Fairly equal angles from dividing the cueball

[Angle Detective]

I'm new to this forum and very glad to have found it. Just got back into pool and find myself frustrated and on the same plateau that keeps driving me out of the game. If I'm not getting better and can't figure out why, I find something else to pursue.

Anyway, I'm a decent player who plays mainly straight pool with a high run of mid-50s and typically when I do play have a high daily run of a couple of racks. But shotmaking is always my downfall. Easy shots very often end my runs. I figure I need a more consistent way of aiming and recognizing angles. So I've been searching for a good aiming system through old threads here and have scoured the web.

As my first post I figured I would show you what I've been working on. I'd never tried dividing the cueball or object ball into equal segments, assuming that the progression of release angles going from a straight shot to a thin cut couldn't possibly be linear enough to be useful, since we're dealing with spheres and nonlinear calculations. But I'm desperate so I did some basic stuff drawing some paper pool balls with a compass and figuring out angles with a protractor.

As it turned out, dividing the cueball into 8 equal segments from edge to edge, and using the dividing points between those segments as aiming points toward the edge of the object ball yields surprisingly linear results:

Ex. Cuts to Left Using Right Edge of OB as Target
CB Right Edge 0 degrees
CB Right 1/8 7 degrees
CB Right 1/4 14 degrees
CB Right 3/8 21 degrees
CB Center 30 degrees
CB Left 3/8 39 degrees
CB Left 1/4 48 degrees
CB Left 1/8 60 degrees
CB Left Edge 90 degrees

This shows that the first 4 shots are an equal 7 degrees apart, shots 5-7 are an equal 9 degrees apart, and shot 8(at 12 degrees) is just an extra 3 degrees wider than the previous 9 degree shots. Only from the 8th to the final shot is there a large enough range to require significant adjustment, whether by feel or further division.
I created a visual, showing the actual angles using my protractor on the computer screen, of this in the link below. Forgive me if there's a simpler way to create this link. I realize it's quite bulky.

http://CueTable.com/P/?@2AaqX2BULV2COPQ2DIcK2EBIs1FGGW1GMBn1HROh4IUjW3Qapr2UaqX3Uaxb2VULV3Vapc2WOXR3Wapc2XIcK3Xapb3Xapb2YBIs3Yapb1aGGW3aapb1bLkm3baxc1cROg3cbGb4dUjW3dahc3lapr3lbCn3qWbPDividing_the_cueball_into_8_equal_parts_from_left_to_right_edge_and_using_the_dividing_lines_as_aiming_points_towards,_in_this_case,_the_object_ball's_right_edge_gives_the_shooter_7_practically_equally_spaced_shot_angles_to_work_with._The_8th_is_only_slightly_wider_at_12_degrees.&My_rough_calculations_in_degrees_for_the_9_shots_available_using_these_aiming_points_are:_0,7,14,21,30,39,48,60,90_&ZZ4rDcW________________________12&&&30&ZZ3safS__7&_degree&angles&ZZ3tRfp_______9&___degree_&angles&ZZ@

Thanks for reading. Hopefully this is of use to some of you who haven't visualized these angles before. As for recognition of these angles when they come up, I guess that's where lots of practice comes in.

Jeff

 

[Black-Balled]

... If I'm not getting better and can't figure out why, I find something else to pursue.Jeff

Welcome- I am th same way...(I am an ISTP )

Good luck with the calqumalations. Looks like Sanskrit to me!

 

[Jude Rosenstock]

I'm new to this forum and very glad to have found it. Just got back into pool and find myself frustrated and on the same plateau that keeps driving me out of the game. If I'm not getting better and can't figure out why, I find something else to pursue.

Anyway, I'm a decent player who plays mainly straight pool with a high run of mid-50s and typically when I do play have a high daily run of a couple of racks. But shotmaking is always my downfall. Easy shots very often end my runs. I figure I need a more consistent way of aiming and recognizing angles. So I've been searching for a good aiming system through old threads here and have scoured the web.

