Combining weight, balance and swingweight

[stoneage]

Originally Posted by 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.

There certainly are! The purpose of the curve is to visualize some important parameters and hopefully make it easier so see the difference between racquets. It is not a prescription how to optimize a racquet.

The level of tennis you can achieve is only to a small degree determined by the balance of your racquet (Federer would beat me with an iron spade). But getting a racquet that feels fine will make it more fun och you will probably play better. The placebo effect is at least as important as the physics.

[floydcouncil]

tennis nerds...........

[A.Reader]

@stoneage Thanks for your response explaining the correct Ip for the uniform reference racquet. My mangling of the parallel axis theorem and inability to figure out your correct expression might be more embarrassing than your extra factor of 2! I'll get over it someday.

Now that (hopefully) the math is checked out, we can talk about the interpretation of the model and its results. The "effective mass" was an interesting idea, but I wasn't comfortable with the mixing of linear and angular forces. I didn't know what to make of effective masses of 500 (or 700) grams at small values of r. So the "mass" numbers were no more intuitive than swingweights.

The normalization was an improvement, certainly, but since it's now dimensionless quantity, there's no concept of "mass" anymore. And since me/me0 = Ip/Ip0, you only need starting equations 5 and 6 in your proof. Equations 1-4 aren't needed, and we're just plotting the ratios of moments vs. radius of swing.

Still, this is pretty cool. You can plot the moments of two racquets and say something like Racquet A takes 21% less effort to swing on serves than Racquet B, and 11% less effort on forehands. Just need to pick values of r that represent the serve and the forehand. (Let's ignore the fact that the serve is a complex motion involving multiple radii at different phases.) I think that would be about as readily understandable as you can get. And it's a big improvement over just taking the ratios of the conventional swingweights. Your fundamental insight is that 10cm from the butt is the wrong axis of rotation to care about, and looking at longer radii shows that swingweight numbers understate the differences in swing effort.

After we revolutionize the reporting of swingweight, we can tackle the endless argument whether racquet speed or weight is more important when the racquet hits a tennis ball.

[T-Vex]

Originally Posted by stoneage

The level of tennis you can achieve is only to a small degree determined by the balance of your racquet (Federer would beat me with an iron spade). But getting a racquet that feels fine will make it more fun och you will probably play better. The placebo effect is at least as important as the physics.

I see this so often on this boards that I just can't believe people that read Tennis Talk (which means they have more than average knowledge and interest in tennis) are able to overlook this important field!

No doubt a perfectly tuned racket wouldn't make you win against Federer, nor even against your best club player!

But it will give you some leverage that's for sure.
If it will improve your game for only 5-10% - great! I would take any factor that would improve my game by that much and put me slightly ahead in fron of my competition at 4.0 level!


People just aren't able to put things into perspective!

[anubis]

Originally Posted by stoneage

There certainly are! The purpose of the curve is to visualize some important parameters and hopefully make it easier so see the difference between racquets. It is not a prescription how to optimize a racquet.

The level of tennis you can achieve is only to a small degree determined by the balance of your racquet (Federer would beat me with an iron spade). But getting a racquet that feels fine will make it more fun och you will probably play better. The placebo effect is at least as important as the physics.

It looks like, from your graphs, that adding weight in a non-polarized manner makes it harder for you to achieve the same end result (swinging the racquet along any axis from your body) than adding it in a polarized manner.

Say I want a SW of 350. I do this by adding 8g in the hoop and 8g in the butt. My balance remains the same, and my curve on your graph will be parallel between the unmodified racquet and the modified racquet. This means that I have access to this added mass in a predictable and linear manner, as it's deviation from the mean is equal across all data points.

If I want the same SW of 350 but I do it by adding 5 g in the hoop and nowhere else, then its a de-polarized customization and my balance is thrown off... its more or less head heavy now. My access to the added mass increases exponentially away from the mean the further my axis point travels from the core of my body. This means that depending on where my axis is, it will be harder to swing the racquet by a factor that is exponentially larger than any point prior to that axis. I think that can confuse the mind-body mechanics and negatively affect timing.

IMO, a depolarized setup gets you to a point of diminishing returns quicker because the added mass you may want will not equal what you need depending on where the axis is. It certainly does for a while, but if for some reason you're stretched out far trying to make a stab volley and the axis is at your wrist, a depolarized racquet will actually make it harder for you to access that added mass -- and may even hurt you -- due to the fact that it requires so much more effort on your part than it did when you were swinging from your shoulder.

[henryshli]

Hi this thread is amazing. Would it be possible for someone to produce a graph for the ps85 please? That racket has also been so mysterious in that it swung so easily.

