# MgR/I where I = Swingweight + 20MR - 100M

#### frear

##### New User
Could someone please explain me where the +20MR part comes from?

Thank you in advance.

#### frear

##### New User
Thank you, I have extensively read the threads around the subject and I'm fine with the information with the exeption of the +20MR part of the formula for I about the pivot point. I thougth it was calculated at the butt, but I must be missing something.

#### Irvin

##### Talk Tennis Guru
@frear I still cant help you with the 20MR - 100M but I just got me a new racket. I wanted to add just a little mass and the best feature of the racket was how fast I could move the racket through the ball. I wanted to increase mass but not SW any more than I had to so I added 7 g at 6 o'clock. I loved the result. Just out of curiosity I wanted to check the MgR/i value and I used this link http://www.racquettune.com/MgR_I/.

I think I can measure the swing time (period) and length with exceptional accuracy and no math using the link. Long story short my time for 10 swings was 13.72 sec, axis of 64 cm, and a balance of 32 cm. That gave me an MgR/I of 20.97. I was very surprised.

#### travlerajm

##### G.O.A.T.
SW = "Swingweight" = swingweight moment of inertia about 10-cm axis
Ic = "Recoil Weight" = swingweight moment of inertia about center of mass
I = Swingweight moment of inertia about butt end
M = mass
R = distance from butt to center of mass

Ic = SW - M(R-10)^2
I = Ic + MR^2
I = SW - M(R-10)^2 + MR^2
I = SW - M(R-10)(R-10) + MR^2
I = SW - M(R^2 - 20R + 100) + MR^2
I = SW -MR^2 + 20MR -100M + MR^2
I = SW + 20MR -100M

#### floydcouncil

##### Professional
Useless gibberish.... I'd rather go hit 1k balls and hone my skills.

#### travlerajm

##### G.O.A.T.
Useless gibberish.... I'd rather go hit 1k balls and hone my skills.
I challenge you to a match - me and my finely-tuned racquet and minimal practice against you and your many hours of drilling.

#### frear

##### New User
I = SW - M(R^2 - 20R + 100) + MR^2
Thanks for taking the time and answering. That's now so obvious that I must say it's time to refresh my math..

Since you were so kind, I would take advantage to further ask you if it's to consider deprecated the steps 6-8 of your 2006 guide, ie finding the r' to add mass in order to optimize the plough-through.

I have found it possible to achieve both goals, but I should add a 16 full grams at the throat, which I'm not convinced of doing, and it clearly is quite a higher place than the 7", here often referred as the optimal location (I couldn't find any reference to support this though..).

Thank you.

#### frear

##### New User
@frear I still cant help you with the 20MR - 100M but I just got me a new racket. I wanted to add just a little mass and the best feature of the racket was how fast I could move the racket through the ball. I wanted to increase mass but not SW any more than I had to so I added 7 g at 6 o'clock. I loved the result. Just out of curiosity I wanted to check the MgR/i value and I used this link http://www.racquettune.com/MgR_I/.

I think I can measure the swing time (period) and length with exceptional accuracy and no math using the link. Long story short my time for 10 swings was 13.72 sec, axis of 64 cm, and a balance of 32 cm. That gave me an MgR/I of 20.97. I was very surprised.
Thank you, I've been using @stoneage apps quite a lot in the last few years.
They're nice, and I've learned a lot by using them (the stiffness is brilliant).
I also get consistent results, even if I get slightly different Swingweights when I measure with the iPhone versus the iPad. There's some device related error, but each device is self consistent and the delta is usually a fixed 2 points. So I'm fine

The guy didn't (won't, probably) add a mgr/I tool, and I perfectly see his point, but I won't complain about that until I'll have proved it works for me thoroughly. oh, if anything, I complain that the uniform rod graph is too little..

#### topspn

##### Legend
I challenge you to a match - me and my finely-tuned racquet and minimal practice against you and your many hours of drilling.
Lool..assuming you guys lived in relative proximity and can actually play, what would it actually prove? Nothing other then a better player on the day won or one of you is simply a much better tennis player. However out of curiosity, is anyone aware of this formula being used by anyone customizing in the professional ranks? And if so, how did you come about this information?

