Tire

Tire refers to the ring of rubber around the wheel (or rim) that is in contact with the ground. Tires are the only link between a FSAE car in the ground and thus are extremely important (duh)

Characteristics

You probably think this page is stupid; everyone knows what a tire is. I thought I knew too.

Balance

In order to rotate smoothly a tire must have an even distribution of mass around its circumference. An unbalanced tire will vibrate. This can be corrected by applying weights on the wheel to balance it.

Centrifugal expansion

When a tire turns at a high rate of speed, it has centrifugal force. If a tire spins fast enough, the centrifugal force generated may be enough to increase the diameter of the tire through "pulling" on the rubber sidewalls. This is not a notable issue on FSAE cars.

Slip angle

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. Slip angle causes a deformation in the tire tread, which in turn acts as a spring. This "spring" has a returning force which is the cornering 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.

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 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.

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.

Spring rate

Yep. Tires are also a spring. The spring rate of a tire is the k-constant of its vertical stiffness. The magnitude of the k-constant determines the tire vertical deflection under load. This is largely influenced by the sidewall stiffness and air pressure.