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paddle mass and speed

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Post Options Post Options   Thanks (0) Thanks(0)   Quote davidzou Quote  Post ReplyReply Direct Link To This Post Posted: 10/28/2010 at 6:12pm
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Krantz Quote  Post ReplyReply Direct Link To This Post Posted: 10/28/2010 at 7:00pm

Isnt it that in the past heavier blades simply WERE faster - just because the construction of a "fast" blade required using heavier, thicker woods? Looks to me that this observation was indeed true by just coincidence and now become obsolete with the rise of light composite materials.

edit: and that it is the “correlation does not imply causation” kind of problem.



Edited by Krantz - 10/28/2010 at 7:17pm
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Hookshot Quote  Post ReplyReply Direct Link To This Post Posted: 10/28/2010 at 8:19pm

Here is a thing that I saw in person. No guessing.

My partner had two of the same blades. One weighed 99gm, one 103. Both played like OFF+.  One was for a spare. He wanted a third and asked Paddla Palace to pick the lightest one they had in stock. They sent one that was 74. The first two played very much the same as each other. This one was like a defensive blade. All three looked the same and the same kind of wood. Same rubber on all three. The light one obviously had less dense wood to make it so light.     
 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote BH-Man Quote  Post ReplyReply Direct Link To This Post Posted: 10/28/2010 at 9:18pm
Originally posted by nicefrog nicefrog wrote:

I always switch between blades during practice to get a feel for what I can do with each one, I can consistently swing much faster, hit the ball harder and get more spin with a light balsa blade 100% of the time all the time. Not only that I can block balls I otherwise wouldn't' have timed well. So I agree with you on this one :). Also like you say it's MUCH easier on your wrist and shoulder which means you can hit more high speed big winning shots than you can with a heavier blade, it's a huge advantage over a two day tournament. I think any blade over 80 grams is in the too heavy range
 
If you get along with such light blades and bat weights, moar power to you my man. I recently had a TBS that felt under 90 grams, so I agreed to mail it off oversees to another forum mmeber for his heavier TBS. I add grip tape and heavy Tenergy and Chinese rubber max thick. I don't have a scale, but I would not be surprised if the weight of the bat is over 200 grams. Yet, it feels so balanced, it doesn't feel all that heavy at all. Zero issues with the weight. In fact, when I was using Lissom, a blade at least 10 grams lighter, I really missed the solidness, but Lissom taught me to value setting up shots for higher percentage finish. Now I have the TBS back in the fight, I am better for the experience and can do more. I don't regret using the setup that was easily under 180 grams, but I feel very well using my HEAVY as brick TBS setup and am happy as a kid with sliced cheese for teh first time.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote nicefrog Quote  Post ReplyReply Direct Link To This Post Posted: 10/28/2010 at 11:37pm
Originally posted by Krantz Krantz wrote:

Isnt it that in the past heavier blades simply WERE faster - just because the construction of a "fast" blade required using heavier, thicker woods? Looks to me that this observation was indeed true by just coincidence and now become obsolete with the rise of light composite materials.

edit: and that it is the “correlation does not imply causation” kind of problem.


I think this is a accurate statement :), pretty hard to make a blade faster from the same tree unless you use a denser and heavier selection of wood. But that all goes out the window with super hard non wood materials

BH-man I can see how a heavier blade might make a more consistant shot just because once it's moving it's less likely to move and probably accelerates in a more consistant way but being able to vary the angle on the blade just before you hit the ball and while you are hitting the ball is a nice thing also. In the end everyone should play with what makes them play the best. But I just don't like the idea that there are people out there missing out on a good thing so I'm trying to share the theory that light blades are good, for the people that haven't realised it yet, that's all :) 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 10/29/2010 at 12:14am
as

Edited by pnachtwey - 03/20/2012 at 4:24am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote stiltt Quote  Post ReplyReply Direct Link To This Post Posted: 10/29/2010 at 1:38am
Originally posted by pnachtwey pnachtwey wrote:

