# Coefficient of Rolling Friction

by Ron Kurtus (20 November 2016)

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

## Coefficient relationship

The Standard Friction Equation is:

Fr = μrN

Dividing by N, you can get the equation for the coefficient of rolling friction:

μr = Fr/N

where:

• 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.

## Values

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 cobblesÂ  - 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

## Summary

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

Ron Kurtus' Credentials

### Websites

Friction Resources - Extensive list

Rolling friction and rolling resistance - includes coefficients - Engineering Toolbox

Rolling Resistance - Wikipedia

### Books

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## Students and researchers

www.school-for-champions.com/science/
friction_rolling_coefficient.htm

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