The operation of a bicycle is visibly simple, but moving a bicycle through the crown, chain, ratchet, pedal movement and wheels follow the fundamentals of Mathematics and Physics. When moved, the pedals rotate the crown, which transmits the movement to the ratchet through a chain, which is connected to the rear wheel, setting the bicycle in motion. The complete wheel travel depends on the diameters of the crown, ratchet and the wheel itself. Note the following example:
The following illustration demonstrates a bicycle with the following diameters:
Crown: 30 cm
Ratchet: 10 cm
Rear wheel: 80 cm
To perform these calculations we will use the expression that allows us to calculate the length of a circle: C = 2*π*r, where π = 3.14 and r the radius.
Let's determine the length corresponding to a complete turn of the crown and ratchet
Crown length (diameter 30 cm, then radius 15 cm)
C = 2*π*r
C = 2 * 3.14 * 15
C = 94.2 cm
Ratchet Length (diameter 10 cm, then radius 5 cm)
C = 2*π*r
C = 2 * 3.14 * 5
C = 31.4
We have that the ratio between the crown and the ratchet is 94.2 / 31.4 = 3, that is, while the crown makes one turn, the ratchet makes three turns, making the rear wheel also make three complete turns. Based on this information, we have that the distance covered by the bicycle for each ride will be:
Rear wheel diameter is equal to 80 cm, therefore the radius is 40 cm.
C = 3 * (2*π*r)
C = 3 * 2 * 3.14 * 40
C = 753.6 cm or 7.536 m
Therefore, the bicycle will travel approximately 7.5 meters per complete pedal stroke.
We saw that the space traveled by a bicycle at each pedal stroke will be determined by the diameter of the crown, of the turnstile and rear wheel, as the measurements can be different between the different models of bicycles existing.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Circumference - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/sistema-transmissao-por-correntes.htm