This paper is prepared for staff use and is not for publication. The views expressed are Those of the author and not n*ceasarily those of the Bank. INTERNATIONAL BANK FOR RECONSTRUCTItON AND D1SVELOPT INTERNATIONAL DEELOPMENT ASSOCIATION Economics Department Working Paper No. 63 Railroad Cost Performance Model Febrqary 25, 1970 This paper is one of a series of papers from the Transport Planning Models Study under the direction of Mr. Jan de WeillU and Mr. Leon H. MiLler. The overall objective of the Study is the continuing inveesigation of mathematical models developed for use in transport planning. The Study will. analyze existing transport models, revise and extend the models where practical, and develop new models where needed. An svaluation of the models will include their application in transport planning studies and a critical review of the methodology. This paper is based on Appendix 4 of the Harvard University Transport Research Program report "An Analysis of Investment Alternatives in the Colombian Transport System", by Paul 0. Roberts, David T. Kresge, and John R. Meyer, (Cambridge, Massachusetts, Septembers 1968). The member of the Bank Study working on this portion of the study was Leon H. Miller. The Harvard presentation has been amplified by includLng sample caputer inputs and outputs, a listing of the computational equations, and a dictionary of terms. Also, editorial and other changes in the text have been made to improve the presentation. This paper is expository in nature; no attempt has been made to critically evaluate the model. A critique will be covered in a subsequent paper. Bank staff members are invited to make comments and suggestions for improvement of the model. Sector and Projects Studies Division II TABLE OF CONTENTS Page No. I THE MODEL 1 A. Computational Procedure 2 B. Input Data 3 C. Link Characteristics 5 D. Volume Characteristics 6 E. Vehicle Characteristics 6 F. Cost Information 7 II. DETAILS OF MODEL COST PERFORMANCE CALCULATIONS 8 A. Computation of Allowable Train Tonnage 8 B. Computation of Miniriium Running Time 11 C. Train Delayv Calculations 12 D. Decermination of Equipment Requirements 16 E. Operating Cost Calculations 18 F. Model Output 22 Table Table 1 16 Figures Figure 1 4 Figure 2 14 Appendices Appendix A A.1 Colombian Rail-Vehicle Characteristics 25 A.2 Colombian Railroad Model -- Factors and Costs Input 26 A.3 Other Rail Factors and Costs 27 Appendix B Details of Computer Print-Out 29 Appendix C Mode Summary Table 32 Appendix D Railways Dictionary 39 Appendix E Railroad Model Equations 43 Bibliography 24 ... ...... .... RAILROAD COST PERFORKANCE MODEL I. T MODUL. Tlhe Railrload cost performance model is used to develop the operational costs and performance measures for a single track rail link. T'he objective of thie model is to transfom the operational demands, physical cha;racteristics of' different road-links and the rail equipmert into operational costs and the performance measures for a link. Ferformance mea:s0res are silch tlhings as travel time, waiting for service time, delivery Lfine variabili.ty and probability of loss. The operational and performance restilts may be used to analyze alternative options for a part.icular link or may be used as input to a transportation network systu mode]. The model is deterministic in that average values are used rather than random values for the model variables. The model is designed to analyze the rail system on e link-to-link basis using the traffic demands, the individual link's characteristics, i.e. no. of sidings, ruling grade, average grade, and type of sigralling and the associated rail equipment. With the model, the effect upon oiperating costs and perfornance measures can be obtained under the dififerent conditions. Tlhus the model can be used to analyze present conditions alorig with alternative proposals - increased traffic, different locomotives, number of sidings, grades, etc. A considerable number of trade-offs exist in determining the number of trai.ns that can be operated in any one direction over an oxisting rail line. Unlike a highway, where flows in both directions are usually permitted, railroad flows are oftern uni-directional. Even where a sing:l.e lane highway exists, passing requirements are less stringent since opposinlg vehicles may si.iriply reduce speed and share the paved portion. In order to increase the poLenliial for opposing raii traffic, siding spacing may be roduced, sidings i.engthened or signal systems may be improved. At one extreme), a single Lrack line may be operated entirely as a one way route, havinig neither B;ignals nior sidiings. At the other extreme, a continuous sid:lng, i.e., second or tElird track, with centralized traffic control may be employed. The filrst case requires niore rolling stock and locomotive power to handle a specified tonniage whereas in the second case, the rolling st-ck requirements .ALe reduced at the expense of increased investment in siding3 and signal equipment. Of course, intermediate cases exist, such as the use of a single track with sidings and trains proceeding under special orders and time table rules. -2- In most cases, the specifics of the situation, tonnage, nature of the cargo, topography, lengthl of the line, and extent of the railroad syrstem, will determine which technology or operating procedure is to be prefer'ed. For this reason, it is difficult to generalize on railroad cost f mctions. The procedure to be followed in the following sections involv,s simulating the pbrformrance of a simple ra{Vxoad line, operatingr. over a stated distance witlhout intermediate stops.-' A. C1-putAtional Procedure The procedure by which the data are combined to compute various perfor,nance characteristics for a particular rail link is described in flow ciart form in Figure 1. This simaulation model is designed to provide such p3rformance measures as average cost per l;on and average run;iing timets for alL trains using the link as opposed to the specific details about partic ilar train performance that can be obtained from a Train Performance CalculatorS2 Thus, calculations are made for an "average" size train, as detem:.ned by avai-lable locomotive power and ruling grade, even though in specif:Lic instances both larger and smaller trains might be operated in accordance -with fluctuations in traffic volume. Details of the computational procedure will be described later in the paper. Briefly, however, this procedure can be summarized by the following steps. 1. Allowable tonnage per train for the available locomot:ive power and ruling (maxinum) grade of link is conputed. 2. Given the characteristics of the cars available to haul. each commodity group, such as tire weight and payload, the revenue load capacity of a single train is determined. 