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.

本文推导了一个骑自行车的人在崎a不平的地形上骑行的数学模型。该模型非常通用。它用任意函数来表示，这些函数描述了海拔高度如何随水平距离变化以及骑车人的功率输出如何变化，并且还考虑了道路摩擦和空气阻力。通过考虑特殊情况（例如水平和倾斜表面）对模型进行了验证。尽管控制方程过于复杂，无法精确求解一般情况，但仍提出并测试了数值求解程序。此外，还概述了一种近似的分析解决方案程序。作为说明，给出了一些数值结果，用于骑车人在起伏的山丘上骑行的情况。所采用的方法非常适合数学物理学的本科生。该公式同样适用于在可变景观上行驶的车辆。这项工作还将物理学中的概念与数学建模和编码结合在一起。最后，还提供了视频摘要。