Graph comparing speed (output) vs input of different rubber types

Jedi powers are for sale on TT11, but I've adjusted the graph for those without.

Made the differences smaller, and gave them equal top speed.

Further changes in labels and axis'. Added illustratory examples of the type of rubber described.
View attachment 28795
Seriously doubt there is something like a true linear rubber. At the most in a short section of the graph. And also all curves shall flatten at the top (air resistance...).

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Would you guys stop with the fake data? Do it right or not at all.
The x scale of low impact to high impact is meaningless. What are the units?
When the ball first hits the rubber, the force is zero, but it increases as the ball imbeds itself into the rubber. The above graph doesn't reflect that.
Also, it ignores the coefficient of restitution. There is a speed after impact formula.
The Tiefenbacher document shows the speed after impact changes with impact speed. In other words the coefficient of restitution drops as the speed of impact increases.
Tiefenbacher had some interesting observations about tacky rubbers.
I must have posted a link to this document 50+ times over the years.
The high-speed cameras and other sensors are MUCH superior to what Tiefenbacher had to use.

@Johnniedarko, you are headed for a lot of frustration. Most TT players are totally ignorant of physics and prefer to believe in myths. I posted the video of the TT ball compressing about 3 months ago. No one seemed to care.
Years ago PathfinderPro did some testing of rubbers and TT balls. No one remembers. You can find his YouTube channel.

If you want to know how to do it right, then pm me.

Just play.

Hi Brokenball,

Thanks for that paper! Super fascinating, I read it all in one go instead of going to sleep. Maybe this sounds sarcastic, but it isn't. This is a long reply so I'm going to be a bit more structured and use headers and stuff.

Interesting things in the Tiefenbacher paper
  • First and foremost: the model of Epar and Tpar and the measurements of common rubbers of the time is really cool, wonderfully analysed and summarised. It was a joy to read, and it also covers pretty much what I was looking to do.
  • Epar and Tpar declining with speed is interesting. This means more energy is absorbed at higher speeds. Translating this to a spring damper system means there's non-linear damping going on (not necessarily a non-linear spring). This could be due to the rubbers. But it can also be caused by the ball deformation: more energy is absorbed by the ball, and by the time the energy is propagated to the other side of the ball and back, the ball has already left the bat, and thus the excess energy results in some fluttering in the ball. I have not yet checked the other links you shared, so perhaps this gets answered in those.
  • The immense influence of speed glue on Tpar, at least with the glues and rubbers tested. Speed gluing a 2.1mm rubber increases speed and spin with the same difference as between using a 1.3mm and 2.1mm rubber... wow. No wonder everyone did/does it.
  • Grip strength is irrelevant above 10 m/s! Thus having a loose grip on the bat is, on its own, not detrimental for speed and spin generation with fast balls.
  • There is or was an international Journal of Table Tennis Sciences. Probably the most surprising thing to me. The latest papers seem to be from 2013.
Possible next steps building on Tiefenbacher
Building a model is the most difficult part. Now with the heavy lifting already done (30 years ago), it's, the next step could be:
  1. An update with measurements of modern rubbers and the modern ball
    The paper is 30 years old and doesn't name rubbers by brand. So it has a theoretical use but not so much practical use for players.

  2. A better visualisation of the measured parameters
    The information in the paper and graphs used don't translate to the general public. The Epar (x-axis) vs. Ppar (y-axis) graph on page 11 is useful, but also limited. It doesn't show the decline of the Epar and Tparat higher impact speeds. A 3d graph, with impact speed on the third axis, could be the answer. This tells players:
    1. How fast the Ball is in flat hits (Epar).
    2. Roughly how fast and spinny the ball is on loop hits (Ppar).
    3. This is for both touch play and full power.

