Physics-Minded..How does the CB know?

[CueAndMe]

The stick transfers energy to the cue ball by compressing like a spring along its whole length. The compression wave happens at the speed of sound in the stick, which is about 13000 feet per second. This speed is the fastest that the butt can learn of something colliding with the tip. Some people make the mistake of thinking of the cue stick as being perfectly rigid and incompressible, but it's not. So, the shot proceeds like this: the stick is coming forward and the tip meets the ball. The tip starts to compress, force and acceleration of the cue ball start to build up. The ball also starts to compress, since it too is not incompressible. The ball has started to move, but is not up to the speed of the stick yet, and the stick has started to slow down as its energy is transferred to the cue ball. This continues until the tip (and ferrule and joint and butt) reach maximum compression along the length. At this exact point some amazing things are happening. The stick and ball are moving at the same speed. The force between stick and ball are at their maximum. The compression along the length of the stick (including the tip) is at its maximum. The energy stored in the spring-like compression of the tip (and stick and ball) are at their maximum. For a typical ball and stick, the speeds of the ball and stick are 75% of the original stick speed.

After this point of maximum compression, the ball is pushed forward from the tip by the compression of system. The ball starts to move even faster from this force and the stick continues to slow down. This "unwinding" process continues until the ball finally leaves the tip. At that point, the ball is going at about 130% of the original stick speed, and the stick has slowed down to about 50% of its original speed. (The 130% would be 150%, but the tip is not perfect in springing back to its original shape, and energy is lost.)

Now the hand comes in. Human flesh makes a much "softer" spring than the leather of a tip or the wood that is compressed along the length of the stick. Think of the tip as about the stiffest car spring you can imagine and your hand like a rubber band. The cue ball is gone by the time your hand -- which is still moving forward at full speed -- can wind up even a little. As the hand winds up on the stick and relaxes, which takes about 20 milliseconds, the hand is slowed to about 80% of its initial speed and the stick goes from 50% back up to 80% of its initial speed. Of course this re-acceleration of the stick by your hand is useless in that the cue ball is long gone.

How does a heavier stick affect things? It changes that 130% number. The formula is in Byrne's Advanced book, and somewhere in my columns in Billiards Digest and certainly in Ron Shepard's paper and Dr. Dave's book. A heavier stick through the spring action, puts slightly more energy into the cue ball.

As for how the weight of the stick affects the squirt, I think the answer is that it doesn't, much. Squirt is caused by the spinning cue ball pushing the stick to the side during the contact time of an off-center hit. The amount of squirt is determined by the mass that is being pushed to the side. Since the stick is very floppy side-to-side (as compared to length-wise compression), only the front part of the stick can participate in the squirt during the 1 millisecond or so of contact time. A heavier stick will increase the contact time a little, and that will increase the squirt a little, but I think this effect is pretty small.

Phrased technically, the transverse wave has a very slow propagation velocity along the length of the stick, and so the joint and butt cannot participate in the sideways push that causes squirt.

You should find Mike Page's discussion of his experiment with vise grips on the shaft which determined how much of the shaft participates in squirt.

As Fred mentioned, a major problem with some of the Jacksonville Project was that Iron Willie had too stiff a grip -- like vise grips -- and too hard a bridge. I have heard that Predator's current cue testing robot has fixed those problems to hold the cue more like a human at both ends.

As for some of your other questions, in theory the squirt should depend on stiffness of the cue since that should change the speed of the transverse wave. In practice, "end mass" seems to be a much better indicator of squirt than stiffness. There are stiff cues with little squirt and stiff cues with lots of squirt. A major red herring along the path of squirt studies was the fact that carom cues tend to be stiff but have relatively low squirt. They usually have smaller tips than pool cues.

Excellent! Thanks for such a thorough description. I'm beginning to see the light.
One thing I don't get is if the sideways shaft pushing from the spinning cueball causes squirt, and this happens too quickly for the rest of the cue to take part, when does the slower full-stick system-compression/force-transfer stuff take place on an offcenter hit? Afterwards?
If the cue is still in contact long enough to transfer its shotward force to the cueball, why isn't squirt affected during this time? Is squirt decided, over and done with, after only the inital stage of contact?
Thanks,
Jeff

 

[David Beck]

Here.
http://www.billiards.colostate.edu/physics/Shepard_squirt.pdf

 

[CueAndMe]

In practice, "end mass" seems to be a much better indicator of squirt than stiffness. There are stiff cues with little squirt and stiff cues with lots of squirt.

Isn't it about resistance to the spinning cue ball's force, rather than end mass necessarily? I'm picturing WorriedBeef's stiff stainless steel yet hollow light-end-mass cue striking the cueball right of center. But what if the right side of the cue, close to the cueball, was brushing against a dense immovable object?
Thanks,
Jeff

 

[Patrick Johnson]

Bob:
Many carom shafts have nearly conical tapers which makes them feel "stiff." The also often have fairly small tips (12mm or less) and short (very light) ferrules. If a carom cue like that were modified by removing wood in the first six inches, it would probably have less squirt as a result.

You've described the shaft I play with, but with a very small (10mm) tip. Ed Young made it for me and it plays pretty stiff because of the conical taper, but very low squirt because of the small tip, 1/4" ferrule and hollow front end.

pj
chgo

 

[Skeezicks]

Ed Young made it for me and it plays pretty stiff because of the conical taper, but very low squirt because of the small tip, 1/4" ferrule and hollow front end.

What's the SPP?

 

[Bob Jewett]

I ... But what if the right side of the cue, close to the cueball, was brushing against a dense immovable object?
Thanks,
Jeff

That's exactly how the scoop shot works as explained by Dr. Dave. You slide your stick along the cloth to hit the bottom of the ball and the cue ball jumps not because of a miscue but because the table is the mass on the other side. It's a totally unnatural shot, but try it to see if you can jump without a miscue. Make sure the edge of your tip is chalked well.

 

[Jaden]

This is exactly how I understood it with two exceptions.

The stick transfers energy to the cue ball by compressing like a spring along its whole length. The compression wave happens at the speed of sound in the stick, which is about 13000 feet per second. This speed is the fastest that the butt can learn of something colliding with the tip. Some people make the mistake of thinking of the cue stick as being perfectly rigid and incompressible, but it's not. So, the shot proceeds like this: the stick is coming forward and the tip meets the ball. The tip starts to compress, force and acceleration of the cue ball start to build up. The ball also starts to compress, since it too is not incompressible. The ball has started to move, but is not up to the speed of the stick yet, and the stick has started to slow down as its energy is transferred to the cue ball. This continues until the tip (and ferrule and joint and butt) reach maximum compression along the length. At this exact point some amazing things are happening. The stick and ball are moving at the same speed. The force between stick and ball are at their maximum. The compression along the length of the stick (including the tip) is at its maximum. The energy stored in the spring-like compression of the tip (and stick and ball) are at their maximum. For a typical ball and stick, the speeds of the ball and stick are 75% of the original stick speed.

After this point of maximum compression, the ball is pushed forward from the tip by the compression of system. The ball starts to move even faster from this force and the stick continues to slow down. This "unwinding" process continues until the ball finally leaves the tip. At that point, the ball is going at about 130% of the original stick speed, and the stick has slowed down to about 50% of its original speed. (The 130% would be 150%, but the tip is not perfect in springing back to its original shape, and energy is lost.)

Now the hand comes in. Human flesh makes a much "softer" spring than the leather of a tip or the wood that is compressed along the length of the stick. Think of the tip as about the stiffest car spring you can imagine and your hand like a rubber band. The cue ball is gone by the time your hand -- which is still moving forward at full speed -- can wind up even a little. As the hand winds up on the stick and relaxes, which takes about 20 milliseconds, the hand is slowed to about 80% of its initial speed and the stick goes from 50% back up to 80% of its initial speed. Of course this re-acceleration of the stick by your hand is useless in that the cue ball is long gone.

How does a heavier stick affect things? It changes that 130% number. The formula is in Byrne's Advanced book, and somewhere in my columns in Billiards Digest and certainly in Ron Shepard's paper and Dr. Dave's book. A heavier stick through the spring action, puts slightly more energy into the cue ball.

As for how the weight of the stick affects the squirt, I think the answer is that it doesn't, much. Squirt is caused by the spinning cue ball pushing the stick to the side during the contact time of an off-center hit. The amount of squirt is determined by the mass that is being pushed to the side. Since the stick is very floppy side-to-side (as compared to length-wise compression), only the front part of the stick can participate in the squirt during the 1 millisecond or so of contact time. A heavier stick will increase the contact time a little, and that will increase the squirt a little, but I think this effect is pretty small.

