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

[sophiecentaur]

The same impulse results in the same linear momentum change:
https://en.wikipedia.org/wiki/Impul...ion_in_the_case_of_an_object_of_constant_mass

Oh, I get that BUT the forces are different, aren't they? So the Impulses will be different. Show me that the forces, radial and tangential are the same for a dumbel and I will believe I have it all wrong.

 

[A.T.]

Are you saying that an impulse applied radially for a brief period will have precisely the same initial effect as an impulse applied tangentially?

So the Impulses will be different.

Then your question makes no sense, because you aren't comparing applied radially vs. applied tangentially, just different impulses.

 

[sophiecentaur]

Then your question makes no sense, because you aren't comparing applied radially vs. applied tangentially, just different impulses.

Why do you have a problem with this? The resolved radial and tangential forces can be found from the applied force vector. They are different and they are applied for the same time. Is it not reasonable that their net effect can also be calculated? Additionally, if the tangential force is beyond limiting friction, the tangential effect will be even less.
Where is the hole in that argument? We are. after all, discussing the net effect on the ball and where it will go.

 

[A.T.]

Why do you have a problem with this? The resolved radial and tangential forces can be found from the applied force vector. They are different and they are applied for the same time.

There is no problem with the above, and It's not what I criticized.

We are. after all, discussing the net effect on the ball and where it will go.

The net acceleration is parallel to the net force.

 

[sophiecentaur]

'Net produces net' is something I would have said was obvious. Whether or not I made that clear, is hardly part of the answer to the OP.
What is your opinion about the actual situation and whether this net force can be in line with the cue?
If a player is aware of a sideways force on the cue (and they tell us that the cue actually bends) then that suggests to me that the net force on the ball is to the left. Some other force is needed for the ball to end up going straight.
Rather than just pointing out that part of the above is "wrong", it could help if you could add something positive.

 

[A.T.]

'Net produces net' is something I would have said was obvious.

Well, I hope we mean the same thing by "net force". I mean a simple vector sum of the force components, without any extra weighting based on whether they act radially or tangentially.

What is your opinion about the actual situation and whether this net force can be in line with the cue?

The friction coefficient required to produce the result in the videos by impact alone is way below 1, so not completely unrealistic. I don't know whether it's feasible for that particular material pairing with the chalk in between.

 

[sophiecentaur]

You don't like the term "weighting" but you must agree that the two forces will not be the same. They are both reactive forces. The radial force is due to the mass and the tangential force is due to the MI divided by the radius. They are different and that is what the weighting is about. It isn't necessary to calculate the actual value as the direction is all that counts.
I have scribbled some calculations which suggest that the value of tangential reactive force is 2/5 of the radial reactive force for a uniform sphere. I have to go out and chop some wood in the sun but I will try to present the sums in a readable form. Would you disagree with my earlier idea that a cue hitting a rigid sphere with all its mass concentrated at the centre would (could only) experience a zero tangential reaction force?

 

[A.T.]

you must agree that the two forces will not be the same.

Sure, in the first video the friction would have to be about 1/4-1/3 of the normal force, in order to explain the result by impact alone. These aren't completely unrealistic friction coefficients.

 

[sophiecentaur]

Sure, in the first video the friction would have to be about 1/4-1/3 of the normal force, in order to explain the result by impact alone. These aren't completely unrealistic friction coefficients.

You seem to be completely ignoring the relevance of Moment of Inertia. Can you disagree that it is crucial and that the ratio of forces is calculable? The effect of friction will be very non-linear in view of the cue tip material and the chalk so you can't do more than say it could reduce the tangential effect. The MI is always with us yet you still don't seem to be acknowledging it. Do you, in fact, get my point about a sphere with all its mass at the centre?

 

[A.T.]

You seem to be completely ignoring the relevance of Moment of Inertia.

To verify this, you could measure the angular velocity, and check if it is consistent with the tangential impulse required for the observed linear velocity.

 

[sophiecentaur]

To verify this, you could measure the angular velocity, and check if it is consistent with the tangential impulse required for the observed linear velocity.

How would one know the tangential impulse? It would not be possible to measure or even apply just a tangential Impulse under these conditions (without any radial force)
In any case, would there be any point in adding experimental error to what the Maths of such well established theory can tell us? I get the feeling that you really don't feel able to go along with what I'm saying. What objection can you have? Could I put it another way that would be more convincing? Nothing in the above couple of posts violated Newton.

