## How to Improve Running — With Mathematical Equations

Connected objects are everywhere in a sportsman’s life. Every day, new applications to improve fitness can be downloaded on your smartphone. They involve a lot of measurements and statistics but how reliable are they from a scientific point of view? How should we train to improve our running performance? How should my favorite champion should run his race and how should i run my 10km or 1500m tomorrow? By modeling running in the form of equations, and then solving them, we can now predict the optimal strategy to run a given distance in the shortest amount of time thanks to powerful mathematics. If turned into a software, this could become a revolutionary tool for training.

Our model takes into account physiological parameters such as maximal oxygen uptake and total available anaerobic energy and involves several differential equations coupling the unknown variables of the runner: velocity, propulsion force, and anaerobic energy, which the body uses when in oxygen deficit. The equations rely on two basic principles of physics: energy is preserved, and acceleration (or velocity variations) is equal to the sum of all the forces. This second principle is also called the fundamental principle of dynamics.

The difficulty in the numerical simulations —> Read More Here