400 % more edge holding - convex vs flat

[Obsessed with Edges]

I'm with Josh's comments above, in that fundamentally, it all comes down to 'thinner cuts better', regardless of which shape it happens to be. And there are also some circumstances where removing or easing the hard, crisp shoulders of a V-bevel, by convexing, makes a big difference in cutting ease in tougher materials like heavy cardboard or wood. Going beyond that, polishing a convex makes things even more slick, to a scary degree at times. My favorite edge for heavy cardboard is either a polished, shallow convex (for thicker blades), or an extremely thin hollow grind for thinner blades, on which the edge profile (V or convex) really doesn't matter much anyway; it's all about being thin, in that profile.

I don't worry too much (or at all, truthfully) about whether one lasts longer than another, based only on the shape (V or convex) of the edge. Most of the durability issues are due to thinness of geometry, heat-treated hardness and steel type (which plays into how hard it can be made in the first place, depending on carbon content). I've never believed in making an edge thicker just to protect it's fundamental shape from deformation, especially if doing so means it won't cut very well to begin with. I've become spoiled on thinner edge geometries, even if it means I need to tune it up a little more often (and thinner makes that job easier too).

 

[FortyTwoBlades]

As others have stated above, there is a lot going on here. The basic principle is that 'thinner cuts better'. So the goal for every knife and knife maker should be - "go as thin as possible while still holding up for the hardest use this blade will see".

I was just stating above that low angles cut better, whether it's convex or V it doesn't matter. What Mike is pointing out in the video is that, for wood processing if you go with too low of an angle then the edge will not be supported enough and will deform or chip (depending on the steel). So he is saying that a flat grind of the same height will actually be thinner behind the edge and cut better, but he doesn't believe it has the support to process wood (and he would be right with certain steels at certain heat treats at certain hardnesses - lol). To determine the best geometry for a specific task, Cliff Stamp has an amazing video on how to do this and it's spot on (see below)

flat vs. convex geometry... Theoretically convex should cut better because it doesn't have any shoulders right? The only problem with this is that, while it doesn't have any shoulders it generally has much more meat behind the edge (as Mike is pointing out in the video). Why does it have more metal?

I've been grinding knives for several years now. I have 3 main methods of doing convex, depending on how deep I want to go (i.e. how much curvature). If I want it really obtuse (a LOT of curve and metal behind the edge) then I will use a slack belt. For medium curve I will use a soft platen, and for a shallow convex grind (almost imperceptible) I use a rubber belt as a backing that spins underneath my abrasive belt. If I scribe a line mid way up the blade that I will grind to, the convex (in all three situations) will have more metal behind the edge than the flat grind to the same point. If you want a lower angle convex grind, then you will need to raise the grind height up towards the spine and then, yes, you can make it probably cut better than a flat grind - but not a flat grind at the same geometry.

What I have found that works REALLY well is a full flat grind with a convex edge blended into the flat grind (i.e. remove the shoulders w/ out all the metal in the primary grind). There are other benefits that wood workers can appreciate to a full height convex grind, but I believe that the primary one is probably that it is more beefy and won't penetrate as deep (when chopping) thus, not getting stuck.

Sorry for being so long winded lol

I would personally caution against using visual bevel width as the fixed value. Really it's the effective edge angle that must be held as fixed. That does mean that the visual bevel width will be wider on a convex of equal edge angle to a flat ground edge, but this is necessary for comparing flat vs. convex if what we're discussing is both cutting ability and strength. At equal edge angle a convex is thinner at the shoulder than a flat grind, but is (in most cases) equally strong at the edge itself. It's sort of like a mini relief/primary grind right behind the edge. When visual bevel width is held fixed all you're proving is that a thicker edge angle is stronger when resisting plastic deformation, and a flat ground edge of equal edge angle would have even more resilience to torquing than the convex would. Visual bevel width is an artifact of imposing certain geometries onto the blade stock, and so changing the variables of that geometry can end up changing the visual effect of the bevel. A similar conundrum comes up with axes when people talk about "banana grinds" where the bevel looks way wider in the middle of the bit and narrower at the heel and toe. Conventional descriptions cite this as the edge being a thinner angle in the middle and thicker at the heel and toe for durability, and this would certainly be true on flat-cheeked axes. However, a uniform edge angle applied to the bit of an axe with a high centerline (a lenticular or lens-shaped cross section) would also have a bevel that looked like that, despite being the same angle at all points of the edge.

