# Optimum Racquet Balance for Performance II - MgR/I Data for ATP Pros

Discussion in 'Racquets' started by travlerajm, Jul 5, 2011.

1. ### sykeProfessional

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Travelerajm, may I ask what is the SI unit for the individual variables for calculating effective mass?

I got 0.1556???

M= grams? or kilos?
b= cm
L= cm
R= cm
SW= kg/cm2

For excel, would this be right?
Effective Mass=M/(1+(M*(POWER(b,2)/Ic)))
Ic=SW-M*(POWER(b-10,2))

Which of the 3, MgR/I, MR^2 or Effective Mass should have the highest importance? Which should I achieve first?

Lastly, thanks for the insightful post!

Last edited: Mar 14, 2012

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Some basic questions.

Do you need MGR/I and MR^2 to be optimal. If not which is better to have optimal?

What is the optimal MR^2 rating?

Can these formulas ever become popular and used worldwide?

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replica...

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Also, do these apply to one handed backhand? The OHB is supposed to have different requirements to a 2hb, like lower swing-weight.

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bump. Really need an answer, I have a club match coming up.

6. ### sykeProfessional

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I have waiting for an answer much longer than yourself..

7. ### Circa 1762Rookie

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Syke, I had the exact same problem as you and spent some time playing with the formula last night. Unless I'm still doing something wrong, you are correct that b, L, and R are in cm and that SW is in kg cm2. However, M should be in kg, not grams.

See the first post by TW Professor in this thread: http://tt.tennis-warehouse.com/archive/index.php/t-243818.html

The formula is simplified slightly differently, but it gives the same result as travlerajm's formula above.

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Forget about my questions, syke asked it here. This is the one I need an answer to.

Also, how much should I reduce the MgR/I for a wristband.

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Just looking through the thread. This was never rebuffed by travlerajm. Doesn't muscle mass affect the pendulum?

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Is optimal MgR/I good for a ohb? Found out that it does
Does MgR/I help a serve, using the continental grip? Is it easier to serve with a higher mgr/i? Found out that MGR/i doesn't matter. A good swingweight is needed.

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13. ### jstoutNew User

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I'm not travelerjam but I have done this to my racquet.

MgR/I = Accuracy (Equation uses Mass, Balance, Swingweight)
MR^2 = Byproduct of MgR/I (Equation uses Mass and Balance)
Effective Mass = Power/Shock Absorption (Equation uses Length, Mass, Balance, Swingweight)

For a quick adjustment, MgR/I and Effective Mass would have the most importance depending on what you are wanting.

To adjust to all the equations.
2. Increase the Swingweight to the 340-380 range changing the Effective Mass keeping your MgR/I value as same as possible
3. Adjust the Mass for the MR^2 keeping your MgR/I value as same as possible

14. ### Mig1NCProfessional

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Has anybody figured out the exact distance from the bottom of the racquet yields the highest gain in MgR/I for the smallest increase in static weight?

15. ### stoneageRookie

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Maybe many great racquets have the same MgR/I (e.g. 21), but the reverse is not true.
Very few racquets with MgR/I = 21 are great. So as a design criterion for customizing racquets it is a very dangerous concept and would avoid it if I were you!

If you still want to find the minimum added weight m you can use:
m = (M*R-c*J)/r(cr-1)

Where M, R and J are the values for the original racquet. m and r are for the added weight and c = 21/g (or what ever value you are striving for).

You can find the r that gives you the minimum m by taking the derivative dm/dr = 0.
But that leads to a fourth order equation, so it is not so fun. It is probably easier to plot the equation in Excel and see where min lies.

You can also see from the equation that you should avoid r=1/c (46.7 cm) since that will require an infinite weight to achieve the right value.

/Sten

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16. ### Mig1NCProfessional

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Thanks, I'll plug that into Excel and see what it looks like.

PPS: What is J?

Last edited: Sep 4, 2012
17. ### travlerajmHall of Fame

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Sten,
The MgR/I formula can be used as a mass distribution design criterion as long as other design criteria are used along with it.

For example, when I design my own racquets, I use 3 critical mass distribution design criteria:
1. MgR/I = 21.0 (this assures a tuned forehand for an eastern to semiwestern grip).
2. MgR'/I' = 22.5 to 22.6, where R' = R - 10cm, and I' = the sw about the axis 10cm from butt. (this assures that my 2hb is tuned).
3. I' (SW) = 360 to 370. This assures that my serve will have maximum velocity without wearing my shoulder out. I start to lose speed on the serve if I go lower than that range (as measured by how high it hits on the back fence after a bounce in the service box). And if I go higher than that range, my serve is still fast, but my arm runs out of gas and I start to labor and lose accuracy after serving several sets.

