A ball struck by a cue in billiards with English goes straight at first....

[poolplayer]

'Stroking' along the side may well affect the accuracy of that approximation. Would I be right unsaying that stroking is sometimes used for some shots?

Some players including professional players use that kind of shots when they have to hit with right/left English. I think it is not like stroking or scratching on the ball, but rather an attempt not to push against the impact of cue-to-ball collision, which results in a sudden change of the cue direction to the side during/after the collision. They believe that it makes the ball go more straight (more parallel to the initial cue direction). Massive 'stroking' might be used in some masse shots, but this is not related to this thread.

This kind of shots may affect the ball direction. However, many people do not use that shot, but still can make a ball go almost straight with right/left English. So, I guess its effect would be small, maybe ~1-2° at most. I don't use that shot because it hurts consistency of shots.

 

[poolplayer]

Yes, exactly. If F is the only relevant force, then the velocity will be parallel to it's average value during impact. This is the simple part.

You are absolutely right.. but this is a kind of tautology. When I was asking about applied force F by the cue, I was talking about a simple case in theory where some unknown parameters can be ignored.

When force F (whose direction is off the normal) is applied to a ball, is the tangential acceleration of the ball F/m sinθ if there is enough friction between the force and ball (enough friction means Fsinθ < μFcosθ , where μ is static friction coefficient)?

Is this an ill-posed problem? If not and if it is right, maybe this was the simplest answer that I could get. My problem was that I thought that all of the tangential force Fsinθ cannot be used for linear acceleration (I even thought that the tangential force only spins a ball...). But, it seems that all the force can be used for linear acceleration of center-of-mass after a little research. (if there is enough friction on the contact surface)
1) Application: pull on two hockey pucks
https://books.google.co.jp/books?id=8oyNPd5QbYgC&pg=PA350&lpg=PA350&dq=puck+string+center+of+mass+velocity+google+book&source=bl&ots=61cEZe4Zaj&sig=blaDAk_ZGOhw0PbgPsm-6To0X7U&hl=en&sa=X&ved=0ahUKEwisivLSvLPRAhWr1IMKHVcaC68Q6AEIIzAB#v=onepage&q=puck string center of mass velocity google book&f=false
2) Puck-to-stick collision and fusion on frictionless ice
http://web.mit.edu/8.01t/www/materials/InClass/IC_Sol_W11D2-4.pdf

Of course, we now know that some factors such as cue flex or player's arm movement do not guarantee that the force is always in the direction of the cue during the collision, which makes the case complex. But, I would say the applied force is almost always near to the initial direction of the cue. Because players usually try to push a cue straight forward.

 

[A.T.]

When force F (whose direction is off the normal) is applied to a ball, is the tangential acceleration of the ball F/m sinθ ...

Yes.

But, it seems that all the force can be used for linear acceleration of center-of-mass after a little research.

Yes.

 

[poolplayer]

I think I am done here if no one points to a flaw in the logic. Thank you.

What still confuses me is some videos that I posted before. I hit the ball with a metal cue (so small cue flex. tip is normal, so there should be the same friction as a normal cue) and it seems that the ball went rather to the normal direction. Do you think this is just a sort of double hit? It seems that the ball already started to go oblique immediately after the first contact.

This video is still mysterious, though... maybe some unidentified leftwards force makes the ball go significantly off from parallel to the cue direction, but I will think about this in other occasions.

 

[sophiecentaur]

Because players usually try to push a cue straight forward.

I believe that is true but that doesn't imply that there is no lateral force from the cue (the fact that it requires some effort must imply there is some lateral force). So how could one measure the actual impulse? Answer has to be by observing the actual direction of the resulting motion of the ball when hung on a string. You have already done that on a few (or one) occasions and you would really need to do several runs (>10) with the same contact point etc. and analyse the result by taking the mean after discarding any that don't fit the pattern. It may need a mechanical actuator, rather than a human. Also, it would be interesting to find out the coeff of friction, which could be dominated by the cue tip, so a flat ceramic plate could be used with a cue tip under a known mass and a spring balance used to pull it along the surface of the plate. There have been various values suggested but I wonder how well justified they are. Varying the applied weight could show how linear the friction is - which could really spoil your day if you wanted to make real sense of it.

 

[sophiecentaur]

maybe some unidentified leftwards force

. . . or lack of friction force between tip and ball. No friction would mean only a normal force would be applied.

