What does blade flexing mean?

There is another forum where this topic has gone astray. There are people that know little that talk too much. I know Der Echte ( the real ) has participated on this topic.

First there is the issue as to whether the blade flexes or vibrates. The answer is yes. The blade flexes when it vibrates. We all know the blade vibrates because we can hear it. This should be obvious and simple. I am an old engineer. I know even steel vibrates, compresses or deforms. Look up Young's Modulus. Put this issue to rest.

I have a high speed video camera that can easily take videos at 2000 FPS. It costs over $16K. In theory it can record over 38K FPS but lighting limits this. I have posted the pictures here maybe 2 or 3 years ago but no one seemed to take notice. I have a video of a toxic 5 with Peacekeeper 0X on it. The Toxic 5 vibrates a lot. One can see the blade vibrate long after the ball leave the paddle. What does this mean? In this case the Toxic 5 is in a vise and a Newgy 2050 is shooting balls at it. The vibrations are caused by the balls hitting the paddle. Any vibrations that occur after the ball has left the paddle is a sign of energy that is not moving the ball. An engineer would call this wasted energy. Basically all vibrations that occur after the ball leave the paddle are a sign of wasted energy.

I also have a video of me looping a TT ball thrown by a newgy 2050. Even at 2000 FPS one can't see the blade flex but I can hear the ping from my Firewall Plus so I know it is vibrating but at a higher frequency than my Toxic 5. So what does this mean? I know but it would be best if some of you would contribute.

Are there any spring board divers out there? Your experience with "riding the board" would be helpful in explaining the interaction with the paddle and ball at a non technical level. Why spring board divers? I suppose people that jump on trampolines would do but spring board divers "tune" the board by adjust the fulcrum by moving a big wheel by the side of the board. What does this have to do with TT? I think it is Nexy that has a paddle that one can tune by putting wood in some notches in the blade and therefore making the board stiffer.

How will this affect your play? It shouldn't. The paddle you are playing with now is not the limiting factor in your game. You are. If you play with anything that is close to normal there isn't any force or impulse that one can generate with one setup that can be generated by another therefore achieving the same trajectory. It may require a slightly different stroke but the results can be the same using many different setups.

If a person that knows a lot about spring board diving chimes in that will be good. Otherwise I may need to settle for someone that jumps on a trampoline.

BTW, I do have a coach who is about 2500 US. He doesn't seem to be interested in what I am using at all. It is all about foot work, timing and whether I am moving my forearm or my upper arm. I think too many pay too much importance on the equipment. If you play with anything norma they can all generate the same impulse and trajectory.

