What Are The Advantages of a Convex Grind?

For all the convex edges that show they're thicker, its not note worthy that a blade with a higher edge or apex angle has more metal.
 
*Puts pinky finger up in the air while sipping tea from nice China*
Well actually, where the rhombus meets the integral on the "Z" plane in quadrant 2...
:D:D:D
 
Twindog said:
There has been no "common math" showing the convex edges have angles. The only math was for intersecting tangents. But tangents are straight lines, not curved lines, so they don't represent a convex edge. If you balance a yard stick on a beach ball, the yard stick is a tangent. The beach ball has an infinite number of tangents, all of them are straight lines and many of them will intersect at some point to form an angle. But that doesn't mean the beach ball has an angle.

I haven't tried your method to approximate a comparison of a V edge to a convex edge, so I don't know how well it works.

But the more shallow the curve of a convex edge -- meaning the more it approximates a V edge -- the better your system is likely to work. In fact, most convex edges are so close to a V edge that there is not much difference between them.

The more aggressive the curve of a convex edge -- meaning the curved sides are arcs with a very short radius --the more poorly your system will work.
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The beach ball doesn't have an angle, but the convex edge does because it's the intersection of two arcs.

The more aggressive the curve, the thicker its edge angle. You literally cannot cut something if the edge apex isn't contacting the target material. For it to bite in, your angle of approach has to be any angle greater than the edge bevel. When your angle of approach is exactly equal to your edge bevel, the bevel is running totally parallel with the target surface. Any lower and it's pointed up and away from it. Any higher and the edge will actually engage with the material and cut. However, targets can deform or yield under pressure, which causes the material to realign itself with the edge at a more obtuse angle, meaning that an angle of approach that wouldn't cut wood might cut rubber because the rubber deforms under the pressure of the bevel (not edge) until it's meeting the edge and then becomes cut. Hence why using a rigid surface is useful in angle approximation and low pressure should be used.
 
sharp_edge said:
A convex egde could have more or less materail than a V edge or even equal material, all depending what you are comparing. See the diagram below (sorry about my hand drawing).

Lets say for the same blade, (1) if we want the primary grind to be the same, which is Case B, then a convex edge will have more material, whereas (2) if we want the angle at the blade tip (apex) to be the same, which is Case A, a convex edge will have less material.

The argument throughout this thread is like saying "A's daddy is stronger than B's daddy" for which A is comparing his daddy in the age of 20 with B's daddy in the age of 60 while B is comparing his daddy in the age of 20 with A's daddy in 60.

20170521_154919_zps5k74c8yf.jpg
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I really don't see why this is hard for some to grasp.
 
I've found a fun way to read these convex grind arguments; page through fast reading snipits from each. Beach ball on the Z plane etc.

I used to argue for non convex.
Now I just shallow out the edge angle until the edge starts to break down, go a bit more obtuse until the edge holds up and . . . OK you win . . . round over the transition between main bevel and edge angle.

I still do not like micro bevels though if I can help it.
 
No, I don't think that is how sharpness works...

You don't round off anything, because that induces inconsistencies, and inconsistencies make apex touch ups laborious: Instead of just one instant swipe that hits all of the apex all the way through in one pass, you have to go over and over... Even the flattest hand-applied V edge will still be slightly rounded, and roundness is precisely what you want to minimize to hit the apex everywhere easily in one pass (upon touch up)... A convex edge just means you have to open more grossly the touch up angle to insure this apex contact happens all the way... (When this gets really bad, convex fans then proudly resort to stropping...)

The first sign of weakness of a really sharp edge is usually not "edge breakdown", but micro-folding: Most do not look hard for it with nail rubbing (wrongly), but micro-folding should be minimal and tend to wear off with further use, not get more pronounced... Readily visible apex breakdown (excluding of course the narrowly focused impact of tiny and hard impurities) means that the edge is either quite open (dull), which will tend to concentrate the damage on the apex(!), or that the steel is poor... Visible parts of the edge breaking off is not what I consider normal...

You try not to let the knife dictate to you what sharpness it can take: If you don't have a minimum standard that at least half your knives fail (no matter how expensive), then you don't know which half of your knives is the better half...

Gaston
 
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First off, I want to say that Marinek's math is absolutely spot on, and anyone who at least paid attention in high school should see that plainly.

Gaston444 said:
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 behavior 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
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But here I want to reply to two things...first "because the theoretical "drag" of the V's side ridge only affects the dynamics of fluids, and fluids are not what knives cut..."

In a way you've got this backwards....if we were talking about cutting through fluids than the material would be in contact with the blade all the way to the spine and friction at the cutting edge would not be that important. Since we are cutting through solids what's important is that convex edges push said material away from the blade thus reducing friction after cutting AND the slope from edge to body is softer on convex knifes so even if you were talking about cutting through water(unless this is magic weightless water) the resistance from friction would be less from the gradual slope....there's a reason boats and canoes aren't headed by triangles.

So a FG or beveled grind stays in contact with the material longer, the longer said material pushes against the knife the more friction and thus resistance it creates. This is more important for some materials, often much more, than others. If we were cutting trough liquid the liquid would stay in contact with the entirety of the blade through the entire cut...and even in such a case the grind with the steepest angle to the body of the blade would create the most resistance.

Along that same line of thinking, unless the material you are cutting is about the thickness of a human hair, an extremely soft material, or filled with a resistance free material AND the blade is completely indestructable/undullable then the apex angle and cutting edge isn't the most important thing. Sharpness != less cutting resistance, and how a knife will perform in the week/month after sharpening it is more important than how it performs in the few minutes after.

BUT, what you were saying at the end is spot on. The alloy of the knife determines what grinds will work best for it, assuming the intended uses are the same...and even then convex grinds can work will for just about everything while other grinds may only perform them for certain tasks and even then it only makes sense with the proper alloy...or else it may only outperform a convex grind for a very short length of time.

There aren't that many cases where a flat/concave grind will outperform a convex grind over time, and in then they will only do with with certain(often expensive) alloys and those alloys come with drawbacks such as less corrosion resistance, difficult to sharpen, or prone to chipping.

Convex grinds are plenty sharp if done right, will stay sharp, extremely durable and low maintenance, have less resistance after the initial cut, are suitable for any alloy knife, and work well for a wide variety of tasks. They are the jack of all trades...sure there are certain times where a flat/convex grind will outperform convex grinds on silly benchmarks right after sharpening...but but for practical use and wide range of suitability they can not be beat.
 
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