On the measurement of court speeds

Benhur

Hall of Fame
Requests for proper speed tests that would attempt to measure the court speeds of different surfaces relative to one another, are sensible and reasonable requests. A brief reflection on what these tests would involve to be properly conducted, makes me be pessimistic that they will ever be conducted.

First you define what you need to measure. Let’s say it is the horizontal speed of the ball, post-bounce, off various different shots on different surfaces.

Some essential things in no particular order:

- devise a good enough variety of shots to be tested. Two or three different kinds of topspin shots at different rpms, different speeds, and different angles when leaving the ball machine. Same thing with flat shots, underspins, and serves.

- ensure that the exact same machinery is used in all tests and calibrated prior to each test so that the parameters (speed of shot of the machine, angle, rpm) are indeed the same, as well as the measuring techniques for the horizontal speed post bounce.

- ensure that atmospheric conditions that vary from day to day (temperature, humidity, wind and air pressure) and that affect the speed and trajectory of the ball, are the same on all tests. This may well be the most difficult condition to attain, next to impossible, and the only way to compensate for its impossibility would be to increase the sample size under various conditions hoping they would cancel each other out.

Though such comparative tests would not be impossible in principle, they would be expensive to carry out, and they are very unlikely. On the other hand, if they are not conducted properly, and only a few shots are measured without regard to all these factors, the potential for large skewing would be too large for them to have much validity.
Now, in the absence of such tests, there is simply no objective measure to rank court speed directly. Anecdotal evidence that so and so said he felt the courts were faster or slower when he played so and so on such and such day are really not what you call “hard data”. They are in fact pretty meaningless as a measure of anything.

So in the absence of any reliable direct speed tests, it seems to me the next best measure is some kind of proxy measurement that can rely on hard objective data and be free of subjective impressions. One can think of several such proxy measurements, among them length of points, percentage of points won by the receiver, and percentage of games won by the receiver.

The easiest of these to compute based on existing data is the latter. Demonstrating that there is a general relation between percentage of breaks and court speed is not difficult. Which surfaces are faster and which are slower in general, is already known, even though without precision. This we call generally perceived speed. You would need to be slightly deranged to argue this carries no weight and that MC might just be faster than Lyon, for all we know, etc. Since the general relation between perceived court speed and breaking frequency has long been known intuitively and can easily be confirmed through comparisons of breaking percentages on different perceived court speeds (again, by perceived court speeds I mean court speeds whose ranking relative to one another is generally accepted as known; for example, the fact that clay is generally slower than grass, etc.) then there is no question but that breaking percentage can act as a fairly reasonable and reliable proxy measurement for this variable. In fact, it is probably more reliable than many others that are routinely used on other fields:

http://en.wikipedia.org/wiki/Proxy_(climate)
http://en.wikipedia.org/wiki/Proxy_(statistics)

Finally, I will mention that those who continue arguing against the lack of objectivity or "science” in using breaking percentage as a proxy indicator of court speed, have themselves nothing whatsoever to offer in the way of objectivity and "science", except purely anecdotal trivialities based on the “feeling” of such or such player, or on their own impressions, or on the fact that such and such player made it to such and such round. Not particularly impressive.

Even more absurd is the supposition that these analysis are prompted by a need to defend or attack particular players.

When these discussions about Wimbledon "turning to clay" began a few years ago, I quickly realized there were no reliable available direct measurements to confirm this. I also realized there was an enormous amount of confusion about what is meant by “court speed”. It was then I began to think of possible proxy indicators that could shed some light away from all that muddy chatter. I first thought that the percentage of points won by receivers vs total points played, over entire tournaments year after year, would be a pretty good indicator. But since this data is not readily available, obtaining in the necessary amounts to get large sample sizes would be extremely lengthy. Next best thing would be to focus on games won by receivers vs total games. When NF presented his first set of results on this, I was in a sense not surprised to see the correlation with perceived court speeds easily confirmed. But on the other hand I was surprised at how clear and smooth the correlation was when using these very large samples. This completely convinced me that, in the absence of those direct tests, breaking percentage is by far the best available proxy indicator of this variable.

Those who deride it as outlandish and “unscientific” should have better things to offer than the reproduction of anecdotal comments about the impressions some players or people have.
 
