Combining weight, balance and swingweight

[JohnB]

Give me a couple of hours

[DEH]

Thanks for posting all the good info. Here is what I got. I have tune my daughter's racquet (she is 15) for a long time using Travlerajm's method and it seem to work very well. I ended up with 324g with a balance of 32.7 and swingweight of 310. She was using a windsheild style forehand and it seemed that the shots where very spinny but not a lot of power. I tried all kinds of strings and tensions and I could not get any more power out of it. So we changed here swinging style to a Djokovic style swing which took about a month to do. Now that racquet will not work at all. The balls fly all over the place. No control at all. Tried more strings and no luck. So I tried another racquet. It was an nTour Wilson and it has some weird specs so it could be fake I don't know. Well she started hit a little better. So I just started adding lead to the top of the racquet and it got better and better and better. I added 18 grams at 12. So now her shots are controlled with a lot of spin and power. The specs are 314g with a balance of 34 and 337 swingweight. Not really close to the other specs. So I was just trying to figure out what is so different between the two styles of hitting and the curve on the racquet map. Here is a link for some WTA specs.
http://www.hdtennis.com/grs/pro_racq...ance-open.html
Look at Sloane Stevens racquet. Thanks again.

[JohnB]

What puzzles me is that the lighter Travlerajm racket has virtually the same MgR/I and the same shape of the curve. But if you add weight at the center of a racket, the shape of the curve also remains the same, but MgR/I increases.

[JohnB]

Originally Posted by DEH

Thanks for posting all the good info. Here is what I got. I have tune my daughter's racquet (she is 15) for a long time using Travlerajm's method and it seem to work very well. I ended up with 324g with a balance of 32.7 and swingweight of 310. She was using a windsheild style forehand and it seemed that the shots where very spinny but not a lot of power. I tried all kinds of strings and tensions and I could not get any more power out of it. So we changed here swinging style to a Djokovic style swing which took about a month to do. Now that racquet will not work at all. The balls fly all over the place. No control at all. Tried more strings and no luck. So I tried another racquet. It was an nTour Wilson and it has some weird specs so it could be fake I don't know. Well she started hit a little better. So I just started adding lead to the top of the racquet and it got better and better and better. I added 18 grams at 12. So now her shots are controlled with a lot of spin and power. The specs are 314g with a balance of 34 and 337 swingweight. Not really close to the other specs. So I was just trying to figure out what is so different between the two styles of hitting and the curve on the racquet map. Here is a link for some WTA specs.
http://www.hdtennis.com/grs/pro_racq...ance-open.html
Look at Sloane Stevens racquet. Thanks again.

I think that the relatively low static weight in combination with the relatively high sw gives a longer dwelltime, a whippier feel and thus more spin.

My guess is that with her old racket the rackethead was feeling light to her in relation to the static mass and balance. Resulting in high rackethead speed and thus easier spin, but less plow. Djokovic drives thru the ball flatter which would be harder to do when you don't feel enough weight in the rackethead.

[stoneage]

Originally Posted by JohnB

What puzzles me is that the lighter Travlerajm racket has virtually the same MgR/I and the same shape of the curve. But if you add weight at the center of a racket, the shape of the curve also remains the same, but MgR/I increases.

I don't think it is strange that they behave differently since they describe different things. The curve describes a swing, admittedly a very simplified and crude swing, but a least a swing where you apply a force to the racquet. MgR/I describes what happens when you attach the racquet to a cuckoo clock (exaggerating a little .

You can find other placements of the weight that might change the curve, but not MgR/I. For example you can add 10 kg at the but end or at a point around 48 cm without changing MgR/I.

[JohnB]

Originally Posted by stoneage

I don't think it is strange that they behave differently since they describe different things. The curve describes a swing, admittedly a very simplified and crude swing, but a least a swing where you apply a force to the racquet. MgR/I describes what happens when you attach the racquet to a cuckoo clock.