 

[A.T.]

How would one know the tangential impulse?

From a video where spin is around vertical axis you can get the linear and angular velocities. Then you can check if their relationship is consistent with a single impulse applied at the queue contact point.

 

[sophiecentaur]

From a video where spin is around vertical axis you can get the linear and angular velocities. Then you can check if their relationship is consistent with a single impulse applied at the queue contact point.

No doubt but I was asking you a question about the theory. That is much more reliable. I thought you could help me, in the light of your earlier remarks.

 

[A.T.]

From a video where spin is around vertical axis you can get the linear and angular velocities. Then you can check if their relationship is consistent with a single impulse applied at the queue contact point.

A single short impulse on an uniform resting sphere should result in the following relationship:

w/v = 5/2 * r/R²

where:

w : angular speed
v : speed
r : lever arm of the force around the center
R : radius of the sphere

In the below video a quick & dirty analysis yielded an error <10%. Thus the observed kinematics can be explained without significant forces other than the cue impact.

 

[sophiecentaur]

A single short impulse on an uniform resting sphere should result in the following relationship:

w/v = 5/2 * r/R²

where:

w : angular speed
v : speed
r : lever arm of the force around the center
R : radius of the sphere

In the below video a quick & dirty analysis yielded an error <10%. Thus the observed kinematics can be explained without significant forces other than the cue impact.

That's interesting and the 5/2 factor is familiar. But could you translate that into direction of motion? Remember, the force on the ball is not necessarily in the direction of the cue (or the cue wouldn't bend*.
What was your quick and dirty analysis? Looking at the linear and rotational motion between frames? That is not the complete kinematics of the situation.

* In fact, the net motion will be in the direction of the net force, which is patently not in the line of the cue. That's putting it in a nutshell.

 

[A.T.]

Looking at the linear and rotational motion between frames?

Yes

net motion will be in the direction of the net force,

Yes.

 

[sophiecentaur]

YesYes.

Glad to read those positive responses.
And do you have an answer about the direction?

 

[A.T.]

And do you have an answer about the direction?

The second "Yes" is about the direction.

 

[sophiecentaur]

Only if you know the direction of the force and that goes without saying. Can you help with calculating the actual direction of the force? You seem to imply that you could but I should do it myself. Can you do it?

 

[A.T.]

Can you help with calculating the actual direction of the force?

As you said yourself, it's the direction of motion.

 

[sophiecentaur]

And that is. . . ?

 

[A.T.]

And that is. . . ?

Look at the video.

 

[sophiecentaur]

Is this a game in which you have to avoid giving an answer to my questions?
If you cannot say what the theory tells us then you cannot say whether or not the video (experiment) agrees with a theory. Does 'your' theory account for the ball motion being in the direction that the cue points, despite the acknowledged fact that the cue experiences a lateral force? Do you claim that contact with the table is not relevant? There would be a logical inconsistency if you do.

 

[A.T.]

Does 'your' theory account for the ball motion being in the direction that the cue points

I used the ball motion from the video. See post #112 & #114.

Do you claim that contact with the table is not relevant?

From what I have seen so far in this specific case, it seems not very relevant for the initial horizontal motion of the ball, right after the hit.

 

[sophiecentaur]

I used the ball motion from the video. See post #112 & #114.From what I have seen so far in this specific case, it seems not very relevant for the initial horizontal motion of the ball, right after the hit.

Have you observed that the motion appears to be in the line of the cue? Are you aware that there is a extra, lateral force involved (Described by players) which would produce a lateral motion. How are those two things reconciled if simple (2 D) theory tells us the ball travels in the direction of the force? There has to be another force involved. Can you think of a better mechanism than contact with the table?

 

[A.T.]

Are you aware that there is a extra, lateral force involved (Described by players) which would produce a lateral motion.

When? By what? On what?

 

[David VH]

Something that you could help me with would be to 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.

As an aside, as far as I know there are two distinct reasons to play with side (English). First is to swerve the cueball around an obstacle. The motion has two phases, first it goes fairly straight as it slips over the table, then it slows down and as it starts rolling, the side "takes" and the ball curves into the direction of the side. It's an easy way to get out of a snooker. The second common shot with side is to affect cueball position after it hits the object ball. The collision slows the cueball, the side takes from the collision onwards and the cueball rolls off into a direction different from the collision tangent.

