QAs about the trajectory of a shuttlecock’s flight path

Badminton shuttlecocks are an odd piece of sports equipment. Typical shuttles have 16 feathers stuck in a piece of cork and can fly at speeds over 250 mph, making badminton the world’s fast racquet sport. (Indeed, Lee Chong Wei holds the Guinness World Record for the fastest smash speed at 254 mph)

The New York Times recently looked at the professional shuttlecocks used at the Rio Olympic games. It describes how the shuttles played a key part in the badminton matches. My favourite part relates to how Yonex sent almost 15,000 F-90 Yonex shuttles from its factory in Japan to Brazil. Shuttles were then tested and selected to suit the venue and match conditions.

A shuttle’s trajectory is different to most the ball sports. After a high initial speed, the shuttle rapidly slows down due to air drag. Studies on the trajectory of the badminton shuttlecock are scarce but below are some research highlights. Honestly this is a snapshot. So here we go.

Why does the shuttle flip? Researchers from Ecole Polytechnique sought to understand how a player can use shuttlecock flip to lure an opponent. Texier et al. explained there’s 2 reasons for the flip: (a) the centre of mass is closer to the cork because the cork is heavier than the skirt, and (b) the aerodynamic centre is closer to the centre of volume. Advanced players put a spin on the shuttlecock to make it flip so that it’s harder for their opponent to hit the cork.

Shuttlecock flip movie
Fig 1. Slow motion capture of a shuttlecock taken at 5 millisecond intervals, flipping after being hit by a racket from the left. Image from Texier et al. (2012).

What’s the difference between a plastic and feather shuttlecock? Researchers from RMIT compared the air drag properties of feather and plastic shuttlecocks under a range of wind speeds. Alam and co-workers rigged up a shuttle to a sensor, placed it in the RMIT Industrial wind tunnel and blasted it with wind speeds up to 120 km/h. They confirmed plastics have the most drag. Perhaps more interestingly, they found feathers deformed more than plastic shuttles at low speeds, and deformed less at high speeds. Also, Verma et al found that the pressure difference between the inside and outside of the skirt is the main contributor to air drag. This is caused by gaps in the skirt.

types of shuttlecocks
Fig 2. Computational models of a synthetic, feather and gapless shuttlecock. Image from Verma et al. (2013)

How can you predict the trajectory of a shuttlecock? Just construct a motion equation of the shuttlecock’s flight path. Taiwanese researchers Chen et al (2009) looked at the effect of stroke angle and force on shuttlecock speed. They found that the trajectory could be best expressed in terms of its terminal velocity. This meant the speed, time, direction and path could be more accurately predicted for sports training. Useful for matches, no?


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