Slip angle

The cornering force would be perpendicularly left of the wheel direction. The direction of travel of the wheel in this instant is straight vertical.

Slip angle is the angle between the direction a tire is pointing and the direction it is traveling. Slip angle results in a force perpendicular to the direction the tire is pointing called cornering force.

How does it help?

Slip angle causes a deformation in the tire tread, which in turn acts as a spring. This "spring" has a restoring force which points perpendicular to the wheel direction. This restoring force is called cornering force. Cornering force points towards the center of the curve. For example, a wheel turning left will have a cornering force pointing perpendicularly left of the wheel's direction. This can be best visualized with a Circle of Forces diagram.

You can demonstrate this with your hand to better understand the force and how the tire acts like a spring. Form your hand into a fist and press the bottom of it into a table. Slightly twist it to the left while maintaining pressure. You will feel that the skin on your palm does not rotate relative to the table. You will also feel a slight restoring force wanting to twist your fist back straight. That force has an opposite which will wants to twist your skin to match the direction your fist is pointing (direction of motion). This is how the tire's cornering force is generated.

Cornering force helps a car change direction by pulling the car in towards the center of a curve.

The ratio of slip angles for the front to rear tires determines the car's behavior in a turn. A ratio greater than 1:1 demonstrates understeer while a ratio less than 1:1 demonstrates oversteer. This ratio can be changed by modifying a car's relative roll couple; changing roll center, spring rates, or anti roll bars relative front to rear.

Circle of Forces

Circle of forces is a way in which to visualize the forces acting between a tire and the road. It is a 2D visualization viewing the tire from the top, with the tire rolling on the xy-plane which acts as the ground. The y-axis is the direction of travel of the vehicle of which the tire is attached. The diameter of the circle is the maximum magnitude of lateral force the tire can generate. The diameter of the circle depends on the road surface, load, and condition of the tire, so basically the amount of friction available. In real life, the circle is usually an ellipse with the y direction being longer than the x.

In this example the tire is turned to the right. The tire is pointed in a different direction than the direction of travel and thus must slip. It generates a horizontal force (F) by the mechanism of slip. F is perpendicular to the wheel direction. The X component of the force is transferred through the suspension to the chassis thus causing the vehicle to turn right.

Relationship to corner force

At low angles of slip, corner force increases linearly with slip angle. As the angle of slip increases, it will eventually reach a point at which the corner force increases non-linearly with slip angle. Finally, the tire will reach a peak cornering force and thereon after an increase in slip angle will decrease cornering force.

This means to drive fast, it is beneficial to be at a "large" angle. "Large" meaning the slip angle which provides the most lateral force without destroying the tires. What determines the optimum slip angle is ultimately the friction between the tire and the ground surface.

Relaxation Length

Relaxation length describes the delay between a slip angle occurring and the time it takes for the corner force to reach a steady state. It can be calculated as cornering stiffness over lateral stiffness. Cornering stiffness is the ratio of cornering force over slip angle. Lateral stiffness is the ratio of lateral force over lateral displacement.