Vehicle operating cost equations are disaggregated by vehicle type (small auto, medium/large auto, 4-tire trucks, 6-tire trucks, 3+ axle single-unit trucks, 3-4 axle combination trucks, and 5+ axle combination trucks) and by cost component (fuel, oil, tires, maintenance, and depreciation), under constant speed conditions. Also, additional operating costs due to speed variability are provided for all seven vehicle types and all five cost components, and additional operating costs due to horizontal curvature are provided for all seven vehicle types for three of the cost components (fuel, tire wear, and maintenance). Finally, a set of pavement condition adjustment factors to constant-speed operating costs are generated for each of the five cost components (fuel and oil are combined in one equation) as functions of pavement surface quality (PSR).
The computations for the operating cost components in HERS are based on the report "Vehicle Operating Costs, Fuel Consumption, and Pavement Type and Condition Factors", by J.P. Zaniewski, et. al., Texas Research and Development Foundation, June 1982. This report was prepared for the U. S. Department of Transportation, Federal Highways Administration.
In the Zaniewski report, operating costs are listed in tables in Appendix B. There are three categories of tables matching the HERS categories: constant-speed operating costs; excess cost due to speed change cycles; and excess costs due to horizontal curvature. The Zaniewski tables for constant-speed operating costs are given as a matrix of speed in miles per hour and gradient. The miles per hour are given from 5 to 70 in increments of 5-m.p.h. The gradient is given from −8% to 8% in increments of 1%.
The tables for excess cost due to horizontal curvature are organized as a matrix of degrees of curvature (1°, 2°… 6°, 8°, 10°… 20°, 25°, 30°) and speed in miles per hour (5 to 70 in 5-m.p.h. increments).
The Zaniewski data were scanned and converted to spreadsheet form. Some corrections were applied where it appeared that the original data were misleading. In two cases, data from the Zaniewski report demonstrated constant-speed fuel consumption of 0.0 over a broad range of gradient and speed. In these cases, data from alternate sources were used in place of the Zaniewski data. These sources were P. J. Claffey and Associates, "Running Costs of Motor Vehicles as Affected by Road Design and Traffic," NCHRP Report 111, Highway Research Board, National Research Council, Division of Engineering, 1971; and Daniels, C. Vehicle Operating Costs in Transportation Studies, E.S.U Technical Series No. 1, London: Spencer House, 1974. Both these sources were referenced by the Zaniewski report.
For constant-speed operating costs, the data between gradients of −3% and 3% (inclusive) are considered important. Speeds of up to 90 miles per hour are also important, and are extrapolated from existing data. Data for speeds of 2 miles per hour are also extrapolated.
For excess cost due to curvature, only speed/curvature settings below the value of VCURVE (Equation 5.39) are considered important. In some cases, at a low degree of curvature, data must be extrapolated to 90-m.p.h.
An analysis of the operating cost equations of the December 2000 version of HERS revealed discontinuities within some of the equations. As a result, many of the operating cost equations have been revised to provide better accuracy and to eliminate the discontinuities within the constant-speed operating cost equations. The equations for excess cost due to curvature were updated as well to establish complete coverage of the equations, thus eliminating the practice of interpolating values obtained from a look-up table.
Table E-1 displays the complete array of operating cost equations, and indicates which constant-speed and excess cost due to curvature equations were updated.
Existing constant-speed operating costs equations were examined graphically within the region of interest (−3% to 3% gradient, 2-90 m.p.h.) to look for discontinuity or other forms of error (e.g. values less than 0; arcing towards infinity, especially in the extremes). The results were also compared, graphically, to the source data. If the results show a noticeable discontinuity or a poor resemblance to the source data, then the equations for that component were updated. The graphical examination used gradient increments of 0.25% between the range of −3% to 3%, and increments of 1- m.p.h. between 2- and 90-m.p.h. Gradient ranges of between −8% to −3% and 3% to 8% were also examined for erratic behavior, though this examination was not as exacting as within the region of interest.
In the case of excess operating costs due to curvature, the previously equations applied to cases of speeds of greater than or equal to 55-m.p.h. New equations were generated for the complete region of interest.
Microsoft Excel was used for graphic display of the data to examine for discontinuity and to compare, graphically, against the original data. Curves were also segmented or re-segmented in spreadsheets (different equations may be used for different portions of the speed or gradient, and segmentation may have been increased or, more often, simplified).
Data from the spreadsheets were then read by a software package called ‘TableCurve 3D', by SPSS. TableCurve produces a list of equations to predict the output based on the two input variables (gradient and speed). The equations are ranked by adjusted r^{2} score. The first pass attempts to find a reasonable fit with a maximum of five terms. If a good fit is not found, then the term count is stepped until either a reasonable fit is found or that it becomes apparent that resegmenting is necessary. Final equations were tested for continuity and conformity to the original data.
Component | Vehicle Type | ||||||
---|---|---|---|---|---|---|---|
Small Auto | Med/Large Auto | 4-Tire Truck | 6-Tire Truck | 3+ Axle Single-Unit Truck | 3-4 Axle Combo Unit Truck | 5+ Axle Combo Unit Truck | |
♦ = equation updated | |||||||
Constant-Speed Fuel Consumption | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ |
Constant-Speed Oil Consumption | ♦ | ♦ | ♦ | ||||
Constant-Speed Tire Wear | ♦ | ♦ | |||||
Constant-Speed Maintenance and Repair | ♦ | ♦ | ♦ | ||||
Constant-Speed Depreciation | |||||||
Speed Variability Fuel Consumption | |||||||
Speed Variability Oil Consumption | |||||||
Speed Variability Tire Wear | |||||||
Speed Variability Maintenance and Repair | |||||||
Speed Variability Depreciation | |||||||
Curvature Fuel Consumption | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ |
Curvature Tire Wear | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ |
Curvature Maintenance and Repair | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ | ♦ |
For reasons noted above, the data from the Zaniewski report were not used directly for constant-speed fuel consumption (CSFC) for 3-4 axle combination unit trucks and 5+ axle combination unit trucks. Data from the Claffey study, adjusted to scale, were used for 3-4 axle CU trucks. It should be noted that the Zaniewski data are consistent with the Claffey data at steep uphill gradients (GR ≥ 3) across the range of speed, and at lesser gradients up to 30 m.p.h.
The Zaniewski report states that the data for 3-S2 semi (5+ axle CU) trucks were extrapolated from 2-S2 semi (3+ axle CU) trucks, yet the report does not state the method applied for this extrapolation. For the HERS equations, the following method was applied to obtain constant-speed fuel consumption equations for 5+ axle CU trucks:
The new data tables for both 3-4 Axle CU trucks and 5+ axle CU trucks were then rendered using Microsoft Excel and processed using TableCurve, as shown above.
The equations below are grouped by vehicle type, then by component. Equations are typically segmented, and the conditions to define the range of the segments are given along with the equation for that segment. The tables are presented in the following order:
Within each vehicle type, equations are presented in the order shown in Table E-1.
