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# Circle of forces

The Circle of Forces is a useful way to think about the dynamic interaction between a vehicle's tyre and the road surface. In the diagram below we are looking at the tyre from above, so that the road surface lies in the x-y plane. The vehicle that the tyre is attached to is moving in the positive y direction.

In this example, the vehicle would be cornering to the right (i.e. the positive x direction points to the center of the corner). Note that the plane of rotation of the tyre is at an angle to the actual direction that the tyre is moving (the positive y direction). That angle is the slip angle.

A tire can generate horizontal force where it meets the road surface by the mechanism of slip. That force is represented in the diagram by the vector F. Note that in this example F is perpendicular to the plane of the tyre. That is because the tyre is rolling freely, with no torque applied to it by the vehicles's brakes or drivetrain. However, that is not always the case.

The magnitude of F is limited by the dashed circle, but it can be any combination of the components Fx and Fy that does not exceed the dashed circle. (For a real-world tyre, the circle is likely to be closer to an ellipse, with the y axis slightly longer than the x axis.)

In the example, the tyre is generating a component of force in the x direction (Fx) which, when transferred to the vehicle's chassis via the suspension system in combination with similar forces from the other tyres, will cause the vehicle to turn to the right. Note that there is also a small component of force in the negative y direction (Fy). This represents drag that will, if not countered by some other force, cause the vehicle to decelerate. Drag of this kind is an unavoidable consequence of the mechanism of slip, by which the tyre generates lateral force.

The diameter of the circle of forces, and therefore the maximum horizontal force that the tyre can generate, is affected by many things, including the design of the tyre and its condition (age and temperature, for example), the qualities of the road surface, and the vertical load on the tyre.

03-10-2013 05:06:04