#### Irvin

##### Talk Tennis Guru
The guy didn't (won't, probably) add a mgr/I tool, and I perfectly see his point, but I won't complain about that until I'll have proved it
LOL Ya think not? Think again - http://www.racquettune.com/MgR_I/
All you need to measure is balance and hang point accurately and SwingTool will give you the period.

#### travlerajm

##### G.O.A.T.
Thanks for taking the time and answering. That's now so obvious that I must say it's time to refresh my math..

Since you were so kind, I would take advantage to further ask you if it's to consider deprecated the steps 6-8 of your 2006 guide, ie finding the r' to add mass in order to optimize the plough-through.

I have found it possible to achieve both goals, but I should add a 16 full grams at the throat, which I'm not convinced of doing, and it clearly is quite a higher place than the 7", here often referred as the optimal location (I couldn't find any reference to support this though..).

Thank you.
My advice is to ignore anything I posted prior to 2010 or so. Prior to that I was just getting into the experimentation process of figuring out how the physics of racquets and strings work. You've probably seen the thread below, but it's a good place to start if you are serious about learning how to fine-tune a racquet for high performance:

#### smirker

##### Hall of Fame
@frear I still cant help you with the 20MR - 100M but I just got me a new racket. I wanted to add just a little mass and the best feature of the racket was how fast I could move the racket through the ball. I wanted to increase mass but not SW any more than I had to so I added 7 g at 6 o'clock. I loved the result. Just out of curiosity I wanted to check the MgR/i value and I used this link http://www.racquettune.com/MgR_I/.

I think I can measure the swing time (period) and length with exceptional accuracy and no math using the link. Long story short my time for 10 swings was 13.72 sec, axis of 64 cm, and a balance of 32 cm. That gave me an MgR/I of 20.97. I was very surprised.
Being a complete dunce with anything mathematical (languages are my thing) how do you measure the pivot point in the link above? Swings from the top string as in the TW swing weight measurement tool?

#### frear

##### New User
My advice is to ignore anything I posted prior to 2010 or so. Prior to that I was just getting into the experimentation process of figuring out how the physics of racquets and strings work. You've probably seen the thread below, but it's a good place to start if you are serious about learning how to fine-tune a racquet for high performance:

Got it, thank you.

Of course I know the thread, I think I've read almost everything about the subject, and it surely is the reference for whom -like me- is curious about the outcomes. I'm still in the experimental part of the process, so leading all the way up.

#### frear

##### New User
LOL Ya think not? Think again - http://www.racquettune.com/MgR_I/
All you need to measure is balance and hang point accurately and SwingTool will give you the period.
Yes yes, I meant he is not adding it to the app (I know that calculator), as in the other threat he did not converge on the theory behind the mgr/i stuff. To be honest, I'm sceptical also, but what works works, so I'm checking that out before judging.

I've set up my own excel file and am tracking my few racquets...

#### GBplayer

##### Hall of Fame
@frear I still cant help you with the 20MR - 100M but I just got me a new racket. I wanted to add just a little mass and the best feature of the racket was how fast I could move the racket through the ball. I wanted to increase mass but not SW any more than I had to so I added 7 g at 6 o'clock. I loved the result. Just out of curiosity I wanted to check the MgR/i value and I used this link http://www.racquettune.com/MgR_I/.

I think I can measure the swing time (period) and length with exceptional accuracy and no math using the link. Long story short my time for 10 swings was 13.72 sec, axis of 64 cm, and a balance of 32 cm. That gave me an MgR/I of 20.97. I was very surprised.
Thanks for that link, my racquet has a value of 21.07 . Purely by accident over a year and a half of adding and subtracting weight. I could have saved a lot of time

#### Irvin

##### Talk Tennis Guru
Being a complete dunce with anything mathematical (languages are my thing) how do you measure the pivot point in the link above? Swings from the top string as in the TW swing weight measurement tool?
Just using a metric steel tape measure. It does not matter if you use the top string or some other string. I don't use the TW method to support my racket though I use cup hooks in the end of a 1x4 board. If the racket slides back and forth on the pencils you will have errors.