Those 3 design criteria are in my opinion the most important.
Other design criteria, such as length, stiffness, string pattern, string type, head size, matter less and can be varied as long as I work within the first three constraints. If I want a bigger serve, I might go longer (and use SW at the upper edge of the range). If I want more control on groundies and volleys, I might go shorter.

Last edited: Sep 4, 2012
18. ### Circa 1762Rookie

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travlerajm, quick question for you about MgR/I and racket length. For standard length rackets, I've had good luck keying in on an optimal MgR/I and MgR'/I' for my 2hb (21.1 and 23.0, roughly). I'm thinking about moving to an extended length racket and want to make sure I set it up properly. I don't see anything in the MgR/I formula that would change with racket length, but I want to make sure I'm not missing anything. Say my standard length racket is at 357 g, 32.3 cm, and 340 SW. Should I still be aiming for these exact specs with the extended length racket?

All your help in this thread is much appreciated! MgR/I has really helped me understand why some rackets work for me and some don't.

19. ### stoneageRookie

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Thanks for the clarification!
I have had two problems with MgR/I:

1. I have yet to hear an explanation why this parameter is relevant to the mechanical behavior of the racquet in tennis. MgR/I describes how the racquet swings freely in a gravitational field, i.e. like a pendulum. MgR/I=21 means that frequency of a racquet swinging from the but is 0.73 Hz. But unless you are building a cuckoo clock of the racquet I have difficulties to see the relevance. Gravity is the least of forces involved in a tennis swing. But if you have some explanation that could shed some light on this I would be most interested (no irony intended).

2. There are an infinite number of racquet configurations that fulfill MgR/I=21 most of them very strange and unplayable. So if you use only that to find an optimal racquet you could easily go wrong.

However, you say that MgR/I should be combined with a certain swingweight. And then it becomes something different entirely! By saying that MgR'/I' = 22.5 and I' = 360 to 370 you are saying that MgR' should be around 8200. And MgR'/I' (and MgR/I) has disappeared.

1. setting MgR' (or MgR), which is the static force (moment) you feel when you hold the racquet in the handle parallel to ground.
2. Setting the moment of inertia (swingweight) which is good description of the rotational behavior

So there is obviously no need for MgR/I at all, which I think is fine since the two above criteria are better.

/Sten

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Last edited: Sep 4, 2012
20. ### travlerajmHall of Fame

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Sten,
You misinterpreted my post.
The MgR/I formula works for swingweights in the 300 range to 400 range.

And so does the MgR'/I' formula.

The physics of a pendulum are relevant to a tennis stroke even in the absence of gravity, because the centrifugal force is always present.

But the laws that govern the motion of a pendulum are easiest to apply by using the laws of motion for a pendulum in a vertical plane - rotating the plane of motion closer to the horizontal plane has little effect on the formula.

I have found that a groundstroke can be reduced to the swing of a double pendulum, with the frequency of the upper pendulum (the arm and torso) almost independent of the racquet specs. Adding a kg to the butt of racquet would obviously affect the speed of the upper (arm+torso) pendulum, thereby reducing the optimum MgR/I value for the lower (racquet) pendulum. Thus the formula does not "break down" as you suggest - rather, it is the assumption that the upper pendulum is unaffected by changes to the racquet mass distribution that breaks down. The principles of the formula still hold.

An easy way to see see the significance of the MgR/I formula is to start the racquet high overhead with your forehand grip, and allow the racquet to sweep through a high-to-low-to-high stroke in a mostly vertical plane (much like a golf stroke). If you keep the wrist relaxed through the stroke, the racquet will exert a moment on your hand as it passes through the hitting zone. If MgR/I is > 21.0, the moment from the racquet handle will pull forward on your index finger. If MgR/I is < 21.0, the moment from the handle will push back on base knuckle of your index finger. If MgR/I is tuned properly, there will be virtually zero moment.

Zero moment acting on your wrist joint is highly desirable, because it means you do not need to apply any forces from the wrist during your swing to keep the racquetface aimed toward the target. This increases your ability to control the ball significantly.