1/ Generalized work stops, delays, etc. could be included, however. 2/ Train Performance Calculators are used by some operating railroads to dei;ermine speed and time profiles and fuel consumption for a train of a specific make up (that is, number and horsepower of locomotives andt number and weight of cars), operating over a line for which de-.ailed profile and alignment information is available. Several such programs are available including programs developed by the Pennsylvania Ra2lroad, Canadian National Railways, Cailadcan Pacific and the Southern Ra .lroad, -3- 3. Thle number of daily trains required for the time ,eriod under consideration is determined by dividing the re'!enue loAd capacity of a single train into the average daily traffic. 4z. For a single train, the average running speed is calculated by determining the speed at which the tractive effort developed by the locomotive just equals the rolling and grade resistance encounter.3d onl the average grade. 5. Average runLing time over the link is adjusted to account for delays enroute. These delays depend upon daily traffic, length of link, number of sidings and type of signal systen. 6. Rolling stock requirements are calculated on the basis of adjusted runuing time and terminal turnaround -ime. 7. Operating statistics, such as train-miles, train-lours and car-miles, are EJummarized for the link. Tota.. costs of operation, maintenance and depreciation costs are then determined on the basis of these operating statistics. The necessary link information and volume data are provided as exogenous input for the programn. Other information, such as ;ire weight and payload of veliJcles for eaclh of the commodity groups, horn;epower and weight of different locomotive types (also specified excgonously) and various operating cost coefficients are stored internal to the program in the forni of data tables. A sample of this data is shown in Appendix A. B. u The computational procedures for the model with the aXisociated input's were depicted in Figure 1. There are four general areas of data: 1) Vehicle Equipment Characteristics, 2) Link Characteristi(s, 3) Traffic Volume Data, L4) Cost Data. The volume of traffic data and the link characteristic d.ita are input for each link analysis; whereas. the vehicle ec(;uipment and cost data are i qFut to the basic prcgranr and remain constant for a partLicular set of runs.D--- / T'his design) of the model. is not essential. The program m.ly be altered easily to take the equipment data as input and not part of the basic program. Figure 1 Conputational Procedure Employed in the Rail Simulation Model COST VEMCLE INK TRA C VOLUME DATA CHARACTRS2ICS CHARACTERISTICS Dl ANDS INPUT IMAXIMU MODEL DAILY TRAIN REQUIREKETS ThAIN DELAYS WNOUTE . ROLLING ST'OCK REQUIRENTS -- - OEATING COB TS MODEL OUTPUT LINK AND TRAIN PFRFORMANCE CHARACTERISTICS ............. C. Lirk Characteristics The costs associated with moving a given quant-ity of cargo over a railxoad linlc depend to some extent on thty physical characteristics of that link and the makeup of trainis. In particular, costs wil) depend upon: 1. Length of the link, DIS 2. Speed limitations diue to excessive curvature, condition of the track or other physical features of the line that cause the train to travel at less than its maximum possi.ble speed, VMWAX 3. Minimum allowable speed which can be tolerated due to locomotive overheating., etc., VMIN l. Ruling or maximum grade in each direction, GMAX 5. Average grade or rate of rise and fall. in each direction, GAV 6. Number of sidings, NS 7. Signal system waiting time cate-ory, ISTD 8. Switching system waiting time category, ISC 9. Locomotive type, LT 10. Number of locomotives per train, 2TJL Items 1 and 2 are more or less self-explaanatory. Items 3 and 4h make it necetssary to provide sufficient locomotivo potier to assure a minimum speed :'or the ruling grades. In such cases, it will usually be wore efficient to reduce locomotive power for the overall line and provide hlelper locomotives on the ruling grade sectLion. Item ; 1is the? average grade encountered over the linLk. Grade (listinctiont; :ive indica ted b.,r- direct4-on. Item 6 gives the nurmber of' siding anid items 7 and 8 give some indica ;ion of the quality of the signal and switching systems. The switch-.ng delay at sidings, for example, depends upon whether switchles are opc rated manually or automatically by remote controlled power devices. Ry spetifying switch and signal categories as inpiAs, appropriate coefficients for ca-.culating delays are obtained from a data table that is part o[' tlhe s.lmula,ion program. See Table 1. A sample link characteristic in1'ut card is given in Appendix A. 6- D. Vol'ume Characteristics Because of differeiices in equipment relq.ireineuts anl(A the Lratn make-u and classification) iAmes a3sociaLed with diifferent type,s of equipm 3nt, volume data are separated into conmiodl Ly classifications. ThLree 'reight commodity categories are used as indicatedl by the approp 'iate index shain below in addition to one passenger cate uay. 1. Bulk cargo, ICLAS 1 2. General cargo, ICLAS 2 3. Special cargo, ICLAS = 3 4. Passenger, ICLAS = 4 Bulkl c)mmnodities are assumed to move in open gondola cars or flabtcar;s, general cargo in box cars anid special cargo ia rofri.geraLed, taink cars or othar specialized equipment. For each caLegrwJy, volumes for Llhe Liinme period under considera tion, such as annu al or seasonal volume:;, ar1'c specified in terms of average daily tonnages for each category, A)1T (ICLAS). From tie tonnage flows the vehicle requirements, ADV (ICLAS) ar*t - deU-cirmined. A sampLe Traffic Voliune data card is given in Appenlix A. Tlhe traCific Clow may al30 be irnput as vehicles required per day as well as in tonLm por day. E. Ve dcle Characteristics Information on the equipment available for the make-up of trains is nec3ssary for determining ina.xnimwn brain length, avei'age trairn speed and ov:rall equipment requirements. The followinig daLa are neces,;ary: L/ 1. Horsepower of each locomotive type, HP (LT) 2. Weight of locomotive, WL (LT) 3. Frontal area, A(LT) 4. Fuel consumption rate in gallons per h.p. ' hour, FUEL (LT) 5. Number of driving axles, AXLES (LT) 6,, Standard locomotive life, SLOCLF (LT) 7. Reserve factor for locomotives, RFLOC (LT) 8. Yard time for locomotives., YTL (LT) LT Locomotive Type -7- 9. Capital recovery factor for locom,otives, CRFL (LT) 10. Weiglbt. of car by class, W(ICLAS) 11. Typical car lire, CARLIF (ICLAS) 1,2 Car reserve factor, CARRF (ICIAS) 13. Typical yard time for cars, YTC (ICLAS) ' 14 H Handling time by class of car, THAND (ICLAS) 15. Capital recovery factor for cars, CRF (ICLAS) Saimple values for vehicle characteristics