# Thread: The Balance of a Racquet

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Originally Posted by R20190

I believe, what you may be feeling is the difference in the slight variance in the diameter of the handle which certainly would affect playability as tightening of your forearm muscles are affected.
it is not! on my z-slash i paste the tape around the sides of the butt cap only, i'm extremely picky about the diameter of how my racquets are gripped and have a plastic vernier caliper to measure each time i re-grip my racquets. my target is usually 25mm x 28mm if not i will re-grip it (sorry.. pedantic scientist here..)

little bit of tape peeking out from side of butt cap

both Z-slash and I-slash are gripped to 28mm x 25mm

your calculation in using the distance 0.625m to calculate the moment is interesting, i would prefer to calculate it based on the centre of gravity since we are looking at free swing. the moment acts through the centre of gravity (there is no external force applied since there is no shuttle contact)

the reason why i chose exactly 2.6 grams on butt cap, was because i wanted to replicate the similar swing feel of the i-slash on the Z-slash, i have the BP down to exactly 283mm from the usual 295mm of the Z-slash, identical to the i-slash. this was how i managed to adapt to the Z-slash's swing speed immediately, with no need to re-calibrate my hitting timings at point of contact

I slash moment = W1 x D1
Z-slash original moment = W1 x (D1+12mm) since the centre of gravity was 12mm away

so what happens if i add lets say 1.2 grams on the head of the i-slash..
the BP shifts by abt 5mm!..
so in principle the moment that i will feel now, is (W1 + 5mm) x D1

vice versa.. which is why headheavy, even balance or light head balance is just a permutation of a narrow range of a couple of centimetres, yet significant swing differences..

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Originally Posted by visor
@vajrasatvva : we've been thru many times in previous threads. Obviously +1g on the top of the frame would have a significant effect on swing weight. But at the handle or butt, very negligible. Try wearing a heavy ring on your racket hand next time and see if you notice any difference.
having a ring on the racquet hand doesnt change anything significant because the ring is on the pivot!.. having some weight on the buttcap changes things because it affects the centre of gravity of the racquet by which the moment is calculated....

i know this had been debated before, but i thought i had to revive the discussion because i have a different opinion as to how the physics should be calculated...

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just to be clear here, i disagree with only the separate calculation of W1 and W2 in the original diagram in post 1.. i dont believe W1 and W2 to exist separately in a circular moment about a pivot.

i believe the contributions of both W1 and W2 (weights of shaft and head) to exist combined at the balance point of the racquet, because if you shift the pivot to below the balance point, the racquet is horizontal, the sum of moments is zero. there is no separate W1 and W2, if not the racquet will be lop sided if W1 is independent.

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5. Recently over the past year, instead of depending on wt and BP when choosing rackets, I've been weighing the racket head in a scale on a level surface with the tip of the racket on the scale while the tip of the handle rests on a box that is the same ht as the scale.

This is way more consistent for me in predicting swing wt than just the spec numbers. After getting Panda P Pros, Revelations, Victor MX80, MX70, Yonex VT80, VTZF, RKEP XP70, now I know that I prefer a very narrow range of 38.0-38.7g head wt, bare (ie unstrung, no overgrip) for a good balance between attack and defence for me. When I have time over the next wk, I'll start a thread more about my measurements.
Last edited by visor; 02-15-2013 at 04:33 PM.

6. ^^ PS: So now, to me it doesn't matter which overgrip and how much it weighs, and the handle wt inconsistencies from the factory is taken out of the equation.

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Originally Posted by blableblibloblu
do the experiments!! i was in agreement with R20190 theory/concept till i tried it myself to see a significant difference despite a tiny 2-3 grams at the end of the buttcap! leadtape's cheap, if you're worried you can try AC180 tangsten by yonex.

in swinging with the wrist as the pivot, it is still a single moment from the CG of the racquet

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Originally Posted by visor
Recently over the past year, instead of depending on wt and BP when choosing rackets, I've been weighing the racket head in a scale on a level surface with the tip of the racket on the scale while the tip of the handle rests on a box that is the same ht as the scale.

