Improving your performance, losing weight, boosting your fitness level...there are an increasing number of mobile apps designed for ‘connected’ sport. Now researchers at the French National Centre for Scientific Research (CNRS) have published a mathematical model to help you optimise your running.

How Maths Can Help You Optimise Your Running

How can you run better? There are already quite a number of apps available in the ‘connected’ sport space. At the moment however, all they can do is gather data – such as distance run and average speed – for statistical purposes. Last month however, Amandine Aftalion from the Mathematics Laboratory at the University of Versailles-Saint-Quentin-en-Yvelines just outside Paris, and Frédéric Bonnans from the Centre of Applied Mathematics at the École Polytechnique, both funded by the CNRS, unveiled the results of their latest research, which seeks to put maths at the service of the runner. The researchers have devised a mathematical model based on algorithms which can draw up a full programme of personalised training sessions for any runner. The major innovation is that their app goes further than simple statistics, incorporating parameters such as the runner’s energy, maximal oxygen consumption and anaerobic energy storage capacity so as to guide the runner in improving his/her performance.

Continuous real-time personalised monitoring

The application will be able to draw up an appropriate programme suited to each person’s physiology and characteristics. To this end it gathers a range of data on the runner, which it then feeds into a set of differential equations. The app links speed, acceleration, propulsive force and frictional forces. Combined with the initial data at the start of the run – zero speed and zero energy consumed; and the constraints – energy and the propulsive force must be positive, i.e. the runner cannot go backwards, the system is able to predict how the person should run throughout the race or session. It will carry out an ongoing real-time check to determine to the nearest second the runner’s optimal speed plus the energy s/he is using along the way.

A range of sports applications

The application is designed for two different audiences: ‘semi-professional’ runners, and ‘amateurs’ who do not have the opportunity to train with a sports coach. In addition the CNRS researchers should perhaps consider making their model available for use in physical and sports education at schools. A software project to create programmes for personalised training is now underway. This will identify the physiological parameters that need developing and suggest detailed strategies for achieving optimal speeds at each moment of the race or session. And as the set of differential equations can be adapted to any variable, it can also give the runner the exact number (rather than just an average) of calories burned during the run. The system is already up and running, but the researchers are looking to make further improvements, integrating additional parameters such as altitude and (head- or back-) wind speed. The algorithms could also be harnessed to help boost performances in other sports such as cycling, swimming and kayaking.