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09-16-2012, 01:06 AM   #53
stoneage
Rookie

Join Date: Apr 2010
Location: Stockholm, Sweden
Posts: 243

Quote:
 Originally Posted by travlerajm The two racquets have the same swingweight when measured in the plane normal to the stringbed, but if you mounted them in an RDC machine with the handle rotated 90 degrees to measure the swingweight in the plane of the stringbed, the racquet with higher twistweight would measure higher swingweight than the other because the added weight on the sides of the hoop is farther from the pivot point than if the weight were placed in the center of the stringbed. Your actual swing occurs in a plane that is neither completely normal nor completely parallel to the stringbed, so the twistweight contributes to the "effective" swingweight, which is always slightly higher than the measured swingweight. In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference. But the example presented (with 2 frames of equal mass, balance, and measured SW, but different mass distributions) is a case where the difference does come into play. I have to go catch a plane this morning, so I'll leave a drawing to someone else.

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.

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Last edited by stoneage; 09-16-2012 at 11:58 PM.