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Rolling Resistance

Rolling friction and rolling resistance

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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 as

Fr = c W                                   (1)

where

Fr = rolling resistance or rolling friction (N, lbf)

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

W = m ag

    = normal force - or weight - of the body (N, lbf)

m = mass of body (kg, lb)

ag = acceleration 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 - dimension length (coefficient of rolling friction) (mm, in)

r = radius of wheel (mm, in)

Rolling Friction Coefficients

Some typical rolling coefficients:

Rolling Resistance Coefficient 
ccl (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)

where

c = rolling coefficient

p = tire pressure (bar)

v = velocity (km/h)

  • 1 bar = 105 Pa = 14.5 psi
  • 1 km/h = 0.6214 mph

Example - The Rolling Resistance of a Car on Asphalt

The rolling resistance of a car with weight 1500 kg on asphalt with rolling friction coefficient 0.03 can be estimated as

Fr = 0.03 (1500 kg) (9.81 m/s2)

= 441 N

= 0.44 kN

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