Mathematical modeling of an athletic track surface

Development of a 3D mathematical model of an athletic track in co-operation with Politecnico of Milan.

The incorporation of air cells into the lower layer of prefabricated rubber track surfaces is thanks to the innovative intuition of Elio Stroppiana, founder of Mondo, who, already in 1976, understood that air spaces below track surfaces would create an elastic effect that was unattainable with dense track bases.

Since then, the size, depth and shape of the air cells have been modified to continuously improve athletes’ performance. The result is the current patented honeycomb design, which gives directionality to the track’s elastic response.

Today, modern techniques to calculate finite elements (FEM) and the mathematical modeling of the physical characteristics of materials contribute to research into the relationship between their form and physical properties, allowing for the optimization of their technical features.

Cooperation between MONDO and the Politecnico di Milano has led to the development of a 3D mathematical model of a running track that is being tested for its interaction with the Berlin artificial athlete, which is an apparatus used to measure energy absorption and vertical deformation of a track subjected to the pounding of athletes’ feet.

This study represents a first step towards designing virtual prefabricated track surfaces whereby the elastic response can be precisely measured before a physical prototype is built.

Initial evaluation regarding the size and shape of the air cells and the response of the track materials led to Mondotrack WS’ current chemical formula, which optimizes the lower layer’s density and the upper layer’s polymeric composition.

The MONDOTRACK WS’ top layer contains pre-vulcanized, three-dimensional rubber granules that were designed to improve track elasticity and improve energy return during the propulsion phase.

The new polymeric system makes the granules more elastic and optimizes their deformability.

Thanks to their new composition, the granules bind permanently with the track’s structure during the vulcanization process, creating a three-dimensional network with improved flexibility and resistance.

As a result, the track is more elastic while maintaining optimal deformability and helps athletes to control the length of their strides, running rhythm and stability, which are essential for competitors that must run to, and then take off from, a specific point, such as hurdlers, pole vaulters, and long, triple and high jumpers.

References

A 3D numerical model for the optimization of running track performance, 11th conference of the International Sports Engineering Association, ISEA 2016


L. Andena, a,c, S. Aleo, a, F. Caimmi, a, S. Mariani, b, c, F. Briatico-Vangosa, a and A. Pavan, a


a Department of Chemistry, Materials and Chemical Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy
b Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy
c E4Sport - Engineering for Sport Laboratory, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy