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

1. Originally Posted by craigandy
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.
That's an interesting idea. Ofc its known arm players prefer more flex to maximise contact time. Wristy players prefer stiff so they can transfer power faster due to their shorter swings. But now I'm thinking there could be even more to it, Like the wrist flexibility so he is able to do a longer swing and transfer energy over a greater distance unlike FHF and LD. Yh, LYB is a good example. But then I'm wondering why PG can't do the same. Ofc he moves his racquet faster than any other player when he does his deceptive shots with extraordinary control and he displays that flexibility in his wrist a lot, but he doesn't seem to be able to generate power as comfortably in overheads or backhand shots in the same way that TH does. Thanks for your input, its given me a lot to think about. Might have to learn some biology now and figure this out. I think the sliding-filament model of muscle might be worth looking at.

2. Originally Posted by visor
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...
Thanks!
This would be a good statistical test if someone can compare e.g. average racket + shuttle speed with head heavy racket, and then compare with head light racket.

Those equations say that for head heavy racket with approximated mass at 40g, and a head light racket with approximated weight at 35g, the head light racket need only be swung 1.05% faster!

I'm pretty sure that if we got a large enough sample, we would disprove this!

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

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

Plugging in those example wts give 1.59% difference in swing speeds, not 1.05%. Not much difference, but still... something somehow doesn't add up.

4. Also another thought, since craig and Notorious have brought up shaft flex and matching biomechanics:
do any of you play golf?

I ask because I don't but I've seen and heard how the pros have their clubs customized with respect to shaft flex, swing wt, angle, length, etc according to the player's swing profile.

Would be interesting for someone to do that for badminton. I would be the first to sign up.

5. Originally Posted by visor
Also another thought, since craig and Notorious have brought up shaft flex and matching biomechanics:
do any of you play golf?

I ask because I don't but I've seen and heard how the pros have their clubs customized with respect to shaft flex, swing wt, angle, length, etc according to the player's swing profile.

Would be interesting for someone to do that for badminton. I would be the first to sign up.
Yeah I play golf and was kinda in someway looking to get the ball rolling with this discussion to get ideas and facts that i could use to at least video analyse myself and customize to some extent, and yes golf was the inspiration. In golf this is common, Joe Public can walk into one of the fitting centers and get customized clubs.

I don't think it would work in badminton though because imagine all "those" folk that use 28lb+ tension Voltric z force's or MX 80's After analyze the swing you have to tell them you need to use a 21lb flexi racket with an enlarged sweet spot or be better off with a Yonex mp2 junior.

6. Originally Posted by visor

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

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

Plugging in those example wts give 1.59% difference in swing speeds, not 1.05%. Not much difference, but still... something somehow doesn't add up.
No, I believe I am correct
Code:
```>>> mr1 = 0.04
>>> mr2 = 0.035
>>> ms = 0.005
>>> vr1 = 40
>>> vr2 = vr1 * mr1 / mr2 * (mr2+ms) / (mr1+ms)
>>> vr2
40.63492063492064
>>> vr2 / vr1
1.015873015873016```

7. Originally Posted by amleto
No, I believe I am correct
Code:
```>>> mr1 = 0.04
>>> mr2 = 0.035
>>> ms = 0.005
>>> vr1 = 40
>>> vr2 = vr1 * mr1 / mr2 * (mr2+ms) / (mr1+ms)
>>> vr2
40.63492063492064
>>> vr2 / vr1
1.015873015873016```
Hey Smart guy. You are partially correct at best but who is nitpicking

1.0158... is 1.016 is 1.02. If you want to do rounding or lazy ok as 1.01 but DON'T calculate it as 1.05

one step at a time and check your math specially when you are sticking with your point. Specially taking deep dive in complex equations

SZ

8. Originally Posted by visor
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...
when you go on such granular details of physics dealing with force, momentum, torque, mass, velocity as scientifically measurable characteristics as end output the input to cause this becomes secondary and non-relevent.

folks can use
basic, Bevel, Panhandle or any other damn grip based on situations ...

