I'll post it when I get home, TB. By the way, even the shot-string over water demonstration is the opposite of what it appears to be. That is, it shows pattern diameter, not shot string.
Think of it this way. Imagine you had the longest shot string possible, every pellet lined up behind every other one, from the place where the first one hits the water all the way back to the gun. What does that shot-string look like on the water? Answer: It doesn't look like a shot string at all; it is just one hole in the water the diameter of the shot.
Now imagine the contrasting case, all the shot in a 30-inch-diameter disk of 0.090 thickness. What does that look like as it enters the water at a very low angle?
Neil