Calculation Overview

hp 5 (146.19 3 50)/375 5 19.49 or approximately 20 hp

Only about 20 hp is necessary—at the wheels—to propel this pickup truck along at 50 mph on a level road without wind. In fact, a rated 20-hp electric motor will easily propel a 4,000-lb. vehicle at 50 mph—a fact that might amaze those who think in terms of the typical rated 90-hp or 120-hp internal combustion engine that might just have been removed from the pickup.

The point here is to condition yourself to think in terms of force values, which are relatively easy to determine, rather than in terms of a horsepower figure that is arrived at differently for engines versus electric motors, and that means little until tied to specific force and speed values anyway.

Another point (covered in more detail in Chapter 6’s discussion of electric motors and Chapter 9’s discussion of the electrical system) is to think in terms of current when working with electric motors. The current is directly related to motor torque. Through the torque-current relationship, you can directly link the mechanical and electrical worlds. (Note: The controller gives current multiplication. In other words, if the motor voltage is one-third the battery voltage, then the motor current is slightly less than three times the battery current. The motor and battery current would be the same only if you used a very inefficient resistive controller.)

Calculation Overview

Notice that the starting point in the calculations was the ending point of the force value required. Once you know the forces acting on your vehicle chassis at a given speed, the rest is easy. For your calculation approach, first determine these values, then plug in your motor and drivetrain values for its design center operating point, be it a 100-mph speedster, a 20-mph economy flyer, or a 50-mph utility vehicle. A 50-mph speed will be the design center for our pickup truck utility vehicle example.

In short, you need to select a speed, select an electric motor for that speed, choose the RPM at which the motor delivers that horsepower, choose the target gear ratio based on that RPM, and see if the motor provides the torque over the range of level and hillclimbing conditions you need. Once you go through the equations, worksheets, and graphed results covered in this section, and repeat them with your own values, you’ll find the process quite simple.

The entire process is designed to give you graphic results you can quickly use to see how the torque available from your selected motor and drivetrain meets your vehicle’s torque requirements at different vehicle speeds. If you have a microcomputer with a spreadsheet program, you can set it up once, and afterwards graph the results of any changed input parameter in seconds. In equation form, what we are saying is Available engine power 5 Tractive resistance demand Power 5 (Acceleration 1 Climbing 1 Rolling 1 Drag 1 Wind) Resistance

Plugging into the force equations gives you:

Force 5 F a 1 Fh 1 F r

1 Fd 1 F w Force 5 CiWa 1 Wsin f 1 C r Wcos f 1 CdAV2 1 C w Fd

You’ve determined every one of these earlier in the chapter. Under steady-speed conditions, acceleration is zero, so there is no acceleration force. If you are on a level surface, sin f 5 0, cos f 5 1 and the force equation can be rewritten as

Force 5 C r Wcos f 1 CdAV2 1 C w

Fd

This is the propulsion or road-load force you met at the end of the rolling resistance section and graphed for the Ford pickup in Figure 5-5. You need to determine this force for your vehicle at several candidate vehicle speeds, and add back in the acceleration and hill-climbing forces. This is easy if you recall that the acceleration force equals the hill-climbing force over the range from 1 mph/sec to 6 mph/sec.

You can now calculate your electric motor’s required horsepower for your EV’s design center. Horsepower (hp) 5 (Torque 3 RPM)/5252 5 2p/60 3 FV/550 Wheel RPM 5 (mph 3 Revolutions/mile)/60

The previous equation can be substituted to give

but,

HPwheel 5 (Torquewheel 3 mph 3 Revolutions/mile)/(5252 3 60)

hpmotor 5 hpwheel/no

where n o is the overall drivetrain efficiency. Substituting the previous equation into this gives you:

hpmotor 5 (Torquewheel 3 mph 3 Revolutions/mile)/(315120 3 n o))

Plugging the values for torque, speed, and revolutions/mile (based on your vehicle’s tire diameter) into the equation will give you the required horsepower for your electric motor.

After you have chosen your candidate electric motor, the manufacturer will usually provide you with a graph or table showing its torque and current versus speed performance based on a constant voltage applied to the motor terminals. From these figures or curves, you can derive the RPM at which your electric motor delivers closest to its rated horsepower. Using this motor RPM figure and the wheel RPM figure, which gives you the wheel RPM from your target speed and RPM, you can determine your best gear or gear ratio from Overall gear ratio 5 RPMmotor/RPMwheel

This—or the one closest to it—is the best gear for the transmission in your selected vehicle to use; if you were setting up a one-gear-only EV, you would pick this ratio. With all the other motor torque and RPM values you can then calculate wheel torque and vehicle speed using the following equations for the different overall gear ratios in your drivetrain:

Torquewheel 5 Torquemotor/(overall gear ratio 3 n o)

Speedvehicle (in mph) 5 (RPMmotor 3 60)/(overall gear ratio 3 Revolutions/mile)

You now have the family of torque available curves versus vehicle speed for the different gear ratios in your drivetrain. All that remains is to graph the torque required data and the torque available data on the same grid. A quick look at the graph tells you if you have what you need or if you need to go back to the drawing board.