Fairly equal angles from dividing the cueball

[Bob Jewett]

But, but, Bob, everyone knows you don't play 1pocket. How about at 14.1?

Lou Figueroa

While it's true that I need 10-5 from nearly everyone, and especially you and JoeyA, I think I would have also lost at 14.1 to that guy.

 

[pletho]

 

[Jal]

VERY interersting post Jim. Great that you included the throw and non-throw cb paths since SO many diagrams fail to do that and are therefore, quite misleading.


But you threw me a curve with your comment in bold above. Can you give me the quick and dirty about why follow or draw would eliminate CIT?

THANKS!

Jim

Thanks Jim.

As Pat described, draw and follow tend to reduce horizontal throw by changing it more to vertical throw, and by increasing surface speed (which reduces the friction force itself). Vertical throw doesn't really affect the shot, only the remaining horizontal component does.

On top of this, the contact time is finite (not instantaneous) , which means the balls travel along a chord of a circle (more or less) while in contact. This shifts the tangent line a little, ie, the balls emerge from the collision at a different "contact point" than the initial one. This means there is always a little "negative throw" built in and this further reduces "positive throw" (positive throw being in the direction of the cueball along the tangent line, "negative in the opposite direction of the cueball). The faster the shot, and the greater the cut angle, the larger this effect.

All in all, with medium to fast speed and a fully rolling cueball (or reverse rolling, as in lots of draw), throw is reduced to something like a few tenths of a degree according to calculations (less than 0.5 degrees at all cut angles and considerably less at small cut angles). But throw theory, namely the dependence of the coefficient of friction on surface speed and normal pressure, isn't exactly rock solid, imo. The specific numbers spit out by the computer can't be taken as gospel. (Maybe I should have mentioned that above, but it gets tedious when you're forever qualifying everything.)

Jim

 

[Jal]

...I also know that a higher speed impact reduces horizontal throw, but I don't know the mechanism for that - can you explain how that works for the physicsaholics among us?

I have a model in mind, but from what I've read, I don't think the people who study and theorize about friction (tribologists) put much stock in it. Since it works for me, I'll just mention that surfaces, even polished ones, are riddled with tiny protrusions (asperities). You can imagine them colliding with each other, and these collisions would tend to push the surfaces apart. If the asperities are generally less steeply sloped near the top than near the bottom, the friction force (the sum of all the tiny individual collision forces) will tend to point more perpendicular to the surfaces as the surfaces separate, thus less parallel or tangential force remains. For some particular surface speed, the surfaces separate until equilibrium is reached and the normal force force trying to push the surfaces together equals the collision force trying to separate them.

I thing the surface separation aspect might be right, but tribologists seem to describe friction as the result of molecular attractions, ie, temporary bonds getting established and then severed (ah, what do they know). Sorry, but I can't say anything more, and probably should have stopped sooner. It's a complicated subject and various surface to surface interactions are quite different from each other.

Do you know the relative magnitudes of these two effects when combined like this?

Yes, more or less. "More or less" because while the geometry is straightforward, the measurements of how the friction force varies with the pressure between the balls and surface speed, still leave some doubt. But going with Dr. Dave's model, let's compare 15, 30 and 60 degree cut shots at stun and natural roll, using a cueball speed of 7 mph (a little faster than lag speed) and no sidepsin.

The predicted throw angles with stun are 2.19, 1.70, and 0.89 degrees, respectively. With natural roll, they are 0.20, 0.39 and 0.67. The percentage reductions in the throw angles due solely to the shifting of the friction to a more vertical orientation are, 74%, 50%, and 13%, respectively. The percentages drop as the cut angle increases because the cut angle itself supplies more surface speed, which reduces the coefficient of friction, and keeps the orientation of the overall surface speed more horizontal. (Friction acts in the anti-direction of the overall surface speed.)

The numbers aren't to be taken too literally, but describe the overall trend. Not figured in is the "negative throw" due to the finite contact time (shift of the tangent line). This is small, but reduces the apparent (net) throw further and increases with cut angle.