are shown in Appendix A. F. Cost Information The necet,ssry co:31, information for depreciation, operation and mai.ntenance musit be provided for the model. This data is broken dowan into the cos;t, of locomotives and cars, fixed annual costs, variable costs, crews and fiie].s. Othier factoirs inc.luided are ratios of overhead costs and lubricating til -onsumpl,in. TItese items are: 1.. Cost of car (CAICST) (I) P. Cost of' locomotive (CSTLOC) 3. Annual. fixed component of maintenance costs for other rolling stock (Al.) Li. Annual fixed nornToonent of maintenance costs for locomotive (A2) 5. Annual track fixed component of maintenance costs in $/mile (A3) 6. Variable componelnt of maintenance costs/car for other rolling stock per car-mile (MB) 7. Variable complonent of maintenance costs per locomotive,o per locomo tive-mile (B2) 13. Annual variable comrponent of maintenance costs in $/grosE ton- mile (B3) P. Crew costs in dollars/train-mile (B4) 10. Fuel cost in "P.gallon (B5) 11.. Cost of lubricants in $/gallon (B6). 12. Ratio of traffic costs to total maintenance and operatin;: cost (B7) 13. Ratio of overhead costs/total maintenance and operating costs (BO) 1)4. Oil ratio in gallons of fuel oil/gallon of lubricating oil (OR). Sample values for the cost information are shown in Appendix A. -8- II. DETAIIS OF MODEL COST PORMANCE CALCUlATlIOS This section is devoted to the details of the calculations for determiaing the equipment requirements and the operating costs o r the rail linlc being considered. Each of the model relationships is given below in computaUional sequeiCoe. A. Comnutation of Allowable Train TonnacrA' The maximum tonnage which can be hauled in one train depends upon the tractive effort which can be developed by the locomotive, the ruling ,rade and the minimum acceptable speed on that ruling gra(de anid the physical chlaracteristics of' the locomotives and c:ars used, suclh as weigiit, number of axl? and payload. Tractive effort depends upon the net rated horsepower-~/of the locomotives arid locomoLLve speed as given by the equation. 375 * (.82) (HP) (TNL) V 308 (HP) (TNL) V where, .82 = efficiency factor TE = tractive effort in lbs. HP = net horsepower of one locomotive TNIL total number of locomotives per train V = train speed in m.p.h. In this case, tractive effort is computed for VNIN, the iiiinimwn acceptable train soeed on the ruling grade. 1/ The references used to obtain *the allowable train toriages used Americarn units - e.g. short tons, miles, mph, etc. and the equatiaons are presented as such. However, the conputer program is designied to use either metric units or American units in the input and output. 2/ net horsepower = rated output-horsepower furnished auxiliaries. . .........~ -9- Tractive effort can be increased by reducing the mini num speed. For diesel-elec'ric locomotives, however, the minimum speed Ls usuially limited to about 10 m.p.h., due to overheating of elestric moLors at low speeds. Level tangernt rolling resistances for the first locomotive and suiccessive loconmotives are given by Equations 2 and 3 respectLvely. Thlere is a difference in the two equations because the first locomotive eiicounbers a higher air resistance than successive locomotives. SR()=.+ 29 AXLES O03+0.0024 A* (2) SRR (1) = 1.3 + - + 0.03 V* .04 'v (2) WL WL SR (2) =1.3 + 29 AXLES + 0.3 V +0.00 A' V WL WL whiex, e, SR(1) = level tangent rolling resist'ance for the first locomotive, in pounds per ton, SRR(2) = level tangent rolling resistance for each successive locomotive, in pounds per ton, AXLES - number of driving axles on each locomotive, WL = weight of the locomotive in tons and A = cross section area of the locoigotive, in square feet. Net tractive effort available for hauling cars is given by Equation 4. SNETE = TE - WIL /-RR(l) + SM(2) 8 (TNL- 1) + 20G e TNL 7 (4) wh e e , SNETE = net tractive effort, in pounds and G = grade, in percent. For this computation, the ruling grade, GMAX,, is used. The Lotal number of cars that can be hauled depends u.pon the resistance encounm,ered by each car. Since cars used to carry the various comitiodity types diC'rer wii,h respect to their physical chara(.teristics (tare weight and payload capacity), a weighted average resistance is comnputed, based on the relative numbers of each car type. Tlhus, for each cair ocf Type 1, WEIGII(I) -vW(I) + P(I) VLODFC(I) (5) - 10 - TR(I) = 116.0 + o.045v + WEIGH(I) /173 + o.o45v + 20G7 (6) where, IMGH(I) = combined weiglht, in tons, W(I) = weight of car, in tons, P(I) = payload capacity, in tons., VJ.O2FC(I) = load, factor and TR(I) total resistance,in pounds. If it is assumed that the relative proportion of different car types .n an average train is related to thre average daily volurme for each commodity group weighted by the payload facLor for that groupu, L'hert the weighted average total resistanace per car is given by Equatioul 7. N WTR = ADT(I) e TR(I) WTR IJm P(x) * VLOD1M(I) e DEN0I4 Furthermore, 'NCARS SNETE (8) WTR where, WTR = weighted average tobal resistance per car, in pounds, 21/ TIJCARS - total number of cars per train, N ADT(I) D>2JNIK QE.. (8a) I=1 P(I) * VLODEC(I) AD)T(I) = average daily traffic for comnodity group I and 1/ Because of line operating restrictions an absolu-te maximun number of cars per train may be imposed. & u f ; - auN e hl< r $@SfSsX&W<~/>Srsele}irE StsSsGjahaA5s4ow-5:F: .4u1--bNs+. .......... S -:. *X.:.:~...... . . .. . . . ~=.h->v AI N- NTYPES = number of commodity groups carried over the line. For a particular groul), CARS(I) ADT(I) TNCA(RS P(I ) *VLODFC(I ) DENOM and TOTLOD - iCARS(I) * P(I) VLODFC(I) (10) I where, CARS(I) = number of cars of Type I per train and TOTLOD = total tonnage per train. The number of daily trains, DT, required to handle the averat;e total daily traffic is thus given by Equation 11. N E ADT(I) I1=1 DT (11) TOTLOD 1B. Computation of Minimum Running Time Determination of train running speed involves a cubic equation, which is a function of tractive effort and train resistance lror the average grade. Balancing speed is that speed at which the resistance to motion encountered by the train is just equal to the tractive effort dleveloped by the locomotive. As previous equations have shown aon increase in train speed increases train resistance and decreases tractive effort. These computations are made on thie basis of the average gradient encountered arid a train coraposition determined by the ruling grade, as discussed in the preceding section. The cubic equation is developed from setting SNETE = TRR (12) wlhere SNETE is developed in Equation 4 and TRR E TR(I) CARS(I) (13) I - 12 - where, TRR - total train resistance, in pounds and TR(I) AND CARS(I) are obtained fronm Equations 6 and 9, respec,tively. Both E: ,uations 4 and 6 are functions of the unknowni value V. Rearranging the tew'ms which result from the equality defined by Equation 12 will produc.