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. Both rolling body and base are subject to deformations during rolling and large bodies rolls more easily than small bodies. Harder roller and base surfaces results in lower resistance coefficients. The rolling resistance coefficient for a car tire on asphalt is approximately 0.2 and the rolling resistance for a ball bearing is approximately 0.002.
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, ball bearings |
| 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
Related Topics
• Dynamics
Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.
• Mechanics
The relationships between 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.
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 - Coefficients for Common Materials and Surfaces
Find friction coefficients for various material combinations, including static and kinetic friction values. Useful for engineering, physics, and mechanical design applications.
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.
New vs. Old Car Costs: A Comprehensive Cost Comparison
Compare the total cost of owning a new car versus an old car, including purchase price, maintenance, fuel efficiency, insurance, and depreciation. Use our detailed breakdown to make an informed financial decision before buying the next vehicle.
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.