Towards a mathematical theory of athletic training. Part 1. The mathematical model of the training process and the equation of athletic performance by Nikolai Nikolaevich Engwer

Relevance. The 1960s and 70s in the USSR were marked by the beginning of the active application of mathematical methods in sports, which made it possible to move from intuitive training planning to accurate calculations of training loads and prediction of athletic performance. One of the first mathematicians who thought about translating the empirical rules and principles of sports training into mathematical language was Nikolai Nikolaevich Engver, Doctor of Economics. The ideas expressed and the mathematical models proposed by him are undeservedly forgotten. This article will allow a wide range of readers to get acquainted with the ideas and legacy of this scientist. The objectives of this work were the systematization, interpretation and comparative analysis of the ideas, methods and results of Doctor of Economics, Professor Nikolai Nikolaevich Engwer, who developed an original mathematical model of the relationship between training loads and sports results, which allows predicting the growth of the best results based on controlled parameters - intensity and volume of training, as well as to determine the patterns of adaptation of the athlete’s body to increased loads. Materials and methods. The analysis of scientific papers and biographical materials by N.N. Engwer devoted to the development and application of methods of mathematical statistics and the theory of automatic control systems to the analysis of athletes’ training and the construction of training plans was carried out. Results. The results of scientific research by N.N. Engwer are systematized, who built a mathematical model of the training process, including 1) the dependence of the maximum result of an athlete on the average intensity of training and their volume; 2) the equation of effectiveness of training loads; 3) the equation of habituation (adaptation) of the body to work with increased intensity. He developed practical recommendations on load dosing and planning of the training process. It has been experimentally confirmed that the model makes it possible to accurately predict the growth of athletic performance. The model of N.N. Engwer is compared with the model of E. Banister. It was found that the Engwer model is suitable for operational planning of microcycles (weeks/months), and the Banister model is optimal for long-term management of the training process (months/years).