# MgR/I Question/Example

#### dave t

##### Rookie
So I took a shot at using MgR/I (thanks @zalive) - I was a bit surprised I ended up pretty close to 21.

Here are my current stats:
M: .340
R: 32.385
SW: 327 (as measured by my stringer - I've always thought his numbers are slightly low...going with it here)

MgR/I = 21.03 (if my math is correct)

How could I lower that number? Would it have to become more HH? How could I keep it relatively close to 21 while increasing SW?

Also I don't know if this is significant but I'm about 6'0" and do not use a wristband...

#### Irvin

##### Talk Tennis Guru
Inertia is a function of Mass and Radius. As mass and balance (M&R) go up so does SW (I.) Therefore, all you need to do is add mass above the center of mass.

As far as checking the MgR/I, @stoneage had an app that used the swing time, balance point, and axis alone to compute the MgR/I value. http://www.racquettune.com/MgR_I/index.php I think that is much more accurate that any calculation you may use.

EDIT: The reason I think it is more accurate is normally the axis used for the SW axis is unknown. You may assume the axis was 10 cm or 10.16 cm but more often than not that's not the case. And there is too much rounding off of too many measurements to make you SW figure accurate. The more rounding and false assumptions you can eliminate the more accurate you results will be.

But on the other hand if you SW, mass, and balance are the same it is IMPOSSIBLE for your MgR/I to be any different unless you have some method of changing gravity. Therefore do you really think there is any added value to MgR/I? MgR/I is nothing but a scientific babble.

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#### dave t

##### Rookie
Interesting stuff but I'm not really looking to get into a right/wrong debate - MgR/I was suggested to me as a starting point for figuring out the mass I'm adding to the handle of my racquets (and more specifically how much at 7" and how much at the butt). I don't know if it's right/wrong but my racquet feels better now that it's closer to 21, so i think it may have some merit.

But if you don't recommend paying attention to MgR/I - could you point me in the right direction? Thanks.

#### Irvin

##### Talk Tennis Guru
Interesting stuff but I'm not really looking to get into a right/wrong debate - MgR/I was suggested to me as a starting point for figuring out the mass I'm adding to the handle of my racquets (and more specifically how much at 7" and how much at the butt). I don't know if it's right/wrong but my racquet feels better now that it's closer to 21, so i think it may have some merit.

But if you don't recommend paying attention to MgR/I - could you point me in the right direction? Thanks.
I'm not looking to getting into a argument either. But it seems like everyone get caught up on numbers that have no real meaning to them and may or may not be obtainable. I'm not saying that SW and MgR/I have no value or meaning they do but no one knows what it really is.

Let's assume you like a racket that weighs x grams or ounces and has a balance of y cm, inches, or points. To obtain that exact mass and balance there are an infinite (not quite but most believe it) number of z inertia values. Really there is a finite number because your accuracy goes out the window when you fine tune down far enough.

So let's assume there is a finite number of SWs, TWs, MgR/I values or what ever you want to use to measure or fine tune your racket. Let say you want to narrow down the mass to whole numbers only, and you want to narrow down the balance to millimeters only. I say that because it gives you a finite number of weights and balance points. If your racket's weight or balance is less than +/- 0.5 g or mm you will never know it no matter how good your are. If you can tell the different you can buy more exact measuring devices.

So now we are left with the Inertia of your racket. Inertia is often measured using SW, TW, RW, MgR/I, or whatever else someone may dream up. But for and 1 combination of x mass, y balance, and z inertia (SW, TW, RW, & MgR/I) around any specific axis there will be 1 period of the Racket. The period of a physical pendulum (racket) is determined by the distance from the balance point to the center of mass and the inertia around the axis. The period is the time it takes for the bracket to swing back and fourth once around an axis.

Swing tool is an iOS device app that will measure the period down to 1/1,000th of a second with usually witching 0.002% accuracy. Match the mass, balanance, and period to what you like and nothing else really matters. Match the mass, balance, and period to within +/- 1 g, +/- 1 mm, and +/- 0.01 sec and your SW, TW, RW, and MgR/I are all exactly the same.

EDIT: If you don't have an iOS device to use Swingtool you can use a stopwatch and time for 10-20-30 or more swings. Even a stop watch is so accurate you can't tell the difference.

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#### zalive

##### Hall of Fame
So I took a shot at using MgR/I (thanks @zalive) - I was a bit surprised I ended up pretty close to 21.

Here are my current stats:
M: .340
R: 32.385
SW: 327 (as measured by my stringer - I've always thought his numbers are slightly low...going with it here)

MgR/I = 21.03 (if my math is correct)

How could I lower that number? Would it have to become more HH? How could I keep it relatively close to 21 while increasing SW?

