 E 6.21 6.08 6.11 6.14 6.32 6.38 .13 .022 .081 .954 80 B 6.45 6.35 6.27 6.54 6.46 6.62 .14 .022 .073 .82 CA12 20 1 .8 .9 .9 .71 .75 .75 .09 .117 -.048 -.804 32 B 1.22 1.11 1.49 1.1 1.06 1.33 .19 .153 2E-03 .013 50 .8 1.3 1.25 1.32 1.22 1.38 1.32 .06 .048 .019 .487 80 B 1.46 1.35 1.44 1.43 1.59 1.48 .09 .059 .04 .725 CA13 20 e 1.11 1.21 1.19 .92 1.02 1.22 .14 .122 -.014 -.167 32 8 1.38 1.33 1.49 1.14 1.48 1.44 .15 .105 .021 .225 50 9 1.31 1.25 1.3 1.33 1.35 1.33 .04 .029 .021 .861 80 B 1.72 1.67 1.64 1.83 1.67 1.79 .09 .05 .029 .527 128 Table B.6. Summary of Results from Mays Meter #2 on the Surface Treatment Roads. INTERNIATIONRL RORD ROUGHiHNE3SS EXPERIMENT - BRRSILIR - JUNE .1962 MAYS METER #2 SIIE SPEED TRACK ROU6HNESS MEASUREMENT (SLOPE I 1000) (KIHI MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA SIN TREND R TSOI 20 B 7.69 7.29 7.48 7.67 7.890 8.130 .33 .043 .21 .999 32 B 6.22 6.03 6.14 6.16 6.3 6.45 .16 .026 .098 .974 50 B 5.46 5.41 5.54 5.41 5.37 5.59 .09 .017 .017 .291 80 B 7.01 6.56 6.91 7.16 7.18 7.25 .29 .041 .167 .923 TS02 20 B 9.83 9.64 9.86 9.99 9.89 9.76 .13 .014 .029 .34 32 B 8.39 8.43 8.03 8.38 8.38 8.72 .24 .029 .092 .6 50 B 6.63 6.75 6.67 6.41 6.67 6.64 .13 .019 -.022 -.279 80 B 5.52 5.48 5.33 5.57 5.57 5.64 .12 .021 .056 .748 TS03 20 B 9.56 9.21 9.67 9.7 9.54 9.7 .21 .022 .086 .648 32 B 8.28 7.76 8.37 9.38 8.45 8.45 .29 .035 .144 .783 50 B 7.78 7.59 7.91 7.81 7.79 7.81 .12 .015 .033 .451 80 B 7.1 6.76 7.02 7.19 7.18 7.35 .22 .031 .133 .949 TS04 20 B 8.25 8.25 8.19 8.14 8.45 8.24 .12 .014 .022 .306 32 B 8.43 8.48 8.6 8.32 8.45 8.3 .12 .015 -.051 -.648 50 B 6.86 6.4 6.87 6.86 7.02 7.16 .29 .042 .167 .92 8o B 9.23 8.6 9.33 ?.18 9.41 9.64 .39 .042 .214 .872 TS05 20 B 10.66 11.08 10.37 10.41 10.6 10.86 .3 .028 -.021 -.108 32 B 9.44 9.64 9.08 9.51 9.46 9.49 .21 .022 .01 .072 50 B 7.72 7.56 7.59 7.76 7.79 7.92 .15 .02 .094 .976 80 B 11.72 10.94 11.89 11.89 12 11.89 .44 .038 .202 .723 TS06 20 B 4.64 4.54 4.6 4.81 4.78 4.46 .15 .033 2E-03 .017 32 B 4.22 4.19 4.3 4.05 4.24 4.32 .11 .026 .019 .278 50 B 3.42 3.52 3.29 3.48 3.48 3.33 .1 .03 -.019 -.292 80 B 3.11 3.3 2.84 3.33 2.98 3.11 .21 .067 -.024 -.18 TS07 20 B 3.97 3.98 4.06 4.03 3.79 3.95 .1 .026 -.033 -.502 32 B 4.25 4.03 4.32 4.3 4.35 4.24 .13 .03 .044 .552 50 B 3.61 3.76 3.62 3.54 3.48 3.65 .11 .03 -.037 -.529 80 B 3.3 3.35 3.13 3.38 3.27 3.35 .1 .031 .014 .22 TSO8 20 B 5.61 5.62 5.54 5.6 5.75 5.52 .09 .016 2E-03 .029 32 B 4.65 4.6 4.52 4.81 4.79 4.54 .14 .03 .014 .164 50 B 3.8 4.03 3.67 3.71 3.73 3.87 .15 .039 -.025 -.269 80 B 4.08 4.06 4 4.11 4.11 4.11 .05 .012 .021 .667 TS09 20 B 5.89 5.51 5.78 6.11 5.95 6.08 .25 .042 .132 .838 32 B 5.6 5.46 5.67 5.72 5.67 5.49 .12 .021 6E-03 .087 50 B 5.21 5.06 5.16 5.25 5.3 5.27 .1 .019 .056 .901 80 B 4.56 4.56 4.52 4.59 4.43 4.7 .1 .022 .019 .307 TSIO 20 B 6.06 6.22 5.92 5.95 5.92 6.27 .17 .029 .01 .087 32 B 5.61 5.49 5.43 5.6 5.68 5.86 .17 .03 .098 .925 50 B 5.3 5.32 5.21 5.57 5.06 5.35 .19 .035 -BE-03 -.067 80 B 4.72 4.6 4.67 4.91 4.68 4.75 .11 .024 .03 .415 TSII 20 B 3.57 3.49 3.83 3.41 3.7 3.43 .18 .051 -.025 -.221 32 B 3.2 3.06 3.11 3.33 3.19 3.29 .11 .036 .052 .728 50 B 2.51 2.64 2.6 2.32 2.52 2.44 .13 .051 -.046 -.568 80 B 2.32 2.11 2.4 2.3 2.43 2.35 .12 .054 .051 .643 TS12 20 B 3.47 3.46 3.59 3.59 3.37 3.35 .12 .033 -.044 -.609 32 B 3.44 3.24 3.62 3.54 3.48 3.3 .16 .047 -2E-03 -.016 50 B 2.38 2.46 2.37 2.29 2.43 2.37 .07 .028 -.013 -.298 80 B 2.44 2.46 2.48 2.38 2.46 2.41 .04 .016 -.011 -.441 129 Table B.7. Summary of Results from Mays Meter #2 on the Gravel Roads. INTERN/ATIONAL ROeAD RO7UGHNESS EIXPERIMENT - BRASILIA - JUNE 1982 MAYS METER #2 SITE SPEED TRACK ROUSHNESS HEASURENENT (SLOPE X 1000) (KJH) KEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGM(A S/N TREND R MRO1 20 B 3.72 3.73 3.57 3.79 3.79 3.73 .09 .024 .022 .387 32 8 3.58 3.65 3.79 3.46 3.46 3.52 .14 .04 -.059 -.647 50 8 3.24 3.24 3.1 3.3 3.43 3.14 .13 .041 .014 .171 80 8 2.86 2.75 3.06 2.78 2.92 2.81 .13 .045 -2E-03 -.019 6R02 20 B 4.47 4.56 4.06 4.54 4.56 4.65 .23 .052 .068 .463 32 B 3.76 4 3.52 3.68 3.91 3.67 .19 .051 -.029 -.234 50 8 3.33 3.33 3.24 3.33 3.38 3.38 .06 .017 .024 .645 80 8 3.52 3.49 3.51 3.46 3.7 3.43 .11 .03 6E-03 .095 6R03 20 B 11.4 11.65 11.03 11.26 11.41 11.65 .27 .023 .038 .226 32 B 9.94 9.65 9.95 9.87 10.02 10.21 .2 .02 .117 .914 50 B 8.85 8.7 8.68 8.95 8.97 8.92 .14 .016 .073 .815 80 B 8.11 7.79 8.21 8.14 8.25 8.16 .18 .023 .078 .673 6R04 20 8 9.36 9.52 9.35 9.24 9.4 9.29 .11 .012 -.043 -.614 32 B 7.9 7.62 7.97 7.91 7.94 8.06 .17 .021 .086 .811 50 B 7.54 7.32 7.490 7.41 7.640 7.84 .2 .027 .119 .919 80 8 6.52 6.38 6.45 6.52 6.59 6.67 .11 .017 .071 .999 6R05 20 B 15.42 15.51 15.26 15.4 15.64 15.29 .16 .01 -6E-03 -.064 32 B 15.17 15.56 14.78 15.26 15.03 15.24 .29 .019 -.038 -.209 50 B 13.71 13.48 13.7 13.87 13.49 14 .23 .017 .084 .576 80 B 12.77 12.32 12.08 13.02 13.18 13.26 .53 .042 .297 .879 R.06 20 B 13.39 13.43 13.53 13.56 13.3 13.13 .18 .013 -.083 -.742 32 B 12.96 12.97 12.89 12.75 13.35 12.84 .23 .018 .021 .14 50 B 11.69 11.54 11.8 11.75 11.67 11.7 .1 BE-03 .019 .313 80 B 10.8 10.72 10.27 11.05 10.75 11.22 .36 .034 .149 .648 GR07 20 B 8.22 8.06 8.25 8.51 7.91 8.35 .24 .029 .022 .148 32 B 7.490 7.6 7.59 7.52 7.41 7.32 .12 .016 -.075 -.97 50 B 7.18 7.03 7.02 7.22 7.3 7.3 .14 .02 .083 .922 80 B 6.39 6.14 6.35 6.64 6.33 6.490 .18 .029 .068 .585 GROB 20 B 5.47 5.73 5.45 5.45 5.32 5.41 .15 .028 -.076 -.779 32 B 4.95 4.87 4.98 5.08 4.91 4.92 .08 .016 2E-03 .031 50 B 4.35 4.27 4.4 4.14 4.48 4.48 .14 .033 .049 .539 80 B 4.08 3.97 4.05 3.95 4.18 4.25 .13 .032 .07 .841 6R09 20 8 12.18 12.11 12 12 12.24 12.56 .23 .019 .113 .77 32 B 10.71 10.78 10.49 10.64 10.78 10.86 .14 .014 .044 .485 50 8 10 ?.94 9.51 10.14 10.21 10.19 .29 .029 .121 .649 80 B 11.05 10.38 10.92 11.51 11.21 11.24 .43 .039 .2 .738 6RIO 20 B 10.09 9.94 10.22 10.14 10.16 9.97 .13 .012 0 0 32 B 8.87 8.7 8.89 9.3 8.7 8.76 .25 .029 -6E-03 -.04 50 B 8.68 8.62 8.72 8.62 8.67 8.76 .06 7E-03 .024 .606 80 B 9.64 9.16 9.48 9.84 9.95 9.78 .32 .033 .171 .841 6RI1 20 B 18.65 19.35 18.54 18.68 18.29 18.38 .42 .023 -.219 -.824 32 B 19.59 19.27 19.76 19.45 19.83 19.64 .23 .012 .079 .547 50 B 20.31 20 20.16 20.45 20.78 20.18 .31 .015 .097 .501 6R12 20 B 20.21 20.65 20.43 19.88 20.21 19.89 .34 .017 -.175 -.815 32 B 21.62 21.49 21.37 21.81 22.05 21.35 .31 .014 .04 .205 50 8 19.58 18.8 19.78 19.61 19.57 20.15 .49 .025 .249 .798 130 Table B.8. Summary of Results from Mays Meter #2 on the Earth Roads. INTERNATIONAL ROAD ROG&HNESS EXPERIMENT - RRASILfIA - JULNE 1982 MAYS METER #2 SITE SPEED TRACK ROUGHNESS MEASUREMENT (SLOPE X 1000) (K/H) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA S/N TREND R TEOI 20 B 7.54 7.48 7.65 7.72 7.27 7.6 .18 .023 -.013 -.114 32 B 5.96 5.65 6.05 5.87 6.02 6.21 .21 .035 .108 .817 50 B 4.88 4.46 4.62 4.98 5.14 5.18 .32 .066 .195 .963 80 B 4.49 4.16 4.59 4.57 4.46 4.67 .2 .044 .089 .707 TE02 20 B 7.12 7.11 7.3 7.29 6.89 6.98 .18 .026 -.067 -.58 32 B 5.76 5.52 5.65 5.76 5.89 5.95 .17 .03 .11 .995 50 B 4.31 4.02 4.32 4.22 4.44 4.52 .2 .046 .114 .909 8Q B 4.13 3.73 4.02 4.13 4.35 4.41 .27 .066 .17 .979 TE03 20 B 14.04 14.35 14.45 13.75 14.1 13.57 .38 .027 -.191 -.799 32 B 12.77 12.59 12.68 12.56 13.18 12.83 .25 .02 .097 .608 50 B 9.26 8.87 9.22 9.18 9.19 9.84 .35 .038 .191 .851 80 B 8.25 7.97 7.91 8.32 8.46 8.57 .3 .036 .176 .941 TE04 20 B 14.67 15.03 14.65 14.4 14.75 14.53 .24 .016 -.092 -.603 32 B 12.91 12.76 13.02 12.67 12.97 13.14 .19 .015 .071 .583 50 B 10.07 9.64 9.84 10.02 10 10.84 .46 .046 .257 .885 80 B 8.35 7.91 8.29 8.49 8.43 8.62 .27 .033 .157 .906 TEOS 20 B 26.88 27.81 26.81 26.43 26.5 26.83 .55 .021 -.229 -.653 32 8 23.88 22.42 23.43 23.88 24.83 24.84 1.02 .043 .625 .968 50 B 20.55 19.94 20.67 20.34 20.97 20.81 .41 .02 .205 .786 TE06 20 B 33.45 34.08 33.5 32.75 33.04 33.89 .56 .017 -.084 -.237 32 B 29.46 27.8 28.8 29.62 30.58 30.53 1.18 .04 .724 .966 50 B 25.7 24.78 25.54 25.86 26.21 26.11 .58 .022 .333 .915 TE07 20 B 7.61 7.29 7.57 7.79 7.6 7.78 .21 .027 .102 .783 32 B 7.06 6.98 7.16 7.05 7.16 6.95 .1 .014 -6E-03 -.104 50 8 5.92 5.51 5.94 6.02 6.02 6.13 .24 .041 .132 .866 80 B 5.37 5.38 5.3 5.38 5.38 5.38 .04 7E-03 8E-03 .354 TEOB 20 B 8.41 8.180 8.19 8.68 8.32 8.67 .25 .03 .111 .7 32 8 7.54 7.45 7.46 7.67 7.52 7.6 .09 .013 .038 .637 50 B 6.12 5.57 5.89 6.24 6.46 6.45 .38 .063 .232 .955 80 e 5.61 5.43 5.57 5.81 5.54 5.68 .15 .026 .048 .518 TEO9 20 8 16.13 15.45 16.1 16 16.51 16.59 .46 .028 .27 .931 32 e 12.76 12.7 12.21 12.54 13.14 13.22 .42 .033 .198 .74 50 e 9.19 8.68 8.72 9.52 9.45 9.56 .45 .048 .248 .879 80 B 8.36 7.890 8.24 8.49 8.56 8.62 .3 .036 .178 .938 TEIO 20 B 22.23 21.54 22.27 22.46 22.19 22.65 .42 .019 .214 .804 32 B 17.7 17.41 17.7 17.89 17.89 17.61 .2 .011 .057 .447 50 B 12.87 12.24 12.21 13.41 13.16 13.32 .6 .046 .311 .826 80 B 11.25 11.26 11.19 11.51 11.19 11.1 .16 .014 -.032 -.321 TEII 20 B 21.13 21.07 21.11 20.78 21.43 21.26 .24 .011 .07 .457 32 B 17.22 16.64 16.94 17.67 17.4 17.48 .42 .025 .214 .799 50 B 12.36 12 12.3 12.62 12.18 12.7 .3 .024 .127 .68 80 B 10.7? 10.48 10.57 10.76 11.05 11.1 .28 .026 .171 .979 TE12 20 B 16.91 16.41 17.07 17.03 17.07 16.97 .28 .017 .111 .628 32 B 14.62 14.54 14.99 14.29 14.73 14.56 .26 .018 -.022 -.136 50 B 10.74 10.4 10.46 10.78 10.97 11.08 .3 .028 .187 .981 80 B ?.89 10.13 9.79 9.6 10.18 9.76 .25 .025 -.035 -.223 131 Table B.9. Summary of Results from Mays Meter #3 on the Asplhaltic Concrete Roads. SITE SPEED TRACK RDOUHNESS MEASUREMENTS (SLOPE X E3) (KIH) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA SIN TREND R CAOI 20 B 2.65 2.64 2.22 2.54 2.83 3.05 .31 .117 .143 .729 32 B 3.83 3.91 3.84 3.68 3.97 3.75 .12 .03 -.019 -.26 50 B 5.55 5.4 5.46 5.49 5.78 5.62 .15 .027 .076 .796 s0 B 5.19 4.95 5.27 5.43 5.05 5.24 .19 .036 .035 .293 CA02 20 B 3.98 4.06 3.91 3.84 3.87 4.22 .16 .04 .029 .283 32 B 4.11 4.32 4.19 4.06 4.13 3.84 .18 .043 -.102 -.912 50 B 5.4 5.46 5.68 5.37 5.46 5.05 .23 .043 -.105 -.719 80 B 5.11 4.64 5.18 4.95 5.33 5.43 .32 .062 .175 .867 CA03 20 B 6.64 6.76 6.89 6.51 6.6 6.45 .18 .028 -.092 -.796 32 B 4.94 4.98 4.92 4.89 4.83 5.08 .1 .02 .01 .156 50 B 6.17 6.22 6.51 5.87 6.29 5.97 .25 .041 -.073 -.454 80 B 6 5.56 5.68 5.68 6.73 6.35 .51 .086 .264 .812 CA04 20 B 5.98 5.52 6.06 6.35 5.91 6.03 .3 .05 .086 .452 32 B 6.54 6.45 6.7 6.16 6.6 6.79 .25 .038 .06 .383 50 8 6.740 6.83 6.7 6.67 6.54 6.98 .17 .025 .016 .149 80 B 5.74 5.37 5.21 6.06 6.1 5.97 .42 .073 .21 .787 CA05 20 B 7.59 7.27 7.91 7.97 7.68 7.11 .38 .05 -.054 -.224 32 8 6.76 6.48 6.6 6.86 6.7 7.14 .26 .038 .143 .878 50 B 7.63 7.240 7.37 7.59 7.94 8 .34 .044 .21 .981 80 B 6.65 6.41 6.57 6.92 7.11 6.22 .36 .055 .016 .069 CA06 20 B 8.74 8.73 8.45 8.92 8.92 8.7 .2 .022 .041 .332 32 B 8.62 8.67 8.38 8.79 8.86 8.38 .23 .026 -.01 -.067 50 B 9.14 9.14 8.83 8.86 9.33 9.52 .3 .033 .127 .666 80 8 8.77 8.29 8.7 8.79 9.02 9.05 .31 .035 .184 .947 CA07 20 8 1.37 1.56 1.62 1.08 1.46 1.14 .25 .179 -.098 -.634 32 B 3.06 3.94 2.73 2.86 2.89 2.89 .49 .161 -.194 -.62 50 B 2.81 2.79 2.83 2.92 2.89 2.64 .11 .04 -.025 -.361 90 B 3.04 3.43 2.95 2.83 3.27 2.73 .3 .098 -.108 -.574 CA08 20 B 1.19 1.49 1.14 1.21 1.08 1.02 .18 .155 -.102 -.87 32 B 2.06 1.9 2.25 2 2.16 1.97 .14 .07 3E-03 .035 50 B 2.31 2.29 2.25 2.38 2.32 2.32 .05 .02 .013 .426 80 B 3.19 2.95 3.4 3.4 2.95 3.24 .22 .07 .013 .09 CA09 20 B 3.86 3.91 3.49 3.97 3.65 4.29 .31 .079 .092 .476 32 8 3.66 3.84 3.81 3.49 3.78 3.37 .21 .059 -.098 -.725 50 B 4.13 4.1 4.1 4.35 4.13 4 .13 .031 -.016 -.193 80 B 4.85 4.51 5.11 5.18 4.83 4.6 .3 .061 -.01 -.051 CA10 20 B 3.09 3.3 3.24 3.02 2.98 2.89 .18 .057 -.108 -.97 32 B 3.71 3.62 3.78 3.71 3.65 3.78 .07 .02 .019 .416 50 B 3.87 3.75 3.91 3.91 3.94 3.84 .08 .02 .022 .464 80 B 4.34 4.06 4.22 4.73 4.35 4.32 .25 .057 .064 .407 CAII 20 B 6.31 6.38 6.41 6.25 6.22 6.25 .09 .014 -.044 -.819 32 B 6.78 6.67 6.51 6.64 7.11 6.95 .25 .037 .117 .747 50 B 6.19 5.91 5.59 6.45 6.48 6.54 .42 .068 .216 .808 80 B 6.83 6.6 6.73 6.76 7.33 6.73 .29 .042 .086 .472 CA12 20 B .57 .73 .6 .57 .54 .38 .13 .223 -.076 -.958 32 B .42 .6 .35 .38 .35 .41 .11 .254 -.038 -.567 50 B 1.03 1.17 .98 .95 1.02 1.02 .09 .083 -.029 -.527 80 B 1.66 1.59 1.4 1.75 1.75 1.84 .17 .105 .086 .776 CA13 20 B .94 1.43 1.17 .83 .76 .51 .36 .386 -.225 -.983 32 B .65 .7 .57 .67 .54 .76 .09 .141 .01 .165 50 B 1.09 1.05 1.08 1.05 .98 1.27 .11 .1 .035 .508 80 B 1.94 1.84 1.81 2.03 2.16 1.87 .15 .076 .041 .441 132 Table B.10. Summary of Results from Mays Meter #3 on the Surface Treatment Roads. SITE SPEED TRACK ROUGHNESS NEASURENENTS (SLOPE X E3) (KJHI) EAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIBNA SIN TREND R TSOI 20 B 7.58 7.62 7.18 7.94 7.4 7.75 .3 *039 .048 .253 32 R 5.61 5.43 5.72 5.4 5.87 5.65 .2 .036 .06 .477 50 B 5.6 5.4 5.52 5.65 5.65 5.78 .14 .026 .089 .971 80 B 7.41 7.11 7.33 7.87 7.14 7.59 .32 .043 .076 .375 TS02 20 B 8.95 9.02 8.89 9.05 9.92 8.89 .07 8E-03 -.022 -.472 32 B 7.4 6.98 7.18 7.43 7.81 7.59 .33 .044 .194 .891 50 B 6.14 6.38 6.41 6.03 5.91 5.97 .24 .039 -.133 -.881 80 B 5.23 5.43 5.11 4.92 5.18 5.52 .24 .047 .025 .164 TS03 20 B 9.87 9.49 9.97 10.06 10.03 9.91 .23 .023 .098 .693 32 B 8.07 7.62 7.84 8.41 8.32 9.16 .33 .041 .156 .74 50 0 8.35 8.48 8.38 8.19 8.32 8.38 .11 .013 -.025 -.381 80 B 7.16 7.02 7.21 7.56 7.14 6.89 .25 .035 -.032 -.2 TS04 20 B 9.8 9.97 10.13 9.49 9.52 9.91 .28 .029 -.073 -.41 32 B 8.31 8.45 8.83 8.22 8.25 7.78 .38 .046 -.19 -.792 50 B 7.18 6.79 7.43 7.27 7.3 7.11 .24 .034 .051 .329 80 B 9.73 9.27 10.1 10.29 9.97 9.02 .55 .057 -.064 -.182 TS05 20 B 10.95 10.8 11.3 10.99 11.05 10.64 .25 .023 -.057 -.356 32 B 10.04 9.97 9.87 10.22 10.03 10.1 .13 .013 .041 .496 50 B 8.040 7.65 8.16 7.97 8.32 8.1 .25 .031 .105 .662 90 B 11.91 11.72 12.13 12.06 12.45 11.21 .47 .04 -.07 -.234 TS06 20 B 5.51 5.3 5.59 5.4 5.68 5.56 .15 .028 .06 .622 32 B 4.22 4.1 4.51 4.16 4.06 4.29 .18 .043 -6E-03 -.055 50 B 3.66 3.81 3.78 3.59 3.59 3.56 .12 .033 -.07 -.92 80 B 3.47 3.78 3.46 3.46 3.56 3.11 .24 .069 -.124 -.815 TS07 20 8 5.27 5.3 5.4 5.24 5.3 5.11 .11 .02 -.048 -.715 32 B 4.58 4.32 4.7 4.64 4.83 4.44 .2 .044 .038 .297 50 B 3.66 3.62 3.52 3.68 3.75 3.71 .09 .024 .041 .741 80 8 3.64 3.78 3.52 3.75 3.56 3.59 .12 .032 -.035 -.477 TSQ8 20 9 5.47 5.46 5.21 5.43 6.13 5.11 .4 .073 .022 .088 32 B 4.48 4.6 4.44 4.6 4.35 4.41 .12 .026 -.049 -.653 50 B 3.94 4.29 3.3 4.25 3.84 4.03 .4 .102 3E-03 .013 80 B 4.39 4.38 4.44 4.1 4.25 4.76 .25 .057 .057 .364 TS09 20 B 5.91 6.29 5.46 5.14 6.64 6 .61 .103 .06 .158 32 B 4.78 5.4 5.05 4.98 4.6 3.87 .58 .121 -.349 -.951 50 B 5.23 5.46 5.33 5.27 5.21 4.86 .23 .043 -.133 -.932 80 B 3.04 2.89 3.02 2.89 3.17 3.24 .16 .053 .086 .942 TSI0 20 B 5.91 6.25 5.97 5.37 5.75 6.19 .36 .061 -.035 -.153 32 B 5.12 5.56 5.14 4.83 5.05 5.02 .27 .053 -.117 -.686 50 B 5.35 5.52 5.11 5.65 5.43 5.02 .27 .051 -.07 -.406 80 B 2.9 2.92 2.79 2.92 2.95 2.92 .06 .021 .016 .406 TSII 20 B 2.3 2.67 1.9 2.73 2.25 1.94 .39 .17 -.111 -.45 32 B 1.92 1.59 1.9 1.94 2.06 2.13 .21 .109 .124 .937 50 B 3.04 3.08 3.05 2.89 3.27 2.92 .15 .05 -.01 -.1 80 B 2.27 2.16 2.7 3.08 1.71 1.71 .61 .267 -.187 -.489 TS12 20 B 1.58 1.62 1.46 1.56 1.65 1.62 .08 .048 .019 .397 32 B 1.8 1.46 2.22 1.78 1.81 1.71 .27 .153 .01 .055 50 B 3.12 2.98 3.05 3.27 3.14 3.14 .11 .035 .041 .601 80 B 1.92 2.22 2.67 1.78 1.52 1.43 .52 .269 -.273 -.836 133 Table B.ll. Summary of Results from Mays Meter #3 on the Gravel Roads. INTERNHATION4AL RO/4D Rc'U&HHESS EX'PERIMENT - BRASILZ1A - JUNE 2982 MAYS METER #3 SITE SPEED TRACK ROU8HNESS MEASUREMENTS ISLOPE I E3) (K/H) KEAN RUN I RUN 2 RUN 3 RUN 4 RUN S SIGMA S/N TREND R BROI 20 B 3.19 3.21 3.33 2.98 3.17 3.27 .13 .041 -3E-03 -.036 32 B 2.6 3.81 2.22 2.03 2.44 2.48 .7 .27 -.244 -.551 50 B 2.25 1.97 2.41 2.32 2.29 2.29 .17 .075 .051 .478 80 B 2.74 1.59 2.73 2.16 3.52 3.71 .9 .328 .505 .889 6R02 20 B 3.3 3.27 3.56 3.46 3.08 3.14 .2 .062 -.073 -.566 32 B 2.52 4 2.22 2.13 2.16 2.1 .83 .329 -:397 -.739 50 B 2.08 1.71 1.65 2.6 2.32 2.1 .4 .194 .143 .561 s0 B 3.08 2.06 3.14 3.21 3.27 3.71 .61 .198 .343 .838 6R03 20 B 7.29 7.59 7.18 7.21 7.240 7.240 .17 .023 -.063 -.594 32 B 5.87 6.32 5.78 5.33 5.87 6.06 .37 .062 -.041 -.179 50 B 8.19 9.11 7.84 8.1 7.08 8.83 .81 .099 -.133 -.261 80 B 7.83 6.92 7.81 7.87 7.91 8.64 .61 .078 .352 .915 9R04 20 B 5.79 5.49 5.65 5.68 6.38 5.75 .34 .059 .124 .571 32 B 4.46 4.25 4.54 4.7 4.38 4.44 .17 .039 .022 .21 50 B 6.43 7.72 5.87 5.33 5.43 7.76 1.22 .19 -.032 -.041 80 B 5.69 4.44 4.86 6.92 6.51 5.68 1.05 .195 .413 .62 BRO5 20 B 17.67 17.08 19.32 17.72 17.05 18.19 .6 .034 .095 .252 32 8 16.86 17.11 17.24 16.67 16.64 16.64 .29 .017 -.156 -.838 50 B 14.58 14.29 14.76 14.57 13.84 15.43 .59 .04 .137 .367 80 B 12.23 12.38 11.24 13.05 12 12.48 .67 .055 .095 .225 8R06 20 B 15.48 16.51 14.51 15.18 16.07 15.14 .8 .052 -.117 -.233 32 B 14.08 14.03 14.1 14.22 14.22 13.84 .16 .011 -.025 -.254 50 B 11.98 12.03 11.97 11.78 11.91 12.19 .15 .013 .025 .263 d0 B 10.3 9.68 9.75 10.73 11.11 10.22 .62 .06 .244 .623 BR07 20 B 9.8 10.03 9.3 9.87 10.19 9.62 .35 .036 6E-03 .029 32 B 7.92 8.38 8.64 6.67 8.25 7.65 .79 .099 -.184 -.37 50 8 7.240 6.98 7.3 7.240 7.02 7.65 .27 .037 .105 .617 g0 B 6.5 5.37 6.16 6.92 7.27 6.76 .75 .115 .391 .825 BROf 20 B 7.44 6.95 7.240 7.62 7.3 8.1 .44 .059 .235 .853 32 8 5.31 5.56 5.56 4.16 5.33 5.97 .69 .129 .06 .139 50 B 4.48 5.08 4.57 5.11 4 3.62 .66 .147 -.349 -.938 80 B 3.83 2.89 2.92 4.79 5.24 3.3 1.11 .289 .314 .449 6R09 20 B 13.79 13.3 13.46 14.19 13.46 14.51 .53 .039 .241 .717 32 B 11.09 11.68 10.73 10.45 10.57 12.03 .72 .065 .054 .119 50 B 10.12 9.84 9.27 10.32 11.14 10.03 .69 .068 .225 .518 80 B 11.99 11.49 12.29 12.32 12.64 11.21 .61 .051 -.022 -.058 BRiO 20 B 10.88 11.02 10.57 10.99 10.83 11.08 .2 .018 .038 .305 32 B 9.11 9.4 9.25 8.76 9.59 9.56 .58 .064 .165 .447 50 B 9.65 10.13 9.84 9.78 9.05 9.43 .42 .043 -.219 -.633 90 8 9.71 8.7 9.43 10.32 9.4 10.7 .8 .082 .397 .786 BRil 20 B 18.62 19.15 18.57 18.48 18.35 18.54 .31 .016 -.143 -.737 32 B 20.29 19.97 20.38 20.51 19.97 20.61 .3 .015 .086 .451 50 B 20.19 20 19.81 20.51 20.48 20.13 .3 .015 .092 .48 6R12 20 B 20.74 21.49 20.86 20.29 20.57 20.48 .47 .023 -.232 -.78 32 B 20.56 20.51 20.26 20.7 20.95 20.38 .27 .013 .044 .256 50 B 19.91 19.64 19.46 20.07 20.19 19.97 .28 .014 .098 .557 134 Table B.12. Summary of Results from Mays Meter #3 on the Earth Roads. SITE SPEED TRACK ROUGHNESS MEASUREMENTS (SLOPE X E3) (K/H) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SI6GA S/N TREND R TEOI 20 B 8.41 B.16 8.79 8.51 8 8.57 .32 .030 3E-03 .016 32 B 6.43 6.06 6.64 6.41 6.38 6.64 .24 .037 .089 .598 50 8 4.82 4.32 4.57 5.02 5.46 4.73 .44 .091 .171 .617 8o B 4.32 4.19 3.65 3.94 4.73 5.08 .58 .135 .286 .776 TE02 20 B 7.890 8.25 8.76 7.59 7.11 7.75 .63 .08 -.267 -.664 32 B 6.02 6 6.32 5.65 5.94 6.19 .26 .042 0 0 50 B 4.83 4.76 4.67 4.95 4.79 4.95 .12 .026 .051 .643 80 B 3.77 3.27 3.62 3.84 3.62 4.48 .45 .119 .241 .853 TE03 20 B 14.94 15.24 15.46 14.92 14.32 14.76 .44 .03 -.21 -.751 32 B 12.15 11.94 11.94 12.19 12.35 12.32 .2 .016 .117 .927 50 B 9.12 9.08 9.11 8.22 9.78 9.43 .58 .063 .137 .374 80 B 7.3 5.97 6.48 8.51 8.45 7.08 1.15 .157 .419 .577 TE04 20 B 15.36 15.53 15.18 15.34 15.56 15.21 .18 .011 -.025 -.228 32 B 13.12 13.11 12.95 13.33 13.05 13.14 .14 .011 .016 .178 50 B 9.57 9.43 10.19 8.76 9.46 10 .56 .059 .041 .116 80 B 7.91 7.84 7.02 8.76 8.03 7.91 .62 .079 .114 .291 TE05 20 B 24.59 24.57 24.51 24.86 24.61 24.39 .17 7E-03 -.029 -.259 32 B 19.11 18.07 17.53 17.72 17.43 24.8 3.19 .167 1.337 .663 50 B 21.47 21.56 21.34 21.49 21.65 21.3 .15 7E-03 -.019 -.204 TE06 20 B 32.2 31.56 32.26 32.29 32.48 32.42 .37 .011 .194 .828 32 B 26.31 25.46 24.8 25.21 25.21 30.86 2.56 .097 1.121 .693 50 B 28.11 28.13 27.65 27.94 28.32 28.48 .32 .012 .137 .668 TE07 20 B 8.76 8.83 8.76 9.05 8.73 8.41 .23 .026 -.086 -.594 32 B 7.63 7.56 7.62 7.240 8 7.75 .28 .036 .076 .433 50 B 6.9 6.13 6.98 7.14 7.18 7.08 .44 .064 .21 .754 80 B 4.47 4.19 4.38 4.57 4.67 4.54 .19 .042 .098 .832 TE08 20 B 9.94 10.45 9.68 10.03 10.16 9.4 .41 .041 -.162 -.625 32 B 7.85 7.56 7.68 7.75 8.32 7.97 .3 .038 .146 .772 50 B 6.94 6.76 6.35 7.08 7.05 7.46 .41 .06 .21 .802 80 B 4.28 4.32 4.13 4.38 4.25 4.32 .1 .023 .013 .209 TE09 20 B 17.18 17.91 16.1 18 17.14 16.76 .8 .046 -.124 -.245 32 B 12.81 12.35 12.83 13.46 12.67 12.76 .41 .032 .067 .26 50 B 10.35 10.13 9.97 10.35 10.73 10.57 .31 .03 .165 .837 80 B 7.91 7.52 7.72 8 8.29 5.03 .3 .037 .159 .847 TEIO 20 B 19.62 19.08 19.43 19.88 19.75 19.97 .36 .019 .21 .91 32 B 17.08 15.65 19.11 17.88 15.72 17.02 1.47 .086 -.067 -.072 50 B 13.6 13.46 13.27 13.72 13.46 14.1 .32 .023 .146 .724 80 B 10.73 10.76 10.86 10.73 10.92 10.35 .22 .021 -.076 -.541 TEII 20 B 16.8 16.73 16.61 16.95 16.61 17.08 .21 .013 .07 .516 32 B 12.69 13.05 12.54 12.13 13.08 12.64 .39 .031 -.029 -.115 50 B 11.18 11.18 11.21 10.73 11.4 11.37 .27 .024 .057 .339 80 B 10.57 10.86 10.6 10.41 10.54 10.45 .18 .017 -.089 -.795 TE12 20 B 17.13 17.14 17.11 16.73 17.4 17.24 .25 .014 .048 .305 32 B 13.08 13.33 13.21 12.76 13.14 12.95 .22 .017 -.083 -.581 50 B 9.47 9.08 9.56 9.68 9.56 9.49 .23 .024 .083 .566 s0 B 8.46 8.67 8.41 8.35 8.57 8.29 .16 .019 -.06 -.603 135 Table B.13. Summary of Results from the Car-Mounted BI on the Asphaltic Concrete Roads. SITE SPEED TRACK ROUSHNESS MEASUREMENT (SLOPE X 1000) (K/H) KEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA S/M TREND R CAOI 20 B 2.16 2.22 2.06 2.06 2,22 2.22 .09 .04 .016 .289 32 B 2.98 3.33 3.17 3.02 2.7 2.7 .28 .095 -.175 -.972 50 8 3.97 3.81 3.97 3.97 4,13 3.97 .11 .028 .048 .671 80 B 6.32 6.35 5.72 6.83 6.83 5.87 .52 .082 .016 .048 CA02 20 B 3.11 3.33 3.02 3.02 3,17 3.02 .14 .046 -.048 -.53 32 B 4.03 4.44 3.97 4.13 3.65 3.97 .29 .072 -.127 -.696 50 B 4.95 4.92 5.08 4.92 4.92 4.92 .07 .014 -.016 -.354 80 B 6.35 6.19 6.35 6.35 6,67 6.19 .19 .031 .032 .258 CR03 20 B 6.19 6.03 6.19 6.03 6.19 6.51 .19 .031 .095 .775 32 B 6.57 6.67 6.35 6.67 6,67 6.51 .14 .022 0 0 50 B 7.33 6.83 7.3 7.78 7.3 7.46 .34 .047 .127 .503 80 B 10.57 10.32 9.84 9.84 11.43 11.43 .81 .076 .381 .747 CA04 20 B 5.43 5.24 5.72 5.56 5,24 5.4 .21 .038 -.016 -.121 32 B 6.13 6.03 6.03 6.19 6.03 6.35 .14 .023 .063 .707 50 B 6.48 6.03 6.51 6.51 6.83 6.51 .28 .044 .127 .707 80 B 7.62 7.62 6.98 8.25 7.62 7.62 .45 .059 .063 .224 CR05 20 B 7.27 7.14 7.46 7.3 7,3 7.14 .13 .018 -.016 -.189 32 B 7.91 7.78 7.78 7.78 8.25 7.94 .21 .026 .079 .606 50 B 7.67 7.46 8.25 7.46 8.25 7.94 .4 .051 .095 .378 80 B 10.51 10.32 9.21 10.8 11.27 10.95 .8 .077 .333 .655 CR06 20 B 8.130 B.1 8.1 8.25 7,78 8.41 .24 .029 .032 .213 32 B 8.6 8.73 8.41 9.05 8.41 8.41 .28 .033 -.063 -.354 50 a 9.62 9.37 9.52 9.68 9.84 9.68 .18 .019 .095 .832 B0 B 13.72 12.7 13.97 12.54 14.76 14.6 1.04 .076 .46 .697 CA07 20 B 1.78 1.59 1.75 2.22 1.75 1.59 .26 .147 0 0 32 8 2.35 2.38 2.38 2.38 2.06 2.54 .17 .074 0 0 50 B 2.57 2.54 2.54 2.54 2.7 2.54 .07 .028 .016 .354 80 B 4.19 3.65 4.44 4.29 4.44 4.13 .33 .079 .095 .457 CA08 20 B 1.75 1.9 1.75 1.59 2.06 1.43 .25 .144 -.063 -.4 32 B 1.87 1.75 2.06 1.9 1.75 1.9 .13 .071 0 0 50 B 2.25 2.38 2.22 2.22 2.22 2.22 .07 .031 -.032 -.707 80 8 4.29 3.97 4.13 4.76 4.29 4.29 .3 .069 .079 .423 CA09 20 B 3.11 3.17 3.17 3.17 3.02 3.02 .09 .028 -.048 -.866 32 B 3.52 3.49 3.65 3.49 3.49 3.49 .07 .02 -.016 -.354 50 B 3.97 3.97 3.97 3.97 3.97 3.97 0 0 0 0 80 B 5.52 5.72 5.72 5.08 5.4 5.72 .28 .051 -.032 -.177 CA10 20 8 2.51 2.54 2.38 2.54 2.86 2.22 .24 .094 -.016 -.107 32 B 3.05 3.02 3.02 3.17 3.02 3.02 .07 .023 0 0 50 B 3.71 3.49 3.65 3.97 3.65 3.81 .18 .049 .063 .555 80 B 5.24 5.08 5.24 5.4 5.08 5.4 .16 .03 .048 .474 CAJI 20 B 6.16 6.19 6.19 5.87 6.19 6.35 .17 .028 .032 .289 32 B 6.41 6.51 6.19 6.51 6.51 6.35 .14 .022 0 0 50 B 6.22 6.03 6.03 6.35 6.51 6.19 .21 .033 .07? .606 80 B 6.7 6.67 6.98 6.51 6.83 6.51 .21 .031 -.048 -.364 CA12 20 B .95 1.11 .95 .79 .95 .95 .11 .118 -.032 -.447 32 B 1.27 1.27 1.27 1.27 1.27 1.27 0 0 0 0 50 B 1.59 1.75 1.43 1.59 1.59 1.59 .11 .071 -.016 -.224 CA3 20 B .98 1.11 1.27 .79 .95 .79 .21 .21 -.095 -.726 32 B 1.24 1.27 1.11 1.27 1.27 1.27 .07 .057 .016 .354 50 B 1.56 1.75 1.43 1.59 1.43 1.59 .13 .085 -.032 -.378 136 Table B.14. Summary of Results from the Car-Mounted BI on the Surface Treatment Roads. INTERNA TIONAL ROAD ROUGHNE SS E PERIMENT - BRASILIIR - JUNE 1982 CAR-MOUNTED BUMP INTEGRATOR SITE SPEED TRACK ROUGHNESS MEASUREMENT (SLOPE I 1000) (KIR) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 S16MA S/N TREND R TSOI 20 B 6.54 6.35 6.67 6.67 6.51 6.51 .13 .02 .016 .189 32 B 5.84 6.03 5.72 5.72 5.87 5.87 .13 .023 -.016 -.189 50 B 5.46 5.4 5.56 5.56 5.4 5.4 .09 .016 -.016 -.289 TS02 20 B 8.19 7.78 8.1 8.41 8.41 8.25 .27 .032 .127 .756 32 B 7.33 7.46 7.3 6.98 7.3 7.62 .24 .032 .032 .213 50 B 6.29 6.51 6.19 6.19 6.35 6.19 .14 .023 -.04B -.53 TS03 20 B 8.7 8.57 8.73 8.57 9.21 8.41 .31 .035 .016 .082 32 B 7.72 7.46 7.78 7.62 7.78 7.94 .18 .023 .095 .832 50 B 7.240 6.98 7.14 7.3 7.3 7.46 .18 .025 .111 .971 TS04 20 B 7.68 7.46 7.78 7.78 7.78 7.62 .14 .018 .032 .354 32 B 7.21 7.14 7.14 7.14 7.14 7.46 .14 .02 .063 .707 50 B 6.76 6.83 6.83 6.67 6.83 6.67 .09 .013 -.032 -.577 TS05 20 B 9.75 9.68 9.84 9.52 10 9.68 .18 .019 .016 .139 32 B 8 7.94 7.94 8.1 7.94 8.1 .09 .011 .032 .577 50 B 7.490 7.62 7.46 7.3 7.46 7.62 .13 .018 0 0 TS06 20 B 4.51 4.44 4.44 4.6 4.29 4.76 .18 .04 .048 .416 32 B 4 3.97 3.97 3.97 3.97 4.13 .07 .018 .032 .707 50 B 3.49 3.49 3.33 3.49 3.65 3.49 .11 .032 .032 .447 TS07 20 B 4 4.13 3.97 3.97 3.97 3.97 .07 .018 -.032 -.707 32 B 3.68 3.97 3.65 3.49 3.65 3.65 .17 .047 -.063 -.577 50 B 3.43 3.33 3.49 3.33 3.49 3.49 .09 .025 .032 .577 TSO8 20 B 4.86 4.92 4.92 4.76 4.92 4.76 .09 .010 -.032 -.577 32 B 4.29 4.13 4.44 4.13 4.29 4.44 .16 .037 .048 .474 50 B 3.59 3.65 3.49 3.65 3.49 3.65 .09 .024 0 0 TS09 20 B 5.49 5.72 5.72 5.4 5.4 5.24 .21 .039 -.127 -.943 32 B 5.05 5.24 5.08 5.24 4.76 4.92 .21 .041 -.095 -.728 50 B 4.83 4.92 5.08 4.76 4.6 4.76 .18 .038 -.079 -.693 TS1O 20 B 5.43 5.87 5.4 5.4 5.24 5.24 .26 .048 -.143 -.866 32 B 5.08 4.92 5.24 5.08 5.00 5.08 .11 .022 .016 .224 50 B 4.98 5.08 4.92 4.92 5.08 4.92 .09 .017 -.016 -.289 TSII 20 B 2.67 2.7 2.54 2.7 2.7 2.7 .07 .027 .016 .354 32 B 2.98 3.02 3.17 2.86 3.02 2.86 .13 .045 -.048 -.567 50 B 2.51 2.54 2.54 2.38 2.54 2.54 .07 .028 0 0 TS12 20 B 3.24 3.02 3.17 3.17 3.49 3.33 .18 .056 .095 .832 32 B 3.17 3.33 3.02 3.17 3.17 3.17 .11 .035 -.016 -.224 50 B 2.51 2,,54 2.54 2.54 2.54 2.38 .07 .028 -.032 -.707 137 Table B.15. Summary of Results from the Car-Mounted BI on the Gravel Roads. INTERNI1T1ONAL ROAID ROUGHNESS EX'PERIMENT - BRASILI,A - JLUNE 1982 CAR-MOUNTED BUMP INTEGRA TOR SITE SPEED TRACK ROUGHNESS MEASUREMENT (SLOPE X 1000) (K/H) NEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA S/N TREND R 6ROQ 20 B 2.98 2.7 3.33 3.02 3.02 2.86 .24 .079 0 0 32 B 3.14 3.02 3.33 3.17 2.86 3.33 .21 .066 .016 .121 50 B 3.05 3.02 3.17 3.02 3.02 3.02 .07 .023 -.016 -.354 6R02 20 B 3.59 3.49 3.49 3.65 3.65 3.65 .09 .024 .048 .866 32 B 3.52 3.65 3.49 3.33 3.65 3.49 .13 .038 -.016 -.189 50 B 3.27 3.49 3.17 3.33 3.33 3.02 .18 .055 -.079 -.693 6R03 20 B 10.13 10.16 10.48 10.32 9.94 ?.984 .28 .02B -.127 -.707 32 B 8.8? 8.57 8.73 9.37 8.57 9.21 .37 .042 .111 .472 50 B 8.06 7.78 7.78 8.1 7.94 8.73 .4 .049 .206 .826 6RQ4 20 B 8.45 8.89 8.57 8.25 8.25 8.25 .28 .034 -.159 -.884 32 B 7.27 7.14 7.14 7.3 7.3 7.46 .13 .018 .079 .945 50 B 6.98 6.83 7.14 7.3 6.67 6.98 .25 .036 -.016 -.1 OR05 20 B 12.73 12.86 12.7 12.7 12.54 12.86 .13 .01 -.016 -.189 32 B 12.41 12.38 12.86 11.91 12.54 12.38 .34 .028 -.032 -.146 50 B 12.16 11.91 12.38 12.06 12.38 12.06 .21 .018 .032 .236 6R06 20 B 12.89 13.02 13.18 12.86 12.54 12.86 .24 .018 -.095 -.64 32 B 11.43 11.11 11.43 11.43 11.75 11.43 .22 .02 .095 .671 50 B 11.49 11.59 11.59 11.43 11.27 11.59 .14 .012 -.032 -.354 6R07 20 B 7.4 7.46 7.46 6.98 7.62 7.46 .24 .033 .016 .104 32 B 6.73 6.98 6.67 6.51 6.83 6.67 .18 .027 -.048 -.416 50 B 6.57 6.51 6.51 6.51 6.98 6.35 .24 .037 .016 .104 GR06 20 B 4.95 4.92 4.76 4.76 5.24 5.08 .21 .042 .079 .b06 32 B 4.35 4.6 4.13 4.29 4.29 4.44 .18 .042 -.016 -.139 50 B 4.13 3.81 4.29 4.13 4.13 4.29 .19 .047 .079 .645 6R09 20 B 11.81 11.59 12.06 11.75 11.75 11.91 .18 .015 .032 .277 32 B 10.13 9.84 9.84 10.32 10.64 10 .34 .034 .111 .511 50 B 9.4 9.21 9.52 9.37 9.52 9.37 .13 .014 .032 .378 6R10 20 B 8.99 8.89 9.05 8.73 9.21 9.05 .18 .02 .048 .416 32 B 7.75 7.46 7.78 9.25 7.46 7.78 .33 .042 .032 .154 50 B 7.37 7.46 7.46 7.46 7.3 7.14 .14 .019 -.079 -.884 6R11 20 B 18.89 19.21 18.73 18.57 19.05 18.89 .25 .013 -.032 -.2 32 B 18.38 18.73 17.78 18.1 18.26 19.05 .51 .028 .111 .347 50 B 18 18.73 18.73 17.46 17.62 17.46 .67 .037 -.365 -.962 6R12 20 B 19.21 19.53 19.53 19.05 18.73 19.21 .34 .018 -.143 -.671 32 B 18.89 18.73 18.73 18.26 19.05 19.68 .53 .028 .222 .667 50 B 17.49 18.26 16.99 16.99 17.14 18.1 .63 .036 -.016 -.04 138 Table B.16. Summary of Results from the Car-Mounted BI on the Earth Roads. CAR-MOUNTED BUMP INTEGRATOR SITE SPEED TRACK ROUGHNESS MEASUREMENT (SLOPE X 1000) (K/H) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIBMA SIN TREND R TEOI 20 B 6.45 6.83 6.03 6.67 6.35 6.35 .31 .048 -.063 -.324 32 B 5.68 5.72 5.72 6.03 5.72 5.24 .28 .05 -.095 -.53 50 B 4.79 4.76 4.92 4.6 5.08 4.6 .21 .043 -.016 -.121 TE02 20 B 6 6.03 6.03 5.87 5.87 6.19 .13 .022 .016 .189 32 B 5.11 4.92 5.56 4.92 5.08 5.08 .26 .051 -.016 -.096 50 8 4.38 4.13 4.29 4.44 4.6 4.44 .18 .041 .095 .032 TE03 20 B 12.7 12.86 12.86 12.7 12.7 12.39 .19 .015 -.111 -.904 32 B 12.16 12.38 12.06 11.75 12.54 12.06 .31 .025 -.016 -.081 50 B 11.05 10.95 10.95 10.64 11.75 10.95 .41 .037 .079 .303 TE04 20 B 13.84 12.86 13.97 13.81 14.45 14.13 .6 .043 .302 .797 32 B 13.53 13.02 13.49 13.33 13.49 14.29 .47 .035 .254 .858 50 B 12.67 13.02 12.38 12.7 12.22 13.02 .36 .029 -.016 -.069 TE05 20 B 24.54 23.97 24.45 24.29 24.92 25.08 .46 .019 .27 .933 32 B 21.18 19.84 20.48 21.11 22.23 22.23 1.06 .05 .651 .974 50 B 20.83 19.84 20.16 20.64 21.43 22.07 .91 .044 .572 .988 TE06 20 B 32.51 31.75 32.54 32.23 32.86 33.19 .55 .017 .317 .905 32 e 27.4 26.19 27.15 27.46 27.62 28.57 .86 .031 .524 .964 50 B 26.48 25.56 26.19 26.35 27.15 27.15 .68 .026 .413 .964 TE07 20 B 6.92 6.98 6.98 6.83 6.98 6.83 .09 .013 -.032 -.577 32 B 6.48 6.03 6.51 6.35 6.98 6.51 .34 .053 .143 .656 50 B 5.81 5.72 5.87 6.03 5.72 5.72 .14 .024 -.016 -.177 TEOS 20 B 6.7 6.51 6.67 6.83 6.83 6.67 .13 .02 .048 .567 32 B 6.22 6.35 6.19 6.19 6.19 6.19 .07 .011 -.032 -.707 50 B 6.03 5.87 6.03 6.19 6.03 6.03 .11 .019 .032 .447 TE09 20 B 13.68 13.65 13.49 13.81 13.65 13.81 .13 .01 .048 .567 32 B 10.86 10.8 10.95 10.8 10.95 10.8 .09 8E-03 0 0 50 B 9.33 9.37 9.52 9.05 9.21 9.52 .21 .022 0 0 TEIO 20 B 19.27 19.21 18.89 19.21 19.53 19.53 .27 .014 .127 .756 32 B 15.43 15.4 15.08 16.03 15.08 15.56 .4 .026 .032 .127 50 B 13.27 13.18 13.65 13.49 12.7 13.33 .37 .028 -.063 -.275 TEII 20 B 18.7 18.73 18.41 18.89 18.57 18.89 .21 .011 .048 .364 32 B 14.54 14.45 14.13 14.76 14.45 14.92 .31 .021 .127 .649 50 B 11.59 11.75 11.59 11.27 11.75 11.59 .19 .017 -.016 -.129 TE12 20 B 13.49 13.65 13.18 13.18 13.49 13.97 .34 .025 .095 .447 32 B 11.4 11.59 11.11 11.27 11.27 11.75 .26 .023 .048 .289 50 B 10.16 9.68 10.16 9.84 10.64 10.48 .4 .04 .206 .006 139 Table B.17. Summary of Results from the NAASRA Meter on the Asphaltic Concrete Roads. INTERNI7TIc/NRL ROAD Rfc/&HNE.S EXPERIMEHT - 9PRA:S3Lli -- JVNE 19e2 CAR-MOUNTED NAASRA METER SITE SPEED TRACY ROUGHNESS KEASUREtENT (SLOPE I 10001 (K/H) HEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA S/H TREND R CAQI 20 B 1.98 1.? 1.8 1.99 2.09 2.09 .12 .063 .066 .849 32 B 3.02 3.42 3.23 2.95 2.66 2.85 .3 .1 -.171 -.891 50 B 3.97 3.7 3.89 4.27 3.8 4.18 .25 .062 .085 .55 80 B 5.61 5.7 5.61 5.7 5.7 5.32 .16 .029 -.066 -.639 CA02 20 B 3.15 3.13 3.04 3.32 3.13 3.13 .1 .033 9E-03 .144 32 B 3.93 4.18 3.99 4.08 3.8 3.61 .23 .058 -.133 -.919 50 B 4.69 4.75 4.65 4.75 4.46 4.84 .14 .031 0 0 80 B 5.72 5.51 5.7 5.8 5.7 5.89 .14 .025 .076 .853 CA03 20 B 6.29 6.08 6.36 6.46 6.17 6.36 .16 .025 .038 .385 32 B 6.54 6.17 6.740 7.03 6.55 6.17 .37 .057 -.019 -.081 50 B 6.71 6.46 6.55 6.65 6.84 7.03 .23 .034 .143 .985 80 B 8.07 8.07 8.17 7.88 8.26 7.98 .15 .019 -9E-03 -.1 CA04 20 B 5.34 5.61 5.32 5.22 5.22 5.32 .16 .029 -.066 -.674 32 B 6.1 6.17 6.08 6.17 6.08 5.99 .08 .013 -.038 -.756 50 B 6.18 5.8 6.27 6.17 6.27 6.36 .22 .036 .114 .809 80 B 6.54 6.46 6.36 6.46 7.03 6.36 .28 .043 .048 .268 CA05 20 B 7.22 7.41 7.12 7.31 7.12 7.12 .13 .019 -.057 -.671 32 8 7.56 7.22 7.31 7.41 7.98 7.88 .35 .046 .199 .91 50 8 7.11 6.65 7.5 7.12 7.22 7.03 .31 .044 .048 .242 80 a 8.19 8.26 7.98 8.07 8.36 8.26 .16 .019 .038 .385 CA06 20 B 8.15 7.69 8.26 8.36 8.07 8.36 .28 .034 .114 .643 32 B 8.4 8.45 8.17 8.36 8.26 8.74 .22 .026 .066 .481 50 B 8.42 8.07 8.45 8.17 8.93 8.45 .33 .04 .123 .586 80 B 9.82 9.31 9.78 9.59 10.07 10.35 .41 .041 .237 .924 CA07 20 B 1.48 1.52 1.52 1.52 1.52 1.33 .08 .057 -.038 -.707 32 B 2.11 1.99 2.28 2.09 1.9 2.28 .17 .081 .019 .177 50 B 2.49 2.56 2.37 2.47 2.56 2.47 .08 .032 0 0 80 B 3.82 3.61 3.8 3.99 3.7 3.99 .17 .044 .064 .619 CA08 20 B 1.41 1.52 1.43 1.33 1.43 1.33 .08 .057 -.038 -.756 32 B 1.77 1.9 1.71 1.61 1.52 2.09 .23 .129 .019 .131 50 B 2.15 2.09 1.99 2.37 2.18 2.09 .14 .067 .019 .209 80 B 3.74 3.7 3.9? 3.89 3.7 3.42 .22 .058 -.085 -.618 CA09 20 B 3.02 3.23 2.95 2.85 3.04 3.04 .14 .047 -.028 -.32 32 B 3.31 3.13 3.32 3.32 3.23 3.51 .14 .043 .066 .746 50 B 3.72 3.7 3.61 3.8 3.89 3.61 .12 .033 9E-03 .121 80 B 5 4.?4 5.13 4.84 4.94 5.13 .13 .026 .019 .236 CA10 20 B 2.3 2.18 2.28 2.37 2.37 2.28 .08 .035 .029 .567 32 B 2.87 2.76 2.85 2.85 3.13 2.76 .16 .054 .029 .289 50 B 3.46 3.42 3.7 3.42 3.51 3.23 .17 .05 -.057 -.522 80 B 4.64 4.56 4.65 4.46 4.46 5.03 .24 .051 .076 .508 CAII 20 B 6.29 6.17 6.27 6.17 6.27 6.55 .16 .025 .076 .77 32 B 6.48 6.65 6.17 6.65 6.55 6.36 .21 .032 -.019 -.146 50 B 5.97 5.99 5.99 6.08 5.99 5.8 .1 .017 -.038 -.577 80 B 6.42 6.17 7.03 6.27 6.27 6.36 .35 .054 -.038 -.173 CA12 20 B .8 1.04 .76 .67 .76 .76 .14 .181 -.057 -.626 32 B 1.03 1.04 .95 .95 1.04 1.14 .08 .077 .029 .567 50 B 1.3? 1.52 1.33 1.43 1.43 1.23 .11 .078 -.047 -.693 CA13 20 B .78 .76 .85 .76 .76 .76 .04 .055 -9E-03 -.354 32 B 1.1 1.04 .95 1.23 1.04 1.23 .13 .116 .048 .589 50 8 1.35 1.33 1.43 1.33 1.43 1.23 .08 .059 -.019 -.378 140 Table B.18. Summary of Results from the NAASRA Meter on the Surface Treatment Roads. CAR-MOUNTED NAASRA METER SITE SPEED TRACK RQU8HNESS MEASUREMENT ISLOPE X 10001 (K/HI MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA S/H TREND R TSOI 20 8 6.59 6.55 6.46 6.740 6.740 6.46 .14 .022 9E-03 .104 32 B 5.66 5.7 5.99 5.51 5.7 5.42 .22 .039 -.085 -.618 50 8 5.47 5.32 5.51 5.51 5.32 5.7 .16 .029 .057 .567 TSO2 20 B 8.21 7.98 7.88 8.45 8.36 8.36 .26 .031 .123 .761 32 B 7.11 7.22 6.84 6.740 7.31 7.41 .3 .042 .085 .457 50 B 6.04 6.17 5.99 5.8 6.27 5.99 .19 .031 -9E-03 -.081 T103 20 B 8.45 8.17 8.55 8.74 8.55 8.26 .23 .028 .019 .129 32 B 7.79 7.88 8.07 7.22 7.79 7.98 .34 .043 -9E-03 -.045 50 B 7.18 6.65 6.93 7.69 7.12 7.5 .42 .059 .19 .711 TS04 20 B 7.68 7.69 7.79 7.69 7.79 7.41 .16 .02 -.057 -.577 32 B 7.05 7.22 7.03 6.93 6.93 7.12 .12 .018 -.028 -.364 50 B 6.740 6.55 b.36 7.22 7.03 6.55 .36 .054 .066 .291 TS05 20 B 9.5 9.12 9.69 9.5 9.5 9.69 .23 .024 .095 .645 32 B 7.98 7.88 8.07 7.98 7.88 8.07 .1 .012 .019 .316 50 B 7.45 7.41 7.6 7.31 7.6 7.31 .14 .019 -.019 -.209 TS06 20 B 4.71 4.65 4.84 5.03 4.46 4.56 .23 .049 -.057 -.394 32 B 3.86 3.8 3.89 3.8 3.99 3.8 .08 .022 9E-03 .177 50 B 3.34 3.32 3.23 3.51 3.23 3.42 .12 .037 .019 .243 1S07 20 B 4.12 4.27 4.08 4.37 3.8 4.08 .22 .053 -.066 -.481 32 8 3.74 3.89 4.08 3.51 3.61 3.61 .24 .064 -.104 -.693 50 B 3.33 3.61 3.23 3.32 3.32 3.13 .18 .053 -.085 -.761 TS08 20 B 5 5.22 5.03 5.13 5.03 4.56 .26 .051 -.133 -.819 32 B 4.14 3.8 4.56 4.08 4.37 3.89 .32 .077 0 0 50 B 3.51 3.51 3.42 3.61 3.32 3.7 .15 .043 .029 .3 TS09 20 B 5.55 5.51 5.89 5.22 5.61 5.51 .24 .043 -.028 -.189 32 B 4.96 5.22 4.75 5.22 4.56 5.03 .3 .06 -.057 -.305 50 8 4.67 4.56 4.56 4.84 4.75 4.65 .12 .027 .038 .485 TSIO 20 8 5.53 5.8 6.08 5.32 5.22 5.22 .39 .07 -.199 -.813 32 B 4.98 5.03 4.94 4.84 4.94 5.13 .11 .022 .019 .277 50 B 4.75 4.84 4.84 4.75 4.75 4.56 .12 .024 -.066 -.904 TSII 20 B 2.6 2.37 2.47 2.76 2.76 2.66 .17 .066 .085 .783 32 B 2.72 2.76 2.56 2.76 2.bb 2.8S .11 .04 .029 .416 50 B 2.28 2.37 2.18 2.28 2.37 2.18 .1 .042 -.019 -.316 T912 20 B 3.08 2.95 3.04 3.04 3.13 3.23 .11 .035 .066 .971 32 B 2.95 3.23 2.95 2.85 2.76 2.95 .18 .06 -.076 -.676 50 B 2.37 2.56 2.37 2.37 2.37 2.18 .13 .057 -.076 -.894 141 Table B.19. Summary of Results from the NAASRA Meter on the Gravel Roads. CA*R-MOUNTED NAASRA METER SITE SPEED TRACK RDW HNESS MEASUREMENT (SLOPE X 1000) (Ki/) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 S16A SMll TREND R SROI 20 B 2.51 2.47 2.56 2.56 2.47 2.47 .05 .021 -9E-03 -.289 32 B 2.85 2.95 2.85 2.95 2.85 2.66 .12 .041 -.057 -.775 50 B 2.77 2.76 2.85 2.66 2.85 2.76 .08 .029 0 0 6R02 20 B 3.27 3.13 3.32 3.32 3.23 3.32 .08 .026 .029 .53 32 B 3.17 3.32 3.13 2.95 3.23 3.23 .14 .045 -9E-03 -.104 50 B 2.96 3.04 2.95 3.04 3.04 2.76 .12 .042 -.047 -.606 6R03 20 B 9.58 9.59 10.07 9.4 9.4 9.4 .29 .03 -.104 -.573 32 B 8.32 8.07 8.17 8.64 8.17 8.55 .26 .031 .095 .585 50 B 7.640 7.6 7.41 7.5 7.5 8.17 .3 .04 .123 .64 6R04 20 B 7.81 8.07 7.79 7.69 7.6 7.88 .18 .023 -.057 -.493 32 B 6.84 6.740 6.740 6.93 6.93 6.84 .1 .014 .038 .632 50 B 6.59 6.36 6.65 6.740 6.46 6.740 .17 .026 .057 .522 6R05 20 B 12.2? 12.63 12.16 12.44 11.88 12.35 .29 .024 -.085 -.467 32 B 11.87 12.06 12.25 11.31 11.88 11.88 .36 .03 -.076 -.338 50 B 11.59 11.5 11.88 11.4 11.78 11.4 .22 .019 -.028 -.202 6RO6 20 B 12.67 12.92 13.11 12.44 12.44 12.44 .32 .025 -.161 -.8 32 B 11.1 10.93 11.12 11.21 11.21 11.02 .12 .011 .029 .364 50 B 10.94 10.45 11.02 11.12 11.02 11.12 .28 .026 .133 .75 6R07 20 B 7.03 7.41 6.84 6.84 7.03 7.03 .23 .033 -.057 -.387 32 B 6.4 6.55 6.27 6.27 6.65 6.27 .19 .029 -.019 -.162 50 B 6.18 6.08 6.36 6.08 6.27 6.08 .13 .022 -9E-03 -.112 8R08 20 B 4.81 4.65 4.65 4.94 5.03 4.75 .17 .036 .057 .522 32 B 4.1 4.18 3.99 3.99 4.08 4.27 .12 .03 .029 .364 50 B 3.86 3.89 3.8 3.99 3.7 3.89 .11 .028 -9E-03 -.139 6R09 20 B 11.29 11.21 11.5 11.12 11.21 11.4 .16 .014 9E-03 .096 32 B 9.78 9.69 9.5 10.07 10.07 9.59 .27 .027 .038 .224 50 B 8.84 8.45 8.83 9.02 8.93 8.93 .22 .025 .104 .742 6R}O 20 B 8.59 8.36 8.83 8.45 8.45 8.83 .23 .027 .057 .394 32 B 7.56 7.12 7.41 7.98 7.79 7.5 .33 .044 .114 .541 50 B 7.2 7.31 7.31 7.03 7.22 7.12 .12 .017 -.047 -.606 6RI1 20 B 18.9 19.28 18.81 18.71 18.9 18.81 .22 .012 -.085 -.607 32 B 18.03 18.43 17.29 17.48 18.33 18.62 .6 .033 .143 .374 50 B 18.51 18.43 18.33 18.81 18.33 18.62 .21 .011 .038 .292 6R12 20 B 18.89 19.28 19.28 18.71 18.33 18.81 .41 .021 -.19 -.741 32 B 18.24 18.14 18.14 17.67 18.52 18.71 .4 .022 .152 .596 50 B 17.9 17.67 17.38 17.86 18.05 18.52 .43 .024 .237 .877 142 Table B.20. Summary of Results from the NAASRA Meter on the Earth Roads. INTERNI)TIONAL ROiCD R0USHNESS EXPERIMENT - BRASILIA - JUNE 1982 CAR-MOUNTED NAASRA METER SITE SPEED TRACK ROUGHNESS MEASURENENT (SLOPE X 1000) (K/H) MEAN RUN I RUN 2 RUN 3 RUN 4 RUN 5 SIGMA SIM TREND R TEOI 20 B 6.21 6.36 5.8 6.65 5.89 6.36 .36 .058 9E-03 .042 32 9 5.05 5.22 5.03 5.13 5.03 4.84 .14 .028 -.076 -.853 50 B 4.29 4.27 4.46 4.27 4.27 4.18 .1 .024 -.038 -.577 TE02 20 B 5.61 5.7 6.17 5.32 5.32 5.51 .36 .063 -.123 -.549 32 B 4.96 4.84 5.03 4.94 4.75 5.22 .18 .037 .048 .411 50 B 4.31 4.08 4.37 4.27 4.18 4.65 .22 .051 .095 .687 TE03 20 8 12.14 12.63 12.25 12.25 11.88 11.69 .37 .031 -.228 -.973 32 B 11.21 11.4 10.93 11.21 11.21 11.31 .18 .016 9E-03 .085 50 B 8.91 8.64 8.83 8.93 9.02 9.12 .18 .021 .114 .986 TE04 20 B 13.17 12.54 12.82 13.58 13.39 13.49 .46 .035 .247 .852 32 B 11.89 12.44 12.06 11.5 11.78 11.69 .37 .031 -.18 -.771 50 a 9.98 9.78 10.35 9.78 9.88 10.07 .24 .024 9E-03 .062 TE05 20 B 24.23 23.47 24.03 23.94 24.6 25.09 .63 .026 .38 .959 32 B 20.63 19.57 19.85 20.61 21.38 21.76 .94 .046 .589 .989 50 8 20.06 19.09 19.28 19.76 20.8 21.38 .99 .049 .608 .973 TEO6 20 B 32.34 32.2 32.3 32.11 32.3 32.77 26 8E-03 .114 .702 32 B 26.94 26.31 26.69 26.5 27.17 28.02 .68 .025 .39 .901 50 B 25.88 24.7 25.55 25.84 26.6 26.69 .82 .032 .504 .972 TEO7 20 B 6.54 6.55 6.46 6.55 6.55 6.55 .04 7E-03 9E-03 .354 32 B 6.04 5.8 5.89 5.99 6.36 6.17 .23 .038 .123 .853 50 B 5.36 5.32 5.51 5.32 5.42 5.22 .11 .02 -.028 -.416 TEOS 20 B 6.46 6.36 6.27 6.55 6.740 6.36 .19 .029 .048 .395 32 B 5.99 5.89 5.89 5.8 5.89 5.99 .07 .011 .019 .447 50 B 5.68 5.32 5.7 5.8 5.8 5.8 .21 .036 .104 .802 TEO9 20 B 13.07 13.01 12.92 13.2 13.01 13.2 .13 .01 .048 .589 32 B 10.26 10.26 10.45 10.07 10.26 10.26 .13 .013 -.019 -.224 50 B 8.82 9.02 8.83 8.45 8.64 9.12 .27 .031 0 0 TEIO 20 B 18.68 18.52 18.33 18.62 18.9 19 .27 .015 .152 .878 32 B 14.78 14.44 14.34 15.29 14.82 15.01 .4 .027 .162 .646 50 B 12.64 12.44 12.73 12.82 12.44 12.73 .18 .014 .029 .254 TEII 20 B 18.33 18.05 17.86 18.71 18.52 18.52 .36 .02 .162 .706 32 B 13.93 13.87 13.87 13.96 13.87 14.06 .08 6E-03 .038 .707 50 B 11.02 10.93 11.21 10.93 10.83 11.21 .18 .016 .019 .169 TE12 20 B 13.28 13.3 12.92 13.2 13.58 13.39 .25 .019 .085 .55 32 B 11.15 11.4 10.83 11.12 11.02 11.4 .25 .022 .019 .121 50 B 9.84 9.69 9.78 9.59 10.07 10.07 .22 .022 .104 .755 143 Table B.21. Summary of Results from the BI Trailer on the Asphaltic Concrete Roads. INTERNHT10NAL ROAD RO&GHNESS EX(PERIMENT - BRASILIA - JUNE 1982 BUMP INTEGRATOR TRAILER SITE SPEED TRACK ROU8HNESS MEASUREMENTS (SLOPE X E3) (K/H) HEAN RUN I RUN 2 RUN 3 SIGMA S/H TREND R CAOI 20 R 4.92 4.76 4.92 5.08 .16 .032 .159 1 20 L 4.82 4.92 4.6 4.92 .18 .038 0 0 32 R 3.86 3.97 3.81 3.81 .09 .024 -.079 -.866 32 L 4.02 3.97 3.97 4.13 .09 .023 .079 .866 50 R 3.49 3.49 3.49 3.49 0 0 0 0 50 L 3.76 3.81 3.81 3.65 .09 .024 -.079 -.866 CA02 20 R 5.03 5.08 4.92 5.08 .09 .018 0 0 20 L 5.77 5.72 5.72 5.87 .09 .016 .079 .866 32 R 4.39 4.29 4.6 4.29 .18 .042 0 0 32 L 4.97 5.08 4.92 4.92 .09 .018 -.079 -.866 50 R 3.92 4.13 4.13 3.49 .37 .094 -.317 -.866 50 L 4.76 4.76 4.92 4.6 .16 .033 -.079 -.5 CA03 20 R 8.57 8.25 8.73 8.73 .27 .032 .238 .866 20 L 8.47 8.25 8.41 8.73 .24 .029 .238 .982 32 R 7.83 7.94 7.62 7.94 .18 .023 0 0 32 L 6.93 7.14 6.67 6.98 .24 .035 -.079 -.327 50 R 7.04 7.3 6.98 6.83 .24 .034 -.238 -.982 50 L 6.61 6.67 6.51 6.67 .09 .014 0 0 CAQ4 20 R 7.25 7.3 7.46 6.98 .24 .033 -.159 -.655 20 L 7.83 7.78 7.62 8.1 .24 .031 .159 .655 32 R 6.19 6.19 6.19 6.19 0 0 0 0 32 L 6.93 6.83 6.98 6.98 .09 .013 .079 .866 50 R 5.82 5.72 5.72 6.03 .18 .031 .159 .866 50 L 6.46 6.83 6.19 6.35 .33 .051 -.238 -.721 CA05 20 R 9.15 9.52 8.89 9.05 .33 .036 -.238 -.721 20 L 9.63 9.21 9.52 10.16 .48 .05 .476 .982 32 R 8.1 8.1 8.1 8.1 0 0 0 0 32 L 8.78 8.73 8.73 8.99 .09 .01 .079 .866 50 R 6.93 6.83 6.98 6.98 .09 .013 .079 .866 50 L 7.41 7.62 7.3 7.3 .10 .025 -.159 -.866 CA06 20 R 10.37 10.32 10 10.9 .4 .039 .238 .596 20 L 11.06 11.27 10.64 11.27 .37 .033 0 0 32 R 9.37 9.37 9.52 9.21 .16 .017 -.079 -.5 32 L 10.74 10.32 10.95 10.95 .37 .034 .317 .866 50 R 8.63 8.73 8.41 8.73 .18 .021 0 0 50 L 9.94 9.84 9.84 9.B4 0 0 0 0 CA07 20 R 4.02 3.97 3.97 4.13 .09 .023 .079 .866 20 L 5.34 5.24 5.4 5.4 .09 .017 .079 .866 32 R 2.96 3.17 2.86 2.86 .18 .062 -.159 -.866 32 L 4.18 4.29 4.44 3.01 .33 .079 -.238 -.721 50 R 2.7 2.7 2.7 2.7 0 0 0 0 50 L 3.55 3.81 3.49 3.33 .24 .068 -.238 -.982 CAO8 20 R 4.18 4.13 4.13 4.29 .09 .022 .079 .866 20 L 4.71 4.6 4.76 4.76 .09 .019 .079 .866 32 R 3.07 3.17 3.02 3.02 .09 .03 -.079 -.866 32 L 4.02 3.97 3.97 4.13 .09 .023 .079 .866 50 R 2.75 2.86 2.7 2.7 .09 .033 -.079 -.866 50 L 3.17 3.17 3.17 3.17 0 0 0 0 CA09 20 R 4.97 5.08 4.92 4.92 .09 .018 -.079 -.866 20 L 6.56 6.83 6.51 6.35 .24 .037 -.238 -.982 32 R 4.13 4.13 3.97 4.29 .16 .038 .079 .5 32 L 5.56 5.4 5.72 5.56 .16 .029 .079 .5 50 R 3.49 3.49 3.65 3.33 .16 .045 -.079 -.5 50 L 4.5 4.44 4.44 4.6 .09 .02 .079 .866 144 Table B.21 (Cont.) INTERNRT.ZONL RO4AD ROIU&HNESS EXPER1MENT - BRPSILZI - JUNE .982 BUMP INTEGRATOR TRAILER SITE SPEED TRACK ROUGHNESS MEASUREMENTS (SLOPE I E3P IKJH) MEAN RUN I RUN 2 RUN 3 SIGMA S/H TREND R CAIO 20 R 4.44 4.44 4.44 4.44 0 0 0 0 20 L 6.3 6.35 6.35 6.19 .09 .015 -.079 -.866 32 R 3.7 3.65 3.81 3.65 .09 .025 0 0 32 L 5.24 5.08 5.24 5.4 .16 .03 .159 1 50 R 3.39 3.33 3.33 3.49 .09 .027 .079 .866 50 L 4.34 4.13 4.44 4.44 .18 .042 .159 .866 CAII 20 R 8.94 9.21 8.89 8.73 .24 .027 -.238 -.982 20 L 7.94 8.25 7.62 7.94 .32 .04 -.159 -.5 32 R 7.14 7.14 7.14 7.14 0 0 0 0 32 L 7.04 6.83 7.14 7.14 .18 .026 .159 .866 50 R 6.19 6.19 6.03 6.35 .16 .026 .079 .5 50 L 6.4 6.19 6.51 6.51 .18 .029 .159 .866 CA12 20 R 3.76 3.65 3.97 3.65 .18 .049 0 0 20 L 4.07 4.29 3.97 3.97 .18 .045 -.159 -.866 32 R 2.7 2.7 2.7 2.7 0 0 0 0 32 L 2.54 2.7 2.38 2.54 .16 .063 -.079 -.5 50 R 2.06 2.06 2.06 2.06 0 0 0 0 50 L 2.06 2.06 2.06 2.06 0 0 0 0 CA13 20 R 3.55 3.49 3.49 3.65 .09 .026 .079 .866 20 L 3.86 4.13 3.81 3.65 .24 .063 -.238 -.982 32 R 2.59 2.54 2.7 2.54 .09 .035 0 0 32 L 2.7 2.86 2.7 2.54 .16 .059 -.159 -1 50 R 2.17 2.22 2.22 2.06 .09 .042 -.079 -.866 50 L 2.22 2.22 2.22 2.22 0 0 0 0 145 Table B.22. Summary of Results from the BI Trailer on the Surface Treatment Roads. INTERNATIONAL ROsD ROIEGHNE;S EXPERIIEHT - BRASILIA - JUfNE J982 BUMP INTEGRATOR TRAILER SITE SPEED 7RACK R0U6HNESS MEASUREMENTS (SLOPE I E3) (K/H) MEAN RLN I RUN 2 RUN 3 SISKA SIN TREND R TSO1 20 R 9.37 9.37 9.52 9.21 .16 .017 -.079 -.5 20 L 8.94 8.73 9.05 9.05 .18 .02 .159 .866 32 R 6.77 6.83 6.83 6.67 .09 .014 -.079 -.866 32 L 6.56 6.83 6.51 6.35 .24 .037 -.238 -.982 50 R 5.29 5.24 5.08 5.56 .24 .046 .159 .655 50 L 5.45 5.24 5.72 5.4 .24 .044 .079 .327 TS02 20 R 11.38 11.59 11.43 11.11 .24 .021 -.238 -.982 20 L 10.69 10.64 10.64 10.8 .09 9E-03 .079 .866 32 R 8.1 7.94 8.1 8.25 .16 .02 .159 1 32 L 8.15 9.1 7.94 8.41 .24 .03 .159 .655 50 R 6.35 6.51 6.19 6.35 .16 .025 -.079 -.5 50 L 6.14 6.03 6.35 6.03 .18 .03 0 0 TSo3 20 R 10.37 10.16 10.48 10.48 .18 .018 .159 .866 20 L 11.06 11.43 10.8 10.95 .33 .03 -.238 -.721 32 R 8.25 8.41 8.1 8.25 .16 .019 -.079 -.5 32 L 8.73 8.89 8.73 8.57 .16 .018 -.159 -1 50 R 6.77 6.98 6.83 6.51 .24 .036 -.238 -.992 50 L 7.36 7.46 7.3 7.3 .09 .012 -.079 -.866 T904 20 R 10.74 10.8 10.8 10.64 .09 9E-03 -.079 -.866 20 L 9.05 9.05 8.89 9.21 .16 .019 .079 .5 32 R 8.63 8.57 9.73 9.57 .09 .011 0 0 32 L 7.41 7.3 7.46 7.46 .09 .012 .079 .866 50 R 7.36 7.3 7.3 7.46 .09 .012 .079 .866 50 L 6.35 6.35 6.35 6.35 0 0 0 0 TSQ5 20 R 11.06 10.95 11.43 10.8 .33 .03 -.079 -.24 20 L 11.91 12.06 12.06 11.59 .27 .023 -.238 -.866 32 R 8.89 8.73 9.05 8.89 .16 .018 .079 .5 32 L 9.84 9.52 10 10 .27 .028 .238 .866 50 R 7.62 7.62 7.62 7.62 0 0 0 0 50 L 8.68 8.57 8.09 8.57 .18 .021 0 0 7SO6 20 R 5.77 5.87 5.72 5.72 .09 .016 -.079 -.866 20 L 7.2 7.3 6.98 7.3 .18 .025 0 0' 32 R 4.5 4.6 4.44 4.44 .09 .02 -.079 -.866 32 L 5.45 5.56 5.4 5.4 .09 .017 -.079 -.866 50 R 3.7 3.65 3.65 3.81 .09 .025 .079 .866 50 L 4.13 4.13 4.29 3.97 .16 .038 -.079 -.5 TS07 20 R 5.66 5.72 5.56 5.72 .09 .016 0 0 20 L 6.35 6.51 6.35 6.19 .16 .025 -.159 -1 32 R 5.13 5.24 5.24 4.92 .18 .036 -.159 -.866 32 L 5.08 5.08 5.08 5.08 0 0 0 0 50 R 4.13 4.13 4.13 4.13 0 0 0 0 50 L 3.86 3.97 3.81 3.81 .09 .024 -.079 -.866 TS08 20 R 7.990 7.78 7.94 8.25 .24 .03 .238 .982 20 L 7.73 7.46 7.78 7.94 .24 .031 .238 .982 32 R 6.24 6.19 6.19 6.35 .09 .015 .079 .866 32 L 5.93 6.03 5.72 6.03 .18 .031 0 0 50 R 4.6 4.6 4.6 4.6 0 0 0 0 50 L 4.39 4.29 4.44 4.44 .09 .021 .079 .866 TS09 20 R 7.93 7.78 7.78 7.94 .09 .012 .079 .866 20 L 8.1 8.1 8.1 8.1 0 0 0 0 32 R 6.4 6.35 6.35 6.51 .09 .014 .079 .866 32 L 6.19 6.35 6.1q 6.03 .16 .026 -.159 -1 50 R 5.29 5.24 5.4 5.24 .09 .017 0 0 50 L 5.13 5.24 5.08 5.00 .09 .018 -.079 -.866 146 Table B.22 (Cont.) INTERNATIONAL ROAD ROUGHNESS EXPERIMENT - BRIOSILIq - JUNE .1982 SUMP INTEGRATOR TRAILER SITE SPEED TRACK ROUWHNESS MEASUREMENTS ISLOPE I E3) (K/H) MEAN RLU I RUN 2 RUN 3 S16A S/H TREND R TS1O 20 R 8.2 9.1 8.25 8.25 .09 .011 .079 .866 20 L 8.41 8.41 9.57 9.25 .16 .019 -.079 -.5 32 R 6.51 6.67 6.35 6.51 .16 .024 -.079 -.5 32 L 6.83 6.83 6.83 6.83 0 0 0 0 50 R 5.13 5.24 4.92 5.24 .18 .036 0 0 50 L 5.45 5.56 5.4 5.4 .09 .017 -.079 -.966 TSII 20 R 5.66 5.56 5.87 5.56 .19 .032 0 0 20 L 5.77 5.56 5.72 6.03 .24 .042 .238 .982 32 R 4.44 4.44 4.44 4.44 0 0 0 0 32 L 4.39 4.6 4.29 4.29 .18 .042 -.159 -.966 50 R 3.29 3.17 3.33 3.33 .09 .026 .079 .966 50 L 3.17 3.33 3.17 3.02 .16 .05 -.159 -1 TS12 20 R 6.14 6.19 6.19 6.03 .09 .015 -.079 -.866 20 L 6.56 6.51 6.51 6.67 .09 .014 .079 .866 32 R 4.29 4.13 4.44 4.29 .16 .037 .079 .5 32 L 4.97 4.92 4.92 5.09 .09 .018 .079 .866 50 R 3.12 3.17 3.17 3.02 .09 .029 -.079 -.966 50 L 3.44 3.49 3.33 3.49 .09 .027 0 0 147 Table B.23. Summary of Results from the BI Trailer on the Gravel Roads. INTERNATIONAL ROAD ROU&HNESS EX'PERIMENT - BRASILIA - JUNE 1982 BUMP INTEGRATOR TRAILER SITE SPEED TRACK ROUGHNESS MEASURENENITS (SLOPE X E3) (K/H) MEAN RUN I RUN 2 RUN 3 SIGMA S/H TREND R 6ROI 20 R 5.45 5.4 5.4 5.56 .09 .017 .079 .866 20 L 6.3 6.35 6.35 6.19 .09 .015 -.079 -.866 32 R 4.02 3.97 3.97 4.13 .09 .023 .079 .866 32 L 5.24 4.92 5.56 5.24 .32 .061 .159 .5 50 R 3.39 3.17 3.49 3.49 .18 .054 .159 .866 50 L 4.55 4.44 4.6 4.6 .09 .02 .079 .866 6R02 20 R 5.93 5.87 5.72 6.19 .24 .041 .159 .655 20 L 6.4 6.35 6.51 6.35 .09 .014 0 0 32 R 4.5 4.6 4.44 4.44 .09 .02 -.079 -.866 32 L 5.45 5.24 5.72 5.4 .24 .044 .079 .327 50 R 3.39 3.49 3.33 3.33 .09 .027 -.079 -.866 50 L 4.55 4.44 4.44 4.76 .18 .04 .159 .866 6R03 20 R 12.12 11.91 12.86 11.59 .66 .055 -.159 -.24 20 L 11.38 11.75 11.27 11.11 .33 .029 -.317 -.961 32 R 10.11 10.16 10.48 9.68 .4 .04 -.238 -.596 32 L 11.17 11.27 10.95 11.27 .18 .016 0 0 50 R 7.78 8.41 7.46 7.46 .55 .071 -.476 -.866 50 L 10.58 10.48 10.48 10.8 .18 .017 .159 .866 uRO4 20 R 10.8 11.27 10.64 10.48 .42 .039 -.397 -.945 20 L 10.16 10 10.16 10.32 .16 .016 .159 1 32 R 8.78 8.89 8.57 8.89 .18 .021 0 0 32 L 9.47 9.84 9.21 9.37 .33 .035 -.238 -.721 50 R 7.2 7.3 6.98 7.3 .18 .025 0 0 50 L 9.05 8.73 9.21 9.21 .27 .03 .238 .866 GRO5 20 R 13.44 13.49 13.02 13.81 .4 .03 .159 .397 20 L 16.88 17.3 16.83 16.51 .4 .024 -.397 -.993 32 R 11.75 11.59 11.59 12.06 .27 .023 .238 .866 32 L 16.19 16.83 16.35 15.4 .73 .045 -.714 -.982 50 R 10.95 10.8 11.11 10.95 .16 .014 .079 .5 50 L 14.76 15.24 15.24 13.81 .82 .056 -.714 -.866 6RO6 20 R 14.18 13.97 14.13 14.45 .24 .017 .238 .982 20 L 15.29 15.4 14.92 15.56 .33 .022 .079 .24 32 R 13.44 13.49 13.65 13.18 .24 .018 -.159 -.655 32 L 14.6 14.45 14.45 14.92 .27 .019 .238 .866 50 R 11.06 11.11 10.95 11.11 .09 8E-03 0 0 50 L 14.08 13.81 14.29 14.13 .24 .017 .159 .655 6R07 20 R 7.25 6.83 7.46 7.46 .37 .051 .317 .866 20 L 11.85 11.91 11.59 12.06 .24 .02 .079 .327 32 R 5.82 5.87 5.72 5.87 .09 .016 0 0 32 L 10.05 9.68 10.48 10 .4 .04 .159 .397 50 R 5.08 4.92 5.24 5.08 .16 .031 .079 .5 50 L 8.52 8.41 8.25 8.89 .33 .039 .238 .721 GR08 20 R 6.77 6.51 6.98 6.83 .24 .036 .159 .655 20 L 8.41 8.1 8.73 8.41 .32 .038 .159 .5 32 R 5.08 5.24 4.92 5.08 .16 .031 -.079 -.5 32 L 6.56 6.67 6.51 6.51 .09 .014 -.079 -.866 50 R 4.39 4.44 4.29 4.44 .09 .021 0 0 50 L 6.03 6.03 6.03 6.03 0 0 0 0 6R09 20 R 11.85 11.59 12.22 11.75 .33 .028 .079 .24 20 L 15.03 14.76 15.4 14.92 .33 .022 .079 .24 32 R 10.69 10.48 10.64 10.95 .24 .023 .238 .982 32 L 13.55 13.81 13.49 13.33 .24 .018 -.238 -.982 50 R 9.31 9.21 9.52 9.21 .18 .02 0 0 50 L 11.43 11.27 11.75 11.27 .27 .024 0 0 148 Table B.23 (Cont.) INTERNRTIONRL RO/%D ROU&/GNESS EXPERIMENT - BRASILIR - JUNE 298"2 BUMP INTEGRATOR TRAILER SITE SPEED TRACK ROUGHNESS MEASUREMENTS ISLOPE I E3) (K/H) MEAN RUN I RUN 2 RUN 3 SIGMA S/H TREND R 6RIO 20 R 8.89 8.57 9.05 9.05 .27 .031 .238 .866 20 L 12.81 13.02 12.54 12.86 .24 .019 -.079 -.327 32 R 7.51 7.3 7.94 7.3 .37 .049 0 0 32 L 11.11 10.95 11.11 11.27 .16 .014 .159 1 50 R 6.72 6.67 6.83 6.67 .09 .014 0 0 50 L 10.37 10.48 10.48 10.16 .18 .018 -.159 -.866 6RI 20 R 20.08 20.8 19.37 1.01 .05 -1.429 -1 20 L 25.64 25.72 25.56 .11 4E-03 -.159 -1 32 R 19.9 20.64 19.37 19.68 .66 .033 -.476 -.721 32 L 23.65 23.34 22.23 25.4 1.61 .068 1.032 .64 50 R 16.35 16.51 16.19 .22 .014 -.317 -1 50 L 21.99 21.75 22.23 .34 .015 .476 1 6R12 20 R 16.75 16.83 16.67 .11 7E-03 -.159 -1 20 L 25.08 24.92 25.24 .22 9E-03 .317 1 32 R 17.09 17.46 16.99 16.83 .33 .019 -.318 -.961 32 L 24.45 24.45 23.81 25.08 .64 .026 .317 .5 50 R 13.57 13.49 13.65 .11 8E-03 .159 1 50 L 22.38 23.65 21.11 1.8 .08 -2.54 -1 149 Table B.24. Summary of Results from the BI Trailer on the Earth Roads. 1NTERNATIONAL ROID ROUGHNESS EXPERI1ENT - BRASILIA - JUNE 1982 BUMP INTEGRATOR TRAILER SITE SPEED TRACK ROUGHNESS MEASUREMENTS (SLOPE I E3) (K/H) HEAN RUN I RUN 2 RUN 3 SIGMA SIN TREND R TEOI 20 R 7.04 6.67 6.98 7.46 .4 .057 .397 .993 20 L 10 10 9.84 10.16 .16 .016 .079 .5 32 R 5.87 5.72 6.03 5.87 .16 .027 .079 .5 32 L 7.73 7.78 7.46 7.94 .24 .031 .079 .327 50 R 4.6 4.29 4.6 4.92 .32 .069 .317 1 50 L 5.98 5.56 6.19 6.19 .37 .061 .317 .866 TE02 20 R 7.73 7.46 7.62 8.1 .33 .043 .317 .961 20 L 9.52 9.37 9.52 9.68 .16 .017 .159 1 32 R 5.93 5.87 5.87 6.03 .09 .015 .079 .866 32 L 7.14 6.98 7.14 7.3 .16 .022 .159 1 50 R 4.87 4.6 5.08 4.92 .24 .05 .159 .655 50 L 5.29 5.24 5.24 5.4 .09 .017 .079 .866 TE03 20 R 10.74 10.64 10.32 11.27 .48 .045 .317 .655 20 L 18.26 18.1 18.57 18.1 .27 .015 0 0 32 R 8.63 8.57 8.89 8.41 .24 .028 -.079 -.327 32 L 16.77 17.14 16.35 16.83 .4 .024 -.159 -.397 50 R 7.62 7.3 7.46 8.1 .42 .055 .397 .945 50 L 13.86 13.33 14.13 14.13 .46 .033 .397 .966 TEO4 20 R 13.92 13.81 13.97 13.97 .09 7E-03 .079 .866 20 L 16.77 16.83 16.99 16.51 .24 .014 -.159 -.655 32 R 11.75 11.75 11.43 12.06 .32 .027 .159 .5 32 L 16.51 16.99 15.87 16.67 .57 .035 -.159 -.277 50 R 9.95 10 9.68 10.16 .24 .024 .079 .327 50 L 14.45 14.13 14.45 14.76 .32 .022 .317 1 TE05 20 R 32.17 31.75 32.23 32.54 .4 .012 .397 .993 20 L 31.59 30.32 32.07 32.39 1.11 .035 1.032 .929 32 R 27.46 27.46 27.15 27.79 .32 .012 .159 .5 32 L 25.93 25.08 26.03 26.67 .8 .031 .794 .993 50 R 23.65 23.5 23.81 .22 9E-03 .317 1 50 L 21.75 21.91 21.59 .22 .01 -.317 -1 TEO6 20 R 37.84 37.78 37.94 37.78 .09 2E-03 0 0 20 L 40.38 40.48 40.64 40 .33 8E-03 -.238 -.721 32 R 33.5 33.34 32.86 34.29 .73 .022 .476 .655 32 L 32.44 31.91 32.23 33.19 .66 .02 .635 .961 50 R 26.51 26.19 26.83 .45 .017 .635 1 50 L 26.19 26.51 25.88 .45 .017 -.635 -1 TE07 20 R 8.94 8.73 9.05 9.05 .18 .02 .159 .866 20 L 9.47 9.68 9.37 9.37 .18 .019 -.159 -.866 32 R 7.36 7.14 7.62 7.3 .24 .033 .079 .327 32 L 7.62 7.62 7.62 7.62 0 0 0 0 50 R 6.24 6.19 6.03 6.51 .24 .039 .159 .655 50 L 6.67 6.51 6.83 6.67 .16 .024 .079 .5 TEOB 20 R 9.58 9.68 9.52 9.52 .09 .01 -.079 -.866 20 L 9.79 9.68 9.94 9.84 .09 9E-03 .079 .866 32 R 7.73 7.46 7.78 7.94 .24 .031 .238 .982 32 L 7.88 7.94 7.78 7.94 .09 .012 0 0 50 R 6.35 6.35 6.19 6.51 .16 .025 .079 .5 50 L 6.3 6.19 6.51 6.19 .18 .029 0 0 TE09 20 R 17.25 16.67 17.14 17.94 .64 .037 .635 .99 20 L 14.29 14.29 14.76 13.81 .48 .033 -.238 -.5 32 R 12.44 12.22 12.38 12.7 .24 .02 .238 .982 32 L 13.12 13.02 12.7 13.65 .48 .037 .317 .655 50 R 7.79 7.62 7.62 8.1 .27 .035 .238 .866 50 L 9.58 9.21 10.16 9.37 .51 .053 .079 .156 150 Table B.24 (Cont.) INTERNPTIONIL ROD ROUGHNESS EXPERIMENT - BRPSIL14 - JUNE 19f2 BUMP INTEGRATOR TRAILER SITE SPEED TRACK ROUGHNESS MEASUREMENTS (SLOPE X E3) IJHI MEAN RUN I RUN 2 RUN 3 S16GA S/H TREND R TEIO 20 R 21.22 22.38 20.32 20.95 1.06 .05 -.714 -.676 20 L 24.77 24.76 24.76 24.76 0 0 0 0 32 R 16.56 16.19 16.51 16.99 .4 .024 .397 .993 32 L 20.64 20.48 20.48 20.95 .27 .013 .238 .866 50 R 12.7 12.39 12.86 12.86 .27 .022 .238 .866 50 L 14.29 14.29 14.76 13.81 .48 .033 -.238 -.5 TEII 20 R 17.41 17.3 17.46 17.46 .09 5E-03 .079 .866 20 L 23.18 23.34 22.7 23.5 .42 .018 .079 .189 32 R 13.71 13.97 13.33 13.81 .33 .024 -.079 -.24 32 L 20.11 20.48 19.68 20.16 .4 .02 -.159 -.397 50 R 11.8 11.59 11.75 12.06 .24 .021 .238 .982 50 L 15.98 16.35 16.19 15.4 .51 .032 -.476 -.933 TE12 20 R 20.11 20.32 19.68 20.32 .37 .018 0 0 20 L 15.24 15.4 15.08 15.24 .16 .01 -.079 -.5 32 R 18.04 17.94 18.1 18.1 .09 5E-03 .079 .866 32 L 13.39 13.33 13.33 13.49 .09 7E-03 .079 .866 50 R 14.02 14.13 13.65 14.29 .33 .024 .079 .24 50 L 10.69 10.64 10.64 10.8 .09 9E-03 .079 .866 151 Table B.25. Summary of Results from the BPR Roughometer on the Asphaltic Concrete Roads. 