# Thread: Calculations of Momentum P=mv, and Kinetic energy KE=(mv^2)/2 of a racket on shuttle

1. Wow... now this is getting very interesting. Thanx for the work @craigandy !

I have a few broken rackets that I can also chop off to measure the head wts.

2. The Tracker itself, the link is on this thread, I did not create it, it was out their free to use so have a look. It included all sorts of readings that you could use(which i couldn't understand). I used the Vx reading which is linear, there was Vmagnitude/Vy and stuff but I never bothered with it.
The problems with the tracker was each frame is only available to plot every 0.4 seconds and that the shuttle got blurry. I would assume each frame every 0.05second would be waayy more suitable. So that is a big let down. (also I did not experiment enough, only a handful of times with one racket)(just so nobody gets confused the experiments I posted earlier in the thread were not used this time because for instance I could not get a hold of FHF's racket)

For cor the formula was just the ratio speed in speed out. V found using the tracker.(problem is I didn't spend all day getting different results to compare, did it a couple times one type racket clamped )

I stated in my post a couple above how I went about measuring the head weights and guessed the head weight of the racket used in the experiment using this technique(I chopped them 1/2 inch down from middle of the T).
Problems - this was a bit weird both the rackets I used and chopped were head heavy, don't know if doing this would correlate with for instance a head light racket or any other rackets, maybe just luck. No idea)

The formula used to check all of this stacked up was given up by Line & length and is explained in one of the quotes in post #1

I don't know it would be such a good idea to improve this experiment but to completely reinvent it.

3. Originally Posted by amleto
Nice. How did you do the CoR test? Throw a shuttle at a clamped racket?

In summary:
CoR ~= 0.69.
pseduo-head-weight is a good approximation of the mass of the actual head of the racket.

The linear approximation equation closely matches tracker values.

TBC: Exact methodology for the tracker needs to be determined:
What axis do you set up to measure the velocity? horizontal? or aligned with shuttle exit velocity vector?
I calibrated the video with a length of wood in the close background level with where I was chucking the shuttle.

I used the Vx reading(horizontal) and to be fair the shuttle went in and out fairly horizontal with regards to where the points got plotted. The tracker gave me the speeds and I took the velocity reading of the plotted spot that was closest in and again the velocity reading of the closest plotted point out.

4. Oops tired, I said the video frame allowed the plot every 0.4seconds but meant to say 0.04 seconds and 0.005 seconds would be more suitable.

5. I'm thinking about this racquet business and distribution of weight and contact area and it would be easier if someone with an unused/ broken racquet and familiar with the removal of the handle and cone of the racquet could post if they are willing to sacrifice their racquet for this as the method I am thinking would be much easier and more reliable with a uniform shape and density throughout the frame( including shaft). Handle and strings would affect this. I'm just about to sleep so it's a sketchy idea at best atm but I'll mull it over tomorrow and post a proper method for calculating weight distribution when I have the time for someone else to do and post the results of for people to use in their calculations. Thanks in advance

6. @craigandy : why did you cut off the head where you did instead of right at the T? You probably added extra 1-2 g to the head wt measurement.

7. Originally Posted by visor
@craigandy : why did you cut off the head where you did instead of right at the T? You probably added extra 1-2 g to the head wt measurement.
I thought the T joint might be a place where a lot of the head weight might be put, in a head heavy racket so thought it would be unfair to chunk into it, probably completely wrong. I took the head to be where, for reference in an old racket where the metal t joint would end down the shaft.

8. Originally Posted by craigandy
I thought the T joint might be a place where a lot of the head weight might be put, in a head heavy racket so thought it would be unfair to chunk into it, probably completely wrong. I took the head to be where, for reference in an old racket where the metal t joint would end down the shaft.
Hmmm... makes sense. Looks like I'll cut mine right at the T, and then also cut and weigh a little 1/2 inch of shaft from the T to see how much that section weighs.

