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

1. Originally Posted by amleto
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?

2. Originally Posted by todjo
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...
You could maybe try the tactic explained here http://twu.tennis-warehouse.com/lear...wingweight.php
Trial and error adding lead tape to racket untill the swing weight calculator gives the same end figure for both?

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Even then ... medium flex A =/= medium flex B.
Grip A =/= grip B (so you might hold it differently)
and the list grows.

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Originally Posted by craigandy
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?
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...

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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'.
@craigandy , 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?

6. Originally Posted by Line & Length
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'.
@craigandy , 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...1Badminton.pdf
Page 3. 9.7x10-4 metres squared.

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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.

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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.

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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.

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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.
Last edited by amleto; 06-04-2013 at 05:03 PM.

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Originally Posted by amleto
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.

12. @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.

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sorry, you (@Notorius) are right about the shape having an effect. I don't know what I was thinking

14. My Anti science results are done.
Disclaimer - If you have been part of this thread you will have figured out I am no mechanical engineer nor physicist(just ask @amleto ).

I have done several real life measurements on a digital scale and used the tracker software I linked earlier in the thread. Take these results for what they are worth(and no I am not going to give a full presentation). I understand they are going to be frustrating to a few of you, but at the moment this is the best I can do

Ok.
I did the "cor" tests and got 0.69. using Vs in Vs, out clamped racket.String tension 25lb(bg65), isometric head. This was calculated total between/including racket and shuttle.

I got a set of digital scales which measure to .1 of a gram. I balanced the handle at the tip on a screwdriver(it was the same height as the scales) and rested the head on the scales at the tip. I then chopped the head off two of these rackets. My finding was that one head gave exactly the same reading to .1 of a gram and the other was .4g off.

I weighed the racket I used on one of the tracker vid's in the same balancing manner to find the head mass.(I did not chop this one though as it ain't broken and that really would be crazy)

I used the formula @Line & Length gave and left shuttle speed blank to see how it matched the tracker speed and it was damned close, within 1 m/s.

I am pretty much done with this. I will be happy to plot any vids for people on tracker if they wish, and I wait for a more complete experiment and report (to confirm) from someone far more versed in mechanical engineering than I. Good Luck.

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Nice. How did you do the CoR test? Throw a shuttle at a clamped racket?

In summary:
CoR ~= 0.69.
pseduo-head-weight is a good approximation of the mass of the actual head of the racket.

The linear approximation equation closely matches tracker values.

TBC: Exact methodology for the tracker needs to be determined:
What axis do you set up to measure the velocity? horizontal? or aligned with shuttle exit velocity vector?
Last edited by amleto; 06-04-2013 at 06:46 PM.

16. Originally Posted by amleto
Nice. How did you do the CoR test? Throw a shuttle at a clamped racket?
HaHA yip that is exactly correct, I tried hitting it in with another racket but struggled to either hit or see if it hit the middle of the clamped racket.

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Originally Posted by amleto
sorry, you (@Notorius) are right about the shape having an effect. I don't know what I was thinking
No worries. Hopefully someone will be able to resolve the equations I suggested to a general formula. I have time now but I'm too tired for the integration and combination of the principles right now. I suspect I'll be like this for the next few days so if someone else understand what I was suggesting and feels like doing some (relatively) simple agelbra, go for it
@craigandy , could you give a quick summary of the principles and equations you used and information on the tracker you used? e.g. linear/angular dynamics equations, constants used, software tolerances and limits in functionality etc. Just a brief point summary will do. I'll have a look at it and see if I can find any ways of improving the experiment or choice of principles used. I'll also run it by my dad who did his degree in mech eng next time I see him and we have enough free time to seriously think about this stuff.

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