OOAK Table Tennis Forum

I'm trying to measure the spin and speed characteristics of table tennis rubbers independent of blade (blade testing will be done later as will combining blade and rubber combinations).

I'm not scientifically trained - I go by what I see and investigate what makes me curious. In the past I've tested rubbers glued to a sheet of 6mm glass.

Now I'm thinking of switching to having a small sheet of acrylic polymer screwed in to a camcorder tripod mount. I'm using the tripod mount as I can accuratley control the angle the acrylic is placed at when testing how a table tennis ball reacts on impact to a sheet of table tennis rubber glued to the acrylic. The ball will be fired at different, spin and speed rates vertically down on to the rubber. The angle of the rubber will be changed to reflect different contact points dependent on type of shot.

I've chosen acrylic polymer as based on my research it's got a coefficient of restitution as close to 1.0 as anything else I can find which I'm hoping means any variation between incoming and out going spin and speed and trajectory of a ball will be down to the rubber, not the material the rubber is attached to. In short, the acrylic will allow me to test the rubbers performance.

The next step would be to have a custom blade made out of acrylic polymer and to measure how peoples technique changes dependent on the rubber they are using - hardware is being created which can hopefully measure this type of thing in a quick and easy way (speaking to the manufacturers it's intended for tennis analysis but should be able to be used for table tennis too).

For any scientists out there, two questions:

1. would acrylic be the closest realistic material I could get to a substance with a COR of 1.0 and
2. what would it's weight be in comparision to the woods used in blades eg would a blade made of acrylic polymer weigh similar to, more, or less than a wood table tennis blade

Cheers

I guess first you need to define this coefficient of restitution by showing us the equation it's used in. Coefficients are multipliers used in equations. Here I'm guessing a restitution coefficient of 1.0 means that the energy of an object hitting a (solidly mounted, infinitely thick) surface of a substance with a c.r. of 1.0 will bounce off with no reduction of velocity, and thus no loss in kinetic energy. The impactor itself must also have a c.r. of 1.0 for this to be true - V(after bounce)=V(before bounce) x c.r. (surface) x c.r. (impactor). Whether or not "acrylic" - I think you actually mean methyl methacrylate, i.e. Perspex (British) or Plexiglass (US), acrylic being a VERY LOOSE term indeed - look it up on Wikipedia - has a c.r. of 1.0, I have absolutely no idea. What makes you think it's better than marble, or high carbon steel, or glass? The thing though - even if it DOESN'T have a c.r. of 1.0, I don't see why it wouldn't be a valid substrate for comparative experiments, as long as it's close (maybe 0.95 and above) and repeatable, and does not degrade over time.

As for weight comparisons - we know a middle-of-the-road allround blade will weigh between 75 and 90 grams or so, and the rubber covering the head is 200 sq. cm. (yes, I've measured them..). You'd have to add the area not covered by the rubber (the wings) - probably 10 sq. cm - and the tang - about 2cm x 10cm? Say a total of 230 sq. cm. Looking up methyl methacrylate on Wikipedia, it's density is 0.93 g per cu.cm (it floats! So do a lot of plywoods, and I think most all-wood blades.. a good sign..). So you have to figure out the weight of 230 sq. cm of Perspex of a given thickness. How thick would a 75g acrylic blade (sans handle pieces, let's allow 5 g each for those for a total blade weight of 85g..) be? Hmm... fifth grade algebra. 230 sq. cm x T cm x 0.93 g/cu. cm = 75 g. So rearrange - T = 75/(230x0.94). T=0.347cm. NOT good - a 3.5mm thick piece of Perspex (about 0.2 inch) will flop around like.. uh.. I think someone has already done this experiment - do a search for "3D printing" and you'll see.

Iskandar

That is my understanding from the research I have done. I'm fully aware of the effect the "second" object can have, that's one of the reason's I asked this question. Did anyone know?

I can buy it locally here http://www.cutplasticsheeting.co.uk/cle ... st-acrylic and I can ask them to cut it to size - it's not just for a bat. It's also as a small block which I can mount to a tripod. The block will be thick enough for the tripod not to impact on the acrylic's COR and small enough to help manage inconsistencies in direction of feed in a way that is quickly visible to me - miss the block and I don't count it without having to watch hundreds of slow motion video bits of footage back - may need to make it bigger to fit in with the concept expressed by ITTF of 20mm thick by 200mm square. Ideally I want to keep the test simple and visible ie easy to see the difference in rebound trajectory, spin rates etc hence using highspeed cameras.

