The effect of string shape on diameter (gauge), and area

[SpinToWin]

So I thought I'd make a thread about how different shaped strings' gauges are measured and what this means relative to a regular round string.

Now, there are two assumptions I will make in order to make the calculations possible and more simple:
1) the gauge is 1.25mm.
2) The shape is that of a regular polygon.

I will calculate a few values:

• The gauge of a circle (round string) into which the shape is inscribed.
• The area of the shaped string with this gauge relative to a round string with the same gauge (if necessary, using different axes along which this gauge is measured)
• The gauge a round string would have in order to have the same area as the shaped string

Triangular shaped strings:
Since we're discussing regular polygons, this is a equilateral triangle. The only sensible value for the gauge seems to be the altitude of the string (h in the diagram below):

By making h=1.25mm, we get values of a=b=c=1.443mm (pythagoras). Now, if this triangle was inscribed in a circle, the lines from the centre to the corners of the triangle are congruent (and all radii) and thus form similar triangles:

Using this geometric property, I can use the sin rule to find the radius of the circle in which the triangle is inscribed:
r=0.83333mm, which means that the diameter is 1.667mm!
Of course, the string doesn't play nearly that thick, so let's move on to the areas…
The area of a circle with a 1.25mm diameter = 1.227mm^2.
The area of a triangle with an altitude of 1.25mm = 0.902mm^2.
What would the gauge of a round string have to be to have the same area? 1.07mm!

Square shaped strings:
Of course, the first problem we face here is how is the gauge of this string measured? Is it the altitude or is it the diagonal? I will analyze both scenarios, though I put my money on the gauge being measured on the flat edges (a lot easier), so the altitude seems to be the better value (in general for polygons with an even number of sides).

Having said that, let's start out with the diagonal being the gauge:

If the diagonal has a length of 1.25mm, then the side length is 0.8839mm. Obviously, the diameter of the circle in which this square is inscribed = 1.25mm (it is the diagonal).

Essentially, we get an area of 0.78125mm^2 for the square (1.227mm for circle).
For a round string to have the same area, its gauge would have to be 0.997mm!

Next let's take the more realistic case where the gauge is the altitude ( = side length a in the diagram below) of the square.

In that case, the diameter of the circle encompassing the square is 1.768mm!
The area of the square is 1.5625mm^2 (1.227mm for circle).
For the round string to have the same area, it would have to have a 1.41mm gauge!

Pentagonal shaped strings:
As with any polygon with an odd number of sides/corners, there is really only one way to measure the gauge, and that is the altitude.

Now, the calculations here are slightly more complicated, but I got the following values:
The diameter of the encompassing circle is 1.382mm.
The area of the pentagon is 1.135mm^2 (relative to 1.227mm^2 for a round string with the same gauge).
For a round string to have the same area, its gauge would have to be 1.202mm.

Hexagonal shaped strings:
Once again there are two possibilities to measure the gauge, using the altitude or the diagonal.

Let's start with the diagonal:

As you can see, the diagonal equals the diameter of the circumscribing circle (1.25mm). The area of the hexagon = 1.015mm^2 (circle 1.227mm^2). For a circle to have the same area as the hexagon, its diameter would have to be 1.137mm.

Next is the altitude:

In this case, the diameter of the circumscribing circle would be 1.443mm. The area of a hexagon with a 1.25mm gauge in this sense is 1.353mm^2 (1.227mm^2 circle). For a circle to have the same area, it would have to have a diameter of 1.313mm.

Heptagonal shaped strings:
Again, here there's only one way to measure the gauge, namely the altitude:

The diameter of the circumscribing circle here is 1.315mm.
The area of the heptagon is 1.183mm^2 (1.227mm^2 circle).
For a circle to have the same area, its diameter would have to be 1.227mm.