Have you observed that the motion appears to be in the line of the cue? Are you aware that there is a extra, lateral force involved (Described by players) which would produce a lateral motion. How are those two things reconciled if simple (2 D) theory tells us the ball travels in the direction of the force? There has to be another force involved. Can you think of a better mechanism than contact with the table?

I think your reasoning is sound. I only read 4 pages of this thread and skimmed over the rest (sorry) but it seems one factor has not been discussed in any detail, and that is that the cueball bounces off the table. It is nearly impossible to play a shot with a horizontal cue, so the friction contact between cue and cueball is pushing the cueball into the cloth. As the cue releases the cueball, the cueball bounces up off the cushion. Depending on the shot this is more or less pronounced, but in my experience (and backed up by your reasoning about the origin of lateral force) it always happens to some extent.

What I'm trying to say is, because of the downward angle of the cue, you are always pushing the ball into the cloth, so the spin axis of the ball is tilted forwards even on a vertically neutral (no top or back spin) shot.

 

[sophiecentaur]

@AT. Read higher up the thread for comments on cue deflection and rigidity. In fact, try the whole thread for some background.

 

[sophiecentaur]

As an aside, as far as I know there are two distinct reasons to play with side (English). First is to swerve the cueball around an obstacle. The motion has two phases, first it goes fairly straight as it slips over the table, then it slows down and as it starts rolling, the side "takes" and the ball curves into the direction of the side. It's an easy way to get out of a snooker. The second common shot with side is to affect cueball position after it hits the object ball. The collision slows the cueball, the side takes from the collision onwards and the cueball rolls off into a direction different from the collision tangent.
I think your reasoning is sound. I only read 4 pages of this thread and skimmed over the rest (sorry) but it seems one factor has not been discussed in any detail, and that is that the cueball bounces off the table. It is nearly impossible to play a shot with a horizontal cue, so the friction contact between cue and cueball is pushing the cueball into the cloth. As the cue releases the cueball, the cueball bounces up off the cushion. Depending on the shot this is more or less pronounced, but in my experience (and backed up by your reasoning about the origin of lateral force) it always happens to some extent.

What I'm trying to say is, because of the downward angle of the cue, you are always pushing the ball into the cloth, so the spin axis of the ball is tilted forwards even on a vertically neutral (no top or back spin) shot.

Yes. It's definitely more complex than a simple 2D problem. Your comment on vertical cue angle is interesting. It would control slip and encourage the steering action. It's all very non linear so limiting friction is probably very relevant at all points of contact.

 

[A.T.]

It's definitely more complex than a simple 2D problem.

As I have been saying throughout the thread. But for the specific case with the ball spinning around a close to vertical axis, a simple 2D approach seems to explain the result quite well.

 

[sophiecentaur]

As I have been saying throughout the thread. But for the specific case with the ball spinning around a close to vertical axis, a simple 2D approach seems to explain the result quite well.

So a lateral force explains a motion with no apparent lateral component? Not much of an explanation, I would say.

 

[A.T.]

So a lateral force explains a motion with no apparent lateral component?

Maybe you can draw a diagram to explain better what you mean here. It's to vague.

 

[sophiecentaur]

Maybe you can draw a diagram to explain better what you mean here. It's to vague.

Only 'vague' because I presumed you had read all the comments about cue deflection. Lateral cue deflection is evidence of a lateral force. Irrespective of the stiffness, the force will exist. That force acts on the ball and will cause some lateral (leftwards, here) motion. Do you object to that?
You claim that the ball should follow the line of the cue. (Am I right in my understanding of what you have written?)
The lateral motion is not observed. So another force must be present. Ok?
Why do you claim that's not relevant on the basis of videos which do not measure forces?

 

[A.T.]

You claim that the ball should follow the line of the cue.

Where did I claim that? In the videos it's close but quite parallel.

 

[sophiecentaur]

A video is just a video. Errors can't be avoided. What does "close" and "quite" mean? This is why I say theory is important; 2D theory is not enough for such a complex 3D situation.
You cannot tell what lateral forces are operating in the video so there is little useful information - except that the ball appears to go straight. You do not say how. I say it will need 3D analysis because the radial force is so significant. N

 

[rcgldr]

Going back to an early video, note that the cue ball doesn't quite follow the path of the cue stick. The cue stick is angled slightly to the right in order for the ball to go straight in the video. It's best to watch the video in full screen to note the angle between the cue stick direction line and the ball direction line.

