How does bicycle gearing affect mechanical advantage?

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    Bicycle Gearing
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Discussion Overview

The discussion revolves around how changes in bicycle gearing, specifically the size of the front sprocket and its effect on mechanical advantage and torque at the rear wheel, impact performance. Participants explore theoretical scenarios while considering various assumptions and constraints related to gearing ratios, chain tension, and mechanical leverage.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether a smaller front sprocket increases mechanical advantage or torque at the rear wheel, assuming the cassette is adjusted to maintain the same gear ratio.
  • Another participant suggests that changing the front sprocket alone does not lead to a mechanical advantage if the rear sprocket is also adjusted to keep the ratio constant.
  • There is a discussion about the definitions of mechanical advantage (MA) and velocity ratio (VR), with some participants emphasizing the importance of terminology in understanding the mechanics involved.
  • One participant proposes that a smaller front sprocket increases chain tension for a given pedal effort, which could affect torque, but this is countered by the smaller rear sprocket maintaining the same overall torque output.
  • Another participant raises concerns about the implications of higher chain tension, suggesting it may lead to increased wear and friction, while also noting that the actual work done against friction is more complex than simply considering chain tension.
  • There is a suggestion that the performance of the bike and rider is influenced by various factors, including body dimensions and preferred pedaling speed, complicating the analysis of gearing effects.

Areas of Agreement / Disagreement

Participants express differing views on whether a smaller front sprocket alone provides a mechanical advantage or changes torque at the rear wheel. The discussion remains unresolved, with multiple competing perspectives on the implications of gearing changes.

Contextual Notes

Participants acknowledge limitations in their assumptions, such as the neglect of factors like inertia and chain deflection, which could affect the analysis. The complexity of the relationship between gearing, rider dynamics, and mechanical efficiency is also noted.

  • #31
Baluncore said:
Surely not.
A cyclist is an inverted pendulum who positions the bike wheels so as to “fall” in the direction they want to turn. Gravitational acceleration is not dependent on the mass of the cyclist so the speed of a manoeuvre is determined by how quickly they can reposition the bike.

The fulcrum of the inverted pendulum is the line between the wheel contact patches. The energy cost of manoeuvring is proportional to the bike mass and speed2 used to reposition the fulcrum = bike.

I guess you are right: that aspect of manoeuvrability is affected by bike mass (Moment of Inertia, actually) than rider mass (what about his legs, though?)
But there are other reasons for wanting a light bike. Manouvering is mainly restricted to cut and thrust competition. Just accelerating must be pretty important, surely - and going uphill. In those cases, it will be Mechanical Advantage and not Velocity Ratio that counts, though. The bike mass and friction contribute to - reduce MA.
 

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