Jim

 

[Jal]

But for this to be worthwhile, he needs offsets he can align using ball fractions, doesn't he?

pj
chgo

Well, for what it's worth, my thinking is that it's best not to think in terms of ball fractions (unless you're Bob Jewett's opponent). I mean, even if you set the practice balls up according to Jeff's in-line method (or the circle method) where you know what the correct fractional hit should be, it might be better to put that out of your mind and just sort of get the "feel' of the shot. In normal play, with random cut angles, no one is going to be reporting the right fraction.

It seems plausible to me then that "burning in" various fractions, even if they occur at irregular intervals, might be as good. It was just an afterthought though, while looking for a more convenient way of doing it.

Jim

 

[Patrick Johnson]

JAL:
It seems plausible to me then that "burning in" various fractions, even if they occur at irregular intervals, might be as good.

The point of the ball fractions system is the ball fractions, which aid accurate replication of the "reference" angles. Your idea is probably good, but it's a fundamentally different approach to learning aiming, maybe for a different kind of player.

pj
chgo

 

[Bob Jewett]

... The predicted throw angles with stun are 2.19, 1.70, and 0.89 degrees, respectively. With natural roll, they are 0.20, 0.39 and 0.67. The percentage reductions in the throw angles due solely to the shifting of the friction to a more vertical orientation are, 74%, 50%, and 13%, respectively. ...

I just wanted to highlight this part of Jim's response. Stated simply: if you change a fullish cut shot (about a 3/4-full hit) only by going from stun to draw, you change the cut angle by 2 degrees. That's a significant change for a 4-diamond long cut shot. Any aiming system worth its salt needs to get the aiming line to better than 2 degrees. The conclusion will be obvious to some.

 

[Angle Detective]

I just wanted to highlight this part of Jim's response. Stated simply: if you change a fullish cut shot (about a 3/4-full hit) only by going from stun to draw, you change the cut angle by 2 degrees. That's a significant change for a 4-diamond long cut shot. Any aiming system worth its salt needs to get the aiming line to better than 2 degrees. The conclusion will be obvious to some.

Good point.
Jeff

 

[Angle Detective]

The predicted throw angles with stun are 2.19, 1.70, and 0.89 degrees, respectively. With natural roll, they are 0.20, 0.39 and 0.67. Jim

Jim, is it the same figures for draw? If so, then I have been deluding myself with the extreme draw for a steeper cut shot.

Jeff

 

[Angle Detective]

Jeff, sorry for the delay. Wow, you've been doing some work! I'm wondering how you figured it all out using compass and protractor....or maybe you did the trig?

As you say, you could make some sort of gauge to set them up quickly. If you don't have their locations along the line in numerical form, I could help, if you like.

As for the circle setup, I did come up with it, but likely many others have as well.

I was thinking that you might be able to get a good distribution of offsets just by placing the balls at selected intersections of the diamonds. I thought about writing a small program to figure the various cut angles, but laziness won out. Still, it might be a good alternative, though the cut angles would be a bit dependent on table size. I think your way might be more accurate, although it also depends on table size, and it should allow for the fact that diamond markers are not a fixed distance from the edge of the cushion in going from table to table style.

Jim

I certainly did no trig. Nearly failed it in school. Just used the protractor on the computer screen for the lines and angles.
I didn't realize that the diamonds could be different from table to table. I also didn't know about the throw reduction with vertical spin. So thanks for the info.
As for the numerical ball positions, if it's easy for you to do that would be great, but don't go out of your way. I can probably figure it out next time I'm at a table.
Already learning a lot here. Thanks.
Jeff

 

[Jal]

Jim, is it the same figures for draw? ...

Yes they are when you have the same amount (magnitude) of backspin as you would have in topspin if the ball were rolling. This happens when the cueball is struck with a tip offset 2/5'ths of its radius below center, and doesn't have time to lose any of that backspin before reaching the object ball (ie, fairly fast shots where the balls aren't too far apart). In both cases, draw and roll, the cueball has a spin/speed ratio of 1.

Jim

 

[av84fun]

Quote:
Originally Posted by Bob Jewett
Well, there are exceptions. I know one good player in this area who divided the ball into 64ths. Yes, 63 hits on each side. I know this because he had me program his HP calculator to give him the angles when he got tired of working them out one by one. If a ball was sitting half a diamond off the third diamond on the long rail, he could tell you that it's path to the pocket made a 9.5-degree angle with the cushion. If the line for the cue ball for the shot went from the third diamond on the short rail to the sixth diamond on the long rail, he knew that it made a 26-degree angle with that same rail, and that the needed cut was therefor 16.5 degrees and a 46/64ths hit was needed. As for how well he could play, the last time we played he gave me 10-5 at one pocket and beat me.


