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Journal of Special Topics P2_7 Power Curves and Gear Ratios in Bicycles J. Anand, A. Buccheri, M. Gorley, I. Weaver Department of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH. November 19, 2009 Abstract This article investigates how the power exerted by a cyclist varies with cyclist speed, and gear ratio. From Hill’s relation, both relations are determined and plotted. Suggestions are made on how these results might be useful to recreational and competitive cyclists. P2_2 Sports Science pedalling rates than contraction velocity (as in Hill’s relation), so we substitute v=ωr where r Introduction is the pedal crank arm length. Originally, Hill Gears in bicycles are often misused. Many used parameters for the mechanics of muscle people have experienced that pedalling in a fibres to determine the unknowns in this high gear from stationary is very difficult, and equation. However, since the cyclic pedalling produces very little acceleration. Equally, a motion is not as well studied as basic linear low gear at high speeds is inefficient. This contraction, values for a, b and c must be article explores the relationship between found from the special cases. That it, at ω=0 bicycle gearing, and the cyclist power output. where F=F0, and at F=0 where ω=ω0. Power Functions (1) (2) The force exerted by any engine is always applied in 2 different areas. The first is These 2 equations alone are not enough to accelerating engine components, and the determine values for the 3 unknowns. other is in the system on which you want to However, by considering the maximum power do work. -