The list below gives the variable names used in the equations:
AES | = | average effective speed |
---|---|---|
GR | = | grade (in percent) |
CSMAX | = | maximum speed during speed change cycle |
DCA | = | degrees of curvature |
CSFC | = | constant-speed fuel consumption (gallons/1000 miles) |
CSOC | = | constant-speed oil consumption (quarts/1000 miles) |
CSTW | = | constant-speed tire wear (% worn/1000 miles) |
CSMR | = | constant-speed maintenance and repair (% avg. cost/1000 miles) |
CSVD | = | constant-speed depreciation (% new price/1000 miles) |
PCAFOC | = | pavement condition adjustment factor for oil consumption |
PCAFTW | = | pavement condition adjustment factor for tire wear |
PCAFMR | = | pavement condition adjustment factor for maintenance and repair |
PCAFVD | = | pavement condition adjustment factor for depreciation expenses |
SCCFC | = | excess fuel consumption for speed change cycles (gallons/1000 cycles) |
SCCOC | = | excess oil consumption for speed change cycles (quarts/1000 cycles) |
SCCTW | = | excess tire wear for speed change cycles (% worn/1000 cycles) |
SCCMR | = | excess maintenance and repair for speed change cycles (% average cost/1000 cycles) |
SCCD | = | excess depreciation for speed change cycles (% new price/1000 cycles) |
CFC | = | excess fuel consumption due to curves (gallons/1000 vehicle miles) |
CTW | = | excess tire wear due to curves (% worn/1000 vehicle miles) |
CMR | = | excess maintenance and repair due to curves (% average cost/1000 vehicle miles) |
PSR | = | pavement serviceability rating |
1 | Condition | GR ≥ 0 |
---|---|---|
Equation | CSFC = 100.82 − 4.9713 × AES + 0.11148 × AES^{2} − 0.0011161 × AES^{3} + 5.1089e−06 × AES4 + 3.0947 × GR | |
2 | Condition | GR < 0 and AES ≤ 40 |
Equation | CSFC = (91.045 − 4.0552×AES + 0.060972×AES^{2} + 4.0504×GR + 0.4227×GR^{2})/(1 − 0.014068×AES + 0.0004774×AES^{2}−0.045957×GR + 0.0054245×GR^{2}) | |
3 | Condition | GR < 0 and AES > 40 |
Equation | CSFC = 23.373 + 3.6374×GR + 0.21681×GR^{2} + (72.562/(1 + exp(−((AES − 81.639)/7.4605)))) |
1 | Condition | GR > 0 and AES < 55 |
---|---|---|
Equation | CSOC = exp(2.7835 − 0.79034×ln(AES) − 1.1346/(AES^{(1.5)}) + 0.65342×(GR^{(0.5)})) | |
2 | Condition | GR ≥ 0 and 55 ≤ AES < 70 |
Equation | CSOC = −170.4 + 34.02×ln(AES) + 1939/AES + 0.4747×GR − 0.003296×AES×GR | |
3 | Condition | GR ≥ 0 and AES ≥ 70 |
Equation | CSOC = −170.4 + 34.02×ln(AES) + 1939/AES+0.27×GR | |
4 | Condition | GR ≤ 0 and AES < 55 |
Equation | CSOC = 1.0435 + (327.89/((1 + (((AES + 7.1977)/3.0141)^{2})) × (1 + (((GR + 8.0484)/2.8984)^{2})))) | |
5 | Condition | Otherwise |
Equation | CSOC = −170.4+34.02×ln(AES)+1939/AES |
1 | Condition | GR ≥ 2.5 and AES < 55 |
---|---|---|
Equation | CSTW=exp(−2.55+0.0001621×AES^{2}+0.01441×AES+1.473×ln(GR)−0.001638×AES×GR) | |
2 | Condition | GR ≥ 2.5 and AES ≥ 55 |
Equation | CSTW=1.314+0.000733×AES^{2}−0.05758×AES+0.01514×GR^{2} +0.003997×AES×GR | |
3 | Condition | (0 < GR < 2.5 and AES < 15) or (−AES/20 < GR < 2.5 and AES ≥ 15) |
Equation | CSTW=0.1959+2.51×10^{−6}×AES^{3}−0.0352×ln(AES)+0.01754×GR^{2}+0.00348×AES×GR | |
4 | Condition | (−1.5 < GR ≤ 0 and AES < 15) or (−AES/10 < GR ≤ −AES/20 and AES ≥ 15) |
Equation | CSTW=0.0604+2.92×10^{−8}×AES^{4}+0.0000796×AES^{2}+0.0274×GR^{2}+0.074×GR+0.0000568×AES^{2}×GR | |
5 | Condition | otherwise |
Equation | CSTW=exp(−5.39−0.000895×AES_{2}+0.0962×GR+2.83×ln(−GR)−0.00397×AES×GR) |
1 | Condition | GR ≥ 0 |
---|---|---|
Equation | CSMR=48.3+0.00865×AES^{2}+0.0516×AES×GR | |
2 | Condition | (−1.5 ≤ GR < 0 and AES ≤ 25) or (GR < 0 and 25 < AES < 55 and AES ≥ −12.2×GR+4) |
Equation | CSMR=45.1+0.00582×AES^{2}+0.23×AES+0.0502×AES×GR | |
3 | Condition | (GR < −1.5 and AES ≤ 25) or (GR < 0 and 25 < AES < 55 and AES < −12.2×GR+4) |
Equation | CSMR = −5.83−0.01932×AES^{2}−23.4×GR | |
4 | Condition | −0.14×AES+3.6 < GR < 0 and AES ≥ 55 |
Equation | CSMR=73.35+0.01397×AES^{2}−0.7398×AES+0.04994×AES×GR | |
5 | Condition | otherwise |
Equation | CSMR=4.27−0.0208×AES^{2}−23.63×GR |
1 | Condition | all |
---|---|---|
Equation | CSVD = 2.2+0.001596×AES−0.38×ln(AES) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCFC=0.00424×CSMAX^{3} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCFC=0.04547+0.08559×CSMAX+3677×10^{−8}×CSMAX^{3} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCOC=0.00004×CSMAX^{3} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCOC=0.000879+0.000934×CSMAX−1612×10^{−8}×CSMAX^{2}+193×10^{−9}×CSMAX^{3} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCTW=0.0008×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCTW=exp(−7.112+1.999×ln(CSMAX)− 8384×10^{−8}×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCMR=0.0016×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCMR=exp(−6.284+0.006889×CSMAX+1.881×ln(CSMAX) −7388×10^{−8}×CSMAX^{2}) |
1 | Condition | CSMAX < 60 |
---|---|---|
Equation | SCCD=0.0004×CSMAX | |
2 | Condition | CSMAX ≥ 60 |
Equation | SCCD=exp(−4.327+0.000168×CSMAX^{2}) |
1 | Condition | AES ≥ (1/(0.001147 + 0.008062×DCA^{(0.5)} + 0.008862/DCA)) |
---|---|---|
Equation | CFC = MAX(0, 18387.7115×(1/(1 + (DCA/39.459)^{(−3.0419)}))× 1/(1 + (AES/104.38)^{(−6.2768)})) | |
2 | Condition | DCA ≥ 6 and AES > 10 and AES ≤ (−0.6807×DCA + 30.944) |
Equation | CFC = MAX(0, −0.046905 + 0.95904×LN(DCA) − 0.02218×AES − 0.17662×(LN(DCA))^{2} + 0.000957×AES^{2} − 0.021388×AES×LN(DCA)) | |
3 | Condition | (DCA ≥ 6 and AES ≤ 10) or (DCA < 6 and AES ≤ 25) |
Equation | CFC = MAX(0, −1.9503 + 1.0112×LN(DCA) + 0.31328×AES − 0.16763×(LN(DCA))^{2} − 0.012903×AES^{2} − 0.031507×AES×LN(DCA)) | |
4 | Condition | Otherwise |
Equation | CFC=0 |
1 | Condition | (DCA≥16 and AES ≥ (−0.031746×DCA^{2} + 0.74603×DCA + 21.19)) or (16 > DCA ≥ 6 and AES ≥ (45 − 1.9167×DCA + 0.041667×DCA^{2})) or (DCA < 6 and AES ≥ (−442.3 + 2959.4/DCA^{(0.5)} − 6735.1/DCA + 6810.6/DCA^{(1.5)} − 2582.5/DCA^{2})) |
---|---|---|
Equation | CTW = MAX(0, 351887 × EXP(−EXP(−(DCA − 51.408)/19.756) − (DCA−51.408)/19.756 + 1) × EXP(−EXP(−(AES − 122.22)/38.201) − (AES−122.22)/38.201 + 1)) | |
2 | Condition | (DCA ≥ 16 and AES < (−0.031746×DCA^{2} +0.74603×DCA + 21.19)) or (16 > DCA ≥ 8 and AES < (45 − 1.9167×DCA + 0.041667×DCA^{2})) |
Equation | CTW = MAX(0, −21.508 + 13.474×LN(DCA) + 19.67×LN(AES) − 1.5206×(LN(DCA))^{2} − 3.5315×(LN(AES))2 − 3.6298×LN(DCA)×LN(AES))^{3} | |
3 | Condition | (8 > DCA ≥ 6 and AES < (45 − 1.9167×DCA + 0.041667×DCA^{2})) or (DCA < 6 and AES < (−442.3 + 2959.4/DCA^{(0.5)} − 6735.1/DCA + 6810.6/DCA^{(1.5)} − 2582.5/DCA^{2}) |
