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
F_{r} = c W (1)
where
F_{r }= rolling resistance or rolling friction (N, lb_{f})
c = rolling resistance coefficient  dimensionless (coefficient of rolling friction  CRF)
W = m a_{g}
= normal force  or weight  of the body (N, lb_{f})
m = mass of body (kg, lb)
a_{g} = acceleration of gravity (9.81 m/s^{2}, 32.174 ft/s^{2})
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
F_{r} = c_{l} W / r (2)
where
c_{l} = 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  c_{l}(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 = 10^{5} 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
F_{r} = 0.03 (1500 kg) (9.81 m/s^{2})
= 441 N
= 0.44 kN
 compare car rolling resistance with car air resistance (drag)
The rolling resistance for one wheel can be calculated as
F_{r} = 0.03 (1500 kg / 4) (9.81 m/s^{2})
= 110 N
= 0.11 kN
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