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travlerajm 07-05-2011 09:48 PM

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

..............Fig.1 .............................. Fig. 2. ........................... Fig. 3 .............

............Fig. 4. ...............

In summary, these data show that ATP players with both optimized racquet MgR/I value and high swingweight have significantly superior rankings compared to other players.

The raw data comes from a combined list of 99 Top-200 ATP pros whose racquet specs were posted either on Greg Raven's website, or by Jura in his 2005 Pro Racquet Specs post.
Swingweights for the players on Jura's list were approximated from M, R, and L using Rod Cross's 2-segment beam method.

Fig. 1 compares Performance vs MgR/I value for the 36 players on the list with swingweights in the 350-370 range. Of those 36 players, 25 had MgR/I less than 20.7, 10 were in the 20.7-21.1 range, and 1 was over 21.1. Statistically, the players in the 20.7-21.1 group have significantly superior rankings to those with lower MgR/I values.

Fig. 2 shows that ATP player racquet specs are clustered around the apparent optimal MgR/I range of about 20.9, while WTA player distribution is shifted toward a higher apparent optimum of about 21.1.

Fig. 3 shows that for the 53 ATP players on the list within the 'optimum' 20.7-21.1 MgR/I range, players with higher swingweights have superior rankings -- a very statistically significant result!

Fig. 4 shows that both ATP player and WTA player rankings correlate positively with increasing Effective Mass. For both men and women, Effective Mass of >160g (calculated 12cm from tip) seems to be key to performance. Note that Effective Mass is different than Swingweight, because an extended length racquet might have a high swingweight, but still have little mass in the racquethead. It also shows that players near the optimum MgR/I range benefit most from high effective mass.

Enjoy!

For instructions for tuning your frame to find your personal optimum value for MgR/I, see second post of this thread.

For 2 closely related threads, see:
http://tt.tennis-warehouse.com/showthread.php?t=387620

http://tt.tennis-warehouse.com/showthread.php?t=390065

travlerajm 07-05-2011 09:49 PM

Analysis
 
Reserved for analysis of data:

The MgR/I value gives a measure of the racquet's natural swing frequency as it pivots about the wrist axis on a forehand.

A groundstroke can be simply modeled as a double pendulum, with the upper pendulum swinging from the shoulder, and the lower pendulum swinging from the wrist. The speed of the upper pendulum is mostly related to the length of the player's arm, while the speed of the lower pendulum is largely a function of the racquet's weight's distribution. The angular acceleration of a pendulum is proportional to MgR/I, where M is the mass of the pendulum (here in kg), g is the acceleration of gravity (here assumed 980.5 cm/s^2), R is the distance from the pivot point to the center of mass (here in cm), and I is the moment of inertia about the pivot point (here equal to Swingweight + 20MR - 100M). Thus, a racquet's MgR/I value gives a measure of its natural swing frequency.

If MgR/I is perfectly tuned to the optimum value, the racquetface angle will naturally stay constant through the hitting zone, greatly improving accuracy. If MgR/I is too low, the racquethead will lag behind the hand unless the player compensates by applying a force from the wrist, making control more difficult and the forehand stroke more sensitive to timing errors. And if the MgR/I value is too high, the racquethead will naturally move through the hitting zone faster than the hand, also making the stroke difficult to control.

The optimum MgR/I value is not the same for every player. It depends on the player's height because players with longer arms have naturally slower swings. For players about 6'2" in height, I believe that the optimum MgR/I value is about 20.8 (this is supported by the data above). For players about 5'11" tall, I believe the optimum MgR/I value is about 21.0 (this is further supported by my own personal experimentation, as I stand 5'11" tall). And for players about 5'8" tall, I believe the optimum MgR/I value is about 21.2 (this is supported by my analysis of WTA specs, which I plan to post soon).

