Ooh, I like this!
Quote: However, if the angle ψ is less than 90°, then the component of FR parallel to the plane of the ski, will point outward (towards the left), and the ski will slip outward (out of the "trench").
I hadn't thought of that in those terms, but that's the angulation that's so critical to hard carving. ψ greater than 90 degrees makes the trench deeper, which supports more force. I love it when math further explains something we "know" from real-world experience!
/nerdout