Slip angle

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In vehicle dynamics, slip angle^[1] or sideslip angle^[2] is the angle between the direction in which a wheel is pointing and the direction in which it is actually traveling (i.e., the angle between the forward velocity vector ${\displaystyle v_{x}}$ and the vector sum of wheel forward velocity ${\displaystyle v_{x}}$ and lateral velocity ${\displaystyle v_{y}}$, as defined in the image to the right).^[1][3] This slip angle results in a force, the cornering force, which is in the plane of the contact patch and perpendicular to the intersection of the contact patch and the midplane of the wheel.^[1] This cornering force increases approximately linearly for the first few degrees of slip angle, then increases non-linearly to a maximum before beginning to decrease.^[1]

The slip angle, ${\displaystyle \alpha }$ is defined as
$${\displaystyle \alpha \triangleq -\arctan \left({\frac {v_{y}}{|v_{x}|}}\right)}$$