The moment produced by forward shift of the resultant ground reaction force is called rolling resistance moment (Figure 4a), and can expressed as

                                                                          (2)

Figure 4a: Force acting on a tyre vs. deformation in loading and unloading on a soft surface

To keeps the wheel rolling, a force F_r, acting on the centre of the wheel is required to balance this rolling resistant moment. This force is expressed as

                (3)

The rolling resistance moment can be equivalently replaced by horizontal force acting on the wheel centre in the direction opposite to the movement of the wheel. This equivalent force is called the rolling resistance and its magnitude is given by

                    (4)

When a vehicle is moving up a gradient, the normal force (P), in equation 4, is replaced by the component that is perpendicular to the road surface. Hence, equation 4 is rewritten as

                       (5)

The rolling resistance coefficient, f_r, is a fucntion of:

• • tire material

• tire structure

• tire temperature

• tire inflation pressure

• tread geometry

• road roughness

• road material

• presence of absence of liquids on the road