^ an equation which is a cubic function of V. The value of the coeffi(;ients of this equation are such that only one real value of V exists that i:; greater than or equal to VMIN, nanmely VAV. Minimtum running time i; then determined from Equation 14, ¢ mo) DIS (JL4) VAV where, TRO minimum running time in hours (outbound) and VAV - average speed, in m.p.h., where Equationi 12 holds. A distinction is made between outbound and inbound running times for purposos of the train delay calculations discussed in the fo.ollwing section. Inboun(d running time is calculated in the same manlier for average grade', ruling grade and daily traffic. C. Tr.iin Delay Calculations Calculations of delays encountered enroute due to traffic congestion are batod on the assumption of a single track line with sidings sufficiently long btoatnmodate one train. 7ime-distance curves for inbound and outbound trains along such a line are shown in Figure 2. In the following equations, the su'fixn "i0" and "I" denote outbound and inbound directions respectively. In developing the model for traindelays, the following symbols are used: DT0, DTI = daily trains out; daily trains in, TRO, TRI minimum rumdng times (as determined in the previous section), in hours, '.RAVO,, TRAVI - average running times, in hours, K average delay per meet, in hours, ST - switching time per train taking the siding, iII hours, WT = waiting time per train taking the aiding, in hours, and M = number of mets. If an outbound traill leaves at time t - O, it will encounter two groups of inbound trains, namely (1) those inbound trains already on the line and (2) those inbound trains leaving after time t = 0 and before the outbound train has arrived at the other end, TRAVO hours later. The first, group includes all trains leaving during the period t = - TRAVI to t = 0. Assuming departures at both ends of the link are unliformly distributed over a 24 hour period, the total number of trains encountered by an outbound train is given by: DTI Meets = /RAVI + TRAVO 7 (15) TRAVO = TRO + KXM (16) TRIVO = TRO + DRAVI + TRAVO7 (16a) 2kb wlich reduct s -to TRO + K DTI /TRAVI 7 24 TRAVO (16b) 1- K' DTI 24 Similarly, TRAVI = TRI + K'M (17) TRAVI = TRI + K DTO /TRAVO + TRAvi 7 (17a) 24 TRI + K'DTO /TRAVO 7 TRAVI = (17b) 1- KDTO 24 - 14 - Figure 2 TimeI-Ditance Curves for a Single Track Line TIME" zA TINEIA IN. N I-I T S DISTANCE Sub.stituting Equation 17 in Equation 16b, TRLTRI + ]DTO TRAVO 1 ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ TRAVO (18) K d- DTI 1 - __._-_- 24 If the assumption is made that DTI DTO - DT, then :3quation 18 can be .reduce*cd l.o 576 TRO + 24 K DT * /TR- TRO7 'I'liA VO - (19 ) 576 - 48 K DT S:i nilarly, 576 TRI + 2_4 KI DT */TRO - TRI 7 TRAVI (20) 576 - 48 K *DT IThe value of K, waiting time per meet, depends upon the nature of the sigLial system, thie type of switches and the efficiency of the train dispatch. These characteristics are suniiarized by the two indices provided as input to the program, such that K = ST(I) + WT(J) (21) wnere, ST(I) = switching time associa bed with switch type I and WT(J) = waiting time associated with signal syt3tem J. Under optimum conditions, trains would pass "on the run" and no train would be forced to stop at the siding. Under the worst conditions, inbound and outbound trains would arrive at opposite ends of the single t,rack section simultaneously. In this case, one train wovld be forced to wait for lhe opposing train to travel the distance between the two sidings. Since only one train is Lorced to stop, on the average this waiting time would be one half the running time between successive sidings. For - 16 - inter,iediate situations, train delays would range between zero and one-I6,lf the running time between sidings. The program now allows for three different signal and switch categories. The delays associated with each are extracted from a data table for the appropriate index provicded as input, as shown in Table 1. Table 1 Switching and Waiting Time Delays Siding Switching Delay Waiting Time categz in hours in hours I or J ST(I) WT(J) 1 0.10 TRO/lO (NS+l) 2 0.25 TRO/ 4 (NS+1) 3 0.25 TRO/ 2 (NS+1) D. Determination of Equipment Requirements Equipment requirements depend principally upon the daily tonnage of eac h coimnodity type, payload and load factor of the appropriate car and the t:.me required for a car to make one trip. The latter is referred to as the block time and is given by 7M(I) - TLU(I) + TRAVO + YTC (I) (22) where. TBC(I) - block time for Type I cars, in hours, 'TLU(I) = time to connect and/or disconlect the cars carrying Type I commodities, in hours, - THAND (I) I CARS (I), THAND(I) average "handling" time for cars carrying Type I commodities, in hours and YTC(I) - yard time for Tjpe I cars, in hiours. Loading and unloading times depeind upli the nature of the car jo and the ratio of backhaul to outbound cargo. Handling rates, THAND(I), are incorporated as internal data and are respectively 0.01, 0.10, and 0.01 hours per car for. bulk, general and cargo requiring specialized eqjuipment. - 17 - The number of "sets" of Type I cars is given by Equation 23, rounded to the next whole number, which is then used to determine th'3 total number of cars reqjuired for each commodity group, as in Equation 24. AXTT (I) = DT TBC(I) (23) e-4 ANO (I) = ANT (I) * cARS (I) j g + CARRF (I) 7 (24) where, ANT(I) = number of sets of Type I cars, where a "SAIt is defined as a group of cars of the same type in ons train, ANO(I) = total number of Type I cars required and CARRF(I) - reserve factor for Type I cars to allow for routine maintenance periodic overhaul and stand-by expressed as a decimal fracti\on. Values of CARRF are included in the internal data table. The total number of locomotives required to operate the line are determined in a sirmilar manner. The relevant equations are: TBL = TRAVO + YTL (25) STLOCS = DT TBL (26) 24 TLOCO03 = STLOCS e TNL 5 Cl + RFLOCO7 /LUF (27) whiere, TBL = locomotive block time, in hours, STLOCS - nunber of sets of locomotives, TLOCOS = total number of locomotives and RFLOC = loconmotive reserve factor, expressed as a decimal fraction of TLOCOS. LUF = Locomotive Utilization Factor E. erating Cost Calculations Operating cost calculations are based on various operatinig statistics that can now be summarized from the above calculatiorns. These operating statistics include gross tori-miles, train-miles and car-miles. These can be computed from the following equations: TRAMIL DT - DIS - DAYS (28) CA L 2 TNCARS TRAIIIL (29) TllOC4L TNL * TRAMIL (30) TGTN DT DAYS C CARS(I) W w(I) + P(I) * VLDDFC(I) (31) where, TRAMIL total