Review of Truck Characteristics as Factors in Roadway Design (2003)

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E-1 APPENDIX E TRUCK SPEED PROFILE MODEL A truck speed profile model (TSPM) for truck perfor- mance on upgrades has been developed as a design tool to permit highway agencies to anticipate when an added climb- ing lane may be warranted. TSPM is implemented in a Micro- soft Excel spreadsheet. This appendix illustrates how the speed profile model operates and documents the truck performance equations that form the basis for that model. The current Green Book contains several truck speed pro- file plots (i.e., plots of truck speed versus distance along a grade) for use in determining the critical length of grade that might warrant a climbing lane. These plots are not as useful as they might be because they assume a single initial truck speed, a constant percent grade, and a single truck weight-to- power ratio (120 kg/kW [200 lb/hp]). The TSPM spreadsheet allows the user to input the actual vertical alignment for any site of interest and to choose any appropriate value for initial truck speed and weight-to-power ratio. This flexibility should improve the ability of highway agencies to determine whether the climbing lane criteria are met at any particular site. INPUT DATA The input data for the TSPM include both roadway and truck characteristics. The specific input data are as follows: • Roadway Characteristics: – Vertical profile—percent grade for specific ranges of position coordinates – Elevation above sea level (ft) • Truck Characteristics: – Desired speed (mph) – Initial speed of truck at beginning of analysis section (mph) – Weight-to-power ratio (lb/hp) – Weight-to-front-area ratio (lb/ft2) The input data are entered on the first page of the TSPM spreadsheet, which is illustrated in Figure E-1. The grades that constitute the vertical profile of the analysis site are entered for ranges of position coordinates, such as stationing, in units of feet. The profile should begin at coordinate zero and subse- quent grade ranges should appear in order of increasing coor- dinates. The end of each coordinate range should be equal to the beginning of the next coordinate range. Vertical curves have little effect on truck speeds, so grades can be entered as continuous constant grades from one vertical point of inter- section (VPI) to the next. Grades for any number of coordinate ranges may be entered. The desired speed of the truck, entered in miles per hour, is the speed that the truck driver would prefer to travel where not limited by the presence of an upgrade. The TSPM logic will never show the trucks as traveling faster than this speed. The initial speed of the truck, entered in miles per hour, is the speed of the truck at coordinate zero. This speed typically represents the truck speed prior to entering the grade and can be any speed greater than or equal to zero. If the truck is entering the grade from level terrain, the initial speed may be equal to the desired speed. If the truck is entering the grade from a stopped position, the initial speed may be zero. The weight-to-power ratio, entered in lb/hp, represents the performance ability of the truck. The lower the weight-to- power ratio, the better will be the truck performance on any grade and the greater will be the truck’s final crawl speed. The weight-to-frontal-area ratio, entered in lb/ft2, repre- sents the ability of the truck to overcome aerodynamic resis- tance. If the cell representing weight-to-frontal-area ratio is left blank or set equal to zero, the spreadsheet will estimate a typical default value of weight-to-frontal-area ratio, based on the weight-to-power ratio. In general, aerodynamic resis- tance has limited effect on truck speed profiles, so it is best in most cases to use the typical default value. However, the TSPM permits the user to include a specific value for weight- to-frontal-area ratio where this is available. The elevation above sea level, in feet, of the site being evaluated is also entered for the site being evaluated. The ele- vation of the site influences the aerodynamic resistance. However, as noted above, the effect of aerodynamic resis- tance on truck performance is minimal, so the accuracy of the elevation used is not critical. TSPM is applicable to diesel trucks, so there is no horse- power correction for elevation as there would be for gasoline engines. When all input data for a problem have been entered, the user should click the button marked “Calculate Speed Pro- file” to generate output data. OUTPUT DATA TSPM generates two types of output data. On the sheet labeled “Results,” TSPM displays the speed profile calcula- tions for each second of elapsed time after the truck passes coordinate zero. The tabulated values include all position coordinates from zero to the maximum coordinate specified in the input data. This detailed, second-by-second output is illustrated in Figure E-2. The individual columns in the spread- sheet are defined in the next section of this appendix.

