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jondrums
11-13-2007, 02:23 PM
Hey guys, I posted this over at azbilliards, but nobody seems to care much about this kind of stuff there. So I thought I would put it here and see if anyone here is interested.

Ok, so I lied a little in the title - this is an AUGMENTATION to the very popular "quarter ball aiming system". Basically the same system as SAM, and the billiards aim trainer system (http://www.billiardaimtrainer.com/). For more information about these systems, do a quick archives search.

So I have always had a little trouble estimating the cut angle to start with, so that when I thought it was supposed to be a half ball hit, I might miss the shot. So I present here, my method for determining the hit angle. Once you get calibrated, you could easily and quickly determine the angle to a few degrees precision!

A disclaimer: I MADE THIS SYSTEM UP MYSELF, using lots of external input from books, other people, and forum advise. There are probably lots of other people who have done something just like it, so I claim no property to it. I'd rather just share it freely, since I thought of it myself.

To recap the quarter ball aiming system: a 15 degree cut is called a 3/4 ball hit, a 30 degree cut is called a 1/2 ball hit, and a 45 degree cut is called a 1/4 ball hit.

Using my cue and my hand as a distance measuring tool, I used some basic trigonometry to come up with a very simple method to find those three angles. First some background info:

My father taught me very early a simple way to estimate length using my hand. All you have to do is hold your pinky and thumb stretched out as far as you can, and measure that span with a ruler. From then on, you can use your "hand span" as a unit of measure. My hand span is 9.25". Your hand size may vary. Yes, I also have big feet (reference: http://www.vendian.org/mncharity/dir3/bodyruler/)

My pool cue is 58" long. The joint is 29" from the tip. The wrap begins 42" from the tip.

To use this system, you must first find your personal hand span distance, and using that then find your magic number. To find your magic number, multiply your hand span by 3.86. My hand span is 9.25, and my magic number is 35.7. Then you must locate a point on your cue that is exactly your magic number in inches from the tip of the cue. For me, it is a little more than halfway from the joint to the wrap (35.7 inches from the tip).

For me, a picture is a 1000 words, so take a look at the sketch of me measuring a 30 degree cut (1/2 ball hit). Then realize that one hand span = 15 degrees (3/4ball hit). three hand spans = 45 degrees (1/4ball hit). I have found this system to be VERY accurate, and fairly simple to execute on the fly.

http://i237.photobucket.com/albums/ff105/jondrums/Aiming_system.jpg

I don't use this aiming system for pocketing balls very often at all!!! I actually just look at the shot, and know how to hit it, and then go ahead and do it. Or if I'm feeling particularly off that day, I use something like the ghost ball system.

WHAT THE HELL IS IT FOR THEN???

I've found the quarter ball system really useful for the following three situations:
Tricky combination shots
Balls very close to the pocket
Safety play, where this is no clear spot to aim an OB at
Very long cut shots

These are situations where I find it very tricky to aim because I do not have a solid reference to aim at (like a pocket).

I'm sure a few of you are going to jump on me saying that aiming systems are useless, but I don't really care, because I know that they have a time and place in my game!

Jon

ps. the math behind it here (http://s237.photobucket.com/albums/ff105/jondrums/?action=view&amp;current=aiming_system_math_2.jpg)

SPetty
11-13-2007, 02:37 PM
That's fun. I like it. The link to the math behind it, though, is the same as the pic you provided in the post. I was curious to know what the 3.86 number is. I'm sure I could figure it out, but since you have already, and I'm feeling lazy, I thought maybe you could tell me.

And isn't there some school of thought that 1/4 ball isn't really 45 degrees, and 3/4 ball isn't really 15 degrees? Well, and half ball isn't really 30 degrees? Have you found that to be true as well?

