Combining weight, balance and swingweight

[Circa 1762]

Originally Posted by JohnB

Today I went on the court with two customized rackets. I played with both of them and adjusted the weight until they felt the same except for the weight difference.(feel as close as possible)

I know it's hard to do this objectively, but I tried to get the same swingdynamic/swingfeel with both rackets. Both rackets gave me virtually the same control and the same connected feel.

Here are the specs:

Völkl Quantum Energy II, 320 g, 32.15 cm balance, 302 sw

Babolat APDGT, 359 g, 32.65 cm balance, 342 sw

JohnB, just curious, did you focus mostly on getting the forehand to feel the same, or were you also thinking about backhand?

[JohnB]

Originally Posted by Circa 1762

JohnB, just curious, did you focus mostly on getting the forehand to feel the same, or were you also thinking about backhand?

Mostly forehand, but backhands (one handed) also felt about the same. When I was satisfied with similar feel I switched between the rackets and it took me virtually no time to adjust. I just played and felt very in tuned with both of them.

Also with volleys, smashes etc.

[Circa 1762]

Originally Posted by JohnB

Mostly forehand, but backhands (one handed) also felt about the same. When I was satisfied with similar feel I switched between the rackets and it took me virtually no time to adjust. I just played and felt very in tuned with both of them.

Also with volleys, smashes etc.

Interesting. The reason I ask is that based on the specs you provided, the MgR/I values of your two rackets are almost exactly the same (21.20 and 21.26). The MgR'/I' values (for two-handed backhand) are much farther apart (23.01 and 23.31), but since you have a one-handed backhand, you wouldn't have noticed. I'm very curious what Sten's curves end up looking like. (Sten, I apologize for bringing MgR/I into this thread - just thought it was an interesting observation. I'm excited to see how useful your equation/curves can be.)

[stoneage]

Originally Posted by JohnB

Today I went on the court with two customized rackets. I played with both of them and adjusted the weight until they felt the same except for the weight difference.(feel as close as possible)

I know it's hard to do this objectively, but I tried to get the same swingdynamic/swingfeel with both rackets. Both rackets gave me virtually the same control and the same connected feel.

Here are the specs:
Völkl Quantum Energy II, 320 g, 32.15 cm balance, 302 sw
Babolat APDGT, 359 g, 32.65 cm balance, 342 sw

Thanks for the data, here are the curves:


Dividing one with the other shows that you have succeeded well with getting both follow the same curve. The Babolat is about 13% heavier for all swings.



/Sten

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

[stoneage]

Originally Posted by Circa 1762

Interesting. The reason I ask is that based on the specs you provided, the MgR/I values of your two rackets are almost exactly the same (21.20 and 21.26). The MgR'/I' values (for two-handed backhand) are much farther apart (23.01 and 23.31), but since you have a one-handed backhand, you wouldn't have noticed. I'm very curious what Sten's curves end up looking like. (Sten, I apologize for bringing MgR/I into this thread - just thought it was an interesting observation. I'm excited to see how useful your equation/curves can be.)

Don't apologize, it deals with the same stuff (swingweight, mass etc) as the curves, so it is relevant to discuss it here. I think that there might be some interesting stuff buried in there somewhere and that is why I spent time discussing it. The problem is that travlerajm treats it as some kind of holy grail and applies it everywhere. Like the unfounded statement that you should use MgR/I for one handed swings and MgR'/I' for two handed (sorry, no critique of you), not to speak of the hilarious theory that you need to include g since gravity varies in different places in the world.

As an example of the connection I took the two Wilson racquets I used in the first post and modified them to MgR/I = 21.0. I think that they are interesting since they are very different to begin with. The Pro Staff has a MgR/I = 21.5 which is fairly close to the magical number so it was enough to add 8 g to the top leading to m=365 g, sw=354, balance=22.6 cm. The Cierzo Two has MgR/I = 19.1 and to bring it up to 21.0 the least I could get away with was adding 85 g at 25 cm. It resulted in a racquet with m=363 g, sw=369, balance=34.3 cm (1 pt HL). And the resulting curves:



Giving them equal MgR/I certainly brought the curves closer together. On the other hand the original racquets are close together for short swings despite having radically different MgR/I.

[toly]

The formula (4) acc = ω(r + d) in http://appmaker.se/racquetTune/equivalent_mass.pdf defines linear speed Vlin, not acceleration. Thus, Vlin = ω(r + d), and formula (1) Me =F/acc is meaningless???

[stoneage]

Originally Posted by toly

The formula (4) acc = ω(r + d) in http://appmaker.se/racquetTune/equivalent_mass.pdf defines linear speed Vlin, not acceleration. Thus, Vlin = ω(r + d), and formula (1) Me =F/acc is meaningless???