#### Irvin

##### Talk Tennis Guru
Thanks for that link, my racquet has a value of 21.07 . Purely by accident over a year and a half of adding and subtracting weight. I could have saved a lot of time
I was adding weight to my new racket new stick at 6 o'clock and quite by accident came up with what I liked at 20.97 I think. The big benefit of changing the weight at or very near the COM is it will not change the balance and you know the hang point does not change. If you add weight at the top of the grip you may have to check the balance when adding or taking off weight.

Then there is the 10 cm axis using @travlerajm's method. If you use SwingTool and measure your balance, hang point, and weight weight to calculate your SW you probably have some error. Then you start calculating MGR/I and create more error rounding off. The simpler the process the better off you are. But rather than having a link I would very much prefer to see the MgR/I tool incorporated into @stoneage's SwingTool app. I don't think Sten thinks MgR/I is all that great and many people agree with him but then are a lit of people that like it too.

EDIT: Using RacquetTune MgR/I you can change the period until you get exactly the period you want for your specific MgR/I value. Then add or remove weight near balance point until your period matches the time you need for your MgR/I. If you add weight at other locations that will change you Radius, SW, or Balance you may need to measure everything every time you change the weight. Of course adding weight at the top of the grip better hides the mass and a smaller amount of mass can make a bigger change in the period, and at the same time a lower change in SW and a larger change in RW.

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#### RanchDressing

##### Hall of Fame
Lool..assuming you guys lived in relative proximity and can actually play, what would it actually prove? Nothing other then a better player on the day won or one of you is simply a much better tennis player. However out of curiosity, is anyone aware of this formula being used by anyone customizing in the professional ranks? And if so, how did you come about this information?
There are plenty of instances where weight is placed at the top of the handle. P1 does it on novak djokovic's frame:
http://tinypic.com/view.php?pic=143ictu&s=8
Wilson has put weights at that same location inside the grips of their pro staffs:
http://i39.tinypic.com/b536uv.jpg
http://i43.tinypic.com/r1a2k7.jpg
http://i39.tinypic.com/2irb2g2.jpg

#### Nicholas Kakatsis

##### Rookie
I have been monitoring and implementing the theory behind MgR/I and although I am by no means an experienced player, I must admit that I have enjoyed the search and play around. Also the results have been satisfactory to say the least. Lastly a huge ge respect on all that devote theor time to post here their resewrch and findings.

My only comment is that i don't feel confident on the ways to measure MgR/I accurately. It is an output of certain variables in any way way you measure it - SW via SwingTool or a hand stopwatch - when ch both have margin errors. Any deviation or rounding causes big jumps in the output of the MgR/I. For instance i have used xls and Swingtool and got 20.99, and by using the Racketune the time for the 10 swings i used was 13.70 which on my racket specs gave me 20.66. If my timing was 13.79 it would have been 21. That 9 miliseconds could have been an error on my behalf....or not.

Any suggestions/method to make results less "volatile"?

#### Irvin

##### Talk Tennis Guru
Use RacquetTune MgR/I (http://www.racquettune.com/MgR_I/.) Measure your balance and hang point accurately and let SwingTool measure the period. Multiple the period from SwingTool by ten and you should be good to go.

#### Nicholas Kakatsis

##### Rookie
Use RacquetTune MgR/I (http://www.racquettune.com/MgR_I/.) Measure your balance and hang point accurately and let SwingTool measure the period. Multiple the period from SwingTool by ten and you should be good to go.
Irvin, thanks for the reply, how does one measure the period from teh Swing tool?

#### Irvin

##### Talk Tennis Guru
Irvin, thanks for the reply, how does one measure the period from teh Swing tool?
In SwingTool you need hang the racket, hit preview to make sure the camera is looking at the racket, swing the racket and hit start. After 15 periods it will tell you the average time. Multiply by 10 and your done. Mine always come up to the hundredth of a second (for ten swings) and +/- 0.02 seconds error (after multiplying the error +/- 0.002 by 10.)

#### travlerajm

##### G.O.A.T.
I have been monitoring and implementing the theory behind MgR/I and although I am by no means an experienced player, I must admit that I have enjoyed the search and play around. Also the results have been satisfactory to say the least. Lastly a huge ge respect on all that devote theor time to post here their resewrch and findings.

