Calculate tractive force: maximum traction from vehicle weight and road surface friction, or the wheel force needed to accelerate and climb grades.

Largest forward force the tires can transmit before slipping: friction coefficient × weight on the driven wheels.

Slope and driven-wheel share
Blank = level road. Positive uphill; negative downhill.

Blank = 100% (all-wheel drive). Use about 50–60% for a typical two-wheel-drive car.

Tractive Force Formula

Required wheel force is acceleration force plus the selected road loads. The adhesion ceiling is a separate limit, not the force required to drive.

Frequired = m a + m g sin(theta) + Crr m g cos(theta) + rho Cd A v²/2
  • Where Frequired is the signed required wheel force (N), a is target acceleration, Crr is rolling resistance, and rho, Cd, A and v define aerodynamic drag
  • mu is the tire-road adhesion coefficient used only in the optional grip check
  • m is the mass of the vehicle (kg)
  • g is the acceleration due to gravity (m/s2)

For moving forward, sum acceleration, grade, rolling and aerodynamic terms. At standstill the modeled rolling term is zero. With grade percent =100 tan(theta), the simplified propulsion grip limit is mu × driven normal-load share × m g cos(theta). Acceleration before this limit is explicitly uncapped; negative wheel force does not establish actual braking capacity.

What is a Tractive Force?

Definition:

In mechanics, the tractive force is the component of a force vector parallel to the ground that is applied to a body to cause it to move in the desired direction. Tractive force is also commonly used synonymously with traction force.

How to Calculate Tractive Force?

Example Problem:

The following example calculates an adhesion ceiling, separate from required wheel force.

First, determine the mass of the vehicle. In this example, the vehicle weighs 950 kg.

Assume a tire-road adhesion coefficient of0.7 for this example; this is not a universal tire-road average. Assume level ground and100%of normal load on the driven wheels.

The estimated propulsion-grip ceiling is then:

Fgrip = mu × driven share × m × g

Fgrip =0.7 ×1 ×950 ×9.80665

Fgrip =6521.42225N. Required force still depends on target acceleration and selected road loads; load transfer, actual tire slip and braking distribution are not modeled.