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# Rolling Friction and Automobile Tires

by Ron Kurtus (revised 27 October 2016)

When an automobile coasts along the road, the resistive force of * rolling friction on the automobile tires* slows down the motion.

The rolling friction of the tire is slightly affected by the static friction of the rubber on the pavement. The adhesion effect of the rubber adds a little more to the rolling friction. But the major contribution to the rolling friction is the deformation of the tire while rolling.

The coefficient of friction for the automobile tire can be determined experimentally, but it only applies to the specific configuration.

Questions you may have include:

- How does the rolling coefficient of friction compare with the others?
- How does deformation of affect rolling friction?
- How does adhesion of affect rolling friction?

This lesson will answer those questions. Useful tool: Units Conversion

## Friction effects

Rolling friction for a hard wheel on a hard surface is quite small and is a combination of contributions of static friction and friction from molecular adhesion. For example, the coefficient of rolling friction for a train wheel on a steel rail is only 0.001. That is less than the coefficient of sliding friction on ice.

But an automobile tire is made of rubber and is filled with air. It deforms under the weight of the car, and that deformation contributes greatly to the rolling friction. The result is that the coefficient of rolling friction is about 15 times as great. A typical automobile tire has an average coefficient of rolling friction of **μ _{r}** = 0.015.

## Rolling friction equation for tires

You can apply the standard friction equation for rolling wheels to try to determine the value of rolling friction. That equation is

F_{r}= μ_{r}W

where:

**F**is the resistive force of rolling friction_{r}**μ**is the coefficient of rolling friction for the two surfaces (Greek letter "mu" sub R)_{r}**W**is the weight of the wheel plus the weight of the automobile**μ**is_{r}W**μ**times_{r}**W**

This equation is not as straightforward as with sliding friction for hard surfaces, since ** μ _{r}** varies with the radius, width, treads, amount of inflation and temperature of the tire, as well as the type of rubber and the value of

**W**. The surface roughness of the pavement is also a factor.

What this means is that **μ _{r}** can vary considerably depending on the experimental conditions.

## Measuring coefficient of rolling friction

One way to measure the tire's coefficient of rolling friction is to roll the tire at a given velocity and then measure how long it takes to come to a stop. The equation used is

μ_{r}= vg/t

where:

**μ**is the coefficient of rolling friction_{r}**v**is the initial velocity (m/s or ft/s)**g**is the acceleration of gravity (9.8 m/s² or 32 ft/s²)**t**is the time in seconds it takes to stop**vg/t**is**v**times**g**divided by**t**

### Problem of tire by itself

The problem is that since you are just rolling the tire by itself, the deformation effects from the weight of the car are not included. Thus the coefficient would not be accurate.

### Problem of other friction

On the other hand, if you started a car rolling at velocity **v**, the tires would be deformed as in actual use. The problem now would be that there would be an added friction from the wheels turning on their axles that would also slow down the car. Thus the coefficient again would not be accurate.

### Separate measurements needed

The only way around that problem would be to take a separate measurement of the friction of the axles and their bearings and then subtract that from the previous measurement.

My head hurts from all this! But I guess you have to go through all this trouble if you want to find an accurate coefficient of rolling friction for a tire. But then, if you would change the air pressure, you'd have to repeat the test.

## Summary

When an automobile coasts along the road, the resistive force of rolling friction on tires slows down the motion. The rolling friction of the tire is slightly affected by the static friction of the rubber on the pavement and the adhesion effect of the rubber. The major contribution to the rolling friction is the deformation of the tire while rolling.

The coefficient of friction for the automobile tire can be determined experimentally, but it only applies to the specific configuration.

Learn by being observant

## Resources and references

### Websites

**Friction Resources** - Extensive list

**How Tires Work** - How Stuff Works

**Rolling friction and rolling resistance** - includes coefficients - Engineering Toolbox

**Rolling Friction** - simple explanation - Davidson College

**Rolling Resistance** - mathematical approach - MathWorks

**Tire-Road Interaction** - equations - MathWorks

**Rolling Resistance Equations** - derivations - Real World Physics Problems

**Rolling Resistance** - Wikipedia

### Books

**Top-rated books on Friction Science**

**Top-rated books on Friction Experiments**

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## Rolling Friction and Automobile Tires