Abstract

This paper describes the use of Pareto-optimal solutions for the screw kick in rugby. We attempted to optimise the initial conditions for a screw kick. The optimisation was carried out using an elitist non-dominated sorting genetic algorithm. Distance achieved in flight is considered as an objective function, as well as the lateral deviation between the ball and the touchline, or the flight time. Six initial conditions were defined as control parameters: the magnitude of the velocity vector, the flight path angle, the azimuth angle, the spin rate, the pitch angle and the yaw angle. The results are summarised as follows: it is impossible for both objective functions to be satisfied simultaneously, although the greatest distance achieved in flight and the smallest value of the lateral deviation between the ball and the touchline, or the least flight time, is the ideal situation. This kind of conflicting solution is called a ‘Pareto-optimal solution’. The optimal kick in Pareto-optimal solutions made by the leg nearest the touchline produces a greater flight distance than the optimal kick in Pareto-optimal solutions made using the leg furthest from the touchline. The initial pitch angle, which is the angle between the longitudinal axis of the ball and the horizontal plane, should be comparable to or slightly greater than the initial flight path angle in order to satisfy the Pareto-optimal solutions. Verf.-Referat