The rolling tyre
Let us discuss the rolling tyre in more detail, see figure below . With the tread entering and moving through the contact area, the distance to the wheel centre changes from the unloaded radius to the loaded radius and back to the unloaded radius. With the peripheral speed in the contact area corresponding to the effective rolling radius in between these values, points in the contact area need to catch up with this peripheral speed at the both ends of the contact area where the distance of contact points to the wheel centre exceeds Re. As a consequence, one observes rearward slip at these parts. With a similar argument, the points of the tyre circumference are slowed down in speed in the centre part of the contact area, corresponding to forward slip. Integration of the slip over contact area results in the global performance related to the shear stress as indicated in figure below. The peripheral speed with respect to the wheel centre is shown in the lowest graph in figure below, reducing from the unloaded speed Ω.R just before the contact area to the speed Ω.Re within the contact area.
The total longitudinal net force, determined from integrating the shear stress over the contact area will be a nonzero, negative force, known as the rolling resistance force . This rolling resistance force corresponds to a moment acting around the wheel centre, being balanced by the moment resulting from the tyre load. Consequently, the net tyre load will have to act along a force line, slightly in front of the wheel centre.
Free rolling tyre