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

[sophiecentaur]

Absolutely, CK. The issue is more that there seems to be no deviation, rather than the actual amount. Pairs of contacting balls seem to behave pretty much textbook, exchanging Momentum when they're the same masses. Their surfaces do not seem to transfer rotation in the short time of contact, normally. The cue is much more complex, with a soft tip, an almost 'infinite mass' acting along its line (incompressible and bolted to the pushing arm and Earth) but a high amount of flexibility, as the movie shows, and not a lot of mass at the tip region. I have been looking at skill, rather than simple Physics for the best explanation. That sort of attitude tends not to satisfy the non-Physicist but it's the way Physicists tend to operate.

 

[Cutter Ketch]

There must be another force (or set of forces) at work that the skilled player is introducing (perhaps sub-consciously).

It is just friction. It is not in the subconscious of the skilled player. It is in the softness of the cue tip and the coating of chalk. Note that the contact between the cue and the ball persists for a significant distance. The ball did not bounce off the cue in an elastic collision.

English can be applied at various locations but this is the result you get even when it is directly right of center on the equator. I'm sure that is what poolplayer will tell you he did as that is what he was trying to demonstrate. Practically everyone who plays pool with any regularity does this all the time and we know that the cue pretty much goes straight regardless of where around the center we strike the ball unless we miscue. (We exceed the limit of static friction and the cue slides)

 

[sophiecentaur]

It is just friction.

But the friction force between tip and ball isn't acting to the right hand. At best, it is acting in the cue direction. Won't that plus the normal contact force still produce a leftwards resultant? I still feel that there needs to be a relevant force from the table surface. The problem is that doing a good, appropriate diagram is proving difficult!
Edit: PS, we had a similar kind of discussion about how an arrow appears to sneak round the front of the bow and end up heading in the right direction. It's a similar example of Man and Machine where you can't easily measure what the Man is putting in.

 

[sophiecentaur]

Practically everyone who plays pool with any regularity does this all the time

Which part of the tip makes contact with the ball and is the cue actually horizontal? I don't think it can be. Now, there's another thing!

 

[rcgldr]

Wait... does the less effective inertia of the cue perpendicular to its direction affect the direction of the ball? (or force normal to the contact point to the ball?)

To some degree the inertia of the cue matters, but don't forget you are holding the cue. It is constrained by the force of your hands. If the cue was sliding through a fixed bearing instead of your bridge hand so that it really couldn't move, then the contribution of the inertia of the cue to the left/right deflection would become almost completely unimportant and the elastic bending of the cue would be the dominant contribution to the deflection of the cue at the contact point. I suspect a good bridge hand is closer to this highly constrained case than the free body case that makes the inertia of the cue important.

By "effective inertia", I meant how easy it is for the cue to flex a bit and allow the cue tip to move sideways by a small amount. However the cue stick is virtually incompressible, so the forward "effective inertia" is much greater. So during the time of the collision, the cue tip moves forwards and sideways, effectively making an angled collision with the ball, with enough friction to induce a spin on the ball.

 

[sophiecentaur]

I meant how easy it is for the cue to flex a bit and allow the cue tip to move sideways by a small amount.

The movie implies that the lateral movement is around the thickness of the cue tip. It shows that that contact time is fairly lengthy. Shame that a frame with actual contact seems to be missing. It would be necessary to for several takes or 10X the frame rate in order to see that. The movement of the tip will be well damped, I guess as the later frames show no movement.
This is more and more interesting.

 

[rcgldr]

The movie implies that the lateral movement is around the thickness of the cue tip.

I think that's the key aspect of this; the cue tip moves at an angle to the side (and not just straight forward) during the collision.

 

[poolplayer]

friction force between tip and ball isn't acting to the right hand. At best, it is acting in the cue direction. Won't that plus the normal contact force still produce a leftwards resultant?

I thought that the friction force between the cue and ball if any is the right hand, parallel to the contact surface. When you say the cue direction, is it the initial cue direction before the contact or actual cue direction during the contact?

