# MgR/I is useless!

Discussion in 'Racquets' started by stoneage, Oct 9, 2010.

1. ### stoneageRookie

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Sorry for starting another thread and sorry for the harsh title. But as I will hopefully show below, well founded. The relation MgR/I has has been kicked around as a supposedly good help to customize a racquet. I didn't find any information about why this would work, so I decided to dig a little deeper into equation. Unfortunately it turns out that it gives an infinite number of racquet configurations, most of them useless.

First a general observation: The laws of mechanics have been used fairly successfully for a couple of hundred years to describe more advanced objects than a swinging tennis racquet. The parameters you need to describe how a racquet behaves when a force is applied to it, is mass, center of mass and MOI (moment of inertia/swing weight). If you take two of these parameters and divide by the third, you don't gain any information, but you loose a lot!

If you assume that you want to keep MgR/I constant (e.g. =21) and we are playing on earth so g is constant we end up with MR/I = c where c is a constant (for example c=21/981= 0.214 if we talk kg and cm).

Further assume that we have a racquet with mass m0, center of gravity r0 and MOI I0 to which we ad a number N of point weights mi at a distance ri. We then get (MOI for a point weight is m*r^2):

Here we already see a scary thing. Any weight added at r=0 doesn't contribute to the total MR/I at all, which means that the idea of MR/I being a description of mass distribution falls apart. And anyone who thinks that adding a 1 kg lump to the handle of a racquet doesn't affect the playability raise a hand.

Further, since we want to keep c constant while adding weights we can simplify the above expression to:

This is the relation that added weights should fulfill to keep MR/I constant. Let us look at some practical cases.

1. Adding one weight means that the relation is m*r=c*mr^2
This has two solutions one is r=0 (as said before) the other is r=1/c. This means that you can add any weight you want at r=0 or r= 46.7 cm but nowhere else!

2. Two weights. The idea behind the concept is to add a weight to increase swingweight, then tweak it a little to achieve the right MgR/I. So lets add a first weight of 30g at the top of the racquet, say at 70 cm. You then end up with a relation for the second weight to fulfill:
0.03*70+m*r=c*(0.03*70*70+m*r^2) which can be simplified to
m=1/(r*(1-c*r))
If you plot the relation between m and r for the second weight you get:

This means that you have have an infinite number of solutions for r<46.7 giving very varying combination of m and r. Which in its turn leads to huge differences in mass and swingweight of racquets that fulfills MgR/I=21

The conclusion is thus:

1. MgR/I does not describe any mechanical behavior of the racquet (apart from being proportional to swing time of if you hold the racquet at the but and let it swing like a pendulum)

2. MgR/I does not describe the mass distribution

3. Using MgR/I=const leads to an infinite number of very varying solutions making it impossible to use as a design criterion.

/Sten

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2. ### travlerajmHall of Fame

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Actually, I use the fact that MgR/I stays constant when I add mass to the buttcap to my advantage. Once I have MgR/I tuned for my forehand by adding weight to the top of the handle, I can subsequently tune the MgR/I value for my 2hb by adding additonal mass to the end of the buttcap (assuming the 2hb MgR/I needs to be reduced) without disturbing the tuned MgR/I value for forehand. This method allows me to tune a racquet for both wings when I don't have the luxury of a scale or yardstick.

Of course adding 1kg to the butt will affect playability, but we're only dealing with weights and balances within the very narrow range that is practical for a tennis racquet. And within that range, there exists an optimal MgR/I value for each of your groundstrokes.

3. ### cellofaanSemi-Pro

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1. I thought that pendulum swing property was the whole point of the formula. Adjusting its natural (pendulum)swing to somehow match or cooperate with your personal tennis swing.

3. It does lead to an infinite number of solutions, but it also excludes a lot of other combinations.

So, what I'm trying to say is, while all your statements and eamples are true, I don't agree that it is completely useless, as it does provide information.
Your opinion is that the relation between swing time for a pendulum and a tennis swing have no relation what so ever and changing the first does not affect the other, but the whole theory as far as I understand it, is based on the assumption that it does.
When that assumption has been made, it is usefull as it excludes a lot of configurations, and in practice, there is a relatively limited number of reaching 21 (though the actual value is supposed to be different for different people) without adding large amounts of weight.