Equation | CTW = MAX(0, −3.3578 + 3.5095×DCA + 0.080638×AES − 0.18665×DCA^{2}−0.00054297×AES^{2} − 0.061173×DCA×AES) |
1 | Condition | (DCA > 10 and AES ≥ −0.65×DCA + 34.5) or (DCA < 10 and AES ≥ −2.4444×DCA + 52.444) |
---|---|---|
Equation | CMR = MAX(0, EXP(−19.624 − 1.0614×DCA^{(0.5)}×LN(DCA) + 6.4853×DCA^{(0.5)} +0.033374×AES^{(1.5)} − 0.00046284×AES^{2}×LN(AES))) | |
2 | Condition | 5 ≤ DCA ≤ 10 and (−1×DCA + 20) ≤ AES ≤ (−1×DCA + 25) |
Equation | CMR = 0.1 | |
3 | Condition | Otherwise |
Equation | CMR = 0 |
1 | Condition | AES ≤ 40 |
---|---|---|
Equation | CSFC = 88.556 − 3.384×AES + 1.7375×GR + 0.053161×AES^{2} + 0.18052×GR^{2} + 0.076354×AES×GR | |
2 | Condition | AES > 40 |
Equation | CSFC = 85.255 − 2.2399×AES + 2.7478×GR + 0.028615×AES^{2} + 0.041389×GR^{2} + 0.046242×AES×GR |
1 | Condition | GR > 0 and AES < 55 |
---|---|---|
Equation | CSOC = exp(−1.5698 + 9.8768/AES^{(0.5)} − 7.6187 /AES + 0.70702×GR^{(0.5)}) | |
2 | Condition | GR ≥ 0 and 55 ≤ AES < 70 |
Equation | CSOC = 9.5234−0.29873×AES +0.0026913×AES^{2} + 0.28997×GR^{1.00129} | |
3 | Condition | GR ≥ 0 and AES ≥ 70 |
Equation | CSOC = −173.3 + 34.6×ln(AES) + 1973/AES + 0.29×GR | |
4 | Condition | −3 ≤ GR ≤ 0 and 15 ≤ AES < 55 |
Equation | CSOC = 0.42295 + 0.35839×AES − 0.029984×AES^{2} + 0.0010392×AES^{3} −0.000016196×AES^{4} + 9.3539e−08×AES^{5} − 0.0024×GR | |
5 | Condition | GR < −3 and 15 ≤ AES < 55 |
Equation | CSOC = 1/(−0.18739 + 0.0014953×AES^{(1.5)} − 1.7461/GR) | |
6 | Condition | GR ≤ 0 and AES < 15 |
Equation | CSOC = exp(1.7713 − 0.12178×AES^{(0.5)}×ln(AES) + 0.14636×GR + 0.11002×GR^{2} + 0.0082804×GR^{3}) | |
7 | Condition | Otherwise |
Equation | CSOC = −173.3 + 34.6×ln(AES) + 1973/AES |
1 | Condition | GR ≥ 2.5 and AES < 55 |
---|---|---|
Equation | CSTW=exp(−2.39+0.0001564×AES^{2}+0.01367×AES+1.475×ln(GR)−0.001586×AES×GR) | |
2 | Condition | (0 < GR < 2.5 and AES < 15) or (−AES/20 ≥ GR < 2.5 and 15 ≥ AES < 55) |
Equation | CSTW=0.229+2.65×10^{−6}×AES^{3}−0.0403×ln(AES)+0.0214×GR^{2}+0.00392×AES×GR | |
3 | Condition | (−1.5 < GR ≥ 0 and AES < 15) or (−AES/10 < GR < −AES/20 and 15 ≥ AES < 55) |
Equation | CSTW=0.08+3.0×10^{−6}×AES^{3}+0.029×GR^{2}+0.0828×GR+0.000056×AES^{2}×GR | |
4 | Condition | (GR ≥ −1.5 and AES < 15) or (GR ≥ −AES/10 and 15 ≥ AES < 55) |
Equation | CSTW=exp(−5.22−0.000771×AES^{2}+0.0843×GR+2.81×ln(−GR)−0.00323×AES×GR) | |
5 | Condition | GR ≥ 0.5 and AES ≥ 55 |
Equation | CSTW=1.318+0.000743×AES^{2}−0.05661×AES+0.01941×GR^{2}+0.00417×AES×GR | |
6 | Condition | (−AES/10+1 < GR < 0.5 and AES ≥ 55) or (GR < 0.5 and AES ≥ 80) |
Equation | CSTW=−0.2022+0.000237×AES^{2}+0.0213×GR^{2}−1.0322×GR+0.3099×ln(AES)×GR | |
7 | Condition | otherwise |
Equation | CSTW=−0.2613+0.000164×AES^{2}+0.02065×GR^{2}+0.005452×AES×GR−0.03975×ln(AES)×GR |
1 | Condition | GR≥0 |
---|---|---|
Equation | CSMR=48.4+0.00867×AES^{2}+0.0577×AES×GR | |
2 | Condition | (−1.5 ≤ GR < 0 and AES ≤ 25) or (GR < 0 and −12.2×GR+4 ≤ AES and 25 < AES < 55) |
Equation | CSMR=45.19+0.00584×AES^{2}+0.229×AES+0.0562×AES×GR | |
3 | Condition | (GR < −1.5 and AES ≤ 25) or (GR < 0 and −12.2×GR+4 > AES and 25 < AES < 55) |
Equation | CSMR=−6.67−0.018×AES^{2}−23.4×GR | |
4 | Condition | −0.14×AES+3.6 < GR < 0 and AES ≥ 55 |
Equation | CSMR=72.46+0.01373×AES^{2}−0.7081×AES+0.05597×AES×GR | |
5 | Condition | otherwise |
Equation | CSMR=−5.415−0.01912×AES^{2}−23.51×GR |
1 | Condition | all |
---|---|---|
Equation | CSVD=1.725+0.001892×AES−0.311×ln(AES) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCFC=0.008×CSMAX^{3} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCFC=0.03401+0.1902×CSMAX+4491×10^{−8}×CSMAX^{3} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCOC=0.00004×CSMAX^{3} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCOC=0.000801+0.000869×CSMAX−1617×10−8×CSMAX^{2}+197×10^{−8}×CSMAX^{3} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCTW=0.0012×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCTW=exp(−6.64+1.947×ln(CSMAX)−9909×10^{−8}×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCMR=0.0016×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCMR=exp(−6.277+0.007347×CSMAX+1.876×ln(CSMAX)−7275×10^{−8}×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCD=0.0004×CSMAX | |
2 | Condition | 5 ≤ CSMAX < 50 |
Equation | SCCD=0.001+0.0002×CSMAX | |
3 | Condition | CSMAX ≥ 50 |
Equation | SCCD=exp(−4.973+0.000228×CSMAX^{2}) |
1 | Condition | DCA ≤ 5 and AES ≤ 1/(−0.0137 + 0.0123×DCA^{0.5} + 0.0299/DCA^{0.5}) |
---|---|---|
Equation | CFC = MAX(0, −0.34211 + 0.28291×DCA + 0.014828×AES − 0.016971×DCA^{2} − 0.00024465×AES^{2} − 0.0047869×DCA×AES) | |
2 | Condition | DCA > 5 and AES ≤ 1/(−0.0137 + 0.0123×DCA^{0.5} + 0.0299/DCA^{0.5}) |
Equation | CFC = MAX(0, −0.79434 + 1.1403×LN(DCA) + 0.052408×AES − 0.1933×(LN(DCA))^{2} − 0.00060403×AES^{2} − 0.028889×AES×LN(DCA)) | |
3 | Condition | AES > 1/(−0.0137 + 0.0123×DCA^{0.5} + 0.0299/DCA^{0.5}) |
Equation | CFC = MAX(0, EXP(−18.864 − 0.02183×DCA^{(1.5)} + 2.6113×DCA^{(0.5)} + 1.80792×AES^{(0.5)})) |
1 | Condition | (DCA ≥ 16 and AES ≥ (−0.031746×DCA^{2} +0.74603×DCA +21.19)) or (6 ≤ DCA < 16 and AES ≥(45 − 1.9167×DCA + 0.041667×DCA^{2})) or (DCA < 6 and AES ≥ (−442.3 + 2959.4/DCA^{(0.5)} − 6735.1/DCA + 6810.6/DCA^{(1.5)} − 2582.5/DCA^{2})) |
---|---|---|
Equation | CTW = MAX(0, 519464×EXP( −EXP( −(DCA − 48.665)/18.647) − (DCA − 48.665)/18.647 + 1) × EXP( −EXP( −(AES − 127.84)/39.862) − (AES − 127.84)/39.862 + 1)) | |
2 | Condition | (DCA ≥ 16 and AES < (−0.031746×DCA^{2} +0.74603×DCA +21.19)) or (6 ≤ DCA < 16 and AES < (45 − 1.9167×DCA + 0.041667×DCA^{2})) |
Equation | CTW = MAX(0, −31.7 + 20.767×LN(DCA) + 22.783×LN(AES) − 2.5841×(LN(DCA))^{2} − 3.9522×(LN(AES))^{2} − 4.4831×LN(DCA)×LN(AES)) | |
3 | Condition | DCA < 6 and AES < (−442.3 + 2959.4/DCA^{(0.5)} − 6735.1/DCA + 6810.6/DCA^{(1.5)} − 2582.5/DCA^{2}) |
Equation | CTW = MAX(0, −4.4955 + 4.542×DCA + 0.088792×AES − 0.27253×DCA^{2} − 0.00042329×AES^{2} − 0.07399×DCA×AES) |
1 | Condition | (DCA > 12 and AES ≥ (−0.5×DCA + 30))
or (DCA < 12 and AES ≥ (−2.3636×DCA + 52.364)) |
---|---|---|
Equation | CMR = MAX(0, EXP(−37.927 + 3.2935×LN(DCA) + 1.8096/DCA + 7.8477×LN(AES))) | |
2 | Condition | 5 ≤ DCA ≤ 10 and (−1×DCA + 20) ≤ AES ≤ (−1×DCA − 25) |
Equation | CMR = 0.1 | |
3 | Condition | Otherwise |
Equation | CMR = 0 |
1 | Condition | GR ≥ 0 and 20 < AES < 55 |
---|---|---|
Equation | CSFC = 115.41 − 3.6397×AES + 7.0832×GR + 0.050662×AES^{2} − 0.34401×GR^{2} + 0.096956×AES×GR | |
