31 Vehicle Mechanics V 0 t t f FIGURE 2.10 Plot of velocity profile. F TR inc β V FIGURE 2.11 Tractive force versus steady-state velocity characteristics. cruising speed and at the maximum speed on a specified slope. The useful design information is contained in the vehicle speed versus time and the steady-state tractive force versus constant veloc- ity characteristics, illustrated in Figures 2.10 and 2.11. In the sections to follow and in the remainder of this book, we will always assume the velocity to be in the tangential direction and denote it by v instead of v xT for simplicity. The steady-state constant velocity will be denoted by the upper case V . dv tion of motion (Equation 2.5).
When steady-state velocity is reached, = 0 ; and hence, Σ = F 0 . dt Therefore, we have The tractive force versus steady-state velocity characteristics can be obtained from the equa- F F TR − − AD F F ROLL − = gxT 0 ρ ⇒ = F m TR g C [ ] sin s β + + 0 1 gn( V V ) sgn( ) mgC C + A V 2 D F . 2 Note that dF TR ρ C A 1. = + 2 s V V D F gn( ) mgC V 2 1 > ∀ 0 and dV 2. lim F F TR ≠ lim . TR → → + − V 0 0 V The first equation reveals that the slope of F TR versus V is always positive, meaning that the force requirement increases more than the velocity increase as the vehicle speed increases, which is due v(t) Steady state constant ve Transient vf