Blade Performance Vs Wood Type and Design

JRSDallas wrote: I use blade frequency as an predictive measure for blade speed since (1) it is tied to system stiffness, i.e. to the (square root of the) ratio of elastic modulus divided by the density

1              If blade frequency can be used to predict blade speed because of its relationship to system stiffness, then does it follow that calculating stiffness will also give us a measure of blade speed?

2              The formula quoted above uses “density”.  Are you using average dried weight (measured in kg/m³) rather than specific gravity?

3              How is the formula applied?  (I said I had trouble with numbers!)  For example, if I know that PO cedar has an average dried weight of 430 kg/m³ and MoE of 11.35 GPa, then stiffness = √(430/11.35) ?

Again, I’m sorry if I have no idea what I’m talking about, but I would be really interested to know if this produces some meaningful way of comparing different timbers.  Thanks.

AgentHEX wrote: > You're assuming that those frequency calcs are directly correlated which is very much in question (they certainly aren't with respect to size, and who knows what else), ie. a case of begging the question.

It seems that you like to argue (and a good argument can be fun) but your apparent strategy is to mix misuse of concepts with the innuendo and incomplete statements (such as your first sentence above). You also like to put words in the mouths of others even though the facts of what they have presented are on the page.  No matter, I’ll play along.     

1.  You accuse that - "I am assuming frequency is directly correlated which is very much in question".   Well since you have by omission left me with my choice of what frequency is correlated with, I hereby claim that frequency is directly correlated with frequency, i.e. f = f.          I win.

2.  Your parenthetic statement (they certainly aren’t with respect to size, and who knows what else) says you claim that (frequency) is not correlated with blade size or other physical parameters.    I disagree and claim that for a symmetrically laminate cantilevered beam (as a 1-D approximation to a table tennis blade face) exhibiting vibration mode frequencies f_{n ,} THAT frequency is in fact correlated with the causal function:

Blade frequency of vibration mode n vs blade stiffness:    where:

E ^k      is the modulus of the k^th lamina relative to the midplane

I ^k     is the moment of inertia of the k^th laminate layer relative to the midplane, where  I ^k = b h_k³/12 + bh_k d_k ²

d_k     is the distance from the midplane of the laminate beam to the center of the kth laminate ply where k = 1 to N.

h_k    is the thickness of the kth laminate layer

d_k     is the distance from the midplane to the center of the kth ply

b      is the width of every laminate layer

L      is the length of the every laminate layer

N     is the number of layers in the laminate beam

n    is an integer identifying specific modes of vibration where  n = 1, 2, 3…..

r     is the mean density of the laminate beam

A     is the area of the end face of the laminate beam, wher A = width b * sum of h_k, for k= 1 to N

Further the above correlation is causally based on the physical parameters of blade size (parameters length L, width b, cross section face area A), and other physical parameters (density r, Young’s modulus E, Moment of Area I ).    Since this relationship was derived from the (1) accepted theory of beams, and (2) accepted rules for mathematical manipulation, it is widely accepted as correct as it stands.      Finally, as this is the same claim I made in 2008 when I originally posted this derivation and in 2013 when I reposted it, the evidence suggests that your understanding correlates with unskilled.   I win again.

You of course are free to contest this by showing that the theory of beams is wrong (to first order, and not at some limit of relativistic speeds or other silly flapping about), or show that the mathematical solution to the differential equation is in substantially in error.   I won’t hold my breath.

Please also refrain from using Wolfram Alpha to pull up some non-physical function (as you did earlier in this thread) to argue that it is a better predictor.  We all know that the declining number of pirates is strongly negatively correlated with the increase in global temperatures.  Of course the pirate correlation IS true, but only the unskilled believe it to be causal.

3.  HEX said  “To elaborate further, if what you're claiming about the relative significant of surface vs inner plies is true it should certainly show up in this category of theories as some relative weighted factor with respect to distance from center (then integrated over the thickness of the plate).” 

Well lets look….….yes the contribution of plies that are displaced from the plywood mid-plane correctly does show up as a distance squared weighting factor per the Parallel Axis theorem, and by golly the weighing has been there since the original posting of this thread in 2008, and since this MyTT.net reposting in 2013.  Maybe you should get your eyes checked?

