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.
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 appears to be apparent sliding between outer surface of the rim and the road in addition to rolling due to deformation of the part of tire above the area in contact with the road.
When driving on dry pavement the fraction of slip that is caused by actual sliding taking place between road and tire contact patch is negligible in magnitude and thus does not in practice make slip ratio dependent on speed.
This slippage is caused by the forces at the contact patch of the tire, not the opposite way, and is thus of fundamental importance to determine the accelerations a vehicle can produce.
is the effective radius of the corresponding free-rolling tire, which can be calculated from the revolutions per kilometer, and