# Rolling Resistance

The force that resists the motion of a body rolling on a surface is called the **rolling resistance** or the **rolling friction**.

The *rolling resistance* can be expressed by the generic equation

*F _{r} = c W (1)*

*where *

*F _{r }= rolling resistance or rolling friction (N, lb_{f})*

*c = rolling resistance coefficient - dimensionless (coefficient of rolling friction - CRF)*

*W = m a _{g} *

* = normal force - or weight - of the body (N, lb _{f})*

*m = mass of body (kg, lb)*

*a _{g} = acceleration of gravity (9.81 m/s^{2}, 32.174 ft/s^{2})*

Note that the rolling resistance coefficient - *c* - is influenced by different variables like wheel design, rolling surface, wheel dimensions and more.

The rolling resistance can alternatively be expressed as

*F _{r} = c_{l} W / r (2)*

*where *

*c _{l} = rolling resistance coefficient - dimension length (coefficient of rolling friction) (mm, in)*

*r = radius of wheel (mm, in)*

### Rolling Friction Coefficients

Some typical rolling coefficients:

Rolling Resistance Coefficient | ||
---|---|---|

c | c_{l}(mm) | |

0.001 - 0.002 | 0.5 | railroad steel wheels on steel rails |

0.001 | bicycle tire on wooden track | |

0.002 - 0.005 | low resistance tubeless tires | |

0.002 | bicycle tire on concrete | |

0.004 | bicycle tire on asphalt road | |

0.005 | dirty tram rails | |

0.006 - 0.01 | truck tire on asphalt | |

0.008 | bicycle tire on rough paved road | |

0.01 - 0.015 | ordinary car tires on concrete, new asphalt, cobbles small new | |

0.02 | car tires on tar or asphalt | |

0.02 | car tires on gravel - rolled new | |

0.03 | car tires on cobbles - large worn | |

0.04 - 0.08 | car tire on solid sand, gravel loose worn, soil medium hard | |

0.2 - 0.4 | car tire on loose sand |

### Rolling Coefficients Cars

The rolling coefficients for air filled tires on dry roads can be estimated

*c = 0.005 + (1 / p) (0.01 + 0.0095 (v / 100) ^{2}) (3)*

*where *

*c = rolling coefficient*

*p = tire pressure (bar)*

*v = velocity (km/h)*

#### Example - Wheel Pressure & Rolling Resistance Coefficient

The standard wheel pressure in a Tesla Model 3 is *2.9 bar (42 psi)*. The rolling friction coefficient at *90 km/h (56 mph)* can be calculated from (3) as

*c = 0.005 + (1 / (2.9 bar)) (0.01 + 0.0095 ((90 km/h) / 100) ^{2})*

* = 0.011*

Increasing the pressure to 3.5 bar reduces the rolling resitance coefficient to

*c = 0.005 + (1 / (3.5 bar)) (0.01 + 0.0095 ((90 km/h) / 100) ^{2})*

* = 0.010*

- or

*((0.011 - 0.10) / 0.011) 100% = 9%*

*1 bar = 10*^{5}Pa = 14.5 psi*1 km/h = 0.6214 mph*

### Example - The Rolling Resistance of a Car on Asphalt

The rolling resistance for all four wheels in a car with total weight *1500 kg* on asphalt with rolling friction coefficient *0.03* can be estimated with the generic equation 1 as

F_{r}= 0.03 (1500 kg) (9.81 m/s^{2})

= 441 N

= 0.44 kN

- compare car rolling resistance with car air resistance (drag)

The rolling resistance for one wheel can be calculated as

F_{r}= 0.03 (1500 kg / 4) (9.81 m/s^{2})

= 110 N

= 0.11 kN

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