7NTERNH4TItJNHL RORD ROHUGHNESS EXPERINENT - BRASILIR - JUNE 1982 BPR ROUGHOMETER SITE SPEED TRACK ROUSHNESS MEASUREMENTS (SLOPE X E3) (KIN) MEAN RUN I RUN 2 RUN 3 SIGMA SIN TREND R CAoI 20 R 1.7 1.6 1.59 1.9 .18 .105 .151 .843 20 L 1.67 1.71 1.6 1.7 .06 .036 -SE-03 -.132 32 R 2.36 2.24 2.29 2.56 .17 .073 .159 .927 32 L 2.53 2.7 2.52 2.38 .16 .063 -.159 -.998 50 R 1.67 1.64 1.57 1.79 .11 .069 .079 .b93 50 L 1.43 1.64 1.6 1.05 .33 .231 -.294 -.889 CAo2 20 R 1.45 1.48 1.43 1.44 .02 .017 -.016 -.655 20 L 2.21 2.25 2.16 2.22 .05 .022 -.016 -.327 32 R 2.52 2.24 2.44 2.87 .32 .129 .317 .98 32 L 2.85 3.05 3.03 2.48 .33 .114 -.286 -.875 50 R 1.78 1.87 1.59 1.87 .16 .093 0 0 50 L 2.07 2.19 2.19 1.83 .21 .102 -.183 -.866 CAO3 20 R 2.97 3.19 2.86 2.87 .19 .063 -.159 -.844 20 L 4.18 4.27 4.2? 3.97 .18 .043 -.151 -.843 32 R 5.33 5.52 5.06 5.4 .24 .045 -.064 -.267 32 L 5.82 5.6 6.33 5.51 .45 .078 -.048 -.105 50 R 4.02 3.75 4.57 3.75 .48 .119 0 0 50 L 3.55 3.91 3.43 3.32 .31 .088 -.294 -.941 CAO4 20 R 2.3 2.56 2.27 2.08 .24 .104 -.238 -.993 20 L 3.72 3.6 3.97 3.59 .22 .058 -sE-O3 -.037 32 R 4.43 4.48 4.3 4.51 .11 .025 .016 .143 32 L 5.52 5.6 5.48 5.49 .07 .013 -.056 -.803 50 R 2.98 3.11 2.84 3 .14 .045 -.056 -.41 50 L 3.57 3.92 3.51 3.27 .33 .092 -.325 -.988 CAO5 20 R 3.74 3.56 3.78 3.8? .16 .044 .159 .974 20 L 5.49 5.14 5.52 5.79 .33 .06 .325 .995 32 R 10.75 11.94 10.65 9.65 1.15 .107 -1.143 -.997 32 L 13.08 12.72 13.45 13.08 .37 .028 .183 .5 50 R 3.55 3.84 3.41 3.4 .25 .071 -.222 -.881 50 L 5.31 4.78 4.06 7.08 1.58 .297 1.151 .73 CA06 20 R 4.81 4.98 4.67 4.78 .16 .033 -.103 -.64 20 L 4.8 5 4.64 4.76 .19 .039 -.119 -.642 32 R 11.85 11.73 11.53 12.29 .39 .033 .278 .705 32 L 13.45 13.49 13.33 13.51 .1 7E-03 SE-03 .082 50 R 4.18 4.11 4.33 4.08 .14 .033 -.016 -.115 50 L 3.94 5.24 4.59 2 1.71 .435 -1.619 -.945 CA07 20 R 1.06 .95 1.11 1.11 .09 .087 .079 .866 20 L 1.7 1.97 1.38 1.75 .3 .175 -.111 -.375 32 R 1.9 1.97 1.86 1.87 .06 .032 -.046 -.792 32 L 2.13 2.32 1.9 2.16 .21 .098 -.079 -.381 50 R .94 .76 .98 1.06 .16 .167 .151 .965 50 L 1.39 1.32 1.54 1.32 .13 .092 0 0 so R .98 1.06 .98 .89 .09 .089 -.087 -.999 80 L 1.6 1.35 1.54 1.92 .29 .181 .286 .982 tA08 20 R 1.04 .95 1 1.16 .11 .104 .103 .955 20 L 1.42 1.3 1.32 1.64 .19 .133 .167 .886 32 R 1.87 1.86 1.76 1.99 .11 .06 .063 .569 32 L 2.05 2.21 1.9 2.03 .15 .074 -.087 -.577 50 R .77 .75 .78 .79 .02 .031 .024 .982 50 L 1.15 1.16 1.13 1.16 .02 .016 0 0 80 R 1.39 1.41 1.44 1.3 .08 .054 -.056 -.741 80 L 1.31 1.16 1.22 1.54 .2 .156 .191 .933 152 Table B.25 (Cont.) INTERNH4TIOW'L RO&V ROLt7HNESS EX PERIMENT - BRISILliQ - JUNE 1982 BPR ROUGHOMETER SITE SPEED TRACK ROUGHNESS NEASUREMENTS (SLOPE X E3) (KINH) EAN RUN I RUN 2 RUN 3 SIGMA SIH TREND R CAO9 20 R 2.17 2.24 2.17 2.1 .07 .033 -.071 -.998 20 L 1.56 1.64 1.64 1.41 .13 .082 -.111 -.866 32 R 1.06 .92 .98 1.27 .19 .176 .175 .939 32 L 1.64 1.62 1.48 1.81 .17 .102 .095 .569 50 R 1.11 1.08 1.02 1.24 .11 .103 .079 .693 50 L 2.3 2.21 2.25 2.44 .13 .055 .119 .945 80 R 1.22 1.29 1.24 1.14 .07 .06 -.071 -.982 80 L 2.13 2.03 2.08 2.27 .13 .059 .119 .945 CAIO 20 R 1.19 1.11 1.38 1.08 .17 .139 -.016 -.096 20 L 1.59 1.49 1.62 1.67 .09 .057 .087 .967 32 R .8 .81 .73 .86 .06 .00 .024 .371 32 L 1.83 1.83 1.71 1.95 .12 .065 .063 .533 50 R 1.21 1.11 1.38 1.13 .15 .126 8E-03 .052 50 L 1.69 1.56 1.46 2.05 .32 .187 .246 .781 80 R 1.64 1.68 1.56 1.67 .07 .042 -8E-03 -.115 80 L 1.65 1.44 2.1 1.41 .39 .233 -.016 -.041 CAll 20 R 3.34 3.21 3.3 3.51 .15 .046 .151 .978 20 L 3.13 3.21 3.21 2.97 .14 .044 -.119 -.866 32 R 3.2 3.06 3.13 3.41 .19 .058 .175 .939 32 L 3.32 2.98 3.41 3.56 .3 .09 .286 .961 50 R 3.39 3.65 3.51 3 .34 .101 -.325 -.951 50 L 3.03 3.06 3.03 3 .03 .01 -.032 -1 80 R 3.34 3.44 3.14 3.43 .17 .051 -8E-03 -.047 80 L 2.87 2.84 2.67 3.1 .22 .075 .127 .589 CA12 20 R 1.66 1.7 1.65 1.64 .03 .02 -.032 -.961 20 L 2.05 2.05 2.08 2.03 .02 .012 -8E-03 -.327 32 R 1.57 1.49 1.6 1.6 .06 .041 .056 .866 32 L 1.55 1.51 1.62 1.52 .06 .039 8E-03 .132 50 R 1.21 1.24 1.17 1.22 .03 .027 -8E-03 -.24 50 L 1.19 1.17 1.21 1.19 .02 .013 8E-03 .5 CA13 20 R 1.59 1.64 1.54 1.6 .05 .03 -.016 -.327 20 L 1.8 1.86 1.79 1.76 .05 .027 -.048 -.982 32 R 1.48 1.51 1.46 1.46 .03 .019 -.024 -.866 32 L 1.59 1.56 1.62 1.59 .03 .02 .016 .5 50 R 1.29 1.29 1.3 1.27 .02 .012 -8E-03 -.5 50 L 1.33 1.33 1.32 1.35 .02 .012 8E-03 .5 153 Table B.26. Summary of Results from the BPR Roughometer on the Surface Treatment Roads. INTERNATIONIPL R0AD ROU&HNESS EXPERIMENT - BRqSILZIQ - JUNE 1982 BPR ROUGHOMETER SITE SPEED TRACK ROU&HNESS MEASUREMENTS (SLOPE X E3) (K/H) MEAN RUN I RUN 2 RUN 3 S16tA S/H TREND R TSOI 20 R 5.43 5.59 5.32 5.38 .14 .026 -.103 -.731 20 L 5.09 4.97 5.08 5.21 .12 .023 .119 .999 32 R 4.33 4.44 4.06 4.48 .23 .053 .016 .069 32 L 4.2 4.13 4.29 4.19 .08 .019 .032 .397 50 R 3.61 3.6 3.51 3.71 .1 .029 .056 .538 50 L 3.51 3.49 3.6 3.44 .08 .023 -.024 -.292 TS02 20 R 5.92 5.89 5.97 5.89 .05 8E-03 0 0 20 L 6.42 6.48 6.45 6.35 .07 .01 -.063 -.961 32 R 5.56 5.6 5.64 5.45 .1 .018 -.079 -.778 32 L 5.71 5.83 5.86 5.46 .22 .039 -.183 -.828 50 R 4.06 3.78 4.02 4.4 .31 .077 .31 .991 50 L 4.08 4.03 4.16 4.05 .07 .017 8E-03 .115 TS03 20 R 6.04 6.13 6.02 5.97 .08 .013 -.079 -.974 20 L 6.68 6.81 6.65 6.59 .11 .017 -.111 -.971 32 R 5.11 5.18 5.03 5.11 .07 .014 -.032 -.444 32 L 6.37 6.6 6.13 6.38 .24 .037 -.111 -.466 50 R 4.69 4.71 4.78 4.57 .11 .023 -.071 -.676 50 L 5.23 5.29 5.25 5.14 .08 .014 -.071 -.952 TS04 20 R 8.98 9.32 9.06 8.56 .39 .043 -.381 -.982 20 L 6.43 5.84 7.35 6.1 .81 .126 .127 .157 32 R 5.19 5.11 5.3 5.16 .1 .019 .024 .24 32 L 5.74 5.3 6.14 5.78 .42 .073 .238 .564 50 R 4.39 4.33 4.37 4.46 .07 .015 .063 .%61 50 L 3.91 3.78 3.91 4.03 .13 .033 .127 1 TS05 20 R 10.17 10.32 10.81 9.38 .73 .071 -.468 -.645 20 L 9.28 9.21 9.41 9.22 .11 .012 8E-03 .069 32 R 5.73 5.86 5.62 5.7 .12 .021 -.079 -.655 32 L 7.08 6.52 7.7 7.02 .59 .083 .246 .417 50 R 4.93 5.19 4.67 4.92 .26 .053 -.135 -.515 50 L 5.03 5.1 4.97 5.03 .06 .013 -.032 -.5 TS06 20 R 3.78 3.98 3.71 3.65 .18 .047 -.167 -.942 20 L 4.47 4.41 4.57 4.43 .09 .02 8E-03 .091 32 R 3.05 3.03 3.16 2.95 .1 .034 -.04 -.381 32 L 3.58 3.6 3.6 3.54 .04 .01 -.032 -.866 50 R 2.36 2.24 2.41 2.43 .11 .045 .095 .901 50 L 2.66 2.67 2.59 2.73 .07 .027 .032 .444 TS07 20 R 3.8 3.95 3.79 3.67 .14 .038 -.143 -.998 20 L 4.19 4.41 4.16 3.95 .23 .055 -.23 -.998 32 R 3.19 3.1 3.25 3.22 .08 .026 .063 .756 32 L 3.23 3.25 3.22 3.22 .02 6E-03 -.016 -.866 50 R 2.42 2.46 2.41 2.38 .04 .017 -.04 -.993 50 L 2.5 2.54 2.46 2.51 .04 .016 -.016 -.397 TS08 20 R 4.79 4.79 4.76 4.83 .03 7E-03 .016 .5 20 L 4.5 4.49 4.52 4.49 .02 5E-03 -8E-03 -.327 32 R 3.86 3.91 3.84 3.83 .04 .011 -.04 -.945 32 L 3.89 3.75 3.97 3.97 .13 .033 .111 .966 50 R 3.96 3.83 4.05 4 .12 .03 .087 .746 50 L 4.07 4.13 4.08 4 .06 .016 -.063 -.99 154 Table B.26 (Cont.) INTERNI TIOIURL ROiqD ROU6LHHESS EXPERINEHT - BRRSILI,A - JUNE 19G2-1 EPR ROUEGHOMETER SITE SPEED TRACK ROUDHNESS HEASURENENTS (SLOPE I E3) (K/H) MEAN RUN I RUN 2 RUN 3 SISNA &/H TREND R TS09 20 R 4.57 4.59 4.57 4.56 .02 3E-03 -.016 -1 20 L 4.61 4.64 4.7 4.51 .1 .021 -.064 -.655 32 R 3.6 3.57 3.62 3.6 .02 7E-03 .016 .655 32 L 3.76 3.75 3.76 3.76 .01 2E-03 BE-03 .866 50 R 3.17 3.17 3.21 3.14 .03 .01 -.016 -.5 50 L 3.23 3.35 3.16 3.19 .1 .032 -.079 -.778 TSIO 20 R 4.51 4.57 4.41 4.56 .09 .019 -6E-03 -.091 20 L 4.77 4.83 4.76 4.73 .05 .01 -.04B -.982 32 R 3.56 3.52 3.49 3.67 .09 .026 .071 .768 32 L 3.85 3.87 3.84 3.83 .02 6E-03 -.024 -.982 50 R 2.95 2.94 2.94 2.97 .02 6E-03 .016 .866 50 L 3.27 3.35 3.19 3.27 .08 .024 -.04 -.5 TSII 20 R 3.37 3.4 3.33 3.37 .03 9E-03 -.016 -.5 20 L 3.27 3.29 3.25 3.27 .02 5E-03 -BE-03 -.5 32 R 2.58 2.65 2.52 2.57 .06 .025 -.04 -.619 32 L 2.59 2.54 2.62 2.6 .04 .016 .032 .756 50 R 1.88 1.92 1.84 1.89 .04 .021 -.016 -.397 50 L 1.9 1.89 1.89 1.92 .02 .01 .016 Jb66 TS12 20 R 3.75 3.68 3.79 3.76 .06 .015 .04 .693 20 L 3.85 3.84 3.83 3.87 .02 6E-03 .016 .655 32 R 2.66 2.65 2.68 2.64 .02 9E-03 -SE-03 -.327 32 L 2.93 2.94 2.92 2.94 .01 3E-03 0 0 50 R 1.88 1.83 1.94 1.89 .06 .03 .032 .569 50 L 2.1 2.11 2.11 2.08 .02 9E-03 -.016 -.866 155 Table B.27. Summary of Results from the BPR Roughometer on the Gravel Roads. INTERNi4TIONiQL RO/AD ROLi&HNESS EXPERiMENT - BRRSILIR - JLUNE 1982' BPR ROUGHOMETER SITE SPEED TRACK ROUGHNESS MEASUREMENTS (SLOPE X 10001 (KIH) MEAN RUN I RUN 2 RUN 3 SI6NA SIH TREND R &ROI 20 R 2.91 2.95 2.86 2.91 .05 .016 -.024 -.5 20 L 3.31 3.29 3.3 3.33 .02 7E-03 .024 .982 32 R 2.37 2.35 2.37 2.4 .02 .01 .024 .982 32 L 2.79 2.86 2.73 2.79 .06 .023 -.032 -.5 50 R 1.9 1.92 1.9 1.89 .02 BE-03 -.016 -1 50 L 2.42 2.37 2.48 2.41 .06 .023 .024 .427 6R02 20 R 3.22 3.27 3.14 3.25 .07 .021 -8E-03 -.115 20 L 3.67 3.6 3.86 3.56 .16 .044 -.024 -.147 32 R 2.67 2.41 2.73 2.87 .24 .088 .23 .977 32 L 3.03 2.87 3.13 3.08 .14 .045 .103 .764 50 R 2.15 2.16 2.14 2.14 .01 4E-03 -8E-03 -.866 50 L 2.67 2.7 2.67 2.65 .02 9E-03 -.024 -.982 6RQ3 20 R 6.85 6.81 6.79 6.94 .08 .011 .063 .811 20 L 7.33 7.29 7.41 7.3 .07 9E-03 8E-03 .115 32 R 5.72 6.05 5.59 5.52 .29 .05 -.262 -.916 32 L 6.96 6.87 7.16 6.84 .17 .025 -.016 -.091 50 R 4.04 3.97 4 4.16 .1 .025 .095 .933 50 L 5.79 5.72 5.84 5.83 .07 .012 .056 .803 BR04 20 R 5.2 5.21 5.25 5.13 .06 .012 -.04 -.619 20 L 7.16 7.16 7.22 7.11 .06 8E-03 -.024 -.427 32 R 4.22 4.19 4.21 4.27 .04 .01 .04 .945 32 L 6.51 6.46 6.57 6.51 .06 9E-03 .024 .427 50 R 3.59 3.6 3.54 3.64 .05 .013 .016 .327 50 L 5.78 5.37 5.94 6.05 .37 .063 .341 .932 SR05 20 R 6.66 6.52 6.72 6.75 .12 .018 .111 .924 20 L 9.61 10.18 9.4 9.26 .5 .052 -.46 -.929 32 R 6.12 6.3 5.86 6.19 .23 .038 -.056 -.24 32 L 7.25 7.33 7.1 7.32 .13 .018 -8E-03 -.06 50 R 4.87 4.81 5.06 4.75 .17 .034 -.032 -.189 50 L 6.51 6.51 0 0 0 0 6R06 20 R 6.32 6.25 6.46 6.24 .12 .02 -8E-03 -.064 20 L 7.92 8.11 7.86 7.79 .17 .021 -.159 -.?45 32 R 5.49 5.68 5.54 5.25 .22 .04 -.214 -.982 32 L 7.33 7.16 7.37 7.48 .16 .022 .159 .985 50 R 4.27 4.21 4.32 4.27 .06 .013 .032 .569 6R07 20 R 4.65 4.27 4.92 4.76 .34 .073 .246 .725 20 L 7.1? 7.18 7.240 7.14 .05 7E-03 -.016 -.327 32 R 3.47 3.49 3.41 3e49 .05 .013 0 0 32 L 6.3 6.24 6.35 6.3 .06 9E-03 .032 .569 50 R 2.98 3.02 2.97 2.95 .03 .011 -.032 -.961 50 L 3.84 4.16 3.52 .45 .117 -.635 -1 GROB 20 R 4.16 3.92 4.14 4.41 .25 .059 .246 .998 20 L 5.45 5.33 5.79 5.22 .3 .056 -.056 -.183 32 R 3.07 3.08 3 3.14 .07 .023 .032 .444 32 L 4.06 3.76 4.1 4.33 .29 .071 .286 .995 50 R 2.55 2.57 2.57 2.49 .05 .018 -.04 -.866 50 L 3.41 3.37 3.44 .06 .016 .079 1 156 Table B.27 (Cont.) INTERNATIONAL ROAD ROUfGHNESS EXPERIMENT - BRRSILIR - JUNE 19f G- BPR ROUGHOMETER SITE SPEED TRACY ROUGHNESS HEASURENENTS (SLOPE X 1000) (KIH) MEAN RUN I RUN 2 RUN 3 SIGMA S/H TREND R 6R09 20 R 7.95 7.97 7.95 7.92 .02 3E-03 -.024 -.982 20 L 9.35 9.29 9.4 9.37 .06 6E-03 .04 .693 32 R 6.66 6.72 6.68 6.59 .07 .01 -.063 -.961 32 L 8.61 8.52 8.62 8.7 .09 .01 .087 .999 50 R 5.55 5.62 5.45 5.59 .09 .017 -.016 -.171 50 L 6.9k 6.91 0 0 0 0 6R10 20 R 6.36 6.48 6.29 6.32 .1 .016 -.079 -.778 20 L 7.97 7.990 8.020 7.92 .05 6E-03 -.032 -.655 32 R 4.6 4.65 4.6 4.56 .05 .01 -.048 -1 32 L 6.95 6.15 7.13 6.98 .19 .028 .119 .619 50 R 4 4 4.13 3.87 .13 .032 -.063 -.5 50 L 6.46 6.46 0 0 0 0 157 Table B.28. Summary of Results from the BPR Roughometer on the Earth Roads. 1NTERP TINONfAL RO.4D ROVSHNES-S EXPERIMENT - BR/4SlLID - JUfNE 198,2 BPR ROUGHOMETER SITE SPEED TRACK ROUGHNESS HEASUREHENTS (SLOPE X 1000) (K/H) MEAN RUN I RUN 2 RUN 3 SIGMA S/X TREND R TEOI 20 R 4.22 4.09 4.13 4.46 .21 .049 .191 .919 20 L 5.22 5.19 5.22 5.25 .03 6E-03 .032 1 32 R 3.55 3.49 3.67 3.48 .11 .03 -SE-03 -.075 32 L 4.22 4.16 4.32 4.18 .09 .021 8E-03 .091 50 R 2.7 2.79 2.67 2.64 .08 .031 -.079 -.945 50 L 3.34 3.4 3.29 3.33 .06 .017 -.032 -.569 TE02 20 R 4.75 4.89 4.75 4.6 .14 .03 -.143 -1 20 L 4.83 4.78 4.79 4.91 .07 .014 .063 .918 32 R 3.82 3.89 3.62 3.95 .18 .046 .032 .179 32 L 3.79 3.79 3.83 3.75 .04 .011 -.024 -.596 50 R 3.2 3.08 3.37 3.16 .15 .046 .04 .269 50 L 3.08 3.27 3.02 2.95 .17 .055 -.159 -.945 TE03 20 R 6.47 6.59 6.3 6.52 .15 .023 -.032 -.212 20 L 10.53 10.51 10.37 10.7 .17 .016 .095 .569 32 R 5.28 5.41 5.3 5.13 .14 .027 -.143 -.992 32 L 8.93 8.6 9.16 9.02 .29 .032 .206 .715 50 R 4.31 4.24 4.25 4.43 .11 .025 .095 .901 50 L 6.9 7.13 6.62 6.94 .26 .037 -.095 -.371 TE04 20 R 8.24 8.06 8.3 8.37 .16 .019 .151 .948 20 L 11.21 11.08 11.49 11.05 .25 .022 -.016 -.064 32 R 6.58 6.22 6.56 6.97 .37 .057 .373 .998 32 L 9.17 9 8.97 9.54 .32 .035 .27 .84 50 R 5.41 5.86 4.91 5.48 .48 .089 -.19 -.397 50 L 7.13 6.86 7.41 7.11 .28 .039 .127 .457 TE05 20 R 19.22 21.65 20.54 15.48 3.29 .171 -3.088 -.938 32 R 16.45 16.62 16.29 .24 .014 -.333 -1 TE06 20 R 22.05 22.65 25.88 17.62 4.16 .189 -2.516 -.605 32 R 19.4 18.29 20.51 1.57 .081 2.222 1 TE07 20 R 5.35 5.41 5.35 5.29 .06 .012 -.063 -1 20 L 5.94 6 6.16 5.67 .25 .042 -.167 -.664 32 R 4.4 4.51 4.35 4.35 .09 .021 -.079 -.866 32 L 4.82 4.87 4.79 4.78 .05 .011 -.048 -.933 50 R 3.48 3.48 0 0 0 0 TEO0 20 R 6.02 6 5.92 6.13 .1 .017 .063 .61 20 L 5.89 5.76 5.86 6.05 .15 .025 .143 .982 32 R 4.75 4.64 4.76 4.86 .11 .023 .111 .997 32 L 4.99 4.95 5.14 4.87 .14 .028 -.04 -.286 50 R 3.54 3.54 0 0 0 0 TE09 20 R 11.63 12.57 11.46 10.84 .88 .075 -.865 -.987 20 L 12.06 12.26 11.7 12.22 .31 .026 -.016 -.051 32 R 8.2 7.84 8.27 8.48 .32 .04 .317 .98 32 L 9.22 8.87 9.37 9.43 .3 .033 .278 .913 50 R 5.37 5.37 0 0 0 0 158 Table B.28 (Cont.) INTERNI)TIONAL ROI9D RAO$HNESS EXiPERIhENT - BRPSILI - JUNE 19,22 BPR ROUGHOMETER SITE SPEED TRACK ROUGHNESS MEASUREMENTS (SLOPE X 1000) (KIf) MEAN RUN I RUN 2 RUN 3 SIGMA SIR TREND R TEIO 20 R 16.1 16.3 16.35 15.64 .4 .025 -.333 -.835 20 L 15.01 15.07 15.18 14.8 .2 .013 -.135 -.689 32 R 11.48 11.45 11.46 11.54 .05 4E-03 .048 .933 32 L 12.55 13.05 12.22 12.38 .44 .035 -.333 -.761 50 R 5.84 5.84 0 0 0 0 TEII 20 R 12.14 12.16 12.21 12.06 .07 6E-03 -.048 -.655 20 L 17.4 17.4 0 0 0 0 32 R 9.4 9.54 9.49 9.18 .2 .021 -.183 -.92 32 L 14.07 14.02 14.11 .07 5E-03 .095 1 TE12 20 R 11.73 11.96 11.3 12.02 .38 .032 .079 .212 20 L 11.4 11.4 0 0 0 0 32 R 9.23 9.48 9.1 9.13 .21 .023 -.175 -.B26 159 Table B.29. Summary of All ARS Numerics Obtained Directly with RTRRMSs at 20 km/h. Opala Cars with Caravan Car BI Trailer BPR Roughometer Site Mbdified Maysmeters with 2 meters (Wheeltrack) (Wheeltrack) MM 01 MM 02 MM 03 BI NAASRA Left Right Ave. Left Right Ave. CA01 2.54 2.56 2.65 2.16 1.98 4.82 4.92 4.87 1.67 1.70 1.69 CA02 3.26 3.80 3.98 3.11 3.15 5.77 5.03 5.40 2.21 1.45 1.83 CA03 6.01 6.57 6.64 6.19 6.29 8.47 8.57 8.52 4.18 2.97 3.57 CA04 5.34 5.95 5.98 5.43 5.34 7.83 7.25 7.54 3.72 2.30 3.01 CA05 7.47 7.75 7.59 7.27 7.22 9.63 9.15 9.39 5.49 3.74 4.61 CA06 7.77 8.79 8.74 8.13 8.15 11.06 10.37 10.72 4.80 4.81 4.80 CA07 2.10 2.16 1.37 1.78 1.48 5.34 4.02 4.68 1.70 1.06 1.38 CA08 2.00 1.78 1.19 1.75 1.41 4.71 4.18 4.44 1.42 1.04 1.23 CA09 3.60 3.65 3.86 3.11 3.02 6.56 4.97 5.77 1.56 2.17 1.87 CAIO 2.81 2.91 3.09 2.51 2.30 6.30 4.44 5.37 1.59 1.19 1.39 CAll 6.43 6.66 6.31 6.16 6.29 7.94 8.94 8.44 3.13 3.34 3.23 CA12 1.23 0.80 0.57 0.95 0.80 4.07 3.76 3.92 2.05 1.66 1.86 CA13 1.16 1.11 0.94 0.98 0.78 3.86 3.55 3.70 1.80 1.59 1.70 TSO1 7.47 7.69 7.58 6.54 6.59 8.94 9.37 9.15 5.09 5.43 5.26 TS02 9.39 9.83 8.95 8.19 8.21 10.69 11.38 11.03 6.42 5.92 6.17 TS03 8.73 9.56 9.87 8.70 8.45 11.06 10.37 10.72 6.68 6.04 6.36 TS04 8.17 8.26 9.80 7.68 7.68 9.05 10.74 9.90 6.43 8.98 7.70 TS05 9.47 10.66 10.95 9.75 9.50 11.91 11.06 11.48 9.28 10.17 9.73 TS06 4.69 4.64 5.51 4.51 4.71 7.20 5.77 6.48 4.47 3.78 4.13 TS07 3.90 3.97 5.27 4.00 4.12 6.35 5.66 6.01 4.18 3.80 3.99 TS08 5.36 5.61 5.47 4.86 5.00 7.73 7.99 7.86 4.50 4.79 4.65 TS09 5.60 5.89 5.91 5.49 5.55 8.10 7.83 7.96 4.61 4.57 4.59 TS10 5.85 6.06 5.91 5.43 5.53 8.41 8.20 8.31 4.77 4.51 4.64 TS11 3.71 3.57 2.30 2.67 2.60 5.77 5.66 5.72 3.27 3.37 3.32 TS12 3.67 3.47 1.58 3.24 3.08 6.56 6.14 6.35 3.85 3.75 3.80 GROI 3.81 3.72 3.19 2.98 2.51 6.30 5.45 5.87 3.31 2.91 3.11 GRD2 4.12 4.47 3.30 3.59 3.27 6.40 5.93 6.16 3.67 3.22 3.45 GRO3 10.23 11.40 7.29 10.13 9.58 11.38 12.12 -11.75 7.33 6.85 7.09 GRO4 8.14 9.36 5.79 8.45 7.81 10.16 10.80 10.48 7.16 5.20 6.18 GR05 13.40 15.42 17.67 12.73 12.29 16.88 13.44 15.16 9.61 6.66 8.14 GRO6 12.34 13.39 15.48 12.89 12.67 15.29 14.18 14.74 7.92 6.32 7.12 GR07 8.52 8.22 9.80 7.40 7.03 11.85 7.25 9.55 7.19 4.65 5.92 GRO8 5.76 5.47 7.44 4.95 4.81 8.41 6.77 7.59 5.45 4.16 4.80 GRO9 12.27 12.18 13.79 11.81 11.29 15.03 11.85 13.44 9.35 7.95 8.65 GR10 9.48 10.09 10.88 8.99 8.59 12.81 8.89 10.85 7.97 6.36 7.17 GRll 21.73 18.65 18.62 18.89 18.90 25.64 20.08 22.86 .... .... .... GR12 24.30 20.21 20.74 19.21 18.89 25.08 16.75 20.92 .... .... .... TE01 6.67 7.54 8.41 6.45 6.21 10.00 7.04 8.52 5.22 4.22 4.72 TE02 6.44 7.12 7.89 6.00 5.60 9.52 7.73 8.63 4.83 4.75 4.79 TE03 12.60 14.04 14.94 12.70 12.14 18.26 10.74 14.50 10.53 6.47 8.50 TE04 13.05 14.67 15.36 13.84 13.17 16.77 13.92 15.35 11.21 8.24 9.73 TE05 19.09 26.88 24.59 24.54 24.23 31.59 32.17 31.88 .... 19.22 19.22 TE06 .... 33.45 32.20 32.51 32.34 40.38 37.84 39.11 .... 22.05 22.05 TE07 4.03 7.61 8.76 6.92 6.54 9.47 8.94 9.21 5.94 5.35 5.65 TE08 4.85 8.41 9.94 6.70 6.46 9.79 9.58 9.68 5.89 6.02 5.95 TE09 12.41 16.13 17.18 13.68 13.07 14.29 17.25 15.77 12.06 11.63 11.84 TEIO 17.77 22.23 19.62 19.27 18.68 24.76 21.22 22.99 15.01 16.10 15.55 TEll 19.60 21.13 16.80 18.70 18.34 23.18 17.41 20.29 17.40 12.14 14.77 TE12 15.92 16.91 17.13 13.49 13.28 15.24 20.11 17.67 11.40 11.73 11.56 160 Table B.30. Summary of All ARS Numerics Obtained Directly with RTRRMSs at 32 km/h. Opala Cars with Caravan Car BI Trailer BPR Roughometer Site Modified Maysmeters with 2 meters (Wheeltrack) (Wheeltrack) MM 01 MM 02 MM 03 BI NAASRA Left Right Ave. Left Right Ave. CAOI 3.13 3.68 3.83 2.98 3.02 4.02 3.86 3.94 2.53 2.36 2.45 CA02 3.78 4.53 4.11 4.03 3.93 4.97 4.39 4.68 2.85 2.52 2.69 CA03 6.12 7.37 4.94 6.57 6.54 6.93 7.83 7.38 5.82 5.33 5.57 CAO4 5.86 6.91 6.54 6.13 6.10 6.93 6.19 6.56 5.52 4.43 4.98 CAO5 7.27 8.32 6.76 7.91 7.56 8.78 8.10 8.44 13.08 10.75 11.91 CA06 7.50 9.26 8.62 8.60 8.40 10.74 9.37 10.05 13.45 11.85 12.65 CA07 2.11 2.36 3.06 2.35 2.11 4.18 2.96 3.57 2.13 1.90 2.01 CA08 1.75 1.71 2.06 1.87 1.77 4.02 3.07 3.55 2.05 1.87 1.96 CA09 3.47 3.78 3.66 3.52 3.31 5.56 4.13 4.84 1.64 1.06 1.35 CAIO 2.98 3.48 3.71 3.05 2.87 5.24 3.70 4.47 1.83 0.80 1.31 CAll 6.72 7.03 6.78 6.41 6.48 7.04 7.14 7.09 3.32 3.20 3.26 CA12 1.32 1.22 0.42 1.27 1.03 2.54 2.70 2.62 1.55 1.57 1.56 CA13 1.14 1.38 0.65 1.24 1.10 2.70 2.59 2.65 1.59 1.48 1.53 TS01 5.72 6.22 5.61 5.84 5.66 6.56 6.77 6.67 4.20 4.33 4.27 TS02 7.44 8.39 7.40 7.33 7.11 8.15 8.10 8.12 5.72 5.56 5.64 TSO3 7.68 8.28 8.07 7.72 7.79 8.73 8.26 8.49 6.37 5.11 5.74 TS04 7.85 8.43 8.31 7.21 7.05 7.41 8.63 8.02 5.74 5.19 5.47 TSO5 8.53 9.44 10.04 8.00 7.98 9.84 8.89 9.37 7.08 5.73 6.40 TSO6 3.84 4.22 4.22 4.00 3.86 5.45 4.50 4.97 3.58 3.05 3.32 TS07 3.72 4.25 4.58 3.68 3.74 5.08 5.13 5.11 3.23 3.19 3.21 TSO8 4.51 4.65 4.48 4.29 4.14 5.93 6.24 6.09 3.89 3.86 3.88 TS09 5.25 5.60 4.78 5.05 4.96 6.19 6.40 6.30 3.76 3.60 3.68 TS1O 5.15 5.61 5.12 5.08 4.98 6.83 6.51 6.67 3.85 3.56 3.70 TS11 3.11 3.20 1.92 2.98 2.72 4.39 4.44 4.42 2.59 2.58 2.58 TS12 3.15 3.44 1.80 3.18 2.94 4.97 4.29 4.63 2.93 2.66 2.79 GROl 3.68 3.58 2.60 3.14 2.85 5.24 4.02 4.63 2.79 2.37 2.58 GRO2 3.90 3.76 2.52 3.52 3.17 5.45 4.50 4.97 3.03 2.67 2.85 GRO3 8.70 9.94 5.87 8.89 8.32 11.17 10.11 10.64 6.96 5.72 6.34 GR04 7.25 7.90 4.46 7.27 6.84 9.47 8.78 9.13 6.51 4.22 5.37 GR05 12.71 15.17 16.86 12.41 11.88 16.19 11.75 13.97 7.25 6.12 6.68 GRO6 11.12 12.96 14.08 11.43 11.10 14.60 13.44 14.02 7.33 5.49 6.41 GRO7 7.64 7.49 7.92 6.73 6.40 10.05 5.82 7.94 6.30 3.47 4.88 GRO8 4.89 4.95 5.31 4.35 4.10 6.56 5.08 5.82 4.06 3.07 3.57 CR09 10.88 10.71 11.09 10.13 9.78 13.55 10.69 12.12 8.61 6.66 7.64 GR10 8.58 8.87 9.11 7.75 7.56 11.11 7.51 9.31 6.95 4.60 5.78 GR1l 26.92 19.59 20.29 18.38 18.03 23.65 19.90 21.78 .... .... .... GR12 18.15 21.62 20.56 18.89 18.24 24.45 17.09 20.77 .... .... .... TE01 5.26 5.96 6.43 5.68 5.05 7.73 5.87 6.80 4.22 3.55 3.88 TE02 5.09 5.76 6.02 5.11 4.96 7.14 5.93 6.54 3.79 3.82 3.80 TE03 11.11 12.77 12.15 12.16 11.21 16.77 8.63 12.70 8.93 5.28 7.10 TE04 11.24 12.91 13.12 13.53 11.89 16.51 11.75 14.13 9.17 6.58 7.88 TE05 15.79 23.88 19.11 21.18 20.63 25.93 27.46 26.70 .... 16.45 16.45 TE06 .... 29.46 26.31 27.40 26.94 32.44 33.50 32.97 .... 19.40 19.40 TE07 5.11 7.06 7.63 6.48 6.04 7.62 7.36 7.49 4.82 4.40 4.61 TE08 5.77 7.54 7.85 6.22 5.89 7.88 7.73 7.81 4.99 4.75 4.87 TE09 10.92 12.76 12.81 10.86 10.26 13.12 12.44 12.78 9.22 8.20 8.71 TE10 14.40 17.70 17.08 15.43 14.78 20.64 16.56 18.60 12.55 11.48 12.02 TEll 16.60 17.22 12.69 14.54 13.93 20.11 13.71 16.91 14.07 9.40 11.73 TE12 14.12 14.62 13.08 11.40 11.15 13.39 18.04 15.72 .... 9.23 9.23 161 Table B.31. Summary of All ARS Numerics Obtained Directly with RTRRMSs at 50 km/h. Opala Cars with Caravan Car BI Trailer BPR Roughometer Site Modified Maysmeters with 2 meters (Wheeltrack) (Wheeltrack) MM 01 MM 02 MM 03 BI NAASRA Left Right Ave. Left Right Ave. CAO1 3.92 5.03 5.55 3.97 3.97 3.76 3.49 3.62 1.43 1.67 1.55 CA02 4.32 5.11 5.40 4.95 4.69 4.76 3.92 4.34 2.07 1.78 1.92 CA03 5.70 7.45 6.17 7.33 6.71 6.61 7.04 6.83 3.55 4.02 3.79 CA04 5.98 7.11 6.74 6.48 6.18 6.46 5.82 6.14 3.57 2.98 3.28 CA05 6.98 5.21 7.63 7.87 7.11 7.41 6.93 7.17 5.31 3.55 4.43 CA06 7.43 8.72 9.14 9.62 8.42 9.84 8.63 9.23 3.94 4.18 4.06 CA07 2.62 2.72 2.81 2.57 2.49 3.55 2.70 3.12 1.39 0.94 1.16 CA08 2.31 2.31 2.31 2.25 2.15 3.18 2.75 2.96 1.15 0.77 0.96 CAO9 3.79 3.98 4.13 3.97 3.72 4.50 3.49 4.00 2.30 1.11 1.71 CA10 3.44 3.88 3.87 3.71 3.46 4.34 3.39 3.86 1.69 1.21 1.45 CAll 5.70 6.21 6.19 6.22 5.97 6.40 6.19 6.30 3.03 3.39 3.21 CA12 1.26 1.30 1.03 1.59 1.39 2.06 2.06 2.06 1.19 1.21 1.20 CA13 1.36 1.31 1.09 1.56 1.35 2.22 2.17 2.20 1.33 1.29 1.31 TSO1 5.21 5.46 5.60 5.46 5.47 5.45 5.29 5.37 3.51 3.61 3.56 TS02 5.62 6.63 6.14 6.29 6.04 6.14 6.35 6.24 4.08 4.06 4.07 TS03 6.90 7.78 8.35 7.24 7.18 7.36 6.77 7.06 5.23 4.69 4.96 TS04 6.33 6.86 7.18 6.76 6.74 6.35 7.36 6.85 3.91 4.39 4.15 TS05 7.05 7.72 8.04 7.49 7.45 8.68 7.62 8.15 5.03 4.93 4.98 TS06 3.48 3.42 3.66 3.49 3.34 4.13 3.70 3.92 2.66 2.36 2.51 TS07 3.41 3.61 3.66 3.43 3.32 3.86 4.13 4.00 2.50 2.42 2.46 TS08 3.38 3.80 3.94 3.59 3.52 4.39 4.60 4.50 4.07 3.96 4.01 TSO9 5.05 5.21 5.23 4.83 4.67 5.13 5.29 5.21 3.23 3.18 3.20 TS10 4.66 5.30 5.35 4.98 4.75 5.45 5.13 5.29 3.27 2.95 3.11 TS11 2.34 2.51 3.04 2.51 2.28 3.18 3.28 3.23 1.90 1.88 1.89 TS12 2.43 2.38 3.12 2.51 2.38 3.44 3.12 3.28 2.10 1.88 1.99 GRO1 2.80 3.24 2.25 3.05 2.77 4.55 3.39 3.97 2.42 1.90 2.16 GR02 3.25 3.33 2.08 3.27 2.96 4.55 3.39 3.97 2.67 2.15 2.41 GRO3 7.49 8.85 8.19 8.06 7.64 10.58 7.78 9.18 5.79 4.04 4.92 GRO4 6.45 7.54 6.43 6.98 6.59 9.05 7.20 8.12 5.78 3.59 4.69 GRO5 11.15 13.71 14.58 12.16 11.59 14.76 10.95 12.86 6.51 4.87 5.69 GRO6 10.13 11.69 11.98 11.49 10.94 14.08 11.06 12.57 .... 4.27 4.27 GR07 6.79 7.18 7.24 6.57 6.18 8.52 5.08 6.80 3.84 2.98 3.41 GRO8 4.28 4.35 4.48 4.13 3.86 6.03 4.39 5.21 3.41 2.55 2.98 GRO9 9.53 10.00 10.12 9.40 8.84 11.43 9.31 10.37 6.91 5.55 6.23 GR10 7.57 8.68 9.65 7.37 7.20 10.37 6.72 8.55 6.46 4.00 5.23 GR1l 18.57 20.31 20.19 18.00 18.51 21.99 16.35 19.17 .... .... GR12 17.01 19.58 19.91 17.49 17.90 22.38 13.57 17.98 .... .... .... TE01 4.39 4.88 4.82 4.79 4.29 5.98 4.60 5.29 3.34 2.70 3.02 TE02 4.07 4.31 4.83 4.38 4.31 5.29 4.87 5.08 3.08 3.20 3.14 TE03 8.30 9.26 9.12 11.05 8.91 13.86 7.62 10.74 6.90 4.31 5.60 TE04 8.60 10.07 9.57 12.67 9.98 14.45 9.95 12.20 7.13 5.41 6.27 TE05 14.75 20.55 21.47 20.83 20.06 21.75 23.65 22.70 TE06 .... 25.70 28.11 26.48 25.88 26.19 26.51 26.35 .... TE07 5.31 5.92 6.90 5.81 5.36 6.67 6.24 6.46 .... 3.48 3.48 TE08 5.56 6.12 6.94 6.03 5.68 6.30 6.35 6.32 .... 3.54 3.54 TEO9 8.84 9.19 10.35 9.33 8.82 9.58 7.78 8.68 .... 5.37 5.37 TEIO 12.23 12.87 13.60 13.27 12.64 14.29 12.70 13.49 .... 5.84 5.84 TEll 11.34 12.36 11.18 11.59 11.02 15.98 11.80 13.89 .... TE12 9.99 10.74 9.47 10.16 9.84 10.69 14.02 12.36 .... 162 Table B.32. Summary of All ARS Numerics Obtained Directly with RTRRMSs at 80 km/h. Opala Cars with Caravan Car BI Trailer BPR Roughometer Site Modified Maysmeters with 2 meters (Wheeltrack) (Wheeltrack) MM 01 MM 02 MM 03 BI NAASRA Left Right Ave. Left Right Ave. CA01 4.29 4.91 5.19 6.32 5.60 .... .... .... .... .... .... CAO2 4.50 5.16 5.11 6.35 5.72 .... .... .... CA03 6.18 7.78 6.00 10.57 8.07 .... .... .... .... .... .... CA04 5.55 6.32 5.74 7.62 6.54 .... .... .... .... .... .... CA05 6.50 7.68 6.65 10.51 8.19 .... .... .... .... CA06 7.53 9.32 8.77 13.72 9.82 .... . .... . . .. . .. . .. CA07 3.00 2.85 3.04 4.19 3.82 .... .... .... 1.60 0.98 1.29 CAO8 2.89 2.87 3.19 4.29 3.74 .... .... .... 1.31 1.39 1.35 CA09 4.25 4.29 4.85 5.52 5.00 .... .... .... 2.13 1.22 1.67 CAIO 3.72 3.95 4.34 5.24 4.64 .... .... .... 1.65 1.64 1.64 CAll 5.95 6.45 6.83 6.70 6.42 .... .... .... 2.87 3.34 3.10 CA12 1.96 1.46 1.66 .... .... ... . .... .... .... .... .... CA13 2.09 1.72 1.94 .... .... .... .... .... TSO1 6.14 7.01 7.41 .... .. .. .... .... .... TS02 4.92 5.52 5.23 .... .... .... .... .... TS03 5.90 7.10 7.16 .... .... .... .... .... TS04 7.89 9.23 9.73 .... .... .... .... .... TS05 9.58 11.72 11.91 .... .... .... .... .... TS06 3.22 3.11 3.47 .... .... .... .... .... TS07 3.14 3.30 3.64 .... .... .... .... .... TSO8 3.74 4.08 4.39 .... .... .... .... .... .... TSO9 3.93 4.56 3.04 .... .... .... .... .... TS10 4.00 4.72 2.90 .... .... .... .... .... TS11 2.82 2.32 2.27 .... .... .... .... .... TS12 2.79 2.44 1.92 .... .... .... .... .... GROI 3.28 2.86 2.74 .... .... .... .... .... GRO2 3.18 3.52 3.08 .... .... .... .... .... .... .... .... GRO3 6.58 8.11 7.83 .... .... .... .... .... GR04 5.73 6.52 5.68 .... .... .... .... .... GRO5 10.79 12.77 12.23 .... .... .... .... .... GRO6 9.25 10.80 10.30 .... .... .... .... .... GRO7 5.91 6.39 6.50 .... .... .... .... .... GRO8 4.04 4.08 3.83 .... .... .... .... .... .... .... .... GRO9 9.19 11.05 11.99 .... .... .... .... .... GR1O 8.36 9.64 9.71 .... .... .... .... .... GRIl 4.1 4 4.32 .... .... .... .... .... .... ..... GR12 .98 .1 3. .... .... .... .... .... .... .... .... TE01 4.19 4.49 4.32 .... .... .... ..... .... TE02 3.98 4.13 3.77 .... .... .... ..... .... TE 0 3 7.02 8.25 7.30 .... .... .... ..... ..... .... TE04 6.76 8.35 7.91 .... .... .... .... .... .... .... TE05 .36 .91 .... .... .... .... .... .... .... TE06 .... .... .... .... .... .... . .... . .... . .... . .... . .... TE07 3.50 5.37 4.47 .... .... .... . .... . .... . .... . .... . .... TE08 3.91 5.61 4.28 .... .... .... . .... . .... . .... . .... . .... TEO9 5.06 8.36 7.91 .... .... .... . .... . .... . .... . .... . .... TE10 7.68 11.25 10.73 .... .... .... .... .... .... .... .... TEll 10.90 10.79 10.57 .... .... .... .... .... .... .*.. TE12 9.16 9.89 8.46 .... .... .... .... .... .... .... .... 163 APPENDIX C CORRELATIONS BETWEEN RTRBMS MEASURES In this appendix, the average rectified slope (ARS) measures that were obtained from the response-type road roughness measuring systems (RTRRMSs) are compared between instruments and across operating speed. A number of scatter plots are presented that show how the different RTRRMSs "see" roughness, relative to each other. A simple correlation exercise was performed, in which the ARS measures from each RTRRMS were regressed against those of the others. The squared correlation cofficients (R-squared) are presented for comparative purposes, and are all based on linear regressions. Purpose of the Comparisons It is generally recognized that RTRRMSs change with time. The data obtained in the IRRE should not be used to estimate the measures of one RTRRMS from the measure of another, since the mechanical properties of the participating RTRRMSs are now only historical. Recognizing that there is little merit in attempting to estimate one RTRRMS measure from another, the objective of this appendix is to indicate the best agreement that is possible between two RTRRMSs, by comparing measures made at the same time under the same conditions over the same test sites. This level of agreement establishes a standard against which a calibration methodology can be evaluated. In this report, the source of error (differences in measures obtained from two systems) are classified into three categories: Repeatability. Whenever repeated measurements are made, there will not be perfect agreement due to sources that are uncontrolled and random. Because the error is random, it can be reduced by averaging, either by using longer test sites or by making repeated runs. 165 Calibration Error. The measures from one system are consistently higher than those of the other. If the difference is consistent for a class of measurement conditions, it can be determined experimentally and compensated by using a calibration curve. This is done for a RTRRMS by experimentally determining an equation for estimating the reference measure from the RTRRMS measure. The regression equation is the calibration curve, and the method is a calibration by correlation. If the calibration curve is in error then the calibrated measures will be biased. Reproducibility. Even when two systems are properly calibrated to a reference, and repeat measures are made to eliminate the effect of random error, the measures obtained with one system will generally not be perfectly reproduced by another. This error exists because no two RTRRMSs respond exactly the same to road roughness. If a number of roads are measured with two RTRRMSs, they will be ranked in a different order. No amount of rescaling or manipulating of data can avoid the fact that two roads can be ranked differently by two RTRRMSs. This appendix deals with the reproducibility error, which cannot be eliminated by calibration. If a calibration reference is "perfect" for one RTRRMS, then it must have a correlation with another RTRRMS that is no better than the correlation that exists directly between the two RTRRMSs. (And since a "perfect" calibration reference has yet to be found for any RTRRMS, the reproducibility will always be less than what is demonstrated in direct comparisons between RTRRMSs.) Correlations Tables C.1 - C.10 (located at the end of this appendix) show the correlation matrices of r-squared values for all simple speed combinations of measurements when the results are segregated by surface type. Tables C.11 - C.14 show correlation matrices that are obtained when the data sub-sets are lumped together by surface type and speed. Before calculating linear regression equations between the different measures, the measures obtained from the trailers (Bump Integrator Trailer and BPR Roughometer) for each wheel track were used to calculate an average and difference numeric for each 166 section/speed condition. The average of the measures should approximate the roughness input to a vehicle that causes bounce and pitching motions, while the difference is representative of the roll input to a vehicle. In addition to the correlation tables, a number of scatter plots were prepared and examined, which more directly show the relationships between the ARS measures obtained from the different systems. Some of these plots are also attached at the end of the appendix. The scatter plots and the correlation tables lead to these observations: !easuresent speed. Correlations between the measures obtained with different systems are best when the two systems are operated at the same test speed. Correlations are degraded when the difference in speed of the two systems is increased. Figure C.1 compares measures made at different speeds. In all of the plots shown, regression lines are plotted, based on a quadratic regression using the data points shown in the plot. Figures C.2 - C.5 show similar plots made when ARS measures made at the same speeds are compared. (The figures are attached at the end of the appendix.) Surface type. When the same speed is used for two RTRRMSs, the regression lines obtained for different surface types are nearly the same, indicating that the underlying relationship is not influenced strongly by surface type. Distribution of Scatter. The variance about the regression lines is fairly uniform over the entire range of roughness. An assumption of equal scatter over the range is a much better approximation than an assumption of scatter proportional to roughness. Interaction between speed and surface type. When ARS measures made at different speeds are compared (Fig. C.1), the regression lines for different speeds diverge, and would indicate that scatter increases with roughness if the data for the different surface types were combined. Thus, the interrelationship between scatter and roughness that appears when measures are made at different speeds is not due to random effects, but to an interaction between surface type and measurement speed. 167 Appendix I shows that the spectral contents of road profiles differ with surface type, and Appendix F shows appproximately the waveband seen by a RTRRMS at the different test speeds. On the unpaved roads, there is more short-wave roughness, which is "seen" more by the RTRRMSs at lower speeds. On the asphaltic concrete (CA) roads, there is relatively little short-wave roughness. Therefore, when a paved and unpaved road have the same roughness when measured at a high speed, the unpaved road will have more roughness input to the RTRRMS at a lower speed. Choice of roadmeter. Figure C.6 compares the ARS measures from the BI and NAASRA meters mounted in the same vehicle. The agreement is nearly perfect except for a few of the 80 km/h tests. (Comparisons with the other systems indicate that the NAASRA readings are more consistent.) Except for the 80 km/h tests, the BI and NAASRA results are equivalent for all practical purposes, and can be considered to be redundant measures made by one system. The BPR Roughometer. The BPR Roughometer tends to have the lowest correlation with the other instruments. Not suprisingly, its measures usually agree closest with those of the BI Trailer. The problem appears to be that this RTRRMS was not rugged enough for the conditions included in the IRRE, with the result that many of the readings were faulty due to vehicle damage. Range of conditions for correlation. Any given instrument has certain combinations of speed and surface type that show either high or low correlations with the other instruments, but overall, no trend is evident. Agreement between the different instruments is more-or-less equivalent over all of the test conditions when the test speeds are equal (with the exception of the BPR Roughometer). Sum and difference measures. The difference measures obtained from the two trailers do not appear useful for predicting measures made with other systems. The simple average of the roughness measures of the right and left wheeltracks has such a high correlation with the other measures that little can be gained by adding the difference measures to a regression. Correlation across speed. The form of vehicle response to road 168 roughness that is measured by a roadmeter is the rate of motion of the suspension, technically called the average rectified velocity (ARV). ARV is measured by dividing the accumulated axle-body deflection measured by the roadmeter by the elapsed time of the measurement, yielding a numeric with the units "length/time." The ARV thus measures the severity of vibration (in the vehicle suspension) caused by the road roughness. When the accumulated deflection is divided by the length of the road test section, the result has the units of average rectified slope (ARS). ARS is not a measure of the vertical deviations in the road surface per unit of road length. Rather, it is the ratio of mean suspension (vibration) velocity to travel velocity. The difference is subtle, but explains why ARV should be used when comparing measures made by different RTRRMSs over a range of speeds. A simple relationship can usually be found between the responsiveness of one RTRRMS relative to another, but due to nonlinearities in the vehicles, the roadmeters, and also the presence of extra vibration from tire and wheel nonuniformities, the relationship will not be linear and may have an offset, such that a zero reading for one system corresponds to a non-zero reading for the other. The nonlinearities are due to vehicle properties, and are primarily influenced by the amplitude of input as perceived by the vehicle, regardless of the travel speed. This is illustrated in Figure C.7, which shows the ARV measures from different RTRRMSs plotted together for three of the IRRE test speeds. The separate regression equations computed for each speed collapse into a single relation. But because ARS is the ARV rescaled by travel speed, the simple offset that appears in the plots in Figure C.7 will vary with speed when the data are compared as ARS measures. Figure C.8 shows that different relations between ARS measures exist for the different measurement speeds. The data show that a relationship found between two RTRRMSs when both are operated at one speed will usually be valid at other speeds, if the roadmeter numerics are converted to ARV units. 169 Table C.l. Correlation Tables of R-Squared Values for 20 km/h. ASPHALTIC CONCRETE TEST SITES MN 01 KM 02 MN 03 BI CAR NAASRA Bl TRL BI TRL BPR BPR (AYE) (DIFF) (AVE) (DIFF) MN 01 1 .9914 .973 .9941 .9928 .9846 4.2E-03 .8821 .1645 MN 02 .9914 1 .9882 .995 .9947 .9846 3.9E-03 .8695 .1553 MN 03 .973 .9882 1 .977 .9803 .9633 3.3E-03 .8467 .1554 DI CAR .9941 .995 .977 1 .9986 .9921 9.6E-03 .8994 .1594 NAASRA .9928 .9947 .9803 .9986 1 .9886 .0105 .8968 .1559 81 TRL (AYE) .9846 .9846 .9633 .9921 .9886 1 5.3E-03 .9038 .1221 B TRL (DIFF) 4.2E-03 3.9E-03 3.3E-03 9.6E-03 .0105 5.3E-03 1 .0767 .0134 8PR (AYE) .8821 .8695 .8467 .8994 .8968 .9038 .0767 1 .1506 BPR M 01FF) .1645 .1553 .1554 .1594 .1559 .1221 .0134 .1506 1 TEST SITES WITH SURFACE TREATMENT NM 01 MN 02 MN 03 8I CAR NAASRA 8I TRL 8I TRL BPR BPR (AYE) (DIFF) (AYE) (DIFF) MN 0l 1 .9908 .882 .9587 .958 .9799 .1136 .7554 .2339 MN 02 .9908 1 .8905 .9767 .9723 .9836 .0917 .78 .1955 ON 03 .882 .8905 1 .9372 .9538 .8453 .2415 .7856 .3544 Bl CAR .9587 .9767 .9372 1 .9964 .9587 .1463 .8336 .2461 NAASRA .958 .9723 .9538 .9964 1 .9526 .1574 .8172 .2532 DI TRL (AYE) .9799 .9836 .8453 .9587 .9526 1 .0718 .7648 .1932 81 TRL (DIFF) .1136 .0917 .2415 .1463 .1574 .0718 1 .2257 .7152 BPR (AYE) .7554 .78 .7856 .8336 .8172 .7648 .2257 1 .4008 DPR (0IFF) .2339 .1955 .3544 .2461 .2532 .1932 .7152 .4008 1 BRAYEL SURFACED TEST SITES MM 01 MN 02 MN 03 RI CAR NAASRA BI TRL DI TRL BPR DPR (AYE) (DIFF) (AYE) (DIFF) MM 01 1 .9411 .8338 .9636 .9658 .9605 .6771 .9249 .3483 KM 02 .9411 1 .8775 .9829 .9778 .9559 .5338 .8729 .342 MN 03 .8338 .8775 1 .8619 .8671 .8445 .609 .7069 .4743 Bl CAR .9636 .9829 .8619 1 .999 .9839 .5408 .8979 .2936 NAASRA .9658 .9778 .8671 .999 1 .9883 .5456 .8889 .2976 DI TRL (AVE) .9605 .9559 .8445 .9839 .9883 1 .5393 .8685 .3303 DI TRL (DIFF) .6771 .5338 .609 .5408 .5456 .5393 1 .2513 .4732 BPR (AVE) .9249 .8729 .7069 .8979 .8889 .8685 .2513 1 .3095 BPR (DIFF) .3483 .342 .4743 .2936 .2976 .3303 .4732 .3095 1 EARTH (CLAY) SURFACE TEST SITES MN 01 M 02 MM 03 8I CAR NAASRA 8I TRL 81 TRL BPR BPR (AVE) (DIFF) AYE) (0DIFF) NM 01 1 .9075 .8263 .8823 .8821 .7933 .2283 .8597 .1563 NM 02 .9075 1 .9653 .9887 .9882 .9722 .0207 .989 IE-04 MM 03 .8263 .9653 1 .9675 .9672 .9653 .0109 .9415 6.8E-03 BI CAR .8823 .9887 .9675 1 .9996 .9806 .0134 .9666 2E-04 NAASRA .8821 .9882 . %72 .9996 1 .9837 .012 .9656 0 BI TRL (AYE) .7933 .9722 .9653 .9806 .9837 1 8E-04 .957 .0102 EI TRL (DIFF) .2283 .0207 .0109 .0134 .012 8E-04 I 8.5E-03 .5384 8PR (AVE) .8597 .989 .9415 .9666 .9656 .957 8.5E-03 I 4E-04 BPR (DIFF) .1563 IE-04 6.8E-03 2E-04 0 .0102 .5384 4E-04 I 170 Table C.2. Correlation Tables of R-Squared Values for 20 and 32 km/h. ASPHALTIC CONCRETE TEST SITES 20 MN 01 MN 02 MN 03 B1 CAR NAASRA 81 TRL 3} TRL BPR BPR 32 (AYE) (DIFF) (AYE) (DIFF MN 01 .9838 .983 .9761 .9779 .9013 .9569 7E-03 .841 .1698 MN 02 .971 .9864 .9888 .9776 .9796 .961 .0115 .8537 .1676 H" 03 .8881 .9107 .8997 .8819 .876 .8751 4.2E-03 .6783 .083 8I CAR .9865 .9955 .9863 .9915 .9908 .9784 9.2E-03 .8816 .1768 NAASRA .9834 .994 .9863 .989 .9897 .9729 .0118 .8662 .1656 8} TRL (AYE) .9745 .9838 .9695 .9848 .9796 .9929 3.8E-03 .8874 .1161 8} TRL (DIFF) .0369 .0469 .0488 .038 .0317 .0546 .4335 2.7E-03 .0138 BPR (AYE) .7157 .7172 .6872 .738 .7193 .7565 .0699 .8654 .1305 BPR (D1FF) .5086 .5014 .5094 .5016 .478 .5067 7.9E-03 .5307 .2909 TEST SITES VITH SURFACE TREATMENT 20 MN 01 MN 02 MN 03 BI CAR NAASRA BI TRL BI TRL BPR BPR 32 (AYE) (DIFF) (AYE) (DIFF) NM 01 .9496 .9507 .9209 .9684 .9628 .9475 .1661 .8537 .3474 NM 02 .9534 .9551 .9239 .9743 .9697 .9469 .1729 .8534 .3308 MN 03 .8617 .883 .9739 .9433 .9497 .8476 .2362 .8764 .3658 DI CAR .9706 .9716 .9271 .983b .9791 .9623 .1527 .7992 .2919 NAASRA .9544 .9625 .9386 .986 .9815 .9494 .1524 .7976 .2841 DI TRL (AVE) .9352 .9568 .8985 .9719 .9646 .9638 .0965 .8437 .2484 8I TRL (D1FF) .0645 .0596 .118 .1106 .1061 .0641 .6062 .2963 .5324 BPR (AYE) .946 .9589 .9163 .9746 .9669 .9432 .1755 .8673 .308 BPR (D1FF) .3762 .4299 .4428 .5201 .4842 .3987 .1786 .5643 .1526 GRAVEL SURFACED TEST SITES 20 NM 01 MN 02 MN 03 B1 CAR NAASRA BI TRL B! TRL BPR BPR 32 (AYE) (DIFF) (AYE) (DIFF) MN 01 .8627 .8094 .7106 .8635 .8762 .9334 .5104 .8895 .3902 NM 02 .9695 .9832 .8846 .9736 .9736 .9663 .5885 .7976 .373 MN 03 .8843 .9006 .9743 .893 .9017 .9046 .6181 .6424 .4723 BI CAR .9825 .9757 .8606 .9878 .9893 .9886 .5831 .8501 .3354 NAASRA .9821 .9728 .8655 .9884 .9907 .9914 .587 .8559 .3409 BI TRL (AYE) .9679 .9601 .8398 .9859 .9895 .9966 .5339 .8258 .2864 B} TRL (DIFF) .5681 .4836 .5857 .4462 .4453 .4268 .9303 .2481 .5296 BPR (AYE) .9247 .8762 .646 .9233 .9099 .8831 .1633 .9745 .2271 BPR (DIFF) .2409 .1823 .1612 .2345 .2301 .1968 .3712 .3294 .3842 EARTH (CLAY) SURFACE TEST SITES 20 MN 01 MM 02 MN 03 DI CAR NAASRA B} TRL 8I TRL BPR BPR 32 (AYE) (0IFF) (AYE) (DIFF) MM 01 .978 .9029 .8373 .8724 .873 .7828 .2218 .8615 .1643 MM 02 .8685 .9891 .9748 .9896 .9905 .9852 .0142 .97 0 MN 03 .7903 .9477 .9853 .9596 .9575 .9528 8.4E-03 .9168 6.3E-03 B} CAR .8193 .9573 .9626 .9835 .9822 .9683 .0114 .9229 4E-04 NAASRA .8268 .966 .9697 .9887 .989 .983 8.2E-03 .9345 IE-04 81 TRL (AYE) .8147 .97 .9722 .9799 .9825 .9945 3.1E-03 .9482 5.5E-03 8I TRL (D0FF) .338 .0192 5.5E-03 .0131 .0113 IE-03 .8139 8.7E-03 .7005 8PR (AYE) .835 .9895 .9573 .9838 .9855 .9876 3.6E-03 .9878 2E-03 BPR (DIFF) .1644 7E-04 3.6E-03 8E-04 3E-04 8.4E-03 .5222 0 .9788 l/i Table C.3. Correlation Tables of R-Squared Values for 20 and 50 km/h. ASPHALTIC CONCRETE TEST SITES 20 MN 01 MN 02 NH 03 E} CAR NAASRA Dl TRL Dl TRL BPR BPR 50 (AYE) (DIFF) (AYE) (DIFF) MN 01 .9414 .9588 .9654 .9382 .936 .917 3.9E-03 .7745 .1727 NH 02 .7592 .8121 .8412 .7841 .7911 .7729 .0103 .592 .0618 MN 03 .8476 .8795 .8995 .8475 .846 .8329 J.4E-03 .6944 .1004 81 CAR .9422 .9698 .9791 .958 .9586 .9512 .0135 .8415 .1377 NAASRA .9381 .9651 .9761 .9487 .9506 .934 .0121 .8034 .1463 DI TRL (AYE) .9557 .9785 .9685 .9753 .9719 .9807 7.7E-03 .8618 .1042 El TRL (DIFF) .1026 .1354 .1482 .1049 .0991 .1222 .4018 .0262 2.6E-03 EPR IAYE) .9355 .9295 .9204 .9467 .9481 .9232 .0572 .9413 .2639 EPR 015FF) .2214 .1855 .1866 .1798 .1706 .163 .0599 .1518 .4813 TEST SITES W17H SURFACE TREATHENT 20 NH 01 "H 02 MN 03 BE CAR NAASRA Bl TRL B} TRL EPR BPR 50 (AYE) (DIFFI (AYE) (DIFF) MN 01 .8722 .8872 .9208 .9389 .9371 .8725 .1435 .7616 .2781 MN 02 .9063 .9208 .9216 .952 .9501 .9123 .1125 .7461 .2534 NH 03 .8582 .8791 .8732 .9241 .9076 .8727 .1219 .7691 .2798 Bl CAR .9233 .9311 .9337 .9632 .9605 .9192 .1445 .7876 .2954 NAASRA .9174 .9256 .9391 .9626 .9596 .9128 .1524 .7969 .308 dI TRL (AYE) .8904 .9174 .9166 .9612 .953 .9104 .132 .8832 .2938 8! TRL (DIFF) .3223 .3348 .4505 .4341 .4161 .3263 .4887 .7306 .6305 BPR (AYE) .8231 .8575 .8418 .8743 .8748 .8629 .0707 .7157 .1972 BPR (D1FF) .057 .0499 .1121 .0895 .086 .0616 .2846 .0636 .3317 GRAYEL SURFACED TEST SITES 20 NH 01 MN 02 NH 03 8I CAR NAASRA BI TRL BI TRL BPR DPR 50 (AYE) (DIFF) (AVE) (DIFF) nH 01 .9723 .94 .8503 .9695 .9757 .9922 .6162 .8863 .4085 NO 02 .9699 .9663 .8619 .9749 .9781 .9892 .595 .8309 .4084 "H 03 .9541 .9666 .9146 .9655 .9694 .9715 .6276 .8322 .4515 DI CAR .9664 .9693 .8713 .9831 .9866 .9926 .5598 .8031 .3705 NAASRA .9746 .9553 .8519 .9755 .9805 .992 .503 .8079 .3739 Bl TRL (AYE) .9555 .9656 .856 .9841 .9878 .9958 .5209 .8128 .3205 Dl TRL (DIFF) .8514 .7437 .6769 .7355 .7379 .7166 .8316 .517 .4902 BPR (AYE) .782 .7662 .5243 .7682 .7465 .7355 .1801 .9283 .2207 BPR (DIFF) .0821 .1072 7.IE-03 .0774 .0647 .0617 .0875 .2267 .0776 EARTH (CLAY) SURFACE TEST SITES 20 NH 01 NH 02 NH 03 Bl CAR NAASRA Bl TRL Bl TRL BPR BPR 50 (AYE) (DIFF) (AVE) (DIFF) NN 01 .8804 .9893 .96 .9776 .9796 .9603 .0528 .9769 .0407 PH 02 .7427 .9457 .9576 .9678 .972 .9892 IE-04 .9231 8.8E-03 "H 03 .6112 .9014 .9364 .9354 .9397 .9697 6.4E-03 .8823 .0325 Bl CAR .7023 .914 .9482 .9505 .9508 .9581 1.1E-03 .8776 2.6E-03 NAASRA .7131 .9316 .9573 .9604 .9639 .9846 2E-04 .9051 .0146 Bl TRL (AYE) .7441 .9301 .9297 .951 .9545 .9706 1.7E-03 .9043 1.4E-03 Bl TRL (DIFF) .3005 J.3E-03 2.6E-03 3.8E-03 2.7E-03 4E-04 .6821 1.8E-03 .661 BPR (AVE) .8033 .7667 .8528 .83 .8188 .7332 .3319 .6908 .42 BPR (DIFF) .101 .0198 .0453 .0465 .0433 .0136 .6174 0 .9358 172 Table C.4. Correlation Tables of R-Squared Values for 20 and 80 km/h. ASPHALTIC CONCRETE TEST SITES 20 MM 01 MN 02 NH 03 8i CAR NAASRA 8l TRL DI TRL BPR BPR 80 (AVE) (01FF) (AVE) (IEFF) "H 01 .9471 .9661 .9739 .948 .9498 .9375 6.IE-03 .7837 .115 MM 02 .9141 .9413 .9543 .9251 .9264 .9162 .0177 .776 .1168 "H 03 .8652 .8897 .9046 .8587 .8604 .8586 0 .6634 .0343 Di CAR .7787 .8202 .8312 .8198 .813 .8437 .2109 .8721 .0456 NAASRA .8553 .8926 .9124 .8848 .8864 .8902 .2171 .9106 .0532 BI TRL (AVE) 0 0 0 0 0 1 0 0 0 8} TRL (DIFF) 0 0 0 0 0 0 1 0 0 BPR (AYE) .9701 .9632 .882 .9847 .9797 .9804 .0119 .9557 .5472 BPR (D1FF) .0658 .0726 .0716 .0471 .0534 .0483 .0478 .094 .3066 TEST SITES WITH SURFACE TREATHENT 20 NH 01 Mn 02 NH 03 3I CAR NAASRA B8 TRL ?I TRL BPR BPR 80 (AYE) (I1FF) (AYE) (0IFF) MN 01 .7165 .7287 .7582 .772 .7575 .7049 .2051 .9364 .4244 MA 02 .7398 .7592 .798 .8104 .7985 .7398 .1806 .9408 .3912 m 03 .677 .6891 .7652 .7361 .7259 !6451 .2635 .8952 .4565 GRAVEL SURFACED TEST SITES 20 MN 01 KM 02 MN 03 B} CAR NAASRA D} TRL 8I TRL 8PR BPR 80 (AYE) (0IFF) (AVE) (D1FF) H" 01 .9397 .9224 .896 .9074 .9096 .9241 .2666 .8659 .3819 IM 02 .9553 .9448 .8607 .9309 .9308 .9389 .2291 .8942 .3358 H" 03 .9358 .6891 .8525 .8943 .8936 .8933 .2867 .9099 .3003 EARTH (CLAY) SURFACE TEST SITES 20 MM 01 NH 02 MN 03 8I CAR NAASRA 8I TRL DI TRL BPR BPR 80 (AVE) (DIFF) (AVE) (IIFF) "N 01 .8758 .7393 .6014 .725 .7438 .7158 .5714 .6732 .4364 MN 02 .9089 .9688 .9334 .9485 .9546 .9698 .3885 .9409 .2366 MH 03 .9461 .9911 .9114 .9923 .9952 .9781 .3968 .9645 .2881 173 Table C.5. Correlation Tables of R-Squared Values for 32 km/h. ASPHALTIC CONCRETE TEST SITES KM 01 MN 02 MN 03 8I CAR NAASRA 81 TRL 8I TRL BPR BPR (AYE) (DIFF) (AYE) (DIFF) MN 01 1 .9869 .9128 .9854 .9905 .9 455 .0187 .6527 .4588 ON 02 .9869 1 .915 .9934 .9966 .9619 .0306 .6988 .4923 MN 03 .9128 .?15 1 .9088 .9154 .8905 .0693 .5969 .461 B1 CAR .9854 .9934 .9088 1 .9978 .9786 .038 .7415 .5246 NAASRA .9905 .9966 .9154 .9978 1 .9715 .0303 .7125 .4882 81 TRL (AYE) .9455 .9619 .8905 .9786 .9715 1 .0741 .7813 .5432 81 TRL (DIFF) .0187 .0306 .0693 .038 .0303 .0741 1 .0345 .1724 BPR (AYE) .6527 .6988 .5969 .7415 .7125 .7813 .0345 1 .7036 SPR (DIFF) .4598 .4923 .461 .5246 .4882 .5432 .1724 .7036 1 TEST SITES PITH SURFACE TREATMENT M 01 MN 02 MN 03 8I CAR NAASRA 8I TRL 31 TRL BPR BPR (AYE) (DIFF) (AYE) (DIFF) MM 01 1 .9949 .9364 .9876 .9828 .9761 .127 .969 .4616 MN 02 .9949 1 .9442 .9878 .984 .9725 .1181 .9721 .4568 NH 03 .9364 .9442 1 .9225 .9364 .9296 .1529 .9414 .5103 Of CAR .9876 .9878 .9225 1 .9969 .96 .102 .9649 .4718 NAASRA .9828 .984 .9364 .9969 1 .9706 .0996 .9634 .4962 BI TRL tAYE) .9761 .9725 .9296 .969 .9706 1 .094 .9634 .4842 8I TRL (DIFF) .127 .1181 .1529 .102 .0996 .094 1 .1286 .3702 SPR (AYE) .969 .9721 .9414 .9649 .9634 .9634 .1286 1 .5068 SPR (DIFF) .4616 .4568 .5103 .4718 .4962 .4842 .3702 .5068 1 6RAVEL SURFACED TEST SITES Nf 01 NH 02 Mn 03 BI CAR NAASRA BI TRL 8I TRL BPR MPR (AYE) (DIFF) (AYE) (DIFF) NM 01 1 .8406 .8114 .8875 .8956 .9144 .3579 .8807 .2125 MN 02 .8406 1 .9314 .991 .?886 .9749 .5296 .7919 .1366 MN 03 .8114 .9314 1 .9146 .9195 .902 .5723 .5888 .1132 8I CAR .8875 .991 .9146 1 .9995 .994 .4926 .8643 .1742 NAASRA .8956 .9986 .9195 .9995 1 .9953 .4914 .8669 .1851 BI TRL (AYE) .9144 .9749 .902 .994 .9953 1 .4282 .8574 .165 8I TRL (DIFF) .3579 .5296 .5723 .4926 .4914 .4282 1 .1579 .2026 BPR IAYE) .8807 .7919 .5888 .8643 .8669 .8574 .1579 1 .3098 BPR (0IFF) .2125 .1366 .1132 .1742 .1851 .165 .2026 .3098 1 EARTH (CLAY) SURFACE TEST SITES MN 01 MM 02 MM 03 BI CAR NAASRA 81 TRL Bl TRL SPR BPR (AYE) (DIFF) (AYE) (DIFF) NH 01 1 .8793 .7989 .8173 .826 .8138 .3379 .8371 .1742 M 02 .8793 1 .9592 .9797 .9878 .9906 .0166 .9896 0 MM 03 .7989 .9592 1 .9657 .9675 .9608 6.8E-03 .9351 3.6E-03 BI CAR .8173 .9797 .9657 1 .9967 .9804 .0177 .9565 IE-03 NAASRA .826 .9978 .9675 .9967 1 .9902 .0112 .9697 0 BI TRL (AYE) .8138 .9906 .9608 .9804 .9902 1 SE-03 .9817 4.7E-03 BI TRL (DIFF) .3379 .0166 6.BE-03 .0177 .0112 5E-03 I 4.6E-03 .6449 BPR (AYE) .8371 .9896 .9351 .9565 .9697 .9817 4.6E-03 1 9E-04 BPR (DIFF) .1742 0 3.6E-03 IE-03 0 4.7E-03 .6449 9E-04 I 174 Table C.6. Correlations Tables of R-Squared Values for 32 and 50 km/h. ASPHALTIC CONCRETE TEST SITES 32 RH 01 Ni 02 MN 03 B1 CAR NAASRA BI TRL Bl TRL BPR BPR 50 (AVE) (DIFF) (AVE) (DIFF) HN 01 .9649 .978 .9507 .9692 .9728 .9322 .0478 .6754 .5244 IN 02 .8179 .8606 .8459 .8165 .8402 .7904 .0499 .4479 .2541 NM 03 .8879 .9189 .9361 .8965 .9044 .0639 .0439 .6383 .4714 81 CAR .9494 .9036 .9006 .9783 .9783 .9679 .0542 .7383 .5067 NAASRA .9604 .9874 .9203 .9749 .98 .9482 .045 .6856 .4731 BI TRL (AYE) .9425 .9697 .9043 .9759 .9746 .9909 .0685 .7527 .4927 BI TRL (DIFF) .0891 .1189 .227 .1241 .1132 .1623 .7639 .098 .2072 RPR (AVE) .9293 .936 .7515 .9441 .9391 .9041 4.3E-03 .7538 .5170 BPR I(IFF) .1879 .1643 .1439 .1984 .1686 .1664 .1147 .177 .4747 TEST SITES WITH SURFACE TREATMENT 32 MM 01 RM 02 MN 03 8I CAR NAASRA BI TRL B1 TRL BPR BPR 50 (AVE) (DIFF) (AYE) (DIFF) NH 01 .9404 .934 .9102 .9507 .9624 .9246 .1094 .9767 .5049 RH 02 .9582 .9539 .9153 .9709 .9805 .9572 .0738 .9058 .4746 RM 03 .9358 .9211 .8921 .?441 .9563 .9315 .1239 .8956 .5936 B1 CAR .9714 .9681 .9284 .9813 .9966 .9573 .1041 .9198 .4893 NAASRA .9687 .9634 .9319 .9776 .984 .9528 .114 .9198 .4966 Di TRL (AVE) .9703 .9639 .9531 .9542 .9622 .9799 .1378 .939 .5466 DI TRL (DIFF) .4803 .472 .5542 .419 .4277 .4429 .6994 .4852 .6377 BPR (AVE) .8461 .8206 .8354 .8461 .8567 .8937 .0764 .8829 .4485 BPR (8IFF) .1091 .0932 .1048 .1166 .1258 .0906 .3716 .088 .304 GRAYEL SURFACED TEST SITES 32 MN 01 MN 02 RM 03 DI CAR NAASRA BI TRL El TRL BPR BPR 50 (AYE) (DIFF) (AYE) (DIFF) Mn 01 .9442 .9624 .9152 .9851 .9888 .9873 .495 .877 .2385 Ni 02 .9138 .9857 .9265 .9932 .9943 .9888 .5029 .8193 .1844 RN 03 .8928 .9802 .9578 .9773 .9803 .9668 .5491 .7867 .2033 BI CAR .9031 .9864 .9299 .9956 .9966 .9953 .4681 .8141 .1748 NAASRA .9174 .9815 .9202 .9944 .996 .9948 .4791 .0146 .1814 BI TRL (AYE) .9108 .9773 .916 .9904 .9924 .9967 .4232 .8276 .1625 B1 TRL (DIFF) .6106 .9033 .7211 .7823 .779 .7341 .7744 .4375 .3603 BPR (AVE) .7567 .6694 .4755 .72 .7219 .6961 .1887 .904 .249 BPR (DIFF) .0743 .0596 3.0E-03 .0605 .0589 .0433 .0843 .1758 .1651 EARTH (CLAY) SURFACE TEST SITES 32 MM 01 MM 02 MN 03 DI CAR NAASRA DI TRL BI TRL BPR BPR 50 (AVE) (DIFF) (AYE) (DIFF) nn 01 .598 .9908 .9454 .9428 .9623 .9663 .1427 .978 .0496 NM 02 .7508 .9769 .945 .975 .9864 .9923 5E-04 .9695 7.0E-03 MN 03 .616 .9345 .9324 .9427 .9593 .9599 7.3E-03 .9343 .0273 BI CAR .7044 .9544 .9535 .9866 .9843 .9727 4.8E-03 .9281 1.9E-03 NAASRA .7132 .9651 .952 .9742 .9845 .9869 0 .955 .0127 DI TRL (AYE) .7513 .9693 .918 .9723 .9779 .9848 8.5E-03 .9539 1.8E-03 0} TRL (8IFF) .3164 7E-03 1.8E-03 .0107 4.5E-03 9E-04 .8607 4E-04 .6379 0PR (AVE) .8921 .8511 .859 .9345 .9034 .9443 .4539 .7359 .5536 EPR (DIFF) .1071 .0623 .0506 .159 .117 .0577 .7812 4.7E-03 .875 175 Table C.7. Correlation Tables of R-Squared Values for 32 and 80 KM/h. ASPHALTIC CONCRETE TEST SITES 32 fffl 01 fffl 02 ffff 03 Bl CAR NAASRA Pl TRL Bl TRL BPR BPR 80 (AYE) (DIFF) (AYE) (DIFF) flfl 01 .9626 .9779 .9304 .9672 .9742 .9497 .0493 .6572 .4453 MN1 02 .9302 .9633 .8909 .9483 .9556 .9349 .0518 .6755 .4411 MN1 03 .8865 .8992 .9389 .883 .8942 .8845 .0604 .5764 .3885 3I CAR .7463 .8335 .6977 .8366 .8262 .8819 9E-04 .8377 .4419 NAASRA .8538 .9203 .7872 .9098 .9089 .9157 8.5E-03 .7896 .4035 Pl TRL (AYE) 0 0 0 0 0 0 0 0 0 RI TRL (DIFF) 0 0 0 0 0 0 0 0 0 BPR (AYE) .976 .9518 .9384 .9675 .9806 .9683 .6757 .6223 .0721 BPR EDIFF) .0512 .0515 .0454 .0619 .0486 .0423 IE-04 1.2E-03 .0636 TEST SITES VITH SURFACE TREATNENT 32 flff 01 fffl 02 19 03 El CAR NAASRA Of TRL BI TRL BPR BPR 80 (AYE) IDIFF) (AVE) (DIFF) "H 01 .8 .7879 .8107 .7523 .7481 .77 .2825 .7767 .4933 ffff 02 .8309 .819 .8505 .7865 .7875 .8158 .2541 .8025 .509 NH1 03 .746 .7351 .8005 .7057 .7068 .7089 .2832 .7633 .4949 6RAVEL SURFACED TEST SITES 32 MNf 01 191 02 MN1 03 81 CAR NAASRA BI TRL Pl TRL PPR BPR so (AYE) (DIFF) (AYE) (DIFF) 1H" 01 .9645 .923 .8884 .9255 .9373 .9034 .3249 .8299 .206 M 02 .9713 .9302 .8507 .9417 .9503 .9213 .2848 .8695 .1928 11 03 .9445 .8657 .8211 .8919 .9037 .8697 .3259 .8841 .2089 EARTH (CLAY) SURFACE TEST SITES 32 191 01 MN1 02 111 03 DI CAR NAASRA DI TRL El TRL DPR BPR 80 (AYE) (DIFF) (AYE) (DIFF) ffff 01 .8969 .7804 .522 .6923 .7304 .7673 .6397 .7337 .4027 N 02 .9555 .9932 .9052 .9127 .9529 .9847 .431 .966 .2613 11 03 .9528 .9854 .8831 .9358 .9666 .9749 .4294 .9817 .3203 176 Table C.8. Correlation Tables of R-Squared Values for 50 kmn/h. ASPHALTIC CONCRETE TEST SITES NH 01 NH 02 MH 03 DI CAR NAASRA D} TRL Bl TRL BPR BPR (AYE) (DIFF) (AYE) (DIFF) NH 01 1 .,8665 .9673 .969 9841 .9403 .1658 .8709 .208 NH 02 .8665 .1 .8921 .8811 .9068 .8522 .1831 .6925 .031 MM 03 .9673 .8921 1 .9358 .9557 .8885 .199 .7639 .1449 DI CAR .969 r8811 .9358 1 .9937 .982 .1673 .9 .1404 NAASRA .9841 c9068 .9557 .9937 1 .9673 .1586 .8879 .1438 DI TRL (AYE) .9403 .8522 .8885 .982 .9673 1 .1686 .8926 .1185 BI TRL (DIFF) .1658 o1831 .199 .1673 .1586 .1686 1 .0314 .0743 BPR (AYE) .8709 .6925 .7639 .9 .8879 .8926 .0314 1 .1996 BPR (DIFF) .208 .031 .1449 .1404 .1438 .1185 .0743 .1996 1 TEST SITES WITH SURFACE TREATMENT MM 01 NM 02 MM 03 Bl CAR NAASRA DI TRL DI TRL BPR BPR (AYE) (DIFF) (AYE) (DIFF) MM 01 1 .9849 .9715 .9876 .9889 .9582 .4329 .8047 .1485 NM 02 .9849 1 .9725 .993 .988 .963 .3928 .8361 .1377 MN 03 .9715 .9725 1 .9735 .9749 .9558 .4786 .8234 .2064 Bl CAR .9876 .993 .9735 1 .9981 .9699 .4374 .8229 .1426 NAASRA .9889 .988 .9749 .9981 1 .97 .4517 .8325 .1483 BI TRL (AYE) .9582 .963 .9558 .9699 .97 1 .5264 .8601 .1107 BI TRL (DIFF) .4329 .3928 .4786 .4374 .4517 .5264 1 .3529 .2939 8PR (AYE) .8047 .8361 .8234 .822g .8325 .8601 .3529 1 .1007 DPR (DIFF) .1485 .1377 .2064 .1426 .1483 .1107 .2939 .1007 1 GRAVEL SURFACED TEST SITES MN 01 MN 02 MN 03 Bl CAR NAASRA DI TRL BI TRL BPR BPR (AYE) (DIFF) (AYE) (DIFF) Mn 01 1 .9907 .9759 .9872 .9922 .9835 .7622 .7401 .0672 MN 02 .99q7 1 .9884 .9952 .9961 .991 .7785 .7089 .0829 NM 03 .9759 .9884 1 .9814 .9784 .9763 .784 .6924 .0851 BE CAR .9872 .9952 .9814 1 .9971 .9963 .7543 .6598 .0404 NAASRA .9922 .9961 .9784 .9971 1 .9934 .7766 .6662 .0466 El TRL (AYE) .9835 .991 .9763 .9963 .9934 1 .7224 .6871 .0527 Bl TRL (DIFF) .7622 .7785 .784 .7543 .7766 .7224 1 .3696 .1371 BPR (AYE) .7401 .7089 .6924 .6598 .6662 .6871 .3696 1 .4031 BPR (DIFF) .0672 .0829 .0851 .0404 .0466 .0527 .1371 .4031 1 EARTH (CLAY) SURFACE TEST SITES MN 01 MN 02 MM 03 81 CAR NAASRA B} TRL BI TRL BPR DPR (AYE) IDIFF) (AYE) (DIFF) MM 01 1 .9366 .8743 .884 .9196 .9038 .1437 .7966 .0282 MM 02 .9366 1 .981 .9793 .9963 .9867 IE-04 .8606 .0647 MM 03 .8743 .981 1 .9619 .9886 .9445 .0125 .7537 7.8E-03 BI CAR .884 .9793 .9619 1 .986 .977 3.4E-03 .9553 .2035 NAASRA .9196 .9963 .9886 .986 1 .9791 9E-04 .8746 .0675 BI TRL (AVE) .9038 .9867 .9445 .977 .9791 1 4.4E-03 .9014 .1767 DI TRL (DIFF) .1437 IE-04 .0125 3.4E-03 9E-04 4.4E-03 1 .5127 .9027 6PR (AYE) .7966 .8606 .7537 .9553 .8746 .9014 .5127 1 .2403 BPR (DIFF) .0282 .0647 7.8E-03 .2035 .0675 .1767 .9027 .2403 1 177 Table C.9. Correlation Tables of R-Squared Values for 50 and 80 km/h. ASPHALTIC CONCRETE TEST SITES 50 NN 01 MN 02 MN 03 Dl CAR NAASRA Bl TRL Bl TRL BPR BPR 80 (AYE) (DIFF) (AYE) (DIFF) MN 01 .9818 .898 .9546 .9804 .99 .9615 .1606 .8639 .1591 PM 02 .9643 .9108 .9507 .9832 .9882 .9559 . 159 .8557 .1334 Mi 03 .9331 .8819 .955 .9158 .9305 .9 .217 .7199 .1158 El CAR .8233 .735 .8267 .918 .8828 .9009 .0258 .7989 .0212 NAASRA .9133 .8126 .9117 .9727 .9589 .9372 6.6E-03 .8721 .0238 Bl TRL (AVE) 0 0 0 0 0 0 0 0 0 Bl TRL (DIFF) 0 0 0 0 0 0 0 0 0 BPR (AVE) .9357 .9211 .9054 .9303 .9432 .9834 .4048 .9768 .0364 BPR (DIFF) .064 .0418 .0628 .0485 .051 .0297 .0767 .0594 .4952 TEST SITES WITH SURFACE TREATNENT 50 NM 01 NH 02 NH 03 Bl CAR NAASRA 81 TRL Bl TRL BPR BPR 80 (AYE) (DIFF) (AYE) (DIFF) HN 01 .7551 .7141 .7546 .7701 .79 .8336 .6775 .6561 .0696 IM 02 .8061 .7673 .8 .8145 .8331 .8795 .6599 .7061 .0759 IM 03 .6914 .6523 .6938 .7094 .7364 .7679 .6696 .6646 .0719 GRAVEL SURFACED TEST SITES 50 N 01 MN 02 RN 03 BI CAR NAASRA El TRL DI TRL BPR BPR 80 (AVE) (DIFF) (AYE) (DIFF) im 01 .9596 .9476 .9698 .9213 .9291 .9177 .6089 .7662 .0999 MN 02 .9649 .9513 .9584 .9268 .9334 .9269 .5847 .8063 .1142 MN 03 .934 .8925 .9135 .868 .8735 .8651 .5549 .8217 .1083 EARTH (CLAY) SURFACE TEST SITES 50 Ni 01 Ni 02 NN 03 DI CAR NAASRA Bl TRL BI TRL BPR DPR 90 (AYE) (DIFF) (AYE) (DIFF) NH 01 .738 .764 .512 .6083 .6852 .8384 .4695 .912 .3032 NN 02 .9951 .9911 .9132 .8576 .9674 .9331 .3234 .927 .0473 MM 03 .9805 .9762 .9024 .8536 .9567 .9136 .3212 .8206 .0431 178 Table C.lO. Correlation Tables of R-Squared Values for 80 km/h. ASPHALTIC CONCRETE TEST SITES MN 01 NM 02 NN 03 BI CAR NAASRA BI TRL EI TRL BPR BPR (AVE) (DIFF) (AYE) tDIFF) MN 01 1 .9892 .9599 .0721 .955 0 I- .9368 .0743 NM 02 .9992 1 .94 .9275 .9972 0 Q .9502 .0398 NM 03 .9599 .94 1 .7954 .8831 0 d .9169 .0476 31 CAR .8721 .9275 .7954 1 .9712 0 0 .8677 .0444 NAASRA .955 .9872 .8831 .9712 1 0 0 .9178 .0614 Bl TRL (AVE) 0 0 0 0 0 1 0 0 0 B} TRL (DIFF) 0 0 0 0 0 0 1 0 0 BPR (AVE) .9368 .9502 .9169 .8677 .9178 0 0 1 .0116 BPR (DIFF) .0743 .0398 .0476 .0444 .0614 0 0 .0116 1 TEST SITES WITH SURFACE TREATMENT M 01 MN 02 MN 03 MM 01 1 .9917 .9629 MM 02 .9917 1 .9453 MM 03 .9629 .9453 1 GRAVEL SURFACED TEST SITES NN 01 KM 02 MN 03 Nm 01 1 .9918 .9751 MN 02 .9918 1 .9921 MM 03 .9751 .9821 1 EARTH (CLAY) SURFACE TEST SITES "H Q1 MM 02 NM 03 MN 01 1 .7742 .7666 NMN 02 .7742 1 .9707 Km 03 .7666 .9707 1 179 Table C.ll. Correlation Tables of R-Squared Values without Segregating Surface Type. MEASURES MADE AT 20 K/H MN 01 MN 02 NH 03 BI CAR NAASRA BI TRL BI TRL BPR BPR (AVE) (DIFF) (AVE) (DIFF) NH 01 1 .917 .8778 .9348 .9366 .8867 .5444 .8853 .2745 MN 02 .917 1 .9552 .9901 .9867 .9719 .3169 .956 .0863 MN 03 .8778 .9552 1 .95 .A483 .9219 .359 .8997 .0925 BI CAR .9348 .9901 .95 1 .9988 .9817 .3087 .9486 .0822 NAASRA .9366 .9867 .9483 .9988 1 .9834 .2997 .9458 .0762 DI TRL IAVE) .9867 .9719 .9219 .9817 .9934 1 .2462 .9408 .0382 BI TRL (DIFF) .5444 .3169 .359 .3087 .2997 .2462 1 .2237 .4801 BPR CAVE) .8853 .956 .8997 .9486 .9458 .9408 .2237 1 .0666 BPR (DIFF) .2745 .0863 .0925 .0822 .0762 .0382 .4801 .0666 1 HEASURES MADE AT 32 K/H MN 01 MN 02 NH 03 DI CAR NAASRA 81 TRL BI TRL BPR BPR (AVE) IDIFF) (AYE) (DIFF) NH 01 1 .8866 .8713 .8907 .8978 .8802 .4513 .7267 .3054 MN 02 .8866 1 .9486 .9902 .9912 .9823 .3019 .8458 .0912 MM 03 .8713 .9486 1 .9411 .9417 .9195 .3271 .7459 .0856 BI CAR .8907 .9902 .9411 1 .9978 .9846 .2927 .8516 .0991 ' NAASRA .8978 .9912 .9417 .9978 1 .9862 .2721 .8574 .0866 1I TRL CAVE) .8802 .9823 .9195 .9846 .9862 1 .253 .8443 .0612 DI TRL (DIFF) .4513 .3019 .3271 .2927 .2721 .253 1 .1239 .5201 DPR IAYE) .7267 .8458 .7459 .8516 .8574 .8443 .1239 1 .0998 BPR IDIFF) .3054 .0912 .0856 .0991 .0866 .0612 .5201 .0998 1 MEASURES MADE AT 50 K/H MH 01 NM 02 MN 03 El CAR NAASRA BI TRL BI TRL BPR BPR CAVE) (DIFF) CAVE) (DIFF) MH 01 1 .9696 .9571 .9406 .9657 .9365 .5834 .8012 .1511 MN 02 .9696 1 .9814 .9716 .9871 .974 .3435 .7626 .1474 M 03 .9571 .9814 1 .9677 .9849 .9562 .2882 .7434 .125 DI CAR .9406 .9716 .9677 1 .9902 .9831 .3058 .7897 .1708 NAASRA .9657 .9871 .9849 .9902 1 .981 .2916 .7921 .134 91 TRL CAVE) .9365 .974 .9562 .9831 .981 1 .3293 .8107 .1929 BI TRL (DIFF) .5834 .3435 .2882 .3058 .2916 .3293 1 .367 .5473 BPR (AVE) .8012 .7626 .7434 .7897 .7921 .8107 .367 1 .2275 BPR (DIFF) .1511 .1474 .125 .1708 .134 .1929 .5473 .2275 1 MEASURES HADE AT 80 K/H MM 01 MN 02 MH 03 BI CAR NAASRA BI TRL BI TRL BPR BPR (AVE) (DIFF) (AVE) (DIFF) MM 01 1 .9349 .9178 .8721 .955 0 0 .9368 .0743 MN 02 .9349 1 .9544 .9275 .9872 0 0 .9502 .0398 NM 03 .9178 .9544 1 .7954 .8831 0 0 .9169 .0476 BI CAR .8721 .9275 .7954 1 .9712 0 0 .8677 .0444 NAASRA .955 .9872 .8931 .9712 1 0 0 .9178 .0614 BI TRL (AVE) 0 0 0 0 0 1 0 0 0 BI TRL (DIFF) 0 0 0 0 0 0 1 0 0 BPR IAYE) .9369 .9502 .9169 .8677 .9178 0 0 1 .0116 BPR (DIFF) .0743 .0398 .0476 .0444 .0614 0 0 .0116 1 180 Table C.12. Correlation Tables of R-Squared Values without Segregating Measurement Speeds. ASPHALTIC CONCRETE TEST SITES MN O MN 02 ON 03 8I CAR NAASRA BI TRL B} TRL BPR BPR (AYE) (DIFF) (AVE) (DIFF) MN 01 0 .9539 .9455 .8383 .947 .8492 .0126 .4949 .2605 NO 02 .9539 1 .9203 .8568 .9438 .8067 .0182 .5304 .2065 MN 03 .9455 .9203 1 .8116 .9147 .7658 .0237 .4021 .2121 BI CAR .8383 .8568 .8116 1 .954 .7913 .0128 .474 .2185 NAASRA .947 .9438 .9147 .954 1 .8118 .01 .4935 .2254 8I TRL (AYE) .8492 .8067 .7658 .7913 .8118 1 .0411 .5083 .252 81 TRL (DIFF) .0126 .0182 .0237 .0128 .01 .0411 1 .0119 .0445 8PR (AYE) .4949 .5304 .4021 .474 .4935 .5083 .0119 1 .3956 BPR (DIFF) .2605 .2065 .2121 .2185 .2254 .252 .0445 .3956 1 TEST SITES HITH SURFACE TREATHENT MN 01 MN 02 MN 03 DI CAR NAASRA DI TRL 8I TRL BPR BPR (AYE) (D1FF) (AYE) (DIFF) Mn 01 0 a.9783 .9119 .9574 .9615 .8889 .2116 .8181 .3172 NH 02 .9783 1 .9227 .978 .975 .8472 .1823 .8038 .2803 NM 03 .9119 .9227 1 .9291 .9401 .7479 .278 .774 .3875 BI CAR .9574 .978 .9291 1 .9958 .7991 .2103 .7894 .292 )NAASRA .9615 .975 .9401 .9958 1 .8156 .2215 .7945 .3043 Bi TRL (AYE) .8889 .8472 .7479 .7991 .8156 1 .201 .8645 .3005 8I TRL 8I1FF) .2116 .1823 .278 .2103 .2215 .201 1 .2626 .531 BPR (AYE) .8181 .8038 .774 .7894 .7945 .8645 .2626 1 .4303 BPR (DIFF) .3172 .2803 .3875 .292 .3043 .3005 .531 .4303 1 GRAVEL SURFACED TEST SITES RH 01 MM 02 MN 03 81 CAR NAASRA 5} TRL BI TRL BPR 8PR (AYE) (DIFF) (AYE) (DIFF) NM 01 0 .9004 .8573 .9256 .9245 .9433 .5227 .834 .2148 NM 02 .9004 1 .9384 .986 .9833 .9593 .5777 .743 .1862 MN 03 .8573 .9384 1 .9166 .9187 .8949 .6214 .6178 .2066 8I CAR .9256 .986 .9166 1 .9979 .9787 .565 .7431 .1622 NAASRA .9245 .9833 .9187 .9979 1 .9751 .5786 .7448 .1718 81 TRL (AVE) .9433 .9593 .8949 .9787 .9751 1 .4982 .8065 .1783 DI TRL (DIFF) .5227 .5777 .6214 .565 .5786 .4982 1 .1374 .2385 8PR (AYE) .834 .743 .6178 .7431 .7448 .8065 .1374 1 .3193 BPR (DIFF) .2148 .1862 .2066 .1622 .1718 .1783 .2385 .3193 1 EARTH (CLAY) SURFACE TEST SITES MM 01 MM 02 M 03 B1 CAR NAASRA 8I TRL B1 TRL BPR PPR (AYE) (DIFF) (AYE) (DIFF) NM 01 0 .9114 .8411 .8546 .872 .8349 .2491 .8505 .1822 MO 02 .9114 1 .9561 .968 .9792 .9817 .0195 .9913 .0109 MH 03 .8411 .9561 1 .9502 .9619 .9374 4.8E-03 .934 1.1E-03 BI CAR .8546 .968 .9502 1 .9945 .9639 .0165 .9298 .0134 NAASRA .872 .9792 .9619 .9945 1 .9736 9.6E-03 .9474 7.6E-03 DI TRL (AVE) .8349 .9817 .9374 .9639 .9736 1 8.9E-03 .9643 IE-03 BI TRL (D0FF) .2491 .0195 4.8E-03 .0165 9.6E-03 8.9E-03 1 .0331 .6188 BPR (AYE) .8505 .9813 .934 .9298 .9474 .9643 .0331 1 8.2E-03 BPR (DIFF) .1822 .0109 .1IE-03 .0134 7.6E-03 IE-03 .6188 8.2E-03 1 181 Table C.13. Correlation Tables of R-Squared Values after Conversion to ARV, without segregating Measurement Speeds. ASPHALTIC CONCRETE TEST SITES NM 01 MA 02 NN 03 O1 CAR NAASRA Bl TRL BI TRL BPR BPR (AYE) (DIFFI (AYE) (DIFF) "M 01 1 .9708 .9775 .9428 .9837 .9524 .1431 .5061 .293 MN 02 .9708 1 .9542 .9507 .9743 .9199 .159 .5325 .212 NH 03 .9775 .9542 1 .912 .959 .9141 .1913 .448 .2524 BL CAR .9428 .9507 .912 1 .9906 .9726 .1597 .4621 .2533 NAASRA .9837 .9743 .959 .9806 1 .9694 .1463 .4975 .2625 BI TRL (AYE) .9524 .9199 .9141 .9726 .9694 1 .1648 .5901 .2766 BI TRL IDIFF) .1431 .159 .1813 .1587 .1463 .1648 1 .0583 .1178 BPR (AYE) .5061 .5325 .448 .4621 .4875 .5901 .0593 1 .3584 BPR (DIFF) .293 .212 .2524 .2533 .2625 .2766 .1178 .3504 1 TEST SITES VITH SURFACE TREATNENT NI 01 MM 02 MN 03 BI CAR NAASRA B1 TRL DI TRL BPR BPR (AVE) (DIFF) (AVE) IDIFF) NH 01 1 .9902 .9589 .9813 .983 .9751 .289 .8782 .1334 MN 02 .9902 1 .9612 .9847 . 939 .977 .2671 .8922 .1228 Nh 03 .9589 .9612 1 .9538 .9596 .9378 .3292 .8829 .1753 Bl CAR .9813 .9847 .9538 1 .9974 .9728 .286 .9821 .1076 NAASRA .983 .9839 .956 . 9974 1 .9752 .2967 .8851 .I179 El TRL (AYE) .9751 .977 .9378 .9728 .9752 1 .3038 .8958 .1141 Bl TRL (DIFF) .208 .2671 .3292 .286 .2967 .3038 1 .2835 .3284 BPR (AYE) .8782 .8922 .8929 .8821 .8851 .0959 .2935 1 .1799 BPR (DIFF) .1334 .1228 .1753 .1076 .1179 .1141 .3284 .1799 1 6RAYEL SURFACED IEST SITES MM 01 MN 02 MH 03 Bl CAR NAASRA Bl TRL Bl TRL BPR BPR (AYE) (DIFF) (AVE) (DIFF) NH 01 1 .9424 .9286 .9395 .9422 .9529 .6594 .8626 .2495 MN 02 .9424 1 .9744 .9932 .9923 .9848 .7487 .8227 .2384 MMN 03 .9286 .9744 1 .9578 .9589 .9495 .7611 .7289 .2219 91 CAR .9395 .9932 .9578 1 .9975 .9935 .7327 .8157 .2096 NASRA .9422 .9923 .9589 .9975 1 ."907 .7442 .8191 .2162 Bl TRL (AVE) .9529 .9848 .9495 .9935 .9907 1 .6903 .8267 .2227 BI TRL (DIFF) .6594 .7487 .7611 .7327 .7442 .6903 1 .4598 .3116 EPR IAVE) .8626 .8227 .7289 .8157 .8191 .8267 .4598 1 .4662 BPR (DIFF) .2495 .2384 .2219 .2086 .2162 .2227 .3116 .4662 1 EARTH (CLAY) SURFACE TEST SITES MN 01 iM 02 MN 03 BI CAR NAASRA Bl TRL BI TRL BPR DPR CAVE) (DIFF) (AVE) 1DIFF) MM 01 1 .8912 .8483 .8808 .8977 8734 .2767 .7517 .115 MN 02 .8912 1 .9542 .97 .9862 .9859 .0202 .9486 7.ME-03 NH 03 .8483 .9542 1 .963 .9772 .9296 4.9E-03 .8343 0 01 CAR .8808 .97 .963 1 .9905 .9662 .0337 .8428 .0237 NAASRA .8977 .9862 .9772 .9905 1 .976 .0155 .894 6.7E-03 Bl TRL (AYE) .8734 .9859 .9296 .9662 .976 1 .0216 .9399 2.5E-03 Bl TRL (DIFF) .2767 .0202 4.9E-03 .0337 .0155 .0216 1 .0388 .6738 8PR (AYE) .7517 .9486 .8343 .8429 .894 .9399 .0388 1 5.7E-03 BPR (DIFF) .115 7.6E-03 0 .0237 6.7E-03 2.5E-03 .6738 5.7E-03 1 182 Table C.14. Correlation Tables of R-Squared Values for No Segregation of Data. NH 01 NH 02 MN 03 Bl CAR NAASRA 8I TRL DI TRL BPR BPR (AVE) (DIFF) (AYE) (DIFF) MN 01 1 .9195 .893 .8916 .9181 .8998 .5078 .8091 .2828 MM 02 .9195 1 .9572 .9684 .9819 .9685 .3171 .8917 .1124 MN 03 .893 .9572 1 .9352 .9518 .9188 .326 .8119 .109 8I CAR .8916 .9684 .9352 1 .9915 .9635 .3019 .8639 .1117 NAASRA .9181 .9819 .9518 .9915 1 .9673 .2074 .8762 .1001 8I TRL (AYE) .8998 .9685 .9188 .9635 .9673 1 .2649 .8939 .0761 8I TRL (DIFF) .5078 .3171 .326 .3019 .2874 .2649 1 .1809 .508 8PR (AVE) .8091 .8917 .8119 .8638 .8762 .8939 .1809 1 .1122 BPR (DIFF) .2828 .1124 .109 .1117 .1001 .0761 .508 .1122 1 Measurements of ARS MN 01 MN 02 NH 03 B} CAR NAASRA II TRL PI TRL BPR BPR (AYE) (DIFF) (AYE) (DIFF) MN 01 1 .9484 .9327 .8734 .9295 .9188 .5571 .7347 .2361 NH 02 .9484 1 .9682 .9389 .9778 .9775 .3668 .8234 .1241 MN 03 .9327 .9682 1 .9082 .9576 .9401 .3489 .7216 .1168 EI CAR .8734 .9389 .9082 1 .9791 .9764 .3452 .7558 .1349 NAASRA .9295 .9778 .9576 .9791 1 .9784 .3299 .7829 .1163 BI TRL (AVE) .9188 .9775 .9401 .9764 .9784 1 .3322 .8488 .1055 8I TRL (D1FF) .5571 .3668 .3489 .3452 .3299 .3322 1 .2031 .5309 BPR (AYE) .7347 .8234 .7216 .7558 .7829 .8408 .2031 1 .1243 BPR (D1FF) .2361 .1241 .1168 .1349 .1163 .1055 .5309 .1243 1 Measurements of ARV 183 O m CA O" m CA X TS e oTS oGR + o . GR m ~+ TE X - + TE/ + E EN 0/. g 0o 0 0 N~~~~~~~~ 0 _ _ _ _ _ _ _ 0 10 20 30 0 10 20 30 ARS32 from MM #2 ARS50 from MM #2 O m CA imCA _ * TS 0 TS O~~ GR A,GR m , + TE . + TE +t, E Eo oc%O 17. N _ _ _ _ ___0 ___ ___ 0 10 20 30 0 5 10 15 ARS50 from MM #2 ARS80 from MM #2 Figure C.1. Comparison of ARS measures made at different speeds by two RTRRMSs. 184 o inCA 0o m CA t tD TS /< QTS 7 o A GR + °GR o0 0 10 2 0 00 1 2 0 4 +~~~~ 04~~~~~~~ 0 10 20 30 40 0 10 20 30 40 ARS20 from MM #2 ARS20 from MM #2 oI m CA 0 * CA e TS / TS A GR + A GR m + TEH + TE Eo + E . o 0 0 I _ _ _ _ __ __ ____ 0 10 20 30 40 0 10 20 30 ARS20 from NAASRA ARS20 from BPR Trailer Figure C.2. Comparison of ARS20 measures made by four RTRRMSs. 185 O m CA a m CA _ a TS < TS £GR AGR m *TGREX < >. + TE o~~~~~~~~~ o E O. ~ ~ AE 04 C4 0 0 10 20 30 0 10 20 30 ARS32 frorA MM #2 ARS32 from MM #2 °T m CA 0" m CA a) D TS a) e TS > ^ ~~GR m GRX C~~~~~~~~~4~~. E _ _ E ___ __ o o 0 10 20 30 0 5 10 15 20 ARS32 from NAASRA ARS32 from BPR Trailer Figure C.3. Comparison of ARS 32 measures made by four RTRRMSs. 18B o m CA s m CA _ e~oTS OTS EGR GR TEO< + TE n ZXm E E o 0 0:: 0 10 20 30 0 10 20 30 ARS50 from MM #2 ARS50 from MM #2 O FigCA C.. CCA o TS a TS 1 GCR +A0 GR+ O' + TE O + TE Fn~~~~~~~~~~i E E i o 0 n CP LOLC U) U) 0 10 20 30b 0 24 68 ARS50 f rom NAASRA ARS50 from BPR Trailer Figure C.4. Comparison of ARS 5 measures made by four RTRRMSs. 187 o m CA tn m CA o TS o TS A GR ~~~~GR N TS TE + TE 0 +~~~~~ E + E o 0 o + 0OLO O ~~~~~~~~~~IL 0 5 l0 15 0 5 10 15 ARS80 from MM #1 ARS80 from MM #3 Figure C.5. Comparison of ARS80 measures made by three RTRRMSs. 188 O 320 km/h .32 km/h o 50 km/h + 80 km/h 0C~ I- cn wY C: < v- 0 10 20 30 40 ARS from NAASRA Figure C.6. Comparison of ARS measures made with two roadmeters in the same vehicle. 189 @-.4 (P) *-4 Jw -I 8 28 48 66 BeS 1e 120 MAYS METER #2 - M"MS SUJF:F= C;e: S3 s c '% ! 0P I E . I 83 28 48 68 80 188 120 MIAYS METER *2 - ""M S E;EE; P DI: 2C 32 5O N, Jo a s -4 20 48 _ 6 t 20 53 EJF FR P'00 C E=- 53 c C fO= ES PF IE EE ID a a ;2 C0 -- 2 S O Figure C.7 Comparison of ARV Measures from Three RTRRMSs Taken at Three Speeds on Asphaltic Concrete Roads. 190 N. S.D 1-j In- 2 4 6 8 10 MAYS METER *2 - M'KM E3 U Ft 9 ck=e: S3 a C-- C-. IC ~ ~ ~ E;FEEEDSz 20 32S 1-1 De -'J ,[ I-. 8e 2 4 6 8 14 MAYS METER #2 MzKM ;FESEF:DSu s C 20 ac:50 Speed on APhicf - Cnrete Rods 191 < cm" W %D e 2 ~ ~ ~~~4 I 8 l HAASRA Mf 'KM 5 IUR F A C:-z ER: 5 oa C- Fn S P FE: E:t S f= :Z O) 3_ 2 5s 4D Figure C-8 Comparison of ARS Measures from Three RTRRMSs Taken at Three Speeds on Asphaltic Concrete Roads. 191 APPENDIX D SUBJECTIVE RATINGS Experiment At the completion of the experiment, a short study was performed in which a panel of 18 persons assigned a subjective ride rating to each test section. The staff at GEIPOT had performed a similar study in late 1978 for the project "Research on the Interrelationships Between Cost of Highway Construction, Maintenance and Utilization" (ICR) to relate the QI scale to user opinion [7]. The procedures used to gather data in the earlier study were repeated, using an international panel of men and women, whose backgrounds are summarized in Table D.1. All of the panel members were driven over the test sections by a staff member familiar with the route in one of three Chevrolet Opala passenger cars. These were the same three cars equipped with Maysmeters that were used in the main experiment. The vehicle speed was 50 km/h for all of the unpaved sections and 80 km/h for all of the paved sections. The panel members rated the section by marking a graphical scale on a field form, which showed as scale ranging from 0 to 5, with 5.0 being a perfect road. Back in the office, the location of the mark was measured with a ruler and entered into the computer, which converted the measure to a value between 0 and 5. Data Normalization The data collected in the study are presented in Table D.2. The mean and standard deviation (MEAN and SIGMA) are listed for each test section and for each panel member. The mean value for all ratings is 2.7 and the average standard deviation for all the members is 1. When the ratings from each rater are simply averaged, the results are more influenced by those members who used more of the available scale (signified by larger SIGMA values) than those who used only a small portion. To give each member equal weighting in the final average, the ratings for each member were normalized by the process of subtracting the mean value for that rater from all of his/her ratings, and dividing the results by his/her standard deviation. After normalization, the 193 Table D.1. Description of panel of raters Number Country Occupation Sex I United States Mechanical Engineer Male 2 Brazil Secretary Female 3 Brazil Secretary Female 4 Brazil Draftsman Male 5 Brazil Accountant Male 6 United States Economist/Editor Male 7 Brazil Civil Engineer Male 8 Brazil Civil Engineer Male 9 Brazil Translator Male 10 Brazil Clerk Male 11 Brazil Draftsman Male 12 Brazil Secretary Female 13 Brazil Technician Male 14 New Zealand Civil Engineer Male 15 France Civil Engineer Male 16 France Civil Engineer Male 17 Brazil Clerk Male 18 Brazil Civil Engineer Female 194 Table D.2. SUBJECTJEVE RATINGS WITH NO CORRECTION SITE 1 2 3 4 5 b 7 8 9 10 11 12 13 14 15 16 17 18 KEAN SISNA CAOI 3.5 3.4 4.2 3.2 3.4 3.3 3.7 3.7 3.4 4 2.7 4.1 3.4 2.3 2.5 3 3.9 2.0 3.4 .5 CA02 3 3.1 3.5 2.7 3.2 3.2 3.6 3.5 3.5 4.3 2.7 4.2 3.5 2.5 2.5 2.5 3.4 3 3.2 .5 CA03 2.7 2.7 2.6 2.5 2.5 2.8 3.3 3.3 2.6 4.4 2.3 2.7 3.3 2.7 1.5 2 2.5 2.7 2.7 .6 CA04 2.6 2.7 1.7 2.5 2.4 2.5 3.2 3.2 3.2 3.7 2.b 2.8 3.2 3 .5 2.5 3.4 2.4 2.7 .7 CA05 2.5 1.7 1.5 2.4 2.4 2.3 3.2 3 2.5 4 1.7 2.7 3.2 2.6 . . 2.5 . 2.5 .6 CA06 1.5 1.5 1.8 2.7 2.2 3.2 2.5 2.7 1.6 2.7 1.3 2.7 3.1 2.6 . . 1.8 1.0 2.2 .6 CA07 3.4 3.4 2.7 3.5 3.2 3.5 4.4 3.5 3.6 4.7 4.3 4.1 3.4 3.5 4.5 4 3.5 3.2 3.7 .5 CAO8 3.7 3.2 2.7 3.7 3.5 3.5 4.4 3.5 3.5 4.5 4.4 4.1 3.4 3.5 3.5 4 3.5 3.6 3.7 .4 CA09 2.7 3.2 1.7 3.8 3.3 2.7 2.8 3.7 3.2 4.5 2.5 4.1 3.4 3.2 2.5 4.5 3.4 2.2 3.2 .7 CAIO 3.1 2.8 1.2 3.3 3.1 2.5 2.8 3.7 3.5 3.7 3.4 4.1 3.4 3.3 3.5 4 3.6 2.2 3.2 .7 CAll 2.5 3.1 .5 2.2 2.8 2.4 2.6 3.3 2.2 2.6 1.7 3.1 2.7 2.7 1.5 3.5 2.4 1.9 2.4 .7 CA12 4.4 4.3 4.7 4.3 4.3 4.5 4.9 4.5 4.5 4.7 4.5 4.5 4.5 4.3 4.5 5 4.6 4.2 4.5 .2 CA13 4.1 4.5 4.7 4.2 4.3 4.5 4.7 4.4 4.4 4.6 4.5 4.5 4.5 4.1 4.5 5 4.7 4.5 4.5 .2 TSOI 2.7 3.1 2.7 3.3 3.3 4.4 3.4 3.6 2.5 4 2.4 3.5 3.4 3.1 4.3 4 3.7 3.2 3.4 .6 TS02 2.3 2.8 2.6 3.1 3.3 3.8 3.4 3.4 3.5 4 2.7 3.5 3.5 3.1 4.3 4 3.8 2.9 3.3 .5 TSQ3 2.6 2.7 1.7 3 3.4 3.6 3.4 3.2 3.4 4.3 2.6 3.1 3.2 2.8 2.5 3 3.7 2.2 3 .6 TSQ4 2.5 2.8 1.2 3.1 3.2 3.3 3.3 3.3 2.6 4.1 2.6 3.7 3.2 3 2.2 2.8 3.1 2.5 2.9 .6 TS05 2.1 2.5 1.7 3 3.1 3.3 3.2 3.2 2.7 3.5 2.7 . 3.2 3 2.3 2.7 3.1 2.4 2.8 .5 TS06 3.5 3.1 3.7 3.3 3.7 3.5 3.5 3.5 3.5 4.6 2.7 3.5 3.5 3.5 3.3 3.7 3.3 2.5 3.4 .4 TS07 2.7 2.5 3.7 3.3 3.7 3.5 3.5 3.3 3.5 4.6 2.7 3.5 3.4 3.2 3.3 4 3.5 2.7 3.4 .5 TS08 2.7 3.5 2.8 2.7 3.4 3.6 3.1 3.3 3.3 4.5 2.4 3.5 3.5 3.2 3.3 3 3.4 3.1 3.2 .4 T509 3 3.2 4.2 3.4 3.7 3.8 4.4 3.5 3.4 4.4 3.7 3.4 3.5 . . . 3.6 3.4 3.6 .4 TSIO 2.5 3.1 4.5 3.1 3.6 3.9 4.4 3.5 3.6 4.5 3.6 3.4 3.4 . . . 3.5 3.3 3.6 .5 TSII 4 ' 4 3.7 3.5 3.9 4.5 4.1 3.7 3.8 4.6 4.6 4.4 3.5 3.7 4.5 4.3 4.1 2.6 4 .5 TS12 3.7 4.1 3.7 3.5 3.8 4.5 4.1 3.7 3.8 4.6 4.4 4.4 3.5 3.5 4.5 4.5 4.1 2.5 3.9 .5 6ROI 3.6 1.3 3.5 2.3 3.1 3.3 1.7 2.5 3.4 3.1 3.7 3.5 2.5 3 2.5 4 3.1 1.8 2.9 .7 6R02 3.2 2.1 3.5 2.4 3.1 3.2 1.8 2.5 3.4 3.3 3.7 3.5 2.5 3 2.5 4 2.8 1.5 2.9 .6 6R03 2.3 1.2 2.2 2.2 2.5 2.6 1.6 2.3 2.6 2.7 3.3 3.5 2.5 2.7 3.5 3.5 2.4 1.9 2.5 .6 6R04 2.4 1 2.3 1.9 2.5 2.6 1.5 2.3 2.5 2.8 3.7 3.5 2.5 2.3 1.5 3.2 2.5 1.6 2.4 .7 BRO5 2 .6 .2 1.2 2.2 1.5 1.5 2.2 2.3 2.1 2.7 3.1 1.8 2.5 1.5 2.5 2.7 1.7 1.9 .7 6R06 2.5 .5 .5 .8 2.2 1.5 1.3 2 1.4 2.1 2.4 3.2 1.6 2.3 1.4 2.2 2.4 1.6 1.8 .7 6R07 2.5 2.1 2.7 2.2 2.6 2.5 2.7 2.5 2.5 3.5 3.5 3.1 2.3 3.4 2.3 4 2.5 2.5 2.7 .5 6R08 2.1 2.1 3.5 2.4 2.7 3.3 2.5 2.5 2.5 3.5 4.5 3.1 2.4 3.3 2.4 4 2.7 2.8 2.9 .6 6R09 1.6 1.3 2.7 2.3 2.4 2.5 2.2 2.2 1.5 2.7 3.3 2.6 2.3 2.8 1.7 3 2.1 2.4 2.3 .5 BRiO 1.5 1.2 2.7 2.1 2.4 2.7 2.4 2.3 1.6 2.7 2.5 2.5 2.5 3 1.7 3 1.9 2.1 2.3 .5 6RII .6 .3 1.8 1.7 1.5 .2 .6 1.3 1.4 2.3 2.4 1.5 .5 1 .7 1.8 3.1 1.1 1.3 .8 6R12 .4 .2 1.8 1.2 1.4 .4 .6 1.4 1.3 .7 1.6 1.5 .4 1.4 .6 1.5 2.2 .7 1.1 .6 TEOI 2.5 2.6 1.2 2.7 3.1 2.6 1.4 2.2 3.3 4.1 3.4 3.5 2.5 2.6 1.5 4 2.5 2.1 2.7 .8 TE02 2.2 2.7 .8 2.7 3 2.5 1.4 2.3 2.7 4.2 3.4 3.5 2.5 2.8 2.5 4 2.6 2.2 2.7 .6 TE03 1.4 2.5 1.3 2.5 2.b 2.5 1.3 2 1.5 3.b 3.4 3.5 2.4 2 1.5 3.5 2.3 1.8 2.3 .8 TE04 1.2 1.8 .7 2.7 2.4 2.5 1.2 1.8 1.5 3.5 3.4 3.5 2.5 1.9 1.5 3 2.4 1.5 2.2 .8 TE05 .6 .2 .6 .7 .4. .5 .5 1 1.5. 2.5 1.4 2.1 .3 1.5 1.2 1.5 1.5 .8 1 .6 TE06 .2 .1 .3 .2 .3 .4 .3 .7 1.4 2 .6 1.7 .4 .5 .5 1 1.3 .5 .7 .5 TE07 2.4 1.5 1.3 2.4 2.4 2.5 2.2 2.3 2.7 3.1 3.7 3.1 2.4 3.4 2.4 3.5 3.4 2.2 2.6 .7 TEOS 2 1.1 1.7 2.3 2.4 2.5 2.1 2.3 2.5 3.1 1.5 3.1 2.4 3.4 2.4 3.5 3.1 1.9 2.4 .6 TE09 1.4 .8 1.2 1.6 2.3 1.5 1.9 1.7 2.4 2.1 2.7 2.1 1.5 2 1.6 2 2.4 1.8 1.8 .5 TEJO .6 .4 1.2 1.4 1.9 1.2 1.2 1.5 1.3 1.9 3.7 2.1 1.5 1.6 1.5 1.8 2.1 1.5 1.6 .7 TEII 1 .2 .7 1.5 2.4 .7 .8 1.5 1.3 2.5 2.3 1.9 .7 1.3 .9 2 2.4 1.5 1.4 .7 TE12 1.2 .3 .7 1.3 2.3 .6 .7 1.8 1.4 3.2 2.3 1.9 .9 1.7 .8 2 2.6 1.5 1.5 .8 MEAN 2.4 2.1 2.2 2.5 2.8 2.7 2.6 2.7 2.7 3.5 3 3.2 2.6 2.7 2.4 3.2 3 2.3 2.7 .4 SISMA I 1.2 1.3 .9 .9 1.1 1.2 .9 .9 1 .9 .8 1 .8 1.2 1 .7 .8 1 .2 195 ratings of each member had a mean value of zero and a standard deviation of 1.0. The normalized ratings are presented in Table D.3. Ideally, there should be no missing data, because the calculated values of the mean and standard deviation can then be erroneous. In this case, there were ten missing values out of a total of 882. The test sections that were missing were not extremely smooth or extremely rough; hence the errors introduced to the final rating for the sections are assumed to be negligible. A critical phase of analyzing subjective rating (SR) data is called '"anchoring the scale" to assign absolute roughness values to each road section, based on a comparison of the range of SR values obtained from the raters to a reference range. Since the interest here is in seeing the correlation of SR with the other measures and comparing the roughness rankings, the arbitrary normalized scale of Table D.3 was considered sufficient. If desired, the SR numerics can be "anchored" to any one of the many objective roughess measures used in the IRRE. Fxample Correlations With Objective Roughness Measures Figure D.1 shows scatter plots of SR against the roughness measures obtained from one of the response-type road roughness measurement systems (RTRRMSs). The plots also include quadratic regression lines, whose coefficients were computed separately for each surface type. The standard error (SE) is indicated for each regression, and has the same arbitrary units as SR. The plots also include the r2 value for each of the regressions. The figure reveals that about the same quality of correlation is obtained at all four speeds, and that surface type influences the regressions the most when the RTRRMS was run at 80 km/h. These are unexpected findings, given that the SR values are based on travel speeds of 80 km/h for the paved roads and 50 km/h for the unpaved. Better correlation was expected when the RTRRMS measurement speed matches the travel speed during the SR experiment. In these examples, a single non-linear relationship seems to exist that relates the RTRRMS measure to SR for three of the surface types as a function only of roughness, as measured by either the SR or RTRRMS scale. But a separate relationship is needed for the sections with surface treatment (TS). The SR ratings do not discriminate among these sections as much as the RTRRMS, and the SR is generally high compared to comparable RTRRMS roughness levels for 196 Table D. 3. SUBJECTIVE RATINGS AFTER RE-SCALING SITE 1 2 3 4 5 & 7 8 9 10 11 12 13 14 15 lb 17 18 MOANSIGNA CAOl 1.2 1 1.6.7 .7 .6.9 1.1 .9.5 -.31.2 .8-.6 .1-.21.2 .7 .7 .6 CA02 .7 .81 .2 .5.4 .8 9.9 ..8-.3 1.2 .8-.3 .1-.7.6 1 .5 .5 CA03 .4 .4 .3 0 -.4 .1 .6 .7 0 .9 -.7 -.6 .b -.1 -.7 -1.2 -.6 .6 0 .6 CA04 .3 .5 -.4 0 -.5 -.2 .5 .5.6 .2 -.3 -.5 .6 .3 -1.5 -.7 .6 .2 0 .6 CA05 .1 -.3 -.6 -.2 -.5 -.3 .5 .3 -.3 .5 -1.4 -.6 .6 -.2. . -.7 . -.2 .5 CAO6 -.9 -.6 -.4 .2 -.7 .5 -.10 -1.2 -.8 -1.8 -.6 .4 -.1. . -1.6 -.6 -.5 .6 C407 I 1.1 .4 1.1 .6.7 1.5 .9 1 1.3 1.5 1.1 .8 .9 1.3 .9 .7 1.1 1 .3 CAO81.3 .8.4 1.3 .9 .7 1.5 .9.9 1 1.5 1.2 .7 1 .9 .9.7 1.7 1 .3 CA09 .3 .8-.4 1.5 .6 0 .2 1.1 .6 1 -.5 1.1 .7 .6.1 1.3 .6-.1 .5 .5 CAlO .7.6 -.8 .9.4-.2 .21.1 .9.2.51.1 .7 .7.9 .8.8 -.1 .5 .5 CAII .1 .8 -1.4 -.4 0 -.3 .1 .6 -.5 -.9 -1.4 -. I0 0 -.7 .3 -.7 -.4 -.3 .6 CA12 2.1 1.7 2 2 1.9 1.6 1.9 2 2 1.2 1.7 1.6 1.9 2 1.8 1.9 2.2 2.3 1.9 .2 CA13 1.7 1.9 2 1.9 1.8 1.5 1.7 1.9 1.9 1.2 1.7 1.6 1.9 1.8 1.9 1.9 2.3 2.7 1.8 .3 TSOI . 3 .8 .4 . 8 .6 1.5 . 7 .9 -.2 . 5 -.6 .4 .8 .5 1.6 .8 .9 1.2 .7 .5 TS02 -.1I .6 .5 .7 .6 1 .7 .8 .9 .5 -.3 .4 .8. .5 1.6 .8 1.1 .8 .7 .4 TS03 3.2 .5-.4 .5.7 8.7 .6.8 .8-.3 -.1 .6.2 . 1-.2 1 -.1 .3 .4 TS04 .2 .5 -.8 .6.6 .5.6.6 0 .7 -.3 .7 .6.3-.1 -.4 .2.2 .2 .4 TS0 5 -.3.3 3-.4 .6.3 .5 .5.50 0 -.3. .6.3 -. 1-.5 .2 .2 .1 .4 TS06 1.1 .9 i.2 .S1.2 .7 .8 .9.91.2 -.3.3 .9 1 .8 .5.4.2 .7.4 TS07 .4 .3 1.2 . 8 1.2 .7 .8 .7 .9 1.2 -.2 .3 .8 .7 .6 .9 . 7 .6 7 .3 TSO S.3 1.1 . 5.2 .7.84 .6 7 1 -.6 .3 .8 7.8-.2.6 1 .5 .4 TS09 6 .8 1.5 1 1.1 .9 1.5 .9 .9 1 .8 .2 .8. . 81.4 . 9.3 TSIO0I.181.B .61I 1 1.5 .9 1.1 1.1 .7 .3 .8. .7 1.3 .9 .4 TSII 1.7 1.6 1.2 1.1 1.3 1.5 1.3 1.1 1.2 1.1 1.7 1.5 .9 1.2 1.8 1.1 1.5 .4 1.3 .3 TS12 1.4 1.6 1.2 1.1 1.2 1.5 1.3 1.1 1.2 1.2 1.6 1.5 .9 1 1.8 1.3 1.6 .2 1.3 .3 BR01 1.2 -.7 1 -.2 .3 .6 -.7 -.2 .8 -.4 .8 .4 -.1 .3 .1 .9 .2 -.6 .2 .6 8R02 .9 -.11 -.2 .4 .4 -.6 -.2 .9 -.2 .8 .3 -.2 .3 .1 .8 -.2 -.6 .2 .5 8903 -.1 -.8 -.1 -.4 -.3 -.1 -.8 -.6 .1 -.9 .4 .3 -.2 0 .9. .3 -.9 -.4 -.2 .5 9904 0 -.90 -.7 -.4 -.1 -.9 -.5 -.2 -.7 .8.3 -.1 -.5 -.7 0 -.6 -.9 -.3 .4 GROS -.4 -1.3 -1.6 -1.5 -.7 -1.1 -.8 -.7 -.4 -1.5 -.3 -.1 -.9 -.3 -.7 -.7 -.3 -.8 -.8 .4 6R06 .1 -1.4 -1.3 -2 -.7 -1.1 -1 -.8 -1.4 -1.5 -.6 0 -1.1 -.6 -.9 -1 -.8 -.9 -.9 .5 8907 .10 .4 -.3 -.3 -.2 .1-.3 -.2 0 .5 -.1 -.3 .8-.1 .8-.7 .3 0 .4 GR09 -.3 0 1.1 -.2 -.1 .5 0 -.3 -.2 0 1.6 -.1 -.3 .7 0 .8 -.3 .& .2 .5 8909 -.8 -.7 .4 -.3 -.5 -.2 -.3 -.6 -1.3 -.9 .4 -.9 -.3 .1 -.6 -.2 -1.2 .2 -.4 .5 SRIO -.9 -.7 .4 -.5 -.5 0 -.1 -.b -1.3 -.8 -.4 -.9 -.1 .4 -.6 -.2 -1.4 -.2 -.5 .5 6911 -1.9 -1.5 -.3 -.9 -1.6 -2.2 -1.5 -1.6 -1.5 -1.3 -.6 -2.2 -2.1 -2.2 -1.4 -1.4 .2 -1.4 -1.4 .6 9912 -2. -1.6 -.3 -1.5 -1.7 -2 -1.6 -1.6 -1.6 -2.9 -1.4 -2.2 -2.2 -1.6 -1.5 -1.7 -1 -1.9 -1.7 .5 TEOI .1 .4 -.I.2 .40 -.9 -.6.7 .6.5 .3 -.1-.2 -.7 .8-.7-.2 9 .5 TE02 -.2 .5 -1.1 .2 .3 -.2 -1 -.5 0 .8 .4 .4 -.2 .1 .1.8 -.4 -.2 0 .5 TE03 -1 .3 -.8 -.1 -.3 -.2 -1 -.8 -1.3 .1 .5.3 -.2 -.9 -.7 .3 -.9 -.6 -.4 .5 TE04 -1.2 -.3 -1.2 .2 -.5 -.2 -1-1 71-1 -13 .4 .3 -.2 -1 -.7 -.2 -.7 -.9 -.5 .6 TE05 -1.9 -1.6 -1.3 -2.1 -2.9 -2 -1.7 -2 -1.3 -1.1 -1.7 -1.4 -2.3 -1.5 -1 -1.7 -2 -1.8 -1.7 .4 TE0& -2.3 -1.7 -1.6 -2.6 -3. -2 -1.8 -2.4 -1.4 -1.6 -2.6 -1.9 -2.2 -2.8 -1.6 -2.3 -2.3 -2.1 -2.1 .4 TE07 0 -.6 -.8 -.2 -.5 -.2 -.3 -.5 .1 -.4 .8 -.2 -.2 .9 0 .3 .6 -.2 -.1 .4 TEOB -.4 -.8 -.4 -.2 -.5 -.2 -.3 -.5 -.2-.4 -1.5 -.1 -.3 .8 0 .3 .2 -.5 -.3 .5 TEO9 -1 -1.1 -.8 -1 -.6 -1.1 -.6 -1.1 -.3 -1.5 -.2 -1.4 -1.1 -.9 -.6 -1.2 -.7 -.6 -.9 .3 TEIO -1.8 -1.4 -.8 -1.3 -1.1 -1.3 -1.1 -1.4 -1.5 -1.7 .8 -1.4 -1.1 -1.4 -.7 -1.4 -1.2 -1 -1.2 .5 TEII -1.5 -1.6 -1.2 -1.2 -.5 -1.8 -1.4 -1.4 -1.6 -1.1 -.7 -1.7 -1.9 -1.9 -1.2 -1.2 -.7 -.9 -1.3 .4 TE12 -1.2 -1.5 -1.2 -1.4 -.6 -1.9 -1.5 -1.1 -1.4 -.3 -.7 -1.7 -1.7 -1.3 -1.4 -1.2 -.5 -1 -1.2 .4 197 04 N - ( GE r~se r z 0 Im CA .Lo .95 0 CA .19 .93 .'e 0!t O l TS .23 .60 0 0 TS .22 . o "teS A GR li1 .95 A GR .13 '96 e o X + ~~TE 1 4 .95 e o + TE .1(o .94 ,0 1______I_+ un I I (n C-4 n) C- 0 10 20 30 40 0 10 20 30 ARS20 - m/km ARS32 - m/km ARS20 from Opola-MM #2 E IDCA .I .94 se r2' oTS .20 11 Dm CA .24 .89 A GR.14 .-b( db 0 TS .22 . (3 _. <, + TE 15 .91 'c 3 TE .15 SL+ TE A .91 o 0 _ __,_ _ _ 4. ,, ,, . '',,,,,Ill .0~~~~~~~~ (n 04~~~~~~~~~~~~~~~4 0 10 20 30 0 5 10 15 ARS50 - m/km ARS80 - m/km ARS50 from Opala-MM #2 ARS80 from MM #2 Figure D.l. Correlations between SR and ARS measures from a RTRRMS. 198 other surface types. The cause of these results over the TS sites is revealed by the PSD functions in Appendix I, which show that the four "roughest" of the TS sections have a periodic variation that is seen by the vehicle at 11 Hz when the speed is 80 km/h. This frequency will typically excite axle motions, because the vehicle has a lightly damped vibration mode in which the mass of the axle and wheels vibrates against the siffness of the tires. These axle vibrations, having small deflection amplitudes but high frequncy, are sensed by the roadmeter but apparently not by the passenger. Figure D.2 shows similar plots and regression results for the RARS numeric computed from profile using the reference quarter-car simulation (RQCS) described in Appendix F. The regressions are very similar to those obtained from the RTRRMS for the lower speeds, but for the higher speeds, the regression equations collapse approximately into a single relationship. Thus, the sensitivity of the "reference" RTRRMS appears to match the panel judgement better than the ARS measures obtained from the same vehicle used to transport the raters. Figure D.3 shows the relationships between SR and three other profile-based numerics: the short-wave CP2.5, the medium-wave CPlo. and QIr. Just as the RTRRMS speed does not strongly influence the quality of the correlation, the choice of a moving average baselength for the CP analysis does not appear critical unless the analysis emphasizes the longest wavelengths, in which case (not shown) poor correlations exist. The Qlr numeric is seen to be one of the best predictors of SR. The correlation between QIr and SR on the unpaved roads, is the best obtained, and the correlation for the paved roads is nearly as good as seen for the RARS80 numerics. The regression equations for the different surface types collapse approximately into a single relationship between Q0r and SR, as do the regression equations for RARS50 and RARS80. 199 C9- . S E ra-~C C14. se t- C14s r, 0 10 20~C 30 o 1 132 O 9 m CA .26 .63 E ,cl9 CA .22 .91 m te o e TS .23 , 'WoT 1 7 H ^ ~~~~~GR.211 .@-n R.92 90 C S .S+ TE .15 .95 0* a TEAS .l9 0~~~~~~~~~ A' , 0 5 10 1520 25 0 5 10 15 20 RARS20 m/km RARS32 - mlkm RARS from SAPLc 25sue RARS from Satic 72sue Fiur9D2 CAreain bet2e CAR 22o th QS9ndSR 20 A 0 10 1520 30 0 5 10 15 20 RARS,50 m r/km RARS32 - rn/km RARS from SaPLc 25sue RARS from SaPLc 72sue Fiue D..2Creaiosbten ASfo the QCS Can S.2 oTS21 (i, corSj200l 04 se T CV r S m CA AI .8(0 CA , .o TS . 9 -75 _ TS GR5, .0 .19 TE .2 6+ TE 2(o ,13 -4-', - 4)A o XA N~~~~~~~~ AN 1.~~ . I,,l,,I, 0 50 100 150 200 0 100 200 300 CP2.5 CP 1o CP 2.5 from APL 72 CP 10 fSrom APL 72 o TS -lb A GR,1 .92 0 ~~~~+ TE .09 U4) + A 1~~~~~0 re) 0 100 -200- 300 Qr- counts/km Qt from Static Measures Figure D.3. Correlations between SR and seVeral profile-based numerics. 201 APPENDIX E QI ANALYSIS prepared by The University of Michigan Transportation Research Institute (UMTRI). The Brazilian Road Research Institute (IPR/DNER), The French Bridge and Pavement Laboratory (LCPC), and The Belgian Road Research Center (CRR) QI is the name given to the roughness scale used in Brazil during and after the project, "Research on the Interrelationships Between Costs of Highway Construction, Maintenance and Utilization" (PICR). In actuality, there are several Q1 scales, which have subtle differences. During the PICR project, the Q0 scale evolved from a numeric that depended on the specific properties of a reference instrument (designated QI, which stands for Quarter Car Index), to a calibrated measure from a response-type road roughness measuring system (RTRRMS) (the calibrated measure is designated QI*) E7], to a roughness numeric defined by the true longitudinal profile of the road (designated QIdr [8]. The QI* scale is of particular interest, because the cost equations developed in the PICR project that involve road roughness are based on measurements of QI*. Although it is not completely equivalent to the QI* scale, the Ql scale is also of interest because it is a profile-based roughness measure that has been suggested as a standard for future calibration of RTRRMSs. In addition to the testing reported in this report, the Qlr scale has also seen limited use in Bolivia 126] and South Africa 127]. Further, MO, a nearly identical scale, has been used in Texas [28]. This appendix describes 1) the development of the various versions of QI in Brazil, 2) the mathematical properties of the profile-based QI numeric, 3) 203 requirements in profile measurement for valid measurement of QI- and 4) the compatibility of the QI' scale with the RTRRMSs that participated in the IRRE. Many of the details of the procedures used for the QI and Qlr numerics have been reported previously [7, 81, so this appendix mainly covers new findings that have emerged during the IRRE. DEVELOPMENT OF THE QI ROUGHNESS SCALE QI: The Quarter-Car Index The roughness scale initially used in the PICR project was based on the output from a GMR-type Inertial Profilometer (also called a Surface Dynamics Profilometer) used in the project [7]. The Profilometer is equipped with a special purpose analog computer called a Quarter-Car Simulation (QCS) that is intended to replicate the dynamics of a BPR Roughometer [24]. To avoid confusion between this particular QCS and others mentioned in this report, it is designated BPR/QCS. (See Appendix A for descriptions of the two BPR Roughometers that participated in this experiment, and Appendix F for a description of the BPR/QCS.) At the start of the project, both the profilometer speed and the simulation speed were set at 55 km/h, to correspond to the usage of a similar unit at The Pennsylvania State University. The BPR/QCS device produces a number of counts over each 1/10 mile of travel as a measure of road roughness. The scaling is such that each count corresponds to 1/10 inch of accumulated positive suspension deflection of the simulated vehicle. Since the test length is 1/10 mile, the units can also be expressed as "inches/mile," as normally reported for a BPR Roughometer. Because the accumulation in a BPR roadmeter is only for deflection in one direction, the statisic produced is exactly half of the ARS (average rectified slope) numeric produced by roadmeters that accumulate in both directions. This number was multiplied by 0.6214 to convert to kilometers, and the result was reported as "QI" (Quarter-Car Index) with the assumed units "counts/kilometer." The simulator was able to process only one profile at a time, so the QI was found for both the right and left wheel-tracks separately, and these measures were averaged to obtain the official QI for a test section. 204 The Profilometer and its related equipment experienced constant operational problems during the PICR project. Also, the output of the electronic QCS was found to vary with a number of testing conditions, such as speed, gain setting, and choice of follower-wheel. These variations were consistent and large, indicating that the instrument was not actually measuring "profile" as it is designed to do. (When used only on the smoother paved roads in the United States, the same roughness numeric can be obtained over a range of testing conditions with a GMR-type Inertial Profilometer.) Nonetheless, when operated under the same testing conditions (speed, etc.) the measurements were more time-stable and thus more reliable than those of the RTRRMSs used to gather the bulk of the roughness data for the project. In this regard, the QI measures from the Profilometer helped provide a more time stable roughness scale. During the project, survey profile measures were made of the control sections (used for calibrating the RTRRMSs) with the rod and level technique, as the Brazilian researchers anticipated even further problems with the equipment. Efforts were made to find an alternative to the BPR/QCS "QI" that could be calculated from the rod and level profile measurements. These efforts were successful, and in 1979, after the Profilometer reached the point where the cost and effort needed to keep it operational were too great, it was "mothballed." From then on, the alternative definition of QI that could be applied to Rod and Level measures was used in the project [8]. Qlr: A Statistic Computed from Rod and Level Profile Because of the problems associated with the Profilometer, a method for estimating QI from rod and level measurements was developed. Rod and level profiles were made of the control sites, whose QI roughness values were known. Several roughness statistics that had been proposed in the literature were calculated from measured profiles tested for agreement with the QI numerics obtained from the Profilometer: 1. RMSVA (root-mean-square vertical acceleration) [25] calculated for several baselengths, 2. MAVA (mean absolute vertical acceleration = average rectified 205 acceleration), also calculated for several "characteristic baselengths," 3. Slope variance, also calculated for several characteristic baselengths, including the one for the published geometry of the CHLOE profilometer, and 4. Waveband analysis, in which profile elevation variance is computed for specific wavebands. Using each type of analysis, the "best" model for predicting the QI as determined by the Profilometer was developed, using least squares methods to maximize fit and using ridge analyses to choose the independent variables. It was found that excellent correlations were obtained using either a waveband or an RMSVA model. In either case, two independent variables were needed (that is, two different wavebands were needed for the waveband analysis, and two different baselengths were needed for the RMSVA analysis). Computationally, the RMSVA statistic is much simpler to obtain, and thus it was adopted to redefine QI for continuing work [8]. QI*: Rescaled Measurements from RTRRMSs During the PICR Project, the roughness scale was defined by either the QI numeric obtained from the BPR/QCS or the QIr statistic; however, the actual roughness measurements were made with RTRRMSs, composed of Chevrolet Opala passenger cars equipped with modified Maysmeter Roadmeters (see descriptions in Appendix B and Reference [4]). With few exceptions, the RTRRMSs were operated at speeds of 80 km/h on paved roads and at 50 km/h on unpaved roads. A third standard speed of 20 km/h was used on the worst roads, which amounted to only a few percent of the total. When operated at 80 km/h (paved roads), the "raw" measures (as read directly from the roadmeter display) of the RTRRMS were transformed to QI *through the use of a linear regression equation, which was in essence the calibration for that particular RTRRMS. The measures made at 50 km/h were converted to QI* through a two-step process: first, the "raw" measure was used to estimate what the RTRRMS would have measured if operated at 80 km/h. Then, the resulting estimated 80 km/h measure was converted to QI* by using the calibration equation. On those rare occasions 206 that actual measures were made at 20 km/h, a three-step process was used, in which the measure was transformed into an estimate of a 50 km/h measure, which was in turn transformed into an estimate of an 80 km/h measure, which was then transformed into QI . Although the roughness scale has been described in terms of the QI and QIr scales, the roughness data collected in the PICR project, used as the basis of the roughness-related cost equations, are composed completely of QI values: rescaled (calibrated) RTRRMS measures. MATHEMATICAL DEFINITIONS OF THE QI SCALES QI: Quarter Car Index Ideally, the mathematical properties of the QI numeric would be determined by the published response properties of the BPR/QCS device [9, 241. Due to a number of circumstances, the QI numeric includes a number of equipment-related characteristics as well, which also affect the total roughness definition. In order to understand the significance of the QI numeric, it is necessary to also know something about the factors that influence the operation of the Profilometer and the BPR/QCS. Calibration Error. The electronic BPR/QCS produces a voltage in proportion to a simulated axle-body velocity, rectifies this signal (takes the absolute value), and integrates the rectified signal over the test length of 0.10 mile (0.160 km) to obtain accumulated displacement. The accumulated displacement signal runs a counter that increments every time a voltage threshold is reached and resets the output of the integrator to zero. The "counts" produced as the output are thus due to 1) the rate at which the signal increases (i.e., average rectified velocity, ARV), and 2) the voltage level used as a reference for "one count." Part of the calibration of the BPR/QCS electronic box involves the careful setting of this threshold, such that each count shown corresponds to .10 inch of accumulated movement in one direction (0.20 inches in both directions). The calibration is achieved by using a sine wave input of specified amplitude and frequency, and adjusting 207 the threshold value until a specified count is obtained. During the PICR project, however, the calibration procedure outlined by the manufacturer was not followed. The speed setting on the QCS was not adjusted correctly, and a square wave was used rather than a sine wave. Not until the Profilometer was prepared for the IRRE were the effects of these errors found [23]: 1. The gain was in error such that the output had the units of .204 inch/count in one direction (.408 inch/count in both directions) 2. The gain pushed the voltage threshold near the limits of the electonic circuitry, where behavior is non-linear due to saturation of the op-amps. The sensitivity of the calibration was reduced, such that fluctuations in performance that would normally be corrected by an accurate calibration were not easily detected. Hence the main purpose of the calibration was partially thwarted. The square wave input was used rather than the sine wave because the output drifted with a sine wave input, making calibration difficult. The use of a square wave input eliminated the symptom, but not the cause, which was found to be a defective electonic component (replaced) during the course of preparing for the IRRE. Use of the Profiloseter at low speeds. The GMR-type Profilometer senses vehicle-to-road distance using a spring-loaded follower wheel. On medium-quality paved roads, the follower wheel bounces when the Profilometer is operated at highway speeds (50 km/h and higher). In order to prevent bounce of the follower wheel, lower speeds were used during the PICR project. This introduces an additional error into the BPR/QCS numeric, however, because the instrumentation in the Profilometer and the BPR/QCS were designed for higher speeds. Specifically, the BPR/QCS has a high-pass electronic filter that attenuates "very low" frequencies. The cut-off frequency, which is the frequency at which attenuation becomes significant, can be set by the operator to match conditions. The problem is that in order to run the Profilometer without overloading the amplifiers (indicated by lights and beepers), the cut-off filter had to be set at the medium settings, near 0.5 Hz. The corresponding wavelength is determined by the Profilometer travel speed, and is 18 m/cycle at a measurement speed of 32 km/h. The response range of the 208 BPR/QCS depends on the simulation speed, with the 1.0 Hz lower limit corresponding to a wavelength of 15 m at the simulation speed of 55 km/h. Although the high-pass filter transmits most of the wavelengths that affect the QI numeric, those near 15 m and longer are attenuated due to the low profilometer speed. Therefore, the QI measures probably did not contain all of the long wavelength content that would be expected if the input to the BPR/QCS had been the "true" profile. Speed Correction. The BPR/QCS is supposed to correct for profilometer measurement speed. During the PICR project, the circuit was found to be defective, the manufacturer was contacted, and a modification to fix the circuit was developed. The modification was never implemented, however, so that the numerics produced by this particular BPR/QCS had a speed sensitivity. While the overall effect can be corrected by a speed ratio, variations in speed during measurement go undetected and can lead to variability. Summary of "True" QI. The above factors could possibly be taken into account to determine a quantitative definition of QI. But for all practical purposes, QI can be considered as "the number produced by the BPR/QCS and the Profilometer as operated during the PICR." Because the original Q1 was so specific to a particular piece of hardware and operational procedures, it cannot be replicated with any assurance. The Profilometer was only rarely used on surface treatment and unpaved roads. Since very few measurements were obtained, the original QI is effectively undefined for these conditions. Rather than attempting to determine exactly how to describe the original QI, it has been recommended that the alternative description, designated Qlr and described below, be used as the definition of "true" QI as determined from profile measurement 18]. 209 QI,: Defined by Profile Geometry Definition of QIr. The QIr statistic is computed directly from measured profiles. First, the profile is "filtered" to yield a variable that has been called "Vertical Acceleration," although it will be shown later that the name is not truly appropriate. The "filter" is defined by the equation: VA(x)= [ y(x + b) + y(x - b) - 2 y(x) ) b-2 (E-1) where x = longitudinal distance (m) y(x) W elevation of wheeltrack at position x (mm) b = baselength (m). Given measures of y(x) that are equally spaced, Eq. 1 can be re-written: VA(i) [y(i + k) + y(i - k) - 2 y(i) I b-2 (E-2) where k - b/dx (E-3) and i = index, corresponding to the ith profile elevation measure dx - distance between profile measurements therefore n-k 2l2 RMSVAb 1 1 / (n - 2 k)i= +k VA(i)2 alI2 (E-4) where n - number of measurements 210 The Estimate of QI that was developed through regression methods is: E [QI] = QIr = -8.54 + 6.17 RMSVA1 0 + 19.38 RMSVA2.5 (E-5) where E [QI] - expected value of Ql, and RMSVAb has the units: slope x 106. (These units arise when b is measured as m and elevations are measured as mm.) Waveband Response of RMSVA and Qlr. The wavelength sensitivity of the VA "filter" can be calculated using Laplace Transforms, which consider a sinusoidal input: y(w,x) = YO ejwx = input (E-6) where ejwx = coswx + j sinwx (E-7) w - spatial circular frequency (rad/m) - 2" / wavelength - 2" wavenumber, YO = sinusoidal amplitude, and j - /-i = the "imaginary" part of a "complex" vector, 900 out of phase with the "real" part. Eq. 6 describes a variable that is sinusoidal over longitudinal distance. Combining Eqs. 1 and 6 yields: VA(w,x) = [ Y0 eJw(x + b) + y0 ejw(x - b) - 2 YO ejwx I b2 3 Yo [ ejwx eJwb + eJwx e-jwb _2 eJwx I b-2 - y(w,x) [ eiwb + eiwb - 2 1 b-2 = y(w,x) [ cos(wb) + j sin(wb) + cos(-wb) + j sin(-wb) - 2 lb 2 211 2 y(w,x) i cos(wb) -1 ] b 2 - 4 y(w,x) sin2(wb/2) b-2 (E-8) The "gain," IVA / Y|, is therefore: IVA / YI - 4 sin2(wb/2) b-2 (E-9) or IVA / YI - 4 sin2(ib/L) b-2 (E-10) where L - wevelength 2n/w (E-11) This relationship is shown in Figure E.1. The figure also shows the wavelength sensitivity of double differentiation, which defines the true form of vertical acceleration. Differentiation of a variable is very simple in the frequency domain: y'(w,x) - dy/dx = jw YO ejwx - jw y(w,x) (E-12) The amplitude response of a double differentiation is obtained by applying Eq. 12 twice: ly" / Y| - |iw iwl - I-w21 _ w2 _ (2n/L)2 (E-13) When the wavelengths are large relative to the RMSVA baselength, Eq. 10 and 13 yield similar results. In order for the difference to be less than 10%, the wavelengths must be at least 5.6 times longer than the baselength. For the QIr numeric, which uses a baselength of 2.5 m, this means that the transform approximates vertical acceleration only for wavelengths longer than 14 m, even though most of the "roughness" derives from shorter wavelengths. Thus, the name "RMSVA" is a misnomer, because the roughness statistic has virtually no relation to vertical acceleration of the profile. Eq. 10 also shows that the VA variable has no response to the wavenumber 212 true vertical acceleration VA = [ y(x+b) + y(x-b) - 2 y(x) ] / b2 x 0 0.0 0.5 1.0 1.5 2.0 2.5 Wavenumber x b - cycle/baselength NOTE: Wavenumber = I/wavelength Figure E.I. Sensitivity of RMSVA to Wavenumber 213 = 1/b and all multiples (harmonics) of this value. It has maximum sensitivity at wavenumbers .5/b, 1.5/b, 2.5/b, ... The VA variable does not have a bandwidth for an arbitrary elevation input, being equally responsive to wave numbers .5/b and 1000.5/b. The RMSVA filter is linear, but Eq. 5 is not because it adds two RMS numerics to yield the QIr statistic. Therefore, QIr does not have a true waveband response that applies to broad-band road inputs. (That is, if the Qir numerics that result for two separate inputs are known, there is no relation between those two numerics and the QIr value that would be obtained from the linear sum of the two inputs.) Nonetheless, the response of the QIr analysis can be calculated for a purely sinusoidal input by combining eqs. 5 and 10. (Note that the substitution of the ratio of output/input from eq. 10 into eq. 5 implies that the sinusoidal input is characterized by RMS amplitude.) (QIr + 8.54) / RMS Y = response to sinusoidal profile input = 4 x 6.17 sin2(G. 1.0/L) 1.0-2 + 4 x 19.38 sin2(, 2.5/L) 2.5-2 = 24.7 sin2(in/L) + 12.4 sin2(2.5./L) (E-14) Eq. 14 is shown plotted in Figure E.2a. While the figure shows that the Qir analysis amplifies the profile input for shorter wavelengths, it should be noted that there is substantially more road roughness content at long wavelengths when elevation is used to define profile. (See Appendix I, which contains the PSD's of the 49 test sections of the IRRE.) Eq. 14 can be re-written to show the relative importance of wavelengths to the QIr numeric, by considering a profile input defined by slope. Combining Eqs. 12 and 14 gives: 214 E E O E -Y. NI) co 0 0 2 5 .1 2 1 2 5 Wavenumber - cycle/m a. Sensitivity of Qlr to pure sinusoidal displacement cq 0 2 2 2 5 Wavenumber - cycle/m b. Sensitivity of Qlr to pure sinusoidal slope input Figure E.2. Sensitivity of QIr to Wavenumber 215 (QIr + 8.54) / RMS Y' - response to sinusoidal slope input [ 24.7 sin2("/L) + 12.4 sin2(2.5w/L) ] / w ' L 1 24.7 sin2(r/L) + 12.4 sin2(2.5n/L) 1 / 2w 3 L [ 3.95 sin2(W/L) + 1.97 sin2(2.5Y/L) I (E-15) Eq. 15 is plotted in Fig. E.2b. One of the motives for determining the sensitivity of an analysis to different wavelengths is to help determine whether the analysis is compatible with band-limited measurements. In this case, the question is whether dynamic profilometers such as the APL trailer can be used to directly measure RMSVA and QIr. In an absolute sense, they cannot. Fig. E.2a shows that the QIr analysis is not band-limited. The bandwidth of the APL profilometer is limited, however, such that it is not capable of transducing very short wavelengths. If these wavelengths contribute to the RMSVA or QIr numerics when measured statically, then measures made using the profilometers will be in error since these wavelengths are omitted. If, on the other hand, most of the RMSVA numeric derives from wavelengths that are transduced by the profilometer, then the error can be negligible. The factor that determines whether or not Qlr can be measured with a dynamic profilometer is the spectral content of the road itself. On roads having less short-wavelength roughness, the errors are slight, while on roads having significant short-wavelength roughness, results obtained from a dynamic profilometer will be more in error. The response to slope input shown in Fig. E.2b gives a fairly reasonable view of the significance of different wavelengths for typical road inputs. Effect of Measurement Interval. Eqs. 2 - 4 indicate that RMSVA can be computed using any baselength that is a multiple of the measurement interval (the distance between successive profile elevation measurements). The limiting case, of course, is where the baselength equals the measurement 216 interval. When the measurement interval is shorter, such that the baselength is an integer multiple of the measurement interval, Eq. 4 can be re-written: m-i m-i RMSVAb [ 1/(m - 2) 5: VA(ik)2 + l/(m - 2) 5 VA(ik+1)2 + 1/(m - 2) 7 VA(ik+2)2 + . ]1/2 k-i rn-i - [ 1/[ k (m - 2)]j S 5 VA(ik+j)2 ]1/2 (E-16) j=0 i=i where m = n/k (E-17) and it is assumed (for mathematical convenience in this discussion of measurement interval) that the quantity n is an integer multiple of k. Eq. 16 can be further simplified: k-I 2 (E-i2 RMSVAb = [ i/k 57 R. (E-18) where R. = [ i/(m - 2) 7 VA(ik + j)2 1 (E-19) The above equations have a simple interpretation, since Eq. 19 is equivalent to Eq. 4 for the case of k=i (baselength = sample interval). The RMSVA value obtained with a small sample interval, in which case k > 1, is the RMS sum of all of the possible RMSVA values that can be obtained by skipping data points. Although the RMSVA formulation has always been presented in terms of a finite number of data points [8, 25, 28], the definition of RMSVA given in Eqs. 2 - 4 can be extended to a limit, where the sample interval dx approaches zero. The "true" RMSVAb value is thus: k-i / "true" RMSVAb = Lim [ i/k 57 R.j/ (E-20) b 1Ik->O jO =02 217 Since the selection of the beginning point of the profile measurement is essentially random over a distance lying within the baselength b, as opposed to being systematically selected on the basis of profile properties, the best estimate of any particular R value must be independent of the starting point j. That is, the best estimate of Rj will be the same, whether the computation starts at the first profile elevation measurement (j=O), the second (j=1), or any arbitrary position between the start of the data set and a distance corresponding to the baselength b. This is true for a stationary signal, and qualifies as a valid "engineering assumption" as long as the length of the profile is much larger than the baselength. If the expected value of R. is independent of j, then all R. variables computed for a given (long) profile must have the same expected value, and thus: "true" RMSVAb = Lim { 1/k k E[R.2] }1/2 1 /k->-O = E[R.] (E-21) In other words, there is no bias error associated with having a profile measurement interval equal to the RMSVA baselength. The only error is a random one, which is determined by the (random) selection of a starting point for the RMSVA computation. If a profile has the same properties as a stationary random signal, the random error is inversely proportional to the square root of n, the number of independent elevation measures. The error is thus reduced by increasing n in either of two ways: 1) use a shorter sample interval, or 2) use a longer section length. In actuality, no profile is truly stationary, nor random. Therefore, the random error can be decreased by increasing the section length only to the extent that the roughness properties are consistent over the entire length, in accordance with the assumed stationarity. On the other hand, decreasing the sample interval will always bring the estimate of RMSVA closer to the "truth" for that particular segment of profile. Given the application of RMSVA, in which high accuracy for a short segment is not the primary motive, increasing the section length is preferable to decreasing the measurement interval when possible. This is because the 218 longer profile tends to better approach the assumption of a stationary random signal, and is less dominated by any singularities in its vertical geometry. Since the RMSVA numerics have been suggested as a means for calibrating RTRRMSs, there is another reason to use longer section lengths when possible, because the RTRRMS measurements also include random errors that are decreased with longer sections. Physical Interpretation of RMSVA and Qlr RMSVA. Even through the RMSVA statistic is not a measure of vertical acceleration, the VA "filter" has a very simple interpretation: it is equivalent to the mid-chord deviation that would be obtained from a rolling straightedge. As shown in Figure E.3, the deviation of the center of the chord is the difference between the profile elevation at that point and the average of the elevations at the two endpoints of the chord: MCD(x) = [ y(x+b) + y(x-b) 1/2 - y(x) (E-22) In comparing Eq. 22 to Eq. 1, it can be seen that the two differ only by the scale factor 2 b-2. Eq. 22 yields a numeric with units of deflection (mm) and the simple interpretation of the figure. "RMSVA" is simply the RMS value of a mid-chord deviation, as would be obtained from a three-point moving straightedge having a length of 2b. oIr. The Qlr numeric does not have any direct physical interpretation. It is a weighted sum of two RMS mid-chord deviations, based on chord lengths of 2.0 and 5.0 m. Since it has been used primarily for the calibration of RTRRMSs, it can be thought of as a reference RTRRMS, particularly since the measures are reported as "counts/km." One problem with this interpretation is that the QIr numeric has certain characteristics that are not reflected in RTRRMSs. For example, wavelengths of 0.5 m are completely "invisible," as can be expected from the concept of RMSVA as shown in Fig. E.3, even though they affect the measure obtained from a RTRRMS. Also, the VA variable defined in Eq. 1 is defined at all times by the profile at three discrete locations. Thus, a singular roughness event, such as a big 219 b -- b a. Schematic Representation of a Mechanical Rolling Straightedge MCD(s) = Mid Chord Deviation = measure v=moving reference y(x-b) t ytx+b) y(x) Y MCD(x) = [ y(xb) + y(x-b)1/2 - y(x) x b. Geometry of Mid Chord Deviation Figure E.3. Physical Model of RMSVA analysis. 