 

[REK Knives]

I would personally caution against using visual bevel width as the fixed value. Really it's the effective edge angle that must be held as fixed. That does mean that the visual bevel width will be wider on a convex of equal edge angle to a flat ground edge, but this is necessary for comparing flat vs. convex if what we're discussing is both cutting ability and strength. At equal edge angle a convex is thinner at the shoulder than a flat grind, but is (in most cases) equally strong at the edge itself. It's sort of like a mini relief/primary grind right behind the edge. When visual bevel width is held fixed all you're proving is that a thicker edge angle is stronger when resisting plastic deformation, and a flat ground edge of equal edge angle would have even more resilience to torquing than the convex would. Visual bevel width is an artifact of imposing certain geometries onto the blade stock, and so changing the variables of that geometry can end up changing the visual effect of the bevel. A similar conundrum comes up with axes when people talk about "banana grinds" where the bevel looks way wider in the middle of the bit and narrower at the heel and toe. Conventional descriptions cite this as the edge being a thinner angle in the middle and thicker at the heel and toe for durability, and this would certainly be true on flat-cheeked axes. However, a uniform edge angle applied to the bit of an axe with a high centerline (a lenticular or lens-shaped cross section) would also have a bevel that looked like that, despite being the same angle at all points of the edge.

I'm not sure I understand what you mean by visual bevel width? could you explain more? I didn't use that term personally so I am not sure why you think I was using that as a fixed value...

 

[FortyTwoBlades]

How wide the bevel appears to be. It will not have more metal if edge angle is held consistent. The convex will only have more metal behind the edge if the visual bevel width (the "height" of the bevel) is kept as the fixed variable, and in such a situation, the edge angle will inherently be thicker on the convex because a flat grind is taking the shortest possible path between the two points (edge and edge shoulder.)

I was just stating above that low angles cut better, whether it's convex or V it doesn't matter. What Mike is pointing out in the video is that, for wood processing if you go with too low of an angle then the edge will not be supported enough and will deform or chip (depending on the steel). So he is saying that a flat grind of the same height will actually be thinner behind the edge and cut better, but he doesn't believe it has the support to process wood (and he would be right with certain steels at certain heat treats at certain hardnesses - lol). To determine the best geometry for a specific task, Cliff Stamp has an amazing video on how to do this and it's spot on (see below)

flat vs. convex geometry... Theoretically convex should cut better because it doesn't have any shoulders right? The only problem with this is that, while it doesn't have any shoulders it generally has much more meat behind the edge (as Mike is pointing out in the video). Why does it have more metal?

[...]

If I scribe a line mid way up the blade that I will grind to, the convex (in all three situations) will have more metal behind the edge than the flat grind to the same point. If you want a lower angle convex grind, then you will need to raise the grind height up towards the spine and then, yes, you can make it probably cut better than a flat grind - but not a flat grind at the same geometry.

 

[Twindog]

FortyTwoBlades The problem with saying "at equal edge angle" when comparing V edges and convex edges is that the convex edge has no "edge angle." V edges and convex edges cannot be compared that way. A convex edge can be thought of as an edge with an infinite number of angles, each different from the other. The convex edge is a curve. Curves do not have angles. A V edge has just one angle.

You can see this played out with a laser protractor. It will show a sweep of angles, with each point on the edge having a different measured angle than the points on either side of it.

If the edge height is consistent, a V edge will be more acute and a convex edge will have more metal behind the edge. If you vary the edge heights, you can get any result you want.

It's also important to remember that a V edge can be functionally identical to a convex edge -- or wildly different.

Josh's explanation of how he can vary the backing of his belt can make a big difference is spot on.

 

[FortyTwoBlades]

FortyTwoBlades The problem with saying "at equal edge angle" when comparing V edges and convex edges is that the convex edge has no "edge angle." V edges and convex edges cannot be compared that way. A convex edge can be thought of as an edge with an infinite number of angles, each different from the other. The convex edge is a curve. Curves do not have angles. A V edge has just one angle.

You can see this played out with a laser protractor. It will show a sweep of angles, with each point on the edge having a different measured angle than the points on either side of it.

