36 Electric and Hybrid Vehicles 2.6.1.4 Energy Required The energy requirement for a given acceleration and constant steady-state velocity is necessary for the design and selection of the energy source or batteries to cover a certain distance. The rate of change of energy is the tractive power given as de P t ( ) = TR TR dt where e TR is the instantaneous tractive energy. The energy required or energy change during an interval of the vehicle can be obtained from the integration of the instantaneous power equation as e TR ∫ ∫ ( ) t f f t de TR = P d TR t e TR (0) t = 0 (2.20) ⇒∆ e t TR = f T P R Example 2.1 An EV has the following parameter values:
m = = 800 kg, C A 0.2, = = 2.2 m , 2 C C 0 1 0.008, = 1.6*10 s –6 2 2 D F /m , The vehicle is on level road. It accelerates from 0 to 65 mi/h in 10 s such that its velocity profile is given by Also, take density of air ρ = 1.18 kg/m 3 , and acceleration due to gravity g = 9.81 m/s 2 . v t ( ) = ≤ 0.29055 t t 2 for 0 ≤ 10 s. a. Calculate F TR ( t ) for 0 1 ≤≤ t 0 s . b. Calculate P TR ( t ) for 0 1 ≤≤ t 0 s . c. Calculate the energy loss due to nonconservative forces E loss . d. Calculate Δ e TR . Solution a. From the force balance equation, dv F F TR − − AD F m roll = dt dv ρ ⇒ = F t + + 2 TR ( ) m C A v mg C ( ) 2 2 0 1 + C v dt D F = + 464.88 t t 0.02192 4 + 62.78 N. b.
The instantaneous power is P t TR ( ) = Ч F t TR ( ) v t ( ) = + 135.07 t t 3 6 0.00637 + 18.24 t 2 W.