[stoneage]

Originally Posted by A.Reader

@stoneage Thanks for your response explaining the correct Ip for the uniform reference racquet. My mangling of the parallel axis theorem and inability to figure out your correct expression might be more embarrassing than your extra factor of 2! I'll get over it someday.

Now that (hopefully) the math is checked out, we can talk about the interpretation of the model and its results. The "effective mass" was an interesting idea, but I wasn't comfortable with the mixing of linear and angular forces. I didn't know what to make of effective masses of 500 (or 700) grams at small values of r. So the "mass" numbers were no more intuitive than swingweights.

The normalization was an improvement, certainly, but since it's now dimensionless quantity, there's no concept of "mass" anymore. And since me/me0 = Ip/Ip0, you only need starting equations 5 and 6 in your proof. Equations 1-4 aren't needed, and we're just plotting the ratios of moments vs. radius of swing. This curve loses a part for the very long swing radii, but instead shows the part where you go from r=0 where meausure swing to just outside the handle

Still, this is pretty cool. You can plot the moments of two racquets and say something like Racquet A takes 21% less effort to swing on serves than Racquet B, and 11% less effort on forehands. Just need to pick values of r that represent the serve and the forehand. (Let's ignore the fact that the serve is a complex motion involving multiple radii at different phases.) I think that would be about as readily understandable as you can get. And it's a big improvement over just taking the ratios of the conventional swingweights. Your fundamental insight is that 10cm from the butt is the wrong axis of rotation to care about, and looking at longer radii shows that swingweight numbers understate the differences in swing effort.

After we revolutionize the reporting of swingweight, we can tackle the endless argument whether racquet speed or weight is more important when the racquet hits a tennis ball.

Great input, you are right about a lot of things here. The original equation is very simple and contains some unspoken simplification (like assuming that the racquet is attached to a massless rod). I also agree that the effective mass becomes a little hard to understand for short swing radii. However, I still thought it was useful since my aim was to compare racquets, not to give absolute values. Normalizing made the difference more clear, but I am aware that, as you point out, I am really leaving the equivalent mass idea. I still kept it since I started talking about equivalent mass. But you are probably right that it is better to just talk about relative swing weight.

If I keep the reference racquet as before an plot a curve of Ip/Ipref it will look the same as the Me/Meref (not surprise).



The advantage is that we longer need the equations as background. While we are at it we might as well plot it against the the swing radius r instead of 15/r since it is easier to understand. The reason for using 15/r was that Me had no relevance for r=0, whereas MOI has. So instead we get a figure like this:



It shows the same relation as the first figure, but with short swings to the left instead of to the right. The advantage is that you can see the actual values of the swing radius, which is more intuitive. This curve looses a part for very long radii (probably not so interesting). But instead shows the difference between r=0, where you measure swing weight and the wrist at r=15.

[stoneage]

Originally Posted by henryshli

Hi this thread is amazing. Would it be possible for someone to produce a graph for the ps85 please? That racket has also been so mysterious in that it swung so easily.

It looks very much like the Pro Staff 90 in my diagrams, just 2% lower along the whole curve.

[stoneage]

Originally Posted by anubis

It looks like, from your graphs, that adding weight in a non-polarized manner makes it harder for you to achieve the same end result (swinging the racquet along any axis from your body) than adding it in a polarized manner.

I would say the opposite. A "polarized" racquet has a higher swing weight than a non polarized with the same weight and balance. Increasing the swing weight more than the weight will push up one of the curve.

If add a weight around 42 cm from the but end, shape of the curve will remain pretty much the same, it will just be pushed upwards.

[A.Reader]

Yes, plotting r instead of 15/r is much better. An alternative option for plotting is to plot the ratio of the racquet moments to each other, avoiding the need for a reference broomstick--although I like the idea of an official reference broomstick, maybe gold-plated and enshrined somewhere.

An example of the swingweight-ratio-of-two-racquets plot:



In this plot it's easy to see the Pro Staff has roughly equal swingweight at the wrist, roughly 8-10% more at the elbow, roughly 13-14% more at the shoulder. That's why your arm will fatigue faster with that racquet, even though it's the "lower" swingweight racquet at the traditional reference axis.

I really like the results of this thread, even if all we have done is a) think about a realistic axis of rotation, and b) use the parallel axis theorem.