If the edge height is consistent, a V edge will be more acute and a convex edge will have more metal behind the edge. If you vary the edge heights, you can get any result you want.

It's also important to remember that a V edge can be functionally identical to a convex edge -- or wildly different.

Josh's explanation of how he can vary the backing of his belt can make a big difference is spot on.

Except you can measure the angles of the intersection of two arcs. It's done using the tangent of the radius at the given point (the apex, in this case.) On a practical level, the effective edge angle can be found with any cutting tool by choosing a given cutting medium with a relatively flat, firm surface, laying the blade flat on it, and (using very light pressure) lift the spine until the edge actually contacts and is just barely able to bite the target material. The edge angle is just a smidgen lower than that, as it's when the apex is riding parallel with the flat surface.

 

[Twindog]

Except you can measure the angles of the intersection of two arcs. It's done using the tangent of the radius at the given point (the apex, in this case.) On a practical level, the effective edge angle can be found with any cutting tool by choosing a given cutting medium with a relatively flat, firm surface, laying the blade flat on it, and (using very light pressure) lift the spine until the edge actually contacts and is just barely able to bite the target material. The edge angle is just a smidgen lower than that, as it's when the apex is riding parallel with the flat surface.

The tangents of an arc are straight lines. You can measure angles of two intersecting straight lines. You cannot measure the angle of two curved lines. Tangents share only one point with the arc. To say the arc is the same as the tangent is obviously incorrect. One is a straight line and one is a curved line. They are not the same.

To compare a V edge to a convex edge, the edges have to have the same edge height and you have to know the radius of the arc of the convex edge.

The only practical way to compare a V edge to a convex edge is to overlay the profiles of each edge. The differences will then be apparent.

 

[FortyTwoBlades]

Factually incorrect. The angle of intersection can be measured. And, as mentioned, an easy way of determining the angle for all practical consideration is to see at what angle the edge starts biting. The following images show two identical quarter-circles, given a 15° rotation each time. A very small radius is used to simplify the visuals. Convexes on actual knives are usually a compound curve rather than a uniform arc, and the closest uniform arc to it would have a VERY large radius. If you want a fairly precise approximation of the apex angle other than using the edge-biting method, you can use a digital protractor and see at what point the apex touches the bottom of the angle.

180° edge angle (dead flat):

150° edge angle:

120° edge angle:

90° edge angle:

 

[Twindog]

The mathematical definition of an angle is the separation, usually measured in degrees, of two intersecting lines.
A line in math is straight.

Your method of approximating the angularity of a convex edge is clever, but flawed.

How fast the apex bites depends on the keenness of the apex (sharper bites faster), coarseness of the edge, the material you're pressing the apex into (softer bites faster than hard -- rubber vs. glass) and the pressure you're using (harder bites faster).

Your test will produce wildly different results than someone else whose edge is less keen, who uses a harder surface and who uses less pressure. For your system to be useful to anyone other than you, you'd have to standardize all the variables. You have standardized none of them. You method has many confounding variables.

 

[FortyTwoBlades]

The mathematical definition of an angle is the separation, usually measured in degrees, of two intersecting lines.
A line in math is straight.

Your method of approximating the angularity of a convex edge is clever, but flawed.

How fast the apex bites depends on the keenness of the apex (sharper bites faster), coarseness of the edge, the material you're pressing the apex into (softer bites faster than hard -- rubber vs. glass) and the pressure you're using (harder bites faster).

Your test will produce wildly different results than someone else whose edge is less keen, who uses a harder surface and who uses less pressure. For your system to be useful to anyone other than you, you'd have to standardize all the variables. You have standardized none of them. You method has many confounding variables.

Again, the angle of intersection of two arcs is taken from the tangent to the point of intersection. There is actual established math for this. For that purpose. If you choose to deny that this is the way of doing things, that's on you. But it's a very real thing with no mystery behind it.

