It has been stated that some people think that I am unconsciously compensating as these shots should not, theoretically, be made. This is possible but I do not think it is true. I have now made well over 200 shots using this method and various arrangements of balls with the contact point defined as indicated above. I have attempted to pay particular attention to not compensating.
Dr. Joe,
With the OB positioned around center table or thereabouts, you can only hope to make shots at cut angles of roughly 3-4 degrees or less by aiming at the contact point, and actually propelling the center of the cueball in that direction. It all depends, of course, on the the amount of slop the pocket will allow, but you must be making some sort of adjustment on most of the shots in your diagram.
Let's say you need to drive the OB at some angle "P" with respect to the CB-OB line of centers, with a margin of error of +/- delta P. With an infinite separation between the CB and OB, aiming at the contact point will produce an error of about P/2 (the exact value, ignoring throw and compression effects, is sin(P')=(1/2)sin(P), where P' is the actual angle in which the OB is driven, as compared to the desired angle P). As CB-OB separation distance is reduced, this relation is still a fairly good approximation until they're about a foot apart, at which point P' begins to drop off much more rapidly. (It depends on the value of P).
At best then, aiming at the contact point drives the OB at 1/2 the angle needed with respect to the CB-OB line of centers direction. Thus, you can only expect to make shots where the margin of error is roughly equal to 1/2 P. With the OB around center table, for instance, the margin of error is typically around 1-1/2 to 2 degrees. With a little bit of luck, you might be able to pocket balls with P as much as 3-4 degrees. At CB-OB distances of a foot or more, the cut angle is very close to P in value, so you're limited, accordingly, to cut angles of about 3-4 degrees, as mentioned earlier. Throw makes matters a little worse, but not much at these small angles.
Jim