Editing Rolling resistance (section)

==Physical formulae==
The coefficient of rolling resistance for a slow rigid wheel on a perfectly elastic surface, not adjusted for velocity, can be calculated by <ref>{{cite book |last1=Guiggiani |first1=Massimo |title=The Science of Vehicle Dynamics |date=5 May 2018 |publisher=Springer Cham |isbn=978-3-319-73220-6 |page=22}}</ref>{{citation needed|date=September 2018}}
<math display="block"> C_{rr} = \sqrt {z/d} </math>
where
*<math>z</math> is the sinkage depth
*<math>d</math> is the diameter of the rigid wheel

The empirical formula for <math> C_{rr} </math> for cast iron mine car wheels on steel rails is:<ref>Hersey, equation (2), p. 83</ref>
<math display="block"> C_{rr} = 0.0048 (18/D)^{\frac{1}{2}}(100/W)^{\frac{1}{4}} = \frac{0.0643988}{\sqrt[4]{WD^{2}}}</math>
where
*<math>D</math> is the wheel diameter in inches
*<math>W</math> is the load on the wheel in pounds-force

As an alternative to using [[#Rolling resistance coefficient|<math> C_{rr}</math>]] one can use <math> b</math>, which is a different '''rolling resistance coefficient''' or '''coefficient of rolling friction''' with dimension of length. It is defined by the following formula:<ref name = "Hibbeler" />
<math display="block"> F = \frac{N b}{r} </math>
where
* <math>F</math> is the rolling resistance force (shown in figure 1),
* <math>r</math> is the wheel radius,
* <math>b</math> is the '''rolling resistance coefficient''' or '''coefficient of rolling friction''' with dimension of length, and
* <math>N</math> is the normal force (equal to ''W'', not ''R'', as shown in figure 1).

The above equation, where resistance is inversely proportional to radius <math>r</math> seems to be based on the discredited "Coulomb's law" (Neither Coulomb's inverse square law nor Coulomb's law of friction){{citation needed|date=November 2020}}. See [[#Dependence on diameter|dependence on diameter]]. Equating this equation with the force per the [[#Rolling resistance coefficient|rolling resistance coefficient]], and solving for <math>b</math>, gives <math>b</math> = <math>C_{rr}r</math>. Therefore, if a source gives rolling resistance coefficient (<math>C_{rr}</math>) as a dimensionless coefficient, it can be converted to <math>b</math>, having units of length, by multiplying <math>C_{rr}</math> by wheel radius <math>r</math>.