And my practical test of increasing the presentation angle of the blade until it bites into a hard flat surface is just that: practical. Is it 100% accurate? No. But it gives you a reasonable approximation of the angle on that side. Using something like wood or a hard plastic like acrylic (plexiglass) and light pressure will minimize deflection that would give you an artificially low angle. Because some deflection will occur even on fairly hard surfaces, the angle at which biting occurs can be used as the actual effective angle. That is to say, it is the angle at which the edge becomes effective; starts doing its job. Light pressure on a hard surface minimizes the interfering factors enough for it to be a reasonable approximation of the edge angle. One could even say that all edge angles are essentially nominal rather than actual. The same goes for things like blade length measurements--depending on how you choose to measure it, you may have something like ±1/8" on the length, but it's still useful for comparing against a knife that has a blade length >1" of difference. The granularity of the data matters, and for most purposes, getting in the ballpark is close enough. You would simply be testing both blades on the same target medium, with as close to equal pressure as you can (LIGHT) and any significant difference will be made visible. You could even use something relatively standardized like a sheet of copy paper on top of that hard flat surface for finding that initial bite point.

And, again, you can just use a digital protractor to get a very close reading on the edge angle at the apex. The edge itself won't touch the bottom corner of the V until you're at the edge angle. This is on a macro scale, of course. On a micro scale all edges are rounded completely over.

 

[Twindog]

Well, we're repeating ourselves. But a tangent is a straight line. The two intersecting tangents of a convex edge are straight lines and so do have an angle. But the convex edge is not a straight line, and that convex edge is far more acute than the angle of the tangents.

I emailed the maker of the laser protractor I use, and my position was confirmed. When you measure a V edge, the laser beam is reflected at an exact angle -- a near pinpoint of light at the given angle mark. If your V edge isn't perfect, the light beam will illuminate a wider area, reflecting the imperfection of the edge.

In other words, a V edge has a specific angle. A convex edge has an infinite number of differing angles.

With a convex edge, you get either a crescent shaped line (ground edges) or a straight line (for polished edges). Those lines will cover a range of angles, from acute near the shoulders to less acute near the apex. The angles represent straight lines because the light moves in a straight line and it deflects off the edge in a straight line. The angle is the straight line from the laser emitter to a point on the edge and then a second straight line from the edge to the measuring grid.

The convex edge is not an angle, but a whole series of angles that can be measured only at one point. Each point on the convex edge has a different angle.

Nothing in math says you can measure the angle of a convex edge, only the tangents (straight lines) of those edges, and those tangents are not anywhere close to the actual convex edge.

 

[ScottsBad]

He is just making a case for convex. And I understand that, because it is superior for most uses if it is the appropriate convex for the application. I put convex edges on most of my fixed blade knives even if they had some type of "V". I leave folders in a "V" just because I can put them on a flat stone and boom their done. I don't bother to strop them.

This is from an end user perspective. JMHO

 

[FortyTwoBlades]

Well, we're repeating ourselves. But a tangent is a straight line. The two intersecting tangents of a convex edge are straight lines and so do have an angle. But the convex edge is not a straight line, and that convex edge is far more acute than the angle of the tangents.

I emailed the maker of the laser protractor I use, and my position was confirmed. When you measure a V edge, the laser beam is reflected at an exact angle -- a near pinpoint of light at the given angle mark. If your V edge isn't perfect, the light beam will illuminate a wider area, reflecting the imperfection of the edge.

In other words, a V edge has a specific angle. A convex edge has an infinite number of differing angles.

With a convex edge, you get either a crescent shaped line (ground edges) or a straight line (for polished edges). Those lines will cover a range of angles, from acute near the shoulders to less acute near the apex. The angles represent straight lines because the light moves in a straight line and it deflects off the edge in a straight line. The angle is the straight line from the laser emitter to a point on the edge and then a second straight line from the edge to the measuring grid.

The convex edge is not an angle, but a whole series of angles that can be measured only at one point. Each point on the convex edge has a different angle.

Nothing in math says you can measure the angle of a convex edge, only the tangents (straight lines) of those edges, and those tangents are not anywhere close to the actual convex edge.

Except you're very confused about what the tangents represent. A tangent to a point on an arc is a line passing through that one point only meaning that any deviation from that line's trajectory through that point would cause it to intersect two points on the arc. That is to say, the tangent represents the straight-line-equivalent of the trajectory of the arc at that precise point.