As my first post I figured I would show you what I've been working on. I'd never tried dividing the cueball or object ball into equal segments, assuming that the progression of release angles going from a straight shot to a thin cut couldn't possibly be linear enough to be useful, since we're dealing with spheres and nonlinear calculations. But I'm desperate so I did some basic stuff drawing some paper pool balls with a compass and figuring out angles with a protractor.

As it turned out, dividing the cueball into 8 equal segments from edge to edge, and using the dividing points between those segments as aiming points toward the edge of the object ball yields surprisingly linear results:

Ex. Cuts to Left Using Right Edge of OB as Target
CB Right Edge 0 degrees
CB Right 1/8 7 degrees
CB Right 1/4 14 degrees
CB Right 3/8 21 degrees
CB Center 30 degrees
CB Left 3/8 39 degrees
CB Left 1/4 48 degrees
CB Left 1/8 60 degrees
CB Left Edge 90 degrees

This shows that the first 4 shots are an equal 7 degrees apart, shots 5-7 are an equal 9 degrees apart, and shot 8(at 12 degrees) is just an extra 3 degrees wider than the previous 9 degree shots. Only from the 8th to the final shot is there a large enough range to require significant adjustment, whether by feel or further division.
I created a visual, showing the actual angles using my protractor on the computer screen, of this in the link below. Forgive me if there's a simpler way to create this link. I realize it's quite bulky.

http://CueTable.com/P/?@2AaqX2BULV2COPQ2DIcK2EBIs1FGGW1GMBn1HROh4IUjW3Qapr2UaqX3Uaxb2VULV3Vapc2WOXR3Wapc2XIcK3Xapb3Xapb2YBIs3Yapb1aGGW3aapb1bLkm3baxc1cROg3cbGb4dUjW3dahc3lapr3lbCn3qWbPDividing_the_cueball_into_8_equal_parts_from_left_to_right_edge_and_using_the_dividing_lines_as_aiming_points_towards,_in_this_case,_the_object_ball's_right_edge_gives_the_shooter_7_practically_equally_spaced_shot_angles_to_work_with._The_8th_is_only_slightly_wider_at_12_degrees.&My_rough_calculations_in_degrees_for_the_9_shots_available_using_these_aiming_points_are:_0,7,14,21,30,39,48,60,90_&ZZ4rDcW________________________12&&&30&ZZ3safS__7&_degree&angles&ZZ3tRfp_______9&___degree_&angles&ZZ@

Thanks for reading. Hopefully this is of use to some of you who haven't visualized these angles before. As for recognition of these angles when they come up, I guess that's where lots of practice comes in.

Jeff

It's a very interesting analysis but something else you might want to consider is margin of error. The underlying feedback a shooter uses is whether or not he actually pockets the ball and fact is, you don't need to execute a shot perfectly in order for the ball to go in. As you progress through the shots, the margin of error diminishes so that by the time you reach the 9th shot, the shooter's accuracy must be absolutely precise.

Although there is surprisingly little difference in angle as you move through the segments of the object ball, the margin of error is decreasing exponentially.

 

[Bob Jewett]

... But I'm desperate so I did some basic stuff drawing some paper pool balls with a compass and figuring out angles with a protractor. ...

You don't have to use a protractor. The geometric function you want is the arcsin(1-fullness), where "fullness" means how full you are hitting the ball. A full-ball hit is a fullness of 1, and half-ball is 1/2. OK, now go to google (www.google.com) and for any "fullness" stick it into the search box in the form:

arcsin(1-3/4) in degrees

Yes, just like that -- that's the exact text you put into the search box to find the angle for a 3/4-full hit. The result you get back from google is:

arcsin(1 - (3 / 4)) = 14.4775122 degrees

Of course, you don't need that much precision for most shots -- usually half a degree is more than enough. If you would like to see a plot of cut angle versus fullness, it is available on the page http://www.sfbilliards.com/misc.htm as the third link under item 17 -- fractional ball aiming. A direct link to the plot: http://www.sfbilliards.com/fract.pdf

Also under item 17 are some diagrams by Pat Johnson that give good illustrations of fractional cuts.