Phrased technically, the transverse wave has a very slow propagation velocity along the length of the stick, and so the joint and butt cannot participate in the sideways push that causes squirt.

You should find Mike Page's discussion of his experiment with vise grips on the shaft which determined how much of the shaft participates in squirt.

As Fred mentioned, a major problem with some of the Jacksonville Project was that Iron Willie had too stiff a grip -- like vise grips -- and too hard a bridge. I have heard that Predator's current cue testing robot has fixed those problems to hold the cue more like a human at both ends.

As for some of your other questions, in theory the squirt should depend on stiffness of the cue since that should change the speed of the transverse wave. In practice, "end mass" seems to be a much better indicator of squirt than stiffness. There are stiff cues with little squirt and stiff cues with lots of squirt. A major red herring along the path of squirt studies was the fact that carom cues tend to be stiff but have relatively low squirt. They usually have smaller tips than pool cues.

I know JoeyA had talked to you about what I had described to him and this is almost exactly what I had described to him with two exceptions. The first isn't really an exception but a correction. The speed of sound is approximately 1100 feet per second not 13000. The other thing that is different in what I perceive is happening has to do with the compression during an off center hit. The compression is not going to be perfectly tangential to the contact because one side of the tip or the other is making contact.

This means that the compression of an off center hit is going to be off center itself causing the compression of one side of the cue shaft. When the contact ceases, it is then that the compression of the shaft rebounds in the opposing direction. I believe that high speed video shows that shaft deflection does not occur until after contact ceases and this is cohesive with what I described as happening. If what you decribed of the CB "pushing" the shaft away from it is what was occurring, then high speed video should show the "pushing away" as happening "during" contact instead of after contact.

Jaden

 

[Jaden]

see my response on the off center hit.

Excellent! Thanks for such a thorough description. I'm beginning to see the light.
One thing I don't get is if the sideways shaft pushing from the spinning cueball causes squirt, and this happens too quickly for the rest of the cue to take part, when does the slower full-stick system-compression/force-transfer stuff take place on an offcenter hit? Afterwards?
If the cue is still in contact long enough to transfer its shotward force to the cueball, why isn't squirt affected during this time? Is squirt decided, over and done with, after only the inital stage of contact?
Thanks,
Jeff

I believe the answer to this is that the compression itself is off center causing the shaft to compress toward the side closest to the CB. What I believe really causes squirt is the off center compression of the shaft so that the shaft is actually pointing in a slightly different direction when the CB leaves the tip. When there is less end mass there is less opposing mass and therefore contact time is lessened allowing for less compression and therefore a lesser degree of angle differential that is caused by said compression.

Bob, I still think that I am right on this. Do me a favor and really think about what I am describing here and see if it doesn't fit a little more neatly with what you have seen in the experiments done with high speed video, etc... than the idea of teh CB pushing sideways on the shaft.


Jaden

 

[Patrick Johnson]

Jaden:
The speed of sound is approximately 1100 feet per second not 13000.

1,100 fps is the speed of sound through air. 13,000 fps is the speed of sound through maple.

Still think you're right?

pj
chgo

 

[CueAndMe]

What I believe really causes squirt is the off center compression of the shaft so that the shaft is actually pointing in a slightly different direction when the CB leaves the tip. When there is less end mass there is less opposing mass and therefore contact time is lessened allowing for less compression and therefore a lesser degree of angle differential that is caused by said compression.
Jaden

What you're describing certainly makes sense. Very interesting.
Jeff

 

[Jal]

...The other thing that is different in what I perceive is happening has to do with the compression during an off center hit. The compression is not going to be perfectly tangential to the contact because one side of the tip or the other is making contact.

This means that the compression of an off center hit is going to be off center itself causing the compression of one side of the cue shaft. When the contact ceases, it is then that the compression of the shaft rebounds in the opposing direction. I believe that high speed video shows that shaft deflection does not occur until after contact ceases and this is cohesive with what I described as happening. If what you decribed of the CB "pushing" the shaft away from it is what was occurring, then high speed video should show the "pushing away" as happening "during" contact instead of after contact.

