Let me just start off by saying that respect for others and empathy mean a lot to me, but I don't like you very much, so I'm not going to be politically correct with you. You're a bully, rude and full of yourself, and I get the impression that you start these threads every now and then just to feel like the center of attention, and to make yourself look smart. You probably don't like me that much either, and I'm fine with that.
A 2000Hz blade will (almost) always be faster than a 1500Hz blade. This is not a question, this is a fact. Empirical knowledge is just as important, if not more, than theoretical knowledge. Every player that has tried some examples of these blades know this is real, they might not know why, but they can feel it. Sometimes you have to step out of the lab or wherever you work, and actually try things for yourself, not only theorize things. Although I've seen your videos, so any of your remarks on throw angle, control, feedback, speed or whatever, lose all meaning...
I don't need to study any of those things, I'm a Civil Engineer and I specialized in the seismic retrofitting of old buildings, which included Modal Analysis with numerical models calibrated by experimental measurements of their vibration frequency. Now I make blades for a living, and that background gave me enough knowledge to understand what is going on. So, while you are playing with your high speed camera, I'm building blades, testing them, making experiments with different compositions and reaching conclusions, getting feedback from costumers and learning from that too.
Right now I know better than arguing with you, so I will answer my own questions, not for you, but for others who might want to learn a little.
- Why and how does it deform?
A blade deforms because an external force is applied (obvious). How it deforms depends on the type of contact, the amount of force that is being applied and where. Modal analysis helps us to understand how this happens, zeio posted a great video which explains a lot about these vibration modes. Every vibration mode has an associated deformed shape, but that deformation only happens for a certain excitation. This is where your incorrect thought process starts, you just speak of "vibrations" and don't differentiate.
- What is the frequency we read?
As I stated above, you have a severe problem of understanding some pretty basic things. NextLevel already said it, but I think it's pretty clear I meant "what is the frequency that we, as players, read on our phones" not you on your lab. The frequency we read is related to the membrane mode, which correspond to the out-of-plane deformation. This is the 1500Hz we read, but you talk about this like it corresponds to pure bending, which is the fundamental mode. The fundamental mode is closer to the 100Hz range, so this statement is completely flawed
"So what if the paddle has a frequency of 1000 Hz?
In this case a complete cycle is 1 millisecond = 0.001 second.
A half cycle where the paddle is deformed and springs back is 1/2 a millisecond.
This would be optimal if the contact time is also 1/2 millisecond because the blade would be pushed back by the ball for the first quarter millisecond and then the blade would push the ball back during most of the second quarter of a millisecond. "
If you truly analysed your toxic 5 video, you could also see some twisting modes happening.
- What variables can we change in the composition of a blade to change the frequency?
"Basically the density and thickness of the wood."
Incomplete. We can change the shape and size of the blade, the density and thickness of each ply, and consequently their relative distance and the total thickness and mass of the blade, but we can also change the orientation of the plies and the direction of the cut. Flat sawn wood has roughly the same mass as quarter sawn wood, but quarter sawn pieces are stiffer due to the grain direction. And we are just talking about all wood blades, don't even get me started on composite blades...
And here we have your very weak springboard analogy. A much better analogy would be, well, a tennis racket.
View attachment 26236
If you look at slow motion videos of a ball impacting the racket, you can clearly see the most important vibration modes. The whole frame bends backwards, which is the first mode, but then the strings deform out of their plane too, "swallowing" the ball, which is the membrane mode. In tennis they use different materials, shapes and sizes to manipulate the stiffness of the frame, and different types of strings and string tension to control the amount of "swallowing". The "swallowing" is what we, as TT players, perceive as dwell time, and we can make an analogy between the layers on the blade and the strings on the racket.
- Why do we have blades with the same composition but with different frequency?
"Different thicknesses and sizes."
Again, a real lack of understanding of a simple question. What I meant was, why do we have blades from the same model with different frequency. The answer is above basically, and this is where the problem gets tricky. You like equations, so here's one for you, this is how we calculate the fundamental mode of a cantilever: (1/2PI)*√(k/m). k stands for the stiffness of the cantilever, so it's pretty easy to see that higher stiffness produces a higher fundamental mode. However, there is an inverse proportion to mass.
Wood is a natural product, and there is a lot of deviation in terms of mechanical properties, but as a general rule we can assume that, within the same species, if a piece has a higher density, then it's also stiffer and harder. As an example we have two 5 ply blades with the same total mass and structure, but one has heavy outer layers and a light core, and the other has lighter outer layers and a heavy core. It's not easy to say what will happen in terms of frequency, it depends on the stiffness/mass relation of each layer, but this causes some differences in the relation of the 1st and 6th mode. From experience, what I can say is that a heavy core causes a lower frequency, but that doesn't mean it's slower. This is why I say that frequency doesn't matter much... Unless you really know and understand what's in the blade.
Saying that any blade is faster than another just because it has a higher frequency is of course a misconception, there are just too many variables at play. When we look at two identical compositions there is a more fair ground for comparison, more so if the mass and thickness are similar. In those cases, the frequency reading is a good and ready available tool that players have.