My only comment is that i don't feel confident on the ways to measure MgR/I accurately. It is an output of certain variables in any way way you measure it - SW via SwingTool or a hand stopwatch - when ch both have margin errors. Any deviation or rounding causes big jumps in the output of the MgR/I. For instance i have used xls and Swingtool and got 20.99, and by using the Racketune the time for the 10 swings i used was 13.70 which on my racket specs gave me 20.66. If my timing was 13.79 it would have been 21. That 9 miliseconds could have been an error on my behalf....or not.

Any suggestions/method to make results less "volatile"?
I agree that accurate timing is not easy. I have found that using an internet stopwatch is not accurate enough, since other background processes slow it down - I use the stopwatch on my iPhone.

I measure 20 swings. Then repeat the 20-swing measurement at least a couple more times, until I'm getting reproducible results. I can usually get the times reproducible to within +/- 0.02s , which would mean +/-0.01s for the 10-swing time.

#### Nicholas Kakatsis

##### Rookie
I agree that accurate timing is not easy. I have found that using an internet stopwatch is not accurate enough, since other background processes slow it down - I use the stopwatch on my iPhone.

I measure 20 swings. Then repeat the 20-swing measurement at least a couple more times, until I'm getting reproducible results. I can usually get the times reproducible to within +/- 0.02s , which would mean +/-0.01s for the 10-swing time.

Thanks guys for this. I implemented your methodology and the results now are more consistent between racketune and my xls spreadsheet. I am 5.8 but with long hands so looks like my optimal MgR/I is around 20.95.

#### Irvin

##### Talk Tennis Guru
I agree that accurate timing is not easy. I have found that using an internet stopwatch is not accurate enough, since other background processes slow it down - I use the stopwatch on my iPhone.

I measure 20 swings. Then repeat the 20-swing measurement at least a couple more times, until I'm getting reproducible results. I can usually get the times reproducible to within +/- 0.02s , which would mean +/-0.01s for the 10-swing time.
You may be able to reproduce your time within 0.02 seconds but I doubt it for 20 periods. Getting an accuracy of 0.02 seconds I'll never believe.

EDIT: Let's assume you can start and stop your stop watch with 1/4 second accuracy. Those two events account for +/- 1/2 second in 20 periods so the more periods you measure the better off you are. But those two events account for +/- 0.025 sec error in 20 periods and halving the number does not halve the error. SwingTool has an accuracy of +/- 0.002 sec per period (or that's what's claimed.)

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#### frear

##### New User
In SwingTool you need hang the racket, hit preview to make sure the camera is looking at the racket, swing the racket and hit start. After 15 periods it will tell you the average time. Multiply by 10 and your done. Mine always come up to the hundredth of a second (for ten swings) and +/- 0.02 seconds error (after multiplying the error +/- 0.002 by 10.)
Well, since SwingTool calculates swingweight right from the same data, I'd say just pick that SW number from SwingTool and use it in your excel.
The formula in the subject does the conversion of inertia from SW (@ 10 cm) to I (@ butt).
I think this provides a consistent method that does not require strarstopping any stop watch: no human error.
The better your phone's video resolution, the more accurate the sampling.

#### Irvin

##### Talk Tennis Guru
NO HUMAN ERROR? Do you seriously think SwingTool calculates the balance point, weight, and hang point of a racket? And if I had a SW of X with +/- 2 Kgcm^2 I would be happy. The period of a pendulum is a ratio of the pendulum axis to the balance point distance and the inertia at the axis (MgR/I.) If you can measure the period with +/- 0.002 sec accuracy why would you want to use any other method that just compounds the error? If you have two of the same frames where you can get the balance and weight the same, and the periods matched to 2/1000th second, why would you want to complicate everything with a spreadsheet? I want to play tennis with a racket that feels right to me and looking at numbers on a spreadsheet does not work for me.

EDIT: Many people have enough problem with just finding the SW or balance they like. So they start adding mass all around the racket searching for that mass placement that feels good. FACT - adding mass to a racket slows the racket down no matter where you add mass. FACT - adding mass to a racket may increase ball speed. So you go out and buy a racket you like. Then add mass. What happens when you add mass?