Imagine you have a flat material that a knife is hard enough to readily cut, but (unlike in reality) it will not flex or deflect under pressure in any way--it remains perfectly flat regardless of the downward pressure on it. A knife sharpened with a 15° per side flat-ground edge laid with the bevel flat on the stone (running parallel to the surface) will not cut, but the instant it is tilted even the tiniest bit above that angle, the edge is suddenly able to engage the material, and a cut is initiated. Until the apex contacts the surface, the knife is not cutting. The same applies with a convex edge. Only at any angle greater than the edge angle will allow the apex to bite into the target. Call it something else if you want -- maybe the "minimum engagement angle" for a given material. But the fact remains that until that apex touches the target material, a cut will not be initiated. When deflection occurs, the material is buckling under pressure in such a way that it is presenting itself to the apex at an angle greater than the edge angle.

And you keep talking about a laser protractor. The laser protractor won't work on a convex for the reason you mention, but that's because of the fashion in which you're trying to measure it. Use a physical digital protractor. It's trivial to do.

 

[Twindog]

Every convex edge has an infinite number of tangents. Which are you using? Are you averaging them all? How do you do that?

I did contact the engineers who make edge-measuring laser protractors as a profession. They agree with me. They say you are wrong. This is what they do for a living.

Laser protractors are just as useful for V edges as convex edges. They show you exactly what the edge profile is. In the case of a convex edge, they show you the full range of the edge's angularity.

You could look up the definition of angles and lines and see where you have gone astray.

Your seat-of-the-pants way to measure the angularity of a convex edge doesn't work unless you control for the many confounding variables. For example, a keen edge will grab a surface more easily than a dull edge, giving you different "angles," even though the edge angle hasn't changed.

We've had this argument before. You never change your mind. I never change mine.

The reason that this is important is that so many people on this forum have been mislead by myths that a convex edge is superior to a V edge. It ain't so. Either one can be better than the other for any specific use, depending on the underlying geometry. They can be virtually identical.

 

[Dangerously]

There’s always the same nonsense in these threads.

At least no one here is seriously arguing that there is a 400% edge retention increase with convex edges. That’s a testable claim, and, to my knowledge, no one has ever offered a test that showed it to be remotely true.

I like convex edges, but their reputation has suffered as fallout from from a particular manufacturer’s hucksterism.

 

[FortyTwoBlades]

Every convex edge has an infinite number of tangents. Which are you using? Are you averaging them all? How do you do that?

I did contact the engineers who make edge-measuring laser protractors as a profession. They agree with me. They say you are wrong. This is what they do for a living.

Laser protractors are just as useful for V edges as convex edges. They show you exactly what the edge profile is. In the case of a convex edge, they show you the full range of the edge's angularity.

You could look up the definition of angles and lines and see where you have gone astray.

Your seat-of-the-pants way to measure the angularity of a convex edge doesn't work unless you control for the many confounding variables. For example, a keen edge will grab a surface more easily than a dull edge, giving you different "angles," even though the edge angle hasn't changed.

We've had this argument before. You never change your mind. I never change mine.

The reason that this is important is that so many people on this forum have been mislead by myths that a convex edge is superior to a V edge. It ain't so. Either one can be better than the other for any specific use, depending on the underlying geometry. They can be virtually identical.

There's a number of strawman arguments in the above that seem to deliberately misrepresent my position, and at this point I feel as though I've said everything I need to on the subject for other members who are interested in it to get a firm grasp of the concepts. I'm very sorry that you've been unable to wrap your head around this, but it's really not at all complicated. For testing purposes one must obviously presume that a sharp blade is being used rather than a dull one, and as I've said before, it's for rough approximation purposes only. Use a physical digital protractor if you want a more accurate reading and it'll readily give you a precise reading. It's painfully simple.

I'll be bowing out now.

 

[REK Knives]

How wide the bevel appears to be. It will not have more metal if edge angle is held consistent. The convex will only have more metal behind the edge if the visual bevel width (the "height" of the bevel) is kept as the fixed variable, and in such a situation, the edge angle will inherently be thicker on the convex because a flat grind is taking the shortest possible path between the two points (edge and edge shoulder.)