So…..just to be clear…..your claim that I was not correct about the impact of ply placement is and has been pointless from the beginning.        I win this one as well – Just saying what’s true.        

To assist you, the detail of how the area moment of inertia for the kth lamination of the laminate beam is calculated below.  The correct weighting of course is there as it was in the beginning and ever will be. 

Finally, I’ve just tonight discovered an article in Procedia Engineering, Volume 34, 2012, Pages 604–609, ENGINEERING OF SPORT CONFERENCE 2012  that addresses the same topic that my original 2008 thread addressed.     The abstract clearly includes the approach I took in my original 2008 work.   Makes me feel pretty damn good that I took this same path six years ahead of them.  --  I think this counts as another win for me.  Just sayin’.  

Vibro-acoustic of table tennis rackets at ball impact: influence of the blade plywood composition

Lionel Manina, Florian Gaberta, Marc Poggib, Nicolas Havardc

Abstract - The performances of a table tennis racket can be qualified with several adjectives like: fast, slow, stiff, adhesive, controllable, etc. These qualifications are subjective since they are relative to the sensory analysis made by each player. It appears that the noise produced at the ball impact on a racket has a great influence on the opinion that a player can give about a racket. Moreover, the sound emitted at the stroke can be appreciated differently among several players. Hence a good sound may give a positive a priori to the player racket appreciation. The work presented first demonstrates the correlation between the acoustic frequency spectrum and the vibration frequency spectrum of a racket following the ball impact. The analysis is first performed on the racket blades without rubbers glued on. The vibration modes that produce the sound at the ball impact were identified experimentally. It is shown that there are two essential modes responsible of the sound emitted. In second, comparisons were made between several rackets composed of different composite plywoods. Their influence on the sound emitted is shown experimentally. Indeed, depending on the wood essences of the different plies, their thickness and their fibers relative orientation the sound produced will be different. Then the influence of the rubbers glued on both blade sides is studied. The vibration modes are the same but the frequencies are lower. The sound can be qualified as sharp, long, clear, deep, hollow, and plain. Some correlations with the player appreciations are made.

References

        [1]      Y. Kawazoe, D. Suzuki  - Prediction of Table Tennis Racket Restitution Performance Based on the Impact Analysis, Theoretical and Applied Mechanics Japan, 52 (2003), pp. 163–174

        [2]     K. Tienfenbacher, A. Durey -  The impact of the table tennis ball on the racket, Int.  Journal of Table Tennis sciences, 2 (1994), p. 1994

4.  Earlier in this thread, you said that the dwell time of a TT ball bounce on a racket was 1ms and that a supersonic TT ball impact on a hard bat and a molecular (hard sphere) model of a TT ball bounce proved this.     You are adamant about 1ms and have used it to argue against popular belief that blade flex and recovery contributes to catapulting the ball off the racket.   I said I thought that dwell was 3 – 5 msec,  but as I could not find my original source that perhaps my memory of an article I saw in 2008 was wrong. 

I have now found the article I saw in 2008.  What is more, it shows table tennis ball on racket contact times (dwell) of 4-5 ms (see Fig 15 below), a marginal 400% to 500% longer than the forcefully claimed 1ms.   The article is in: Science and racket sports III : the proceedings of the Eighth International Table Tennis Federation Sports Science Congress and the Third World Congress of Science and Racket Sports / Published London ; Routledge, 2004.   Y. Kawazoe and D. Suzuki -- Characterization of table tennis racket and sandwich rubbers (Tamasu Corporation aka Butterfly ).  Selected excerpt below – Just saying. 

BTW – These Butterfly research guys also physically characterized the BISIDE racket they used in the experiment.  Not too surprisingly, one of the few parameters they felt was important to record was the racket frequency. – Again, just sayin’

5.  > HEX talks plate theory but does not recognize that the plate theory equation he has seen assumes an isotropic and homogeneous material

I very much recognize this, so the issue is that my point hasn't been understood. To elaborate further, if what you're claiming about the relative significant of surface vs inner plies is true it should certainly show up in this category of theories as some relative weighted factor with respect to distance from center (then integrated over the thickness of the plate).