This is significant because the traditionally-defined swingweight axis clearly doesn't give us the best number to predict arm fatigue, or even indicate how easy or hard it feels to swing a forehand! If it ever worked for such purposes, it was a coincidence owing to racquets under comparison being very close in mass distribution. If I had to pick a single replacement without further study, I'd choose swingweight at the elbow radius, say r=40. That radius applies to arm-stressing portions of the groundstrokes and the middle phase of the serve. And "tennis elbow" is the epidemic, not "tennis wrist" or "tennis shoulder" although those are bad too.

Maybe the traditional axis was intended to be more relevant to the effects of ball-impact, since it represents the axis where torque is applied to resist the ball, but those dynamics depend more specifically on mass distribution than the static swingweight number can capture. We're lucky that TWU is now full of better measurements--power potential, plowthrough, etc.--which quantify and summarize impact effects.

What I'd like to see developed is the most realistic number for predicting arm fatigue, so if I had that number, and I knew what my limit was, I'd know whether the racquet was too heavy or not. This thread shows the significance of swingweight on a more realistic axis of rotation, which is the torque required for a given angular acceleration. Right now, I'd use the swingweight at r=40 (or maybe an average of the swingweights at r=15, 40, and 60) as my magic number for "racquet heaviness."

For me, the next theoretical step would be to consider the maximum centrifugal force caused by the racquet, which would occur at the point of contact of a serve, and try to figure out if that tells me anything different about racquet heaviness. If the racquet speed is high enough, I wonder if centrifugal force outweights torque as a cause of arm fatigue.

[kaiser]

Hey guys, this is one hell of a thread, keep it going!!!

[stoneage]

Originally Posted by A.Reader

Yes, plotting r instead of 15/r is much better. An alternative option for plotting is to plot the ratio of the racquet moments to each other, avoiding the need for a reference broomstick--although I like the idea of an official reference broomstick, maybe gold-plated and enshrined somewhere.

OK, then plotting against r is decided by the International Relative Swing Weight Comity (IRSWC).

Plotting the two racquets against each other is really useful when you want to compare them and make them similar. And you don't have to deal with the somewhat arbitrary reference stick. However, if you have more than two racquets it can be confusing. You also miss the information whether they are heavier for shorter or longer swings, i.e. both can have a descending curve without it being visible. So I think that both ways to plot have their merit and can be used in parallel.

I have therefore made a new excel sheet with both curves that you can download here.

I have also made a new theory background available here.

The relative swing weight for two racquets is:


And for a racquet and a reference stick.


Where sw is the standard swing weight, M is the weight and c is the balance minus 10 cm.

/Sten

PS The reference frame made of irridium, gold and platina will be placed in the vault in Paris together with the standard meter and kg.

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

[JohnB]

Originally Posted by 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.

Having done so, here are my findings.

When I matched the polarized racket's swingweight to the effective swingweight of the high twistweight racket while keeping balance and mass equal, they felt pretty much the same. The polarized one felt slightly whippier, but I had just about the same control over the rackethead.

When I matched balance, swingweight, static weight and twistweight I couldn't tell them apart swingwise. The only difference was during impact. The polarized one had a longer dwelltime.

[newyorkstadium]

MgR/I uses swingweight as part of it's formula. Should swingweight be replaced with relative swingweight in the MgR/I formula?

[stoneage]

Originally Posted by newyorkstadium

MgR/I uses swingweight as part of it's formula. Should swingweight be replaced with relative swingweight in the MgR/I formula?

No, you should not, since relative swing weight is not one value but a curve. You could of course play with it by putting in relative swing weight and vary R the same amount. But I have no idea what that would say (on the other hand, I don't understand what MgR/I is supposed to say to begin with).

Sten

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

[newyorkstadium]

Thanks. Hopefully you and travlerajm can get together and work on mgr/i.

Do you think relative swingweight should replace swingweight in racket specs and RDC machines?

[stoneage]

Originally Posted by newyorkstadium

Thanks. Hopefully you and travlerajm can get together and work on mgr/i.

Sorry, but that is not going to happen.
I have tried both to get some useful information about what mgr/i is supposed to mean and to contribute, but the response has been discouraging to say the least.

Do you think relative swingweight should replace swingweight in racket specs and RDC machines?

No. Moment of inertia (swingweight) is, together with balance and weight, one of the fundamental parameters that describe the behavior of the racquet. And you need that to create the relative swingweight curve.

My aim with the curve was to increase the understanding of how these three parameters affect the racquet for different swings.

[newyorkstadium]

Thanks. I have no more questions.

[LeeD]

Yes, there is a specific mathmatical formula to match racket specs with players.
As is in the rest of life's puzzles.

[kaiser]

Hej stoneage, downloaded and extracted your Excelsheet, but can't open it. Only found a bunch of .xml files which open up as xml source code in IE8. What am I doing wrong?