11-13-2007, 04:08 PM
You might want to take a look at a similar approach:

jondrums
11-13-2007, 04:13 PM
I fixed the link to the math. Thanks for the comment, I think the calculations will answer your questions, but basically, you're right, the quarterball system is not exactly 15,30,45 deg. The system I showed approximates the exact angles well enough to use an excellent starting point for more practice.
Jon

dr_dave
11-13-2007, 05:56 PM
<blockquote><font class="small">Quote jondrums:</font><hr>To recap the quarter ball aiming system: a 15 degree cut is called a 3/4 ball hit, a 30 degree cut is called a 1/2 ball hit, and a 45 degree cut is called a 1/4 ball hit.<hr /></blockquote>In case you didn't know this already, the angles you report are only approximate. See TP A.11 (http://billiards.colostate.edu/technical_proofs/new/TP_A-11.pdf) for the exact values.

Also, if you want to see a bunch of other stuff written on this forum about aiming systems, you can find many highlights and summaries here (http://billiards.colostate.edu/threads.html) under aiming.

Regards,
Dave

Jal
11-14-2007, 11:58 AM
jondrums,

I knew a fella who had an ingenious method for replacing a light bulb in the dark. He would first stumble around for a while, but eventually manage to insert a 100-watt lamp. At this point he had plenty of light to screw in the new 60-watt bulb.

Your system, though a noble attempt since it involves math, is, I'm afraid to say, equivalent to the above. In order to do an accurate measurement, you first establish the aim line. With this accomplished, you then make a measurement to do what?...to determine the aim line. The only purpose of the measurement then is to introduce some error, or for some reason, to get a numerical estimate of the cut angle.

Most of us have probably been guilty of circular reasoning at some point. I certainly am and have done it on this forum. And I hope to do it again so as to provide another example of this logical trap, which one should avoid at all costs.

Jim

wolfdancer
11-14-2007, 12:25 PM
My system i believe is vastly superior to yours, it only reguires a builder's transit
http://www.surveyhistory.org/images/transit.JPG

a basic understanding of Fibonacci numbers

and A TI scientific calculator, to input the data....

http://education.ti.com/images/rightcolumn/products/scientific/TI36XSolar_L.jpg

No magic numbers are needed, although a magic 8 ball is very useful
http://lord.xopl.com/ulpage3a/m8-ball.gif

11-14-2007, 01:08 PM
************
Most of us have probably been guilty of circular reasoning at some point. I certainly have and have done it on this forum. And I hope to do it again so as to provide another example of this logical trap, which one should avoid at all costs.

Jim
*************

If you "know" the cut angle, then you "know" where to aim, which for the beginning to intermediate player is probably 1/3 of the game.

I've been measuring angles and translating them into aim points for a few months now. Of the many reasons that I miss shots, incorrect choice of aim point is the least of them. It takes maybe 5 seconds, which is a lot less than the pros take when planning a shot without a shot clock. I'm probably accurate to within a degree or two, which translates into a millimeter or two in aim point.

When someone misses using invisible references such as ghost ball or contact points, how do they know whether they blew the stroke or misjudged the aim point?

I see nothing circular about solving the problem at hand by calculating the solution. That such tangible approaches have been neglected by teachers astounds me.

jondrums
11-14-2007, 01:22 PM
[ QUOTE ]
In order to do an accurate measurement, you first establish the aim line. With this accomplished, you then make a measurement to do what?...to determine the aim line. The only purpose of the measurement then is to introduce some error, or for some reason, to get a numerical estimate of the cut angle. <hr /></blockquote>

Actually your logic is fairly flawed. If you roughly know the aim line within a degree or two, you can then use my (or other) systems and determine the aiming line to within a fraction of a degree. That's the whole idea of systems like this! Its like progressive approximation - you use a close estimate and some other information to refine your estimate.

This is not for everybody, and certainly I wasn't thinking that many of us would be all that interested - we already know how to aim (I hope!). I do think its an incredibly valuable tool to have in the arsenal for specific situations where our other aiming techniques fall short.

