From Individualism to Collectivity: Wash Riding Interactions in Canoeing.

In both cases endurance sports and long distance animal displacement large groups are commonly observed. In these collective phenomena the efficiency is key and is achieved through pairwise interactions. As a result some individuals take advantage of part of the energy dissipated by others, a efficiency oriented self-organization dynamic is created and groups appear. In endurance canoeing the interaction is called wash-riding and it is characterized by a well-defined geometry. By simplifying the interaction and defining both a efficiency and connectivity metrics we introduce a parametric model for this sport. Our results reproduces the structure and groups observed in competitions. The most efficient the groups will be the fastest and most numerous they are, also the most connected. More connected groups imply shorter lateral distances, at intermediate distances a topological transition is observed and finally there is a critical distance, in terms of the displacement velocity, beyond which no groups are formed. The parametric model here presented not only reproduces the particular case of canoeing but also delimits the driving mechanisms of these kind of interactions.