220 pothole, will cause only three large VA values. A RTRRMS, on the other hand, will respond to the singularity for some time after encountering it. The QI* Calibration Method. All of the road roughness data measured in the PICR Project, as reported and stored in the Brazilian computer data files, are on a scale called QI QI* is the calibrated roughness measure obtained with the RTRRMSs used in that project, which were the Opala/modified Maysmeter systems described in Appendix A. When operated at 80 km/h (96% of paved road length was measured in the vehicle cost study at 80 km/h [14]), the direct ARS measures (as read directly from the roadmeter display) of the RTRRMS were transformed to QI* through the use of a linear equation having the form: QI* = A + B ARS80 (E-23) The values of A and B were found for each RTRRMS during "calibration" by regressing measures of QI (in the early part of the project) or QIr (in the later part of the project) against the ARS80 measures obtained from that RTRRMS on special calibration sites that were periodically re-measured to determine current QI/QIr roughness levels. The calibration sites were all on paved roads and had mostly asphaltic concrete surfaces. Only a few sections had double surface treatment construction, and these were usually omitted from calibration computations because they were "outliers," deviating from the correlation equation found for the majority of the sites. On unpaved roads, the RTRRMS was typically operated at 50 km/h (94% of the total length measured in the vehicle operating cost study [14]). A single "speed correction equation'" E [ARS80] = -0.275 + 1.04 ARS50 (E-24) was used for all RTRRMSs, and surface types, to rescale the 50 km/h measurement to an approximation of what the RTRRMS might have measured at 80 km/h. (Eq. 24 requires the ARS measures to have units of m/km, as used for presenting all of the IRRE data. The original version [7] used -275 as the 221 offset, based on ARS measures with the units: mm/km.) To determine QI, the estimate of ARS80 from Eq. 24 would be re-scaled according to Eq. 23. When a speed of 50 km/h could not be used, a third standard speed of 20 km/h was allowed. In this case, a third conversion equation was also needed: E [ARS50] = 1.023 + 0.658 ARS20 (E-25) The estimate of ARS50 is then rescaled to an estimate of ARS80 using Eq. 24, which is in turn re-scaled to QI using the calibration equation determined for that RTRRMS (Eq. 23). The roughness range used in determining the critical "calibration equation" for Eq. 23 was much less than the range covered by the RTRRMS, because only paved roads were used. The roughness of the calibration sites never exceeded 100 counts/km, while many of the QI values obtained for unpaved roads were higher than this, ranging up to 300 counts/km. Therefore, characteristics of the RTRRMS that were dependent on road roughness were not corrected by this procedure. To maintain consistency, all RTRRMSs were based on the same make, model, and year of passenger car. When vehicle components such as shock absorbers were damaged or wore out, they were replaced only with OEM equivalents. Mathematically, the QI* roughness scale cannot be completely quantified, because it depends in part on the calibration procedure (Eqs. 23 - 25), and in part on the response properties of those particular RTRRMSs during the PICR. Since different methods were used on different surfaces, the QI* scale is defined by several procedures, each of which was applied over some of the conditions. By surface type, these are: Asphaltic Concrete. The QI measures are more-or-less equivalent to the Qlr scale, since the calibration equation (Eq. 23) is valid over the roughness range (0 - 100 counts/km), surface type (asphaltic concrete), and measurement speed (80 km/h) that were used to obtain the actual field measurements (96%). Surface Treatment. The calibration sites included a few surface 222 treatment sites, but the roughness measures were often excluded from the regression equation because there was poor agreement between the ARS80 measures from the RTRRMS and the QI/QIr reference measures. Nearly all of the ARS measures were obtained at 80 km/h in the PICR project; thus, the QI values obtained are ARS80 measures rescaled according to Eq. 23. Because the calibration sites did not include enough surface treatment sections, QI is determined by 1) the response of the Opala (as maintained in the PICR project) at 80 km/h over a surface treatment road, and also 2) its response over asphaltic concrete roads at that speed. Unpaved Roads. Nearly all (94%) field measurements on unpaved roads in the user cost survey were made at 50 km/h. On these roads, the QI* values are determined by: 1) the response of the Opala at 50 km/h over unpaved roads, 2) its response at 80 km/h over asphaltic concrete roads, and 3) an aggregate speed conversion equation (Eq. 24). MEASUREMENT OF QIr IN THE IRRE Technical Requirements for Measuring QIr Measuresent Interval. The effect of profile measurement interval on the QIr numeric has been tested and reported previously, with the conclusion that a 500 mm interval is sufficient [8]. The analyses of the Qlr computation method, presented in the previous section (Eqs. 16 - 21), prove that use of alternate intervals cannot bias the expected value of the QIr numeric, but that repeatability should be improved when a shorter interval is used. Profiles obtained from the TRRL Beam (100 mm intervals) and the APL 72 system (50 mm intervals) were decimated to yield profiles with 500 mm spacings. QIr numerics computed before and after the decimation agreed closely, as had been found earlier. Precision in the Elevation Measurement. Based on experience with QCS numerics, it was anticipated that the precision needed in profile measurement for acceptable accuracy in QIr depends on the roughness. A candidate specification was considered in which the required precision of the profile elevation measurement is simply proportional to the roughness of a road, when 223 expressed as QIr. An analysis of the profile data obtained from the TRRL Beam was performed to determine: 1) if this type of specification is reasonable, and 2) if it is reasonable, what quantities are involved? In this analysis, the precision of the measurement was assumed to be limited solely by the quantization of the continuous height variable into digitized quantities, which were originally 1.0 mm. The random measurement errors that also degrade precision were not considered. For each of the 28 measured profiles, the QIr value obtained with the original profile was used to determine a new quantization level (greater than 1 mm). The profile was then quantized to the nearest multiple of this new level, and re-processed to yield a new QIr numeric. Figure E.4 shows the results for four levels of increased quantization (degraded precision). In all cases, the effect of the degraded precision is an increase in the computed roughness numeric. The changes were calculated from the difference in the (solid) quadratic regression lines and the (dashed) equality line (x = y), and were found to be nearly constant across the range of roughness when expressed as a percentage. (For example, for the case of precision = 0.03 Qlr, shown in Fig. E.4b, the errors were 1.8% at QIr = 50, and 1.9% at QIr =100, 150, and 200 counts/km.) This indicates that the candidate method of specifying required precision in proportion to roughness is valid. For QIr accuracy within 1.0%, the precision (mm) should be about 0.02 QIr (counts/km), while for accuracy within 2%, the precision should be less than 0.03 Qir. Thus, on the smoothest sites, which had QIr values near 20 counts/km, the actual measurement precision of 1.0 mm probably led to numerics that are several percent higher than the "true" QIr values. A measurement precision of 0.5 mm would have been better. At the other end of the scale, where roughness levels were greater than 150 counts/km, a measurement precision of 3 mm (less than 0.02 QIr) gave the same results as the original precision of 1 mm. Sumary of QIr Data The summary QIr numerics that were obtained from four methods of profile measurement are presented in Table E.1. Some of the paved sections were measured before and during the IRRE via rod and level. Those measured prior are indicated as "RL 1" and those measured during the IRRE are designated "RL _ 224 - o - - - 0 ON O N 0. Ecrr-- E c-4 3 10~~~~~~~~~~~ 00 0 MO cm E o X ~ BIAS ERROR < 0.7% BIAS ERROR < 2% E 0 Ur) I 0. .4 7i 0 i-4~~~~~~~~~~~~~~~~~~I 0 0 100 150 200 250 0 50 100 150 200 250 Qlr from original Beam Profile Qlr from original Beam Profile a.-PRECISION (mm) = .02 Qir (counts/km) 6. PRECISION (mm) = .03 Qlr E o E a.. 0 °. ; C / a- -O'-' 0 5 10 102020 0~ 50 10 1070 5 Qir / o B E ~~~BIAS ERROR < 5% E~ i 31A5 ERROR <19% .4- L4- Lo ~ ~ ~ IL O 50 1600-- 150 200 250 0 50 100 150 200 250 Qlr from original Beam Profile Qlr from original Beamn Profile c.PRECISION (mm) = .05 Qlr (counts/kim) a.PRECISION (mm) = .1 Qir (counts/km) Figure E.4. Effect of Profile Measurement Precision on the QI numeric 225 Table E.1 Simvmry of the Qlr Nu&nsrics Obtained In the IFN Left WhueeI rmk Right Whelfrack Bth Wheelfracks: Average site Static FL IR ~2 Bow A 72 A 25 Static RL I RL2 Bem A 72 A 25 Static RL I RL 2 Bun A 72 A 25 CAO 1 47 48 45 ... .. 46 57 64 49 .... 50 60 52 56 47 .. .... 53 CAO2 68 67 69 .... 59 46 55 58 53 .... 70 44 62 63 61 .... 64 45 CPO3 84 79 89 .... 72 77 81 83 78 .... 78 69 82 81 84 .... 75 73 CAO4 78 77 80 77 70 71 68 69 69 66 64 62 73 73 75 71 67 67 CAO5 93 98 94 87 96 78 80 80 80 80 69 52 86 89 87 84 82 65 CA06 106 108 106 104 101 83 88 92 84 88 89 72 97 100 95 96 95 78 CA07 32 31 32 .... 43 35 25 25 25 .... 31 28 28 28 29 .... 37 31 CA08 26 26 26 .... 31 28 28 28 28 .... 30 23 27 27 27 .... 30 25 CA09 45 46 43 .... 60 37 33 34 31 .... 37 35 39 40 37 .... 49 36 CAIO 39 40 39 .... 54 46 36 41*33 34 44 33 38 40 36 .... 49 40 CAII 81 84 78 .... 56 46 64 64 64 .... 72 44 72 74 71 .... 64 45 CA12 18 16 15 22 15 25 17 15 18 .... 15 22 17 16 17 .... 15 23 CA13 17 17 18 .... 16 17 18 19 17 .... 17 17 18 18 17 .... 16 17 TSOI 45 45 .... 45 43 40 47 47 ..... .. 40 46 46 . . ....... 40 TS02 59 599.. .... 51 46 56 56 ... .. 49 45 57 57 .... .. 50 46 TS03 58 58 ......55 54 50 50 .. ......48 54 54 ......... 51 TS04 56 55 .... 56 50 54 63 63 .. . . .... 49 59 59 ... ...... 51 TS05 64 65 63 65 68 57 53 54 51 .. 58 52 59 60 57 .. 63 55 TSO6 37 39 35 38 35 30 35 34 35 35 31 31 36 36 35 36 33 30 TS7 36 39 33 37 35 32 4 1 39 42 .. 37 33 39 39 38 .. 36 32 TSD8 43 43 44 .. 39 35 47 47 48 .. 43 36 45 45 46 .. 4 1 36 1S09 48 55 42 .. 39 38 42 43 42 .. 42 44 45 49 42 .. 4 1 4 1 TS1O 4 1 41 .. .... 42 35 42 42 .. .... 4 1 34 42 42 .... .. 42 34 TS11 25 25 ...... 23 20 26 26 ......25 18 26 26 .. ... 24 19 TS12 26 26 ...... 23 24 24 24 ......22 17 25 25 .. ... 23 20 - GRIl1 52 .... 52 .... 33 44 37 .... 32 42 .. 38 45 .... 42 .. .... 41 GRD2 45 .... 45 .... 47 26 41 .... 41.. .. .. 22 43 .... 43 .. .... 24 GF03 114 .... 114 .... 74 81 71 .... 71 ... .. 65 93 .... 93 .. .... 73 GR4 95 .... 95 .... 88 73 71 ... 71 .. .... 60 83 .... 83 ... .. 66 GRI5 117 117 * 117 116' 119 91 108 112 0108 105 ... 92 112 115 112 110 ... 92 GR06 108 .... 108 .... 112 82 98 .... 98 .. .... 90 103 .... 103 .. .... 86 GF7 86 .... 82 89 62 43 52 .... 52 52 .. 34 69 .... 67 71 .. 39 GRI8 55 .... 55 .... 48 41 48 .... 48 .. .... 33 51 .... 51.. .. .. 37 GRI09 119 .... 119 .... 105 65 102 .... 102 .. .... 73 110 .... 110 .. .... 69 GRIO 96 .... 96 .... 102 77 73 .... 73 .. .... 78 84 .... 84 .... .*. 77 GRll 202 .... 202 .... .... 158 187 .... 187.. .. .. 136 194 .... 194.. .. .. 147 GR12 205 .... 205 205 .... 138 176 .... 181 172 ... 140 190 .... 193 188 ... 139 TEOI 54 .... 50 59 49 57 50 481*51 52 43 50 52 .... 50 55 46 54 TE02 49 .... 49 .. 43 44 47 .... 47 *... 51 36 48 .... 48 .. 47 40 TEO3 .100 .... 102 99 99 69 76 .... 79 73 75 55 88 .... 90 86 87 62 TE04 93 .... 93 ... 107 82 85 .... 85 .... 76 67 89 .... 89 ... 91 75 TEOS 185 182' 189 ..... 161 184 182* 185 .... .... 154 185 182 187...... 157 TE06 240 .... 240 .. ... 205 202 .... 202 202 .... 160 221 .... 221 .. ... 182 TEN7 61 .... 61 .... 56 53 47 .... 47 .... 53 51 54 .. 54 .. 55 52 TE08 67 .... 67 ... 64 58 49 .... 49 .... 51 41 58 .... 58 ... 58 49 TEO9 109 .... 109 ... 99 78 110 .... 110 .... 80 74 109 .... 109 ... 90 76 TEIO 156 .... 156 ... 135 84 120 .... 120 .... 98 85 138 .... 138 ... 117 84 TEII 163 .... 170 156 139 118 98 .... 98 97 99 71 130 .... 134 126 119 94 TE12 164 .... 164 ... 101 131 117 .... 117 .... 110 94 140 .... 140 ... 105 112 *rod and level measures using 100 mm interval between elevation measurements. 226 2." In addition, 6 wheeltracks were measured by rod and level using a measurement interval of 100 mm. These are also shown in the "RL 1" column, and are identified with an asterisk. The labels "Beam," "A 72," and "A 25" indicate profiles measured with the TRRL Beam, the APL Trailer in the APL 72 configuration, and the APL Trailer in the APL 25 configuration. The results indicated under the headings "Static" are averages of the numerics obtained with the static profile measurements, that is, rod and level and the TRRL Beam. When examining correlations with other measures and statistics, the numbers under the "Static" heading were used. Accuracy of QIr Computed from Statically Measured Profiles Repeatability with Rod and Level. Most of the sources of error that plague roughness measurements using RTRRMSs are eliminated when profiles are measured statically with rod and level: the same roughness computation method can be used, eliminating variations due to different definitions of roughness; and surveying equipment is sufficiently interchangeable to eliminate problems of reproducibility. The only remaining variation is the repeatability that can be achieved in measuring a profile. The repeatability that can be achieved is, in this case, the accuracy of the roughness measurement. Since most of the paved sites were profiled twice with the rod and level method, the IRRE data give an idea of the repeatability achievable in using QIr as a roughness measure. Figure E.5a shows the comparison of QIr measures obtained in two independent rod and level surveys. As in other plots, the dashed line is the line of equality (x=y), while the solid line is the "best fit" as obtained with a quadratic regression. The RMS errors shown in the figures are with reference to the line of equality, rather than the regression line, since regression methods would never be used to "correct" profile-based numerics. Note that the accuracy limits shown in the figures apply only to the IRRE section length of 320 m, and should not be considered universal for all section lengths. For roads whose roughness is more-or-less constant, it can be expected that better accuracy would be obtained for longer test site lengths, because the random sources of variation would tend to average out. The expected change in accuracy is proportional to the square root of length, 227 > 0-~ ~ ~ ~ ~ ~~~~~0 0~~~~~~ 0 50 10 5 0 5 0 S 0 0 E E 00 C9 RMS RMSf Diff.14.7 counts/km Dif N MSDff 1. counts/km/ 00 4d 0 5 160 20 aa Ro &f Lee Reetblt bCmarsnofBa Cy - C) I I LO F4RMS Digure 4..75.ounts/k C r RMS Diffen 1If. cn5str nts/km 228 0 .0 __ _ __ _ _ 0 50 100 150 200 0 50 100 150 20025 Qir from SttiRo &M evsuel Qir from StRRLc Beamue a. Rod . ALel Repatbiitb C AParso of2ea F' igSurff 11.3 Counts/kmn of QIMaurmnt rom Diff.ere19. consts/kmens 0228 such that the random variations indicated in the figure would be cut in half if the section length were increased by a factor of four. On the other hand, larger errors should be expected for shorter sections. Validation of the TRRL Beam. Figure E.5b compares the Qlr numerics obtained with rod and level and the TRRL beam. Approximately the same repeatability is obtained as with repeated measures with rod and level, indicating that the TRRL Beam is a valid means for measuring longitudinal profile for the purpose of computing QIr. Direct Computation of Qlr from Dynamically Measured Profiles APL 72. Figure E.5c compares the QIr numerics computed from the profile signals obtained from the APL Trailer in its APL 72 configuration with the QIr numerics computed from the statically measured profiles. The measures obtained from the APL 72 are lower than those obtained statically, as evidenced by the fact that the quadratic regression line lies below the line of equality. In addition to this bias error (for the rougher sites), the amount of scatter (random error) is much greater than when static profile measurement methods are used. The results obtained with the APL 72 systenl can be explained by the power spectral density (PSD) plots presented in Appendix I. At 72 km/h (20 m/sec), the APL Trailer attenuates inputs having wavelengths shorter than 1.0 m, as shown in Figure G.1. When profiles were obtained by the TRRL Beam using an interval of 100 mm, the PSDs obtained from the APL 72 can be compared with static measures for wavelengths shorter than 1.0 m (wavenumbers higher than 1.0 cycle/m). The comparisons verify that the APL 72 is attenuating the profile for those short wavelengths. Since the QIr numeric is influenced by wavelengths shorter than 1.0 m (Fig. E.2b), it includes the full amplitude of the shorter wavelengths when computed from statically measured profiles, but is "missing" some of the amplitude when measured dynamically, due to the limitations in the response of the APL Trailer. Note that the wavelengths attenuated by the APL 72 do not influence the APL 72 numerics normally computed by LCPC. 229 APL 25. Figure E.5d compares the QIr numerics computed from the profile signals obtained from the APL Trailer in its APL 25 configuration with the QIr numerics computed from the statically measured profiles. The errors indicated when QIr is computed directly from the APL 25 signal are also low, resulting in larger errors than with the APL 72. The reason for this can also be seen by examining the PSD plots shown in Appendix I. The APL 25 attenuates wavenumbers below 0.07 (wavelengths longer than 14 m), which are transduced by the static measurement methods, and also the APL 72. The PSD plots also indicate that the APL 25 signals are consistently low for wavenumbers between 0.4 and 2 cycle/m (wavelengths from 0.5 - 2.5 m long). These wavenumbers contribute little to the CAPL 25 numeric, and therefore the erroneous response is probably not a problem when the APL 25 system is used solely for measuring the CAPL 25 coefficient. Overall, the APL 25 profile signal simply doesn't cover the range required by the QIr analysis. Other Alternatives for the Calculation of APL QI Values It is useful to recall that the choice of the two RMSVA baselengths (1 m and 2.5 m) and the numerical coefficients of the QIr equation (Eq. E.5) were determined empirically during a correlation study (which took place before the IRRE) between the GMR-type Profilometer results and the RMSVA values obtained from rod and level profiles. These regressions reflect the spectral contents of the profiles as measured by the rod and level method, the Profilometer, and the various factors that influenced the original QI numeric. Because the transfer functions of the APL are different from those of the rod and level system and of the TRRL Beam, the spectral contents of the profiles are also different, and it is not surprising that the differences shown in Figs. E.5c and E.5d were found. A new statistical analysis has been performed by the French Bridge and Pavement Laboratory (LCPC) in order to determine a better equation for estimating QI when using the APL Trailer. Multilinear regressions were computed between rod and level QI values and the RMSVA1 0 and RMSVA2.5 values as computed from APL 25 and APL 72 profiles. The statistical 230 population of the test sections on which the computations were carried out is the same as the one which was considered for the comparisons between rod and level QIr and TRRL Beam QIr. Figure E.6 shows that it is possible to find several estimators for QI which are different from those used for the rod and level profiles, while still using the 1.0 and 2.5 m RMSVA baselengths. Note that the standard errors shown for the paved sites are about the same as obtained for the repeated rod and level measures, and for the comparisons between TRRL Beam and rod and level. If QI is measured in the future with APL systems, further improvement might be possible by optimizing the RMSVA baselengths through a study similar to the one which was done for the rod and level method [7]. The CP2.5 coefficient, described in Appendix G, can also constitute an estimator for QI. Figure E.7 gives the correlation between QI determined for right and left tracks on all sites CA, TS, GR, TE measured with the TRRL Beam and the CP2.5 values obtained from APL 72 signals. The value of the coefficient of correlation reveals a significant linear relationship between the two scales. No bias induced by surface types was visible. I CALIBRATION OF RTRRMSs A primary purpose of a profile-based roughness numeric such as QIr is viewed in this report as being for the calibration of RTRRMSs, using a "calibration by correlation." In a calibration by correlation, the "raw" measures from the RTRRMS are used to estimate what the reference measure would be, based on a regression equation. The objective is to produce the most accurate estimates of "true roughness," over the entire range of conditions that will be covered. To this end, one or more regression equations must be used to estimate the "truth" from the RTRRMS "raw" measure. In this case, QIr is the candidate for "true roughness." Before testing the calibration by correlation method, results are presented using the QI* procedures described earlier. 231 ALL TYPES OF SECTION . CA A:;D Ts S -CTONS QI 01 APL 25 - -71.61+13.0 RMSVA (1)+25.43 RMSVA (2.5) QI 01 APL 25--69.05+7.87 RMSVA(1)+44.37 RMSVA(2.5) 2 ~~~~~~~~~~~~~~~~2 2 = .88 r = .96 | zzz z / RMS Diff. - 4.6 counts/km C), ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C), nso / * o / ~~RMS Diff. =12.3 counts/km 0 «o *ono o so *o0 Ql Rod and Level QI Rod and Level =CP TS .=TE G R CA AND TS SECTIONS 4 o r 98 CY * S .RMS Diff. 4.9 counts/km 0 50 *00 15 00 *s0 APL QI APL 72 Figure aL6. Comparison of QI values calculated from rod and level with QI values calculated from APL.25 and APL 72 profiles 232 ALL SECTIONS INCLUDED CA, TS, GR, TE CP (2.5) = 14.0 + 1.06 * QI 160 120 C P 2.5 80 RMS Diff. = 14 CP 40 40 80 120 160 Figure E-7. Comparison of QI values calculated from TRRL Beam profiles with CP (2.5) derived from APL 72 signal 233 Calibration Using the QI* Method The QI* calibration method was tested by adopting the procedures followed in the PICR project [7], using the RTRRMS speeds that were used for the majority of the PICR roughness measurements: 80 km/h on paved roads and 50 km/h on unpaved roads [14]. Using the data obtained during the IRRE, a calibration equation was determined for the five Opala and Caravan-based RTRRMSs that were operated at 80 km/h on the Asphaltic Concrete (CA) surfaces (Eq. E-23). ARS80 measures on the paved sites were rescaled according to that equation, while ARS50 measures on the unpaved surfaces were rescaled according to Eqs. 23 and 24 together. Figure E.8 shows how the QI* numerics compare with the profile-based QIr reference. The four plots in Figure E.8 indicate that the QI* calibration method results in a scale that is not equivalent to QIr on all surface types. Figs. E.8a and E.8b show that the non-equivalence of gravel and earth surfaces (GR and TE) was evident mainly at high roughness levels. This effect can be attributed to the inaccuracy of the speed conversion used [14]. The four outliers on surface treatments are again the result of the tuning of the Opal vehicles to a 2m periodicity (corrugation). The PICR method required that the calibration (linear regression obtained on CA surfaces) be extrapolated to cover other surface types and a wider range of roughness amplitude than was covered in the actual calibration. Also, the single speed correction equation (Eq. 24) introduces bias errors that are unique for each RTRRMS. The figure also shows that the QI* calibration method does not rescale the ARS measures from the different RTRRMSs the same way; the "calibrated" QI* numerics depend on both the procedure and the response properties of the individual RTRRMS. Thus, the method does not allow comparison of roughness data obtained from different sources. Due to differences that occurred only on the CA sites at 80 km/h, the nearly identical "raw" ARS measures obtained with the BI and NAASRA roadmeters (the measures are compared in Appendix C) on the rougher unpaved roads are rescaled differently, such that the QI* numerics obtained from the BI units tend to be less than the reference QIr measures, while the QI* numerics from the NAASRA unit are greater than the QIr measures. 234 E E 0" mCA O" mCA + t o o TSA v) o TS c A / o * GR o A GR 0 GR0 0 0 + TE + 0 ° + TE A A 0 .4~ Al /- E E 0 0 -,,I g m CA 0" m CA uz- v,> o GR GR :3 ' TE / M TE L. // a 0 100 100 150 2003 QIlr fromn Profile - counts/km Qir from Profile - counts/km a.C. pAlA- Ays-e #. CALAMAY-NAASRA Fu e ETEE ATE 2 o 00 L0 0~~~~~~~~~~~~~~~- : 0Y o 0 20 30 IY o1020 '0 oir fom Prfile couts/kmQlr fom Pofile- couts/k /. CAAVNBID CRVA AAR Fiur -8 CmarsosbewenQIfom~ th7TRS n Q rmpoie a::~~~~~~~~~~~~~~~~~~~ F-O A~~~~42A I- V~23 Although the QI* numerics obtained from the Opala systems differ from those obtained with the Caravan systems, the QI* calibration method does rescale the three Opala-Maysmeter ARS measures about the same. (The QI data from the third Opala-Maysmeter system are not included in the figure, but showed the same relation to QIr as the other two.) This is the critical finding, in terms of the quality of the PICR roughness data, since it implies that the QI* data collected in the PICR project from a fleet of Opala-Maysmeter systems is internally consistent. That is, the QI calibration succeeds in terms of bringing the measures from different Opala-Maysmeter systems into agreement, even though it fails in bring measures from other RTRRMSs into agreement. In summary, the QI calibration method probably helped to maintain a roughness scale during the PICR project that was consistent and reasonably stable with time. The method requires that the RTRRMS have response properties very similar to the Opala-Maysmeter system as maintained at GEIPOT, so the method is not valid for other RTRRMSs, and should not be used in future work. The QI* scale is not completely equivalent to the QIr scale on three of the four surface types that were included in the IRRE. (This has largely been compensated in subsequent work [14].) Calibration through Correlation The comparisons between ARS measured with four of the RTRRMSs and QIr are illustrated in Figures F.9 - 12. Results from the Caravan-BI system (not plotted) are virtually the same as for the Caravan-NAASRA system. Results for the two Opala-Maysmeter systems that are not plotted are generally similar to those of the system that is shown in the figures. In all plots, the "static" Q:r values from Table E.1 were used. Comparisons with the two single-track RTRRMSs (BI Trailer and BPR Roughometer) are on the basis of single wheeltracks, while those with the two-track RTRRMSs use the average QIr for both wheeltracks. Thus, the plots involving the trailers generally have twice as many data points. In each figure, the solid curved line is a quadratic regression line obtained from all of the data points shown, based on minimizing the RMS error in estimating QIr. 236 o o CA g i CA r') o TS r TS *GR *GR o + TE ao + TE o- 0 04 ~~~A AN OC ++ + +~~~ O ' w 0 in 0 0 10 20 30 40 0 10 20 30 40 ARS20 - m/km ARS20 - m/km a. Opala-Maysmeter #2 b. Caravan-NAASRA O 0 )x CA + ol X , o + x* TS E E - 0C lO 20 30 4050 0 lGOR '%AR2 -. m/k AR,, - /k Figure E.9.xamplcalirin p x TE 2374++jCN C + =3 ~~~ + + o 0+ 0 A A ~ wxA .)A' *TS M +At £ *GR + x TE 0 ~~~X~~~~CI~~~IB--I 0 1020 3040 50 0 10 20 30 ARS20 -Mr/km ARS20 - rn/km Figure E.9. Example calibration plots to estimate QIr from AS0 237 o" m CA 0 m CA o 0 ) eo TS o TS * GR * GR o + TE o + TE o 0 0 50+Jel 0e +~~~~~~~~~~~4 0 0~~~~*4 0 10 20 30 0 10 20 30 ARS32 - rn/km ARS32 - m/km a. Opala-Maysmeter #2 b. Caravan-NAASRA O t x CA 0 ) O* oTS r * m x CA E + GR + E * TS -) + x TE * + GR co ~~'Lx 0' o >% ~~+ o m x TE o 0 I0 0 0 ~~~~~0 0 10 20 30 40 0 5 10 15 20 ARS32 - m/km ARS32 - m/km c. B Trailer d. BPR Roughometer Figure E.10. Example calibration plots to estimate QIr from ARS32. 238 o m CA m *CA o 0o TS o TS * GR * GR o + TE o + TE o ~~~~~0 I.- cY ++ Oc + O A a 0 _ _ _ _-__ _-_ _ _-_ __- 0 10 20 30 0 10 20 30 ARS50 - m/km ARS50 - rn/km a. Opala-Maysmeter #2 b. Caravan-NAASRA o" inxCA0 O - en x CA 'r') * TS e * TS IC | &x Xo + G E xeG TEG A A 0 0~~~~~~~~~~. A xTE aI + t C A~~~~~+X o 0 o 0U0 - 30 0 4 6/k 10 ~~RS0 m/mAR5 ' m/k c. Bl Trailer d. BPR Roughometer Figure E.11. Example calibration plots to estimate QIr from ARS50. 239 on m CA + o TCA a TS + 4T A GR AR GR o + TE + + TE I 0~~~~~~~~~~~~~~~~ A o . 0 5 10 15 2 4 6 8 10 ARS80 - m/km ARS80 - m/km a. Opala-Maysmeter #2 b. Caravan-NAASRA Figure E.12. Example calibration plots to estimate Qlr from ARS80. 240 These four figures lead to the following observations: Overall correlation. By and large, QIr is highly correlated with the ARS numerics obtained from all types of RTRRMSs that participated in the IRRE. Most of the data points lie close to the regression curve in each figure. Error distribution. Errors, as defined by the scatter about the regression curves in the vertical direction, are fairly uniform across the roughness range. Therefore, least-squares regression models should assume equal significance of error across the scale. Transformations of the variables that change the weighting of error, such as linear regressions of log values, should be avoided (for calibration purposes) because they place less priority on the errors on rougher roads. Sensitivity to surface type. Surface type systematically affects the regressions in most of the plots. The data points for the asphaltic concrete (CA) roads typically lie above the regression line (indicating that the QIr analysis is relatively more sensitive than the RTRRMS to roughness on those surfaces), while points for the surface treatment sites (TS) lie below the line (indicating that the QIr analysis is less sensitive). The implication of this finding is that separate calibrations for each surface type can give better accuracy. The degree of sensitivity to surface type varies with the RTRRMS and the speed, and generally is worse at the lower speeds. The effect is minimal at 50 km/h, such that the bias is less than the random error (scatter about the regression line) associated with individual sites. The effect of surface type can be expected when considering the sensitivity of the QIr analysis to wavenumber, shown in Fig. E.2b. The sensitivities of the RTRRMSs are not known precisely, but are generally very similar to that of the RQCS described in Appendix F, particularly in terms of the range of wavenumbers sensed by the RTRRMS. Figure F.2 in that appendix shows the sensitivity of the simulated RTRRMS to wavenumber at all four of the RTRRMS speeds. The bandwidth of a RTRRMS is somewhat broader than that of the QIr analysis, such that the QIr numeric reflects a narrower portion of the spectrum than affects a RTRRMS. 241 The PSD plots in Appendix I indicate that the CA, TS, and unpaved (GR and TE) roads have different aggregate spectral characteristics. The CA surfaces have a higher proportion of roughness contributed at low wavenumbers (longer wavelengths, such as 5 m where the QIr has its maximum sensitivity (Fig. E.2b). The QIr "tunes in" to this portion of the spectrum, resulting in an upward bias for this surface type. The TS sites have more of the roughness deriving from higher wavenumbers, to which the QIr analysis is less sensitive. Comparison of single-track trailers. Although both the BI Trailer and the "BPR Roughometer" made by Soiltest, Inc., are similar in appearance and are both based on the BPR Roughometer [13], they contrast in performance. The Soiltest BPR Roughometer, which proved to be too fragile for the roads covered in the IRRE (see Appendix A), produced measures that had the least correlation with QIr. On the other hand, the TRRL BI Trailer measures showed about the same correlations as the RTRRMSs based on passenger cars. Outliers. The four roughest surface treatment sites appeared as "outliers" when measured by the Opala-Maysmeter systems at 80 km/h (Fig. E.12a). (Although the results are plotted for only one of these systems, all three showed the same behavior.) On these sites (TS01, TS03, TS04, and TS05), the RTRRMS responded much more than the QIr analysis. The power spectral density (PSD) plots shown in Appendix I for these four sites are similar, and differ from the PSD plots for most of the other test sites. All four have more of the roughness concentrated at higher wavenumbers, to which the QIr analysis is less sensitive. Further, three of the sites show a singular peak at wavenumber 0.5 cycle/m (2 m wavelength, which appears as a frequency of 11.1 Hz when traversed at 80 km/h). The presence of a singular peak at 0.5 cycle/m signifies that the road site has a periodic disturbance occurring every 2 m. Although the Qlr analysis shows a near-maximum gain at that wavenumber (Fig. E.2b), it is not as sensitive as the typical passenger car at that frequency [9]. Due to nonlinearities, a passenger car can over-respond when subjected to a purely periodic excitation. This is particularly true with lightly damped vehicles. From the simple comparison of the ARS80 and RARS80 numerics in Appendix F, 242 the Opala vehicle is seen to be less damped than the RQCS, as evidenced by the higher ARS80 numerics. This indicates that stiffer shock absorber could be used with the Opala, with the expected result of bringing the "outliers" closer to agreement with the rest of the ST data. Correlations and Accuracy. Table E.2 presents the r2 values obtained when the QIr numerics are regressed against the ARS numerics from the RTRRMSs using a linear prediction model. The regressions were performed using only the data corresponding to the combination of speed and surface type indicated. When the surface type is indicated as "ALL," then the regression included all measurements made at that speed, and the r2 describes a calibration across surface type. Table E.3 presents the r2 values obtained when a quadratic model is used. Both models use a simple least-squares error approach, but the quadratic model is slightly more versatile, as it involves less in the way of assumptions about the linearity of the RTRRMS. In comparing the two tables, it can be seen that there are a number of cases where much better correlation is obtained with the quadratic model, including most of the regressions performed for TS surfaces. Since there is no real penalty for using the quadratic model (other than a more complex computation--typically performed by computer), the quadratic model is recommended to allow for the occasional case in which a linear model would not fit the data or would lead to an erroneous extrapolation. The correlation coefficients are presented as one basis for comparing the accuracy that can be obtained. Yet it should be understood that r2 values are only one measure, with limited utility. The r2 value is essentially the fraction of the variances of the two variables that is accounted for by the (linear or quadratic) regression model. Thus, r2 values depend both on the agreement between the measures (as related by the regression model) and the range of roughness included in the data set. Since r2 values can always be improved simply by adding more very smooth and very rough sites, they should never be used as the sole basis for quantifying a calibration quality. The actual accuracy of an estimate of QIr based on an ARS measure can be defined as the Standard Error: the RMS difference between the estimate of QIr and the true QIr value. The standard errors associated with the quadratic model are presented in Table E.4. Whereas the r2 values were dimensionless, 243 Table E.2. R-Squared Values Obtained from Linear Regressions Between QI and ARS from the RTRRMSs. Opala Passenger Cars Caravan Car Single-Track Surface with Modified Maysmeters with 2 meters Trailers Speed Type MM 01 MM 02 MM 03 BI NAASRA TRRL BI BPR 20 CA 0.9068 0.9343 0.9451 0.9191 0.9242 0.8552 0.7226 TS 0.8484 0.8439 0.9295 0.8731 0.8984 0.8104 0.6724 GR 0.9814 0.9262 0.7785 0.9617 0.9636 0.9121 0.8540 TE 0.8555 0.9675 0.9572 0.9408 0.9444 0.8993 0.8929 ALL 0.8830 0.8692 0.8437 0.8848 0.8869 0.8404 0.7244 32 CA 0.9435 0.9695 0.8824 0.9517 0.9615 0.8790 0.6621 TS 0.8975 0.8928 0.9070 0.8792 0.8825 0.8590 0.8475 GR 0.9175 0.9476 0.8474 0.9770 0.9781 0.9436 0.9121 TE 0.8697 0.9674 0.9207 0.9096 0.9283 0.8890 0.9674 ALL 0.8878 0.9324 0.8792 0.9206 0.9271 0.8909 0.8036 50 CA 0.9660 0.8941 0.9476 0.9736 0.9861 0.9167 0.8308 TS 0.8482 0.8694 0.7841 0.8654 0.8668 0.8492 0.8243 GR 0.9805 0.9712 0.9403 0.9653 0.9758 0.9137 0.8746 TE 0.9539 0.9336 0.8823 0.8811 0.9149 0.8510 0.7521 ALL 0.9448 0.9424 0.9138 0.9234 0.9355 0.8975 0.6957 80 CA 0.9700 0.9780 0.9039 0.8496 0.9395 .... 0.8413 TS 0.6589 0.7048 0.6507 .... .... .... GR 0.9041 0.9317 0.9114 .... .... .. TE 0.7502 0.9365 0.8978 .... .... . ALL 0.7088 0.7658 0.6709 0.8496 0.9395 0.. 0.8413 244 Table E.3. R-Squared Values Obtained from Quadratic Regressions Between QIr and ARS from RTRRMSs. Opala Passenger Cars Caravan Car Single-Track Surface with Modified Maysmeters with 2 meters Trailers Speed Type MM 01 MM 02 MM 03 BI NAASRA TRRL BI BPR 20 CA 0.9172 0.9402 0.9460 0.9310 0.9351 0.8644 0.7348 TS 0.8757 0.8912 0.9344 0.9206 0.9279 0.8120 0.8930 GR 0.9814 0.9587 0.8288 0.9886 0.9864 0.9123 0.8553 TE 0.8688 0.9675 0.9602 0.9438 0.9493 0.9049 0.8933 ALL 0.8866 0.8695 0.8478 0.8872 0.8899 0.8567 0.7255 32 CA 0.9481 0.9721 0.8825 0.9605 0.9676 0.8918 0.7996 TS 0.9346 0.9333 0.9451 0.9128 0.9250 0.8763 0.9058 GR 0.9538 0.9536 0.8797 0.9835 0.9848 0.9436 0.9158 TE 0.8738 0.9683 0.9250 0.9120 0.9352 0.8940 0.9692 ALL 0.8982 0.9326 0.8845 0.9220 0.9294 0.9009 0.8056 50 CA 0.9664 0.8956 0.9492 0.9826 0.9866 0.9339 0.8615 TS 0.8711 0.8974 0.8602 0.8895 0.8958 0.8893 0.8583 GR 0.9822 0.9766 0.9576 0.9736 0.9783 0.9155 0.8985 TE 0.9554 0.9568 0.9229 0.8903 0.9449 0.8556 0.8372 ALL 0.9448 0.9454 0.9201 0.9303 0.9466 0.9059 0.6958 80 CA 0.9700 0.9785 0.9039 0.9398 0.9709 .... 0.8442 TS 0.8103 0.8533 0.7633 .... .... .... .... GR 0.9261 0.9441 0.9236 .... .... .... .... TE 0.8013 0.9398 0.9023 .... .... .... .... ALL 0.7303 0.7738 0.7032 0.9398 0.9709 .... 0.8442 245 Table E.4. Standard Error for Estimating QI with a Quadratic Regression Equation and ARS Measurements. Opala Cars with Caravan Car Single-Track Surface Modified Maysmeters with 2 meters Trailers Speed Type MM 01 MM 02 MM 03 BI NAASRA BI BPR 20 CA 7.6 6.4 6.1 6.9 6.7 9.9 13.8 TS 4.0 3.7 2.9 3.2 3.0 5.0 3.8 GR 6.5 9.7 19.8 5.1 5.6 14.6 10.4 TE 15.6 9.6 10.6 12.6 12.0 17.0 15.3 ALL 14.5 17.1 18.5 15.9 15.7 18.3 19.7 32 CA 6.0 4.4 9.0 5.2 4.7 8.8 12.0 TS 2.9 2.9 2.7 3.3 3.1 4.1 3.6 GR 10.3 10.3 16.6 6.1 5.9 11.7 7.9 TE 15.3 9.5 14.6 15.8 13.6 18.0 8.0 ALL 13.7 12.3 16.1 13.2 12.6 15.2 16.0 50 CA 4.8 8.5 5.9 3.5 3.0 6.9 10.0 TS 4.1 3.6 4.2 3.8 3.7 3.9 4.4 GR 6.4 7.3 9.9 7.8 7.1 14.3 8.7 TE 9.1 11.1 14.8 17.6 12.5 21.0 10.6 ALL 10.1 11.1 13.4 12.5 11.0 14.8 15.0 80 CA 4.6 3.9 8.2 5.7 4.0 ... 6.8 TS 4.9 4.3 5.5 ... ... ... GR 6.8 5.9 6.9 ... ... ... TE 15.7 8.6 11.0 ... ... ... ALL 16.4 15.0 17.2 5.7 4.0 ... 6.8 246 a standard error has the units of the QIr measure: counts/km. In essence, Table E.4 quantifies the accuracy involved when a "raw" ARS measure is re-scaled (according to the quadratic regression equation) to a "Calibrated" QI measure. The standard error data show that a speed of 50 km/h gives the best accuracy for all of the RTRRMSs. Therefore, RTRRMS measures should be conducted at 50 km/h if the QIr numeric is used as the calibration reference. The table also indicates the tradeoff in accuracy that occurs when a single calibration is used across all surface types, instead of conducting separate calibrations for each surface type. 247 APPENDIX F QUARTER-CAR SIMULATION The roughness measure from an "ideal" response-type road roughness measurement system (RTRRMS) can be obtained mathematically using a quarter-car simulation (QCS). The roughness numerics obtained via QCS are inherent characteristics of the true longitudinal road profile, and can be obtained with a variety of instrumentation and computation methods. To distinguish the particular set of QCS parameters used in this report from alternate sets used in other QCS applications, the analysis used in the IRRE is called the "Reference Quarter Car Simulation" (RQCS). This appendix describes 1) the development of the RQCS, 2) its mathematical properties, 3) computational details, and 4) the results obtained during the International Road Roughness Experiment (IRRE). Although the use of a QCS to quantify roughness is not new, there is presently no single source in the literature that covers the details of implementing a QCS. Therefore, this appendix includes additional background information in all sections when such information is useful but not readily available elsewhere. DEVELOPMENT AND HISTORY Mathematical models of vehicle response have been used since the 1940s by engineers charged with the design and/or evaluation of airplanes and military vehicles. At that time, the effort associated with obtaining a profile with conventional survey methods and converting it into a form compatible with the computation methods of the day (analog computers) was far too great to consider using vehicle simulation for evaluating road roughness. But given the dire consequences of an aircraft failure while traversing a runway, or of a military vehicle traversing rugged terrain, the effort involved in conducting simulations was justified for those applications. In the early 1960s, General Motors Research (GMR) developed a "Profilometer," using modern instrumentation, that was capable of measuring the "dynamic" portion of a road profile responsible for inducing vehicle ride 249 motions [21]. Shortly after that, the Michigan Dept. of Transportation (MDOT, then called the Mich. Dept. of State Hwys and Transp.) built a second GMR Profilometer in cooperation with GMR [22]. At about the same time, GMR licensed K.J. Law, Inc. to market the Profilometer commercially. At that time, the most well known roughness measuring system was the BPR Roughometer RTRRMS. In the late 1960s, both MDOT and K.J. Law, Inc. developed electronic "equivalent" BPR Roughometers, which employed a vehicle simulation using an analog computer 122, 241. Since the BPR Roughometer has but one wheel, that vehicle simulation was called a BPR Roughometer Quarter-Car Simulation (BPR/QCS). The BPR/QCSs used by MDOT and K.J. Law, Inc. have equations identical in form to a textbook mathematical model used to characterize various dynamic systems, and are the first applications of that model for quantifying road roughness. The QCS is in fact that model, with parameter values representative of vehicles. (The two BPR/QCSs used two different sets of parameter values, each based on measurements of a different "standard" BPR Roughometer.) Most of the profilometers produced by K.J. Law, Inc. have included the BPR simulation. Several years later, K.J. Law, Inc. introduced a second set of parameter values for a QCS to simulate a 1968 Chevrolet Impala passenger car. One of the GMR-type profilometers with a BPR/QCS was the basis for the 01 scale used in the PICR project, although, due to a number of factors, the device never actually measured profile during the project with the accuracy normally associated with that instrument. The QI scale is therefore not equivalent to the published characteristics of the BPR/QCS. (See Appendix E for details.) During the late 1970s, a large-scale NCHRP research project was undertaken at UMTRI (then called The Highway Safety Research Institute) to: 1) study RTRRMSs, 2) determine correlations between the different systems in use, and 3) devise a valid calibration methodology. The research included extensive testing of the RTRRMS in a laboratory environment, along with a formal theoretical analysis of the RTRRMS concept and instrumentation. It became apparent that a main source of the problems lay in the fact that the instruments were invented without a clear concept of what "roughness" is or how it should be measured. Instead, "roughness" had been defined rather 250 loosely as: "Whatever it is that the RTRRMS measures." Since calibration requires comparing the measures from the instrument being calibrated to "true" values of the variables being measured, it was necessary to define, mathematically, a measurable aspect of the true longitudinal profile that would serve as a calibration reference. The reference that was selected is the QCS, with new model parameters chosen to offer maximum correlation with existing RTRRMSs. In addition to a new set of parameters, the QCS was "upgraded" to a half-car simulation, because nearly all of the RTRRMSs used in the United States are based on two-track vehicles (passenger cars and two-wheeled trailers). The way a tire "envelops" small bumps was found to have a critical influence when the QCS was used to simulate low speeds. Accordingly, tire enveloping was added to the model when low-speed simulations were performed. The RQCS described in this report is nearly identical to the NCHRP reference, differing only in the tire enveloping parameter, which was changed inconsequentially from 1 ft (300 mm) to 250 mm to simplify the measurement requirements for rod and level methods. The NCHRP Report 228 recommended a roughness statistic called "reference average rectified velocity" (RARV) which is useful when comparing measurements made by RTRRMSs at more than one measurement speed. The other statistic associated with the RQCS is called "reference average rectified slope" (RARS). Since the RARS numeric obtained with a simulation speed of 80 km/h (RARS80) is selected in this report as the best choice for an International Roughness Index, most of the results obtained with the RQCS are reported as RARS values. MATHEMATICAL DEFINITION OF THE QUARTER CAR SINULATION Sumaary of the Reference Quarter-Car Simulation (RQCS) Figure F.1 illustrates the concept of the RQCS analysis in terms of the mechanical model (la) and its frequency response (lb and 1c). The RQCS consists of three distinct mathematical procedures: 1. Geometrically smooth the profile. A pneumatic tire contacts the 251 0 Sprung Mess Displacement ms ) O of the t (I,_/ Sprung Malss zs Linear Linear Spring Damper ks |Cs k tm Unsprung Mass k I/ Displacement I m ~ k=ks /s 0L() of the U Unsprung Mass ZU M./S C = Cs/ms/ Lineer Spring 0 01 1||tkt 0 5 10 15 20 25 Prof ile Input | b| Fixed Contact Frequency - Hz y(x) Length b b. Frequency Response of RQCS to Elevation Input C~ o LO COI 0 (0 o 0 5 10 15 20 25 Frequency - Hz c. Frequency Response of RQCS to Slope Input Figure F.1. The Reference Quarter Car Simulation (RQCS) 252 road over an area, rather than at a single point, and effectively "envelops" small, sharp roughness features. It has been shown that this effect is simulated quite well with a "moving average" smoothing technique, using a "moving average" baselength approximately 50% longer than the contact patch between tire and road [91. The moving average is defined for a continuous profile measurement by an integral over the baselength of the filter: Y5(x) = 1/b J b/2Yr(X) dX (F-1) where x = distance travelled Yr(x) = unfiltered "raw" vertical profile elevation ys(x) = smoothed vertical profile elevation b = baselength of moving average X = dummy variable of integration Due to the practical advantage of measuring profile manually at conveniently marked intervals, a baselength of b = 250 mm is proposed in this report, which differs from the 1 ft (300 mm) baselength used in the NCHRP work. The effect of smoothing is often negligible for high simulated speeds, but assumes greater importance for lower speeds, as shown later in this section. 2. Filter the profile signal. The mathematical model shown in Figure F.la is defined mathematically by two second-order differential equations: Zs + C (2s - Ad + K2 (zs - zu) 0 (F-2) Zs + zu + K Zu = KI y (F-3) where 653 sec2, k2 = 63.3 sec 2, u = .150, C 6.00 sec1 (F-4) and y = profile elevation input 253 The mechanical system shown in the figure and described by the above equations is a band-pass filter, so-called because it transmits only a band of frequencies, "filtering out" the rest. The figure shows the frequency response plot of the RQCS filter, in the form of "amplitude out"/"amplitude in." Note that the sprung mass, indicated in the Figure as mi, is used to normalize the other parameter and is itself not used in the filter specification. Methods that are used to perform the filtering are mentioned later in this section, and computational details are provided in the next section for one approach that is particularly suited for manual profile measurement and computation with microcomputers. 3. Rectify and average the filtered profile signal. To simulate a roadmeter, the axle-body velocity from the QCS is rectified and averaged to yield an ARV statistic similar to that obtained from the roadmeter in a RTRRMS. The ARV numeric can be rescaled from units of velocity to units of slope, to yield the ARS numeric. Deriving from the Reference, the statistic is called RARS in this report to differentiate it from the "raw" ARS measure obtained from a mechanical RTRRMS. When the RQCS is implemented as described later in this appendix, the output of the filter has the units of slope, and RARS is computed simply by rectifying and averaging that output. Half-Car Simulation (RCS) The QCS is converted to a HCS by adding one more step, which is to average the left- and right-hand wheeltrack profiles, point-by-point, prior to processing with the QCS. This step is included because roadmeters in two-track RTRRMSs are installed at the center of the vehicle axle, where they detect virtually no roll motion of the vehicle body or axle. This step is not equivalent to processing the two profiles independently and then averaging the summary statistics; when the profiles are processed separately, a higher roughness numeric is obtained because the independent profile roughness numerics include crosslevel variations that would not register on a roadmeter at the axle center. The NCHRP Reference is a HCS, while most of the results obtained in the IRRE were for a QCS (each wheeltrack processed independently). 