Curvature away from the tangent line

[Bluewolf]

Let's for hypothetetical purposes assume 2 givens: 1)the student has an accurate stroke and cb hit 2)The student has good ball speed control.

In terms of curving the ball away from the tangent line, I have a few questions.

1) In putting top or bottom on the cb, will the cb curve away from the tangent line sooner with a firm hit vs a soft hit and if so, why?

2) In terms of top and bottom deviating from the tangent line, is there a difference in which one will curve away from the tangent line sooner. IE will bottom leave the tangent line sooner than top, for instance?

3) When varying degrees of top or bottom, ie, 1 tip vs two, will the resulting curvature be greater with bottom with top, vice versa, or is the deviation given the same amount of vertical spin the same?

Laura

 

[mjantti]

First of all, when cueball has a spin, the friction between the table and the cueball will "bend" the cueball to the direction of the spin until the cueball is going to the direction of the spin or the spin wears out before that.

1) if you shoot hard, the curve will have a longer & wider arc than on a soft shot. So, you will get the cueball curve earlier if you shoot softly. But usually you can't create so much spin with a soft stroke so you'll have an early curve but not much of it. The condition of the cloth and humidity has also some effect on this. With a new cloth and dry conditions, the friction between the cloth and the cueball is smaller and so the curve is wider but the cueball spins longer thus making wide and long curves possible. With worn cloth and humid conditions the friction is high, thus making curves short and "tight".

2) and 3) there is no difference between follow and draw, it's just spin. But you must realize that draw wears out sooner than follow before the cueball contacts the object ball. So, if you have a long distance between the object ball and the cueball, you must shoot more draw than follow to create equal amount of spin on the impact.

extra: cueball will follow the tangent line only if the spin is zero at the impact. If you roll the cueball or the spin has already disappeared before the impact, you will have a slight curve to the "follow" direction after the impact. That's because when the cueball is rolling, it works as a slight follow after the impact.

Hope this helps... would be nicer to draw some diagrams to make things more clear....

 

[Colin Colenso]

Some Clarifications

Not bad Mikko, but a few points need clarification.

First of all, when cueball has a spin, the friction between the table and the cueball will "bend" the cueball to the direction of the spin until the cueball is going to the direction of the spin or the spin wears out before that.

The cueball actually curves toward a final direction which is essentially the vector addition of the tangential deflection speed and the spin momentum that through friction will convert into speed in that direction.

It is not about spin wearing out, it is about 2 additional forces.

On near straight shots, tangential deflection force is low but at 90 degrees, therefore the cue ball goes mostly in the direction of the spin. On cut shots the two forces are almost alligned.

you must realize that draw wears out sooner than follow before the cueball contacts the object ball. So, if you have a long distance between the object ball and the cueball, you must shoot more draw than follow to create equal amount of spin on the impact.

extra: cueball will follow the tangent line only if the spin is zero at the impact. If you roll the cueball or the spin has already disappeared before the impact, you will have a slight curve to the "follow" direction after the impact. That's because when the cueball is rolling, it works as a slight follow after the impact.

Well it is more accurate to say that follow does not wear out at all...not until the cue ball stops.

It is actully very hard to put overspin on the cue ball. That means, more spin than rolling rate spin. There are perhaps only a few trick shot applications where you can or may want to.

You can test this by puting object ball on head spot. Hit it with medium follow from 12" away so the object ball travels about 16 feet (just missing the cue baall on the way back). Now try it from about 4" away and try to get overspin on the cue ball.

Meaasure the distances travelled by both balls. You'll see that it is hard to get more than rolling follow spin on the cue ball, even in these conditions. In play, I expect overspin never occurs enough to account for any significant changes in tangent line curve.

 

[Colin Colenso]

I should add, for Laura, that with close draw shots, you might attain the same ratio of vertical spin as for follow shots, and hence the same arc, but on longer shots, in order to maintain a high backspin ratio against the cloth friction, more power is needed, and this will send the cue ball further out on the tangent line before the arc takes full effect.