Your movie does not show the height at which the ball is struck and that, imo, is a vital factor. If it's hit at its equator, it will spin anticlockwise. The table surface is designed with friction in it. If the ball is struck above the mid line The ball will rotate away from the cue and contact with the table will produce an impulse to the right, cancelling the slight leftwards impulse from the cue. ... My guess is that the side shots would show that the cue is hitting the ball slightly above mid height.

I tried to strike the ball right of center on the equator, although it is possible that I accidentally hit slightly above mid height. As Cutter Ketch knows, even if the ball is hit below the mid height, it goes almost straight as when it is hit above the mid height. I didn't think that the contact between the table and ball is relevant to the ball direction, but could you explain a bit more how the impulse to the right is generated when the ball is struck above the mid line?

Which part of the tip makes contact with the ball and is the cue actually horizontal? I don't think it can be.

It should be the left hand side of the cue tip that makes contact with the ball. But, it could be a little above the mid height of the cue tip because the cue is often pointing slightly downward although we always try to make it horizontal as much as possible.

 

[poolplayer]

The movie implies that the lateral movement is around the thickness of the cue tip. It shows that that contact time is fairly lengthy. Shame that a frame with actual contact seems to be missing. It would be necessary to for several takes or 10X the frame rate in order to see that. The movement of the tip will be well damped, I guess as the later frames show no movement.
This is more and more interesting.

I think the contact time is a few milliseconds at most. I only have GoPro and its maximum is 240fps. I could increase lighting to get clearer videos, but 240fps is not good to capture the details of the cue during contact... Dr. Dave has some videos taken with high-speed camera if you want to see the cue movement during the contact (this is a draw shot though... the ball was hit below the center). Frame rate seems 2000 fps and it looks that the contact persists 4 frames, so contact time would be ~2 ms.

 

[sophiecentaur]

Full marks for the evidence gathering. That's the advantage of a near-perfect system.
I still have a problem in explaining all of what happens in terms of just cue-ball interaction. All forces on the ball from the cue are in the leftwards direction and that can't account for lack of leftwards motion. Is that argument OK with you?
The table must also be contributing a significant force to account for what happens. The rotation of the ball will be due to two couples - one from the cue impact and reaction force of the CM of the ball (would happen in free space) and another from cue impact and reaction due to friction with the table. Imo, the latter must produce an effect of steering to the right. As skilled players, you guys seem to be finding it hard to accept that the player is actually making a contribution to getting the effect just right. As an unskilled player (A level Physics is the limit to my certainties about the situation), I can tell you that what happens to the ball is usually a bit of surprise to me when I strike it. I have not acquired the subconscious control that good players have. I would guarantee that, in a movie of what would happen if I did the experiment, the ball could go every which way in different shots.
A suitable diagram of the situation (3D) would, I am sure, resolve my problem.

 

[AstroChris]

So I happen to be a pro/am pool player myself and know a bit about physics. One thing that I didn't see mentioned and forgive me if it was but the reason that the ball will go almost straight but not quite straight is due to the shaft deflection. Because the shaft also deflects and recoils from the initial impact of the cue, it does slide a bit.

Someone said that the cue ball will always slide when you hit, that is also false. It will depend on many different things as to whether or not the cue ball will slide but most times it won't.

Oh and lastly, to demonstrate what I'm talking about poolplayer, go to your pool room and ask to use anyone's OB shaft or Predator shaft. Those are no to low deflection shafts and you can use extreme English and watch the ball travel in a direct line to where you hit it. Undoubtedly someone at your pool room has one of those too lol.

 

[poolplayer]

All forces on the ball from the cue are in the leftwards direction and that can't account for lack of leftwards motion. Is that argument OK with you?

Again, how about friction between the cue and ball? Why can you be so sure that the friction is not the key factor? I am still not convinced by your suggestion that the direction of friction force is leftward or straight at most (during right English). I feel it is rightward because the cue is moving rightward during the contact. It could be even deemed as clockwise rotation of the cue tip.

I am not sure that the rotation/spin of the ball is relevant to the initial direction of the ball after contact... It definitely affects the cue ball path, but I think that the ball usually slides on the table especially when the cue speed is fast (in my video the cue speed is ~2-3 m/s, which I believe is sufficient to induce slip of the ball on the table).