" Check the COR for those substances. Acrylic has the closest to COR I can find reference to of 1.0. If you check the steel plate used by the ITTF to test balls they use "A standard steel plate is made of Steel S235" I have purchased one, but much thinner than the 20mm the ittf used, mainly to check for vibrations which I will monitor to give an idea of "feel". The ITTF test has the ball dropped at a height of 305mm and it's expected to bounce back between 240 and 260mm. If Wikepdia is correct it lists stainless steel - i know, its not the same as steel S235. Presumably someone therefore knows the COR of a plastic ball and the COR of steel S235 and can use that information to work out what they would expect the rebound height to be. That's what I'm after. Some way of knowing for sure what the COR of the plastic I link to above is. Then I have a starting point to work from.

Regarding the weight of a blade made of the "perspex", this website gives me some hope - http://www.allplastics.com.au/architect ... of-perspex.

"How do I work out the weight of Perspex® Acrylic sheet? By using a specific gravity of Perspex® Acrylic sheet (1.19) you can use the following simple formula to work out the weight of any Perspex® Acrylic sheet or cut to size panel:
length (in metres) x width (in metres) x thickness (in mm) x 1.19 = weight in kg

Way too heavy.



Don't do it as square - do it as a circle with a radius of 75mm and a thickness of 3mm. Circle area now equals 17.671*3= 53g and you have spare weight for the handle. As for perspex 3mm flopping around. Mmmm. if that's the case

And this is why I ask these questions.

Thank you

Considering we both get thicknesses of around 3mm, we're calculating the same thing, more of less, which is encouraging.

I am curious as to where you found the c.r. of Perspex. To be honest, while it might not be 1.0 or better than steel (which I suspect is pretty close to 1.0) it might be plenty close enough. Why does the table tennis ball lose height? Because it's c.r. is less than 1 (it would be, say, 250/305 or 250^2/305^2 depending on whether your c.r. ratio depends on velocity or kinetic energy and if you assume rebound height/drop height is proportional to the velocity after impact/velocity before impact, which it isn't, there's also aerodynamic drag involved).

Iskandar

COR OF 1.06 was obtained from Wikepedia here https://en.wikipedia.org/wiki/Coefficie ... estitution. Wikipedia is not my favourite source of information but a good starting point, hence my question here. If you look at metals and ceramics you'll see stainless steel as listed between 0.63 to 0.93. Whilst you talk of the ball losing height because of it COR being less than 1, it could also be the case that being plastic, the ball is actually closer to 1 than the steel and the percentage drop is allowed to reflect the lower COR of steel not the ball. However, what I am after is a substance where the COR is known in advance and which is light enough to take the place of a bat - being close to 1 was a "best case scenario" and not essential eg https://hypertextbook.com/facts/2006/restitution.shtml


As for velocity, aerodynamic drag etc, I'm assuming you are referring to things like gravity and magnus effect. This is being considered separately and I'm talking to manufacturers about spin, speed rates and vertical ball feeds on table tennis robots and ensuring measurable consistency in this factors. Yes there are many factors to suggest what I hope to do is problematic or it would have been done before but I prefer to focus on trying to do something and work on "fail fast" approach than do nothing except think of why it can't be done. Been there done that and very little else.

There are major problems with the list of coefficients of restitution listed. Note that some are greater than 1. Silicon, for instance, has a c.r. of 1.79. This would mean something hitting a surface made of silicon (the element, not the oxide, I presume) would bounce off with 79% MORE velocity than it had before the collision. This makes absolutely no sense. They list plastics and rubbers after metals, with this warning:

"Plastics and rubbers will give higher values than their actual values because they are not as ideally elastic as metals, glasses, and ceramics because of heating during compression. So the following is only a guide to ranking of polymers." This means what? Their c.r. s should be LOWER than those of metals, glasses and ceramics.

