TRACTIVE EFFORT AND RESISTANCE

Tractive effort (also referred to as thrust) and resistance are the two primary opposing forces that determine the straight-line performance of road vehicles. Tractive effort is simply the force available, at the roadway surface, to perform work and is expressed in lb. Resistance, also expressed in lb, is defined as the force impeding vehicle motion. The three major sources of vehicle resistance are (1) aerodynamic resistance, (2) rolling resistance (which originates from the roadway surface and tire interface), and (3) grade or gravitational resistance. To illustrate these forces, consider the vehicle force diagram

Ra = aerodynamic resistance in lb, W = total vehicle weight in lb,

Rrlf = rolling resistance of the front tires in lb, θg = angle of the grade in degrees,

Rrlr = rolling resistance of the rear tires in lb, m = vehicle mass in slugs, and

Ff = available tractive effort of the front tires in lb, a = acceleration in ft/s2.

Fr = available tractive effort of the rear tires in lb,

Summing the forces along the vehicle’s longitudinal axis provides the basic

equation of vehicle motion:

f r a rlf rlr gF F ma R R R R+ = + + + + (2.1)

where Rg is the grade resistance and is equal to W sin θg. For exposition purposes, it is convenient to let F be the sum of available tractive effort delivered by the front and rear tires (Ff + Fr) and similarly to let Rrl be the sum of rolling resistance (Rrlf + Rrlr). This notation allows Eq. 2.1 to be written as

a rl gF ma R R R= + + + (2.2)