Octagonal shaped strings:
Gauge measured as diagonal:

Diameter of circumscribed circle = diagonal = 1.25mm.
Area of octagon = 1.105mm^2 (1.227mm^2 circle).
Diameter of a circle with the same area = 1.210mm.

Gauge measured as height (A):

Diameter of circumscribing circle = 1.353mm.
Area of octagon = 1.294mm^2 (1.227mm^2 circle).
Diameter of circle with the same area = 1.284mm.

Conclusion:

Now let us sum up what we found, however, using only values with altitudes as measures for the gauge size (simply because this seems like the more realistic assumption). In case you know there is an exception, you can refer to the other values above for guidance

First is a graph, with the amounts of sides of the polygon as the x-axis and the diameter of the circumscribing circle as the y-axis. At first it seems like there is no relationship. However! If you isolate odd and even sided polygons respectively, you will find that the two data sets correlate in a similar way (what seems to be two negative regressive exponential functions, only vertically/horizontally translated). Essentially, the less sides a shape has, the further the maximum distance from the center point to the edges is. However, shapes with even numbers of sides have a relatively higher maximum displacement relative to shapes with odd numbers of sides.
Conclusions:
1) Among odd/even sided strings, those with less sides will feel thicker.
2) For sides with close numbers of sides, even sided shapes will feel thicker.

The next diagram has the amounts of sides of the polygon as the x-axis and the gauge of a round string for which the cross sectional area is equal to that of a 1.25mm shaped string as the y-axis. Here too we can split odd and even sides and find interesting results. Odd sided strings show a positive regressive relationship, whereas even shaped strings show a negative regressive relationship and are always above the level of odd shaped strings! Additionally, it seems like both curves are approaching the regular gauge of the round string (1.25mm), so it seems like that may be a asymptote the two curves approach as they get more and more sides.
Conclusions:
1) Strings with odd numbers of sides have a thinner equivalent gauge than those with even side numbers.
2) The more sides a odd sided string has, the thicker its equivalent gauge is.
3) The more sides a even sided string has, the thinner its equivalent gauge is.
4) Shaped strings with odd numbers of sides have a lower equivalent gauge than comparable round strings.
5) Shaped strings with even numbers of sides have a higher equivalent gauge than comparable round strings.

Thoughts:
The most interesting statistical outlier here is the square shaped string, for its shape takes up the most space (measured as a circumscribing circle, which is the grommet hole shape), and it has by far the highest cross sectional area relative to its gauge. Due to this it is reasonable to suggest that these strings will feel considerably thicker than other shapes (at the same gauge) and that they will be heavier due to their added cross sectional area. Very stiff offerings of these strings are likely to play relatively more uncomfortable and should be treated carefully.

Furthermore, this data seems to suggest that strings with odd numbers of sides play relatively thin, whereas strings with even numbers of sides play relatively thick.

It is entirely possible that these values influence our perception of liveliness and ball feel, which we often attribute to thinner gauges of round strings.


Questions for you: What (other) kinds of implications could these numbers have, and are there any other values that should be calculated?

 

[esgee48]

Your answer may be here
http://tt.tennis-warehouse.com/inde...uge-to-shaped-polyesters.542607/#post-9658687

 

[SpinToWin]

I have entered the values from triangles up to pentagons, I will update this thread with values up to hexagons soon (gotta do something first).

 

[SpinToWin]

Your answer may be here
http://tt.tennis-warehouse.com/inde...uge-to-shaped-polyesters.542607/#post-9658687

I am doing something slightly different and more mathematical than that #geekout

 

[Mongolmike]

Um... can you do it without all the math-y stuff? You lost me after polygons.

 

[SpinToWin]

Um... can you do it without all the math-y stuff? You lost me after polygons.

Haha I'll try to sum it up in the end

 

[SpinToWin]

I think I am finished here

Um... can you do it without all the math-y stuff? You lost me after polygons.

