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
Related Topics

Dynamics
Motion  velocity and acceleration, forces and torque. 
Mechanics
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Related Documents

Acceleration
Change in velocity vs. time used. 
Bodies Moving on Inclined Planes  Acting Forces
Required forces to move bodies up inclined planes. 
Car  Required Power and Torque
Power, torque, efficiency and wheel force acting on a car. 
Car  Traction Force
Adhesion and tractive force between car wheel and surface. 
Car Acceleration
Car acceleration calculator. 
Car Fuel Consumption  liter/100 km
Calculate fuel consumption in liter per km  consumption chart and calculator. 
Cars  New vs. Old Car Cost Calculator
Calculate and compare the costs between owning a new vs. an old car. 
Centripetal and Centrifugal Acceleration Force
Forces due to circular motion and centripetal / centrifugal acceleration. 
Disk Brakes  Torque and Force
Forces and torque activated with disk brakes. 
Drag Coefficient
The drag coefficient quantifies the drag or resistance of an object in a fluid environment. 
Efficiency of Small Machine Elements
Friction and efficiency in bearings and roller chains. 
Electrical Vehicle Charging  Power vs. Voltage and Amps
EV Charging  AC vs. DC, single phase vs. three phase and power vs. voltage and amps. 
Formulas of Motion  Linear and Circular
Linear and angular (rotation) acceleration, velocity, speed and distance. 
Friction  Friction Coefficients and Calculator
Friction theory with calculator and friction coefficients for combinations of materials like ice, aluminum, steel, graphite and many more. 
Fuel Consumption  mpg
Calculate fuel consumption in miles per gallon  mpg  calculator and consumption charts. 
Impact Force
Impact forces acting on falling objects hitting the ground, cars crashing and similar cases. 
Impulse and Impulse Force
Forces acting a very short time are called impulse forces. 
Kinetic Energy
Energy possessed by an object's motion is kinetic energy. 
Piston Engines  Compression Ratios
Cylinder volume and compression ratios in piston engines. 
Piston Engines  Displacement
Calculate piston engine displacement. 
Vehicle  Distance Traveled vs. Velcocity and Time Used (mph)
Speed (mph) and time (hours) and distance traveled (miles) chart. 
Vehicle  Distance Traveled vs. Velocity and Time (km/h)
Speed (km/h) vs. time (hours) and distance traveled (km). 
Vehicles Traffic Flow and Density
Traffic flow and density as used in highway design.