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Mathline

Math of Bicycles: Gearing Up (Grades 7-10)

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bike

The other factor that influences the bike is the relationship between how one turn of the pedal effects the turn of the wheel.

1. Look at the tricycle. Stand the tricycle upside down, with the wheels pointed up so you can watch what happens. One complete turn of the pedal produces how many complete turns of the wheel? Why?

2. For the tricycle, you have a pedal to wheel ratio of 1:1. This means that one complete revolution of the pedals creates 1 complete revolution of the wheel. At this point, do not worry about the size of the wheel, just the number of times it goes around.

3. Now look at a standard bike. Gently place the bike so the wheels are up in the air. Start with a pedal at top of its turn and the valve stem on the wheel at the top of the wheel. Very slowly turn the pedals one complete revolution and watch how far the wheel turns. Do not keep the wheel spinning or coast after you have stopped turning the pedals. One turn of the pedal produced how many turns of the wheel? What is the pedal to wheel ratio for this bike? Why do you think the ratio is different from that of the tricycle?

4. Set one of the bikes with multiple gears upside down. Count the number of teeth in the largest gear attached to the pedals. Count the number of teeth in the smallest gear attached to the wheels. How many of the small wheel gears would it take to have the same number of teeth as the large pedal gear?

5. Now shift the bike so the chain is on the large pedal gear and the small wheel gear. In this setting, one turn of the pedals produces how many turns of the wheel? How does this compare with the comparison of the number of teeth in each gear? Why? What is the pedal to wheel ratio for this setting?

6. Now count the teeth on the largest wheel gear. How does it compare with the number of teeth in the largest pedal gear? Estimate the pedal to wheel ratio for this setting. Shift the bike so the chain is in this setting, and test out your estimate.

7. What setting has the smallest pedal to wheel ratio? Why?

8. What would have to be true for the pedal to wheel ratio to be the same as that of the tricycle?