I have been busy and waiting for a spring board diver to show up.
During impact the ball, rubber and blade deform. During the period when the ball, rubber and blade are restoring to their normal shape they are all pushing against each other until they are no longer in contact. If the most energy is to be returned to the ball the ball, rubber and blade must return to their normal shape at the same rate. If the rubber and blade push the ball away and the ball has not returned to its normal shape then that energy is lost.
The point I wanted to make with the spring board diver is that the diver times his jump with the spring board so he is pushing off the board while the board is coming up and wants to leave the board just about the time the spring board is level and moving up at its highest speed. That is what the divers call "riding the board". It allows the divers to jump higher. If the diver pushes off the board while the board is moving down the jump will fail.
In table tennis we don't have control of how the ball pushes off the rubber and blade. We don't really have control of how efficient the rebound is. On top of that, when the ball stops relative to the blade and the ball, rubber and blade are at their max deformation then all the kinetic energy of the ball is now in the form of potential energy. When springing back some of this energy is used to spring back the blade, the rubber and finally the ball. The ball gets only a small part of the energy it imparted on the paddle back.
My point here is that the impact isn't very efficient and each combination of different types of blades, rubber and ball make this hard to predict and provides some justification for EJing where one tries different combinations until one seems to be close to optimal or just feels right.
There have been previous posts about blades vibrating at different frequencies. What isn't mentioned is the amplitude of those frequencies. This makes a big difference. Since the blade vibrations are largely sinusoidal in nature peak velocity of the vibration is Amplitude*(2*PI*Hz)^2 and the peak acceleration is Amplitude*(2*PI*Hz)^3. So now lets sanity check using some numbers. Lets assume the primary mode or HZ is 100. This comes from JRS Dallas's work. Lets assume the blade bends back 0.0001 meter or 0.1mm. That isn't much. The peak velocity at that point would be 0.0001*(2*PI*100)^2=39.5 m/s or 88.3 mph or 142 kph. That is fast, too fast. The blade will not bend back faster than the ball impacting it due to the conservation of momentum. Since the blade and rubber have much more mass they would be moving back at a small fraction of the impact speed. Since there are only two variables either the frequency or amplitude must be smaller. I think the amplitude must be smaller since I believe the primary mode of vibration must be 100 HZ or higher. We can hear the pitch of the vibration. So how much smaller must the amplitude of vibration be? I am still thinking about that but I bet it is too small in most cases to have real impact on the path of the ball relative to the ball and rubber deformation. Although we may not be able to model the impact exactly I am sure that if the proper constraints are used then the problem can be narrowed down so it isn't just an opinion any more.
"No, the ITTF sanctions the study, supposedly declares the issue, then we can further debate it almost forever"
That is because no one does the physics and math and a lot of people doing the debating don't know how to do the physics and math and go by what other good TT players say that also don't know the physics and math.
BTW, my company does consulting for government testing applications. FAA, DOE/Sandia and JPL through another contractor.
"We could get the GOVERNMENT to sanction a study and declare the issue to be such and such. Don't we all blindly accept and trust what governments decide without question like good sheep? "
No, I have also been involved in a disputed between the Army Corp of Engineers and a private contractor. I had to prove the contractor was not at fault for some problems. I had to use accelerometers on that one to measure vibrations.

"Also, does any of this really matter? "

This is my point. It doesn't unless one is using a very flexible blade that vibrates at a much lower frequency than other like my Toxic 5. When I do the math it seems that the amplitude of the primary mode must be measured in microns not millimeters if you believe the vibration data that JRS Dallas provided. JRS Dallas didn't provide the amplitudes of the vibrations. Now do you think the amplitude in microns will make that much difference? I think technique will make a much bigger difference and I said something to this effect in my first post.

I can't see my Firewall Plus flex or vibrate at all with my high speed camera but I wouldn't expect to if the amplitude of vibration was in the 10s of microns.
"If could work out the math behind why ...."
It isn't clear what point you are trying to make. In the end we play with what feels good and our ability out weighs small difference in equipment. As I said at the beginning, one can generate the same impulse and trajectory with a wide range of equipment. It just requires a slightly different stroke.

"I could go on the UC Berkley math/physics lecture tour. That would be cool as one of our Korea Foreign ringers is in grad school there."

Not so cool. I doubt there would be any money in it. You have to be a useless politician to get speaking fees. I know. You might get free hotel room and meals. You have to be selling a product. Writing technical books doesn't pay either unless you can use them to get people to buy a product.

For the TT manufacturers sake, EJ on everybody. The next paddle must be significantly different from all the previous paddles. The TT manufacturers say so and too may believe them.

Der_Echte. I am not a poor college professor. I am an old grumpy engineer/entrepreneur that has made lots of money because I am will to tell people they are doing it all wrong or are simply wrong. I do not believe the customer is always right. If the customer was always right he wouldn't need me but that isn't the case. I don't have a PhD but I have learned a lot over many years from the school of hard knocks and by being willing to take on all sorts of applications relying only on my physics and math ability.

I am surprised no one on any TT forum has figured out who I really am. It is easy to use my user name to find my real name and my company and what I do. The fact that two other TT forums have failed to do this shows how stupid and ignorant they really are. Hopefully this forum will be more inquisitive.