Jim, I appreciate very much the offort you have put in your post. But to use it and understand it fully I need to know what units your numbers refer to. What I am looking for is variance in millimeter (distance) measurement of contact points for given distances. For example, if the cueball squirts .2 degrees, and you are aiming at the rail from 3 feet away, how many millimeters of error do you hit on the rail from your intented target? This information might verify what I have taught people all these years, that for each cue you play with, it is nice to find a speed that gives you a predictable amount of squirt so that aiming can be trusted with english. And if your speed is too low the tip won't grab the ball whereas if your speed is too fast the cueball may be pushed out of the way enough to cause a squirted, missed ball.
What are the units of the numbers you are giving me? Thanks so far....
Hunger, the units for every number (except the 3' CB-OB separation) are degrees. For example, if you need a three-quarter ball hit to bring the OB to exact center-pocket, but instead the cueball squirts 0.3 degrees off the exact line needed to accomplish this (i.e., your squirt compensation is off by 0.3 degrees), the OB's direction will be off by 4.72 degrees if the "excessive" squirt is to the outside, or -4.60 degrees if to the inside.
But to answer your question directly, 1 degree of error is equivalent to being 1" (25.4 mm) off line (to the side) after traveling 57.3 inches in the forward direction. So an error of 0.3 degrees over 3' of travel results in the CB being off line by:
d = (36"/57.3) x (0.3 deg/1 deg) = 0.19" or 4.8mm
You can do the same to figure how far the object ball will be off line after traversing some distance. In the first example, with a 4.72 degree error in direction, after the OB travels 2', it'll be off by:
d = (24"/57.3) x (4.72 deg/1 deg) = 2.0"
So if the pocket is 2' away, instead of hitting center-pocket, it'll be off to the side of center-pocket by 2.0". These numbers aren't exact, but very close for smallish angles (i.e., the method of calculating doesn't work very well when you get to angles of several tens of degrees).
To calculate the error in OB direction from some error in CB direction, as in my earlier post, requires a bit more math.
Hope that's what you're looking for.
Jim