Maroński R
Institute of Aeronautics and Applied Mechanics, Warsaw, Poland.
J Biomech. 1994 Feb;27(2):205-13. doi: 10.1016/0021-9290(94)90210-0.
This paper focuses on the solution of two problems related to cycling. One is to determine the velocity as a function of distance which minimizes the cyclist's energy expenditure in covering a given distance in a set time. The other is to determine the velocity as a function of the distance which minimizes time for fixed energy expenditure. To solve these problems, an equation of motion for the cyclist riding over arbitrary terrain is written using Newton's second law. This equation is used to evaluate either energy expenditure or time, and the minimization problems are solved using an optimal control formulation in conjunction with the method of Miele [Optimization Techniques with Applications to Aerospace Systems, pp. 69-98 (1962) Academic Press, New York]. Solutions to both optimal control problems are the same. The solutions are illustrated through two examples. In one example where the relative wind velocity is zero, the optimal cruising velocity is constant regardless of terrain. In the second, where the relative wind velocity fluctuates, the optimal cruising velocity varies.
本文聚焦于与骑行相关的两个问题的解决方案。一个是确定速度作为距离的函数，该函数能使骑行者在给定时间内覆盖给定距离时的能量消耗最小化。另一个是确定速度作为距离的函数，该函数能使在固定能量消耗下的时间最小化。为了解决这些问题，利用牛顿第二定律写出了骑行者在任意地形上骑行的运动方程。该方程用于评估能量消耗或时间，并结合米莱方法（《应用于航空航天系统的优化技术》，第69 - 98页（1962年），学术出版社，纽约）使用最优控制公式来解决最小化问题。两个最优控制问题的解是相同的。通过两个例子对解进行了说明。在一个相对风速为零的例子中，无论地形如何，最优巡航速度都是恒定的。在第二个例子中，相对风速波动，最优巡航速度也会变化。
