That's a nice level of quotes, Phil. Almost recursion . The forum software apparently cannot keep up anymore .

You make some very interesting points.

PhilipPasteur wrote:


I understand. Good point.



I don't understand this. Why is this the case? Is it always the case, or does this depend on the type of material?

Also, you're talking about fully convex blades and fully flat blades. Before we were talking about edges only. Does you argument scale down to edges?



Me too. Very interesting! Also outside the scope of our discussion. Many thanks, even though right now I don't have the intellectual energy to try and understand them.

Mark,
My original point was that the difference in resistence to cutting between a convex edge and a V would be swamped by the differences in resistence contributed by the blade grind. Therefor this aspect alone would not make one geometry inherently superior to the other. That is it. As you are correct the conversation is wondering... I can't go into answers to your questions without promoting this diversion.

If there is interest, someone could start another thread and I will be happy to attempt further explanation.

BTW, It is not helpful to ask a bunch of questions and then point out that the answers would be off topic...

As to the articles that I linked, the second one deals primarily with how the angle at the edge contributes to friction and therefore percieved and measured sharpness. It fits pretty closely with where we started on the latest tangent.. discussing whether a convex edge would contribute less to cutting effort than a V. The idea that I take from the second paper, which requires the basis established in the first one (which is why I linked both), is that any change in edge geometry, even fairly gross angle changes, are pretty inconsequential in regard to changing cutting effort.. and the resulting measured sharpness. Again, the method for measuring this is etablished in the first paper. Take a closer look when you have a chance.

Phil

PhilipPasteur wrote:


Yes they were very intriguing, iirc from while back when I deep dive into these type of interactions. This older study linked by Thom Brogan via FF Haptic Rendering of Cutting. All these studies are confined by pseudo finite elements model, and most study material cells are too uniform, therefore I am not sure how much they translate to our knives usage world.

Back to convex - I guess it's up to one's interpretation what convex (curve and or angle and or shoulder). Also interpretation of performance for the 'what' V or C pros/cons; however studies/researchs such as above attempt to cover the 'why' fell short IMO. In WE world - bevel angle precision & repeatability - convex doesn't add much if your blade is thin behind the edge, a few micron micro-bevel will stable acute angle edge. If thick behind the edge, well thin it out (if has the mean), otherwise just blend the shoulder so there is less of an abrupt change from bevel to blade (the wedge - e.g. try to cut a crisp apple with scandi grind, hey don't cut it in hands unless you've bandage handy heheh.).

Hey Phil,

I guess you miss-interpreted my words. I must admit I gave room for that.

Please don’t interpret them as if I don’t want our conversation to wander. In fact, I’m really happy with it, since this maybe the first conversation I’ve had on convex edges that gets a lot further than “convex has more steel behind the edge”.

Also, I didn’t mean to say that the links to the articles were off-topic. In contrast, they’re really interesting. My words “also outside the scope of our discussion” were short for “they are also very interesting outside the scope of our discussion”. Not for “they are outside the scope of our discussion”.

Please go on! I’m very interested in what you are saying.

Good point about wedging, Bluntcut. I guess most of us can relate to that.

Great article, too! I have some reading to do... There was a small typo in the link you gave. For those who cannot find the article: it is here.

I just want to clarify my earlier posts on convex edges - stated C in V, or V in C or V intersect C. For me, most of the time, convex means 'Practical convex'.



For 'Extreme', we are looking at nearly double or half the bevel angle. Even in the cases of micro-bevel - e.g. inclusive * 15/25 (67%); 20/30(50%); 30/40(33%) - we're far from doubling the angle. Stropped edges are mostly convex micro-bevel anyway

Hey guys,

I intended to write a summary of this thread, since I found it interesting and I have learned a lot from you. But then I found myself jumping to my own conclusions. I guess blood is thicker than water... I’ll post it anyway and please shoot! The reason for being here (other than having fun) is that I want to learn, so I can stand a good deal.

This thread started off with the question by Ken who wondered what the advantage is of a convex edge over a double-beveled or multi-beveled edge. I then generalized this question into what the use is of a convex edge anyway.

Lots of claims are made about convex edges. Some in this thread, some elsewhere. And some claims were supported in this thread, others debunked. What did I learn?


A convex edge is millennia old

This point was most prominently made by Leo, who claimed that even in the bronze age people made blades with convex edges. Now when you think about this, this could be true. Our ancestors didn’t have a WEPS, but we all know you don’t need a WEPS to create a convex edge. A mousepad and some sandpaper is enough. Uhm... but hey, they didn’t have mousepads in the bronze age! Not even sandpaper...

OK, it’s true. There’s lots of empirical evidence that is beautiful, too.


A convex edge is marketing blurb

This point, made by Curtis (with a smiley), was appealing to me. I’m a naturally inquiring guy and I only believe things I have seen with my own eyes or at least understand with my own mind. Perhaps that’s one of the reasons why the sometimes traditional world of knife sharpening appeals to my investigative senses.


A convex edge is stronger than a single bevel

This claim is often followed by “because it has a better geometry” or “because it has more material behind it”. However, this claim says nothing. That’s because it omits the angles we are comparing. As Tom wrote, “angles are everything”.

Yes, a convex edge that varies between 17 and 22 degrees is stronger than a straight edge of 17 degrees. However, it is not stronger than a straight edge of 22 degrees.

Yet the idea that a convex edge is stronger is appealing. This is Tom’s pencil point theory. We all know that by rounding the point of a pencil, the probability that it breaks off is much reduced.

This is similar to what we do when we put a micro-bevel on straight primary bevel. We still benefit a lot from the steeper primary bevel, but we make it less fragile by putting on a blunter micro-bevel.