Please tell me if there's something I need to clarify (and what )

 

[Aretium]

So... exams finished? Plenty of time? XD

or is it the opposite? Procrastination? I am at my most productive when I have a deadline or exam coming up haha

 

[Aretium]

Great work though, interesting...

 

[SpinToWin]

So... exams finished? Plenty of time? XD

or is it the opposite? Procrastination? I am at my most productive when I have a deadline or exam coming up haha

How did you know?

Got a presentation for law on Friday which I'm kinda pushing ahead

 

[Aretium]

How did you know?

Got a presentation for law on Friday which I'm kinda pushing ahead

How do I know? I have an exam on monday hahaha All of a sudden I have a million ideas. None of them to do with my exam. I sold some rackets, 2 of my pro staff 90s for not a lot but I was surprised someone wanted to buy.

 

[Shroud]

Images arent showing

 

[SpinToWin]

Images arent showing

Really? They're showing on all devices for me

 

[Shroud]

Really? They're showing on all devices for me

the ones in the conclusion werent there earlier. They are now though!

 

[SpinToWin]

the ones in the conclusion werent there earlier. They are now though!

Ok good, those are kinda the cornerstone of this thread haha

 

[Karma Tennis]

All your theoretical stuff is very interesting but it still doesn't tell me which string shape will guarantee me a French Open Singles Title.

Seriously though, excellent stuff. One thing though, what happens to all of your theory when each string has been used for a little while and the string shape starts to change due to tension changes, stretching, and string wear?

 

[SpinToWin]

All your theoretical stuff is very interesting but it still doesn't tell me which string shape will guarantee me a French Open Singles Title.

Seriously though, excellent stuff. One thing though, what happens to all of your theory when each string has been used for a little while and the string shape starts to change due to tension changes, stretching, and string wear?

Hmm... Well it depends on how the string wears off with time...

I don't find that entirely relevant in this case, because that has more to do with how a string ages rather than how a string plays from the get go.

However, here is what I think:
For shaped strings with fewer sides (triangular and square shaped), I think the shaped profile will remain (though perhaps less sharp than in the beginning) even when the string has been played for a while, due to how emphasised the edges are. The shape certainly will last long enough for the string to need to be restrung due to being dead I would say. Shaped strings with fewer sides (pentagonal and up) will (depending on their composition and thus their resilience) lose their characteristic shape more easily and approach the shape of the inscribed circle, essentially playing like a thinner round string in the case of odd numbers of sides, and playing more like a normal round string in the case of even numbers of sides (due to the nature of the inscribed circle).
Overall, shaped strings will probably lose more surface area than comparable round strings I would say, though the triangular shaped string may be an outlier in that regard.

 

[ShahofTennis]

I look at this and wonder, gosh, this guy is doing law? Put down the calculator and study man. Lol, nice work though.

Sent from my SAMSUNG-SM-G920A using Tapatalk

 

[SpinToWin]

@Roland G here is the thread which I had mentioned. It summarises how different string shapes affect the implication of gauges in theory.

 

[El_Yotamo]

While this data is quite interesting, I'm not too sure as to how it helps with string characteristics. Here's why: you calculated the area of a two dimensional regular polygon, and while there might be some correlations to the string's actual shape and gauge, it is certainly not the best results which can be achieved. While I don't have the results quite yet, I propose that you look at the surface area of a string based on shape, and how much of that surface area impacts the ball/the other string in the stringbed. This is important, since the polyester stringbed is elastic, in that it snaps back into place with the ball still on the stringbed, and therefore the magnitude (amount) of friction (force) may change dramatically based on how much area of contact there is between the string and whatever it's impacting, which as I've elaborated, can be either the other string in the racket, or it can be the ball. For further (somewhat) guidance, when you look at string-ball contact area, the edges of the string will have the highest friction with the ball, and should be taken into consideration slightly more than the sides of the string as to how much frictional force they exert on the ball. Also, I recommend you to see how many edges are on the string due to shape, and thus how many may impact the ball each time, as that will be crucial to see which string shape(s) will have the least string-string friction as well as which will have the most string-ball friction. Finally, note that the crosses and mains have different types of friction with the ball, since one is parallel to impact and the other is perpendicular. Based on my findings so far, even sided strings, especially ones with more edges or unique shapes (such as diadem strings like solstice power) were most efficient in these two regards. To conclude, this is looking past the standard μ (COF), and as well as looking into deformation, and thus how the elastic string really behaves under full pressure, and how that not only dramatically changes the normal force pushing the two surfaces together, but also changes the μ itself to some degree, and gives new meaning to how you regard data given the shape of each particular string it is on. Hope I could help and didn't rant too long!