254 Bandwidth of the RQCS In order to derive the frequency response functions of the above-described operations, it is convenient to consider complex sinusoidal variables of the form: y(w,x) = y 0ej (F-5) y(w,t) = YO ejwt (F-6) where eiwX = coswX + j sinwX (F-7) w = circular frequency = 2nf, and j = /-1 = the "imaginary" part of a "complex" vector, 900 out of phase with the "real" part. Eq. 5 describes a variable that is sinusoidal with distance travelled, x, while Eq. 6 describes a variable that is sinusoidal with time t. Depending on the context, the letter w designates either spatial circular frequency, with units of radians/length in Eq. 5; or temporal circular frequency with units of radians/sec in Eq. 6. Whether the variable is temporal or spatial, differentiation is simple: y' = dy/dx = YO jw ejwx = jw y (F-8) or y = dy/dt = YO jw ejwt = jw y (F-9) The Moving Average. The spatial frequency response of a moving average, defined as the ratio of the output "smoothed" profile ys, to the "raw" profile, Yr' is found by combining Eqs. 1 and 5: x+b/2 ys/yr = 1/b [ J YO eiwx dX ] / (YO eJwx) (F-10) x-b/2 where X = dummy integration variable. Solving Eq. 10, 255 y/yr = 1/b [ ei w(x+b/2) / jw - eJw(x-b/2) / jw I e-jwx = 1/(jwb) [ ejwb/2 e-jwb/2 i = 1/(jwb) [ cos(wb/2) + j sin(wb/2) - cos(-wb/2) - j sin(-wb/2) ] = 1/(jwb) 2j sin(wb/2) = sin(wb/2) / (wb/2) = sin(n,b/L) / (rTb/L) (F-il) where L = wavelength = 2"/w. The moving average filter is described in more detail in Appendix J, which includes the effect of samnple interval on the wavenumber sensitivity. The OCS Filter. Eqs 2 and 3 can be converted to algebraic equations dependent on frequency by substituting jw for the derivatives, as shown in Eq. 9: _=2 Zs + jw C (Zs - zu) + K2 (zs - zu) = 0 (F-12) _w2 Z -w2 u z + K, zu = K1 y (F-13) Eqs. 12 and 13 can be solved for the two variables Zu and zs to yield the temporal frequency response function of the QCS: Zr/Y zs/y - zu/y = K, w2 / D (F-14) where zs/y Ki (K2 + j C w) / D (F-15) Zu/Y = K1 (K2 - w2 + j C w) / D (F-16) and 256 D = Dr + j Di (F-17) Dr = u w4 -[K1 + K2 (1 + u)] w2 + K, K2 (F-18) Di= C w [K1i - (1 + u) w2] (F-19) Eq. 14 contains both amplitude and phase information. The amplitude of the Frequency Response Function is: IZr/YI = K1 w2 / (Dr2 + Di2)1/ (F-20) Eqs. 14 and 20 are dimensionless, meaning that the output (Zr) will have the same units as the input. Thus, to obtain a slope output, the input should be profile slope. Eq. 20 is shown plotted as a function of frequency in Fig. F.1c. When the input is a profile elevation, then the frequency response function should include the differentiation involved in transforming a displacement to a slope. When the differentiation (jw) is combined with Eq. 20, the result is: Izr/YI = Ki w3 / (Dr2 + Di2)1/2 (F-21) Eq. 21, with units 1/sec is shown plotted in Fig. F.lb. Frequency Response of RQCS at four simulation speeds. As shown in Figure F.1c, the bandwidth of the OCS filter covers temporal frequencies between 0.8 - 17 Hz, which can be related to spatial wavenumber (1/L, L = wavelength) by the simulation speed: i/L (cycle/m) = 3600 (sec/h) .001 (km/m) f (cycle/sec) / V (km/h) (F-22) In addition, the geometric smoothing limits the response to shorter wavelengths according to Eq. 11, regardless of the simulation speed. Figure F.2 shows the combined effects of the filtering and smoothing for the four speeds used in the IRRE, obtained by combining Eqs. 11, 20, and 22. When expressed as wavelengths, the bands are approximately: 257 WAVELENGTH - M/CYCLE 50 20 10 5 2 1 0.5 0.2 C%J without 250 mm smoothing Z a. 20 km/h with 250 mm smoothing a 2 5 .1 2 1 2 5 without 250 mm smoothing { / ~~~~with 250 mm smoothing C, 2 55 2 2 , without 250 mm smoothing 8 ~c /0 km. 0 m/ z > ~~~~with 250 mm smoothing 2 5~~~~~~5 without 250 mm smoothii z d. 80 km/h WAVE NUMBER -CYCLE/M Figure F.2. Sensitivity of RQ4CS to Different Wavelengths 258 20 km/h: 0.5 - 7 m 32 km/h: 0.5 - 11 m 50 km/h: 0.8 - 17 m 80 km/h: 1.3 - 28 m (F-23) Physical Interpretation of the RARS Statistic. The RQCS analysis described above has three simple interpretations: Reference RTRRMS. As shown in Figure F.la, the analysis simulates an idealized RTRRMS, sometimes called the "Golden Car," equivalent in concept to a gold-plated reference measure. The RQCS has the same approximate sensitivity to surface type, roughness, and (simulated) measurement speed as observed with a RTRRMS, but has none of the nonlinearities that exist with most vehicles and roadmeters. The RQCS gives the operator of a RTRRMS an opportunity to see how the RTRRMS compares with an "ideal" system, in terms of such performance features as: suspension damping, roadmeter nonlinearity, and tire/wheel nonuniformity. Profile Slope. Alternatively, the RQCS can be viewed as providing a statistic summarizing profile geometry. RARS is, as the name implies, the average rectified slope of the profile when wavelengths are attenuated that fall outside the range specified in Eq. 23. Vehicle Excitation. When the roughness statistic is converted to RARV, it is proportional to the vertical excitation perceived by a vehicle traversing that road at the simulation speed. Thus, roads can be compared in terms of their roughness as perceived by the vehicle, even when different speeds are involved, by using a simulation speed that corresponds to the traffic speed. A higher number always implies more vehicle excitation, regardless of the simulation speed. Exauples of the RQCS "Filter." To illustrate the nature of the RQCS, Figures F.3 and F.4 show the profile inputs and the resulting QCS output. Figure F.3 shows three plots derived from a single profile measured with the TRRL Beam during the IRRE. Note that the roughness information is not very 259 E . E01 (0 0 0 0 10 20 30 40 50 60 70 80 90 c. Slope Profile as Filtered by the RQCS E ) 0. 0 LO 0 00 0 30410 20 3 4 50 60 70 80 90 b. Approximate Slope: Elevation change per Measurement Interval 0- - 0 C10 0 10 20 30 40 50 60 70 80 90 Longitudinal Position - m a. Original Elevation lvleasurement Figure F.3. Analysis of Profile Obtained With TRRL Beam. (Left Wheeltrack, Section CA06) 260 aE, E .- LO 00 L. - 0 10 20 30 40 50 60 70 80 90 c. Slope Profile as Filtered by the RQCS 0~~~~~~~~~~~~~~~~~~~9 0 ' 10 20 30 40 50 60 70 80 90 b. Approximate Slope: Elevation Change per Measurement Interval .~ I I** I*|** g||**@I| I| t2o > 'U; 0 0 10 20 30 40O 50 60 70 80 90 Longitudinal Position - m a. Original Elevation Measurement Figure F.4. Analysis of Profile Obtained with APL 72. (Left Wheeltrack, Section CA06) 261 clear from the elevation profile (Fig. F.3a) due to 1) the underlying slope of the road, and 2) the fact that road elevation profiles are dominated by the longest wavelengths included in the measurement. The plot of profile slope (Fig. F.3b), obtained by taking point-by-point differences in elevation, normalized by the measurement interval, more clearly shows "roughness." The filtered slope, as seen through the RQCS (Fig. F.3c), is very similar to the "raw" slope, however, the high frequency "hash" is removed by the RQCS bandpass filter. Also, the non-zero mean slope is removed with the longer wavelengths. Figure F.4 shows corresponding measurements obtained with the APL Trailer (in the APL 72 configuration), described in Appendices A and G. Figures F.3 and F.4 show that direct comparison of the elevation "profile" signals (Figs. 3a and 4a) is meaningless, since the APL signal does not include wavelengths longer than 40 m. Direct comparison of the slope "profile" signals (Figs. 3b and 4b) is much closer, yet the signals are still not comparable due to differences in the instrumentation approaches of the TRRL Beam and APL Trailer. After the signals are filtered by the RQCS, the waveband of the slope profile has been limited to the band that excites the RQCS at the simulation speed of 50 km/h. While exact agreement is not obtained, the signals now appear much more similar, and have close RARS values. COMPUTATIONAL DETAILS Due to the way the RQCS is formulated, the output of the model has the same units as the input. Thus, a single RQCS algorithm can provide RARS directly from a slope input or RARV directly from a vertical velocity input, without modification. Since this report emphasizes the RARS statistic, rather than the RARV statistic, spatial descriptors are used when possible. 262 Computational Methods for Simulating Vehicle Dynamics The RQCS can be implemented any number of ways, since the analysis is defined by Eqs. 2 and 3, rather than a specific means of their solution. Four approaches that have been used successfully are mentioned here: Analog Computer. As noted earlier, the first QCSs used for roughness evaluation were electronic [22, 24]. An electronic filter is designed that follows Eqs. 2 and 3, thus defining an electronic analog of the ideal mechanical system. An analog computer requires that the profile be measured continuously, to provide a voltage proportional to profile over the proper frequency range. Therefore, it cannot easily be used with measurement methods that only provide the profile numerically at discrete intervals, such as the Rod and Level and TRRL Beam. An analog computer has several potential advantages: 1) it operates in "real time," and therefore does not require that profile be stored on magnetic tape, 2) summary results are obtained immediately, and 3) it is ideally suited to an analog dynamic profilometer, such as the APL 72 (digitization is not necessary). In practice, the analog QCSs have proven troublesome to maintain. (For example, problems with the BPR/QCS used as the basis of the QI, are mentioned in Appendix E.) Numerical Integration. The differential equations can be numerically integrated on a digital computer, using one of many possible integration approximations (Euler, Runge-Kutta, Hammings Predictor-Corrector, etc.). The variables are calculated at discrete times, spaced closely by the small "time step." At each time step, the derivatives are evaluated (according to Eqs. 2 and 3) and used to estimate the variables at the next step. While numerical integration is an approximation, the errors can be kept at negligible levels by proper choice of the time step interval [361. Estimation through Correlation. A number of alternative analyses can be devised that yield statistics correlated with RARS. While a rigorous mathematical relationship might not exist, a statistical relation can be developed through regression analyses. The QIr analysis, described in Appendix E, estimates the output of a BPR/QCS using mid-chord deviations (RMSVA) from two baselengths. The RMSD analysis, described in Appendix H, estimates the ARS numeric obtained from a BI Trailer as it existed in July 263 1982 during the IRRE. Although alternate statistics combined with regression equations are not universally equivalent to direct computation of a QCS numeric from the profile data, the alternate statistics can sometimes be "converted" to the RARS roughness scale with little loss in accuracy. State Transition Matrix. Because the differential equations of the QCS are linear, the exact solution can be calculated if the profile input has a known shape between measurements. The solution method is called the state transition matrix (STM) method, because the differential equations are used to define two fixed matrices of constant coefficients that are used to compute the transition of the QCS over each time step [37]. This method is described below. Filtering the Profile: The State Transition Matrix The state of the mathematical model shown in Fig. F.1 can be described completely (for purposes of determining RARS) by the four state variables Zs s Zs''' Zu' and Zu*'' The displacements of the sprung and unsprung masses, zs and Zu, can also be computed, but are not necessary for determining the suspension motion detected by a roadmeter. Because the RQCS is linear, the new value of each variable can be calculated at a position x along the road if the values of the four variables are known at a previous position, and if the profile shape is known over the measurement interval. For assumed constant profile slope between measurements, and a constant measurement interval, the values of the state variables at a given point are computed as: Zs Si1 Zs + 512 Zs + s13 Zu' + s14 Zu" + P1 Y' (F-24) Zs s21 Zs + S22 Zs + s23 Zu + s24 Zu" + P2 Y' (F-25) Zu s31 Zs + 832 Z5t + s33 Zu + s34 Zu" + P3 Y' (F-26) Zu s41 Zs' + 542 zs' + s43 Zu + s44 Zu" + P4 Y' (F-27) where 264 Zs'' Zs't, Zu'' and Zu'' are the values of the state variables for the current position, Zs5s Zs, Zu and Zu" are the values known for the previous position, and y'= profile slope input. The coefficients sjk and pj (j,k = 1...4) are constants, which are fixed by the "time step," which is the time that would be needed for a vehicle to advance over one profile measurement interval at the simulation speed. In essence, the RQCS consists of Eqs. 24 - 27. Table F.1 lists the coefficients required for simulation speeds of 50 and 80 km/h, and measurement intervals of 50, 100, 250, and 500 mm. The above computation method is recursive, meaning that it "marches" through the profile, basing new computed values on both the new input and the previous values. As such, it is always responding to past excitation, just as a physical vehicle does. Computation of the RQCS Coefficients When a simulation speed/measurement interval combination is required that is not included in Table F.1, the necessary coefficients can be computed directly. To simplify the mathematical expressions, matrix notation will be used below. In the following equations, all one-dimensional (1x4) matrices are indicated in bold print, while two-dimensional matrices (4x4) are both underlined and shown in bold print. Although the state transition computation method can be used to give a slope output, Eqs. 2 and 3 have time derivatives. To solve those equations, it is more convenient if all derivatives are temporal, and therefore only time derivatives are indicated in this section. Eqs. 24 - 27 can be re-written in matrix form with temporal derivatives as: 265 Table F.1 RQCS Coefficients dt = 3.6 x 10 3 sec, dx = 50 mm, V = 50 km/h (Valid for any road surface) ST = R999611699 3.56272188 x 10-3 1.92070642 x 10 4 3.71002355 x 10]5 PR = 1.96228971 x 10 4 _ -.209863995 .979719377 .0483543033 .0200843925 3 .161509692 2.57625371 x 10-3 2.47334903 x 10 .970650997 3.32009264 x 10- .0267727492 1.38542279 .13389595 -15.8388928 .839331301 14.4534699 dt = 7.2 x 10-3 sec, dx = 100 mm, V = 50 km/h (Valid for road surfaces not having isolated "bumps" shorter than 150 mm) ST = r.998527757 7.0568212 x 10-3 -3.69240955 x 10 5 1.40418015 x 10 Pt R,= 1.50916745 x 10 3 -.38744038 .3 961803551 -.223846046 .0366872825 -1 .611286426 9.6237219 x 10 9.36120101 x 10 .889589221 6.01437205 x 10 .100787057 2.4788086 .244581883 -28.661375 .65463106 J 26.1825663 dt = .018 sec, dx = 250 mm, V = 50 km/h (Valid for road surfaces not having Isolated "bumps" shorter than 300 mm) ST = .992040026 .0171948155 -.0124196184 7.08544757 x 10 4 PR = .0203795897 _ -.789425935 .917212924 -2.29510558 .0624074845 3.0845315 .0465278304 4.72363171 x 10- .453113538 9.9465964 x 10-3 .500358633 3.89845779 .416049897 -47.1993075 .0835914715 4 43.3008497 dt = .036 sec, dx = 500 mm, V = 50 km/h (Valid for road surfaces not having significant "short wave roughness." Less accurate than when dx = 250 mm.) ST = .972753756 .0330653765 -.0908549945 1.71168531 x 10 3 PR = .118101242 _ -1.37070714 .842828908 -6.08082958 .0390698522 7.45153671 .102287289 .0114112354 -.275579675 5.66614513 x 10-3 1.17329239 1.66878205 .260465682 -26.3354005 -.433758069 24.6666185 dt = 2.25 x 10 -3 sec, dx = 50 mm, V = 80 km/h (Valid for all road surfaces) ST = .999845186 2.23520857 x 10-3 1.06254529 x 10-4 1.47639955 x 10- PR = 4.8559593 x 10 5 -_ I -.135258296 .987024495 .0709857026 .0129269461 .0642725938 1.03017325 x 10-3 9.84266368 x 10-5 .988294046 2.14350069 x 10- 1.0106757814 898326884 .0861796409 -10.2296999 .903144578 9.33137299 dt = 4.5 x 10-3 sec, dx = 100 mm, V = 80 km/h (Valid for road surfaces not having isolated "bumps" shorter than 150 mm) ST = ,999401438 4.44235095 x 10 3 2.18885407 x 10 i4 5.72179098 x 1015 PR = 3.79676767 x 10 4 _ -.257054857 .975036049 7.96622337 x 10-3 .0245842747 .249088634 3.96037912 x 103 3.81452732 x 10 .954804848 4.05558755 x 10 3 .041234773 1.68731199 .163895165 -19.3426365 .794870062 17.6553245 dt = .01125 sec, dx 5 250 mm, V 5 80 km/h (Valid for road surfaces not having Isolated "bumps" shorter than 300 mm) ST = .996607069 .0109151441 -2.08327474 x 10 3 3.19014531 x 10 4 PR = 5.47620359 x 10 1 _ -.55630449 .943876786 -.832472102 .0506470087 1.38877659 .0215317589 2.12676354 x 10 .750871363 8.22188868 x 10o3 .227596878 3.33501289 .337646725 -39.1276349 .434756397 35.792622 dt = .0225 sec, dx = 500 mm, V = 80 km/h (Valid for road surfaces not having significant "short wave roughness") ST = .988172567 .0212839445 -.0252093147 9.92316691 x 10 4 PR = .0370367529 _ -.928516044 .900161568 -3.39136929 .0628016846 ] 4.31988533 .0638632609 6.61544461 x 10 .240289418 9.86268262 x 10- .695847322 3.74329442 .418677898 -46.6788394 -.114525219 42.935545 266 Z(i) = ST Z(i-1) + PR 9(i) (F-28) where zT = [ s) Zs) 2uX zu ](F-29) and ST = 4x4 State Transition Matrix (with coefficients sll ... s44) PR = 1x4 Partial Response Matrix (with coefficients p1 ... P4) i = present time step , i-1 = previous time step To make Eqs. 2 and 3 compatible with Eqs. 24 - 27, both sides of Eqs. 2 and 3 are differentiated with respect to time. They can then be expressed in the following matrix form using the four state variables of the Z vector, defined in Eq. 29: Z(t) =A Z(t) + B y(t) (F-30) A = r ° 1 0 0 B 0 -K2 -C K2 C 0 I O 0 1 O LK2/u C/u -(K1+K2)/u -C/u Kl/u (F-31) The form of the solution for Eqs. 30 and 31 has already been presented (Eq. 28). For a constant time step, over which the input y(i) is a constant, the ST and PR matrices can be computed from the A and B matrices: ST = eA dt (F-32) PR = A71 (ST - I ) B (F-33) where dt (sec) = dx (m) 360C (sec/h) .001 (km/m) / V (km/h) (F-34) 267 and I is a 4 x 4 identity matrix. The PR matrix as defined in Eq. 33 is based on the assumption of an input that remains constant over the profile measurement interval. That is why the generalized input in Eqs. 24 - 27 should be a slope, rather than elevation: an assumption of constant slope between profile measures is more reasonable than an assumption of constant elevation. (Note that if an elevation input is used, the output signal will also be an elevation, and that a simple average would not yield RARS.) Eq. 33 requires a matrix inversion, which is not detailed here because it is such a common computer subroutine. The matrix exponent in Eq. 32 is less common, but can be evaluated with a Taylor series expansion: ex = 1 + x + x2/2 + x3/(3 2) + x4/4! + ... eA dt =I + A dt + A A dt2 / 2 + A3 dt3 / 3! + N = I+ A' dt' / i! (F-35) - i=l- For Eq. 35 to be perfectly exact, N must approach infinity. In practice, however, the series converges rapidly to the precision of a computer when dt is small. In calculating the coefficients shown in Table F.1, the computer program checked the coefficients after each new term in the series was added to determine if a change in eA dt could be detected; when a change was not detected for any of the 16 coefficients, then the program stopped since the coefficients were precise to the limits of the computer. This generally occurs after about 10 terms (N=10). Conversion of Elevation Profiles to a Smoothed Slope Input. As mentioned earlier, the RQCS includes a smoothing of the input profile, using a 250 mm "moving average," and also uses elevation changes (slope) as the input to the QCS filter. When the two operations are combined, the resulting operation is very simple: The slope input used for the QCS filter is the change in elevation over the moving average baselength. If the profile is measured continuously, then 268 y'(x) = [yr(x + b) - yr(x)] / b (F-36) where y'(x) smoothed slope input to the RQCS Yr(x) raw profile elevation (It is recognized that Eq. 35 introduces a phase shift, equivalent to the distance b/2 = 250/2 = 125 mm). This has no effect on the roughness numerics and simplifies the conversion of the equations into computer code. For zero phase, the equation would be: y'(x) = [yr(x+b/2) - Yr(x-b/2)] / b.) When profile elevations are measured at constant intervals, there are two possible relations between dx, the measurement interval, and b, the baselength of the moving average: 1. dx > b. In this case, the input to the RQCS should be: Y'(i) = [y(i+l) - y(i)] / dx (F-37) The input is the equivalent of a profile smoothed with a moving average equal to dx. If dx = b = 250 mm, then the resulting slope input values agree perfectly with the definition of the RQCS. Should dx be greater than b (for example, 500 mm), then the result is equivalent to the filter portioa of the RQCS with a longer moving average baselength, equal to dx. 2. dx < b. (Example: dx=100, b=250 mm.) If b is not an integer multiple of dx, then interpolation of profile points is needed to employ the correct baselength in the moving average: y'(i) = A y(i+k) + B y(i+k+1) - y(i) ] / b (F-38) where k = INT( b/dx ) , B = ( b - k dx) /dx , and A = 1 - B (F-39) The function INT in Eq. 39 is the INTeger function in the BASIC and FORTRAN computer languages, and designates truncation. 269 If b is an integer multiple of dx (for example, dx=50, b=250 mm), then Eq. 38 is simplified because A=1 and B=O. Eq. 38 then reduces to: y'(i) = [y(i+k) - y(i)] / b (F-40) Initialization. Because the RQCS is always responding to both new profile input and its present "state" (as defined by the spatial equivalents of vertical acceleration and vertical velocity of the simulated body and axle), the assumed initial values of the four state variables can influence the RARS numeric. This replicates the behavior of a physical RTRRMS which is responding to the road surface immediately prior to the test site upon entry. In order to obtain the true initial state of the RQCS, the profile must be measured for some distance prior to the start of the test site. The simulation should begin on the lead-in, to determine the proper values of the variables zs , Zs , Zu , and Zu at the start of the test site. In the IRRE, lead-in data were not available from the static profile measures obtained from Rod and Level and the TRRL Beam, and initial conditions had to be assumed. The assumed initial conditions are: Zs51 = Zuw = ° (F-41) Zs = zu' = [y(i + k) - y(i)] / (k dx) (F-42) where k = INT( 0.5 / dt) (F-43) The above initial conditions assumed for the RQCS have a physical interpretation: it is as if the Reference RTRRMS is approaching the test site on a perfectly smooth road, with a grade equal to the average grade of the profile over the first 0.5 second of simulated travel time. Note that Eq. 42 270 initializes the RQCS for a slope input, suitable for direct computation of RARS. When RARV is computed, the dx variable in Eq. 42 is replaced with dt to yield an initial vertical velocity. Also, the primes used to indicate spatial derivative should be replaced with dots to indicate time derivatives. The profiles obtained during the IRRE were analyzed to determine the errors introduced using Eqs. 41 and 42 and, as shown in the next section, they were negligible. (A different initialization was used at first in the IRRE analyses, which used only the first two profile points (k=l in Eq. 42). The resulting RQCS numerics, included in the December 1982 draft of this report, showed slightly higher and more erratic results for the profiles measured with the Beam and APL 72 system. The shorter measurement intervals made that initialization more sensitive to the values of the first two elevation measures, introducing a random effect that degraded the agreement between RQCS numerics obtained by different profile measurement methods.) A Demonstration Computer Program. Figure F.5 presents a demonstration computer program to calculate RARS80, using the BASIC computer language. The profile values needed to compute the slope input are kept in a buffer, which is the array, Y. The State Transition Matrix is stored in the ST array (and read by the program from the DATA statements at the bottom); the Particular Response Matrix is stored in the array PR (these coefficients are also read from the DATA statements); DX is the measurement interval (0.25 m in the program); the Z array contains the current values of the four state variables; and the Zi array contains the old values of the state variables, from the previous time step. Although smoothing is not needed, due to the sample length of 0.25 m, the program has provision for smoothing with smaller intervals. When DX is changed to values smaller than 0.25, then more elements In the Y buffer are used for smoothing. The program was written as a demonstration and is not particularly efficient. For example, it should be modified to read the profile from a file, rather than for keyboard input. In order to convert the program for other sample intervals and/or simulation speeds, lines 1510-1550 should be replaced with new values. 271 1000 REM This program demonstrates the IRI computation. 1010 REK 1020 REM 1030 REM ------------------------------------- Initialize constants 1040 DIN Y(26),Z(4),Z1(4),ST(4,4),PR(4) 1050 READ DX 1060 K = INT (.25 / DX +...5).+ 1 1070 IF K < 2 THEN K = 2 1080 BL = (K - 1) * DX 1090 FOR I = 1 TO 4 1100 FOR J = 1 TO 4 1110 READ ST(I,J) 1120 NEXT J 1130 READ PR(I) 1140 NEXT I 1150 REM -------------------…------------------ Initialize variables. 1160 INPUT "profile elevation 11 m from start:", Y(K) 1170 INPUT "X = 0. Elevation = ",Y(1) 1180 Z1(1) = (Y(K) - Y(1)> I 11 1190 Z1(2) = 0 1200 Z1(3) = Z1(1) 1210 Z1(4) = 0 1220 RS = 0 1230 IX = 1 1240 I = 0 1250 REM -------------- Loop to input profile and Calculate Roughness 1260 I = I + 1 1270 PRINT "X = ";IX * DX, 1280 IX = IX + 1 1290 INPUT "Elev. = "; Y(K) 1300 REM ----------------------------------------- Compute slope input 1310 IF IX < K THEN Y(IX) = Y(K) 1320 IF IX < K THEN GOTO 1270 1330 YP = (Y(K) - Y(1)) / BL 1340 FOR J = 2 TO K 1350 Y(J-1) = Y(J) 1360 NEXT J 1370 REM ---D______---------------------- Simulate vehicle response 1380 FOR J = 1 TO 4 1390 z(J) = PR(J) * yp 1400 FOR JJ = 1 TO 4 1410 Z(J) = Z(J) + ST(J,JJ) *.Z1(JJ) 1420 NEXT JJ 1430 NEXT J 1440 FOR J = 1 TO 4 1450 Z1(J) = Z(J) 1460 NEXT J 1470 RS = RS + ABS (Z(1) - Z(3)) 1480 PRINT "disp = ";RS * DX, "IRI = ";RS / I 1490 GOTO 1260 1500 END 1510 DATA .25 1520 DATA .9966071 , .01091514,-.002083274 , .0003190145 , .005476107 1530 DATA -.5563044 , .9438768 ,-.8324718 , .05064701 , 1.388776 1540 DATA .02153176 , .002126763 , .7508714 , .008221888 , .2275968 1550 DATA 3.335013 , .3376467 ,-39.12762 , .4347564 , 35.79262 Fig. F.5 Demonstration program for computing IRI with a microcomputer 272 MEbSURENENT OF RQCS NUMERICS IN THE IRRE The profile data obtained in the IRRE provided a number of new quantitative findings concerning the accuracy of RQCS numerics obtained using different methods. Alternatives in the Quarter-Car Model Tire Enveloping. The tire enveloping (moving average) smoothing portion of the RQCS is not always used in the United States. This is justified by an earlier finding that the smoothing had a very slight effect on paved roads at the highway speeds (60 - 80 km/h) normally associated with RTRRMS use in the United StaLtes [9]. To determine the significance of the smoothing over the much broader range of surface type and speed covered in the IRRE, the profiles obtained from the TRRL beam and the APL 72 trailer were processed with and without the smoothing. Fig. F.6 shows the RARS statistics as obtained with and without the 250 mm moving average. As predicted from the plots shown earlier in Fig. F.2, the effect is slight at high speeds, but more significant at lower speeds. Figs. 6a and 6b show that smoothing must be included for the simulation speeds of 20 and 32 km/h. Figs. 6c and 6d show that a small but noticeable effect is present for 50 km/h. For a simulation speed of 80 km/h (data not shown), there was no visible difference between RARS numerics obtained with and without smoothing. Half-Car or Quarter Car. When possible, the ARS statistic was computed from both wheeltracks together, simulating a half-car. This computation requires that the profiles of both wheeltracks begin at the same point, so that the point-by-point averaging can be performed. Because of this requirement, only the static profile measures were processed in this way. Figure F.7 compares the measures obtained processing both wheeltracks together with the measures obtained by processing the profiles separately and then averaging the RARS obtained for each. The figure shows that for the conditions covered in the ITtRE, the two methods give highly correlated results, which can be approximately "converted" using a regression equation determined from the IRRE data: 273 c c~~~~~// 0 10 20 30 40/0 / RASs wih20m mohn 0AS ih20m mohn E / Q.) /0 CkR 5 00 0 / -C~~~~~~~~~~~~- 8 0 ~ / 0 10 20 30 40 0 10 20 30 RARS. with 250 mm Smoothing RARSSR with 250 mm Smoothing 2. 20 km/h, data from TRRL Beam b32 km/h, data from TRRL Beam 274 u- 0 o~~~~~~~~~ E E/ 0 0' 0 5 10 15 20 25 0 5 10 15 20d RARS. with 250 mm Smoothing RARS.. with 250 mm Smoothing C. 50 km/h, data from TRRL Beam &. 50 km/h, APL 72 data Figure F.6. Effect of Smoothing (Enveloping) on the RARS Numeric 274 0 o4 m 20 krr /h o 32 krr /h *50 krr /h 0E 0 0 5 10 15 20 25 fRARS from Quarter Car Figure F.7. Comparison of t]he RARS Obtained from QAuarter-car and hsalf-car 275 ARSh = 0.760 RARSA (F-44) where ARSh = numerics computed from point-by-point average of both wheeltrack profiles (HCS), and RARSA = Average of two RARS numerics computed independently from the two wheel track profiles. Eq. 44 reflects the fact that most of the test sites used in the IRRE had very similar roughness levels in the two wheeltracks. When one wheeltrack is substantially rougher than the other, this equation will not be valid. In fact, the case for one wheeltrack much rougher than the other is relatively easy to analyze. In the limit, where one wheeltrack is perfectly smooth, then ARSh = RARSA. When one wheeltrack is much smoother than the other, but not perfectly smooth, the ratio of ARSh to RARSA should be expected to lie between 0.76 and 1.0. Technical Requirements for Profile Measurement Initialization and/or Lead-In. To obtain the "true" RARS numeric, the profile preceding a test site must be measured. To determine the amount of lead-in required, the errors introduced by the assumed initial conditions of Eqs. 41 - 43 were evaluated. One of the test sites was divided into 16 consecutive sections, 20 m long. The RQCS was run over the site, starting first at x=O, and finishing at x=320. The RARS50 numeric was printed for each of the 20 m sections, rather than simply for the total length. This was repeated 14 times, starting at x=20, x=40, ... x=300. The results are shown in Table F.2. The test site, CA05, was chosen because it was known to have highly variable roughness over its length. In the table, the first (top) numeric in each column is based on the assumed initial conditions of Eqs. 41 - 43, while all subsequent numerics are initialized "correctly" (the initial condition for the 20 m section is the ending condition for the preceding 20 m section), as the RQCS proceeded continuously. The table shows that the effect 276 Table F.2. Effect of ROCS Initialization Sub-Section Starting Position Where RQCS was started (m) Position 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 3300 0 8.20 ...... .. .... .. .... .. .... .. .... .. .... .. .... .. .... .. .... .. ..... .. .... .. ..... .. ... ... .. ..... 20 5.11 5.21 ..... ..... ..... ..... ..... ..... ..... ..... . . . . . ... ...... . 40 7.19 7.19 7.13 ......... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .. . .... 60 4.10 4.10 4.09 3.50 ..... ..... ... .. ..... .. ....... ..... ..... ..... ..... ..... ..... 80 5.34 5.34 5.34 5.34 5.21 ..... ..... ..... ..... ..... .... .. ..... 100 4.05 4.05 4.05 4.05 4.05 3.93 . . ..... ..... ..... ..... ..... ..... 120 6.08 6.08 6.08 6.08 6.08 6.08 5.76 .. ....... ..... ..... ..... ..... .......... ..... 140 9.80 9.80 9.80 9.80 9.80 9.80 9.81 9.72 .. ..... ..... ..... ..... ..... ..... 160 6.11 6.11 6.11 6.11 6.11 6.11 6.11 6.11 6.01. ..... ..... .. 180 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.94 4.61 ..... . .... ..... ..... ..... ..... 200 4.37 4.37 4.37 4.37 4.37 4.37 4.37 4.37 4.37 4.37 4.37 ..... .......... ..... ..... 220 6.68 6.68 6.68 6.68 6.68 6.68 6.68 6.68 6.68 6.68 6.68 6.30 ......... ..... ..... 240 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.87 13.86 ..... ..... 260 11.37 11.37 11.37 11.37 11.37 11.37 11.37 11.37 11.37 11.37 11.37 11.37 11.35 10.89 ..... 280 10.67 10.67 10.67 10.67 10.67 10.67 10.67 10.67 10.67 10.67 10.67 10.67 10.67 10.68 10.27 300 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.56 6.57 6.33 NOTE: The above results are for the left wheeltrack of site CA05. Simulation speed = 50 km/h. of the initialization is extremely slight, and disappears after 20 m (at the simulation speed of 50 km/h). That is, the same roughness numerics are obtained for each 20 m section, as long as the RQCS is started on a preceding 20 m section. Even the roughness numerics computed for the first 20 m section in each of the 15 runs show only slight errors. The large variations in roughness between some of the sections (from 4.05 to 14.88) are actual variations in road roughness, duly reflected in the RARS50 statistic. The section of CA05 from 60 - 80 m appears in the Table as one in which there is the greatest difference between RARS50 using the assumed initialization of Eqs. 41- 43 and the correct value. Therefore, it was used to show the differences between the output of the RQCS filter as it is affected by initialization in Figure F.8. The figure shows three filtered profiles: 1) the RQCS output signal for the theoretically correct initialization, determined by the 60 m of profile preceding this 20 m section, and designated "true RQCS output" in the figure; 2) the signal obtained using the initial conditions of Eqs. 41 - 43; and 3) a deliberately erroneous initialization, obtained by stopping the computer simulation in progress and changing one of the variables drastically before restarting. The third trace shows that even with an unreasonable initialization, which might be caused by a computer programming error, the output of the RQCS reached the "correct" response within the 16 m shown in the plots. These results indicate that, for all practical purposes, no lead-in is required if: 1) the initializations of Eqs. 41 - 43 are used, and 2) calibration sites are selected such that the preceding 20 m have similar roughness qualities. Measurement Interval. The "true" RARS value is obtained with a sample interval approaching zero. In order to show the effects of sample interval on the roughness statistics, the 28 profiles obtained with the TRRL beam were decimated to yield profiles having intervals that were multiples of the original 100 mm. Some of the data obtained are plotted in Figure F.9 to show the effect of sample interval on the RARS50 numeric. In each plot, the dashed line is the line of equality, on which the data points should lie for perfect agreement. The solid lines are quadratic regression curves, which indicate trends in the data. The plots indicate that as the measurement 278 Eo RQCS output using assumed initial values, starting at x=60 m E 7 ( r ,,- - True RQCS output, which started at x=O 0~ (0 CO O - Demonstration of Erroneous RQCS output caused by deliberate error. ,~~~~ O. 60 62 64 66 68 70 72 74 76 Longitudinal Position - m Figure F.8. Initialization of RQCS 04~~~0 4-I~~~~~~~~~~~I o / X0 ELOaL 0 0 1 20 25 5 10 16 20 2 RARSo with Original Data RARSIC from Original Data a. 200 mm Interval b. 300 mm Interval 0 ~~~~~~0 .E Lo ELoL O 0 VC~~~~~~~~~~4~V w 0 .... .. ~~~ ~~~~~~~~~~C-)'--- - - 0 5 10 15 20 2 0 16 RARS.o from Original Data RARS. from Original Data c. 500 mm Interval d. t. O m Interval Figure F.9. Effect of Measurement Interval on RARS 50' 280 interval increases up to 500 mm, there is negligible bias introduced, but that the random error (scatter) increases slightly. (A possible exception might be the two roughest measures shown in Fig. 9c, in which the RARS50 values from the decimated profile data are slightly lower; however, it is not possible to say whether this bias is due to a characteristic of rough unpaved roads, or simply chance, since the error is of the same magnitude as the random scatter.) Fig. 9d illustrates the bias error that occurs when the sample interval is so large that significant variations in profile between measurements are missed: RARS50 numerics calculated from a profile with the 1.0 m spacing are low by 50%. The data shown in Figure 9, along with similar data from the APL Trailer (not shown), indicate that random error in the RARS50 computation can be held to negligible levels by using a measurement interval less than 250 mm, while unbiased but less accurate measures can be obtained using an interval of 500 mm. The interaction of speed and required measurement interval is illustrated in Figure F.10, which shows that a sample interval of 500 mm is not adequate for the lower simulation speeds of 20 and 32 km/h, but that good results are obtained for a simulation speed of 80 km/h. For the higher speeds of 50 and 80 km/h, there is negligible bias error, but the random error still exists, indicating that a shorter interval (250 mm) is needed for the best accuracy. Precision in the Elevation Measurement. It has been known that the precision needed in profile measurement for analysis through QCS is a function of the roughness, with better precision needed on smoother roads [381. A statement of necessary precision therefore depends on the range of roughness being evaluated. A candidate specification was considered in which the required precision is simply proportional to the roughness of a road, when expressed as RARS50. An analysis of the profile data obtained from the TRRL Beam was performed to determine: 1) if this type of specification is reasonable, and 2) if it is reasonable, what quantities are involved? In this analysis, the precision of the measurement was assumed to be limited solely by the quantization of the continuous height variable into digitized quantities, which were originally 1.0 mm. The random measurement 281 0 0 RARSX/ / l Lo ~a 20 kmhb.3Ok E ~~~~~~~~E °- T / E~~~~~~~~~~~ U) / I 0 ~ ~~~~30 0 5 lb 20 40 0 30 20 RARS.O from 100 mm data RARS. from 100 mm Data a. 20 km/h b. 32 km/h 14RAR Copuaton 282 0 LO~ ~~~~ o a0 E o E o V- ~~~~~~0 LO LO 0 RARSIG from 100 mm Data RARS.O f rom 100 mm Data c. 50 km/h d. 80 km/h Figure F.10. Interaction of Measurement Interval and simulation Speed on the RARS Computation. 282 errors that also degrade precision were not considered. For each of the 28 measured profiles, the RARS50 value obtained with the original profile was used to determine a new quantization level (greater than 1 mm). The profile was then quantized to the nearest multiple of this new level, and re-processed to yield a new RARS50 numeric. Figure F.11 shows the results for four levels of increased quantization (degraded precision). In all cases, the effect of the degraded precision is an increase in the computed roughness numeric. The changes were calculated from the difference in the (solid) quadratic regression lines and the (dashed) equality line (x = y), and were found to be nearly constant across the range of roughness when expressed as a percentage. (For example, for the case of precision = 0.3 RARS, shown in Fig. F.11c, the errors were 1.7% at RARS50 = 5, 2.0% at RARS50 = 10, 1.7% at RARS50 = 15, and 1.2% at RARS50 = 20.) This indicates that the candidate method of specifying required precision in proportion to roughness is valid. For RARS50 accuracy within 1.0%, the precision (mm) should be less than 0.2 RARS50 (m/km), while for accuracy within 2%, the precision should be less than 0.3 RARS50. Thus, on the smoothest sites, which had RARS50 values near 2 m/km, the actual measurement precision of 1.0 mm probably led to numerics that are several percent higher than the "true" RARS50 values. A measurement precision of 0.5 mm would have been better. At the other end of the scale, where roughness levels were greater than 15 m/km, a measurement precision of 3 mm (better than .2 RARS50) gave the same results as the original precision of 1 mm. Summary of RQCS Data The summary RARS numerics that were obtained from four methods of profile measurement are presented in Tables 3 - 6. All of the RARS numerics have the units: slope x 10O3 (m/'km, mm/m, etc.). Only those numerics are presented for which the profile bandwidth covered the RQCS bandwidth, as defined in Eq. 23. For the lower speeds of 32 and 20 km/h, the 500 mm spacing used with the rod and level is inadequate, and the RARS numerics are not shown. But at the higher simulation speeds of 50 and 80 km/h, the 500 mm spacing used with the rod and level was adequate (although a shorter interval is recommended for future work to improve repeatability), and thus at least one RARS numeric computed from a statically measured profile is presented for 283 0 0 - - - - L. ~~~~~~~~~~~~~L. 0-~~~~~~~ m _ 7 ? m Lo 0 O IA E /X~~/0 C4 0 W i~~~~~~ry 0 U|-t OV~~~ 0: 0 10 2--0 30 10 20 30 RARS20 from Static Measures RARS. from Static Measures cc. APL 25 for Sim. Speed of 20 b. APL 25 for Sim. Speed of 32 0 04~ ~ ~ / N / E I e~~~~m RMS Diff. 1.6 rn/km 0 5 10 15 20 RARSI. from Static Measures c. APL 25 for Sim. Speed of 50 Figure F.14. Accuracy of RARS as measured with APL 25. 295 Calibration when Simulation Speed = Measurement Speed. The comparisons between ARS measured with four of the RTRRMSs and RARS are illustrated in Figures F.15 - 18. Results from the Caravan-BI system (not plotted) are virtually the same as for the Caravan-NAASRA system. Results for the two Opala-Maysmeter systems that are not plotted are generally similar to those of the system that is shown in the figures. In each comparison, the simulated speed of the RQCS matches the RTRRMS speed. For the passenger car-based systems, the "Ave." RARS values from Tables F.3 - F.6 were used. Comparisons with the two single-track RTRRMSs (BI Trailer and BPR Roughometer) are on the basis of single wheeltracks. Thus, the plots involving the trailers generally have twice as many data points. In each figure, the solid curved line is a quadratic regression line obtained from all of the data points shown, based on minimizing the RMS error in estimating RARS. For the lower speeds of 20 and 32 km/h, there are only valid static measures of RARS on 19 of the test sites (30 wheeltracks), and therefore the RARS numerics computed wfrom the APL signals are shown. (For the speeds of 50 and 80 km/h, RARS was measured statically for all 49 test sites (98 wheeltracks).) These four figures lead to the following observations: Overall correlation. By and large, the RARS numeric is highly correlated with the ARS numerics obtained from all types of RTRRMSs that participated in the IRRE. Most of the data points lie very close to the regression curve in each figure, and the measures on all four types of surface are uniformly distributed about the curve in most cases (exceptions are noted below). Error distribution. Errors, as defined by the scatter about the regression curves in the vertical direction, are fairly uniform across the roughness range. Therefore, least-squares regression models should assume equal significance of error across the scale. Transformations of the variables that change the weighting of error, such as linear regressions of 296 o X CA X m CA a TS ~ + + T E A GR E *GR NE +TE N-Q + TE + ~ ~ ~ ~ A + A + o 0 0 10 20 30 40 0 ?0 20 30 40 ARS20 - m/km ARS20 - m/km a. Opala-Maysmeter #2 b. Caravan-NAASRA El A0 S+. E1k~(I S o 10 20 30 40 5010l 20 30 4 ARS20 - rn/km ARS20 - rn/km o &A0* <~c Bl. ,1 x A u) o + C 0 I. TS0+T O ~~~~~~~~~O- 0 10 20 30 0 10 20 30 ARS50 - m/km ARS50 - m/km a. Opala-Maysmeter #2 b. Caravan-NAASRA Fg 2xCA c r o t exCA o.TS + #3TS E LO A +GR A E '+R N--I+x TE 2 10 A +A + x+ V) V~~~~~~~~~~) 0 10 20 30 0 2 4 6 8 ARS50 mlrnkm ARS50 - rn/km c. B1 Trailer d. BPR Roughometer Fig. F.2l. Example calibration plots to estimate RARS80 from ARS50 measures. 310 Table F.l1 ,Standard Errors for Estimating RARS80 from Quadratic Regression Equations and ARS Measurements. Opala Cars with Caravan Car Single-track Surface Modified Maysmeters with 2 meters Trailers speed Type MM 01 MM 02 MM 03 BI NAASRA BI BPR 20 CA 0.49 0.41 0.36 0.44 0.43 0.59 0.87 TS 0.33 0.33 0.25 0.29 0.27 0.42 0.30 GR 0.61 0.74 1.28 0.51 0.51 0.73 0.70 TE 1.14 0.45 0.48 0.59 0.56 0.68 0.64 ALL 0.95 1.02 1.09 0.90 0.89 1.01 1.22 32 CA 0.42 0.31 0.61 0.36 0.33 0.52 0.81 TS 0.24 0.25 0.24 0.29 0.29 0.34 0.32 GR 0.43 0.78 1.10 0.56 0.53 0.64 0.61 TE 1.16 0.40 0.81 0.80 0.65 0.83 0.51 ALL 0.81 0.70 0.96 0.74 0.69 0.81 1.17 50 CA 0.35 0.51 0.40 0.19 0.18 0.40 0.65 TS 0.38 0.36 0.38 0.33 0.32 0.33 0.44 GR 0.44 0.56 0.69 0.59 0.58 0.75 0.67 TE 0.43 0.51 0.68 0.93 0.57 1.07 0.77 ALL 0.58 0.59 0.74 0.68 0.58 0.76 0.95 80 CA 0.23 0.14 0.47 0.30 0.16 ... 0.36 TS 0.36 0.32 0.43 ... ..... GR 0.48 0.39 0.44 ... ... ... TE 1.03 0.41 0.44 ... ... ... ALL 1.00 0.84 1.02 ... ... ... 311 Table F.11. r2 Values Obtained from Quadratic Regressions Between RARS80 and the ARS Measurements. Opala Cars with Caravan Car Single-track Surface Modified Maysmeters with 2 meters Trailers speed Type MM 01 MM 02 MM 03 BI NAASRA BI BPR 20 CA 0.9186 0.9415 0.9557 0.9325 0.9365 0.8848 0.7478 TS 0.8951 0.8989 0.9401 0.9227 0.9291 0.8445 0.9197 GR 0.9633 0.9457 0.8373 0.9745 0.9742 0.9501 0.8922 TE 0.8487 0.9859 0.9833 0.9754 0.9779 0.9683 0.9597 ALL 0.8949 0.9035 0.8901 0.9246 0.9262 0.9074 0.7852 32 CA 0.9385 0.9679 0.8720 0.9547 0.9616 0.9113 0.7827 TS 0.9462 0.9423 0.9459 0.9176 0.9180 0.8976 0.9100 GR 0.9812 0.9390 0.8791 0.9687 0.9722 0.9614 0.9183 TE 0.8437 0.9887 0.9529 0.9547 0.9705 0.9530 0.9755 ALL 0.9224 0.9539 0.9140 0.9494 0.9561 0.9407 0.8005 50 CA 0.9583 0.9107 0.9454 0.9878 0.9892 0.9464 0.8614 TS 0.8660 0.8796 0.8611 0.8943 0.9008 0.9057 0.8255 GR 0.9806 0.9684 0.9524 0.9647 0.9669 0.9469 0.8994 TE 0.9781 0.9813 0.9668 0.9382 0.9769 0.9210 0.8517 ALL 0.9609 0.9677 0.9495 0.9568 0.9690 0.9472 0.7753 80 CA 0.9817 0.9936 0.9227 0.9603 0.9883 ..... 0.8838 TS 0.8798 0.9030 0.8264 ..... .. .... ... .. . ... GR 0.9409 0.9606 0.9520 ..... ..... ..... ... . TE 0.7883 0.9662 0.9624 ... .. .. ... .. ... ALL 0.7923 0.8532 0.7850 ..... ..... ..... 312 because the wavebands covered by the RTRRMS no longer match that of the RQCS, due to the speed difference. The relationship between the two depends on the relative spectral content of the road, which differs with surface type. One physical reason for the fairly good results obtained at lower speeds is that some of the random errors in the RTRRMS measurement are reduced by greater averaging, since a longer time is spent making the measurement. The same effect can be obtained for higher speeds by using longer calibration sites. A second reason for better results at low speeds appears to apply to the BPR Roughometer. When operated at the lower speeds, the RTRRMS is subjected to less excitation (ARV). Errors due to vibration levels exceeding the design limits of the vehicle and roadmeter are reduced by reducing the vibration levels. Of course, this effect disappears when more rugged RTRRMSs are used. Calibration Across Speed The IRI selected in this report is based on the concept that a given road has only a single "true" roughness value, regardless of how it is used by the public. An alternative concept is that a road roughness measure should reflect how the road is used, such that a high-quality road used at high speeds might be rated the same in terms of perceived roughness as a lower quality road used at low speeds. When ARS numerics are used to estimate RARS over a range of speeds, there is a question of how many calibration curves are needed. Should a separate curve be used for every speed encountered? Or can a single calibration curve be used across speed? Prior to the IRRE, it has been shown that substantial calibration errors can be introduced when ARS measures taken at different speeds are compared to the corresponding RARS measures, and that the errors are eliminated by using ARV as the roughness numeric [9, 29]. Figure F.22 confirms that a single ARS/RARS calibration across speed does not exist for the RTRRMSs that participated in the IRRE. On paved roads, substantial errors would be introduced by using a ARS-to-RARS regression obtained for one speed for ARS-to-RARS rescaling at a different speed. 313 O 0 m 20 km/h z o 32 km/h cU E ' 50 km/h + '-. 80 km/h ED EA 0 5 10 15 0 10 20 30 40 ARS -m/km ARS - m/km a. MM #2 on Paved Sites b. MM #2 on Unpaved Sites OT °T ig 20 km/h , m @ ~~~~~32 km/h <~ ~~~~~1 A- 507 km2 kmhh C~~~~~~.J~~~~' cr- 2~+ 0 km/h y,/#/ ^ e32 km/h 0 . * 50 km/h 0 5 10 15 0 10 20 30 40 ARS - m/km ARS - m/km c. BM Tr#iler on Paved Sites. d. MM Tr#iler on Unpaved Sites. Figure F.22. Calibration across speed using ARS and RARS numerics. 314 Figure F.23 shows the same data points, rescaled to ARV units (mm/sec). When converted to ARV, the agreement is much better, such that it would be reasonable to use a single calibration across speed. This is because the ARV is the vehicle response variable actually measured by the RTRRMS. It is easy to show that if a valid ARV relation exists, then a corresponding ARS relation cannot exist except under certain conditions. A valid ARV calibration across speed would have the form: E [RARV] = CARV = A + B ARV + C ARV2 (F-45) Since ARV and ARS are related by measurement speed, Eq. 45 can be converted to an ARS equation: CARS = CARV / V = A / V + B ARV / V + C ARV2 / V = A / V + B ARS + C V ARS2 (F-46) Eq. 46 cannot be independent of speed unless the offset A and the curvature C are both zero. Although a calibration across speed can be demonstrated for the RTRRMSs that participated in the IRRE, an ARV calibration across speed is not guaranteed due to the presence of nonlinearities in RTRRMSs [9]. Often, however, the factors that introduce a speed dependency are small enough that a calibration equation obtained at one speed (e.g., 50 km/h) can be used at another speed (e.g., 32 km/h) if the RTRRMS and RQCS measures are converted to ARV units. 315 O c 20 km/h 8 m 20 km/h ol 0. cJ 0 32 km/h " 032 km/h u c - 50 km/h + A50 km/h ( LO, , (D , I , , , ,O co, + 20 km/h o 5 20 km/,h E i > _ E + +~~~~~~~~~~~~~ >0 > 0 0~~~~~~~ 0 50 200 30 0 100 200 300 400 ARV - mm/sec ARV - mm/sec a. MM #2 on Paved Sites. b. MM #2 on Unpaved Sites 0" w20 km/h 0" m20 km/h LO I 0 a 32 km/h o 032 km/h C) A 50 km/h A *50 km/h 0 A U)~~~~~~N O' E E um A I 3 0 > 0 50 ~100 150 0 100 200 300 400 ARV- mm/sec ARV - mm/sec c. BI Trailer on Paved Sites. d. BI Trailer on Unpaved Sites. Figure F.23. Calibration across speed using ARV and RARV numerics. 316 APPENDIX G APL ANALYSES USED IN EUROPE prepared by The French Bridge and Pavement Laboratory (LCPC), The Belgian Road Research Center (CRR), The University of Michigan Transportation Research Institute (UMTRI), and The Brazilian Road Research Institute (IPR/DNER). The Longitudinal Profile Analyser (APL) Trailer, developed by LCPC, produces a profile signal which replicates the frequency content of the longitudinal profile of a pavement section over the frequency range 0.5 - 20 Hz. The profile signal obtained from the APL Trailer can then be processed any number of ways to provide simple and quantified roughness information appropriate to a particular application. The CAPL 25 measurement is used for low-speed (21.6 km/h) evaluation of road quality during construction, while the APL 72 system provides for the high-speed measurement (72 km/h) of three independent roughness numerics to describe the condition of existing roads in greater detail. A very similar roughness analysis, which results in three evenness coefficients (CP), is used by CRR in Belgium. Appendix A describes the APL instrument itself and the methods used to record profile data during the International Road Roughness Experiment (IRRE). This appendix presents: 1) mathematical properties of the CAPL 25, APL 72, and CP numerics, 2) the measures of these numerics obtained in the IRRE, 3) correlations between these measures and those obtained from response-type road roughness measuring systems (RTRRMSs), and 4) examples of how plotting the APL profile can be used to visually diagnose pavement condition. Plots of power spectral density (PSD) functions obtained from the APL Trailer are included in Appendix I along with similar plots obtained from static profile measurements. Additionial CP-type analyses are presented in Appendix J, in which the moving average analysis is applied to both the APL 72 profiles and statically 317 measured profiles. The results reported in this appendix were obtained during two analysis operations. The first was done in Brazil by the LCPC team during the IRRE, and provided the CAPL 25 coefficients and the APL 72 indices. Further analyses were performed in Europe by carrying out spectral density analysis, energy analysis (LCPC method), and coefficient of evenness (CP) analysis (CRR method). DESCRIPTION OF THE APL SUMMARY NUMERICS CAPL 25 The APL 25 configuration of the APL trailer was originally designed to evaluate the quality of roughness of road layers during construction. It had to meet the objectives of great ease of use and of simplicity of data analysis. A relatively low standard speed of 21.6 km/h (6.0 m/sec) is used because high-speed measurements can give rise to problems on a construction site. The name of the measure is based on the standard test length of 25 meters which is used for the calculation of a roughness numeric called the APL 25 coefficient (CAPL 25). During testing, the transducer signal is recorded graphically (scale 1/200) on an analog paper recorder, and at the same time, digitized every 0.25 meter. The digitizing equipment is set so that the value varies about zero, with the value zero being obtained when the system is at rest. The absolute values of the samples are summed, and averaged over the 25 m test section (100 samples). This average is the CAPL 25 coefficient, which can be converted to millimeters by a scale factor associated with an amplifier gain setting. Physically, the CAPL 25 is the average rectified displacement of the arm on the trailer supporting the follower wheel, relative to the horizontal pendulum used as an inertial reference. The computation of the CAPL 25 coefficients is carried out during the measurement and their values are printed on the recorder strip chart. When the sections that are measured are several kilometers long, it is more convenient to record the digitized signal on magnetic tapes and have it processed with a mini-computer. Further .318 information about the APL 25 methodology is available in Reference [151. The transducer signal processed to yield the CAPL 25 result is filtered only by the mechanical properties of the APL trailer, which are shown by the Bode plot in Figure G.1. At the 6.0 mts towing speed, the bandwidth of the APL signal (approximately 0.4 - 20 Hz) includes wavelengths from 0.3 to 15 m, as shown in the figure. The normal spectral content of roads is such that when profile is characterized by a displacement (elevation) measure such as the CAPL 25 numeric, the measure will be dominated by the lowest wave numbers (longest wavelengths) within the response range of the trailer. (See Appendix I for more information on spectral content of simple roughness numerics.) It will be seen later that the mode for quantifying roughness represented by the CAPL 25, which is very well adapted to judge the quality of a road construction or to evaluate the present state of a road network, is not the best method available to provide an appreciation of the typical dynamic response of the vehicle. But in the same way that coefficients of roughness were determined (CRR method, described later) from APL 72 signals, it would have been possible to obtain analog coefficients with the APL 25 signal offering better correlations with the RTRRMSs. For example, CRR uses both the APL 25 signal and the APL 72 signal to compute CP numerics. However, these analyses were not performed during the IRRE because they would have been redundant to those applied to the APL 72. APL 72 Analyses used in France The APL 72 analyses are the most commonly used in France by the Road Administrations for the purpose of routine surveying of the road networks [161. The measures are taken at 72 km/h (20 m/sec), because at this speed, the APL Trailer detects profile variations for wavelengths between 1 and 40 m (Fig. G.1). As described in Appendix A, the profiles are stored on magnetic tape, to be played back later in the laboratory for analysis. The APL 72 analysis used in France is based on the global energy (mean square value) of a signal. Road roughness is characterized by three numerics, 319 output/input displacement O,9/ Lo) 0 ,L 0,5 0,6 0,7 0,8 0,9 1 1,5 2 2,5 3 4 5 5 7 F 9 10 15' 20 25 30 frequenciesHertz APL '72' ' I I I I ' 5om 40m lom 2,5m 1,25m lm I a | wavelength range at 20.0m/ speed I I I APL -25- I - ___I 15m 12m 3m 1,Om 0,3m wavelength range at 6.Om/s speed Figure G.1 Frequency Response of APL Trailer to displacement input computed for every 200 m. The three values are obtained by playing the signal back from the tape recorder through three electronic band-pass filters. During playback, the tape speed is increased to reduce processing time and to avoid the need for filters with extremely low frequency characteristics. The filters are set to separate the short, medium, and long wavelength roughness content. These ranges (wavebands) were chosen to distinguish between profile roughness affecting user safety (shorter wavelengths) and those affecting user comfort (longer wavelengths). The three wavebands are: 1.0 - 3.3 m/cycle Short Wavelength (SW) 3.3 - 13 m/cycle Medium Wavelength (MW) 13 - 40 m/cycle Long Wavelength (LW) The intermediate limits (3.3 m and 13 m) where chosen to be related to the characteristics of devices used previously in France (3 m straightedge, viagraphe). The signal delivered by each filter is squared and integrated over a length of 200 meters. Thus, for every 200 meters of road three mean-square values of energy (W) are obtained for the signal (one for each wavelength range). To each of these energy values, one can associate a value of "equivalent amplitude" (Y) expressed in mm, which would be the amplitude of a sinusoidal signal, the wavelength of which is the median value of the filter range, and which would deliver the same energy. More usually, the energy values (W) are spread within 10 classes (called Index (I) for the IRRE) graded, from 1--the worst level of roughness to 10--the best level, in an approximately logarithmic way. Further details of this APL 72 Analysis are available in Reference [171. In normal operation, the profiles of the right and left wheel-tracks are measured simultaneously with two APL trailers. In this experiment, the tracks were analyzed separately, and roughness measures were reported for each wheeltrack. 