Physics and Power, by Kirbosmash


As a high school student, I am required to take math and science courses- this year, I took Calculus and Physics. With my obsession with badminton rackets and my gifts in physics, I have decided to write a report on what gives badminton rackets their power. For those too lazy to read the whole thing :rolleyes:, scroll down to the bottom for the summary.

First off, what is the scientific meaning of power? Answer: Momentum. By the law of conservation of momentum, the momentum of the racquet is completely transferred to the birdie. Thus, to find what makes rackets powerful, we must find what gives the racket the most momentum.

Physics equation: Momentum = Velocity x Mass

The variable that affects both velocity and mass is of course, the specs of a racket - head heavy/ head light/, etc. For a greater velocity, the mass of the racket must be less. No, I take that back, the swing must be fast.
A "head light" racket swings faster than an "even balanced racket" which swings faster than an "even balanced racket."

The "overall racket weight/mass" is not as influential to the speed of the racket as much as where the weight is located - since the contact point with the birdie is at the head (where the strings are), it is only logical that the accountable mass for momentum is located there.

Thus, to determine power, we must use the velocity of the swing, and the mass of the head. Of course, ordinary badminton players can not measure this as accurately as scientists, so we must use comparative reasoning instead.
1. as stated above, head light rackets swing faster. However, head light rackets have less mass at the head. The faster swing generates more power, but the lack of mass lessens it.
2. Even balanced are in between.
3. Head heavy rackets swing the slowest, but with the most mass at the head, they are naturally powerful.

Finding the right balance is key - if one can swing a racket very fast, then a head heavy racket would be beastly, however, an even balanced or head light racket would do just fine - according to the equation momentum = m x v. For someone not swinging as fast, they will benefit in terms of power by using a head heavy racket, as opposed to a head light racket (which would give them almost no power).

More skill = increased racket speed = more racket options.


Conclusively, this means that the power of the racket is based on the "specs" of the racket almost soley. That makes us wonder, what differentiates between two rackets with the same specs then? It isn't power, at all - don't be confused by the Company's slogans that the extra $$$$ means more power. The extra $$ must equate to better feel and/or durability, as opposed to power, since power is based upon the laws of physics.


Summary: rackets vary by balance and mass in order to change how powerful a racket is. A racket that has a lot of mass at the head, while still being able to swing fast (not hard, fast), would generate the most power. However, that is extreme and of course sacrifices control and sometimes, your arm (injuries). It is much easier to swing a racket with less weight at the head but since it has less mass, it will not have as much power. Swing speed and mass are inversely proportional with power, increasing swing speed but decrease head mass, decrease swing speed but increase head mass --> "power" can come in many ways.

extra $$ leads to better feel and durability, but not necessarily power. On a final note, physics makes power, it is power. Let this advise your next racket purchase.


Thanks for reading,
Kirbosmash

you kinda missed a key point. The racket itself.

the racket is composed of wood, and carbon fibers/ graphite. this brings into play torsion, tensile strength, flexibility, etc. these also contribute to power generation.

The strings are another component. they are strung at certain tension, and have different characteristics that allow for power generation.

You are right about the general physics of human physiology. If you punch someone in the face at 30km/h is of course more powerful than at 5km/h. If you add a iron knuckle to your fist, the damage can be double because of the weight. But for badminton, you have to take in consideration of the racquet itself as well. Like jymbalaya said, the density of material and flexibility of an racquet will greatly contribute to how much power you will have when you swing. If you have learned Pivot-Theory, then you might want to read on more about that as in badminton, there are many pivot points. Shoulder pivot -> Elbow pivot -> Wrist pivot -> Shaft pivot -> Frame pivot...Something like that I believe. So, head heavy racquets are not necessarily more powerful than head light or even balanced racquets due shaft stiffness. Think of this, why would racquet company release many different specs of racquet of the same line?

I'm pretty sure what you have described is already a general understanding. There are definitely, as others have said, many other different variables that would affect it. There is no real objective way to measure the strength of a racket itself, as it is the person wielding the instrument that generates the power.

You completly missed strings, strings, act as a spring to amplifly the momentum created by the swing.

The strings are the torsion coefficient that multiplys the force created by the swing, focusing it on the shuttle. Tension is stored energy in the racket, this, also, gives rackets there power.

The thickness, and elastic qualitys of the string play a huge role in the performance of the racket.

Gotta love your "gifts in physics" rofl

Kirbosmash, are you implying that..