I have not acquired the subconscious control that good players have

It may require some skill to push the cue straight, but it is not so difficult if you apply chalk to the tip and strike it slowly. As Cutter Ketch said, this phenomenon is very robust and reproducible by anyone. Any unskilled player can just go to a pool bar, grab any cue, apply chalk to its tip, strike the right hand side (above/mid/below the equator), and he/she will see the ball goes pretty much straight. No professional tricks there.

explain when and why the "English" shot is choses, over a straight impact. Something to do with bending the path of the ball, I guess. Those professionals do some annoyingly clever stuff with how the ball behaves.

We use English to spin the ball. It is sometimes chosen to make the cue ball curve, but in most cases it is for positioning the cue ball where we want in order to pocket balls in a row. It is sometimes used to deflect the object ball direction hit by a cue ball. I think this is due to small friction between balls. Clockwise spin of a cue ball makes the object ball go rightward from the expected direction.

 

[poolplayer]

Someone said that the cue ball will always slide when you hit, that is also false. It will depend on many different things as to whether or not the cue ball will slide but most times it won't.

Right, that was what I thought! But, probably you would agree that a ball usually slides when it is hit hard, right?

use anyone's OB shaft or Predator shaft. Those are no to low deflection shafts and you can use extreme English and watch the ball travel in a direct line to where you hit it.

I actually have a Predator Z2 shaft and Meucci Ultimate Weapon shaft! So, do you have any ideas about how the cue shaft deflection makes the cue ball go straight rather than normal to the contact surface?

 

[sophiecentaur]

Again, how about friction between the cue and ball? Why can you be so sure that the friction is not the key factor?

You have to be right that friction is necessary for this to happen. A non friction contact with cue and ball and ball and table cannot cause any rotation and the ball would have to move to the left. But in what direction can this friction force act? Any force that rotates a ball isolated in space can't affect the direction it heads off in. That direction of the linear momentum change can only be radial from the contact point. The impact is prolonged, due to flexing of the cue and slippage so the contact point changes a bit and you have to consider the integral over the contact time but it's always to the left. Prove it for yourself with a force diagram and draw a circle and a contact point. You cannot obtain a rightwards resultant force, even allowing for the cue displacement. It's only when the ball has a contact point with the table that friction can have any effect on the final velocity of the cm of the ball. Once you allow the ball to rotate about a non vertical axis, it can 'walk' either way, depending on the angle of that axis. Being pushed forward will naturally tilt the rotation axis forward, which will cause a rightwards walk.

 

[sophiecentaur]

So, do you have any ideas about how the cue shaft deflection makes the cue ball go straight rather than normal to the contact surface?

Unless you give deliberate back spin, the ball will always have a roll-forward component as it will not slip on the table. That forward roll and the rotation about a near vertical axis will cause the sideways movement component.
Again, I have to insist that there are many additional variables involved here - even down to the nature of the cloth surface. One of the qualities for a 'good' cloth will probably involve a 'good feel' and you haven't quantified what is meant by that. Too slippy would not be acceptable, would it?

 

[AstroChris]

I actually have a Predator Z2 shaft and Meucci Ultimate Weapon shaft! So, do you have any ideas about how the cue shaft deflection makes the cue ball go straight rather than normal to the contact surface?

I don't really understand your question due to the wording but I'll run through it once more, no worries. The low or no deflection shafts combat the side way "skid" that you will see from using English. Even in cases of extreme English the cue ball will go straight vs "pushing" to the side a bit first as a regular shaft would do, much like your Muecci. Muecci by the way is one of the "livest" shafts out there, by that I mean it has tons of deflection and with that you can add large amounts of English on the cue ball without moving to the either side as much.

Too slippy would not be acceptable, would it?

Too slippy is what happens when a table gets recovered in new cloth. Because the cloth is stretched out so after it plays for a while it loosens a bit correctly, the grain is almost pulled out of it so to say and it causes a bunch of sliding when using English and just hitting at faster speeds.

 

[poolplayer]

Any force that rotates a ball isolated in space can't affect the direction it heads off in.