Jaden

Jaden, the direction of the cueball tells us things. When you contact it on the right side, for instance, it scoots off to the left a little (squirt). This can only happen because the force exerted on it by the stick is pointing slightly to the left. This is the average direction of the force over the contact period. If you don't accept this fact, then you're going to have a very hard time explaining why the cueball ends up heading left. This is what forces do: they propel things, and they propel them in specific directions.

If you accept that, then consider Newton's Third Law. It tells us that whatever force the stick is exerting on the cueball, the cueball must be exerting an equal but oppositely directed force on the stick. If the force on the cueball is pointing forward and slightly to the left, as in our example, then the force on the stick is pointing backward and slightly to the right.

Now, if the force on the stick is pointing to the right, that's the direction the stick will be deflected. Why? Because that's how objects respond to forces: they get propelled in the direction the forces push them. They have no choice.

The models of squirt that are available (R. Shepard, Dr. Dave) do not tell the whole story. They are necessary simplifications of a very complex phenomena. Your off axis compression no doubt plays a part in any real life deviations from theory. But watch the cueball. It's giving us a summary of what's taking place during the collision.

Jim

 

[Andrew Manning]

Nobody's really given direct and correct answers (although a few have provided some not-quite-to-the-point correct physics):

1)Say you're the cue ball. You're struck at the same speed and contact point by the same modern low-squirt shaft placed on two different butts. The first contact is from a 17 oz. total weight cue. The second contact is from a 25 oz. total weight cue. How do you know to react differently?

Every action has an equal and opposite reaction. The collision between cue and ball makes the END of the cue deflect away from the ball. There is an IMPULSE during contact that causes this deflection. However, since every action has an equal and opposite reaction, the impulse deflects the ball in the other direction. Now, the more mass the DEFLECTED PORTION of the cue contains, the more lateral impulse there will be during contact (impulse is directly proportional to mass). So the mass of the part of the cue that deflects (the last few inches) is what causes the ball to deflect the other way in direct proportion.

2)Same scenario, but the 17 oz. cue is being held with a death grip, and the 25 oz. cue is being held with a feather touch that allows the cue to be thrown into the cueball. Still both cues contacting the cueball at the same speed. How does this change things? Does the arm's mass with the 17 oz. shot come into play, in essence, fusing with the cue's mass?

No. The arm's linkage with the cue is too loose to provide much effective mass to the cue due to the skin and flesh of the hand being too soft and flexible, and even if it did provide mass, it would not provide mass to the deflected portion of the shaft.

3)How about 2 cues with the same shaft and overall weight but the first has most of its weight forward, the second has most of its weight rearward?

It depends on the exact weight distribution. If the first shaft has more mass in the first few inches (the part that deflects away from the ball during contact), then it will cause the ball to deflect more.

4)How about 2 cues with the same shaft and overall weight but the first has most of its weight around the perimeter, the second has most of its weight in its core?

Should not change deflection.

What answers above would change depending on stick speed or CB contact point?

More stick speed means more impulse means more deflection. The cue will deflect much more quickly away from the ball with a faster stroke, and so the ball will deflect with more lateral momentum equally and oppositely.

For CB contact point, the further away from center the hit is, the faster the stick will deflect laterally, due to the ball's center of mass deflecting it from an angle more orthogonal to the cue. In a close to center hit, most of the deflection is back toward the cue (decelerating the stick), and only a little is directed to the side. In a hit further from center, the deflecting energy is directed more laterally, meaning the stick will deflect with more momentum in that direction, meaning the ball will equally and oppositely deflect more laterally.

I hope I've cleared things up more completely for you, it seemed like other answers were not meeting your questions head-on.

-Andrew

 

[hang-the-9]

I see it's been generally agreed upon that the mass in the first few inches of a shaft determines the amount of squirt. I can sort of grasp that, but I don't understand the effects of overall cue weight and weight distribution.

1)Say you're the cue ball. You're struck at the same speed and contact point by the same modern low-squirt shaft placed on two different butts. The first contact is from a 17 oz. total weight cue. The second contact is from a 25 oz. total weight cue. How do you know to react differently?

2)Same scenario, but the 17 oz. cue is being held with a death grip, and the 25 oz. cue is being held with a feather touch that allows the cue to be thrown into the cueball. Still both cues contacting the cueball at the same speed. How does this change things? Does the arm's mass with the 17 oz. shot come into play, in essence, fusing with the cue's mass?