number of train miles during the time period under consideration, DAYS number of days in the timne period, CA L =. total number of car-miles in the time period and NTYPES total number of different commodity groups. Using these operating statistics, operating cost calculations are broken down Into the following categories: rolling stock depreciation, rolling stock maijatenance cos Ls, maintenance of way and sttructure-, train operating. costs and transportation and overhead costs. Locomotive and other rolling stock depreciation costs are given by Eqtations 32 and 33 respectively. Thiese equations are based on a straight ratio of days in the time period under consideration to the total number of operating days in the year, which is assumed to be 365. Tllus, two tiqie periods of equal length would produce the -rame depreciation chargEs, even though utilization of the equipment might be greater during one period than the other. DEPRLC - DAYS TLOCOS CSTLO (LT) CBL(LT)_7 DFAC (32) 365 DAYS DEPRC (I) D S CARC S T(I CRF(I) 7 TBC(I (33) 365 24 where, DEPRLC = total locomotive depreciation cost, CSTLOC(LT) = initial cost of Type LT locomotive, CRFL(LT) - c.apital recovery factor for Type LT locomot,ive, DEPRC(I) = total depreciation cost of Type I car, CARCST(I) = initial cost of Type I car and CRF(I) = capital recovery factor for Type I car DFAC = TBIV24 = percent of day locomotive was usedl on link DAYS = no. of days in a season The c,apital recovery factors for locomotives and rol.ling stock depend upon oquipment. life (in years) and the rate of interest used in amortizing the investment in rolling stock. These factors are included in the internal diata table for each type of car. Equipmerit maintenance costs for a single car or loco:notive are conmpri.sed of an anr:ual fixed component that is independent f car usage and .x variable component that varies with usage (or car-miles per' car). Total maintenance of equipment costs for the time period are given by CARMIT = A(1) DAYS B(1) CAM L 365 N ANO (I) (3) -ANO (I) =1 aind SLOCMT FA(2) DAYS + B(2) . LOCIL TLOCOS (35) 315 TLOCOS j C=4 T - total maintenance costs for rolling stock, excJuding locomotives, - 20 SLOCMT - total Miaintenance costs for locomotives, A(1), A(2) = annual fixed component of maintenance costs for other rolling stock and locomotives respectively, per car-mile or locomotive-mile, in dollars and B(1), B(2) - variable component of maintenance costs per car for other rolling stock and locomotives respectively, per car-miie or locomotive-mile, in dollars. Values of A and B are provided as internal data. Mainltenance coats for track and structures also display a certain fixed component necessary to keep the line operative and a variable component That depends upon the traffic. For this cost category, the best measwe4 of traffic appears to be gross ton-miles per mile of track. For the to al length of the line then., maintenance of way costs are given by WAM4T DIS.LA(3) * DAYS + B(3) . myTN_7 A (36) where WAMIT - total maintenance of way costs, in dollars, A m annual fixed component of maintenance costs, in dollars per mile and B3 annual variable component of maintenance costs,in dollars per gross ton-mile per mile. Train operating costs include crew costs, fuel costs and oil costs, as given by Equations 37 to 39 respectively. CRMSCT - TRAMIL B(4) X NT x DIS x DAYS 7 B(4) (37) FUI1,ST = TRAVO DAYS * DT * FUEL (LT) * B( ) HP(LT) TNL (38) FULCST B(6 OITX;ST S (39) OR B(t5) where CRLUST total cost of train operating crews, in dollars, -21- t B(h) = crew costs in dollars per train-mile, FULCS? = total cost of fuel consumption, in dolars3, FUEL(LT) = rate of fuel consumption in gallons per H?- hour for Type LT locomotive, B(5) - fuel coat in dollars per gallon, OILCST = total cost of lubricating oils, in dollar3, OR = oil ratio in gallons of fuel oil per gallon of lubricating oil and B(6) = cost of lubricants in dollars per gallon. The first expression of Equation 38 involves converting train-miles and average speed information into train-hours. Total basic cost is given by the sun of the costs determined above, as in Equation 40. BASE = CArT + SLMT + IJAfMT + CRUWST + FLCST + OIST (40) Traffic costs (advertising, management, ticketing, billing and so on) and overhead costs are then related to this basic cost, aa in Equations 141 and 142. TRACST = BC;) . BASE (141), OVHCST = B(8) . BASE (42) where, BASE = total maintenance and operating costs, in dollars, TRACST = traffic cost, in dollars, B(7) ratio of traffic costs to total maintenance and operating costs and B(8) = ratio of overhead costs to total maintenance and operating costs. Total costs of operation, maintenance, overhead and traf'fic are given by Equation 43. Thus, TO34T = BASE + OVHCST + TRACST (43) For each commodity group, this cost is distributed in proportioxn to the relative traffic volumes for each type. Locomotive depreciation costs aie also allocated in a similar manner so that TO04(I) = ADT(I) L. OEMT + DEPRLC 7 + DEPRC(I) (44) N. ADT(I) I1= - 22 - UC(I K() 1L) (45) ADT(I) * DIS where TO4X (I)= total costs of rail transport for Type I commodity, in dollars per time period and TIC(I) =unit costn for Type I commodity, for the time period under consideration, in dollars per ton-mile. F. Mode) . t ¶.he program has two main outputs. The first section is the train operating cost components measures; the second section gives the Link PerformaiLce Measures in the same format as in the Highway and Transfer Model. A'he Link Performance Measure output is described in detail in Apperidix B. 'Lhe operating cost and the train make-up output includes for each directioni on a link the following: 1. net %ractive effort of the locomotive(s) for the ruling grade; 2. aver;age tractive resistance for an average train up the ruling grade; 3. cars required to carry each volume; 4. cars per train of each class; 5. required number of trains per day; 6. average speed of each train; 7. roll:ing stock depreciation costs for a season by class of .car and for locomotives; 8. operating and maintenance costs for rolling stock for a season; 9. fuel costs per season; 10. oil co-ts per season; 11. crew costs per season; 12. overaead costs per season; 13. mainteance of way costs per season; Train Performance Measures include a wide variety of indications of the way in which the rail link is being operated and thie resultiug consequences. The trains per day, the number of cars of each type, the net and average 'ractive resistance, the number of average cars and train speed are all summarized in the output. The specific measur.es included in this portion by shipping class, are: 1. Costs/ton-mile 2. Total, Handling Time 3 Tot&l Yard Time 4. Totel B£lock Time 23 - 5. Travell Time 6. Waiting Time 