If MgR/I is too low, you need to apply a forward moment from the wirst to keep the racquetface aimed toward the target through the hitting zone. This is not easy, but it is doable.

Similarly, if MgR/I is too high, the racquetface will come around too fast relative to the hand, making control difficult because you would need to apply a reverse moment to the racquet in order to control the ball (or convert the excess racquetspeed into extra vertical velocity for more spin, which is not easy to do). This is more difficult than the former situation, which is why very few stock racquets (or pro customized racquets) have specs with MgR/I > 21.

The ideal situation, however, is to have zero moment required, allowing a relaxed wrist through the hitting zone. This is why, I believe, that most of the top players in the world have MgR/I values very close to 21.0, as I have shown in the data I presented.

Last edited: Sep 4, 2012
21. ### cornersLegend

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The following were questions posed to Travlerajm, but I'd like to add a bit of response as well.

Rod Cross has been modeling tennis strokes, including the serve, as double pendulums for several years, with two papers appearing in the past twelve months.

This isn't the case. Many racquets on the market are reasonably close to 21.0, especially traditional players' frames like the Pro Staff 6.0 and the Prestiges. I support your skepticism but I think you're misinterpreting this notion of MgR/I and its use. It's not meant as a stand-alone, be all/end all.

I suspect that if you try some on-court experiments, like the following two, you'll find some value in the approach:

Experiment #1: Alternate between two frames with very different MgR/I values but with very similar swingweights and static weights. The two frames will differ only in balance point.

For example: Racquet A at 335 grams / 31.5 cm balance / 320 swingweight (MgR/I = 20.8 ) and Racquet B at 335 grams / 33.0 cm balance / 320 swingweight (MgRI = 21.37).

Experiment #2: Alternate between two frames with the same MgR/I values (how about 21.0?) but with very different static weight, balance and swingweights, such as:

Racquet A at 350 grams / 31.5 cm balance / 330 swingweight (MgRI = 21.0), and Racquet B at 335 grams / 32.0 cm balance /320 swingweight (MgRI = 21.0). Or better yet, your preferred specs and another very different configuration with the same MgR/I ratio as your preferred specs.

If the ratio doesn't make some sense to you after these experiments then we can confidently add your report to the "MgR/I is rubbish." pile of anecdotes.

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22. ### stoneageRookie

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Do you mean that you should fix the swingweight or not? If you aim for a certain swingweight when doing the calculation my argument still holds, it doesn't matter if the target is 320 or 380. If you are saying the swingweight could become anything between 300 and 400, then you are saying something else than in you last post.

The physics, Yes. The specific solution, No. They are both controlled by forces, weight, moment of inertia etc. MgR/I is a solution to one situation/configuration, but it is not the solution to other problems, and definitely not the double pendulum.

You, or Rod Cross? Because that is what he has been saying in a couple of papers. Except that he is talking about swing speed, which is something different.

If adding a weight changes behavior of the system it does. You can't say that it only affects one part and the other can be treated as if nothing happened. Apart from that MgR/I doesn't describe the lower pendulum.

I would love to see a proof of this, or at least an indication how this has been calculated.

Just a note here. I am not out on a crusade against you concept, I was intriuged when I first saw it and really tried to understand relevance of it. But so far I haven't seen anything that supports it. You have obviously studied a lot of racquets and found that certain values for swingweight and balance gives great racquets. That is very interesting and commendable. I just think you confuse those findings by combining them into a new parameter with doubtful mechanical relevance.

/Sten

23. ### stoneageRookie

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I have read his A double pendulum model of tennis strokes in American Association of Physics Teachers. I can find nothing there that even remotely support the use of MgR/I. He is studying a double pendulum with an applied force and without gravity (see fig 1 and the appendix) which have a very different behavior.
Any other sources?

Say you have two parameters A=10 and B=5

1. If you say that A=10 and B=5, then saying that A/B = 2 doesn't ad any information, it follows automatically.

2. If you say that B = 5 and A/B = 2, it is the same as in 1. just a slightly more complicated way of saying that A=10 and B=5

3. If you only say that A/B = 2 then you have solutions like A = 5 800 and B = 2 400

You admit that 3. is not sufficient and you have to set B as well. If you want to describe your relation as 2. fine, as long as you are aware that it is the same as 1.

So I don't doubt that your customization work. But it does so because you set the fundamental properties, not the relation.

24. ### jmnkProfessional

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I do not think there's anything particularly theoretically special about claiming that a racket with MgR/I = 21 is 'the best'.

