Is All Hand Sharpening, Convex Sharpening? Murray Carter Says It Is

[HeavyHanded]

HH, Looking at your diagrams #3 & 4 this depiction and it's subsequent description, perhaps inadvertently express why one should use the least number of stones possible to obtain a sharp edge. Because the conclusion is 'the more strokes & stones one uses = more chances for the edge to become more convexed. One could easily gather in this discussion to stay as much away from stropping as possible. Utilizing the stone to remove the burr. DM

Is all just speculation, but it does explain a few things that seem to crop up consistently. I think the most important thing to remember is to always work from the shoulder out and not try to just set the bevel flat on the stone and grind away. This works well enough at the coarser grit levels, but as you climb to a finer polish it becomes more and more critical to have a plan, and that plan should involve deliberately working from the shoulder. This also falls in with my habit of undershooting the angle by a few degrees so when it opens up a tiny bit I'm still at (or under) my target angle.

Stropping is a science all is own, it factors heavily in my maintenance strategy but only on very hard surfaces so I can get some material removal as well as a finer finish.

 

[Twindog]

.... The whole point of the convex is to make a more acute angle with less friction going into a cut, not necessarily a tougher one unless its convexed right to the apex - something that is liable to happen with convex or V bevel if stropped aggressively.

There are several issues in this thread, but this is the one where you and I are not on the same page.

If we just look at the edge grind, and not the blade grind, an edge is defined by three points that make a triangle. Points A and B are the mark the edge's shoulders, the points where the edge grind meets the blade grind. Point C is the apex. We have to keep these three points equal in order to compare the qualities of the various types of edges.

1-- V edge: In a V edge (often called a flat grind in this thread), the edge is created by two straight lines, one running from A to C and the other from B to C.

2-- Convex edge: In a convex edge, the edge is created by two arcs that run outside of the straight lines of the V edge, one of those arcs connects point A to C the other B to C. By definition, a convex edge is less acute and has more metal behind the apex than a V edge. I think what you are saying, Heavy, is that you can thin out a convex edge so it is more acute than a V edge, but you can do that thinning only by moving points A and B farther up the blade to make the edge taller. To give a convex edge the advantage of being more acute, you have to compare a tall convex edge to a short V edge.

3-- Hollow ground edge (concave): The hollow ground edge is like the convex edge in that it is created by two arcs, one of those arcs connects A to C and the other B to C. The difference between a convex edge and a hollow ground edge is that the arcs are inside the profile of the V edge. This edge is more acute than either the V edge or the convex edge, and also less robust.

4-- Compound bevel: The compound bevel is what Murray is calling a convex edge, but it isn't. You can create a compound bevel in many ways. The two simplest ways are to put a microbevel on the V edge or to round off the shoulders of the edge. Or you can do both or you can do several bevel facets.

If you change the three points, you will drastically change the profiles and characteristics of the edges. For example, you can make a V edge extremely short, with the shoulder points A and B barely above point C. Imagine a V edge with an inclusive angle of 179.99999 degrees. It would technically be a V edge, but it would look like the knife had two spines and no edge. You can make a convex edge or a hollow ground edge that are equally short and all three of these edges would look to anyone without a powerful microscope as having no edge at all.

Conversely, you can raise the shoulder points all the way to the spine of the blade, in which the edge grind is basically a blade grind. The full-ground V edge will be more acute than the convex edge and the hollow ground edge will be more acute than the V edge.

Further complicating the issue are the characteristics of the arcs the define the convex and hollow ground edges. When the edge shoulder points are connected to the apex at point C by an arc that is severe, say by the arc equal to a segment of a small circle, such as a marble, the edge geometry will be very acute. If instead, you connect the edge shoulder points to the apex at point C with an arc equal to a segment of a very large circle, such as the size of the earth, you will make the convex and hollow ground edges so much more acute that for all practical purposes, they are identical to the V edge.

 

[Twindog]

Here's a diagram of the edges:

 

[Jason B.]

