Racquet Mod Formulas: Matching Specs

[nikolaih]

Amone, I appreciate the work and look forward to any further fine tuning! What would be neat would be a way to plug in specs, including pre-modded, to figure out the hitting wieght that travlerajm speaks of.

And does increasing the static weight really only affect volleys? I thought this also affected a racquets stability, but I'm guessing that this factor is better represented in the recoilweight and as such static weight loses much of it's meaning?

Thanks again.

[Duzza]

I have a question... tested with a Pure Storm
Weight 312
Balance 32.65
SwingWeight 326

and say...desired

Final Weight 335
Final Balance 32
Final SwingWeight 340

so then...wat do these 2 figures mean and what locations?
Weight 1 Location 10.63679351
Weight 2 Location 36.86895253

[Greg Raven]

Originally Posted by Amone

[...]Now, without further ado, the spreadsheet.[...]

Once you get the bugs worked out, you could post it on Google Spreadsheets so anyone could use it, whether or not he had Microsoft Excel.

[Greg Raven]

I'm curious as to how your derived your formula for Effective weight (AKA Hitting weight). I have a completely different formula, which yields completely different results.

[Greg Raven]

I have a spreadsheet I've been using for a couple of years now to help me match racquets. The results of my spreadsheet correspond with the on-line tool Crawford Lindsey developed for USRSA members at racquettech.com. However, if I plug the same numbers into each of our spreadsheets, there are differences in the results.

Here is an example, starting with my spreadsheet:

Starting mass 331.50
Starting balance 32.20
Starting swing weight 310.00

COP 52.12
Recoil weight 147
Hitting weight @ COP 175

Added mass 0.00
Location 0.00

Added mass 0.81
Location 53.34

Added mass 3.19
Location 58.42

New mass 335.50
New balance 32.50
New swing weight 319
New COP 52.26
New recoil weight 149
New hitting weight 179

Note that I am calculating the Hitting weight at the COP.

When I plug these same numbers into your spreadsheet, I get these results:

Starting mass 331.50
Starting balance 32.20
Starting swing weight 310.00

Starting recoil weight 146.624
Starting hitting weight 0.789
Starting polarization index 0.442

Final mass 335.50
Final Balance 32.50
Final swing weight 319.00
Additional mass 1 0.81
Additional mass 2 3.19

Swing weight increase 9.00
Total added mass 4.00
Mass Location 57.362

Location of added mass 1 17.305
Location of added mass 2 67.534

Final recoil weight 149.153
Final hitting weight 0.837
Final Polarization Index 0.445

I haven't yet had the time to track down the reason(s) for the differences.

[travlerajm]

Originally Posted by Greg Raven

I'm curious as to how your derived your formula for Effective weight (AKA Hitting weight). I have a completely different formula, which yields completely different results.

The hitting weight is mathematically derived using the momentum balance, assuming that the swing has only translational motion at impact (neglecting the rotational component of the swing).

It is highly accurate for predicting power level on groundstrokes, because groundstrokes hit with sound technique have minimal rotational motion at impact. The correction factor to account for the Serve/Groundstroke Power Ratio (SGPR) must be applied to accurately predict relative power on the serve, because the serve has a large rotational component. If two racquets have the same hitting weight, but one has a longer balance, the power level will be about the same on groundstrokes, but the frame with the longer balance will generally be more powerful for serves.

The derivation of the formula for hitting weight is as follows.

We assume the impact of the ball on the racquet causes the racquet to pivot about the wrist joint, and that the racquet is otherwise constrained by the wrist joint (i.e., we neglect momentum losses transferred into the forearm). Let’s also neglect the momentum contribution of the hand to keep this simple.

The ball’s rebound momentum is determined by balancing the moments of the momentum vectors about the wrist joint.


Let’s define variables:

m = mass of ball
v = change in velocity of ball during impact
V = change in velocity of racquet center of mass during impact
r = distance from butt to point of impact
M = mass of hand
R = distance friom butt to balance point
d = distance from butt to wrist axis of rotation (about 4cm for a forehand, or 8cm for a 2hb).

The momentum balance is given by:

M*(R – d)*V = m*(r – d)*v

Rearranging gives:

M*(R – d) = m*(r – d)*(v/V)

m*(r – d) is a constant (neglecting any changes in sweet spot location due to weight distribution), and v/V is the ratio of the ball’s change in velocity to the racquet’s change in velocity. Clearly, v/V is a measure of the power level of the racquet.

So the power level of the racquet (v/V) is proportional to M*(R – d).