 

[poolplayer]

I believe that is true but that doesn't imply that there is no lateral force from the cue (the fact that it requires some effort must imply there is some lateral force). So how could one measure the actual impulse? Answer has to be by observing the actual direction of the resulting motion of the ball when hung on a string. You have already done that on a few (or one) occasions and you would really need to do several runs (>10) with the same contact point etc. and analyse the result by taking the mean after discarding any that don't fit the pattern. It may need a mechanical actuator, rather than a human. Also, it would be interesting to find out the coeff of friction, which could be dominated by the cue tip, so a flat ceramic plate could be used with a cue tip under a known mass and a spring balance used to pull it along the surface of the plate. There have been various values suggested but I wonder how well justified they are. Varying the applied weight could show how linear the friction is - which could really spoil your day if you wanted to make real sense of it.

I agree that these are necessary experiments to know the actual force applied by the cue. But, I am now satisfied by the simple model because in the model the ball always goes straight.

 

[poolplayer]

. . . or lack of friction force between tip and ball. No friction would mean only a normal force would be applied.

Yeah, this might be possible. Even if the cue tip is the same as a usual cue (so the friction coefficient should be the same in the simplest case), there may be nonlinearity of friction coefficient as a function of amount of force. If the force applied by the metal cue is too strong due to the larger effective mass of the cue, the tangential force might have exceeded the static friction. I cannot know the amount of slippage even though slippage is not apparent in the video. This is a good point.

 

[sophiecentaur]

even though slippage is not apparent in the video

Contact is only brief. Would your frame rate show up the actual contact time? I reckon you'd need to find a way of actually measuring the friction. Perhaps with ball secured in a hole and the cue resting on top (with added weights) measure force needed to shift the tip.
Question: When players chalk their cue so regularly, is it for a physical reason or just a ritual to help them settle to each shot? Also, when the commentator says they got a 'kick', what is meant? Is it the chalk sticking to the ball?

 

[poolplayer]

Contact is only brief. Would your frame rate show up the actual contact time?

You are right. I cannot know the contact time and slippage from my 240fps video.

When players chalk their cue so regularly, is it for a physical reason or just a ritual to help them settle to each shot?

If I shoot a ball several times (<10-20) without putting additional chalk, the cue readily slips on the ball (miscue) if my shot is off center. This is because a significant amount of chalk is removed from the cue tip in every shot.

Also, when the commentator says they got a 'kick', what is meant? Is it the chalk sticking to the ball?

It means that a ball went to unusual direction and many think that it is due to accidentally increased friction between balls. I think it is mostly due to the chalk on the ball. But, I heard that a clean new ball often induces a 'kick' in an unpredictable way because the friction is sometimes higher on the surface of a clean ball.

 

[David VH]

Question: When players chalk their cue so regularly, is it for a physical reason or just a ritual to help them settle to each shot?

It is both. If you forget to chalk before a significantly off-center shot, you risk a miscue. It's easy to forget how long it's been since you chalked it, so many players have developed a habit of chalking while they plan the shot so they never forget, turning it into a ritual. 90% of billiard chalk is being wasted though, that's for sure (and it's also a health hazard).

 

[sophiecentaur]

It is both. If you forget to chalk before a significantly off-center shot, you risk a miscue. It's easy to forget how long it's been since you chalked it, so many players have developed a habit of chalking while they plan the shot so they never forget, turning it into a ritual. 90% of billiard chalk is being wasted though, that's for sure (and it's also a health hazard).

So the chalk increases the effect of friction between the surfaces and probably makes it more consistent. It wouldn't be hard to do the measurement I was suggesting, though. I do not have a cue or a snooker ball so I can't help there. It is easy for me to suggest a whole range of possible experiments but what about a set of measurements with different amounts of offset (English). You're going to need a bigger memory stick!

 

[David VH]

This video may be of interest to this thread:


The most interesting part IMO is around the 5:55 mark where consecutive shots are being performed, depleting the chalk from the cue. You can see that the cueball deflection from the cue direction exceeds 1 degree, time after time.

From this video I learned that the deflection of the cueball from the cue direction is called "squirt". This led me to this very comprehensive page:
http://billiards.colostate.edu/threads/squirt.html

This page basically confirms our findings, and comes up with the same influencing factors (e.g. immediate swerve because of downward cueing angle). To summarize: our minds work pretty well, but our google-fu is below par.

 

[Steeve Leaf]

Any computer simulation programs for this game ?