 

[SpinToWin]

While this data is quite interesting, I'm not too sure as to how it helps with string characteristics. Here's why: you calculated the area of a two dimensional regular polygon, and while there might be some correlations to the string's actual shape and gauge, it is certainly not the best results which can be achieved.

How it can help? It's rather intuitive, but sure, I'll explain: gauges for different shapes can refer to vastly different perceived thicknesses. One way of perceiving this difference is by the circumscribed circle, which could be the grommet holes for instance. This value is most easily perceived by how thick a string feels in the hands and while stringing. It also explains why many report triangular and rectangular strings to be a more snug fit in grommet holes. The other way of perceiving thickness that I could think of is the area of the cross section, which would show how much (more) material there is in a given length. Is it unreasonable to suggest that a string may feel thicker than it's advertised gauge when it has the equivalent amount of cross sectional surface area/material of a significantly thicker string?

While I don't have the results quite yet, I propose that you look at the surface area of a string based on shape, and how much of that surface area impacts the ball/the other string in the stringbed.

These are entirely different values than what I was looking at (string thickness), but that should be rather easy to calculate. The surface area of the string that is in contact with the ball is a uninteresting measure in my opinion, firstly because experiments have shown that all strings grab the ball regardless of shape; secondly as there is a lack of consideration for and understanding of the contact angle between the ball and the side; finally because there is no distinction between the different sides that potentially could be in contact with the ball.

The surface area of contact between the strings may affect how good the string movement is and how long it lasts, though I am not sure in which way. I could calculate that and post it here though, that shouldn't be a problem.

This is important, since the polyester stringbed is elastic, in that it snaps back into place with the ball still on the stringbed, and therefore the magnitude (amount) of friction (force) may change dramatically based on how much area of contact there is between the string and whatever it's impacting, which as I've elaborated, can be either the other string in the racket, or it can be the ball. For further (somewhat) guidance, when you look at string-ball contact area, the edges of the string will have the highest friction with the ball, and should be taken into consideration slightly more than the sides of the string as to how much frictional force they exert on the ball.

You are suggesting that string shape leads to a measurably higher friction when striking the ball, but you have no evidence for that, in fact, TWU seems to suggest that there is no such correlation at all. Your argument is based on unsound assumptions.

Also, I recommend you to see how many edges are on the string due to shape, and thus how many may impact the ball each time, as that will be crucial to see which string shape(s) will have the least string-string friction as well as which will have the most string-ball friction.

... Triangle 3. Square 4. Pentagon 5. This is a redundant exercise. How many impact the ball is irrelavant as we already established. You still haven't said how this number is crucial in any way.

Finally, note that the crosses and mains have different types of friction with the ball, since one is parallel to impact and the other is perpendicular. Based on my findings so far, even sided strings, especially ones with more edges or unique shapes (such as diadem strings like solstice power) were most efficient in these two regards.

That is a unsound conclusion. You are not only changing string shape, but composition, density, colouring, etc. You cannot isolate the shape and call it the deciding factor.

To conclude, this is looking past the standard μ (COF), and as well as looking into deformation, and thus how the elastic string really behaves under full pressure, and how that not only dramatically changes the normal force pushing the two surfaces together, but also changes the μ itself to some degree, and gives new meaning to how you regard data given the shape of each particular string it is on. Hope I could help and didn't rant too long!

