4.2 Rolling friction

Rolling friction force is generated when two bodies roll on each other without sliding. Let's imagine a wheel with radius r subjected to a load N. As the wheel approaches the contact point, the material is compressed and afterwards, once the contact point has been surpassed, undergoes an elastic release. If the material used to manufacture the wheel is not perfectly elastic, some of the energy required for compression is lost in the subsequent return phase dissipated in the form of heat to counteract internal frictional resistance of the material. If we think in terms of forces, instead of energies, we could say that the distribution of pressure in the contact is not symmetrical compared to the direction of force N.

The diagram of pressure generates, therefore, a resultant equal to N but moved forward with respect to the wheel axis by a distance bv (arm of the rolling friction). The displacement of the resultant generates a moment of resistance.To keep the wheel turning evenly it is necessary to apply a motive moment identical to and opposite Mr or a traction force F parallel to the forward direction and such that.
From the previous formulas we obtained:

Where:

With fv known as the rolling friction coefficient which can be found with experimental tests.