Thank you for the response but I just don’t understand how a straight edge when tilted will maintain the same angle. It is on a completely different plane. I do partially understand what you mean about the radius though and how there’s going to be a "sweet spot" although it would still have some sort of slight variation unless you got it completely perfect.
Hi Larry, this is definitely a brain teaser. Different visual aids work better for different people, so maybe this one will help. I find it easier to visualize on a Wicked Edge type of system for whatever reason.
Think of the line of the blade’s edge that you’re grinding a bevel on as just "a line on a plane."
In the drawing I have a plane (in green). Maybe think of this as a piece of thin, inflexible plexiglass (or metal or whatever) but where you have it mounted to the pivot point of the sharpening rod (the red dot) so it’s co-planar with the sharpening rod.
Lay that plane across the blade edge (first with the blade edge horizontal). The blade is shown in orange.
The dotted red lines represent the different angles you could pivot the sharpening rod at, and these are all lines on the green plane. I also have a profile view of this setup.
The WE sharpening stones go on the rods, and the face of each sharpening stone lays flat on the plane no matter which side-to-side angle the rod is at (because the sharpening stones can rotate on the rods). As you scrub the sharpening stones up and down to abrade the edge, they stay in constant contact with the plane. Since the plane is fixed at the same angle everywhere, so too are the faces of the stones.
Now tilt the blade in the vise so it’s no longer horizontal:
Note that the line of contact between the plane and the blade edge is still just a line on the plane. But the spherical pivot joint allows the plane to still conform to the blade's edge no matter what the tile angle is. So, while the angle of the plane itself may change slightly between the 2 drawings, it is fixed at a constant angle in both individual cases.
If you set your sharpening angle to the same in both cases (using an angle cube, not the relative angle markings on the WE angle bar scale) with the sharpening stone at the centerline of the vise, the constant sharpening angle will also be the same in both cases.
Does this help?