Eventually, you learn all these angles by eye, but I think it helps to put them into a framework like you have developed.

 

[Jal]

...As for recognition of these angles when they come up, I guess that's where lots of practice comes in.

But therein lies a problem. You have to know how full to hit the object ball in order to determine the cut angle, or you have to know the cut angle in order to determine how full to hit the object ball. Maybe I don't get where you're going with this, but knowing the cut angle as a number is redundant.

Memorizing the direction of the object ball after being hit at a finite number of offsets, such as the 1/8'th ball increments in your diagram, could be very helpful. We're talking about really burning them into your brain through long repetition so that there simply is no question where the OB will go at these particular offsets. But it's not clear if that is the end goal of your calculations.

OB direction varies with throw as well. Knowing how throw varies with different cueball speeds, spins and cut angles is also important, whether learned at the table or in the "classroom". There is much information available now.

Jim

 

[Angle Detective]

Although there is surprisingly little difference in angle as you move through the segments of the object ball, the margin of error is decreasing exponentially.

That's something I've always assumed and is exactly why I never even considered a fractional system before, opting for feeling my way through shots, or visualizing the ghost ball. But I was surprised, after measuring, just how many shots, up to that very thin cut area, can be relied upon if aimed and set up properly.

Jeff

 

[Angle Detective]

You don't have to use a protractor. The geometric function you want is the arcsin(1-fullness), where "fullness" means how full you are hitting the ball. A full-ball hit is a fullness of 1, and half-ball is 1/2. OK, now go to google (www.google.com) and for any "fullness" stick it into the search box in the form:

arcsin(1-3/4) in degrees

Yes, just like that -- that's the exact text you put into the search box to find the angle for a 3/4-full hit. The result you get back from google is:

arcsin(1 - (3 / 4)) = 14.4775122 degrees

Thanks for the info. So to be more accurate, using the arcsin calculations, after rounding, the 9 cut angles come to:
0
7
15
22
30
39
49
61
90

Jeff

 

[Angle Detective]

But therein lies a problem. You have to know how full to hit the object ball in order to determine the cut angle, or you have to know the cut angle in order to determine how full to hit the object ball. Maybe I don't get where you're going with this, but knowing the cut angle as a number is redundant.

Memorizing the direction of the object ball after being hit at a finite number of offsets, such as the 1/8'th ball increments in your diagram, could be very helpful. We're talking about really burning them into your brain through long repetition so that there simply is no question where the OB will go at these particular offsets. But it's not clear if that is the end goal of your calculations.

OB direction varies with throw as well. Knowing how throw varies with different cueball speeds, spins and cut angles is also important, whether learned at the table or in the "classroom". There is much information available now.

Jim

Good point. I suppose "burning in" applies to any method. And if you experiment too often and don't give any one method its full burn in time, you'll probably end up burning in inconsistency. Which I think I've done. I have to unlearn and unburn some bad habits.

Jeff

 

[cleary]

I dont know if you saw this on the cue table site, but it might help you.

http://cuetable.com/project/CueTableCutAngleCalIntro.html

 

[Angle Detective]

I dont know if you saw this on the cue table site, but it might help you.

http://cuetable.com/project/CueTableCutAngleCalIntro.html

Thanks. Actually I did know about this but it was too small to get accurate enough. I just looked again and notice they have a bigger version which would have been much more helpful.

Jeff

 

[Patrick Johnson]

OP With Wei Table Displayed

Fairly equal angles from dividing the cueball

I'm new to this forum and very glad to have found it. Just got back into pool and find myself frustrated and on the same plateau that keeps driving me out of the game. If I'm not getting better and can't figure out why, I find something else to pursue.

