Research interests include all those aspects of ball games that can be represented by mathematical models although current interest centres on the biomechanics of soccer, specifically the modelling of the flight of a soccer ball in a direct free kick. Coaches and players alike are aware of the goal-scoring potential of this important set play. In the 1998 World Cup, for example, of the 171 goals scored, 50% originated from set plays of all kinds and 50% of these in turn were from free kicks. Biomechanical treatments of kicking have tended to concentrate on instep kicking and have looked almost exclusively at maximal ball velocity as the key output. This is not the most important ingredient in beating a defensive wall, however, as elite players use a combination of speed and spin to swerve the ball over or around the defensive wall. A spinning ball in flight is subject to three distinct forces: gravity, drag and a deflecting force associated with the ball's spin, the Magnus force. Work at Bath has concentrated on modelling the flight by solving the three dimensional differential equations representing the motion. The differential equations include parameters representing the orientation of the ball's spin axis, as well as the aerodynamic coefficients for spin and drag. Solutions of the equations are related to a realistic mathematical model of the defensive wall. The constraints imposed by the wall on a free kick can then be explored by varying the model parameters. As there is very little published data for soccer balls it has been necessary to determine the aerodynamic parameters from a series of trial free kicks. The trajectory of a ball has been determined experimentally by fast video analysis of the flight, the resulting data being reduced using the DLT transformations in conjunction with the TARGET analysis system. By comparing trajectories predicted by the mathematical model with those measured in the trials the aerodynamic spin and drag coefficients have been determined, together with the ball's spin axis. The results are in close agreement with the kinds of deflections achieved in free kicks by elite footballers in actual match conditions. The work is likely to be extended to determination of the initial conditions of the flight much more precisely than has been possible so far, as the initial conditions have an important bearing on the resultant flight. This will entail measurement of the launch velocity, spin rate and spin axis of the ball. A review of this work, together with the use of a mathematical modelling software, can be viewed at Adept Scientific in the MathCad User Journal.
© Copyright 2004 The Engineering of Sport 5, Volume 1. Veröffentlicht von International Sports Engineering Association. Alle Rechte vorbehalten.