Bicycle speed through different gears with drag

Authors

Ian Larson, University of South Florida

Publication Year

2019

Abstract

When riding a bicycle, the rider experiences two forces: the force of the road that acts upon the rear wheel while pedaling, and an opposing force that exerts on the bicycle/cyclist, called aerodynamic drag force (drag). When adjusting Newton’s equation in the second law of motion, the instantaneous change in velocity is equal to the object’s net force divided by its mass. The corresponding differential equation has not been solved analytically. With the bicycle starting at rest at t=0, we solved the equation numerically for any time t by using what is known as Euler’s Method to plot the velocity as a function of time of the bicycle through gear shifts.

Recommended Citation

Larson, Ian (2019) "Bicycle speed through different gears with drag," Undergraduate Journal of Mathematical Modeling: One + Two: Vol. 10: Iss. 1, Article 4.
DOI: https://doi.org/10.5038/2326-3652.10.1.4909
Available at: https://digitalcommons.usf.edu/ujmm/vol10/iss1/4

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