9. Originally Posted by visor
Hmmm... makes sense. Looks like I'll cut mine right at the T, and then also cut and weigh a little 1/2 inch of shaft from the T to see how much that section weighs.
I'm thinking that actually the weight of the shaft will also be part of the head weight but I'm still thinking this through so don't take my word for it.

10. that's true, but it may not be significant - have to pick a head light racket to find the worse case scenario.

11. Originally Posted by amleto
that's true, but it may not be significant - have to pick a head light racket to find the worse case scenario.
or make one yourself - attach some dowling or something to one of the beheaded rackets so that the total length is restored to ~680mm and repeat the weighing measurements

12. Just thinking further on craigandy's idea of comparing rackets of differing head wts swung at differing max racket speeds, without the need to measure those pesky shuttle speeds.

Assumptions:
1. That one swings a racket with a certain head wt at a certain max speed, and that another racket with the heavier head wt will be swung at a max speed that is lower than the lighter head wt.
2. That these max racket speeds are comfortably reproducible over many successive swings, ie good technique (please, no panhandle grip! ) and near but not 100% effort, to avoid muscle fatigue and also more accurately reflect reality.
3. Linear collision at strike.
4. C is the same for both rackets. Obviously, same strings, tension, shuttle, conditions.

From Line and Length's equation for partially elastic linear collisions:
Vs/Vr = (C + 1)*Mr/(Mr+Ms)

Vs = (C + 1)*Mr*Vr/(Mr+Ms)

Now if Vs of racket 1 is set to Vs of racket 2, ie you want the heavier racket to hit at least the same shuttle speeds as the lighter one:

(C + 1)*Mr1*Vr1/(Mr1+Ms) = (C + 1)*Mr2*Vr2/(Mr2+Ms)

Mr1*Vr1/(Mr1+Ms) = Mr2*Vr2/(Mr2+Ms)

Hence we can see, as expected from conservation of momentum, how much faster one needs to swing a lighter racket to compensate for lower head wt, or alternately how much more head wt one needs to compensate for a maxed out swing speed.

Now, time to check out that tracking software link to check out my swing speeds with my various rackets...

13. Forgot to summarize the final equations for racket 2:

Vr2 = Vr1*Mr1/Mr2*
(Mr2+Ms)/(Mr1+Ms)

Mr2 = Mr1*Vr1/Vr2*(Mr2+Ms)/(Mr1+Ms)

14. You could be only something here visor, but if my theory is correct, head weight will actually be acting from the pivot of the racquet (the handle) and so the weight of the player and their arm+shoulder plus loss of energy down the arm would affect this massively as different biological tissue has different density. This is would affect the reading for head weight you get due to different mass on the other side of the pivot and the rules regarding coupling and angular momentum. This means what is true for one player isn't true for the other. e.g. Taufik hitting a 300km smash and FHF doing it would do it totally differently.

But perhaps the differences between intermediate players would be smaller due to the lower string tensions, longer+less powerful swings etc. There are quite a lot of variables here which is why I'm taking so long thinking this through.

15. Originally Posted by TheNotoriousLIG
You could be only something here visor, but if my theory is correct, head weight will actually be acting from the pivot of the racquet (the handle) and so the weight of the player and their arm+shoulder plus loss of energy down the arm would affect this massively as different biological tissue has different density. This is would affect the reading for head weight you get due to different mass on the other side of the pivot and the rules regarding coupling and angular momentum. This means what is true for one player isn't true for the other. e.g. Taufik hitting a 300km smash and FHF doing it would do it totally differently.

But perhaps the differences between intermediate players would be smaller due to the lower string tensions, longer+less powerful swings etc. There are quite a lot of variables here which is why I'm taking so long thinking this through.

I think you must be on to something. I have tried headlight rackets before and the racket speed feels much faster, but smashes not as fast even though swing feels fast. With the formulas, Vr needs only to be increased slightly to negate head mass benefit. So their is something in all that that needs to be discovered.