As noted many times by now, there are lateral component forces (Newton third law pair) between the cue tip and the cue ball, but since the cue stick flexes to the right, the cue tip has more of a reaction to the lateral component forces than the cue ball, so that the cue ball isn't deflected to the left much by the impact.

As for the reason behind putting pure side english on the cue ball, this is usually done to affect how the cue ball will react when it bounces off a cushion after striking a target ball (there's some interaction between the balls due to spin, but the biggest reaction occurs due to a bounce off a cushion). This is done to control where the cue ball ends up to setup the next shot. To curve a cue ball, a combination of back spin and side spin are used.

 

[A.T.]

the ball appears to go straight.

But not parallel to the cue line. The ball goes left of the original cue line, while the cue goes right.

 

[A.T.]

What I'm trying to say is, because of the downward angle of the cue, you are always pushing the ball into the cloth, so the spin axis of the ball is tilted forwards even on a vertically neutral (no top or back spin) shot.

Yes, I also made this point earlier in the thread. But how relevant is this effect really, during the short impact phase, if you strike as horizontal as possible, at mid height?

A quick estimate: With the queue at ~5° the downwards component is about 1/10 of the horizontal component. That adds to the table-normal force by gravity, which is negligible compared the the horizontal cue impact force. If the table-normal force is ~0.1 of the horizontal cue impact force, the table friction can be around 0.02 of it. So even if all that table friction acts to the right (which it most likely doesn't), you still have a very small effect compared to the cue impact force (~1deg change for the initial ball direction)

Later, over a longer time period, the friction due to spin can curve the path to the right, as described in the link I posted earlier.

 

[sophiecentaur]

As noted many times by now, there are lateral component forces (Newton third law pair) between the cue tip and the cue ball, but since the cue stick flexes to the right, the cue tip has more of a reaction to the lateral component forces than the cue ball, so that the cue ball isn't deflected to the left much by the impact.

A complicating factor here is that a flexing cue will extend the contact time and a different amount of slip across the surface of the ball, which will (could) mean that there is more imparted spin round a vertical axis.
But N3 says that the two forces have the same magnitude. I am thinking that the radial Momentum imparted by the cue is not too much affected by this extended contact (it's more of an ideal collision because the mass of player + cue could be regarded as infinite) but the tangential Momentum could be affected much more with an extended contact because it can't be considered in the same simple way.

Yes, I also made this point earlier in the thread. But how relevant is this effect really, during the short impact phase, if you strike as horizontal as possible, at mid height?

Is the cue ever horizontal? I watch a fair amount of Snooker on TV and the close up shots suggest there is nearly a significant downwards tilt when a hand bridge is used, True, the X rest is a bit lower than the hand but isn't the cue axis still higher than the centre of the ball? That downwards angle helps to strike with the flat end of the cue tip and will help to avoid unwanted slip against the table. The 1/10 factor you quote would be easily enough to control slip and a steeper attack would cause bounce and make control harder. Unsurprisingly, the angle has been chosen to work optimally.
Unfortunately, all these extra factors that we're bringing in only serve to show just how complex the system is that we're dealing with. A slippery disc is just not an adequate model and, in any case, it predicts a significant lateral motion. So we need to look for something else, to explain how this is eliminated by good players. And they may well be very unsuitable witnesses to what goes on because there is a massive amount of 'insulation' between their bodies' behaviour and what the ball does. Our brains just don't naturally do good Maths and Physics because they don't need to. Look at the way a Swallow or a Bat flies - dumb but amazing at the same time.

 

[A.T.]

The 1/10 factor you quote would be easily enough to control slip...

The 1/10 factor is for the table normal force. The max. table friction is just a fraction of that (~0.2). And the lateral friction component is some fraction of that. This limits the lateral table friction to ~0.02 of the horizontal cue impact force (in the specific case I was considering).

 

[sophiecentaur]

The 1/10 factor is for the table normal force. The max. table friction is just a fraction of that (~0.2). And the lateral friction component is some fraction of that. This limits the lateral table friction to ~0.02 of the horizontal cue impact force (in the specific case I was considering).

