Slip (vehicle dynamics)

In (automotive) vehicle dynamics, slip describes the relative motion between a tire and the road surface it is moving on. This slip can be generated either by the tire's angular velocity being greater or less than the free-rolling speed (referred to as slip ratio), or by the tire's front facing direction being at an angle to its direction of motion (referred to as slip angle). When both of these measurements do not equal zero, the tire enters a state called combined slip.

Longitudinal slip ratio

The longitudinal slip (commonly referred to as longitudinal slip ratio) is used to describe the rotational state of a tire at any given speed. The most common definition is given as the ratio between the tire's slip velocity and the forward facing component of the tire's linear velocity. Mathematically, this definition can be expressed as:

${\displaystyle \sigma ={\frac {r_{e}\Omega -v_{x}}{v_{x}}}}$

where ${\displaystyle \Omega }$ is the tire's angular velocity along the axle, ${\displaystyle r_{e}}$ is the effective radius from the hub to the center of the contact patch, and ${\displaystyle v_{x}}$ is the forward facing component of the tire's linear velocity. A slip ratio of zero indicates that the tire is free-rolling at its zero-slip velocity (${\displaystyle r_{e}\Omega =v_{x}}$). A positive slip ratio indicates that the tire is rolling at an angular velocity greater than its ideal zero-slip velocity, which would ideally generate a force that speeds up the assembly^[1]. Accordingly, a negative slip ratio means that the tire is spinning at an angular velocity less than its ideal zero-slip velocity, which would ideally generate a force that slows down the assembly to resolve the slip ratio.

Lateral slip angle

Main article: Slip angle

The lateral slip of a tire is the angle between the direction it is moving and the direction it is pointing. This can occur, for instance, in cornering, and is enabled by deformation in the tire carcass and tread. Despite the name, no actual sliding is necessary for small slip angles. Sliding may occur, starting at the rear of the contact patch, as slip angle increases.^[2]

The slip angle can be defined as:^[2]

${\displaystyle \alpha =\arctan \left({\frac {v_{y}}{|v_{x}|}}\right)}$