Racket head speed should be relative to the ground. Body motion and joint motions should be considered, in 3D, to get racket head speed vs time, especially for impact.
First cut,
You determine location of the body rotation axes and the distances,
r, from each axis to the racket head. For circular ground strokes, the
main rotation axes are usually through the spine at the neck area,
r1, and through the shoulder joint,
r2. The
rs change during the strokes as the arm angles, forearm-to-racket angles and other angles change. Typically for ATP forehand drives and 1HBHs, mainly I see the uppermost body turn first and then the shoulder joint works before impact. For rec players, it's a mix of uppermost body and shoulder joint. There may be other considerable axes and rotations also. See videos for details.
Next, there are the instantaneous rotation rates, of the uppermost body at spine,
ω1, and the shoulder joint,
ω2 and any other rotations.
I don't think that the defined joint motions are enough. But for the forehand, the uppermost body turn and the shoulder joint account for much of the forward racket head speed. I ignore, for example, the forward running of the player. Sometimes I consider the wrist joint.
I also don't attempt to calculate actual racket head speeds, not because it is easy but because it is hard.
For high speed videos, if you view squarely to the side of the ball's outgoing trajectory, then you can get a reasonably accurate racket head speed. If the ball is traveling toward or away from the camera, that velocity component cannot be accurately measured.
To measure more accurately than video cameras,
3D Motion Capture Systems with multi-cameras and computers are used. $300K. These systems can probably do a very good job on most of the swinging sub-motions. But
rotations, such as
intenal shoulder rotation (ISR), cause inaccuracies because the measurements of reflective balls, strapped onto the arm or leg, does not show bone rotation angles accurately. That's because the reflective ball position lags the bone position - because the ball is mounted on the surface of flesh and flesh flops around and lags the desired bone position.
Shortening the distance while the arm and racket are swinging does increase racket head speed and that has a special name,
parametric acceleration. This tennis racket speed increase has been much more thoroughly explored for golf and is more widely known there. Search:
parametric acceleration golf
Thread on Parametric Acceleration in tennis.
if the fh is no longer 'hitting 3 balls in a row down the target line', why is the 1hbh still taught to 'stay side ways'. it should be a mirror image of the fh, where the parametric acceleration means pulling the right shoulder hard left towards the left shoulder and have racket finish around...
tt.tennis-warehouse.com
The ice skater's feet are on ice. C
onservation of angular momentum shows by the ice skater spinning up as they pull in two arms and a leg. It may be that
parametric acceleration for golf and tennis is the same principle as the ice skater uses but it is no longer so visible because the feet are on the ground for golf and tennis vs on ice.