That seems the wrong way round to me. The limiting friction force is less than the normal force but the normal component of the cue's force will increase the normal force (usually just the weight) considerably. 1/10 of the net, brief force from the cue will be greater (or at least as great) than the weight of the ball, which is easy to show from the fact that a struck ball can be lifted to a significant height above the table in some trick shots. So the net friction force, which is what will cause the ball to rotate, will be significantly higher with a slightly downwards stroke. It will be approximately proportional to the angle, aamof, because sin and tan are about the same as the angle for small angles (radians of course). Even if there is slippage, the tangential force against the table will still be greater than with a horizontal impact.
I have played very little pool but I have heard comments about 'controlling the ball' by digging in a bit, which justifies my view.

 

[A.T.]

So the net friction force, ..., will be significantly higher with a slightly downwards stroke.

Higher than from gravity alone. But still just ~2% of the horizontal force from a 5° downwards stroke. So at most ~1° horizontal direction change.

 

[David VH]

Higher than from gravity alone. But still just ~2% of the horizontal force from a 5° downwards stroke. So at most ~1° horizontal direction change.

How did you come to the 1 degree (could be correct, I don't see all the relevant math in my head)? 1 degree is enormous for a snooker player by the way. For a not-that-hard half table shot of ~1.7m a 1 degree deviation is more than the radius of a snooker ball, in other words the difference between a full ball contact and a miss.-

 

[A.T.]

How did you come to the 1 degree (could be correct, I don't see all the relevant math in my head)?

If the friction is 0.02 of the impact force, then it can change the direction of the net force by max. atan(0.02) ~= 1°. But that assumes that it acts perpendicularly to the impact force, so it's actually even less than 1°.

1 degree is enormous for a snooker player by the way.

Not for the question of the OP, which is to explain the ~15° deviation from the contact normal in his video.

 

[David VH]

Not for the question of the OP, which is to explain the ~15° deviation from the contact normal in his video.

I am lost. I thought this was the discussion we were having:
- if there were no friction between cue tip and cueball and both were undeformable, the cueball would go 15 degrees left of the cue direction;
- there is friction in the contact, causing the force to be mostly imparted in the longitudinal direction of the cue, keyword mostly;
- the residual part causes the cue to flex away after the contact, and should cause the cueball to veer off to the left noticeably;
- pool and snooker players do not cue significantly out of line with their intended cueball path even when applying significant side however;
- therefore we are looking for any forces which explain the straighter-than-expected cueball trajectory.

You could even ask "is the majority of the cue deflection force converted into extra spin instead of cueball deflection?" and it would be the same analysis.

Did I misinterpret the problem? I thought we did away with most of the 15 degrees from the start assuming friction contact.

 

[A.T.]

I thought we did away with most of the 15 degrees from the start assuming friction contact.

If you agree that cue friction explains most of the ~15°, and table friction accounts for merely ~1° at best, then we have no disagreement.

 

[sophiecentaur]

If you agree that cue friction explains most of the ~15°, and table friction accounts for merely ~1° at best, then we have no disagreement.

I thought the point of the top of this thread was that the ball goes more or less along the line of the cue and that needed explanation. No one would be surprised if it went as far as 15° off. The videos seem to show very nearly a parallel course and that's what I've been working to. No wonder you (A.T.) and I have been arguing the toss so much.

 

[A.T.]

No one would be surprised if it went as far as 15° off.

It goes ~15° off the contact normal. That was what the OP asked about.

 

[sophiecentaur]

It goes ~15° off the contact normal. That was what the OP asked about.

In the video I am referring to (Post #24) the ball path is parallel with the cue. That was what the question needed an explanation for, as far as I can see. Have you seen it?
I am not sure how your 15° angle is relevant here when what counts is surely the direction relative to the line of the cue - which is how the player views the event.

 

[poolplayer]

It goes ~15° off the contact normal. That was what the OP asked about.

Exactly. I don't think the cue ball goes dead parallel with the cue, and I don't care 1° difference for now.

Even if there is slippage, the tangential force against the table will still be greater than with a horizontal impact.

How can you be sure that? You really push the friction between the ball and table... The cue angle would be always downwards in the game because there are rails, but we always try to strike horizontally as possible. So, the angle should be less than 5° in most cases. In my videos, I would say shots are very horizontal because there is no rail on my table.

Anyway, I am going to post probably decisive evidence against the friction between the ball and table. I hang a ball with a rope in the air and stroke the ball with right English.

I am sorry for the low quality experiment, but you would agree that the ball still goes straight without contact with the table.

So, now we can focus on the real force that makes the ball goes rightwards from the normal direction.