Swingweight measuring or calculating??

[Technatic]

and in fact yesterday i tried ti calculate with this kind of formula (com*com*Mass) the swingweight of my wilson prostaff 6.0 85.
but the result proved to high for me (354 kg*cm^2) as tw warehouse calculated this sw at 329.

The calculationi that you made z * z * mass can not go very wrong.
Even the pivot point should not influence it too much because you have to add z^2 * G on both sides of it.
(It is not so that you have to deduct Mass of intertia on above the pivot from that below it!!)

 

[Irvin]

This is a nice quick approximation, but nothing more. The flaw is that this assumes uniform distribution of weight along the racquet.

To illustrate, imagine a racquet with perfectly even balance. We place a small weight on each side of the balance point and perform your calculation. If we then move each weight the same distance away from the balance point towards the tip/tail of the racquet, the real swingweight would change, whereas nothing in your calculation changes.

A polarized racquet will have an obviously different swingweight than a racquet with most of the mass at the balance point. Your equation does not appear to account for this. The TW and USRSA ones do.

I could not agree with you more, but didn't I start out by prefacing my quick and dirty method saying it had some problems of its own? Please don't take this as me being argumentative or arrogant I am just trying to contribute to the thread and explain problem with these methods. They are all good and will produce approximate swing weight measurements under ideal conditions.

Maybe I am a dumb arrogant and argumentative stringer that is all wet and does not know what he is talking about. MAYBE I am!!! I tried a little experiment with the method of swinging the racket from the head and added 8 grams of lead tape and it did not make any difference in the time for a period. If the period did not change, the swing weight did not change according to the TW method. By the way here is a video of my experiment.

http://www.youtube.com/watch?v=UNAkzMeR5AE

Is anyone able to explain how I can add 8 grams of lead tape to the top of the racket and not change the swing weight? I understand the tape will fall off the first time I hit a ball so the swing weight will revert back. And it is against the rules to place any object inside the string pattern. LOL

Irvin

 

[Irvin]

and in fact yesterday i tried ti calculate with this kind of formula (com*com*Mass) the swingweight of my wilson prostaff 6.0 85.
but the result proved to high for me (354 kg*cm^2) as tw warehouse calculated this sw at 329.

Daniele these methods will get you in the ball park but unless you are prepared to spend a lot of money for an RDC or similar machine or take you racket to someone who has one you are just going to have to wait for a better method.

Who is to say that your racket does not really have a swing weight of 354 or 329? My racket was listed with a swing weight of 331 but when I have it measured on an RDC it comes out to 356. If you have two rackets you are trying to match up and you can get the balance and weight the same it is good enough. If you can get the weight and swing weight to match up (no matter which method you use) it is good enough.

IF IT WERE ME!!!!! I am not saying this is the best way but the method that makes more sense to me. I would use the balance and weight method.

Irvin

 

[SW Stringer]

To be just a little more specific see Chapter 5, page 45, second paragraph, first sentence. He states the ideal way to measure SW and why he doesn't use the ideal way.

I do believe the TW way is a true measure of the MOI of a tennis racket if the racket swings from the head end of the racket. But the formula to convert the TW way to the ideal way is a bit complicated. That formula is on on page 46 in the middle of the page. Swinging the racket from the head and not the handle introduces errors. The reason for the error is any mass added at the pivot point will not change the period time for the pendulum. Any weight added at the ideal pivot point makes a world of difference using the TW method and should not make any difference at all.

Irvin

Quote of paragraph 2, chapter 5 (Cross & Lindsey), page 45 of "The Physics and Technology of Tennis" : "Ideally, one should swing the racquet about the actual axis of rotation of interest (near the end of the handle), but it is not easy to mount a racquet in this way. It is much easier to mount the racquet as a pendulum so that it rotates about an axis in the string plane. The swingweight about a parallel axis in the handle can then be calculated using the formula on the next page. . . . " The formula may seem complicated but all the calculations are automatic using the swingweight calculator at the TW site. See the instructions for using this at http://twu.tennis-warehouse.com/learning_center/howto_swingweight.php . The TW professor is Crawford Lindsey who co-authored the book. Page 47 analyzes the errors that can be introduced in the calculations by picking different cross strings. Using the bottom cross string gives a measurement error of plus or minus 2.6%. Using the top or middle cross string for the pendulum measurement gives an error of plus or minus 0.3 %. The TW swingweight calculator uses the top cross.

Irvin states that "Swinging the racket from the head and not the handle introduces errors. The reason for the error is any mass added at the pivot point will not change the period time for the pendulum." I have no idea how this conclusion was reached. It is certainly not supported by the formula nor in Cross and Lindsey's error analysis that says (p 47) that the errors come from small errors in measuring the distance from the balance point to the rotation axis and small errors in the timing measurement. By following their recommendations (TW Swingweight calculator) you can keep the errors below one percent ( 0.3 %) .

 

[DEH]

I could not agree with you more, but didn't I start out by prefacing my quick and dirty method saying it had some problems of its own? Please don't take this as me being argumentative or arrogant I am just trying to contribute to the thread and explain problem with these methods. They are all good and will produce approximate swing weight measurements under ideal conditions.

Maybe I am a dumb arrogant and argumentative stringer that is all wet and does not know what he is talking about. MAYBE I am!!! I tried a little experiment with the method of swinging the racket from the head and added 8 grams of lead tape and it did not make any difference in the time for a period. If the period did not change, the swing weight did not change according to the TW method. By the way here is a video of my experiment.

http://www.youtube.com/watch?v=UNAkzMeR5AE

Is anyone able to explain how I can add 8 grams of lead tape to the top of the racket and not change the swing weight? I understand the tape will fall off the first time I hit a ball so the swing weight will revert back. And it is against the rules to place any object inside the string pattern. LOL

Irvin

When you add the weigh to it changes the balance point and total weight of the racquet. So if you go and rebalance your racquet, it will be more head heavy and then you have to put that info into the TW swingweight tool with the new weight. It will chance the swingweight on the TW swingweight calculator.

 

[Irvin]

When you add the weigh to it changes the balance point and total weight of the racquet. So if you go and rebalance your racquet, it will be more head heavy and then you have to put that info into the TW swingweight tool with the new weight. It will chance the swingweight on the TW swingweight calculator.

Thank you 'DEH' and 'SW Stringer' I will check this out. I appreciate you feedback.

Irvin

 

[SW Stringer]

I could not agree with you more, but didn't I start out by prefacing my quick and dirty method saying it had some problems of its own? Please don't take this as me being argumentative or arrogant I am just trying to contribute to the thread and explain problem with these methods. They are all good and will produce approximate swing weight measurements under ideal conditions.

Maybe I am a dumb arrogant and argumentative stringer that is all wet and does not know what he is talking about. MAYBE I am!!! I tried a little experiment with the method of swinging the racket from the head and added 8 grams of lead tape and it did not make any difference in the time for a period. If the period did not change, the swing weight did not change according to the TW method. By the way here is a video of my experiment.

http://www.youtube.com/watch?v=UNAkzMeR5AE

Is anyone able to explain how I can add 8 grams of lead tape to the top of the racket and not change the swing weight? I understand the tape will fall off the first time I hit a ball so the swing weight will revert back. And it is against the rules to place any object inside the string pattern. LOL

Irvin

" Is anyone able to explain how I can add 8 grams of lead tape to the top of the racket and not change the swing weight? "

I used the TW calculator with the following data sets: Set 1: 300 grams racquet weight, BP = 13.5 inches, dist from butt to hang string = 65.9 cm, time for ten swings = 13.3 seconds; Set 2 308 grams racquet weight, the same for rest of data.

