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

[travlerajm]

Originally Posted by kaiser

So what about big vs small hands, wide vs narrow wrists? Aren't your theory and equations suggesting far more accuracy and preditive power than they really have?

I have no basis to compare hand size for the players, so I can't comment on that. But experimenting by adding mass to my wrist is something I have tested carefully.

Anyway, the point of the MgR/I formula is not predictive power for other players. Rather, the point is that awareness of the MgR/I value allows you to predict how adjustments to your racquet mass distribution will affect the timing of your swing, and that this formula is an effective tool for tuning your racquet to optimize your performance.

Also, once you find your personal optimum MgR/I value, you can use it to predict what specs will work for you when you go up or down in swingweight. In other words, it allows you to decouple swing dynamics from impact dynamics when you experiment with different weight distributions.

[kaiser]

So you are saying that because of the many possible differences in body proportions between different players, the optimal configuration of a racket can vary considerably? That would make sense to me.

This leaves one crucial component in your theory I never understood. In your formula there is only one acceleration term, g, which in your posts you have related to a high take-back. Does this mean that the primary force acting on the racket in your model is gravity? In other words, that in your model the tennis stroke is treated as a dual pendulum consisting of racket and arm swung through an arc from the highest takeback position by the force of gravity alone?

Does your model account for the acceleration of the racket and arm due to the hip and shoulder turn? Why is there no term in your formula which expresses this acceleration?

[ART ART]

@travlerajm:

and the MR^2= 392 ? it's far from 385

Maybe we need real specs like those from Novak and Almagro, in order to conclude something, but all in all it's allways a personal preference for each player, not some right or wrong numbers...

But, I apreciate a lot your efforts and theory, and there's allways some fire on it...

Cheers

[floydcouncil]

Originally Posted by ART ART

@travlerajm:

and the MR^2= 392 ? it's far from 385

Maybe we need real specs like those from Novak and Almagro, in order to conclude something, but all in all it's allways a personal preference for each player, not some right or wrong numbers...

But, I apreciate a lot your efforts and theory, and there's allways some fire on it...

Cheers

We can ALL conclude that the point is MOOT.

[travlerajm]

Originally Posted by kaiser

So you are saying that because of the many possible differences in body proportions between different players, the optimal configuration of a racket can vary considerably? That would make sense to me.

This leaves one crucial component in your theory I never understood. In your formula there is only one acceleration term, g, which in your posts you have related to a high take-back. Does this mean that the primary force acting on the racket in your model is gravity? In other words, that in your model the tennis stroke is treated as a dual pendulum consisting of racket and arm swung through an arc from the highest takeback position by the force of gravity alone?

Does your model account for the acceleration of the racket and arm due to the hip and shoulder turn? Why is there no term in your formula which expresses this acceleration?

When I first started trying to relate a tennis swing to physical parameters, I made some of the same misassumptions that most people make. I wrongly assumed that the swingweight is what determines how much effort goes into getting the racquet to "come around."

I eventually found that a much more accurate way to model a swing is to divide it into two distinct parts. The first part is the mostly gravity-powered part of the swing where the racquet goes from the top of the backswing to the bottom of the swing. The second part is the portion of the swing where the player adds force behind the racquet handle to accelerate the racquet forward and upward against gravity and through the hitting zone.

During the first part of the swing, the face of a the racquet naturally rotates toward the ball. If the racquet has a "tuned" MgR/I value, then no added torque from the wrist muscles is needed to ensure that the racquet is facing the target at the end of the this part of the swing. Since gravity is providing nearly all of the acceleration, the final angle of the racquetface at the end of this gravity-powered first portion of the swing is nearly entirely determined by the MgR/I value (assuming a relaxed wrist is used).

I believe that our brains sense the bottom of the swing as the cue to "switch on" the applied force that starts the acceleration through the hitting zone. However, without a tuned MgR/I value, you cannot use a relaxed wrist, and your arm will tend to wear out over the course of a match from exerting the wrist muscles on every shot.

Once the second part of the swing begins, most of the acceleration is applied by the player. As long as the racquet starts the hitting zone with the right racquetface angle, the player can easily vary the applied force to achieve different results on the ball. But if MgR/I is not tuned, then the second part of the swing will begin with the racquetface not quite at the right orientation, leading other adjustment forces from the wrist to be needed during the second part of the swing as well.

[kaiser]

So the MgR/I theory only applies during the backswing phase while the racket drops from high to low. Can you illustrate graphically what you mean when you say "the final angle of the racquetface at the end of this gravity-powered first portion of the swing is nearly entirely determined by the MgR/I value" and "if MgR/I is not tuned, then the second part of the swing will begin with the racquetface not quite at the right orientation"? How does the racket face orientation change during this phase?

I always understood that you were referring to the racketface orientation at the end of the stroke when it strikes the ball. As I understand it (see for a more authoritative description this article by Rod Cross: http://www.racquetsportsindustry.com...ing_and_m.html), the orientation of the racket face prior to impact changes as follows: During the second phase of the swing, as you defined it, the racketface first lags behind the wrist as the arm moves forward through the force applied by the player. Then, as the arm slows down at the end of the stroke, the racketface quickly catches up and accelerates forward through an arc around the wrist (dual pendulum), ideally striking the ball at the exact moment when the racketface is perpendicular to the intended hitting direction. Hence, slight variations in the timing of these processes during the second phase of the stroke will lead spraying of the ball from left to right. That's why I always thought you were referring to this second phase of the stroke when you were discussing MgI/R.

