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 by the generic equation
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)
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
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 | ||
|---|---|---|
| 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) (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 = 105 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
Fr = 0.03 (1500 kg) (9.81 m/s2)
= 441 N
= 0.44 kN
- compare car rolling resistance with car air resistance (drag)
The rolling resistance for one wheel can be calculated as
Fr = 0.03 (1500 kg / 4) (9.81 m/s2)
= 110 N
= 0.11 kN