# Mgr/I and racquet length - question for Trav

#### Nicholas Kakatsis

##### Rookie
Hoping Trav will read the below consideration of mine:

i had been playing with a shortened racquet by 1cm. 348,5gram, 31.5 balance 326 SW. I decidedto test out again a normal 68.5. All the lengths are strung lengths. Assuming you extend the above by 1 cm the new balance point would move to roughly 31.9cm. However such a move would materially change the mgr/I since the latter is dependent on the balance point in cm. So initially decided to maintsin the same 31.5 balance so as to keep mgr/I unchanged. I could not hit a normal ball! Felt too HL. So i am thinking for a different racquet length there is a different optimum mgr/I. A factor that i think supports this is that 31.5cm of balance for a 67.5cm racquet in points in almost 1 point different (more HH) than for a 68.5cm racquet. So i modded the racquet to maintain the same balance in points while obviously increasing the mgr/l. I will try this on Friday, but any input in advance would be greatly appreciated.

#### travlerajm

##### G.O.A.T.
Hoping Trav will read the below consideration of mine:

i had been playing with a shortened racquet by 1cm. 348,5gram, 31.5 balance 326 SW. I decidedto test out again a normal 68.5. All the lengths are strung lengths. Assuming you extend the above by 1 cm the new balance point would move to roughly 31.9cm. However such a move would materially change the mgr/I since the latter is dependent on the balance point in cm. So initially decided to maintsin the same 31.5 balance so as to keep mgr/I unchanged. I could not hit a normal ball! Felt too HL. So i am thinking for a different racquet length there is a different optimum mgr/I. A factor that i think supports this is that 31.5cm of balance for a 67.5cm racquet in points in almost 1 point different (more HH) than for a 68.5cm racquet. So i modded the racquet to maintain the same balance in points while obviously increasing the mgr/l. I will try this on Friday, but any input in advance would be greatly appreciated.
It is most likely that your MgR/I after extending was not matched as closely as you thought to your old spec. Usually, extending the frame will lower the MgR/I (because the swingweight is increased by a larger percentage than R). And then you will need to add mass above the top of the handle to restore the MgR/I to where it was. The swingweight will of course be higher, but the feel of the swing will be similar.

#### Nicholas Kakatsis

##### Rookie
I did not explain myself correctly And i apologize. Once i extended the racquet, SW went up significalty. I then removed weight from the head and re-distributed weight from top and bottom of the handle in order to reach same specs as before the extension. Smae specs = same mgr/l. Only now it does feel a totally different racquet.
what you suggest would make sense if i wanted to increase overall static weight which i don’t.
is there a way fr the mgr/ formula variables to take into consideration balance not in cm but in points? That way the difference would be accounted for when the racquet is extended/shortened. Now it does not.

#### Nicholas Kakatsis

##### Rookie
So mgr/i formula does not take into account racquet length. Only balance in cm for an unknown length. Sounds like the formula needs work to adapt to different lengths.

#### travlerajm

##### G.O.A.T.
So mgr/i formula does not take into account racquet length. Only balance in cm for an unknown length. Sounds like the formula needs work to adapt to different lengths.
No. I use it almost every day. It works the same for different lengths.

It is not my formula. It is the formula for the angular acceleration of a pendulum about the pivot point.

#### Nicholas Kakatsis

##### Rookie
I think it does not. Empirically speaking as i have not spent time to re adjust the formula: 34.25cm of Balance on a 68.5cm racquet is even right? But on a 67cm racquet is not - yes? All other variables equal (same SW AND STATIC) and same 34.25cm balance would yield same mgr/i for both racquets. Yes? Yet they play totally differently.

replacing balance in cm with balance in points would fix that issue (since ooints can take into consideration the length). Need to spendtime on the math though..

#### travlerajm

##### G.O.A.T.
I think it does not. Empirically speaking as i have not spent time to re adjust the formula: 34.25cm of Balance on a 68.5cm racquet is even right? But on a 67cm racquet is not - yes? All other variables equal (same SW AND STATIC) and same 34.25cm balance would yield same mgr/i for both racquets. Yes? Yet they play totally differently.

replacing balance in cm with balance in points would fix that issue (since ooints can take into consideration the length). Need to spendtime on the math though..
The laws of physics work the same for long pendulums as they do for short ones.