Also I don't know if this is significant but I'm about 6'0" and do not use a wristband...
Lowering MgR/I means slowing racquet's head a bit - is that what you want to do?
Lower MgR/I means slower, while higher MgR/I means faster. Value 21 is considered as some approximately neutral point at which swing speed feels natural, though it's really personal.

You can lower MgR/I by putting some mass in the upper hoop - putting lead at 12 decreases MgR/I the most.
You can increase MgR/I by putting some mass at the top of the handle (7'' from the butt cap) or anywhere at the throat.
Even dampener increases MgR/I, especially if placed next to grommets at 6 o'clock.

#### Irvin

##### Talk Tennis Guru
So I took a shot at using MgR/I (thanks @zalive) - I was a bit surprised I ended up pretty close to 21.

Here are my current stats:
M: .340
R: 32.385
SW: 327 (as measured by my stringer - I've always thought his numbers are slightly low...going with it here)

MgR/I = 21.03 (if my math is correct)

How could I lower that number? Would it have to become more HH? How could I keep it relatively close to 21 while increasing SW?

Also I don't know if this is significant but I'm about 6'0" and do not use a wristband...
How far is the top cross from the butt of the racket, and how far would like to lower your MgR/I, and raise your SW?

EDIT: Do you want your balance to stay the same?

#### dave t

##### Rookie
The distance from butt to top cross is approx 24 7/8" or 63.1825 cm. I guess my goal would be to increase swingweight but keep the balance similar or slightly more HL if the racquet gets heavier.

I like the way my racquet plays and feels now. But I've also ended up liking every addition of weight i've tried (I've gone up in pretty small increments), so I'm kind of curious how I should go about further customizing...

As you can tell, I'm not a physics or math nerd - but this stuff is intriguing to me. So adding weight at 7" increases MgR/I because it adds mass/SW without affecting balance much? Or is there something else going on?

#### Irvin

##### Talk Tennis Guru
The distance from butt to top cross is approx 24 7/8" or 63.1825 cm. I guess my goal would be to increase swingweight but keep the balance similar or slightly more HL if the racquet gets heavier.

I like the way my racquet plays and feels now. But I've also ended up liking every addition of weight i've tried (I've gone up in pretty small increments), so I'm kind of curious how I should go about further customizing...

As you can tell, I'm not a physics or math nerd - but this stuff is intriguing to me. So adding weight at 7" increases MgR/I because it adds mass/SW without affecting balance much? Or is there something else going on?
Let me do some math for you and I get back later.

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#### Irvin

##### Talk Tennis Guru
Here is a link to computing MgR/ using the period timing, balance, and hang point:
http://www.racquettune.com/MgR_I/index.php
Plugging in your figures (assuming the SW you were given is correct) your time for 10 periods should be around 13.95 seconds. If your period times 10 is not that you will get a different MgR/I. You'll have to work backwards then to compute your SW if that's a concern for you.

So you want to raise your SW. I'm going to assume 327 was correct and you want to go up to 330.
New SW = Old SW + mdd where m is the mass in Kg and d is distance in cm from 10 cm axis
330 = 327 + m*57*57 I'm assuming the inside of top of frame is 57 cm from 10 cm axis
3 = 3249m
.009 = m that's in Kg though so you're looking at about 1 g @ 12 o'clock to raise SW to 330 (2 g is 333 etc.)

Here now is where you start chasing your tail adding any amount of mass at the head will raise you center of mass. Raising the COM will will speed up the period of time for 10 swings. Think of it as a weight on a string. The shorter the string between the weight and the axis the faster the period. But at the same time you increased the recoil weight or inertia of the racket which will have the opposite effect slowing down the period. So let's just assume they are pretty close to cancelling each other out.

Now let's look at the opposite end of the racket (the butt.) You want to slow down your period which will in turn drop you MgR/I value. To slow down your period you want to move the COM away from the axis on that top string and you want to increase the inertia. The best place to add weight to lower the COM and increase the inertia is as far down on the butt as you can possibly add it. If you add mass at 7" your COM does not drop as much and your inertia does not increase as much so it will take more mass to do the same thing. I hope that helps explain what I said earlier where you should be more concerned with the period than MgR/I. Because the period is actually controlling your Inertia, SW, and MgR/I.

If I were customizing for mysel I would first add mass to the outer portion of the hoop if I wanted to raise TW. Then add mass to the top of the racket if I wanted to raise the SW. Finally I would add mass to the lower end to fine tune the racket.

Granted matching multiple rackets is a lot more complicated than that but you should have the idea I hope.

EDIT: If I were matching rackets I would get the mass and balance the same then match the periods when swinging from identical axes.