You can find other placements of the weight that might change the curve, but not MgR/I. For example you can add 10 kg at the but end or at a point around 48 cm without changing MgR/I.

That is probably why MgR/I isn't a personal ideal number, but differs with different weightdistributions.

[JohnB]

Originally Posted by stoneage

It is included. If you look at the formula:



You can see that both the swing weight (sw) and the balance (c) are in the numerator. So increasing either will increase me and make the curve steeper, but in a slightly different way.

Tonight I played with 2 identical rackets and customized to same endspecs, 327 g, 33.3 balance, 335 sw.

One racket had all the added weight at the sides and the other one in a more polarized manner.

The played very different despite having the same curve (and the same MgR/I). I am not only referring to ball trajectory, but also the felt racketheadcontrol. The polarized one has a whippier feel than the other one.

The equivalent mass is the same for both rackets, but do you know why they play so different? I think I know why just by experience, but it would be great if there was a scientific explanation.

[travlerajm]

Originally Posted by JohnB

Tonight I played with 2 identical rackets and customized to same endspecs, 327 g, 33.3 balance, 335 sw.

One racket had all the added weight at the sides and the other one in a more polarized manner.

The played very different despite having the same curve (and the same MgR/I). I am not only referring to ball trajectory, but also the felt racketheadcontrol. The polarized one has a whippier feel than the other one.

The equivalent mass is the same for both rackets, but do you know why they play so different? I think I know why just by experience, but it would be great if there was a scientific explanation.

You measure SW in the plane perpendicular to the stringbed, but your swing is not in that plane.

The higher twistweight frame has higher SW in the plane of your actual swing, so effective MgR/I is lower for that frame.

[jmnk]

Originally Posted by travlerajm

You measure SW in the plane perpendicular to the stringbed, but your swing is not in that plane.

The higher twistweight frame has higher SW in the plane of your actual swing, so effective MgR/I is lower for that frame.

Could you elaborate on what you mean by that? Perhaps a drawing would help.....

[travlerajm]

Originally Posted by jmnk

Could you elaborate on what you mean by that? Perhaps a drawing would help.....

The two racquets have the same swingweight when measured in the plane normal to the stringbed, but if you mounted them in an RDC machine with the handle rotated 90 degrees to measure the swingweight in the plane of the stringbed, the racquet with higher twistweight would measure higher swingweight than the other because the added weight on the sides of the hoop is farther from the pivot point than if the weight were placed in the center of the stringbed.

Your actual swing occurs in a plane that is neither completely normal nor completely parallel to the stringbed, so the twistweight contributes to the "effective" swingweight, which is always slightly higher than the measured swingweight. In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference. But the example presented (with 2 frames of equal mass, balance, and measured SW, but different mass distributions) is a case where the difference does come into play.

I have to go catch a plane this morning, so I'll leave a drawing to someone else.

[jmnk]

Originally Posted by travlerajm

The two racquets have the same swingweight when measured in the plane normal to the stringbed, but if you mounted them in an RDC machine with the handle rotated 90 degrees to measure the swingweight in the plane of the stringbed, the racquet with higher twistweight would measure higher swingweight than the other because the added weight on the sides of the hoop is farther from the pivot point than if the weight were placed in the center of the stringbed.

Your actual swing occurs in a plane that is neither completely normal nor completely parallel to the stringbed, so the twistweight contributes to the "effective" swingweight, which is always slightly higher than the measured swingweight. In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference. But the example presented (with 2 frames of equal mass, balance, and measured SW, but different mass distributions) is a case where the difference does come into play.

I have to go catch a plane this morning, so I'll leave a drawing to someone else.

sure, I get all of that. But you never said before that 'I' in your MgR/I equation is (as you call it) 'effective swingweight'. And if it is - than aren't all your line of thinking based on observed correlation between ATP player's racket specs and MgR/I of those rackets kind of baseless? Since I'm pretty sure that all data about player's rackets refers to what commonly is known as 'swingweight' and not 'effective swingweight'?
Also, isn't saying "In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference." a bit misleading? As you pointed out yourself - if you add weight to the sides of the racket the 'effective swingweight' actually changes apparently noticeably. Isn't adding weight to the sides of the racket like at least as common as adding the weight at the top or bottom of the racket? In other words 'most cases' is like 50% of the cases, no?

