Optimum Gear Ratios for a Human-Powered Vehicle

by Jessica Arce

Submitted : Spring 2012

For this project, I needed to find various values. I needed to find the value for GR₃, which is a gear on a human-powered vehicle. I was also required to find the gear ratios GR₁ and GR₂ that will minimize the total time needed to reach a velocity of 8 m/s. In addition, I had to calculate the total time needed to reach 8 m/s, the times t₁, t₂, and t₃ that the vehicle spends in each gear, and the velocities v₁ and v₂ at the shift points from first to second gear and from second to third gear. I accomplished this by integrating the function of dv/dt that was given. I created values for v₁,v₂, and v₃ and plugged those into the function of dv/dt that was given and differentiated the function. I then solved for GR₁ and GR₂. I made a function for the total time needed to reach 8 m/s as well as a function for each individual t₁, t₂, and t₃. I concluded values for GR­₁, GR₂, GR₃, the individual times that the vehicle spent in each gear, and the velocities v₁ and _v2 at the shift points from first to second gear and from second to third gear.

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