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

[newyorkstadium]

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.

[Circa 1762]

Originally Posted by travlerajm

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.

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.

[newyorkstadium]

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.

[jmnk]

Originally Posted by newyorkstadium

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.

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'.

[newyorkstadium]

To qoute travlerajm "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 indicates there is an ideal number.

What does make a good racket?

[Circa 1762]

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.

[Vlad_C]

Here’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 head–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

Here’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
That’s pretty close to travlerajm’s ideal numbers.
I really don’t think this is just a coincidence. Physics don’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.

[travlerajm]

Originally Posted by Circa 1762

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.

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

[travlerajm]

Originally Posted by newyorkstadium

1) Does muscle mass affect the pendulum?

Not that much - other factors such as arm length are more significant.

Originally Posted by newyorkstadium

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?

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.

Originally Posted by newyorkstadium

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

There is no rule about where to add lead. Adding lead at about 9" from the butt will provide maximum increase in MgR/I for the amount of lead added, but it will also tend to stiffen the frame. The top of the handle is simply a good place to add lead to increase MgR/I without affecting the feel of the impact as much as adding higher. Adding lower works too, but more is needed. If you plan to optimize for both forehand and backhand simultaneously, then you will need to add a specific amount to the handle at a specific location to satisfy both constraints.

Originally Posted by newyorkstadium

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.

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).

Originally Posted by newyorkstadium

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.

[/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.

[stoneage]

Originally Posted by 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.

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.

[yemenmocha]

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

[travlerajm]

Originally Posted by stoneage

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.

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.

[stoneage]

Originally Posted by travlerajm

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.

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.

I think perhaps you are underappreciating the importance of gravity to a tennis stroke....
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.

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

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.

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.

Originally Posted by travlerajm

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.

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?

[newyorkstadium]

Originally Posted by travlerajm

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).

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.

[TaihtDuhShaat]

^^^ Use Mg(R-10)/SW for the 2hbh. Should equal around 22.5 +- 0.1.

[newyorkstadium]

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

[T-Vex]

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!

[Circa 1762]

Originally Posted by T-Vex

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!

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?

[travlerajm]

Originally Posted by stoneage

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?

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.

[stoneage]

Originally Posted by travlerajm

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.

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)