Circle of forces

The Circle of Forces is a useful way to think about the dynamic interaction between the tyres of a vehicle and the road surface. It is a more intuitive way to understand these interactions without having to delve into complex mathematics - it can be used while actually driving to get a better understanding of the vehicle dynamics.

A tyre in contact with a road has a certain value of friction force. If a force greater than this amount is applied to the tyre, the tyre will slip or skid across the surface. This applies no matter what direction the tyre is pushed in (consider the tyre to be locked rather than on a rotating wheel). This value of friction can be seen as a circle surrounding the tyre. The diameter of the circle represents the amount of friction - a smaller friction value gives a smaller circle of forces than a larger value. The circle's diameter will constantly change as the vehicle is driven on different surfaces, and as the vehicles weight shifts from wheel to wheel. If at any time the force on a tyre exceeds the circle, the tyre will skid.

As the vehicle is steered, accelerated and braked, forces are applied to the tyres and a variety of directions - cornering produces a sideways force for example, and braking applies a force acting to push the tyre backwards. The vector sum of these applied forces muct remain within the circle of forces for the tyre to remain useful. If, for example, a car is being cornered so hard that the cornering force is equal to the friction force of the tyre, any further force applied, such as by applying more power or braking, will take the total force outside the circle and the tyre will break contact. Such an event may well cause loss of control.

This approach immediately shows why four-wheel drive vehicles are able to corner faster than two-wheel drive ones - the force arising from the power is shared across four tyres instead of two, allowing a greater cornering force component per tyre than would otherwise be available.