This:
http://www.germes-online.com/direct/dbimage/50175948/Badminton_Racket_Set.jpg

is more powerful than..

this? ( If the swing speed, strings and string tension remain constant ):
http://www.just-rackets.co.uk/gfx/uploads/img_1_26082008233024199_m-tec70page.jpg

Aw give him a break. He's just expressing his enthusiasm :)

Maybe if he was him. http://news.yahoo.com/s/afp/20090528/od_afp/swedeneducationoffbeatiraq_20090528124335 :p It's alright. We're just giving friendly criticism. ;)

Something else to consider is that as you learn to swing faster, you will begin to approach a maximum speed that is dependent on limb length, CNS speed, muscle insertion angle and muscle-tendon ratio. The idea is that for an explosive movement, once an object starts moving your leverage on it changes, plus your muscles generate less force at high speeds. This is why you want to accelerate your arm with as much initial force as possible, to maximize impulse. You do this instinctively when using the stretch reflex.

What this means is that with a light racquet, you might get to a point where you just can't get the racquet to a faster swing speed. It just has too little inertia to allow you to load it fully. With a heavier racquet, you might be able to get it to a faster speed.

However, be careful with your terminology. With the light racquet, you can still improve "power" by having the same swing speed at contact but with less preparation time for the stroke. Remember that power is force over time, so minimizing time is a valid way to improve power. Just remember that in this case the improvement in power means you can get your smash off more quickly, and therefore use it in more situations. It doesn't mean that the smash will have a higher shuttle speed.

you guys are so mean...c'mon, he is only in high school and trying to show off a little by applying what he learnt.

but the general consensus is right, there are many more variables than the momentum of the racket that ultimately determine the power of the stroke/speed of the bird.

Well, in a way, we're not really chastising him, but elaborating on the general conditions he already laid out.

Kirbosmash, sorry to tell you this, but your report elaborates only at a mediocre highschool level, if i were you, i wouldn't dare type the sentence "my gifts in physics". Don't take this as an insult, but please NEVER, EVER, initiate an unnecessarily long post with self-righteousness and ignorance.

"Power" not only can be based on the racquet's balance and weight..
You have to take in all these other variables like frame stability, tensile modulus (stiffness)~shaft/frame flexibility and length, aerodynamics, etc, when the swing speed, string, string tension, hitting angle, air density, shuttle used, etc are all constant.. it gets quite complicated IMO.

Kirbosmash, I suggest you to read through all of taneepak's... physics talk ;)

"Power" not only can be based on the racquet's balance and weight..
You have to take in all these other variables like frame stability, tensile modulus (stiffness)~shaft/frame flexibility and length, aerodynamics, etc, when the swing speed, string, string tension, hitting angle, air density, shuttle used, etc are all constant.. it gets quite complicated IMO.

Kirbosmash, I suggest you to read through all of taneepak's... physics talk ;)

That, my good sir, completely blew my mind. I could've sued taneepak for murdering my brain cells.:D:D:D

wow so mean. I had to leave early because I went to play at Bintang Badminton so I did not get to finish my report. I"m not trying to show off - to be honest, I"m trying to stop my urges to keep buying more rackets.

I forgot to mention, as many of you kindly pointed out, the string tension and strings. Well of course that is important. The repulsion rate is directly related with the speed of the swing, - less tension for a slow swing, more tension for a fast swing. This leads to my next point, the stiffness of the racket. A flexible racket helps a slow swing because after the racket hits the bird, it rebounds faster than the swing. However if the player swings faster than the racket, then its useless.

In order for companies to truly make rackets more powerful, they would have to find a way to make it flexible, so flexible that its' faster than any human swing. That material is too futuristic- not only must it be ultra elastic it must also be ultra durable - this is star trek and stargate material.


And wow you all focused on "gifted in physics." I was only trying to get your attention. Maybe I got it too much.

I"m trying to stop my urges to keep buying more rackets.
TwoBeer would probably tell us all that one TC700 is enough ;)

I don't quite get how a racket is supposed to be "faster than any human swing" and how manufacturing a flexible shaft will allow for this? Wouldn't a durable stiff shaft be more helpful for that goal?

And wow you all focused on "gifted in physics." I was only trying to get your attention. Maybe I got it too much.

Haha, maybe many of us are very envious of you having "the gift", so we all started bashing your statements for fun.

Just kidding, you are alright.:D

And wow you all focused on "gifted in physics." I was only trying to get your attention. Maybe I got it too much.

We are not intentionally focusing on your "gifts for physics", there's just nothing else to focus on :rolleyes:. Please, don't think of us as mean :D.