2 | Condition | GR ≥ 0 and AES ≤ 20 |
Equation | CSFC = 120.7 + −5.0201×AES + 0.1088×AES^{2} + 9.8816×GR − 1.3755×GR^{2} + 0.11582×GR^{3} | |
3 | Condition | GR < 0 and AES ≤ 10 |
Equation | CSFC = 161.2 − 6.622×AES − 87.758×ln(AES)/AES − 1.0889×GR^{2} − 0.13217×GR^{3} | |
4 | Condition | GR < 0 and 10 < AES ≤ 20 |
Equation | CSFC = 106.31 − 2.7456×AES + 5.0147×GR − 0.001281×AES^{2} + 0.94555×GR^{2} + 0.19499×AES×GR | |
5 | Condition | GR < 0 and 20 < AES < 55 |
Equation | CSFC = 351.5 − 184.42×ln(AES) + 0.71838×GR + 28.297×(ln(AES))^{2} + 1.0105×GR^{2} + 2.8947×GR×ln(AES) | |
6 | Condition | GR ≥ 1.5 and AES ≥ 55 |
Equation | CSFC = 110.4 + 0.000249×AES^{3} − 18.93×ln(AES) + 8.06×GR | |
7 | Condition | −2.5 ≤ GR < 1.5 and AES ≥ 55 |
Equation | CSFC = (28.77 + 0.183655×AES + 3.34032×GR) / (1 − 0.0074966×AES − 0.049703×GR) | |
8 | Condition | Otherwise |
Equation | CSFC = exp(2.784 + 0.02014×AES + 0.06881×GR) |
1 | Condition | Condition GR > 0 and AES < 50 |
---|---|---|
Equation | CSOC=exp(2.47−0.604×ln(AES)−0.00994×GR^{2}+0.277×GR−0.001248×AES×GR) | |
2 | Condition | GR > 0 and 50 ≤ AES ≤ 70 |
Equation | CSOC=16.41+0.004424×AES^{2}−0.5255×AES+1.296×GR−0.2664×ln(AES)×GR | |
3 | Condition | GR > 0 and AES > 70 |
Equation | CSOC=16.41+0.004424×AES^{2}−0.5255×AES+0.19×GR | |
4 | Condition | min(−3.5, −AES/6.0) < GR≤ 0 and AES < 50 |
Equation | CSOC=8.45+0.0000352×AES^{3}−0.00567×AES^{2}+0.370×AES−4.12×ln(AES) | |
5 | Condition | GR < min(−3.5, −AES/6.0) and AES < 50 |
Equation | CSOC=exp(0.92−0.000295×AES^{2}−0.751×ln(AES) −0.0269×GR^{2}−0.584×GR) | |
6 | Condition | otherwise |
Equation | CSOC=16.41+0.004424×AES^{2}−0.5255×AES |
1 | Condition | GR ≥ 2.5 and AES < 55 |
---|---|---|
Equation | CSTW = EXP(−2.08 + 0.0001517×AES^{2} + 0.012×AES + 1.367×LN(GR) − 0.001389×AES×GR) | |
2 | Condition | (0 < GR < 2.5 and AES < 15) or (−AES/20 < GR < 2.5 and 15 ≤ AES < 55) |
Equation | CSTW = 0.297 + 2.9×10^{(−6)}×AES^{3} − 0.0421×LN(AES) + 0.0234×GR^{2} + 0.00429×AES×GR | |
3 | Condition | (−2.5 < GR ≤ 0 and AES < 15) or (−AES/10 < GR ≤ −AES/20 and 15 ≤ AES < 55) |
Equation | CSTW = 0.1294 + 3.64×10^{(−6)}×AES^{3} + 0.0324×GR^{2} + 0.1085×GR + 0.0000631×AES^{2}×GR | |
4 | Condition | (GR ≤ −2.5 and AES < 15) or (GR < −AES/10 and 15 ≤ AES < 55) |
Equation | CSTW = EXP(−5.45 − 4.13×10^{(−6)}×AES^{3} − 0.01377×AES + 2.79×LN(−GR)) | |
5 | Condition | GR ≥ 0.5 and AES ≥ 55 |
Equation | CSTW = 1.365 + 0.000736×AES^{2} − 0.05471×AES + 0.0197×GR^{2} + 0.004395×AES×GR | |
6 | Condition | ((−AES/10+1) < GR < 0.5 and AES ≥ 55)
or (GR < 0.5 and AES ≥ 80) |
Equation | CSTW = ABS(−0.1554 + 0.000258×AES^{2} + 0.0205×GR^{2} − 0.05138×GR + 0.005058×AES×GR) | |
7 | Condition | Otherwise |
Equation | CSTW = MAX(0.01, −0.2177 + 0.000208×AES^{2} + 0.02376×GR^{2} + 0.005895×AES×GR − 0.03288×LN(AES)×GR) |
1 | Condition | GR ≥ 0 |
---|---|---|
Equation | CSMR=49.2+0.00881×AES^{2}+0.0545×AES×GR | |
2 | Condition | (−1.5 ≤ GR < 0 and AES ≤ 20) or (GR < 0 and 20 < AES < 55 and AES≥−10×GR+6) |
Equation | CSMR=46.0+0.00595×AES^{2}+0.231×AES+0.0531×AES×GR | |
3 | Condition | (GR < −1.5 and AES ≤ 20) or (GR < 0 and 20 < AES < 55 and AES < −10×GR+6) |
Equation | CSMR=−12.43−0.019×AES^{2}−23.5×GR | |
4 | Condition | (GR <0 and AES ≥ 55 and GR > −0.1×AES+0.75) or (GR < 0 and AES>70) |
Equation | CSMR=72.36+0.01373×AES^{2}−0.6841×AES+0.0532×AES×GR | |
5 | Condition | otherwise |
Equation | CSMR=−13.83−0.0197×AES^{2}−24.01×GR |
1 | Condition | all |
---|---|---|
Equation | CSVD = 0.742+0.000589×AES−0.1307×ln(AES) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCFC=0.00904×CSMAX^{3} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCFC=0.8137+0.1576×CSMAX+7327×10^{−8}×CSMAX^{3} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCOC=0.0002×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCOC=exp(−6.242+0.5935×ln(CSMAX)+0.000131×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCTW=0.0012×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCTW=exp(−6.568+1.906×ln(CSMAX)−7502×10^{−8}×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCMR=0.0016×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCMR=exp(−6.39+1.958×ln(CSMAX)−1781×10^{−8}×CSMAX^{2}) |
1 | Condition | CSMAX < 60 |
---|---|---|
Equation | SCCD=0.0002×CSMAX | |
2 | Condition | CSMAX ≥ 60 |
Equation | SCCD=exp(−5.0007+0.000162×CSMAX^{2}) |
1 | Condition | (DCA < 6 and AES ≥ (−0.5682×DCA^{2} + 0.75×DCA + 55.818)) or (DCA ≥ 6 and AES ≥ (−0.0055×DCA^{2} − 0.7634×DCA + 43.597)) |
---|---|---|
Equation | CFC = MAX(0, EXP(779.63 − 1.2743×DCA + 3.1889×DCA^{(0.5)}×LN(DCA) − 2.9306×DCA^{(0.5)} − 25.106×AES^{(0.5)} − 10108.5/AES^{(0.5)} + 10588.5×LN(AES)/AES)) | |
2 | Condition | (DCA ≥ 10 and AES ≤ (57.993 + 1.1162×DCA − 13.963×DCA^{0.5})) or (8 ≤ DCA < 10 and AES ≤ 25) |
Equation | CFC = MAX(0, −0.45381 + 0.98231×LN(DCA) + 0.10049×AES − 0.15×(LN(DCA))^{2} − 0.0011603×AES^{2} − 0.046122×AES×LN(DCA)) | |
3 | Condition | 4 ≤ DCA < 8 and AES ≤ (−2.5×DCA + 45) |
Equation | CFC = MAX(0, −2.0296 + 2.4402×LN(DCA) + 0.087398×AES − 0.50234×(LN(DCA))^{2} − 0.0012841×AES^{2} − 0.036879×AES×LN(DCA)) | |
4 | Condition | (2 ≤ DCA < 4 and AES ≤ 35) or (DCA < 2 and AES ≤ (2.5×DCA + 30)) |
Equation | CFC = MAX(0, EXP(0.0010091 − 5.4673/DCA^{2} − 0.082805×AES + 0.011991×AES^{2} − 0.0018375×AES^{(2.5)})) | |
5 | Condition | Otherwise |
Equation | CFC = 0 |
1 | Condition | (DCA ≥ 16 and AES ≥ (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (6 ≤ DCA < 16 and AES ≥ (35 − 125/DCA + 750/DCA^{2})) or (DCA < 6 and AES ≥ (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3})) |
---|---|---|
Equation | CTW = MAX(0, 450515×EXP( −EXP( −(DCA − 49.07)/18.816) − (DCA − 49.07)/18.816 + 1) × EXP( −EXP( −(AES − 124.84)/38.88) − (AES − 124.84)/38.89 + 1)) | |
2 | Condition | DCA ≤ 16 and AES < (0.02381×DCA^{2} − 1.4524×DCA + 42.143) |
Equation | CTW = MAX(0, −13.126 + 79.095/DCA + 254.26/AES − 39.567/DCA^{2} − 694.97/AES^{2} − 217.62/(DCA×AES)) | |
3 | Condition | (6 ≤ DCA < 16 and AES < (35 − 125/DCA + 750/DCA^{2})) or (DCA < 6 and AES < (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3}) |
Equation | CTW = MAX(0, −2.743 + 3.5215×DCA + 0.077273×AES − 0.16376×DCA^{2} − 0.00069592×AES^{2} − 0.064592×DCA×AES) |
1 | Condition | (DCA ≥ 12 and AES ≥ (−0.45×DCA + 30.4)) or (DCA < 12 and AES ≥ (−2.2727×DCA + 52.273)) |
---|---|---|
Equation | CMR = MAX(0, EXP(594.56 − 0.021279×DCA^{(1.5)} + 2.6656×DCA^{(0.5)} − 19.444×AES^{(0.5)} − 7777/AES^{(0.5)} + 8121.8×LN(AES)/AES)) | |
