Math CentralQuandaries & Queries


Question from Dennis, a parent:

I would like to calculate the distance traveled on a bike based on the size of the tire and on the number of revolutions per minute. This is based on the rider traveling at a constant speed.

Hi Dennis.

Each revolution, the bike travels the distance equal to the circumference of the tire (unless you are skidding!) Bike tires are usually measured using the diameter though.

To calculate the circumference, you can just multiply the diameter by π, which is about 3.142. That gives you the distance for each revolution.

Then you can multiply by the number of revolutions per minute. That will give you the distance traveled in each minute.

Finally, multiply by the number of minutes you are traveling at this speed and you will get the total distance traveled.

For example, my bike tire has a diameter of 0.73 m (that's 73 cm). My wheel speed is 180 rpm and I ride for 30 minutes. How far did I go? To answer, I just multiply these together along with π:

0.73 x 3.142 x 180 x 30 = 12 386 m. About 12.4 km.

Hope this helps,
Stephen La Rocque.

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