84 Electric and Hybrid Vehicles The vehicle is to accelerate uniformly (i.e., constant acceleration) from 0 to 60 mph in 10 s. a. Find an expression for traction force as a function of time F TR ( t ) for this initial acceleration period. b. Find an expression for traction power as a function of time P TR ( t ) for the initial acceleration period. c. Find the energy Δ e TR required for initial acceleration between 0 and 10 s. 3.2 The vehicle parameters and performance requirements of the vehicle are used for sizing calculations: Description Requirements Vehicle mass 1,800 kg Driver/one passenger 176 lbs./80 kg Trailering capacity 1,000 kg Rolling resistance coefficients:
C 0 , C 1 0.01, 0 Wheel radius, r wh 0.3305 m Aerodynamic drag coefficient, C AD 0.45 Frontal area, A F 2.5 m 2 0–60 mph 8.0 s 50–70 mph 6.3 s Sustained cruising speed (with trailer) 55 mph at 7% grade Sustained cruising speed (without trailer) 70 mph at 0.5% grade Zero emission range (without trailer) 5 miles at 40 mph The initial acceleration requirement is without the trailer, but the total mass must account for the driver and one passenger. a. Calculate the velocity and power at the end of 5 s for a constant force initial acceleration. The constant force is 7,600 N. b.
The vehicle accelerates in the constant power mode after the initial constant force accel- eration period of part (a) with a constant power of 140 kW. Write the dv / dt equation for constant power acceleration for the given conditions. What is the velocity after a total time of 8 s. (You can solve the equation numerically.) c. Calculate the power required for a steady-state velocity of 55 mph at 7% with trailer. REFERENCES 1. C.C. Chan and K.T. Chau, Modern Electric Vehicle Technology , Oxford University Press, Oxford, UK, 2001. 2. R. Hodkinson and J. Fentos, Lightweight Electric/Hybrid Vehicle Design , SAE International, Warrendale, PA, 2001. 3. R. K.
Jurgen (editor), Electric and Hybrid Electric Vehicles , PT-85, SAE International, Warrendale, PA, 2002. 4. A. Nagasaka, M. Nada, H. Hamada, S. Hiramatsu, Y. Kikuchi, and H. Kato., “Development of Hybrid/ Battery ECU for the Toyota Hybrid System, Technology for Electric and Hybrid Vehicles,” SAE Publication, SP-1331, SAE International, Warrendale, PA, 1998. 5. J.F. Ronning and G.L. Grant, “Global Hybrid Electric Vehicle Markets and Missions,” Electric and Hybrid Electric Vehicles and Fuel Cell Technology, SAE Publication, SP-1466, SAE International, Warrendale, PA, 1999.