2 | Condition | (3.5 < DCA < 8.5 and 17.5 ≤ AES < 22.5) or (4.5 < DCA < 10.5 and 12.5 ≤ AES ≤ 17.5) or (7.5 < DCA < 12.5 and 7.5 < AES <= 12.5) |
Equation | CMR = 0.1 | |
3 | Condition | Otherwise |
Equation | CMR = 0 |
1 | Condition | GR ≥ 0 and AES < 55 |
---|---|---|
Equation | CSFC = 298.60 − 13.131×AES + 53.987×GR + 0.30096×AES^{2} − 4.7321×GR^{2} − 0.88407×AES×GR − 0.0020906×AES^{3} + 0.22739×GR^{3} + 0.02875×AES×GR^{2} + 0.0045428×AES^{2}×GR | |
2 | Condition | GR < 0 and AES < 55 |
Equation | CSFC = 273.05 − 9.2427×AES +58.195×GR + 0.14718×AES^{2} + 6.7665×GR^{2} − 1.3785×AES×GR − 0.00046068×AES^{3} + 0.13884×GR^{3} − 0.079555×AES×GR^{2} + 0.012622×AES^{2}×GR | |
3 | Condition | GR ≥ 1.5 and AES ≥ 55 |
Equation | CSFC = 361.11 − 8.1978×AES + 11.186×GR + 0.077607×AES^{2}−0.27665×GR^{2} − 0.035211×AES×GR | |
4 | Condition | GR < 1.5 and AES ≥ 55 |
Equation | CSFC = 101.5 + 0.000186×AES^{3} + 1.102×GR^{2} + 18.22×GR |
1 | Condition | GR > 0 and AES < 55 |
---|---|---|
Equation | CSOC = exp(3.8424 − 0.93964×ln(AES) − 1.7418/AES + 0.80327×GR^{(0.5)}) | |
2 | Condition | GR > 0 and AES ≥ 55 |
Equation | CSOC = 51.76 + 0.002513×AES^{2} − 14.29×ln(AES)+ 0.7485×GR | |
3 | Condition | (−1.5 < GR ≤ 0 and AES < 55) or (−AES/10 ≤ GR ≤ 0 and AES < 55) |
Equation | CSOC = 13.98 + 0.0000603×AES^{3} − 0.00857×AES^{2} + 0.523×AES − 6.17×ln(AES) | |
4 | Condition | GR < −AES/10 and AES ≥ 70 |
Equation | CSOC = exp(1.41 + 0.000519×AES^{2} − 0.0845×AES − 0.0344×GR^{2} − 0.649×GR) | |
5 | Condition | Otherwise |
Equation | CSOC = 51.76 + 0.002513×AES^{2} − 14.29×ln(AES) |
1 | Condition | GR ≥2.5 and AES<55 |
---|---|---|
Equation | CSTW=exp(−1.572+0.0000943×AES^{2}+0.01509×AES+1.65×ln(GR)−0.001535×AES×GR) | |
2 | Condition | GR ≥2.5 and AES ≥ 55 |
Equation | CSTW=2.206+0.001267×AES^{2}−0.09683×AES+0.07733×GR^{2}+0.01096×AES×GR | |
3 | Condition | (0 < GR < 2.5 and AES<15) or (−AES/25 < GR <2.5 and AES≥15) |
Equation | CSTW=0.353+4.5×10^{−6}×AES^{3}−0.0556×ln(AES)+0.0855×GR^{2}+0.01012×AES×GR | |
4 | Condition | (−1.5 < GR ≤ 0 and AES < 15) or (−AES/14 < GR < −AES/25 and AES ≥ 15) |
Equation | CSTW=0.104+5.37×10^{−8}×AES^{4}+0.0001578×AES^{2}+0.1282×GR^{2}+0.222×GR+0.000168×AES^{2}×GR | |
5 | Condition | otherwise |
Equation | CSTW=exp(−3.16−3.35×10^{−6}×AES^{3}−0.0308×AES+2.28×ln(−GR)−0.00377×AES×GR) |
1 | Condition | −4 ≤ GR ≤ −1 and AES > (−1.6667×GR^{3} − 17.5×GR^{2} −70.833×GR −45) and AES < (−1.6667 ×GR^{3} − 17.5×GR^{2} −70.833×GR −40) |
---|---|---|
Equation | CSMR = 1/(0.96223 + 2.3017e−06×AES^{3} − 0.33129×exp(AES/44.4878) + 0.48203/GR − 0.00029083×exp(−GR)) | |
2 | Condition | (GR ≥ −1) or (GR < −1 and AES ≥ (−1.6667 ×GR^{3} − 17.5×GR^{2} −70.833×GR −40)) |
Equation | CSMR = 44.2 + 0.01147×AES^{2} + 0.1462×AES×GR | |
3 | Condition | Otherwise |
Equation | CSMR = −0.722 − 0.00697×AES^{2} − 15.9×GR |
1 | Condition | AES < 55 |
---|---|---|
Equation | CSVD=1.126+0.0028×AES−0.247×ln(AES) | |
2 | Condition | AES ≥ 55 |
Equation | CSVD=0.2006+4.936/AES |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCFC=0.1184×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCFC=3.09+0.02843×CSMAX^{2} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCOC=0.00068×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCOC=exp(−5.069+0.6392×ln(CSMAX)+0.000169×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCTW=0.0016×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCTW=exp(−6.387+1.984×ln(CSMAX)−988×10^{−7}×CSMAX^{2}) |
1 | Condition | CSMAX ≤ 5 |
---|---|---|
Equation | SCCMR=0.0012×CSMAX^{2} | |
2 | Condition | CSMAX>5 |
Equation | SCCMR=exp(−6.427+0.01826×CSMAX+1.758×ln(CSMAX)−0.000103×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCD=0.0004×CSMAX | |
2 | Condition | 5 ≤ CSMAX < 40 |
Equation | SCCD=0.001429+0.000221×CSMAX | |
3 | Condition | CSMAX ≥ 40 |
Equation | SCCD=exp(−4.957+0.000294×CSMAX^{2}) |
1 | Condition | (DCA ≥ 10 and AES ≥ (27.9 − 0.0144×DCA^{2} + 300/DCA^{2})) or (2 ≤ DCA < 10 and AES ≥ (1/(0.0127 + 0.00484×DCA − 0.000675×DCA^{2} + 3.97e−05 × DCA^{3}))) or (DCA < 2 and AES ≥ (1/(0.0286 + 0.00429×DCA − 0.00429×DCA^{2}))) |
---|---|---|
Equation | CFC = MAX(0, EXP(−50.349 − 0.98363×DCA − 0.05974×DCA^{2} + 59.476×EXP(DCA/ 31.649) − 90.158/AES^{(0.5)})) | |
2 | Condition | DCA ≥ 5 and AES ≤ (27.9 − 0.0144 × DCA^{2} + 300/DCA^{2}) |
Equation | CFC = MAX(0, −9.7649 + 7.88×LN(DCA) + 6.036×LN(AES) − 1.0423×(LN(DCA))^{2} − 1.053×(LN(AES))^{2} − 1.464×LN(DCA)×LN(AES)) | |
3 | Condition | 1 < DCA < 5 and AES ≤ (30 + 70/DCA − 100/DCA^{2}) |
Equation | CFC = MAX(0, EXP(1.604 − 4.6423/DCA^{(1.5)} − 0.000062414×AES^{3})) | |
4 | Condition | Otherwise |
Equation | CFC = 0 |
1 | Condition | (DCA ≥ 16 and AES ≥ (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (6 ≤ DCA < 16 and AES ≥ (35 − 125/DCA + 750/DCA^{2})) or (DCA < 6 and AES ≥ (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3})) |
---|---|---|
Equation | CTW = MAX(0, 377675×EXP( −EXP( −(DCA − 51.703)/19.791) −( DCA − 51.703)/19.791 + 1) × EXP( −EXP( −(AES − 120.93)/37.611) − (AES − 120.93)/37.611 + 1)) | |
2 | Condition | (DCA ≥ 16 and AES < (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (6 ≤ DCA < 16 and AES < (35 − 125/DCA + 750/DCA^{2})) |
Equation | CTW = MAX(0, −26.586 + 17.42×LN(DCA) + 19.303×LN(AES) − 2.1482×(LN(DCA))^{2} − 3.3487×(LN(AES))^{2} − 3.81×LN(DCA)×LN(AES)) | |
3 | Condition | DCA < 6 and AES < (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3}) |
Equation | CTW = MAX(0, −4.0066 + 3.8372×DCA + 0.11043×AES − 0.2262×DCA^{2} − 0.0011358×AES^{2} − 0.064529×DCA×AES) |
The fourth equation for 6-Tire Truck excess maintenance and repair due to curves is incremental - the condition is true when certain other conditions are true and the equation adds value to the existing CMR value.
1 | Condition | DCA ≥ 8 and AES ≥ (−0.0038×DCA^{2} − 0.3106×DCA + 27.272) |
---|---|---|
Equation | CMR = MAX(0, EXP(9.6157 + 0.12975×DCA − 157.95/DCA^{2} + 7095.5×EXP(−DCA) − 106.49×LN(AES)/AES)) | |
2 | Condition | DCA < 8 and AES ≥ (−0.625×DCA^{2} + 3.125×DCA + 40) |
Equation | CMR = MAX(0, EXP(−314.6 + 2.5973×DCA×LN(DCA) − 1.4569×DCA^{2} + 0.30227×DCA^{(2.5)} + 2642/LN(AES) − 2565.9/AES^{(0.5)})) | |
3 | Condition | (1 ≤ DCA ≤ 3 and (−10×DCA + 37.5) < AES < (10×DCA + 2.5)) or (3 < DCA ≤ 5 and AES < 32.5) or (5 < DCA < 8 and AES < (0.8333×DCA^{2} − 14.167×DCA +85)) or (DCA ≥ 8 and AES < (−0.0038×DCA^{2} − 0.3106×DCA + 24.5)) |
Equation | CMR = 0.1 | |
4 | Condition | DCA > 4.5 and 12.5 < AES < (−0.35×DCA^{2} + 3.85×DCA + 12) |