Thanks for the clarification. But I wasn't referring to how wide the bevels appear to be, I was referring to the same specific grind height on two different blades. This isn't just visual, it is measurable. If I have a 1" wide blade (from edge to spine) and put a full height zero grind on it, one convex and the other flat, the convex grind will have more metal on the blade and will hinder cutting performance. In some cases (e.g. if additional strength is needed) then it is a good thing. In other situations it is not. But I think we are saying the same thing here, as your last line in the above quote indicates

That does mean that the visual bevel width will be wider on a convex of equal edge angle to a flat ground edge, but this is necessary for comparing flat vs. convex if what we're discussing is both cutting ability and strength.

yes I understand what you and twindog are discussing, you are using 'edge angle' to refer to the angle at the very apex. so if the apex angle is the same on a convex and flat grind, yes the convex grind would need to be wider (i.e. higher, closer to the spine).

I think part of the issue for me, is that I'm coming at it from a different perspective than most. I truly do understand both sides of the argument and see where they are coming from.

But this is my issue w/ convex grinds, often times when I'm regrinding knives I can't simply raise the grind height because maker's logos are on the flats. So the issue comes in that my customer can either choose flat, convex (or hollow of course) but without being able to raise the grind height the convex won't cut as well.

At equal edge angle a convex is thinner at the shoulder than a flat grind, but is (in most cases) equally strong at the edge itself.

I used to make this argument myself actually until I started grinding a lot of knives. Because to make it 'thinner than a flat grind' and remove the shoulders, you will almost always have to do a decently shallow, full height, zero convex grind (that's a mouthful!!). It isn't feasible on a lot of knife styles and blades, esp. ones that are already made and being worked on. If you are making a knife from scratch then sure, set it up however.

In my experience, as soon as you try to convex the primary and secondary grinds and blend them together, your abrasives medium will walk up into the blade flats and scratch it up (on a deep/obtuse convex anyway, which most convex knives I've seen have, and most seem to prefer for visual appeal I think). you could do a shallow convex saber grind, which will be a decent performer but it would be a toss up between doing a zero flat grind and putting a microbevel on it.

Here is one I made from scratch that had a double, shallow convex saber grind. I zero ground it before the DLC, and then added a secondary (slightly larger than a microbevel) after.

Here's a Busse TGLB I reground - full height convex grind. If I had done a full flat grind then there is no comparison which one would cut better - I thin you would agree on this correct?

 

[FortyTwoBlades]

Well, I said I was bowing out, but since you quoted me I suppose I'll respond regardless.

Thanks for the clarification. But I wasn't referring to how wide the bevels appear to be, I was referring to the same specific grind height on two different blades. This isn't just visual, it is measurable. If I have a 1" wide blade (from edge to spine) and put a full height zero grind on it, one convex and the other flat, the convex grind will have more metal on the blade and will hinder cutting performance. In some cases (e.g. if additional strength is needed) then it is a good thing. In other situations it is not. But I think we are saying the same thing here, as your last line in the above quote indicates

By visual I mean that the bevel is being judged by how wide it looks on the given stock rather than by its specific geometry being imposed on the stock and the bevel width being determined by the combination of that geometry and the thickness of the stock. A 1/4" wide grind on 1/8" stock will be a lot thinner than a 1/4" wide grind on 1/4" thick stock. This is especially an issue when dealing with distal tapered blades. Condor's golok, for instance, is 1/4" thick with a strong distal taper, and while I'm not sure quite how they do it, they grind their blades in such a way that they are a consistent width rather than consistent angle. This makes the edge angle near the tip properly thin, but the edge at the base of the blade is literally like a cold chisel. Absurdly thick and won't cut anything worth damn. When I regrind them to a consistent edge angle, the width of the bevel is greater at the base of the blade and reduces towards the tip due to the reduction in thickness from the distal taper.

yes I understand what you and twindog are discussing, you are using 'edge angle' to refer to the angle at the very apex. so if the apex angle is the same on a convex and flat grind, yes the convex grind would need to be wider (i.e. higher, closer to the spine).

I think part of the issue for me, is that I'm coming at it from a different perspective than most. I truly do understand both sides of the argument and see where they are coming from.

But this is my issue w/ convex grinds, often times when I'm regrinding knives I can't simply raise the grind height because maker's logos are on the flats. So the issue comes in that my customer can either choose flat, convex (or hollow of course) but without being able to raise the grind height the convex won't cut as well.