This makes sense to you?

 

[El_Yotamo]

How it can help? It's rather intuitive, but sure, I'll explain: gauges for different shapes can refer to vastly different perceived thicknesses. One way of perceiving this difference is by the circumscribed circle, which could be the grommet holes for instance. This value is most easily perceived by how thick a string feels in the hands and while stringing. It also explains why many report triangular and rectangular strings to be a more snug fit in grommet holes. The other way of perceiving thickness that I could think of is the area of the cross section, which would show how much (more) material there is in a given length. Is it unreasonable to suggest that a string may feel thicker than it's advertised gauge when it has the equivalent amount of cross sectional surface area/material of a significantly thicker string?



These are entirely different values than what I was looking at (string thickness), but that should be rather easy to calculate. The surface area of the string that is in contact with the ball is a uninteresting measure in my opinion, firstly because experiments have shown that all strings grab the ball regardless of shape; secondly as there is a lack of consideration for and understanding of the contact angle between the ball and the side; finally because there is no distinction between the different sides that potentially could be in contact with the ball.

The surface area of contact between the strings may affect how good the string movement is and how long it lasts, though I am not sure in which way. I could calculate that and post it here though, that shouldn't be a problem.



You are suggesting that string shape leads to a measurably higher friction when striking the ball, but you have no evidence for that, in fact, TWU seems to suggest that there is no such correlation at all. Your argument is based on unsound assumptions.



... Triangle 3. Square 4. Pentagon 5. This is a redundant exercise. How many impact the ball is irrelavant as we already established. You still haven't said how this number is crucial in any way.



That is a unsound conclusion. You are not only changing string shape, but composition, density, colouring, etc. You cannot isolate the shape and call it the deciding factor.



This makes sense to you?

Perhaps I didn't word it in the best way I could. For the first part, I thought it would be rather futile to simply calculate the string thickness, as it gives you nothing except for the string's thickness, and won't change any of the string's parameters. Therefore, I assumed maybe you were taking it in some direction, which lead me to spin, seeing as that's not only your username, but also something that (correct me if I'm wrong) seems to at least have interested you in the past. I also never said anything about unreasonability.

Next, for my seemingly rash recommendation: again, I was taking it in the spin direction (sorry), as (again) I thought that might've been a topic of interest. Firstly, I'd like to note that I'm aware of past experiments and how they've proven that all strings grab the ball, as that is obvious, but just how all polyester strings slide and snap back, and some do it to a greater extent, some strings grab the ball more than others, and yes, it can be affected by the string's shape. Here's why: firstly, from a physics standpoint, and how sharper objects exert more force, it is somewhat obvious that the edges on the string will have more friction than the sides of the string, and seeing how many edges there are could be noteworthy therefore. Nothing unsound there. Furthermore, notice how all values in TWU are only frictional coefficients, I was simply trying to show that in an elastic material like a PET-based tennis string, the surface area in contact with anything matters, as it will deform and cause more force pushing it together compared to a regular inelastic collision. Moreover, I do hear you out on the contact angle part, but that is simply something that must be taken into account as an assumption based on a regular topspin (or slice) shot, and I do acknowledge that it is somewhat of an approximation to do so, but I believe that when it comes to comparing, that is alright. Furthermore, it is again interesting, at least to me, the surface area in contact between the strings during impact, since they deform as a cause of the ball impacting them, meaning that the total frictional force (compared to just the COF) could be different among strings of different shapes. Again, the TWU values, which I'm not demeaning in any way (they are extremely important), are only the coefficient of friction in a somewhat relaxed mode, since the strings there are experiencing the force divided by the number of strings usually in contact with the ball (which is also an assumption, shows that those can be ok for certain situations). Therefore, depending on surface area of contact between the strings, not only can the force pushing the strings together (normal force) change a lot, but even the μ can change. This, again, is because there is an elastic collision here.