[Amone]

@ AJK1: The assertion that I have ever tried to put myself forth as an expert is fallacious. I'm a high school student, at a public high school near Detroit. I've made no claim at any of my own knowledge, except this one piece of work, which is a work in progress. All my other assertions are made on other people's word which I believed above yours.

However, you haven't the right to assert anything without proving it. So if you won't prove it, then keep your mouth shut.

@ Nikolah: Static Weight may have an effect on stability, but I think that there is no direct correlation. Consider, for instance, the effects of adding 4 oz to the butt end of your racquet. I've done it before, it doesn't add any considerable stability or power. In fact, I lost some stability. So take that idea with a grain of salt.

@ Duzza: The locations are measured in CM from the butt end, and they're the center of mass. So if you were to add the weight in 4 inch strips, you'd start 2 inches below the reccomended position. I'd also suggest rounding up to one decimal place, so that it's easier to find.

@ Greg Raven: As I've said a few times, I'm not done yet, because my formulae are the tiniest bit off. I don't see where it is, but I know it's there because in my tests, my swingweight usually ended off by about .23 points, hence not perfect. And the Effective Mass formula is calculated badly somewhere, I don't know where. I got it right on paper, but on Excel I had trouble with it. So regarding that issue: Agreed. Effective Mass is wrong.

As to my formulae in the rest of the spreadsheet, I think they need some tweaking, and I don't know why yours say so differently (as the difference is pretty huge) but they are pretty close.

[FitzRoy]

Amone- I like what you're doing with the spreadsheet. Keep up the good work and try not to get discouraged by any negative feedback.

I apologize if the rest of my post is slightly off-topic for the thread. I'm hoping that it could lead to a better understanding of the application of the formulas which are being discussed.

Originally Posted by travlerajm

The hitting weight is mathematically derived using the momentum balance, assuming that the swing has only translational motion at impact (neglecting the rotational component of the swing).

travlearjm- I've been adjusting the lead on my LM Radicals to try different things. I decided to put more lead on the handle (18 grams, to be exact), but I wrapped it too high. The center of mass is above the 4 cm line, which when using your formula leads to a relatively high hitting weight. This explains what I noticed when hitting with it yesterday, chiefly that it was equally (possibly more) powerful after adding weight to the butt than before, which struck me as odd before I read this post. I had thought that adding the weight should reduce power and it didn't. When I introduced the hitting weight formula to my spreadsheet, I noticed that the 18g didn't reduce the hitting weight at all. So that now makes sense.

The question I have is related to something I saw you mention a while back, in your Sampras setup post - that, at a certain point, increasing swingweight will begin to increase spin (due to ball flattening). My desire is to achieve a higher level of spin on the racquet. Is this measure of ball flattening an actual product of swingweight, or is it more related to the ratio of hitting weight to swingweight? Looking at the numbers, it seems to me that if you have two racquets with the same swingweight, the one with lower hitting weight should be more adequate for hitting a ball with more spin. Do you have a direct formula for calculating this ball-flattening, and what are your general thoughts on this?

[AJK1]

Amone, i don't have to prove anything to you, my racquet tech's knowledge is all the proof i need. To other kids on these boards you might sound important and smart, but to me you and your statements are just full of holes. Even Greg Raven is telling you it's all wrong, your figures suck.

[Amone]

Ha ha ha, AJK. You're funny. If you wanted to play tagalong with Greg, you should've said so. I would've argued less, because he has a point which I have agreed with repeatedly. I don't need to sound smart, I just need to be useful. If I can give someone an answer, then my job's done. And you know what? This gives them that answer, in a public way that you don't give.

Your role is only that of the destroyer, dissenting and questioning with nothing other than a desire to dissent and question, no facts or realities. At least Greg has a contribution to make. I'm done with this discussion, I hope. Though you know, I am a young one, my fiery tempermentality might get me back in.

[Amone]

Excuse me, I was wrong. Silly me and my quick replies. I don't even need to be useful to you folks. I started the project for my own purposes, just like the reason I've been a keen follower of Travler's 'lectures,' same as I've read JohnCauthen's old posts, same as I took physics class this year to try to understand the things they don't talk about, and make my own decisions. I just like the feeling I get inside when people say 'Thanks Amone,' so I shared my own tool.

[FitzRoy]

Originally Posted by AJK1

Amone, i don't have to prove anything to you, my racquet tech's knowledge is all the proof i need. To other kids on these boards you might sound important and smart, but to me you and your statements are just full of holes. Even Greg Raven is telling you it's all wrong, your figures suck.