2-- Convex edge: In a convex edge, the edge is created by two arcs that run outside of the straight lines of the V edge, one of those arcs connects point A to C the other B to C. By definition, a convex edge is less acute and has more metal behind the apex than a V edge. I think what you are saying, Heavy, is that you can thin out a convex edge so it is more acute than a V edge, but you can do that thinning only by moving points A and B farther up the blade to make the edge taller. To give a convex edge the advantage of being more acute, you have to compare a tall convex edge to a short V edge.


This is false.

A convex grind DOES NOT run on the outside of a V edge it is inside it. You cannot add metal.

Only apex angle change makes a edge stronger or weaker not the shape behind it.

 

[HeavyHanded]

Pretty sure I understand what you're saying, my only point is that if you compare a range of edge grinds that all have the same inclusive angle, the situation becomes a little more simple to visualize (the inclusive angles above are all different). Take the diagram of the pure V edge upper left, and convex it starting about 1/3 of the way up the backbevel. The only way to apply a more acute V bevel would be to grind the entire thing way back and make another FFG. Instead of picturing the oversized convex from the diagram, simply picture arcs that fit within all the other grind types (on the chisel grind, just imagine it on the angled side). The convex will always fit within other grind types at the same inclusive angle and stock thickness.

From my POV, folks that claim there's more meat behind a convex are only talking about very thick, relatively inefficient ones, otherwise just about any grind type can be converted to a convex without making the angle more acute or obtuse, leading the convex to have less meat behind the edge and less resistance as it goes into a cut - that's the real advantage of the convex. On the other hand, converting a full convex to a V bevel requires a considerable amount of stock removal unless you're OK with making the inclusive more broad. I have several full convex edges that are very close to a full flat grind - only a couple degrees of deviation from the spine to apex define the entire arc - these were ground down from overbuilt sabre grind edges. To make a V bevel with the same inclusive apex angle fit within the convex would require both sides be thinned out flat all the way back to the spine with a lot of metal taken off. I could then grind the shoulders down and make a convex with the same or more acute inclusive apex angle and less resistance....

Not all my edges are convex, but the properties that make it appealing are based on solid principles - has nothing to do with more meat behind the edge.

Martin

 

[Twindog]

2-- Convex edge: In a convex edge, the edge is created by two arcs that run outside of the straight lines of the V edge, one of those arcs connects point A to C the other B to C. By definition, a convex edge is less acute and has more metal behind the apex than a V edge. I think what you are saying, Heavy, is that you can thin out a convex edge so it is more acute than a V edge, but you can do that thinning only by moving points A and B farther up the blade to make the edge taller. To give a convex edge the advantage of being more acute, you have to compare a tall convex edge to a short V edge.


This is false.

A convex grind DOES NOT run on the outside of a V edge it is inside it. You cannot add metal.

Only apex angle change makes a edge stronger or weaker not the shape behind it.

What makes the statement true is that it compares a convex edges to V edges bounded by the same three points. That's simple geometry. Yes, you can move those points around and come up with all kinds of situations where one edge will be inside or outside of the other. But for a fair comparison, the edges have to have comparable boundaries.

You second point is incorrect, too. The hollow edge can have a less acute edge and still be much less strong than a convex or V edge. You'd see that difference if you tried to chop wood with a hollow edge, even if it's a little less acute than the convex or V edge.

 

[Twindog]

Pretty sure I understand what you're saying, my only point is that if you compare a range of edge grinds that all have the same inclusive angle, the situation becomes a little more simple to visualize (the inclusive angles above are all different). Take the diagram of the pure V edge upper left, and convex it starting about 1/3 of the way up the backbevel. The only way to apply a more acute V bevel would be to grind the entire thing way back and make another FFG. Instead of picturing the oversized convex from the diagram, simply picture arcs that fit within all the other grind types (on the chisel grind, just imagine it on the angled side). The convex will always fit within other grind types at the same inclusive angle and stock thickness.

From my POV, folks that claim there's more meat behind a convex are only talking about very thick, relatively inefficient ones, otherwise just about any grind type can be converted to a convex without making the angle more acute or obtuse, leading the convex to have less meat behind the edge and less resistance as it goes into a cut - that's the real advantage of the convex. On the other hand, converting a full convex to a V bevel requires a considerable amount of stock removal unless you're OK with making the inclusive more broad. I have several full convex edges that are very close to a full flat grind - only a couple degrees of deviation from the spine to apex define the entire arc - these were ground down from overbuilt sabre grind edges. To make a V bevel with the same inclusive apex angle fit within the convex would require both sides be thinned out flat all the way back to the spine with a lot of metal taken off. I could then grind the shoulders down and make a convex with the same or more acute inclusive apex angle and less resistance....