The swingweight calculator said Set 1 = 294, and Set 2 = 302 .

Your times didn't change but the total racquet weight went up 8 grams so of course the swingweight increased.

Plug in your actual parameters and use the TW swingweight calculator and you'll get a difference in SW between the two experiments.

 

[stangaele]

as i've already red in this thread i think irvin's formula is quite precise.
but this one does not introduce the variable of weight distribution.
this could be the most important thing when you are going to calculate swingweight.

 

[loubapache]

I used the TW calculator with the following data sets: Set 1: 300 grams racquet weight, BP = 13.5 inches, dist from butt to hang string = 65.9 cm, time for ten swings = 13.3 seconds; Set 2 308 grams racquet weight, the same for rest of data.

The swingweight calculator said Set 1 = 294, and Set 2 = 302 .

Your times didn't change but the total racquet weight went up 8 grams so of course the swingweight increased.

Plug in your actual parameters and use the TW swingweight calculator and you'll get a difference in SW between the two experiments.

Exactly. Time does change does not mean the swingweight does not change because the calculation depends also on the total mass and balance point (COM). The 8 g added in the racket on the video changed both the total mass and the balance point.

To build up on your example, the 8 g added at 65.9 cm will also change the balance point (COM). It will make the distance higher from the butt end to the COM. The swingweight is very sensitive to this. For your 300 g evenly balanced racket (13.5"), 8 g will change the balance to slightly greater than 13.6". If one uses 13.7", then the swingweight is 312.

The swingweight will then be 307 (but still the same oscillation period of 1.33 seconds). Therefore, the 8g increased the swingweight from 294 to more than 307

 

[Bud]

I really like this method as it's very quick and easy.

I prefer taking the measurements from the very tip of the frame and/or from the end of the butt cap. The distance (L) will then be the total length of the frame.

When you do that, you only have to make one measurement - which you can do by placing the 12 o'clock position of the racquet head onto the edge of the scale while supporting the butt cap with you finger. It helps to make the frame as level as possible, but makes very little difference in the weight (Gh) if it's slightly off.

**edit**

To verify my above assumption in red was correct, I went ahead and weighed the tail of the racquets to verify that the head and tail weights (Gh + Gt) = the total frame weight (G). They did.


- - -

In my case, I just modified (2) Babolat APD+ frames by shortening 1/2" while adding silicone inside the handles (see thread here: http://tt.tennis-warehouse.com/showthread.php?t=357497) and wanted to determine their SW's. Both frames are approximately 9 pts. HL. (slightly lighter frame #2 is about 8.5 pts. HL). To perfectly match the strung frames, I should add another 2g of weight just inside the buttcap of frame #2. This will bring the weight up to 344g and the balance closer to 9 pts. HL. I feel that is really splitting hairs, however.


Here are the steps and results:


Frame #1

1. Weigh the frame: 344g (G)
2. Place the racquet head near the edge of the scale and support the butt with a finger: 157g (Gh)
3. Gt will then equal 344g - 157g: 187g (Gt)
4. Z = (157g ∙ 68.58cm) ÷ 344g: 31.30cm (also COM)
5. SW = (31.30cm)² ∙ 344g: 337 kg∙cm² ◄◄


Frame #2

1. Weigh the frame: 342g (G)
2. Place the racquet head near the edge of the scale and support the butt with a finger: 157g (Gh)
3. Gt will then equal 342g - 157g: 185g (Gt)
4. Z = (157g ∙ 68.58cm) ÷ 342g: 31.48cm (also COM)
5. SW = (31.48cm)² ∙ 342g: 339 kg∙cm² ◄◄


This is about what I predicted, based on their weight and balance.

 

[stangaele]

I really like this method as it's very quick and easy.

I prefer taking the measurements from the very tip of the frame and from the end of the butt cap. The distance (L) will simply be the total length of the frame.

When you do that, you only have to make one measurement - which you can do by placing the 12 o'clock position of the racquet head onto the edge of the scale while supporting the butt cap with you finger. It helps to make the frame as level as possible, but makes very little difference in the weight (Gh) if it's slightly off.

- - -

In my case, I just modified 2 Babolat APD's and wanted to determine their SW's. Both frames are approximately 9 pts. HL. (lighter frame is about 8.5 pts. HL).


Here are the steps and results:


Frame #1

1. Weigh the frame: 344g (G)
2. Place the racquet head near the edge of the scale and support the butt with a finger: 157g (Gh)
3. Gt will then equal 344g - 157g: 187g (Gt)
4. Z = (157g ∙ 68.58cm) ÷ 344g: 31.30cm (also COM)
5. SW = (31.30cm)² ∙ 344g: 337 kg∙cm² ◄◄


Frame #2

1. Weigh the frame: 342g (G)
2. Place the racquet head near the edge of the scale and support the butt with a finger: 157g (Gh)
3. Gt will then equal 342g - 157g: 185g (Gt)
4. Z = (157g ∙ 68.58cm) ÷ 342g: 31.48cm (also COM)
5. SW = (31.48cm)² ∙ 342g: 339 kg∙cm² ◄◄


This is about what I predicted, based on their weight and balance.

actually the weight distribution variable IS in this formula as you consider only the weight of the head.my error was to calculate the COM with a ruler.
i also try a very very accurate measurement with the tw calculator and i arrived to a very precise result.
in the end i would say that both method are equal very precise.
my only question remained is:In what way the 10 cm axis is involved in those kind of formulas???

 

[Bud]

actually the weight distribution variable IS in this formula as you consider only the weight of the head.my error was to calculate the COM with a ruler.
i also try a very very accurate measurement with the tw calculator and i arrived to a very precise result.
in the end i would say that both method are equal very precise.
my only question remained is:In what way the 10 cm axis is involved in those kind of formulas???

Yes, this is an excellent method which is also very easily accomplished, IMO.

 

[Irvin]

I tried another experiment by measuring a racket with no weight and a 31 gram weight added at three different points on the racket. I put painter's tape on a racket at three different locations so I could add weight at almost the same locations for each test and to protect my racket. I also put another small strip of tape on my weight and the racket so I could make sure the weight was oriented the same every time. Here is a picture of the racket and weight with the tape:

First I went to my local big box store and asked to use their RDC and measured the swing weight with no weight added and with the weight added at the three locations where the tape was located. Then I did the same tests all over again. Then I came home and did all the same type of tests, and a lot of calculations to come up with the data I needed to use the TW calculator. Here are my results:

No weight added:

RDC SW - 325 - 326 / Average 325.5
Weight - 346 g - 346 g / Average 346 g
COM distance - 29.2 cm - 29.2 cm / Average 29.2 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 296 - 286 / Average 291
Difference between RDC and TW = -34.5

Weight added in lower position

RDC SW - 330 - 331 / Average 330.5
Weight - 376 g - 376 g / Average 376 g
COM distance - 31.0 cm - 31.0 cm / Average 31.0 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 359 - 341 / Average 350
Difference between RDC and TW = +20

Weight added in middle position

RDC SW - 356 - 357 / Average 356.5
Weight - 376 g - 376 g / Average 376 g
COM distance - 33.1 cm - 33.1 cm / Average 33.1 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 381 - 381 / Average 381
Difference between RDC and TW = +24.5

Weight added in top position

RDC SW - 410 - 412 / Average 411
Weight - 346 g - 376 g / Average 376 g
COM distance - 35.8 cm - 35.8 cm / Average 35.8 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 451 - 452 / Average 451
Difference between RDC and TW = +40.0

I think it is interesting to note the biggest difference came when I added weight near the top which was close to the head string pivot point.

