Sports Engineering

, Volume 21, Issue 2, pp 103–114 | Cite as

Free kick goals in football: an unlikely success between failure and embarrassment

  • Søren Nørgaard Sørensen
  • John Rasmussen
Original Article


We develop and use a numerical model to investigate the window of opportunity of free kicks in association football. The planar multibody forward dynamics model comprises a two segment leg model with joint actuations, a football, a wall and the turf. Contact mechanics is defined to model the impact of the foot and the ball’s interaction with the different elements in the environment. The optimum kick is determined using the global optimization algorithm differential evolution, requiring millions of kick simulations. The sensitivity of various solutions to parameter perturbation is investigated. It is concluded that toe kicks are theoretically superior to instep kicks, but are difficult to perform reliably. The results also show that small perturbations in parameters can lead to embarrassingly failed kicks.


Football free kick Forward dynamics Motion prediction Computer simulation Optimization Soccer 


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Copyright information

© International Sports Engineering Association 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Manufacturing EngineeringAalborg UniversityAalborgDenmark

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