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Rolling Resistance
Rolling friction and 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 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 = c l W / r
(2)
where
cl = rolling resistance coefficient - dimension length (coefficient of rolling friction) (mm, in)
r = radius of wheel (mm, in)
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Rolling Friction Coefficients
Some typical rolling coefficients:
Rolling Resistance Coefficient
c
cl (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)
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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
compare car rolling resistance with car air resistance (drag)
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