      A 3d graph like this would allow players to select between, for example:
      1. Slow but very spinny rubbers (low Eret, high Pret) or
      2. Slow and less spin-sensitive, but still capable of a lot of spin (low Eret, relatively lower Pret at low speeds but doesn't lose much Pret at high speeds).
  3. A physical model
    of rubber+sponge+glue to predict Epar-Ppar based on parameters such as sponge hardness, top sheet elasticity, friction, tackiness, etc.
Will I do any of that? No.
My main goal was solving a problem, as that is the most interesting part of research to me. I thought there was an unsolved problem here. But the Tiefenbacher paper already does a wonderful job. The three possible follow-ups above are not so interesting to me:
  1. Gathering more data is not a problem to solve. It is 'simply' work and a lot of it. It's a lot of effort to set up a testing environment, test, parse data, and acquire all sorts of rubbers. I would be interested in doing that if it would support the process of building a model, but since a model has already been established, there's no reward for me in there.
  2. Thinking about clear visualizations is fun (that's why I started this thread). Without data, as many pointed out already, it makes no sense to do anything more elaborate than illustratory. And since there's already no agreement on a simple 2D representation by EmRatTich,
  3. Building a physical model of rubber is what the R&D department of rubber producers is for. There's no practical use for players at all. I would only do this if I worked for ESN or DHS.
Can something simple but still good still be made?
I think so. My made-up graph is not as wrong as you might think. With some small improvements, it can fall in line with the paper.

Quick graph adjustments:
  • it describes only a submaximal topspin ball against topspin.
  • x-axis is the speed differential between the ball and bat before impact.
  • y-axis is the speed differential between the ball and bat after impact.
  • No Epar and Ppar more than 1. However, there aren't units on the graph so this doesn't matter.
  • Epar and Ppar taper off.
Perhaps something like this could be of use for the TT community even if not backed by data, if enough knowledgeable people agree that it helps explain concepts. In the same way that a lot of what you learn about physics and biology in high school is oversimplified to the point of being wrong, but it's still useful to transfer knowledge.


Perhaps this 'feels' okay to some, and not to others.

But we can do more.

Using the research paper of Tiefenbacher, 1994.
In Tiefenbacher 1994, there's a figure that describes the Epar of a unnamed rubber on an unnamed all-wood bat.


What this basically shows is that the bigger the difference between ball speed and bat speed, on a flat hit, the less your effort gets rewarded. If you hit twice as hard, the ball will not go twice as fast, but a bit less than that. But how much?

Let's "reverse engineer" this graph to a situation with a known ball speed. In actual terms we reverse the transfer of the frame of reference. Let's assume a stationary ball, 0 m/s. This yields:


How to read the above? This graph assumes a ball speed of 0 m/s (X-axis). This doesn't happen in actual play but assume you let the ball bounce on the table, then hit it at it's highest point.

For a bat speed of 6m/s (first blue bar, left Y-axis), the ball will fly over the table with speed 10.2m/s (first red bar, left Y-axis). The Epar of this is 0.7 (first grey bar, Y-axis on the right).

In summary:
  • The value of 6 m/s (blue) and the Epar (grey) is from the Tiefenbacher plot.
  • The initial ball speed of 0 m/s was chosen by me.
  • The resulting ball speed of 10.2 m/s is the result.
  • The ball speed is 70% (10.2/6) faster than the bat speed.

If you hit much harder, 24 m/s (last blue bar), then the ball flies with 34 m/s (last red bar). Even though everything is faster, the ball speed is now 34/24 = 1.4, only 40% faster than the bat speed.

We can make a plot of the bat speed vs ball speed in this situation:


Surprisingly, this looks like a straight line! This must be wrong (was my first thought). But it isn't. You can see that the values correspond perfectly with the graph above. On the left, bat speed (x-axis) of 6 m/s corresponds to a 10 m/s output speed. On the right, batspeed of 24 m/s, corresponds to a 34 m/s output speed. The angle of the line does decrease for higher bat speeds, but not as much as I'd expected, given there's now only 40%.

But it still just looks wrong.
Yes I know, I still feel the same way. So let's plot the extremes for some better context.
If the rubber is perfectly sticky, the ball loses all energy and sticks to the bat. The bat pushes the ball forward with it's speed. This is the red line below.
If the rubber is perfectly bouncy, no energy lost (Epar = 1), then the ball flies off with twice the bat speed. This is the yellow line.


