Coefficient of Rolling Friction
by Ron Kurtus
The coefficient of rolling friction is the indication of how great the rolling resistance is for a given normal force between the wheel and the surface upon which it is rolling. This ratio is based on the Standard Friction Equation.
Because of the various factors, the coefficient of rolling friction is usually determined experimentally.
Questions you may have include:
- What is the coefficient of rolling friction relationship
- How is the coefficient of rolling friction determined?
- What are some sample values?
This lesson will answer those questions. Useful tool: Units Conversion
The Standard Friction Equation is:
Fr = μrN
Dividing by N, you can get the equation for the coefficient of rolling friction:
μr = Fr/N
- μr is the coefficient of rolling friction for the two surfaces (Greek letter "mu" sub r)
- Fr is the resistive force of rolling friction
- N is the normal or perpendicular force of the wheel on a surface
Other factors in coefficient
The coefficient of rolling friction, μr, isn't a simple number as in the case of sliding friction for hard materials. Instead, it is proportional to the width of the wheel and inversely proportional to the radius. In the case of soft wheels and tires, μr the surface area of the tire on the ground is also a factor.
Determining the coefficient
Since rolling resistance can be very small, determining the coefficient of rolling friction is not an easy task. For example, if you put a 50 kg weight on a bicycle that has tires with a coefficient of rolling friction of 0.002, the rolling resistance would be 0.002 * 50 = 0.01 kg = 10 grams. That's not much.
One way to determine the coefficient of rolling friction between a wheel and some surface is to measure the torque required to keep the wheel rolling at a constant velocity.
Another way is the start the wheel rolling at some velocity and time how long it takes to for the wheel to stop.
Some values of the coefficient of rolling friction or resistance are shown the the chart below:
Coefficients of Rolling Friction
|0.001 - 0.002||
railroad steel wheels on steel rails
|0.001||bicycle tire on wooden track|
|0.002||bicycle tire on concrete|
|0.004||bicycle tire on asphalt road|
|0.008||bicycle tire on rough paved road|
|0.006 - 0.01||truck tire on asphalt|
|0.01 - 0.015||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 tires on solid sand, gravel loose worn, soil medium hard|
|0.2 - 0.4||car tires on loose sand|
Source: Engineering Toolbox
The coefficient of rolling friction or resistance is the indication of how great the rolling resistance is for a given normal force between the wheel and the surface upon which it is rolling. This ratio is based on the Standard Friction Equation. Because of the various factors, the coefficient of rolling friction is usually determined experimentally.
Roll with the punches
Resources and references
Friction Resources - Extensive list
Rolling friction and rolling resistance - includes coefficients - Engineering Toolbox
Rolling Resistance - Wikipedia
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Coefficient of Rolling Friction