Irvin

 

[Irvin]

...my only question remained is:In what way the 10 cm axis is involved in those kind of formulas???

Danielle I guess 'Bud' is just going to ignore you so I will answer your question. Nothing

'Bud' let me ask you another question. Let's assume your racket weighs 344 grams and it is 9 points HL. Why is there any need to do any more calculations? You know your balance point is 31.4325 cm ((13.5" - 1.125") * 2.54 - that is mid point minus 9 points converted to cm) so the force at that point is 31.4325*344 or 10,812.78 gcm. So if you go out 68.58 cm (27 * 2.54) you will still have 10,812.78 gcm so the weight will be 157.67 grams (10,812.78/68.58.) of course if you just lay the racket on the scales and it hits the scales a little inside the 27" mark you will have something a little less than 157.67 grams.

This doesn't mean that all 27" rackets that weigh 344 grams and are 9 point HL will have the same swing weight.

Irvin

 

[Bud]

Danielle I guess 'Bud' is just going to ignore you so I will answer your question. Nothing

'Bud' let me ask you another question. Let's assume your racket weighs 344 grams and it is 9 points HL. Why is there any need to do any more calculations? You know your balance point is 31.4325 cm ((13.5" - 1.125") * 2.54 - that is mid point minus 9 points converted to cm) so the force at that point is 31.4325*344 or 10,812.78 gcm. So if you go out 68.58 cm (27 * 2.54) you will still have 10,812.78 gcm so the weight will be 157.67 grams (10,812.78/68.58.) of course if you just lay the racket on the scales and it hits the scales a little inside the 27" mark you will have something a little less than 157.67 grams.

This doesn't mean that all 27" rackets that weigh 344 grams and are 9 point HL will have the same swing weight.

Irvin

Wow... snarky :shock: I didn't see the question buried at the bottom of his post so don't get you knickers in a wad.

The OP's method takes into account the weight distribution along the longitudinal axis of the frame. If the pivot point is 9-10 cm away from the handle and you have a significant amount of weight just inside the buttcap, it would seem that the weight distribution from the pivot point to the top of the frame will be inaccurate since you'd have a seesaw effect... making the head appear lighter than it actually was versus checking the (head) weight from the very end (of the buttcap). Again, this is why it seems more logical, IMO, to measure SW from the extreme ends of the frame.

To answer your other question, two different racquets with the same balance point and static weight should have similar COM and swingweights (assuming they aren't extremely polarized). However, again... weighing the head (using the OP's method) will reveal small difference in both frames' weight distributions along the longitudinal axis and thus their different centers of mass.

This is what common sense is telling me... But, perhaps, my logic is unsound and I need to experiment around with a few different scenarios to check. IMO, extremely polarized racquets may give a false reading on a RDC machine.

- - -

Here's a thread with a link to a video (and the direct link to the video) of someone performing all the racquet measurements on a RDC for those who aren't sure how these things are measured.

http://tt.tennis-warehouse.com/showthread.php?t=306096

http://www.youtube.com/watch?v=T0ZDlBQam7U

 

[DEH]

Irvin,

Watching your video I see that when you push the racquet to start the movement it looks like you are pushing it 4-5". I read in the TW instructions for the swingweight, it said that you should only push it 1-2", maybe that is why you are getting different readings. Give that a try and let us now.

 

[stangaele]

Irvin,

Watching your video I see that when you push the racquet to start the movement it looks like you are pushing it 4-5". I read in the TW instructions for the swingweight, it said that you should only push it 1-2", maybe that is why you are getting different readings. Give that a try and let us now.

and n fact up to 1 or 2 inches the result is the same as the velocity of the racket n even balanced by the dstance covered from the racket during the pendulum movement.After 2 or 3 inches the dstance to cover for the racket becames too high and the tme increases rapidly.

 

[SW Stringer]

I tried another experiment by measuring a racket with no weight and a 31 gram weight added at three different points on the racket. I put painter's tape on a racket at three different locations so I could add weight at almost the same locations for each test and to protect my racket. I also put another small strip of tape on my weight and the racket so I could make sure the weight was oriented the same every time. Here is a picture of the racket and weight with the tape:

First I went to my local big box store and asked to use their RDC and measured the swing weight with no weight added and with the weight added at the three locations where the tape was located. Then I did the same tests all over again. Then I came home and did all the same type of tests, and a lot of calculations to come up with the data I needed to use the TW calculator. Here are my results:

No weight added:

RDC SW - 325 - 326 / Average 325.5
Weight - 346 g - 346 g / Average 346 g
COM distance - 29.2 cm - 29.2 cm / Average 29.2 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 296 - 286 / Average 291
Difference between RDC and TW = -34.5

Weight added in lower position

RDC SW - 330 - 331 / Average 330.5
Weight - 376 g - 376 g / Average 376 g
COM distance - 31.0 cm - 31.0 cm / Average 31.0 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 359 - 341 / Average 350
Difference between RDC and TW = +20

Weight added in middle position

RDC SW - 356 - 357 / Average 356.5
Weight - 376 g - 376 g / Average 376 g
COM distance - 33.1 cm - 33.1 cm / Average 33.1 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 381 - 381 / Average 381
Difference between RDC and TW = +24.5

Weight added in top position

RDC SW - 410 - 412 / Average 411
Weight - 346 g - 376 g / Average 376 g
COM distance - 35.8 cm - 35.8 cm / Average 35.8 cm
Pivot distance - 62.1 cm - 62.1 cm / Average 62.1 cm
TW SW - 451 - 452 / Average 451
Difference between RDC and TW = +40.0

I think it is interesting to note the biggest difference came when I added weight near the top which was close to the head string pivot point.

Irvin

Interesting experiment. I Googled "calibrating Babolat RDC" and found the following posts at the GSS site:


Full Member

Offline

Posts: 155
Vista, California
Gender:

​

Re: RDC Calibration
Reply #7 - Sep 21st, 2004, 1:51pm
Geoff wrote on Aug 28th, 2004, 11:06am:
(snip) But I was comparing a couple of rackets to figures I got off the USRSA website......ie Head I radical (MP) sw 283, flex 63 where I'm measuring sw 312 and flex 64.

Just wondered if this was within the tolerance you would expect? or could it be the published figures are unstrung? (I'm measuring strung!) (snip)



The flex is definitely "close enough," but the swingweight difference is worrysome. The swingweight portion of the USRSA RDC machine is calibrated to racquets of known swingweight provided by Ken in machine services at Babolat. If you call Ken and tell him the current compensation numbers on your machine, he can tell you if they have changed since the last calibration, as he keeps records on these matters. (After calibrating your machine, you should of course call Ken and give him the new figures.) After calibrating the USRSA RDC machine, I made up three racquets that tested the same as the calibration sticks from Babolat, so calibration retesting is now a snap. (If anyone cares, I used three new Wilson Hyper Pro Staff 6.1s. After stripping off all the plastic except the butt cap, I had one racquet that was already at the mass I needed, and I weighted up the other two with lead tape to get the other two calibration points.)
Back to top

[FONT=verdana,sans-serif]Greg Raven, MRT
Vista, California

"If it can't be expressed in figures, it is not science; it is opinion."
-- Robert A. Heinlein, Time Enough for Love[/FONT]
​

Richard_Parnell
GSS Pro Board Member
GSS Panel Member
21 Club
Symposium Seminar Leader

Offline

Posts: 646
Fuengirola,Malaga,Spain
Gender:

​

Re: RDC Calibration
Reply #5 - Aug 29th, 2004, 2:48pm
Geoff,
are you putting the frame on the weighing plate before pressing the button? This would explain the no readings at all . If so press the weight button and then place the frame on the plate.
The RDC should be switched on for 30 mins to warm up and then once it is warm you need to switch it off put the tulip into the string deflection tester and switch the machine back on (then take the tulip back out) and then your readings will be as exact as possible.
Hope this helps,
Richard 8)
Back to top



So, my questions are these: Did they warm up the machine for at least 30 minutes and was the machine's swingweight section recently calibrated? I don't know what SW the three calibration sticks are set to but that would be a good data point too. As Lindsey explained in the error analysis of his method on pages 45 - 47 if the pivot point is too close to the BP (COM) inaccuracies in measuring this distance can lead to errors. What was that distance on the last test. Food for thought. Personally I'd put more faith in a method under which I had more control like the TW (USRSA) method. You have no control or knowledge of how accurate or how well the big box store maintains it's equipment.