In addition I would like to add: I find it very interesting to work out and discuss the math/geometry/physics behind pocket billiards. This forum is perhaps the only place around where I could possibly find like minded souls to throw ideas around.

Jon
ps. thanks wolfdancer, I think I need one of those mounted sighting scopes...

wolfdancer
11-14-2007, 05:40 PM
I think if your system works for you, stick with it. over the years I've tried many, and seem to have the best luck with estimating the angle then using a fractional ball aim....
I've tried to show that to my struggling team mates but it doesn't work for them...I once read that all aiming systems fail as the distance increases....so I think they get you into the aiming ball park, and then your own "intuition", makes the adjustments for you to pocket the ball.
In the end it's better to trust your own judgment , then rely on any absolutes of an aiming system....but that's just my opinion, gleaned from years of watching excellent players, and asking them how do you aim?

Jal
11-14-2007, 06:47 PM
Most of us have probably been guilty of circular reasoning at some point. I certainly have and have done it on this forum. And I hope to do it again so as to provide another example of this logical trap, which one should avoid at all costs.

Jim
*************

Circular? What is circular about this.<hr /></blockquote>Once you've established the aim line, why not use it directly. For instance, just site along the line through the center of the cueball to the tip, which is at the center of the ghostball position. You could either extend it to establish a reference point on the cushion (not marked of course), or visualize the fractional offset (ie, the ghostball). Once you've gone through the calculation of cut angle, etc., you're going to have to do some visualization anyway to set the aim line, no?

Maybe "roundabout" would have been a better word than "circular".

<blockquote><font class="small">Quote DeadCrab:</font><hr>If you "know" the cut angle, then you "know" where to aim...<hr /></blockquote>Yes, sort of. But there's the matter of the sine calculation (or recalling it from a memorized table) and then some visualization (ie, where is the aim line for a .67 ball hit?)

<blockquote><font class="small">Quote DeadCrab:</font><hr>I've been measuring angles and translating them into aim points for a few months now. Of the many reasons that I miss shots, incorrect choice of aim point is the least of them. It takes maybe 5 seconds, which is a lot less than the pros take when planning a shot without a shot clock. I'm probably accurate to within a degree or two, which translates into a millimeter or two in aim point.<hr /></blockquote>But what is visible that sets the aim line after you've figured the fractional ball offset, or the offset of the contact point, or whatever? Even if it works out to a nice neat, say 3/4 ball hit, how do you know where to aim?

Jim

Jal
11-14-2007, 07:01 PM
<blockquote><font class="small">Quote jondrums:</font><hr>Actually your logic is fairly flawed. If you roughly know the aim line within a degree or two, you can then use my (or other) systems and determine the aiming line to within a fraction of a degree. That's the whole idea of systems like this! Its like progressive approximation - you use a close estimate and some other information to refine your estimate.<hr /></blockquote>Can you tell us more about this?

<blockquote><font class="small">Quote jondrums:</font><hr>... In addition I would like to add: I find it very interesting to work out and discuss the math/geometry/physics behind pocket billiards. This forum is perhaps the only place around where I could possibly find like minded souls to throw ideas around.<hr /></blockquote>Unfortunately, I'm one of them. /ccboard/images/graemlins/smile.gif I hope nothing said here on the forum will discourage you from presenting your ideas. As far as I'm concerned, and I'm sure this is true of a few others, they will be welcomed.

Jim

jondrums
11-14-2007, 08:44 PM
Jal-
I punched out a few quick calcs to illustrate my point. What I did was calculate how much error there is in the system's resultant aiming line when the user uses an approximate aim line to input into the system.