[spectastic]

whoever's a physics phd should write his dissertation on this stuff.

[stoneage]

Originally Posted by travlerajm

The two racquets have the same swingweight when measured in the plane normal to the stringbed, but if you mounted them in an RDC machine with the handle rotated 90 degrees to measure the swingweight in the plane of the stringbed, the racquet with higher twistweight would measure higher swingweight than the other because the added weight on the sides of the hoop is farther from the pivot point than if the weight were placed in the center of the stringbed.

Your actual swing occurs in a plane that is neither completely normal nor completely parallel to the stringbed, so the twistweight contributes to the "effective" swingweight, which is always slightly higher than the measured swingweight. In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference. But the example presented (with 2 frames of equal mass, balance, and measured SW, but different mass distributions) is a case where the difference does come into play.

I have to go catch a plane this morning, so I'll leave a drawing to someone else.

Some corrections and clarifications: The swing weight (Ix) is measured around an axis in the plane of the string bed (x-axis), not normal to it (but you probably mean that).

The twist weight (Iy) is measured around an axis along the length of the racquet (y-axis) and affects the swing very little (but is important at an off-line impact).

It is right that a normal swing not is entirely around the string bed plane and that the actual swingweight is a little higher. The moment of inertia (Iz) around the third axis is higher than the swingweight, which follows from perpendicular axis theorem Iz=Ix+Iy. However, in a racquet these two "swingweights" (Ix and Iz) are similar since Iy is small, so their combined effect from not swinging entirely around the x-axis is fairly small.

An example: assume an evenly balanced racquet with a weight of 320 g, a swing weight (Ix) of 325 kg cm^2 and a twist weight (Iy) of 15 kg cm^2 ( a typical value). Using the the parallel axis and perpendicular axis theorems you get that Iz is 340 kg cm^2 . That is the swingweight if you swing with edge towards the ball (not so common). If you swing with racquet with the head tilted at some other angle it is much more complicated and you have to involve the products inertia as well. But assuming that the racquet is flat ( a fair assumption) you approximate the moment of inertia at an angle a with Ia = Ix*(cos a)^2+ Iz*(sin a)^2 if a is 45 degrees Ia becomes the average of the two. So the swingweight of a swing with the head at 45 degree angle is 332 or 2% higher. More importantly, this increase is almost the same for all racquets, so it is hardly worth bothering about.

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

[stoneage]

Originally Posted by JohnB

Tonight I played with 2 identical rackets and customized to same endspecs, 327 g, 33.3 balance, 335 sw.

One racket had all the added weight at the sides and the other one in a more polarized manner.

The played very different despite having the same curve (and the same MgR/I). I am not only referring to ball trajectory, but also the felt racketheadcontrol. The polarized one has a whippier feel than the other one.

The equivalent mass is the same for both rackets, but do you know why they play so different? I think I know why just by experience, but it would be great if there was a scientific explanation.

travlerajm is correct that they have a different twist weight (moment of inertia around the y-axis). As I discussed above that doesn't influence the speed of the swing that much (and thus not the curve). However, it does influence the feel of the racquet, especially at impact. Placing weights at 3 and 9 increases the twist weight whereas placing it at 12 doesn't. A racquet with high twist weight feels less "wobbly" i.e. it is more difficult to rotate around its length axis. It can also handle an off line hit a little better (if you ever miss the sweet spot) and transfers a little less twist to the arm.

[jmnk]

Originally Posted by stoneage

Some corrections and clarifications: The swing weight (Ix) is measured around an axis in the plane of the string bed (x-axis), not normal to it (but you probably mean that).

The twist weight (Iy) is measured around an axis along the length of the racquet (y-axis) and affects the swing very little (but is important at an off-line impact).

It is right that a normal swing not is entirely around the string bed plane and that the actual swingweight is a little higher. The moment of inertia (Iz) around the third axis is higher than the swingweight, which follows from perpendicular axis theorem Iz=Ix+Iy. However, in a racquet these two "swingweights" (Ix and Iz) are similar since Iy is small, so their combined effect from not swinging entirely around the x-axis is fairly small.

An example: assume an evenly balanced racquet with a weight of 320 g, a swing weight (Ix) of 325 kg cm^2 and a twist weight (Iy) of 15 kg cm^2 ( a typical value). Using the the parallel axis and perpendicular axis theorems you get that Iz is 340 kg cm^2 . That is the swingweight if you swing with edge towards the ball (not so common). If you swing with racquet with the head tilted at some other angle it is much more complicated and you have to involve the products inertia as well. But assuming that the racquet is flat ( a fair assumption) you approximate the moment of inertia at an angle a with Ia = Ix*(cos a)^2+ Iz*(sin a)^2 if a is 45 degrees Ia becomes the average of the two. So the swingweight of a swing with the head at 45 degree angle is 332 or 2% higher. More importantly, this increase is almost the same for all racquets, so it is hardly worth bothering about.

Originally Posted by stoneage

travlerajm is correct that they have a different twist weight (moment of inertia around the y-axis). As I discussed above that doesn't influence the speed of the swing that much (and thus not the curve). However, it does influence the feel of the racquet, especially at impact. Placing weights at 3 and 9 increases the twist weight whereas placing it at 12 doesn't. A racquet with high twist weight feels less "wobbly" i.e. it is more difficult to rotate around its length axis. It can also handle an off line hit a little better (if you ever miss the sweet spot) and transfers a little less twist to the arm.

@stoneage - yes, this is excellent explanation, and more importantly based on physics and not 'feel'. I never had any doubts you understand the nuances. I get all of that.
But what I do not understand is whether in MgR/I equation one shall use:
a) Ix (which is what is being published as 'swingweight')? or
b) Ix + Iz (which would take into account twistweight as well)?

Because in all previous threads and posts the only value ever mentioned or discussed was Ix.
Now, when JohnB points out that two rackets with identical mass, balance, and swingweight (Ix) - which obviously means that MgR/I is also identical - do feel differently, travlerajm says that this is expected since the twistweight (Iy) of those two rackets is different.
well, which is it than? Either 'I' in MgR/I is just Ix and you at least can claim you are using published specs to back up your claims. Or 'I' in MgR/I is 'Ix+Iy' and than the entire line of thinking backing up this MgR/I idea needs to be redone since:
- no one measures Ix+Iy unless specifically told to do so, and
- therefore people were tuning rackets to MgR/I=21.0 using incorrect value of I, and
- there's no way to compare that to pro's racket specs since they do not publish Iy of pros rackets.

[JohnB]

I am planning on a couple more experiments.

Namely, first I will up the swingweight enough of the polarized racket to match it to the effective swingweight of the higher twistweight racket and then compare.

Second I will try to set-up both rackets, one more polarized than the other, but now not only with identical mass, balance and swingweight, but also with the same twistweight and then compare.

[stoneage]

Originally Posted by jmnk

@stoneage - yes, this is excellent explanation, and more importantly based on physics and not 'feel'. I never had any doubts you understand the nuances. I get all of that.
But what I do not understand is whether in MgR/I equation one shall use:
a) Ix (which is what is being published as 'swingweight')? or
b) Ix + Iz (which would take into account twistweight as well)?

