MR - Changing Tires Lesson

Changing Tires Lesson

Adapted from Course materials (1.A Student Activity Sheet 5) for AMDM developed under the leadership of the Charles A. Dana Center, in collaboration with the Texas Association of Supervisors of Mathematics and with funding from Greater Texas Foundation.

What do each of the numbers on the side of a tire mean, and why are they important?

A labeled diagram of a tire showing the components of its sidewall, including size, aspect ratio, type, load index, speed symbol, tire composition, and other identifiers.

Changing Tire Size

Changing tire size is one of the most common things car owners do that can affect speedometer accuracy. That's because larger tires cover more ground in one complete revolution. All speedometers must be calibrated to make sure the rotation indicated accurately reflects the speed of the car. When an axle makes one complete turn, the tire it's connected to makes one complete revolution. But a tire with a larger diameter will travel farther than a wheel with a smaller diameter. That's because the distance a tire covers in one revolution is equal to its circumference. For example, a tire with a diameter of 20 inches will cover about 62.8 inches of ground in one revolution. A tire with a diameter of 30 inches will cover more ground — about 94.2 inches.

Let's explore more from our example

Diagram showing the aspect ratio of the tire is the height of the sidewall (from the edge of the inner rim to the tread) in relation to the section width. We are given the diameter of the rim but how do we determine the diameter of the tire? Look at the tire!

The diameter of the entire tire is equal to the diameter of the rim + 2 x (height of the sidewall).

The aspect ratio is the height of the sidewall (from the edge of the inner rim to the tread) in relation to the section width.

Use the aspect ratio to solve for the height in inches of the tire and diameter of the 205 / 55R16 tire in our example. To help you better understand what these numbers mean, the diagram has been filled in for you below.

Image displaying tire size specifications and measurements, highlighting dimensions

Use the aspect ratio of 55% to solve for the height in inches of the sidewall.

Aspect ratio (decimal) = Height (mm) / width (mm)

Next, convert the height of the sidewall to inches. (2.54 cm = 1 in., 1 mm = 0.0393701 in.)

112.75 mm X 0.0393701 / `1mm = 4.44 in

You can then find the entire height of the tire by adding the sidewall height (2 times) to the diameter of the rim.

math equation 4.44 + 16 in + 24.88

Now, using the equation: circumference = ∏ x diameter, you can solve for the circumference of the tire

Note: the equation is typically written circumference = 2∏r, where r is the radius, but in this case, we have already solved for the diameter which is equal to two times the radius.

circumference descriptions

Using the above example as a guide, check your answers with the following chart given these tire sizes.

Answers to Practice Question
Tire	Width (mm)	Aspect Ratio	Sidewall Height (in.)	Diameter (in.)	Circum (in.)
P1845/60R15	185 mm	60 % = .60	4.4 in.	23.8 in.	74.7 in.
P225/40R18	225 mm	40 % = .40	3.5 in.	25 in.	78.5 in.
P195/75R14	195 mm	75 %= .75	5.8 in.	25. 6 in.	80.4
P225/45R17	225 mm	45% = .45	4.0 in.	25 in.	78.5 in.
P315/40R26	315 mm	40 % = .40	5.0 in.	36. 0 in.	113.0 in.

View the presentation below. It contains an example of how to find and use differential ratios that you will need in the changing tires assignment.

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