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 and moving your hand forward. 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. The force has an opposite which will change the direction your fist is moving toward the left as it moves forward. 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.

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.