Handplane Challenge: Does Skewing the Plane Lower the Cutting Angle?

Almost everyone skews the handplane when planing a board. This makes it easier to obtain good shavings. One reason (among a few) is that it lowers the cutting angle and the low angle is better for slicing the fibers (more cutting, less scraping). It is difficult visualize this effect and so I have make some wooden models to make it easier to understand. Enjoy.
Reference: for those who like geometry, here is a good reference. investigations...