38 Electric and Hybrid Vehicles dv Σ = F m dt dv ⇒ − F F TR AD − − F F roll gxT = m dt (2.21) dv ⇒ = F m TR + + mg sin β F F AD + roll dt dv ρ = m + + mg sin β + mgC A C v 2 + mgC 1 F D 0 . dt 2 The instantaneous tractive power P t TR ( ) is dv = + mv v F ( ) gxT A + + F F D roll .
(2.22) dt P t TR ( ) = F t TR ( ) v t ( ) The change in tractive energy ∆ e TR is f ∆ = TR TR ( ) t dt e P ∫ t t i m vdv v F gxT dt ∫ v t ( ) f t f t f ( ) + + ( ) v F ( ) AD F d roll t (2.23) = + ∫ ∫ v t ( ) i t i t i The energy supplied by the propulsion unit is converted into various forms of energy, some of which are stored in the vehicle system, while others are lost due to the non-constructive forces. It is inter- esting to note the type of energy associated with each term in Equation 2.23.
Let us consider the first term on the right side of Equation 2.23 v t ( ) f m ∫ 1 vdv m = − v t 2 2 ( ) f i v t ( ) = ∆ (kinetic energy) 2 v t ( ) i Also, t ∫ ∫ t i t i s t ( ) ∫ ∫ f t f s t ( ) f f t ( ) f ( ) v F gxT dt = = mg v d sin s β β t mg d in s m = g df i f t ( ) i = − mg f t ( ) f i f t ( ) = ∆ (potential energy) The above term represents change in vertical displacement multiplied by mg , which is the change in potential energy.