Patrick Johnson said:
It appears to me that your diagram shows the "adjusted aim" offset being more in the same way as if you simply moved the stick sideways more without adjusting the aim. Why wouldn't that produce greater spin/speed?
pj
chgo
The black arrow emanating from the center of the cueball (labeled
v) is the direction you want the cueball to go. The blue arrow at the bottom represents the direction of the stick for a perfect compensation, given the anticipated squirt angle gamma (the small "y" ...don't mean to be insulting, you probably know more Greek than I do.)
Since the cueball is driven in the direction indicated by
v, that's the overall direction of the force applied at the contact point, despite the direction of the cue. It's the direction of the force, not the aim line of the cue that determines the effective offset. So it's as if you initially lined up in the direction of
v (with offset b'), then made the squirt adjustment by pivoting about the contact point and ending up in the blue arrow's direction. You now have a greater apparent offset (b), but the same working offset b'. In your particular case, b' is (1/2)R, although the diagram was not drawn with this offset in mind.
The torque, b' x F, puts the spin on the ball. (F is not shown, but as just mentioned, it points in the same direction as
v, and extends from the contact point.)
Is the rebound angle shown in your diagram a fairly accurate representation of the actual angle, say within a degree or two? I suspect it is, but ask anyway because I want to see how well a simple friction model of the cushion does in predicting it.
Jim