 

[Mark Davidson]

This subject is more complicated than most of these answers have suggested. It is pretty well understood by serious practitioners of the billiards arts. For a good introduction see the links at this website: http://billiards.colostate.edu/threads/squirt.html. Basically there are a number of effects that contribute to the cueball motion after being struck by a cuestick. These are

1. Deflection or squirt
2. Swerve ( massé is an extreme form: )
3. Throw
4. Bounce

The flexibility and mass profile of the cue stick make a difference, as does the tip hardness and the type of stroke and english is used.

An early but rather complete treatise on billiards physics was done by Coriolis: http://www.coriolisbilliards.com/. A number of other texts have appeared since then delving into the classical mechanics underlying billiards.

Another good source of information are the articles by Bob Jewett over the years in Billiards Digest: http://www.sfbilliards.com/articles/BD_articles.html

Bob is arguably one of the leading experts in the world on the physics of billiards. The easiest way to understand these effects is to play the game.

 

[poolplayer]

It is so weird that these billiard lovers do not give a straight answer to my original question. These links are of some help, but I could not find an answer probably because my question is too basic.

But, I think I got a simple answer in this thread:
It is *friction* between the cue tip and cue ball that makes the cue ball go almost straight (parallel to the cue direction) rather than to the oblique/normal direction (much deflection/squirt) predicted by the Newton's law. With enough friction, the tangential force can accelerate the cue ball as well as the normal force. The vector sum of the tangential force and normal force is in theory parallel to the cue direction, so the ball goes straight.

 

[DWT]

It is so weird that these billiard lovers do not give a straight answer to my original question. These links are of some help, but I could not find an answer probably because my question is too basic.

But, I think I got a simple answer in this thread:
It is *friction* between the cue tip and cue ball that makes the cue ball go almost straight (parallel to the cue direction) rather than to the oblique/normal direction (much deflection/squirt) predicted by the Newton's law. With enough friction, the tangential force can accelerate the cue ball as well as the normal force. The vector sum of the tangential force and normal force is in theory parallel to the cue direction, so the ball goes straight.

As a billiard player for most of my life I will say that the ball does not go straight when struck with right or left English.
It squirts off line in the opposite direction of the english. The heavier the tip of the cue stick the more exaggerated this squirt is. Many companies have been working towards creating low deflection shafts for cues which minimize this squirt, and the key component in these is reducing the weight at the tip of the cue.

I hit with a cue that had a lead weighted tip and when putting any type of side spin on the cue it would shoot off at a sever angle from the aim point.

 

[poolplayer]

As a billiard player for most of my life I will say that the ball does not go straight when struck with right or left English.

We all know that. Please read the thread first...
My question was why the ball goes more straight in cue-to-ball collision than the ball-to-ball collision.

And my answer is the friction between the cue tip and cue ball makes the cue ball go almost straight (parallel to the cue direction) rather than to the oblique/normal direction (much deflection/squirt) predicted by the Newton's law. With enough friction, the tangential force can accelerate the cue ball as well as the normal force. The vector sum of the tangential force and normal force is in theory parallel to the cue direction, so the ball goes straight.

 

[DWT]

Put a tip on the cue made of the same material as the balls and as long as the weight of the tip is less than the object ball, i guarantee you the ball will still follow the almost straight direction.

It is not due to friction. As a matter of fact the harder the tip the straighter the ball goes as long as you don't miss cue.

One thing that happens at impact is the cue shaft will flex away from the cue ball in the same direction of the english. This is where the loss in angular momentum is.

 

[zwierz]

There is a good exercise nearby by the way. Let ball moves on a horizontal table and there is a Coulomb friction between the ball and the surface. Show that the center of the ball describes a parabola until the slipping stops. What about slope?

 

[Buckleymanor]

What about slope?

The table should be flat unless you are referring to the nap of the cloth.

 

[zwierz]

I meant to consider the problem for inclined table. There is a ball on the inclined table; there is a Coulomb friction between the ball and the surface. Describe the motion of the ball while the ball slips. There is something to think about :)

 

[A.T.]

Put a tip on the cue made of the same material as the balls and as long as the weight of the tip is less than the object ball, i guarantee you the ball will still follow the almost straight direction.

Do you have links to videos demonstrating this with low friction tips?

 

[DWT]

Do you have links to videos demonstrating this with low friction tips?

I will work on one. Going to have to make tip and apply it to an old shaft may take a few days.

Until then you can search for using a phenolic tip. These are the lowest friction tips on the market. They were designed for breaking and jumping but a good practitioner can impart english to the cue ball without chalk.
The chances of a mis-cue are higher but with a good stroke it is doable.

 

[poolplayer]

Put a tip on the cue made of the same material as the balls and as long as the weight of the tip is less than the object ball, i guarantee you the ball will still follow the almost straight direction.

