Slip Angle

#glossary

Slip angle $\alpha$ is defined as the angle between the direction in which a wheel is pointing and the actual direction in which the wheel is moving. It's an indicator of the lateral deformation of the tire as it travels along the road surface, and it plays a vital role in generating cornering forces.

Definition

$α=arctan \left(\frac{v_y​+\omega \cdot l}{v_x​}​\right)$

Where:

• $v_x$ is the longitudinal velocity of the tire (or the vehicle) in the direction the tire is pointing.

• $v_y$ ​ is the lateral velocity of the tire.

• $\omega$ is the yaw rate of the vehicle (angular velocity about the vertical axis).

• $l$ is the distance from the vehicle's center of mass to the tire in question (positive for front tires, negative for rear tires).

Alternative

$α=arctan \left(\frac{v_y​}{v_x​}​\right)$

Where:

• $v_y$ is the lateral velocity of the tire contact patch

• $v_x$ is the longitudinal velocity of the tire contact patch

Relation to Steering

• During Cornering: When a driver steers the vehicle, the front wheels are turned to a certain angle (steering angle). Due to the lateral forces acting on the tires, they deform, and the vehicle travels along a path that is slightly different from the direction the wheels are pointed. This difference is the slip angle.

• Understeer and Oversteer: Slip angles are critical in understanding understeer and oversteer behavior:

  • Understeer: The front tires have a larger slip angle than the rear tires, causing the vehicle to turn less than intended.

  • Oversteer: The rear tires have a larger slip angle than the front tires, causing the vehicle to turn more than intended.

In Practice

1. Tire Grip and Handling: The slip angle is directly related to the lateral grip of the tires. Tires generate maximum lateral force (cornering force) at an optimal slip angle. Beyond this optimal angle, the lateral force decreases, leading to a loss of grip.

2. Vehicle Stability Control (VSC): Modern vehicles use sensors to monitor slip angles and adjust braking and throttle inputs to maintain stability and control, preventing understeer or oversteer.

3. Performance Driving: In high-performance driving, managing slip angles is essential for maximizing cornering speed and vehicle control. Drivers aim to maintain slip angles within the optimal range to achieve the best handling performance.