What Are The Advantages of a Convex Grind?

Well put, sir. My simple brain understands this.

Then get ready to have your mind blown! Look at my pic. On the bottom half it is showing a convex grind in red, and a v grind of the same edge angle in black.

Now look at the top half! Vee in black, and....concave/hollow in red!! The hollow ground has more steel behind the edge for a given edge angle than a vee or convex. (it quickly gets thicker.)

Sometimes mathematics just slaps you around just because it can.
 
So far, I see one person endorsing it for kitchen duty and whittling, and one other person endorsing it for heavy camp chores and skinning. I have two people saying it is not good for shaving.
 
So far, I see one person endorsing it for kitchen duty and whittling, and one other person endorsing it for heavy camp chores and skinning. I have two people saying it is not good for shaving.
Given all the stroping required on a classic razor (15 times on each side with the cloth side then same game with the leather side, per Böker, before each shaving session), I believe my razor must have gotten convexed somehow ! It shaves smooth and fine. But I'm still reluctant to take it to the WorkSharp, though...
 
You can't compare a V edge to a convex edge unless you know the underlying geometry of each edge. Asking which is better without knowing the specifics of the underlying geometries is like asking which is faster, a car or a truck. Either can be faster than the other.

A V edge and a convex edge can be virtually identical for all practical purposes, meaning there is no difference in performance.

A V edge can be more or less acute than a convex edge, meaning there can be a large difference in performance, favoring one or the other.

Convex edges have no angles. An angle is defined by the intersection of two straight lines. A convex edge is defined by the intersection of two arcs.

If you compare a a convex edge to a V edge -- and the boundaries of those edges are identical, meaning the two shoulder points and the apex are exactly the same distance from each other for each edge -- then by definition the V edge will be more acute and the convex edge will have more metal behind the apex. But the differences can be small or large, depending on the nature of the arcs that define the convex edge.
 
Convex edges have no angles. An angle is defined by the intersection of two straight lines. A convex edge is defined by the intersection of two arcs.

Demonstrably false and already covered earlier in the thread. :)
 
If you prefer a convex either sometimes or all the time, what do you do with it? Hunting? Whittling? Carving? What applications does it excel at? Where does it fall short? Does it hold an edge longer? I never had a knife that was completely convexed.

I have one convex ground knife, a custom warncliffe trapper by Don Hanson. It's a heavy duty knife to meet the hard-use needs of the over-the-road truck driver who commissioned it (e.g. opening things and cutting off pieces of hose, blown tires, etc.) The O1 convex edge excels at this job as an all-around-heavy-duty-EDC. It holds a good edge, but the O1 is hardened to 60RC.

The only negative about a convex grind is that you need to learn how to sharpen it, but that's not too hard. Just use sandpaper on a top of a hard/soft surface. I use a notepad with the sandpaper on top of the cardboard back and the pad sitting on a board. Don Hanson suggested sandpaper on top of leather on top of wood. He suggested 400grit for this grind/steel/application and that's what I use to good effect. Don't even try to sharpen it on a fixed angle sharpener (e.g. spyderco sharpmaker.)
 
You can't compare a V edge to a convex edge unless you know the underlying geometry of each edge. Asking which is better without knowing the specifics of the underlying geometries is like asking which is faster, a car or a truck. Either can be faster than the other.

And, at a given time, which is faster can be easily measured. The one with the larger MPH is going faster. Which illustrates my point nicely. To compare things you need a fixed quantity to compare - like edge angle or MPH at 12:37:52 PM.

Convex edges have no angles. An angle is defined by the intersection of two straight lines. A convex edge is defined by the intersection of two arcs.

Yes, it is. And the angle at which those two arcs intersect is a mathematically measureable quantity. It is. Again, sorry.

Its like you are saying one cannot divide fractions because you don't remember how.
 
Demonstrably false and already covered earlier in the thread. :)
Twingdog is right. You are wrong. Sounds like you need a picture you comprehend this.

To simplify what he said, draw a straight line from the point of the edge to the shoulder (back bevel). This is the only way to measure a consistent edge angle. You can do this for any edge. It should have been obvious that the convex edge has no real edge angle. Therefore, convex has more metal behind the edge.

I'll post a pic if you still don't get it. But basically, whoever thinks a V edge has more metal than a convex edge (at the same sharpening angle obviously) needs to do more research before posting nonsense.
 