The 4 critical variables for curvature arc are 1. Shot speed 2. Vertical spin amount 3. Shot angle and 4. Surface friction of cloth

 

[Colin Colenso]

Test to determine if backspin can be created which is spinning at the same rate as rolling follow.

Place balls as described above. Object ball on head spot, cue ball 4" behind. Hit ball to the bottom rail with follow and measure how far the cue ball rolled forward. Then hit to the rail with low draw, and measure the distance the cueball rolls back.

 

[DoomCue]

Let's for hypothetetical purposes assume 2 givens: 1)the student has an accurate stroke and cb hit 2)The student has good ball speed control.

In terms of curving the ball away from the tangent line, I have a few questions.

1) In putting top or bottom on the cb, will the cb curve away from the tangent line sooner with a firm hit vs a soft hit and if so, why?

2) In terms of top and bottom deviating from the tangent line, is there a difference in which one will curve away from the tangent line sooner. IE will bottom leave the tangent line sooner than top, for instance?

3) When varying degrees of top or bottom, ie, 1 tip vs two, will the resulting curvature be greater with bottom with top, vice versa, or is the deviation given the same amount of vertical spin the same?

Laura

1. The harder you hit the ball, the farther down the tangent line the CB will travel before it deviates on a line resembling half of a parabolic curve. If the tangent line is the x axis, and the line of centers is the y axis, then the curve can be graphed as either x squared or negative x squared, depending on your point of reference. When planning your intended CB path, make sure you take into account the speed at which you hit the CB.

2. I think that follow leaves the tangent line sooner. This is mostly from personal observation. I believe this is due to forward momentum and forward spin working together.

3. I haven't tested this, but I would think you'd have to use more backspin to see the same parabolic curve on the opposite side of the tangent line compared to the curve using topspin. The reason I think this is because the forward momentum of the CB will help a forward spinning CB leave the tangent line, while it will fight against a backspinning CB.

-djb

 

[DoomCue]

Mikko and Colin, you're fast! I was typing my response to Laura's question, and by the time it posted, all of your responses were there before me.

-djb

 

[Colin Colenso]

1. The harder you hit the ball, the farther down the tangent line the CB will travel before it deviates on a line resembling half of a parabolic curve. If the tangent line is the x axis, and the line of centers is the y axis, then the curve can be graphed as either x squared or negative x squared, depending on your point of reference. When planning your intended CB path, make sure you take into account the speed at which you hit the CB.

2. I think that follow leaves the tangent line sooner. This is mostly from personal observation. I believe this is due to forward momentum and forward spin working together.

3. I haven't tested this, but I would think you'd have to use more backspin to see the same parabolic curve on the opposite side of the tangent line compared to the curve using topspin. The reason I think this is because the forward momentum of the CB will help a forward spinning CB leave the tangent line, while it will fight against a backspinning CB.

-djb

Doomcue,
There are some reasons for what you are observing, but it is not due to any forward momentum somehow helping the cue ball forward.

One reason that the tangent line deflection is actually around 88 degrees, slightly forward of the tangent. This is due to frictional losses in the collision. Draw has to fight against this, where follow is aided by it.

Try the test I show above and you will realize that it is quite rare to get the same ratio of backspin as you the spin you get on common follow shots. Therefore, follow shots have the equivalent arc of the most ripped draw shots and probably even more due to the tangent line frictional losses.

In all cases,the cue ball leaves the line at a time infinitely close to collision time. The deviation may be minimal, but it begins immediately. This is akin to the assymtote of a parabola never reaching the line. So we can't say which one begins to arc sooner, only that follow arcs to a greater degree, or more sharply than draw.

btw: The shape of the curve appears parabolic y=k(x*x) +c but that is just an appearance. You could create parabolas that closely trace many curves, but I doubt they would be exact.

 

[Colin Colenso]

Mikko and Colin, you're fast! I was typing my response to Laura's question, and by the time it posted, all of your responses were there before me.

-djb

DoomCue,
I think maybe you hadn't refreshed your main forum screen for a while before you replied as Mikko's post was nearly 90mins before yours

 

[mjantti]

Colin is right, I stand corrected. The final direction cueball takes is actually a vector sum of translation vector and rotational vector.

