This recently published article explains how a shuttle travels. It's free to download: The physics of badminton Caroline Cohen, Baptiste Darbois Texier, David Quéré, and Christophe Clanet 2015 New J. Phys. 17 063001 http://iopscience.iop.org/1367-2630/17/6/063001/article And here's a simulation of the equations described in the article. I've checked a couple of them and it seems to be a very nice model: http://community.wolfram.com/groups/-/m/t/515609