Optimal pacing for running 400- and 800-m track races

We present a toy model of anaerobic glycolysis that utilizes appropriate physiological and mathematical consideration while remaining useful to the athlete. The toy model produces an optimal pacing strategy for 400-m and 800-m races that is analytically calculated via the Euler-Lagrange equation. The calculation of the optimum v(t) is presented in detail, with an emphasis on intuitive arguments in order to serve as a bridge between the basic techniques presented in undergraduate physics textbooks and the more advanced techniques of control theory. Observed pacing strategies in 400-m and 800-m world-record races are found to be well-fit by the toy model, which allows us to draw a new physiological interpretation for the advantages of common weight-training practices.