No. ω is angular acceleration (as said in the document). You can also see that I have used M=ω*I which indicates that it is angular acceleration. So the formula is correct.

However, ω is often used to denote angular velocity so you are right that it is confusing. I will change in the document. Thanks for being a careful reader.

/Sten

[JohnB]

If the shape of the curve is a personal preference, regardless how high or low it is situated (within reason) I have a few thoughts about it:

If one increases MgR/I by putting mass on top of the handle, the curve remains the same, but situated higher, thus the racket will feel the same, only heavier, despite that the rackethead should travel faster relative to the handle.

If one decreases or increases MgR/I by subtracting or adding swingweight, the curve will flatten or steepen, thus the rackethead will travel faster or slower and feel different.

Is this what you mean Sten, that MgR/I is a consequence of weightdistribution and not the cause of what makes a racket play sweet?

[toly]

Originally Posted by stoneage

No. ω is angular acceleration (as said in the document). You can also see that I have used M=ω*I which indicates that it is angular acceleration. So the formula is correct.

However, ω is often used to denote angular velocity so you are right that it is confusing. I will change in the document. Thanks for being a careful reader.

/Sten

According to all textbook about angular motion, Ѡ is angular velocity. So formula 4 was wrong.
Right now you start using α – angular acceleration without proper corrections and all your formulas become wrong.

[stoneage]

Originally Posted by toly

According to all textbook about angular motion, Ѡ is angular velocity. So formula 4 was wrong.
Right now you start using α – angular acceleration without proper corrections and all your formulas become wrong.

ω isn't angular velocity, but it is often used to denote (stand for) angular velocity. But you can use any symbol you like as long as you are consistent (and I was). I have changed so now I am using the more common α to denote angular acceleration to avoid confusion. While at it I also changed the Moment (torque) from M to the more common τ in the latest version.

There are no standards saying what symbol you must use for a certain variable, just common practice. I agree that the common practice helps avoiding confusion, but it doesn't change the equations. And the common practice has changed since I taught at the university

As for eq 4 there is a good explanation here

[stoneage]

Originally Posted by JohnB

If the shape of the curve is a personal preference, regardless how high or low it is situated (within reason) I have a few thoughts about it:

If one increases MgR/I by putting mass on top of the handle, the curve remains the same, but situated higher, thus the racket will feel the same, only heavier, despite that the rackethead should travel faster relative to the handle.

If one decreases or increases MgR/I by subtracting or adding swingweight, the curve will flatten or steepen, thus the rackethead will travel faster or slower and feel different.

Is this what you mean Sten, that MgR/I is a consequence of weightdistribution and not the cause of what makes a racket play sweet?

The swing radius tells you the relation between racquet head and handle speed. At the left side of the curve they are the same, at the right side the handle speed is close to zero. So if you pick a point say 15/r = 0.5, r is 30 cm and the acc point moves (30+40)/30 = 2.3 times faster than the handle. And that is the same for all curves at that point. (I am not sure if that answers your question).

And yes, MgR/I is a measure of weight distribution. It is taking one such measure (MR) and dividing it with another (I). It also means that a very heavy racquet (100 kg) and a very light racquet (10 g) with similar weight distribution can have the same MgR/I.

A fun exercise in connection with this is to assume that the racquet has a completely even weight distribution. MgR/I=21 will then lead to the result that the ideal racquet is 70 cm long, but of arbitrary weight!

[JohnB]

Originally Posted by stoneage

The swing radius tells you the relation between racquet head and handle speed. At the left side of the curve they are the same, at the right side the handle speed is close to zero. So if you pick a point say 15/r = 0.5, r is 30 cm and the acc point moves (30+40)/30 = 2.3 times faster than the handle. And that is the same for all curves at that point. (I am not sure if that answers your question).

And yes, MgR/I is a measure of weight distribution. It is taking one such measure (MR) and dividing it with another (I). It also means that a very heavy racquet (100 kg) and a very light racquet (10 g) with similar weight distribution can have the same MgR/I.

A fun exercise in connection with this is to assume that the racquet has a completely even weight distribution. MgR/I=21 will then lead to the result that the ideal racquet is 70 cm long, but of arbitrary weight!

Yes I understand.

This method/formula is truly amazing. I have set-up 5 rackets differently (different specs) and they are all very playable.

Sten, I have also tested (before this thread) the influence of mass locations, instead of just the specs. I went on the court with two rackets with the same specs, as close as I could, but with a different weightdistibution. They played quite differently. One was hitting flatter than the other. I don't think this is covered in the formula, or is it?

If it isn't, you can determine your favorite specs. Then finetune the playingcharacteristics by adjusting the weightdistribution within the specs you like.