If I follow travlerajm posts properly he just observed statistical correlation between player's rank and player's rackets MgR/I value, and from that he therefore deducted that 21 is the optimal value.

Now, it is interesting but in my opinion unfortunately a bit far fetched.

Per his own data the accuracy of MgR/I needs to be calculated with 0.1 precision. that means to back up his claims with empirical data (that is player's rackets specs) that data must be pretty darn accurate. However per his own admission he just estimated the mass and swing weight of the player's rackets based on available specs for mass and balance for unstrung rackets (see http://tt.tennis-warehouse.com/showthread.php?t=387620). Is that possible - well, estimation is, but you can't really use the result of the approximation in cases where the very exact number is needed. Or in other words - the formula used to calculate swing weight based on mass and balance of the racket, and assumption about racket's weight distribution, developed by Cross (I think), while indeed gives pretty decent result as far as swingweight is concerned, is by no means an absolute theoretical truth in the sense for example the parallel axim theorem is.

Now if you add to this the fact that you are supposed to adjust the value if you wear a sweatband - than I think we are leaving the realm of physics....

25. ### stoneageRookie

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I most wholeheartedly agree and it should never have tried to enter the realm of physics

It is a pity since there are obviously a lot of data behind it (even if you doubt the accuracy of some of it) and there are people who are happy with the result when using it. So can you use it as some kind of rule of thumb if you leave all that unfounded talk about double pendulum and zero moment on the wrist behind? Maybe.

Start by dividing by g, since it is only there to confuse things. You then get:
MR/I= 2.14

Now invert it to get a more practical unit, you then get:
I/MR = 0.467 m or 46.7 cm

Call it a normalized balance (NB) or something like that and say that a rule of thumb is that NB should be around 47 cm, without claiming any physical background. It would be like a BMI for a racquet. BMI doesn't claim any deeper background, just based on observations it says that a healthy normal person has a BMI between 20 and 25.

But as a rule of thumb you should also open up for other values. Why should recreational player have the same value as a pro?

Last edited: Sep 6, 2012
26. ### travlerajmHall of Fame

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Correct - the formulas do not need to be adjusted when you go to a longer racquet, and you can use approximately the same target specs. But keep in mind that while the swing dynamics will stay the same, the impact dynamics will change with a longer racquet. That is, the effective mass at the hitting zone will be lower with longer racquet - so the feel and ball response of the impact will change. The longer racquet will be less solid and less powerful for the same groundstroke or volley stroke. But the added leverage may make it easier to produce spin and ball velocity on the serve.

Because of the lower hitting weight for a given mass, balance, and SW, you may find that you prefer a higher SW for the extended racquet. I would recommend keeping the MgR/I and MgR'/I' values the same, but bump the SW up a bit to compensate for the lower hitting weight, thereby preserving a similar level of mass in the racquet head.

Last edited: Sep 6, 2012
27. ### travlerajmHall of Fame

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The exact distance for maximum gain in MgR/I depends on the starting specs, but it is usually around 9" from the butt.

Keep in mind that adding mass to the throat region can have a considerable stiffening effect on frame (which may or may not be desirable for you), especially for thin-beamed frames.

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Curious to see what travlerajm says in reply to stoneage and jmnk. I think my game has improved for mgr/i. That may just be the increased mass and swing-weight i have added to my racket, though.

Last edited: Sep 6, 2012
29. ### DEHRookie

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I just don't see where Stoneage formula will help a person out. All it shows me is how to compare two different racquets. Their most be something I am missing. At least Travlerjm compared and came up with a formula that is based on the Pro's and how we can apply it to a Male player and Female player. What am I missing.

30. ### travlerajmHall of Fame

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The method of letting the racquet sweep through a high-to-low-to-high swing with a relaxed wrist in order to determine the optimum MgR/I is not a calculation -- rather, it is a method of measurement. You can easily feel the moment that the racquet applies to your hand. You don't know the magnitude of the moment, but you can perceive the direction in which it acts (either backward or forward).

If the racquet pushes back on your hand (i.e., pressing against the base knuckle of your index finger) as it comes forward through the hitting zone, then MgR/I is below the optimum (which is roughly 21.0 for an average sized male, but slightly higher for shorter players, and slightly lower for taller players). If the racquet handle pulls forward on you fingers as it comes through the hitting zone, then MgR/I is higher than your optimum.