 

[Irvin]

Irvin,

Watching your video I see that when you push the racquet to start the movement it looks like you are pushing it 4-5". I read in the TW instructions for the swingweight, it said that you should only push it 1-2", maybe that is why you are getting different readings. Give that a try and let us now.

"The book" says to keep the angle under 15 degrees which is maybe 1'. I just timed it with a different racket and got 13.75 for 10 periods for 2" swing. Then I moved it out to a 6" swing and got 13.75 seconds for 10 periods.

and n fact up to 1 or 2 inches the result is the same as the velocity of the racket n even balanced by the dstance covered from the racket during the pendulum movement.After 2 or 3 inches the dstance to cover for the racket becames too high and the tme increases rapidly.

Not sure what you are saying here Daniele but the amplitude of the swing (according to Galileo Galilei) does not effect the period of a pendulum. As strange as it may seem only the length of the pendulum determines the period see http://honolulu.hawaii.edu/distance/sci122/SciLab/L5/lenform.html Everything but the length and time is a constant.

Irvin

 

[Irvin]

'SW Stringer' I think what you are trying to say is the RDC could be off and that is true enough. No telling when it was last calibrated. But the listed SW on that Prince racket is 331. I have an overgrip on it and 3 g lead tape under the grip near the bottom of the handle. I removed the lead tape that was at the head. So I would expect the SW to be somewhat lower than 331 but not below 300. The RDC measured it at 325.

One or both of the methods has got to be false I would agree with that. Possibly both, but IMHO I feel the RDC is close.

Irvin

 

[SW Stringer]

'SW Stringer' I think what you are trying to say is the RDC could be off and that is true enough. No telling when it was last calibrated. But the listed SW on that Prince racket is 331. I have an overgrip on it and 3 g lead tape under the grip near the bottom of the handle. I removed the lead tape that was at the head. So I would expect the SW to be somewhat lower than 331 but not below 300. The RDC measured it at 325.

One or both of the methods has got to be false I would agree with that. Possibly both, but IMHO I feel the RDC is close.

Irvin

I guess one way to scientifically resolve this dilemma would be to get your hands on three calibration sticks of known SW that cover the whole range and verify the accuracy of both the RDC and the SW Tool at TW University. Then it wouldn't be mere opinion on either of our parts. Happy Turkey Day.

 

[stangaele]

i measured the swingweight of my racquet with the tw tool.this gave me 325 kg*cm^2 reall really close to that 329 of the review.

 

[bugeyed]

I guess one way to scientifically resolve this dilemma would be to get your hands on three calibration sticks of known SW snip

How is this "known" SW derived? I thought one issue here was the definition of SW. I have missed a few posts here, but is there a consensus on what test best measures true SW? Was the question of allowing for the actual arc of the racquet resolved or was it decided that using a point on the handle is adequate for our purposes?

Cheers,
kev

 

[stangaele]

Hi guys,

I was at a Stringing Happening of Stringway in the Netherlands.
They explained a way to calculate the Swingweight of a racquet out of weighing the racquet.

Last week they sent out the explanation of this calculation, perhaps it is interesting for you:

ok..first i weighted the head of my prostaff 85 with the irvin's method and then used this formula posted by technatic to calculate the swingweight.
simply incredible!!!!!! the result was 329.467 vs 329 posted on tw....to be continued

 

[SW Stringer]

How is this "known" SW derived? I thought one issue here was the definition of SW. I have missed a few posts here, but is there a consensus on what test best measures true SW? Was the question of allowing for the actual arc of the racquet resolved or was it decided that using a point on the handle is adequate for our purposes?

Cheers,
kev

SW is the moment of inertia. I looked it up in a couple of reference books and the mathematical formula is: I(cm) = 1/4 * M * r * r + 1/12 * M * l * l
where I(cm) is the moment of inertia at the center of mass axis
M is the mass in kilograms of the beam
r is the radius of the uniform circular beam
l is the length of the beam

To get the SW of the beam referenced to 4 inches (reference point for RDC machine's SW measuring) from the end the parallel axis theorem is used which is

I(parallel axis) = I(cm) + d * d * M
where d = distance from (cm) axis to parallel axis, M is the same mass as above.

With the above equations you can build reference "sticks" from dowel rods. I found two wooden rods in the garage, one a 30 inch long leg from a cheap craft table, the other a 47.5 inch section of a market umbrella stand. The leg was 1.174 inches in diameter and weighed 217 grams. The umbrella stand stick was 1.4125 inches in diameter and weighed 964 grams.

Using the above equations the theoretical SW's were 276.8 and 3611.4 kg-cm^2 respectively.

Using the TW empirical method I got 278.1 and 3571.3 kg-cm^2 respectively.

For the 30 inch leg the empirical method is within 0.47 % of the theoretical.
For the 47.5 inch stick the empirical method is within 1.11 % of the theoretical.

My conclusions:

One - the TW empirical method for measuring swingweight is extremely accurate.

Two - some big box store in the Marietta, Georgia area should get their Babolat RDC calibrated.

 

[Bud]

Question for SW Stringer and/or Technatic

I've been determining the SW of my frames using your guide. It seems to be very close to what I'm estimating in my head, when measuring Gh and Gt from the ends of the frame. However, the calculated SW seems to be quite far off when measuring Gh and Gt from 9 cm inside the buttcap. The 9 cm is based on where an RDC would measure the frame's SW.

- -

Scenario: I modified a Babolat Pure Storm Tour by adding a leather grip and 8g of silicone inside the buttcap (handle). I also removed the optional headguard (which removed 10 g of static weight and made the frame an additional 4 pts. HL). The total frame weight is 365 g and the balance is ≈10.5 pts. HL


Example 1: using the total length of the frame (27 in. or 68.58 cm)

G = 365 g
Gh = 165 g
Gt = 200 g
L = 68.58 cm
Z = (165 g · 68.58 cm) ÷ 365 g = 31.00 cm (also COM)
SW = (31.00 cm)² · 365 g ÷ 1000 = 351 kg · cm² ← ← this SW seems close to what it should be

- -

Example 2: Using the length from 9 cm (≈ 3.5 in.) inside the buttcap to the end of the head (23.5 in. or 59.69 cm)

G = 365 g
Gh = 130 g
Gt = 235 g (the last 9 cm of the frame to the buttcap must weigh about 35 g)
L = 59.69 cm (≈ 23.5 in.)
Z = (130 g · 59.69 cm) ÷ 365 g = 21.26 cm
SW = (21.26 cm)² · 365 g ÷ 1000 = 165 kg · cm² ← ← this SW seems too low


Discussion: from the two examples above, when I perform the SW calculation from 9 cm inside the buttcap, the SW is way off (see example 2). Does this method work when calculating from 9 cm inside the buttcap or does it require and extra step, like calculating the parallel axis value for the additional 9 cm?


