trig & sharpening

[hardheart]

using this applet, http://www.carbidedepot.com/formulas-trigright.asp , I stuck some numbers in just to give me something to think about with angles and blade thickness. Thinking in millimeters and microns is best, imo, since it's simply 1000 micron = 1 mm, so thinking in terms of either relief or microbevel is easy.

for a height of 1 unit, width is roughly (degrees per side)

0.246 at 7[SIZE=-1]°
0.353 at 10[/SIZE][SIZE=-1]°
0.425 at 12[/SIZE][SIZE=-1]°[/SIZE]
0.536 at 1[SIZE=-1]5°
0.611 at 17[/SIZE][SIZE=-1]°
0.728 at 20[/SIZE][SIZE=-1]°
[/SIZE][SIZE=-1]0.933 at 25[/SIZE][SIZE=-1]°
1.155 at 30[/SIZE][SIZE=-1]°

[/SIZE][SIZE=-1]I think these are pretty common angles mentioned here, or used in sharpening systems. For me, having something to look at in this regard helps me consider the actual implication of changing sharpening angles. It's obvious that higher angles mean thicker edges, but to see the numbers sometimes makes things a bit more clear.

*waits for someone to ask about convex edges*


[/SIZE]

 

[HoB]

Well, yes and no. The numbers are of course correct, but it is really misleading in some respects because it applies to a material of infinite width, which is not the case for a knife. In a knife you usually have TWO intersecting angles. So depending on the intersecting angle (the blade angle and blade width) you can have a fairly thin edge at fairly thick edge angles, because your "one unit height" is never reached (unless you adjust your one unit hight dependent on shoulder width which is not very illustrative. This is why you really need both measurements: thickness behind the edge AND edge angle.

If this wasn't clear, drawing it out should hopefully explain what I mean.

 

[sputnick]

I picked up a digi caliper for just that reason (well, they wouldnt let me take any home from college either). It was tough to make real observations about an edge and its performance when you can't describe it.

"Uh, I sharpened it with a narrower edge than factory and it slices better" is less useful than "I decreased the edge angle from 35 degrees to 22 degrees and effort required to slice 1/2" hemp rope was decreased by half."

As for the description of the curvature in a convex edge, I would get as many data points on the curve as possible and plot a graph. The average of ten separate collections would likely yield a reasonable representation. I'm glad i dont have any convex edges, as this doesn't sound like much fun.

I don't calculate half angles at the edge because I cant actually measure where the centerline between the two right triangles would be so i calculate for a scalene triangle for the edge. For the primary grind though i calculate for a trapezoid and then extrapolate for a triangle to give what the angles of the primary grind would be if they actually met at a point.

I think this is more or less what HoB was trying to say too, but I might not be picking up what he is putting out.

 

[hardheart]

I guess I understand. But, if I sharpen at 15 degrees, 1mm above the edge the blade should be no more than 0.536mm, 100 microns above the edge would be 53.6 microns wide, thinner if the stock used is thinner (that's pretty thin ) The top of the bevel naturally can't be wider than the blade stock.

 

[db]

I have to say I just hold my knife at around 10 degrees or so and sharpen away on it. If I find it chips or rolls too easily I’ll raise it up the next time I sharpen it. I’ll also relief grind if I think it’s still a little too thick behind the edge. I use to be concerned with angles and measuring but I don’t really care about it anymore.

 

[HoB]

I guess I understand. But, if I sharpen at 15 degrees, 1mm above the edge the blade should be no more than 0.536mm,

Correct, but it could be in principle a whole lot less, if at 1 mm above the edge you are already on the blade grind.

 

[Cliff Stamp]

As for the description of the curvature in a convex edge, I would get as many data points on the curve as possible and plot a graph. The average of ten separate collections would likely yield a reasonable representation. I'm glad i dont have any convex edges, as this doesn't sound like much fun.

You generally only need two, anything more than that is actually beyond the precision significance anyway.

-Cliff

 

[sputnick]

By any means available to me at home, any more than 2 or 3 measurements is very much beyond precision. I'll have to actually try it of course, but i would expect several seperate collections could be compiled to achieve a reasonable representation. In practice I've only done this on parabolic reflectors which are much larger the a knife edge.

 

[Cliff Stamp]

With knives, even 2-3 points is enough on an edge that further measurements cause changes in < a degree. The edge will never be that static anyway.

-Cliff