Longitudinal force and slip ratio

For a tyre to produce a longitudinal force (driving or braking) it must slip (stretch then release). This means that its rotational velocity is not equal to its translational velocity. The amount of slipping “Slip Ratio” is expressed either as a fraction or a percentage.

SR = (Rotational Velocity / Translational Velocity) -1

The actual definition of slip ratio differs worldwide, depending on how the rotational velocity is calculated. Some notable ones are:

Rl= Wheel centre above the road surface, (loaded radius) Calspan
Re= Effective rolling radius (zero slip angle, free rolling) revs/m SAE
Free rolling, SR = 0; Braking limit, SR = -1; Driving limit, SR = +1

The three dimensional visualization of Longitudinal Force with Slip Ratio and Normal Load is shown in the diagrams. The chart on the left is for pure longitudinal force (zero slip angle). The chart on the right is for 3.5° slip angle.

Longitudinal force and slip ratio - White-Smoke

As with the 3D lateral response surface, the longitudinal response surface provides us with a wealth of information. The curvature of the surface with slip ratio, normal load and slip angle dictates how the car will respond to changes in parameters and its eventual CONTROL, STABILITY and HANDLING behavior.

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