Bicycle speed through different gears with drag

by Ian Larson

Submitted : Fall 2018

When riding a bicycle, two forces that you experience are the force of the road that acts upon your rear wheel while pedaling, and an opposing force, drag. When adjusting Newton’s equation for his second law of motion, we have that the instantaneous change in velocity (dv) is equal to the object’s net force divided by it’s mass. We have a differential equation, but it hasn’t been solved analytically. With the bicycle starting at rest at t=0, I solved the equation numerically for any time t by using what is known as Euler’s Method to plot the velocity as a function time of the bicycle and the rider through gear shifts. Euler’s Method is applicable for differential equations that haven’t been solved analytically.   

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