Since we're talking about edges you have room to raise the bevel height on all but zero grinds. When dealing with non-zero grinds, doing primary bevel regrinds, that's a different story. Sometimes you have constraints on the location of the plunge line due to things like the aforementioned makers' marks, but in such cases you're still changing the thickness at the shoulder (essentially the "edge" of the primary grind) rather than keeping that thickness consistent.

I used to make this argument myself actually until I started grinding a lot of knives. Because to make it 'thinner than a flat grind' and remove the shoulders, you will almost always have to do a decently shallow, full height, zero convex grind (that's a mouthful!!). It isn't feasible on a lot of knife styles and blades, esp. ones that are already made and being worked on. If you are making a knife from scratch then sure, set it up however.

In my experience, as soon as you try to convex the primary and secondary grinds and blend them together, your abrasives medium will walk up into the blade flats and scratch it up (on a deep/obtuse convex anyway, which most convex knives I've seen have, and most seem to prefer for visual appeal I think). you could do a shallow convex saber grind, which will be a decent performer but it would be a toss up between doing a zero flat grind and putting a microbevel on it.

Except then what's making it stronger is still because it's a thicker edge angle. Again, we're talking about edges, not primary grinds. And you're talking about constraints set by the overall pre-existing geometry of a knife rather than designing from scratch. A lot of weird design decisions get made by companies, usually for aesthetic rather than functional reasons, that severely impair their knives cutting ability, and they can be difficult to "fix" with modifications if you're limited by logo placement. And you really don't have to do full height grinds for this sort of stuff. Just facet it in with one or more flat grinds behind the edge bevel and then blend them together. Also, a convex edge doesn't inherently have to blend seamlessly into the primary grind--when I convex edges there's still usually a distinct shoulder between the bevel and the primary grind, it's just a lot shallower than if I were using a flat-ground edge, and the shoulder is located further up on the blade.

Here is one I made from scratch that had a double, shallow convex saber grind. I zero ground it before the DLC, and then added a secondary (slightly larger than a microbevel) after.

Here's a Busse TGLB I reground - full height convex grind. If I had done a full flat grind then there is no comparison which one would cut better - I thin you would agree on this correct?

When spine thickness is held constant (and it usually is) then definitely a full flat zero will produce a thinner geometry than a full convex zero edge, but the edge angle will be different between the full flat zero grind and the full convex zero. The same full height convex could be "polygon-ized" into multiple flat bevels using tangents at points along the arc and produce a thicker overall geometry. If holding the edge angle constant, this means that it would be like laying hinged line segments over the curve of the convex rather than nesting within it (because doing that would reduce the edge angle.)

Long story short, if edge angle is held fixed, and bevel width allowed to shift, convex edges are thinner due to their reduced volume at what would have been the shoulder of the flat-ground edge, but the bevel width is increased. If edge angle is allowed to shift and bevel width kept the same instead, convexes are thicker, but edge angle is increased. When comparing edges, keeping angle fixed makes the most sense due to this established dynamic. If one were trying to design a knife using a particular aesthetic layout of the grind boundaries, or producing a zero-ground tool and keeping spine thickness fixed, keeping bevel width fixed and altering the grind type to adapt that visual look to the context of use would make the most sense.

This is actually a reason why so many small blades (pen blades and the like) on traditional folders have a hollow primary grind. Spine thickness plays a huge role in rigidity of the blade, and traditionals often are fairly thin stock with narrow blades due to their overall small proportion. If they want the blades to both be sufficiently rigid and have any chance of cutting reasonably well without being zero-grinds, a hollow makes the most functional sense. The wider a blade the lower the angle of a flat grind you can put on the knife without reducing the spine thickness and losing significant rigidity, but the harder that becomes to steer in a cut (although it tracks a straight line better) and the bigger it makes the overall blade. Tiny blades risk either becoming foil-like and flimsy or becoming too thick to cut well. The hollow primary grind addresses both of those concerns while keeping the edge bevel narrow and quick to sharpen thanks to the small contact surface.

 

[HeavyHanded]

From my POV, with the gear I have, I can make a convex with a known finish angle at the spine or primary if it has one, and a known edge angle at the apex. I cannot guarantee the shape of the arc - whether it is a consistent arc the entire face.

Forum member EdgePal (IIRC) showed off a magnetic widget for convexing axe bits that uses a curved rod, this will give you an exact stem to stern arc value.