Any thoughts?


Addendum: After thinking about this a bit more... I may have figured it out. The initial SW should be calculated from the ends of the object, like example 1. Then, the 9 cm should be subtracted, using the parallel axis calculation. In this case, I'd subtract (9 cm)² · 365 g ÷ 1000 or 30 kg · cm² ... which would be (351 kg · cm² - 30 kg · cm²) or 321 kg · cm²

 

[SW Stringer]

I've been determining the SW of my frames using your guide. It seems to be very close to what I'm estimating in my head, when measuring Gh and Gt from the ends of the frame. However, the calculated SW seems to be quite far off when measuring Gh and Gt from 9 cm inside the buttcap. The 9 cm is based on where an RDC would measure the frame's SW.

- -

Scenario: I modified a Babolat Pure Storm Tour by adding a leather grip and 8g of silicone inside the buttcap (handle). I also removed the optional headguard (which removed 10 g of static weight and made the frame an additional 4 pts. HL). The total frame weight is 365 g and the balance is ≈10.5 pts. HL


Example 1: using the total length of the frame (27 in. or 68.58 cm)

G = 365 g
Gh = 165 g
Gt = 200 g
L = 68.58 cm
Z = (165 g · 68.58 cm) ÷ 365 g = 31.00 cm (also COM)
SW = (31.00 cm)² · 365 g ÷ 1000 = 351 kg · cm² ← ← this SW seems close to what it should be

- -

Example 2: Using the length from 9 cm (≈ 3.5 in.) inside the buttcap to the end of the head (23.5 in. or 59.69 cm)

G = 365 g
Gh = 130 g
Gt = 235 g (the last 9 cm of the frame to the buttcap must weigh about 35 g)
L = 59.69 cm (≈ 23.5 in.)
Z = (130 g · 59.69 cm) ÷ 365 g = 21.26 cm
SW = (21.26 cm)² · 365 g ÷ 1000 = 165 kg · cm² ← ← this SW seems too low


Discussion: from the two examples above, when I perform the SW calculation from 9 cm inside the buttcap, the SW is way off (see example 2). Does this method work when calculating from 9 cm inside the buttcap or does it require and extra step, like calculating the parallel axis value for the additional 9 cm?


Any thoughts?


Addendum: After thinking about this a bit more... I may have figured it out. The initial SW should be calculated from the ends of the object, like example 1. Then, the 9 cm should be subtracted, using the parallel axis calculation. In this case, I'd subtract (9 cm)² · 365 g ÷ 1000 or 30 kg · cm² ... which would be (351 kg · cm² - 30 kg · cm²) or 321 kg · cm²

" . . . It seems to be very close to what I'm estimating in my head, when measuring Gh and Gt from the ends of the frame. However, the calculated SW seems to be quite far off when measuring Gh and Gt from 9 cm inside the buttcap. . . "

Both Gh and Gt are measured at the ends of the frame. The equation G*Z = Gh*L is the simplified moment equation in which they left out the first term at the point where Gt is measured. The complete equation of moments about the butt capp is: G*Z = Gt*0 + Gh*L which simplifies to G*Z = 0 + Gh*L since the moment arm at Gt is zero.

These simplified SW equations only appear to work if the racquet is 'nearly' a uniform beam, i.e. - the balance point is not too far off neutral or even balance. The more radical the racquet is Head heavy or head light the larger the error in estimating the true SW.

To get the true SW use the TW swingweight calculator or a Babolat RDC that you know is actually calibrated correctly (Good luck with that!). Hope that helps.

 

[Technatic]

Bud Question for SW Stringer and/or Technatic

--------------------------------------------------------------------------------
I've been determining the SW of my frames using your guide. It seems to be very close to what I'm estimating in my head, when measuring Gh and Gt from the ends of the frame. However, the calculated SW seems to be quite far off when measuring Gh and Gt from 9 cm inside the buttcap. The 9 cm is based on where an RDC would measure the frame's SW.

- -

Scenario: I modified a Babolat Pure Storm Tour by adding a leather grip and 8g of silicone inside the buttcap (handle). I also removed the optional headguard (which removed 10 g of static weight and made the frame an additional 4 pts. HL). The total frame weight is 365 g and the balance is ≈10.5 pts. HL


Example 1: using the total length of the frame (27 in. or 68.58 cm)

G = 365 g
Gh = 165 g
Gt = 200 g
L = 68.58 cm
Z = (165 g · 68.58 cm) ÷ 365 g = 31.00 cm (also COM)
SW = (31.00 cm)² · 365 g ÷ 1000 = 351 kg · cm² ← ← this SW seems close to what it should be

- -

Example 2: Using the length from 9 cm (≈ 3.5 in.) inside the buttcap to the end of the head (23.5 in. or 59.69 cm)

G = 365 g
Gh = 130 g
Gt = 235 g (the last 9 cm of the frame to the buttcap must weigh about 35 g)
L = 59.69 cm (≈ 23.5 in.)
Z = (130 g · 59.69 cm) ÷ 365 g = 21.26 cm
SW = (21.26 cm)² · 365 g ÷ 1000 = 165 kg · cm² ← ← this SW seems too low


Discussion: from the two examples above, when I perform the SW calculation from 9 cm inside the buttcap, the SW is way off (see example 2). Does this method work when calculating from 9 cm inside the buttcap or does it require and extra step, like calculating the parallel axis value for the additional 9 cm?


Any thoughts?


Addendum: After thinking about this a bit more... I may have figured it out. The initial SW should be calculated from the ends of the object, like example 1. Then, the 9 cm should be subtracted, using the parallel axis calculation. In this case, I'd subtract (9 cm)² · 365 g ÷ 1000 or 30 kg · cm² ... which would be (351 kg · cm² - 30 kg · cm²) or 321 kg · cm²

Hi Bud,
Good thinking this is exactly as it works:
When you want to know the SW at a different position you multiply the square of the change in position with the weight.
Like you did in red.

Using this method it is possible to compare the RDC measurements with the calculation.

 

[Bud]

" . . . It seems to be very close to what I'm estimating in my head, when measuring Gh and Gt from the ends of the frame. However, the calculated SW seems to be quite far off when measuring Gh and Gt from 9 cm inside the buttcap. . . "

Both Gh and Gt are measured at the ends of the frame. The equation G*Z = Gh*L is the simplified moment equation in which they left out the first term at the point where Gt is measured. The complete equation of moments about the butt capp is: G*Z = Gt*0 + Gh*L which simplifies to G*Z = 0 + Gh*L since the moment arm at Gt is zero.

These simplified SW equations only appear to work if the racquet is 'nearly' a uniform beam, i.e. - the balance point is not too far off neutral or even balance. The more radical the racquet is Head heavy or head light the larger the error in estimating the true SW.

To get the true SW use the TW swingweight calculator or a Babolat RDC that you know is actually calibrated correctly (Good luck with that!). Hope that helps.

Hi Bud,
Good thinking this is exactly as it works:
When you want to know the SW at a different position you multiply the square of the change in position with the weight.
Like you did in red.

Using this method it is possible to compare the RDC measurements with the calculation.

Thanks for the excellent responses. I'll try and locate a RDC machine (or buy a wooden dowel with a uniform cross section) to determine how close my calculations are to true SW. It's also clear now why tail-weighting also changes the expected result. I assume this is also why the RDC machines incorrectly subtracts SW when weight is placed below the 9 cm testing location.