Not all my edges are convex, but the properties that make it appealing are based on solid principles - has nothing to do with more meat behind the edge.

Martin

Yes, if you compare inclusive angles, the convex comes out better. But that's because convex edges are naturally less acute than a V edge. So if you grind metal off the V edge to create a convex edge, the convex edge will have a more acute profile, but that's only because you would be comparing a tall convex edge to a short V edge.

And your newly created convex edge could be made more acute still if you converted it to a V edge by grinding down the profile.


For any given blade stock, a short edge will be less acute than a tall edge. And that hold's whether you're comparing a short V edge to a tall V edge. So if you compare a tall convex edge to a short V edge, you can get a more acute edge. But when the blade stock is constant and the edge heights are the same, the V edge will be more acute than the convex edge and the hollow edge will be more acute than the V edge.

 

[Jason B.]

It might look good on paper but it does not translate to reality.

From what you are saying the convex example would need to be of thicker blade stock than the V edge or your example simply wouldn't work.

With convex grinding you have a thinning of the material behind the edge apex which causes a reduction on the drag of the blade which can translate to lower pressures exerted on the edge apex. This is a misunderstood part of the convex grind and why many will say its a "stronger" edge. The only thing that makes a edge stronger is to change the angle which is never discussed. If you convex a edge without changing angle the only difference will be drag, you will not get a tougher edge and your edge retention will not go up.

Cutting and chopping are two very different actions causing VERY different stresses to the edge. If you want to change the disscussion from edge grinds to blade grinds then you have a valid point, otherwise it's just getting off track.

 

[Twindog]

It might look good on paper but it does not translate to reality.

From what you are saying the convex example would need to be of thicker blade stock than the V edge or your example simply wouldn't work.

With convex grinding you have a thinning of the material behind the edge apex which causes a reduction on the drag of the blade which can translate to lower pressures exerted on the edge apex. This is a misunderstood part of the convex grind and why many will say its a "stronger" edge. The only thing that makes a edge stronger is to change the angle which is never discussed. If you convex a edge without changing angle the only difference will be drag, you will not get a tougher edge and your edge retention will not go up.

Cutting and chopping are two very different actions causing VERY different stresses to the edge. If you want to change the disscussion from edge grinds to blade grinds then you have a valid point, otherwise it's just getting off track.

I've said consistently that if you grind a V edge into a convex edge, you will end up with a more acute cutting profile. Conversely, if you grind a convex edge into a V edge, you will also end up with a more acute cutting profile.


But my point is about fairly comparing one type of edge to another. The height of the edge made from any bar stock is a key variable. As is the width of the edge shoulders. Take a piece of bar stock 1/8 of an inch thick and two inches wide. Then you grind a convex edge and I grind a V edge. The only requirement being that the final edge has to remain 2 inches. The V edge will be more acute when the bar stock and the edge height are kept constant.

The convex edge is an edge that curves outward. The hollow (concave) edge curves inward. The V edge is straight and the shortest line from the edge shoulders to the apex.

When people grind a V edge into a convex edge, they are raising the height of the edge. It's that taller edge height -- not the conversion of a V edge to a convex edge -- that makes the cutting profile more acute. Taller edges cut better than short edges on any given stock.

 

[somber]

When people grind a V edge into a convex edge, they are raising the height of the edge. It's that taller edge height -- not the conversion of a V edge to a convex edge -- that makes the cutting profile more acute. Taller edges cut better than short edges on any given stock.

I don't agree, because you're not factoring in that the height of the primary bevel (the edge that initiates the cut) is dependent on the thickness of the secondary edge (the bevel behind the primary edge). If I have a .1" secondary edge and a primary edge ground at 15degrees, the height of the bevel will be smaller than if I have a a .2" secondary edge with a primary edge ground at 15degrees -- the thinner knife will cut better than the thicker one every time, no matter the 'height' of the primary bevel.