This is the method I use to tune a racquet in a pinch, when I don't have access to a wall. A more precise way to tune MgR/I is to use the wall targeting method I described in other threads.

Also, I choose to keep the convention of including g in the formula because g can vary significantly enough between different cities around the globe to make a noticeable difference in how my racquet plays, and I travel a lot for work, and always bring a racquet with me. For example, I will at my office in Belgium next week , where g = 981. I also travel to Buenos Aires a couple of times per year, where g = 978. The difference in racquet swing dynamics affects my swing enough that I like to look up the g value when I travel and adjust accordingly.

That reminds me: I'm looking for a hitting partner in the following cities over the next 2.5 weeks: Vienna, Barcelona, Glasgow, Paris, Madrid. Any takers (I'm a 4.5-5.0)?

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1) Does muscle mass affect the pendulum?

2) You say lead on the butt effects mgr/i for a 2hb. Lead on the butt has minimal effect on mgr/i on the spreadsheet. Does lead on the butt affect mr^2?

3) Why does lead have to be 7" to reduce mgr/i? Why can't it be lower?

4) How do you tune your mgr/i for a backhand. Is there a formula, or do you tune till it feels right? I play ohb.

I've noted that on a 27 " frame, adding lead at 18.5" has minimal effect on mgr/i. Strangely 17.5 " increases mgr/i. Just informing you.

32. ### Circa 1762Rookie

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Thanks for the advice! I've had much better luck settling on MgR/I than on weight/SW, so I'll keep this in mind if I go extended.

Also, to everyone else: for those of you who are skeptical of MgR/I, I'd highly recommend playing around with it if you aren't happy with your current racket setup. After a very long racket search, I settled on a Prestige MP, but it still didn't feel quite right. After stumbling on this thread, I realized that stock Prestiges have a much higher MgR/I than most other rackets. They started feeling better and better as I brought the MgR/I down until I finally found an ideal level (~21.15 - I'm 5'8", so I think the slightly higher than normal MgR/I makes sense). Then I started to think about all the rackets I'd demoed, and began calculating their stock MgR/I - most had MgR/I's around 20.8! The two with which I felt I had the best control, though - Bio 200 and TFight 325 - both had MgR/I's around 21.1. Certainly there were other factors at play here, and I don't completely understand the physics, but these two things together have convinced me that MgR/I is a valuable tool.

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I too know nothing about physics.

If travlerajm could rebuff the claims that the physics are wrong, I would be delighted, as i have tuned my racket to optimal mgr/i.

34. ### jmnkProfessional

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it's not that the MgR/I formula is somehow against physics. It's just that having MgR/I = 21.0 has as much relevance to the racket being 'good' as the racket being 'red', or 'painted in stripes'.

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replica

Last edited: Feb 9, 2016
36. ### Circa 1762Rookie

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The very simplified idea (I think) is that each person has an ideal MgR/I such that the racket face comes through the hitting zone perpendicular to the ball, meaning that you don't need to apply any extra wrist action to keep the head perpendicular. The result - assuming your footwork and stroke is sound - is that you'll have more (or at least easier) control right around your ideal MgR/I. To jmnk's point, ideal MgR/I is going to be different for every person. Again, I don't understand the physics, but travlerajm has said it tends to vary by height (probably as a proxy for arm length, I would guess). Taller players will have lower ideal MgR/I, while shorter players (like myself) will have higher ideal MgR/I. Again, MgR/I is not the whole story. If you're primarily a doubles player and care more about serves and volleys (for which MgR/I isn't important), your ideal racket setup may not give you an ideal MgR/I. Nonetheless, MgR/I can be an important data point.

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Hereâ€™s my 2 cents on this:

When I started customizing my racquet a few months ago, I had never heard of this MgR/I, or any other magical formula. I started modifying the racquet through trial and error, based on what felt right for my game.
I started with a 300g (strung) racquet. After OG and dampener, 312g.
I started adding lead at 9 and 3, which reduced twisting considerably and increased the swingweight. Then I added a little lead at 12, for more swingweight. Then it felt too headâ€“heavy, so I added 15g of silicone in the handle.
At this point, my racquet feels great for my forehand. I am still struggling a little with my 1hbh, but I think it is just a matter of getting used to the new balance, after adding silicone in the handle.
The current specs: 350g, 4.5pHL, 350SW

Hereâ€™s the fun part.
A couple of weeks ago I stumbled upon this thread.
So out of curiosity, I checked my numbers and the results are:
MgR/I = 20.7
MR^2 = 378
Thatâ€™s pretty close to travlerajmâ€™s ideal numbers.
I really donâ€™t think this is just a coincidence. Physics donâ€™t lie, you just have to know the formulas and how to apply them to real-world situations.

