It is interesting applying mathematics to the trajectories of a double and under and over.

Another variable would be the increasing group size in the same propertion as a minute of angle ie if you get a 1 1/2 inch group at 60 metres theoretically you will get a 3 inch group at 120 metres, so the width of the barrels is not actually dupllicated at that distance instead the group size is straddling each other ???

With the U/O I guess he is saying as the lower barrel is crossing with a greater angle it will shoot higher for a while than the lower barrel until they trajectories cross again ???

For me and looking at them scientifically I have always associted doubles with mysticism, magic and full moons. It just happens! Especially if a "Guru" tells me it will.