All rubbers fall in between these lines.
Btw, the curve would be more noticeable if the speed went up higher. But as the paper doesn't have measurements for that, I won't make them up here.

Despite the decline of bouncyness of rubbers the harder you hit, the resulting effect is visually not that large.

Let's put add this graph to my illustratory graph. Scaling for the same maximum top speed, this gets:


Ignore the vertical line part. Also let's ignore that the Tiefenbacker graph describes flat hits, and I earlier said I tried to make my graph for topspin hits. It's not relevant at this point.

It is clear that I've exaggerated the decline of speed at higher stroke impact. The lines are nearly horizontal at the end, and that's pretty much impossible, as speed cannot 'top out'. If you hit faster, the ball will go faster too. This will be the case until the ball breaks.

A line graph is not the ideal way to plot characteristics of rubber, since the lines pretty much all look the same. The devil is in the details, the minor deviations in the lines.

At some point I'll continue, for now time for a little break. For those still reading, respect.

I appreciate criticisms and feedback.

Could you give a clear-cut definition of tensor rubber.? None of you can, I surmise.
Sure: A collection of rubbers produced by ESN, bearing the "Tensor" brand stamp.
If by clear-cut you mean data-driven, then no.

Seriously doubt there is something like a true linear rubber. At the most in a short section of the graph. And also all curves shall flatten at the top (air resistance...).

The paper shared by Brokenball supports your point strongly (no linear rubber).
The air resistance at speed comes into play after the ball has traveled, but it is of no relevance yet the at immediate moment after a hit, and it is also the same for every ball/rubber. So it may be ignored for these purposes.

Air resistance might play another role in table tennis:
  • If you flat hit, the bat moves the air around the ball forward as well, so in the beginning the ball experiences less air resistance than it would in clean air.
  • However, the bat moving away from the ball after a hit, from the balls perspective, can create a (turbulent) low pressure zone, sucking the ball backwards.
But if that was noticable, I expect top players would've noticed it by now.
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Random comments.

Don't think in terms of absolute speeds. Think in terms of relative speeds. The paddle is the reference frame. The balls absolute speed is important when moving through the air.

Assuming the paddle is the reference frame its speed is zero. All the kinetic energy of the ball is absorbed by the paddle and the ball. Then it becomes potential energy but there is some energy lost due to internal friction. The speed relative to the paddle is used to compute the kinetic energy. Some energy is lost in the paddle which is why the CORs are less than 1.0

This is important. There is a formula for the speed after impact. It is derived using the COR and the conservation of momentum.
Obviously the COR changes as a function of impact speed.
If the speed after impact can be calculated, then the impulse required to generate that change in speed can be calculated too. The impulse is the integral of force over the contact time. The contact time is what most people call dwell time. The impact force is not constant. It starts at 0 when the ball first touches the rubber and then increases to maximum when the ball is stopped relative to the paddle. At that time all the kinetic energy of the ball has been transferred to potential energy minus some frictional losses. Another reason the COR is less than zero is that the potential energy must accelerate both the ball AND the rubber.

Air resistance is significant. The air resistance increases with the velocity squared. A ball will lose half its speed in about 5 meters. Considering the table is about 3.9 m long you can see the ball speed decreases to about half when it gets to the other player. There is resistance coefficient that changes a function of air speed.

Do you know what Reynolds numbers are? The Reynolds number determines which one of the 5 types of air flow are occurring around the ball.
There is a part that covers spheres. Notice coefficient of drag changes but more significantly it increases a lot as the speed is lower. Normally once assume the Cd to be 0.5 because that is the Cd for most speeds but TT balls go fast and then slow down. When it gets to the very low speeds the Cd increases. This is why balls seem to just drop.

Think about it.
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Thanks for your comments. It's been a while since I've used a reybolds number if I was familiar with Stokes law, I've certainly forgot. But its very inteesting.

I was quick to dismiss air resitance, as it isn't strickly part of to the collison of ball and paddle. But it becomes relevant when using for example drop tests to determine COR at different speeds. As that'be easier than going the high speed photography and data analysis route.