I must also add that I play with an Eastern grip and hit fairly flat, with a long swing.
I believe that these specs are better suited for this style.

38. ### travlerajmHall of Fame

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Yes. This sums up the main point of the concept.

39. ### travlerajmHall of Fame

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Not that much - other factors such as arm length are more significant.
Yes, lead on the butt decreases the MR^2 value. But I don't think it's important to worry about MR^2 value. I believe that the apparent optimum MR^2 value for the pros of ~385kg-cm^2 arises as a consequence of having both MgR/I and SW optimized.
In my experience, a 1hb feels about right when MgR/I is tuned for my forehand at high SW. But I have never specifically tried to tune for a 1hb. I tune my own racquets for a 2hb by assuming that the racquet pivots about an axis 10cm from the butt (where the left wrist pivots).
[/quote]
Yes. Depending on the starting specs, the inflection point (where adding mass does not affect MgR/I) could be at around 18.5" from the butt. Adding mass anywhere below the inflection point would increase MgR/I.

40. ### stoneageRookie

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My formula? It is MgR/I
I just indicated a way to save the concept by skipping the erroneous physics. But it was obviously misguided since most people on this thread just want to believe.

Last edited: Sep 6, 2012
41. ### yemenmochaProfessional

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Are there any stock racquets that are optimal or close to optimal in this analysis?

42. ### travlerajmHall of Fame

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Sten,
Hundreds of people on this forum have tested this formula and benefited from this simple way to tune a racquet for their strokes. There is nothing erroneous about the formula, and it is indeed based on simple laws of physics.

I think perhaps you are underappreciating the importance of gravity to a tennis stroke. Consider that the takeback on the forehand of every single high level player, regardless of grip or swingpath, has something in common: every player takes the racquet back with the racquethead higher than his head. And there are important reason this:
1. To take advantage of the potential energy of a high takeback, which accounts for a large fraction of the total racquet head speed through the hitting zone.
2. Racquethead speed generated from the potential energy of a high takeback is highly reproducible (because gravity is the same for each swing). This gives a more consistent shot.

In order to best take advantage of the reproducible conversion of potential energy to gravity-assisted kinetic energy during the swing, a racquet must have a mass distribution that ensures that the racquethead rotates through the hitting zone at the speed that keeps the racquetface perpendicular to the target. The MgR/I formula (and the wall targeting tuning method for optimizing MgR/I) gives a very simple way to ensure that your racquet is set up optimally for this.

Please try out the wall tuning method yourself before you dismiss this.

43. ### stoneageRookie

Joined:
Apr 8, 2010
Messages:
256
Location:
Stockholm, Sweden
Yes a lot of people like it, then why not be satisfied with that? Put up the specs and say "try this, I have no clue why, but it works". Instead you have decided to ice the cake with a lot of quasi physics. You are repeating time after time that it is based on simple laws of physics, but you have never been able to show it, or even tried.

Wrong both from a mechanical and tennis perspective. Gravity acts downwards and is difficult to convert to the forward motion of the racquet when you hold it from the side. And even if you could the contribution would not be that great, 0.5 m drop would add 3 m/s to the swing speed at most. And the high take back is part of a circular swing so when the acceleration starts the position is fairly low
Federer
Djokovic

Another example of the quasi physics I was talking about. When I asked about a proof or background to a similar statement earlier you replied that there was no calculation or measurement but " that you could feel it in you hand". I guess that this is about as well founded.

I am trying to decide whether this statement is outrageous or just plain funny. You need a precision that would make NASA envious: The force on the hand in a normal forehand swing parallel to the ground is about 0.00003% higher in Belgium than in Buenos Aires due to difference in gravity.

Do you take the position of Venus and Mars into account as well?

Last edited: Sep 6, 2012

Joined:
Jan 12, 2012
Messages:
658
Location:
Rotherham, United Kingdom

Do you have a number in mind for your 2hb, or do you tune till you like the feel? Does tuning the 2hb mess up the mgr/i?

As you can probably tell, I'm considering trying a 2hb for the first time.