In these cases we don't only make the edge stronger. We sacrifice a bit of sharpness in favour of strength. We are trying to optimize the balance sharpness-strength.

As Phil said it, “it [convexing the edge] makes sense, but more so in a case where you are doing something that will make the knife steel fail at your chosen angle”.


A convex edge dulls faster

This point is made more often. The idea is that a convex edge is thicker right behind the edge, so as the edge wears, it gets thicker faster too.

But again, as Bluntcut, pointed out, this doesn’t say much about convex versus V-edge, but more about angles (“not so much about V or C, IMO”). A convex edge that varies between 17 and 22 degrees dulls faster than a straight edge of 22 degrees. However, it doesn’t dull faster than straight edge of 17 degrees.


A convex edge doesn’t wedge

Well, at least not as much as a straight edge, so goes the claim. One of the most annoying features of an axe is that it may wedge. This is the reason everybody prefers a convex edge on their axe.

Wedging is also a big annoyance for cooks when cutting harder materials like carrots or onions. In the world of high-end kitchen knives, blades should have such a profile that they are thin behind the edge. Some cooks go as far as recommending thinning out a knife every time it is sharpened.

Indeed, here a convex edge has an advantage over a straight edge. The convex edge acts as a wedge: there is simply a smaller part of the edge in contact with the material being cut, so there is less friction or stiction. This is illustrated by a picture I found on the Net (here).



Phil brought up the same argument for entire blades. “For instance a full flat grind would have more of the main part of the blade in contact with the material at one time versus a hollow grind or a convex grind. If you are cutting something where a major portion of the blade is engaged with the material, the sides of the blade will contribute more friction or resistance to cutting to the overall effort required than the bevel.”

Also Ken supported this. “With a typical FFG knife cutting a firm moist substance, I get a lot of resistance from (what in the stropping threads we've termed stiction) the material.”

Even though a convex edge may have an advantage over a straight edge here, does it also have an advantage over a multi-beveled edge?


A convex edge cut doesn’t cut (much) better than a multi-beveled edge

Bluntcut made the point that a convex edge is more aerodynamic than a multi-beveled edge. However, Phil wrote that “those designs are done using fluid dynamics as the basis. We typically are not cutting fluids nor gasses.” This was supported by a statement by Jay Fischer:



Does the fact that a convex edge is more aerodynamic than a multi-beveled edge make it a better cutting edge? Probably not much. As Bluntcut wrote: “In WE world - bevel angle precision & repeatability - convex doesn't add much if your blade is thin behind the edge.”


Conclusion

My conclusion is that some of the claims made in the knife world about convex edges are not so much true or false, but instead rather meaningless. A convex edge is not inherently stronger than a straight edge. Convex edges allow for different trade-offs between angle steepness and strength than straight edges.

This different trade-off between angle steepness and strength is similar to what we achieve when putting a micro-bevel on a straight edge. We make the edge stronger, but at the cost of a little cutting efficiency.

Similarly, a convex edge does not inherently dull faster than a straight edge. It all depends on the angles.

However, a convex edge does have an advantage over a straight edge in that it doesn’t wedge as much. There is a smaller part of the edge in contact with the material being cut, so there is less friction.

It seems that this advantage is most prominent when cutting hard, rigid materials. Perhaps that is the reason everyone prefers a convex edge on their axe. And cooks never complain that a knife is wedging when cutting tomatoes. But they may complain when cutting potatoes.

Does a convex edge have an advantage over a proper double-beveled or multi-beveled edge? Probably not: convex doesn't add much if your blade is thin behind the edge.

The fact that we even ask this latter question shows we are from the Wicked Edge world. In the rest of the world nobody is able to create multi-beveled edges where the bevel angles are 1 or 2 degrees apart. If they try do so so, they end up with convex edges. Even if they try to create a straight edge, it will be somewhat convex. It has been that way since the bronze age.

This is a great topic with a lot of great insights! I have a couple of thoughts on convex edges as well:

As several others have pointed out, axes are generally convex ground. Wedging is a major factor in why they have their shape. Another factor is edge durability, but maybe not for the reasons that most people assume. Imagine striking into a tree with an ax; the very edge of the blade bears the initial impact, but as the rounded shoulders force their way into the cut, they spread the wood, splitting it apart like a maul and mitigating further contact from the edge itself as the ax penetrates. This process happens relatively quickly and spares the very edge from the majority of the force. While this is valid for axes and choppers, I'm not sure it really helps with everyday cutting tasks, especially those that utilize a slicing motion.

Accuracy - convex edges are not as crisp as V-ground edges and allow deflection through the material being cut. For extreme cutting, chisel ground blades are often chosen though they are limited to precision only on the flat side of the grind. A V-grind or compound V-grind is an excellent choice for precision cutting when precision is required on both sides of the blade.

Let me begin by saying I have never (intentionally - in my days of hand sharpening who knows what I may have done by accident) sharpened a convex edge.

How do you touch up a convex edge? I assume small touch ups with strops are possible (free hand and/or WE?). For anything more than strops do you have to completely redo the edge? For me the advantage of the V grind with WE is when stropping is not enough I can pull out the finest or 2nd finest stone and quickly touch up the edge at the same angle without starting from the beginning every time. (I rarely trash a blade to the point that starting out with 100# stones is required).

Mark, thanks for the summary, excellent job. Did the people from the bronze age make convex edges on purpose or by accident?

Geocyclist wrote:


I believe that the theory (if you follow Leo's post...aand I tend to agree) is that they did it by accident, at least initially. How precise a V would anyone get by sharpening on a stone... as in a stone you pulled out of the ground... ?? But, of course I was not there, so cannot say for sure...


Phil