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.
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.
The code with NDSolveValue is attached. Here is the resulting simulation of the flight of badminton shuttlecocks:
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?
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
corresponds to the stabilizing torque generated by the aerodynamic drag.The damping term
results from the drag associated with the orthoradial movement of the shuttlecock as φ varies.
Oscillating time approximation provides to:
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! :)
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?
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. :)
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 = 2, and would stabilize much farther from the net.
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)
And here is a refined GIF from my link above:
Yes, that's it.
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