 

[KennyB]

Your process of producing a convex edge is extremely complicated, and even with all those instructions, there is not enough information to mathematically model the final edge.

Your example starts with an insanely thick edge -- producing an edge bevel more than a quarter of an inch tall for the 20-degree angle. Your next step makes the edge even taller, but you don't give enough information to know how much taller. Even my ZT 0560CBCF, reground to a 30-degree edge, is just 0.1 inches tall.

But here's the bottom line: You can make whatever convex edge you want, and I can quickly and easily convert it to a V edge that will have a more acute edge angle and cut better.

Convex and V edges come in an infinite variety of edge profiles, including edge profiles so similar that you'd need an electron microscope to detect a difference in profiles.

What I object to is the common notion expressed in this thread that convex edges are somehow better, sharper or more robust than V edges. No such general statement can be made. You can only compare specific profiles -- or hybrid profiles -- of each type.

Edges are bounded by three points: the two edge shoulders and the apex. When convex edges are compared to V edges bounded by those same three points, the V edge will be more acute and the convex edge will be more robust. But those differences can be reduced to almost zero, depending on the arcs that further define the convex edge.

As a general matter, neither convex edges nor V edges are superior to the other.

Where did we come up with an edge bevel over a 1/4" tall? I think we're confusing the vernacular here. When I speciefied a bevel width of .100" that is WIDTH i.e. what you're referring to as "tall". I think you inferred I meant thickness behind the edge. Then with your example of your ZT with a 30 degree inclusive angle being that "tall" I'm pretty sure that's where we got mixed up. So yeah, replace bevel "width" with "height" or "tall, NOT thickness and I'm sure it will make much more sense.

But beyond that you're still being too insistant on extreme precision which in this example is just not needed. The .100" tall bevel was an example to make the approximations easier for one to imagine when reading. In all reality the bevel height for the V bevel you set will probably be at some random height, and rather than measure it you will grind in new bevels at the percentages I mentioned. So for example, the first more acute bevel to be ground in should cover somewhere between 1/4th and 1/2 of the original bevel. This also creates a new bevel with an undetermined height but one does not have to be concerned with that because it is the proportions that count here. The over-all shape is much more important to replicate than the actual dimensions, especially since going from one knife to the next if you were to specify "Grind in a new bevel exactly this wide, with the top end exactly this far from the spine, and the bottom end exactly this far from the edge," it wouldn't actually translate to what you wanted because every knife geometry is different--think about it, you can't tell someone to put a .050" "tall" bevel on a blade that is only .250" wide and have the proportions be the same.

Nothing here is precise, it's approximation entirely, but what I'm telling you is that as inprecise as it is, it will still reproduce the intended shape which is actually what will make a convex edge perform any differently than a V edge. This is not even a "formula" either, one could leave off the final more obtuse bevel entirely, but the point is just communicating to a person the angle of the new bevel and how much of the old bevel it should cover is enough to reproduce it in a close-enough fashion.

The irony here is that even with a V edge, one person's 30 degree inclusive edge could be a lot different than another person's even on the same knife because some people have sharpened theirs more than others, and on most knives the more you sharpen it the thicker the edge gets as you travel higher up the blade grind. So if the implication is specifying a V edge of one geometry will reproduce it exactly even that isn't necessarly true. Now, does it really make a difference if one is a few thousanths of an inch thicker behind the edge or the bevel face is a few thousanths thicker or thinner on one? Not very likely right? So why would it make a differnce if these were different for a convex edge either?

Other than not I'm not really sure if you thought I was implying that convex edges are somehow better but that's not really what I was saying at all. I don't think convex shapes make much of a difference unless close attention is paid to the actual shape and even then it might not be a really tremoundous difference or only something you will notice improvement in for something task-specific. A good example is cutting cheese... A lot of people think that a convex edge will do it better because it reduces friction, that the V edge's shoulders slow it down or that the convex one can get thinner and so on and so forth but it's none of these reasons. A V edge will cut cheese with just as ltitle resistance as a convex edge, but the SHAPE of the V will not cause the cheese to part away from the blade like certain convex shapes can, so the user must be more careful to angle the knife blade in such a way that the cheese doesn't ride along the blade surface--the convex edge does this "separating" for you.