#### Nicholas Kakatsis

##### Rookie
Of course they do. I am not questioning the laws of physics.

#### travlerajm

##### G.O.A.T.
Of course they do. I am not questioning the laws of physics.
MgR/I is simply the formula for angular acceleration of a pendulum.

If two racquets have the same MgR/I and swingweight and one is longer than the other, they will feel the same when you swing them, but the feel and response of the ball will differ because the longer one has less mass in the head and slightly higher speed at the impact point.

#### tennisbike

##### Professional
Re MgR/I， swingweight，Balance point...
I am assuming that we are all modding rackets to achieve a certain feel. I want a stick to hit good n to be honest and I do not always know what that is. And often what is good can changes from day to day.
Those spec. the numbers are all numbers that we human invented to mean something, to approximate something. But as far as how a racket play, those numbers suggest something. I am not saying they are not valid. For me they are guidelines. Each one of us need to determine how to use those number.
For me, a high mass is more difficult to accelerate linearly. Yes, difficult to muscle at the last second for adjustment during a stroke. Does it swing slower? Maybe, maybe not. Once the stick gets moving it can come around quickly. T2000 actually whips around pretty good.
High moment of inertia stick less Manuverable? What does that mean? Difficult to volley？depending on how you swing or move the stick, I is different depending on where your axis is located.
MgR/I is even more tricky. I get force x lever arm/ I, but what and where is the force vector acting in relation to the object, where is r and that again will define your I.

Then even if you can define all that and do the math, you still need to coorelate to your experience. I think you discovered that the matching no. do not match performance.

I guess ultimately you have to find your answer. Only your hand can tell you what to do. Good luck and have fun.

#### Nicholas Kakatsis

##### Rookie
they will feel the same when you swing them,
I will disagree with that based on exactly what you said

because the longer one has less mass in the head and slightly higher speed at the impact point.

#### travlerajm

##### G.O.A.T.
I will disagree with that based on exactly what you said
The angular acceleration will be the same, so they will feel exactly the same when you shadow swing without the ball. But they won’t feel the same when the ball hits the stringbed.

#### Nicholas Kakatsis

##### Rookie
With all due respect i personally don't care about shadow swings. I have used your formula in the same context as tennisbike suggested for many years now and definitely thank you for introducing it to us. That said, I am no physics guy so I rely on the more cognizant to make statements. What i do understand is that once you have collision in the double pendulum system - which by definition is chaotic in the second part - things change quite a bit. And since center of mass is a vital component in the process having only the R (ie 31cm) and not R relative to the length (ie 31cm but for an xcm of legth) is not enough.

#### travlerajm

##### G.O.A.T.
With all due respect i personally don't care about shadow swings. I have used your formula in the same context as tennisbike suggested for many years now and definitely thank you for introducing it to us. That said, I am no physics guy so I rely on the more cognizant to make statements. What i do understand is that once you have collision in the double pendulum system - which by definition is chaotic in the second part - things change quite a bit. And since center of mass is a vital component in the process having only the R (ie 31cm) and not R relative to the length (ie 31cm but for an xcm of legth) is not enough.
It sounds like you are trying to use the MgR/I formula for something else. The formula just tells you how fast the racquet will swing into the ball and how much force you need to apply to get the racquet to the ball. It doesn’t tell you anything about the impact of the ball on the strings.

#### tennisbike

##### Professional
I think it does not. Empirically speaking as i have not spent time to re adjust the formula: 34.25cm of Balance on a 68.5cm racquet is even right? But on a 67cm racquet is not - yes? All other variables equal (same SW AND STATIC) and same 34.25cm balance would yield same mgr/i for both racquets. Yes? Yet they play totally differently.

replacing balance in cm with balance in points would fix that issue (since ooints can take into consideration the length). Need to spendtime on the math though..
Compare (a) your example, i.e. same 34.25 cm balance point from end between 68.5 cm and 67 cm length sticks, to (b) zero points on 68.5cm and 67 cm length sticks. (mass added to identical, but how to add to same SW?)
Would (a) or (b) play more similar to each other?

For me, personally, balance point reference to end cap is more useful. And I only use trial and error method and typically reach between 31.5 to 32 cm. And for me SW and Mgr/I and double pendulum are interesting ideas but not useful, I am ignorant to them.

Most people are confused between mass and weight already so.. adding r and moment of inertial, which is the sum of mr^2 is beyond even me. That is calculus stuff, integrals. And seriously we do not all swing the racket the same way (atp vs wtp, old school, modern, neo-modern...)