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Rolling Resistance
Rolling friction and rolling resistance
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The force resisting the motion when a body rolls on a surface is called the rolling resistance or rolling friction.
The rolling resistance can be expressed as
Fr = c W (1)
where
Fr = rolling friction (N, lbf)
c = rolling resistance coefficient - dimensionless (coefficient of rolling friction - CRF)
W = m g = normal force or weight of body (N, lbf)
m = mass of body (kg, lb)
g = accelaration of gravity (9.81 m/s2, 32.174 ft/s2)
The rolling resistance can alternatively be expressed as
Fr = cl W / r (2)
where
cl = rolling resistance coefficient with 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 | cl (mm) | |
| 0.0002 - 0.001 | 0.5 | steel wheels on steel rails |
| 0.0015 - 0.0025 | low resistance tubeless tires | |
| 0.005 | tram rails | |
| 0.006 - 0.01 | truck tire on asphalt | |
| 0.01 - 0.015 | ordinary car tires on concrete | |
| 0.03 | car tires on tar or asphalt | |
| 0.04 - 0.08 | car tire on solid sand | |
| 0.2 - 0.4 | car tire on loose sand | |
Rolling Coefficients Cars
Rolling coefficients for a pneumatic tyres on dry roads can be calculated as
c = 0.005 + 1/p (0.01 + 0.0095(v/100)2)
where
c = rolling coefficient
p = tyre pressure (bar)
v = velocity (km/h)
Example - Normal car on asphalt
The rolling resistance of a normal car 1500 kg on asphalt with rolling friction (rolling coefficient from the table above) can be estimated like
Fr = 0.03 (1500 kg) (9.81 m/s2)
= 441 N
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