So, during the course of me and Pointy's obsessive quest in the realm of sharpening, we hit a very distinct problem. When you sharpen a v-grind, determining the angle is a fairly simple process, especially if you have a sharpening system like a KME or other that shows what angles you are sharpening an edge at. So, how does one determine the angle of a convex edge?
We have a working theory that seems to have merit, so I figured I would post it up here. The difficulty in establishing the angle of a convex edge is that quite simply there is no one single answer, the edge is curved convexly and this means that something as simple as laying it on a KME won't quite work.
So how do we do it? For our working theory, we have to first ask what is accomplished by the edge angle? The edge angle of a knife is the angle at which the very apex will do what a bladed instrument is designed to do; cut. We sharpen the apex by removing material and refining the face such that the edge apex is in fact "sharp". We do this with a convex edge by dragging the edge away on a somewhat yielding material such as leather.
And here's the answer; what happens when you go the other way? That simple question was the single item that changed our entire outlook on developing a method of determining the angle of a convex edge. What angle does the edge begin to cut into material? The angle where the edge begins to dig into the material. On a convex edge you can find this by slowly rotating the knife until the point at which it just begins to cut on something flat. Once you hit that angle, you have thus determined the angle of your edge (in theory at least).
See, the only part of the edge that matters is the very, very edge, and that is the part that really determines what the angle could be, so if you rotate your knife on the convex portion whilst cutting it towards the material, when it catches, that is your angle.
If you knife has flats, you can use an angle finder to see just what that angle is, (angle finder shown below) as the flats will be parallel to the centerline that you are using to determine your actual angle.
Got mine at Lowe's this morning. So far, the theory seems to work. Thought I might toss this out there and see if any like-minded individuals might be willing to undertake the same experiment to independently verify our results.