I suppose... but still a greater m will have more P and KE, although it's a matter of optimizing the m so that you can still swing it at a very high v. Obviously due to differences in our musculature and technique, our individual optimal m and v will vary.
lol sorry that was what i was trying to say in that last paragraph. measure your own personal swing speed for each of the rackets the use the appropriate v and m to see what gives you the higher Vs using LL's formula. Any better?
But still, let's say I swing fastest with the Arc FB, that doesn't mean that I'll get the fastest smash with it as it has a really low m. Otherwise you'll see everyone using very light rackets. Somehow m also plays a large role eg for LCW, LD.
correct just because you swing fastest doesn't mean fastest smash but that's why you need to use line & length's formula as stated. So for instance lets say you have a racket with a 35g head mass and can swing(record it) at 150mph (67.05m/s) and then you get a flashboost with head weight 28g and you can swing that 170mph(75.99m/s)(record this). Then use vs/vr=(c+1)*mr/(mr+ms) to see what has worked out best for you. (I think c is more 0.7 and a 5g shuttle) first racket: the 35gram one Vs/67.05= (0.7+1)*0.035/(0.035 + 0.005) vs=99.74m/s (223.11mph) Flashboost one: the 28 gram one vs/75.99 = (0.7+1)*0.028/(0.028+0.005) vs = 109.6m/s (245.16mph) So if you can swing that 28g that faster than the 35g one then hey presto!
It's too simplistic a model anyway. Just because you can swing it with a lot of momentum, doesn't mean you'll be good at transferring it to a shuttle.
this http://link.springer.com/content/pdf/10.1007/s12283-010-0053-0.pdf#page-1 says that racket speed of 40m/s *at the tip* is elite badminton player level, so 67m/s - 75m/s is totally unrealistic.
Whilst the vast majority of us (myself included) will only ever achieve a string-bed-speed of 20-30m/s, a speed in the region of 67-75m/s was probably needed to set the 421kph record. Re: wind resistance. I was trying to find a formula to solve: a = -k.v*v, v(0) = V. Maclaurin series diverges too quickly to be useful. Anyone know a good method? If there is one, craigandy could plot several frames after impact and work back to what the contact speed would have been. That said, taking the average speed over the first 2-3 frames after contact will be within a few percent. Re: momentum transfer to the shuttle. Whilst no contact is instantaneous, this one is short enough for additional force at the handle to make no significant influence what-so-ever. Just watch super slo-mos of balls striking cricket bats or snooker cues. The supposedly rigid timber wobbles like a tuning fork! To get the best shuttle speed for the weight you have, the velocity of the racket head needs to be as square to the shot as possible (no slicing) and as quick as possible at the point of impact.
about drag: general approach with short/long time approximation equation: http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/mechan/air0.pdf matlab: in 2d for golfball with drag www.engr.wisc.edu/cmsdocuments/COE-ULC-Numerical-ODE-MATLAB.pdf
No, you can too easily get a bad reading because who knows where on the racket string bed the shuttle came off or if their was slight slice during the test. Maybe a few mm off center makes no difference to feel or sound but big enough difference to speed. I just don't know.
I think the model formula that line and length came up with is maybe not incredibly accurate for the actual speed of the shuttle but I see no reason why it is not an excellent formula for comparing rackets.
Eh? Direct measurement of shuttle is surely more accurate and... direct, no? After all you're just guesstimating what the "c" is in L&L's formula.
Imo for comparisons of rackets I think ignore real shuttle speed and calculate hypothetical. I think this would be more accurate to work out the rackets capeabilty in your hands. If you could get a camera to record from the front as well and some sort of sound device so you could tell if you have peached it out the middle and then only use those results, then then Shuttle speed would be more accurate for comparison, yes! Guesstimating the "c" does not make a notable difference when comparing different weighted rackets as I would imagine the "c" would be the same regardless of racket weight so it's the same difference it won't hurt the formula for comparisons.
If you're doing this as a practical test, then of course you measure the shuttle speed! common technique is to measure a decent sized sample, remove outliers, then obtain the average. Do for both rackets and compare. Then it doesn't matter about slight slices etc as the effects will be the same (averaged) in both data sets. What you are left with is average smash shuttle speed for your rackets.
that's terrible logic. If a model isn't accurate then it is missing some physics. So why use it to compare that which it does not model well? Crazy.
you've just assumed that the model is accurate in that statement so it's a bit of a self fulfilling sentence.
I understand why you think it's bad logic. But I am under the assumption that the model is only inaccurate because of the estimation of the "cor" which is fine, ergo perfect logic. It seems to model really well, I don't understand for comparisons of rackets what could be missing.
Under what basis can you assume that? The model has not been validated at all. The fudge factors at the moment are CoR estimates - total guesses, and also the racket head mass that is being used - total guess. There is not a clear defined method of obtaining the mass used in the calculations from the actual mass of the racket. Since you have not been recording the masses and BPs of the rackets, you have no idea if this model is more or less accurate when trying to predict shuttle velocity for rackets with hi/medium/low BPs. I think a lesson in The scientific Method might be needed How can you say that when there has been no comparison at all done between theory prediction and empirical evidence? There has only been 'well, it's in the ball park' hand waving. We have covered elsewhere that there is a lot of physics missing from this linear approximation of a badminton swing & shuttle contact.
Yeah you are right, The whole mass thing does need to be defined properly, that is a given(can you help by doing an example of method specific to the situation?). The cor I am not so concerned about although i will try doing that on the software hitting shuttles into a clamped racket.