So if you approximate the aiming line with 5 degrees of error (entire width of a ball at 24"), the system's answer on the resultant aiming line will be off by something between .5 and .75 degrees! (depending on cut angle)

CUT ANGLE (deg): 15 30 45
AIM LINE APPROXIMATION ERROR (deg): 5 5 5
RESULTANT AIM LINE ERROR (deg): .734 .669 .558
(above is supposed to be a table)

The resultant aim line error is fairly linear based on approximation error (for small angles of error). So that means if you can approximate the aiming line to within 1-2 degrees, you'll end up with an aiming line around .1-.3 deg. That's about a quarter of an inch at 9 feet.

You could theoretically start with just about any aiming line, and within 3 steps or so, converge on an aiming line to within a very tight tolerance. (I don't recommend this!)

Does this make more sense?
Jon

Jal
11-15-2007, 01:29 AM
Thanks for doing the calcs.

But I reread your first post along with the linked to math page, and I can't find how you're generating successive approximations. Are you assuming that the true cut angle is 14.5, 30.0 or 48.6 degrees (or pretty close to one of these) and then correcting your aim until the measurements jive?

I also reread DeadCrab's thread farther down on the main forum's page to refresh myself as to how he determines his aim line, given some cut angle. It doesn't appear that he uses a series of approximations (but I didn't read the whole thread).

Jim

11-15-2007, 11:44 AM
******
Yes, sort of. But there's the matter of the sine calculation (or recalling it from a memorized table) and then some visualization (ie, where is the aim line for a .67 ball hit?)
*******

Nope. It has to do with some convenient properties between the hypotenuse and "opposite" side of the right triangle formed by the cut line and the CB-OB line. By aligning your cue along the cutline, and the tip close to the OB, the joint of the stick will be about 30" from OB center, and the butt of the stick about 60".

The length of the perpendicular line from the joint line of the stick to the CB-OB line (in inches) will be half of the cut angle (in degrees). From the butt end of the stick to the CB-OB line, the distance of the short side of the triangle formed will equal the cut angle in degrees. I have a chalker with some hash marks at .5" intervals that I can use to measure, but I can usually judge the distance by visual inspection for the narrow angles, and use known dimensions on my hand + wrist for the others.

Knowing the cut angle, line up on the CB-OB line. the aim point for cut angle= Z degrees, will be Z mm off of the center of the OB.

Example: a cut angle of 10 degrees has an aim point 10 mm off of the center of the OB

If a visual cue is needed, the tip of most cues will be 13 or 14 mm, a small paperclip is about 5mm wide, a large paperclip 10mm wide, a dime 18mm, a penny 20mm.

I'm not exactly sure what is meant by a .67 ball hit, but it sounds like a 9.43 degree cut, which would have an aim point 9.43mm off the center of the object ball.

If I had a digital video camera, I would make a demo, because this method is not difficult, even though it sounds that way.

Jal
11-15-2007, 06:57 PM
Yes, sort of. But there's the matter of the sine calculation (or recalling it from a memorized table) and then some visualization (ie, where is the aim line for a .67 ball hit?)
*******

Nope.<hr /></blockquote>I was refering to what you have to do once you have the cut angle figured, in order to translate that into an aim line. In the thread where you presented your method, you described identifying the target point with the help of a point on the edge of the OB below the target point. After doing some measurements, you developed a table for the height of this edge point at different target point displacements from centerball. But this involves a trig function implicitly, namely:

h = R(1 - Sqrt[1 - (2sin(A))^2])

where R is the ball's radius, and A is the cut angle.

Yes, you can avoid the calculation or the table by aiming x number of millimeters off-center (another neat observation by you), but I thought the whole point of your system was to provide a tangible target?

<blockquote><font class="small">Quote DeadCrab:</font><hr>It has to do with some convenient properties between the hypotenuse and "opposite" side of the right triangle formed by the cut line and the CB-OB line. By aligning your cue along the cutline, and the tip close to the OB, the joint of the stick will be about 30" from OB center, and the butt of the stick about 60".

