39 Vehicle Mechanics The third and fourth terms on the right side of Equation 2.23 represent the energy required to overcome the non-constructive forces that include the rolling resistance and the aerodynamic drag force. The energy represented in these terms is essentially the loss term. Therefore, t f ∫ ( ) v F ( ) AD + = F d roll t E loss . t i ρ Let K m 3 0 = = gC , K m 4 1 gC + C A D F . For, v t ( ) > ≤ 0, t t i f ≤ t , 2 f t f ds E loss = + K 3 4 dt K v 3 dt ; dt t i t i t f = ∆ K s 3 4 + K v ∫ t ∫ ∫ 3 dt .
t i In summary, we can write t f 1 ∆ = e m v t 2 2 TR − ( ) f i v t ( ) + − mg f t ( ) f i f t ( ) + + ( ) v F ( ) AD F d roll t or 2 ∫ t i ∆ = e E TR ∆ + (kinteic energy) ( ∆ + potential energy) loss Exercise 2.3 The vehicle with parameters given in Exercise 2.2 accelerates from 0 to 60 mph in 13.0 s for the following two acceleration types: (i) constant F TR and (ii) uniform acceleration. a. Plot on the same graph, the velocity profile of each acceleration type. b. Calculate and compare the tractive energy required for the two types of acceleration. F TR = = const. 1,548 N. Ans. (b) Δ e TR = 0.2752 MJ for constant F TR and Δ e TR = 0.2744 MJ for uniform acceleration.
2.7 TIRE–ROAD FORCE MECHANICS A number of forces including the traction force act at the tire-ground contact plane of a moving vehicle. The traction torque from the propulsion system is converted into a traction force through an interaction of the pneumatic tire and the road surface at the tire–road interface. The pneumatic tire is designed to perform several functions of a ground vehicle including support of the vehicle weight and provide traction for driving and braking.
The performance potential of a vehicle depends not only on the characteristics of the propulsion system and transmission but also on the maximum trac- tion (or braking) force that can be sustained at the tire–road interface. The maximum friction force sustainable is determined by the friction coefficient of the pneumatic tire which depends on its road adhesion characteristics and the normal load on the drive axle or axles. The smaller of the propul- sion system traction (or braking) force and the maximum sustainable friction force determines the