But, but, Bob, everyone knows you don't play 1pocket. How about at 14.1?

LOL! And he was SERIOUSLY delusional to think that he actually could SEE such thinly sliced targets...let alone hit them.

Regards,
Jim

 

[av84fun]

In my experience, the sharpest cuts occur when using extreme draw. Maybe I'm deluding myself, but whenever faced with cinching an extreme cut, I draw the ball.

Jeff

Hi Jeff. To each his own of course, but given an extreme cut angle precision re: the CB path is obviously critical. I prefer to use a tip of high center to get true roll asap and avoid both side and low cueing to avoid squirt and swerve. Maybe a TOUCH of outside but never low.

Regards,
Jim

 

[av84fun]

Thanks Jim.

As Pat described, draw and follow tend to reduce horizontal throw by changing it more to vertical throw, and by increasing surface speed (which reduces the friction force itself). Vertical throw doesn't really affect the shot, only the remaining horizontal component does.

On top of this, the contact time is finite (not instantaneous) , which means the balls travel along a chord of a circle (more or less) while in contact. This shifts the tangent line a little, ie, the balls emerge from the collision at a different "contact point" than the initial one. This means there is always a little "negative throw" built in and this further reduces "positive throw" (positive throw being in the direction of the cueball along the tangent line, "negative in the opposite direction of the cueball). The faster the shot, and the greater the cut angle, the larger this effect.

All in all, with medium to fast speed and a fully rolling cueball (or reverse rolling, as in lots of draw), throw is reduced to something like a few tenths of a degree according to calculations (less than 0.5 degrees at all cut angles and considerably less at small cut angles). But throw theory, namely the dependence of the coefficient of friction on surface speed and normal pressure, isn't exactly rock solid, imo. The specific numbers spit out by the computer can't be taken as gospel. (Maybe I should have mentioned that above, but it gets tedious when you're forever qualifying everything.)

Jim

Great explanation Jim...I even understood some of it!! (-:

The reason I asked is that in Sciene of Pocket Billiards,(1989) Koehler wrote that in his experiments, the speed of the CB "did not discernibly effect the throw angle." (p. 38)

The magnitudes of variations you cite seem to confirm that few shots would be made or missed based solely on the single variable of speed. Is that right do you think?

THANKS!

Jim

 

[Jal]

...As for the numerical ball positions, if it's easy for you to do that would be great, but don't go out of your way....

Jeff, I completed the math and will have the numbers for you this evening. (I have to write a small program.) It won't take much work to do the program, but if you've decided not to go ahead with this for some reason, please let me know.

Jim

 

[Jal]

Great explanation Jim...I even understood some of it!! (-:

The reason I asked is that in Sciene of Pocket Billiards,(1989) Koehler wrote that in his experiments, the speed of the CB "did not discernibly effect the throw angle." (p. 38)

The magnitudes of variations you cite seem to confirm that few shots would be made or missed based solely on the single variable of speed. Is that right do you think?

THANKS!

Jim

Thanks Jim.

I think what you said about speed is true when the object ball isn't very far from the pocket and the shot speed variation isn't too great. But if you look at a 30 degree cut, for instance, shot with stun and zero english at 3 mph and 10 mph, the calculated throw angles are 3.55 deg and 1.11 deg, respectively. That 2+ degree difference is enough to miss quite a few shots.

These numbers are from Dr. Dave's model, which are based on measurements done by Wayland Marlow (The Physics of Pocket Billiards). I don't know if he (Marlow) used frozen object balls, one acting as a proxy cueball, to obtain his numbers. If so, this puts them in question, a little. But going with them, it appears that the coefficient of friction, which is the ratio of the friction force to the force acting normal to the surfaces (the latter being the one that propels the OB in its forward direction), can vary by as much as a factor of 10 from very slow to very fast surface speeds. Maybe the actual variation is less, but it seems likely that there is still some considerable difference, whatever it is. I doubt that the actual variation is something like, say, 30%, compared to Marlow's data which indicates something like 1000%. I've done some crude tests myself and indeed the variations were roughly what Marlow got, but alas, I used frozen OB's.

