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A Simple Model for the Tyre

The torque from the engine is used to turn the wheel. Friction between the tyre and the road surface is responsible for preventing the tyre slipping across the road surface and hence for propelling the car forwards (Fig. 4).

Figure 4: A schematic diagram showing the forces acting on a tyre and the road

Figure 5: The traction force that a tyre generates as a function of the torque applied to the wheel.

The tyre is pushed onto the road by the weight of the vehicle supported by that wheel. There is a maximum force that can be generated by the friction. If this is exceeded, the tyre `breaks loose' and spins. A simple model for an ideal tyre is shown in Fig. 5. As the applied torque rises, the force increases, but if too much torque is applied, the tyre begins to slip and no extra accelerating force is generated. If we go on increasing the torque, the tyre spins and the force generated drops rapidly.

The maximum force that can be applied is approximately given by

where W is the reaction force pressing the tyre onto the road (Tipler, p. 107). If the car is stationary, W=Mg where M is the mass of the car supported on the particular wheel. For a road tyre, , for a race tyre, .

This is an oversimplified description, but it will be adequate for this course. In Part 5, we'll briefly introduce `slip angle'.

Richard Bower
Thursday October 8 16:09:30 BST 1998