Anyway, I'm a decent player who plays mainly straight pool with a high run of mid-50s and typically when I do play have a high daily run of a couple of racks. But shotmaking is always my downfall. Easy shots very often end my runs. I figure I need a more consistent way of aiming and recognizing angles. So I've been searching for a good aiming system through old threads here and have scoured the web.

As my first post I figured I would show you what I've been working on. I'd never tried dividing the cueball or object ball into equal segments, assuming that the progression of release angles going from a straight shot to a thin cut couldn't possibly be linear enough to be useful, since we're dealing with spheres and nonlinear calculations. But I'm desperate so I did some basic stuff drawing some paper pool balls with a compass and figuring out angles with a protractor.

As it turned out, dividing the cueball into 8 equal segments from edge to edge, and using the dividing points between those segments as aiming points toward the edge of the object ball yields surprisingly linear results:

Ex. Cuts to Left Using Right Edge of OB as Target
CB Right Edge 0 degrees
CB Right 1/8 7 degrees
CB Right 1/4 14 degrees
CB Right 3/8 21 degrees
CB Center 30 degrees
CB Left 3/8 39 degrees
CB Left 1/4 48 degrees
CB Left 1/8 60 degrees
CB Left Edge 90 degrees

This shows that the first 4 shots are an equal 7 degrees apart, shots 5-7 are an equal 9 degrees apart, and shot 8(at 12 degrees) is just an extra 3 degrees wider than the previous 9 degree shots. Only from the 8th to the final shot is there a large enough range to require significant adjustment, whether by feel or further division.
I created a visual, showing the actual angles using my protractor on the computer screen, of this in the link below. Forgive me if there's a simpler way to create this link. I realize it's quite bulky.

CueTable Help

Thanks for reading. Hopefully this is of use to some of you who haven't visualized these angles before. As for recognition of these angles when they come up, I guess that's where lots of practice comes in.

Jeff

 

[Angle Detective]

Cool. Thanks Patrick. I just checked out how to do this. Next time I'll use it.
Jeff

 

[Patrick Johnson]

If you just consider your odd numbered "interior" angles (3, 5 & 7, not counting straight and 90 degrees) you've got the "3 angle" system, which divides the balls into 1/4s (3/4, 1/2 & 1/4 below), for cut angles of 14.5, 30 and 48.6 degrees. I guess your 1/8s would be the "7 angle" system.

Here's a graph of the cut angles for 1/8 ball fractions. I show the aim as fractions of "CB/OB OVERLAP", where a straight-on hit is an overlap of 1, a half-ball hit is an overlap of 1/2 and a thin cut is an overlap of 0.

pj
chgo

 

[Patrick Johnson]

I was surprised, after measuring, just how many shots, up to that very thin cut area, can be relied upon if aimed and set up properly.

Sure, there's no reason you can't use index angles to "map" the fuller hits and something else better suited for thinner cuts, like maybe the "double overlap" system.

pj
chgo

 

[Angle Detective]

Sure, there's no reason you can't use index angles to "map" the fuller hits and something else better suited for thinner cuts, like maybe the "double overlap" system.

pj
chgo

Is there a double overlap system?
Nice chart. It really shows how even the angles are. It's interesting to see how 1/3 of all available paths for an object ball in any situation are engulfed by that last 8th. Makes you want to stay the heck away from thin cuts.

I think the division of the cueball in either 4 or 8 makes sense because of the width of a standard cue tip. 14mm I suppose would be ideal because 4 tips would be practically the dead on width of a pool ball which is 57mm. But I'd guess that 13mm and up would be close enough to be useful.

You probably know this, but for a practical way of finding the points between the 8 cueball divisions, the edge of the tip from a center ball address gives the first point to one side of center. Placing a tip edge on center ball gives the 1/4 ball point on the other edge. Then from addressing the cueball edge you can find the final 1/8 point with the tip edge that remains on the cueball.

Jeff

 

[Patrick Johnson]

Me:
...there's no reason you can't use index angles to "map" the fuller hits and something else better suited for thinner cuts, like maybe the "double overlap" system.

bluepepper:
Is there a double overlap system?

