I hereby declare the entire airspace over the court with only three terms: ROLL, PITCH, YAW.
You only need to understand the first picture, and suddenly you can talk about the undercut, topspin etc, in much more detail. Or doing the yaw as in sweeping like Lars Paaske. So, pilots, use ROLL, PITCH, YAW, or RPY for short.
All else, IGNORE. Yes, I mean it.
«Covering the angles» is a nice misnomer you hear badminton commentators and coaches saying. But which ones do they mean? They usually use the hands and rackets to show what they mean. But we cannot do this in text, so we need a better way.
Since everybody has seen Lars Paaske, or Cai Yun, turning their trunk in short service, like a turret looking for a target, and since we essentially run into fuzzy naming like «woobling» flight, turret-style «turning», not to mention what side is it in the «side spin» ...
I declare the court as an airspace.
Why? Yonex already had introduced the Z-FORCE, so why not take it seriously, because there is this aerospacey XYZ and RPY.
AIRSPACE over the badminton court
It is easiest to imagine the shuttlecock being the aircraft. However, what about players? Well, take your nose, take the aircraft's nose, take the shuttlecock's nose ... that's «x» and the rest goes as is. It's easiest with the space shuttle, as shown in the graphic, because suddenly you can get a feeling where the shuttlecock «orbit» is.
Some conventions, even used by Yonex and Forza racket designers.
COURT is the «local frame».
the alleys to have a forecourt/rearcourt = x
the net = y
the heights = z
PLAYER is like the space shuttle
front back, or nose = x
shoulders width = y
body height = z
x = front-back = index finger = to roll
y = left-right = thumb = to pitch
z = up-down = middle finger = to yaw
You actually can use your thumb, index fingers and middle fingers for both hands: «hold» a pistol with thumbs and indeces, «roll» so that the right thumb points to left (and left thumb right), pistol as in a Hong Kong movie, so that the middle fingers must point to the floor ... and then you have your own frame if you aim.
RACKET, from the studies I read
head-handle axis = x
racket face = y
in a push the shuttle goes = z, as in «VT Z-Force»
SHUTTLECOCK: That's a bit tricky because we don't have a true belly. But the cork-skirt axis = x, and use the horizontal flight (as after a drive stroke) as normal position, similar to the space shuttle.
A common reference frame would be useful. I also agree that we need up to 3 XYZRPY frames to describe motion relative to the court, player and (possibly) shuttle.
However, we need to stick to completely right-hand or left-hand convention, otherwise it's just going to get confusing. Most items in engineering are right-hand rule, so I propose that we adopt right-hand rule throughout.
It's also worth stating that axes need to have a direction specified too:
Therefore referencing from the individual:
x-direction would be straight ahead
y-direction would be from right-to-left
z-direction would be upwards
Therefore the court would be:
x-direction is from your rear-court to the rear-court of your opposition
y-direction is from your forehand side to your backhand side (if you're a right-hander)
z-direction would be upwards
It is worth noting that if a player is facing square to the net, then these 2 reference frames are equal.
I saw no mention of a datum/origin through. Shuttle and player are fairly arbitrary, though for the court, I'd pick the floor below the center of the net (i.e. the middle of the court surface). However, you could pick the center of your side of the court?
If you take the halfs of the entire floor as origin, you have the positive and negative coordinates flipping all the time. The short service from one T corner to the other T corner is about four+ meter on the floor, and you would have to jot down that you serve from [-2 , +0.5 (right) , z ] to [ 2 , -0.5 (left) , z ].
That's like the civilian time zones on the globe with plus/minus hours, and with November-Zulu-Alpha zones.
Then, many consider the "compass" for doubles rotatiion an intuitive way to speak about the court, so a point behind the T mark would be nil. A rear court would be negative, the net is about +2m away, and playing too long would be about +10 m.
How about the rear-left-floor as an origin, all positive numbers, I guess. It's obvious that y = nil would be "left", and y = 6__ m "right" and 3__ m is the " usual centerline" .
I also remember that some Chinese coaching book splits the one-player court into fields of three equals, so you have nine fields and they start count field names [ 1 , 2 , 3 ] from the left, net corner to right, and next row left is [ 4 , 5 , 6] etc. So the right-hander's backhand is in [ 7 ].