I think I'm right but not on this particular case. In masse shots, the final direction of the cueball is often the direction of the spin imparted if the spin is strong enough and the cue elevation has been near 90 degrees.

Yes, follow wears out too, but slower than draw. It's difficult to explain things and get all points clear with just a few sentences.

Djb, we're faster than lightning

 

[mjantti]

DoomCue,
I think maybe you hadn't refreshed your main forum screen for a while before you replied as Mikko's post was nearly 90mins before yours

No help living in different time zone, eh ?

 

[Colin Colenso]

I think I'm right but not on this particular case. In masse shots, the final direction of the cueball is often the direction of the spin imparted if the spin is strong enough and the cue elevation has been near 90 degrees.

With Masse that is only true if elevated at 90 degrees or if alligned along the centre line of the ball.

Check my diagram on the Masse thread and you'll see the final direction, as determined by Coriolis 200 years ago, is parallel to a line between the centre of the cue ball and the point on the cloth your tip is aimed aat.

The angle of spin is not in this direction, but along the line between the center of the cue ball and where your tip hits the cue ball. Shots at just 45 degrees elevation clearly illustrate this, the nearer vertical you get, the closer the two lines converge.

 

[Bluewolf]

Up with physics, geometry etc.

Thank-you colin, doom and everyone else who shared your knowledge, including any more posts that may come. Lots to fill this head with, but all great stuff.

I agree with you Colin, that concepts should be introduced early on. I was introduced to things like the tangent line, transfer of energy, etc, at Randy gs poolschool after playing for about six weeks. I could pocket simple shots at that time only. Having some understanding, IMO, even if preceeding the ability to execute, can give a person understanding, which can then be beneficial once more proficiency is achieved resulting in more rapid growth in the sport with practice and experience in pool. Even as a sl2, knew how to not scratch (unless I did something dumb like hit the wrong side of the ball LOL) and how to predict that a ball would have little energy or a lot for the rail, based on transfer of energy due to one instructor giving me some knowledge.

Laura

 

[chefjeff]

Another point to consider is the weight/size of the cueball. Nowadays, this isn't such a big deal as most coin ops have better cueballs than before. I remember those fat, heavy balls traveling right through the object ball, creating some unique opportunities for shape.

But I'm wondering, does the composition of these new cueballs affect the billiard?

Thanks,

Jeff Livingston

 

[mjantti]

Another point to consider is the weight/size of the cueball. Nowadays, this isn't such a big deal as most coin ops have better cueballs than before. I remember those fat, heavy balls traveling right through the object ball, creating some unique opportunities for shape.

I was playing one day at our club and we have very good sets of balls there but they have been in heavy club use for... I dunno... 5-10 years. The balls are in very good shap and I always polish them before I play. BUT. I got one of our tournament ball sets out and practised a few hours with them. Of course they have had quite a little use because they are used only in tournaments. What I found out was that the cueball follows quite a bit more than with the regular set !! Only reason for this is that the cueball is smaller on the worn rack making it more difficult to follow. The playing conditions are alike but the difference between soft roll-in shots were considerable between these two sets !! At least it made a difference to me for position shots...

So, the differences between cueballs are not only in coin-op tables but also with good Brunswick Centennial balls if they have been used a lot....

 

[Bob Jewett]

btw: The shape of the curve appears parabolic y=k(x*x) +c but that is just an appearance. You could create parabolas that closely trace many curves, but I doubt they would be exact.

Well, Coriolis thinks that it is a parabola until the cue ball loses its excess spin and starts rolling in a straight line. This assumes three things which are not always true:

1. The cue ball is on the surface of the table and not bouncing. In fact, it is usually bouncing a little right after contact with the object ball and while it is in the air, it moves in a straight line as seen from above. Each time the cue ball lands while bouncing, it makes a quick change in direction, so as seen from above the path is a series of straight lines until the cue ball stops hopping. This is hard to see on the table, but it is well-modeled in Virtual Pool, which shows you the path of the cue ball in three dimensions.

2. The coefficient of friction between the cue ball and the cloth is independent of the speed of rotation of the cue ball. So far as I know, this has never been measured, and it is difficult to do so.