Anyway, to be continued.
says Shoo...nothing to see here. - zeio
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Jan 2018
Hmm, the first few graphs actually encapsulate better what table tennis players experience in actual play, like a Japanese blogger has done (check out the various blogs to see the graphs).

The biggest problem with most data obtained through real-world experiments is that they don't replicate what players attempt in reality (in practice) and care most about - landing the shots. Normal and tangential coefficients of restitution, drag and lift coefficients, Reynolds number, spin ratio, and what not become irrelevant if the shots don't land, and that's the one thing that differentiates tacky rubbers from grippy rubbers above a certain input threshold. Graphing the transfer characteristics of table tennis rubbers from data obtained under real yet unrealistic scenarios then becomes moot.

There are 2 types of real-world experiment:
Passive, in which a robot shoots a ball horizontally at a stationary racket [1], or a ball is dropped vertically over a stationary racket [2, 3, 4];
Active, in which a robot swings a racket at a stationary ball horizontally (with a modified golf swing robot like at Sumitomo [5]), or drives a racket at an approaching ball shot out of a robot (with a custom conveyor belt like at Butterfly [6]), or a ball is dropped vertically over a sliding platform with a rubber attached (as in the spin test).

The passive type is useless for comparing between tacky and grippy rubbers. Grippy rubbers always come out on top as they are the best at returning energy, e.g. redirecting the incoming shots (blocking). The thing is, tacky rubbers are rarely used that way. OTOH, the active type is better in that regard but the problem is that most experiments only test at one initial velocity, and like mentioned above, the focus is never about making shots land.
Here is the ad for Super Ventus where strong and weak impacts with and without ORC are compared
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@zeio , Thank you for your insight. Your post got me thinking what the goal I had in mind really was.
And that is a more intuitive, accessible way to present and compare rubbers than exists now.

So here are my latest musings.

There are two 'systems' currently popular:
  1. Rating rubbers on 3 parameters Speed, Spin and Control. Sometimes the parameters 'Chop', 'Loop' and 'Smash' are added to these three. This is most popular by reviewers.
  2. Showing one "speed curve" with a relation between impact speed, or hit power, and output ball speed. This is what manufacturers use to distinguish their rubbers from each other. This is what you also shared, and what the blogger is making.
With shortcomings in both:
  1. In the 'reviewer system' all facets of the rubber in play (Speed, Spin and Control (and Smash, Chop, Loop)),are presented, but not it's non-linearities.
    Example: good spin, does that mean that it spins easily, or that it's maximum spin is very high, IF you put in massive effort? Also, Control is a hotly debated term.
  2. In the 'manufacturer system' where a speed curve is shown (like on the blog and manufacturers you shared), there's only one axis presented, and it isn't even said which one. So likely Tpar under a fixed angle of for example 45 degrees, but you don't know.
    Example: one rubber gives a faster ball than another at medium input speeds. But is it good for my flat hitting play style?
I think that the main thing that can be improved on is presenting non-linearity, on both the Perpendicular axis (Epar, flat hit) and the Tangential axis (Tpar, spin and loop ability) which describe most of the behavior and feel of rubbers.

Basically the improvement is: Show two "speed curves", one for flat hits, one for super loop hits. With these two, you can compare every rubber on every aspect to every other rubber. (I think). This doesn't cover everything a rubber does, such as how much it vibrates, how sensitive to heat and moisture it is, but I think it should cover 99% of the important stuff.

Also, if you have two X-Y graphs describing a rubber, then they can be combined in a single 3D X-Y-Z graph, to show the complete behavior of a rubber. Will this be intuitive and easy to use? I don't know but lets find out!

I moved away from Google Sheets and remade everything in Python in a much better way.

So first: 2D graphs.


The top graphs show Perpendicular speed, so Epar in Tiefenbacher's research, or simply Flat hit.
You'd expect a medium tensor to give more speed at medium speed hits than a "linear" rubber. (As discussed, linear rubber is not actually linear, but that's what they're called).

The bottom graphs show Tangential speed , so basically "how spinny is it at any impact", or Spin and Loop
You would expect tacky hybrids to be spinnier than classic tensors at low speeds for example. This is the type of behavior you can read from this graph.

