Explanation of Rolling Friction and Automobile Tires by Ron Kurtus - Succeed in Understanding Physics. Key words: physical science, coefficient, deformation, train, truck, car, wheels, rubber, forces, velocity, time, pressure, temperature, Ron Kurtus, School for Champions. Copyright © Restrictions

# Rolling Friction and Automobile Tires

by Ron Kurtus (revised 3 November 2005)

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. 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 μR = 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

FR = μRW

where:

• FR is the resistive force of rolling friction
• μR is the coefficient of rolling friction for the two surfaces (Greek letter "mu" sub R)
• W is the weight of the wheel plus the weight of the automobile
• μRW is μR times W

This equation is not as straightforward as with sliding friction for hard surfaces, since μR 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 μR 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

μR= vg/t

where:

• μR is the coefficient of rolling friction
• 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

Ron Kurtus' Credentials

### Websites

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

Friction Resources - Extensive list

### Books

Friction Science and Technology (Mechanical Engineering Series) by Peter J. Blau; Marcel Dekker Pub. (1995) \$89.95

Tribology: Friction and Wear of Engineering Materials by I. M. Hutchings; CRC Press (1992) \$68.88

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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