I do understand it quite a bit better now, as well. I think the uniform beam concept is also why the COM is not exactly matching the balance point (it baffled me a bit at first but assumed it was something related to weight distribution)... the weight distribution varies slightly. If I was to cut the frame into many equal pieces, weigh each piece and then add them together it would become clear how the small variation in weight distribution affect the result.

So my final question or thought is this... when measuring the swingweight of a non-uniform object (i.e. beam), using either the swinging method or the RDC machine... will the SW ever be exactly correct? Will the swinging method of determining SW give an inaccurate result if a racquet has quite a bit of weight just inside the butt cap as well?

 

[SW Stringer]

Thanks for the excellent responses. I'll try and locate a RDC machine (or buy a wooden dowel with a uniform cross section) to determine how close my calculations are to true SW. It's also clear now why tail-weighting also changes the expected result. I assume this is also why the RDC machines incorrectly subtracts SW when weight is placed below the 9 cm testing location.

I do understand it quite a bit better now, as well. I think the uniform beam concept is also why the COM is not exactly matching the balance point (it baffled me a bit at first but assumed it was something related to weight distribution)... the weight distribution varies slightly. If I was to cut the frame into many equal pieces, weigh each piece and then add them together it would become clear how the small variation in weight distribution affect the result.

So my final question or thought is this... when measuring the swingweight of a non-uniform object (i.e. beam), using either the swinging method or the RDC machine... will the SW ever be exactly correct? Will the swinging method of determining SW give an inaccurate result if a racquet has quite a bit of weight just inside the butt cap as well?

" . . . So my final question or thought is this... when measuring the swingweight of a non-uniform object (i.e. beam), using either the swinging method or the RDC machine... will the SW ever be exactly correct? Will the swinging method of determining SW give an inaccurate result if a racquet has quite a bit of weight just inside the butt cap as well? . . . " If every racquet were uniform in weight such that every minute slice of the frame weighed the same as every other minute slice then we wouldn't need an RDC machine or the SW measuring method at the USRSA or TW. We could just use the moment of inertia equations for uniform beams. But since most racquets are non-uniform in weight distribution the swinging of the RDC (and other similar machines) and the pendulum swing of the TW method are what determines the exact distribution of the weight in the racquet and adjusts the swingweight accordingly. If you carefully measure the distances and times in the TW method you should be within 1% or less of the actual swingweight. Unfortunately I don't know what the accuracy of a properly calibrated Babolat RDC machine is. The usefulness of the RDC or TW swingweight measuring method lies not in it's absolute accuracy to a "standard" but in their ability to let the user match two or more of his racquets to the same swingweight number. Either the RDC (and other like machines) or the TW (USRSA) method should be more than adequate for that task.

 

[Bud]

" . . . So my final question or thought is this... when measuring the swingweight of a non-uniform object (i.e. beam), using either the swinging method or the RDC machine... will the SW ever be exactly correct? Will the swinging method of determining SW give an inaccurate result if a racquet has quite a bit of weight just inside the butt cap as well? . . . " If every racquet were uniform in weight such that every minute slice of the frame weighed the same as every other minute slice then we wouldn't need an RDC machine or the SW measuring method at the USRSA or TW. We could just use the moment of inertia equations for uniform beams. But since most racquets are non-uniform in weight distribution the swinging of the RDC (and other similar machines) and the pendulum swing of the TW method are what determines the exact distribution of the weight in the racquet and adjusts the swingweight accordingly. If you carefully measure the distances and times in the TW method you should be within 1% or less of the actual swingweight. Unfortunately I don't know what the accuracy of a properly calibrated Babolat RDC machine is. The usefulness of the RDC or TW swingweight measuring method lies not in it's absolute accuracy to a "standard" but in their ability to let the user match two or more of his racquets to the same swingweight number. Either the RDC (and other like machines) or the TW (USRSA) method should be more than adequate for that task.

It seems even the swinging method would operate based on average distribution of weight along the frame.

For example, what if 40 grams of weight was placed directly at 12 o'clock on the head of the frame (as the swinging method determines SW by swinging the frame from the middle of the stringbed)?

Would such a frame swing differently than a similarly weighted and balanced racquet, without so much polarized mass in one extreme location?

 

[Technatic]

I think that the swinging time on the RDC systems depends completely on the Moment of inertia and every difference should come out of the measurement, independent of the weight-distribution.

When you calculate with the weights you have to calculate the moment of inertia for the weights separately and add that to the total.

 

[corners]

My conclusions:

One - the TW empirical method for measuring swingweight is extremely accurate.

Two - some big box store in the Marietta, Georgia area should get their Babolat RDC calibrated.

Thanks for sharing your results/conclusions. TW uses the empirical method to calibrate their RDCs.

Everytime I see posts with people saying the at-home, empirical method is inherently, hopelessly flawed I kind of want to pull out my hair. I guess I should be thinking: go ahead, throw out established elementary physics principles, get yourself two scales and invent your own physics. It's absolutely not necessary, little Newton, but knock yourself out.

 

[Bud]

I think that the swinging time on the RDC systems depends completely on the Moment of inertia and every difference should come out of the measurement, independent of the weight-distribution.

When you calculate with the weights you have to calculate the moment of inertia for the weights separately and add that to the total.

However, when weight is added to a frame below the pivot point and then tested on the RDC (which uses the swinging method with the pivot point on the handle) the SW (moment of inertia) decreases.

Therefore, is it possible (in terms of physics) to decrease the true moment of inertia (i.e. swingweight) by adding weight to an object, regardless of the location?

Wouldn't this also be true for the TW swinging method if there was weight above the pivot point (which is located within the stringbed)?

 

[SW Stringer]

However, when weight is added to a frame below the pivot point and then tested on the RDC (which uses the swinging method with the pivot point on the handle) the SW (moment of inertia) decreases.

Therefore, is it possible (in terms of physics) to decrease the true moment of inertia (i.e. swingweight) by adding weight to an object, regardless of the location?

Wouldn't this also be true for the TW swinging method if there was weight above the pivot point (which is located within the stringbed)?

Statement 1: "However, when weight is added to a frame below the pivot point and then tested on the RDC (which uses the swinging method with the pivot point on the handle) the SW (moment of inertia) decreases."

I've never personally used an RDC machine or any of the other commercially available machines that measures swingweight. So I don't know the veracity of that statement. If that statement is true then there are three possible explanations: 1 - the operator doesn't know how to use the machine correctly, 2 - the machine is out of calibration, or 3 - the machine has an inherent design flaw.

Question 1: "Therefore, is it possible (in terms of physics) to decrease the true moment of inertia (i.e. swingweight) by adding weight to an object, regardless of the location?"

Answer: NO. Absolutely not.

Question 2: "Wouldn't this also be true for the TW swinging method if there was weight above the pivot point (which is located within the stringbed)?"

Answer: No.

Discussion: The generalized physics equation that describes the definition of moment of inertia (swingweight as used in tennis) is the integral of MD^2. Where M is the mass of the object and D is the distance(squared) from the rotational axis. The integral in discrete form is the summation of all MiDi^2, where Mi is the ith particle of mass located at Di distance (squared) from the rotational axis. The discrete integral (summation) can be simulated on a computer using a simple spreadsheet. I did this with the 30 inch table leg in an Excel spreatsheet. I broke the wooden dowel into 762 one millimeter (30 inches) slices each weighing 0.284777 grams and multiplied that weight by the distance squared from the pivot point which I chose at 4 inches (10 mm) from one end, which is the tennis industry standard reference for SW calculations. I added up all 762 MOI's. The calculated SW from the spreadsheet was 275.7648 kg-cm^2 versus the 276.8 that I got from the specific MOI equation for uniform rods given in a previous post. The two results agree with 0.38%. You could use this same model and add weights anywhere to the rod and NEVER decrease the MOI.