But, if you think something like a treadmill moving rightward, and push this treadmill against a ball, isn't the ball receive rightward force through friction? I don't think that curve induced by rotation/spin of the ball significantly affects the initial direction. If the rotation/spin is that strong, we see that the ball greatly curves rightward and crosses the straight line in its later path, which is not the case.

I have to insist that there are many additional variables involved here ... Too slippy would not be acceptable, would it?

I stroke a ball on a smooth table and it was indeed almost the same as usual table with cloth. So, I think that the friction between the table and ball is not significant. The table was quite smooth as it was really hard to set the ball (this indicates that the table was not completely horizontal, but I don't think it matters).

 

[poolplayer]

Muecci by the way is one of the "livest" shafts out there, by that I mean it has tons of deflection and with that you can add large amounts of English on the cue ball without moving to the either side as much.

I agree. I once tried to abandon Meucci because of their poor reputation, but it seems that I was so used to Meucci cues and could not accommodate myself to other cues.

My question was why the ball goes relatively straight even when we use a usual cue shaft. You know that a ball goes to the left during ball-to-ball collision when the aim is thin. But a ball goes almost straight even if it is extreme right English. I have never wondered this thing as most people, but I noticed that I don't know its physics.

 

[AstroChris]

Ok, so over emphasize the experiment and you'll understand what I am saying. At a very low stroke speed, line up at extreme right hand English and almost "push" through it and it will definitely move to the left, line up dead middle and it will go dead straight. If you are using a regular cue, it will most certainly move slightly to the opposite direction of the English you're using.

 

[poolplayer]

Ok, so over emphasize the experiment and you'll understand what I am saying. At a very low stroke speed, line up at extreme right hand English and almost "push" through it and it will definitely move to the left, line up dead middle and it will go dead straight. If you are using a regular cue, it will most certainly move slightly to the opposite direction of the English you're using.

Of course I know that cue ball deflection. What I am saying is that the cue ball direction is not perpendicular from the contact point between the cue tip and the ball... You see that the cue ball does not go on the red line in the movie above.

 

[poolplayer]

Sophiecentaur would be able to explain how mysterious it could be. We are pretty much used to playing games and never wondered the difference between ball-to-ball collision and cue-to-ball collision.

 

[AstroChris]

Of course I know that cue ball deflection. What I am saying is that the cue ball direction is not perpendicular from the contact point between the cue tip and the ball...

Right, it won't be. It can't be. If you do not hit directly down the middle of the cue ball, it will not leave your cue perpendicular. The other factors are the conditions surrounding you in the environment: humidity, cloth, the cleanliness of the cloth etc etc. We're using a rounded tip to hit a ball. There is compression between both surfaces at contact, mostly the tip though. All those factors play into your question.

 

[sophiecentaur]

The table was quite smooth as it was really hard to set the ball (this indicates that the table was not completely horizontal, but I don't think it matters).

You are not getting this. If the ball rolls along the table without skidding then there is enough friction for what I am describing to happen. If you stick a piece of cotton to a ball, with bluetack, and pull. you will feel a resistance. That's due to friction and it is what makes all wheels roll and allows car wheels to drive the car forward.

The flex of the cue will have some influence on what happens but the whole system of cue weight and flexibility plus the rigidity of your bridge will have a pretty unquantifiable result. Your brain / body is good at finding, by experiment, how to achieve what you want in this sort of circumstance without knowing any Physics at all. You must have seen birds doing stunning aerobatics and they know no Physics at all.
If you really want an answer to this then you will need to involve a lot more Physics than that you are trying to get away with at the moment. You have to address how the ball would react if hit in space, before you try to analyse this situation. Try to answer the purple passage in post 44 before you try to progress further along those lines. Without doing that then you are just ignoring the real Physics behind your question. There is no answer in that direction, which doesn't detract in any way from learning the skills of the game.

 

[poolplayer]

Try to answer the purple passage in post 44 before you try to progress further along those lines. Without doing that then you are just ignoring the real Physics behind your question.

You said "draw a circle and a contact point. You cannot obtain a rightwards resultant force, even allowing for the cue displacement" in the purple passage. But, the diagram is just the force normal to the contact surface to the ball and opposite force to the cue, isn't it? If the diagram has no rightward force to the ball, it obviously cannot explain the result. So, do you think that a treadmill running rightward does not induce rightward friction force to a ball when it is pushed against a ball? I guess this is happening during contact: cue tip is pushed against a ball and moving rightward.

