Whenever the subject of "x angles" aiming systems comes up (and when doesn't it?), a predictable bone of contention is exactly how many angles are necessary to make all possible shots, taking into account the "margin of error" provided by pockets being bigger than balls. I don't think it's ever been answered in those terms, and it's easy to do, so here's the answer in a nutshell:
For a wide range of pocket widths (4.5 to 5.5 inches), an aiming system needs only 6-8 cut angles in each direction to make all balls within 1 foot of pockets.
So far, so good, but that number multiplies quickly as shots get longer.
To make all balls within 3 feet of pockets, 18-24 cut angles in each direction are needed. And for all balls within 5 feet of pockets, 30-40 cut angles in each direction.
The systems we hear about all have 10 cut angles or less, which means 2/3 of 3-foot shots and 4/5 of 5-foot shots can only be made with some kind of adjustment from the system.
I'm not making a point, just passing along the information for future reference because I happened to be thinking about it. The math for this is simple - anybody's welcome to it.
pj
chgo
For a wide range of pocket widths (4.5 to 5.5 inches), an aiming system needs only 6-8 cut angles in each direction to make all balls within 1 foot of pockets.
So far, so good, but that number multiplies quickly as shots get longer.
To make all balls within 3 feet of pockets, 18-24 cut angles in each direction are needed. And for all balls within 5 feet of pockets, 30-40 cut angles in each direction.
The systems we hear about all have 10 cut angles or less, which means 2/3 of 3-foot shots and 4/5 of 5-foot shots can only be made with some kind of adjustment from the system.
I'm not making a point, just passing along the information for future reference because I happened to be thinking about it. The math for this is simple - anybody's welcome to it.
pj
chgo
Last edited: