Rolling Resistance Coefficient - slow rigid wheel on a perfectly elastic surface

Description

Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc. is recovered when the pressure is removed. Two forms of this are hysteresis losses (see below), and permanent (plastic) deformation of the object or the surface (e.g. soil). Another cause of rolling resistance lies in the slippage between the wheel and the surface, which dissipates energy.
In analogy with sliding friction, rolling resistance is often expressed as a coefficient times the normal force. This coefficient of rolling resistance is generally much smaller than the coefficient of sliding friction.
The coefficient of rolling friction for a slow rigid wheel on a perfectly elastic surface, not adjusted for velocity, can be calculated as shown.

Related formulas

Variables

Crrrolling resistance coefficient (dimensionless)
zsinkage depth (m)
ddiameter of the rigid wheel (m)