7. Time Variability G . ?robability of Loss Itenms 5-8 are transferred to the Linlk Performance Vector (LPV) along with the shipping charge. Thlis LPV is the source of the mAde meiastros used in tlhe System Transportation Model to analyze the botal tratisLwoirtation systemi. - 24 - Bibliography De Salvo, Joseph S., "A Process Function For Linelaul Operations"l, Journal of Transport Economics and Policy, Vol. III, No. , Jan. 1 969. f7loyd, D. P., Simulation of the Colombian Railway. Network thesis submitted to School of Graiduate School, Department of Civil Engineering, University of Toronto, October, 1968. Hay, William W.,Railroad Engineering, Vol. 1, Johni Wiley and Soris, nc, New York, N.Y., 1953. - 25 - Appendix A A.1 Colombian Rail-Vehicle Characteristics Class Bulk General Special Characteristics cargo cargo cargo Passenger Weight or car (w) 13.8 13.8 15.2 17.8 Tons (2204 lbs.) Cost of car (CARCST) 90,000 86,000 103,000 258,000 '69 Col. Pesos Typical car life 30 30 30 30 (CARLIF) (years) Car reserve factor 0.15 0.15 0.15 0.33 (CARRE) Typical yard time for cars (YTC) (Hours) 6.0 12.0 6.o 1.0 Capi tal recovery factor for cars (CRF) 0.09 M.09 0.09 0.09 Hand].ing time by class of car (TiIAND) (hours) 1.0 2.0 1.0 .5 Capacity of care (fAYLOAD) 31.5 214.5 28. 17.5 - 26 - A.2 Colombian Railroad Model Factors and Costs Input Locomotive type CharacteristicsI III Horsepower (HP) 2,000 1,350 950 Weight of locomotive (WL) (tons 2204a lbs.) 91.s 91.4 61.0 Fuel consumtion Rate in liters per h.p.-hour (FUEL) (LT) .045 .035 Frontal area (A) m2 8.t326 8.826 8.826 Cost of 2ocomotive by type (CSTLOC) 1969 Gcl. Pesos 3,096,000 - 2,?73,500 2,752,000 Number of driving axes (AXLES) 6 6 4 Standard locomotive life (SLODLF) 20 20 20 Reserve factor for locomotive (RFLOC) 0.25 0.22 0.23 Yard time for locomotive (YTL) hours 1.0. 1.0 2.0 Capital recovery faotor for locomotive (CRFL) 0.10 0.10 0.110 Switching: time (ST).hours 0.15 0.15 0.15 - 27 - A.3 Other Rail Factors and Costs Al. = annual fixed. compolient of maintenance costs for other rolli ig stock, (per car-year), in dollars = US$ 76 dollars/year. $ col. (69) 1,307 PS/year A2 arnual fixed component of maintenance costs for locontotive ?er (locomotive-year), in dollars = US $4,000 dollars/year. $ Col. (69) = 68,80i) PS/year.. A3 annual track fixed component of maintenance costs $ Col.. (69) = 24,080 PS/mile $ Col. (69) = 14,963 PS/K- Bi variable component of maintenance cos ts/car for other rolling stock $ Col. (69) = 0.157 PS/mile $ Col. (69) = 0.098 PS/KM B2 =-variable component of maintenance costs per locomotive $ Col. (69) = 1.08 PS/mile $ Col. (69) = 0.67 PS/KM. B.3 = annual variable component of way maintenance costs $ Col. (69) = 0.0134 PS/Ton-mile $ Col. (69) = 0.0083 PS/Ton-KM. 34 = crew costs = $ Col. (69) 1.73 PS/train-mile $ Col. (69) 1.08 PS/train-KM. B-- .U=el cost = $ Col. (69) 1.64 PS/gallon $ Col. (69) .433 PS/liter B6 = cost of lubricants = $Col. (69) 7 PS/gallon $Col. (69) 1.849 PS/liter B7 = ratio of traffic costs to total maintenance and operating (ost = 0.012 B8 = ratio of overhead costs/total maintenance and costs - 0.08C ;)1 = oil ratio in gallons of fuel oil/gallon of lubricating oil 130 ¶ D A NO. TYE PE ITNCF ;$'MAX IdN' -,,ÆR)E RADE t siGr NALIL)jG LOCo. L.OCO LIN' 21 20 33400.00 60.00 10.00 2,90 1 ,5010.00 2. 00 2.00 3,.00 I, -0.00 -0.00 -, .e VOL 20 21 600,00-0.00 1 AO,00-0,o0 600.00,-000 -0,00-0.00 -in0.0-O.00 nn. T A*** -~ . V OL 21 2 20o.non00 So.on-0 ,0o.00-o0 -o,oo-.0 -0.oo0oon -o T A*** ENDL ~ _ __ _ _ \BE6T.;J, fiN(i) VOLVME£ \OLU?K-___ 'J)ILJME - - OJLI)M1; -- - -~ -.~~~~-- -- - ------- - -~ \ 40DE 40DE COMM I . c~CA:tM.T 12AS37&.64 0.06R40.084 0.090 '~.-LCCDFP 177205'%.10 0.n9t ^.II? 0.120 L)4T 6275A0.13 0,0330.4 0.4 __ _ __ _ _ F IIE~L 4462T67.'i0 O.'~34 0.291 0.311 _ _ _ _ _ _ _ _ _ _ _ O IL 146591.72 0.008 0.01-1 0,010 5194.A 0.024 .3 0.036 -~=-Tf TALI 143'.3741.58 0.761 0.937 I.COO TPACST 176044.08 0,00? 1.000 ff)V4FAD 914 34 3.77 0.049 A0 .f6 0 t~,-TnTAL 2 15414134.952 n.R17 l,000 ~iYI 34-59747.43 l. 18 3 -ITnTAL3 1,48733531.95 1.000 T ET ~ EA S i 4E S-' 0 0-- ---- -- _ _ _ _ _ _ _ : 11 -~ ILK -GF NJF iA L SDECIAL PAS~%!R___ ~-COSTS/";TON.%I(Un,5 0.0777 M0..579 '.n."00 -TOT ~T0T 2L43 TUE 3.3-i97 25.44141 1.76A4 0.nof ___ -. TOTAL 'tAQfl TluE'- i.r,000 12.00010 A. e)on 1.000 lo- - -- - --_ ~- TOTAL 3LCK TJvE 380.3 70* 77.4700 3A.7943 2A.1299______________ 4 200 .fl0ona- 7,001m ___ RVLTIME 47.4802 44.8? 4,523.4802 Ž o-AIT T1'mE 7.11103- 2.1103 7.1103 2.1103 - C..TIEVARIARTLTY A.4591 5.59 4.45Q1 399 )VFRR 3FLCSS t),'00)3 - 0.0003 n. 0003 0.0002 iŽ _LI'.K Cr.ARACTEQISTICS rR1I. 21 TO 20 400.000 60.000 1n0.000 2.500 1.500 10.000 7.000 2.000 3.000 1.000 04TrR/AyYITE0L0iN NTS 'AND COSTS/SCASO.4 -(AVG. S1PEEn 74TWi.46KPH) (MWIN4. REQUIRE0 TRAINS 4 00 - 32 - Apendix C Mode SLmmnary Table A summary table of the coats and link performance measues are computed fdr each link - bwth dirctions - an& fbor each mode.* This suRary table cdmputes the details of each cOat and breake. out the tax revuen and foreign ekchange copponents. Thoee charts arw computed each year far & li*x but the chart is divided. izito five columns: 1) "PRZ5T bTff To Present Worth of the cost d1scounted back to the. bqiring year. 2) ACC1Ul&TED PW TNfRU i Thle is the accumulated Pfreent Worth through the present year. 3) "C1JT VALUE (IN f±8J it the current cost of the items considered. 14) "AVM VALUE PIS TOIK 5 Ih1* Is the cost given In the '"CURRENT LUE" columms divided by the total tow AMpped over the link. 5) "RELArONSHIPS" %L divides the component& a) Total costs, bJ Operations Costs, cJ) W Revenue, and d) Foreign Exchange into pereentages. The followint, 4*Lanation for each r@w, corresponding to the rw nwnber as given in t]s cwtput, are presented in torms of the "CURRENT VAL&"" column. * This is a general format output for all modes. Therefore exne items for a partioul'a?r de - such as TIRES on Railway will not apply. In the case where the ite1 does not apply th. entry will be (0.0). - 33 - Th-e othlr elements ot' tU,e row are calculat4ed from the current v3lue as di scutsssed3 above. Row Item Eplanation 1. TOTAL COST Sum of the WAYKNT + RFAC 2. WAYMNT WAY MN4T is calculated .by Equation 36. 3. RFAC Sum of rows 4-8 which are th3 components of the RFACTOR. I WAIT TIME (I) X W TIME C)ST (I) .;. lTTrMIe = TRAVEL TIME (I) X TRAVEL COST(I) I -1 6. hl. ft TIME VARIABILITY (I) X VTIME COST(I) I1=1 i'. PRLOSS 4 5 PROB OF LOSS (I) X PROB-LOSS COST (I) 3. Ci, If liGE - OTONS (I) X RATE(I) .9. (0PITR Sumn of the operation cost components. Rlows 10-16. 1TO. CffIC1W LSum of the link CREW cost for both directions. 1l. FELEW' Sum of link FU13L cost for both directions. 12. LUBE Sum of link LUBE cost for both directiolns. 