The speed profile spreadsheet includes the minimum and maximum truck speeds computed by the spreadsheet and their difference. If the maximum speed represents the truck speed in advance of the upgrade, then the difference between the maximum and minimum speeds represents the speed reduc- tion on the grade. If the speed reduction is 16 km/h [10 mph] or more, a climbing lane may be warranted. The sheet labeled “Chart1” presents a speed versus dis- tance plot that illustrates the truck speed profile. The speed profile plot is simply a graph of Columns 17 and 19. A typi- cal plot is illustrated in Figure E-3. Such a plot allows the user to review the expected speed of the truck at each loca- tion along the specified grade. SPEED PROFILE COMPUTATIONS The speed profile computations are conducted as follows, using the truck performance equations from the TWOPAS model (85, 86): • Column 1 represents the elapsed time, in seconds, since the vehicle passed coordinate zero. • Columns 2 and 3 represent the user-specified desired speed, in units of miles per hour and feet per second, for the truck in question. • Columns 4 and 5 represent the actual speed of the truck, in miles per hour and feet per second, at the time shown in Column 1. • Column 6 represents the position of the truck (distance from coordinate zero) at the time shown in Column 1. E-2 • Columns 8 through 10 represent the coasting accel- eration, horsepower-limited-acceleration, and effective acceleration, respectively, during the 1-s interval begin- ning at the time shown in Column 1. The accelerations are determined as follows: (1) (2) (3) (4) where ac = coasting acceleration (ft/s2) during gear shifts ap = horsepower-limited acceleration (ft/s2) ae = effective acceleration (ft/s2) including an allow- ance of 1.5 s for gear shift delays a 10a 1 1.5a a (a a ) , V 10 ft/se o o o p c = + − < 0 a 0.4V a 0.4V 1.5a a (a a ) , V 10 ft/se o o o p c = ′ ′ + − ≥ a 15368C (W/NHP)V 1 14080(W/NHP)V p pe 2 = ′ + ′ a 0.2445 0.004V 0.021C (V )(W/A) 222.6C (W/NHP)V gG c de 2 pe = − − ′ − ′ − ′ − Desired speed (mph) = 65.0 or 95.3 (ft/sec) Initial speed (mph) = 65.0 Weight/power ratio (lb/hp) = 100.0 Weight/frontal area ratio (lb/ft2) = 0.0 Elevation (ft) = 1000.0 Location (legend) = ROUTE 3 Begin End 0 528 6.1 529 1056 5.9 1057 1584 5.8 1585 2112 5.7 2113 2640 5.6 2641 3168 6.2 3169 3696 6.1 3697 4224 5.7 4225 4752 5.8 4753 5426 5.6 5427 6052 5.8 TRUCK SPEED PERFORMANCE MODEL Position (ft) (Beginning of first segment must equal 0) Percent Grade enter volume or enter zero to use default estimate Vertical Profile Calculate Speed Profile Figure E-1. Input screen for TSPM.