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#### Nicholas Kakatsis

##### Rookie
Let me elaborate a bit on what I did.

I have been until today using swing tool to calc SW which was then hard coded in my xls to calculate RW, MgR/I etc.... I used yesterday racket tune and got a significantly different MgR/I than the one in my xls, guessing that my stopwatch might be a bit off as it is my hand/eye coordination that plays a significant role.

So i took up Irvin's suggestion and used the period from SWingTool. After some minor tuning I got almost identical resutls from both methods. My xls and racket tune. Obviously this is dependent on use of the same variable (period from Swing Tool), which since it is a machine calculated and not hand/eye coordination result, I trust more as not necessarily 100% correnct but with significnatly lower margin error.

Thanks again guys

#### Irvin

##### Talk Tennis Guru
While I'm on my bandwagon let me say that I don't care what my SW is, that is just a number that I don't understand. What I do care about is how the racket feels in my hand, what it feels like to swing the racket and what it feels like when I hit the ball. It is much easier for me to tell when a racket feels like. And when it's right I don't need to come back and measue it unless I want two or more identical. When I drive a car I adjust my steering wheel and seat so I'm comfortable. I don't have to measure it it just feel right. But I wish when it all gets messed up I knew exactly where to put it back. So I measure specs but they don't help me play.

#### esgee48

##### Legend
Completely agree. Us damn humans can mod racquets to feel right, but that does not guarantee that we can hit the ball well because of a lot of factors that make us human (like lack of sleep, no focus, etc.) It just means we can't look at the racquet when we hit the ball out.

#### GBplayer

##### Hall of Fame
Completely agree. Us damn humans can mod racquets to feel right, but that does not guarantee that we can hit the ball well because of a lot of factors that make us human (like lack of sleep, no focus, etc.) It just means we can't look at the racquet when we hit the ball out.
Definitely the strings when thhe ball goes out, more than the racquet!

#### zalive

##### Hall of Fame
Thanks for taking the time and answering. That's now so obvious that I must say it's time to refresh my math..

Since you were so kind, I would take advantage to further ask you if it's to consider deprecated the steps 6-8 of your 2006 guide, ie finding the r' to add mass in order to optimize the plough-through.

I have found it possible to achieve both goals, but I should add a 16 full grams at the throat, which I'm not convinced of doing, and it clearly is quite a higher place than the 7", here often referred as the optimal location (I couldn't find any reference to support this though..).

Thank you.
Math says that MgR/I gain difference between 7'' spot and throat area is actually small. It's about the same.

The 7'' spot choice is therefore natural simply because of being invisible to the eye (lead on throat doesn't look as nice as on hoop). The second reason is that influence on swing weight is lower at 7'' (which some will prefer - I personally don't mind as much), with some increase of recoil weight (RW), which is also good. Also, it lowers balance towards head light - which is as well good (maneuverability and less recoil because of COM closer to the hand).

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#### Nicholas Kakatsis

##### Rookie
Thanks for taking the time and answering. That's now so obvious that I must say it's time to refresh my math..

Since you were so kind, I would take advantage to further ask you if it's to consider deprecated the steps 6-8 of your 2006 guide, ie finding the r' to add mass in order to optimize the plough-through.

I have found it possible to achieve both goals, but I should add a 16 full grams at the throat, which I'm not convinced of doing, and it clearly is quite a higher place than the 7", here often referred as the optimal location (I couldn't find any reference to support this though..).

Thank you.
Frar may i ask if you can post a link to this 2006 guide please?

Tks

#### frear

##### New User
I got almost identical resutls from both methods. My xls and racket tune. Obviously this is dependent on use of the same variable (period from Swing Tool), which since it is a machine calculated and not hand/eye coordination result, I trust more as not necessarily 100% correnct but with significnatly lower margin error.
That's just what I meant. @Irvin I didn't want to suggest that either one method was wrong, just that using the period form SwingTool (+racquet tune site) or the swingweight (+anyexcel) it's the same since both are based on the solid period from SwingTool.
Nothing more than this, really, may anyone use the same right math in the tool of choice!

EDIT: of course, just to be crystal clear, being the weight, bal, etc the same in both cases and input the proper way in the racquetune or excel.

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