Rolling Resistance - Physical Formulas

Physical Formulas

The coefficient of rolling friction for a slow rigid wheel on a perfectly elastic surface, not adjusted for velocity, can be calculated by

where

is the sinkage depth

is the diameter of the rigid wheel

Empirical formula for Crr for cast iron mine car wheels on steel rails.

where

is the wheel diameter in in.

is the load on the wheel in lbs.

As an alternative to using one can use which is a different rolling resistance coefficient or coefficient of rolling friction with dimension of length, It's defined by the following formula::

where

is the rolling resistance force (shown in figure 1),

is the wheel radius,

is the rolling resistance coefficient or coefficient of rolling friction with dimension of length, and

is the normal force (equal to W, not R, as shown in figure 1).

The above equation, where resistance is inversely proportional to radius r. seems to be based on the discredited "Coulomb's law". See #Depends on diameter. Equating this equation with the force per the #Rolling resistance coefficient, and solving for b, gives b = C_rr·r. Therefore, if a source gives rolling resistance coefficient (C_rr) as a dimensionless coefficient, it can be converted to b, having units of length, by multiplying C_rr by wheel radius r.