It is not due to friction. As a matter of fact the harder the tip the straighter the ball goes as long as you don't miss cue.

One thing that happens at impact is the cue shaft will flex away from the cue ball in the same direction of the english. This is where the loss in angular momentum is.

Thank you for your answer. My thought is that as long as we don't miscue, there is enough friction between the tip and ball due to chalk.

But, I have never tried English with a phenolic tip without chalk. If we can make the ball go straight without miscue, it might not be friction because now the friction should be same as ball-to-ball collision. To avoid miscue I guess we can only strike around the center without chalk though.

 

[A.T.]

Until then you can search for using a phenolic tip. These are the lowest friction tips on the market

Note that "lowest friction tips on the market" doesn't mean "no friction". If friction was irrelevant to ball direction, it should work even when the low friction is tip lubricated.

 

[DWT]

Thank you for your answer. My thought is that as long as we don't miscue, there is enough friction between the tip and ball due to chalk.

But, I have never tried English with a phenolic tip without chalk. If we can make the ball go straight without miscue, it might not be friction because now the friction should be same as ball-to-ball collision. To avoid miscue I guess we can only strike around the center without chalk though.

We will not be able to put anything more than a tip of english for sure bu

 

[DWT]

We will not be able to put anything more than a tip of english for sure bu

Above are links to videos showing results of the experiment.
Made a tip out of a cue ball, was not able to put anymore than a tip of english on the ball or i would miscue.
Was not able to get spin on the ball due to lack of friction but the angle of travel was really consistent.

 

[poolplayer]

Made a tip out of a cue ball, was not able to put anymore than a tip of english on the ball or i would miscue.
Was not able to get spin on the ball due to lack of friction but the angle of travel was really consistent.

Did you make the tip from a cue ball?? So cool!
It's hard to tell, but it looks like the ball goes to the normal direction rather than parallel to the cue direction... What do you think?

I have a break cue with a phenolic tip, so I could also try some experiments when I have a chance. Though I am not sure if the phenolic tip is the same material as the cue ball (probably different, right?)...

 

[DWT]

Did you make the tip from a cue ball?? So cool!
It's hard to tell, but it looks like the ball goes to the normal direction rather than parallel to the cue direction... What do you think?

I have a break cue with a phenolic tip, so I could also try some experiments when I have a chance. Though I am not sure if the phenolic tip is the same material as the cue ball (probably different, right?)...

Yep here's the cue ball i used.

The ball is splitting the angle from the natural to parrallel to the cue very consistently.

Phenolic tip i think is a little softer than the stone balls but i do not have anything to test that.

 

[DWT]

I have a better way to test this which will remove any potential human error.

I am going to take a ball and core it out to reduce its mass, we will see what happens when the object ball is struck by a ball identical in every way except its weight. This may take me a day or so i will post video of results asap.

 

[poolplayer]

I have a better way to test this which will remove any potential human error.

I am going to take a ball and core it out to reduce its mass, we will see what happens when the object ball is struck by a ball identical in every way except its weight. This may take me a day or so i will post video of results asap.

Wow. I don't know how you can core it out, but it's going to be great to see if you are right and the ball goes straight when hit by the light ball!

Just some quick comments:
In your last video, the impact point was a bit unclear, but it seems that the ball did not go parallel to the cue direction. So, I believe that friction is indeed the key factor. Also, your cue stroke seemed to go off a bit to the side after impact (I believe it is to avoid miscue) and that may also affect the ball direction. I was wondering if we can stop the cue stroke at the contact point, which might make our interpretation easier. Maybe I can try that when I have time.

 

[DWT]

I think we may find out that it is a combination of friction and mass. After I use the cored out ball i can put some chalked felt or maybe leather at impact point. That should give same results as hitting with chalked cue tip.

 

[poolplayer]

I think we may find out that it is a combination of friction and mass. After I use the cored out ball i can put some chalked felt or maybe leather at impact point. That should give same results as hitting with chalked cue tip.

That's a great idea!

By the way, I just found this .pdf where a guy from Argonne National Laboratory explained the cue ball direction with friction as I did (please see p.19).
ftp://ftp.tcg.anl.gov/pub/shepard/pool/old_versions/physics.PDF
But, a model is just a model. Nobody has done your experiment. It's exciting to see what happens.

 

[poolplayer]

I think we may find out that it is a combination of friction and mass. After I use the cored out ball i can put some chalked felt or maybe leather at impact point. That should give same results as hitting with chalked cue tip.

Maybe you can apply chalk between the balls if felt or leather does not work well.