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French Researchers Harness Power Of Maths To Optimise Running

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A couple of French mathematicians have developed a mathematical model that aims to ensure optimal results for runners. Amandine Aftalion from the Mathematics Laboratory in Versailles and Frederic Bonnans from the Center of Applied Mathematics recently presented their work at the Futurapolis international meeting held in Toulouse. The duo believe that their model could promote the development of personal e-coaching programmes tailored to the physiological state of every runner.

It has long been known that speed variation allows for longer and more effective runs. The solution helps athletes to redistribute their available energy throughout the training session or competition.

The model is a combination of differential equations which correlate variables such as speed, acceleration, friction, propulsion forces, oxygen uptake and anaerobic energy. The system is paired with initial conditions and constraints, the latter including a requirement for positive energy and propulsion force.

Using the model, researchers can make predictions about the best running strategy for a given race. This includes projections about optimal speed and initial energy expenditure. The results of the French study show that speed variation allows athletes to run longer with less energy expenditure. In addition, a comparison with the results obtained from professional athletes enables the researchers to determine the physiological parameters that need improvement.

The mathematical model is designed for two groups of runners: semi-professionals and occasional runners. It is now being developed further as the researchers take into consideration other variables, for example wind and altitude. In this way, the model will also be suitable for application in sports such as cycling and swimming.