Does super sharp mean less durable???

hardheart said:
The confusion over geometry and sharpness seems to be thinking that they are separate. Sharpness measurements are done of cutting force required, which is affected by geometry, and the tests reflect this.

The closest I can think that this discussion has been revolving around is the level of refinement at the meeting of the two edge bevels. This is also a question of geometry, as what is measured is the radius of the curve joining the two sides. As this is less than a micron for highly refined edges, this has little to do with cutting. That is why geometry is such a critical component of sharpness, the blade needs to penetrate the media to some depth, and I think that we have always needed that depth to be greater than a millionth of a meter. The real challenges in measuring sharpness are the differences in elastic ranges and fracture mechanics of the various materials we cut.

Check up on ISO 8442.5 and related discussions for measuring sharpness in knives, scalpels, needles, etc. There are several papers on sharpness tests outside of CATRA REST/REDS, such as non-destructive tests in gel and fiberglass test media.
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Personally I consider sharpness to mean the degree of refinement of the meeting of the two sides of the blade, while the general term geometry is used to describe everything behind the point making initial contact with the cutting medium. So sharpness is an extension of geometry in the same way that a square is a rectangle. The edge is the face that experiences the most significant degree of wear during cutting, and is the aspect of geometry that we, as users, maintain. So it is part of the geometry of the blade, yes, but it's also a little more distinct than that. It represents a specific and localized aspect of the blade geometry.
 
i am not an expert.... my knowledge is limited to what i've read here and what i've done with my own knives.. that said, IMHO, the best compromise is a razor sharp convexed edge.

you get more durability than you get from a similarly sharp flat grind, and it massively improves the chopping abilities of larger blades.

Just my $.02
 
I suppose another way to define edge sharpness would be the degree of refinement of the two bevels which are intended to meet, since a dull edge represents an interruption of the meeting of those bevels. Like I mentioned before it's analogous to a pyramid vs. one missing its top. The one with a point represents a fine degree of sharpness, with the bevels all meeting or very nearly so. The topless pyramid represents a dull edge, with the planes halting before they reach the point of intersection due to the horizontal plane that they connect with instead. Does that make sense? :confused:
 
BePrepared said:
i am not an expert.... my knowledge is limited to what i've read here and what i've done with my own knives.. that said, IMHO, the best compromise is a razor sharp convexed edge.

you get more durability than you get from a similarly sharp flat grind, and it massively improves the chopping abilities of larger blades.

Just my $.02
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How do you get more durabilty and what do you mean by "similarly sharp"?
 
The thing is, sharpness is a measure of work done, depth of cut versus force applied.

I know what you are talking about though, I tried to look at sharpness this way for a while. It's just that the term 'sharpness' doesn't actually apply to that when measured and discussed by either regular folks or scientists measuring peak and mean moments of cutting force.

In either case, the pyramid is always going to have a flat top, it just depends on how closely you have to look at it to see that the two faces cannot meet at zero width since there's a whole mess of atoms taking up space at the point. So yes, that measure is all about how small you can make the distance between the two planes.

... there really isn't any reason to think a convex edge similarly sharp (same final edge angle) to a flat grind will be more durable. With the same final edge angle the convex grind has less steel in the blade. but measuring the final edge angle is not something that can be eyeballed.
 
hardheart said:
... there really isn't any reason to think a convex edge similarly sharp (same final edge angle) to a flat grind will be more durable. With the same final edge angle the convex grind has less steel in the blade. but measuring the final edge angle is not something that can be eyeballed.
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Exactly!!! And for some reason people will not accept that. But it's blatantly obvious when you look at a simple picture...

flatgrind.jpg


If this is an over-exaggerated cross section of a flat-ground knife with a flat-ground edge bevel (B), the convex edge with the same edge angle would have to be thinner (and less durable) than the v grind edge. And if the convex has more steel...then it has a more obtuse edge angle.

There's nothing mysterious or confusing about it. Simple geometry. Geometry matters.

And I happen to like a full flat grind with a convexed edge (which most "convex" knives are).
 
effectively the same angle for a hand tool after sharpening by hand? it's pretty easy.

geometry is important, but tenths of degrees difference probably isn't setting the world on fire.
 
Brian Sargent said:
I'm dumb.

