32 Electric and Hybrid Vehicles F TR mg F TR β cg mgsin β __________ √(mg) 2 -F TR 2 (a) (b) FIGURE 2.12 (a) Force diagram to determine maximum gradability. (b) Tractive force and mg with respect to the grade. to the aerodynamic drag force opposing the vehicle motion. Also, the discontinuity of the curves at zero velocity is due to the rolling resistance force. 2.5.2 m aximum g radabiliTy The maximum grade that a vehicle will be able to overcome with the maximum force available from the propulsion unit is an important design criterion as well as performance measure.
The vehicle is expected to move forward very slowly when climbing a steep slope, and hence, we can make the following assumptions for maximum gradability: 1. The vehicle moves very slowly ⇒ v ≅ 0. 2. F AD and F roll are negligible. 3. The vehicle is not accelerating, i.e., dv / dt = 0. 4. F TR is the maximum tractive force delivered by motor (or motors) at near zero speed. At near stall condition, under the above assumptions, F Therefore, sin β = TR . The maximum percent grade is mg Max.% grade = 100tan β 100 F TR (2.10) ⇒ = Max.% grade ( ) mg 2 − F 2 TR The force diagram for the maximum gradability condition is shown in Figure 2.12.
2.6 VELOCITY AND ACCELERATION The energy required from the propulsion unit depends on the desired acceleration and the road load force that the vehicle has to overcome. The maximum acceleration is limited by the maximum trac- tive power available and the roadway condition at the time of vehicle operation. Although the road load force is unknown in a real-world roadway, significant insight about the vehcile velocity profile and energy requirement can be obtained through studies of assumed scenarios. The vehicles are typically designed with a certain objective, such as maximum acceleration on a given roadway slope on a typical weather condition.
Two simplified scenarios that will set forth the stage for designing electric and hybrid EVs are discussed in the following.