Last edited: Sep 7, 2012
45. ### TaihtDuhShaatSemi-Pro

Joined:
Sep 29, 2010
Messages:
556
^^^ Use Mg(R-10)/SW for the 2hbh. Should equal around 22.5 +- 0.1.

Joined:
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Messages:
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Location:
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Again, I hope travlerajm can rebuff stoneage, as my racquet is perfectly set up, to 0.01, for mgr/i.

47. ### T-VexRookie

Joined:
Aug 6, 2010
Messages:
141
MgR/I for my racket is 33.2

0.360 kg strung weight (with overgrip and dampener)
31.9 cm balance point
340 kg/cm2 rated swingweight

And btw I have a double-handed backand!

48. ### Circa 1762Rookie

Joined:
Apr 28, 2012
Messages:
103
That comes out to MgR/I = 21.10 and MgR'/I' = 22.74 with the formula I've been using. Would someone else mind confirming which one of these is right?

49. ### travlerajmHall of Fame

Joined:
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Messages:
4,703
Location:
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For someone who is so interested in equations, I'm not sure why you continue to argue against a concept based on Physics 101:
http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

Your arm behaves very much as a physical pendulum. And so does the racquet. And yes, using the assumption that MgR/I = 21.0 to estimate the gravity contribution to the velocity of the hand at the bottom of the swing (from potential energy of the arm), you get about 3m/s. Since a typical high level forehand has forward racquet velocity of about 20m/s, gravity contributes about 15% of the forward racquet velocity of a forehand.

But that is not the point. The point is that, over the first half of the stroke (from top of backswing to the bottom of the swing), if your wrist is relaxed, almost 100% of the racquet's angular acceleration comes from the gravity contribution, which depends on the MgR/I term. So in the absence of any adjustment from the wrist muscles, the angle of the racquetface at the moment you start to apply force to further accelerate the racquet is almost entirely dependent on the MgR/I term.

The point is that tuning the racquet's natural swing frequency to match the natural swing frequency of the arm will significantly improve control. by ensuring that your racquetface naturally stays perpendicular to your target as it passes through the hitting zone.

Also, I point out again that g value can indeed vary by as much as 0.3%, depending on your location on the globe, even for two cities both at sea level. This can make a difference in MgR/I of up to 0.06, enough to throw off your timing if your racquet is perfectly tuned (as I like mine to be). I'm currently building a customized frame identical to my own racquet for a friend I met through TTW who lives in Singapore that tried my frame when he visited in Seattle. The g value in Singapore is only 9.78, so I will need to adjust for that.

Last edited: Sep 7, 2012
50. ### stoneageRookie

Joined:
Apr 8, 2010
Messages:
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Location:
Stockholm, Sweden
I have said several times that my main complain is that MgR/I is the frequency of a single freely swinging pendulum and nothing, I repeat nothing, more. Now you tell me "you see it is a pendulum"!!!!!! Yes, it is the frequency of a pendulum, if you hold the racquet at the but end between your thumb and forefinger MgR/I=21 means that it will swing with 0.73 Hz. But only if the swings are small and you don't move your hand.

I repeatedly ask for some kind proof that you can apply this formula everywhere like you do, and you reply by telling me to take the physics 101! After a number of years of research and teaching at the post doc level, including helping several student to their PhD:s in mechanical engineering, I think I know my physics 101.

You have obviously seen Rod Cross writings about the double pendulum (I recognize some of the statements, even if you write as if they were your own findings). You probaly saw the word "pendulum" and then you found a formula somewhere on the net that also said "pendulum" and used that without understanding what you did.

Rod Cross model includes some radical simplifications, like one that you don't use your wrist, and should be used carefully. But since you re so attached to it lets assume that it is a perfect description. Then behavior of the racquet involves solving eq A10a and A10b in A double pendulum model of tennis strokes. And I can assure you that the result won't be MgR/I.

As to your hilarious statement that you need to take the variation in gravity into account. The air resistance of the racquet has a much greater influence than the gravity, shouldn't you include the air pressure and temperature as well?

There are a lot of helpful people at this forum and if you had chosen so you could have received help from them (me included) and maybe made this into something useful where you know how and when to apply it. Instead you have the attitude that you know it all and can apply it everywhere, even when it obvious that you don't have a clue what you are talking about. Pity.

Since you not are interested in any feedback except praise of your great finding I won't bother you with comments any more.

/Sten
________________________________
Ph.D. (Aerospace Eng.), M.Sc. (Eng. Physics)