Hi all,

I've got a goniometer that aids in determining the angle at which a knife has been sharpened. It works quite well for knives with a flat grind, as for example my Swamprat Ratmandu:



The edge has got an angle of about 20 degrees per side.

It also works quite well for thin knives with a convex grind, However, I cannot interpret the results the goniometer gives for a thick knife with a convex grind, my Fallkniven A1:



Can you help me interpret what my goniometer tries to tell me?

Thanks!

Hi Mark
I have had similar problems with the goniometer...I believe that the problem lies in the fact that the meter requires a flat facet to reflect the laser so it points to the correct reading. In a fully convexed blade, as the edge approaches zero the job for the meter becomes more and more difficult until a point is reached near zero when the laser reflects not only from the actual edge but even more from the steel at the base of the edge.Big sprays of red laser light all over the dial.
The reading I see there is very unclear but my best guess is between 4 and 6 degrees. You might try the following...turn the knife in the slot so it rests flat on one of the V sides...take a reading of the laser at its furthest reach...do the same with the knife lying flat on the other side of the V...if the readings are the same then you are at zero or approaching zero. If there is a difference e,g, one reading is 30 degrees and the other is 35 degrees then the angle is 5 degrees.
Having said all that I may be full of baloney. I will trust that those with more scientific minds than mine will see this just that or maybe not!!

Leo the nut case LOL!

leomitch wrote:

Thanks guys, for responding so quickly. (And for even calling Don )

I guess I’ll have to live with the fact that my knife is too thick for exact results with the goniometer. Depending on how I hold the knife exactly, the light pattern is quite different: just a tiny bit of a degree already makes a world of difference. And there must be some unevenness in the knife, because the patch of light on the right (around 15 degrees) is consistently larger than the patch of light on the left (around 9 degrees).

You are probably right that these large patches of light are just reflections from anywhere on the blade. I was puzzled for some time, thinking: “a convex edge varying from 10 degrees till 28 degrees, that cannot be right”. But now I come to think of it, the 28 degrees (in the photograph 22 and 31 degrees, but twice 28 when I slightly twist the knife) must be the dullest angle of the edge. And since it is convex, that must be the final angle of the edge of the blade. Does this make sense?

I also mailed Fallkniven with the question what the angle is of the final edge. They answer quite nicely every time. But the mail exchange is getting sillier and sillier. I ask them the angle and they respond with more and more detailed explanations on how to sharpen a convex edge . They are really worried I am going to end their beautiful convex edge with a guided sharpening system .

From the convex picture, it looks like the knife isn't exactly quite perpendicular, which would account for the wide reflection on the "right" side and almost nothing on the left.

Also, even if it is convexed, the edge of the edge should still split the beam, even if it spreads it out as in right side of the convex. The highest reading should be the edge angle, while the convexing of the bevel should produce the spread of lower angles. (Don't forget, while the edge may approach zero degrees, the actual edge angle increases on convex grinds).

I'd play with the knife position on the Falkniven a little more.

jendeindustries wrote:


I agree with Tom.

Thanks guys! You're right the knife position is not optimal. I did manage to get a somewhat optimal knife position (however, without a third hand, I didn't manage to photograph that) and then the light marks furthest from the knife are at about 28 degrees on each side. The large patch of light at the right remains there.

An acquaintance of mine also mailed Catra (makers of the goniometer) and got a response from them. Nice guys! (And of course their goniometer can do a large convex knife .) This is their response:



I don't understand everything they say (21 to 23° and 21 to 31° ?), but I am happy they conclude the final edge angle should be about 54° inclusive. That is almost the 28 degrees per edge I inferred.

It took me a while to respond, but finally I had time to figure out the real angle of the edge of the edge.

And boy, was I wrong. That Fallkniven A1 is sharpened a lot more acutely than you'd probably think for such a big knife. The true angle is... 13.5 degrees . However, if you consider them carefully, the goniometer readings do make sense.

Sharpening the A1 on the WEPS involved some challenges, too. But I conquered them and now this knife shaves arm hair again .

You can read the full story on my blog.

I haven't time just now to explain everything I want to. So here is a brief sketch of what I understand. Later on, if I have time, I'll make a more detailed post.

For now, let's pretend the knife is a perfect wedge, meaning a perfect V-edge without any convexing or hollow-grind (it isn't, but let's understand this case first):

If you remember:
(1) Your ray-optics from high-school
(2) Your 2d plane geometry from high-school
Then you can work out that the angle subtended by the two reflected beams are twice the total included angle of the knife. Later if I have time, I'll make another post to show the mathematical proof; it's fairly straightforward.

If you don't remember (1) and (2), Prof. John Verhoeven works out the math for you in the Appendix of his tech report on knife sharpening (he talks about building a laser goniometer for knife edges based on a laser pointer):
www.mse.iastate.edu/fileadmin/www.mse.ia...even/KnifeShExps.pdf

Here is one extreme examples that should make sense to everyone: If your knife has an included angle of 90 degrees (super blunt!) then the two reflected beams will be 180 degrees apart. Notice that 2*90 = 180. It turns out this formula works in general: 2*(inclusive angle of the knife edge) = angle between the two reflected beams. This will be true so long as the laser reflects off of both sides. If you turn the knife so far that one side of the bevel is in the shadow of the laser, then this is no longer true.

The most interesting part of this result, is that the angle between the two reflected beams is unaffected by small twists in the knife's orientation. By twist, I mean a rotation through a line along longest axis of the knife.

There are some complications both from fine-scratches in the knife edge, as well as curved surfaces such as convexing or a hollow-grind. In the simple analysis sketched above, we ignore these additional complications. However, we may have to deal with them in practice. I'm still in the process of playing around to gain more practical experience with this. But for now, the math is pretty clear to me.

Currently, I'm very busy working out extremely detailed mathematics of guided sharpening systems and knife geometry. I also hope to build my own laser goniometer for measuring knife angles. This is a ton of stuff. Part of it is actually just doing all that, but it seems that explaining all of that in a good way might be a huge amount of work as well. I hope to have stuff for you guys in the coming week or two.

Sincerely,
--Lagrangian

Hi Anthony,

Great to have someone knowledgeable in this area as well!

Theory does not only work nice in theory, but also in practice, for the goniometer.

If you have a knife with a flat bevel on top of a blade with sides of 0 degrees, it is quite easy to read the results. See the picture of my Ratmandu in my first post.

One thing that complicates the use of the goniometer is that it usually shows multiple patches of light: usually two per side. This may be due to the fact that the laser isn't a perfect point laser. The patch at the lowest angle is usually, I think, due to some laser light creeping past the edge (so not being reflected by the edge) and hitting one of the sides of the blade, which then reflects it. You can see this in the picture of the Ratmandu from 4-17 degrees.

A second thing that complicates the use of the goniometer is that the light reflected from the edge usually does not end up in one point (or line), but makes a patch. This may be due to the fact that the edge isn't a perfect flat surface, but contains scratches. In the picture of the Ratmandu, the reflected light is between 17 and 23 degrees. It is quite a step to conclude from that that the angle per side is 20 degrees.

And, as the remainder of the posts are about, if the blade does not have 0 degree sides and a flat edge, the reflection patterns can be much more complicated. In case of the Ratmandu, which not only has a convex edge, but an entirely convex blade, it was the patch of light at the lowest angle that represented the angle at the edge of the edge.



This is true and this is why the 13.5 degrees per side makes sense for the A1 (included angle 27 degrees). However, the exact patterns of multiple patches vary wildly even with small rotation twists.