Because in all previous threads and posts the only value ever mentioned or discussed was Ix.
Now, when JohnB points out that two rackets with identical mass, balance, and swingweight (Ix) - which obviously means that MgR/I is also identical - do feel differently, travlerajm says that this is expected since the twistweight (Iy) of those two rackets is different.
well, which is it than? Either 'I' in MgR/I is just Ix and you at least can claim you are using published specs to back up your claims. Or 'I' in MgR/I is 'Ix+Iy' and than the entire line of thinking backing up this MgR/I idea needs to be redone since:
- no one measures Ix+Iy unless specifically told to do so, and
- therefore people were tuning rackets to MgR/I=21.0 using incorrect value of I, and
- there's no way to compare that to pro's racket specs since they do not publish Iy of pros rackets.

To elaborate a little more on my previous answer and my view on this:
The twist weight is Iy, i.e. around the y-axis. The swing occurs mainly around the x and z axis, and is "controlled" by a combination of Ix and Iz, but since they are fairly similar the error by using only Ix, i.e. the swingweight, is small. So my first conclusion is: you can continue to use swingweight as before.

The twistweight will affect the feel of the racquet, but it doesn't influence the swing that much and can therefore be treated as a separate problem. Still I think twistweight is a neglected parameter that is worth keeping an eye on. Some more about twist weight here:

I am not going to comment on what to use in MgR/I since I don't know (I have yet to see a reasonable explanation how MgR/I influence a tennis swing).

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

[A.Reader]

@stoneage Thanks for your many technical posts. This is an interesting attempt to develop a new way of looking at the weight parameters of racquets.

However, I believe there is a mistake in the formula in your effective_mass.xlsx spreadsheet. There is an extra factor of 2 in the denominator there. When you take that out, the plots become monotonic with 15/r and you get much larger effective masses on the right side.

In the eqv_mass_norm.xlsx spreadsheet, I don't understand the expression for the reference racquet that you use in the denominator there. Can you explain how Ip for the reference racquet equals 320 (1033 + 50*r + r*r) ?

Using I[end] = (M*L^2)/3 for a uniform rod, I get
Ip = 320 (70*70/3 + r*r) for the reference racquet. This makes the curves look quite different.

Anyways, thanks for posting something that was motivating enough to get me to finally de-lurk!

[LeeD]

When matching racket/weights to players, there is NO direct corelation between a certain fix and the player's ability to PLAY better. Too many X factors come to play.

[stoneage]

Originally Posted by A.Reader

@stoneage Thanks for your many technical posts. This is an interesting attempt to develop a new way of looking at the weight parameters of racquets.

However, I believe there is a mistake in the formula in your effective_mass.xlsx spreadsheet. There is an extra factor of 2 in the denominator there. When you take that out, the plots become monotonic with 15/r and you get much larger effective masses on the right side.

I hate to admit it, but you are absolutely right! The 2 shouldn't be there. I have updated the Excel sheet. The change alters the curves as you have noticed. I don't think that there is a much difference in the relation between the racquets, but since the curve rises faster it is more difficult to see the difference. It is therefore even more motivated to use the normalized diagram instead (which never had the irritating 2). Thanks a lot for pointing it out even if it was embarrassing

In the eqv_mass_norm.xlsx spreadsheet, I don't understand the expression for the reference racquet that you use in the denominator there. Can you explain how Ip for the reference racquet equals 320 (1033 + 50*r + r*r) ?

Using I[end] = (M*L^2)/3 for a uniform rod, I get
Ip = 320 (70*70/3 + r*r) for the reference racquet. This makes the curves look quite different.

Not quite. r is defined as the distance to the point 10 cm up the handle where the force is applied. So starting with the MOI around the midpoint, Ip for the rod is:
Ip=M*L^2/12+M*(c+r)^2

and c for an evenly balanced rod is L/2-10 = 25 so I get
Ip=M*70*70/12+M*(25+r)^2= M*(1033+50*r+r*r)

Also remember that the parallel axis theorem can only be used in relation to the MOI around the center of mass, so you can't calculate Ip the way you did, even if r would have been to the endpoint of the racquet.