The length of the perpendicular line from the joint line of the stick to the CB-OB line (in inches) will be half of the cut angle (in degrees). From the butt end of the stick to the CB-OB line, the distance of the short side of the triangle formed will equal the cut angle in degrees. I have a chalker with some hash marks at .5" intervals that I can use to measure, but I can usually judge the distance by visual inspection for the narrow angles, and use known dimensions on my hand + wrist for the others.<hr /></blockquote>Somebody should market billiard shirts with scales along the sleeves.

<blockquote><font class="small">Quote DeadCrab:</font><hr>Knowing the cut angle, line up on the CB-OB line. the aim point for cut angle= Z degrees, will be Z mm off of the center of the OB.

Example: a cut angle of 10 degrees has an aim point 10 mm off of the center of the OB

If a visual cue is needed, the tip of most cues will be 13 or 14 mm, a small paperclip is about 5mm wide, a large paperclip 10mm wide, a dime 18mm, a penny 20mm.<hr /></blockquote>You've gotten rid of the trig (or memorized table), but at a cost. I don't doubt that you could get pretty good at estimating so many millimeters, but I have serious doubts that this would be as accurate as noting the original aim line which was used to figure the cut angle in the first place.

<blockquote><font class="small">Quote DeadCrab:</font><hr>I'm not exactly sure what is meant by a .67 ball hit, but it sounds like a 9.43 degree cut, which would have an aim point 9.43mm off the center of the object ball.<hr /></blockquote>I was just wondering what to do after you've measured the cut angle and (perhaps) determined the ball fraction. This was before I looked at your method again, which uses the OB edge height to find the target.

Since the accuracy of the cut angle measurement depends on the accuracy of the aim line estimate, which in turn depends on the accuracy of the tip placement at the center of the ghostball, locating the center of the ghostball is crucial. I'll concede that positioning oneself over the object ball, rather than looking from the normal shooting position, should yield more accuracy here. Jondrum's and your systems exploit this through the intermediary of a cut angle determination. I think there's a better, more direct way, but each to his own.

Jim

jondrums
11-16-2007, 04:10 PM
[ QUOTE ]
Since the accuracy of the cut angle measurement depends on the accuracy of the aim line estimate, which in turn depends on the accuracy of the tip placement at the center of the ghostball, locating the center of the ghostball is crucial. <hr /></blockquote>

Actually I was trying to make the point that in both my and DeadCrab's systems, the accuracy of the tip placement at the center of the ghostball IS NOT CRUCIAL. In fact, the whole idea is that even with a few degrees of error in this placement, you can end up with an aiming line which has very little error - approximately 10 times less than the ghostball approximation error.

In fact, for shots where the cueball is 24" or more away from the objectball, you could use a centerball hit as the approximate aim line, and calculate an aiming line that still pockets the ball on a moderately tight table!
Jon

av84fun
12-01-2007, 09:26 PM
I hope nothing said here on the forum will discourage you from presenting your ideas. As far as I'm concerned, and I'm sure this is true of a few others, they will be welcomed.

Maybe on THIS forum but not necessarily so on certain others as you have witnessed! (-:

My point in posting here is that I see a lot of math/geometry being discussed here and that is certainly an appropriate baseline for all studies of aiming methods.

HOWEVER...As I pointed out on the other forum, the notion that shots go because they are geometrically correct and cannot go if they are not is an utterly flawed thesis.

In Jack Koehler's landmark book The Science of Pocket Billiards, he points out that collision induced throw will cause up to a FOUR DEGREE variation from the geometric path of travel even with clean balls and up to an ELEVEN DEGREE error depending on such factors as powder, palm prints, chalk marks etc.

For the same reason (collision-induced throw) Robert Byrne in his legendary Standard Book of Pool and Billiards, advises that some shots must be shot thinner than raw geometry would suggest.

All I am saying is that when assessing aiming systems, while math skills are a GREAT place to start, one should be awfully careful of being too dogmatic about it.

Regards,
Jim

Jim <hr /></blockquote>