Optimal design for speed distribution of marathon runners

Using the methods of least squares and optimization, a mathematical model is established based on the running model of Joseph B. Keller, and combining the running characteristics and actual conditions of athletes. Whole marathon is divided into three phases: the starting section, the halfway section and the sprint section. Different from previous studies, this study designs athletes to accelerate in the starting and the last stage of the race. But in the middle segment, it is an uniform motion. The study finds that the model design is in line with the objective facts of the marathon. Through this model, the relative errors between theoretical results and actual competition results can be found out realistically, so as to provide scientific training basis for marathon coaches and athletes to improve their running results. At the same time, this search proves that high-level athletes use uniform speed running in the middle of the competition, which is more conducive to exerting their level and showing better performance.