How does the timing of the first, backswing phase of the stroke affect the orientation of the racket face at impact? And doesn't the timing of the second, player-powered, phase of the stroke have a much more direct effect on the orientation of the racketface at impact and hence the accuracy of the shot?

[jstout]

Originally Posted by ART ART

@travlerajm:

check this post with Novak racket specs:
http://tt.tennis-warehouse.com/showthread.php?t=441393

Specs strung+overgrip+dampener, are:
Mass: 360gr
Balance: 33cm
SW:371

So the MgR/I = 20,35 and MR^2= 392

Far away from the ideal MgR/I = 21,0 and MR^2= 385

Any comments about it ?

A different way to look at the MgR/I is by a pendulum period.

M = kg, g = cm/s^2, R = cm, I = kg*cm^2
MgR/I is (kg * cm/s^2 * cm) / kg*cm^2 = 1/s^2 so Period = 2 * PI * SQRT(I/MgR) which will be in seconds

Travlerajm's optimal 21.0 is ~1.371s and Djokovic's 20.237 is ~1.397s. The difference between values are generally in hundredths of a second. I've tried to collect as many measured pro racquet specs as possible and the range tends to be 19-22 (1.44s-1.34s) with the average being 20.5 (1.38s)

MR^2 is a byproduct and ranges can be very extreme: 315-450 with the average being 374. Djokovic's 392 is actually close to 385 and not far away in that regard.

I've used travlerajm's equations myself and in my opinion adjusting Swingweight, Effective Mass, and MgR/I is a good way to tweak a racquet to what feels best to you.

[travlerajm]

Originally Posted by kaiser

So the MgR/I theory only applies during the backswing phase while the racket drops from high to low. Can you illustrate graphically what you mean when you say "the final angle of the racquetface at the end of this gravity-powered first portion of the swing is nearly entirely determined by the MgR/I value" and "if MgR/I is not tuned, then the second part of the swing will begin with the racquetface not quite at the right orientation"? How does the racket face orientation change during this phase?

I always understood that you were referring to the racketface orientation at the end of the stroke when it strikes the ball. As I understand it (see for a more authoritative description this article by Rod Cross: http://www.racquetsportsindustry.com...ing_and_m.html), the orientation of the racket face prior to impact changes as follows: During the second phase of the swing, as you defined it, the racketface first lags behind the wrist as the arm moves forward through the force applied by the player. Then, as the arm slows down at the end of the stroke, the racketface quickly catches up and accelerates forward through an arc around the wrist (dual pendulum), ideally striking the ball at the exact moment when the racketface is perpendicular to the intended hitting direction. Hence, slight variations in the timing of these processes during the second phase of the stroke will lead spraying of the ball from left to right. That's why I always thought you were referring to this second phase of the stroke when you were discussing MgI/R.

How does the timing of the first, backswing phase of the stroke affect the orientation of the racket face at impact? And doesn't the timing of the second, player-powered, phase of the stroke have a much more direct effect on the orientation of the racketface at impact and hence the accuracy of the shot?

I think Cross's statement is interesting:
"Having extra weight in the handle therefore allows a top player to control what he is doing. It slows down the forward motion of the handle and the backward motion of the head just enough so that he can swing the head around with a reasonable effort rather than an excessive amount of wrist torque."
The extra weight in the handle that Cross refers to (that permits swinging without wrist exertion) is the weight required to bring MgR/I up to a player's personal optimum value (most lightweight stock racquets lack enough handle mass for MgR/I to be optimized).

However, according to Cross's explanation, adding weight to the butt of the racquet would accomplish the task. But according to my findings, that is not true. The handle weighting must be higher in the handle to have the desired effect (i.e., increasing MgR/I). Thus Cross's explanation can be easily disproved (with a simple on-court experiment).

[travlerajm]

Originally Posted by ART ART

@travlerajm:

and the MR^2= 392 ? it's far from 385

Maybe we need real specs like those from Novak and Almagro, in order to conclude something, but all in all it's allways a personal preference for each player, not some right or wrong numbers...

But, I apreciate a lot your efforts and theory, and there's allways some fire on it...

Cheers

ART ART,
As jstout pointed out, 392 is very close the the statistical apparent optimum. Also, notice that the sample size is lower at the high end of the player list than at the low end. And you may have noticed that my racquets are at 390, which I find to work best for me after years of experimentation.

[corners]

Originally Posted by jstout

I've used travlerajm's equations myself and in my opinion adjusting Swingweight, Effective Mass, and MgR/I is a good way to tweak a racquet to what feels best to you.

I've also found it useful, and matching MgR/I of two sticks with quite different swingweight and static weight seems to give the same "swing feel" to both sticks, even though they are both very different from the conventional racquet-tech point of view.