Why some people think that convex edges of any shape are just all-around better... I don't know. Honestly task-specific edges, tailored for say cheese cutting, probably won't perform as well "all-around". Sometimes that 'separating' effect of certain convex shapes is not beneficial. But I already said most of this stuff in my post BEFORE the one you quoted so I don't want to reiterate.

Long story short... Convex versus flat V edge doesn't really make a difference uness the convex shape was designed and intended to do something specific to aid the user. Now whether that's making a knife slice cheese better ( dental floss works the best ), or having an edge that's seemingly "faster" to sharpen, either are fine with me. The only thing about convex edges I don't think I agree with this that they lend any more strength or robustness than a V edge will.

 

[HeavyHanded]

But when the blade stock is constant and the edge heights are the same, the V edge will be more acute than the convex edge and the hollow edge will be more acute than the V edge.

I can only go back to the same observation I made earlier. If you compare two knife edges of equal thickness and width, say a piece of flat stock .125" by 1", and ground a V cutting edge into both at the same angle (say 30* inclusive), then convexed one of the specimens, it will have less drag than its cousin, it will have less steel behind the cutting edge, yet have the same inclusive apex angle. It will also be more easily made more acute, as some of the steel one would have to pull off of the V bevel to make it more acute, has already been removed during the convex conversion.

If by the term "edge height" you mean the region where its actually been ground, you cannot make them equal between a V bevel and a convex (all other factors being identical) and still have the same inclusive apex angle - it isn't possible.

Martin

 

[Fred.Rowe]

I don't think its a convex at all, but more of a spiral ground edge. It is surely impossible to hold the correct angle and pressure that will produce the points on curve, that make up an actual curved surface. I guess thats why it was referred to as the apple seed edge early in its existence. When you consider this it makes the arguments almost moot.

 

[Twindog]

I can only go back to the same observation I made earlier. If you compare two knife edges of equal thickness and width, say a piece of flat stock .125" by 1", and ground a V cutting edge into both at the same angle (say 30* inclusive), then convexed one of the specimens, it will have less drag than its cousin, it will have less steel behind the cutting edge, yet have the same inclusive apex angle. It will also be more easily made more acute, as some of the steel one would have to pull off of the V bevel to make it more acute, has already been removed during the convex conversion.

If by the term "edge height" you mean the region where its actually been ground, you cannot make them equal between a V bevel and a convex (all other factors being identical) and still have the same inclusive apex angle - it isn't possible.

Martin

Hey Martin:

See if this diagram gets us on the same page. The dark blue outline on the left represents a blade with a convex grind. Distance H1 represents the height of the edge. Distance W1 represents the width of the edge, or the distance between the edge shoulders.

The inside line (separated from the convex grind by the red space) shows how the convex edge can be ground into a V edge without changing either the height or the width of the edge. The V edge is more acute and the convex edge is more robust.

The dark blue outline on the right represents a V edge (the same V edge in the diagram on the left). The line inside the V edge represents a convex edge that was created out of the V edge. It’s a little difficult to see that it’s a convex edge because to convert a V edge into a convex edge, you have to soften the radius of the edge profile making the arc more difficult to see, but it’s there. To make this conversion, you have to raise the height of the edge to distance H2. I believe that this is the edge you are talking about. By converting a V edge to a convex edge, you can create an edge that has a more acute edge profile. But you can’t do that conversion unless you increase the height of the edge and/or reduce the width of the edge.

What I’m saying is that the superior cutting profile of the edge on the right is not because it was converted to a convex edge, but because the edge height was raised. You could also raise the height of the V edge to H2 and that new V edge will have a more acute cutting profile than either the original V edge or the convex edge that was ground out of the first V edge. In other words, the improved cutting performance you see was the result of raising the edge height from H1 to H2, not because the V edge was converted to a convex edge.

What I do agree with you is that you can improve a V edge by converting it into a convex edge. A convex edge doesn’t always have a less acute cutting profile than a V edge nor does it always have more metal behind the apex.

However, when the edge height and edge width are held constant, the V edge will be more acute and the convex edge will be more robust.

