Forces involved

In addition of the inertia force (ma) and the tire friction force (F_f = μF_v), two other forces must be considered for evaluating longitudinal acceleration: the rolling resistance and the aerodynamic drag.

Rolling resistance

The rolling resistance (F_r = f_rF_v) is a force that acts in a way similar to the friction force. The only difference is that the rolling resistance direction depends on the rolling direction of the tire and the friction force direction depends on the torque application. So sometimes the rolling resistance acts against the friction force (acceleration) and sometimes it works with the friction force (braking).

Since the rolling resistance and the friction force are always in the same plane, you could say that the result is a tire with «net» friction coefficient (= μ ± f_r) that is greater or smaller depending if the vehicle is accelerating or braking.

The rolling resistance is very small and can be omitted in most cases. The net effect is usually a variation of 1-2% of the original tire friction coefficient. It is more important in off-road situations where that variation can go up to 30% (tire on sand for example).

Aerodynamic forces

Drag

The drag force (F_D = 0.5ρC_DAv²) is acting at height h_D above the ground. Although unrelated, we can assume that the drag force height is equal to the center of gravity height (h). This will simplify the mathematical equations.

Lift

A lift force (F_L = 0.5ρC_LAv²) is generally produced by a typical vehicle. It is relatively small though, so it can be ignored in most cases. However, with race cars, not only do we try to avoid lift but we actually create «negative» lift, or downforce, with the help of inverted wings or ground effects.

This force will be distributed between the front and rear axle according to the vehicle design. Since it is the reaction forces at each axle that are important, we will divide the total lift force into two: the front lift force (F_Lf = 0.5ρC_LfAv²) and the rear lift force (F_Lr = 0.5ρC_LrAv²), such that F_L = F_Lf + F_Lr (or C_L = C_Lf + C_Lr).