Equation | CMR = CMR + 0.1 | |
5 | Condition | Otherwise |
Equation | CMR = 0 |
1 | Condition | Condition GR ≥ 3 and AES ≤ 20 |
---|---|---|
Equation | CSFC = 68.536 + 12.823×AES + 122.45×GR + 0.023896×AES^{2} + 0.36758×GR^{2} − 6.2014×AES×GR | |
2 | Condition | 3 ≥ GR ≥ 0 and AES ≤ 20 |
Equation | CSFC = 254 − 3.0854×AES − 2.177×GR − 0.063346×AES^{2} + 24.848×GR^{2} + 4.3101×AES×GR + 0.0012816×AES^{3} − 1.2432×GR^{3} − 1.6437×AES×GR^{2} + 0.0013556×AES^{2}×GR | |
3 | Condition | GR < 0 and AES ≤ 20 |
Equation | CSFC = (259.66 − 19.925×AES+ 0.49931×AES^{2} − 0.0045651×AES^{3} − 1.5876×GR)/(1 − 0.058535×AES + 0.00077356×AES^{2} − 0.14916×GR + 0.024241×GR^{2}) | |
4 | Condition | GR > 3 and AES > 20 |
Equation | CSFC = 290.45 − 2.598×AES + 25.823×GR + 0.024983×AES^{2} − 2.2654×GR^{2} + 0.21897×AES×GR | |
5 | Condition | 3 ≥ GR ≥ 0 and AES > 20 |
Equation | CSFC = 1208.8 − 586.87×LN(AES) + 80.955×(ln(AES))^{2}+ 93.99×GR − 13.477×GR^{2} | |
6 | Condition | 0 > GR ≥ −3 and AES > 20 |
Equation | CSFC = exp(6.0673 − 0.1139×AES + 0.023622×AES×ln(AES) + 0.79191×GR − 0.022171×GR^{3}) | |
7 | Condition | GR < −3 and AES > 20 |
Equation | CSFC = (−1.3978/(1 + (((AES − 40.215)/−11.403)^{2}))) + (47.024/(1 + (((GR + 0.01611)/5.4338)^{2}))) + (−26.724/(1 + (((AES − 40.215)/−11.403)^{2}))) × (1/(1 + (((GR + 0.01611)/5.4338)^{2}))) |
1 | Condition | Condition GR > 0 and AES<55 |
---|---|---|
Equation | CSOC=exp(4.36+0.00711×AES−0.869×ln(AES)−0.01712×GR^{2}+0.338×GR) | |
2 | Condition | min(−1.5,−AES/12.5) < GR ≤ 0 and AES<55 |
Equation | CSOC=20.2+0.0000724×AES^{3}−0.0103×AES^{2}+0.662×AES−8.52×ln(AES) | |
3 | Condition | GR ≤ min(−1.5,−AES/12.5) and AES < 55 |
Equation | CSOC=exp(1.77+0.00055×AES^{2}−0.0769×AES−0.0343×GR^{2}−0.646×GR) | |
4 | Condition | GR > 0 and AES ≥ 55 |
Equation | CSOC=22.85+0.006514×AES^{2}−0.7188×AES+1.615×GR | |
5 | Condition | (−AES/12.5 ≤ GR ≤ 0 and AES ≥ 55) or (GR ≤0 and AES ≥ 90) |
Equation | CSOC=22.85+0.006514×AES^{2}−0.7188×AES | |
6 | Condition | otherwise |
Equation | CSOC=exp(1.77+0.00055×AES^{2}−0.0769×AES−0.0343×GR^{2}−0.646×GR) |
1 | Condition | Condition GR ≥ 2.5 and AES<55 |
---|---|---|
Equation | CSTW=exp(−1.71+0.0000511×AES^{2}+0.01134×AES+1.575×ln(GR)−0.001038×AES×GR) | |
2 | Condition | GR ≥ 2.5 and AES ≥ 55 |
Equation | CSTW=1.085+0.000405×AES^{2}−0.03274×AES+0.05955×GR^{2}+0.00577×AES×GR | |
3 | Condition | (−0.5 < GR < 2.5 and AES<15) or (−AES/30 < GR <2.5 and AES≥15) |
Equation | CSTW=0.0896+0.0001308×AES^{2}+0.0552×GR^{2}+0.1181×GR+0.00402×AES×GR | |
4 | Condition | −AES/20 < GR ≤ −AES/30 and AES≥15 |
Equation | CSTW=0.0345+0.000387×AES^{2}+0.257×GR^{2}+0.01988×AES×GR | |
5 | Condition | otherwise |
Equation | CSTW=exp(−3.30−0.0275×AES+0.1868×GR+2.92×ln(−GR)−0.00275×AES×GR) |
1 | Condition | −4 ≤ GR ≤ −1 and AES > (−1.6667×GR^{3} − 17.5×GR^{2} −75.833×GR −45) and AES < (− 1.6667 ×GR^{3} − 17.5×GR^{2} −75.833×GR −40) |
---|---|---|
Equation | CSMR = 1046.8 − 499.21×ln(AES) + 106.76×(ln(AES))2 + 601.98×GR + 154.36×GR^{2} + 15.039×GR^{3} | |
2 | Condition | (GR ≥ −1) or (GR < −1 and AES ≥ (−1.6667 ×GR^{3} − 17.5×GR^{2} −75.833×GR −40)) |
Equation | CSMR = 46 + 0.008×AES^{2} + 0.146×AES×GR | |
3 | Condition | Otherwise |
Equation | CSMR = 1.6996 + 0.094776×AES − 0.016324×AES^{2} + 0.00037673×AES^{3} − 4.0767e−06×AES4 + 1.4984e−08×AES^{5} − 14.684×GR |
1 | Condition | AES < 55 |
---|---|---|
Equation | CSVD=1.126+0.00279×AES−0.247×ln(AES) | |
2 | Condition | otherwise |
Equation | CSVD=0.2006+4.936/AES |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCFC=0.174×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCFC=4.477+0.03862×CSMAX^{2} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCOC=0.00136×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCOC=exp(−4.408+0.6632×ln(CSMAX)+0.000148×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCTW=0.0012×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCTW=exp(−6.595+1.918×ln(CSMAX)−6855×10^{−8}×CSMAX^{2}) |
1 | Condition | Condition CSMAX < 5 |
---|---|---|
Equation | SCCMR=0.0008×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCMR=exp(−7.446−0.005514×CSMAX+2.212×ln(CSMAX)+ 5075×10^{−8}×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCD=0.0006×CSMAX | |
2 | Condition | 5 ≤ CSMAX < 55 |
Equation | SCCD=0.001+0.0004×CSMAX | |
3 | Condition | CSMAX ≥ 55 |
Equation | SCCD=exp(−4.439+0.000231×CSMAX^{2}) |
1 | Condition | (DCA ≥ 6 and AES ≥ (44.375 − 1.8236×DCA + 0.02044×DCA^{2} + 0.0018571×DCA^{2} − 0.000053954×DCA^{2})) or (6 > DCA ≥ 2 and AES ≥ (39.5 + 4.1667×DCA − 0.83333×DCA^{2})) |
---|---|---|
Equation | CFC = EXP(371.346 + 5.1878×LN(DCA) + 10.1521/DCA^{(0.5)} − 12.1424×AES^{(0.5)} − 4915.79/AES^{(0.5)} + 5093.19×LN(AES)/AES)) | |
2 | Condition | DCA < 2 and AES ≥ (24.5 − 10×DCA + 10×DCA^{2}) |
Equation | CFC = MAX(0, 1.3873+ 38.977×EXP( −0.5×(((DCA−2.2124)/1.071)^{2} + ((AES−102.44)/16.633)2))) | |
3 | Condition | 2 ≤ DCA ≤ 16 and AES < 10 |
Equation | CFC = MAX(0, −4.0824 + 1.833×DCA − 0.15946×DCA^{2} + 0.0044245×DCA^{3} + 0.56919×AES − 0.038513×AES^{2} + 0.00079158×AES^{3}) | |
4 | Condition | DCA ≤ 1 and AES < 25 |
Equation | CFC = 0 | |
5 | Condition | Otherwise |
Equation | CFC = MAX(0, −8.9743 − 0.099969×DCA +16.366×LN(AES)+ 0.0052265×DCA^{2} − 3.6805×(LN(AES))^{2} − 0.11371×DCA×LN(AES)) |
1 | Condition | (DCA ≥ 16 and AES ≥ (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (16 > DCA ≥ 6 and AES ≥ (35 − 125/DCA + 750/DCA^{2})) or (DCA < 6 and AES ≥ (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{2})) |
---|---|---|
Equation | CTW = MAX(0, 707192×EXP( −EXP( −(DCA − 44.524)/16.77) − (DCA − 44.524)/16.77 + 1) × EXP( −EXP( −(AES − 132.23)/40.729) − (AES − 132.23)/40.729 + 1)) | |
2 | Condition | (DCA ≥ 16 and AES < (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (16 > DCA ≥ 6 and AES < (35 − 125/DCA + 750/DCA^{2})) |
Equation | CTW = MAX(0, 7.4369 + 29.473/DCA + 6.5816×LN(AES) − 541.46/DCA^{2} − 3.8133×(LN(AES))^{2} + 45.797×(LN(AES))/DCA) | |
3 | Condition | DCA < 6 and AES < (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3}) |
Equation | CTW = MAX(0, −4.6194 + 4.5401×DCA + 0.10837×AES − 0.26588×DCA^{2} − 0.00099725×AES^{2} − 0.076619×DCA×AES) |
The third equation for 3+ Axle Single Unit Truck excess maintenance and repair due to curves is used to increment the value for CMR derived from the second equation under certain conditions. These conditions for this may be true when the condition for equation two is true.
