Magnus Effect Soccer Kick

Simulation of soccer ball flight trajectory with fluid drag and magnus effect.

Bend soccer ball flight trajectory with spin, score a goal from three positions on the field, the first to match Roberto Carlos' famous goal against France (looks like the shot is going to miss by 5 meters, and the goalie does nothing), the second is a corner kick, and the third is from the centre spot.

Try scoring on the first scenario without angling the kick towards the goal to explore the effects of spin on the trajectory.

Select the parameter to adjust from radio button group on the left, and slide your finger on the view vertically to modify the vertical value (horizontally for the horizontal value).

This app is meant to be educational, and the flight trajectory is simulated using Apache Commons Math Dormand-Prince integrator to integrate soccer ball flight ordinary differential equations including fluid drag and Magnus effect. Only velocities above 12 m/s can be expected to be simulated realistically, and contact is not simulated at all. Hence simulation stops when the ball would have touched the ground.

Coefficients of drag and lift as a function of velocity and spin are taken from Coff and Carre Eur. J. Phys. 31 (2010) 775–784.