 

[poolplayer]

You are not getting this. If the ball rolls along the table without skidding then there is enough friction for what I am describing to happen.

Right, I was wrong on this point... but I honestly don't understand the diagram you are thinking of. It is related to ball spin/rotation, right? It would be helpful if you can explain that. But, now I am more interested in the possibility of rightward friction, which I think would be more relevant factor.

 

[sophiecentaur]

the possibility of rightward friction,

There isn't any rightwards friction force acting on the ball. There is a leftwards force on the ball and a rightwards force on the cue. (That's why the cue bends to the right).

It would be helpful if you can explain that.

Imagine the ball rotating anticlockwise with its axis vertical. Now tilt it forward (as when you give it any forward motion with the cue). The bit in contact with the ground will be pushing against the ground to the left, which will result in a force steering the ball to the right. That's where your rightwards force comes from. The whole thing requires you to think in 3D and to consider two axes of rotation.
BTW all the time, you are confirming that a knowledge of Physics is not necessary for you to be a good Pool Player. You 'just know' what to do. There is a threshold minimum knowledge to allow understanding of each Physics problem. It is not being patronising to say that you will need at least A level Physics knowledge for this one. There is no simple arm waving answer - although I have been trying to give one.

 

[poolplayer]

There isn't any rightwards friction force acting on the ball.

Then, what force makes the ball spin anticlockwise? Isn't it the friction force rightwards? I understand that you are saying that right English induces rightwards curve so it looks like straight from the beginning, but this is so hard to accept for me for some reasons... Does this explanation make sense to other people?

By the way, I actually really appreciate your inputs. I have been wondering like for months by myself... I learned a lot only within a few days through discussions in this thread.

 

[poolplayer]

Probably the reason that I don't think it is spin is that the ball keeps spinning for no less than a few seconds after the shot but I don't see significant curve after the shot. I think it doesn't make sense that the spin changes the ball path only at the beginning.

 

[rcgldr]

There isn't any rightwards friction force acting on the ball. There is a leftwards force on the ball and a rightwards force on the cue. (That's why the cue bends to the right).

Then, what force makes the ball spin anticlockwise? Isn't it the friction force rightwards?

It's not clear what direction the friction force is, but even if there is zero friction, if the cue strikes the ball off center, the ball will spin. Consider what would happen if a rod in space was struck near the end, the rod would end up rotating in addition to translating due to the collision.

Back to the friction issue, the lateral Newton third law pair component of forces are leftwards from cue to ball, and rightwards from ball to cue, bending the cue tip to the right as seen in the videos. However, the off center forward force imparted by the cue onto the ball would generate a component of friction force to the right onto the cue ball (in addition to the torque related to an off center strike even if there was zero friction). The net torque on the ball results in the cue ball spinning in the direction of the off center strike point.

curve

Generally to get the cue ball to significantly curve, backspin is needed in addition to side spin. It's an issue with how the pool table felt interacts with a spinning ball. In the case of a pure side spin strike, the precession reaction of the ball would be for the balls axis of rotation to tilt to the left in response to the torque from the felt on the pool table, but the ball also starts rolling forwards, so I'm not sure which way the ball would curve with a pure side spin strike.

 

[poolplayer]

but even if there is zero friction, if the cue strikes the ball off center, the ball will spin. Consider what would happen if a rod in space was struck near the end, the rod would end up rotating in addition to translating due to the collision..

Oh, that's right... so the ball could spin without friction...

the off center forward force imparted by the cue onto the ball would generate a component of friction force to the right onto the cue ball (in addition to the torque related to an off center strike even if there was zero friction). The net torque on the ball results in the cue ball spinning in the direction of the off center strike point.

Would it be appropriate to calculate the friction force as the product of the normal force from the cue and friction coefficient in this case? Or is the friction force to the ball dependent on the cue speed? Maybe can I estimate its force by measuring the cue deflection caused by some weight put to the cue tip and comparing it with the deflection during impact...?