Josey

 

[Fred.Rowe]

What happens if you hold the top point on tangent h1 and grind so as to raise the apex?

 

[KennyB]

Okay well since it's time for visual aids... Mind the ruler above the drawing. Resolution is 100 pixels per inch, the cross hair is centered at 5" on each axis

Start with any degree angle, in this case 34 inclusive ( 17 dps )


Now grind in a more acute angle, until the new bevel goes half-way down the old bevel, like shown here. 5-10 degrees is best, here we're doing 7 degrees per side (would probably be about flat on the blade for most knives)


Now grind in a bit of a more obtuse angle. Let's just add 5 degrees to the original angle, just to really demonstrate. So that will end up with 22 degrees per side. As shown in this picture, you grind this bevel in until it travels up about 1/4" of the way up--remember approximation.



Now this is what you end up with, a compound V bevel...



Blend it together as described...



After blending it all together, this will be the new shape.

End result...

 

[Fred.Rowe]

Pictures work for me, text never quite does it. Thanks Kenn.

I have that touched up and it will be headed back your way on Friday, Fred

 

[Twindog]

Kenny B:

What you don't show in your drawings is that you have greatly increased the edge height in your conversion to a modified convex edge. You have also made the near-apex angle less acute.

When you raise the edge height, you will make the overall edge profile more acute, whether you are converting from a V edge to a convex edge or simply raising the edge height on the existing V edge.

Nothing involved in the conversion to the modified convex edge improves the edge profile, only raising the edge height. I can draw a V edge inside your modified convex edge and increase the acuteness of the profile. Unless you control for edge height and edge width, you cannot compare the relative advantages of convex edges to V edges.

And if you notice, as you raise the edge height, the differences between V edge and a convex edge become increasingly less significant.

 

[KennyB]

Kenny B:

What you don't show in your drawings is that you have greatly increased the edge height in your conversion to a modified convex edge. You have also made the near-apex angle less acute.

When you raise the edge height, you will make the overall edge profile more acute, whether you are converting from a V edge to a convex edge or simply raising the edge height on the existing V edge.

Nothing involved in the conversion to the modified convex edge improves the edge profile, only raising the edge height. I can draw a V edge inside your modified convex edge and increase the acuteness of the profile. Unless you control for edge height and edge width, you cannot compare the relative advantages of convex edges to V edges.

And if you notice, as you raise the edge height, the differences between V edge and a convex edge become increasingly less significant.

You're not exactly wrong in what you're saying, but I just don't think we're on the same page of edge acuity being the number one factor. There is simply more that can be done to "tune" an edge or a blade's profile other than simply making the most acute edge angle. I can't really speak a lot for chopping and robustness and all that, but as far as convex edges go for slicing through deep, high-friction materials a convexed blade works so much easier. That is why so many blades that are meant for that purpose, use that grind shape.

I've been saying from the start it makes less of a difference when we're talking about JUST the actual edge grind, but one thing I was trying to point out is that once you begin thinning in the realm of 5-10 degrees per side you're practically changing the entire blade's grind since most relief grinds come in at about ~7 degrees per side. This is a whole different beast than simply rounding off a small .025-050" bevel with a mousepad and sandpaper, it is dramatically changing the overall profile of the blade stock.

I'm not really sure what you're observations about edge height and edge width are... But I'm not sure if it's only pertinent to what you're saying about a V bevel being inherently more acute than a convex grind, or if you're just not factoring in the importance of thickness behind the edge. Between the width of the edge bevel's face, and the distance from the apex to the bevel's shoulder travling along the centerline of the stock ( what I'm inferring you are referencing as edge height ) the thickness of the stock at the edge bevel's shoulder also determines the profile and angle just as much as each factor--it is after all trigonometry.

 

[Fred.Rowe]

One grind that was not pictured is the grind used on some competition knives; where cutting through a hanging rope and chopping through a 2 X 4 is called for. The primary bevel is an extended convex shape where, as the bevel moves toward the spine the curve continues and actually cuts into the spine, thinning it out. This grind reduces friction and the tendency of the blade to get stuck in the material being cut. These blades are thickest through the center of the bevel and not at the spine as in most blades. They are not aesthetically pleasing but they are effective in doing the work called for.