[kaiser]

Originally Posted by travlerajm

I think Cross's statement is interesting:
"Having extra weight in the handle therefore allows a top player to control what he is doing. It slows down the forward motion of the handle and the backward motion of the head just enough so that he can swing the head around with a reasonable effort rather than an excessive amount of wrist torque."
The extra weight in the handle that Cross refers to (that permits swinging without wrist exertion) is the weight required to bring MgR/I up to a player's personal optimum value (most lightweight stock racquets lack enough handle mass for MgR/I to be optimized).

However, according to Cross's explanation, adding weight to the butt of the racquet would accomplish the task. But according to my findings, that is not true. The handle weighting must be higher in the handle to have the desired effect (i.e., increasing MgR/I). Thus Cross's explanation can be easily disproved (with a simple on-court experiment).

Thus? You just stated that MgI/R is only valid for the first, backswing phase of the tennis stroke (the drop from high to low driven by gravity). Cross is talking about the second phase of the stroke, so how can your MgI/R theory disprove that?

[travlerajm]

Originally Posted by kaiser

Thus? You just stated that MgI/R is only valid for the first, backswing phase of the tennis stroke (the drop from high to low driven by gravity). Cross is talking about the second phase of the stroke, so how can your MgI/R theory disprove that?

The first phase of the stroke is the important part for control, because it determines the racquetface angle and the racquetface angular velocity at the start of the hitting zone. Thus what happens in the first part of the stroke determines the forces that the player needs to apply in the second part of the stroke.

My point is that:
A) Cross has made the same observation that I have -- that adding the right amount of mass to the handle can improve control by allowing the player to relax the wrist through the hitting zone.
B) Cross explains the phenomenon with his force balance model, while I explain it with the MgR/I pendulum model.
C) It is easy to determine which model is more correct, because the models predict two completely different results:

Both models predict that adding mass to the top of the handle can enable a relaxed wrist through the hitting zone. But Cross's model predicts that adding mass to the butt of the racquet will work even more efficiently than adding to the top of the handle, while the MgR/I pendulum model predicts that adding mass to the butt of the racquet will have almost negligible effect (for a forehand).

Thus all you need to do to prove which model holds up (and which model fails) is do an experiment adding mass to different parts of the handle and then attempt to hit a moving ball toward a target with a relaxed wrist, see how targeting accuracy is affected, and find the amount of mass needed to maximize control. I have done this experiment hundreds of times. In fact, I do it every time I set up a new racquet or change my setup to ensure that my balance is optimized.

[kaiser]

Originally Posted by travlerajm

The first phase of the stroke is the important part for control, because it determines the racquetface angle and the racquetface angular velocity at the start of the hitting zone. Thus what happens in the first part of the stroke determines the forces that the player needs to apply in the second part of the stroke.

Now this is not clear to me at all, and in my understanding Cross is implying exactly the opposite. Do you have any objective proof for this statement (i.e. beyond your own subjective experience)? Or at least can you illustrate it with a diagram, figure, or something?

[Readers]

How do you calculate I?

[Readers]

Originally Posted by madmanfool

I* = SW + 20MR - 100M or something like that. You get 20,3

Should I just use this? The poster doesn't sound too confident.

[JohnB]

Originally Posted by Readers

Should I just use this? The poster doesn't sound too confident.

That's the one.

[newyorkstadium]

https://docs.google.com/spreadsheet/...1b04ydWc#gid=0

Here's a spreadsheet on mgr/i

[Readers]

Originally Posted by newyorkstadium

https://docs.google.com/spreadsheet/...1b04ydWc#gid=0

Here's a spreadsheet on mgr/i

Thanks, seems that one is correct.

Seems both of my heavily customized gold 99 and stock Blue 99 falls into the ideal range already. Maybe it's a sign that I need to stop change/tweaking and work more on techs.

Still I need a higher SW on the blue. (I am not even going to consider the "ideal" SW in this thread, no way I can swing it).

[mgaia57]

@travlerajm
Hey men, intresting thread here. I was thinking about adding weight in my raquet and didn't know where to start and this pretty much put some light into the subject for me
If it is asking too much, could please make the math for me on my raquet and height? I use the new Head Prestige Pro and I am 177 cm high. Don't know if this is useful but I use Babolat RPM Blast 16 @ 52.5
Thanks!

[LeeD]

Balance.
Sword fighting and tennis racket swinging are similar any many respects.
Several basic strokes, several less used alternative strokes, and as many reposts and replies....
What is the ideal balance for a sword, or a sabre, epee', foil?
There is none! It's based on strength of handle to hilt to blade, since most cutting weapons are made of solid steel of some kind. Balance is determined by usage. It's abliity to not break, strike hard, defend against hard strikes.
But tennis rackets are made of composites, and as such, can have enough strength to make balance a completely different factor. Tennis racket balance is solely to aid the player, not for fear of breakage.
Nobody knows what balance is ideal for the PLAYER. Baseball bats are head heavy, hockey sticks slightly head heavy, golf clubs definetely head heavy, while tennis rackets are mostly head light in heavy weight rackets, and head heavy in lightweight rackets.
Maybe SW has everything to do with it, or at least more to do with it.