Fatt, can yell and scream in big bold letters?  My thread has been high jacked and they are going off topic!!! The thread was never meant to be about paddle mass preferences.
seems like your pond thread became an ocean of supputations, thanks to the rivers flowing with numerous "I'm-interested-so-I-got-to-say-something-no-matter-how-right-and-related-it-is...".
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Post Options Post Options   Thanks (0) Thanks(0)   Quote remmpfremm Quote  Post ReplyReply Direct Link To This Post Posted: 11/05/2010 at 10:10pm


Originally posted by pnachtwey:
You are confusing momentum ( mass x velocity ) with impulse ( mass x the_change_in_velocity ).
******************************************

My answer: Certainly I did not confuse the physical quantities (I meant what I said: mass times speed), but sorry for calling it `impulse' instead of momentum - that is because it is called `Impuls'
in German, my mothertongue.

I had remarked that the resulting curve will show more  dependence on the paddle mass
if one assumes that  the paddle momentum (paddle mass times paddle speed is constant).

***************************
Originally posted by pnachtwey:
I don't think so. Plot it and post it and see for yourself.  Don't believe me. Convince yourself one way or the other.  Take a look at the equation for the speed after impact and you can see what factors it depends on.
*******************

My answer:

The equation for the final ball speed that you used is

                mp*vp0  - vb0*mp             mb*vb0 + mp*vp0 
 (1)   vb = -----------------------  *cr +  ------------------------  .
                     mb + mp                               mb+mp

If one assumes that the paddle momentum mp*vp0 (call it `mom') is constant for all paddle masses, e.g., mom = 160g*10m/sec, then  formula (1) changes to


                 mom - vb0*mp                  mb*vb0 + mom 
 (2)   vb = ------------------------  *cr  + --------------------  .
                      mb + mp                              mb+mp

The assumption of constant momentum is questionable, of course,
but correct if the player always  applies the same force for the same time, independent of paddle mass.

Formula (2)  gives more visible differences for different paddle masses, which is no surprise
from inspecting the formulas. I looked at  plots, but since  comparison of different linear
functions of  cr is not too interesting, let me just give one example calculation:

Setting mom  = 160 g * 10m/sec, cr = 0.8,  vb0 = -5m/sec, mb = 2.7 g (the standard ball mass),
formula (2) produces  the following values:

   For mp = 160g, it gives 

             1600 +5*160            2.7*(-5) + 1600
    vb = [ ---------------- *0.8 + --------------------] m/sec = 21.55 m/sec.
               2.7 + 160                    2.7 + 160

For mp = 180g, it gives 

               1600 +5*180            2.7*(-5) + 1600
    vb = [ ------------------ *0.8 +  -------------------] m/sec = 19.63 m/sec,
                   2.7 + 180                  2.7 + 180

so  the difference is about 0.9 m/sec. With the same values, formula (1) (where mom is not held constant at 1600 g*m/sec, but equals 1800g*m/sec when the paddle mass is 180g) gives a difference  of essentially zero, as you observed before.
Of course, all such  discussions take place  only within the scope of the formula, as other forum members remarked  already.



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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 11/06/2010 at 1:44am
as

Edited by pnachtwey - 03/20/2012 at 4:24am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Chopin Quote  Post ReplyReply Direct Link To This Post Posted: 11/07/2010 at 2:19am
Just out of interest what differences do you consider to be significant, you could change the scale on the graph and make the differences look huge.
 
In cricket for example the difference of 4 mph (say 84-88mph) makes all the difference to world class batsmen. This equates to roughly a yard of pace (i.e. the ball is on you a yard quicker over about 18 yards). 4mph approximates to 1.8 m/s.
 
I am supposing the crux of your argument is that because the paddle mass is so much greater than the ball mass an extra 5/10g doesn't make a huge amount of difference when considering conservation of momentum and energy equations, is this what you are arguing?
 
(I'd rather leave COR out of it as I believe that can be considered seperately to 2 bats of different mass - if your wanting to examine the effects of mass on ball speed that is. By all means consider COR effects after, I am not denegrating that).
 
