Originally Posted by spaceman_spiff
Are you sure you don't just need to readjust your math?
The TW Professor didn't add 100 g to a frame that weighed 0. It was 100 g plus whatever the hitting weight (effective mass at a particular point) of the particular racket used in the test. So, the magic number isn't 100 at 3&9; it's whatever the final total hitting weight of the racket was at 3&9 after the 100 g was added.
If you read the paper you'll see that 100 was grams added at 3&9 to an Exo3 Red 105. The addition of this amount of mass effectively reversed the spin gradient from high (toward the sky when striking a groundy) to low (toward the ground) in the stringbed. Stock, this racquet produced much more spin on low impacts than in the center of the strings, and much less spin on high impacts than in the center. We can assume that all stock racquets share this relationship. By adding 100 grams of mass at 3&9 high impacts became more spin-friendly than in the center and low impacts became less spin friendly than the center. So the relationship observed in the stock condition was reversed.
But reversing this relationship is not the goal. Equalizing the spin production so that the stringbed produces the same amount of spin on high, low and central impacts is the goal. Adding 100 grams does not achieve that goal. The TW Professor mused that, if the addition of mass at 3&9 effectively reverses the relationship in a linear way, there may be an amount of mass that one could add that would achieve this goal. Some simple calculations showed that adding about 60 grams of mass should do this, assuming there is such a linear relationship. For the sake of experiment, I'm willing to run with this assumption.
Instead of trying to find a frame with a SW of 260 so that you can add the 60 g that you have your mind set on, maybe you need to calculate the ideal hitting weight that you are trying to achieve at 3&9. Then, once you know your ideal hitting weight in that location, you can use the hitting weight numbers that the TW Professor has already compiled to find frames that can let you reach your goal with a different amount of added lead.
It would be tempting to assume that the greater hittingweight of added mass at 3&9 is responsible for the altered spin production seen in TWU's experiments with adding lots of mass. But it is not at all clear that hitting weight is the crucial factor here.
In the paper, six physical effects or phenomena were linked to the altered spin production seen at high and low impacts with and without added mass:
1. Short-side effect
2. Rotation effect
3. Friction effect
4. Bending effect
5. String movement effect
6. Weight effect
Increasing hittingweight will definitely have a big impact on numbers 5 and 6 on this list. But the relationship of hittingweight and effects 1-4 on the list is not at all clear.
On the other hand, increasing twistweight will almost certainly alter the rotation effect (#2 on the list) and short-side effects (#1), and the reversal in the spin-gradient from low to high seen in the experiment might be in large, or even most, part due to increasing twistweight by a huge amount because it is likely that these effects are those most amenable to modulation by the addition of mass. Adding those 100 grams to the Exo3 Red 105 pushed the twistweight to around 32.7. The greatest twistweight amongst racquets currently produced is about 21 (Wilson K4 OS), so we're definitely in uncharted territory here. Adding 60 grams at 3&9 to the Exo3 Red would bump the swingweight to around 24. So why not just add a couple grams at 3&9 to a K4 OS and call it a day?
It would be tempting to attribute the results described in the paper to measures that we are familiar with and understand well, like hittingweight and twistweight. But there are several more effects on the above list that are not often considered in conventional racquet customization work using relatively small amounts of mass. The bending effects documented in the paper, for example, are not something that people usually think about when adding a little lead to a racquet. Yes, I could use the the above twistweight number and calculate the hittingweight that would result from the addition of 60 grams at 3&9, and then attempt to target both those numbers. But would that achieve the goal?
Remember that the TWU experiments also included the addition of 100 grams of mass at 1&11. This would have increased the hittingweight much, much more than the addition of that mass at 3&9. So if we focus on a target hittingweight we would only need to add maybe 20 or 30 grams at 1&11 to hit that target. But, the addition of 100 grams at 1&11 did not produce the same effect on spin production at various impact locations as did mass at 3&9. Adding mass at 1&11 intensified the result observed in the stock condition - spin production was already greatest on low impacts and adding mass at 1&11 made this even more pronounced. This would suggest that increasing twistweight, not hittingweight, is most important to reverse the spin gradient observed in stock racquets.
And this is what the paper, at least hesitantly, concludes by noting that the short-side and rotation effects (numbers 1 & 2 on the list) are most responsible for the differences in spin production seen in high and low impacts. Increasing twistweight to around 24 could then, be a worthy goal. It's interesting to note that the short-side effect would be reduced using an oversize frame like the K4 112, because off-center impacts would be further from the frame than they would be in a midplus and even more so than with a mid. This suggests that, at a given twistweight, the difference in spin production for high and low impacts would be less with an oversize than with a midplus. A mid would be the worst. Also, since oversize frames naturally have greater twistweights, because any mass added or existing on the periphery of the frame is located further from the longitudinal axis, you'd have to add less mass to an oversize to achieve the goal of equalizing spin production across the stringbed. Conversely, you may have to add even more mass, perhaps much more, to achieve this goal with a mid. In fact, it could be that the K4 112 achieves the goal in stock form with it's twistweight of 22. But I'm not playing with that ugly thing!
Anyway, yes, it would be tempting to focus only increasing twistweight to a particular target, and in this case that target would be about 24. And in essence that's what I'm doing. What's the best location to add mass to increase twistweight the most while increasing hittingweight the least? At the frame's widest point - at 3&9. So I'm trying to find a frame with a very low swingweight so that I can add 60 grams at 3&9. The good news is that even a very light, low-swingweight frame like those kindly suggested so far have stock swingweights pretty close or only a little less than the Exo3 Red. Whew!
To those who have suggested that I should come down to earth and who have kindly pointed out that adding even modest amounts of mass at 3&9 changes the performance of a racquet: Thanks, you're right. But I'm not looking for performance enhancement; I'm looking to create the ultimate control racquet. LOL
The bummer, though, is that even if I do achieve the objective of making spin production uniform for all impacts across the racquet face from 3 to center to 9, I probably won't even know it. Times like these I wish I had a spin measurement rig in the basement.