The optimum MgR/I value is also likely dependent on the player's style of stroke or grip . For example, for players with full western grips, the importance of optimizing MgR/I may be lessened, or the stroke may be optimized with a lower MgR/I value than for an eastern grip. But for players with eastern or weak semi-western grips, I believe optimizing MgR/I is more crucial. Also, choking up the the handle will increase the effective MgR/I value.

It's my belief that the optimal MR^2 zone of ~385 arises due to circumstance, because those pros that have both high swingweight (>350) and optimized MgR/I value (~21.0) tend to have racquets with MR^2 of about 385.

There are many pros with high swingweight but suboptimal MgR/I value. And there are many pros with optimized MgR/I value but low (suboptimal) swingweight. In both cases, the MR^2 value tends be less than 380.

My opinion is that it is well worth it to tune your MgR/I value to your personal optimum for your body and your swing.

Steps for Tuning MgR/I to find your personal optimum for your swing, for maximum control.


Step 1: Get accurate measurements of racquet mass M (kg), balance R (cm), and swingweight about axis through butt end of racquet (I).

Step 2 is to calculate how much weight should be placed on the handle to move the MgR/I value to ~21.0 (to get it close).

Step 3 is to make the modification.

Step 4 is to remeasure the specs and verify that you are close to 21.0.

Caution: You're not done yet, as the most important step still remains!

Step 5: Tuning the racquet on the court:

I recommend that you grab some extra lead tape and find a wall or racquetball court. You cannot tune the MgR/I value by hitting balls that you drop -- you need the balls to be coming at you with decent velocity in order to tune the angular velocity of your stroke, so a wall is perfect for that.

The key to tuning your forehand is to unlearn your developed habit of compensating for racquet misalignment at impact by applying force with the wrist. You need to learn how to swing the racquet fluidly with a completely relaxed wrist.

A good analogy is when you go to the optometrist for the first time in your life to get glasses for near-sightedness. All of your life, you've been squinting in order to see the world. But when the optometrist is measuring the proper corrective power your eyes, it's important that you stop squinting for the first time in your life and let your eyes relax. Otherwise, you'll still need to squint even after you get your glasses or contacts.

So the same applies to tuning the MgR/I value of your racquet. You can't tell whether your MgR/I value is tuned properly if your wrist is not fully relaxed.

If your MgR/I value is slightly lower than your optimum, when you swing with a completely relaxed wrist, the racquethead will lag behind the hand at the moment of impact, causing you to naturally push your shots wide right (assuming you are righthanded). You need to resist the temptation to compensate by applying force from the wrist. It's kind of like when golfer has a slice swing and is less accurate because he has to always compensate for it.

Conversely, if the MgR/I value is slightly above your optimum, then when you swing with a completely relaxed wrist, the racquethead will get ahead of the hand, and you will tend to pull your shots to the left. The temptation here might be to convert the extra angular velocity into more topspin, but again you need to resist.

When your MgR/I value is perfectly tuned, you can simply fling your arm at the ball with a relaxed wrist, and the racquet will naturally stay perpendicular to your target all of the way through the hitting zone. This means that slight timing errors do not get punished. And you will notice that your targeting accuracy when hitting against the wall improves dramatically.

When my MgR/I value is tuned, I can hit a ball within a 1x1 foot square target almost every time. But if my racquet is slightly off, I can't hit as accurately. Compensating for the mistuned angular velocity might allow me to consistently hit the ball within a 3x3-ft square target, but why settle for that? That difference in accuracy is often the difference between winning a match and losing.

If MgR/I is too low, you can add a little more lead to the top of the handle. If it's too high, you can either remove some lead from that spot or add a dab to the tip. Don't settle for almost! Keep adjusting until you get that "in the zone" feeling.

When you are tuning for the first time, you might find it helpful to keep going beyond where it feels good until it's obvious that you've gone too far. You need to learn the difference in feel between MgR/I too low and too high.

Following all of these steps takes a lot of care and patience, but the end result is worth it.