Can someone explain to me how a convex plane and a flat plane can have the same final angle?
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This is all purely geometric (by that I mean has little to do with reality)...but a convexed edge is formed by two intersecting curves. Let say they intersect at point A. Each of those two curves will have a tangent at point A. Those two tangent lines meet at an angle. There's your angle. Make a flat ground edhe with the same angle, and you have a flat ground edge and a convex ground edge with the "same" final edge angle.

Again, geometry isn't reality. Reality is just an approximation of this stuff.
 
So if the very edge is point A.

.... and the Junction between the primary and secondary bevels is point B.

Wouldn't a convexed curve between A & B have more material than a flat plane?

Of course it could be so slight as to equal almost nothing.
 
Nope.

Here's what is going on

convex2.jpg


The red lines are the two curves that form the convex angle (they are parts of parabolas). The blue lines are the tangents to each of those curves at the point where the curves meet.

A flat ground edge having the same angle will be the blue lines. More steel behind the edge of the flat one.

It's simple geometry no matter what certain convexed-edge knife manufacturers assert.
 
That diagram looks as if the secondary bevels are not the same.

What if you had a two blades that are .125" thick and 1.25" tall that are flat ground to the exact same angle.

If the point where the primary and secondary bevels meet is point B and the very edge is point A.

If there is a curve ... instead of a dead straight line ... isn't there more material ?
 
Here's the picture I made that from, if you are into that kinda thing

6a00e55375ef1c88330153914f330f970b-500wi.jpg


Simplest parabola.

It's a nice pic by the way, since we can really exaggerate. Look at the horizontal center of the graph (x = 0). The tangent to parabola at 0 is a horizontal line. So a parabola is an excellent representation of a convexed edge with a 180 edge angle inclusive. Imagine a v ground edge with an edge angle of 180 degrees inclusive.

That would be "unground." Much thicker than the 180 degree inclusive convex edge.

I know I'm "getting into the nerd weeds" by throwing "tangents" and "parabolas" around, but it's all kinda clear when one looks at a picture.

If a convex edge and a flat ground edge have the same edge angle, the flat ground edge has more steel behind the edge.
 
Brian Sargent said:
If there is a curve ... instead of a dead straight line ... isn't there more material ?
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No. Only if the curves meet at a wider angle do they have more steel.

Draw two "vees" that have the same angle. "Fit" a convex edge into one of the vees. You have to stay inside the vee, or else you are drawing something with a larger edge angle.
 
Marc, your math is over my head.

So, I guess in my head I'm definitely thinking of a wider angle.

My learning never got to the point of measuring angles in curves.

This is where my head is.

IMG_8098.jpg


IMG_8097.jpg
 
hardheart said:
The thing is, sharpness is a measure of work done, depth of cut versus force applied.

I know what you are talking about though, I tried to look at sharpness this way for a while. It's just that the term 'sharpness' doesn't actually apply to that when measured and discussed by either regular folks or scientists measuring peak and mean moments of cutting force.

In either case, the pyramid is always going to have a flat top, it just depends on how closely you have to look at it to see that the two faces cannot meet at zero width since there's a whole mess of atoms taking up space at the point. So yes, that measure is all about how small you can make the distance between the two planes.

... there really isn't any reason to think a convex edge similarly sharp (same final edge angle) to a flat grind will be more durable. With the same final edge angle the convex grind has less steel in the blade. but measuring the final edge angle is not something that can be eyeballed.
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Ok--we're on the same page here, as usual, just using different definitions. I like to think of sharpness as a measure of the surface area per unit of length making initial contact with the cutting medium. So yes, while at a level viewable with an electron microscope there is still surface area to a fine edge, it is significantly less so than that of a knife that has just had its edge dragged across concrete. The increase of surface area contact caused by such deformation results in greater necessary force to make a cut. So essentially I think of sharpness as inverse to the degree to which your applied force is spread out per unit of length during initial material contact.
 
Doesn't sharpness just mean the thickness of the apex of the two planes of the edge? Everything else is geometry, If I'm not mistaken. Cutting performance is a result of a combination of these two plus maybe edge finish(coarseness).
 
singularity35 said:
Doesn't sharpness just mean the thickness of the apex of the two planes of the edge? Everything else is geometry, If I'm not mistaken. Cutting performance is a result of a combination of these two plus maybe edge finish(coarseness).
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There we go--you said it better than I could. My words are running away from me tonight. :p
 
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