This is way more consistent for me in predicting swing wt than just the spec numbers. After getting Panda P Pros, Revelations, Victor MX80, MX70, Yonex VT80, VTZF, RKEP XP70, now I know that I prefer a very narrow range of 38.0-38.7g head wt, bare (ie unstrung, no overgrip) for a good balance between attack and defence for me. When I have time over the next wk, I'll start a thread more about my measurements.
that is interesting but by your method you have created 2 pivots for moment calculation, which does not exist until one swings and makes contact with the shuttlecock, with the shuttle creating the 2nd pivot.

of course the "moment" about the shuttle pivot would be different due to a CG shift in the racquet, but in terms of swinging, free air, it is still a single pivot around the wrist, so a 2 pivot system does not approximate it well..

ignoring the handle wt inconsistency as that is a manufacturing variable, if one carries out the experiments that i had done, the issue is still about shifting the CG of a racquet by 5mm to 1cm by just working on the butt cap itself..

try it!!! particularly if you have a headheavy racquet that feels hard to handle due to the torques from swinging. if you can get some AC182 (its only a few dollars for 4 strips), try 1 strip (abt 4 grams) on the butt cap alone and re-grip the racquet to the exact same diameters. the feel change is.. that significant

9. Yes, people should just try it out themselves instead of working it out in theory and make a significant shift in static bp by adding weight to the extreme end, something like 20mm ... No need for fancy Yonex strips, just add some layers of athletic tape in a strip around the buttcap to create the "bulge".

Out of curiosity though what are the weights of the I-Slash and Z-Slash now with both at 283mm bp?

Originally Posted by visor
Recently over the past year, instead of depending on wt and BP when choosing rackets, I've been weighing the racket head in a scale on a level surface with the tip of the racket on the scale while the tip of the handle rests on a box that is the same ht as the scale.
Is the shaft level this way? Think I tried it once and got nowhere near your values, probably did it wrong .
Last edited by demolidor; 02-15-2013 at 08:52 PM.

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Originally Posted by demolidor
Yes, people should just try it out themselves instead of working it out in theory and make a significant shift in static bp by adding weight to the extreme end, something like 20mm ... No need for fancy Yonex strips, just add some layers of athletic tape in a strip around the buttcap to create the "bulge".

Out of curiosity though what are the weights of the I-Slash and Z-Slash now with both at 283mm bp?

Is the shaft level this way? Think I tried it once and got nowhere near your values, probably did it wrong .
inclusive of string and grip, the overall weights of the I-slash is at about 97.6 grams whilst the Z-slash is at about 99.7 grams, with exactly identical center of gravities at 283mm..

11. I should note, I still have to replicate it myself but a.) have no need to atm and b.) have minimal court time to truly test it

Someone once had had a 275mm 3U AT700 this way (athletic tape to create the bulge). Well also, iirc, athletic tape single layer around the wooden handle and one very thin overgrip and another overgrip, Yonex Strong Grap, as top layer with minimal overlap (obviously no original grip on it anymore). Didn't thoroughly play around with it but thought it was noticeably different. But I already posted this once before and I don't recall anyone actually trying it till you, unaware, of the old thread came posting it here. The usual reply is indeed that "the grip size has changed is what probably makes it feel different".

But like I said until I have also tried it again, don't want to be drawing my own conclusion yet .

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Originally Posted by gundamzaku
come to think of it i do have a lot of free time during the winter because it's not really cycling season, at least not for me. if you do come to norcal bay area, no problem
Talking about winter, Toronto and surrounding areas just had about 30 cm of snow falling on our heads last week. You will see people riding bikes if the temp hit 40F. Just wondering what winter you are talking about. Most of my friends are residing around San Gabriel area, how far away from you place?

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Firstly, let me just clarify that although I have tried to explain my understanding of balance point I only use BP in the absence of being able to physically try a racquet.

I would always prefer to judge for myself as to whether a racquet’s balance or any other characteristic suits me by giving it a few swings and shots – even if it’s just bouncing a shuttle.

However there are times when you are unable to test a racquet physically, this is where I would rely on reviews, specifications and numbers such as balance points. The risk is that two racquets with the same spec and BP may not play the same so this is really a last resort. To help with this, it is often good to make comparisons with other similar racquets rather than just compare numbers.

Anyway, back to responding to the comments.

Originally Posted by ”vajrasattva”
i'm extremely picky about the diameter of how my racquets are gripped and have a plastic vernier caliper to measure each time i re-grip my racquets. my target is usually 25mm x 28mm if not i will re-grip it (sorry.. pedantic scientist here..)

If you are using vernier callipers to measure the width of your grip, I think you need to play more. You’re spending far too much time worrying about numbers than is actually necessary to improving your game on the court. I prefer to be guided by how a racquet feels in my hand than measurements to a hundredth of a millimetre!

Regarding the position of where you take moments, this does not matter. In static equilibrium, you can take moments anywhere – it’s the same.