Great thread. Other proxy factors could include are aces and percentage of first serve points won. All are good indicators of how much difficulty the players are handling the pace combining with the surface. For more baseline analysis, the total amount of winners per total points would be great as well. If there are any sites that have this info, it would help us further.
 
dubai is the fastest.

proof: roddick 56 service games not broken at all. he played nadal and djokovic - great returners
 
dubai is the fastest.

proof: roddick 56 service games not broken at all. he played nadal and djokovic - great returners
Did you read the thread? One player going on fire is not enough proof to say that this surface is the fastest. It might also show how comfortable Roddick is with his movement on hardcourts as he backed up his serve very well.
 
Did you read the thread? One player going on fire is not enough proof to say that this surface is the fastest. It might also show how comfortable Roddick is with his movement on hardcourts as he backed up his serve very well.

yes, i did read the thread, but brought in a theory to prove this.
 
yes, i did read the thread, but brought in a theory to prove this.
I saw some of the rallys of those matches. They were pretty long. Roddick was feeling it. The surface was fast but not too fast. The dry conditions of Dubai also made it a little quicker.
 
When I have nothing to say, I just attach the suffix "****" to the names of various players. ****iness of mind comes naturally to me. I recommend this technique to every one. It is easy and it "feels" better than saying nothing. I am a believer in Feeling and its expression

I tried to answer briefly but got this message:

"The message you have entered is too short. Please lengthen your message to at least 10 characters."
 
Surfaces are unquestionably slower today than in the 90's which is why Federer is certainly a better server than Sampras was, achieving better results despite playing in a much less serve-friendly era.
 
I tried to answer briefly but got this message:

"The message you have entered is too short. Please lengthen your message to at least 10 characters."


Calling you out is so much fun. You have yet to deny you are a Nadal fan. That throws huge bias on your analysis of anything related to surface speeds. And as stated in other threads, you are trying to use statistical science to prove your point, yet you don't follow the rules of statistical science. A basic and fundamental element. Never assume. But hey, I'm just a **** according to you. Don't listen to me :)
 
Surfaces are unquestionably slower today than in the 90's which is why Federer is certainly a better server than Sampras was, achieving better results despite playing in a much less serve-friendly era.

So, to summarize the situation. In the "serve-friendly era," as you call it, servers in the majors were having a harder time holding serve than today. Exactly what you would expect, right? But things have now gotten so un-friendly for servers that they are not only holding serve easier, but they are even having an ace-fest record at Wimbledon.
 
So, to summarize the situation. In the "serve-friendly era," as you call it, servers in the majors were having a harder time holding serve than today. Exactly what you would expect, right? But things have now gotten so un-friendly for servers that they are not only holding serve easier, but they are even having an ace-fest record at Wimbledon.

Stop using logic and common sense, Benhur!

You need correlation statistical analysis tests!
 
Finally, I will mention that those who continue arguing against the lack of objectivity or "science” in using breaking percentage as a proxy indicator of court speed, have themselves nothing whatsoever to offer in the way of objectivity and "science", except purely anecdotal trivialities based on the “feeling” of such or such player, or on their own impressions, or on the fact that such and such player made it to such and such round. Not particularly impressive.

You have really outdone yourself this time,Lestrade.You are quite precipitant with your latest supposition. Break percentage is no more emblematic of overall surface speed than alternative axioms. I aggrandize the International Tennis Federations scientific analysis over your rudimentary hypothesis. It is all rather elementary.

The perception of surface speed is garnered by height of bounce and horizontal speed. I shall trust their scientific formula measuring court speed over the penurious suggestion that break percentage is a preferred proxy.

The ball is bouncing higher at Wimbledon, therefore it is slower.

28mn5ae.jpg

http://www.itftennis.com/shared/medialibrary/pdf/original/IO_39418_original.PDF
 
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I am soooooo glad someone posted one of these threads. I was getting bored with the other 19 that we have. I didn't know what I was going to do without more illogical thoughts, half-truths, and denunciations of common sense.
 
You have really outdone yourself this time,Lestrade.You are quite precipitant with your latest supposition. Break percentage is no more emblematic of overall surface speed than alternative axioms. I aggrandize the International Tennis Federations scientific analysis over your rudimentary hypothesis. It is all rather elementary.

