# Slip (vehicle dynamics)

In (automotive) vehicle dynamics, slip is the relative motion between a tire and the road surface it is moving on. This slip can be generated either by the tire's rotational speed being greater or less than the free-rolling speed (usually described as percent slip), or by the tire's plane of rotation being at an angle to its direction of motion (referred to as slip angle).[1]

In rail vehicle dynamics, this overall slip of the wheel relative to the rail is called creepage. It is distinguished from the local sliding velocity of surface particles of wheel and rail, which is called micro-slip.

## Longitudinal slip

The longitudinal slip is generally given as a percentage of the difference between the surface speed of the wheel compared to the speed between axis and road surface, as:

$slip=\frac{\omega r-v}{v} * 100%,$

where $\omega$ is the lateral component of the rotational speed of the wheel, $r$ is wheel radius at the point of contact and $v$ is vehicle speed. Meaning a positive slip means the wheels are spinning and negative that they are skidding. Locked brakes, $\omega r=0$, means that $slip$ is -100% and spinning on the spot. $v=0$ and $\omega r$$0$, means that $slip=$∞.

## Lateral slip

The lateral slip of a tire is the sideways motion of a tire which occures when the sideway forces of a tire are greater than its friction resistance.[2] This can occur, for instance, in cornering.

The slip angle can be defined as:

$\alpha = \arctan\left(\frac{v_y}{|v_x|}\right)$