I've read Koehler's book too but have forgotten how he did his experiments, if he described them at all, which he wasn't inclined to do as I recall.

Jim

 

[av84fun]

Thanks Jim.

I think what you said about speed is true when the object ball isn't very far from the pocket and the shot speed variation isn't too great. But if you look at a 30 degree cut, for instance, shot with stun and zero english at 3 mph and 10 mph, the calculated throw angles are 3.55 deg and 1.11 deg, respectively. That 2+ degree difference is enough to miss quite a few shots.

These numbers are from Dr. Dave's model, which are based on measurements done by Wayland Marlow (The Physics of Pocket Billiards). I don't know if he (Marlow) used frozen object balls, one acting as a proxy cueball, to obtain his numbers. If so, this puts them in question, a little. But going with them, it appears that the coefficient of friction, which is the ratio of the friction force to the force acting normal to the surfaces (the latter being the one that propels the OB in its forward direction), can vary by as much as a factor of 10 from very slow to very fast surface speeds. Maybe the actual variation is less, but it seems likely that there is still some considerable difference, whatever it is. I doubt that the actual variation is something like, say, 30%, compared to Marlow's data which indicates something like 1000%. I've done some crude tests myself and indeed the variations were roughly what Marlow got, but alas, I used frozen OB's.

I've read Koehler's book too but have forgotten how he did his experiments, if he described them at all, which he wasn't inclined to do as I recall.
Jim

Thanks again Jim. No, he did not describe his experiment on that issue.

Regards,
Jim

 

[Dead Crab]

************
LOL! And he was SERIOUSLY delusional to think that he actually could SEE such thinly sliced targets...let alone hit them.

Regards,
Jim
**************************

Why do you say that?

The radius of a pool ball is 28.6 mm. If you have reasonable vision, you can resolve 1mm distances from several feet away, giving 28 "on ball" aims, and probably another 15-20 that can be reasonably estimated "off-ball" aiming points.

With a little practice, and knowledge of proper technique, it is possible to estimate narrow angles to within a half a degree, large angles to within 2 degrees, and the in-betweens to within a degree.

I don't consider myself delusional, and I do sometimes succeed in hitting a target that I have selected.

 

[Angle Detective]

Jeff, I completed the math and will have the numbers for you this evening. (I have to write a small program.) It won't take much work to do the program, but if you've decided not to go ahead with this for some reason, please let me know.

Jim

Jim, I'll try to figure it out on the table and mark something up like a string and post the measurements I come up with. No need to trouble yourself with writing a program. Cool that you have the ability to though. I'm envious. It will also allow me to adjust to throw and remark the string appropriately. I don't know if the drill is even useful.

I was thinking about how just playing normal shots and guessing which 8th ball shot should apply might be even better for ingraining them, being sure to reposition the shots when I missed to use another 8th division.

I think a drill to practice realignment of the cue after taking aim would be a good idea too.

But for the sake of completeness I'll give the drill a real try on the table when I get to one.
Thanks,
Jeff

 

[Patrick Johnson]

I was thinking about how just playing normal shots and guessing which 8th ball shot should apply might be even better for ingraining them

I think so too. Here's an idea:

Toss the CB and one OB onto the table randomly and start shooting the OB, cycling through the three main "reference" angles (3/4 ball, 1/2 ball and 1/4 ball) one after the other. One possible pattern is left 3/4, right 3/4, left 1/2, right 1/2, left 1/4, right 1/4, repeat. [NOTE: To start you might want to stick with just one angle, say 3/4 ball, until you get familiar with it. Then practice 1/2 ball for awhile, then 1/4 ball. After that you can cycle through all three for awhile, then go to mixing them up randomly.]

You're not trying to pocket the OB; you're just shooting the reference angles one after the other and trying to predict exactly where the OB will hit the rail each time. To be strict with yourself, place a piece of chalk on the rail each time and see how close you come. You should get more and more accurate and consistent over time.

Remember, you have to be able to visualize these reference angles precisely in order for the system to have value.

pj
chgo