On another note -
I found a website for tennis claiming they new the perfect racket weight for tennis but I used it for badminton. The formula was arm mass g times shuttle mass g the sqrt the answer. They say the average human arm is about 2000g and shuttle about 5g mulltiply together and sqrt answer = 100g perfect racket weight for power.
The most powerful racket I have ever owned for smashing is my Zforce, which gripped and strung has a total mass of 100g.
http://www.racquetsportsindustry.com..._ideal_ra.html

16. Originally Posted by craigandy
I think you must be on to something. I have tried headlight rackets before and the racket speed feels much faster, but smashes not as fast even though swing feels fast. With the formulas, Vr needs only to be increased slightly to negate head mass benefit. So their is something in all that that needs to be discovered.

On another note -
I found a website for tennis claiming they new the perfect racket weight for tennis but I used it for badminton. The formula was arm mass g times shuttle mass g the sqrt the answer. They say the average human arm is about 2000g and shuttle about 5g mulltiply together and sqrt answer = 100g perfect racket weight for power.
The most powerful racket I have ever owned for smashing is my Zforce, which gripped and strung has a total mass of 100g.
http://www.racquetsportsindustry.com..._ideal_ra.html
Exactly, its the same for me which is what got me thinking about it. I'm a very short, light, skinny person, but I have never really had any trouble using head heavy racquets or heavy racquets but others much bigger+stronger than me say they think their arms are about to fall off :P so I thought maybe how power and strength is channelled and through what mediums makes a difference perhaps. I don't have much muscle but it is very taut, well-conditioned muscle whereas the people that tried heavy racquets I have had, e.g. N90, VTZF and VT80, MX80 etc have been bigger but their muscle isn't as well conditioned and they also had some fat etc. so I'm thinking of how much energy is put and how much is got out and with what energy release and absorption along the way. Might give a clue to how a tiny guy like Taufik could hit the shuttle the way he did both on his backhand and forehand with power unmatched by much bigger players like Chen Long, Lin Dan, JJS, FHF etc. No one could transfer energy to the shuttle on a backhand or short swing forehand shot like him.

But its all just theory atm, need to get some of these theories tested with paper and pen, and if all makes sense, then practically later. Interesting thing about the ideal racquet weight there. I wonder how much it accounts for bp though. Maybe it could be refined to use a value of swing weight to arm weight which I suspect would be more accurate perhaps?

17. Originally Posted by TheNotoriousLIG
Exactly, its the same for me which is what got me thinking about it. I'm a very short, light, skinny person, but I have never really had any trouble using head heavy racquets or heavy racquets but others much bigger+stronger than me say they think their arms are about to fall off :P so I thought maybe how power and strength is channelled and through what mediums makes a difference perhaps. I don't have much muscle but it is very taut, well-conditioned muscle whereas the people that tried heavy racquets I have had, e.g. N90, VTZF and VT80, MX80 etc have been bigger but their muscle isn't as well conditioned and they also had some fat etc. so I'm thinking of how much energy is put and how much is got out and with what energy release and absorption along the way. Might give a clue to how a tiny guy like Taufik could hit the shuttle the way he did both on his backhand and forehand with power unmatched by much bigger players like Chen Long, Lin Dan, JJS, FHF etc. No one could transfer energy to the shuttle on a backhand or short swing forehand shot like him.

But its all just theory atm, need to get some of these theories tested with paper and pen, and if all makes sense, then practically later. Interesting thing about the ideal racquet weight there. I wonder how much it accounts for bp though. Maybe it could be refined to use a value of swing weight to arm weight which I suspect would be more accurate perhaps?
IMO Taufik can hit it as hard as FHf because Taufiks wrists look a lot more flexible pivot point and relaxed as well. I think he time his hitting so well to have strength at the point of contact exactly.(tighten grip). If you look a LD and others wrists they do not "flow" as much as taufiks and don't look as flexible, they look more rigid.

I don't think it accounts for BP at all.I am starting to think overall weight is king for power and head light and head heavy only preference either a wristy(head light) player or a more arm swing(head heavy). BTW just not to get confused, I don't think Taufik is a wristy player just that he has more flexible wrists. I see for instance LJB as a wristy player Fhf more an arm hitter.

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