35 Vehicle Mechanics For example, let t V T = time to reach 98% of the terminal velocity V T . Therefore, t T tanh − V = 1 T or K K 1 2 V T 1 0.98 V 2.3 2.3 t V T = or . (2.16) K K 1 2 K V 2 T 2.6.1.3 Tractive Power The instantaneous tractive power delivered by the propulsion unit is P t TR ( ) = F v TR ( ) t . Substituting for v ( t ), P t TR ( ) = F V TR T T tanh( K V 2 t ). ⇒ = P t TR ( ) F V TR T T tanh ( ) K K 1 2 t P = tanh ( ) K K 1 2 t . (2.17) The terminal power can be expressed as P F T T = R T V . The tractive power required to reach the desired velocity v f over the acceleration interval ∆ t (refer to Figure 2.15) is P P TRpk = T f tanh ( ) K K 1 2 t .
(2.18) The mean tractive power over the acceleration interval ∆ t is t 1 P TR = ∫ f P t TR ( ) dt t f 0 ⇒ = P 1 P T TR ln cosh 1 2 1 2 ( ) K K t f (2.19) t K f K P TR P t t f ∆ t FIGURE 2.15 Acceleration interval Δ t = t f − 0. R(t) PT