[DEH]

Stoneage,

Could you map Travlerjm racquet which is 383grams with 31.877cm balance and 365 Swingweight and then fine the same curve but in a lighter racquet that is only 320grams? Can you tell me what the balance and swingweight needs to be?

[TaihtDuhShaat]

Reposted below for you DEH

[stoneage]

Originally Posted by JohnB

I have also tested (before this thread) the influence of mass locations, instead of just the specs. I went on the court with two rackets with the same specs, as close as I could, but with a different weightdistibution. They played quite differently. One was hitting flatter than the other. I don't think this is covered in the formula, or is it?

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.

[TaihtDuhShaat]

From this graph, you'll see that if you take or add all the weight from the middle of the racquet, the slope (or should i say derivative?) will be the same it will just be shifted up or down.

So from the TWU customization tool:

subtracting 63.7g from the middle of the travlerajm spec, you get:

320g, 31.4 cm balance, 327.5 sw

This should just be a lower shifted version on the graph

This gives you a MgR/I of:

980.5 x .320 x 31.4 / ((20 x .320 x 31.4) - 32.0 + 327.5) = 19.85 ( A very lagging behind 'slow' racquet head relative to your wrist)

This spec is so polarized (and lower powered than any players frame on the market) it might be nearly impossible to achieve from the specs of 99% of retail frames. It 'might' be doable with a prostock frame, with all the lead at 12 and in the butt, and making sure there is a minimum amount of weight added in between. (ie. no leather grip, no dampener, light strings, etc.)

edit: just tried it on the customization tool for the Ti.radical mp (a very customizable retail frame) and the closest you can get for 320g is around 32.8 cm balance with 327.5 sw (which will give you a much more powerful frame).

[JohnB]

Originally Posted by TaihtDuhShaat

From this graph, you'll see that if you take or add all the weight from the middle of the racquet, the slope (or should i say derivative?) will be the same it will just be shifted up or down.

So from the TWU customization tool:

subtracting 63.7g from the middle of the travlerajm spec, you get:

320g, 31.4 cm balance, 327.5 sw

This should just be a lower shifted version on the graph

This gives you a MgR/I of:

980.5 x .320 x 31.4 / ((20 x .320 x 31.4) - 32.0 + 327.5) = 19.85 ( A very lagging behind 'slow' racquet head relative to your wrist)

This spec is so polarized (and lower powered than any players frame on the market) it might be nearly impossible to achieve from the specs of 99% of retail frames. It 'might' be doable with a prostock frame, with all the lead at 12 and in the butt, and making sure there is a minimum amount of weight added in between. (ie. no leather grip, no dampener, light strings, etc.)

edit: just tried it on the customization tool for the Ti.radical mp (a very customizable retail frame) and the closest you can get for 320g is around 32.8 cm balance with 327.5 sw (which will give you a much more powerful frame).

Would you like to try the following experiment? I would love to know about your opinion/feel on the court if you would play with your current frame and then compare it with a frame customized as if weight is removed from the middle. IOW play with the same, but lower curve and compare whether the lower MgR/I is as noticeable as you would have anticipated if the curve wouldn't have had the same shape.

[TaihtDuhShaat]

Edit:

Now I'm remembering I have tried similar experiments in the past. The result is an extremely spin friendly setup (extreme loopy groundstrokes, great arcing topspin serves), and a flexy feel to the impact. The racquet needed a lot of wrist added before contact on each stroke because the racquet head lagged behind so much (a polarized, disconnected feel between the tip and the handle), like a barbell. It was difficult to hit accurate flat shots, volleys were very grabby and hard to pull off, and I had to prepare earlier for overheads.

[JohnB]

Maybe it is easier to do it the other way, add 20 or 30 gram at the center and check if your timing is off. IOW that the rackethead travels too fast.

[stoneage]

Just when you though you understood it, I am going to hit you with an alternative curve

Well, actually it is showing the same thing and I think it is an improvement. Instead of showing the equivalent mass, I am showing the equivalent mass for the racquet divided by the equivalent mass for a reference frame. And as the reference I am using a 70 cm long 320 g heavy* racquet with a completely even mass distribution and balance. By doing this it will be easier to see the difference between racquets. And the slope of the curve now also means something: A rising slope means that it is relatively heavier to swing at a short radius compared to the neutral racquet. And inverse for the falling curve.

Three examples, first our old friends the Pro Staff and the Cierzo:



Then Johns two racquets:



Finally an answer to DEH's question of taking travlerajm's racquet and make it 320 g. With balance 32 cm and swingweight 305 they look similar:



A new excel sheet is available here for your amusement

Digest and tell me what you think.

/Sten

*Note. I picked the weight of the reference racquet to be 320 g as it is an average of the racquets in the tenniswarehouse database. The value, however, is not so important since it will only shift the scale of the y-axis up or down.