I’m not sure I follow. I’d have just measured the spine thickness t at the place of hone wear, and the width b from edge to spine hone wear and computed the bevel angle as α= 2 arc sin(b/(2w)), just as the central angle of an isosceles triangle . Is the sharpening angle β = α/2? in that case, I agree that β ≈ sin(β), certainly at the precision I’ll have measuring t, and b.
Yes, that’s the sharpening angle. The bevel is formed by laying the razor on the stone at the spine and edge. The razor is sharpened by removing material (abrading) until the centerline from the spine through the edge intersects with the stone’s surface. For a razor, that angle is typically less than ten degrees and within the small angle approximation range. If I have my phone handy, I just use the calculator. Much more convenient than a slide rule :)
Already there, except I think in terms of sharpening angle and save the multiplication step. Since you have a penchant for maths, you’ll be soon to follow :)
I’m not sure I follow. I’d have just measured the spine thickness t at the place of hone wear, and the width b from edge to spine hone wear and computed the bevel angle as α= 2 arc sin(b/(2w)), just as the central angle of an isosceles triangle . Is the sharpening angle β = α/2? in that case, I agree that β ≈ sin(β), certainly at the precision I’ll have measuring t, and b.
Yes, that’s the sharpening angle. The bevel is formed by laying the razor on the stone at the spine and edge. The razor is sharpened by removing material (abrading) until the centerline from the spine through the edge intersects with the stone’s surface. For a razor, that angle is typically less than ten degrees and within the small angle approximation range. If I have my phone handy, I just use the calculator. Much more convenient than a slide rule :)
For the approximation to become useful, we just need to start thinking of bevel angles in units of radians now 😄
Already there, except I think in terms of sharpening angle and save the multiplication step. Since you have a penchant for maths, you’ll be soon to follow :)