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

[ben123]

Originally Posted by ben123

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

could anyone tell me what i do wrong please ? thx

[madmanfool]

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

[ben123]

Originally Posted by madmanfool

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

ah thx

10char

[travlerajm]

Data in OP has been revised to include specs for 99 players!

[kaiser]

Originally Posted by travlerajm

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

So the pendulum action you are referring to is a rotation of the wrist around the axis going through the forarm, and not around the axis perpendicular to that going through the wrist (i.e. from thumb to little finger)?

Because if the latter, the pendulum action would be in the plane of the swing path which is mostly in the horizontal plane, and more so when the player meets the ball higher in the bounce. This means gravity, and hence g, would only play a small role in the pendulum action and g would need to be replaced by a, the accelleration of the racket arm executed by the player.

If the pendulum action you're referring to is a rotation around the forearm axis, as in the modern 'windscreen-wiper' stroke, it would be perpendicular to the plane of the swing path and therefore mostly in the vertical plane. Then gravity does play a role, but not exclusively. When you rotate your forearm to bring the rackethead up during the take-back, you store energy in the forearm by twisting the radius and ulna bones relative to each other. When you then bring arm foreward during the stroke, the radius and ulna are forced back into their original position, releasing this stored energy into a rotation of the wrist and, hence, the racket. This rotational force therefore also affects the pendulum action around the wrist, as well as gravity, creating an angular accelleration on top of g.

Shouldn't this also be accounted for in your formula? How would this affect your conclusions?

[travlerajm]

OP has been revised and updated with additional data!

Data show that the combination of optimized MgR/I and high swingweight (>350) correlates with superior performance.

[julian]

Originally Posted by kaiser

So the pendulum action you are referring to is a rotation of the wrist around the axis going through the forarm, and not around the axis perpendicular to that going through the wrist (i.e. from thumb to little finger)?

Because if the latter, the pendulum action would be in the plane of the swing path which is mostly in the horizontal plane, and more so when the player meets the ball higher in the bounce. This means gravity, and hence g, would only play a small role in the pendulum action and g would need to be replaced by a, the accelleration of the racket arm executed by the player.

If the pendulum action you're referring to is a rotation around the forearm axis, as in the modern 'windscreen-wiper' stroke, it would be perpendicular to the plane of the swing path and therefore mostly in the vertical plane. Then gravity does play a role, but not exclusively. When you rotate your forearm to bring the rackethead up during the take-back, you store energy in the forearm by twisting the radius and ulna bones relative to each other. When you then bring arm foreward during the stroke, the radius and ulna are forced back into their original position, releasing this stored energy into a rotation of the wrist and, hence, the racket. This rotational force therefore also affects the pendulum action around the wrist, as well as gravity, creating an angular accelleration on top of g.

Shouldn't this also be accounted for in your formula? How would this affect your conclusions?

1.An observation by OP ( call it a 21 formula) can make sense
2.A justification to the best of my knowledge has a lot of weak points
If one wants to exchange an E-mail on this subject my E-mail address below

[travlerajm]

Originally Posted by kaiser

So the pendulum action you are referring to is a rotation of the wrist around the axis going through the forarm, and not around the axis perpendicular to that going through the wrist (i.e. from thumb to little finger)?

Because if the latter, the pendulum action would be in the plane of the swing path which is mostly in the horizontal plane, and more so when the player meets the ball higher in the bounce. This means gravity, and hence g, would only play a small role in the pendulum action and g would need to be replaced by a, the accelleration of the racket arm executed by the player.

If the pendulum action you're referring to is a rotation around the forearm axis, as in the modern 'windscreen-wiper' stroke, it would be perpendicular to the plane of the swing path and therefore mostly in the vertical plane. Then gravity does play a role, but not exclusively. When you rotate your forearm to bring the rackethead up during the take-back, you store energy in the forearm by twisting the radius and ulna bones relative to each other. When you then bring arm foreward during the stroke, the radius and ulna are forced back into their original position, releasing this stored energy into a rotation of the wrist and, hence, the racket. This rotational force therefore also affects the pendulum action around the wrist, as well as gravity, creating an angular accelleration on top of g.

Shouldn't this also be accounted for in your formula? How would this affect your conclusions?

This has nothing to do with windshield wiping.

If you look at the slo-mo vids I posted earlier in this thread of Del Potro and Gonzalez hitting forehands, you can see that the racquethead typically drops from about 7 ft high to about 3 feet high before rising again toward the ball. During the portion of the stroke where the racquethead is dropping those 4 feet, the player does not need to exert much force to accelerate the racquet. Rather, it is gravity plus centripetal acceleration that accelerate the racquet (it matters little that the plane of the swing is not vertical, as long as there is a significant vertical component to the motion). In other words, the motion of the racquet still obeys the physics of a mechanical double pendulum even though the plane of the swing is only partly in the vertical plane.