If you have a method or machine that measures MOI (SW) AND that shows a decrease in MOI with added weight anywhere then see the three possible explanations above. The physics says it's impossible.

 

[stangaele]

Hi guys,

I was at a Stringing Happening of Stringway in the Netherlands.
They explained a way to calculate the Swingweight of a racquet out of weighing the racquet.

Last week they sent out the explanation of this calculation, perhaps it is interesting for you:

gh is going to increase by adding weight at the top of the frame.also mass increases but it doesn't affect a lot the new result as gh is multiplied by the lenght of the frame.tell me if i'm wrong

 

[SW Stringer]

It seems even the swinging method would operate based on average distribution of weight along the frame.

For example, what if 40 grams of weight was placed directly at 12 o'clock on the head of the frame (as the swinging method determines SW by swinging the frame from the middle of the stringbed)?

Would such a frame swing differently than a similarly weighted and balanced racquet, without so much polarized mass in one extreme location?

If your question is "can two racquets with different weight distributions (one more polarized) have the same swingweight" then yes. For instance a heavy racquet that's massively head light can have the same SW as a lightweight racquet that's massively head heavy. (note: the word massively is used figuratively and not literally)

 

[Bud]

Statement 1: "However, when weight is added to a frame below the pivot point and then tested on the RDC (which uses the swinging method with the pivot point on the handle) the SW (moment of inertia) decreases."

I've never personally used an RDC machine or any of the other commercially available machines that measures swingweight. So I don't know the veracity of that statement. If that statement is true then there are three possible explanations: 1 - the operator doesn't know how to use the machine correctly, 2 - the machine is out of calibration, or 3 - the machine has an inherent design flaw.

Question 1: "Therefore, is it possible (in terms of physics) to decrease the true moment of inertia (i.e. swingweight) by adding weight to an object, regardless of the location?"

Answer: NO. Absolutely not.

Question 2: "Wouldn't this also be true for the TW swinging method if there was weight above the pivot point (which is located within the stringbed)?"

Answer: No.

Discussion: The generalized physics equation that describes the definition of moment of inertia (swingweight as used in tennis) is the integral of MD^2. Where M is the mass of the object and D is the distance(squared) from the rotational axis. The integral in discrete form is the summation of all MiDi^2, where Mi is the ith particle of mass located at Di distance (squared) from the rotational axis. The discrete integral (summation) can be simulated on a computer using a simple spreadsheet. I did this with the 30 inch table leg in an Excel spreatsheet. I broke the wooden dowel into 762 one millimeter (30 inches) slices each weighing 0.284777 grams and multiplied that weight by the distance squared from the pivot point which I chose at 4 inches (10 mm) from one end, which is the tennis industry standard reference for SW calculations. I added up all 762 MOI's. The calculated SW from the spreadsheet was 275.7648 kg-cm^2 versus the 276.8 that I got from the specific MOI equation for uniform rods given in a previous post. The two results agree with 0.38%. You could use this same model and add weights anywhere to the rod and NEVER decrease the MOI.

If you have a method or machine that measures MOI (SW) AND that shows a decrease in MOI with added weight anywhere then see the three possible explanations above. The physics says it's impossible.

Thanks and excellent reply.

So, to summarize... you broke the uniform object (e.g. dowel) into x number of pieces and then summed the individual MOI's where each piece has the same mass, correct? Have you tried the experiment breaking a non-uniform object into x number of pieces and then summing those pieces... with each piece being slightly different in terms of mass? Also, prior to cutting, making sure to measure the SW of the non-uniform object by either the swinging method or a RDC machine?

A number of TT members have conducted that experiment with a RDC machine... and it does subtract SW when additional mass is placed inside the butt cap (I believe Drakulie is one who has tried it). I'm assuming the additional butt weight, below the pivot point, is acting as a counterweight when the racquet starts swinging... making the head appear lighter than it actually is. This result is why I asked the question about the SW accuracy when measuring from a pivot point that is a significant distance from an object's endpoint.

 

[SW Stringer]

Thanks and excellent reply.

So, to summarize... you broke the uniform object (e.g. dowel) into x number of pieces and then summed the individual MOI's where each piece has the same mass, correct? Have you tried the experiment breaking a non-uniform object into x number of pieces and then summing those pieces... with each piece being slightly different in terms of mass? Also, prior to cutting, making sure to measure the SW of the non-uniform object by either the swinging method or a RDC machine?

A number of TT members have conducted that experiment with a RDC machine... and it does subtract SW when additional mass is placed inside the butt cap (I believe Drakulie is one who has tried it). I'm assuming the additional butt weight, below the pivot point, is acting as a counterweight when the racquet starts swinging... making the head appear lighter than it actually is. This result is why I asked the question about the SW accuracy when measuring from a pivot point that is a significant distance from an object's endpoint.

Q: "So, to summarize... you broke the uniform object (e.g. dowel) into x number of pieces and then summed the individual MOI's where each piece has the same mass, correct?"

A: Yes, figuratively speaking, I divided the 30 inch rod into 762 one millimeter slices, performed 762 MOI calculations for the individual contribution of each 0.284777 gram slice, and added them up to get the total MOI of the object. All done on the spreadsheet.

Q: "Have you tried the experiment breaking a non-uniform object into x number of pieces and then summing those pieces... with each piece being slightly different in terms of mass?"

A: I changed the value of the last slice at the end of the rod to 40 grams and it added over 173 kg-cm^2 to the original dowell that measured 276 bringing it to over 449 kg-cm^2. In a similar manner any one of the slices could be changed to a different weight to observe the change in total MOI. If you would like a copy of the spreadsheet to experiment with I'd be glad to email it to you.

''A number of TT members have conducted that experiment with a RDC machine... and it does subtract SW when additional mass is placed inside the butt cap (I believe Drakulie is one who has tried it).'"

They may well have identified a design flaw within the RDC units since the actual MOI cannot decrease when adding weight to an object.

 

[Bud]

Q: "So, to summarize... you broke the uniform object (e.g. dowel) into x number of pieces and then summed the individual MOI's where each piece has the same mass, correct?"

A: Yes, figuratively speaking, I divided the 30 inch rod into 762 one millimeter slices, performed 762 MOI calculations for the individual contribution of each 0.284777 gram slice, and added them up to get the total MOI of the object. All done on the spreadsheet.

Q: "Have you tried the experiment breaking a non-uniform object into x number of pieces and then summing those pieces... with each piece being slightly different in terms of mass?"

A: I changed the value of the last slice at the end of the rod to 40 grams and it added over 173 kg-cm^2 to the original dowell that measured 276 bringing it to over 449 kg-cm^2. In a similar manner any one of the slices could be changed to a different weight to observe the change in total MOI. If you would like a copy of the spreadsheet to experiment with I'd be glad to email it to you.

''A number of TT members have conducted that experiment with a RDC machine... and it does subtract SW when additional mass is placed inside the butt cap (I believe Drakulie is one who has tried it).'"

They may well have identified a design flaw within the RDC units since the actual MOI cannot decrease when adding weight to an object.

I'd love to look at the spreadsheet (my email is sbinsdca@aim.com)

I'm trying to verify that the RDC does actually subtract MOI for additional weight added below the pivot point. Hopefully, will have the answer within a few days.