1 | Condition | (DCA ≥ 10 and AES ≥ (−0.75×DCA + 40)) or (10 > DCA ≥ 2 and AES ≥ (−2.1875×DCA + 54.375)) or (DCA < 2 and AES ≥ (5×DCA^{2}−2.5×DCA+35)) |
---|---|---|
Equation | CMR = MAX(0, EXP(−50.038+ 0.71092×(LN(DCA))^{2} + 0.50522×LN(DCA) − 0.08522×AES + 13.02×LN(AES))) | |
2 | Condition | (1 ≤ DCA ≤ 3 and (10×DCA + 2.5) ≥ AES ≥ (−10×DCA + 37.5)) or (3 < DCA ≤ 5 and AES ≤ 32.5) or (DCA ≥ 14 and AES ≤ (−0.3125×DCA + 21.875)) or (5 < DCA < 14 and AES ≤ (−1.66667×DCA + 40.8333)) |
Equation | CMR = 0.1 | |
3 | Condition | 4.5 ≤ DCA ≤ 10.5 and AES > (39.3 − 13.497×DCA + 2.215×DCA^{2} − 0.11833×DCA^{3}) and AES < (17.5 + 5/(1 + exp( −((DCA − 7.0222)/−0.07845)))) |
Equation | CMR = CMR + 0.1 | |
4 | Condition | Otherwise |
Equation | CMR = 0 |
1 | Condition | (AES > 20 and 3 ≥ GR ≥ −3) or (AES ≤ 20 and GR ≥ −3) |
---|---|---|
Equation | CSFC = (1087.9 − 576.71×LN(AES) 82.039×(LN(AES))^{2} + 22.325×GR)/(1 − 0.17121×LN(AES) − 0.035147×GR) | |
2 | Condition | GR < −3 |
Equation | CSFC = −239.17 + 61.115×LN(AES) + 2221.9/AES − 4411.6×EXP(−AES) | |
3 | Condition | AES > 20 and GR > 3 |
Equation | CSFC = EXP(4.5952 + 0.0049349×AES×LN(AES) + 0.31272×GR) |
1 | Condition | GR > 0 and AES < 45 |
---|---|---|
Equation | CSOC=exp(3.92−0.661×ln(AES)−0.01718×GR^{2}+0.361×GR−0.000640×AES×GR) | |
2 | Condition | GR > 0 and 45 ≤ AES ≤ 70 |
Equation | CSOC=78.59+0.003813×AES^{2}−21.76×ln(AES)+2.1254×GR−0.0109×AES×GR | |
3 | Condition | GR > 0 and AES > 70 |
Equation | CSOC=78.59+0.003813×AES^{2}−21.76×ln(AES)+1.41×GR | |
4 | Condition | (min(−1.5,−AES/12.5) < GR ≤ 0) or (GR ≤ 0 and AES ≥ 70) |
Equation | CSOC=20.2+0.0000724×AES^{3}−0.01034×AES^{2}+0.662×AES−8.52×ln(AES) | |
5 | Condition | otherwise |
Equation | CSOC=exp(1.85+0.000458×AES^{2}−0.0746×AES−0.0336×GR^{2}−0.638×GR) |
1 | Condition | GR > 3 |
---|---|---|
Equation | CSTW = 0.27453 − 0.016411×AES +0.090845×GR+ 0.00035502×AES^{2} + 0.047978×GR^{2} + 0.0042709×AES×GR | |
2 | Condition | GR < −3 |
Equation | CSTW = ABS(−0.14758 + 0.01337×AES + 0.0040158×GR − 0.000053182×AES^{2} + 0.052391×GR^{2} + 0.0044432×AES×GR) | |
3 | Condition | −3 ≤ GR ≤ 3 |
Equation | CSTW = 0.15566 − 0.0058457×AES + 0.041763×GR + 0.00021374×AES^{2} + 0.056992×GR^{2} + 0.0050156×AES×GR |
1 | Condition | −3 ≤ GR ≤ −1 and AES ≥ (−7.5×GR^{2} − 52.5×GR − 25) and AES < (−7.5×GR^{2} − 52.5×GR − 20) |
---|---|---|
Equation | CSMR = 169.6 + 6.4867×AES + 333.98×GR + 48.825×GR^{2} | |
2 | Condition | (GR > −1) or (GR < −1 and GR ≥ −3 and AES ≥ (−7.5×GR^{2}−52.5×GR−20)) |
Equation | CSMR = 46 + 0.008×AES^{2} + 0.146×AES×GR | |
3 | Condition | Otherwise |
Equation | CSMR = 2.44881 − 0.0404901×AES^{(1.5)} − 15.8112×GR |
1 | Condition | AES<55 |
---|---|---|
Equation | CSVD=0.354+0.000974×AES−0.0806×ln(AES) | |
2 | Condition | otherwise |
Equation | CSVD=0.05657+1.598/AES |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCFC=0.324×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCFC=6.342+0.5855×CSMAX+0.03191×CSMAX^{2} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCOC=0.00136×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCOC=exp(−4.408+0.6632×ln(CSMAX)+0.000148×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCTW=0.0008×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCTW=exp(−7.111+2.0276×ln(CSMAX)−0.000102×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCMR=0.0012×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCMR=exp(−6.639+0.006003×CSMAX+1.912×ln(CSMAX)) |
1 | Condition | CSMAX < 60 |
---|---|---|
Equation | SCCD=0.0002×CSMAX | |
2 | Condition | CSMAX ≥ 60 |
Equation | SCCD=exp(−5.007+0.000162×CSMAX^{2}) |
1 | Condition | DCA < 6 and AES ≤ 20 |
---|---|---|
Equation | CFC = MAX(0,( −0.069855 + 0.4852×LN(DCA) + 0.029223×LN(AES))/(1 − 0.30752×LN(DCA) + 0.10364×(LN(DCA))^{2} − 0.52169×LN(AES) + 0.10545×(LN(AES))^{2})) | |
2 | Condition | 20 < AES ≤ (64 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) and DCA < 6 |
Equation | CFC = MAX(0, −36.549 + 8.3919×DCA + 19.444×LN(AES) − 0.19172×DCA^{2} − 2.6623×(LN(AES))^{2} − 1.9932×DCA×LN(AES)) | |
3 | Condition | 20 < AES ≤ (64 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) and DCA ≥ 6 |
Equation | CFC = MAX(0, −44.639 + 15.079×LN(DCA) + 31.738×LN(AES) − 1.734×(LN(DCA))^{2} − 5.305×(LN(AES))^{2} − 3.6061×LN(DCA)×LN(AES)) | |
4 | Condition | DCA > 1 and AES ≥ (67 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) |
Equation | CFC = MAX(0, EXP(948774.18 + 1.056802×(LN(DCA))^{2} + 11715.15×AES^{(0.5)}×LN(AES) + 54041.58×(LN(AES))^{2} − 133443.12×AES^{(0.5)} − 268395.66×LN(AES) + 309522.12/LN(AES) − 1311374.33/(AES^{(0.5)}))) | |
5 | Condition | DCA ≤ 1 and AES ≥ (67 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) |
Equation | CFC = MAX(0, (−13.559 − 1.1956×DCA + 0.37772×DCA^{2} + 3.5166×LN(AES))/(1 − 0.37771×DCA + 0.1152×DCA^{2} − 0.1529×LN(AES))) | |
6 | Condition | Otherwise |
Equation | CFC = 0 |
1 | Condition | (DCA ≥ 16 and AES ≥ (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (16 > DCA ≥ 6 and AES ≥ (35 − 125/DCA + 750/DCA^{2})) or (DCA < 6 and AES ≥ (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3})) |
---|---|---|
Equation | CTW = MAX(0, 578653×EXP( −EXP( −(DCA − 54.618)/20.44) − (DCA − 54.618)/20.44 + 1) × EXP( −EXP( −(AES − 120.41)/37.427) − (AES − 120.41)/37.427 + 1)) | |
2 | Condition | (DCA ≥ 16 and AES < (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (16 > DCA ≥ 6 and AES < (35 − 125/DCA + 750/DCA^{2})) |
Equation | CTW = MAX(0, −26.305 + 16.264×LN(DCA) + 20.114×LN(AES) − 1.7217×(LN(DCA))^{2} − 3.4077×(LN(AES))^{2} − 4.0945×LN(DCA)×LN(AES)) | |
3 | Condition | DCA < 6 and AES < (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3}) |
Equation | CTW = MAX(0, −3.8937 + 3.8291×DCA + 0.092128×AES − 0.22412×DCA^{2} − 0.00082522×AES^{2} − 0.064764×DCA×AES) |
* The third equation for 3-4 Axle Combination Unit Truck excess maintenance and repair due to curves is, under certain conditions, used to increment the CMR value derived from the second equation. Under some circumstances, the conditions for both equation two and equation three will be true. | ||
---|---|---|
1 | Condition | (DCA ≥ 17.5 and AES ≥ (−0.4×DCA + 29.5)) or (17.5 > DCA ≥ 2.5 and AES ≥ (−1.5×DCA + 48.75)) or (DCA < 2.5 and AES ≥ (4×DCA + 35) |
Equation | CMR = MAX(0, EXP(304.96 − 0.90108×DCA + 2.0321×DCA^{(0.5)}×LN(DCA) − 0.70003×LN(DCA) − 41.773×LN(AES) − 1312.1/AES^{(0.5)} + 2080.7/AES)) | |
2 | Condition | (DCA ≤ 3 and (−6.667×DCA^{2} + 38.33×DCA + −22.5) ≥ AES ≥ (6.667×DCA^{2} − 38.33×DCA + 62.5)) or (3 < DCA ≤ 6 and AES ≤ 32.5) or (6 < DCA < 10 and AES ≤ (−2.5×DCA + 47.5)) or ((DCA ≥ 10 and AES ≤ (−0.5×DCA + 27.5)) |
Equation | CMR = 0.1 | |
3* | Condition | (3.5 < DCA < 6.5 and 12.5 < AES < 22.5) or (5.5 < DCA < 12.5 and 7.5 < AES < 17.5) |
Equation | CMR = CMR + 0.1 | |
4 | Condition | Otherwise |
Equation | CMR = 0 |
1 | Condition | 3 ≥ GR ≥ −3 |
---|---|---|
Equation | CSFC = (1618.8 − 864.83×LN(AES) + 124.88×(LN(AES))^{2} + 32.087×GR)/(1 − 0.16247×LN(AES) − 0.07074×GR + 0.011717×GR^{2} − 0.0011606×GR^{3}) | |
2 | Condition | GR < −3 |
Equation | CSFC = −305.94 + 76.547×LN(AES) + 2737.7/AES − 5493.1×EXP(−AES) | |
