Originally Posted by 10isfreak
In the first place, I never intended to mean that Yandell was addressing this question. I meant that people were using his results improperly.
Secondly, the claim regarding the contact location doesn't rely on a ball's size spot on the string bed. The effect I am looking to get is a fast closure of the racket face upon contact. Any ball struck bellow the geometric center will make it happen to some extent -- that is, you have half a racket string bed to manage getting it right.
The study the SpeedMaster did divided contacts in terms of racket reaction after impact: stable, closed, opened. That is sweet spot, upper half or lower half. You can err a bit toward the tip, the edge or the throat... it still twists the racket. Maybe I worded it poorly by phrasing it the way I did. In my head, it was very clear that relationship wasn't continuous in the sense that each fraction of an inch would give you more spin, but looking at the sentences I wrote, I wasn't accurate enough.
I did provide a chart with three zones, but it's not clear how to use it. To me, you don't use a marginal analysis to make inferences given qualitative data...
OK, I see what you're saying. It would make sense that any hit below center would generate more spin, if we assume a gradient from 2" from center, where 30+% more spin is generated, compared to the center. So, possibly, impacts 1" from center might generate 15% more spin then center impacts. There might be a linear spin gradient from the edge toward the center, in other words. But this is assuming a lot, as the stringbed effects responsible for that extra spin are complex and some of them rely on close proximity to the frame edge.
The rotation effect you mention is one of those effects, but given the physics of racquet rotational instability - twisting moments are much greater the further the impact is from center - one would think that the rotation effect would be much less effective at producing extra spin on impacts 1" from the center than it would be at 2" from the center. But I think another experiment would be needed to sort that out.
For those who are wondering what experiments I'm talking about
The rotation effect can also be applied by the player if he swings so that the top edge of the racquet is accelerating relative to the bottom edge at contact. This will apply a relatively larger force to the top of the ball than the bottom of the ball, producing more spin, even on impacts at locations other than below center and without the racquet spinning in reaction to the ball impact. Rod Cross gives a good explanation of this in a paper on the physics of the kick serve, see Part II, Section 5. Racquet Rotation here: http://twu.tennis-warehouse.com/lear...r/location.php
So there are several racquet rotation events that can generate extra spin:
1. Impacts below the center of the strings produce more spin, all other things equal, due to various stringbed phenomena, one of which is a result of the off-axis impact causing the racquet to "close", which results in greater force being applied to the "top" of the ball.
2. The player can swing in such a way that the racquet-face is closing during impact. In other words, just before impact it is less closed than during and after impact. This will have a similar effect as above, but is not necessarily dependent on impact location. A player could do this by actively pronating the forearm to close the racquet face through impact. I believe coaches sometimes refer to this as "grinding" the ball to produce additional spin at impact. However, there is not enough time during impact for a player to decide, at that point, to do this. The rotation of the racquet would have to be set in motion prior to contact. (Although this could probably be debated by talking about reflex contractions of the forearm muscles, etc., but I'm not sure it would lead anywhere productive.)
3. Racquet tilt should also be considered along with the above. If a racquet is "closed" during the swing, and that angle remains constant so that it is not rotating during contact as in #2 above, it will still produce more spin for the same physical reason as the two rotation events - the closed racquet face will apply greater force to the top of the ball than the bottom of the ball.
I don't know, but I still think it would be better to aim for the center of the strings, or at least along the longitudinal axis. This would seem to give the greatest chance of producing a good shot, although shot speed and spin will vary each time one misses the center, while reducing the chance of clipping the frame and losing the point outright.