The perception of surface speed is garnered by height of bounce and horizontal speed. I shall trust their scientific formula measuring court speed over the penurious suggestion that break percentage is a preferred proxy.

The ball is bouncing higher at Wimbledon, therefore it is slower.

28mn5ae.jpg

http://www.itftennis.com/shared/medialibrary/pdf/original/IO_39418_original.PDF

No information appears on the methods used to calculate SPR, except that it supposedly implies the measurement of horizontal speed as it changes depending on the level of friction the surface offers. This is clear from the paragraph that starts with “rougher surfaces” and the two subsequent ones.

Then they say that CPR uses the previous measurement, and modulates it with the "coefficient of restitution" to take into account the height of the bounce.

The first thing that occurs to me is that this is redundant. If SPR is based on measuring horizontal speed, this measurment ALREADY factors in the coefficient of restitution. This is to say, a ball bouncing on a surface with a lower coefficient of restitution, will show a greater horizontal speed than a ball bouncing on a court with a higher coefficient of restitution, if both balls reached the ground at the same speed and angle.

The really crucial part to know about this is to know how they went about measuring the horizontal speeds. Which in fact is ALL you have to measure. What horizontal speeds you get from equal shots on different surfaces. If you know that, the coefficient of restitution would seem irrelevant (already factored in). If you don’t know that (if you only know the linear speed of the ball along its own trajectory after the bounce) then of course you need the coefficient of restitution, which will give you the angle of the bounce, from which through simple trigonometry you can calculate the horizontal vector.

I would really like to know what kind of tests were used to measure the horizontal speed (or any other speed) on rating any surfaces. What shots were used. What speeds. What regards for replication of speeds and spins and angles off the ball machine. What regards for equality of atmospheric conditions. What specific surfaces where rated. None of this is given to allow anyone to evaluate the soundness of the methods.
 
Stop using logic and common sense, Benhur!

You need correlation statistical analysis tests!



You cannot use common sense to correlate two factors in a statistical analysis. That is wrong and a basic and elementary mistake. If you've ever taken a statistics class you would know this.
 
No information appears on the methods used to calculate SPR, except that it supposedly implies the measurement of horizontal speed as it changes depending on the level of friction the surface offers. This is clear from the paragraph that starts with “rougher surfaces” and the two subsequent ones.

Then they say that CPR uses the previous measurement, and modulates it with the "coefficient of restitution" to take into account the height of the bounce.

The first thing that occurs to me is that this is redundant. If SPR is based on measuring horizontal speed, this measurment ALREADY factors in the coefficient of restitution. This is to say, a ball bouncing on a surface with a lower coefficient of restitution, will show a greater horizontal speed than a ball bouncing on a court with a higher coefficient of restitution, if both balls reached the ground at the same speed and angle.

The really crucial part to know about this is to know how they went about measuring the horizontal speeds. Which in fact is ALL you have to measure. What horizontal speeds you get from equal shots on different surfaces. If you know that, the coefficient of restitution would seem irrelevant (already factored in). If you don’t know that (if you only know the linear speed of the ball along its own trajectory after the bounce) then of course you need the coefficient of restitution, which will give you the angle of the bounce, from which through simple trigonometry you can calculate the horizontal vector.



I would really like to know what kind of tests were used to measure the horizontal speed (or any other speed) on rating any surfaces. What shots were used. What speeds. What regards for replication of speeds and spins and angles off the ball machine. What regards for equality of atmospheric conditions. What specific surfaces where rated. None of this is given to allow anyone to evaluate the soundness of the methods.

The COR is significant ,the height of the bounce contributes to the players perception of time,not only the horizontal speed, as evidenced by the following chart.



IO_39412_staticarticle.JPG

http://www.itftennis.com/shared/medialibrary/image/staticarticle/IO_39412_staticarticle.JPG

The following page clarifies the CPR formula and testing procedures


http://www.itftennis.com/technical/equipment/itfguidetotestmethods/courtpace.asp
 
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Yes a poster that thinks Nadal on steroids probably doesn't appreciate well thought out threads.