321 APL Analyses used in Belgium The characterization of evenness (roughness) that is used is based on a geometric type of representation of the longitudinal profile. This representation makes use of a numerical filtering of the measured profile with a moving average technique. The option taken through this choice of representation offers the advantage of providing a straightforward geometrical interpretation, useful in practice [201. The characterization of the measured profile is obtained by evaluating the difference of the surface profile from the reference line obtained by smoothing the same profile. The process of applying a moving average to the signal acts as a filter attenuating short length irregularities. For its application, this technique requires the numerically sampled signal recorded from the APL trailer. The distance marks for sampling are provided by a pulse train issued from the measuring wheel of the APL mounted as an odometer. The sample interval is such that all of the information contained within the bandwidth of the APL trailer is retained. (Information theory requires a sampling frequency at least equal to twice the higher cut-off frequency of the APL measuring device.) After the recorded profile is sampled and converted to a set of numerical values, those values are, in turn, smoothed using a moving average over an arbitrary baselength. The mean absolute value of the difference between the original profile and the smoothed one over a given section is determined. This mean value, divided by two and expressed per unit length, has been defined as the coefficient of evenness (CP: "coefficient de planeite"). The CP unit has the following dimensions: 1 Cp = 10-5 m (= 104 mm2/km) Since the mean value is divided by two, one mm of the mean absolute value is equal to 50 CP units. It should be noted that the process of summation involving a moving average has a value dependent on the baselength used. Thus, the CP value must be associated with the base length, e.g., CP2.5. For a given baselength, the roughness level increases as the CP increases. 322 The computations performed at the Belgian Road Research Center (CRR) used the APL 72 signals recorded in Brazil at a measurement speed of 72 Km/h (20 m/s). The sampling step length used is 1/3 meter, and the coefficients of evenness (CP) were determined for the baselengths of 2.5 m, 10 m, and 40 m, which are the conventional values used. The CP is normally evaluated for hectometric (100 meters) sections. In the IRRE, the CP of each 320 m profile was therefore chosen as the mean value of the CP of three contiguous hectometric blocs, starting at the beginning of each section track. As mentioned earlier, the same CP statistic is applied in Belgium to APL 25 measurements performed at the speed of 6 m/s (21.6 Km/h). The sampling step length used in that case is of 1/6 meter and the baselengths considered for the moving average are mainly 15 m and 2.5 m. The moving average filter is analyzed in detail in Appendix J, to derive its frequency response, including the effects of sample interval. FINDINGS FROM THE TIRR Measures of APL Sumary Statistics CAPL 25. The APL 25 system produces CAPL 25 numerics for every 25 m of travelled road. Therefore, each 320 test section had 12 or 13 associated CAPL 25 numerics for each wheeltrack. To facilitate comparisons with other numerics, each profile is characterized by the mean of the 12 or 13 CAPL 25 values. The APL 25 results that were obtained in the IRRE are presented in Tables G.1 - G.4. In these tables, the four surface types are: asphaltic concrete, surface treatment, gravel, and earth. They are abbreviated according to their spelling in Portuguese as CA, TS, GR, and TE, respectively. APL 72. During the IRRE, all the paved sections (CA and TS) were measured by the APL 72 in each track (right and left), several times for some 323 Table G.l. Summary of APL Results for the Asphaltic Concrete Roads. INTERNA/JTIc'NL ROAD ROL$&HNESS E)XPERIMENT - BRASI1LIA - JUNE 1982 APL TRAILER SITE MEAS. TRACK ROUSHNESS MEASUREMENTS MEAN RUN I RUN 2 RUN 3 SIGMA SIN TREND R CAOI 25 R 18.5 18 19 .7 .038 1 1 25 L 15 15 15 0 0 0 0 72 SW R 4 4 4 4 0 0 0 0 72 s5 L 3.3 3 3 4 .6 .173 .5 .866 72 NW R 3 3 3 3 0 0 0 0 72 MW L 3 3 3 3 0 0 0 0 72 LW R 3.3 4 3 3 .6 .173 -.5 -.866 72 LK L 3 4 2 3 1 .333 -.5 -.5 CA02 25 R 14 14 0 0 0 0 25 L 16 16 0 0 0 0 72 SW R 2.7 2 3 3 .6 .217 .5 .866 72 SW L 2.7 2 3 3 .6 .217 .5 .866 72 MW R 3.7 3 4 4 .6 .157 .5 .866 72 Mg L 2.7 2 3 3 .6 .217 .5 .866 72 LH R 4 4 4 4 0 0 0 0 72 LM L 4.3 4 5 4 .6 .133 0 0 CA03 25 R 16.5 17 16 .7 .043 -1 -1 25 L 18 18 18 0 0 0 0 72 SW R 1.5 1 2 .7 .471 1 1 72 SW L I I 1 0 0 0 0 72 NW R 3 3 3 0 0 0 0 72 NW L 3 3 3 0 0 0 0 72 L R 3.5 4 3 .7 .202 -1 -1 72 Lk L 4 5 3 1.4 .354 -2 -1 CAo4 25 R 15.5 16 15 .7 .046 -1 -I 25 L 18 18 18 0 0 0 0 72 SW R 2 2 2 0 0 0 0 72 SV L 1.5 1 2 .7 .471 1 1 72 NW R 2.5 2 3 .7 .283 1 1 72M"W L 2 2 2 0 0 0 0 72 LW R 3 3 3 0 0 0 0 72 LW L 3 3 3 0 0 0 0 CA05 25 R 16 16 16 0 0 0 0 25 L 20 20 20 0 0 0 0 72 SW R 2.5 3 2 .7 .283 -1 -1 72 SW L 1.5 2 1 .7 .471 -1 -1 72 NW R 3 4 2 1.4 .471 -2 -1 72 NW L 2.5 3 2 .7 .283 -1 -1 72 LW R 3.5 3 4 .7 .202 1 1 72 LW L 3.5 3 4 .7 .202 1 1 CA06 25 R 18 18 0 0 0 0 25 L 20 20 0 0 0 0 72 SW R 2 2 0 0 0 0 72 SW L I I 0 0 0 0 72 NW R 4 4 0 0 0 0 72 MN L 4 4 0 0 0 0 72 Lk R 3 3 0 0 0 0 72 LH L 3 3 0 0 0 0 CA07 25 R 7 7 7 0 0 0 0 25 .L 7 7 7 0 0 0 0 72 SW R 4 4 4 0 0 0 0 72 S L 3 3 3 0 0 0 0 72 NW R 6 6 6 0 0 0 0 72 Mn L 6 6 6 0 0 0 0 72 LW R 6 6 6 0 0 0 0 72 Lk L 8 8 8 0 0 0 0 324 Table G.1 (Cont.) INTERNiATIONAfL ROPD ROI6GHNESS EAPERIMENT - BRPSILIR - JUNE 19G2 APL TRAILER SITE HEAS. TRACK ROUSHNESS MEASUREMENTS MEAN RUN I RUN 2 RUN 3 SIGMA SIR TREND R CAQ8 25 R 7 7 7 0 0 0 0 25 L 7 7 7 0 0 0 0 72 SW R 4 5 3 1.4 .354 -2 -1 72 SW L 4 4 4 0 0 0 0 72 NW R 6.5 7 6 .7 .109 -1 -1 72 MW L 7 7 7 0 0 0 0 72 LW R 7 7 7 0 0 0 0 72 LW L 6 6 6 0 0 0 0 CA09 25 R 12 12 12 0 0 0 0 25 L 10 10 10 0 0 0 0 72 SW R 3.5 4 3 .7 .202 -1 -1 72 SW L 3 4 2 1.4 .471 -2 -1 72 NW R 5.5 5 6 , .7 .129 1 1 72 MW L 5 5 5 0 0 0 0 72 LW R 4.5 5 4 .7 .157 -1 -1 72 LW L 4 4 4 0 0 0 0 CAIO 25 R 11 11 11 0 0 0 0 25 L 11 11 11 0 0 0 0 72 SW R 3.5 3 4 .7 .202 1 1 72 SW L 2 2 2 0 0 0 0 72 NW R 5.5 5 6 .7 .129 1 1 72 MW L 5 5 5 0 0 0 0 72 LW R 6 6 6 0 0 0 0 72 LW L 5 5 5 0 0 0 0 CAII 25 R 17 17 0 0 0 0 25 L 15 15 0 0 0 0 72 SW R 2 2 0 0 0 0 72 SW L 3 3 0 0 0 0 72 NW R 2 2 0 0 0 0 72 W L 4 4 0 0 0 0 72 LW R 4 4 0 0 0 0 72 LM L 5 5 0 0 0 0 CA12 25 R 5 5 5 0 0 0 0 25 L 5 5 5 0 0 0 0 72 SW R 6 6 6 6 0 0 0 0 72 SW L 6 6 6 0 0 0 0 72 NW R 8 8 8 8 0 0 0 0 72 NW L 8.5 8 9 .7 .083 1 1 CA13 25 R 5 5 5 0 0 0 0 25 L 6 6 b 0 0 0 0 72 SW R 6 6 6 6 0 0 0 0 72 SW L 6 6 6 6 0 0 0 0 72 NW R 7 7 7 7 0 0 0 0 72 MW L 8 8 8 8 0 0 0 0 72 LW R 6 6 6 6 0 0 0 0 72 L L 6 6 6 6 0 0 0 0 325 Table G.2. Summary of APL Results for the Surface Treatment Roads. INTERNATIONAL ROAD ROUGHNESS EXPERIMENT - BRASILIA - JUNE 1982 APL TRAILER SITE HEAS. TRACK ROU6HNESS HEASURENENTS MEAN RUN I RUN 2 RUN 3 SIGMA S/H TREND R TSOI 25 R 7.6 7.6 7.5 .1 9E-03 -. I -I 25 L 7.3 7.5 7.3 7.2 .2 .021 -.15 -.982 72 SW R 2 2 2 2 0 0 0 0 72 SW L 2 2 2 2 0 0 0 0 72 MN R 6.7 7 7 6 .6 .087 -.5 -.866 72 NW L 6 6 6 6 0 0 0 0 72 LW R 6.7 7 7 6 .6 .097 -.5 -.866 72 Lk L 7 7 7 7 0 0 0 0 TS02 25 R 9.4 9.4 0 0 0 0 25 L 9.6 9.6 0 0 0 0 72 SW R 2 2 0 0 0 0 72 SW L 2 2 0 0 0 0 72 NV R 5 5 0 0 0 0 72 HL L 6 6 0 0 0 0 72 LN R 4 4 0 0 0 0 72 LN L 6 6 0 0 0 0 TS03 25 R 10.8 10.8 10.8 0 0 0 0 25 L 10 9.8 10.2 .3 .028 .4 1 72 SW R 2 2 2 2 0 0 0 0 72 SU L 1.3 2 1 1 .6 .433 -.5 -.866 72 NV R 6 6 6 6 0 0 0 0 72 NW L 6 6 6 6 0 0 0 0 72 L R 4 4 4 4 0 0 0 0 72 LW L 5 5 5 5 0 0 0 0 TS04 25 R 10 10 0 0 0 0 25 L 8.7 8.7 0 0 0 0 72 SW R I I I 1 0 0 0 0 72 SW L 1.7 2 2 1 .6 .346 -.5 -.866 72 NW R 6 6 6 6 0 0 0 0 72 NW L 6 6 6 6 0 0 0 0 72 LW R 6 6 6 6 0 0 0 0 72 LH L 6.3 6 7 6 .6 .091 0 0 TS05 25 R 8.5 8.5 0 0 0 0 25 L 9.4 9.4 0 0 0 0 72 SW R I 1 1 0 0 0 0 72 SW L I I I 0 0 0 0 72 NW R 6 6 6 0 0 0 0 72 MN L 6.5 7 6 .7 .109 -1 -1 72 LW R 8.5 9 8 .7 .083 -I -I 72 L L 9.5 a 9 .7 .083 1 1 TS06 25 R 7.9 7.9 0 0 0 0 25 L 8.4 8.2 8.5 .2 .025 .3 1 72 SW R 4 4 0 0 0 0 72 SW L 3 3 0 0 0 0 72 NV R 6 6 0 0 0 0 72 IW L 6 6 0 0 0 0 72 LW R 7 7 0 0 0 0 72 LH L 6 6 0 0 0 0 TS07 25 R 8 8 0 0 0 0 25 1 9.9 8.8 9 .1 .016 .2 1 72 SW R 4 4 0 0 0 0 72 SW L 4 4 0 0 0 0 72 NM R 5 5 0 0 0 0 72 NW L 5 5 0 0 0 0 72 LW R 6 6 0 0 0 0 72 LW L 6 6 0 0 0 0 326 Table G.2 (Cont.) IH7ERNj9TIONHL ROAD ROLUHNESS EXPERIMENT - BRASILIA - JUNE 1982 APL TRAILER SITE fEAS. TRACK ROU6HNESS MEASUREMENTS MEAN RUN I RUN 2 RUN 3 SIGMA S/H TREND R TS08 25 R 11.6 11.5 11.7 .1 .012 .2 1 25 L 10.3 10.4 10.1 .2 .021 -.3 -1 72 SW R 3 3 3 0 0 0 0 72 SW L 3 3 3 0 0 0 0 72 NW R 4 4 4 0 0 0 0 72 NW L 4 4 4 0 0 0 0 72 LO R 3 3 3 0 0 0 0 72 L L 3 3 3 0 0 0 0 TS09 25 R 8.8 8.9 8.7 .1 .016 -.2 -1 25 L 6.8 6.8 6.8 0 0 0 0 72 SW R 2 2 0 0 0 0 72 SW L 3 3 0 0 0 0 72 MW R 7 7 0 0 0 0 72 W L 7 7 0 0 0 0 72 LW R 5 5 0 0 0 0 72 LW L 6 6 0 0 0 0 TS10 25 R 7.4 7.4 7.4 0 0 0 0 25 L 7 7 7 0 0 0 0 72 SW R 3 3 0 0 0 0 72 SW L 2 2 0 0 0 0 72 NW R 6 6 0 0 0 0 72 NW L 7 7 0 0 0 0 72 LW R 8 8 0 0 0 0 72 LW L 9 9 0 0 0 0 ISII 25 R 4.5 4.5 4.5 0 0 0 0 25 L 4.7 4.7 4.6 .1 .015 -.1 -1 72 SW R 4 4 4 0 0 0 0 72 SW L 5 5 5 0 0 0 0 72 NW R 8 8 8 0 0 0 0 72 NW L 7 7 7 0 0 0 0 72 LW R 9 9 9 0 0 0 0 72 L L 8 8 8 0 0 0 0 TS12 25 R 5.5 5.4 5.5 .1 .013 .1 1 25 L 4.8 4.7 4.8 .1 .015 .1 1 72 SW R 5 5 5 0 0 0 0 72 SW L 5.5 6 5 .7 .129 -1 -1 72 MW R 8.5 9 8 .7 .083 -1 -1 72 MW L 10 10 10 0 0 0 0 72 LW R 3 3 3 0 0 0 0 72 Lk L 5 5 5 0 0 0 0 327 Table G.3. Summary of APL Results for the Gravel Roads. INTERNATIONAL RO4D ROUGHNESS EXPERIMENT - BRASILIA - JLNE 1982 APL TRAILER SITE HEAS. TRACK ROU6HNESS HEASUREMENTS KEAN RUN I RUN 2 RUN 3 SIGMA SIl TRED R 6R01 25 R 5.5 5.5 0 0 0 0 25 L 6.1 6.1 0 0 0 0 72 SW L 3 3 3 0 0 0 0 72 MN L 7 7 7 0 0 0 0 72 LW L 6 6 6 0 0 0 0 6R02 25 R 6.8 6.9 0 0 0 0 25 L 7.2 7.2 0 0 0 0 72 SW L 3 3 3 0 0 0 0 72 NW L 7 7 7 0 0 0 0 72 L L 3.5 3 4 .7 .202 1 1 6R03 25 R 14.7 13.8 15.5 1.2 .082 1.7 1 25 L 19.2 19.9 18.4 1.1 .055 -1.5 -1 72 SW L I I 0 0 0 0 72 W L 3 3 0 0 0 0 72 L L 3 3 0 0 0 0 6R04 25 R 14.6 14.8 14.4 .3 .019 -.4 -1 25 L 14.6 12.5 16.7 3 .203 4.2 1 72 SW L I I 0 0 0 0 72M M L 3 3 0 0 0 0 72 L L 5 5 0 0 0 0 6R05 25 R 20.9 21.5 20.2 .9 .044 -i.3 -1 25 L 19 19.7 18.3 1 .052 -1.4 -1 72 S9 B I I 0 0 0 0 72 NW B 3 3 0 0 0 0 72 LM 8 5 5 0 0 0 0 6RO6 25 R 19.4 19.9 18.9 .7 .036 -1 -1 25 L 21 20.4 21.6 .B .04 1.2 1 72 SW i I I 0 0 0 0 72 NM B 3 3 0 0 0 0 72 Lk E 5 5 0 0 0 0 6R07 25 R 7 7 7 0 0 0 0 25 L 8.5 7.9 9.1 .8 .1 1.2 1 72 SW L I I I 0 0 0 0 72 MW L 4.5 4 5 .7 .157 1 1 72 LW L 6 6 6 0 0 0 0 BROS 25 R 6.9 7 6.7 .2 .031 -.3 -1 25 L 7.2 7.2 7.2 0 0 0 0 72 SW L 2 2 2 0 0 0 0 72 NW L 6.5 6 7 .7 .109 1 1 72 LW L 6.5 6 7 .7 .109 1 1 6R09 25 R 17.4 17.6 17.1 .4 .02 -.5 -1 25 L 16.4 16.2 16.5 .2 .013 .3 1 72 SW L I I 0 0 0 0 72 MW L 3 3 0 0 0 0 72 LW L 3 3 0 0 0 0 BRIG 25 R 10.9 10.9 10.9 0 0 0 0 25 L 15.6 15.6 15.5 .1 5E-03 -.1 -1 72 SW L I I 0 0 0 0 72 MN L 3 3 0 0 0 0 72 LW L 6 6 0 0 0 0 6RI 25 R 14.5 14.2 14.7 .4 .024 .5 1 25 L 12.4 12.4 12.3 .1 6E-03 -.1 -1 6R12 25 R 22 29.9 15.2 9.7 .439 -13.7 -1 25 L 13.A 14.3 13.5 .6 .041 -.8 -1 328 Table G.4. Summary of APL Results for the Earth Roads. INTERNATIOHNL ROAD ROUGHNESS EXPERIMENT - BRDSlL18 - JUNE 1982 APL TRAILER SITE MEAS. TRACK ROUGHNESS MEASUREMENTS MEAN RUN I RUN 2 RUN 3 SI6MA S/N TREND R TEOI 25 R 10.1 9.5 10.4 10.4 .5 .051 .45 .866 25 L 12.8 12.6 13 12.9 .2 .016 .15 .721 72 SW R 3 3 3 0 0 0 0 72 SW L 2 2 2 0 0 0 0 72 KM R 5 5 5 0 0 0 0 72 MN L 4.5 4 5 .7 .157 1 1 72 L R 4 4 4 0 0 0 0 72 LL L 3 3 3 0 0 0 0 TE02 25 R 11.5 11.4 11.7 11.5 .2 .013 .05 .327 25 L 9.8 9.3 9.9 10.2 .5 .047 .45 .982 72 SW R 2 2 2 0 0 0 0 72 SW L 2.5 3 2 .7 .283 -1 -1 72 NV R 5 5 5 0 0 0 0 72 NW L 7 7 7 0 0 0 0 72 LL R 5 5 5 0 0 0 0 72 Lk L 4.5 5 4 .7 .157 -1 -1 TEO3 25 R 13.3 13.5 13.2 13.1 .2 .016 -.2 -.961 25 L 15.7 15.2 16.4 15.5 .6 .04 .15 .24 72 SW R 1 1 1 0 0 0 0 72 SW L I I I 0 0 0 0 72 MN R 4.5 5 4 .7 .157 -1 -1 72 NW L 3 3 3 0 0 0 0 72 Lk R 5 5 5 0 0 0 0 72 LM L 5 5 5 0 0 0 0 TEO4 25 R 20.8 21.3 20 21.2 .7 .035 -.05 -.069 25 L 16.4 16.2 16.8 16.3 .3 .02 .05 .156 72 SW R I I I 0 0 0 0 72 SW L I I I 0 0 0 0 72 K R I I I 0 0 0 0 72 W L 2.5 2 3 .7 .283 1 1 72 LM R 3 3 3 0 0 0 0 72 L L 2.5 2 3 .7 .283 1 1 TE05 25 R 15.8 15.8 0 0 0 0 25 L 17.9 18.5 17.3 .8 .047 -1.2 -1 TE06 25 R 20.1 20.1 0 0 0 0 25 L 23.3 23 23.6 .4 .018 .6 I TE07 25 R 8.4 8.3 8.5 .1 .017 .2 1 25 L 10.6 11.7 9.4 1.6 .154 -2.3 -1 72 SW R 2 2 0 0 0 0 72 SW L I I 0 0 0 0 72 MN R 6 6 0 0 0 0 72 MV L 5 5 0 0 0 0 72 LW R 7 7 0 0 0 0 72 LU L 6 6 0 0 0 0 TEO0 25 R 8 8.3 7.6 .5 .062 -.7 -1 25 L 10 10 10 0 0 0 0 72 SW R 2 2 0 0 0 0 72 SV L I I 0 0 0 0 72 NV R 6 6 0 0 0 0 72 NW L 5 5 0 0 0 0 72 LW R 5 5 0 0 0 0 72 LV L 6 6 0 0 0 0 329 Table G.4 (Cont.) INTERNATJOHRL R0ID ROUGHNESS EXPERIMENT - BRfSILIA - JUNE 1982 APL TRAILER SITE MEAS. TRACK ROUGHNESS MEASUREMENTS MEAN RUN I RUN 2 RUN 3 SIGMA S/N TREND R TEO9 25 R 13.7 14 13.4 .4 .031 -.6 -1 25 L 15.7 15.4 16 .4 .027 .6 1 72 SW R I I 0 0 0 0 72 SW L I I 0 0 0 0 72 NW R 4 4 0 0 0 0 72 MW L 3 3 0 0 0 0 72 LW R 6 6 0 0 0 0 72 LN L 5 5 0 0 0 0 TEIO 25 R 15 14.8 15.2 .3 .019 .4 1 25 L 19.5 21.3 17.8 2.5 .127 -3.5 -1 72 SW R I I 0 0 0 0 72 SW L 1 I 0 0 0 0 72 NW R 3 3 0 0 0 0 72 NW L 2 2 0 0 0 0 72 LW R 5 5 0 0 0 0 72 LW L 4 4 0 0 0 0 TEII 25 R 13 13.7 12.2 1.1 .082 -1.5 -1 25 L 20.6 26.9 14.3 6.9 .433 -12.6 -1 72 SW R I I 0 0 0 0 72 SW L I I 0 0 0 0 72 NW R 4 4 0 0 0 0 72 MW L I I 0 0 0 0 72 LW R 5 5 0 0 0 0 72 LW L 3 3 0 0 0 0 TE12 25 R 20.3 20.1 20.4 .2 .01 .3 1 25 L 15.9 21.5 10.3 7.9 .498 -11.2 -1 72 SW R I I 0 0 0 0 72 SW L I 1 0 0 0 0 72 NW R 2 2 0 0 0 0 72 MN L 2 2 0 0 0 0 72 LK R 3 3 0 0 0 0 72 LW L 4 4 0 0 0 0 330 of them. It was also the case for the TE sections (earth roads) with the exception of sections TE 05 and TE 06 which were not measured. For the gravel road sections, the measurement was carried out only in the left track (L) of sections GR 01 - GR 04, GR 9, and GR 10, and between tracks (represented by the letter B) for the sections GR 05 to GR 08. Sections GR 11 and GR 12 were not measured. Tables G.1 to G.4 show the APL 72 indices (I) as they were calculated during the IRRE in Brazil. The values provided are for only a 200 m continuous segment entirely included in each 320 m test section. Of course, when the test sections are not homogeneous along their lengths, the reported values may not truly represent the average APL 72 index of the whole section. But in these cases, the choice of only one numeric to characterize the whole section roughness would not, itself, be very representative. The tables show that nearly all of the earth sections have an APL 72 SW index near 1 (the category for the worst roads), as do more than half of the gravel sections. Indeed, t'he APL 72 index scales used during the IRRE were derived to match the range of observed roughness in the French road network, but they could be modified in order to give representation over a larger roughness range (this was not done in the IRRE). The fact that the APL 72 (I) numeric does not distinguish roughness levels for the unpaved roads is the result of the category definitions, rather than the measurement and analyses preceding the categorization. When the APL 72 index is not used, the roads can be quantified by the mean-square energy (W) and equivalent amplitude (Y) numerics. Tables G.5 and G.6 show the complementary APL 72 results as they are obtained in France by LCPC and in Belgium by CRR. They give (for one run only): - The values of the total (mean square) energy (W) and the equivalent displacement (Y) for a 200-m continuous segment entirely included in each 320-m test section (LCPC method). Both W and Y values are given for the three wavebands described earlier: Short wavelengths (abbreviated as SW), Medium wavelengths (MW), and Long wavelengths (LW) 331 SFCTIONS (W) APL 72 (Y) APL 72 iCP) APL 72 SW MW LW SW MW LW 2,5 m 10 m 40 m CA 01 R 8.8 124.6 1434.4 2.9 11.1 37.8 58 176 536 L 9.9. 119.9 1571.9 3.1 10.9 39.6 54 153 499 CA 02 H 12 83.9 785.4 3.4 9.1 28 62 158 386 L 12.1 76.9 754.6 3.4 8.7 27.4 67 169 453 CA 03 R 31 120.6 829.7 5.5 10.9 28.8 91 184 468 L 27.2 117.6 554.7 5.2 10.8 23.5 90 191 579 CA 04 R 17 143.9 1246.5 4.1 11.9 35.3 72 184 530 L 25.4 139.1 978.7 5 11.7 31.2 88 192 501 CA 05 R 27.8 147.2 318.4 5.2 12.1 17.8 76 172 507 L 33.4 172 665.6 5.7 13.1 25.8 103 207 504 R 22.8 82.6 1026.4 4.7 9 32 100 193 507 CA 06 L 26.6 75.2 1179.1 5.1 8.6 34.3 116 206 493 CA 07 H 6.8 37 298.2 2.6 6 17.2 42 87 218 L 5.7 20.1 102.8 3.6 5.3 10.1 56 89 219 CA 08 R 6 18.3 162 2.4 4.2 12.7 41 78 221 L 7.7 16.6 252.4 2.7 4 15.8 43 87 247 CA 09 R 8.5 38.3 478.7 2.9 6.1 21.8 49 114 302 L 12.8 27.9 759.1 3.5 5.2 27.5 70 126 370 CA 10 R 11.6 42 247.3 3.4 6.4 15.7 56 128 332 CA 10 L 21.4 49 495.9 4.6 7 22.2 69 128 319 CA 11 R 21.7 189.7 845.9 4.6 13.7 29 76 181 421 L 13.9 82.9 546.2 3.7 9.1 23.3 62 157 443 CA 12 R 3.6 14 434.5 1.9 3.7 20.8 28 61 228 L 3.1 8.3 328.4 1.7 2.8 18.1 29 59 262 R 3 12.9 313.3 1.7 3.6 17.7 29 63 236 CA 13 L 2.9 8.1 273.9 1.7 2.8 16.5 27 62 217 TS 01 R 23.2 18.6 214 4.8 4.3 14.6 74 97 238 TS 01 L 15.1 18.1 158.7 3.9 4.2 12.6 66 92 210 R 18.7 42.8 638.8 4.3 6.5 25.2 73 121 402 TS 02 L 18.2 36.9 361.1 4.2 6 19 74 117 353 TS 03 R 20.1 27.7 674.9 4.4 5.2 25.9 75 109 377 L 23.4 27 447 4.8 5.1 21.1 85 118 346 TS 04 R 30.2 29.3 314.3 5.5 5.4 17.7 96 126 261 L 21.5 20.7 215.1 4.6 4.5 14.6 81 107 271 R 25 18.3 102.3 5 4.2 10.1 85 101 179 TS 05 L 33.7 23.4 95.3 5.8 4.8 9.7 102 117 172 R 7.3 23.6 221.4 2.7 4.8 14.8 46 97 304 TS 06 L 10.3 30.9 374.9 3.2 5.5 19.3 54 101 282 R 9 48.6 277 3 6.9 16.6 50 99 276 TS 07 L 9.5 39.4 236.9 3 6.2 15.3 51 99 268 TS08 L 11.6 61.5 1173.1 3.4 7.8 34.2 50 80 239 R 15.9 20.1 438.3 3.9 4.4. 20.9 61 101 252 TS 09 L 13.9 16 289.1 3.7 4 17 59 87 215 TS 10 R 13.4 32 104.5 3.6 5.6 10.2 59 101 212 L 18.5 19.4 82.9 4.3 4.4. 9.1 63 90 171 TS 11 R 7.2 11.8 90.7 2.6 3.4 9.5 35 65 218 L 5.5. 15.5 114.7 2.3 3.9 15.5 37 63 249 R 4.1 9.8 1043.1 2 3.1 32.2 40 69 354 TS 12 L 5.1 5.7 564.1 2.2 2.4 5.7 41 61 272 TABLE G.5 COMPLEMENTARY APL 72 RESULTS OBTAINED ON THE PAVED ROADS (CA AND TS SECTIONS) 332 (W) APL 72 (Y) APL 72 (CP) APL 72 SECTIONS SW I LW SW MW LW 2,5 m 10 m 40 m T 13.2 50.8 844.1 3.6 7.1 29 65 117 367 TE 01 L 21.9 52.6 1328.8 4.6 7.2 36.4 76 136 462 R 18.9 50.2 410.2 4.3 7 20.2 76 133 351 TE 02 L 16.5 20.6 806.3 4 4.5 28.3 68 107 395 TE 03 R 32.4 55.7 498.8 5.7 7.4 22.3 110 171 558 L 37.2 131.7 582 6.1 11.4 24.1 139 206 490 TE 04 R 30.1 225 1138.3 5.4 15 33.7 107 249 575 L 37.2 138.8 1558.4 6.1 11.7 39.4 149 219 592 TE 05 R NO MEASUREMENT L I TE 06 R NO MEASUREMENT L TE 07 R 21.7 35.4 227.6 4.6. 5.9 15 80 111 295 L 24.1 52.3 335.3 4.9 7.2 18.3 86 126 251 TE 08 R 20.9 21.3 477.8 4.5 4.6 21.8 82 110 366 L 24.9 39.6 296.2 4.9 6.3 17.2 91 130 305 TE 09 R 32.8 85.5 374 5.7 9.3 19.3 115 164 341 L 37.2 128.9 507.4 6.1 11.3 22.5 142 203 397 TE 10 R 37.2 109.9 504.5 6.1 10.4 22.4 141 196 408 L 37.2 199.3 866.6 6.1 14.1 29.4 171 254 479 TE 11 R 37.2 85.6 509.3 6.1 9.2 22.5 145 193 316 TE 11 L 37.2 225 1281.7 6.1 15 35.8 172 320 635 TE 12 R 37.2 148.8 1036 6.1 12.2 32.1 136 228 479 L 37 147.3 626.7 6 12.1 25 80 208 406 GROl1 R L 13.3 17.4 355.2 3.6 4.1 18.8 58 85 348 GRO02 R L 12.9 14.2 733.6 3.5 3.7 27 58 91 428 GR3 R L 33.4 94.6 1079.9 5.7 9.7 32.8 103 \184 464 GR 04 L 36 109.9 574.5 6 10.4 23.9 113 176 404 GRO 05 B 37.2 104.1 464.4 6.1 10.2 21.5 169 217 402 GRO06 R. 8 37.2 117.8 525.4 6.1 10.8 22.9 153 231 393 GR 07 R G 30.6 42.4 270.9 5.5 6.5 16.4 89 121 298 GR 08 8 15.3 16.9 179.1 3.9 4.1 13.3 75 108 329 GRO09 R L 37.2 98.6 965.5 6.1 9.9 31 139 200 482 GH 1O R L 37.2 94.6 359.2 6.1 9.7 18.9 134 202 372 GR 11 R NO MEASUREMENT L I GR 12 L NO MEASUREMENT Table G.6 : Complementary APL 72 results obtained on the unpaved roads (GR and TE sections) 333 - The values of the (CP) coefficients determined by the CRR method for a set of three bases (of moving average), namely, the conventional values in practice in Belgium which are 2.5 m, 10 m, and 40 m Additional analyses were performed by LCPC and CRR related to the QI roughness scale, and these results are reported in Appendix E. Additional computations were performed at UMTRI using (approximately) the CP moving average technique, applied to both APL and statically measured profile signals. These results are reported in Appendix J. Comparison of APL Results with RTRRMS Results Linear regressions were calculated between the APL numerics and those obtained from the RTRRMSs. The correlations, defined by the square of the correlation coefficient (R-squared) are summarized in the correlation matrices presented in Tables G.7 - G.10. In performing these regressions, the test data were segregated by speed and surface type. For the APL 72 energy values (W) and the APL 72 equivalent displacement (Y), linear regressions were calculated only with Maysmeter 02 and Bump Integrator trailer results. Linear regressions were used as a first step in the analysis, even while recognizing that higher correlations could often be obtained by nonlinear regression models. The overall examination of Tables G.7 - G.10 shows that the quality of the correlations obtained depends naturally on the type of test sections, the types of RTRRMSs, and their measuring velocity, but that this quality is most of all influenced by the model of processing the APL signal, particularly by the choice of the wavelength range that is used. The correlations obtained for each type of APL analysis are discussed below. CAPL 25. Scatter plots between CAPL 25 and RTRRMS numerics (not included) show that the relationship between the CAPL 25 and a RTRRMS measure is strongly dependent on surface type. As indicated by the correlation matrices in the tables, good correlations are found only on the asphaltic concrete surfaces; correlations are poorest for the surface treatment and gravel sections. As was seen earlier, the CAPL treatment is an amplitude 334 ASPHALTIC CONCRETE TEST SITES (CA) AP. RMRS K 0 1 1K 1 0 2 M 6 0 3 B! CAR NAASRA 8! TRL BEN n.-Orics I AVE) (AVE) CAPL 25 7323 7 6086 8057 7280 7356 6952 - 5645 7., 035 7405 7912 7042 . 7009 I'll847, 4270 NA . 5591 .5805 6155 . 5 385 . 5468 .5825 .3346 LW 4908 . 595 6054 . 4935 .5047 .4608 .46 04 Sw .8~~~~~~~~509 87 U NA . 5~~~~~~~752 48 SW 8439 65 IM..06 5238 ~2. 8676 .9101 92 96 .88 98 .8864 I.88415 7334 P 0 7 53 9 .7908 . 83 57 .7564 . 736 . 711 .528 140 . 6004 . 225 .68 26 .6068 6253 .5650 .5166 TEST SITES WITH SURFACE TREATMENT (TS) API. RTRRVS KM K ? 2 M N 0 3 BI CAR NAASRA 6 8 E nuner 1 CS C~~~~ ~ ~~~~~~~~~~~~~~~~~~~AVE) (AVE) CAPL 25 .3670 {.3620 . 5322 .424,8 .4570 3 3763 .2718 SW .8383 .64 16 .948 .861 1 .8849 .8 2 53 .7046 IKw .0921 . 0966 .212 48 .1000 112 67 .0757 .0483 Lw . 0031 . 0044 . 0095 . 0034 . 0003 . 002 D 363 SW .8553 .8453 A Nwj. 0063 .0062 LW SW . 583 .8444 YKNw. 0259 .0223 LW 2,5 .8738 8 747 .9302 .928 9 9 9283 . 6764 .887 1 CP 10 .64 77 6 6371 8 21 9 .7002 .7346 .5774 4 69 0 40 .0231 .01 38 .0035 .01 13 .0085 .01 32 .0174 GRAVEL SURFACED TEST SITES (GR) API. KS M 0 1 M M 0 2 M K 0 3 81CAR NAASRA 82 TEL BP8 CAPL 25 3880 6054 .4873 5 939 1 16 .4491 .74 78 ISW 7373 .6982 4 4866 .7344 .7260 .6901 .6130 1MW 8005 .8135 .4760 8 373 I.8165 .7692 . 653 3 Lw . 0861 .096I 0020 .10768 0977 .06468 1037 SIW 6103 .7929 6 NW .042 0122 LW 6. SW .8007 .7897 VYKW 8207 .8099 LW 2. .90089 9173 .6412 .9076 .9068 .9242 .8295 CE 10 8759 .8943 .61.73 . 92 23 . 11 .9030 . 632 8 40 .1636 .1855 .0244 .86 .1842 . 730 . 899 EATH) (CLAY) SURFACE TEST SITES (TE) RTNRMI K NO0 1 M 0 2 K M 0 3 85 CAR NAASRA 80 TRIL BEN API. _ _ V(_ AVE) (AVE) CAPL 25 .8120 .7481 .7463 .7331 .7261 .6669 .70466 SW 4 663 .60866 7319 .6174 .6102 .6034 .6002 I NW . 7848 .7279 7800 .7392 .7402 .7228 .6709 LW .2376 .1060 .0912 . 1140 .1175 .1049 .0684 SW .8557 67 Lw 6. . 6~~~~~~~~~~~408 83 S W . 035 72 2.; .175 . 8I0 , 366 . 539 . 838 . 622 . 860 CE 10 . 8168 858~~2F . 01 .684 .8660 268 .77 4 .4142 2 2773 .2951 3 330 ,3219 .2603 .11 TABLE G.7 CORRELATION MATRIX OF R. SQUARED VALUES FOR THE APL RESULTS AND RTRRMS MEASURES MADE AT 20 KM/H 335 ASPHALTIC CONCRETE TEST SITES (CA) -. RTRRMSX[ 0 2 M90 3 DI CAR NAASRA B TRL (P 9801 C~~~~~~~~~~~~~~~~~~~~~~~~~~~~AVE) I(AVE) CAPL 25 8094 8353 804 4 7 86 0 80 72 7120 A705 SW 7361 7600 7859 7403 7492 .70s0o 3701l I MW 6580 .6597 6750 6047 6320 4935 2424 LW 56885 . 6107 . 5433 3 . 5513 5669 3 4 854 .3A67 SW -8722 8375 SW . ~~~~~~~8632 205 SMW .6602 56 L. 2. . 84 2 .9267 .8768 9 9152 9 912 0 9 9196 6 67 07 Ce 0 3 84 1 . 8652 . 355 .8202 . 8350 7 7433 3 . 47 26 40 6.605 .7274 . 264 6 667 8 6 6840 578 6 4 403 3 TEST SITES WITH SURLFACE TREATMENT (TS) ~~~rzcs 9~ ~ m 0 1 9 M 0 2 j MM 0 3 81 CAR NAASRA [ AVE) (AVE CAPL 25 .3872 .37786 4961 3 3924 .4140 .4146 4 45886 SW .8713 .8523 . 6863 .86 60 1 8669 .8647 .8044 I MW .0832 .0825 .1802 .0824 .0924 .0994 . 121 6 SW 9 024 .9095 WMW .0023 r 0097 LW. * SW .8931 .8920 y MW. 01 8 8 02 92 2, 958 so 953 5 9 9482 . 93 68 .9424 9 9189 [ .91 77 CP 30' .798 .7218 7 7765 .71 63 .7267 .6294 .6704 40 .0776 .01 32 .0004 .0205 .0176 .0013 .0195 GRAVEL SURFACED TEST SITES (GR) RT9 m 0 5 9 9 0 2 8 M 0 3 81 088 NAASRA BI TRL 8PR API ~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(AyVE) (AVE) CAPL 25 2476 .5071 4 4338 . 4729 .4645 .4623 .80A4 SW .6823 .6118 .4355 .6645 .6695 .6410 .7862 1KMw . 762 2 .7185 4 4496 . 772 9 .77 38 .7678 .8774 LW .0726 .0598 0014 .0934 .0836 .1029 . 144 SW . 7277 .7705 A MW . 289 .8062 LW W. SW .7197 .7602 Y W 7399 .8082 L. 2.5 .9239 1 947 . 8464 .954 .22 .909 .71 CP 10 .8548 . 493 .6561 ..862 j .8905 .9030 I .846 40 1448B 13.00 0228 . 1719 J . 1 644 4 1958 . 281 EATH SURFACED TEST SITES (TE) ______ RTRRMS 80m02 MM ICR ASA TR L 1 RPR API ~~~~~~~~~~I(AVE) AVE) CAPL 25 .7911 .7312 .7478 7404 .7177 .7123 6 847 SW . 6246 7015 .7261 .6961 .7006 . 673 .6198 I MW .7964 I .7727 .7594 .8121 .7903 .8261 .7024 LW . 1736 j .1084 .0828 .159 .1289 .1557 .0850 SW 9 157 . 979 A MW 7926 . 467 LW SW .9044 .8824 5 MW . 770~~~~~~~~2 . 51 2,5 . 326 . 106 .8352 .9314 . 93 83 .8635 . 979 Ce 10 . 275 . 934 .7654 .6661 .9135 . 9026 3 74 40 .3668 .3245 .3139 .4839 .4254 .3536 .2214 TABLE G.8 CORRELATION MATRIX OF R. SQUARED VALUES FOR THE APL RESULTS AND RTRRMS MEASURES MADE AT 32 KM/H 336 ASPHALTIC CONCRETE TEST SITES (CA) AP)RMS x H 1 1 m 0 2 M Y 0 3 BI CAR NAASRA Bl TRL BPP numOric~~~~~~~~~~~~~~~~~ _ I alAuwE) (AVE) CAPL 25 8832 8711 9352 8380 0789 7534 6939 SW 8119 8123 7845 7702 036 7387 5931 I MW 7335 7247 7672 6246 6942 5327 5220 LW b 610 6898 7429 6236 6568 , 5184 5225 SWI. 6890 8294 ,EN W M- 5764 , 5061 LW . SW 7362 . 8194 r M 6629 5 5497 L- 2.5 9337 H 777 9135 9609 . 9557 9 9366 7972 P 10 9106 89998 9430 8634 9038 . 780? 7123 40 . 7529 7784 7992 71 182 7563 6204 . 6326 TEST SITES WITH SuRFACE TREATMENT (TS) .R McS 36M 2 1 O I | M 0 2 m 0 3 ; I CAR | AAS'A | 81TL BPR numSrics~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7 l AVE) (AVE) CAPL 25 3632 3940 3348 3654 374 6 3781 6432 SW 9021 8964 8361 9018 , 9042 8654 8169 I MW 0694 0911 0463 0770 0800 0826 2370 LW 0157 .011 0124 0171 0142 0205 . 0161 SW 9063 9568 V Kw .0019 .0007 LW N SW . 9193 9368 Y MW 0220 .0125 LW 2,5 . 9442 9244 9198 9578 9639 .994 7691 CP 10 . 7141 . 7189 6290 , 7233 , 7104 . 8392 . 5263 40 . 0010 0048 0032 0037 0026 0006 0043 GRAVEL SURFACED TEST SITES CGO) 7R8M5 N MN11 0 1 N M 0 2 N M 0 3 Bl CAR NAASRA 8B TRL BPR |rumiricsL_ (AVE) (AVE) CAPL 25 . 0384 4411 4615 . 4899 , 4246 4B46 7031 SW | 7047 6647 , 6638 . 6402 . 6493 6409 6863 S W MW 769B 7642 7169 7388 7487 . 7626 8251 LW . 0625 0501 0167 0630 0564 0664 3529 SW . 7883 7660 m v MK w 7657 8100 LW SW. W . 7807 , 7565 Y MW | 7825 . 8092 2.5 9329 9399 . 9440 . 9214 9316 , 9360 7511 CP 10 8671 , 139753 8462 . 8706 881S 6393 7759 40 3 1258 . [210 . 0899 . 1340 . 1254 451588 3187 EATH (CLAY) SURFACE TEST SITES (TE) NIN 0 1 NM 0 2 N N 0 3 8I CAR NAASRA 8I TRL 8PR APL _ (AVE) (AVE) CAPL 25 6 6472 6486 . 5546 . 6841 6 8408 6807 . 8532 SW 8968 . 7251 . 7425 . 7410 . 7321 . 6852 . 7685 M I, 7533 . 8040 6 8265 . 8225 . 7999 8504 . 8629 LW . 0893 . 1186 . 0205 1602 . 1180 . 2044 . 1024 SW 9128 . 8718 w W w .8218 . .791 LW N.r { SWt . f 9031 . 8599 l 5 LW 9. 7297 . 6336 LW 2. . 8934 . 3057 . 9068 . 8628 . 9044 . 8264 . 8901 CP 10 8511 3998 . 7167 , 8742 . 8832 . 9447 7 9410 40 2612 . 3353 . 1848 . 5385 . 3710 . 4641 . 5270 TABLE G.9 : CORRELATION[ MATRIX OF R. SQUARED VALUES FOR THE APL RESULTS AND RTRRMS MEASURES MADE AT 50 KM/H 337 ASPHALTIC CONCRETE TEST SITES (CA) APRMS M M O 1 M M 0 2 MM 0 3 BI CAR NAASRA DI TRL BPR vn,mhrlc( CAVE) (AVE) CAPL 25 8782 8891 8793 6597 7828 8896 SW 8020 8070 7601 7019 7453 5921 I MW 6920 6873 . 6745 2952 4312 9197 N LW 6476 6593 6501 5012 5994 4383 J 2,5S . 9432 9578 8852 9348 9438 6085 CP 10 8943 9047 . 8688 6807 8035 8615 40 7385 7637 6913 5526 6660 8291 TEST SITES WITH SURFACE TREATMENT (TS) APL RMAAJ4S M 1M 0 1 M M 0 2 M M 0 3 BI CAR NAASRA BI TRL BPR num4 rics \ ____________ ____________ ___________ ____________ AVE) (AVE ) CAPL 25 1952 2330 2677 SW 7306 . 7809 6806 I MW . 0323 0449 0825 bN LW 0738 0671 0394 -z 2,5 . 8866 9164 8359 CP 10 4126 4526 4217 40 0523 0542 . 0281 GRAVEL SURFACED TEST SITES (GR) I RTRRMS 1 1 0 1 M M 0 2 M M 0 3 BI CAR NAASRA BI TRL BPR num6ricA= - (CAVE) (AVE CAPL 25 7873 | 8283 , 7546 SW 6217 6335 6157 N I MW . 7264 7576 7221 b LW 0368 0733 0836 -~ 2,5 9631 9535 9055 CP 10 , 8675 . 8884 8388 40 1179 1723 1683 EARTH (CLAY) SURFACE TEST SITES (TE) RTRRMS APL MM 0 1 14M M 0 2 14M M 0 3 BI CAR NAASRA BI TRL BPR APL l , s l l l (AVE) (AVE) CAPL 25 6828 7457 7692 SW * 4207 ' 7202 6219 I MW 6819 7760 7771 NC LW 2676 0987 1301 ..l 2,2 6151 8723 * 9196 f CP 10 8363 8658 9011 40 . 3962 . 2822 * 3222 TABLE G.10 : CORRELATION MATRIX OF R. SQUARED VALUES FOR THE APL RESULTS AND THE RTRRMS MEASURES MADE AT 80 KM/H 338 analysis of the road spectral wavelengths lying between 0.3 m and 15 m (high and medium wavenumbers), dominated by the influence of the longer wavelengths. When the spectrum is very rich in small wavelengths, which is particularly the case for surface treatment sections (TS), the CAPL 25 will less evidently bring out these effects than would the RTRRMS or other APL numerics. APL 72 Index (I). Scatter plots between the SW and MW indices and the RTRRMS measures (not shown) indicate that a definite relationship is evident between the SW index and the RTRRMS measures on the smoother surfaces that is not strongly dependent on surface type. But the correlation is degraded on the rougher surfaces because the roughness range for the SW index does not extend far enough for the unpaved roads. (The SW index is 1--the bottom of the scale--for most of the unpaved roads and many of the surface treatment sites.) For the MW index, relationships can be seen with the RTRRMS measures, which are different for the different surface types. Compared to other correlations observed in the IRRE, the correlations between the MW index and the RTRRMS measures are not very good. For the LW indices, there is virtually no relationship with the RTRRMS measures, as indicated in the correlation matrices. Only on the CA sections do correlations exist, and even these are poor. Good correlations could not be expected because the RTRRMSs do not "see" these long wavelengths. Overall, the comparison of the correlations obtained with the CAPL 25 coefficients or the APL 72 index show that when the small wavelengths are isolated from the rest, the results are clearly better. The remark made earlier for the TS sections (regarding correlation with the CAPL 25 numeric) is illustrated in Tables G.7 to G.10 by the differences obtained between correlations with the SW index and the MW index. APL 72 Energy Values (W) and APL 72 Equivalent Displacement (Y). Some of the problems with correlating RTRRMS measures with the indices are eliminated by considering the W and Y values, which lie on a continuous roughness scale, rather than the discrete intervals 1 - 10. The linear regressions were calculated only with the Maysmeter 02 and the Bumnp Integrator trailer since the principle of global energy (W) and equivalent displacement analysis is not different from the APL 72 Index (I), 339 and that the values (W), (Y), (I) are not independent. Nevertheless, the values of (W) and (Y) are expressed in scales approximately linear and continuous. Tables G.7 to G.9 show that the correlations with the RTRRMSs are generally better for (W) and (Y) than for (I). Figure G.2 shows example scatter plots for the SW energy (W) values, against the ARS measures obtained from one of the RTRRMSs. The regression lines are also shown. The relationship with the SW numerics is dependent on surface type for the lower RTRRMS speeds, but diminishes for the speed of 50 km/h. The correlations shown are good enough, particularly for the RTRRMS speed of 50 km/h, that the SW energy (W) numeric could be considered as a calibration reference for the RTRRMS. Figure G.3 shows similar plots for the MW energy (W) numeric. In this case, the relationships are not as good, and are strongly influenced by surface type. The correlation with the RTRRMS is almost nonexistent for the surface treatment (TS) sites. The results shown in Figs. G.2 and G.3 derive from the differences in wavenumber sensitivity between the APL numerics and the RTRRMS. In comparing the APL 72 wavebands to the Reference Quarter Car Simulation (RQCS) in Fig. F.2 in Appendix F (qualitatively similar to that of any RTRRMS), it can be seen that the RTRRMS responds to a broad band of wavenumbers, whereas the APL numerics selectively isolate narrow bands. Only the SW numerics (W, Y, I) include the shorter wavelengths, which constitute a major portion of the RTRRMS measures on all but the CA roads. The waveband data shown in Tables G.5 and G.6 (and also the Power Spectral Density (PSD) functions plotted in Appendix I) all indicate that the CA surfaces had proportionately more medium wavelength content than the other surface types. At the higher speed of 50 km/h, the RTRRMS is more influenced by the medium wavelengths, which leads to the observed reduced correlation with the SW numerics but improved correlation with the MW numerics (relative to the correlations observed for the lower speeds of 20 and 32 km/h). APL 72 CP Coefficients. Examination of Tables G.7 - G.10 reveals that: 340 *TS zTE ,CA GR ,TS zTE .CP , GR *0~ ~ ~ ~ ~~~~~~~~~~~~~~~G 12 RI9/ CA~~~~~~~~~~~~~~~~~~~~A T TE 75 z ii x / z z ~7 S£ U 25 z*25 30 00O 90 120 A00 60/5 O ISO 606 bE/S 5c is s iC is 25 Is 2KIM SPEEDS 20 KIN/ SPEEDS 32 19NI1 *TS 0T E *CP 1Gf (9) 75 25 TO 140 010 TOO Ml Tb/s 0 $ 0 is 20 AOS K/m SPEEOS : ST Ill/I Figure G.2. Comparison of APL 72 short wave energy results (W) with Mays Meter 02 results 341 ,TS 0TE ,CR XGR ,TS , TE ,CR , GR (WI 0 ~~~~~~~~~~~~~~~~~~~CA TE CA V 200 200~~~~~~~~~r iw 100~~~~~~~0 '~~~ I= O S 10 1S 20 A/M O 10 iS 2tas s Z.D:Z ll SMEES: 32 OM ,TS zTE .CR ,GR il~~~~~~~C :1 X 0 TO~AO 20 08 ~~~~~0 12~~0441/ 1244 IS mlMI O S *C 15 20 ASS n SPEEDS SD MM 11 Figure G.3. Comparison of APL 72 medium wave energy results (W) withY Mays Meter 02 results 342 - The R-squared value of the coefficients of correlation reduces, in general, as the base length for determination of the CP values increases. - Significant and high correlation values are obtained for CP (base 2.5 m) with all RTRRMS devices on all test sites and for all the test speeds. By merging all data belonging to a given RTRRMS device and calculating the linear regression coefficients and the correlation coefficient for each test speed, one can expect to evaluate the effects of speed and site factors that could influence a calibration plot that would be needed to estimate the CP (2.5) numerics from measurements made with one RTRMMS. This case has been examined for both the Maysmeter 02 and Bump Integrator trailers. It has been found that the best fit for the CP (2.5) values is obtained through correlation with both devices traveling at 50 Km/h and that no site type influences the correlation. The two examples are illustrated in Figure G.4. Both correlations are significantly high (r2 > 0.90) and yield nearly identical linear regression equations. Figure G.5 shows the influence of the value of the moving average base (2.5 m or 10 m) and the velocity of measurement of the Maysmeter 02 on the correlations between CP values and Maysmeter 02 values. These CP (10) values bring out, just as do the APL 72 MS (W) values, the peculiarity of TS sections. But, in a general way, they confirm the greater sensitivity of the RTRRMSs to the smaller wavelengths. Of all the APL results reported in this appendix, the CP (2.5) numerics produce the best correlations with the RTRRMSs, and that agreement is best for a RTRRMS speed of 50 km/h. No effort was made to improve the correlations by using alternate baselengths, although it is likely that better correlation could be obtained by adjusting the baselength to obtain appropriate filtering. This hypothesis is supported by the analyses performed by TRRL, reported in Appendix H, where it was found that a baselength of 1.8 m gave improved correlations. 343 160- CP2.5 In u 120_ O 80 _ / ALL SURFACE TYPES: CA, TS, GR, TE CP (2.5) - 13.5 + 0.805 * ARV (50 Km/h) io - _ ,~ *./: r2:,922 u / * Residual Standard Deviation = 10 CP 1' 40_ - _ 11II1;1I11 ARV 160 °40 80 120 160 MM/S MM02 160- C P2.5 X 120_. > t / ALL SURFACE TYPES : CA, TS, GR, TE Q 80 . OCP (2.5) = 12.1 + 0.778 * ARV (50 Km/h) O t X Residual Standard Deviation = 11 CP C.) 40_ -: I - I III -| 11111{ & | | -{ | ARV 40 80 120 160 MM/S Bi TRL Figure G.4. Comparison of APL 72 CP (2.5) values with RTRRMS Measures made at 50 km/h 344 CP2.5 ALL SECTIONS INCLUDED CA, TS, GR, TE CP (2.5) = 13.5 + 0.805 * ARV (50 Km/h) N\ 2 w rr =.9221 .r I CP (2.5) = 23.4 + 0.929 * ARV (32 Km/h) z ~~~~~~~~~~~2 Z 160- r =.8767 w 120-- X 16 80_ / D. 440_ - C- a . l l l l l l l l l ARV 40 80 120 160 MM/S MM02 CPtO ALL SECTIONS INCLUDED CA-, TS, GR, TE | CP(10)= 44 + 1.11 * ARV (50 Km/h) | ~~~~~~~~~~r2 =.7749- 80 o ~ ~~ / \¢ / ~~~~CP(10)= 59.3 + 1.25 ARV (32 Km/h) N~~~~~~~~~~~~ ¢ ;¢/ 0/ ~~~~~~~~r =.7078 0.. 40tm/ 4/ t 9 ....................................... 160 L SECTIONS TS ONLY HP . - // + /8CP(10)==52.8 + 0.811 * ARV (32 Km/h) 2 w i20_ _ y o 4 o r =0.7218 2 80 g / - CP(10)= 54.8 + 0.587 * ARV (50 Km/h) \1 0 r =.7189 b~ ~~~4 . ; 40_ _ - l l i } l l , l l l l l ARV 40 80 120 160 MM/S MMT 02 Figure G.5 Comparison of APL 72 CP (2.5) and APL 72 CP (10) with MaYs Meter 0 2 results 345 IXAMPLE APL PROFILES Adding to the summary results presented, LCPC and CRR have provided a graphical representation of the test section profiles which were run by the APL trailer, since it was the only apparatus present during the IRRE which conveniently produced such results. For each track of each test section measured, but for one run only, the graphs of APL 25 and APL 72 signals were represented for road lengths of about 1000 meters containing these test sections, and were made available to the participants in the IRRE. This representation was achieved with the help of a plotter recorder linked to a micro-computer which treated the digitized signals. (Sample intervals were 250 mm for the APL 25 signal and 50 mm for the APL 72 signal.) In addition to the profile plots, PSD functions were computed immediately after the IRRE from all of the APL 72 signals for which the CP numerics were calculated. PSD functions were also computed at that time for the profiles measured statically with the TRRL Beam, and both sets were distributed to the participants in the IRRE. More recently, PSD functions were computed for all of the profile measurements obtained in the IRRE, and those plots are included in Appendix I. Some examples of graphical representations of the APL profiles are included in this appendix and discussed below. Figure G.6 shows the representations of APL 25 and APL 72 signals recorded on the same test section (CA 01 right track). Figure G.6a gives the complete graphical representation of the APL 72 analog signal (lower part of the figure) and the same signal for which the wavelength components above 18 meters have been eliminated by electronic filtering. Figure G.6b shows that this electronic filtering results in a signal that is nearly identical to the APL profile obtained with the APL 25 system at a lower speed in a different run. Figure G.6c shows the perfect (within the plotting precision) agreement between the digitized representation of the full APL 72 signal and its analog 346 cm C A Q R OQ '1 ~~~~~~~~~~~~~~~3 S~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l o 2~~~CA0 a' CD ~~~~filtered signal C OR- 1 ~~~~~~ Figure~~~~~~~~~~o 200 300 400 t > Figure G.11 b Digitized ~~~~~~~~~~~APL 25 signal Fi r G.1 c igit2edAPL 72 signal .2 ~~~~~~~~~ CM ~~~~CA 1R 0 3 0 2 a ~~~~~~~~~~~~~~~~~0. 0 i. -2 0 full signal ct ~~Figure G.11 a Analogic APL 72 signal ;r ~~- 200 400 m representation. Figure G.7 shows the profiles obtained from the APL 25 and 72 systems, and also the complete record of CAPL 25 numerics as they were measured over the length of the left-hand wheeltrack of test site TS 05. Figure G.8 presents similar measures for the left-hand wheeltrack of site TS 11. Figure G.9 compares the PSD functions of these two TS sections. (In preparing the PSD plots, a sample interval of 1/3 m was used. No extra filtering or windowing functions were applied. A section length of 340 m was transformed, in order to obtain 1024 samples as required by the Fast Fourier Transform (FFT) program used.) The PSD plots show the distribution of the mean square of the APL 72 signal across wavnumber. Thus, the vertical scale has units of displacement2/(cycle/m) = m3. The horizontal scale, which is plotted as wavenumber (cycle/m), is labelled with wavelength (m/cycle) for convenience in the following discussion. (PSDs of all APL profiles are provided in Appendix I.) The content of the spectrum of section TS 05 L reveals the important presence of short wavelengths which appear also on the representation of the road profile as shown in Figure G.9. In contrast, section TS 11 L has a more regular spectrum where the shorter wavelengths do not prevail, which is also confirmed by the profile representation (Fig. G.10). Along with the RTRRMS measures, the APL 72 SW energy and the APL 72 CP (2.5) (Table G.5) reflect this difference between sections TS 05 and TS 11, and illustrate the sensitivity of these modes of roughness quantification for higher wavenumbers (shorter wavelengths). In fact, the TS 05 site was an "outlier" when RTRRMS measures made at 80 km/h were compared to the profile-based numerics. By inspecting the APL profile and PSD, the cause of the high value obtained from the RTRRMSs could be determined (the remarkably rich roughness content at a 2 m wavelength). Figure G.10 shows how the APL profiles identify heterogeneities. Section TS 08 is located at the start of a steep slope (in the direction of measurement) and the road is built partially on an embankment which has settled over a length of about 50 meters. The APL 72 signal reveals the steep slope of the profile over the 200 meters that precede the beginning of the test section. APL 25 and APL 72 signals, together with the elementary values 348 ED CRPL z H C) H O C\D U) 0 4 CM 3 T S 05 -) 2 c< -13 -4 DISTANCE CM) 100 200 500 4 CM 3 I s 05 4: 2 U) -~ 0 c'J~~~~~~~~~~~~q' t- -2 ~1 3 4: 200 400 600 800 Figure G.7. APL signals measured on section test TS 05 left track 349 1) F-- CRFL z 0 Lo O In <~~ - - - - - - - - - - - - -- - - - - 4 CM 3 -I- -T-S 11 ---- - 2 N -1 - - w r E v w l . | . . * § w | ~~~DISTANCE (M) 100 200 500 4 CM 3 TS 11 2 0) a.- -2 D.. 3 -4 10 200 40 60 0 FiueG3 P inl maue nscints TS 11lf rc 3~~~~~~~~5 Densit6spectrale mm3 Densitb spectrale mm3 DB TS1' OS6s18 1S 1L a -- g ' . . . . . 6,8.108 . . . . . . . . . . 6,8j0 r -10. j . P -10 . - l o08 I20. 0 L i] 0 1 7 0 l l I l; O f I _ -30, > . . X l . E -30 . l * * * .. 2 0 -80 101 o I 11~~~~~~~~~~~~~~~~ 0 i 10 40 20 13710 2,5 1 40 20 1310 533, 1 , 51 [IO0E+o L4 G(NR) 2 13000 +O1 . 5U0 03E3[ 0 L2 G01R'0 3 132V01 Figure G.9. POWER SPECTRAL DENSITY FROM APL 72 SIGNAL OF TS 05 LEFT TRACK AND TS 11 LEFT TRACK H 4) C CM 0 0 LO N CL.~ ~ ~ - . -_ - - - - - - - - - - -- - 13 4 - CM 3~~~~~~~5 ____ ___ ____ ___ ____ ___ ____ ___ ___ ___ ____ ___ ____ ___ ___ DISTANCE (M) 100 200 500 4 CM T S 08 3 .~2 -~0 -2 0. 3 -4 200 400 600 800 Figure 0'.10. APL signals measured on section test TS 08 left track 352 of CAPL 25 representation, clearly show this embankment settlement effect. COINCLUSIONS Considered as a profilometer, the APL Trailer is not comparable to static or quasi-static leveling systems which take the absolute profile of a road through an altimetric process based on a fixed horizontal reference. Nevertheless, the profilometric qualities of the APL are largely sufficient to give a significant representation of a road profile in the range of wavelengths from 0.5 m to 40 meters, as shown by the laboratory measurements of the APL frequency response in Fig. G.1 and in the comparisons of PSD functions in Appendix I. This range is, in itself, sufficient to characterize all the defects related to a road. Moreover, the APL Trailer is a dynamic device with automatic modes of recording and of signal processing that allow efficient data collection. During the IRRE, where it experienced practially no failure, the APL Trailer proved that it could be used successfully on all surface types of roads included in the IRRE, paved and unpaved, and under severe environmental conditions. Because it is autonomous and requires little technological support, it can be run in all parts of the world. The quality of correlations between the RTRRMSs measurements and the APL numerics depends on the way the APL signals have been processed and, in particular, on the selection of the wavelength ranges which compose them. For this experimentation, the LCPC and the CRR have applied methods of analysis which are used in a standardized way in France and in Belgium. These methods have been developed for the purpose of evaluating the quality of road construction or for surveying road evolution and its state of deterioration. They were not particularly oriented to represent the response of a vehicle riding on that road and even less to constitute a calibration scale for the RTRRMSs. Nevertheless, analyses based on a separation of the smaller wavelengths produce APL numerics very well correlated with the RTRRMS measures. This is particularly the case for the CP (2.5) numerics, and the results reported in Appendix H indicate that the baselength can be optimized to obtain still higher correlations. 353 In Appendix E, it is shown that it is possible to obtain estimates of QIr' provided that the parameters of the model are properly adjusted to the spectral contents of the APL profiles. In Appendix J, it is shown that the methods of analysis developed for the APL can be applied successfully to profiles obtained by other means. And in Appendix F, it is shown that the RARS numeric (from the RQCS) can be computed directly from the APL signals, using the APL 25 signals for the 20 km/h RTRRMS speed and the APL 72 signal for the other speeds of 32, 50, and 80 km/h. The correlations obtained using the RQCS analysis are the highest obtained. The APL Trailer, like all other profilometer-type systems, offers increased metrological and analysis possibilities when compared to RTRRMSs. As a matter of fact, the continuous representation of a profile, even if it reflects only part of its wavelength spectral content, allows a more precise analysis of the state of degradation of a road and of the variations of its riding quality: it brings into light particular zones, and gives information on the homogeneity of the section tested. Moreover, one can compute from the recording of a profile different roughness indexes adapted to the applications in view and choose the length of the road characterized by this index. This last property is very useful for quantifying local defects of roughness in the studies concerning the safety of road users. These supplementary metrological possibilities become an appreciable advantage when the profilometers have operational qualities equivalent to those of the RTRRMSs. Regardless of the qualities of a device used for measuring a roughness index of a road, the interpretation of that index in view of determining a global level of quality for that road cannot be performed independently from its other characteristics: nature of degradations (stated visually or photographically), state and constitution of the structure, importance of past and future traffic, frequency of maintenance works--and for the regions where the problem exists, the quality of skid resistance of pavements. This remark, which applies to all types of numerical parameters measured by a device on the road, is illustrated by the case of the surface treatment sections. The RTRRMSs ARS values, the APL 72 SW Index, and the CP (2.5) values all award to sections TS 01 to TS 05 a level of quality equivalent to those of sections CA 01 to CA 06 which are very degraded and highly circulated. These 5 surface 354 treatment sections are on a road without degradation of which the constitutions seem to be adapted to the very low volume of traffic, which requires no maintenance, and which has an acceptable level of ride quality. The short wavelengths that dominate their profiles are those of the ancient gravel road which was not trimmed when the surface dressing was added; the short wavelengths cannot be attributed to an evolution of the state of deterioration of this road. 355 APPENDIX H TRRL PROPOSALS FOR ROAD ROUGHNESS CALIBRATION AND STANDARDIZATION prepared by The British Transport and Road Research Laboratory (TRRL) 1. INTRODUCTION The report presents the analysis and findings from the TRRL beam profile data as analyzed by the TRRL, and describes a complete instrument package developed at TRRL to enable users to obtain calibrated and standardized rough- ness measures directly from field measurements using RTRRMS's. The report also presents the results of a short validation exercise that was conducted in the Caribbean island of St. Lucia. Of the 49 test sections selected for the IRRE, the TRRL beam profiled only 18 sections because of the late arrival of the beam in Brasilia. On ten of these sections both wheelpaths were profiled, the nearside wheelpath (right wheeltrack) only on three sections and the offside wheelpath (left wheeltrack) on the remaining five sections. Seven RTRMIMS's were used in the experiment, but in this report only four of these systems were considered for analysis. They are the TRRL Towed fifth wheel B.I. trailer, the car mounted Bump Integrator, the NAASRA meter, and the Maysmeter 02. Maysmeters 01 and 03 and the BPR Roughometer were excluded from the analysis, as the data gathered from these instruments were very variable. 2. TRRL BEAM PROFILE ANALYSIS Objectives The TRRL experimental beam was developed to provide a RTRRMS calibrating capability. This development was based on past TRRL experience in the field of roughness measurement in developing countries. The concept of 'ride com- fort' as adopted in the developed world as a direct measure of the unevenness of a road surface as perceived by the road user was not applicable to the road conditions met in developing countries. 