The left shows an input-output speed relation, x-axis being impact speed of bat and ball before the hit, and y-axis is the speed between bat and ball after a hit. The black lines are the physical outer limits (COR of 0 and 1), the grey area's are the practical limits, as in, it's unlikely that any rubber will be in that area (educated guess).

The right graphs are the Epar and Tpar graphs. The red line is lifted from the Tiefenbach paper, although values above 24 m/s are extrapolated as that's the max speed in the paper. Also I used the same line in both graphs which is incorrect.

Don't take any values in these graphs for fact. I did try to make an as accurate as possible educated guess based on reviews and forum discussions, but there's no fact behind them.

Which is more handy, left or right?

Looking at this, in my opinion, the graphs on the right are clearer and better for understanding and comparing, although the graphs on the left are possibly less abstract.

Now the 3D graphs.

Combining the two graphs on the left, and combining the two graphs on the right:


I'm not really sure whether this is more accessible than the 2D graphs above. Btw, the 'shadow plots' on the walls of the 3D plots are thus exactly the same as the 2D graphs. I'll let this simmer a bit. Let me know wether you think the 3D graphs help.

The process from here on
Ok so a lot of you have pointed out that data must be measured. This will not be that. This is an attempt to improve upon the two existing 'systems' that are also not data-based, and inconsistent and incomplete.

How I see a possible future:
  1. Start by determining the curves for a couple of timeless reference rubbers, such as: Mark V 2.1mm, Tenergy05 2.2mm, DHS H3 Neo 39 OS 2.2mm. Ideally three good and trusted players come to an agreement on how these rubbers should be drawn on the two graphs (Epar and Tpar). The absolute values aren't important, it's all about establishing a baseline from which to compare other rubbers.
  2. More rubbers get added based on playing experience.
    At least a council of three trusted members (could be three TTD forum members for example) must agree on how this new curve gets fit in.
    Why three? To make sure that there's an agreement and a tiebreaker, and also not to have it be a free-for-all like Revspin, where every beginner rates their material a 10.
At the end you end up with an insight in all sorts of playing ability. And it would also be relatively easy to make filters, such as "find a rubber similar to what I have, but then with a bit more spin in the slow game".

Feedback pls
If anyone has something constructive to add I'm happy to hear it.
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Two news things. Data, and I'm going to keep it short.

First of all, I've used the data of TAKKYU LABO / Table Tennis Labo, as compiled by Zaio. Credits:
Takkyu Labo:
Zaio's post:

I've used the data to update my graphs. All rubbers are from the source, except from Mark V which I've got from a different source. The rubbers relative to eachother should be correct, but the speeds are not. Basically: ignore the x-axis and enjoy the graphs.


Interpretation of the Epar graph above:
With regards to flat hits, Tenergy05 is fastest, closely followed by Dignics05 and Rozena. Fastarc G1 and Rakza X are a bit slower but still fast.
Tacky rubbers Rakza Z EH and Dignics 09c are a lot slower, especially when not hitting hard, but in the harder shots they speed up to the other rubbers a bit. This makes them relatively more sensitive to incoming speed, if the opponent hits harder, you'll automatically return harder. But the total speed is still on the low side, so it's still more manageable.
H3 Pro is by far the slowest by itself. Mark V dances to its own tune, pretty fast in the slow stuff but quick to lose out speed wise. It's steep curve makes it very forgiving to incoming power: if the opponent hits harder, the rubber will slow down a lot, giving you a more constant return hit speed. This is possibly a reason why people feel so confident with it.


Interpretation of the Tpar graph above (tangential coefficient of restitution, or spin-ability):
Only relative values count here, not absolute values.
H3 Pro is the king of spin.
Rakza7 EH comes closest in the slow game, Dignics 09c is spinnier in the fast game. Rakza EH has a higher Epar than D09c everywhere, so with equal stroke technique, it'll shoot balls out more straight, and perhaps, therefore, feel less spinny. (It is impossible to hit a 100% Tpar shot, without any perpendicular rebound).