I stand behind my observations (informal though they be) that a convex grind on any hard use chopper will wedge less and bite deeper than a flat sided bit with the same apex angle, distance from edge to poll or spine, and poll/spine width. To outperform it, a flat cheeked bit would have to be ground so thin it will bind, and/or the secondary edge angle will be too fragile.

On regular belt and pocket knives I don't think it will make a difference.

REK Knives I agree running the convex high has its challenges when you don't want to go all the way to the spine, but then again you can only thin a regular sabre grind so much before you hack into the plunge line and have to regrind the whole primary anyway.

 

[REK Knives]

Well, I said I was bowing out, but since you quoted me I suppose I'll respond regardless.

Thank you, I appreciate your response

By visual I mean that the bevel is being judged by how wide it looks on the given stock rather than by its specific geometry being imposed on the stock and the bevel width being determined by the combination of that geometry and the thickness of the stock. A 1/4" wide grind on 1/8" stock will be a lot thinner than a 1/4" wide grind on 1/4" thick stock. This is especially an issue when dealing with distal tapered blades. Condor's golok, for instance, is 1/4" thick with a strong distal taper, and while I'm not sure quite how they do it, they grind their blades in such a way that they are a consistent width rather than consistent angle. This makes the edge angle near the tip properly thin, but the edge at the base of the blade is literally like a cold chisel. Absurdly thick and won't cut anything worth damn. When I regrind them to a consistent edge angle, the width of the bevel is greater at the base of the blade and reduces towards the tip due to the reduction in thickness from the distal taper.

I agree, I think we are on the same page just using different terminology. Yes the edge angle will be much more narrow/acute on a 1/4" high grind on 1/8" stock vs 1/4" stock.

Since we're talking about edges you have room to raise the bevel height on all but zero grinds. When dealing with non-zero grinds, doing primary bevel regrinds, that's a different story. Sometimes you have constraints on the location of the plunge line due to things like the aforementioned makers' marks, but in such cases you're still changing the thickness at the shoulder (essentially the "edge" of the primary grind) rather than keeping that thickness consistent.

This is the chart that I use to determine geometry when discussing grinds just so everyone can follow. I do primary regrinds a lot. So the problem is, if I were to regrind the knife on the right (saber grind) from a flat grind and convert it to a convex, I would have to do it with a very shallow convex (i.e. the belt tracking over the platen, hard backing) to prevent the grind from walking up higher on the blade flats. Even then, it still will. And if I were to do a convex grind w/ a soft backing, then to get the same 'edge angle' (apex angle) I would have to very significantly, probably full height, convex the grind.

Again, we're talking about edges, not primary grinds.

I'm not... I'm talking about either. As you indicate below, for the same edge angle a convex grind will necessarily need to be raised.

Also, a convex edge doesn't inherently have to blend seamlessly into the primary grind--when I convex edges there's still usually a distinct shoulder between the bevel and the primary grind, it's just a lot shallower than if I were using a flat-ground edge, and the shoulder is located further up on the blade.

When a customer asks for a recommendation on a pocket knife between a convex or flat ground edge (secondary grind) I always recommend flat. The reason being is because I set the edge to 15 dps or less. If I tried to make a convex edge apex at 15 dps then there is a high possibility that the convex edge will raise significantly up into the secondary grind, and even scratch it up. For this reason, I must set the convex at a wider angle which will not cut as well.

Long story short

, if edge angle is held fixed, and bevel width allowed to shift, convex edges are thinner due to their reduced volume at what would have been the shoulder of the flat-ground edge, but the bevel width is increased. If edge angle is allowed to shift and bevel width kept the same instead, convexes are thicker, but edge angle is increased.

I couldn't agree more The problem is that in reality, people don't sharpen at the same 'edge angle' imho.

I tried this once. I have a Wicked Edge and wanted a convexing set up. So I custom mounted a mouse pad to the paddles with sandpaper on top. I then used my angle cube to set the angles as I normally would (say 15 dps). You know what I found? I found that even though I was matching the stone to edge angle, the convexing action allowed the edge (secondary grind) to curve all the way around to where the very apex was around 22 dps. For me to have a 15 dps apex I would have to WAAAAY lower the angle, which causes other issues.