357 In such countries ride comfort and level of service do not have the same importance as in the developed countries, as the greater need is for more roads to provide the basic means of transportation and communication which are operable throughout the year. Because of shortage of resources for buil- ding and maintaining all weather roads, a lower serviceability rating is tol- erated by the user. However, the lower quality of the road surface manifests itself in higher vehicle operating costs through greater wear and tear of the mechanical components of the vehicles. Comfort to the vehicle rather than to the rider takes on a greater importance. There is very little evidence to suggest what measure of roughness is most appropriate to relate to the effects of 'vehicle comfort'. Measures in use have been generally selected on the basis of convenience, simplicity and past experience of investigators, and the most popular measure has been the output of RTRRM's which measure the displacement of the axle relative to the body of the vehicle induced by the roughness of the road it is traversing. The magnitude of these response type measurements varies according to the suspension characteristics of the vehicle used and also with time due to a change in these characteristics through usage. Such measurements are accept- able only if they could be calibrated to a given standard enabling measure- ments with different vehicles at different periods in time and space to be related to that standard. Despite these serious drawbacks RTRRMS's enjoy a greater popularity with practising engineers and researchers and are in wide- spread use throughout the world. It is to be accepted that this method of measurement will prevail for some years to come and therefore the necessity to provide a viable and readily available calibration system is urgent. An alternative to the RTRRMS measure of roughness is a profilometry bas- ed measure of roughness, and this is an obvious candidate for providing a ca- libration reference for calibrating measurements of TRRMS. A major require- ment of any profilometer based system is that it should have the ability to accurately measure the longitudinal profiles of test sections of road, and also be able to be calibrated independently of other measuring systems. It also requires a method of processing the profile data to yield a single roughness statistic to describe the profile for subsequent correlation with RTRRMS measures. 358 A successful calibration system based on profilometry for use in devel- oping countries needs to satisfy three important conditions. The calibration system/instrument must be easily transportable particularly from country to country. Appraisal studies undertaken by consultants for developing coun- tries are usually of short duration. This means that unless the instrument is easily transportable to the country and the site, it will not be used by practising engineers and consultants, however good the instrument may be. Secondly the instrument must be reasonably simple to operate, and data man- agement, analysis and interpretation must be available immediately after measurement. Manual data processing cannot be undertaken by field staff, therefore the generation of profiles alone in the field and the creation of a large data bank without the capability of instant computation, analysis and presentation of calibrated results is not acceptable as a viable method of calibrating roughness measurements. The last and equally important consider- ation is the cost of such an instrument. The instruments available at pre- sent are highly sophisticated, and very expensive to acquire, which effec- tively puts them out of the reach of the practitioner. These three conditions guided the TRRL's approach to the IRRE data ana- lysis, the computation of a suitable numeric for correlation with RTRRMS measurements and the subsequent development of the beam as a viable roughness calibrating and standardising instrument, independent of external computa- tional requirements. Method of Analysis When analysing the data, consideration had to be given to the effect of different surface types and speeds of measurement, and also to the effect of variability between wheelpaths. These three factors have been fully examined in the main report, conclusions reached, and analysis proceeded with, on the basis of these conclusions. In this report alternative methods have been examined with a view to simplifying the analysis for practical use but with- out impairing the calibration accuracy. In this report three numerics have been developed as candidate statistics for correlation with RTRRMS, and their performance is discussed and compared with the other reference statistics developed by UMTRI and LCPC/CRR. The three numerics are a profile variance 359 about a moving average datum curve (M. Avg), a root mean square of vertical elevation (RNSVE) from a straight line datum and a root mean square of devia- tion (RMSD) from a linear regression line. All three numerics were examined for various baselengths and profile intervals. Early drafts of the main report (UMTRI-82-45-1) discussed the effect of measuring roughness with RTRRMS's at different speeds and suggested the use of an Average Rectified Velocity (ARV) unit in place of the more popularly used Average Rectified Slope (ARS) unit as this enabled comparison of RTRRMS measurements over more than a single test speed. However, the analysis dis- cussed in this report uses the ARS unit of measurement, as the calibration method proposed is confined to a single standard test speed. This decision was made in the light of analysis results obtained, and is discussed in Chapter 3. Subsequent UMTRI proposals to adopt a single standard speed of measurement resulted also in the choice of an ARS unit, in preference to a traffic speed concept ARV measure. Root Mean Square of Vertical Elevation (RMSVE) This numeric was developed as a method of finding an approximate value of an area under a given datum line to reflect the unevenness of the road profile, and was derived from the formula used to find the root mean square value of a function as used in electrical engineering to describe the properties of alternating currents. The calculation was performed using 'Simpson's Rule' for approximate integration of an area under a curve when equally spaced points are available as was the case with profiles generated by the beam at 100mm intervals. The root mean square of vertical elevation for a baselength b was calculated using the formula: /hr 2 ~2 2 2 2 2 2 2 RMSE y 2+ y + 4(y, + Y3 *Y1n-1) + 2(Y2 + Y4 O-*Y -2)] RMSVE,b = h(n-1) where h is the distance between elevation points, and n is the number of elevation points considered in the baselength, b. 360 The RMSVE for the test section of road containing N baselengths of length b is given by: RMSVE = b The RMSVE numeric was calculated for a number of different baselengths ranging from 0.4 metres through to 10.0 metres and for profile intervals from 100mm to 1000mm in steps of 100mm. These were then correlated with the RTRRMS's measurements, and the R values are tabulated in Tables H.1-H.4 for the four different measurement speeds and for profile intervals up to 500mm. Their performance is discussed in Chapter 3. Moving Average Variance This numeric presents the profile unevenness in terms of the variance of the deviation of the measured profiles about datum curves derived from moving averages. The points (y) of a moving average datum curve n points in length are calculated using the measured profile data points (y) as follows: i+n-1 y n =n-i y. for i > 1 nj=iI For calculation of the profile deviations from the moving average datum, n is always chosen to be an odd number. The profile deviations (d) relative to a moving average datum are given by: d = , - n-i o dk = Yk - Yk wherek= i+ - for i>1 The variance (ab2) of these deviations over a given sequence of N profile points for a given moving average of length b (n x profile interval) is: a 2 = t y kN-n 2 ab Y,~ (dk -d) The variance ab reflects the unevenness in the road profile that is associ- ated with profile features that are approximately b meters in length or less. 361 The profiles of the test sections measured by the TRRL beam are defined at points spaced 100mm apart. Moving average variances were calculated for a number of different baselengths (b) ranging from 0.4 metres to 10.0 metres and for profile intervals of 100mm, 200mm and 300mm. The previous RMSVE ana- lysis indicated that profile intervals greater than 300mm produced weaker correlations, and therefore intervals greater than 300mm were not analyzed. These variances were then correlated with the RTRRMS's measurements made at speeds of 20 km/h, 32 km/h and 50 km/h (and at 80 km/h with the MM02 only) to examine the relationship between the two for use as a calibration measure. The results of these correlations are given in Tables H.5 - H.8, and discuss- ed in Chapter 3 along with the other numerics. Root Mean Square of Deviation (RMSD) The root mean square of deviation is a very simple numeric that suggest- ed itself after examination of the performance of the previous two numerics. It is derived by determining the deviations from a simple linear regression line for a given baselength b, in meters, and profile interval dx, in milli- metres, and then calculating the root mean square of these deviations. For a given baselength b, with n profile points, the regression line y = A + Bx is calculated and the deviations Di evaluated. RMSDb = / n The RMSD for the test section of road containing N baselengths of length b and profile interval dx is given by: RMSDb2 RMSD =b dx,b N RMSDdx,b was calculated for discrete baselengths as well as for contiguous baselengths. For the discrete baselength analysis the baselengths used were consecutive and the last profile point of the first baselength was also the first profile point of the next consecutive baselength, whereas in 362 the contiguous baselength analysis all profile points were used successively to form a baselength. For documentation purposes these RMSDdx,b values are tabulated in Tables H.9 - H.12 for all combinations of baselengths and pro- file intervals examined for all the test sections and wheelpaths measured in Brazil. Tables of R values generated through correlation of RTRRMS's measurements with RMSDdx,b for the nearside wheelpath only for both methods of analysis (i.e., discrete contiguous baselengths) are given in Tables H.13 and H.14. Table H.15 tabulates the R2 values for the offside wheelpath for the discrete baselength analysis only. A detailed examination of these tables is made in Chapter 3. 3. INTERPRETATION AND DISCUSSION OF RESULTS Measurement variables The object of the profile analysis detailed in the previous chapter and tabulated in Tables H.1-H.15 was to develop a suitable statistic to accurate- ly characterize a road profiLle such that it could be correlated with the res- ponse of a roughness measurlng vehicle travelling on it, and thereby produce a stable calibrating equation. The analysis also serves the purpose of exam- ining the effect of different surface types on RTRRMS's, the effect of measu- ring at different speeds, and also the effect of the variation in wheelpath roughness on RTRRMS. 1. Surface types: The main IRRE report examines the effect of surface type in detail and concludes that because of the interaction of surface type and measurement speed it would be necessary to provide separate calibration equa- tions for paved and unpaved roads at 50 km/h or less, and also separate cali- brations for asphaltic concrete and surface treated roads at 80 km/h. In this report surface type was not examined separately as it was felt desirable to consider the phenomenon of roughness as being universal for all roads irrespective of surface type. This could be achieved (as was mentioned in the main report) if the influence of measurement speed could be eliminated. 2. Measurement speed: Examination of the R values calculated for all combinations of baselengths, profile intervals, and wheelpaths with the four 363 RTRRMS's show that all three calibration statistics correlate consistently better at a measurement speed of 32 km/h than at any other alternative measurement speed. One reason for this feature may be that it is easier to propel the vehicle steadily at this speed without interference from spurious acceleration and deceleration inputs and also that the wheelpath can be con- sistently adhered to. As the primary objective of the IRRE was to develop a calibration standard that was robust and could be easily applied universally it is suggested that the standard speed for calibration measurement should be 32 km/h for RTRRMS's irrespective of the actual speeds at which the normal roughness measurements are made. Two immediate benefits that accrue from calibrating at a speed of 32 km/h are the creation of statistically stronger calibration relationships and the elimination of any possible effects due to road surface type on RTRRMS measurements. Routine roughness measurements at speeds other than 32 km/h, although not recommended, could still be under- taken provided the relationship between measurements at 32 km/h and any other desired speed of measurement is established during the calibration period. 3. Effect of wheelpath variation on RTRRMS correlation: When RTRRMS's measure roughness on a road the effect of the unevenness of both wheelpaths are assumed to provide inputs to the numerical measure of roughness. Correl- ation with single wheel trailers is usually improved by measuring both wheel- paths with the trailers and correlating the average measure of the two wheel- paths with RTRRMS measures. This is feasible when measurements are made at reasonable speeds, but profilometry with manual systems such as the Rod and Level and the TRRL beam discourages the measurement of both wheelpaths as these measurements are time consuming. Detailed analysis was therefore undertaken to establish whether any particular wheelpath had a stronger in- fluence on RTRRMS measures or whether it was the rougher or smoother wheel- path that influenced the RTRRMS. A brief examination of correlations of all the rougher wheelpaths and all the smoother wheelpaths measured did not pro- vide any conclusive results for preferring one to the other. Table H.13 tabulates the RMSDdx,b, R values for the nearside wheelpath, and Table H-15 tabulates the comparable R values for the offside wheelpath for all combinations of speed, profile interval, baselength and RTRRMS's. Of the 213 R values generated for each wheelpath in these tables, in every single case the R value for the nearside wheelpath is superior to the offside wheelpath, 364 suggesting that profiles of the nearside wheelpath only need to be measured when using manual profiling methods. [The 1984 version of the TRRL beam per- mits a 320 metre wheelpath to be surveyed in one hour, reducing the survey effort considerably. Improved correlations between RTRRMS and profile based reference numerics can be achieved by using the mean values of the two wheel- paths.] Examination of profile interval and baselength In all the three analyses (i.e., Moving Average, RMSVE and RMSD) many combinations of profile intervals and baselengths have been analysed and cor- related with RTRRMS measures. Examination of the R values derived through the M. Avg. statistic (Tables H.5 - H.8) show that the best R value tends to vary between response vehicles as well as between measurement speed. There is no consistent pattern evident in the improvement of the R2 value with any particular combination of profile intervals or speed, and this makes it dif- ficult to decide on a 'best' profile interval or speed to choose for calibra- tion purposes. Also the R values are inferior to those produced by the other two statistics. The RMSVE statistic on the other hand shows a definite trend towards peaking of the R value around certain profile intervals and baselengths at different measurement speeds, with the 32 km/h speed consistently the best. The Table H.16a summarizes the best R values produced at a measurement speed of 32 km/h for the three best profile intervals and baselengths. The best average R value for the four RTRRMS's used in the IRRE exercise is 0.970 for a baselength of 1.8 metres using a profile interval of 300mm. Thus the RMSVE statistic is capable of producing a calibration relationship with a very high level of statistical significance using profile points at 300mm intervals for a baselength of 1.8 metres. Development of the RMSD profile statistic The successful establishment of an RMSVE profile statistic to character- ize the unevenness of a road surface calculated on a baselength of 1.8 metres using 300mm spaced profile intervals was the result of successive stages of 365 examination of the highly complex theory of waveform analysis. The relative simplicity of the computation of the RMSVE statistic based on profile eleva- tions over a short baselength suggested that this principle could be simplified even further by calculating the root mean square of the deviations of the profile heights from an ideal flat smooth road surface. Thus the RMSD, calculated from the deviations from a linear regression line was considered for correlation with RTRRMS measures. Tables H.9 and H.10 show the RMSDdx,b values computed for discrete baselengths and Tables 11.11 and H.12 list the RMSDdx,b values computed for contiguous baselengths. The R values obtained after regression with the RTRRMS is given in Table H.13 for discrete base- lengths, and Table H.14 for contiguous baselengths. Comparing the discrete baselength R values with the equivalent R values from the RMSVE analysis (Tables H.1-H.4) it is seen that the R values, though very similar, are marginally better for the RMSD statistic. (Direct comparison is not always possible for every baselength, because the RMSD analysis was conducted on baselengths closer to the 'window' of interest (1.8 metres) than the broader spaced baselengths examined in the earlier RMSVE analysis). Table H.16b summarises R2 values produced over the three best profile interval/baselength combinations for the four RTRRMIS's operated at 32 km/h. This shows that the RMSD analysis produces results on a pattern almost identical to the RMSVE analysis and again the overall 'best' baselength/profile interval combination emerges at 1.8 meters and 300mm, producing an average R2 value of 0.970. Comparison of discrete and contiguous baselength analyses Given a large number of consecutive elevation points, baselengths could be defined as discrete or contiguous as explained earlier and it was necessary to examine the results produced by the two different definitions. Therefore the complete RMSD analysis was conducted using both definitions of baselength and the R values produced can be compared between Table H.13 and Table H.14. Here again the pattern of improvement or degradation of the R values with various combinations of profile interval, baselength and speed are almost iden- tical, and overall it is observed that the more complicated contiguous base- length analysis is only marginally better in about fifty per cent of the cases than the much simpler discrete baselength analysis by a few points in the third decimal place. In the particular case of the 1.8 metres baselength which has 366 so far emerged as the most favoured for correlation with RTRRMS, the discrete baselength analysis produces better R2 values in three out of four cases. It is therefore proposed to use the simpler method of calculating the RMSD statistic using discrete baselengths, and RMSD300,1.8 has been selecte as the most appropriate reference numeric for correlation with RTRRMS's opera ting at a speed of 32 km/h. 4. A STANDARD INTERNATIONAL ROUGHNESS INDEX The analysis and discussion so far has concentrated on producing stable calibration relationships for calibrating RTRRMS over a period of time. The second and equally important requirement is to establish a standard roughness scale to which all RTRRMS's throughout the world could be calibrated, enab- ling the effect of road roughness on highway use and maintenance to be asses- sed on a universal basis. The main report discusses the need for an Interna- tional Roughness Index, outlines the requirements such an index has to satis- fy, and finally suggests the use of an RARS80 index as processed via a Quarter Car Simulation (QCS). An alternative Standard International Roughness Index is discussed below, based on the need for a practical and viable system, and on a scale which is familiar and easily understood by the world highway community. In the previous discussion on calibration relationships, it was estab- lished that a statistic generated through road profile, such as RMSDdX,b, provides a satisfactory numeric for correlation with RTRRMS measures. RMSD is thus a statistic that uniquely characterizes a particular road profile and could therefore serve as a common standard roughness index. But such a sta- tistic has several drawbacks when considered as a common roughness index. Its descriptive name would not be commonly understood, its absolute numerical value is small and spread over a very narrow range (0.3 to 7.0 to represent roughness ranging from 800mm/km to 15,000mm/km respectively) and it has no universal association with surface unevenness. The most popular measure of roughness is the output of RTRRMS based on the dynamic motions in the suspension of a passenger car type of vehicle. 367 The measurements obtained with these instruments are in the form of dis- crete counts where each count corresponds to a certain length of cumulative deflection of the vehicle suspension. As the counts themselves are not com- parable for different instruments, they need to be re-scaled to a reference, which should logically be a linear distance per distance such as inches per mile or millimeters per kilometer. The TRRL Towed Bump Integrator Trailer which was developed from the BPR Roughometer was specially designed as a standard response measuring instrument, with known response characteristics and is well known and used in many parts of the world. Roughness measure- ments obtained from the Bump Integrator Trailer in mm/km are easily identi- fied by practitioners with perceived levels of roughness of roads and have been extensively used in the past to assess road and vehicle performance and should therefore appear as a strong candidate for providing a standard rough- ness scale. Moreover, the mm/km roughness statistic has a historical base due to its predominant use in past roughness evaluation studies and is an important input parameter for the RTIM2 and 1DM-II road investment models. However, because of the inherent drawback of response measuring systems, the trailer itself cannot be considered as a standard system/instrument, but an equation derived from an RMSD profile statistic to estimate the Bump Integra- tor Trailer response characteristics would provide an acceptable standard reference roughness measure on a scale familiar to practitioners. One impor- tant qualification for such an acceptance though is that Bump Integrator Trailer measurements should in practice correlate well with other RTRRMS's. Figs. H.1, H.2 and H.3 show the near perfect correlation between the Trailer measurements and the three response instruments used in the IRRE study. Similar correlations have been achieved in previous studies with other RTRRMS's. Therefore a standard reference roughness equation based on the BI Trailer response characteristics would be deemed suitable. Such a standard reference roughness equation has been developed from the IRRE data and is shown in Fig. H.4, where the equation developed is in a quadratic form with an R value of 0.961. The quadratic form marginally improves the goodness of fit at the upper end of the roughness scale. The standard reference roughness equation is: ROUGHNESS (nm/km) = 472 + 1437 (RMSD 300,1.8) + 225 (RMSD300, 1.8) 368 The above standard reference roughness equation will remain a permanent road roughness estimator through time and space, and will not be subject to any change in the future. 5. PROPOSED METROD OF CALIBRATING AND STANDARDIZING OF RTRRMS's In Chapter 3 the analysis of the three profile generated statistics were interpreted and discussed together with the performance pattern of the R2 values with respect to the influence of surface type, speed of measurement and effect of wheelpath roughness variations. Surface type It was argued that roughness should not be discriminated by surface type as it should be regarded as a phenomenon manifesting itself on all surface types in the same manner and affecting vehicle operation and road performance in the same way. Any influence of surface type on roughness measures caused by variations in measurement speed are probably attributable to suspension characteristics rather than surface type. It is proposed in this report that surface type should not be discriminated especially in view of the further proposal that measurement speed should also be held constant. Mwasurement speed The analysis of the IRRE data suggests that measurements made at 32 km/h provide consistently better correlations than at any other measurement speed. Calibration and standardization procedures require robust and stable relation nships, and every stage of conversion of relationships between speeds tends to weaken the stability of the relationship. It is therefore proposed that for calibration and standardization purposes the measurement speed be main- tained at 32 km/h, so that the final calibrated and standardized roughness measure will always be expressed in terms of a measurement speed of 32 km/h and thus directly comparable universally. Users desiring to make routine measures of roughness with RTRRMS's at speeds other than the standard speed of 32 km/h will need to correlate the roughness measures at two different speeds with a particular response system, and then use the equivalent 32 km/h measure for calibration and standardization. 369 Variation in wheelpath roughness Slow manual methods of profilometry have discouraged the measurement of both wheelpaths, if the measurement of one wheelpath alone was sufficient to produce a strong correlation. The analysis has shown that the nearside wheel- path profile statistics always correlated better with RTRRMS than the offside wheelpaths. However, where profiles of both wheelpaths are available, the RMSD300,1.8 of the two wheelpaths should be used to correlate with RTRRMS at 32 km/h. Choice of Profile Statistic Three profile based statistics were generated with the TRRL beam profil- ometer, and a further three statistics were developed and presented in the main report. It was shown in the analysis in this Appendix that the overall best combination of profile interval and baselength was observed to be the 300mm interval for a baselength of 1.8 metres. Table H.17 compares the R2 values produced by these six different statistics when they were correlated against the four RTRRMS's used in the Brazil IRRE on the 28 wheelpaths measu- red by the TRRL beam. All the statistics produced good to excellent correla- tions with the four RTRRMS's, but the computational effort required to pro- duce them varied widely. The statistic requiring the least computational effort and also producing the best correlation with the RTRRI4S is the RMSD300,1.8, and therefore the use of this statistic is proposed for calib- ration and standardization of response type roughness measurements made at 32 km/h. Calibrating and standardizing process The procedure for calibration is to select a number of sections of road approximately 200-300 metres in length, covering a range of roughness levels and containing as many road surface types as possible (a minimum of ten sections is recommended). These sections are then profiled on the nearside wheelpath (and on the offside wheelpath where possible) with the TRRL beam and the Root Mean Square of Deviation statistic (RMSD300,1.8) computed for each section. The sections are also measured with the response type vehicle 370 mounted roughness measuring Lnstrument at a speed of 32 km/h and the results expressed in mm/km. A linear regression of the form y = a+bx is calculated using RMSD as the independent variable (x) and the RTRRMS measured as the dependent variable (y). This equation now constitutes the calibration equation for that particular RTRRMS. Routine field roughness measurements can now be made with the response instrument. The routine measurements need to be standardized in the following manner. Substitute each field measurement for y in the equation y = a+bx and calculate x from x = (y-a)/b, to produce an estimate of RMSD300,1.8 as perceived by that particular RTRRMS. This estimated value of RMSD300,1.8 is then input to the Standard Reference Roughness equation ROUGHNESS (mm/km)'= 472 + 1437 (RMSD300,1.8) + 225 (RMSD300,1.8) to produce a standardized roughness value. All the field measurements are standardized in this manner. 6. VALIDATION STUDY IN ST LUCIA The calibrating and standardizing methodology was developed from data collected from the International Road Roughness Experiment conducted in Brazil in May 1982. It was decided to validate this methodology by obtaining data from a different geographical environment, and using different RTRRMS, and therefore a study was conducted in St. Lucia in the Eastern Caribbean in March 1983. Time and financial constraints restricted this study to two weeks field work, with the use of two locally hired vehicles, a Datsun 120 station wagon and a Cortina estate car, which were both instrumented with Bump Integrator units. The experimental conditions were not as controlled as in the IRRE study, as the TRRL staff were working quite independently without any insti- tutional backup. There was little choice in the selection of the hire vehic- les and their mechanical conditions was an unknown factor. One vehicle was driven by the hire car driver himself who was less amenable to experimental control than would be desirable, and the lack of reliable tire pressure 371 gauges led to the vehicles being operated in a partially uncontrolled condi- tion. These drawbacks, although not desirable, were in retrospect welcome because in the real world transport practitioners are likely to have to oper- ate under similar conditions and the calibration methodology needs to be sufficiently robust to cope with these situations. Nineteen test sections of road were measured with the TRRL beam and the two RTRRMS's, and the details of these sections together with the RTRRMS measures are given in Table H.18. The test section profiles were analyzed in exactly the same manner as the IRRE, Brazil data, and direct comparisons are therefore possible. Table H.19 tabulates the R2 values obtained using the RMSVE statistic, and Table H.20 shows the R2 values obtained with the Moving Average Variance. As the preferred statistic is the RMSD, a fuller documentation of the analysis is given in the following tables. Tables H.21 and H.22 tabulate the root mean square of deviation using the discrete baselength method, and Tables H.23 and H.24 the results obtained using the contiguous baselength method. These RMSDdX,b statistics were correlated against the Datsun and Cortina measures of roughness and the resulting R values are presented in Tables H.25 and H.26 for discrete and contiguous baselengths respectively. It will be observed that the pattern of improvement or degradation of the R2 values is identical to that observed in the IRRE analysis. Table H.16b sum- marised the R2 values obtained for the Datsun and Cortina when correlated with the RMSDdx,b statistic, for profile interval/baselength combinations selected from the IRRE study. The correlations are slightly weaker than those obtained in the IRRE study, but confirm that the calibration methodology derived from the IRRE study is applicable in different environments and with different RTRRMS's. Tables H.27 and H.28 tabulate the uncalibrated and calibrated roughness measurements for the IRRE and St. Lucia study respectively, using the calibrating and standardizing methodology described in the previous section. 372 T. OPERATION OF TRE TRRL ROUGHNESS CALIBRATION AND STANDARDIZATION BEAM The TRRL beam has now been developed as a compact, self contained road roughness calibration and standardization system. The road profiles measured by the beam are processed automatically through its internal micro-processor and the RMSD300,1.8 is printed out on completion of the measurement of the test section. After measuring all the test sections, the operator is requir- ed to input the RMSD300,1.8 values for each section together with the cor- responding RTRRMS measure through the built-in key-pad for computation of the calibration equation. The equation is printed together with the R2 value. The equation is output for the operator's information only, as he does not need to use it. The R value will be printed with a warning that the correl- ation is not satisfactory if the value falls below 0.90. After the equation has been computed and printed, the operator inputs his routine field rough- ness measurements in mm/km and the processor will print the calibrated stand- ard measure of roughness which will be expressed in mm/km for standard speed for 32 km/h. A flow-chart of the operation of the beam is given in Fig. H.5. 373 TABLE H.1 T FEN L FE OF= F; S G;lPLJP FREE PFLUJE r: 1DF F:R M 53 \EF- FT IF lck L- FE L- EES: TF I COV<- FZ xosi Mt T F 31 (USING DISCRETE BASELENGTHS) BRASIL IRRE DATA NEARSIDE WHEELPATH 2(0 Km/hr 100mm INTERVAL 0.4. 0.8a 1.0. 1.2. 1.6. 2.0. 3.03 4.0. 5.0Q 6.0. 7.0. 8.0. 9.0. 10.0. TRAILER 0.765 0.879 0.899 0.911 0.928 0.919 0.896 0.865 0.823 0.817 0.789 0.823 0.817 0.762 CAR 81 0.859 0.925 0.948 0.954 0.967 0.969 0.939 0.915 0.879 0.867 0.840 0.840 0.844 0.813 NAASRA 0.849 0.920 0.944 0.950 0.965 0.967 0.938 0.915 0.879 0.868 0.840 0.842 0.847 0.814 MN-02 0.879 0.932 0.952 0.957 0.962 0.964 0.929 0.901 0.864 0.848 0.826 0.920 0.820 0.792 20(0mm INTERVAL 0.8. 1.2. 1.6. 2.O0 3.2 4.0 4.8. 6.0. 6.8. 8.0. 8.8. 10.0. TRAILER 0.910 0.927 0.931 0.921 0.898 0.863 0.854 0.816 0.816 0.820 0.796 0.759 CAR 91 0.947 0.962 0.963 0.965 0.940 0.908 0.902 0.860 0.849 0.834 0.826 0.810 NAASRA 0.943 0.959 0.962 0.964 0.940 0.908 0.903 0.862 0.850 0.836 0.827 0.811 NM-02 0.947 0.960 0.955 0.956 0.925 0.892 0.887 0.840 0.829 0.812 0.804 0.789 3((0mm INTERVAL 1.2. 1.8. 2.4. 3.0. 4.2. 4.8. 6.0 7.2. 7.8. 9.0. 10.2. TRAILER 0.932 0.925 0.901 0.894 0.869 0.849 0.819 0.810 0.814 0.819 0.792 CAR BI 0.972 0.972 0.956 0.938 0.912 0.905 0.871 0.848 0.847 0.847 0.825 NAASRA 0.970 0.971 0.955 0.937 0.912 0.906 0.872 0.849 0.848 0.849 0.827 NH-02 0.968 0.962 0.945 0.927 0.897 0.891 0.851 0.829 0.829 0.822 0.800 4(1(1mm INTERVAL 1.6. 2.4. 3.2. 4.0 4.8. 5.6. 7.2. 8.0. 8.8. 9.6. TRAILER 0.923 0.892 0.892 0.860 0.849 0.823 0.805 0.811 0.793 0.811 CAR 8I 0.863 0.834 0.835 0.828 0.807 0.795 0.779 0.786 0.780 0.795 NAASRA 0.858 0.830 0.833 0.826 0.805 0.794 0.779 0.787 0.781 0.796 MH-02 0.862 0.829 0.828 0.817 0.797 0.783 0.761 0.767 0.759 0.773 51:0mm INTERVAL 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. TRAILER 0.906 0.888 0.862 0.815 0.811 0.780 0.813 0.813 0.755 CAR 81 0.849 0.856 0.835 0.792 0.793 0.766 0.789 0.791 0.744 NAASRA 0.844 0.852 0.833 0.790 0.793 0.766 0.790 0.793 0.746 NN-02 0.850 0.852 0.828 0.782 0.778 0.753 0.773 0.768 0.723 374 TABLE H.2 -T- P EEI: DF= FR ESC UUiFtFE \.'gLJE E8 F= F;t M1 VE E-F < I t- E -VX I Oll% F; -rF; FIt ISE (USING DISCRETE BASELENGTHS) BRASIL IRRE DATA NEARS IDE WHEELPATH 32 Km/hr 100mm INTER VAL 0.4. 0.8. 1.0. 1.2. 1.6. 2.0. 3.0. 4.0. 5.0 6.0. 7.0 9.0 9.0. 10.0, TRAILER 0.722 0.856 0.B87 0.907 0.944 0.945 0.940 0.920 0.889 0.881 0.858 0.887 0.879 0.834 CAR Bl 0.811 0.887 0.921 0.928 0.965 0.974 0.971 0.960 0.938 0.931 0.915 0.909 0.911 0.889 NAASRA 0.800 0.881 0.917 0.925 0.965 0.974 0.972 0.961 0.941 0.933 0.916 0.914 0.916 0.892 1N-02 0.806 0.872 0.90B 0.915 0.955 0.966 0.965 0.954 0.937 0.926 0.913 0.897 0.894 0.876 200mm INTERVAL 0.8. 1.2. 1.6. 2.0. 3.2. 4.0. 4.8. 6.0. 6.8. 8.0. 9.8. 10.0. TRAILER 0.895 0.927 0.951 0.951 0.944 0.920 0.914 0.882 0.881 0.885 0.863 0.831 CAR DI 0.920 0.945 0.970 0-.975 0.970 0.957 0.955 0.926 0.921 0.904 0.898 0.888 NAASRA 0.916 0.943 0.971 0.976 0.973 0.958 0.958 0.929 0.924 0.909 0.902 0.891 11-02 0.901 0.928 0.958 0.963 0.958 0.949 0.947 0.919 0.910 0.891 0.886 0.874 300mm INTERVAL 1.2. 1.8. 2.4. 3.0. 4.2. 4.8 6.0. 7.2. 7.8. 9.0. 10.2. TRAILER 0.938 0.955 0.943 0.940 0.925 0.909 0.883 0.878 0.877 0.880 0.852 CAR B1 0.960 0.978 0.979 0.972 0.959 0.958 0.934 0.916 0.917 0.912 0.897 NAASRA 0.959 0.980 0.981 0.974 0.963 0.960 0.936 0.920 0.921 0.918 0.902 ;m-02 0.945 0.965 0.971 0.966 0.953 0.952 0.929 0.909 0.909 0.895 0.882 400mm I NTERVAL 1.6. 2.4. 3.2. 4.0. 4.8. 5.6. 7.2. 8.0. 8.8. 9.6. TRAILER 0.950 0.937 0.939 0.918 0.910 0.887 0.875 0.879 0.860 0.874 CAR B1 0.877 0.872 0.878 0.886 0.871 0.863 0.854 0.864 0.853 0.865 NhAASRA 0.873 0.870 0.877 0.885 0.871 0.864 0.857 0.868 0.856 0.868 11-02 0.883 0.880 0.883 0.891 0.878 0.871 0.859 0.863 0.853 0.858 500mm INTERVAL 2.0 3.0 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. TRAILER 0.944 0.936 0.918 0.881 0.B78 0.850 0.879 0.876 0.827 CAR I1 0.876 0.901 0.891 0.860 0.860 0.843 0.864 0.860 0.831 NAASRA 0.872 0.898 0.890 0.861 0.861 0.845 0.868 0.864 0.835 11M1-02 0.885 0.909 0.898 0.873 0.868 0.853 0.863 0.853 0.826 375 TABLE H.3 r P E L E O F FF S RLJ%F / V L LJEE S OF FZ S V ERF T I C PkL. E- L' E: VT I ON J FR T F FZR1 MS (USING DISCRETE BASELENGTHS) BRASIL IRRE DATA NEARSIDE WHEELPATH 50 Km/hr 100mm INTERVAL 0.4. 0.8. 1.O. 1.2. 1.6. 2.0. 3.0. 4.O. 5.0. 6.0. 7.0O 8.0. 9.0. 10.O0 TRAILER 0.686 0.831 0.867 0.890 0.937 0.951 0.947 0.931 0.909 0.891 0.875 0.895 0.892 0.845 CAR B1 0.759 0.850 0.889 0.900 0.948 0.959 0.971 0.964 0.948 0.944 0.936 0.942 0.946 0.923 NAASRA 0.738 0.833 0.876 0.887 0.945 0.958 0.978 0.973 0.962 0.960 0.947 0.954 0.956 0.930 11-02 0.748 0.826 0.867 0.875 0.931 0.944 0.969 0.958 0.955 0.950 0.941 0.941 0.937 0.919 200mm INTERVAL 0.8. 1.2. 1.6. 2.0. 3.2. 4.0. 4.8. 6.0. 6.8. 8.0. 8.8. lO.O0 TRAILER 0.870 0.913 0.944 0.954 0.953 0.930 0.930 0.889 0.886 0.892 0.868 0.840 CAR BI 0.892 0.925 O.959 0.966 0.973 0.963 0.968 0.942 0.945 0.939 0.928 0.923 NAASRA 0.879 0.914 0.958 0.966 0.980 0.973 0.977 0.959 0.955 0.952 0.941 0.930 11-02 0.866 0.898 0.942 0.947 0.958 0.956 0.964 0.947 0.945 0.939 0.928 0.917 3.00mm INTERVAL 1.2. 1.8. 2.4. 3.0. 4.2. 4.8. 6.0. 7.2. 7.8. 9.0. 10.2. TRAILER 0.930 0.965 0.958 0.949 0.939 0.928 0.893 0.893 0.891 0.883 0.849 CAR Bl 0.940 0.969 0.972 0.971 0.970 0.966 0.946 0.940 0.946 0.946 0.934 NAASRA 0.930 0.966 0.976 0.980 0.979 0.974 0.962 0.955 0.954 0.956 0.943 111-02 0.912 0.947 0.960 0.970 0.966 0.961 0.951 0.947 0.940 0.937 0.925 400mm INTERVAL 1.6. 2.4. 3.2. 4.0. 4.8. 5.6. 7.2. 8.0. 8.8. 9.6. TRAILER 0.955 0.956 0.953 0.932 0.931 0.903 0.891 0.890 0.868 0.873 CAR Bl 0.844 0.852 0.863 0.878 0.865 0.858 0.859 0.879 0.857 0.874 NAASRA 0.842 0.856 0.866 0.884 0.873 0.870 0.876 0.891 0.874 0.883 11-02 0.847 0.862 0.863 0.882 0.875 0.869 0.872 0.880 0.861 0.858 500mm INTERVAL 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. TRAILER 0.952 0.943 0.927 0.899 0.886 0.866 0.888 0.879 0.838 CAR El 0.848 0.883 0.881 0.854 0.851 0.842 0.879 0.870 0.850 NAASRA 0.845 0.886 0.888 0.869 0.868 0.858 0.890 0.880 0.858 M1-02 0.849 0.889 0.884 0.875 0.864 0.855 0.878 0.857 0.834 376 TABLE H.4 T %EE'LE E O F FU LJ4FF [ X L-E S O F FRt 5 EB J E FR -T I C- P4L E-= L- FE J%XoT I= or x Fk T F; Ft M S (USING DISCRETE BASELENGTHS) BRASIL IRRE DATA NEARSIDE WHEELPATH 80 Km/hr 100mm INTERVAL 0.41 0.8 I.0. 1.2. 1.6. 2.0h 3.0. 4.0 5.0. 6.0h 7.0 B.h80 9.0. 10.0. N-02 0.58B6 0.683 0.741 0.758 0.845 0.869 0.909 0.906 0.906 0.903 0.897 0.875 0.869 0.857 200mm INTERVAL 0.8. 1.2. 1.6. 2.0h 3.2. 4. 4.8. 6.0. 6.8. 8.0. 8.8. 10.0. NH-02 0.738 0.792 0.868 0.880 0.904 0.909 0.913 0.903 0.889 0.875 0.868 0.859 300mm INTERVAL 1.2. 1.8. 2.4. 3.0. 4.2. 4.8. 6.0. 7.2. 7.8. 9.0. 10.2. NN-02 0.809 0.875 0.907 0.913 0.912 0.909 0.904 0.887 0.880 0.869 0.859 400mm INTERVAL 1.6. 2.4. 3.2 4.0 4.8. 5.6. 7.2. 8.0. 8.8. 9.6. NN-02 0.774 0.813 0.813 0.838 0.831 0.828 0.834 0.835 0.820 0.821 500mm INTERVAL 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. 8.0. 9.0. 10.0. KH-02 0.791 0.838 0.837 0.836 0.831 0.825 0.829 0.814 0.805 377 TABLE H.5 rfEALEE OF FC FE I Ft: L- LUE: OFC3F M 10 v I 1r1 CB *OA v EE- Fti #N G ER: x5 F; -T F;Z F;R M E NEARSIDE WHEELPATH BRASIL IRRE DATA 20 Km/hr 100mm INTERVAL 0.4. 1.0. 1.6. 2.0 3.0. 5.0. 7.0. 10.0. TRAILER 0.831 0.956 0.955 0.931 0.877 0.822 0.801 0.794 CAR DI 0.868 0.892 0.911 0.914 0.891 0.837 0.812 0.787 NAASRA 0.867 0.895 0.915 0.918 O.B94 0.840 0.815 0.792 MN-02 0.859 0.864 0.878 0.880 0.856 0.801 0.775 0.745 200mm INTERVAL 1.2. 1.6. 2.0. 2.4. 3.2. 4.0 5.2. TRAILER 0.964 0.949 0.924 0.900 0.866 0.B43 0.816 CAR 81 0.891 0.905 0.906 0.899 0.875 0.851 0.827 NAASRA 0.895 0.909 0.910 0.902 0.879 0.855 0.831 nM-02 0.857 0.869 0.869 0.862 0.838 0.814 0.791 OOmm INTERVAL 1.2. 1.8. 2.4. 3.0. 3.6. 4.2. 4.8. 5.4. TRAILER 0.961 0.927 0.887 0.863 0.847 0.832 0.819 0.810 CAR 8I 0.903 0.912 0.901 0.884 0.867 0.852 0.841 0.831 NAASRA 0.907 0.916 0.905 0.887 0.871 0.855 0.844 0.835 NN-02 0.869 0.876 0.865 0.848 0.831 0.816 0.805 0.796 378 TABLE H.6 TrP BL-E: QF Ft 8 U UFE 'V L- ULES OF MI"V I NC3 A N,EF E F5 RFTR FMS NEARSIDE WHEELPATH BRASIL IRRE DATA 32 Km/hr i00mm INTERVAL 0.4* 1.0* 16.b 2.0. 3.0. 5.0. 7.0* 10.0m TRAILER 0.770 0.935 0.966 0.959 0.924 0.881 0.861 0.846 CAR Bl 0.800 0.852 0.893 0.910 0.913 0.885 0.869 0.841 NAASRA 0.801 0.859 0.901 0.919 0.921 0.892 0.876 0.850 NN-02 0.768 0.807 0.852 0.874 0.884 0.861 0.843 0.806 200mm INTERVAL 1.2. 1.6. 2.0 2.4. 3.2. 4.0 5.2. TRAILER 0.961 0.966 0.955 0.941 0.917 0.899 0.876 CAR D1 0.865 0.892 0.907 0.910 0.903 0.891 0.879 NAASRA 0.873 0.901 0.916 0.919 0.911 0.898 0.886 MM-02 0.817 0.849 0.869 0.877 0.873 0.883 0.854 300mm INTERVAL 1.2. 1.8. 2.4. 3.0. 3.6. 4.2. 4.8. 5.4. TRAILER 0.968 0.958 0.933 0.916 0.903 0.890 0.880 0.871 CAR DI 0.882 0.910 0.916 0.910 0.902 0.894 0.889 0.883 NAASRA 0.890 0.919 0.924 0.918 0.909 0.901 0.895 0.890 Mf-02 0.837 0.874 0.886 0.883 0.875 0.869 0.865 0.860 379 TABLE H.7 M1 E LEE F kF F; Sf!LJ&FiEE FLJFE8 M OF NEARS IDE WHEELPATH BRASIL IRRE DATA 50 B'm/hr 100mm INTERVAL 0. 4 1.0. 1.6. 2.0 3.0. 5.0. 7.0 10.0. TRAILER 0.712 0.898 0.951 0.953 0.927 0.881 0.857 0.828 CAR BI 0.775 0.854 0.903 0.923 0.930 0.911 0.902 0.886 NAASRA 0.766 0.854 0.911 0.937 0.953 0.938 0.928 0.910 HM-02 0.741 0.811 0.868 0.897 0.921 0.913 0.905 0.877 200mm I NTERVAL 1.2. 1.6. 2.0. 2.4. 3.2. 4.0 5.2. TRAILER 0.935 0.951 0.950 0.940 0.918 0.899 0.874 CAR B1 0.877 0.906 0.923 0.927 0.924 0.915 0.906 NAASRA 0.881 0.916 0.938 0.947 0.948 0.941 0.933 .N-02 0.833 0.870 0.898 0.910 0.915 0.911 0.909 3005m m I NTERVAL 1.2. 1.8 2.4. 3.0. 3.6. 4.2. 4.8. 5.4. TRAILER 0.948 0.955 0.938 0.921 0.907 0.894 0.883 0.874 CAR Bl 0.893 0.924 0.931 0.928 0.922 0.916 0.913 0.909 NAASRA 0.899 0.939 0.952 0.952 0.947 0.943 0.939 0.936 MH-02 0.853 0.898 0.918 0.921 0.919 0.917 0.915 0.914 380 TABLE H.8 -I 1cW 1 L_ EE F= FZ 5 S U iFERE R f LLU 1_ El c F= Mv 0 VE I r4 ID) i=X Vy EE: FZ : (in EU3 F-= w F=t Tr FR F-C Mx 5- NEARS IDE WHEELF'ATH BRASIL IRRE DATA 80 K>ml/hr- 100mm INTERVAL 0.4. 1.0. 1.6. 2.0 3.0. 5.0. 7.0. 10.0o ?W-02 0.582 0.681 0.764 0.809 0.849 0.845 0.836 0.81I 200imm INTERVAL 1.2. 1.6. 2.0. 2.4. 3.2. 4.0 5.2. MN-02 0.720 0.773 0.815 0.836 0.846 0.843 0.843 300Cmm I NTERVAL 1.2. 1.8. 2.4. 3.0M 3.6. 4.2. 4.8 5.4. NK-02 0.744 0.813 0.847 0.853 0.849 0.848 0.847 0.846 381 TABLE H.9 F;:OOT- [= c PIErI%I !S QIUJw F;C E=R: C:F= DEE=- I 0= - I Ol M (USING DISCRETE BASELENGTHS) BRASIL IRRE DATA 100mm INTERVAL SECTION 1.5. 1.8. 2.0s 2.2. 2.4. 2.6h n/s 0/5 n/s o/s n/s 0/s n/s c/s n/s o/s n/s o/s CR04 1.154 1.453 1.356 1.617 1.449 1.690 1.440 -- 1.707 -- 1.638 -- CA05 1.695 1.780 1.869 1.981 1.990 2.154 2.034 -- 2.186 -- 2.292 -- CA06 1.851 2.169 2.100 2.430 2.196 2.671 2.328 -- 2.521 -- 2.517 -- CA10 0.686 -- 0.787 -- 0.865 -- 0.901 -- 0.965 -- 0.996 -- CA12 -- 0.599 -- 0.704 -- 0.748 -- 0.784 -- 0.843 -- 0.876 TSOI -- 1.197 -- 1.360 -- 1.390 -- 1.472 -- 1.576 -- 1.599 TS04 -- 1.368 -- 1.584 -- 1.659 -- 1.694 -- 1.816 -- 1.868 TS05 -- 1.566 -- 1.858 -- 1.931 -- 2.063 -- 2.145 -- 2.183 TS06 0.995 1.103 1.069 1.180 1.137 1.228 1.169 -- 1.178 -- 1.242 -- TS07 -- 1.029 -- 1.074 -- 1.150 -- 1.166 -- 1.220 -- 1.249 TEOI 1.529 1.759 1.637 1.889 1.659 1.965 1.745 -- 1.803 -- 1.839 -- TE03 1.982 2.910 2.163 3.147 2.217 3.239 2.318 -- 2.390 - 2.426 -- TE06 5.015 -- 5.483 -- 5.616 -- 5.914 -- 6.073 -- 6.282 -- TEII 2.970 4.038 3.103 4.269 3.245 4.407 3.284 -- 3.394 -- 3.398 -- GROI 1.345 -- 1.438 -- 1.481 -- 1.538 -- 1.577 -- 1.578 -- 6R05 2.419 3.121 2.672 3.386 2.774 3.464 2.932 -- 2.963 - 3.104 -- 6R07 1.586 2.610 1.682 2.724 1.737 2.885 1.776 -- 1.843 -- 1.843 -- 6R12 3.044 4.371 3.494 5.100 3.770 5.096 4.081 -- 4.327 -- 5.022 -- 200mm INTERVAL SECTION 1.6. 1.8n 2.0n 2.2. 2.4. nis 0/s n/s o/s n/s 0/s n/s 0/s n/s o/s CA04 1.231 1.591 1.373 1.654 1.456 1.720 1.455 -- 1.740 -- Caos 1.777 1.831 1.895 1.999 2.011 2.182 2.045 -- 2.213 -- CA06 2.085 2.213 2.143 2.467 2.246 2.715 2.375 - 2.571 -- CA10 0.748 -- 0.782 -- 0.863 -- 0.915 -- 0.973 -- CA12 -- 0.657 -- 0.695 -- 0.749 -- 0.794 -- 0.849 TSOI -- 1.279 -- 1.368 -- 1.398 -- 1.485 -- 1.582 TS04 -- 1.501 -- 1.601 -- 1.676 -- 1.710 -- 1.821 TS05 -- 1.759 -- 1.902 -- 1.965 -- 2.091 -- 2.165 TS06 0.994 1.104 1.048 1.157 1.122 1.212 1.158 -- 1.157 -- TS07 -- 1.059 -- 1.081 -- 1.147 -- 1.169 -- 1.221 TEOI 1.557 1.808 1.632 1.900- 1.664 1.985 1.761 -- 1.807 -- TE03 2.021 2.987 2.161 3.123 2.200 3.281 2.316 - 2.402 -- TE06 5.260 -- 5.513 -- 5.698 -- 6.002 -- 6.147 -- TE11 2.937 3.973 3.021 4.192 3.151 4.360 3.203 -- 3.310 -- GRO 1.356 -- 1.401 -- 1.458 -- 1.524 -^ 1.562 -- 6R05 2.483 3.209 2.643 3.386 2.762 3.423 2.885 -- 2.944 -- 6R07 1.577 2.650 1.631 2.759 1.673 2.943 1.736 -- 1.810 -- 6R12 3.553 4.511 3.590 5.179 3.839 5.187 4.204 -- 4.427 -- 382 TABLE H.10 FR "CIT M=1EEJn B FtE-: OF D E-V I NT IQN (USING DISCRETE BASELENGTHS) BRASIL IRRE DATA 300mm INTERVAL SECTION 1.5. 1.8. 2.1. n/s 0/s n/s D/s n/s D/s CA04 1.187 1.501 1.422 1.675 1.392 1.853 CA05 1.702 1.817 1.899 2.036 2.094 2.264 CA06 1.873 2.231 2.137 2.500 2.312 2.727 CAIO 0.656 -- 0.788 -- 0.855 -- CA12 -- 0.574 -- 0.721 -- 0.799 TSOI -- 1.199 -- 1.387 -- 1.489 TS04 -- 1.371 -- 1.603 -- 1.712 TS05 -- 1.634 -- 1.951 -- 2.055 TS06 0.973 1.059 1.054 1.152 1.136 1.224 TS07 -- 1.023 -- 1.087 -- 1.172 TEOI 1.366 1.645 1.517 1.832 1.626 1.892 TEO3 1.984 2.904 2.195 3.103 2.299 3.249 TEO6 5.057 -- 5.434 -- 5.721 -- TEII 2.857 3.833 3.005 4.085 3.205 4.317 6RO 1.239 -- 1.359 -- 1.482 -- 6R05 2.363 3.164 2.651 3.433 2.892 3.701 GR07 1.476 2.550 1.608 2.723 1.680 2.880 6R12 3.172 4.552 3.687 5.263 3.849 5.733 500(mm INTERVAL SECTION 1.5. 2.Om 2.5. 3.0O n/s D/s n/s D/s n/s o/s n/s o/s CA04 1.073 1.467 1.463 1.728 1.579 2.139 2.034 2.299 CA05 1.667 1.831 1.991 2.275 2.334 2.459 2.533 2.752 CA06 1.881 2.189 2.249 2.762 2.508 3.085 2.863 3.263 CAIO 0.617 -- 0.859 -- 1.028 -- 1.169 -- CA12 -- 0.528 -- 0.772 -- 0.897 -- 1.073 TSOI -- 1.148 -- 1.401 -- 1.603 -- 1.765 TS04 -- 1.363 -- 1.695 -- 1.869 -- 2.031 TS05 -- 1.543 -- 1.922 -- 2.153 -- 2.160 T906 0.826 0.932 1.033 1.124 1.152 1.243 1.221 1.327 TS07 -- 0.889 -- 1.037- -- 1.133 -- 1.236 TEOI 1.321 1.511 1.540 1.836 1.715 2.016 1.945 2.145 TE03 1.712 2.699 1.988 3.192 2.273 3.457 2.429 3.713 TE06 4.678 -- 5.516 -- 6.094 -- 6.628 -- TEII 2.566 3.715 2.950 4.423 3.145 4.890 3.405 5.087 6ROI 1.119 -- 1.331 -- 1.513 -- 1.685 -- 6R05 2.247 3.020 2.708 3.439 3.087 3.814 3.374 4.051 6R07 1.291 2.481 1.570 2.768 1.720 3.089 1.881 3.135 6R12 3.120 4.418 3.940 5.276 4.694 5.509 5.229 6.180 383 TABLE H.11 FcD O CT trM EIE: kJ SE3 Q UlJP Ft RE O F D% E' V I fPr T I C JN (USING CONTIGUOUS BASELENGTHS) BRASIL IRRE DATA 100mm INTERVAL SECTION 1.5s 1.8. 2.0. 2.2. 2.40 2.6. n/s o/s n/s 0/s n/s a/s n/s a/s a/s o/s n/s o/s CA04 1.189 1.426 1.324 1.594 1.415 1.703 1.508 -- 1.602 -- 1.696 -- CA05 1.692 1.757 1.863 1.955 1.973 2.079 2.078 -- 2.181 -- 2.279 -- CA06 1.905 2.136 2.127 2.422 2.255 2.597 2.368 -- 2.469 -- 2.562 -- CA1O 0.712 -- 0.794 -- 0.850 -- 0.904 -- 0.959 -- 1.012 -- CA12 -- 0.639 -- 0.701 -- 0.744 -- 0.788 -- 0.830 -- 0.872 TS01 -- 1.224 -- 1.345 -- 1.418 -- 1.485 -- 1.545 -- 1.599 TS04 -- 1.412 -- 1.561 -- 1.647 -- 1.722 -- 1.788 -- 1.847 TS05 -- 1.633 -- 1.838 -- 1.953 -- 2.045 -- 2.118 -- 2.172 TS06 1.021 1.115 1.081 1.180 1.121 1.222 1.159 -- 1.197 -- 1.233 -- TSO7 -- 1.042 -- 1.107 -- 1.149 -- 1.188 -- 1.225 -- 1.260 TEOI 1.552 1.789 1.631 1.883 1.682 1.942 1.732 -- 1.781 -- 1.827 -- TE03 2.015 2.957 2.147 3.134 2.229 3.238 2.306 -- 2.377 -- 2.445 -- TE06 5.050 -- 5.429 -- 5.655 -- 5.866 -- 6.065 -- 6.255 -- TEII 2.950 4.049 3.114 4.291 3.212 4.441 3.298 -- 3.373 -- 3.440 -- 6R01 1.357 -- 1.435 -- 1.482 -- 1.526 -- 1.568 -- 1.608 -- 6R05 2.438 3.117 2.642 3.364 2.771 3.506 2.896 -- 3.016 -- 3.131 -- 6R07 1.615 2.602 1.688 2.786 1.737 2.896 1.786 -- 1.835 -- 1.883 -- 8R12 3.142 4.248 3.583 4.772 3.854 5.084 4.107 -- 4.344 -- 4.567 -- 200mm INTERVAL SECTION 1.60 1.8B 2.0s 2.2. 2.4n n/s a/s n/s o/s n/s o/s n/s o/s n/s 0/s CA04 1.244 1.510 1.339 1.626 1.434 1.739 1.530 -- 1.626 -- CA05 1.764 1.845 1.881 1.978 1.994 2.102 2.102 -- 2.206 -- CA06 2.032 2.286 2.176 2.474 2.301 2.646 2.412 -- 2.511 -- CAIO 0.739 -- 0.797 -- 0.855 -- 0.912 -- 0.968 -- CA12 -- 0.655 -- 0.701 -- 0.748 -- 0.794 -- 0.838 TSOI - 1.273 -- 1.355 -- 1.429 -- 1.496 -- 1.557 TS04 -- 1.484 -- 1.581 -- 1.665 -- 1.739 -- 1.803 TS05 -- 1.749 -- 1.878 -- 1.986 -- 2.072 -- 2.138 TS06 1.017 1.110 1.061 1.159 1.103 1.204 1.143 -- 1.182 -- TS07 -- 1.060 -- 1.105' -- 1.148 -- 1.188 -- 1.226 TE01 1.573 1.836 1.631 1.903 1.688 1.965 1.742 -- 1.794 -- TE03 2.047 2.993 2.140 3.119 2.226 3.231 2.304 -- 2.376 -- TE06 5.255 -- 5.503 -- 5.732 -- 5.945 -- 6.146 -- TEII 2.899 4.033 3.014 4.209 3.116 4.369 3.205 -- 3.282 -- 6R01 1.347 -- 1.405 -- 1.457 -- 1.505 -- 1.550 -- 6R05 2.479 3.189 2.617 3.346 2.746 3.489 2.868 -- 2.987 -- 6R07 1.573 2.692 1.629 2.817 1.684 2.929 1.783 -- 1.791 -- 6R12 3.384 4.520 3.677 4.854 3.947 5.158 4.199 -- 4.434 -- 384 TABLE H.12 F'< O3 O3 Tl twEZ= f2 tsJ ID U l_lfF;t EE OD F= I) EE^ r I O tM (USING CONTIGUOUS BASELENGTHS) BRASIL IRRE DATA 300mm INTERVAL SECTION 1.50 1.8s 2.1s n/s o/s n/s ols n/s ols CA04 1.238 1.454 1.390 1.635 1.542 1.811 Ca05 1.715 1.808 1.900 2.020 2.072 2.208 CA06 1.938 2.227 2.161 2.524 2.340 2.779 CA10 0.700 -- 0.799 -- 0.894 -- CR12 -- 0.637 -- 0.721 -- 0.803 TSOI -- 1.230 -- 1.361 -- 1.472 TS04 -- 1.427 -- 1.587 -- 1.719 TS05 -- 1.708 -- 1.912 -- 2.062 TS06 1.000 1.072 1.076 1.152 1.146 1.222 TS07 -- 1.031 -- 1.108 -- 1.176 TEOI 1.414 1.686 1.523 1.813 1.622 1.928 TE03 2.019 2.915 2.169 3.117 2.301 3.278 TE06 5.053 -- 5.449 -- 5.804 -- TEII 2.827 3.874 3.026 4.155 3.190 4.408 BROl 1.267 -- 1.371 -- 1.460 -- BRO5 2.404 3.185 2.631 3.458 2.837 3.684 6R07 1.505 2.552 1.611 2.753 1.711 2.928 6R12 3.312 4.445 3.769 4.966 4.169 5.416 500mm INTERVAL SECTION 1.5s 2.0. 2.5s 3.0s n/s o/s nis a/s n/s o/s n/s o/s CR04 1.147 1.416 1.431 1.737 1.710 2.029 1.975 2.302 CA05 1.670 1.805 2.006 2.189 2.289 2.481 2.539 2.732 CR06 1.975 2.197 2.328 2.682 2.597 3.043 2.825 3.327 C10 0.682 -- 0.857 -- 1.013 -- 1.149 -- CR12 -- 0.624 -- 0.774 -- 0.901 -- 1.005 TSOI -- 1.195 -- 1.434 -- 1.604 -- 1.722 TS04 -- 1.420 -- 1.676 -- 1.856 -- 1.994 TS05 -- 1.622 -- 1.929 -- 2.082 -- 2.173 TS06 0.868 0.956 1.020 1.123 1.145 1.253 1.254 1.367 TS07 -- 0.904 -- 1.040 -- 1.153 -- 1.259 TEOI 1.365 1.553 .1.576 1.799 1.736 1.999 1.875 2.163 TE03 1.769 2.722 2.052 3.115 2.267 3.396 2.441 3.613 TE06 4.681 -- 5.454 -- 6.072 -- 6.574 -- TEII 2.563 3.785 2.941 4.343 3.187 4.779 3.389 5.168 SRO 1.160 -- 1.353 -- 1.502 -- 1.622 -- 6R05 2.267 3.028 2.695 3.477 3.041 3.810 3.332 4.063 6R07 1.356 2.438 1.567 2.777 1.735 3.044 1.877 3.241 6R12 3.262 4.285 4.015 5.134 4.632 5.773 5.170 6.293 385 TABLE H.13 TrOBLEE OF FR lE3 J{4FREM V^L-UJEZ3 OF= FtIlS DEEVJ I {^T I ON4 __ FtFFt (USING DISCRETE BASELENGTHS) BRAZIL IRRE DATA NEARSIDE WHEELPATH Interval Type 20 km/h 32 kr/h 50 km/ Base 1.5. 1.8. 2.0. 2.2. 2.4. 2.6. 1.5. 1.8. 2.0. 2.2. 2.4. 2.6. 1.5. 1.8. 2.0. 2.2. Trailer 0.922 0.922 0.917 0.921 0.913 0.874 0.938 0.950 0.947 0.949 0.946 0.922 0.916 0.931 0.919 0.95 100 m Car Bl 0.967 0.970 0.968 0.963 0.957 0.934 0.957 0.970 0.974 0.975 0.975 0.967 0.937 0.958 0.962 0.96 NAASRA 0.965 0.968 0.966 0.961 0.956 0.933 0.956 0.971 0.975 0.975 0.977 0.968 0.931 0.955 0.961 0.96 NN-02 0.964 0.964 0.961 0.955 0.947 0.922 0.944 0.958 0.965 0.966 0.966 0.963 0.913 0.93? 0.945 0.95 Co 0' Base 1.6. 1.8. 2.0m 2.2. 2.4. 1.6. 1.8. 2.0O 2.2. 2.4. 1.6. 1.8. 2.0. 2.2. Trailer 0.925 0.919 0.916 0.919 0.910 0.952 0.951 0.950 0.952 0.047 0.912 0.931 0.921 0.95 200 - Car BI 0.963 0.967 0.964 0.958 0.950 0.971 0.974 0.974 0.974 0.974 0.960 0.965 0.967 0.9t NAASRA 0.962 0.966 0.963 0.957 0.949 0.972 0.975 0.976 0.975 0.976 0.961 0.963 0.968 0.97 WN-02 0.954 0.959 0.954 0.947 0.937 0.959 0.960 0.963 0.962 0.963 0.943 0.943 0.948 0.9' Base 1.5. 1.8. 2.1. 1.5. 1.8. 2.1. 1.5. 1.8. 2.1., TraiLer 0.924 0.912 0.898 0.952 0.948 0.940 0.932 0.929 0.930 300.. Car BI 0.974 0.968 0.964 0.973 0.980 0.975 0.959 0.972 0.967 NAASRA 0.973 0.967 0.963 0.974 0.982 0.976 0.955 0.972 0.966 _ *-02 0.965 0.959 0.957 0.959 0.970 0.965 0.933 0.953 0.945 Base 1.5. 2.0e 2.5. 3.0e 1.5. 2.0. 2.5. 3.0. 1.5. 2.0r 2.5. 3.Or TraiLer 0.901 0.897 0.883 -- 0.940 0.942 0.933 -- 0.920 0.913 0.886 500 - Car BJ 0.957 0.947 0.927 0.908 0.969 0.970 0.963 0.953 0.963 0.970 0.967 0.9t NAASRA 0.958 0.948 0.927 0.908 0.971 0.973 0.966 9.955 0.964 0.978 0.977 0.9; MN-02 0.949 0.935 0.915 0.894 0.958 0.962 0.957 0.946 0.941 0.958 0.958 0.9! TABLE H.14 T I BE L.E CD F FR S Q LJ )FtFE V L LJ E S O F F CRD LSI-ii'JlE8S RTElE :AS UFRFEMFE r E3 EC FSC 3 S I L. I F;t F FE REFERENCE SECTION RMSD CAR BI NAASRA MM-02 ROUGHNESS (300,1.8) Uncal Cal Uncal Cal Uncal Cal CA04 1.422 3C064 3151 3-050 3248 6906 3161 2970 CA05 1.899 3953 3852 3781 3839 8315 3668 4012 CA06 2.137 4302 i B 4140 4199 4192 9261 4023 4570 C1AO 0.788 1524 2045 1434 2057 3480 2029 1744 CA12 0.721 635 1470 513 1449 1219 1362 1625 TS01 1.387 2921 3042 2831 3077 6217 2921 2898 TS04 1.603 3604 3571 3525 3628 8430 3711 3354 TS05 1.951 4001 3892 3990 4014 9436 4090 4132 TS06 1.054 2000 2372 1929 2404 4220 2261 2237 TS07 1.087 1842 2262 1871 23 63 4248 2270 2300 TE01 1.517 2842 2983 2527 2845 5959 2833r7 3170 TE03 2.195 6080 5718 5605 5456 12767 5434 4710 TE06 5.434 13700 14577 13471 14756 28635 13724 14925 TEII 3.005 72n71 6879 6963 6793 17224 7447 6822 GROI 1.359 1572 2078 1425 2050 3:7578 2060 2840 GRO5 2.651 6207 5838 5938 5773 15173 6490 5863 GRO7 1. 