1.3. TIRES Sum of TIRES in both directiors. Rii. EPAIR Sum of the vehicle MNT in both directions. Does not iriclude WAWMNT. DL'. DLt Sum of the veh DEP in both diiections. - 34 - Row Iten Ep1a t ion Tb. ori Sum of the reanaining items contributing t,o tlhe operdtiii, costs La both tAi.L.,; L ; ,.I Q,t 17. TAX aVRIX Sum of the taxcs - Rows 18-24. 18. FETX FULCST/(1 + TAX (8) ) TAX(Q). 19. LUDETX OILCST/(1 + TAX (9) ) TA (9). 20. TIRETX 21. VEHTI DEPRIC/(1. + TAX (4) ) TX ( 4) 22. PRTSTX (.2x CA1IT + .1 x SLOCMT)/(1+ TAX(3)) TAX( 3) 23. HEOSTX 24. INCHTX (CRUCS T + .5B( 8 ) /gAFM4T + SLOCMT + WAYIIT + CRIJCST + 0iICST 7) x ADT/ ADTOTC x TAX (10) ) 25. FOEIGN EXC. Sum of Ioreigne.X.&arge compornents Rows 26-30. 26. FUEXC FUTLST-/(I + TAX (81) ) ' FRNiXC(8) 27. LUBEXC OILCST X (1 + TAX (2) ) X FR4EXC(Q) 28. T}E;XC 29. PRTSXC /.2 (CARMT) + .1 5LOMC1T 7 / (1 + TAX (3) FWAxC(30) 30. DEPRXC DEPRLC/(i + TAX(h) FEINEXC (4) + SCRDEP (FRME4c F() ) 31. TotaIl tonis moVed. Row I T Xa ntion 32. Total number of v,Zhicles/days required (CARS) (DT) X 365 DAYS X 2 33. S UMARY OF APW Accumulated Preseuit Worth 3R} RAC Accumulated PW co:;t to tlie SHIIPPER 3K OPER Accumulated PW to the TRANSPORTER 3". TAM Accumulated PW Ta;c revenue 3i. FRNX Accumulated PW Foreign Exchange - 36 Taxes on Specific Items Related to Tran-ortation. TAX (1) - IMPORT TAX ON AUTOS AND TRUCKS TAX (2) = IMPORT TAX ON TIRES FOR AUTOS AND TRJCKS TAX (3) = ImPORT TAX ON PARS FOR REPAIRS TAX (4) IMPORT TAX ON L)CC(OTIVES TAX (5) = IMPORT TAX ON RAILCARS TAX (6) IMPORT TAX ON DOCK EQUJIP(ENT TAX (7) GASOLINE TAX TAX (8) = FUEL OIL TAX (RAIL) TAX (9) = LUB1E OIL TAX TAX (10) = INCCiE TAX (AVERAGE ON WAGE) TAX (11) = REGISTRATICN FEE ON CLASS 1 HIGHWAY VEHICLI) TAX (12) - REGISTRATION FEE ON CLASS 2 HIGHIJAY VIGICLES . TAX (13) - REGISTRATION FEE ON CLASS 3 HIGHWAY Va{ICLES TAX (14) - REGISTRATION FEE ON CLASS 4 )HIGHWAY VEHICLES. TAX (15) = REGISTRATON FEE ON CLASS 5 HIGM VEaICLES FRNEXC(N) FOREIGN EXCHANGE PER $ (NO TAXLS IN $) SPET ON ITEM" IN FRNEXC (1)= F. E. ON PURCHASE OF AUTOS AND TRUCKS FRNEXC (2)= F. E. ON PURCHASE OF TIRES FOR AU[OS AND TRUCKS FRNEXC (3)= F. E. ON PURCHASE OF PART FOR REPAIRS FRNEXC (4)- F E. ON PURCHASE OF IC(IOTIVES FEXC (, F. E. ON PURCHASE OF RAIL CARS FRNEXC (5)= F. E. ON PURCHASE OF DOCK EQUIPMENT FRNEXC (7 = F. E. ON PURCHASE OF GASOLINE FRNEXC (3)= F. E. ON PURCHASE OF FUEL OIL (nAIL) FRNEXC (9)= F. E. ON PURCHASE OF LUBE OIL . - - -37- R-FACTORP LINE 4 iN OInIRSi = 8441.1 R-FACTORP LINE 5 IN HOURS z t70870*60 R-FACTOR, LINE 6 IN HOURS = 17911.17 R-FACTOR. LINE 7 IN HOURS s 1.t0 R-FACTORP LINE 8 iN HOURS * 22QrAO90to YEAR 1969p LINK BETWEFN 70 ANn 21. MODE 33 PRESENT WrJRTH ACCUMULATErn PW CURRENT VALUE AVERAGE VALIJF TO 1069 THRU 1969 CIN 1969 ) PER TON S4IPPED RELATIONSHIPS 1. TOTAL COST 125863.94 125863,94 1253863.94 86.2-1 2. MAYMNTo... 4378.37 4378.37 4378.37 3.00 3. RFACee.... 1,1485.57 121485.S7 121485.5, 83.21 1.00 4e WTIMEsE. 1269.37 1269,37 1269.3T 0.67 0,01 5. TTIME... 35r30.50 35730.50 35S30.50 24.4? 0.29 6. vTIEmes 373.87 373,87 373.87 0.26 0,00 7. PRLOSS.. 249*42 249.42 249.42 oat1 0.00 8. CHRGE9*. 83862.40 83862.40 83862.40 57*44 0.69 9. OPER..** 24451.86 24451.66 p4451.86 t1.75 1.00 10. CREW.. 692.45 692.4S 692.45 0.47 0*03 11. FUELEW.. 5410.98 5410.98 541a,98 3.71 0.22 12. LUBE.. 171.74 1t7T.4 177.74 o it 0k00 13. TIRES. 0.00 0,00 o o 0.00 000 14. REPAIR 2697.81 2697.81 2697.8l 1,85 0.11 i5. DEPR.o 9758,78 9758.78 9751878 6.68 0.40 1i6 OTHER. 5714.10 5714 10 5714.10 3.91 0*23 1t? TAX REVENUE. 2296.23 2296,23 2296.2) - 1.53 1.00 18. FUELTX ... 491.91 491.91 491.91 0.34 0.21 19. LUBETX.... 8.46 8,46 A.46 0.01 0.00 20. TIRETX... 0.00 0.00 0,00 0o,00 o0oo 21, VEHTAX.... 1626.46 1626.46 16P6.46 1.11 0.71 22. PRTSTX.... 88.31 88.31 AM.31 0.06 0.04 23. REGSTX.... 0.00 0.00 0.0, 0.00 24. INCMTX .... 81.08 81.08 *1.8 o.6 0.04 25. FOREIGN EXC. 11n38.42 11038.42 11038,42 T.56 1.00 26. EUELX C. ... 2459.53 2459,53 2459.53 1.68 0.22 27. LUBEXC.oo. 93.31 93.3i 93.31 0.06 0.01 26. TIRSXC.... n.no o0oo o0oo 0.00 0.00 29. PRTSXC.... 353.75 353.25 353.25 0.24 0.03 30. DEPRXC.... 8132.32 8t32,32 8132.32 5.57 0.74 31. 1460. TnNS 1460. TONS 32. 83, VEHS S3, VEHS -......- ........-ALL VALIuES nlIVInEr) AY 10oo0---------.--------- THE VALUES PRESENTErn ASSIUME EACH LIN" nPERATED 365 nAYS PER YEAR ( PESOS 3 33, SUMMARY OF APW 34. RFAC 121485.51( SHTPPEP ) 35. OPER 24451,8b( TRANSPnRTER ) - 38 - 36, TAXR 2296,23(GnV T REVFNIIE) 3?. FRNX 11%386,4tFnREI'N EVCNG) .. . . . . . . - - - 39 - Appjendix D Railways Dictionary A(l), A(24) annual fixed component of maintenance costs for other rollitig stock and locomotives respectively, per car-mnile or locomotive-mil.e, in dollars A3 annual. fixed component of maintenance costs, in dollars per mile f(LT) fronltal area, i.e. cross section of the loc3motive in square feet ADT(T) average dai.ly traffic for comwodity group I 11.. Bulk 2. Oeneral 3. "pecial 4. Passenger-commercial ' . Passenger-priva te ADT(IILAS) averag, e (diai ly tonna ge ADV(ICLAS) average daily vehicle requirement ANO(T) total niumber of Type I cars required ANT(I) nuimber' of sets of Type I cars, where a "set" is defined as a g,roup of cars of the same type in one train A2KLES (LT) niunber of driving axles on each locomotive 13(1), B(2) variable component of maintenance costs per car for other rolling stock and locomotives respectively, per car-mile or locomotive-mile in dollars E3 annual variable conmponents of maintenance c)sts in dollars per gross ton-mile per inile 13(4) crew costs in dollars per train-mile B(5) fuel cost in dollars per gallon B (6) cost of luibric.ants in dollars per gallon B (7) ratio of traffic costs to total maintenance and operating costs LB(8) rnt.io of overhead costs to total maintenanci! and operating costs B ASE total nmidntenance and operating costs in dol-lars CARCST(ICLAS) initial. cost of car by class CARLI F (ICLAS) typical car life CARII L sotal ntmlber of car-miles in the time periodl UAW ilT total maintenance costs for rolling stock, 'txcluding locomotives - 4O - CARF(I) reserve factor for Type I cars to allow for routine maintenance and periodic overhaul, expressed as a decinal fraction. CARS(!) number of cars of type I per train CARRF(ICOJS) car reserve factor CO;T(ICLS) coat of Providing the service per ton CRF(ICIX;,) capital recovery factor for cars CRFL(LT) capital recovery factor for locomotives CRJUCST total cost of train operating crews, in dollars CSTLOC(L") initial cost of locomotive by type DAYS number of da7s in the time period N DENOM Z! ODT(I) I-1 P(I ) VLODFC(I) DEPRC(I) total depreciation cost of Type I car DEPRIC total locomotive depreciation cost DIS length of the link DT Number of daily trains DTI daily trains inbound DTO daily trains ouitbound FUEL(LT) fuel