AJK1 - I hate to respond to such a blatant flame, but weren't you the one who several weeks ago posted that adding weight to the butt of a racquet reduced the swingweight (a blatantly and obviously false statement)? To me that brings your credibility into question when you accuse someone else of making statements that are "full of holes". Did you get that info from your racquet tech as well? And honestly, I don't know why you're coming after Amone here. I don't really see him making any bold statements - he's simply taken formulas provided by others and tried to make a spreadsheet for people to more easily utilize said formulas. Where's the harm in that? If, as you say, this is all horribly false information, then at worst people who try to use it will waste a few dollars on lead tape and then abandon the experiment. Your point seems to be that this is all worthless; if that's the case, then you probably don't need to post anything other than "This info is worthless". You've used a lot more space but you really haven't said anything other than that. So, essentially, you think this is worthless. Ok, I think we get it.

[Amone]

Originally Posted by FitzRoy

travlearjm- I've been adjusting the lead on my LM Radicals to try different things. I decided to put more lead on the handle (18 grams, to be exact), but I wrapped it too high. The center of mass is above the 4 cm line, which when using your formula leads to a relatively high hitting weight. This explains what I noticed when hitting with it yesterday, chiefly that it was equally (possibly more) powerful after adding weight to the butt than before, which struck me as odd before I read this post. I had thought that adding the weight should reduce power and it didn't. When I introduced the hitting weight formula to my spreadsheet, I noticed that the 18g didn't reduce the hitting weight at all. So that now makes sense.

The question I have is related to something I saw you mention a while back, in your Sampras setup post - that, at a certain point, increasing swingweight will begin to increase spin (due to ball flattening). My desire is to achieve a higher level of spin on the racquet. Is this measure of ball flattening an actual product of swingweight, or is it more related to the ratio of hitting weight to swingweight? Looking at the numbers, it seems to me that if you have two racquets with the same swingweight, the one with lower hitting weight should be more adequate for hitting a ball with more spin. Do you have a direct formula for calculating this ball-flattening, and what are your general thoughts on this?

I have a similar question/curiosity. I recall your mention of that, but I'd like to know how much the measure of that flattening there should be, because I'd like to know how to make the racquet powerful-- and flat, not spinny.

So I guess what I mean is "Hear, hear!"

[AJK1]

I corrected myself with the SW thing, to say hitting weight, so what's your point? And i do give facts, eg. you're formulas are wrong for a start! Oh, and can you guys learn to spell properly, trying to get credibility is much harder when you show people you can't spell.

[AJK1]

One other thing my friends, you think i flame, troll etc, well the reason i get annoyed with this high school garbage is because if you are going to post info on these boards, make damn sure it is correct. If it is correct, i will praise you, otherwise, make a mistake, correct it, get it right, or don't post.

[Amone]

That's acceptable, AJK, but it's trolling when I say that I tested it, and it's close enough that you won't know the difference, and you won't back up your assessment that it's junk. That's where the difference is. The only reason I bothered to reply is because you sounded like you genuinely didn't understand.

[AJK1]

I didn't have to back it up as wrong, as Greg Raven beat me to it.

[FitzRoy]

Originally Posted by AJK1

I corrected myself with the SW thing, to say hitting weight, so what's your point?

I think my point was simple and quite clear. You're saying that you don't like people posting incorrect stuff; I pointed out a mistake which you made. People told you what was wrong and you fixed it. What you've done is say that Amone is wrong without offering anything to help him improve it. You haven't even said what exactly you thought was flawed about it. Amone's biggest obvious mistake was that he used 10.16cm instead of 10cm; Greg Raven pointed it out, not to sharpshoot Amone's post, but to help him make a more accurate spreadsheet. That's the difference between what your posts are and what his posts are.

Originally Posted by AJK1

And i do give facts, eg. you're formulas are wrong for a start! Oh, and can you guys learn to spell properly, trying to get credibility is much harder when you show people you can't spell.

I assume you're including me in this spelling comment, though I can't fathom why. I'm sure I've made a few spelling errors from time to time, but I don't think I'm exactly firing off a litany of them such that my credibility is going to be tarnished. FWIW, I can clearly see 4 errors in usage/grammar on your part in that one small quote, which is somewhat ironic considering the message.

[AJK1]

There there don't cry Fitzroy, your off the hook. We all make mistakes, myself and Amone included. He just makes bigger ones.

[FitzRoy]

Originally Posted by AJK1

There there don't cry Fitzroy, your off the hook. We all make mistakes, myself and Amone included. He just makes bigger ones.

I do agree that we all make mistakes. That's basically what I was trying to say.