When did I ever say that I thought Nadal was on steroids? This thread isn't well thought out. The OP just threw a bunch of well-constructed sentences together. Other posters have already weighed in on this.

lol. exactly.

Do you even know what you're 'lol-ing' about?
 
You cannot use common sense to correlate two factors in a statistical analysis. That is wrong and a basic and elementary mistake. If you've ever taken a statistics class you would know this.

This is true. I learned this the hard way on a written assignment :(
 
When did I ever say that I thought Nadal was on steroids? This thread isn't well thought out. The OP just threw a bunch of well-constructed sentences together. Other posters have already weighed in on this.
You supported Drakulie and Rabbit's argument on steroids. I would assume that means you think Nadal is on steroids. And I find that the most ridiculous thought on this board.
 
You supported Drakulie and Rabbit's argument on steroids. I would assume that means you think Nadal is on steroids. And I find that the most ridiculous thought on this board.

Not right to say Lifted supported it. But yes lifted wrote a very long serious post about it.
 
You supported Drakulie and Rabbit's argument on steroids. I would assume that means you think Nadal is on steroids. And I find that the most ridiculous thought on this board.

I recall saying that the argument itself can be made from the circumstantial evidence (although there's not really enough to flat out state anything...which, by the way, neither of them did), not that I actually think that it's true. All I'm saying is that I respect Drakulie and Rabbit as posters, so I will furrow my brow and ponder deeply what they post on the subject of weirdness (note: not necessarily doping) surrounding Nadal's withdrawal.

By the by, in case you're wondering, I used to post/lurk here a while ago but I had my account deleted because the time spent lurking and posting was too much, so I decided to just lurk. Not really sure why I got a new account...

Not right to say Lifted supported it. But yes lifted wrote a very long serious post about it.

Hey, a serious post for a serious topic. ;-)
 
This is to say, a ball bouncing on a surface with a lower coefficient of restitution, will show a greater horizontal speed than a ball bouncing on a court with a higher coefficient of restitution, if both balls reached the ground at the same speed and angle.

Are you using coefficient of restitution as a signed number (positive or negative)? Because if you use absolute values for it, lower the coefficient, lower the rebound speed (coefficient = - vfinal/vinitial for bouncing off a stationary surface). This is a vector equation, but again not knowing how the ball reflects off the ground, we do not know how the vertical and horizontal components are related.
 

The COR is significant ,the height of the bounce contributes to the players perception of time,not only the horizontal speed, as evidenced by the following chart.



IO_39412_staticarticle.JPG

http://www.itftennis.com/shared/medialibrary/image/staticarticle/IO_39412_staticarticle.JPG

The following page clarifies the CPR formula and testing procedures


http://www.itftennis.com/technical/equipment/itfguidetotestmethods/courtpace.asp

This is excellent.
My questions are. How do they calculate the correction to be applied due to the perceptional aberration. What I mean to say: take two balls with the same horizontal speed post bounce. But one of them is moving at a lower angle than the other. If I understand this correctly, the player will perceive the lower ball as moving faster toward him, though the horizontal speed is actually the same. How do they calculate how much the player's perception quickens the second ball, in order to apply the correction? And is this misperception constant for all players? Because in fact, in the example I just gave with both balls at the same horizontal speed, the first one (higher bounce) must have a faster linear speed.

The second question regards the third paragraph under Testing Procedure. To quote:
3. "For any surfaces that have an inherent directional pattern – such as natural or artificial grass – test shots should be fired in the typical directions of play, i.e. parallel to the length of the court."

Well, what do they mean by courts having inherent directional patterns? And how can the comparison be made between surfaces by this method, if on certain surfaces the ball is fired at a different angle than on othes?

Also, have they assigned values for the surfaces of the main tournaments by this method? If so, is this information available?

Mi misgivings about equalizing atmospheric conditions are diminished if in fact the distance travelled by the ball between the machine and the ground is greatly reduced, as the illustration seems to indicate (unless the illustration is a simplification of the process).

Other than that, it looks like they've put more thought and work into this than I had previously thought. Great information. Thanks
 
Seems the simplest way is just to measure how high the ball bounces when dropped from the same height. Lower bounce = faster surface (for the surfaces commonly used - of course if you drop a ball on a sand beach and it doesn't bounce at all, you cannot conclude that sand is the fastest surface out there).