3. The normal slowing of the cue ball (rolling friction) is much, much smaller than the sliding friction which is usually acting to speed the cue ball up. This has not been looked at in the studies I've seen, and I suspect that rolling friction will make the path of the cue ball slightly different from a parabola.

The cue ball doesn't go in a straight line off the object ball and then curve unless it is in the air. The curve starts immediately after the cue ball leaves the object ball. It is hard for the eye to catch the initial part of the curve.

There is a very simple system for determining the final direction of the cue ball if the cut angle and amount of draw or follow on the cue ball is known. For this system, if the cue ball is rolling smoothly on the cloth, it has "unit" follow for this system. It is possible to get "unit" draw on the cue ball if it is not far from the object ball. Given the amount of draw or follow and the cut angle, you need to draw (or imagine) two lines on the table going out from the cue ball which represent the cue ball's spin and speed just after the collision, and then the cue ball's final direction and speed are given by a point on the line joining the far ends of those two lines. With a little practice, this system is easy enough to use in play if you don't have a feel for the final path.

As for the original question, draw seems to cause a more dramatic change in the path of the cue ball because for most cases the initial and final paths of the cue ball are separated by a much larger angle -- the cue ball "turns" more with draw. This is not always the case. In the Artistic Pool competition shots, there is a trick shot in which the cue ball is played with follow directly between a pair of balls, so the cue ball is pushed back partly towards you and then when the follow takes, it gives a very dramatic curve. This shot is illustrated in Mike Massey's latest column in "On The Wire," a West Coast monthly pool newspaper.

For an example of "turning more" with draw consider a half-ball shot. If you play it with smoothly rolling follow (call it "unit" follow), the cue ball starts out at 60 degrees from the line of your stick and then bends forward to 34 degrees, a change of 26 degrees. If you play with "unit" draw, the cue ball is pulled back to an angle of 109 degrees (slightly backwards) from the path of your cue stick, for a "turning" of 49 degrees. (In practice, for most people, a half-ball draw shot gets close to a 90-degree final angle because they don't hit the cue ball far enough off center, or there is enough distance to the object ball that some of the draw is lost, or there are some other friction effects as Colin mentioned.)

It is very rare to get more than smoothly rolling follow (the test in a message above was first mentioned in Byrne's "Advanced Technique" book and in BD), but it was observed on the Jacksonville tape. With "excess spin" on the cue ball (more than the "unit" spin mentioned above), the bottom of the cue ball is actually moving back towards you on follow shots, and the top of the ball is moving back towards you on draw shots at the instant the ball leaves the tip. Of course, if there is much distance to the object ball, the extra is gone by the collision.

Here is a related puzzle: We see a freight train going sorth down the track at 60 MPH. I say, "There is a part of that train that is always going nouth." What part is that?

 

[chefjeff]

<snip>

Here is a related puzzle: We see a freight train going sorth down the track at 60 MPH. I say, "There is a part of that train that is always going nouth." What part is that?

How about the bottom of the wheels?

Jeff Livingston

 

[LastTwo]

vector addition of the tangential deflection speed and the spin momentum that through friction will convert into speed in that direction.

This will only work by dividing the scategoriphical nebulas by three astronomical units (AU) and combining the frictional forces to create energy, which powers the cellular respiration of the cueball, which normally takes place in the mitochondrion.

 

[Colin Colenso]

How about the bottom of the wheels?

Jeff Livingston

The bottom of the wheels are momentarily stationary...but never move backward. Just like a naturally rolling ball. Unless of course the tracks are greased and the train is going up ahill. Then the wheels might spin on the track.

Some possible answers to what part of the train is always going north.
The compass needle.
The track.
The passengers with return tickets.
It's shadow.
It's sound.

Not perfect answers, but sure it's a kind of trick question.

 

[LastTwo]

Here is a related puzzle: We see a freight train going sorth down the track at 60 MPH. I say, "There is a part of that train that is always going nouth." What part is that?

Bob, is the fact that you mispelled both north and south part of the trick to this puzzle somehow, or were those just typos?