How does bicycle gearing affect mechanical advantage?

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    Bicycle Gearing
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SUMMARY

The discussion centers on the impact of bicycle gearing on mechanical advantage and torque at the rear wheel. Participants analyze the effects of changing a front sprocket from 38 teeth to 34 teeth while maintaining the same rear cassette. It is concluded that while torque may increase with a smaller front sprocket, if the rear sprocket is adjusted to maintain the same gear ratio, there is no overall increase in mechanical advantage. The terms "Mechanical Advantage" (MA) and "Velocity Ratio" (VR) are clarified, emphasizing that MA is not simply derived from gear ratios alone.

PREREQUISITES
  • Understanding of bicycle gearing systems, including sprocket and cassette configurations.
  • Knowledge of torque and mechanical advantage concepts in physics.
  • Familiarity with the relationship between gear ratios and pedal efficiency.
  • Basic principles of chain tension and its effects on bicycle performance.
NEXT STEPS
  • Research the effects of different gear ratios on cycling performance and efficiency.
  • Explore the relationship between chain tension and wear in bicycle systems.
  • Learn about the physics of mechanical advantage in various mechanical systems.
  • Investigate optimal gearing configurations for different cycling disciplines.
USEFUL FOR

Cyclists, bicycle mechanics, and engineers interested in optimizing bicycle performance through gear selection and understanding the mechanical principles involved in cycling dynamics.

  • #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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