Maximum Tractive Effort

 Maximum Tractive Effort No matter how much force a vehicle’s engine makes available at the roadway surface, there is a point beyond which additional force merely results in the spinning of tires and does not overcome resistance or accelerate the vehicle. To explain what determines this point of maximum tractive effort (the limiting value beyond which tire spinning begins), a force and moment-generating diagram

Vehicle forces and moment-generating distances.

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Ra = aerodynamic resistance in lb, θ g = angle of the grade in degrees,

Rrlf = rolling resistance of the front tires in lb, m = vehicle mass in slugs,

Rrlr = rolling resistance of the rear tires in lb, a = acceleration in ft/s2, Ff = available tractive effort of the front tires in lb, L = length of wheelbase,

Fr = available tractive effort of the rear tires in lb, h = height of the center of gravity above the roadway surface, W = total vehicle weight in lb,

Wf = weight of the vehicle on the front axle in lb, lf = distance from the front axle to the center of gravity, and Wr = weight of the vehicle on the rear axle in lb,

lr = distance from the rear axle to the center of

gravity. To determine the maximum tractive effort that the roadway surface-tire contact can support, it is necessary to examine the normal loads on the axles. The normal load on the rear axle (Wr) is given by summing the moments about point A :

cos sina f g g


R h Wl mah Wh W


θ θ+ + ± = (2.10)

In this equation, the grade moment (Wh sin θg) is positive for an upward slope and negative for a downward slope. Rearranging terms (assuming cos θg = 1 for the small grades encountered in highway applications) and substituting into Eq. 2.2 gives

( )f r rl

l h W W F R

L L = + − (2.11)

From basic physics, the maximum tractive effort as determined by the roadway surface–tire interaction will be the normal force multiplied by the coefficient of road adhesion (μ), so for a rear-wheel–drive car

rF Wμ= (2.12)