The basic equation for determining the hp required for a drive system is:
Required Hp = Hp (Rolling Resistance) + Hp (drag) + Hp (Hill Climbing) + Hp (acceleration)
- Rolling resistance is typically 1% of the vehicle weight. It takes ~1.5 hp per 1000 lbs of vehicle to maintain 50 mph at 0% grade and no aerodynamic drag. So a 4000 lbs vehicle is 4 times as much ~ 6 hp for rolling resistance.
- Aerodynamic Drag is a function of speed squared and frontal area. If you double the speed, the aerodynamic drag increases by 4! With a Drag Coefficient of 0.2 (Cd=0.2) very aerodynamic vehicle, is approximately 0.7 hp at 25 mph and approximately 3 hp is required at 50 mph. With Cd=.4 approximately 7 hp is required at 50 mph. This is based on a frontal area of about 18 sq ft.
- Hills are a major obstacle. A 1% grade is a 1 ft rise in 100 ft. This is the same amount of energy as rolling resistance. A 5% grade (5 ft rise in 100 ft) is five time rolling resistance. That means that it takes 5 times rolling resistance (~8 hp) for a 1000 lb vehicle. For a 4000 lb vehicle, 30 hp is required for the same 5% grade. This is why designing a vehicle for Colorado is considerably different than designing an EV for Florida.
Typically, when we size motors for on-road EV applications, we assume a 2% grade and 50 mph. For a 4000 lb conversion, this would be another 12 hp for a total of 25 hp. Our rule of thumb has been it takes 6- 8 hp per 1000 lbs. That would dictate 24-32 hp. You can see that we are within the range.
- Acceleration can become the dominant requirement. Looking at the totals above for a 4000 lb vehicle with a Cd=.4, approximately only 13 hp is required to maintain 50 mph and 0% grade. A Corvette requires ~ 20 hp at 60 mph and 0% grade. With a 430 hp engine, acceleration is the predominant requirement for the 2010 Corvette.
American auto manufacturers love hp and acceleration. So they require high voltage systems (300+V) in order to maintain reasonable currents. The disadvantage of high voltage systems is more batteries. To minimize the weight and space required, the manufacturers must use smaller and lighter weight batteries.
It is important to remember that as you identify the required motor hp, the entire drive system must also be designed for that hp. For example, if your design requirements dictate 30 hp, then the motor, controller, and battery pack must be designed to deliver 30 hp continuous. That is what system design is all about. For EVs, it is important to convert hp into watts, by multiplying by 746
30 hp x 746 watt/hp = 22380 watts.
So if you have a 144V system, you will need only 155 amps. But a 72V system requires a 310 amps. This is the continuous rating. The FB1-4001A motor is rated at 30 hp continuous and 100 hp peak at 144VDC. To get that 100 hp, you can see that almost 520 amps is required. That means that the controller and battery system must also be capable of delivering much higher amperage than the continuous rating. |