Ducker 07-05-2011 11:08 PM

This is awesome thanks for the hard work.

Can you do me a huge favor and tell me what the rating would come to for a Stock strung Donnay 99 gold would be? Also what would I have to add to the racket to get it to 21.0, id like to test the feel of it.

Id do it myself i see the math is pretty simple i just dont know how to find the balance number in cm....

kaiser 07-06-2011 04:51 AM

Quote:

Originally Posted by travlerajm (Post 5817042)
Reserved for analysis of data:

The MgR/I value gives a measure of the racquet's natural swing frequency as it pivots about the wrist axis on a forehand.

A groundstroke can be simply modeled as a double pendulum, with the upper pendulum swinging from the shoulder, and the lower pendulum swinging from the wrist. The speed of the upper pendulum is mostly related to the length of the player's arm, while the speed of the lower pendulum is largely a function of the racquet's weight's distribution. The frequency of a pendulum is proportional to sqrt(MgR/I), where M is the mass of the pendulum, g is the acceleration of gravity, R is the distance from the pivot point to the center of mass, and I is the moment of inertia about the pivot point. Thus, a racquet's MgR/I value gives a measure of it's natural swing frequency. It is not necessary to take the square root, because only relative values are needed.

Trav, there is something about yopur MgR/I formula I've been wondering about for some time now. What pendulum action around the wrist are you referring to? When you look at slomo movies of e.g. the Federer forehand, you can clearly see that most of the accelleration towards the ball occurs in the horizontal plane (for an example, see http://www.youtube.com/watch?v=xNPaZ...eature=related). So how does g, the accelleration due to gravity, which only occurs in the vertical plane, affect the pendulum around the wrist? Wouldn't the horizontal accelleration component of the racket arm, as generated by the player, be more important here?

Also, when you look at the pendulum action of the wrist, the wrist remains usually completely laid back up untill the point of contact with the ball. That is, the pendulum action around the wrist joint typically occurs after the ball is hit, during follow-through. Then how can this pendulum motion so crucially affect the stroke and, indeed, a player's ranking if it takes place after ball contact?

I'm looking forward to your explantion.

Thanks,
kaiser

corners 07-06-2011 06:00 AM

Trav,

The swingweight about the wrist pivot will be different depending on where the player grips the handle. If one chokes down to the bottom of the grip, the swingweight and MgR/I will be higher; if one chokes up, these values will be lower.

Federer and Nadal, for example, hold their racquets at the bottom of the handle (little finger just barely on the grip) on groundstrokes, making their MgR/I numbers lower than they would appear.

I think it would be helpful to establish a reference handle position for comparing MgR/I numbers, i.e. little finger just above the taper of the buttcap.

It would also be helpful to have a conversion for other grip positions - up or down the handle.

nomie 07-06-2011 06:33 AM

Quote:

Originally Posted by kaiser (Post 5817445)
Trav, there is something about yopur MgR/I formula I've been wondering about for some time now. What pendulum action around the wrist are you referring to? When you look at slomo movies of e.g. the Federer forehand, you can clearly see that most of the accelleration towards the ball occurs in the horizontal plane (for an example, see http://www.youtube.com/watch?v=xNPaZ...eature=related). So how does g, the accelleration due to gravity, which only occurs in the vertical plane, affect the pendulum around the wrist? Wouldn't the horizontal accelleration component of the racket arm, as generated by the player, be more important here?

Also, when you look at the pendulum action of the wrist, the wrist remains usually completely laid back up untill the point of contact with the ball. That is, the pendulum action around the wrist joint typically occurs after the ball is hit, during follow-through. Then how can this pendulum motion so crucially affect the stroke and, indeed, a player's ranking if it takes place after ball contact?

I'm looking forward to your explantion.

Thanks,
kaiser

Good questions, although he did state that its the natural pendulum action, hence why g is used.

