the only thing that I can think of to calculate what mass to use for the head in the linear approximation is to use something like visor's pseudo swing weight, but instead of having the weight at the tip of the frame, consider the weight at the centre of the head.
Just a thought can we work out the head weight that includes the BP by using/plotting the speeds if we anchor the handle and drop the racket so it swings like a pendulum. Is this crazy? is there a formula for it?
T=2.pi.sqrt(I/[m.g.bp]) See pendulum wiki page. http://en.wikipedia.org/wiki/Pendulum Really means you need to measure the bp an then thiswill give you I (MoI)
This is a very good thread. Maybe, we can use it to solve my problem. Pls help. I have 2 rackets, A & B. Both have the same length (675cm), stiffness (medium flex), string type & string tension. The difference is on the weight (wet weight, string & grip included). The weight of racket A is 98 grams, racket B is 94 grams. I set both racket at the same bp=290mm, when I use racket A at first then switch to racket B at the next game, I can feel that I need more energy to push the shuttle when doing dropshot using racket B. If I use the same effort (energy) like when using racket A, the shuttle will meet the net. Maybe, we can solve this by increasing the bp of racket B (usually by cutting the grip shorter). The question is: what is the bp of racket B so it can substitude racket A perfectly? Thank you...
sorry, it does not. I cannot think of a non-arbitrary non-empirical method that will give you the mass to use for the linear approximation case.
What If... Can we balance a racket on something towards the handle, one inch down from the bp and rest on scale and measure on a scale. Then do the same but one inch up towards the head repeat and measure handle side. Find out what mass each of these are then find some relation to get to the correct weight's. I could chop the head off a couple old rackets that are broken to see the real mass of head and handle if it would help to find a correlation we could use for other rackets that would not need to be chopped? Please don't go too mental
You could maybe try the tactic explained here http://twu.tennis-warehouse.com/learning_center/howto_swingweight.php Trial and error adding lead tape to racket untill the swing weight calculator gives the same end figure for both?
Even then ... medium flex A =/= medium flex B. Grip A =/= grip B (so you might hold it differently) and the list grows.
What you are suggesting is anti-science. Just guessing number until you find something that matches a prediction. If you are willing to chop heads off then by all means...
I would recommend against trying to calculate m_r (and c for that matter). Both would be better estimated with a well-designed set of experimental observations. I also think that taking the average shuttle speed across the first 2 frames may be too inaccurate. Doing a simple "v(0) = V, v'(t) = -k*(v(t))^2" within Excel with a very small timestep shows that you could be losing over 10% of 'initial' velocity in the first few feet of travel alone. Using the 2 base equations to generate a Maclaurin series (http://en.wikipedia.org/wiki/Maclaurin_series) produces a stable equation for the first few meters of travel. That should be enough to estimate 'k'. [MENTION=86196]craigandy[/MENTION], what displacement are you getting over the first few frames after contact? I.e. shuttle displacement between the 1st and 2nd frames, and the 2nd and 3rd and the 3rd and 4th etc?
I can only get 2 frames in after contact. If by 'k' you are looking to estimate the drag constant, these guys already did that http://www.isb.ac.th/HS/JoS/vol4iss2/Papers/1Badminton.pdf Page 3. 9.7x10-4 metres squared.
For head weight, I'm not exactly sure of the formulas but I'm fairly sure this is possible using equations for turning moments, coupling and Weight distribution. If you took an unstrung racquet and measured its weight and bp and then you string it and measure weight and bp, delta weight is the mass of string used, and the change in bp would give you the effect that much weight had when applied to the middle of the stringbed (because the string above the middle is roughly equivalent to the amount of string below string bed, and either side is irrelavent because your only using measurments along the axis of the shaft)so you can say all the weight of the string was added in the middle of the stringbed. This gives a distance from the bottom of the handle that is constant and you can treat as a fixed point. You can then use equations relating CoG (balance point) to distance from pivot. Then use an equation to give the change in force due to additional weight with its distance from pivot and new CoG. This change with be proportional to the weight of the racquet head in determining how much weight there is in the handle causing the weight toward the handle and use that to calculate how much weight is above the bp to be counterbalancing that. With that information you can apply weight to areas along the shaft, at known distances from the bottom of the handle and using the change in BP and overall weight, you can find the weight of specific areas of anywhere on the racquet, in this case the head weight. I would figure out which equations to use and derive the overall equation to do this myself but I don't have time atm but if someone else wants to give it a go, then we could finally get a value of actual head weight and force the head can apply at different velocities. I could be wrong in which case I apologise.
If you want the equivalent mass (m') that produces the same torque then it's simple: m' = m r/r' m = racket mass r = distance from butt to bp r' = distance from butt to whatever point you're interested in e.g. centre of head, or harmonic centre of head.
Yh, but that only applies with a shape of uniform mass at any unit^3. The racquet is clearly not uniform so you would need to do several measurements at different points on the head and shaft so see distribution of mass. If you plotted this information on a graph, you could select the area pertaining to the head or mass in front of the bp and use it to find weight of the head.
that calculation is for finding a point mass (called m' at distance r' from the axis) that gives the exact same torque as the racket. It doesn't matter what shape the racket is since torque is perfectly defined by an axis and the systems CoG.
How would you isolate the head weight from your value of torque? Btw, I'm not trying to be frustrating, I too am curious about this relationship between racquets and shuttles and hope this community can figure it out.
@Line & Length It is not calculating the average speed, it is calculating the speed at each tracking point (it has acceleration/distance etc all programmed into it. A couple of times i have matched the shuttle speed directly after and I have never had a plot more than a foot away from the racket. I think I maybe said different a few posts ago but this is what I believe is happening.