4. ### Big BorisRookie

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MgR/I works!! (but might need some fine tuning)

I had a frame I really liked. It looped kind of by itself through the swing giving me spin and ability to get my racket fast to rapid incoming balls. But I thought it lacked power and stability. So I brought it up some 10 SW points using an Excel calculator from these forums combined with your MgR/I equations to keep the MgR/I exactly constant. First time I played after that modification was great. Almost no problems adjusting and massive power and stability. But continuing to play with that frame my strokes have lost some quality in comparison to the first. Maybe this is because my new set up does not force or steer my strokes into the same loops. I tend more to hit straight through the ball and have some trouble getting spin on my drives. I tend to hit too much straight back and forward instead of getting a natural high backswing then drop and up and around. So my new frame performs well but is maybe no good practice tool so to say.

Could this be adjustable via lead in the but or other adjustments like bringing the MgR/I down a bit to "feel" the racquet head better?

Also I have noticed my main problems are on forehands whereas my 1HB has stayed rather good I think. Could there be different optimal MgR/Is also for 1HB and FH?

5. ### courtkingSemi-Pro

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woow.. I thought i was reading the calculus forum or wrong thread.. this is some serious math..

6. ### callmethedoctorBanned

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Wait, what's the formula for anyways? (algebra 2/geom/trig student here)

7. ### sureshsBionic Poster

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I am not sure why someone is surprised that adding weight at r = 0 is counter intuitive. It depends on how you look at it. If a thin guy vs a fat guy sits exactly in the middle of a seesaw, it does not affect its behavior. Of course, if you try to move the see saw by shifting it, it will make a difference. That does not mean moments and torque and center of mass are meaningless.

8. ### frearNew User

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But Sten, the chart shows there's a one only result if the problem you were trying to solve is 'counterbalance' or better said "adding the lowest second weight": as it seems to be from the assumptions.

So this could be the fair point.

I've just found this whole MR/I thing (simplified, I play on earth) and trying to make something out of it.

[edited: I've tried the math but I got a r=1/2c constant result, a constant value of 2,33cm which is strange so I'm not confident in the calcolois and stripped it from the post].

Last edited: Jul 30, 2016

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Agreed. First add huge amount of mass at certain spot won't affect it is huge red flag. Also went from my 2 old frame of 20.9 and 21.1 to my new frame with 20.2 MGR/I and I swing the new one better...

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This is not an opinion, earth's gravity and my hand when swing the frame act upon the frame in completely different ways is a fact.

It's even 2 different fundamental interactions, one is gravitational force, the other is electromagnetic force.

11. ### Fed KennedyHall of Fame

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Bro do you even lift

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12. ### SpinToWinG.O.A.T.

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The dead from their graves you mean?

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13. ### zaliveProfessional

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The bare fact (which can easily be verified by practice) that by changing MgR/I you can either slow down or make faster racquet's head through swing, gives the importance to the MgR/I.

I can understand that someone can question things like whether the best value for playability is around 21. And hence even that there's no single value that racquet designers should pursue - makes sense. But I don't see how you can get from here to the statement that MgR/I is useless.

After all, don't we forget that top pro customizers P1 intentionally change MgR/I by putting lead at 7''? Why if this is useless? the answer is simple: it isn't. It affects playability a lot.

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14. ### frearNew User

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Can you please point me to the source of both information please (A. P1 intentionally change MgR/I, and B. They put lead at 7")? I'm trying to understand the thing in deep. Thanks.

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15. ### zaliveProfessional

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Ask @dr325i for confirmation that P1 used lead at 7'' together with polarization on Novak's setup, he has/had in his hands Novak's frames customized by them, AFAIK.

As for 7'' and its effect of changing MgR/I, you don't need a source, a simple calculation shows that it's one of the best spots on racquet to increase MgR/I. Since polarization with lead on the hoop lowers MgR/I, putting lead at 7'' is the effective way of countering the polarization effect of lowering the MgR/I.

