Abstract
Derived in this article is a mathematical model of a cyclist riding over uneven terrain. The model is very general; it is expressed in terms of arbitrary functions that describe how the elevation changes with horizontal distance and how the cyclist’s power output varies, and also accounts for road friction and air resistance. The model was validated by considering special cases such as horizontal and inclined surfaces. Although the governing equation is too complicated to solve exactly for the general case, a numerical solution procedure is proposed and tested. In addition, an approximate analytical solution procedure is outlined. As an illustration some numerical results are presented for the case of a cyclist riding over rolling hills. The adopted approach is well suited for undergraduate students in mathematical physics. The formulation equally applies to a vehicle driving over a variable landscape. This work also unites concepts from physics with mathematical modelling and coding. Lastly, a video abstract is also provided.
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