consuMption rate in gallons per h.p. hour FULOST total cost of Tuel consunption, in dollars G grade, in percent GAV average grade or rate of rise and fall in eaclh direction GMAX ruling or maximum grade in eacli direction HP rated horsepower of one locomotive HP (LT) horsepower of each locomotive type ICLAS-1 bulk cargo ICLAS=2 general cargo ICLAS-3 special cargo ICLAS=4 passenger ISC switching system waiting time category K average delay per meet, i-n hours LT locomotive type ISTD signal syst waiting time category M number of meets N=NTYPES number of cvaodty groups carried over the line 41 - NS nlnmber of sidings OILCST total cost of lubricating oils, in dollars OR oil ratio in gallons of fuel oil per gallon of lubricating oil OVNC5JT overhead costs P(I) payload capacity, in tons PROBLO(ICLAS) probability of loss of one ton of the shipment AFLOC(LT) reserve factors for locomotives, expressed ,s a decimnal fraction of TLOCOS SLOCLF(LT) standard locomotive life SLOCM' total mnaintenance costs for locomotives SN4ETLe net tractive effort in pounds SRR(l) level tangent rolling resistance for the fii'st locomotive,in poUnd(is per ton SRR(,) level tangent rolling resistance for each suiccessive looomotive, in pounds per ton Sr switching time per train taking the siding, in hours STLOCS niunber of sets of locomotives TBC(I) block time for Type I cars, in hours TIBL locomotive bloclc time, in hours TE; tractive effort in pounds 'rG7lN uotal gross ton-km. TIAWMD(I) average "handling" time for cars carrying T7pe I commodities, ill hours TLOCML TNL TRAMIL TLOCS.O total number of locomotives TLU(I) time to connect and/or disconnect the cars carrying Type I (oriu:iodl ties, in hours TNCARS total number of cars per train n,IL total number of locomotives TOEM(I) total costs of rail transport for Type I coitnodity, in dollars per time period , OENT total cost of operation, maintenance, overh,ad, and traffic TOTLOD t,otal tonnage per train TH(I) total resistance in pounds TRACST traffic cost, in dollars T1tAMIL total number of train miles during the tim'3 period under consideration TRAV(ICLAS) travel time on the link from station to sta-ion, in hours TRAVI aiverage runring times inbound, in hours TRAVO average running times outbound, in hours TRI minimum running time inbound, in hours TRO minimum running time outbound, in hours TAR total train resistance, in pounds UC(I) unit costs for Type I conmodity,for the time period under consideration, in dollars per ton-mile v train speed in m.p.h. VARTIM (ICLAS) travel time variability, in hours VAV average speed, in mph, where SNETE-TRR VLODFC(ICLAS) vehicle load factors VlAAX speed limitations duie to excessive curvature, condition of the track or other physical features of the line that cause the train to travel at less than its maximm possible sdpeed VMEN minimum allowable speed wiich can be tolerated due to locomotive overheating, etc., the mninimum acceptable train speed on the ruling grade W(ICLAS) weight of car by class in tons WAIT(ICIdLS) waiting time on the link -which includes switching time but not loading and unloading time, in hours WADIT total maintenance of way costs, i.n dollars WIGHT(I') combined weight, in tons WL(LT) weight of locomotive in tons WT waiting time per train taking the siding, in hiours WTR weighted average total resistance per car, in pounds YTC(I) yard time for Type I cars., in hours YTL (LT) yard time for locomotives - 43 - Appendix E Railroad, Moe quations 1. Tractive Effort: 308 .(FIr (TNL) TIE v 308 = 375 x 82.2% efficiency 2. Level Tangent Rolling Resistance: 2 29 AXLES 0O.0024 A.,O2hA WL WL 2 3. SRR(2) - 1.3 + 29A + 0.03V + O.000~A WL WL 4. Net Tractive Effort: SNETE = TE - WL /SRR(1) + SRR(2) (TNL - 1) + 20 G TNL_ G = AX: ruling grade 5. Combined Weights: WEIGH(I) = W(I) + P(I) * VLODIF(I) 6. Total Resistance: 2 TR(I) = 116.0 + o.oh5v + WEIGH(I) /T.3 + o.o45v + 200G 7. Weighted Average Total Resistancet WTR - ADT(I) ) (I. 141 P(I) VLODFc(I) DEOM 7a. DENt fi DTI I -1 P(I ) VLODFC(TI) 8. Total No. of Cars per Train: TNCARS SNETS WE 8a. DENON A I11 P(I) * voC (I) 9. N. cf Care of Type I per Traint GARI)AD(I) TNCARS P(I) VLoDFOC(I) *DNOM 10. Total Tonnage per Train: IOTLC - iCARS (I) i P(I) VLODFC (I) I 11. No. of Daily Trains: wADT W TOTLOD MINIMUM FiENIN TIM 12. Tractive Effort: SN1TE - TUf 13. Total Train Resistance: TER TR (I) CARS (I) I 114. Minim= Running Time: TRO w DIS VAV - 45 - TRAIN DELAY CALCULATIONS 15. No. of Trains Encountered by an Outbound Train: M DI + TRAVO 7 1TRAVO = TRO + K M . TRAVO TRO + K*DTRAvi + TRAvo 7 TRO + K D DTI /TRAVIJ 16b. or 1--KDTI 24 TRI + K* TOV 17. and TRAVI K*DTO 21i rK .DTC' eTRAVO 1 24 T DTI ,_X___ DTt-_*_____ TRO + T -- L 24 - 1.- K'bD10 1B. TRAVO 1 K * DTI 24 19. When DTI = DlTO DT 576 TRO + 24 K' DT ' /TRI - TRO J TRAVO = _ - 576 -48 K DT 416 576 T1 + 214 K DT ,/TRo - Tmi 7 20. TRAVI 576 - 48 K 'DT 21. Waiting Time per Meet: K - ST (I) + WT (J) DETERMINATIN OF p gUIP T1 REQUIREMBUTS 22. Car Block Time: TBH (I) - TIU (I) + TRAVO + Y (I) 23. No. of Sets of Cars: AN'(I) - DT TBC (I) RoUnded to next whiole number 24 211. TotLl. No. of Type I Cars Required: ANo(i) = ANT(I) * CA1s (I) /T + CARRF (I)7 Rounded to next whole number 25. Locomotive Block Time: T13L - TRAVO + YTL 26. No. of Sets of Locomotives: STLOCS - DT TBL 24 27. Totftl No. of Locanotives: ThCCJOS STLOCSe TNL * C * RFLOC 7 4- 17 - OIPERA'TING COST CAIClULATIONS 28. Total No. of Train Miles .per season: TRAMIL = DIT - DIS * DAYS 2,. Tot a1 No. of Cai' Miles: CARPIL = TNCARS * TRAMIL 30. Total No. of Loco. Miles TLOCML = TNL * TRAML 31. Tota"l Gross Tons TCTN '- DT *DAYS ; CARS (I) * W (I) + P (I) * VLOL)FC (I) 1=1 32. Total Locomotive Depreciation Cost: DEPRLC 5 DAYS /TLOCOS * CSTLOC (LT) * CRFL(LT) 7 * DFAC 310 DFAC TBL 214 33. Total Depreciation Cost, of Type I Car: DEPRC(I) DAYS /140(I) CARCST(I) CRF(I) 7 * DFAC(I) 310 DFAC(I) TBC(I2 214 - h8 - 34. Toti,l Maintenance Cost of Equipment for Time Period - less Locomotives: CA(1)T Y). S + B(1). CAifIIL 7 310 A ) 35. Totail Maintenance Cost of Locomotives: .JLOCMT nrA(2) DAYS + B(2) 7 oCOS L310 TLOCOS 36e Totkl Roadway Maintenance Cfost: 'IZAYMT - DIS . /A(3) . DAYS + B(3) TV, -7 * ADT(ISW) 310 ADT 37. Tot.,l Coat of Train Operating Crews: JRUCST TRAML B(4) 38. Total Cost of Fuel Consutptiona FUST =TRAO I DAYS DT- FM(L1T) B(5) *HP(LT) TtL 39. TotAl Cost of Lubricating Oils: OILCST FULCST * B(6) OR * B(5) 40. Total Coat of ,asic System: BASE - CAKlT + SLOCMT + WAYNT + CRUCST+ FULCST + OIL.CIT 41. Traffic Costs: TRACST BC) BASE l2. Overhead Cost: OVNCST - B(8) BASE - )49 - 1l3. Total Cost of Operation, Maintenance, Overhead, and Traffic: TOEIT - BASE + OVIICST + TRACST 41i. Total Cos t of Rail Transport for Type I Covnmodity: TOE( I) /-TOEMT + DEPRIL 7 + DEPRC(I)