> So in estimating blade stiffness, can we only look at blade thickness h as HEX says?  No, you have to look at both E and h and the plate theory equation clearly shows this.

Really? Especially when you make the exact same point I do?:
[/QUOTE]

Yes really really Hex and I do it because I made this exact point much earlier in this thread, (originally in 2008 six years ahead of you) and that original point is:

Now because you cannot admit that you have read it, you’ve been claiming that I am ignoring parameters such as blade size (but blade size = A *L so that opinion of yours is now proven false) and blade mass, length, modulus E, area moment of inertia.  You keep repeating this, while willfully ignoring the fact that the parameters are in the equation.  You also willfully ignore that as I derived it so would I know they were there, and since I have written them down, that I have not ignored them.  Since you could not see the elephant in the room, I adopted your strategy.

I thought you would be upset if I adopted the same argument against you as you were making against me – a dose of your own medicine and overdue.  You ignored my results and then claimed that parts of it were yours.   You’ve just complaining that I have unfairly adopted your point that stiffness E*I and thickness matters.    Wow……..I am underwhelmed.    Yes, stiffness and size and mass and area moment of inertia and thickness are clearly in my equation above. Further, the relationship above is much more explicit and carefully thought through than the verbal pondering you have presented (of course you actually have not presented anything other than words).  

 SO…to recap, I am making the exact same point you have made, but its my right since I was the first to make it, and I did it in writing years before you showed up.   I can’t claim a win here since you were never actually in the point.  Of course all of this is simple engineering and well understood by many.

6. ) JRSDallas said "Finally, for any given blade construction, increasing thickness h very quickly makes it stiffer – i.e. stiffness grows as the third power of thickness (as originally posted 05/22/2013 at 7:24am, paragraph 6). "

6). Hex said:  “So it appear you too grasp the differing divergence of a linear vs 3rd-order polynomial function. In practice most TT blade woods don't differ much anyway: most surface species are ~10-13 GPa, and inner ones are in similar relative range.”    

Gee I guess so.   I prefer composites because of the wider design range they offer.  Recently I was surprised by the calculated effect of a hard wood outer ply overwhelming the stiffness contribution from carbon layer below it.   I could just say that all 7mm blades play the same, but I have had too many and I know they don’t.  

> As I remember, that formula also included structural terms that let us understand the connection between the mode frequencies and how the layers of the blade contributed. 

7.) Just because a function contains some of the right variables and seems to go in the right direction doesn't mean it's necessarily accurate. You might recall straight up stiffness contains the same variables without some of the drawbacks of frequency. You might also recall that a relative simple transform to any of these "kind of right" unbounded indicators make them significantly more right. In the real world wood density/hardness tends to vary and it's usually not possible to measure frequency before buying anyway, so in practice considering overall thickness with some compensation for any usual characteristic gets maybe 80% accurate results for very little effort. I seriously doubt more complicated metrics for standard blade is more than 10% better, and in any case probably less so than just pumping the rather trivial aforementioned transform if there are significant differences in thickness/rigidity.

There you go again talking about unbounded indicators.  WWWWOOOOOOUUUUU there must be some sort of deep spooky insight or dark magic danger from an unbound indicator akin to the role that prime numbers density plays in the density of quantum chaos energy levels or in Bessell function eigen modes – Oh my god frequency again!  Nu Nu Nu Nu….  Nu Nu Nu Nu….

It is up to the reader to apply some intelligence as to when a difference of frequency is relevant to their task of comparing the relative stiffness of two blades.   In every case, I have presented the use of frequency as a discriminator in those terms.  It is a very sensitive discriminator and a reasonable tool.  Further, I took pains to point out the variability in wood samples even when building many copies of the exact same blade.  

Yes, most of us know that blade to blade differences for even the same model are large so yes, buying any blade is a crap shoot even after you account for thickness, and compensating for unusual characteristics. Touching the blade and even better playing with it are the best indicators.   But…….don’t forget that the thread topic is to understand the playing characteristics of wood.    SO…..the goal should be to take the effort to actually try to understand rather than argue that it isn’t worth bothering to understand.  

Everyone can argue that they will never use some topic or other that they had to study in school.   I would argue that knowledge for knowledge’s sake creates both a rich internal life and improves the fabric through which we see the world.