Is there really any need to use proxies like first serve %tage etc which depends on the server and returner and so many other variables?
 
Are you using coefficient of restitution as a signed number (positive or negative)? Because if you use absolute values for it, lower the coefficient, lower the rebound speed (coefficient = - vfinal/vinitial for bouncing off a stationary surface). This is a vector equation, but again not knowing how the ball reflects off the ground, we do not know how the vertical and horizontal components are related.

I understand the coefficient of restitution as the percentage of restitution of the angle of incidence after the bounce, which on an ideal non friction, non skid surface, with no spin, should be equal to the post bounce angle, so the coefficient should be 1. In real conditions it can be higher or lower than 1 depending on the characteristics of the surface and on the kind and amount of spin.

What has me a bit perplexed, as I mentioned, is how they calculate the degree of misperception by the player in judging the speed of two balls with equal horizontal speed but at different post bounce angles.
 
Seems the simplest way is just to measure how high the ball bounces when dropped from the same height. Lower bounce = faster surface (for the surfaces commonly used - of course if you drop a ball on a sand beach and it doesn't bounce at all, you cannot conclude that sand is the fastest surface out there).

I disagree. That method would be too simple. If by dropping you mean perpendicular to the ground, a ball dropped on clay would bounce lower than a ball dropped on cement or on wood. But clay is not considered faster than cement or wood.
 
I disagree. That method would be too simple. If by dropping you mean perpendicular to the ground, a ball dropped on clay would bounce lower than a ball dropped on cement or on wood. But clay is not considered faster than cement or wood.

I thought about that, but sort of convinced myself it would bounce higher on clay. On second thoughts, no.

The coeff of restitution in Wikipedia is simply final velocity/initial velocity. If it is smaller, the emerging velocity is smaller. If it is not perpendicular, the results should be the same, isn't it?

What about the simple coefficient of friction? Lower the friction, faster the surface? How does that sound?
 
I disagree. That method would be too simple. If by dropping you mean perpendicular to the ground, a ball dropped on clay would bounce lower than a ball dropped on cement or on wood. But clay is not considered faster than cement or wood.
This is where the firmness of the surface makes a difference. A harder surface absorbs less energy than a softer surface. Same thing with grass. The newer grass absorbs less of the energy to the old grass. Thus why you can have just as fast of grass now while having some pretty high bounces. If you made the grass thicker, the ball would bounce lower and go slower. So this has to be taken into account. The coefficient of friction only partially tells the story.
 
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This is where the firmness of the surface makes a difference. A harder surface absorbs less energy than a softer surface. Same thing with grass. The newer grass absorbs less of the energy to the old grass. Thus why you can have just as fast of grass now while having some pretty high bounces. If you made the grass thicker, the ball would bounce lower and go slower. So this has to be taken into account. The coefficient of friction only partially tells the story.
What is under the top surface has almost no effect whatsoever. A firmer soil under the grass won't make much of a difference. How long the grass is, will. The type of seed, will. If the soil is more compact underneath the grass, wouldn't change much.

Or don't you know a claycourt has 5 feet or a hard surface (compressed clay, crushed stone (or grave), chunks of bricks, smaller chunks of brick, and another layer of compacted clay) underneath the slow, slow top layer of crushed bricks?

Carpet is a really soft surface, yet it comes out really fast because there's almost no friction. Now, put SAND over the carpet, and you'll get a weird surface. Low bounces, but with a vertical component, making the ball SIT UP. A low bounce, slow surface (just like artificial grass with sand on top)

Friction comes into account way more than the firmness of the surface. What's underneath the surface itself is not really relevant.

Put a normal furry carpet on top of the fastest hardcourt, and you ruined the surface by slowing it down.
 
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What is under the top surface has almost no effect whatsoever. A firmer soil under the grass won't make much of a difference. How long the grass is, will. The type of seed, will. If the soil is more compact underneath the grass, wouldn't change much.

Or don't you know a claycourt has 9 feet or a hard surface (compressed clay, crushed stone (or grave), chunks of bricks, smaller chunks of brick, and another layer of compacted clay) underneath the slow, slow top layer of crushed bricks?