In addition what are your thoughts on using paddle weight, paddle and hand weight, paddle and arm weight for the equations? Can the bat be considered completely seperate from the body for the purposes of the relevant equations as the mass of a golf club head can.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote nicefrog Quote  Post ReplyReply Direct Link To This Post Posted: 11/07/2010 at 6:51am
Any table tennis player will probably have noted that lightly built guys that still have good core muscles can hit the ball harder than anyone else. Just like the fastest karate guys are always built like that. The arm definitely is part of the equation and the reason bat weight is such a problem since it's stuck on the very end of the pendulum and extra weight there slows the acceleration heaps.  I guess it impacts the previously mentioned lightly built guy more than it does a heavy set guy too
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Post Options Post Options   Thanks (0) Thanks(0)   Quote zeio Quote  Post ReplyReply Direct Link To This Post Posted: 11/17/2010 at 3:03am
Originally posted by pnachtwey pnachtwey wrote:

The point is that you can see that increasing the mass of the paddle by almost a factor of two makes very little difference in the

speed after impact
whereas the coefficient of restitution, 'speed of the rubber' makes a signficant difference.


Hmm...while I am amazed at your eager embrace of the term COR, you do realize the very term with which you are so obsessed when applied in this case

is actually indirectly derived from and hence dependent on mass?

Originally posted by Wikipedia Wikipedia wrote:

Picture a one-dimensional collision. Velocity in an arbitrary

direction is labeled "positive" and the opposite direction "negative".

The coefficient of restitution is given by

   

for two colliding objects, where

    va is the scalar final velocity of the first object after impact
    vb is the scalar final velocity of the second object after impact
    ua is the scalar initial velocity of the first object before impact
    ub is the scalar initial velocity of the second object before impact

Even though the equation does not reference mass, it is important to note that it still relates to momentum since the final velocities are

dependent on mass.


By the above, the COR is thus not a variable one can pick arbitrarily as in textbook physics.  Disregarding this fact, as is the case in your simulation(same

COR for paddles of different masses with equal initial velocities in an inelastic collision), renders the plot unrealistic and unphysical.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 11/17/2010 at 1:02pm
as


Edited by pnachtwey - 03/20/2012 at 4:25am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote zeio Quote  Post ReplyReply Direct Link To This Post Posted: 11/18/2010 at 8:38am
Originally posted by pnachtwey pnachtwey wrote:

COR is a better term than 'speed' or 'faster rubber' or 'faster blade'.   I think of the fast or speed as the actual motion of an object.   A paddle has speed when I move it or throw it across the room.


There is no better or worse term if COR, speed, faster rubber or faster blade all themselves are quantities presented in a relative manner.  As long as the quantities are derived from experiments carried out under different preset conditions by different manufacturers, the end-users will always find it difficult to compare them in a consistent and reliable manner.  Only a standardized test method across the industry would comparable absolute quantities be produced, but that would be a mission-close-to-impossible since confidential business information like trade secrets would undoubtedly be involved.


Originally posted by pnachtwey pnachtwey wrote:

I have told you why I used the speed after impact formula instead of the simple formula that doesn't take into account mass. Now back up your statement.  Where is your reference?  I don't care if you are right, I just want to know the truth so I can update my model.  Statements that can't be backed up with some sort of research are meaningless.


It looks like bolding the clauses of paramount significance alone has little effect,
Originally posted by Wikipedia Wikipedia wrote:

Even though the equation does not reference mass, it is important to note that it still relates to momentum since the final velocities are dependent on mass.


Just because the mass is not in the equation does not mean it is not there.

By conservation of momentum in a closed system, the final velocities of a one-dimenional collision for two colliding objects are given by:





There you go, mass is now visible in the equation.

Plug one of the final velocities into the COR formula and you get the speed-after-impact formula for that final velocity.  Plug the other in and you get one for the other.





The fact is COR, mass and final velocities are inter-dependent.  Using the speed-after-impact formula does not change that.  Disregarding this fact, you forcefully separate the COR and mass into two independent variables.  This is where the plot becomes unphysical.

Having two independent variables also renders the plot unrealistic because it is in clear violation of fair test:

Originally posted by Science Buddies Science Buddies wrote:


Conducting a fair test is one of the most important ingredients of doing good, scientifically valuable experiments. To insure that your experiment is a fair test, you must change only one factor at a time while keeping all other conditions the same.

To ensure a fair test, a good experiment has only one independent variable.

