How “Ghost Goals” Happen: Mathcad Scores Again!

The football obsessives in the Adept offices seem to be talking about nothing else but Euro 2012 – although our Danish and Swedish colleagues are looking a bit glum now. Ukrainian Marko Devic’s “ghost goal” against England on Tuesday night has brought back memories of Frank Lampard’s disallowed goal for England against Germany at the 2010 World Cup. His shot (as video recordings showed) hit the crossbar, bounced a good metre inside the goal, then, strangely, rebounded in the opposite direction out again.

With England and Germany both through to the Euro 2012 quarter-finals, there’s the tempting possibility that these two old footballing rivals could meet again in the semis. So a new paper by Dr Ken Bray, the Bath-based theoretical physicist who has made a special study of the mathematics of football and the factors affecting the flight of the ball, is very timely. He has recently conducted a series of experiments, using a ball-launching machine and a high-speed digital camera, to show how this sort of “reverse rebound” can happen. The work involved some pretty intensive computations and it was Mathcad’s robust handling of simultaneous equations that, in Dr Bray’s words, made “very short work of the process”.

Devic’s “goal”, which John Terry cleared before it actually hit the ground, is a different kettle of fish, but Dr Bray’s paper breaks new ground in explaining what happened with Lampard’s shot. It’s a fascinating case study, whether or not you’re interested in football. You can read it here.


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