E-3 TRUCK SPEED PROFILE FOR ROUTE 3 Desired speed (mph) = 65.0 Maximum speed (mph) = 63.9 Initial speed (mph) = 65.0 Minimum speed (mph) = 41.9 Weight/horsepower ratio (lb/hp) = 100.0 Speed difference (mph) = 22.0 Weight/frontal area ratio (lb/ft2) = 221.0 Elevation (ft) = 1000.0 Horsepower correction factor for elevation = 1.0000 Aerodynamic drag correction factor for elevation = 0.9710 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) Limiting acceleration (ft/sec2) Limiting acceleration and speed Elapsed Desired speed Start of 1-sec Interval Local New speed based on based on driver preferences time Speed Position grade vehicle performance Speed Acceleration (sec) (mph) (ft/sec) (mph) (ft/sec) (ft) (%) Coasting Power Effective (mph) (ft/sec) (mph) (ft/sec) (ft/sec2) 0.0 65.0 95.3 65.0 95.3 0.0 6.1 -3.11 -1.47 -1.57 63.9 93.8 65.0 95.3 0.00 1.0 65.0 95.3 63.9 93.8 94.5 6.1 -3.08 -1.42 -1.52 62.9 92.2 64.9 95.1 1.37 2.0 65.0 95.3 62.9 92.2 187.5 6.1 -3.05 -1.36 -1.46 61.9 90.8 63.9 93.8 1.53 3.0 65.0 95.3 61.9 90.8 279.1 6.1 -3.03 -1.31 -1.41 60.9 89.4 63.0 92.5 1.69 4.0 65.0 95.3 60.9 89.4 369.1 6.1 -3.00 -1.26 -1.36 60.0 88.0 62.2 91.2 1.84 5.0 65.0 95.3 60.0 88.0 457.8 6.1 -2.98 -1.21 -1.31 59.1 86.7 61.4 90.0 1.99 6.0 65.0 95.3 59.1 86.7 545.2 5.9 -2.90 -1.10 -1.20 58.3 85.5 60.6 88.8 2.13 7.0 65.0 95.3 58.3 85.5 631.2 5.9 -2.88 -1.06 -1.15 57.5 84.3 59.8 87.8 2.26 8.0 65.0 95.3 57.5 84.3 716.2 5.9 -2.86 -1.02 -1.11 56.8 83.2 59.1 86.7 2.39 9.0 65.0 95.3 56.8 83.2 800.0 5.9 -2.84 -0.98 -1.07 56.0 82.2 58.5 85.7 2.51 10.0 65.0 95.3 56.0 82.2 882.7 5.9 -2.83 -0.94 -1.02 55.3 81.1 57.8 84.8 2.62 11.0 65.0 95.3 55.3 81.1 964.3 5.9 -2.81 -0.90 -0.98 54.7 80.2 57.2 83.9 2.73 12.0 65.0 95.3 54.7 80.2 1045.0 5.9 -2.80 -0.86 -0.94 54.0 79.2 56.6 83.0 2.84 13.0 65.0 95.3 54.0 79.2 1124.7 5.8 -2.75 -0.79 -0.87 53.4 78.3 56.0 82.2 2.94 14.0 65.0 95.3 53.4 78.3 1203.4 5.8 -2.74 -0.76 -0.84 52.8 77.5 55.5 81.4 3.03 15.0 65.0 95.3 52.8 77.5 1281.4 5.8 -2.72 -0.72 -0.80 52.3 76.7 55.0 80.6 3.13 16.0 65.0 95.3 52.3 76.7 1358.5 5.8 -2.71 -0.69 -0.77 51.8 75.9 54.5 79.9 3.21 17.0 65.0 95.3 51.8 75.9 1434.8 5.8 -2.70 -0.66 -0.74 51.3 75.2 54.0 79.2 3.29 18.0 65.0 95.3 51.3 