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hubie writes:

Badminton play is characterized by the unusual flight dynamics of the shuttlecock. Although world-class players can launch the projectile almost 140 m/s off the racket (the fastest tennis serves are only about 70 m/s), since aerodynamic drag is the dominant force it not only allows the shuttlecock to travel at manageable speeds by the time it crosses the court, but it permits an analytic solution for the flight path. A very approachable open-access paper by Cohen et al. in the New Journal of Physics covers everything from the history of the game to the effects on the gameplay from subtle differences in shuttlecock design.

Abstract:

The conical shape of a shuttlecock allows it to flip on impact. As a light and extended particle, it flies with a pure drag trajectory. We first study the flip phenomenon and the dynamics of the flight and then discuss the implications on the game. Lastly, a possible classification of different shots is proposed.