By the way it's really cracking me up abt how collective wisdom is progressing on this thread and ultimately coming to same scientific discovery inclination which was made in other threads like with lighter rackets which giver faster swing speed and more wrists game style option panhandle could become more acceptable as compare to last 30-40 years.

please continue .. The more scientific discovery you will do more you will realize the EVOlUTION is already underway

since this thread started becoz of that 'unusual' thread it wld be more ironic the further you will fine tune this thread the more it will support the original thread topic of lighter rackets and grip styles allowed to optimize benefit in terms of Time, Power, Control integration parameters

SZ

9. Originally Posted by amleto
No, I believe I am correct
Code:
```>>> mr1 = 0.04
>>> mr2 = 0.035
>>> ms = 0.005
>>> vr1 = 40
>>> vr2 = vr1 * mr1 / mr2 * (mr2+ms) / (mr1+ms)
>>> vr2
40.63492063492064
>>> vr2 / vr1
1.015873015873016```
Originally Posted by Superzoom
Hey Smart guy. You are partially correct at best but who is nitpicking

1.0158... is 1.016 is 1.02. If you want to do rounding or lazy ok as 1.01 but DON'T calculate it as 1.05

one step at a time and check your math specially when you are sticking with your point. Specially taking deep dive in complex equations

SZ
yeah, ok, I was dumb. twice. That's expected, though because of my low IQ.

10. actually I wont bother

11. Check this vid out, this is the product of evolution.

This ain't gonna get done with a pan handle grip. Pronation/supination is key to being able to swing faster.

But please try to proof this wrong along with the other panhandle theory stuff.
Due to the nature of this thread though and to forward what I have read from you before, I want tracker results and inputted figures to formula's as the only acceptable propositions.

13. Please no panhandling talk on this thread... save it for the other one... :P

14. Originally Posted by TheNotoriousLIG
TIME Advantage could compensate 90 degress limitation (and hence "lack of Power" consideration).

If you notice Power smash does NOT win rally. It's catching your opponent "before he / she recover" to take the shuttle and passing before that recovery wins the point. Naturally at advanced level it's Power Smash which does that and hence people relate More Power smash means better chance of winning rally and hence Power (hence Pronation).

But if you want to to "Apple to Apple" comparison than consider the "trade-off of Power Loss ? against TIME gain".

In a given TH example in (craigandy) .. TH hit that shot as 305Kmph (hitting speed) which caused oppoenent "no chance of recovery by the time his racket in the path of shuttle trajectory" where shuttle already passed him on ground (that split second difference caused by Power 305KMph smash speed).

Now assume it's Panhandle shot. Let's say Power is less but TIME is gained for hitting early (Hitting early is the characteristic of Panhandle grip) . .say by 0.1 second.

So whatever equation these guys are figureing with basic grip and time taken from racket hit to pass the opponent at say 200 km (normal Power smash speed at advanced level) .. add 0.1 second for panhandle grip hit and even probably 120 kmph could give you same effect to catch opponent before he/she recovers.

Also Pronation could be done in Panhandle (not in full effect but 50-75% of basic grip). Panhandle grip (like others is at wrist / finger level) but your elbow .. you can do the pronation of Elbow (50-75% if not 100% of basic grip hit style).

So on BOTTOM LINE effect of hittign before opponent is recovered is managed.

I am sure few genius guys here with frame by frame ability can measure a time on basic hit .. add 0.1 second (assuming it's panhandle grip hit) and figure out how much "equivalent less speed" is needed for same BOTTOM LINE effect.

SZ

15. See? Too late..........

16. Originally Posted by visor
Please no panhandling talk on this thread... save it for the other one... :P
Don't talk panhandle but figure out how 0.1 second TIME addition can allow reduction in speed per your equations.

Consider it as some top level business strategy consultant is helping you in your equations .

SZ

17. @Superzoom Again only formulas, tracker vids, etc to prove this panhandle stuff not semantics, not for this thread. Sure everyone will be happy to look at your findings in this thread if you do that. Real figures though.

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