Carpet is a really soft surface, yet it comes out really fast because there's almost no friction. Now, put SAND over the carpet, and you'll get a weird surface. Low bounces, but with a vertical component, making the ball SIT UP. A low bounce, slow surface (just like artificial grass with sand on top)

Friction comes into account way more than the firmness of the surface. What's underneath the surface itself is not really relevant.

Put a normal furry carpet on top of the fastest hardcourt, and you ruined the surface by slowing it down.
Cliff Drysdale said that the grass now is much firmer. I don't care how it got firmer. A firmer feel equals less energy absorbed. Clay on top of a hard court will definitely change things over clay on top of soft dirt or whatever they use to make the bounces less active. But grass in the 90's was considered very low bouncing due to the softness of the soil or the grass itself. There wasn't much friction either so you got a pretty fast surface with very low bounces. Nowadays you get the same speed about but with more toward medium bounces. The surface underneath it always matters unless you got a lot of top layer to take away most of the effects underneath. Grass isn't thick enough to totally take away the effects of the soil. Especially since a lot of the court is dead grass and dirt sticking out.
 
That's what you don't understand. If the soil absorbs less energy, it could never bounce VERTICALLY. If it regains some of the enery (previously) lost, the ball keeps moving forward, and not UP. It takes FRICTION to make a ball bounce up (gripping the surface. That's why Rebound Ace was considered a slow surface)

Carpet has no friction, the surface absorbs little energy, the ball bounces and keeps his forward momentum. The ball comes off faster, and with a low bounce.

If the ball bounces higher (more vertically), it could NEVER be just as fast. It cannot be fast and have vertical bounces. In order to have high bounces, some energy must be transferred.

The soil doesn't make much of a difference. That's what you don't seem to understand. The soil under a claycourt is as firm as you could get.
 
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That's what you don't understand. If the soil absorbs less energy, it could never bounce VERTICALLY. If it regains some of the enery (previously) lost, the ball keeps moving forward.

If the ball bounces higher (more vertically), it could NEVER be just as fast. It cannot be fast and have vertical bounces. In order to have high bounces, some energy must be transferred.

The soil doesn't make much of a difference. That's what you don't seem to understand. The soil under a claycourt is as firm as you could get.
The new grass could have more friction while absorbing less energy. See what I mean?
 
Physics 101, my friend:

SCIENCE CONCEPT:

When a ball bounces on the court, its speed is reduced significantly by its interaction with the court surface. When the ball slows down a great deal after it bounces, the court is called slow. A fast court does not slow the ball down as much. There are two things that affect the court's speed: The coefficient of restitution (COR) and the coefficient of friction (COF).

The COR characterizes how high the ball will bounce if you drop it from a given height. The high COR court surface gives the ball a higher bounce. The low COR surface gives the ball a lower bounce. The COR is defined as the ratio of the vertical ball speed after the bounce to the vertical ball speed before the bounce. The COF is the measurement of the frictional force of the court surface on the ball. This is in a direction parallel to the surface. Friction slows down the ball. A high value of COF indicates a high frictional force on the ball.

The horizontal speed of the tennis ball is affected more by the friction than by the COR. While the COR does influence the vertical speed of the ball, the friction affects the horizontal velocity of the ball. The horizontal velocity is what determines the speed of the court.

The greater the friction between the ball and the court, the slower the ball will be after it bounces. The greater the friction, the slower the court. If the ball leaves the court before rolling begins, the court is considered fast. Vertical speed loss is affected by the COR. In terms of science, the laws of physics how fast or slow a court is.
 
^^ More friction = Absorbs more energy

What you just described defies the laws of physics.
I was talking about the overall energy. Friction descibes the horizontal/vertical relationship. Think of this way. The old grass described in an equation wouldn't travel as far as the new grass. Thus there has to be less horizontal and vertical length combined. So the old grass in a made up equation of mine is x+y=12 and the new grass is x+y=14. If x is horizontal distance and y is vertical distance than x could be 9 for both while y is 3 for old grass and 5 for new grass. This is what I believe is the case. Just like a gritty hardcourt would bounce pretty high, the same with a grass court that allows for more vertical length. Probably due to it having more similarities to a hardcourt than in the past due to increased firmness.
 