Finally, when I wrote me findings, of course I am aware that there are many other factors to spin, and that is only one of the correlations which can be observed, I'm sorry if I wasn't clear enough, and you are certainly correct here as it is incorrect to say that one of many qualities is a deciding factor of anything without all else being equal, though do remember the values which I'm talking about are theoretical based on contact area, I'm talking about comparing total friction to μ based on the same principle(s), where μ is the given data. I'm truly sorry for not elaborting on that.

Also, for the last bit, I was simply suggesting that there are ways to perceive data and it is not always correct to perceive raw data as absolute. Therefore, I stand by my word that this is sound reasoning, and am deeply sorry if I came off in any sort of negative or rash way. Also sorry if I hijacked the thread, if that happened, it was completely unintentional.

I hope I was a bit more clear this time, and again sorry if I wrote too much or if my reasoning seems unsound. I promise I'm simply trying to help, and of course it is perfectly alright to disagree respectfully. Cheers!

 

[SpinToWin]

Perhaps I didn't word it in the best way I could. For the first part, I thought it would be rather futile to simply calculate the string thickness, as it gives you nothing except for the string's thickness, and won't change any of the string's parameters. Therefore, I assumed maybe you were taking it in some direction, which lead me to spin, seeing as that's not only your username, but also something that (correct me if I'm wrong) seems to at least have interested you in the past. I also never said anything about unreasonability.

So it's futile to point out that the string shape can massively impact how thick a string may feel based on how the gauge is measured? It's futile to point out that the gauge equivalent area of Weisscannon Ultra Cable is that of a 1.38mm round string? This is anything but futile, gauge is easily understood and important to many players, hence misconceptions in regards to gauges based on string shape are a noteworthy issue. Somebody who really loves 1.23mm Ultracable will not find similar properties in a 1.23mm round string (vice versa).

Reading the title should suffice to see what I was going for. Spin indeed is something I had a formerly great interest in, but I am no longer interested in it as I was, simply because I realised that spin is achieved by the player and hence the string that allows the player in question to produce the most spin will help him, not the string which produces the most spin in theory/in the lab.

Next, for my seemingly rash recommendation: again, I was taking it in the spin direction (sorry), as (again) I thought that might've been a topic of interest. Firstly, I'd like to note that I'm aware of past experiments and how they've proven that all strings grab the ball, as that is obvious, but just how all polyester strings slide and snap back, and some do it to a greater extent, some strings grab the ball more than others, and yes, it can be affected by the string's shape. Here's why: firstly, from a physics standpoint, and how sharper objects exert more force, it is somewhat obvious that the edges on the string will have more friction than the sides of the string, and seeing how many edges there are could be noteworthy therefore. Nothing unsound there.

I don't accept "common sense" as an argument. Why do many strings with shape have bad ball to string friction numbers in TWU, especially considering that meanwhile some round strings have great numbers in this regard? The ball is so much larger than the strings, it isn't as obvious as you want to suggest that tiny edges will significantly increase "ball grab" or friction on their own. I recall a Babolat interview where it was said that RPM Blast's shape was not intended to "grab" the ball, but in order to allow for easier string movement. Have you ever considered that the string which slides easiest can perhaps grab the ball best, regardless of shape?

Furthermore, notice how all values in TWU are only frictional coefficients, I was simply trying to show that in an elastic material like a PET-based tennis string, the surface area in contact with anything matters, as it will deform and cause more force pushing it together compared to a regular inelastic collision. Moreover, I do hear you out on the contact angle part, but that is simply something that must be taken into account as an assumption based on a regular topspin (or slice) shot, and I do acknowledge that it is somewhat of an approximation to do so, but I believe that when it comes to comparing, that is alright. Furthermore, it is again interesting, at least to me, the surface area in contact between the strings during impact, since they deform as a cause of the ball impacting them, meaning that the total frictional force (compared to just the COF) could be different among strings of different shapes. Again, the TWU values, which I'm not demeaning in any way (they are extremely important), are only the coefficient of friction in a somewhat relaxed mode, since the strings there are experiencing the force divided by the number of strings usually in contact with the ball (which is also an assumption, shows that those can be ok for certain situations). Therefore, depending on surface area of contact between the strings, not only can the force pushing the strings together (normal force) change a lot, but even the μ can change. This, again, is because there is an elastic collision here.

