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

[newyorkstadium]

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.

[newyorkstadium]

deleted...

[jstout]

Originally Posted by syke

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

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.
1. Find your optimal MgR/I value (sets your optimal swing)
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

[Mig1NC]

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?

[stoneage]

Originally Posted by Mig1NC

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?

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

__________________________________________________ _________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

[Mig1NC]

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

PS: Your avatar is awesome!

PPS: What is J?

[travlerajm]

Originally Posted by stoneage

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

__________________________________________________ _________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

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.

[Circa 1762]

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.

[stoneage]

Originally Posted by travlerajm

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.

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.

So your design criteria are:
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

__________________________________________________ _________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

[travlerajm]

Originally Posted by stoneage

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.

So your design criteria are:
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

__________________________________________________ _________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

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.

[corners]

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

Originally Posted by stoneage

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).

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.

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.

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.

__________________________________________________ _________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.[/quote]

[stoneage]

Originally Posted by travlerajm

The MgR/I formula works for swingweights in the 300 range to 400 range.

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

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.

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.

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.

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.

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.

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.

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

[stoneage]

Originally Posted by corners

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.

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?

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.
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.

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.

[jmnk]

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....

[stoneage]

Originally Posted by jmnk

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....

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?

[travlerajm]

Originally Posted by Circa 1762

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.

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.

[travlerajm]

Originally Posted by Mig1NC

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?

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.

[newyorkstadium]

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.

[DEH]

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.

[travlerajm]

Originally Posted by stoneage

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

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)?