47 Vehicle Mechanics 2.3 An EV has the following parameter values: m = 692 kg, C D = 0.2, A 2 F = 2 m , C 0 = 0.009, C 1 = 1.75 * 10 −6 s 2 /m 2 . Also, take ρ = 1.16 kg/m 3 , g = 9.81 m/s 2 , a. EV at rest The EV is stopped at a stop sign at a point in the road where the grade is + 15%. The tractive force of the vehicle is supplied by the vehicle brakes. i. Calculate the tractive force necessary for zero rolling resistance (the vehicle is at rest). ii. Calculate the minimum tractive force required from the brakes to keep the EV from rolling down the grade. b. EV at constant velocity The EV is moving at a constant velocity along a road that has a constant grade of − 12%. i.
Plot, on the same graph, the magnitudes of the tangential gravitational force ( F gxT ), the aerodynamic drag force ( F AD ) and the rolling resistance force ( F roll ) ver- sus velocity for 0 ≤ V 180 mph . Over that range of velocity, does F gxT dominate? When does F AD dominate? When does F roll dominate? Label these regions on the graph. ii. Derive an expression for the tractive force as a function of velocity. Plot this expression on its own graph. Is the tractive force always in the same direction? 2.4 Showing all steps, derive and plot the velocity profile (i.e., v ( t )) for constant F TR -constant grade acceleration.
(Constant grade means that β is constant but not necessarily zero.) Given: 1. The EV starts from rest at t = 0 . 2. Resultant of F gxT and F TR is enough to overcome the rolling resistance to get the EV moving. 3. v t ( ) ≥ ≥ 0 for t 0. What effect does gravity have on the velocity profile? 2.5 A vehicle accelerates from 0 to 60 mi/h in 10 s with the velocity profile given by v t ( ) = + 20ln(0.282 t t 1) m/s for 0 ≤≤ 10 s. The vehicle is on level road. For the problem use the parameters given in Problem 2.3. (a) Calculate and plot F TR ( t ) and P TR ( t ) for 0 1 ≤≤ t 0 s . (b) Calculate Δ e TR . How much of Δ e TR is D KE ? How much is E loss ?
2.6 Using the vehicle parameters given in Problem 2.3, calculate and plot, on the same graph, steady- state F TR versus V characteristics for β = ± 4 ° and − 60 ≤ ≤ V 60 mi/h, but V ≠ 0.