Lots of hooha for speculation. You have so many currently unproven implicit assumptions that your argument is fully unsupported. Essentially, you're making a more or less baseless hypothesis here; if you want to discuss hypotheses, which might be completely mistaken, I ask you to seek a discussion with the TW Professor. What you are discussing may be helpful to a string producer, but not to a player.

Finally, when I wrote me findings, of course I am aware that there are many other factors to spin, and that is only one of the correlations which can be observed, I'm sorry if I wasn't clear enough, and you are certainly correct here as it is incorrect to say that one of many qualities is a deciding factor of anything without all else being equal, though do remember the values which I'm talking about are theoretical based on contact area, I'm talking about comparing total friction to μ based on the same principle(s), where μ is the given data. I'm truly sorry for not elaborting on that.

The correlation has not been observed to begin with, what are you even talking about?

Also, for the last bit, I was simply suggesting that there are ways to perceive data and it is not always correct to perceive raw data as absolute. Therefore, I stand by my word that this is sound reasoning, and am deeply sorry if I came off in any sort of negative or rash way. Also sorry if I hijacked the thread, if that happened, it was completely unintentional.

Are you being serious? This is simply unscientific thinking.

I hope I was a bit more clear this time, and again sorry if I wrote too much or if my reasoning seems unsound. I promise I'm simply trying to help, and of course it is perfectly alright to disagree respectfully. Cheers!

Unfortunately the main issue seems to be in the basis of what we consider to be reasonable conclusions. You are engaging in what I consider to be speculation and hypothesizing. I clearly presented and processed raw data and numbers in order to reach a reasoned conclusion, whereas you are simply stating your theories as if they were facts.

 

[El_Yotamo]

So it's futile to point out that the string shape can massively impact how thick a string may feel based on how the gauge is measured? It's futile to point out that the gauge equivalent area of Weisscannon Ultra Cable is that of a 1.38mm round string? This is anything but futile, gauge is easily understood and important to many players, hence misconceptions in regards to gauges based on string shape are a noteworthy issue. Somebody who really loves 1.23mm Ultracable will not find similar properties in a 1.23mm round string (vice versa).

Reading the title should suffice to see what I was going for. Spin indeed is something I had a formerly great interest in, but I am no longer interested in it as I was, simply because I realised that spin is achieved by the player and hence the string that allows the player in question to produce the most spin will help him, not the string which produces the most spin in theory/in the lab.



I don't accept "common sense" as an argument. Why do many strings with shape have bad ball to string friction numbers in TWU, especially considering that meanwhile some round strings have great numbers in this regard? The ball is so much larger than the strings, it isn't as obvious as you want to suggest that tiny edges will significantly increase "ball grab" or friction on their own. I recall a Babolat interview where it was said that RPM Blast's shape was not intended to "grab" the ball, but in order to allow for easier string movement. Have you ever considered that the string which slides easiest can perhaps grab the ball best, regardless of shape?



Lots of hooha for speculation. You have so many currently unproven implicit assumptions that your argument is fully unsupported. Essentially, you're making a more or less baseless hypothesis here; if you want to discuss hypotheses, which might be completely mistaken, I ask you to seek a discussion with the TW Professor. What you are discussing may be helpful to a string producer, but not to a player.



The correlation has not been observed to begin with, what are you even talking about?



Are you being serious? This is simply unscientific thinking.