Wouldn't the apex angle of a convex ground blade be the angle between the two tangent lines to the invidual arcs taken at the point where they intersect?

And therefore, the entirety of the convex edge of the blade would be bound by the two tangent lines drawn? And since the edges curve inward away from that tangent line, there would have to be less metal "behind the edge" because you have removed that metal to form the convexed edge. Otherwise, it would just be a typical straight bevel edge.
 
Demonstrably false and already covered earlier in the thread. :)

Only lines or rays (parts of a line) can form an angle.

In geometry a line:
• is straight (no curves),
• has no thickness, and
• extends in both directions without end (infinitely).
https://www.mathsisfun.com/definitions/line.html


Ray: A portion of a line which starts at a point and goes off in a particular direction to infinity.
http://www.mathopenref.com/ray.html


Angle: The amount of turn between two straight lines that have a common end point (the vertex).

https://www.mathsisfun.com/definitions/angle.html
 
Wouldn't the apex angle of a convex ground blade be the angle between the two tangent lines to the invidual arcs taken at the point where they intersect?

And therefore, the entirety of the convex edge of the blade would be bound by the two tangent lines drawn? And since the edges curve inward away from that tangent line, there would have to be less metal "behind the edge" because you have removed that metal to form the convexed edge. Otherwise, it would just be a typical straight bevel edge.

Yup. See my picture above.
 
Actually he's right, and I don't think you're understanding what he's showing. Convexes will have a continuously decreasing angle the further back you get from the edge but at the apex will be identical in angle. The closer to the edge you get the greater the order of magnitude of influence specific geometry has on cutting performance. For equal edge angle, a convex will have superior cutting performance, but less lateral support to resist torque/side-loads. A 50° V edge would have to be compared to a convex with a 50° apex, but of the two the convex would overall be thinner. Convexes, not being limited to a linear geometry, can have more variation in them, though, and so some may be done thinner or thicker while retaining that same edge angle at the apex. When people convex their knives and make them tougher it's because they're not properly accounting for the deflection of their abrasive surface and so are inadvertently just thickening their edge angle. You could do a similar thing by just thickening the apex of a V grind. A straight V grind will thicken continuously, the angle is staying constant. That's kind of what makes it a V instead of a convex or hollow. :)

You and Marcinek are wrong for practical purposes, and here's why: What matters for cutting geometry is blade thickness at the shoulder of the edge: You can put whatever angle you like below that, it is "within" the user's reach in a way the blade thickness is absolutely not... You are using apex angle as a reference point because that leans your way, but apex angle is demonstrably meaningless in technical terms because it is not a fixed and unchangeable characteristic of the edge (for the user), and it is therefore not a solid reference point...

Why on earth would you use a variable reference point when you could have instead a fixed (edge thickness) reference point? Any scientist would laugh at this notion, especially since this is intended as a comparable reference point for determining the practical performance of a tool...

Predictable then as rain follows sunshine, Convex fans will say "but there is no edge shoulder to a full convex edge!": In this deft sleight of hand move, the fact that the corner has been "washed out" is used as an excuse to say the reference point is not visible, and from that it therefore follows that something not clearly marked by a grind line does not exist!

Here on planet earth however, we have a strange high tech tool called "calipers", which we can slide along a convex edge until it gives us a figure equivalent to the desired figure measured at the visible shoulders of the very V edge we wish to compare it to, giving us, as if by miracle, a comparable thickness to be used as a reference line...

A comparable edge thickness is what is the most important, and is the most legitimate comparison point, because it shows how hard material is initially shoved aside... It is doubly significant, on top of performance determination, because, unlike apex angle, it cannot be easily altered by most users, so Convex fans are wrong twice by avoiding it...

When you understand all of the above, you realize that, at comparable edge thicknesses, Convex edges do inevitably feature more metal just behind the apex, which does potentially help a metal deficient in apex stability for a given use (such as many Carbons or, in my experience, several CPM steels). For all other considerations, it is of course inferior in cutting performance (and sharpenability) to a V edge, because the theoretical "drag" of the V's side ridge only affects the dynamics of fluids, and fluids are not what knives cut...

In fact, by reducing the surface of friction to a single point, it is likely the V-edge also reduces friction in splitting tasks etc...

