Torque Required and Available Graph

Torque Required and Available Graph

All that remains is to graph the torque required data from Table 5-10 and the torque available data from Table 5-11 on the same grid versus vehicle speed. This is done in Figure 5-9. Notice its similarity to the curve in Figure 5-8 drawn for the internal combustion engine (except that the torque available curves resemble the electric motor characteristics, a comparison made earlier in Figure 5-7).

How do you read Figure 5-9 and what does it tell you? The usable area of each gear is the area to the left and below it, bounded at the bottom by the torque required at the level condition curve. You want to work as far down the torque available curve for each gear as possible for minimum current draw and maximum economy and range. The graph confirms that 2nd gear is probably the best overall selection. You could put the EV into second gear and leave it there, because it gives you 2 mph/sec acceleration at startup, hill-climbing ability up to 15 percent inclines, and provides you with enough torque to take you up to about 52.5 mph. For mountain climbing or quick pops off the line, 1st gear gives you everything you could hope for at the expense of really sucking down the amps, current-wise. But at the other end of 1st gear, if you drive like there’s an egg between your foot and the accelerator pedal, it actually draws only 100 amps at 45 mph versus the 210 amps required by 2nd gear. At higher speeds, 3rd gear lets you cruise at 60 mph at 270 amps, and 4th gear lets you cruise at 70 mph at 370 amps. At any speed, 5th gear appears marginal in this particular vehicle; though it can possibly hold 78 mph, it requires 440 amps to do so. At any other speed, other gears do it better with less current draw. While current draw is your first priority, too much for too long overheats your motor. You don’t want to exceed your motor’s speed rating either, as you would do if you drove much above 45 mph in 1st gear. Is this a usable motor and drivetrain combination for this vehicle? Definitely. If you want to make minor adjustments, just raise or lower the battery voltage. This will shift the torque available curve for each gear to the right (higher voltage) or to the left (lower voltage). A larger motor in this particular vehicle will give you better acceleration and upper-end speed performance; the torque available curves for each gear would be shifted higher. But the penalty would be higher weight and increased current draw and shorter range. A smaller motor would shift the torque available curves lower while returning a small weight and current draw advantage. But beware of underpowering your vehicle. If given the choice, always go for slightly more rather than slightly less horsepower than you need. The result will almost always be higher satisfaction with your finished EV conversion.

Vehicle gear 1st 1st 2nd 2nd 3rd 3rd 4th 4th 5th 5th

Overall gear ratio 13.66 13.66 7.18 7.18 4.73 4.73 3.45 3.45 2.9 2.9

Motor torque 12.294 6.462 4.257 3.105 2.61

multiplier, equation (12) RPM multiplier, 165.56 87.02 57.33 41.81 35.15

equation (13) Current in amps, Motor Motor Motor Wheel Vehicle Wheel Vehicle Wheel Vehicle Wheel Vehicle Wheel Vehicle torque in ft-lbs, Current Torque RPM Torque Speed Torque Speed Torque Speed Torque Speed Torque Speed vehicle speed in mph

100 10 7750 122.94 46.81 64.62 89.06 42.57 135.19 31.05 185.34 26.10 220.50 125 15 6400 184.41 38.66 96.93 73.54 63.86 111.64 46.58 153.06 39.15 182.09 150 20 5000 245.88 30.20 129.24 57.46 85.14 87.22 62.10 119.58 52.20 142.26 170 25 4600 307.35 27.78 161.55 52.86 106.43 80.24 77.63 110.01 65.25 130.88 190 30 4100 368.82 24.76 193.86 47.11 127.71 71.52 93.15 98.05 78.30 116.65 210 35 3900 430.29 23.56 226.17 44.82 149.00 68.03 108.68 93.27 91.35 110.96 230 40 3700 491.76 22.35 258.48 42.52 170.28 64.54 124.20 88.49 104.40 105.27 250 45 3500 553.23 21.14 290.79 40.22 191.57 61.05 139.73 83.70 117.45 99.58 270 50 3400 614.70 20.54 323.10 39.07 212.85 59.31 155.25 81.31 130.50 96.73 290 55 3350 676.17 20.23 355.41 38.50 234.14 58.44 170.78 80.12 143.55 95.31 305 60 3250 737.64 19.63 387.72 37.35 255.42 56.69 186.30 77.73 156.60 92.47 320 65 3150 799.11 19.03 420.03 36.20 276.71 54.95 201.83 75.33 169.65 89.62 335 70 3050 860.58 18.42 452.34 35.05 297.99 53.20 217.35 72.94 182.70 86.78 355 75 3000 922.05 18.12 484.65 34.47 319.28 52.33 232.88 71.75 195.75 85.35 370 80 2950 983.52 17.82 516.96 33.90 340.56 51.46 248.40 70.55 208.80 83.93 390 85 2900 1045.0 17.52 549.27 33.33 361.85 50.59 263.93 69.35 221.85 82.51 405 90 2850 1106.5 17.21 581.58 32.75 383.13 49.71 279.45 68.16 234.90 81.09 420 95 2800 1167.9 16.91 613.89 32.18 404.42 48.84 294.98 66.96 247.95 79.66 440 100 2750 1229.4 16.61 646.20 31.60 425.70 47.97 310.50 65.77 261.00 78.24

* Values computed for 1987 Ford Ranger pickup; tires = P185/75R14; revolutions/mile = 808; overall drivetrain efficiency = 0.90; dc series traction motor is Advanced DC Motors Model FBI-4001; battery pack is 120 volts; equation (12) is Twheel = T motor/(overall gear ratio x overall drivetrain efficiency); equation (13) is Speedvehicle = RPMmotor x 60)/(overall gear ratio x revolutions/mile). Table 5-11 Torque Available Worksheet for 120-Volt DC Series Motor Powered 1987 Ford Ranger Pickup at Different Motor Speeds and Gear Ratios