Originally Posted by ”vajrasattva”
just to be clear here, i disagree with only the separate calculation of W1 and W2 in the original diagram in post 1.. i dont believe W1 and W2 to exist separately in a circular moment about a pivot.
Admittedly I’m a little surprised at this comment coming from a Scientist. The conventional simple method in calculating the moments and centre of mass of an object is pretty elementary physics.

Originally Posted by ”vajrasattva”
so what happens if i add lets say 1.2 grams on the head of the i-slash..
Originally Posted by ”vajrasattva”
the BP shifts by abt 5mm!..
so in principle the moment that i will feel now, is (W1 + 5mm) x D1
No this is wrong. It’s actually (W1 x D1) + (1.2g x 0.625m approx.)

Originally Posted by ”vajrasattva”
i believe the contributions of both W1 and W2 (weights of shaft and head) to exist combined at the balance point of the racquet, because if you shift the pivot to below the balance point, the racquet is horizontal, the sum of moments is zero. there is no separate W1 and W2, if not the racquet will be lop sided if W1 is independent.

Of course W1 and W2 does not exist separately in reality – it’s not a “mechanism”! We are talking theory. When we work out the moment, CoM, moment of inertia/area etc of a complex object, we break it down into a “system of particles” – the summation of which equates to the global system. I shouldn’t need to explain this.

The other reason why I have separated the frame, shaft and grip into constituent parts is because when calculating the characteristics of a non-uniform element we would separate these into components in order to model and understand their respective contribution. As a Structural Engineer, this is how we would calculate say, the second moment of area of an object or in working out the centre of mass of an object by hand – so we can observe and vary the contribution from different parts of the object. It also shows that the changes in mass of the handle does not have a significant impact to the “balance feel” of the racquet although it does change the overall balance point as I have said before.

Yes, with empirical measurements one could consider the whole object without doing the above theoretical calculations (including any variations such as grips, string, weights etc) and find the distance of the centre of mass quite easily and then amalgamate everything into one mass x distance which statically amounts to the same thing. I.e…

W x D = (w1 x d1) + (w2 x d2) + (w3 x d3)

Where W is the mass of the whole racquet and D is it’s distance to the fulcrum.

However I think you may have missed the point.

If we use your method and hypothetically start to increase the mass of the handle significantly, your total mass “W” would increase and “D” would decrease – which implies that it has become more head light. And on the face of it, that would seem right given that that’s all it is telling us. But is that really true?

I accept the model I have used is only a simple way of explaining the points I have mentioned. In reality this subject is far more complex than is necessary for the purpose of this discussion. A better method may be to adopt a dynamic model and work out the transfer of energy.

When a racquet is unmodified, using say the dry weight we are closer to comparing apples with apples. But often racquets will have different grips, strings and may even have lead tape to tailor it to the user’s requirements. When this happens, the racquet is no longer the same as stock so the BP is less meaningful when compared to another racquet.

As I have stated before, I have used static load / moment calculations to illustrate the concept of BP. However this is by no means the “be all and end all” of the subject. There are many other factors to consider, not least the fact that a racquet is not static during play so moments of inertia, aerodynamics, biomechanics, stiffness, strings, ambient conditions etc etc all affect the perceived feel of the racquet.

At the end of the day, it’s how a racquet feels in the player’s hand that’s important. Not numbers. These are just tools to give us some idea of what it’s like.

@R20190 : over the past 2 years I've started to get away from wt and BP measurements as they're not a very good estimate of swing wt even though it's the easiest way we have now, short of putting the racket on a swing wt machine.

15. double post........
Last edited by visor; 02-18-2013 at 12:44 PM.

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Just my 2 cents as a physicist.

Momentum of inertia
I think that the quantity that describes whether a racket is head-heavy or head-light is indeed the moment of inertia. However this is not described as a sum of W x D but as a sum of W x D^2 (distance squared). The distance D has to be considered from the pivot point, that is, where the hand holds the racket.

- The momentum of inertia is proportional to the energy that one needs to give to the racket to swing it (i.e. rotate) at a given (angular) speed.

- The total weight of the racket determines how hard it is to translate it at a given (linear) speed.

Balance point
The balance point is defined as the point, dividing the racket in two, where the sums of W*D to the left and to the right are equal.

It's clear it is a very different physical quantity from the momentum of inertia, the reason being that one is related to distances from the balance point whereas the other is related to distances squared from the grip.

This explains why changing the grip weight will affect the balance point while not changing the "head heaviness" feeling of the racket. Another way of seeing that is by adding, let's say, 50g at both ends of the racket. The balance point is not changed but the feeling is now extremely head-heavy (and unplayable...).