My question is: The sample for the data seems pretty small. Only data from 2005 onward was used (Or was it just for 2005?). Since then the top five players has pretty much consisted of the same small group of people. So there is a big chance that the dip in the graph for the top five is simple coincidence.

ben123 07-06-2011 07:31 AM

uhm i dont rly get how to use this formula

if we look for example at a stock apdgt

M= 0,32
g=980
R=33
I=331

so 0,32x980x33=10348,8/331
=31?
am i doing smth wrong or is that correct? if thats correct i dont come close near 20 with any racket xD

so what am i doing wrong

sry my native language is not english

travlerajm 07-06-2011 07:39 AM

Quote:

Originally Posted by nomie (Post 5817600)
Good questions, although he did state that its the natural pendulum action, hence why g is used.

My question is: The sample for the data seems pretty small. Only data from 2005 onward was used (Or was it just for 2005?). Since then the top five players has pretty much consisted of the same small group of people. So there is a big chance that the dip in the graph for the top five is simple coincidence.

I agree that the sample size in this thread is indeed small, but If you look at my MR^2 data thread, where the sample size is large enough to be more statistically robust, there are 8 players within the statistically significant apparent optimal zone of MR^2 = 380-390.

I'll soon post another plot on that thread for MR values, showing that there is a statistically significant apparent optimum zone for MR > 11.75, and that MR > 12.0 appears to be even better.

Only four of the 8 players with 'optimum' MR^2 values have MR values over 11.75: Agassi, Robredo, Gaudio, and Grosjean. All of these 4 were top-5 players under 6' tall with unimpressive serves, ho-hum speed, but exceptionally accurate and reliable groundstrokes that made them top-5 players, so I don't think it is coincidence. Of these 4, only 1 of them has MR value over 12.0: Gaudio. Could it be coincidence that he is the only player on the list from Federer's generation to win a Grand Slam title?

Also, all 6 top-20 players in 'optimum' MR^2 zone are under 6 feet with strength as described for the 4 players mentioned above. Coincidence? One of the other 2 players is Ferrer, a top-5 player who led the tour in % return games won (during the Federer-Nadal era) multiple years! Coincidence?

kaiser 07-06-2011 09:05 AM

Quote:

Originally Posted by nomie (Post 5817600)
Good questions, although he did state that its the natural pendulum action, hence why g is used.

Ok, so why is the natural pendulum action, which is driven by gravity and therefore only in the vertical plane, relevant for the pendulum around the wrist which is mostly in the horizontal plane (in the forehand of the pros) and hence largely immune to gravity? This is something I'd like to understand, so what's up Trav?

blackfrido 07-06-2011 09:15 AM

no offense on my words at all;
Do you guys play tennis? just curious about it...........

travlerajm 07-06-2011 09:23 AM

Quote:

Originally Posted by kaiser (Post 5817970)
Ok, so why is the natural pendulum action, which is driven by gravity and therefore only in the vertical plane, relevant for the pendulum around the wrist which is mostly in the horizontal plane (in the forehand of the pros) and hence largely immune to gravity? This is something I'd like to understand, so what's up Trav?

Almost every single pro tennis player brings the racquethead above his head on the backswing. As gravity drops the racquethead from that point, the wrist is free to pivot. How fast the racquethead travels as the racquet travels through a high-to-low-to-high pendulum sweep is largely dependent on the relative weight distributions of the arm and racquet.

The pendulum action is easy to see if you watch these guys in slo-mo, who have pretty good forehands:
http://www.youtube.com/watch?v=UGodD...eature=related
http://www.youtube.com/watch?v=lFibX...eature=related

julian 07-06-2011 09:44 AM

Articles by Rod Cross
 
Quote:

Originally Posted by kaiser (Post 5817445)
Trav, there is something about yopur MgR/I formula I've been wondering about for some time now. What pendulum action around the wrist are you referring to? When you look at slomo movies of e.g. the Federer forehand, you can clearly see that most of the accelleration towards the ball occurs in the horizontal plane (for an example, see http://www.youtube.com/watch?v=xNPaZ...eature=related). So how does g, the accelleration due to gravity, which only occurs in the vertical plane, affect the pendulum around the wrist? Wouldn't the horizontal accelleration component of the racket arm, as generated by the player, be more important here?