I am also beginning to wonder if today's emphasis on Convex edges is not derived from the inferior apex stability behaviour of today's fashionable steels, Carbons and CPMs, which, in the case of CPMs, have high abrasion resistance, but (from what I could observe) truly abyssal lateral stability at thinner V-edge angles: Stranger things do happen...

Gaston
 
Twingdog is right. You are wrong. Sounds like you need a picture you comprehend this.

To simplify what he said, draw a straight line from the point of the edge to the shoulder (back bevel). This is the only way to measure a consistent edge angle. You can do this for any edge. It should have been obvious that the convex edge has no real edge angle. Therefore, convex has more metal behind the edge.

I'll post a pic if you still don't get it. But basically, whoever thinks a V edge has more metal than a convex edge (at the same sharpening angle obviously) needs to do more research before posting nonsense.

It's already been laid out in very clear terms. Your attitude is unwarranted and contributes nothing to the discussion.

For practical purposes you can easily approximate your edge angle by laying your blade on a flat, hard surface that is able to be cut (such as a piece of wood) and gradually raise the spine until the edge just catches the surface of that material. When your angle of approach is equal to the edge angle, your apex is running dead parallel with the surface and does not cut, but the second it's even the tiniest bit above that angle, the edge will then engage. The reason why having a firm surface is important is to minimize how much deformation the target material has, as that can make it look as though your angle is shallower than it actually is. On something like wood the minute amount of deformation is minimal enough that you can consider the angle at which the edge bites the material to be roughly equivalent to your angle for that side of the blade. :)
 
You and Marcinek are wrong for practical purposes, and here's why: What matters for cutting geometry is blade thickness at the shoulder of the edge: You can put whatever angle you like below that, it is "within" the user's reach in a way the blade thickness is absolutely not... You are using apex angle as a reference point because that leans your way, but apex angle is demonstrably meaningless in technical terms because it is not a fixed and unchangeable characteristic of the edge (for the user), and it is therefore not a solid reference point...

Why on earth would you use a variable reference point when you could have instead a fixed (edge thickness) reference point? Any scientist would laugh at this notion, especially since this is intended as a comparable reference point for determining the practical performance of a tool...

Predictable then as rain follows sunshine, Convex fans will say "but there is no edge shoulder to a full convex edge!": In this deft sleight of hand move, the fact that the corner has been "washed out" is used as an excuse to say the reference point is not visible, and from that it therefore follows that something not clearly marked by a grind line does not exist!

Here on planet earth however, we have a strange high tech tool called "calipers", which we can slide along a convex edge until it gives us a figure equivalent to the desired figure measured at the visible shoulders of the very V edge we wish to compare it to, giving us, as if by miracle, a comparable thickness to be used as a reference line...

A comparable edge thickness is what is the most important, and is the most legitimate comparison point, because it shows how hard material is initially shoved aside... It is doubly significant, on top of performance determination, because, unlike apex angle, it cannot be easily altered by most users, so Convex fans are wrong twice by avoiding it...

When you understand all of the above, you realize that, at comparable edge thicknesses, Convex edges do inevitably feature more metal just behind the apex, which does potentially help a metal deficient in apex stability for a given use (such as many Carbons or, in my experience, several CPM steels). For all other considerations, it is of course inferior in cutting performance (and sharpenability) to a V edge, because the theoretical "drag" of the V's side ridge only affects the dynamics of fluids, and fluids are not what knives cut...

In fact, by reducing the surface of friction to a single point, it is likely the V-edge also reduces friction in splitting tasks etc...

I am also beginning to wonder if today's emphasis on Convex edges is not derived from the inferior apex stability behaviour of today's fashionable steels, Carbons and CPMs, which, in the case of CPMs, have high abrasion resistance, but (from what I could observe) truly abyssal lateral stability at thinner V-edge angles: Stranger things do happen...

Gaston

You make the assertion that the most important factor in cutting is the edge shoulder thickness...that's very much not the case. Again, magnitude of influence on cutting performance decreases the further back you move on the blade. The apex has the very most influence by far, followed by the region immediately behind it, and rapidly trailing off in importance the further back you go. The nice thing about science is that the facts exist independently of individual beliefs. Continue to think whatever you'd like, but reality will continue on, unperturbed. I'd suggest doing a little more research before getting so vindictive. :)
 
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