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Post Options Post Options   Thanks (0) Thanks(0)   Quote davidz Quote  Post ReplyReply Direct Link To This Post Posted: 11/18/2010 at 2:16pm
It seems to me that the paddle mass is not that important related to ball speed unless the paddle mass is not much larger than the weight of a table tennis ball. 
 
Based on
 

ma ua + mb ub = ma va + mb vb

1/2ma ua2+ 1/2mb ub2 = 1/2ma va2 + 1/2mb vb2

 

Assuming the initial ball speed ua   is zero before collision, we have

mb ub = ma va + mb vb

mb ub2 = ma va2 + mb vb2

Solving this equation, the ball speed after collision is  va = 2 mb ub/(ma+ mb)
 

For a ball with zero speed and mb >> ma, the maximum speed is about 2 times the blade speed after collision.  This suggests that there is almost no difference for ball speed between 150 gram and 200 gram blades.

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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 11/18/2010 at 3:47pm

as



Edited by pnachtwey - 03/20/2012 at 4:25am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote zeio Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 6:43am
Originally posted by pnachtwey pnachtwey wrote:

The speed after impact doesn't assume that no [I bet you mean kinetic] energy is lost.

O.o?!  The speed-after-impact formula DOES assume perfectly elastic collisions(zero loss of kinetic energy, COR=1), inelastic collisions(some loss of kinetic energy, 0 < COR < 1) and perfectly inelastic collisions(zero kinetic energy in a center of momentum frame, COR = 0).  That is the whole point of having the COR in the equation to start with!

Originally posted by pnachtwey pnachtwey wrote:

You should use the speed after impact formulas and don't assume [again you mean kinetic] energy is conserved or the COR=1.

Yet you used the speed-after-impact formula assuming kinetic energy in both conserved and non-conserved states when generating the plot on the notion that COR is independent of mass.

Originally posted by pnachtwey pnachtwey wrote:

What two independent variables?  Mass can be measured.

Originally posted by Science Buddies Science Buddies wrote:

...A variable is any factor, trait, or condition that can exist in differing amounts or types. An experiment usually has three kinds of variables: independent, dependent, and controlled.

The independent variable is the one that is changed by the scientist. To ensure a fair test, a good experiment has only one independent variable. As the scientist changes the independent variable, he or she observes what happens.


You have two independent variables in the plot: COR[0...1] and mass[160, 180, 200, 250, 300], irrespective of each other.  On the same page now?

Originally posted by pnachtwey pnachtwey wrote:

The simpler equation applies if the paddle isn't allowed to move or change speeds.  In effect the paddle and what is is attached to has infinitely more mass than the ball for all practical purposes.  Adding more weight to the paddle will not make a difference to the COR.


The speed after impact equation applies if the paddle moves or changes speed after impact.  The paddle is not fixed.  For instance if the paddle is stopped and the ball hit the paddle at -5 m/s the paddle will start moving in the negative direction.  There is an equation for how the paddle reacts too.


I hope you aren't trying to imply that adding more weight to the paddle will make any difference to the COR when it is fixed.   If so can I add enough weight to make the COR greater than one?  Obviously not.  When the paddle is fixed and not allowed to move the paddle and what it is attached to is assumed to be infinite with respect to the ball.


Setting the same conditions for the speed-after-impact equation would yield the same result if you solve for the COR, and vice versa.  The two equations are interchangeable.  It does not matter whether the paddle is allowed to move or change speeds as long as the initial conditions are consistently applied to both equations.  This is the whole point of having a fair test, so as to avoid unrealistic results.

Originally posted by pnachtwey pnachtwey wrote:

Again, I was trying to plot how the mass affects speed for any COR to avoid this debate.

Certinally you aren't implying that the speed after impact formula is worng.


Do not use the speed-after-impact equation as a shield.  It is your model in which the COR and mass are treated as two separate entities that renders the plot unphysical.

Originally posted by pnachtwey pnachtwey wrote:

To find the COR of the paddle and ball it would be best if the paddle were fixed.  This locks down the COR of the paddle and ball at the current conditions of temperature, humidity etc.


Then the speed after impact can be calculated for those conditions where the mass must be taken into account.