Since different rackets have more or less the same shapes, the balance point is somehow related to the "head-heaviness" feeling, but that's not the actual parameter that matters.

Hope that helps...

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Originally Posted by R20190
Firstly, let me just clarify that although I have tried to explain my understanding of balance point I only use BP in the absence of being able to physically try a racquet.

I would always prefer to judge for myself as to whether a racquet’s balance or any other characteristic suits me by giving it a few swings and shots – even if it’s just bouncing a shuttle.

However there are times when you are unable to test a racquet physically, this is where I would rely on reviews, specifications and numbers such as balance points. The risk is that two racquets with the same spec and BP may not play the same so this is really a last resort. To help with this, it is often good to make comparisons with other similar racquets rather than just compare numbers.

Anyway, back to responding to the comments.

i dont rely on reviews, specs, numbers, i buy it, try it if i m curious. experience/feel is more important over the all simulated calculations

Originally Posted by R20190
If you are using vernier callipers to measure the width of your grip, I think you need to play more. You’re spending far too much time worrying about numbers than is actually necessary to improving your game on the court. I prefer to be guided by how a racquet feels in my hand than measurements to a hundredth of a millimetre!

Regarding the position of where you take moments, this does not matter. In static equilibrium, you can take moments anywhere – it’s the same.

interestingly, i believe you mentioned the grip size difference as a variable, and i prefer to keep that as a constant particularly when comparing racquets. i play consistently twice a week, on occasion three times, particularly with both old elbow and shoulder injuries, its obvious if a racquet strains me, particular head heavy ones.

Originally Posted by R20190
Admittedly I’m a little surprised at this comment coming from a Scientist. The conventional simple method in calculating the moments and centre of mass of an object is pretty elementary physics.

No this is wrong. It’s actually (W1 x D1) + (1.2g x 0.625m approx.)

Of course W1 and W2 does not exist separately in reality – it’s not a “mechanism”! We are talking theory. When we work out the moment, CoM, moment of inertia/area etc of a complex object, we break it down into a “system of particles” – the summation of which equates to the global system. I shouldn’t need to explain this.

The other reason why I have separated the frame, shaft and grip into constituent parts is because when calculating the characteristics of a non-uniform element we would separate these into components in order to model and understand their respective contribution. As a Structural Engineer, this is how we would calculate say, the second moment of area of an object or in working out the centre of mass of an object by hand – so we can observe and vary the contribution from different parts of the object. It also shows that the changes in mass of the handle does not have a significant impact to the “balance feel” of the racquet although it does change the overall balance point as I have said before.

Yes, with empirical measurements one could consider the whole object without doing the above theoretical calculations (including any variations such as grips, string, weights etc) and find the distance of the centre of mass quite easily and then amalgamate everything into one mass x distance which statically amounts to the same thing. I.e…

W x D = (w1 x d1) + (w2 x d2) + (w3 x d3)

Where W is the mass of the whole racquet and D is it’s distance to the fulcrum.

However I think you may have missed the point.

If we use your method and hypothetically start to increase the mass of the handle significantly, your total mass “W” would increase and “D” would decrease – which implies that it has become more head light. And on the face of it, that would seem right given that that’s all it is telling us. But is that really true?

I accept the model I have used is only a simple way of explaining the points I have mentioned. In reality this subject is far more complex than is necessary for the purpose of this discussion. A better method may be to adopt a dynamic model and work out the transfer of energy.

When a racquet is unmodified, using say the dry weight we are closer to comparing apples with apples. But often racquets will have different grips, strings and may even have lead tape to tailor it to the user’s requirements. When this happens, the racquet is no longer the same as stock so the BP is less meaningful when compared to another racquet.

As I have stated before, I have used static load / moment calculations to illustrate the concept of BP. However this is by no means the “be all and end all” of the subject. There are many other factors to consider, not least the fact that a racquet is not static during play so moments of inertia, aerodynamics, biomechanics, stiffness, strings, ambient conditions etc etc all affect the perceived feel of the racquet.

At the end of the day, it’s how a racquet feels in the player’s hand that’s important. Not numbers. These are just tools to give us some idea of what it’s like.
thanks for the discussion, it was informative and worthy to spend some time myself to re-consider the physics, however the difference was strangely obvious.. i've no interest in the RSL evolution series racquet at the moment but they have a -1, 0, +2 sort base plate that can be changed. i supposed there is something interesting in here

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