48 Electric and Hybrid Vehicles 2.7 An EV racer will attempt to jump five city buses as shown in the Figure P2.7. The vehicle will start at rest at a position 100 m from the beginning of the take-off ramp. The vehicle will accelerate uni- formly until it reaches the end of the take-off ramp at which time it will be traveling at 100 mi/h (miles per hour). The vehicle has the following parameter values: End of take-off ramp 30 0 25m 100m FIGURE P2.7 m = = 2 692 kg, C A 0.2, 2 = = m , C C 0 1 0.009, = 1.75*10 s –6 2 2 D F /m . Also, take density of air ρ = 1.16 kg/m 3 , and acceleration due to gravity g = 9.81 m/s 2 . a.
Sketch and label the velocity profile of the vehicle from the time it starts to the time it reaches the end of the take-off ramp. How much time does the vehicle take to reach the end of the take-off ramp? b. Calculate the change in gravitational potential energy, from start to the end of take-off ramp. c. Calculate energy loss, E loss from start to the end of take-off ramp, if ∆ e = Ч 8.28 10 5 TR J during that period. 2.8 The parameters of a vehicle are given below:
Vehicle mass = 2,000 kg Driver/one passenger = 80 kg Rolling resistance coefficient, C 0 = 0.01 Wheel radius, r wh = 0.3305 m Aerodynamic drag coefficient, C AD = 0.45 Frontal area, A F = 2.5 m 2 The vehicle accelerates from 0 velocity to 21 m/s in 5 s on a 0.5% roadway grade when it reaches the maximum power limit of the propulsion unit. The vehicle then accelerates in the constant power mode for another 7 s. The maximum power limit is 145kW. a. Write the dv / dt equation for constant power acceleration for the given conditions. b. What is the velocity after a total time of 10 s? c. What is the velocity at 12 s if the roadway grade changes to 4% at 10 s?