 

[Technatic]

gh is going to increase by adding weight at the top of the frame.also mass increases but it doesn't affect a lot the new result as gh is multiplied by the lenght of the frame.tell me if i'm wrong

When mass at the top is added the distance Z changes and because the square of Z is in the calculation the SW will certainly change. It is best to calculate the individual MOI of added mass.

They may well have identified a design flaw within the RDC units since the actual MOI cannot decrease when adding weight to an object.

This would be interesting to know, but it also is the question “ why”?
When you hit a ball the actual pivot point will be somewhere in your arm so the extra weight in the butt cap still increases the power of the racquet.

I'm trying to verify that the RDC does actually subtract MOI for additional weight added below the pivot point. Hopefully, will have the answer within a few days.

When MOI is calculated all the mass works positive, it is not so that you deduct the MOI on one side of the pivot point from that on the other side.
In that case the MOI of a cylinder around its axis would be zero.

The MOI determines how much torque is needed to accelerate a total item around its axis.

My question is: For what reason do people add weight in the butt cap?

 

[Bud]

When mass at the top is added the distance Z changes and because the square of Z is in the calculation the SW will certainly change. It is best to calculate the individual MOI of added mass.

This would be interesting to know, but it also is the question “ why”?
When you hit a ball the actual pivot point will be somewhere in your arm so the extra weight in the butt cap still increases the power of the racquet.

When MOI is calculated all the mass works positive, it is not so that you deduct the MOI on one side of the pivot point from that on the other side.
In that case the MOI of a cylinder around its axis would be zero.

The MOI determines how much torque is needed to accelerate a total item around its axis.

My question is: For what reason do people add weight in the butt cap?

For a few reasons:

To increase the maneuverability of a frame. If adding 10g of silicone or lead inside the buttcap, you increase the HL balance of the frame by about 4 pts. So you receive a large return on a small investment, so to speak. This is usually where the debate begins as well. According to the RDC machine, adding weight near the pivot point doesn't change the frame's swingweight or negates it (when added just inside the buttcap). Therefore, according to the RDC, the frame's static weight is increased while maintaining (or even decreasing) the swingweight. However, we know that SW can never decrease when adding weight.

Many people (including pros) also add weight at 3/9 to increase stability of the head (known as twistweight or MOI perpendicular to the longitudinal swingweight axis). To counteract the change in balance along the longitudinal frame axis, weight is added just inside the buttcap to maintain the stock balance.

Silicone is also though to decrease harmful frame vibrations... so some players add 10-12 grams of silicone inside the handle (last 1-1.5" of the handle). To counteract the 3-4 point change in HL balance, weight is added to the head at 12 and/or 3 and 9.

So, in other words... some players add silicone first to remove vibration and then lead to re-balance or lead first and then silicone to re-balance... or both

Hopefully, it's a bit more clear after that explanation

 

[SW Stringer]

When mass at the top is added the distance Z changes and because the square of Z is in the calculation the SW will certainly change. It is best to calculate the individual MOI of added mass.



This would be interesting to know, but it also is the question “ why”?
When you hit a ball the actual pivot point will be somewhere in your arm so the extra weight in the butt cap still increases the power of the racquet.



When MOI is calculated all the mass works positive, it is not so that you deduct the MOI on one side of the pivot point from that on the other side.
In that case the MOI of a cylinder around its axis would be zero.

The MOI determines how much torque is needed to accelerate a total item around its axis.

My question is: For what reason do people add weight in the butt cap?

An additional reason beyond what Bud has added is the extra shock that a heavy racquet will absorb beyond what a light racquet is capable of doing - thus reducing the possibility of tennis elbow, etc.

 

[Irvin]

Patent Pending

Sorry I was so short before but I've been working on this for a long time. Now that my patent is pending I am willing to talk a little more about this.

In order to find the swing weight for a racket you need to determine the distance from a pivot point to the center of mass of the racket first. Unless you want to find the swing weight relative to the bottom of the racket. I have read the industry standard is 10 cm or 4 inches from the bottom of the racket because that is the mean location of the first knuckle on the dominant hand. I am not sure which one is used by which system or if some other distance is used by some manufacturers. In order to find the center of mass relative to some point other than one end of the racket you have to put the racket in motion unless your weight is evenly distributed.

Putting the racket in motion is what the TW and USRSA methods do. They swing the racket from a string located near the top portion of the racket as though it were a pendulum. Then the period of the swing determines distance from the pivot point to the center of mass using basic pendulum formulas for finding the length of a pendulum. It does not matter how much the racket weighs only the center of mass determines the pendulum time period. But the center of mass is controlled by how weight is distributed along the racket. The RDC does the same thing but it swings the racket from the handle and there is no need for conversion.

There are two points on a racket where weight does not affect the center of mass relative to the pivot point and they are the pivot point and the center of mass. Adding weight at either of these point will increase the total weight of the racket, AND SWING WEIGHT but will not change the center of mass relative to the pivot point.

Using the TW or USRSA method of since the racket is not swung by the handle the pivot point must be converted to some point on the bottom of the racket. I have no idea what point TW or the USRSA converts their pivot point to. It could be 4 inches, 10 cm or something else. Because of the blind spots at the pivot point and center of mass you can also get differences entered into the equation. Any or all of these differences could account for the differences in what I measured with the RDC and TW methods. I could have even preformed the procedure wrong. I seen pretty soon that in order to get a correct measurement I needed to swing the racket from the handle.

Rather than using a specific point (10 cm) I like to determine the pivot point depending on how each player grips their racket. My apparatus supports the racket at that point and allows the racket to pivot on that point. The rest is basic math. Right now I am using a stopwatch but I am working on a photointerrupter timer that will eliminate user reaction error.

Using my apparatus and methods I also measured my racket I used to come up with the RDC and TW swing weights. With no weight on the racket my method was the same as the RDC, with the weight in the low position my method was two kg*cm*cm lower than the RDC, with the weight in the middle position my method was the same again as the RDC, and with the weight in the high position I was four kg*cm*cm lower than the RDC.

Irvin

 

[stangaele]

hi irvin finally i came up with your method and i have to say that it was very very useful.are you going to make new tests to prove the validity (or not) of the TW method?

thanks in advance
daniele

 

[Irvin]

^^ I am not going to test any more with the TW method, too many variables. By the way when you say my method which method is that exactly?

Irvin

 

[stangaele]

i was referring to the first method you posted on this thread....i created two scales as you did before and then mesured the head and butt weight...it is incredible as i came up with very good results precisely 331 against 329 posted on tw...

 

[Irvin]

When you add weight to a racket the center of mass will move toward the weight unless the weight is added at the center of mass (or the pivot point.) If the weight is added on one side of the pivot point and the center of mass is on the other the weight at the center of mass will go down. It is not the total mass but the weight at the center of mass relative to the pivot point which is used to calculate swing weight. If weight is added on the opposite side of the pivot point the weight at the center of mass goes down. SW = distance * distance * weight. If distance and weight go down so does the SW.

Irvin

 

[Irvin]

i was referring to the first method you posted on this thread....i created two scales as you did before and then mesured the head and butt weight...it is incredible as i came up with very good results precisely 331 against 329 posted on tw...

OK that is good to identify the SW for the whole racket but not relative to a point somewhere on the racket. Great for finding the Center of mass too. It may work some of the time but there are many errors introduced with that method. It is close only sometimes.

Irvin

 

[stangaele]

by the way i think the tw method is also good and maybe the closest to RDC SW.my result was 325 kg*cm^2 against 329 on the review.not too bad