Only after the racquethead reaches the bottom of the stroke does the player need to apply significant force to keep the racquet moving. This is because the racquet naturally accelerates during the downward part of the stroke (which is mainly gravity powered). But on the upward part of the stroke, the player must apply force to counter the deceleration caused by gravity. I believe that your body naturally senses the inflection point at the bottom of the swing when the motion of the pendulum sweep of your arm switches from acceleration to deceleration, triggering you to begin applying pressure on the handle to keep the racquet moving.

As Corners has mentioned earlier, Rod Cross published an article in 2009 in the American Journal of Physics, showing that the swing of a baseball bat can be modeled as a double pendulum, and that the player must actually apply a reverse-direction couple just before the moment of impact, otherwise the bat pivots too fast from the wrist, causing timing errors. In other words, MgR/I for the baseball bat was too high.

[madmanfool]

Originally Posted by travlerajm

OP has been revised and updated with additional data!

Data show that the combination of optimized MgR/I and high swingweight (>350) correlates with superior performance.

thx for the update

[travlerajm]

I've revised the OP and added the MgR/I distribution for the ladies!

I finally got around to counting strings on string patterns for all the women on Jura's list so that I could convert to strung specs. Then I used 2-segment beam method to approximate swingweights and merged it with Greg Raven's list.

In summary, as I expected, the WTA players cluster at a higher MgR/I value than the men -- shifted up to about 21.1, while the men are at about 20.9.
This was expected because the women are shorter with shorter arms and faster natural swing frequencies.

I haven't posted the chart yet, but I also found that the women with MgR/I within the optimized 20.9-20.3 range and SW > 340 have superior rankings on average. So the women show essentially the same result as the men!

[TennisMaverick]

This exercise is commendable, but irrelevant; the game has changed too much since 2005, and so has the equipment.

[travlerajm]

Originally Posted by TennisMaverick

This exercise is commendable, but irrelevant; the game has changed too much since 2005, and so has the equipment.

A significant portion of the men's specs list is from 2009.

[TennisMaverick]

Originally Posted by travlerajm

A significant portion of the men's specs list is from 2009.

As the exercise is statically based, then the specs from 2009 should be separate, as well as being surface particular.

[travlerajm]

Originally Posted by TennisMaverick

As the exercise is statically based, then the specs from 2009 should be separate, as well as being surface particular.

I initially crunched the datasets separately. The results were virtually identical, so I pooled the results for more statistical robustness.

[NLBwell]

In the OP, Travler only claimed correlation. I'm going to speculate here on possible causations of players with that type setup being better players. Of course, one is a statistical anomaly, which is always possible, but of no value in this conversation.
A direct causation would be players who play with an "optimal" setup will play better - as implied in the title of the thread.
A third possibility is that players with an excellent natural feeling for moving the racket and hitting the ball gravitate toward these racket setups because they feel more efficient and comfortable even if they could play just as well with another setup. At the very top of the tennis game the pros have an ability to sense things unconciously through their innate abilities and repetition. Maybe those with the best sense of tennis in general have the best sense of feeling how the racket moves through the air.

[travlerajm]

I've revised the OP to include Effective Mass vs Ranking for both ATP and WTA players.

In summary, the higher the effective mass of the racquet, the better the ranking. This is true for both men and women.

And for both men and women, there appears to be a big performance drop-off when effective mass drops below 160g.

To calculate the effective mass of the frame, I used:

Effective Mass = M/[1 + M*(b^2)/Ic].
M = Racquet mass.
b = distance from balance point to impact point (assumed to be 12cm from tip) = L - 12 - R.
L = length of racquet
R = distance from butt to balance point
Ic = recoil weight = SW - M*(R - 10)^2

[travlerajm]

OP updated again, with new chart showing that ATP Players near the optimum MgR/I range and effective mass > 160g have superior rankings.
Effective mass of 16g (calculated 12cm from tip) corresponds to around 350 swingweight for a standard length midplus racquet.

[shadowshifter]

How does this tie in with depolarized vs polarized set ups? I recall reading a thread of yours from several years back that talked about that, curious what your take on it is now (I think it's title was how to set up your racket like an ATP pro).

[travlerajm]

With the advances in string technology of the last 5 years, plenty of spin can be found with almost any racquet.

So now what separates the contenders from the rest is whether or not the racquet is heavy enough to counter heavy balls and the balance fine-tuned enough to deliver perfect accuracy on every shot. This thread provides evidence to support this. So this thread is my updated version of "How to set up your racquet like an ATP Pro". Actually, it would be more aptly named, "How to set up your racquet like a Top-10 ATP Pro."

[ben123]

Originally Posted by travlerajm

With the advances in string technology of the last 5 years, plenty of spin can be found with almost any racquet.

So now what separates the contenders from the rest is whether or not the racquet is heavy enough to counter heavy balls and the balance fine-tuned enough to deliver perfect accuracy on every shot. This thread provides evidence to support this. So this thread is my updated version of "How to set up your racquet like an ATP Pro". Actually, it would be more aptly named, "How to set up your racquet like a Top-10 ATP Pro."

yup nice work. its just most ppl cant calculate their sw so too bad ^^