Question

I've been having some trouble figuring out where to start on this maths task:

Investigate how the gears of a multi-speed bicycle allow a rider to increase torque with reduced effort:

 You will need to obtain relevant measurements, such as the length of the moment arm for each of the gears. You may use research or collect your own measurements.

 Consider your assumptions, which should be reasonable (eg, pedal force applied by the rider).

 Simulate the relationship between the applied force and torque for each gear, and how this influences speed. A spreadsheet would be beneficial here.

 Consider how the position of the pedals may affect applied force. Discuss how this influences riding mechanics.

This is a maths task and the topic we are covering is torque and equilibrium: an application of vectors, so that's the vein that the solution needs to follow.

My understanding is that: a force is applied to the pedal, which rotates the chainset, in turn applying a force to the chain and rotating the gear on the back, which then rotates the wheel. As per this diagram:

Chain Chainset Gears Pedal Crank Tire

I am just not sure of the exact relationships and how I would go about deriving the equations needed to find the torque produced from different sized gears and how they affect the distance the bike travels.

Answer 1

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