Originally Posted by stoneage
Some corrections and clarifications: The swing weight (Ix) is measured around an axis in the plane of the string bed (x-axis), not normal to it (but you probably mean that).
The twist weight (Iy) is measured around an axis along the length of the racquet (y-axis) and affects the swing very little (but is important at an off-line impact).
It is right that a normal swing not is entirely around the string bed plane and that the actual swingweight is a little higher. The moment of inertia (Iz) around the third axis is higher than the swingweight, which follows from perpendicular axis theorem Iz=Ix+Iy. However, in a racquet these two "swingweights" (Ix and Iz) are similar since Iy is small, so their combined effect from not swinging entirely around the x-axis is fairly small.
An example: assume an evenly balanced racquet with a weight of 320 g, a swing weight (Ix) of 325 kg cm^2 and a twist weight (Iy) of 15 kg cm^2 ( a typical value). Using the the parallel axis and perpendicular axis theorems you get that Iz is 340 kg cm^2 . That is the swingweight if you swing with edge towards the ball (not so common). If you swing with racquet with the head tilted at some other angle it is much more complicated and you have to involve the products inertia as well. But assuming that the racquet is flat ( a fair assumption) you approximate the moment of inertia at an angle a with Ia = Ix*(cos a)^2+ Iz*(sin a)^2 if a is 45 degrees Ia becomes the average of the two. So the swingweight of a swing with the head at 45 degree angle is 332 or 2% higher. More importantly, this increase is almost the same for all racquets, so it is hardly worth bothering about.
Originally Posted by stoneage
travlerajm is correct that they have a different twist weight (moment of inertia around the y-axis). As I discussed above that doesn't influence the speed of the swing that much (and thus not the curve). However, it does influence the feel of the racquet, especially at impact. Placing weights at 3 and 9 increases the twist weight whereas placing it at 12 doesn't. A racquet with high twist weight feels less "wobbly" i.e. it is more difficult to rotate around its length axis. It can also handle an off line hit a little better (if you ever miss the sweet spot) and transfers a little less twist to the arm.
@stoneage - yes, this is excellent explanation, and more importantly based on physics and not 'feel'. I never had any doubts you understand the nuances. I get all of that.
But what I do not understand is whether in MgR/I equation one shall use:
a) Ix (which is what is being published as 'swingweight')? or
b) Ix + Iz (which would take into account twistweight as well)?
Because in all previous threads and posts the only value ever mentioned or discussed was Ix.
Now, when JohnB points out that two rackets with identical mass, balance, and swingweight (Ix) - which obviously means that MgR/I is also identical - do feel differently, travlerajm says that this is expected since the twistweight (Iy) of those two rackets is different.
well, which is it than? Either 'I' in MgR/I is just Ix and you at least can claim you are using published specs to back up your claims. Or 'I' in MgR/I is 'Ix+Iy' and than the entire line of thinking backing up this MgR/I idea needs to be redone since:
- no one measures Ix+Iy unless specifically told to do so, and
- therefore people were tuning rackets to MgR/I=21.0 using incorrect value of I, and
- there's no way to compare that to pro's racket specs since they do not publish Iy of pros rackets.