Also, when you look at the pendulum action of the wrist, the wrist remains usually completely laid back up untill the point of contact with the ball. That is, the pendulum action around the wrist joint typically occurs after the ball is hit, during follow-through. Then how can this pendulum motion so crucially affect the stroke and, indeed, a player's ranking if it takes place after ball contact?

I'm looking forward to your explantion.

Thanks,
kaiser

Kaiser,Travlerajm

Do u know about two recent articles by Rod Cross on related subjects?

julian 07-06-2011 09:52 AM

Your question
 
Quote:

Originally Posted by blackfrido (Post 5817992)
no offense on my words at all;
Do you guys play tennis? just curious about it...........

There is a tennis coach reading these posts

travlerajm 07-06-2011 09:56 AM

Quote:

Originally Posted by julian (Post 5818061)
Kaiser,Travlerajm

Do u know about two recent articles by Rod Cross on related subjects?

Yes, of course.

julian 07-06-2011 10:25 AM

Vcore and Rod Cross
 
Quote:

Originally Posted by travlerajm (Post 5818089)
Yes, of course. But I didn't find Cross's articles on the pendulum subject that useful. I did appreciate his article on serve speed though.

travlerajm,
couple of points:
1.There are 2 articles by Cross about pendelums
2.The second is in American Journal of Physics
I do NOT know whether you saw both

3.An interesting racket to talk is Vcore 100 S by Yonex.
it has a low swing weight - I think 307
It allows for higher speeds of a head of a racket

4.Some questions touched by kaiser ABOVE are addressed in an article of Cross in the American Journal of Physics

blackfrido 07-06-2011 10:27 AM

Quote:

Originally Posted by julian (Post 5818080)
There is a tennis coach reading these posts

Julian,
I'm glad to know that....for a moment I thought this post was not about tennis rather math and physics.
do you think pro level players know what these guys are talking about?

shadowshifter 07-06-2011 10:34 AM

Quote:

Originally Posted by blackfrido (Post 5818165)
Julian,
I'm glad to know that....for a moment I thought this post was not about tennis rather math and physics.
do you think pro level players know what these guys are talking about?

who cares if pro level players know what these guys are talking about? if you can apply physics and math to model tennis and it works, then it works ...

julian 07-06-2011 10:35 AM

Tennis pros
 
Quote:

Originally Posted by blackfrido (Post 5818165)
Julian,
I'm glad to know that....for a moment I thought this post was not about tennis rather math and physics.
do you think pro level players know what these guys are talking about?

1.Tennis pros do talk to tennis manufacturers.
Some tennis manufacturers know what we are talking about here
2.Some pros are very reluctant to change a racket-
You may talk about Federer and Djokovic and Wozniacki
as representing 3 different cases

shadowshifter 07-06-2011 10:44 AM

Quote:

Originally Posted by julian (Post 5818161)
travlerajm,
couple of points:
1.There are 2 articles by Cross about pendelums
2.The second is in American Journal of Physics
I do NOT know whether you saw both

3.An interesting racket to talk is Vcore 100 S by Yonex.
it has a low swing weight - I think 307
It allows for higher speeds of a head of a racket

4.Some questions touched by kaiser ABOVE are addressed in an article of Cross in the American Journal of Physics

that's cool, thanks for the heads up on the american journal of physics article :)

blackfrido 07-06-2011 11:04 AM

Quote:

Originally Posted by shadowshifter (Post 5818182)
who cares if pro level players know what these guys are talking about? if you can apply physics and math to model tennis and it works, then it works ...

I care buddy, that's what I'm asking.......


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