Slip ratio

Slip ratio is a means of calculating and expressing the slipping behavior of the wheel of an automobile. It is of fundamental importance in the field of vehicle dynamics, as it allows to understand the relationship between the deformation of the tire and the longitudinal forces (i.e. the forces responsible for forward acceleration and braking) acting upon it. Furthermore, it is essential to the effectiveness of any anti-lock braking system.

When accelerating or braking a vehicle equipped with tires, the observed angular velocity of the tire does not match the expected velocity for pure rolling motion, which means there is sliding between the tire and the road in addition to rolling. This difference, expressed as a percentage, is called ‘slip ratio’. This slippage plays a major role in the generation of forces at the contact patch of the tire, and is thus of fundamental importance to determine the accelerations a vehicle can produce.

There is no universally agreed upon definition of slip ratio.^[1] The SAE J670 definition is, for tires pointing straight ahead:^[2]

${\displaystyle Slip\ Ratio\ \%=\left({\frac {\Omega \,R_{C}}{V}}-1\right)\times 100\%}$

Where Ω is the angular velocity of the wheel, R_C is the effective radius of the corresponding free-rolling tire, which can be calculated from the revolutions per kilometer, and V is the forward velocity of the vehicle.

1. Milliken, William; Milliken, Douglas (December 1, 1994). Race Car Vehicle Dynamics. ISBN 978-1-56091-526-3.
2. SAE Vehicle Dynamics Standards Committee (January 24, 2008). "Vehicle Dynamics Terminology". Society of Automotive Engineers.