3)How about 2 cues with the same shaft and overall weight but the first has most of its weight forward, the second has most of its weight rearward?

4)How about 2 cues with the same shaft and overall weight but the first has most of its weight around the perimeter, the second has most of its weight in its core?

What answers above would change depending on stick speed or CB contact point?

Thanks,
Jeff

The cue ball knows, it's smart. Here is another one.. those metal bouncy ball things.. 5 balls, you toss one up, the other end on rebounds. You toss 2 up, 2 rebound, not one double-high. Why? It just knows.

When you hit the cueball, the mass going forward on a heavier cue is more, so the cue-balls mass is less when compared to the cue, it would respond differently. That does not really affect deflection that much though. The reason the new shafts have less deflection, squirt, whatever, is the mass contacting the cue is less, and the design of the shaft causes it to rebound more, giving the cueball less off-angle force. They are also flex more evenly, which makes them more accurate, in theory.

 

[Bob Jewett]

... The speed of sound is approximately 1100 feet per second not 13000. ...

A good source for this sort of information is the CRC handbook of Chemistry and Physics, a copy of which is sitting next to me right now. I urge you to get one and to turn to the table on page E-43 which is labeled "Velocity of Sound." There are sections for solids, liquids and gasses and vapors. Under the section on solids, there are several numbers that are useful for this discussion. In particular:

Ash, along the fiber 4670 meters/second
Ash, across the rings 1390 meters/second
Ash, along the rings 1260 meters/second
Maple, along the fiber 4110 meters/second

Some other woods are listed, but ash and maple are the most common in cues. Since there are about 3.3 feet per meter, the speed of sound along a maple shaft is about 13484 feet per second. Of course this will vary some with the treatment of the wood, how the tree was grown, etc., but it is close enough for this discussion.

The speed of sound in water is about a mile per second, which is five times faster than in air, and is the reason that scuba divers have trouble locating sources of sound around them.

The speed of earthquake propagation, which in a sense is a kind of sound wave but on a grander scale, depends on which way the wiggle goes. The pushing component of an earthquake wave is the fastest, just as the pushing component of the tip-to-ball contact moves fastest down the stick. The side-to-side wiggling of an earthquake travels slightly more slowly but usually has most of the energy. The first, small, quick push alerts savvy earthquake veterans to take cover and is probably what causes animals to make a fuss just before the real shaking starts.

I hope this Freds.

 

[Bob Jewett]

... Bob, I still think that I am right on this. Do me a favor and really think about what I am describing here and see if it doesn't fit a little more neatly with what you have seen in the experiments done with high speed video, etc... than the idea of the CB pushing sideways on the shaft.


Jaden

If you really feel that the current explanation is lacking, then describe an experiment that clearly differentiates between what you claim and the current theory. The current theory has been pretty good at describing what can reduce squirt and what is not important. If your theory is not better at making predictions, then I think it is not useful. I'm afraid that you will need to include a technical discussion to the extent of describing actual forces, conservation of momentum, the time evolution of the forces during contact and other such things. The "other side" has done those things so it's fair to ask you to do them as well.

Since nothing is ever proven in science -- theories can only be disproven, not proven -- maybe you are right, but you will have to provide something more substantial than handwaving to support a hunch.

If it makes you feel any better, I believed for a long time that the hit-side of the stick compressed, and the stick turned into the ball and then shot the ball along the turned line. After seeing the high speed videos and thinking quite a bit about it, I concluded I was wrong.

 

[Patrick Johnson]

If what you decribed of the CB "pushing" the shaft away from it is what was occurring, then high speed video should show the "pushing away" as happening "during" contact instead of after contact.

That's what it shows.

pj
chgo

 

[Cornerman]

The first isn't really an exception but a correction. The speed of sound is approximately 1100 feet per second not 13000.

The speed of sound is through the cuestick, not through air. So, the speed of sound is many times faster through a rigid material.

{edit: I see this was already covered}

Fred <~~~ as slow as this computer

 

[Jaden]

Really Patrick????

