Then use that number for how much to raise the spine
This exploits the fact that sin x = x when x is small and the angle is in radians, it is the 1 in 60 rule that carpenters use, which is based on the fact that 180 degrees is pi radians. The approximation works very well for low angles but you measure from the center of the spine not the distance from the hone to the spine. This is significant for thicker blades at low angles.
http://www.bladeforums.com/forums/showpost.php?p=4000084&postcount=6
Then why don’t you specificly answer the question?
I did, you just don't seem to be able to grasp the concept, it is actually the fundamental way in which equality is defined in physical measurements. You determine it from the inverse, you figure out the ability to discriminate and then work backwards. Everyone who does actual physical measurements knows this process in detail, a carpenter for example when makes something "square" doesn't mean it is perfectly square in an absolute sense, he means you could never tell that it wasn't perfectly square. How much of a difference is significant changes depending on what is being done and for who because there are different tolerances in each case. Thus for example there is a different tolerance for squaring a table than the actual walls of a house. The same would be true of convex bevels on a knife, the more discriminating a user the tighter the tolerance. It would also depend on what you were measuring specifically, the influence on cutting ability, sharpening, durability, etc. .
I was curious as to when you would bring up an old post. About a year or so Thom posted a thread about convex sharpening by hand on flat stones based on a discussion I was having with Alvin on rec.knives. Alvin has always been very critical of jig sharpening and argues that a convex bevel produced by hand is superior. However he is also clear to note that you have to actually intend to create a curvature by varying the bevel significantly intentionally and specifically critized people trying to hold a specific angle. On his knives, the shoulder to apex angle usually doubles, so there is a 100% difference in angle due to the curvature.
http://www.bladeforums.com/forums/showthread.php?t=371297
About that time I had also mentioned several times on the forum that sharpening by hand will pretty much induce a convex bevel due issues such as wear on the stone and variance in angle due to the user. The purpose of these posts was to make the point that the curvature wasn't relevant because in essense all edge primary grinds are convex to some extent but instead try to move the discussion to thick vs thin. Unfortunately this message got perverted by db who has chosen to repeat endlessly since then how he "convexes" edge by hand sharpening and completely ignores the origional intent and just adds to the misinformation on curvature vs cross section which was actually what I was trying to remove.
Yes, I also called a 1-2 increase significant. When I wrote the above I was just after regrinding the edges on a number of blades on a 200 grit silicon carbide stone and attempted to then refine the edges on a 600 DMT pad and ran into a problem because the DMT stone was of course attempting to apply a constant bevel so I had to either regrind to a flatter bevel or rock the blade and I was trying to do constrained edge angle comparisons for a model I was developing on cuttnig ability.
I also realized recently that those posts I made a year or so were not actually correct for reasons I noted in the above. If you argue some minute curvature is convex on hand sharpened bevels then this doesn't hold because there are signficant tangent intersect lengths on hand honed bevels as well (large flat spots) which means they are not convex by defination. Plus the whole notion just confused people as I got a lot of emails like "So I should not use the Sharpmaker and just freehand to produce stronger/sharper edges due to the convexing." No, the origional point was to forget about the curvature and just focus on the thickness/angle.
I also realized that based on some comments gud4u made awhile back I was looking at flat vs convex incorrectly. He noted that if you compared the edge formed by two flat bevels to most convex bevels they were not significantly different, he was speaking of cutting ability and durability. This was about the same time that Hob made mention of tangents in the above linked to thread started by EdgePal about how to quantify convex bevels. I had been looking at the difference in edge angle from shoulder to apex to define curvature but I realized you had to look at the difference to a flat bevel (or bevels) which would best approximate the performance. I noted specifically in the above how to do this and the difference it makes.
Yes db, if you look through old posts I make you will find they often don't agree with current statements I make, it is called learning.
-Cliff