In order for companies to truly make rackets more powerful, they would have to find a way to make it flexible, so flexible that its' faster than any human swing. That material is too futuristic- not only must it be ultra elastic it must also be ultra durable - this is star trek and stargate material.



This is not necesarilly true either, having a material that is flexible, in a sense would be a whip. The problem with that is it would be imposible to be consistant, having to time every shot perfectly. There are reasons why people who like to smash, use stiff rackets. The racket is a mere extension of the body, when you swing, you swing with all of your body's inertia, thats where the power comes from, weight transfer, which then is amplified by the shoulder rotation, which then is amplified by the rist, and finally by the racket itself. You could increase the power simply by making the racket longer, increasing the levrage.

You could increase the "power" simply by making the racket longer, increasing the levrage.That's true because work = force x distance..

Also, Momentum = Mass x ( velocity which is [Distance travelled / time])
The mass and the length of the racquet can both affect the "power", given that the swing speed remains constant.. and also lets say, if racquet A and B have constant "x" mass and "y" "length" ( in general ) and if racquet B has a more aerodynamic frame and shaft profile. The aerodynamic"er" frame will reduce the time taken to swing the racquet if the distance swung remains constant for all racquets, therefore also the "power" will increase as the velocity value in general will also increase.

"Mass" is just too vague as well as Kirbosmash mentionned, it should be taken in context of "sweetspot" or the balance point/centre of gravity from the pivot, and also the total mass of the racquet.
So simply, the balance point can also affect the time taken to swing. Lower bp ( or just lower "mass" ) will give faster swing speed ( there is a limit to this swing speed ). Higher bp ( head-heavy ) racquets will have greater value of "mass" and may take more time to swing the racquet a constant distance, but if the weilder can swing the racquet fast enough ( lets say, at the same speed as the head-light racquet), the head-heavy racquet ( and also heavy in general ) can produce more "power" than a "light" racquet if the racquet length ( most importantly ), strings, etc remain constant.

The stiffness of the material used in the racquet will also affect the "power" and durability. The flexibility/stiffness can change the output "power", but it also depends upon the user as explained by Loopy:
http://www.badmintoncentral.com/forums/showthread.php?t=40187

So pretty much, there can only be "powerful racquets" if everyone are physically the same, which isn't the case. Basing our racquet purchases on the racquet's marketed "power" is just non-sense.

What jhirata says is completly true, rackets don't swing themselves. The power is in the wielder, not the racket.

That's true because work = force x distance..

physically the same, which isn't the case. Basing our racquet purchases on the racquet's marketed "power" is just non-sense.


we agree on something jhirata.

This is not necesarilly true either, having a material that is flexible, in a sense would be a whip. The problem with that is it would be imposible to be consistant, having to time every shot perfectly. There are reasons why people who like to smash, use stiff rackets. The racket is a mere extension of the body, when you swing, you swing with all of your body's inertia, thats where the power comes from, weight transfer, which then is amplified by the shoulder rotation, which then is amplified by the rist, and finally by the racket itself. You could increase the power simply by making the racket longer, increasing the levrage.



Interesting concept with the leverage idea - that physically should work. When I say flexible, I mean that this material is completely out of our league - say, 75 years in the making - it catches the bird for a split seconds then rebounds it faster than any swing - it basically makes "cheating" rackets.

The only comment I have is the above applies fundamental physics which works on rigid systems. Assuming rigid systems helps the students to understand/approximate what they learn as related to what they observe in the general world.

The problem is the world and definitely our racket system is not rigid. The strings stretches, the shaft and racket head flexes, and even the grip/body system of the player introduces flex.

Jhirata: the "work done" calculation is wrongly applied. An increase in length of the racket shaft at the same angular velocity increases the "speed" of the racket head. And Taneepak's version of physics is indeed mindblowing at times.

...First off, what is the scientific meaning of power? Answer: Momentum. By the law of conservation of momentum, the momentum of the racquet is completely transferred to the birdie....

It's a nice report, but your badminton is better than your physics!

Power and momentum are two different things in physics. You've given the correct definition of momentum. Power is defined to be the rate of work done--that is, power equals force times distance divided by time. It's easy to look up these words in wikipedia or other web sites.

Only a part of the racquet's momentum is transferred to the shuttlecock. If the momentum were completely transferred, that would mean the racquet would stop moving at the instant it hit the birdie. (Look up "elastic" versus "inelastic" collisions if you want to learn a little more physics here!)

Thanks for posting your article, it's a good way to get an interesting discussion going!