How do you expect for a COR derived between a ball having non-zero initial and final velocities and constant mass, and a stationary paddle possessing zero initial and final velocities and infinite mass(practically a floor) to apply for conditions where a ball with same constant mass and a paddle possessing non-zero initial and final velocities and finite but differing mass?
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+ Hexer HD 2.1 Red - 49.3g(68.5g 〃 〃)
= 184.8g
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Post Options Post Options   Thanks (0) Thanks(0)   Quote stiltt Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 9:49am
Originally posted by zeio zeio wrote:

How do you expect for a COR derived between a ball having non-zero initial and final velocities and constant mass, and a stationary paddle possessing zero initial and final velocities and infinite mass(practically a floor) to apply for conditions where a ball with same constant mass and a paddle possessing non-zero initial and final velocities and finite but differing mass?
[fist hitting table]Now that's what I call a darned good question! [/fist hitting table] LOL
 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 11:47am
as


Edited by pnachtwey - 03/20/2012 at 4:26am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote JimT Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 12:23pm
Almost off-topic but mass-related:

I just bought a really cheap but decent pocket digital scale (9 dollars from Amazon - free shipping 'cause I needed to buy some other stuff as well, weighs up to 1000 g with 0.1 g precision) and weighed some rubbers and blades. Some results shocked me... Confused

My two primary blades:

Galaxy W-1 (originally 89-90 g) with all the trimmings, including double edge tape (and foam), grip tape, wing triangles: 102.9 g! No frigging kidding, my friends...

Galaxy T-8 (originally 84.5 g) with all the same additions: 94.1 g

Why there is a difference in 2 g between what was added on W-1 and T-8? I have no idea... perhaps a few more centimeters of grip tape?

Furthermore, cut sheets of:

Thors - 49 g
PME 47.5 2.2 - 49.3, 46.3, 49.1
Karate Hard 2.2 - 51.7, 52.3

Just for your general info...
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Post Options Post Options   Thanks (0) Thanks(0)   Quote davidz Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 9:22pm

pnachtwey, 

 
After I read your first post, I realized the result I got is just a special case of yours.  From physics point of view, formula is right! However, it should be caution to apply these results to table tennis.
 
The big assumption to apply your chart (or result from my post) requires constant COR among heavy and light blades.  I do not believe this assumption holds.

 

In realty, heavy blade tends to be faster than light blade within the same brand (heavier ->  faster blade).  One may make a faster blade by decreasing the size of the blade (lighter -> faster blade).  Certainly, there could be another case:  ball speed is not too much related blade’s weight (e.g., very stiff and hard blade)


Thanks for bringing up this interesting topic!
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 11:09pm
as

Edited by pnachtwey - 03/20/2012 at 4:26am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote yogi_bear Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 11:30pm
assumptions even with equations with out proper experiment still isn't convincing....  people you have been SIDomized again hahahahaha
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Post Options Post Options   Thanks (0) Thanks(0)   Quote yogi_bear Quote  Post ReplyReply Direct Link To This Post Posted: 11/19/2010 at 11:33pm
a coach once asked a chinese coach what muscles are involved doing certain strokes the specific muscles... he was told by the chinese coach that even a person who does high jump use a lot of muscles even if its a lot more simple compared to table tennis. 
moral of the story: you do not need to over complicate things to be a good player.. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote zeio Quote  Post ReplyReply Direct Link To This Post Posted: 11/26/2010 at 3:34am
In an effort to clarify the relations between the coefficient of restitution and the mass of a paddle, I have dug around the net and stumbled upon a comprehensive study just on that.  The study, "Prediction of Racket Performance Based on the Table Tennis Impact Analysis", is co-authored by Yoshihiko KAWAZOE of Saitama Institute of Technology and Daisuke SUZUKI of Hitachi Kodaira Semicon Ltd.

