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# 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 Friction 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)                     (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

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

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