gonna try to find a way to show this better
You are kind of half way there to what I found to be true. 30 degrees plus the correction created by your new perspective indeed continues to pocket the ball long after it seems it wouldn't. The comparatively short distances and the working width of pockets are part of the reason the systems work better than I would expect them to. Possibly because we are working with straight lines and a curved surface the automatic correction is not 100% accurate and the closer you get to the outer ranges of the angles that can be pocketed with one aim point the further to the edge of the pocket each ball will hit.
If we look at it mathematically with center pocket being a single infinitely small point then only one positioning of the two balls with a precise half ball hit allows us to perfectly hit the center point of that pocket with the center point of the object ball. However a much wider range will still appear to hit center pocket and a wider range yet continues to pocket balls.
Hu
You are kind of half way there to what I found to be true. 30 degrees plus the correction created by your new perspective indeed continues to pocket the ball long after it seems it wouldn't. The comparatively short distances and the working width of pockets are part of the reason the systems work better than I would expect them to. Possibly because we are working with straight lines and a curved surface the automatic correction is not 100% accurate and the closer you get to the outer ranges of the angles that can be pocketed with one aim point the further to the edge of the pocket each ball will hit.
If we look at it mathematically with center pocket being a single infinitely small point then only one positioning of the two balls with a precise half ball hit allows us to perfectly hit the center point of that pocket with the center point of the object ball. However a much wider range will still appear to hit center pocket and a wider range yet continues to pocket balls.
Hu
PKM said:If you haven't used this before, you can play around with the cuetable cut angle calculator:
http://cuetable.com/project/CueTableCutAngleCal.html
I just chose those angles because they're about the farthest from either side that you might use a SAM 3, if a 3 is approximately a 30 deg cut.
Think of it this way: forget about the pocket for a second. If you shoot a half-ball hit, it will do a 30 deg cut everytime, right? Of course the contact point is changing if you move the cue ball, but how could a half ball hit continue to hit the correct contact point for the center of a given pocket? As the cuetable shows, it would no longer be a half-ball hit once you move the CB from a 30 deg angle.