The following is the abstract of the paper:

"This work investigated the physical properties of the racket and the ball, and predicts the impact force, the contact time, the deformation of ball and rubber, and the rebound power coefficient associated with the impact when the impact velocity and the impact location on the racket face is given. It clarifies the origin of ball speed. It is based on the experimental identification of the dynamic characteristics of the ball-racket system and an approximate nonlinear impact analysis, where the contact time is determined by the natural period of the whole system composed of the mass of the ball, the nonlinear stiffness of the ball and rubber, and the reduced mass of the racket at the impact location on the rubber face. Also considered is the energy loss during the impact. The diameter and the mass of the ball are 38 mm and 2.5 g respectively and the mass of the racket is 171 g including 79.5 g for two sheets of rubbers. This work enables us to predict quantitatively the factors associated with impact between a racket and a ball. The results show that the rebound power coefficient peaks at 18 mm from the center of the racket face and then diminishes because of the mass distribution of the racket. The rebound power coefficient decreases remarkably with increasing impact velocity.

The original paper in Japanese is available in full view here.  An english version has been published in the "Science and Racket Sports III" edited by A. Lees, J.-F. Kahn and I.W. Maynard and is available for preview at Google books.

A follow-up study was conducted by the same authors on the difference between 38 and 40mm balls and has been published in the "Science and Racket Sports III" under the title "Comparison of the 40 and 38 mm table tennis balls in terms of impact with a racket based on predicted impact phenomena."  This paper is available for preview at Google books.

The racket used in both studies is a BISIDE(91.5g) by Tamasu(Butterfly) with Sriver of 1.9mm thickness stuck on both sides(79.5g) resulting in a total weight of 171g(Table 1, Figure 12).  There is no mention of the specific glue used.  The balls used are 38mm and 40mm in diameter with a weight of 2.5g and 2.7g, respectively.


The impact model is comprised of a ball-racket-arm system(Figure 4) in which the spring constant(KRB, a constant of restoring force over deformation) and coefficient of restitution(eRB, a dimensionless ratio of velocity of separation over approach) between the rubber and ball are measured separately.  Of particular interest here is the reduced mass(Mr, the effective mass involved during a collision), which takes into account the mass of racket(MR), the equivalent mass of arm(MH = 1kg), the moment of inertia(IGH), and impact locations(A-H) from the center of mass of the combined racket-arm(Figure 5 and 6).



The effect of the reduced mass(Mr) on the rebound power coefficient(e, based on eRB) derived from equation (13) is illustrated in Fig.13.
The coefficient grows rapidly and starts to fall off for Mr greater than 20g.  It reaches a plateau once Mr goes past 200g.  For reference, the lowest Mr without equivalent arm is at impact location A(78.1g).  In essence, the mass of the ball is simply too low for the arm to cause a huge effect.  In contrast, the impact velocity(VB0 = 8, 16 and 24m/s) has a noticeable impact on the graph where the higher the velocity goes, the lower the coefficient becomes.


The vibration of the racket is also considered in the study and the associated loss of kinetic energy is negligible(Fig.18, (20).)


The rebound power coefficients(e, based on er) for impact locations from A to H at 30m/s of impact velocity are illustrated in Fig.19.  The rebound power coefficient increases along with increased reduced mass.

The ball velocities at impact location A and D are compared in Fig.20.  The graph suggests that the closer the impact location is to the center of mass, the greater the ball velocity gets.  The effect becomes more pronounced as the impact velocity increases but diminishes after 30m/s.


Figures 14 to 19 illustrate the difference between 38mm and 40mm balls.  For 40mm balls, there is a small gain in the rebound ball velocity for impact velocity below 20m/s but a bigger loss above 25m/s(Figure 18.)  The same behavior is seen for the rebound power coefficient in Figure 19.




In a nutshell,
1. The rebound power coefficient increases along with increased reduced mass.
2. A reduced mass above 200g produces little gain on rebound power coefficient.
3. A higher impact velocity results in a lower rebound power coefficient.
4. Vibrations of the racket have negligible effect on rebound power coefficient.  Yet players rely on vibrations to differentiate between good shots(ones hit inside sweetspot) and bad shots.
5. The ball velocity increases as the impact location gets closer to the center of mass, but diminishes once impact velocity goes past 25m/s(40mm) and 30m/s(38mm), respectively.
Viscaria FL - 91g
+ Neo H3 2.15 Blk - 44.5g(55.3g uncut bare)
+ Hexer HD 2.1 Red - 49.3g(68.5g 〃 〃)
= 184.8g
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 01/06/2011 at 4:06am



Edited by pnachtwey - 03/20/2012 at 4:27am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote zeio Quote  Post ReplyReply Direct Link To This Post Posted: 01/06/2011 at 6:17am
Originally posted by pnachtwey pnachtwey wrote:

@Zeio, what is increased reduced mass?  Something didn't translate well.