16. ### BlueBHall of Fame

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MgR/I is a reasonable formula to figure out polarisation/depolarisation.
Play with Bluetack on the racquet, place it all at the tip and butt, then try all towards the centre, keeping the weight and balance the same and watch the MgR/I change. With a bit more effort you'd be able to keep the SW the same, too.

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17. ### frearNew User

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This is interesting, could you possibly elaborate a bit more please?
Why is it better than just, say, sw/weight that we can roughly say >1 is polarised and <1 depolarised?

18. ### BlueBHall of Fame

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Because you can setup the same racquet with the same W and same SW, with a variety of balance points. To make it even harder, even the balace could be the same but still different weight distribution.

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19. ### IrvinG.O.A.T.

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SW is inertia but I like to consider inertia be the inertia at the center of mass or the balance point. Others consider SW to be inertia and SW is sometimes calculated at 4" (4.16 cm,) 10 cm, 9.75 cm, or somewhere in that General. @travlerajm calculates inertia at 0 cm (the butt of the racket) if I'm not mistaken. Any time to add weight to a racket at the axis used to calculate the SW (assuming that axis is not the center of mass) the SW (I in MgR/I) will not change but weight, balance, and inertia at all other points does.

20. ### frearNew User

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I see what you mean. Also, I've noticed this post is very old and the guys have discussed the subject in deep, even though they did not converge.

Since you are so much into inertias I would kindly ask you to explain me the meaning of the +20MR in th MGR/I formula for I:

I = SW + 20MR - 100M

I'm fine with the rest but I don't understand those +20MR.

21. ### Dartagnan64Professional

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Holy cow. Only on a tennis forum would you see obsessive compulsive behavior so entrenched. It's a freaking tennis racquet not a sports car. Grab a racquet, put a little lead here and there and see how it feels.

22. ### fuzz nationLegend

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Have to admit that I've gained much faith in tuning by feel. I respect the math, but I'm no wiz in that department. Glad that it works for some of our pals here, but I've dialed a couple of different racquets into very nice setups over the last couple of years just by adding a bit of lead tape here and there until the smile factor set in. I even did it with a golf driver and it worked there, too.

23. ### ShroudLegend

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Same here. I do it all by feel and not the numbers. You get it right and the racket becomes "quiet" when you swing...meaning you don't have to actively control the racket through contact. Its hard to explain but when you feel it, it will make sense.

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24. ### ShroudLegend

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yes I agree but its nice to know what the racket is doing and where to put the weight and the formulas can help.

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25. ### RanchDressingHall of Fame

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I worked with my old coach on his setup. His racquets came in to 20.8 mgr/i and then I brought him up to 21 with a higher swing weight. I never told him what I did other than "I moved the swing weight up a little" and the results spoke for themselves. His forehand was better than I'd ever seen it, nailing shots easily 100mph in the corner down the line with freakish consistency. Usually he gets a few, but he was painting the lines. And he went on to play what he says the best he'd played in many years a few days later against someone he usually has a tight match up against. That ended up being his favorite racquet, and when he really went for his biggest shots, he just seemed to be timing so purely. Could have been placebo, could have been just the right setup for him.

The only purpose I see in putting time into explaining everything and using formulas and all that, is to demystify the process. Most of it, is basic physics. So that way when you add weight you have an idea of what's going to change on the racquet. Half of the time I have read someone's posts about racquet mods, the info one person says, contradicts what another says, and it's all just sprawled out in all directions. And then you don't know what to believe or what to think.

26. ### IrvinG.O.A.T.

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Maybe that question would be better asked to @travlerajm. I think it's a way of converting the inertia (at the butt of the handle) from the SW of the racket. My guess is m is mass and r is the radius.

27. ### 14OuncesStrungSemi-Pro

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RanchDressing is THE MAN. THE END.

28. ### fuzz nationLegend

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Don't get me wrong - the explanations are great. Although I can't effectively wrap my noodle around all the mathematical breakdowns, etc., it's still really interesting to see what ultimately affects this or that when the ball hits the strings. Even that little book, Technical Tennis was a fun ride along with the science and math heavies, at least for me. I'm probably safe as long as I stay away from the calculus...

