I happened onto a couple of interesting things playing around with Wei's Aiming Table. I'm hoping that, with your help, a useful aiming system can be created from these discoveries.
First, check out the table below. I noticed that for any given cueball position and target pocket, a perfect arc can be plotted to show the placement of object balls that correspond to a specific aiming point, such as half ball or quarter ball. The first page shows a half ball hit(30 degrees) for every one of the 15 balls. The second page is a 3/4 ball hit (15 degrees). The third page is a 1/4 ball hit (49 degrees). The last page is an impossible 90 degree cut, but this arc may provide a reference point for a system. The arcs seem to start about one ball away from the cueball on all shots. And they peak midway between that starting point and the target pocket center. Since the cuetable and the aiming table are different in size, I couldn't place the balls perfectly, but they're close enough to the plots I made from the aiming table to illustrate my point.
If a person can visualize the arcs for each of the aiming points he or she chooses to use, the system can stop there. But I was looking for a simpler way to use this information. What I came up with was a triangle that's formed by the starting point of the arc, the center of the target pocket, and the peak of the arc. The peak of all arcs are found from the midpoint between 1 ball diameter away from the cueball and the center of the pocket. The 7-ball is nearest the center for all of the above diagrams.
Here are the same shots showing the trangle I'm referring to:
You can see that most balls don't fall directly on the triangle lines, but the triangle is fairly easy to find. When a ball falls close, either above or below a certain triangle, there may be some easy way to adjust your aim to account for the error of going from arcs to triangles. The biggest error occurs when the object ball is midway between either the arc starting point and peak, or the pocket center and peak.
A triangle can also be created by using the particular object ball you're shooting. Draw a line through the object ball from either the pocket center(when the object ball is closer to the pocket than it is to the cueball) or the arc starting point (when it is closer to the cueball than the pocket) until you reach the triangle's center peak. Like this:
The resulting triangle will correspond to a slightly more severe cut than is actually necessary to pocket the ball, so an adjustment has to be made, unless the object ball happens to fall exactly at the peak. But again, the triangle is fairly easy to find.
I've only shown one cueball and pocket position so far, but what's interesting is that no matter what distance the cueball is away from the pocket, the triangle peaks all line up to the same angles. Here's an illustration of a half ball hit (though it works for all shots) from different cueball distances from the target pocket. Again, they are eyeballed, but I did check this out on the aiming table. Going from the pocket center through the peak of each triangle, all lines point to the same spot on the far rail:
If all shots were along this particular cueball to pocket line it would be easy to locate the exact points on the rail that correspond to the different aiming points. But of course the entire fanlike spread of angles from 0 to 90 degrees moves with every pocket-to-cueball line. The width of this spread of angles doesn't change, but the 0 degree and 90 degree reference points do.
Here are 3 pages of what I mean:
One thing that I found is that to create a triangle when you have a shot that's near a rail, you can flip the shot like a mirror to create the triangle on the table rather than beyond it. On the following shot, I create a triangle on the table by flipping the 1-ball across the pocket-to-cueball line to create the 2-ball triangle on the second page. Then, on page 3, I create a reference 90 degree triangle with the 3-ball to compare to the triangle I created using the 2-ball:
This is as far as I've gotten. If you have anything to add that can help to make it a useful system, I'd love your input. One thing to keep in mind is that the diamonds aren't that reliable angle-wise, since they don't fall evenly around the table when measuring from a pocket. The angles from pocket to diamond get increasingly smaller the further you go from the 0 degree point out toward the 90 degree point.
Let me finish this post by again thanking Wei for creating the aiming table and the cuetable. I would have never found this stuff without it. Very cool tool.
Thanks
First, check out the table below. I noticed that for any given cueball position and target pocket, a perfect arc can be plotted to show the placement of object balls that correspond to a specific aiming point, such as half ball or quarter ball. The first page shows a half ball hit(30 degrees) for every one of the 15 balls. The second page is a 3/4 ball hit (15 degrees). The third page is a 1/4 ball hit (49 degrees). The last page is an impossible 90 degree cut, but this arc may provide a reference point for a system. The arcs seem to start about one ball away from the cueball on all shots. And they peak midway between that starting point and the target pocket center. Since the cuetable and the aiming table are different in size, I couldn't place the balls perfectly, but they're close enough to the plots I made from the aiming table to illustrate my point.
If a person can visualize the arcs for each of the aiming points he or she chooses to use, the system can stop there. But I was looking for a simpler way to use this information. What I came up with was a triangle that's formed by the starting point of the arc, the center of the target pocket, and the peak of the arc. The peak of all arcs are found from the midpoint between 1 ball diameter away from the cueball and the center of the pocket. The 7-ball is nearest the center for all of the above diagrams.
Here are the same shots showing the trangle I'm referring to:
You can see that most balls don't fall directly on the triangle lines, but the triangle is fairly easy to find. When a ball falls close, either above or below a certain triangle, there may be some easy way to adjust your aim to account for the error of going from arcs to triangles. The biggest error occurs when the object ball is midway between either the arc starting point and peak, or the pocket center and peak.
A triangle can also be created by using the particular object ball you're shooting. Draw a line through the object ball from either the pocket center(when the object ball is closer to the pocket than it is to the cueball) or the arc starting point (when it is closer to the cueball than the pocket) until you reach the triangle's center peak. Like this:
The resulting triangle will correspond to a slightly more severe cut than is actually necessary to pocket the ball, so an adjustment has to be made, unless the object ball happens to fall exactly at the peak. But again, the triangle is fairly easy to find.
I've only shown one cueball and pocket position so far, but what's interesting is that no matter what distance the cueball is away from the pocket, the triangle peaks all line up to the same angles. Here's an illustration of a half ball hit (though it works for all shots) from different cueball distances from the target pocket. Again, they are eyeballed, but I did check this out on the aiming table. Going from the pocket center through the peak of each triangle, all lines point to the same spot on the far rail:
If all shots were along this particular cueball to pocket line it would be easy to locate the exact points on the rail that correspond to the different aiming points. But of course the entire fanlike spread of angles from 0 to 90 degrees moves with every pocket-to-cueball line. The width of this spread of angles doesn't change, but the 0 degree and 90 degree reference points do.
Here are 3 pages of what I mean:
One thing that I found is that to create a triangle when you have a shot that's near a rail, you can flip the shot like a mirror to create the triangle on the table rather than beyond it. On the following shot, I create a triangle on the table by flipping the 1-ball across the pocket-to-cueball line to create the 2-ball triangle on the second page. Then, on page 3, I create a reference 90 degree triangle with the 3-ball to compare to the triangle I created using the 2-ball:
This is as far as I've gotten. If you have anything to add that can help to make it a useful system, I'd love your input. One thing to keep in mind is that the diamonds aren't that reliable angle-wise, since they don't fall evenly around the table when measuring from a pocket. The angles from pocket to diamond get increasingly smaller the further you go from the 0 degree point out toward the 90 degree point.
Let me finish this post by again thanking Wei for creating the aiming table and the cuetable. I would have never found this stuff without it. Very cool tool.
Thanks
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