Then a bit lower follow a whole lot of tensor rubbers. In order of spinny to least: Rakza X, G1, Dignics 05, Tenergy and Rozena.
Rozena is the least spin sensitive (lowest Tpar at low speed) and thus easiest for passive blocks, in the fast game it catches up to the other rubbers.

All of the above can be bullshit of course, it's just my interpretation of these graphs. Calculating Tpar from the measurement values also requires assumptions, which can be wrong, and of course I can have made mistakes in somewhere as well.

That's it for this time!




Ok, I lied, I am going to go on a bit longer. But this is only relevant to those very interested in rubber physics, skip it if you're not.

Wonderful data gives insight into a long-standing debate: does throw angle exist as a separate parameter, or is it 'the same' as Tpar? Are spin and throw angle the same thing or separate things? Answer: it seems to be separate!
The measurements of TT Labo show that there is more to table tennis rubbers than just Tpar and Epar. Or more specifically: it proves that there is a difference between throw angle and spin, and that they are not "the same", as is sometimes claimed.

In the 50cm drop bounce test, rubbers Ventus Extra (Max) and MX-D have the same Epar: 0.64
The Epar stays the equal in the 100cm drop test and very close in the 188cm droptest, so it can be said that these rubbers are very similar if not equal for flat hits.

In the 50cm drop spin test they also generate close to exact the same spin (15.5 rps / 15.4 rps).

Yet their rebound angle is different at 24.5 and 25.7 degrees. This doesn't seem like much, but excluding tacky rubbers, all rubbers are between 23.3 and 25.7 degrees, so it is pretty significant.

So while straight bounce (Epar) and spin generation is equal, their rebound angle differ. This is opposing the view that spin and throw angle 'are the same thing'.

My hypothesis
As the ball sinks into the rubber, it depends on the rubber where it pushes the ball to the side the most. If the sponge pushes more on the deepest tip of the ball (deep in the sponge), you get more spin and less throw angle, if the topsheet pushes more towards the center of the ball , you get more throw angle and less spin.

A simple metaphor
  • if you stand on the ground, and somebody kicks your feet from under you, you rotate in place, but you don't move sideways. (Eventually you'll land face down on the floor). A lot of spin, no throw angle.
  • if you stand on the ground and somebody kicks your knees from under you, you rotate, and you also move sideways a bit. Less spin, more throw angle.
  • Some rubbers kick the ball at their feet, some kick it in the knees.

Methodology and accuracy - only for those interested in the behind-the-scenes of these graphs, skip otherwise.
Epar (Perpendicular Coefficient of Restitution, the speed of flat hits)
This was super easy. The bounce test results are the Epar.

You should ignore the speed values on the x-axis though, as I've not taken drag into account. The absolute speeds aren't the actual speeds, but the relative speeds of the rubber relative to each other are correct.

The test is performed at a slow speed though, so every value for hard hits is an extrapolation. And could be wrong. But it's the best available data at the moment.

Tpar (Tangential Coeffecient of Resitution, important for spin and the speed of loops, together with Epar)
This is a bit more complex. One of the reasons for this is the chosen testing method by TT Labo. In short: he drops the ball from different heights, while a paddle with rubber moves with a constant speed to the side to simulate (top/back/side) spin stroke. The issue is as the ball gets dropped from higher, the paddle doesn't increase in speed. So at low drops, the paddle moves relatively quickly, and thus it's a spinny stroke (loop). At the high drops, the paddle moves at the same speed, so all in all, the hit becomes more drive than loop. Due to this, the graph is more accurate for the low speed values than for the high speed values.

To get the value of Tpar, I took the Tan of the rebound angle and multiplied it with the spin. This is an easy way to get both spin and throw angle in equal scalars into a single number. Then this was divided by the Epar, to take the vertical part out of the rebound angle equation.
The Tiefenbach paper is vague about their math and methods (they skip this step entirely) so I don't know if that's equal to what they did or not. I'll experiment a bit more with other options.

A last remark is that the Epar tests are done at three drop heights, but spin tests at only two. That means for Epar I can plot a curve, but for Tpar only a straight line. Which is likely an oversimplification.

Thanks for reading
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