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29. ### Backhanded ComplimentHall of Fame

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Yeah I tune by feel... for some reason my frames always end up being 9pts hl and I can feel the head coming around the way I like it... frankly Im the least constant part of any tennis equation... somedays I suck, some days I rule so all I want is a frame that feels familiar so it doesnt distract me.

That said all the math is interesting and I like this empirical approach... it is an interesting guideline.

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30. ### saleemRookie

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I am with fuzz nation and Backhanded Compliment on tunning the racket, I go by feel and my priority are in this order balance, swingweight, twist weight, recoil weight, static weight and mgr/i but that does not mean I think mgr/i is useless, one should never dismiss a theory without trying it, I think mgr/i is a great tool for racquet technicians, they can tune up the racquet with their customers desired specs and have the proper mgr/i according to the customers height and hitting style, let customer test the frame and fine tune it if the ball is easier to hit down the line or cross court.
RanchDressing is the BEST and by far the MOST helpful person in my journey to modify my frames, a big kudos to Travlerjam to give us one more tool to perfecting our racquets.

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31. ### AMGFSemi-Pro

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*cough ******** cough*

You can watch days on end of pros play before you see a 100mph winner. Unless your coach is Del Potro (or you had a reliable speed measuring device) this is really hard to believe.

Not saying an amateur can't hit 100mph, just that shots easily 100mph down the line with freakish consistency is not something even the top pros can achieve. But it's the internet so anything's possible.

32. ### zaliveProfessional

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Tuning a racquet by feel indeed changes MgR/I (unless the mass is added at the butt). And tuning by feel is in the end the only method - at least, the only method of finishing the personal customization job.

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33. ### RanchDressingHall of Fame

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Hah! He was a former ITF pro, and beyond that I got measured with a speed gun at 93mph on a stock wilson 90 with full poly.

It is achievable. Actually much easier to do than you think. The reason the pro's don't do that often, is because they don't get balls they can unload on all the time. I gave him some fluffy balls in his wheelhouse, trying to get him to go down the line. The pro's don't give weak attack-able balls often. That's why you don't see it. Also it's low risk to go so big. In a friendly practice set, not in a tournament or for anything of value, some extra stuff comes out.

Even if not every single winner was 100mph I'd bet my last dollar those winners were WELL over 80mph on average.

You put a 5.5-6.0 quality player up against someone who's in the sub 5.0 category and you'll see some winners fly. Depending on how strong that player is, you can see 100mph. The guy is built like wawrinka-a bear, and plays some of the most aggressive big hitting tennis I've ever seen on a public court.

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34. ### RanchDressingHall of Fame

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Lmao you crack me up

Hey man. I hate calculus too. Like I really hate it. It's not all that hard (it just takes soooo much practice), but the amount of time that subject has taken from my life I will never forgive

35. ### ShroudLegend

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Maximagq got as high as 95 and I think troy and Michelle were able to break 90mph. These are off light feeds with no incoming pace and they arent pros.

IMHO 100mph could easily happen with a pro and the right feeds.

36. ### IrvinG.O.A.T.

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i've watched some of Lopez's matches where he's hit 105 mph forehands. For anyone that has just watched the pros on TV and have not been then believe me. there's a difference. Look at it this way the pros care about speed (no doubt zabout it) but they care more about whether or not the ball is in. there is a big difference in hitting the ball as hard as you can and hitting the ball in.

37. ### zaliveProfessional

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Karlovic has some horrific FHs, both on second serve return and on FH putaways (from the baseline lol). I guess his height and SW at about 400 help him, cos he's pretty consistent there too.

I'd gladly know speed of FHs of the guy that hits the wall at my place. When he amps up the power ball changes the sound to a sound of crushing. He told me he used to practice the way he didn't leave the wall until ball fell apart - and at a certain period he did that every time lol

Last edited: Aug 7, 2016
38. ### RanchDressingHall of Fame

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I believe michelle can hit up there. She hits so freakishly flat, deep, down the line, really weird to see actually. Troy hits a different ball and is more interested in working the court angle with spin. Both of them were a lot of fun to hit with, and both are super super nice. Easy to talk to about everything, and just plain chill down to earth people.

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