Did a couple of calculations yesterday to figure out, how much more effort (meaning relatively how much more material) I would theoretically have to put in, in order to rebevel an edge that was sharpened at 22 deg. to 20, 15 or 12 deg. Practical example: I have a knife that was sharpened factory wise to 22 deg. and I have the choice of either taking it to 15 deg on the sharpmaker or to 20 deg.
In my calculation I assumed a straight blade behind the edge bevel, which is clearly not correct for a saber grind, but should be a pretty good approximation for a full flat or hollow ground blade. The problem is pretty basic trigonometry but I fund the result quite surprising. I further assumed that you sharpen to ideal accuteness, without turning a burr. Both turning a burr and a saber grind would greatly aggrevate the general outcome.
Turns out that you would have to remove about 4.5 times more material per side (!) to take an edge from 22 to 15 degrees than from 22 to 20 deg. and over 8 times more material per side to take it from 22 to 12 than from 22 to 20 deg.
Meaning, if you work already on the edge and are ready to go to the whites after 20 strokes (each side) on the greys on the 20 degree setting, it would take about 90 strokes to achieve the same on the 15 degree setting.
Thought that might be interesting to some that are "into sharpening". I personally was just wondering, why it took me so much longer to sharpen a knife to 12 deg in comparison to one that I sharpen to 15. Now I know, I have to remove about 80% more material, meaning, if I spend half an hour on the stone for 15 deg, I have to expect to spend a full hour on the stone for 12.
In my calculation I assumed a straight blade behind the edge bevel, which is clearly not correct for a saber grind, but should be a pretty good approximation for a full flat or hollow ground blade. The problem is pretty basic trigonometry but I fund the result quite surprising. I further assumed that you sharpen to ideal accuteness, without turning a burr. Both turning a burr and a saber grind would greatly aggrevate the general outcome.
Turns out that you would have to remove about 4.5 times more material per side (!) to take an edge from 22 to 15 degrees than from 22 to 20 deg. and over 8 times more material per side to take it from 22 to 12 than from 22 to 20 deg.
Meaning, if you work already on the edge and are ready to go to the whites after 20 strokes (each side) on the greys on the 20 degree setting, it would take about 90 strokes to achieve the same on the 15 degree setting.
Thought that might be interesting to some that are "into sharpening". I personally was just wondering, why it took me so much longer to sharpen a knife to 12 deg in comparison to one that I sharpen to 15. Now I know, I have to remove about 80% more material, meaning, if I spend half an hour on the stone for 15 deg, I have to expect to spend a full hour on the stone for 12.