@amleto Moment of inertia is still a static measurement right? And bakulaw indicated that my "head wt" is essentially a summation of moments of inertia along the rod, ie racket. Reading some more on MOI on a pendulum and a rod, it seems that it is related to mass and the square of the distance of that mass from the pivot. With your background and for the benefit of us on BC, is there a simple equation that can represent this MOI for a racket as related to mass and bp? I suppose we have to assume the racket behaves as a rod of equally distributed mass along its length in order to simplify things? As the little green aliens in Toy Story would say, we would be eternally grateful!
[MENTION=57143]visor[/MENTION]: Those equations are very simple if you apply simplifications for rigid body and evenly distributed masses. BUT exactly these two points define the characteristics of each racket. Therefore if you neglect them you would not be able to get anything near to describe the 'feeling'-characteristics of each racket. The stiffer the rackets are (assuming homogeneous mass density which is wrong) the better the formula could represent that. Your measurements gives you a number for some (not further defined) m' as amleto explained. You can call it "head weight" but thats all. You can still try to get the moment of inertia with this approximation http://en.wikipedia.org/wiki/Mass_moment_of_inertia#Measuring_moment_of_inertia
uhmm, I rethinking what I posted, just to make sure! e: pretty sure I'm right, so I'll put it back!: Yes, my poor explanation there. He's wrong. No, there is not. One can modify the moment of inertia totally independently of mass and bp. In other words, one can modify the MOI whilst keeping mass and bp constant. Therefore it is not possible to use only mass and bp to describe MOI.
Keeping total mass and bp constant, means you need to modify the shape. (eg. two barbells, wood and metal, same mass. rotating around their bp results in different moments of inertia due to the bigger size of the wood-barbell. reason: lower mass-density of wood.) To solve the integral one could maybe split it into parts, defining different constant mass-densities for each handle, shaft and head. Still to think about the shape-functions... but the points to consider: - deformation while playing, deformation by string-tension and string-weight itself - mass-density being manufacturers secret - different fulcrum-points in-game ... therefore I suggest you should just try to get it measured in one pendulum-experiment, taking the time of one period. That makes the setup a little bit more complicated, but still low-cost. That would be an approximation, maybe good enough to compare some rackets.
You don't mean the shape - you mean distribution of weight. If you take dumbbells and keep the distribution of the weight the same (making the wooden one with a larger diameter to make up for the lower density) the moi will be virtually the same despite the shape being different. If you make one longer than the other, it'll be different - that's not due to the shape, in this case. With rackets, as I mentioned earlier, there's a lot of parameters factoring into the equation of the moi. Problem is that usually in mechanics you approximate the real thing by making simplifications (assuming a perfectly rigid body, for example), but most simplifications will take away a significant characteristic from a badminton racket. The way to approximate this would be to differentiate between different areas of the racket. The head can be assumed to be rigid during play (not a lot of deformation, usually), while the shaft is best described as a flexible rod with constant mass distribution. The handle can also be assumed to be rigid and having a constant mass distribution. The problem that we face now is that we can't (without sawing the racket into pieces) find out easily how much each part of the racket weighs and how the weight of the head is distributed. Calculating this would be a rather frustrating endeavour, I believe - so I agree with 96382 that building a machine would actually be easier It would basically have to be a (reverse) pendulum with either constant or adjustable motor power which measures swing time. All that being said, the head weight is a better approximation of the racket's expected behaviour than the BP and weight alone, although it can be derived from those measurements. Measuring the head wt of the rackets you're most comfortable with will give you a good estimation of what to look for when you're browsing the shelves in a badminton store For comparability purposes, measuring it with factory grip+plastic with and without strings would be a good idea as rackets are probably unstrung or factory-strung in stores (which is where you guys in the US and Asia have an advantage over most Europeans - not a lot of walk-in badminton stores in most regions).
read carefully please. i never mentioned moment of inertia. i said summation of moments. entirely different things!
No, you are free to change the density distribution. This is possible with graphite racket design/manufacturing as far as I know.
clarification: what I said: True. What you are doing is actually "Summing Moments" and it does have solid background from Statics.. The moment of a (point load) is naturally affected by the distance from the point you where want to sum moments. The only complication is that the racket weight is not evenly distributed along its length. Nonetheless, any distributed load can be replaced by an equal point load..." what you said: And bakulaw indicated that my "head wt" is essentially a summation of moments of inertia along the rod, ie racket. He's wrong. just to clarify... moment of inertia is different from the moment of a point load.
Sorry, stupid me. Your are right, of course. The density distribution gives the density for a given point of the body. But I wonder. If that had to be kept constant, then the only thing changing the moi should be the shape, shouldnt it?!
For all you experimentalists, I remembered the following. It should be good enough to get some comparable results. Made a fast sketch, hope you get the idea.
How did you arrive at that (mgb^2T^2/(...)) formula? How does the last equation work? It looks like the parallel axis theory, but the axis through the handle is not parallel to the shaft if you want to measure swing weight!
The pendulum measurement is then the concept of the swingTool app for iDevices. Although in our case for badminton rackets, we should hang it by the handle and let the head swing freely instead. "With swingTool you can quickly and easily measure the swing weight of tennis racquets, golf clubs, baseball bats etc. Swing weight is the most important parameter when deciding how a racquet, club or bat feels when you swing it. Unfortunately measuring swing weight has been fairly complicated, until now. With swingTool it is enough to just hang your equipment and let it swing like a pendulum. Place the iPhone close to the swinging end and it will automatically display the swingweight. Characteristics - Can be used for all types equipment - Choose any point to calculate the swingweight at - Choose any point to hang the equipment at (independent of the swingpoint) - Faster and more accurate than the traditional way to measure swingweight - Can be used to measure the swing time of any pendulum with 0.01 s accuracy A demo video is available at appmaker.se/swingTool To golfers: With this app you do MOI-matching i.e. it measures the real dynamic swingweight (moment of inertia). Not the static Lorythmic balance point (D9, C4 etc) that sometimes is called swingweight. NOTE: Requires an iOS device with a video camera, i.e. iPhone 3Gs, 4 or 4s, iPod 4 or iPad 2" [video=youtube;7llkEd_QAMs]http://www.youtube.com/watch?v=7llkEd_QAMs&feature=player_detailpage[/video]
https://docs.google.com/viewer?url=http://www.rose-hulman.edu/~moloney/PH314/bifilar_pendulum_05.doc why not apply parallel axis therom: they are parallel !? Rotation around BP is the same axis as rotation around handle+a
Ok I just tried it. Using the racket as a standalone pendulum really gives me problems due to the friction at the mounting bracket points. Fast build up with the two string 'torsion-pendulum' (referring to the definitions from the picture): (http://www.badmintoncentral.com/for...imation-of-swing-weight?p=2058432#post2058432) - it is easy to get L big (around 2m indoor) - with strings and grip you can determine the BP by balancing the racket on a small edge (uncertainty around 3-5mm) - biggest Problem: Get b big enough to stabilize the racket. I didnt try to attach the strings on handle and racket face. Attached them a few cm along the shaft - Therefore I had to move the racket about 20-30 degree instead of keeping it under 10 degree. Results: MOIs of the handle should be around 3 g m^2 to under 15 g m^2 (estimation interval). 160g Training Racket was around 23 g m^2. This was around 3 times the moi of another racket Maybe someone can provide some more detailed results.
The bifilar pendulum seems too complicated. For only $1, I'll be trying out the SwingTool app, but haven'td figured out how to attach the handle to swing the racket freely. Do you think I can just tie a short piece of string and swing from a point, taking into account the new length in the app?