Refer below:
Originally posted by zeio zeio wrote:

Of particular interest here is the reduced mass(Mr, the effective mass involved during a collision), which takes into account the mass of racket(MR), the equivalent mass of arm(MH = 1kg), the moment of inertia(IGH), and impact locations(A-H) from the center of mass of the combined racket-arm(Figure 5 and 6).


Originally posted by pnachtwey pnachtwey wrote:

It is almost as if they are saying that hitting the ball at different points along the paddle changes its effective mass but I would simply say the COR changes across the face of the paddle and is highest at the sweet spot.


The significance of the study lies in that it bridges the abyss between the clauses underlined above, and that it also brings us back to my original argument:

Originally posted by zeio zeio wrote:

Originally posted by pnachtwey pnachtwey wrote:

The point is that you can see that increasing the mass of the paddle by almost a factor of two makes very little difference in the speed after impact whereas the coefficient of restitution, 'speed of the rubber' makes a signficant difference.

Hmm...while I am amazed at your eager embrace of the term COR, you do realize the very term with which you are so obsessed when applied in this case is actually indirectly derived from and hence dependent on mass?


Originally posted by pnachtwey pnachtwey wrote:

1. What mass are they reducing?

Refer to the first quote.

Originally posted by pnachtwey pnachtwey wrote:

2. It doesn't surprise me that changing the mass as little effect.  They should haven't have used the term power coefficient.

View it this way.  Anything between 20g and 200g, however infinitesimal the differences may be, are significant enough when it means winning or losing the match.  The net weight of the BISIDE blade(91.5g) in this study also rhymes with the median weight that shakehand blades of post-glue generation on the market usually come in.

Originally posted by pnachtwey pnachtwey wrote:

3. That doesn't surprise me but the COR doesn't drop that much.  I don't think anyone would notice.

At least it is not 0 and/or 1 which only appear in textbook physics.

Originally posted by pnachtwey pnachtwey wrote:

4. This surprises me.  I would have thought that the frequency of vibration would have a big effect on the rebound kind of like push a kid on a swing.  If you push at the right frequency the kid on the swing will really move, if not the pushing is difficult and the kid doesn't go far.   Another important aspect that wasn't mentioned is internal friction or damping.  Different woods have different internal friction that will prevent them returning all the energy required to bend or deform the wood.  In effect the wood heats up but not so you would notice.
http://www.primitiveways.com/Bow_and_Arrow_Efficiency.pdf

I would also hope there lies on the net another study on this matter waiting to be dug up.

Originally posted by pnachtwey pnachtwey wrote:

5.  I don't think that surprises anybody.  I think we all know about the sweet spot.   25 m/s is very fast.   The fact that the the rebound speed diminishes is due to the ball deforming and not the paddle.

This is noteworthy whereby many pros are attributed for having a very high swing speed.  Assuming they can consistently attain or even surpass the 25m/s barrier, the logical way to gain a further increase would be in blade weight if that is not already visited before.
Viscaria FL - 91g
+ Neo H3 2.15 Blk - 44.5g(55.3g uncut bare)
+ Hexer HD 2.1 Red - 49.3g(68.5g 〃 〃)
= 184.8g
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 01/06/2011 at 2:54pm
as

Edited by pnachtwey - 03/20/2012 at 4:29am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote yogi_bear Quote  Post ReplyReply Direct Link To This Post Posted: 01/06/2011 at 10:35pm
how bout constructing a robotic arm that swings and hit using a light and heavy paddle.. the amount of force on the robotic arm is the control factor then measure the speed of the balls??? an experiment is the best way to prove that
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pnachtwey Quote  Post ReplyReply Direct Link To This Post Posted: 01/06/2011 at 11:16pm
as


Edited by pnachtwey - 03/20/2012 at 4:28am
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