75.2 1510.4 5.8 -2.69 -0.63 -0.70 50.8 74.5 53.6 78.6 3.37 19.0 65.0 95.3 50.8 74.5 1585.2 5.7 -2.65 -0.57 -0.64 50.4 73.9 53.1 77.9 3.45 20.0 65.0 95.3 50.4 73.9 1659.4 5.7 -2.64 -0.55 -0.61 49.9 73.2 52.8 77.4 3.52 21.0 65.0 95.3 49.9 73.2 1732.9 5.7 -2.63 -0.52 -0.58 49.5 72.7 52.4 76.8 3.59 22.0 65.0 95.3 49.5 72.7 1805.9 5.7 -2.63 -0.50 -0.56 49.2 72.1 52.0 76.3 3.65 23.0 65.0 95.3 49.2 72.1 1878.3 5.7 -2.62 -0.47 -0.53 48.8 71.6 51.7 75.8 3.71 24.0 65.0 95.3 48.8 71.6 1950.1 5.7 -2.61 -0.45 -0.51 48.5 71.1 51.4 75.3 3.77 25.0 65.0 95.3 48.5 71.1 2021.4 5.7 -2.60 -0.43 -0.48 48.1 70.6 51.1 74.9 3.82 26.0 65.0 95.3 48.1 70.6 2092.2 5.7 -2.60 -0.41 -0.46 47.8 70.1 50.8 74.5 3.87 27.0 65.0 95.3 47.8 70.1 2162.6 5.6 -2.56 -0.36 -0.41 47.5 69.7 50.5 74.0 3.92 28.0 65.0 95.3 47.5 69.7 2232.5 5.6 -2.55 -0.34 -0.39 47.3 69.3 50.2 73.7 3.97 29.0 65.0 95.3 47.3 69.3 2302.0 5.6 -2.55 -0.32 -0.37 47.0 69.0 50.0 73.3 4.01 30.0 65.0 95.3 47.0 69.0 2371.2 5.6 -2.54 -0.31 -0.35 46.8 68.6 49.8 73.0 4.05 31.0 65.0 95.3 46.8 68.6 2439.9 5.6 -2.54 -0.29 -0.33 46.6 68.3 49.6 72.7 4.09 32.0 65.0 95.3 46.6 68.3 2508.4 5.6 -2.54 -0.28 -0.32 46.3 68.0 49.4 72.4 4.12 33.0 65.0 95.3 46.3 68.0 2576.5 5.6 -2.53 -0.26 -0.30 46.1 67.7 49.2 72.1 4.16 34.0 65.0 95.3 46.1 67.7 2644.3 6.2 -2.72 -0.44 -0.50 45.8 67.2 49.0 71.8 4.19 35.0 65.0 95.3 45.8 67.2 2711.7 6.2 -2.72 -0.41 -0.48 45.5 66.7 48.7 71.4 4.24 36.0 65.0 95.3 45.5 66.7 2778.6 6.2 -2.71 -0.39 -0.45 45.2 66.2 48.4 71.0 4.29 37.0 65.0 95.3 45.2 66.2 2845.1 6.2 -2.70 -0.37 -0.43 44.9 65.8 48.1 70.6 4.34 38.0 65.0 95.3 44.9 65.8 2911.1 6.2 -2.70 -0.35 -0.41 44.6 65.4 47.9 70.2 4.39 39.0 65.0 95.3 44.6 65.4 2976.7 6.2 -2.69 -0.33 -0.39 44.3 65.0 47.6 69.8 4.43 40.0 65.0 95.3 44.3 65.0 3041.9 6.2 -2.69 -0.31 -0.36 44.1 64.6 47.4 69.5 4.47 (16) (17) (18) (19) End of 1-sec Interval Actual New acceleration New speed position (ft/sec2) (mph) (ft/sec) (ft) -1.57 63.9 93.8 94.5 -1.52 62.9 92.2 187.5 -1.46 61.9 90.8 279.1 -1.41 60.9 89.4 369.1 -1.36 60.0 88.0 457.8 -1.31 59.1 86.7 545.2 -1.20 58.3 85.5 631.2 -1.15 57.5 84.3 716.2 -1.11 56.8 83.2 800.0 -1.07 56.0 82.2 882.7 -1.02 55.3 81.1 964.3 -0.98 54.7 80.2 1045.0 -0.94 54.0 79.2 1124.7 -0.87 53.4 78.3 1203.4 -0.84 52.8 77.5 1281.4 -0.80 52.3 76.7 1358.5 -0.77 51.8 75.9 1434.8 -0.74 51.3 75.2 1510.4 -0.70 50.8 74.5 1585.2 -0.64 50.4 73.9 1659.4 -0.61 49.9 73.2 1732.9 -0.58 49.5 72.7 1805.9 -0.56 49.2 72.1 1878.3 -0.53 48.8 71.6 1950.1 -0.51 48.5 71.1 2021.4 -0.48 48.1 70.6 2092.2 -0.46 47.8 70.1 2162.6 -0.41 47.5 69.7 2232.5 -0.39 47.3 69.3 2302.0 -0.37 47.0 69.0 2371.2 -0.35 46.8 68.6 2439.9 -0.33 46.6 68.3 2508.4 -0.32 46.3 68.0 2576.5 -0.30 46.1 67.7 2644.3 -0.50 45.8 67.2 2711.7 -0.48 45.5 66.7 2778.6 -0.45 45.2 66.2 2845.1 -0.43 44.9 65.8 2911.1 -0.41 44.6 65.4 2976.7 -0.39 44.3 65.0 3041.9 -0.36 44.1 64.6 3106.8 41.0 65.0 95.3 44.1 64.6 3106.8 6.2 -2.68 -0.30 -0.35 43.8 64.3 47.2 69.2 4.51 42.0 65.0 95.3 43.8 64.3 3171.2 6.1 -2.65 -0.25 -0.29 43.6 64.0 46.9 68.9 4.55 43.0 65.0 95.3 43.6 64.0 3235.4 6.1 -2.65 -0.24 -0.28 43.5 63.7 46.8 68.6 4.58 44.0 65.0 95.3 43.5 63.7 3299.3 6.1 -2.64 -0.22 -0.26 43.3 63.5 46.6 68.3 4.61 45.0 65.0 95.3 43.3 63.5 3362.9 6.1 -2.64 -0.21 -0.25 43.1 63.2 46.4 68.1 4.64 46.0 65.0 95.3 43.1 63.2 3426.2 6.1 -2.64 -0.20 -0.23 43.0 63.0 46.3 67.9 4.67 47.0 65.0 95.3 43.0 63.0 3489.3 6.1 -2.63 -0.19 -0.22 42.8 62.8 46.2 67.7 4.69 48.0 65.0 95.3 42.8 62.8 3552.2 6.1 -2.63 -0.18 -0.21 42.7 62.6 46.0 67.5 4.72 -0.35 43.8 64.3 3171.2 -0.29 43.6 64.0 3235.4 -0.28 43.5 63.7 3299.3 -0.26 43.3 63.5 3362.9 -0.25 43.1 63.2 3426.2 -0.23 43.0 63.0 3489.3 -0.22 42.8 62.8 3552.2 -0.21 42.7 62.6 3614.9 Figure E-2. Tabular printout from TSPM.

E-4 TRUCK SPEED PROFILE FOR ROUTE 3 Desired speed (mph) = 65.0 Maximum speed (mph) = 63.9 Initial speed (mph) = 65.0 Minimum speed (mph) = 41.9 Weight/horsepower ratio (lb/hp) = 100.0 Speed difference (mph) = 22.0 Weight/frontal area ratio (lb/ft2) = 221.0 Elevation (ft) = 1000.0 Horsepower correction factor for elevation = 1.0000 Aerodynamic drag correction factor for elevation = 0.9710 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) Limiting acceleration (ft/sec2) Limiting acceleration and speed Elapsed Desired speed Start of 1-sec Interval Local New speed based on based on driver preferences time Speed Position grade vehicle performance Speed Acceleration (sec) (mph) (ft/sec) (mph) (ft/sec) (ft) (%) Coasting Power Effective (mph) (ft/sec) (mph) (ft/sec) (ft/sec2) (16) (17) (18) (19) End of 1-sec Interval Actual New acceleration New speed position (ft/sec2) (mph) (ft/sec) (ft) 49.0 65.0 95.3 42.7 62.6 3614.9 6.1 -2.63 -0.17 -0.20 42.5 62.4 45.9 67.3 4.74 50.0 65.0 95.3 42.5 62.4 3677.4 6.1 -2.63 -0.16 -0.18 42.4 62.2 45.8 67.1 4.76 51.0 65.0 95.3 42.4 62.2 3739.7 5.7 -2.50 -0.02 -0.03 42.4 62.2 45.7 67.0 4.78 52.0 65.0 95.3 42.4 62.2 3801.8 5.7 -2.50 -0.02 -0.03 42.4 62.1 45.6 66.9 4.78 53.0 65.0 95.3 42.4 62.1 3864.0 5.7 -2.50 -0.02 -0.02 42.3 62.1 45.6 66.9 4.79 54.0 65.0 95.3 42.3 62.1 3926.1 5.7 -2.49 -0.02 -0.02 42.3 62.1 45.6 66.9 4.79 55.0 65.0 95.3 42.3 62.1 3988.2 5.7 -2.49 -0.02 -0.02 42.3 62.1 45.6 66.9 4.79 56.0 65.0 95.3 42.3 62.1 4050.3 5.7 -2.49 -0.02 -0.02 42.3 62.0 45.6 66.9 4.79 57.0 65.0 95.3 42.3 62.0 4112.3 5.7 -2.49 -0.02 -0.02 42.3 62.0 45.6 66.8 4.80 58.0 65.0 95.3 42.3 62.0 4174.4 5.7 -2.49 -0.02 -0.02 42.3 62.0 45.6 66.8 4.80 59.0 65.0 95.3 42.3 62.0 4236.4 5.8 -2.53 -0.05 -0.05 42.2 62.0 45.6 66.8 4.80 60.0 65.0 95.3 42.2 62.0 4298.4 5.8 -2.53 -0.04 -0.05 42.2 61.9 45.5 66.8 4.80 61.0 65.0 95.3 42.2 61.9 4360.3 5.8 -2.52 -0.04 -0.05 42.2 61.9 45.5 66.7 4.81 62.0 65.0 95.3 42.2 61.9 4422.2 5.8 -2.52 -0.04 -0.05 42.1 61.8 45.5 66.7 4.82 63.0 65.0 95.3 42.1 61.8 4484.0 5.8 -2.52 -0.04 -0.04 42.1 61.8 45.4 66.6 4.82 64.0 65.0 95.3 42.1 61.8 4545.8 5.8 -2.52 -0.03 -0.04 42.1 61.7 45.4 66.6 4.83 65.0 65.0 95.3 42.1 61.7 4607.6 5.8 -2.52 -0.03 -0.04 42.1 61.7 45.4 66.6 4.83 66.0 65.0 95.3 42.1 61.7 4669.3 5.8 -2.52 -0.03 -0.04 42.0 61.7 45.4 66.5 4.83 67.0 65.0 95.3 42.0 61.7 4730.9 5.8 -2.52 -0.03 -0.03 42.0 61.6 45.3 66.5 4.84 68.0 65.0 95.3 42.0 61.6 4792.6 5.6 -2.46 0.04 0.03 42.0 61.7 45.3 66.5 4.84 69.0 65.0 95.3 42.0 61.7 4854.2 5.6 -2.46 0.03 0.03 42.1 61.7 45.3 66.5 4.84 70.0 65.0 95.3 42.1 61.7 4915.9 5.6 -2.46 0.03 0.03 42.1 61.7 45.4 66.5 4.83 71.0 65.0 95.3 42.1 61.7 4977.6 5.6 -2.46 0.03 0.03 42.1 61.7 45.4 66.5 4.83 72.0 65.0 95.3 42.1 61.7 5039.3 5.6 -2.46 0.03 0.03 42.1 61.8 45.4 66.6 4.83 73.0 65.0 95.3 42.1 61.8 5101.1 5.6 -2.46 0.03 0.02 42.1 61.8 45.4 66.6 4.83 74.0 65.0 95.3 42.1 61.8 5162.8 5.6 -2.46 0.03 0.02 42.1 61.8 45.4 66.6 4.82 75.0 65.0 95.3 42.1 61.8 5224.6 5.6 -2.46 0.03 0.02 42.2 61.8 45.4 66.6 4.82 76.0 65.0 95.3 42.2 61.8 5286.5 5.6 -2.46 0.02 0.02 42.2 61.9 45.4 66.7 4.82 77.0 65.0 95.3 42.2 61.9 5348.3 5.6 -2.46 0.02 0.02 42.2 61.9 45.5 66.7 4.82 78.0 65.0 95.3 42.2 61.9 5410.2 5.6 -2.46 0.02 0.02 42.2 61.9 45.5 66.7 4.81 79.0 65.0 95.3 42.2 61.9 5472.0 5.8 -2.52 -0.04 -0.05 42.2 61.8 45.5 66.7 4.81 80.0 65.0 95.3 42.2 61.8 5533.9 5.8 -2.52 -0.04 -0.04 42.1 61.8 45.5 66.7 4.82 81.0 65.0 95.3 42.1 61.8 5595.7 5.8 -2.52 -0.04 -0.04 42.1 61.8 45.4 66.6 4.82 82.0 65.0 95.3 42.1 61.8 5657.5 5.8 -2.52 -0.03 -0.04 42.1 61.7 45.4 66.6 4.83 83.0 65.0 95.3 42.1 61.7 5719.3 5.8 -2.52 -0.03 -0.04 42.1 61.7 45.4 66.6 4.83 84.0 65.0 95.3 42.1 61.7 5781.0 5.8 -2.52 -0.03 -0.04 42.0 61.7 45.4 66.5 4.83 85.0 65.0 95.3 42.0 61.7 5842.6 5.8 -2.52 -0.03 -0.03 42.0 61.6 45.3 66.5 4.84 86.0 65.0 95.3 42.0 61.6 5904.3 5.8 -2.52 -0.03 -0.03 42.0 61.6 45.3 66.5 4.84 87.0 65.0 95.3 42.0 61.6 5965.9 5.8 -2.52 -0.02 -0.03 42.0 61.6 45.3 66.4 4.84 88.0 65.0 95.3 42.0 61.6 6027.5 5.8 -2.52 -0.02 -0.03 42.0 61.5 45.3 66.4 4.85 89.0 65.0 95.3 42.0 61.5 6089.0 5.8 -2.52 -0.02 -0.03 41.9 61.5 45.3 66.4 4.85 -0.20 42.5 62.4 3677.4 -0.18 42.4 62.2 3739.7 -0.03 42.4 62.2 3801.8 -0.03 42.4 62.1 3864.0 -0.02 42.3 62.1 3926.1 -0.02 42.3 62.1 3988.2 -0.02 42.3 62.1 4050.3 -0.02 42.3 62.0 4112.3 -0.02 42.3 62.0 4174.4 -0.02 42.3 62.0 4236.4 -0.05 42.2 62.0 4298.4 -0.05 42.2 61.9 4360.3 -0.05 42.2 61.9 4422.2 -0.05 42.1 61.8 4484.0 -0.04 42.1 61.8 4545.8 -0.04 42.1 61.7 4607.6 -0.04 42.1 61.7 4669.3 -0.04 42.0 61.7 4730.9 -0.03 42.0 61.6 4792.6 0.03 42.0 61.7 4854.2 0.03 42.1 61.7 4915.9 0.03 42.1 61.7 4977.6 0.03 42.1 61.7 5039.3 0.03 42.1 61.8 5101.1 0.02 42.1 61.8 5162.8 0.02 42.1 61.8 5224.6 0.02 42.2 61.8 5286.5 0.02 42.2 61.9 5348.3 0.02 42.2 61.9 5410.2 0.02 42.2 61.9 5472.0 -0.05 42.2 61.8 5533.9 -0.04 42.1 61.8 5595.7 -0.04 42.1 61.8 5657.5 -0.04 42.1 61.7 5719.3 -0.04 42.1 61.7 5781.0 -0.04 42.0 61.7 5842.6 -0.03 42.0 61.6 5904.3 -0.03 42.0 61.6 5965.9 -0.03 42.0 61.6 6027.5 -0.03 42.0 61.5 6089.0 -0.03 41.9 61.5 6150.5 Figure E-2. Tabular printout from TSPM (continued).