And then they say polybutadiene has a c.r. of 11.8. This would make it very much like that "Flubber" in that Nutty Professor movie. You throw a polybutadiene ball at the wall and it bounces off with 11.8x the velocity it had before it hit the wall. After a few bounces, it's gone supersonic and could kill someone, let along put your eye out. (And then you have people saying table tennis rubber "doesn't bounce back fast enough to add to the speed of the collision.. )

Consider this quote also:

"The COR is not a material property because it changes with the shape of the material and the specifics of the collision, but it can be predicted from material properties and the velocity of impact when the specifics of the collision are simplified. "

Iskandar

hardness of acrylic is comparable to hardwood (walnut)
http://www.pactumax.com/downloads/Plast ... _guide.pdf

http://www.matweb.com/search/datasheet. ... snum=O1303
elastic modulus is around 450,000 psi, which is down there with the softest of woods. An acrylic paddle will be more flexible than a wood paddle of the same thickness, so not the way you want to go.

If I were doing this I'd go with 1-inch thick aluminum plate. Hardness will ensure that you're only measuring properties of the rubber and it will have enough mass that the plate won't move enough when hit to mess with your results.

For a test paddle, easiest thing would be to use a stiff/hard inexpensive blade and glue a graphite plate (0.5mm to 1mm) to the striking face. The paddle doesn't need to be "tournament legal" so use that leeway to create the hardest striking surface you can think of. You also won't need a backside rubber so that will give you an extra 40 gm to work with. Stay away from anything with a softer core like balsa, kiri, etc. in the core. You don't want the striking face to "give" at all. I'd go right up to the limit of 125 or 130 grams blade weight by adding stiffening wood to the backside. Again, no rubber on the backside so it doesn't even have to be flat.

Thank you for your reply wchilton.

Some questions please.

I already have two custom made bats, one with walnut veneer, the other with bamboo. Is using them an option?

Why do you suggest alluminium as opposed to steel?

I'm assuming you mentioned graphite plate because that will be light (based on my knowledge of using graphite badminton rackets).

As for the "alluminium" not moving, I'll be screwing it (the material I glue the rubber to) in to a tripod head so I can control the angle the rubber is at when the ball makes contract with it - I'm particularly interested to see how angle brings in to play the pips structure and friction levels of rubbers). Doing it this way we allow me to repeat the tests with different rubbers at later dates and guarantee some degree of accuracy and consistency in how the tests were conducted.

I think either of those would be ok as long as the core is not something soft like balsa or kiri. Underneath the striking face you want as rigid support as you can achieve. I would still make the striking face something hard like graphite or ipe veneer. I mention graphite (carbon fiber) because it has high stiffness to weight. There's a reason carbon fiber is used to re-enforce things that need to be light weight. It's generally the best option without getting overly expensive




Steel would be fine. Actually may be better because of the added mass.




You'd be surprised how much a "rigid" structure like a tripod can move in an impact. I've seen high-speed video of supposedly rigid mounting brackets flopping around during an impact. With the additional mass, inertia will help keep the plate steady and you won't have to depend on the rigidity of your tripod. A plate of 1 or two pounds mass ought to be sufficient. More mass than that is ok. Thickness of the plate should be 3/4 inch or more so that it is essentially a rigid body.

Be careful with your tripod. There are tripods and there are tripods, ask any serious photographer (or the photographic equivalent of a EJ.. ). Most of the cheap tripods you find for sale in department stores, etc. aren't really good at all, at least not for photography with slow shutter speeds. OK for group photographs in the sun, for what people call "groufies" or "selfies" these days (the photographer wants to be in the photo). For your purposes you'd probably want a really heavy tripod anchored to the ground (camera shutters don't subject the tripod to the impulses you're talking about, after all..).

(Somehow, these days, I can't say the name "Manfrotto" - the really good, really expensive tripods - without snickering anymore.. not since I came across THAT Wikipedia article... )

Iskandar

I appreciate the concern but I make videos guys. I admit I'm no scientist and appreciate the advice but I have 3 dedicated camcorder tripods with suitable dedicated fluid heads, and one camera tripod along with gorilla grips. There is no way the ball will move the mounting on the camcorde tripods, I struggle to move one of them when it's set up

The question was about a blade. Thanks for the feedback on that.