608 3366 3384 3202 3368 7490 3368 33b64 GR12 3.687 9446 9212 912 0 9145 21615 9672r 8829 400 TABLE H. 28 CC3v M F="RF I 8IC3NI OF- CDOL 1. I k-FED L I'jD lC-A L. I E %Itr EL)D FCCL UJgHEESB H S1= rEEINTS C M./,0 12000 - 10000 . -j * 8000 - 6000 4000 BI = 243 + 0.5153*MM02 44 2000 R SQUARE - 0.980 0 C ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 ) 000 0 0 83 C N ° (0 m 0 N a (0 0 8 8 C o - - - - - N N N N N m MAYS METER 02 ( MM/KM ) FIG. H.4 STANDARDISED REFERENCE ROUGHNE%S EQUATION 18000 ( DERIVED FROM BI TRAILER / RMSD (300,1i.5) CORRELATIDN ) 16000 _ ROUGHNESS(mm/km) = 472 + 1437*RMSD + 225*(RMSD)2 14000 R SQUARE = 0.961 E 12000 10000 7 - 8000 cy-~~~~~~~~~~~~~~~7 6000 _ m +. - + + 4000 -+s 2000 +- + 0 C I , , LI o In o I) o ui o I) o In o In o O _2 _ cU r, -T m '5 U i -I (cd ROOT MEAN SQUARE OF DEVIATION (300, 1.8) ( MM 403 FIG. H. 5 FLOW DIAGRAM OF THE OPERATION OF THE TRRL ROUGHNESS CALIBRATION BEAM MEASURE n SECTIONS OF ROAD WITH BEAM xi and RESPONSE VEHICLE yi INPUT n PAIRS OF xi , yi THROUGH BEAM KEY PAD & PRINT CALCULATE y = a + bx PRINT EQUATION and R2 VALUE INPUT A VALUE OF Z (FIELD ROUGHNESS MEASUREMENT) i1 CALCULATE x FROM EQUATION x = (Z-a)/b CALCULATE CAL R FROM CR = 472 + 1437x + 225 x2 PRINT Z and CR 404 APPENDIX I SPECT]RAL CONTENT OF ROAD PROFILES The many measures that have been used to quantify road roughness at first appear to have little in common, yet often result in highly correlated summary statistics. The correlations between dissimilar numerics are determined in part by the mathematical properties of the analyses, and in part by the statistical properties of the road profiles. Much of the correlation between numerics can be caused by correlations within the road profile input and can vary with the type of road. Therefore, information about the nature of the longitudinal profiles of actual roads can give considerable insight to some of the experimental findings dealing with different roughness numerics. The purpose of this appendix is to present a few plots of the spectral characteristics of the 98 wheeltrack profiles (49 lanes) that were obtained in the IRRE. Each wheeltrack profile was measured up to 6 times, using rod and level, the TRRL Beam, and the APL Trailer in both the APL 25 and APL 72 modes of operation. The plots presented serve to quantify the nature of road roughness in great detail over the four surface types included in the IRRE, and also to show the differences resulting from alternative measurement methods. Power Spectral Density (PSD) Functions A longitudinal road profile is fixed in space and, in the short term, is also fixed with time. That is, the same profile should be observed when exactly the same path is followed within a reasonably short period of time (perhaps years for paved roads, and perhaps minutes for unpaved roads during heavy rain). Although a road profile is deterministic, it does have the appearance of a random signal, and statistical descriptions commonly used for random signals have proven to be useful for characterizing road profile. By analyzing the profile using statistical methods, the very large amount of information (hundreds or thousands of independent elevation measurements) are 405 reduced to a manageable number of summary statistics. For reasons that will be discussed below, virtually every roughness numeric computed from profile that has proven useful involves isolating a band of wavenumbers (wavenumber = 1/wavelength) from the original profile signal. It is therefore helpful to view the variations in profile in terms of wavenumber amplitudes, using the statistical power spectral density (PSD) function. Physically, a PSD function is the variance of the variable being measured (elevation, slope, etc.) distributed over wavenumber, having the units: quantity measured2/wavenumber. Thus, an elevation profile measured with the units of mm would have PSD units: mm2 m/cycle, since the quantity measured is mm and a wavenumber (spatial frequency) has units: cycle/m. The integral of a PSD function over a band of wavenumbers (waveband) corresponds to the contribution of that band to the total variance, while the integral over all wavenumbers is equal to the total variance of the variable measured. (An alternate PSD definition, called a "double-sided PSD," is sometimes used in which case negative wavenumbers are also considered. For a double-sided PSD function, the wavenumbers must be integrated from -oo to +oo to obtain the variance. All PSD functions presented in this appendix are single-sided, meaning that the variance is distributed only over wavenumbers ranging from 0 to +oo.) Further information about the usage of PSD functions and other spectral analyses of random (and random-like) signals can be obtained in Reference 139], which also includes formal mathematical definitions of the PSD function. Although PSD functions were developed for describing random signals, error analyses that assume the signal to be random are not appropriate for road profiles, since the profile is not random. The PSD function of a road profile is not an estimate, but rather, an alternate description containing almost as much (up to half) of the information as the original profile measurement. 406 Spectral Contents of Road Profiles Figure I.1 shows three PSD functions, all of which are computed from a single measured profile. Since road profile is measured as an elevation, it is natural to compute the PSD function directly from that measure. As Fig. I.la shows, the contribution to elevation variance is much greater at the lower wavenumbers (longer wavelengths). A PSD function computed for a measured variable such as road elevation can be converted to the PSD function of any other variable, if the two variables are related by a linear operation. Since most of the roughness analyses involve linear filters (the RQCS, RMSVA, moving average, CP, APL 72 energy (W), etc.), the PSD function of the filtered profile can be computed directly from the PSD function of the road profile, together with the frequency response plot of the linear filter. Since differentiation and integration are linear operations, the PSD function can also be computed for the derivatives of the elevation measurement: slope, slope derivative (spatial acceleration, etc.), as shown by Figs. I.lb and I.lc. As a means for characterizing road profiles, the PSD function of slope offers two advantages: 1) The plots can be scaled to show more detail. Note that the elevation and acceleration functions cover a wider range of amplitudes than the slope PSD over the wavenumber range .025 - 1 (wavelengths 1 - 40 m), requiring that the plots be scaled down. 2) Alternate roughness analyses can be compared more readily using their wavenumber response plots. When response plots are calculated for displacement inputs, one must always remember that there is much more input at the lower wavenumbers, and that even if the analysis is less responsive at those wavenumbers, they can constitute much of the numeric. But when response plots are calculated for slope inputs, what you see is what you get. A high sensitivity (gain) at any wavenumber band, high or low, indicates that that band contibutes heavily to the summary numeric. All road PSD functions that follow in this appendix are presented in 407 a. Profile Elevation 1 b (n 0~~~~0 :L \0C b. Profile Slope 0 > v-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 012 .1 2 5 1 .012 .1 2 Wave Number - cycle/m Wave Number - cycle/m 00 Tb c. Profile Acceleration (Spatial) E On / Figure I.1. Comparison of three PSD On / \| N g functions computed from a CL single Measured profile 0 > 01 2 5 .1 2 5 1 Wave Number - cycle/m terms of profile slope. Figure I.2 presents aggregate PSD functions, obtained by graphically overlaying the PSD functions for individual profiles obtained with the TRRL Beam. The amplitudes of each individual plot were normalized by the squared RARS50 roughness value known for that particular wheeltrack. When the PSD functions are normalized in this fashion, many appear to have the same shape, particularly when segregated by surface type. The plots show that: 1) The asphaltic concrete (CA) sites had the least roughness concentrated in the high wavenumbers of any of the surface types. Also, there is little vertical scatter when the PSD functions are normalized, indicating that most of the CA sites had very similar spectral distributions. The PSD shape shown constitutes a "signature" for that type of surface. 2) The surface treatment (TS) sites also had a signature, distinguished by a relative minimum over wavenumbers 0.1 - 0.4 (wavelengths 2.5 - 10 m), with increased roughness content for wavenumbers outside this range. Also, several of the TS sites displayed a spectral peak at wavenumber 0.5, indicating a periodic roughness component occurring at 2.0 m intervals. 3) The PSD functions for the unpaved gravel (GR) and earth (TE) sites show more variation in content than do the paved roads, but this is not unexpected since they also cover a greater range of roughness. Although they do show a slight minimum in the center near wavenumber 0.1, their roughness distribution is more uniform over the spectrum of wavenumbers, with the earth roads showing somewhat more roughness content at the highest wavenumbers than the gravel roads. 4) In all cases, the amplitudes rise at the highest wavenumbers covered (wavenumbers 2 - 5). 'This is due in part to aliasing, and is discussed below. 409 . . . . . . . . ....* . NE ...~~~~ ~ ~~~~~~~~~~~~~ .. .' . . . .'-----. -- . . . '-~~~~~~~~~~~~~~~~~~~~~~~~~~ ."' .. . ". . . .,,.,,,,.,,, ._ ~~~ a) . Ca~ ... ... .~~~~~, *. a) O i ..,._,,,-'--'.".-'.~E- .,,,, ......... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.. ., ,* . N................ ¢ . ... . ,, . . . ~~~~~~~~~~~~~~~. . . . . E;p. . . . . .: . . . .> Q .............. t E-* . . ;. - E < ~ ~~~~~~~~~~.............._ E * a e . - O w w w ... . , . . . . ~~............. ' ~~~~~~~~~~~~~~~~~~~~..... ,,§,I*'f|||. |||||I..I.. N ~ E-4 0) I U OL S Z L S Z [- OL S Z l S Z [-~~~~~~~~l C '44 .... . .. .... 410 U> > .. . . . ... .. .. .. ..... 4.~~~~~~~~~~~~~~~~~~~~'. OSdi 9doIS P8ZILDWJION C]c ado!S PGZIDLDWJON 44 U, U,~~~~~~~~~~~~~~~~~~~~~~~~~~~c _ N~~~~~~~~~~~~~~~~~~~~~~~~~V N~~~~......... ................. '0) a) ........... N0) U ~ ~ ~ ~ ~ ~ ~ ~~~~~~. L. C fl *~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~ ~ ~ ~ ~ ~ l 04 ... .. ... .. ... a 0 . .. . COSd adoIS P9zIIDWUJON C]Sd edolS PGZIIDW.-JON 410 Sensitivity of Simple Variarnce to Measurement Methods Although different types of roads may have unique "signatures," all come closer to having a uniform slope input than a uniform elevation input or uniform acceleration input. This has certain implications regarding the measurement of simple variance and RMS statistics: 1) RMS displacement measures are determined almost completely by the lowest wavenumbers (longest wavelengths) included in the measurement. The lower the wavenumber, the larger will be the RMS displacement. When the measuring instrument does not explicitly filter the profile (e.g., rod and level), then the lowest wavenumber is approximately determined by the length of the profile, and RMS elevation will increase with length. 2) RMS acceleration measures are determined almost completely by the highest wavenumbers (shortest wavelengths) included in the measurement. The higher the wavenumber range, the higher will be the RMS acceleration. When the acceleration is computed from a measured elevation profile, the highest wavenumber can be limited by either the instrument (for a dynamic profilometer), or the sample interval. A shorter sample interval will give higher RMS acceleration numerics. 3) RMS slope measures are determined by the width of the waveband included in the measurement. RMS slope numerics can be increased either by including higher wavenumbers or by including lower wavenumbers. For statically measured profiles, the waveband is not increased so much with profile length as by sample interval. Decreasing the sample interval will increase the slope numeric, although not nearly as rapidly as for an acceleration numeric. Note that simple RMS eLevation, slope, and acceleration numerics all can be increased without bound lby increasing the measurement waveband. Therefore, road roughness cannot be meaningfully characterized by a numeric such as "true slope variance" or "true RMS acceleration," since the measured numerics depend more on the bandwidth of the measurement than on the road. (In fact, "true" -411 slope variance and RMS accelerations are infinite.) Instead, the numeric must either require a standardized measurement method, or else include a means for limiting the bandwidth through processing of the measurement. When terms such as "slope variance" are used, the numerics are inevitably more complicated and specialized than implied by their names. Sumary of the PSD Data from the IRRE The remaining figures in this appendix, Figs. 1.3 - I.10 show the PSD functions measured for each wheeltrack of 8 of the 49 test sites used in the IRRE. Each Figure can have up to eight individual PSD plots, corresponding to measures made by rod and level, the APL 25 system, the APL 72 system, and the TRRL Beam. In order to facilitate comparisons, all plots are made on log-log axes, and cover the same wavenumber range. The vertical scaling was determined automatically by the computer program to include the highest PSD amplitudes. In every case, the vertical scale covers a range of 100:1. Since the plots are logarithmic, they can be shifted up or down to match the y-axis scaling in order to overlay different plots. The same analysis was applied to all of the profiles: 1) The 320 m long profile was converted from an elevation to a slope profile (approximately) by taking the differences in adjacent elevation values, normalized by the sample interval. This step eliminates the mean values, trends, and large amplitudes for the long-wavelength variations that appear when profiles are measured statically. 2) The slope profile was "padded" with zeros to increase the number of data points to the next power of two, which depended on the sample interval used. For the rod and level data, the 641 data points were padded to obtain a total of 1024; for the APL 72 data, the 6401 data points were padded to obtain a total of 8192. 3) The profile was processed via the Fast Fourier Transform (FFT), and the amplitudes of the resulting complex coefficients were squared 412 and scaled to PSD engineering units. 4) The frequency response of the numerical differentiation used in step 1 was used to correct the PSD amplitudes at the higher wavenumbers to the results that would have been obtained by true differentiation. 5) Adjacent PSD values were averaged over a wavenumber interval of .01 cycle/m, which typically meant that 3 - 5 "raw" PSD values were averaged together to obtain the values plotted. Comparison of the Different Measurement Methods Rod and Level. The known limitations of rod and level are in the precision of the individual measures, the need for a large sample interval (to keep the effort reasonable), and the potential for human error. Both precision limits and aliasing can cause the PSD functions to increase erroneously when the wavenumbers approach the upper limit of 1.0 (half the sample frequency of 2 samples/m). Past experience with the precision requirements indicates that the 1 mm interval is adequate for the roughness range covered in the IRRE [38]. Therefore, the fact that the PSD functions obtained by rod and level rise more with wavenumber than the PSD functions obtained by the other methods, including the TRRL Beam, reflects aliasing. The very good agreement: with the TRRL Beam for many of the sites indicate that human error was reduced or eliminated by the routine procedures used in Brazil. TRRL Beam. These measures match those of the rod and level almost perfectly in many of the plots, up until the higher wavenumbers influenced by aliasing. Since the highest wavenumbers for the rod and level measures appear to be artificially high due to aliasing, this is probably true also for the Beam PSD function, for wavenumbers above 2 or 3 cycle/m. The 3 m length of the Beam affects some of the PSD plots for the smoothest roads, appearing as a spectral peak at wavenumber .33 (3 m wavelength). This would be caused by the slight setup error that occurs periodically in the measurement process. The 413 amount of variance contained within that peak is quite small, however, due to its narrow width. Therefore, the setup error, quantified by the PSD, can be seen to be negligible. (The spectral peak is not even visible for the rougher roads.) APL Trailer. The APL Trailer, which is designed to measure profile over the frequency range of 0.5 - 20 Hz, covers a wavenumber range determined by its travel speed. At 72 km/h (APL 72), this wavenumber range is .025 - 1, while for the speed of 21.6 km/h (APL 25) this range is .08 - 3.3. The sample interval for the APL 25 signals was 250 mm, which puts the maximum wavenumber at 2.0, and means that aliasing can be present for wavenumbers above 1. For many of the sites, the agreement between the APL 72 and APL 25 signals and the static measures is nearly perfect over the waveband of the instrument. The PSD plots illustrate very clearly the fidelity that can occur within that range, while also showing how lower wavenumbers are attenuated by the trailer. Like the TRRL beam, the APL spectra show peaks on the smoother sites that are caused by the measurement process. The first peaks occur at wavenumber 0.6 and its harmonics (1.2, 1.8, ...). This is caused by a slight periodic disturbance introduced by the trailer wheel (circumference = 1/.6 = 1.7 m), and, because the peak is too narrow to include much variance, is negligible in terms of roughness measurement. In the case of the APL 72 data, the PSD functions also consistently show a peak lying outside of the design range of the trailer, approximately at wavenumber 3.5. This corresponds to a frequency of 70 Hz during measurement. Most of the analyses are barely influenced by wavenumbers this high, so it also is negligible. The fact that many of the PSD functions from the APL Trailer match those obtained statically is proof that the APL Trailer a valid profilometer (in terms of amplitude response) over the design waveband range. Yet some of the time, the match is not as good between the trailer and the statically measured profiles. These differences may, in many cases, be caused by imprecision in the lateral positioning of the towing vehicle on the test sites, or by 414 starting the signal before or after the markings on the road. In a sense, the careful matching of the rod and level profiles and the TRRL profiles is artificial, since the wheelpaths were marked beforehand and followed almost exactly for repeated static measurements. In actual practice, the choice of where the travelled wheeltrack lies can influence the measurement obtained. The design of the IRRE removed this source of variation from the static measures, but not from the APL measures. Validation for Specific Analyses. Although the good match between the PSD functions tends to confirm that all of the methods used can give "valid" measures of profile, the actual accuracy associated with each method must be determined for the specific application. This is particularly true when high accuracy requirements are set, since very small differences are difficult to see in PSD plots, unless more complicated processing methods are used. 415 Q Cd) a. 0 Left WheUltraLck L. . Rod and Level - Right Wheeltrack Rod and Level .012 | *1 ~ ~ 1 ~ .01 j 2 12 5! 00 -) ALeft Wheeltrack APL 72 o 6 t Right Wheeltrack APL 72 .01 2 5 .1 2 5~ 1 ~ T 2 S .01 2 5 21 2 ' 5 2 5 U ~ av Nubr-ccomWveNme yl/ E CL6~~~~~~~~1 0 Left Wheeltrack Right Wheeltrack APL 25 APL 25 .01 2 ~ .1 2 ~ 1 2 ~ .01 2 5 . 2 5 1, 2 5 Wave Number - cycle/rn Wave Number - cycle/rn Figure [.3. PSD functions for Site CA02. 416 4) 0~ (I, ~~Left Whelltrack a Rod and Level Right Wheeltrack Rod and Level . 1i''5"o 5 1i5 .ol 2 a ' a 2"li''5 E0 *n~ ~ Lf Whetak. Right Wheeltrack *>) ~ ALef 72etrc 1 Z APL 72 0, .01 2 1 2 5 5 i 5 .01 i2 1 i 5 E IT~~~~~~~~~~~~~~~~~~~~~~I Oa.a Figure 1.4. PSDfunctio o Right Wheeltrack o5,6 Left Wheeltrack APL 25 APL725 0 -. Left Wheelrack RightWheeltrac 4)~~~~~~~~1 Left Whelltrack Rod and Level N. \ \Right Wheeltrack F \/&\ V\ Rod and Level .2 C',~~~~~~~~~~~~~~~~~~~~' 221 2 . 2 5 01 ("In~~~~~~~~~~~~~~~~6 Left Wheeltrack ~~~~~Right Wheeltrack 0 ~~~APL 72 1*'APL 72 (V) Rtight Wheeltrack I ~~~Left Wheeltrack APL 25 o ~~~APL 25 C" 2 . 2 5 1 .01 2 5 25 2 5 Wave Number -cycle/rn Wave Number -cycle/rn Figure 1.5. PSD functions for Site CA13. 418 00 0~ Left Wheiltrack Right Wheettrack Rod and Level Rod and Level .01 2 5 1 2 5 2 t 2 2 5 2 @ 1 2 5 Wave Number - cycle/m 0 ~~~Left Wheeltrack = APL 72 0- 0 i a.~~~~~4 LOio .012 5 *' 2 t 1 2 d} 8, AMpRht Wheeltrack APL 25 . \ Left Wheeltrack APL 25 0 1 (j ~ ~ ~ igreI6 S functosfrSt S1 .012 1 2 5 1 2 .012 5 . 1 2 2 2 4 Wave Number -cycle/rn o2 Left Wheeltrack U ~~TRRL Beam 0 m .01 2 .,1 2 1 2 5 Wave Number -cycle/mn Figure I.6 PSD functions for Site TSOI. 419 0 Left Wheeltak Right Wheeltrack Rod and Level Rod and Level 01 i .1 2 ' 1 2 5 .12 a .1 2 ' 1 2 5 Left Wheeltrack APL 72 Right Wheeltrack E °. . oAPL 72 E&- a. ow -~~~~~~~~~~~~0 . 2 .1 2 .01 .1 5 0 Lef Wheltac .9b Left IrWheeltrack Right Wheeltrack >1 ~~APL 25 APL 25 E 0. 02.12 5 2 5 .1 1 2 ~ 1 2 5 0 ~~~~Left Wheeltrack Right Wheeltrack u T~~'RRL BeamTRLem 0 FA- .01 2 ~ .' 2 3 2 ~ 01 2 2 1 2 5 Wave Number - cycle/m Wave Number - cycle/m Figure I.7. PSD functions for Site TS06. 420 V Left Wheeltrack Right Wheeltrack Rod and Level Rod and Level E In 0~~~~~~~~ ol 2 I I I .01 2 ~ 1 2 5 1 2 S .012 5 1 2 5 1 Z 5 Left Wheeltrack ? N t APL 72 Right Wheeltrack E -APL 72 ( 0 06I 0 I Ur20o2 l o1 2 5 2 51 2 5 10 E etWeetak11 Right Wheeltrack 1j oonz;Le sWt V.) .01 2 5 1 2 . 1 2 .01 2 5 .1 2 5 1 2 5 Wave Number -cycle/m Wave Number -cycle/m Figure I.8. PSD functions for Site TS11. 421 Left Wheeltrack and Level Right Wheeltrack Rod and Level 0 U, 01 2 5 1 2.0122 j 2 5 Wave Number - cycle/rn q. Left Wheeltrack APL 72 E 0. C.: ~~ b ~ Left Wheeltrack RgtWelrc >1 ~ PL5 PL 25 422 E a. .01 2 5 .1 2 .01 2 5 .1j 2 0 1 2 5 Wave Number cycle/mn Right Wheeltrack (.3 ~TRRL Beam a. C. .01 2 ~ .1 2 5 1 2 5 Wave Number -cycle/rn Figure I.9. PSD functions for Site GRO1. 422 Right Wheeltrack E Left Wheeltrack Rod and Level Rod and Level 0- 0~~~~~~~~ 0.- l --° .12 5 .1 2 5 . 5 01 2 5 -J 5 1 2 5 Wave Number - cycle/m E IT a. U) Left Wheeltrack APL 72 F; .01 2.1 2 5 1 2 5 4) X . Right Wheeltrack >1 t2- Left Wheeltrack APL 25 o ~AFL 25 E U) 0~ 4) .012 l 5.1 ~. 2 5 4) ~~Left Wheeltrack0 TRIlL Beam -Right Wheeltrack o ~~~~~~~~~~~~~TRRL Beam E 4) a. 06 U) .0 .0 1 01i 5 .1j 2 5 2 5 Wave Number -cycle/rn Wave Number -cycle/rn Figure I.10O. PSD functions for Site GRO5. 423 u , Left Wheeltrack Right Wheeltrack and Level and Level E 0 0. , 012 5 l 2 5 2 5 012 1 2 5 1 2 o Wave Number - cycle/m X_ Left Wheeltrack O ~~APL 72 0. 4)~ ~ ~ ~ ~ ~~~2 06 0~ *2) 0 .01 2 a * ~ etWhetakRight Wheeltrack o1 ALef 25etr APL 25 CL ~ AL2 0 i .01 2 7 1 2 -- 1 5 .0 2 * 2 1 Wave Number - cycle/rn Wave Number -cycle/rn Figure I.11. PSD functions for Site GRO9. 424 e i Left Wheeltrack Right Wheeltrack ? N X Rod and Level Rod and Level U) a. 0 in {0 IC Left Wheeltrack RihtW | ~~APL 72 APL 72 __._. .01 2 S I1 i .01 2 ' c, . ~Left Wheeltrack Right Wheeltrackh 3; ~~APL 25 1 l| +APL 25 1 2L C', u~~~~ I I V 0 ,, ol 2 5 ,1 2 0 l2 e Left Wheeltraclc lTR a TRgrLea Righ 12WPDfuctoseorS terTEO1 4a 0 4,~~~~~~~~~2 0 Rod and Level ^ ~~~~~~~~Rod and Level .01 i2 ' 2 5 1 i' .01 2 5 .1 2 S 1 i' 5 oI 0 Wave Number -cycle/m Wave Number -cycle/m E Rod fandWLeelta Right Wheeltrack .012 5 21 1 51 .01 2 3 .1j 2 5 11 2 51 Warve Number -cycle/rn Wave Number - cycle/rn Figure I.13. PSD functions for Site TE05. 426 E Right Wheeltrack Rod and Level 0 Left Wheeltrack Rod and Level oi.01 2 5 1 2 ' 1 2 ' . o 2 5 1 2 S 2 i 0T V . 1l O Rig ht Wheeltrack APL 72 E Left Wheeltrack 0 ~~APL 72 Ufi 8 TRRL Beam 1illljll ll | T Right Wheeltrack U ~~~~~~~~~~~~~~APL 25 .01 2 5 l2 5 1 1 2 5 C427 E0 0 4)~~~~~~~~~2 APPENDIX J ADDITIONAL ANALYSES WITH THE MOVING AVERAGE A moving average analys.is has been applied to measured profiles by CRR (Appendix G) and by TRRL (Appendix H), to obtain roughness numerics that correlate very well with the measures obtained with response-type road roughness measuring systems (RTRRMSs). In each case, the analyses were applied to profiles obtained with a single measurement method, and the reproducibility of the numerics with different profile measurement methods had not been established. The purpose of this appendix is to derive the response properties of the moving average, as was done for the QIr and RARS numerics (Appendices E and F), and also to apply several of the moving average analyses to profiles measured statically and dynamically. Mathematical Definition of the Moving Average The moving average analysis consists of three steps: 1. Geometrically smooth the profile. A profile can be smoothed at each point by considering an. average over a baselength: x+b/2 Ys(x) = l/b J yr(X)dX (J-1) x-b/2 where x = distance travelled yr(x) = unfiltered "raw" vertical profile elevation at position x y,(x) = smoothed profile elevation at position x b = baselength of moving average X = dummy variable of integration 429 When the profile is sampled, the integral in Eq. 1 is replaced with a summation: m ys(i) = l/(2m + 1) k=2m Yr(i+k) (J-2) where m = INT I (b / dx) /2] (J-3) and i = index, indicating the ith sample. dx = interval between samples (m) INT = INTeger function used in FORTRAN and BASIC, indicating truncation. Eqs. 2 and 3 require that the baselength correspond to an odd integer multiple of dx. Thus, for an interval of 500 mm, moving average baselengths can be 1.0 m (3 points), 2.0 m (5 points), 3.0 m (7 points), and so on. When the baselength requires an even integer multiple of dx, then the smoothed average would correspond to a position between samples, and a slightly different equation can be used: rn-i y5(i-.5) = 1/(2m) 2 Yr(i+k) (J-4) - ~~k=-m where the index (i-.5) indicates that the smoothed value should occur halfway between samples i and i-1. 2. Subtract the smoothed profile from the original profile. yf(i) = Yr(i) - Ys(i) (J-5) where yf(i) is the final, filtered profile. When the number of points included in the average is even, then the smoothed value should lie between samples, and an alternate to Eq. 5 can be used: 430 yf(i-.5) = Yr(i~-5) - ys(i-.5) I Yr(i) + Yr(i-1) I / 2 - ys(i-.5) (J-6) With this step, the smoothed profile is used as a reference or datum, from which deviations can be summarized in the next step. 3. Summarize the filtered profile. The yf variable will vary about zero, and must either be rectified or squared before averaging to obtain a non-zero roughness numeric. In Belgium, the value is rectified and multiplied by 50 (assuming the profile had been scaled in mm) to obtain the CP numeric. In Appendix H, the RMS value is used. Bandwidth of the Moving Average. In order to derive the sensitivity of the moving average filter to wavenumber, it is convenient to consider complex sinusoidal variables of the form: y(w,x) = YO ejwx (J-7) where eix = cos(wx) + j sin(wx) (J-8) w = 2n/L (J9) and L = wavelength ji Y 431 The sensitivity of the moving average smoothing filter to wavelength is found by substituting Eq. 7 into the definition (for a continuous signal) of Eq. 1: X+b/2 Ys/yr = 1/b [ J YO ejwX dX / (Y0 ejwx) x-b/2 (J-10) Where X = dummy variable of integration. Solving Eq. 10, yI/yr = 1/b [ ejw(x+b/2) / jw - ejw(x-b/2) / jw I e-jwx = l/(jwb) e ejwb/2 e-jwb/2 ] = 1/ (jwb) [ cos(wb/2) + j sin(wb/2) - cos(-wb/2) - j sin(-wb/2) ] = 1/(jwb) 2j sin(wb/2) = sin(wb/2) / (wb/2) Ys/yr = sin("b/L) / (nb/L) (J-11) Therefore, the sensitivity of the final filtered variable yf to wavelength is: Yf/Yr = (yr - Ys)/Yr = 1 - Ys /yr - 1 - sin(nb/L) / (nb/L) (J-12) Effect of Sample Interval The numerical equivalents to a moving average given in Eqs. 2 and 4 approach the "true" moving average definition (Eq. 1) when the sample interval is much smaller than the baselength, such that there are 10 or more samples included in the moving average. But the results reported in Appendix H indicate that when the baselength b is not much larger than the sample 432 interval dx, such that there are fewer samples within the moving average, the resulting roughness measure depends on both b and dx. The sensitivity of the numerical equivalents (Eqs. 5 and 6) to wavelength can also be calculated, by substituting Eq. 7 into Eqs. 2 and 4. Noting that ejwx + e-jwx = 2 cos(wx) (J-13) and that all x values are integer multiples of dx, Eq. 5 can be converted to the wavenumber domain as: m Yf/Yr = 1 - 1/(2m + 1) [ 1 + 5: 2 cos(k w dx) (J-14) r ~~~~~~k=1 (for b/dx = odd integer number) while Eq. 6 can be converted as: Yf/Yr = cos(.5w dx) - 1/2m 5 2 cos({k-.5} w dx) (J-15) (for b/dx = even integer number) Eqs. 14 and 15 were used to prepare the four plots shown in Figs. J.1, using the baselength of 2.5 m with measurement intervals of 50 and 500 mm, and the baselength 1.8 m with 100 amd 300 mm intervals. Note that the moving average filter attenuates wavelengths longer than the baselength, and transmits wavelengths that are much shorter than the baselength with a unity gain. For wavelengths slightly shorter than the baselength, the gain is variable, ranging from 1.2 to 0.85. When the sample interval is larger, the properties of the filter are affected, because wavelengths that would be attenuated by the smoothing of a true moving average can appear as a longer wavelength (with less attenuation) due to aliasing. Since these wavelengths are still present in the smoothed signal, they cancel when subtracted from the original, causing the lowered reponse shown in the plots. Although the moving average analysis is a high-pass filter, generally passing wavenumbers higher than the cut-off, the summary numeric is primarily influenced by the longest wavelengths that are transmitted, due to the 433 E0 o EE I ~~~~~~~E6 c E 09 X 0 ~ ~ ~ ~~~ o 2 5 .12 5 1 2 5 2 5.12 5 1 2 5 Wavenumber - cycle/m Wavenumber = cycle/m OL. Base=2.5,dx=.05 D Base=2.5, dx=.5 E E E9 Eo0 E E E E I I LI) o 2 5 1 2 S 1 2 5 2 5 1 2 5 1 2 5 Wavenumber = cycle/m Wavenumber = cycle/m C. Base=1.8,dx=.1 d. Base= 1.8,dx=.3 Figure J.1. Wavenumber Response Functions of the Moving Average for Baselengths and Sample Intervals Used in the IRRE, for an Elevation Input. 434 spectral content of roads (Appendix I). To better show the actual influence of different wavelengths on the roughness numeric, the plots can be converted for the case of a slope inpu.t. For the sinusoidal input, differentiation can be expressed algebraically: y' = dy/dx = jw = j(2n/L) (J-16) Thus, IYf/Yr'l = IYf/Yrl / w = IYf/Yrl L/2,n (J-17) Eq. 17 was used to rescale the four plots in Figure J.1 for the case of a slope input, to obtain the plots shown in Figure J.2. Upon examining the plots for the 2.5 m baselength used for the CP statistic, it can be seen that the CP moving average analysis used by CRR is quite different from the Butterworth band-pass filter as used by LCPC. But when road inputs are considered which have a fairly uniform spectral content in terms of slope input, then the CP filter properties appear more like a band-pass. This is why the LCPC and CRR analyses give highly correlated results when comparing the SW coefficients to CP2.5, the MW coefficients to GPjO, and the LW coefficients to CP40 (Appendix G). The plots shown for the 1.8 m baselength correspond to the RMSD numeric described in Appendix H, although not completely since that analysis uses a linear regression line over a length of 1.8 m rather than a simple mean. The RMSD numeric does not have a true linear wavenumber response, but is so similar to a moving average that generalizations about the wavenumber sensitivity of one should hold for the other. The plots in the two figures indicate why the RMSD numeri.c is dependent on sample interval, and why it is lowered with increasing interval. Comparison of Dynamic and Static Measures of CP Although the moving average analysis was employed by both CRR and TRRL (see Appendix H), time constraints prevented the direct comparison of summary 435 E) E o 0 2 5 .1 2 5 1 2 5 2 5 .1 2 5' 1 2 5 Wavenumber - cycle/m Wavenumber - cycle/m L. Base=2.5,dx=.05 bD Base=2.5,dx=.5 EE o C 2 5 .12 5 1 2 5 2 5 2 ' 5 2 5 Wavenumber - cycle/m Wavenumber - cycle/m C. Base=1.8,dx=.1 d. Base=1.8,dx=.3 Figure J.2. Wavenumber Response Functions of the Moving Average for Baselengths and Sample Intervals Used in the IRRE, for a Slope Input. 436 numerics based on the moving average filter, as computed from statically measured profiles (rod and level or the TRRL Beam) and from the dynamically measured APL profiles, by eiither of those agencies. Since the results reported from CRR and from TRRL were both very encouraging, the moving average analysis was performed more recently at UMTRI on both the APL 72 profiles supplied by LCPC and the rod and level profiles supplied by The Brazilian Transportation Planning Company (GEIPOT), using the same computer program (modified) that produced the QIr and RARS numerics reported in Appendices E and F. These results, scaled with CP units, are listed in Table J.1 The APL 72 signals were the same ones used to compute QIr and RARS numerics, and were obtained at 50 mm intervals as described in Appendix A. The numerical methods used for both the APL and the rod and level profiles are those described in this appendix, and therefore may not exactly match the procedure used at CRR. For example, the data processing at CRR was routinely performed using three adjacent sections 100 m long, whereas the processing at UMTRI was performed continuously for each 320 m site; also a sample interval of 1/3 m is normally used at CRR in contrast to the 50 mm interval used by LCPC. In comparing the numer:ics in Table J.1 to the CP numerics in Appendix G, very good agreement is seen when the baselength was 2.5 m, although agreement is not as close for baselengths of 10 and 40 m. (The numerics reported in this appendix tend to be higher by 5% - 10%.) Even though this indicates that the results in this appendix are not completely equivalent to the CP numeric as computed by CRR, they appear to be similar enough to compare the static and dynamic measurements, as long as the comparisons are limited to the results presented in this appendix. (Unfortunately, time constraints for this report prevented collaboration between UMTRI and CRR to resolve the differences.) For convenience, the numerics are referred to as CP in the following discussion, even though they are "unofficial." For the CP2.5 numeric, the 500 mm sample interval used with the rod and level measures causes the d:igital filter to behave differently than a true moving average, as indicated in Figs. J.lb and J.2b. Therefore, the 28 profiles from the TRRL Beam were processed to obtain the CP2.5 numeric, and these results are listed in the Table, rather than those obtained from rod and 437 Table J.1. Summary of Moving Average (CP) Numerics Obtained at UNTRI from Statically Measured Pprofiles and from the APL Trailer. Test CP(2.5) CP(1O) CP(40) Site Left Right Left Right Left Right Beam APL Beam APL R&L APL R&L APL R&L APL R6L APL CA 01 .. .. .. 57 176 ... 199 190 520 ... 549 579 CA 02 .. 5 .. 84 208 173 171 180 573 487 480 432 CA 03 .. 84 ... 92 228 176 221 197 672 521 584 474 CA 04 90 77 77 70 235 207 212 195 632 562 559 556 CA 05 100 103 94 80 249 235 217 186 644 590 658 568 CA 06 112 116 95 102 241 216 226 200 667 525 667 523 CAO07 ... 58 ... 44 96 96 92 93 259 239 247 241 CA 08 ... 46 ... 46 101 94 94 83 296 266 240 201 CAO09 ... 73 ... 50 141 135 133 128 423 406 354 344 CA 10 ... 69 41 57 138 135 135 139 384 323 368 306 CA 11 ... 61 ... 75 192 160 200 185 426 448 440 436 CA 12 35 ... ... 29 69 ... 77 62 304 ... 334 281 CAI13 ... 27 ... 27 80 66 78 67 242 246 254 261 TS 01 67 70 ... ... 107 96 111 ... 276 212 317 .. TSO02 ... 76 ... 74 145 125 142 127 444 365 522 439 TSO03 ... 88 ... ... 133 123 130 ... 425 364 485 .. TS 04 106 80 . .. 120 105 133 ... 321 261 285 .. TS 05 98 109 .. 3 127 126 111 110 205 188 236 191 TS 06 62 53 57 47 112 104 101 99 302 310 328 339 TS 07 57 52 ... 50 114 104 118 109 307 268 337 287 TS 08 ... 55 ... 57 140 123 149 135 534 547 578 586 TS 09 ... 61 ... 65 99 92 114 106 239 236 269 273 TS 10 ... 67 ... 61 105 99 118 106 207 187 234 221 TS 1L ... 40 ... 41 78 66 75 69 235 233 239 209 TS 12 ... 44 ... 39 78 67 83 73 308 298 .399 397 GRO01 ... 57 60 ... 108 82 86 ... 466 300 426 GR 02 ... 69 ... ... 116 112 106 ... 405 416 359 GR 03 ... 105 .. .. 306 189 175 ... 578 544 575 .. GR 04 ... 110io ... 218 186 181 ... 582 410 574 .. GR 05 152 173 122 . 251 230 264 ... 442 424 443 .. GRO06 ... 153 ... ... 220 243 235 ... 418 427 484 .. GR 07 112 93 66 ... 163 126 125 ... 364 286 358 .. GR 08 ... 76 ... ... 124 112 110 ... 407 346 370 .. GR 09 .. 143 ... ... 254 214 235 ... 565 516 574 .. GR 1O 0 134 ... ... 197 208 155 .. 387 399 372 .. GR 11 ... ... ... ... 317 . .. 389 ... 510 . .. 581 .. GR 12 '201 . 1'57 . 354 ... 349 ... 539 ... 678 . TE 01 82 74 78 65 153 142 138 119 579 504 456 385 TE 02 ... 69 ... 77 128 112 131 137 413 415 392 373 TE 03 138 143 99 103 228 216 198 170 552 521 662 577 TE 04 ... 153 . 96 217 229 238 217 713 627 713 572 TE 05 ... ... . .. 477 .. 399 ... 1025 ... 624 TE 06 .. .. 23 . 595 .. 505 .. 992 ... 856 TE 07 ...9".. 8 158 18 19 123 362 291 301 295 TE 08 ... 93 ... 85 147 138 119 117 349 321 382 396 TE 09 ... 140 ... 118 227 212 210 173 411 426 416 369 TE 10 ... 172 ... 144 289 263 249 204 570 508 490 439 TE 11 ... 167 128 140 337 327 197 190 691 681 417 354 TE 12 ... 122 .. 145 307 226 257 243 522 441 550 499 438 level. Figure J.3 compares the moving average measures statically and from APL profiles. The four scatter plots show that: 1. The CP2.5 numerics computed from the APL 72 signals are higher than those computed from rod and level. This is to be expected from the wavenumber sensitivity plots shown in Figs. J.1 and J.2. The results shown here and in Appendix H indicate that a moving average analysis must require either that the sample interval be fixed (as suggested in Appendix H), or that it be sufficiently small that aliasing will not be significant. A problem with specifying a fixed sample interval is that the magnitude of the aliasing effect depends on the spectral contents of the profile, which is limited by the bandwidth of the APL trailer. Hence, specifying a fixed sample interval could give different relationship between measures obtained with the APL and those obtained statically. A more practical problem is 'that a specified interval decreases the options available for measuring profile. On the other hand, aliasing can be eliminated simply by using a smaller interval. Fig. J.3 indicates good agreement between the APL and Beam measures, which used a 100 mm interval. 2. The CP10 numerics as computed from the APL 72 are nearly identical to those obtained from the rod and level, with the exception of two of the roughest unpaved roads, which appear as "outliers." Excluding the two "outliers," the plot shows the remaining 73 data points lying very close to the line of equality, matching the repeatability of the statically measured RARS numerics, although the APL measures are about 5% lower than the rod and level measures. The "outliers" (GR 03 and TE 12) both have corresponding PSD functions that are quite different in the two wheeltracks (see Appendix I), such that the lateral positioning of the APL Trailer appears to be critical on these sections. For the worst "outlier" (GR 03), the left wheeltrack has a periodic component that occurs exactly at the 10 m wavelength. This peak is seen in the PSD measured with rod and level but not the PSD obtained with the trailer, explaining why the rod and level measure is so much higher. 439 o 0 0 0 1-0 a. 2.4oigAveag b.1/ oin vrg ).. /A/ o- O Eo A o, 0 o /4~~~~~~~~4 0.1~ ~~~~. 0 50 100 150 200 0 100 200 300 400 CP2-5 from Rod and Level CP10 from Rod and Level ca. 2.5 m Moving Average b. 10 m Moving Average 00 00 (N4 04 a. C '4-. '4- Oc 0 ~ ~ ~ ~ ~ ~ ~ N C) x~~~~~~( 200 400 600 800 0 50 100 150 200 OP40 f rom Rod and Level CP2.5 from TRRL Beamn c. 40 m Moving Average d. 2.5 m Moving Average Figure J.3. Comparison of CP Numerics from Statically Measured Profiles and from the APL Trailer. 440 3. The CP40 measures obtained from the APL are about 10% lower than those obtained from the rod and level. In viewing the response plot of the CP analysis (Fig. J.2), it can be seen that wavelengths longer than the baselength are not completely attenuated. For example, the gain at wavenumber 0.2 (wavelength = 5 m) is 3/4 of the gain at wavenumber 0.4 (wavelength = 2.5 m = baselength). For the case of 40 m baselength, this means that the analysis is affected by wavelengths longer than 40 m. But the APL 72 response (Fig. G.1 in Appendix G) does not include these longer wavelengths, whereas the static rod and level method does. Appendix I, which contains PSD functions obtained from the APL Trailer, TRRL Beam, and rod and level, show the difference in slope input at the very long wavelengths (low wavenumbers). The differences shown in Fig,. G.4c may reflect the bandwidth limitation of the APL Trailer. In summary, the CP2.5 and CP1o can be obtained either with a statically measured profile or with an APL Trailer, without any significant error beyond the normal repeatability associated with profile measurement. The sample interval must be small, however, to obtain good agreement with the C.P25 numeric. However, the CP40 numeric is influenced, in part, by the response properties of the APL Trailer because the rod and level measure includes a slight effect of wavenumbers that are too low to be sensed by the APL Trailer. 441 APPENDIX K SUBJECTIVE ESTIMATION OF ROUGHNESS BY SCALE DESCRIPTOR METROD Prepared by William D.O. Paterson (World Bank) Experiment Immediately after the completion of the main experiment a small study was performed in which 4 individual observers estimated the roughness of each test section directly using the 'Scale Descriptor Method'. This method, developed during World Bank studies in Brazil following the PICR project, provides a set of descriptors of the road shape and ride sensations at six levels of roughness on a reference ARS scale from 0 to 25 m/km. Observers match the ride and their assessment of surface shape with the descriptors and estimate roughness directly in m/km units. The method is distinctly differ- ent from the subjective panel rating (Appendix D). In the panel rating, observers rate the ride comfort on a 0 to 5 scale representing their indivi- dual perceptions of poor to perfect road conditions. The subjective panel rating is thus an unanchored scale which is influenced by the observers' pre- conceptions of satisfactory ride comfort and is known to vary from region to region and country to country. The scale descriptor method however employs an anchored scale which is nominally directly equivalent to a RARS scale. The observers were given a set of instructions and two charts summariz- ing the scale for paved roads and unpaved roads respectively, as shown in Figs. K.1 and K.2. The scale was the same for both categories of road, only some of the descriptors differed in examples of typical roads and the types of distress associated with each level of roughness. The scale in the method used for the survey was constructed on the calibrated ARS at 80 km/h of the Opalas used in the PICR. Included with the set of instructions was a set of two photographs of examples of road surface appearance at each of the six levels of roughness (these were not of sections included in the experiment), but in fact the observers made little reference to these and used primarily the written descriptors. 443 The observers were driven in one of the Opala sedan cars that had been used for a Maysmeter in the main experiment, over all 49 test sections in approximately the same random sequence as the main experiment. A speed of approximately 80 km/h was maintained on the paved roads and a speed of approximately 50 km/h on the unpaved roads. There was no stopping at the individual sites and all sections were observed in the course of one day. The observer's estimate of roughness in m/km was written on a field form with the test section number and occasionally a brief comment, for example whether the surface texture was 'noisy', whether the vehicle was 'bottoming' on the suspension, etc. None of the observers had applied the method previously, although two of the four had had some previous experience of the scale. The characteristics of the observers are summarized in Table K.1. Data Analysis The data collected in the study are presented in Table K.2, together with the RARS50 reference value of roughness for each test section from Table F.5, Appendix F. These reference values were not known to any of the observers and had not been computed at the time of the survey. Also presen- ted in the table are the means of the observers' estimates and the absolute deviations from the reference value. The results are plotted for all observers in Fig. K.3 and by individual observer in Fig. K.4 showing surface type effects. The results are summariz- ed by the statistics presented in Table K.3 and are discussed under the aspects of systematic bias, accuracy and correlation. They are evaluated with the expectation that normally only one observer would undertake an esti- mation survey and that averaging across observers is not the norm. Systematic bias is the measure of how the observer's scale compared with the reference scale and indicates whether, on average, there was any systema- tic underestimation or overestimation. The mean reference roughness was 7.58 m/km, and the observers' means ranged from 7.00 to 8.64 m/km, with an average of 7.80 m/km. This is equivalent to a bias ranging from -7.6 to +14.0 per- cent with an average of +3.0 percent. The observers' perceived scales based on the survey scale are therefore very close to the reference RARS50 scale. 444 The bias would be further reduced in applications of the method as the obser- ver gained experience and if a preliminary 'calibration' survey were conduct- ed for the observer. The method is thus successful in both anchoring and controlling the scale. The significance of a low bias is that an observer in the course of a long survey will tend to produce an average result which is within approximately 10 percent of the reference. It is also significant in that the RARS50 scale can be substituted for the survey scale in the method without need for adjustment of the descriptors. The accuracy of estimation of roughness on an individual section is quantified through the root mean square deviation between the observer's estimate and the reference value. For the four observers this ranged from 27 to 48 percent, since the error is proportional to the mean and is best ex- pressed as a percentage. The two observers with some previous experience (A and B) rated slightly better than the two without any previous experience (C and D), i.e. 27 - 35 percent and 35 - 48 percent, respectively. The maximum individual errors were deviations of 3.2 m/km, or 55 percent for the most ac- curate observer and +7.6 m/km or 140 percent for the least accurate. For a subjective method such as this, given that the bias is approximately random and generally less than 10 percent, an error of the order of 36 percent aver- age (and less upon experience) is perfectly acceptable and highly satisfac- tory. It compares with an error of the order of 14 percent for calibrated RTRRMSs and 6 percent for static profilometry methods. The correlation between the observers' estimates and the reference is a measure of the observer's accuracy in ranking the sections by roughness and of how well the estimate relates to roughness. The coefficients of determination (R2-values) range from 0.86 to 0.92 which demonstrates that the method is highly effective in these respects. Although the sample size in this study was small, the results pre- sented are probably representative of what could be expected from competent personnel. The results are sufficient to indicate that the method is able to give satisfactory estimates of roughness with an error of approximately 36 percent, free from significant bias and with high reliability for ranking the roughness of individual sections over a wide range. 445 Following the selection of RARS8O as the International Roughness Index (IRI), the rating scale requires linear adjustment by the factor of 0.80 (which is the ratio of the means of RARS8O and RARS5o in the IRRE data). This relationship between the two scales is not mathematical but empirical: there are differences due to the different wavebands sensed at 50 and 80 km/h but, as these have negligible effects on the primary conclusions, the analysis was not re-run. In order for the rating scales in Figs. K.1 and K.2 to be used for the direct estimation of IRI therefore, the scale values need to be multiplied by 0.80; the new ranges are thus 0 to 10 for paved roads and 0 to 24 for unpaved roads. 446 Table K.1: Description of observers for roughness estimation Code Country Occupation Sex A United States Mechanical Engineer Male B New Zealand Civil Engineer Male C Thailand Systems Engineer Male D United Kingdom Econometrician Male 447 Table K.2: IRRE survey data from roughness estimation by scale descriptor method (Roughness in m/km) SEC 085 085 08S OBS MEAN RARS50 DEVN DEVN DEVN DEVN A 8 C D o0S A B C D CA0I 4.5 7.5 3.5 4 4.88 4.8 -0.3 2.7 -1.3 -0.8 CA02 3.5 7.5 4.0 4 4.75 5.6 -2.1 1.9 -1.6 -1.6 CA03 4.5 8.0 5.0 5 5.63 7.2 -2.7 0.8 -2.2 -2.2 CA04 5.0 7.5 5.0 5 5.63 6.2 -1.2 1.3 -1.2 -1.2 CA05 7.5 8.0 6.0 6 6.88 7.4 0.1 0.6 -1.4 -1.4 CA06 7.0 9.0 7.0 7 7.50 8.2 -1.2 0.8 -1.2 -1.2 CA07 2.5 3.0 2.5 2 2.50 2.7 -0.2 0.3 -0.2 -0.7 CA08 3.0 3.5 2.5 2 2.75 3.1 -0.1 0.4 -0.6 -1.1 CAO9 3.5 3.5 3.5 3 3.38 3.7 -0.2 -0.2 -0.2 -0.7 CAiO 4.5 4.0 4.5 3 4.00 3.6 0.9 0.4 0.9 -0.6 CAil 4.5 7.0 7.5 5 6.00 6.1 -1.6 0.9 1.4 -1.1 CA12 2.0 1.6 1.5 2 1.78 2.2 -0.2 -0.6 -0.7 -0.2 CA13 1.5 2.0 2.0 2 1.88 2.1 -0.6 -0.1 -0.1 -0.1 TSOi 2.5 5.0 2.5 3 3.25 5.1 -2.6 -0.1 -2.6 -2.1 TS02 2.5 6.0 4.0 3 3.88 6.8 -4.3 -0.8 -2.8 -3.8 TS03 4.0 4.0 4.0 3 3.75 6.7 -2.7 -2.7 -2.7 -3.7 TS04 4.5 4.0 6.0 4 4.63 6.8 -2.3 -2.8 -0.8 -2.8 TS05 4.0 4.0 6.0 4 4.50 6.6 -2.6 -2.6 -0.6 -2.6 TS06 3.5 3.0 3.5 2 3.00 4.2 -0.7 -1.2 -0.7 -2.2 TS07 3.5 3.5 3.0 2 3.00 4.3 -0.8 -0.8 -1.3 -2.3 TS08 3.5 5.0 4.0 2 3.63 4.8 -1.3 0.2 -0.8 -2.8 TSO9 3.5 5.0 4.0 . 4.17 5.3 -1.8 -0.3 -1.3 TS1O 3.0 4.8 4.0 . 3.93 5.0 -2.0 -0.2 -1.0 TS11 2.0 3.0 2.5 2 2.38 3.5 -1.5 -0.5 -1.0 -1.5 TS12 2.0 3.5 2.5 2 2.50 3.5 -1.5 0.0 -1.0 -1.5 GROI 3.5 8.0 12.0 5 7.13 5.0 -1.5 3.0 7.0 0.0 GRO2 3.0 8.0 13.0 5 7.25 5.4 -2.4 2.6 7.6 -0.4 GRO3 4.0 9.0 12.0 5 7.50 9.3 -5.3 -0.3 2.7 -4.3 GRO4 3.5 10.0 12.0 5 7.63 8.1 -4.6 1.9 3.9 -3.1 GRO5 13.0 12.0 12.0 14 12.75 11.3 1.7 0.7 0.7 2.7 GRO6 16.0 13.0 13.0 16 14.50 10.4 5.6 2.6 2.6 5.6 GRO7 12.0 10.0 11.0 7 10.00 7.3 4.7 2.7 3.7 -0.3 GROB 10.0 9.0 11.0 7 9.25 5.8 4.2 3.2 5.2 1.2 GRO9 13.0 11.0 10.0 8 10.50 10.9 2.1 0.1 -0.9 -2.9 GRIO 11.0 10.0 10.0 7 9.50 8.9 2.1 1.1 1.1 -1.9 GRII 18.0 18.0 19.0 18 18.25 17.0 1.0 1.0 2.0 1.0 GR12 20.0 22.0 19.0 20 20.25 14.4 5.6 7.6 4.6 5.6 TEOI 5.0 4.0 8.0 4 5.25 5.7 -0.7 -1.7 2.3 -1.7 TE02 5.0 5.0 9.0 4 5.75 5.3 -0.3 -0.3 3.7 -1.3 TE03 6.0 8.0 10.0 5 7.25 9.8 -3.8 -1.8 0.2 -4.8 TE04 8.0 9.0 12.0 6 8.75 9.7 -1.7 -0.7 2.3 -3.7 TE05 19.0 22.0 18.0 20 19.75 17.1 1.9 4.9 0.9 2.9 TE06 21.0 24.0 20.0 22 21.75 20.6 0.4 3.4 -0.6 1.4 TE07 9.0 8.0 14.0 9 10.00 6.0 3.0 2.0 8.0 3.0 TEOS 9.0 7.0 14.0 9 9.75 6.6 2.4 0.4 7.4 2.4 TEO9 11.0 10.0 16.0 10 11.75 12.2 -1.2 -2.2 3.8 -2.2 TEIO 13.0 11.0 16.0 10 12.50 14.8 -1.8 -3.8 1.2 -4.8 TEll 18.0 16.0 17.0 18 17.25 12.5 5.5 3.5 4.5 5.5 TE12 16.0 17.0 15.0 18 16.50 11.6 4.4 5.4 3.4 6.4 448 Table K.3: Summary statistics of accuracy of subjective estimation of roughness by the 'Scale Descriptor Method' (class 4) in the IRRE Method/observer Reference Estimation by observer Average parameter unit' RARS50 A B C D Estimation No. obser- 49 49 49 49 47 194 vations Mean rough- m/km 7.58 7.33 8.24 8.64 7.00 7.80 ness Mean bias m/km 0 -0.25 +0.66 +1.06 0.58 +0.22 Mean bias frac- C0 -.033 +.088 +.140 -.076 +.030 tion RMS Error rm/km j ) 2.6 2.3 3.0 2.8 2.7 RMS Error frac- 0 0.35 0.27 0.48 0.35 0.36 tion R2 1 frac- 1.00 0.89 0.92 0.86 0.89 tion 449 ROUGHNESS (m/km) 0 Ride comfortable over 120 km/h. Undulations barely perceptible at 80 km/h in range 1,5-2,0. No depressions, potholes or corrugations are noticeable; depressions < 2mm/3m. Typical high quality AC 1,5- 2 -2,5, high quality ST 2,0-3,5. Ride comfortable at 100-120 km/h. At 80 km/ih moderately sharp movements 4 or large undulations may be felt. Defective surface:-occasional de - pressions or potholes (e.g. 12-25nmV3m or 20-40imV5m with freq. 3-1 per 50m), or many shallow potholes (e.g. on ST showing extensive rav- elling). Surface without defects: moderate corrugations or large un - dulations. 6 Ride comfortable at 70-90km/h, Frequent sharp rovements and swaying. Nearly always associated with severe defects: frequent deep and un- even depressions (e.g. 20-40mm/3m or 40-80m/5m with freg. 5-3 per 50m), or frequent potholes (e.g. 4-6 per 50m). Surface without de - fects: strong undulations or corrugations. 8 Necessary to reduce velocity below 50knVh. Many deep potholes and severe disintegration (e.g. 40-80 mm deep with freq. 10-20 per 50m). L_ _12 Figure K.1: Road roughness estimation scale for paved roads with asphaltic concrete or surface treatment surfacings 450 ROUGHNESS (m/km) 0 Recently bladed surface of fine gravel or soil surface with excellent longitudinal and transverse profile. 2 Ride ccmfortable at 80-100 km/h, aware of gentle undulations or swaying. 4 Negligible depressions (e.g. < Smn/3m) and no potholes. 6 8 Ride comfortable at 70-80 kloh but aware of sharp movements and sane wheel bounce. Frequent shallow-moderate depressions or shallow potholes (e.g. 6-2OnW3m with freq. 5-10 per 5Dm). Moderate corrugations (e.g. 10 6-20mm/0,7-1,.5m). 12 Ride confortable at 50k/h (40--70 km/h on specific sections). Frequent 14 moderate transverse depressions (e.g. 20-40mV3-5m at freq. 10-20 per 50m) or occaqional deep depressions or potholes (e.g. 40-80mr/3m). Strong corrugations (e.g. > 2OrrYO0,7-1,Sm). - 16 18 Ride ccafortable at 30-40 km/h. Frequent deep transverse depression 20 and/or potholes (e.g. 40-80mm/1-5m at freq. 5-10 per 5Dm); or occasional very deep depressions (e.g. > 80mVl-5m) with other shallow depressions. Not possible to avoid all the depressions except the worst. 22 24 Ride cinfortable at 20-30 km/h. Speeds higher than 40-50 km/h would cause extreme discomfort, and possibly damage to the car. On a good general profile: frequent deep depressions and/or potholes (e.g. 40- 26 80 rtm/1-5m at freq. 10-15 per 50m) and occasional very deep depressions (e.g. > 80mn/0,6-2m). 2 On a poor general profile: frequent nrderate defects and depressions 28 (e.g. poor earth surface). 30 Figure K.2: Road roughness estimation scale for unpaved roads with gravel or earth surfaces 451 ESTIMATED ROUGHNESS (m/km) 24 3 22 B B 0 A 20 a D C 18- oD a B C/ 16- B A CB C/ C 14- C C D C BAA A 12 C A C CC a C C A A B 10- A BIB C B D CmBDi B XB DBBe InD 8-B .BCB* ADB p D OD & AA AD D 4- Bwas a A B S*AA A PE8| A 3 cC £ A 2 a DU sD 0 2 4 6 8 10 12 14 16 18 20 22 24 MEASURED ROUGHNESS. RARS50 (m/km) LEGEND: A A A OBSERVER 'A' B B B OBSERVER 'B' c c C OBSERVER 'C' D 0 0 OBSERVER '0' ~LINE OF EQUALITY Figure K.3: Comparison of observer-estimates of roughness with measured RARS50 index: collectively. 452 ESTIMATED ROUGHNESS (s/ks) ESTIMATED OW4ESS CsH) 24 24- 22 22 4 C 20 + 20 A 18- ( + 16- + IE~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~( 16 4 ( 1 14 12 + I xx 1- 2- 4a 0-~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~2 22+X 22-X 40X A + 4 CX AMM + H A A Ax @~~~~~~~~~~~~~~~~0 x a 4- 4_Z-....... .,,,, a 2 4 a 5 10 12 14 10 15 20 22 24 0 2 4 6 5 10 12 14 IE IS 20 22 24 MEASUREO ROUGHNESS. RARSSO (a/k.) MEASURED ROUGWIdESS. 0ARSSO Cs/H (C) OCSERVER 'A' (6) CHSERVER 'C ESTIMATED RCUCHNESS (aks ESTIMATED ROUONESS (/) 2O X+ L 20 X+ X IM- x 1 1/ XX + 1iur KCComarso o obevresiae ofruheswihmaue 14, CXX 14 /- 12- 4 4 +X + IZ2 4+~~~~~5 10l S ++ I CC+++ XC . Sao ' .A. 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