3 | Condition | GR > 3 |
Equation | CSFC = (1607 − 986.23×LN(AES) + 149.01×(LN(AES))^{2} + 84.747×GR)/(1 − 0.17168×LN(AES) − 0.021455×GR) |
1 | Condition | GR > 0 and AES < 55 |
---|---|---|
Equation | CSOC=exp(4.60−0.668×ln(AES)−0.01879×GR^{2}+0.394×GR−0.000873×AES×GR) | |
2 | Condition | GR > 0 and AES ≥ 55 |
Equation | CSOC=9.383+0.003478×AES−0.271×AES+3.040×GR 3 | |
3 | Condition | min(−1.5,−AES/15.0) < GR ≤ 0 and AES < 55 |
Equation | CSOC=42.6+0.000189×AES^{3}−0.0273×AES^{2}+1.633×AES−18.96×ln(AES) | |
4 | Condition | min(−1.5,−AES/15.0) < GR ≤ 0 and AES ≥ 55 |
Equation | CSOC=9.383+0.003478×AES^{2}−0.271×AES | |
5 | Condition | GR ≤ min(−1.5,−AES/15.0) and AES < 55 |
Equation | CSOC=exp(2.52+0.000397×AES^{2}−0.0675×AES−0.0353×GR^{2}−0.652×GR) | |
6 | Condition | GR ≤ min(−1.5,−AES/15.0) and AES ≥ 55 |
Equation | CSOC=115.8+0.5094×AES−37.27×ln(AES)−3.064×GR |
1 | Condition | GR≥2.5 and AES < 55 |
---|---|---|
Equation | CSTW=exp(−1.6+0.0000684×AES^{2}+0.00608×AES+1.567×ln(GR)−0.000762×AES×GR) | |
2 | Condition | GR≥2.5 and AES ≥ 55 |
Equation | CSTW=1.122+0.000357×AES^{2}−0.03264×AES+0.06295×GR^{2}+0.005081×AES×GR | |
3 | Condition | (−0.5 < GR < 2.5 and AES<15) or (−AES/35 < GR < 2.5 and AES ≥ 15) |
Equation | CSTW=0.1432+1.248×10−6×AES^{3}+0.0639×GR^{2}+0.1167×GR+0.00332×AES×GR | |
4 | Condition | GR < −AES/35 and AES ≥ max(15.,−25×GR) |
Equation | CSTW=−0.1283+1.442×10^{−6}×AES^{3}+0.01044×AES+0.208×GR^{2}+0.01337×AES×GR | |
5 | Condition | otherwise |
Equation | CSTW=exp(−3.05−1.5×10^{−6}×AES^{3}−0.01358×AES+2.13×ln(−GR)−0.001779×AES×GR) |
1 | Condition | GR ≥ 0 |
---|---|---|
Equation | CSMR=44.9+0.01148×AES^{2}+0.254×AES×GR 2 | |
2 | Condition | GR < 0 and AES > 25 and AES ≥ −40×GR−15 |
Equation | CSMR = 78.7+1.545×AES−20.6×ln(AES)+0.254×AES×GR | |
3 | Condition | otherwise |
Equation | CSMR=0.996−0.00149×AES^{2}−15.8×GR |
1 | Condition | AES < 55 |
---|---|---|
Equation | CSVD = 0.395+0.001215×AES−0.0941×ln(AES) | |
2 | Condition | otherwise |
Equation | CSVD = 0.05657+1.598/AES |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCFC=0.3584×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCFC=2.052+1.167×CSMAX+0.03292×CSMAX^{2} |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCOC=0.0028×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCOC=exp(−3.735+0.6849×ln(CSMAX)+0.000112×CSMAX^{2}) |
1 | Condition | CSMAX < 5 |
---|---|---|
Equation | SCCTW=0.0012×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCTW=exp(−6.643+1.947×ln(CSMAX)−721×10^{−7}×CSMAX^{2}) |
1 | Condition | Condition CSMAX < 5 |
---|---|---|
Equation | SCCMR=0.0012×CSMAX^{2} | |
2 | Condition | CSMAX ≥ 5 |
Equation | SCCMR=exp(−6.705+0.008136×CSMAX+1.94×ln(CSMAX)) |
1 | Condition | CSMAX < 60 |
---|---|---|
Equation | SCCD=0.0002×CSMAX | |
2 | Condition | CSMAX ≥ 60 |
Equation | SCCD=exp(−5.007+0.000162×CSMAX^{2}) |
1 | Condition | DCA < 6 and AES ≤ 20 |
---|---|---|
Equation | CFC = MAX(0, EXP(4.892 − 5.8015/DCA^{2} − 0.070341×AES − 6.612/AES^{(0.5)})) | |
2 | Condition | 20 < AES ≤ (64 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) and DCA < 6 |
Equation | CFC = MAX(0, −0.76579 + 9.3637×LN(DCA) + 0.025171×AES − 0.75491×(LN(DCA))^{2} + 0.00010068×AES^{2} − 0.22116×AES×LN(DCA)) | |
3 | Condition | AES ≤ (64 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) and DCA ≥ 6 |
Equation | CFC = MAX(0, −44.672 + 15.308×LN(DCA) + 31.804×LN(AES) − 1.8472×(LN(DCA))^{2} − 5.3075×(LN(AES))^{2} − 3.5085×LN(DCA)×LN(AES)) | |
4 | Condition | DCA > 1 and AES ≥ (67 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) |
Equation | CFC = MAX(0, EXP(−37.185 − 0.0034062×DCA^{2} + 1.262×(LN(DCA))^{2} − 0.00000046205×AES^{3} + 8.9915×LN(AES))) | |
5 | Condition | DCA ≤ 1 and AES ≥ (67 + 0.93749×DCA − 13.928 × DCA^{(0.5)}) |
Equation | CFC = MAX(0, −3.3518 + 58.52/((1 + ((DCA − 3.8448)/3.142)^{2}) × (1+ ((AES − 99.792)/14.486)^{2}))) | |
6 | Condition | Otherwise |
Equation | CFC = 0 |
1 | Condition | DCA ≥ 16 and AES ≥ (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (16 > DCA ≥ 6 and AES ≥ (35 − 125/DCA + 750/DCA^{2})) or (1 ≤ DCA < 6 and AES ≥ (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3})) |
---|---|---|
Equation | CTW = MAX(0, EXP(−40.193 + 14.371×EXP(DCA/−53.803) + 1.2303×(LN(DCA))2 − 1.8886×AES/LN(AES) + 7.0737×AES^{(0.5)})) | |
2 | Condition | DCA < 1 and AES ≥ (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3}) |
Equation | CTW = MAX(0, 1/(1.1442 − 0.015388×DCA^{3} − 9704.3/AES^{(1.5)} + 27917×LN(AES)/AES^{2} − 42372/AES^{2})) | |
3 | Condition | (DCA ≥ 16 and AES < (0.02381×DCA^{2} − 1.4524×DCA + 42.143)) or (16 > DCA ≥ 6 and AES < (35 − 125/DCA + 750/DCA^{2})) |
Equation | CTW = MAX(0, −27.686 + 18.235×LN(DCA) + 24.103×LN(AES) − 2.2305×(LN(DCA))^{2} − 4.3932×(LN(AES))^{2} − 4.4593×LN(DCA)×LN(AES)) | |
4 | Condition | DCA < 6 and AES < (23.334 + 112.5/DCA − 150.83/DCA^{2} + 25/DCA^{3}) |
Equation | CTW = MAX(0, −4.9124 + 4.8372×DCA + 0.12051×AES − 0.2845×DCA^{2} − 0.0011691×AES^{2} − 0.08169×DCA×AES) |
* The third and fourth equations for 5+ Axle Combination Unit Truck excess maintenance and repair due to curves are, under certain conditions, used to increment the CMR value derived from the second equation. These conditions for one or both of these equations may be true when the condition for equation two is true. | ||
---|---|---|
1 | Condition | (DCA ≥ 10 and AES ≥ (−0.5×DCA + 32.5)) or (10 > DCA ≥ 3 and AES ≥ (−2.8571×DCA + 56.071)) or (DCA < 3 and AES ≥ (6.6667×DCA + 27.5) |
Equation | CMR = EXP(703.2 + 0.75135×(LN(DCA))^{2} − 1.3433/DCA^{(0.5)} − 62.464×LN(AES) − 2045.3/LN(AES) + 3128.1/AES)) | |
2 | Condition | (1.5 ≤ DCA ≤ 3 and (5×DCA + 22.5) > AES > (−5×DCA + 17.5)) or (16 ≤ DCA ≤ 25 and AES ≤ 17.5) or (DCA > 25 and AES <= (−1×DCA + 42.5)) or (3 < DCA < 16 and AES ≤ (−1.5385×DCA + 42.115)) |
Equation | CMR = 0.1 | |
3* | Condition | (2.5 < DCA ≤ 6.5 and 12.5 ≤ AES ≤ 27.5) or (3.5 < DCA ≤ 10.5 and 7.5 ≤ AES < 22.5) or (9.5 ≤ DCA ≤ 15 and 2.5 < AES ≤ 17.5) or (15 ≤ DCA ≤ 17 and 7.5 ≤ AES ≤ 17.5) or (17 ≤ DCA < 22.5 and 7.5 ≤ AES ≤ 12.5) |
Equation | CMR = CMR + 0.1 | |
4* | Condition | (3.5 < DCA < 6.5 and 17.5 ≤ AES < 22.5) or (4.5 < DCA < 10.5 and 12.5 ≤ AES ≤ 17.5) or (7.5 < DCA < 10.5 and 7.5 < AES ≤ 12.5) |
Equation | CMR = CMR + 0.1 | |
5 | Condition | Otherwise |
Equation | CMR = 0 |
1 | 4-Tire Vehicles | PCAFOC = 2.64+0.0729×PSR^{2}−0.722×PSR |
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2 | Trucks | PCAFOC = 1.176−0.1348×ln(PSR) |
1 | 4-Tire Vehicles | PCAFTW = 2.40−1.111×ln(PSR) |
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2 | Trucks | PCAFTW = 1.668+0.001372×PSR^{3}−0.581×ln(PSR) |
4-Tire Vehicles | PCAFMR = 3.19+0.0967×PSR^{2}−0.961×PSR | |
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Single-Unit Trucks | PCAFMR = 1.724+0.00830×PSR^{2}−0.661×ln(PSR) | |
Combination Trucks | PCAFMR = 2.075+0.273*PSR−1.622×ln(PSR) |
4-Tire Vehicles | PCAFVD = 1.136−0.106×ln(PSR) | |
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Single-Unit Trucks | PCAFVD = 1.332−0.262×ln(PSR) | |
Combination Trucks | PCAFVD = 1.32−0.254×ln(PSR) |