Physics 201

Ball physics studies would certainly be a lot simpler if we could narrow the variables down - for example, just count the ball spin (which has its own unique issues). However, the majority of ball physics studies must monitor a multitude of simultaneously changing factors to obtain results. Such is the case with ball/court interaction studies.

Aside from environmental factors and atmospheric conditions like wind, altitude, temperature, humidity and air pressure, the ball's trajectory after its bounce is affected by:


* the velocity before bounce;
* the angle the ball strikes the court (angle of incidence or angle in);
court surface material;
* ball spin type and rate;
* the behavior of the ball's materials.

Why examine ball/court interaction at all?

These components affect the angle and velocity off of the court, the distance the ball travels after the bounce and the maximum rebound height. With a variety of court surfaces available, ball/court interaction affects the amount of time you have to get to the ball and the height the racquet can approach and strike the ball. If you have played on a variety of surfaces you know grass courts are considered "fast" (you typically have less time to get to the ball and the angle after the bounce is typically low) and clay courts are "slow." Hard court speeds are somewhere in between.

As a guideline, what results would we expect? According to Professor Howard Brody's book, Tennis Science for Tennis Players, friction between the ball and the court:

* causes the angle out (the rebound bounce) to change from the angle in;
* the smaller the friction the smaller the rebound angle;
* the smaller the friction the faster the court;
* the larger the friction the greater the rebound angle;
* the greater the friction the slower the court.
 
I was talking about the overall energy. Friction descibes the horizontal/vertical relationship. Think of this way. The old grass described in an equation wouldn't travel as far as the new grass. Thus there has to be less horizontal and vertical length combined. So the old grass in a made up equation of mine is x+y=12 and the new grass is x+y=14. If x is horizontal distance and y is vertical distance than x could be 9 for both while y is 3 for old grass and 5 for new grass. This is what I believe is the case. Just like a gritty hardcourt would bounce pretty high, the same with a grass court that allows for more vertical length. Probably due to it having more similarities to a hardcourt than in the past due to increased firmness.
What you believe has no physics basis whatsoever. You're trying to make me look at an 'invented' way with no scientific basis. You're using 5 years old math, INSTEAD OF PHYSICS!!!!
 
What you believe has no physics basis whatsoever. You're trying to make me look at an 'invented' way with no scientific basis. You're using 5 years old math, INSTEAD OF PHYSICS!!!!
Do you believe that every serve goes the same distance from one surface to the next if the serves are exactly the same? This is where it gets complex. The energy absorbed from the surface cuts down the distance. Like a wet clay court would absorb more energy than a dry clay court as an example. I'm sure there is a physics lesson to explain this.
 
Physics 101, my friend:

SCIENCE CONCEPT:

When a ball bounces on the court, its speed is reduced significantly by its interaction with the court surface. When the ball slows down a great deal after it bounces, the court is called slow. A fast court does not slow the ball down as much. There are two things that affect the court's speed: The coefficient of restitution (COR) and the coefficient of friction (COF).

The COR characterizes how high the ball will bounce if you drop it from a given height. The high COR court surface gives the ball a higher bounce. The low COR surface gives the ball a lower bounce. The COR is defined as the ratio of the vertical ball speed after the bounce to the vertical ball speed before the bounce. The COF is the measurement of the frictional force of the court surface on the ball. This is in a direction parallel to the surface. Friction slows down the ball. A high value of COF indicates a high frictional force on the ball.

The horizontal speed of the tennis ball is affected more by the friction than by the COR. While the COR does influence the vertical speed of the ball, the friction affects the horizontal velocity of the ball. The horizontal velocity is what determines the speed of the court.

The greater the friction between the ball and the court, the slower the ball will be after it bounces. The greater the friction, the slower the court. If the ball leaves the court before rolling begins, the court is considered fast. Vertical speed loss is affected by the COR. In terms of science, the laws of physics how fast or slow a court is.

Now i'm confused. Earlier, you said firmness affects speed and friction affects height (more sand>>more friction>>more height).

But here, you say that the COR affects the height and friction affects speed. Am I missing something, or misquoting or something?
 
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