V′ = larger of speed at beginning of interval (V) and 10 ft/s Cde = correction factor for converting sea-level aerodynamic drag to local elevation = (1 − 0.000006887E) 4.255 Cpe = altitude correction factor for converting sea- level net horsepower to local elevation = 1 for diesel engines E = local elevation (ft) W/A = weight to projected frontal area ratio (lb/ft2) W/NHP = weight to net horsepower ratio (lb/hp) Equation 1 represents the coasting acceleration of the truck. Equation 2 represents the acceleration as limited by engine horsepower. Equations 3 and 4 combine the coasting and horsepower-limited accelerations into an effective accelera- tion that allows the truck to use maximum horsepower, except during gear shift delays of 1.5 s, during which the truck is coasting (with no power supplied by the engine). This model of truck performance is based on SAE truck-performance equations which were adapted by St. John and Kobett to incor- porate gear shift delays (86). There are no driver restraints on using maximum acceleration or maximum speed on upgrades E-5 because, unlike passenger car engines, truck engines are designed to operate at full power for sustained periods. • Columns 11 and 12 represent the calculated speed at the end of the 1-s interval in units of miles per hour and feet per second, based on vehicle performance. The speed in feet per second shown in Column 12 is simply the sum of the speed shown in Column 6 and change in speed computed as the acceleration shown in Column 12, mul- tiplied by the interval duration of 1 s. • Columns 13 through 15 show the limiting speed, in units of miles per hour and feet per second, and the limiting acceleration, in units of ft/s2, based on driver prefer- ences. These driver preference limitations are based on research which shows that, even when drivers are not limited by vehicle performance, the driver’s preferred acceleration rate will be limited as a function of the magnitude of the difference between the driver’s current speed and the desired speed (64). Such driver prefer- ences generally come into play only when the accelera- tion rate that would need to be used by the driver in returning to desired speed exceeds 1.2 ft/s2. The follow- ing three equations represent limitations on new speed TRUCK SPEED PROFILE FOR ROUTE 3 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 0.0 1000.0 2000.0 3000.0 4000.0 5000.0 6000.0 7000.0 Distance (ft) Sp ee d (m ph ) Figure E-3. Example of TSPM speed profile plot.

based on maximum preferred accelerations (or deceler- ations) for drivers for three specific cases: If |Vd − V| ≤ 1.2 then, Vn = Vd (5) If |Vd − V| > 1.2 and Vd − V > 0 then, Vn = V + (1.2 + 0.108 |Vd − V|) t (6) If |Vd − V| > 1.2 and Vd − V < 0 then, Vn = V − 1.2 t (7) where Vd = driver desired speed V = vehicle speed (ft/s) at the start of time interval t Vn = new speed (ft/s) at the end of time interval t t = duration of time interval (sec) (generally, t = 1 s) • Columns 16 through 18 show the actual acceleration over the 1-s interval and the new vehicle speed at the end of the 1-s interval considering both vehicle perfor- mance limitations and driver preferences. The new speed, in feet per second, shown in Column 18 is the minimum of the speeds shown in Columns 12 and 14. In other words, if the new speed (based on Equations 5, 6, or 7, as appropriate) is lower than the new speed based on E-6 Equations 1 through 4, then the lower speed based on Equations 5, 6, or 7 will govern. The maximum accel- eration preferences of drivers generally govern speed choices on the level, on downgrades, and on minor upgrades, but not on steep upgrades. Once the speed at the end of the 1-s interval is known, the acceleration during the interval shown in Column 16 can be computed as follows: (8) • Column 19 presents the new position of the vehicle at the end of the 1-s interval, expressed as a distance in feet from coordinate zero. The new position is determined as follows: Xn = Xo + Vt + 0.5 a t2 (9) where Xn = position at end of time interval of length t Xo = position at beginning of time interval of length t • The new speed in Columns 17 and 18 and the new posi- tion in Column 19 on one line of the spreadsheet become the speed at the start of the interval in Columns 4 and 5 and the position at the start of the interval in Column 6 on the next line of the spreadsheet. a V V t n = −