How to measure edge angle on convex knives

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Hunterarrow

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Edge angles on zero grind flat, chisel and saber grinds are easy to measure. It's simple trigonometry.
But how do you measure the edge angle on convex edge or edges with secondary bevels?
I ask this question because I want to change the way I grind the bevel. I like to have a specific target angle (w/o using a jig) instead of going by the feel and what worked before. Thanks.
 
It is also simple trigonometry. The convex edge is the juncture of two arcs, just as the flat grind edge is the juncture of two planes. If the arc was high (small diameter circle), it would make the edge blunt, but since the arc of most convex grinds is in the low number of degrees of arc ( very large diameter circle), just take a thickness measurement at a standard distance from the edge, say .500", and use those two numbers to calculate the edge angle. You will find it is almost the same as if you did the long involved calculation of the junction angle of the two arcs. Thus the edge angle is nearly identical for a flat or convex grind, of the same height as the measured arc.

The difference is that the convex grind will have more meat immediately behind the edge, and will thus take more punishment without rolling or chipping. The flat grind will slice better.
 
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This interest me; how do you go about grinding a specific target angle without the use of some measuring device or "jig"? The human hand finds it hard to distinguish between a 4 and a 3 1/2 degree bevel grind; how do you go about it?

Fred

I have a solution, but it involves a "jig" or device.
 
Thanks bladsmth. I used your method with my BRKT Fox River and got 13.7degrees edge angle. If I measure all the way up from the spine I get a different number, 8.5degrees. I also took measurement at 0.25" from the edge and got 13.7degrees. Does the number seem good? There is no secondary bevel on Fox River.
Fred, I'm thinking about grinding the cutting edge first. Say if I want to make a 20degree convex edge on a 0.156" stock, I put a flat bevel from the edge spine up to 0.88". Then convex/blend the primary bevel from there. Just an idea.
 
Yes. that sounds right. I added some words to the post to make it clearer..... "of the same height as the measured arc." If you measure to the spine, the angle will be incorrect, because the bevel is not an even arc all the way to the spine. The measurements at .500" and .250" are good points for calculation.

Now on your plan to grind a 20° edge and then fair it into the bevels until it is a zero grind convex is a good way to keep the edge centered, and a good way to get a very well regulated edge angle. However, it will not leave a 20° edge angle, as you have removed the planes that formed the 20° angle. Draw it out on a sheet of paper in 10:1 scale. Start with drawing on the 20° angle. Then sketch in the convex grinds. You will see that the edge is more acute than the original angle. This is as it should be.

When doing togi, the final edge angle is rarely pre-set, as the blade's geometry will determine the final angle. I start with a roughly shaped bevel, and smoothly curve it down to the edge. If the blade will be a sword, and needs a strong edge, the curve is fat. If the blade is a slicer, and needs a fine edge, the curve is nearly flat. The final edge is usually given a few final strokes on the stones to make it straight and set a micro-bevel at the desired edge angle.

If you do the same with your knife project, you will get the desired edge. Just make the bevels in the convex shape you desire and take to an edge. This will probably be a really sharp edge, but if examined at magnification, you will observe a rambling edge. It needs a tiny secondary to straighten and stiffen it. This is not the same as the large secondary on most flat grinds. If you want the angle at an EXACT number, use a jig or fixture. However, since the secondary angle is there on a convex grind just to stiffen and straighten the edge. Using a well calibrated eye and a good fine grit stone will work well. Calculate this angle as if the blade was a FFG. Use the blade centerline and the stone surface to determine approximately how high above the stone the spine should be to get your target edge....say 20°.
 
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