Unfortunately the main issue seems to be in the basis of what we consider to be reasonable conclusions. You are engaging in what I consider to be speculation and hypothesizing. I clearly presented and processed raw data and numbers in order to reach a reasoned conclusion, whereas you are simply stating your theories as if they were facts.

However, what each of us has done is extremely different, is it not? And it is certainly not unscientific thinking to look past the numbers and manipulate them to make more sense, which if you noticed is what I did.
Furthermore, hypothesizing is simply the first step of the scientific method. Because sometimes, it is not enough to look at a spreadsheet of coefficients and call it a day. Also, I want to note that the correlation which I was talking about was observed by myself, and I'm again sorry for not elaborating to the fullest, I really thought it was clear enough. Also, one of my philosophies is that if something is important to a player, it will be important to a manufacturer, and vice versa. If not, it shouldn't really be important for either.
Moreover, for the "hooha speculation" part, I want to note that everything I described in that paragraph was one thing, which is not only proven by physics, but also regarded and accounted for in the TWU experiments: that PET co-polyester bends and deforms, and when it does, the numbers change. However, this number can be either smaller or larger based on shape, since that determines the area in contact.
Furthermore, I would like to bring up the part with the ball being bigger than the strings, as that is actually part of my point for this part: if the ball is as large as it is in comparison to the strings and the two deform against each other during impact, then different amounts of edges will be in contact with the ball based on shape, and before you say that does not matter, it is a real physical property that the same mass but sharper (thus less area making it more dense) exerts more force than the same mass but rounded (this is why sharp blades cut through things). The fact that these edges are as small as they are amplifies this effect. Your counter argument against shape here is numbers from these coefficients by the way, and that is exactly the reason that some shaped strings don't have very high numbers and some round strings do; when you account for the shape and gauge of the string, that's when the numbers start to make some more sense. Seriously, there are coefficients there for thick gauges of the same string being higher than thin gauges of the same string.
Also, yes, many people know that RPM's shape was made for sliding, that is also why it has a coating etc. Also, it wouldn't seem like it slides very well according to the posted numbers on TWU, but low and behold, people swear by this string (and one of its couterparts RPM Team) for low inter-string friction. This will make more sense if you regard the numbers as more than just numbers or figures (I'm currently writing a 4000 word essay on these subjects by the way, I might post it here when I'm done). If you realize that not only is contact area minimized with RPM's shape, as well as the fact that its dynamic inter-string friction coefficient will be far lower than its static compared to other strings because of its coating, things might start to be a bit clearer.
Furthermore, about the fact that some strings grab the ball regardless of shape if they slide the best, that is only one of the factors, is it not? It is not only about sliding the best, but also having a higher friction with the ball for sliding further and faster, and thus a mightier snap-back effect. And as a small note, considering all my rants have been about both these factors, is it not a bit negligent or even pretentious to ask if I've considered one of the two which I'm focusing on?
As another note on the actual post you made, I know what you mean by the "feel" of the thickness of the string, don't get me wrong here, but the first thing I look at is the stiffness and energy return before gauge, so I thought that if a triangle shaped string of 1.23mm had an "effective" 1.38 gauge, but the same properties as a 1.23 round string, they'd most likely play quite similarly. However, I understand the point of the post, as I do understand how the feeling and sensation of the string gauge can affect playability (and is one of the things I look at when I look at friction, since it affects the area of contact ). I also do put some small emphasis on this gauge feeling, as I do steer clear of anything thicker than 1.25mm.
And as a final note, I did want to point out that I agree with you on the fact that the player produces spin, and not the string, I am simply interested in these values because I only apply them to strings which must first be control oriented and playable enough, I'd never play a string with a high spin potential in the lab simply due to that, even if it doesn't have great control, feel, tension maintenance, etc. I, as always, just hope I could help, and I hope we can come to understand each other's viewpoints on the subject, it is after all a scientific quality to stay open minded. Cheers and regards as always.