That's what it shows.

pj
chgo

... For instance, much of the sideways deflection of the shaft happens after the cue ball is gone - you can see this in high speed videos.

pj
chgo

Patrick you should really make up your mind which one it is. Either the deflection is shown to be during contact or after contact. You can't have it both ways depending on what you're arguing for or against.

Jaden


And Bob, sorry about the speed of sound thing, I forgot about the different mediums. I have only dealt with it in designing firearms and soundsupressors so I was only aware of the speed of sound through air which is approx. 1100FPS.

Jaden

 

[Andrew Manning]

Patrick you should really make up your mind which one it is. Either the deflection is shown to be during contact or after contact. You can't have it both ways depending on what you're arguing for or against.

I'm not Patrick, but: the impulse that sets the end of the cue in motion laterally happens during contact. After contact, the cue continues to deflect further due to the lateral momentum it gained during contact. Because contact is so short, I think most of the cue's lateral movement takes place after contact is over, but I'm certain all of it is due to the lateral momentum imparted on it during contact.

Also during contact, while these momentum transfers are taking place, a lateral momentum equal and opposite to the one that causes the cue to deflect is imparted on the ball. This is the lateral momentum we call squirt.

Does that clear things up?

-Andrew

 

[Jaden]

no it doesn't "clear things up"

I'm not Patrick, but: the impulse that sets the end of the cue in motion laterally happens during contact. After contact, the cue continues to deflect further due to the lateral momentum it gained during contact. Because contact is so short, I think most of the cue's lateral movement takes place after contact is over, but I'm certain all of it is due to the lateral momentum imparted on it during contact.

Also during contact, while these momentum transfers are taking place, a lateral momentum equal and opposite to the one that causes the cue to deflect is imparted on the ball. This is the lateral momentum we call squirt.

Does that clear things up?

-Andrew

I will have to do as Bob suggested and devise some method of testing. Considering that he believed initially the exact thing that I do, does lead me to want to look further into this. I was prepared to just accept that you are wrong and just accepting the paradigm of the time but now I am influenced to delve deeper into the crux of the matter.

This reminds me of scientists initially creating the ether after the discovery of lightwaves and then switching to particles behaving as waves, when they were closer to the truth the first time. The thing that led them astray was the belief that they had to create an undiscovered medium for the waves to travel on, when they already had space/time. radiowaves travel on speac.time itself, and while I can't prove this as of yet, as Bob already stated and anyone who knows of Descartes' philosophy should know that only that you exist can be proven. In science hypotheses can only be disproven or rather, a better hypothesis that explains phenomena better can be introduced.

I still believe that I am correct and until I have the opportunity to develop some sort of tests and review the high speed video myself, I will believe that I am correct, because the other explanation does not fit as well, IMO.

From what I have seen, from what little high speed photography that I have seen, At the very LEAST, the tip on an off center hit is pointing in the direction that the CB travels and that alone would validate what I say is happening. The funny thing is, is that I don't disagree with what you are saying, although you think that what I am saying is not taking place.

The CB does provide lateral pressure, or rather off center pressure, on the shaft, but the shaft is still traveling forward and as such it must be compressed backward. Since this backward pressure is off center it will compress to one side. That HAS to be occurring, whether it is only a marginal amount remains to be seen. The question then remains, Is the tip compression the majority of the compression or does the shaft compression also have a marginal affect on the outcome of the amount of squirt?

It appears from testing already conducted that flimsyness of shaft does not have a substantial affect on the amount of squirt. I agree with this. The amount that the shaft bows is incidental when compared to endmass, because the endmass of the cue will be a direct correlation to the amount of compression because of the differing masses of the interrelating masses.

If the mass of the end of the shaft is greater then it will have a greater amount of affect on the mass of the CB and the tip or shaft will compress more causing a greater offset angle and greater squirt. Because only the last few inches of the shaft have an opportunity to compress before contact ceases, the mass beyond those first few inches doesn't matter.

If this is true then I would predict that with less endmass there would be less compression and less return of the feel of the hit to the one holding the cue. I do believe that many people HAVE reported that there seems to be less return of feel of hit when using low deflection tech.

This whole attitude of "Do you NOW understand what is happening?" is exactly why science in general has degraded so far. As soon as you develop the attitude that the concensus is all that is true and correct, you are doomed to be stuck in whatever pardigm currently exists and innovation will be left to those who aren't stuck within the current paradigm.

Jaden