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Flight of Badminton Shuttlecocks

GROUPS:

See attached notebook for details. A shuttlecock (previously called Shuttlecork) (also called a bird or birdie) is a high-drag projectile used in the sport of badminton. It has an open conical shape: the cone is formed from 16 or so overlapping feathers, usually goose or duck, embedded into a rounded cork base. The cork is covered with thin leather. The shuttlecock's shape makes it extremely aerodynamically stable. Regardless of initial orientation, it will turn to fly cork first, and remain in the cork-first orientation.

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Image courtesy of IOP Science

The name shuttlecock is frequently shortened to shuttle. The "shuttle" part of the name was probably derived from its back-and-forth motion during the game, resembling the shuttle of a loom; the "cock" part of the name was probably derived from the resemblance of the feathers to those on a cockerel.

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The code with NDSolveValue is attached. Here is the resulting simulation of the flight of badminton shuttlecocks:

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References

Attachments:
POSTED BY: Mariusz Iwaniuk
Answer
2 years ago

Another gem, thank you for sharing! Amazing how simple models couple to produce full dynamics - the shuttlecocks flip model and trajectory model - I hope I understood final equations correctly. But is the flip model is mathematically analogous to pendulum with friction?

POSTED BY: Vitaliy Kaurov
Answer
2 years ago

Got you right ,and is mathematically analogous to pendulum with air friction.

This second order differential equation for φ is one of a damped oscillator. The square of pulsation

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corresponds to the stabilizing torque generated by the aerodynamic drag.The damping term

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results from the drag associated with the orthoradial movement of the shuttlecock as φ varies.

Oscillating time approximation provides to:

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POSTED BY: Mariusz Iwaniuk
Answer
2 years ago

Yes, this is another gem from Mariusz NDSolveValue post series:

Rattleback or Celtic Stone

Tippe Top Toy

Dzhanibekov Effect or tennis racket theorem

Flight of boomerang

Thanks for sharing these! :)

Answer
2 years ago

Clap clap clap!

If you lower the initial velocity V (say V=V/10), then you can see the typical trajectory of a spinning net shot. I did not try to find good mapping between parameters' initial values and for all the shots described in the paper... but maybe Mariusz had not planned anything for the summer?

POSTED BY: Matthias Odisio
Answer
2 years ago

I've never played in Badminton.What is spinnig net shot!. I searched a bit and after Googling and here is the resulting simulation. I hope I understand what is it. :)

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Attachments:
POSTED BY: Mariusz Iwaniuk
Answer
2 years ago

Well that's close! The key is to have the shuttle stabilize only after it goes over the net and thus forcing the opponent to hit the shuttle low. This video in Chinese shows such trajectories in slow motion.

And since I'm having fun an I'm already asking too much, there's no limit anymore: the incoming shot would typically start from a higher altitude, say z[0] = 2, and would stabilize much farther from the net.

POSTED BY: Matthias Odisio
Answer
2 years ago

Also probably this is it too in English - but Matthias should confirm - I am no Badminton sage:

CE2M5V5 Forehand Spin Net Shot (In to Out)

POSTED BY: Vitaliy Kaurov
Answer
2 years ago

And here is a refined GIF from my link above:

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POSTED BY: Vitaliy Kaurov
Answer
2 years ago

Yes, that's it.

POSTED BY: Matthias Odisio
Answer
2 years ago

enter image description here - you earned "Featured Contributor" badge, congratulations !

This is a great post and it has been selected for the curated Staff Picks group. Your profile is now distinguished by a "Featured Contributor" badge and displayed on the "Featured Contributor" board.

POSTED BY: Moderation Team
Answer
1 year ago

Group Abstract Group Abstract