Sure - it's nothing more than recognizing that the CB and OB contact points are always centered in the overlapped parts of the two balls (and then finding the contact point and overlapping the balls until it's centered). You can see that by going to CueTable.com and using the Aiming Tool. The screen capture below shows the overlap for a 61 degree cut. Notice that the red X marking the contact points is centered in the overlapped parts of the two balls.

pj
chgo

http://cuetable.com/project/CueTableCutAngleCalIntro.html

 

[Angle Detective]

Oh okay. I knew of the system, just not what it was called.
Thanks,
Jeff

 

[Angle Detective]

Possible Drill to Learn Fractional Ball Shots

Setting up the object balls perfectly in this drill may be difficult except that they are in a straight line. The edge of the cue stick should help. The 1-ball obviously points to the head spot, and the 2,4,5 and 6-balls point close enough to diamonds or the opposite corner pocket to arrange the rest in between. And the 9-ball aimed at the second diamond would probably be a more practical shot to learn anyway, measuring somewhere in the 80s.

I measured the angles pretty carefully on screen with a protractor. Assuming that the cue table program is to scale, it should look like this on a real table. These are theoretical cut angles, and I haven't been able to try this drill yet, but I was looking for a drill that might ingrain the 9 shots available using 8 divisions of the cueball aimed at one edge of an object ball. I also wanted fairly long shots for more difficulty.

Start with the thinnest cut and work backwards so none of the other balls are disturbed. For a 5 shots(4 divisions) setup just remove the 2,4,6,and 8-balls. Marking the object ball spots with labels would be recommended for easily repeated setup. And of course you should reverse the setup for left-hand cuts.

Tell me what you think and how you would improve the drill.
Thanks,
Jeff

CueTable Help

 

[Jal]

Tell me what you think and how you would improve the drill.

I like the fact that you have them set up in a straight line, but I think there's a problem with placing them accurately along that line. At least you haven't indicated how to do that. An alternative is here:

http://ww2.netnitco.net/users/gtech/CircleDrill.jpg

Here the object balls are placed on a circle going from the side pocket to the corner pocket (intersection of the adjacent cushions). The cueball is shot perpendicular to the end cushion. The offset in which to hit each OB is the same as its location across the width of the table. In other words, the OB at one diamond from the bottom cushion, which is one-quarter way across the table, is hit at an offset of 1/4 ball (3/4 full).

Hitting from medium to brisk speed with full follow or draw all but eliminates throw, so the ball should come close to center pocket when shot that way.

Since the goal is not to sink balls but to memorize the OB's direction when hit at each offset, it would be better to move the whole setup one diamond up table and make the first diamond the target. That way you're concentrating on the OB's direction and not on pocketing the ball. The target is there just to confirm that you're hitting the OB consistently. Also, you get an automatic ball return.

It would help to have your own table to mark up, but a cue stick can be used to set the balls in position.

Another alternative is to just place the CB and OB at various intersections of the diamonds and use some diamond or pocket as a target. You won't be getting offsets in neat 1/8'th ball increments, but is that important?

Just some thoughts. Maybe you can come up with an easy way to position the balls along that line in your diagram.

Jim

 

[Patrick Johnson]

Tell me what you think and how you would improve the drill.

I think this is the "beginner's drill". It practices aligning the ball fractions accurately, but doesn't force you to predict exactly where the OB will go with each fractional alignment, which is the essential skill you need so that in a real situation you can estimate which fractional alignment is closest to the actual cut you need and make the adjustment from it. You'll need to quickly graduate to a drill that tests that, probably with random CB/OB placements.

Also, my instinct tells me that you should start with fewer angles, like the 3, 5 and 7, and add in-between angles (if necessary) once you've mastered those. My guess is that you won't add all the in-between angles because (A) it's hard to memorize so many cut angles accurately and (B) you probably don't need so many. I don't think you really need to practice the 1 and 9 alignments at all for this system (you should already know those).

pj
chgo