Mike Stewart: Convexed blades with convexed edges hold an edge much longer!

[Dangerously]

Next thing you'll claim nothing is free.

I remember when quoting TANSTAAFL made one a subversive on the edge of political reform. Now it's practically paleolithic.

 

[Insipid Moniker]

Convex edges are a perfectly normal V edge badly sharpened so that it is duller.

Manufacturers like Bark River Knives get around that by making the edge much thinner...


I can just see archaeologists in the future digging out one of our knives, and saying:

"Yes, despite the rust, you can still plainly see that this example has what was called then a "convex edge", typical of the early 2000 AD period. There was a mystical belief in that period that this type of edge made knives cut better: We never found any drawings of that time, all of them being on electronic support, and so of course long gone (which is what makes this period so fascinating and obscure to us), but we suspect all these drawings showed the convex lines drawn inside the V edge to support and perpetuate this mystical notion..."

Gaston

So you think in the future they're going to forget math and geometry? I'm not quite so nihilistic myself.

 

[Cobalt]

Jerry Hossom
Master Member KnifeNut!
*
06-30-01 05:47.00 - Post#1143

In response to jgtiffany

I think it basically has to do with what you are trying to cut, though this is probably one of the most contentious subjects in knifemaking. Whatever you hear about it, all anyone can offer is an opinion, including me.
If you are cutting wood, convex is hard to beat since it provides its own wedge to help in the cutting. Also, the sides of the blade are generally prevented by that same wedge from rubbing against the material being cut as it penetrates, thereby reducing friction. It produces the heaviest blade, removing the least amount of steel, and is the most difficult to sharpen without equipment.

If you are cutting rope or wood or most anything else for that matter, a flat grind is probably the best all around grind. The edge on a flat grind can be made convex to give you some of the advantages of the convex grind, yet the primary grind itself can be pretty fine allowing for very delicate cutting as well. While the blade is generally heavier than a hollow ground blade it can be lightened with a distal taper (ie tapering towards the point).

The hollow grind can produce the finest edge and is therefore very good for cutting flesh and most non-rigid or softer materials. It can fail utterly in the wood chopping test, because the top of the hollow grind acts like a barrier to any further penetration. Since the center of the blade is hollowed out, the overall blade weight can be the lightest without reducing the thickness of the blade's spine. Hollow ground blades are probably the easiest to sharpen over time, because the blade thickness remains thin even after the primary edge is sharpened away.

Ask most knifemakers and they will tell you that the one they best know how to grind is clearly the best to have. And most have had many years to completely rationalize that opinion...

In Bold. Removes the least amount of steel. So for same size blade is this not saying there is more steel behind the edge?

Hello Minden:
Sorry to take so long to get back on this topic, Shop has beeen full for a few days.
The article comparing the strength of blade grinds appeared in the April issue of Blade, starting on page 34.

I cut six equal lengths of mild steel from the same bar. Then ground part of the bars to various geometries, leaving one without any grinding.
The resullts of this test were as follows:

weight reduction in Torque in foot pounds
blade mass
Control bar .55 pound 0 31
Hollow Grind .35 .20 pounds 8
Flat Grind .40 .15 10
Light Convex Grind .40 .15 22
medium convex grind .45 .10 25

We ground about 1/2 of the bars to represent the blade, the back or "tang"
was left as a 1/4 x 1, each bar was 7 3/4 inches long. We built a jig to attach the torque wrench and placed it at the exact same spot on the tang for each blade. The blades were placed in a bench vice at exactly the same
depth.
The most suprising result was the increased strength of the light convex grind over the flat grind, it doesn't take much convex geometry in a blade to make a big change in the strength.

There is a book "Cats Paws and Catapults" by Steven Vogle that describes why this kind of event is perfectly natural.

I hope this answeres your question.
Thanks and Take Care

The stuff I wrote did not come into the reply as I wrote it, The first number you read is the weight of the bar, second number the reduction in blade mass and the third number the required foot pounds to flex the blade to 90 degrees. Hope this makes it a little more undestandable.

And this explains it further. The convex blade grind left more metal all the way through, giving more lateral bend strength than either flat or hollow. This has been my point. I guess for the same edge angle the above would not apply, but when you make a blade out of a bar of steel, the convex blade should have more metal.

 

[Cobalt]

I think it is my way of thinking it. In my example, I am taking two knives or even three. All the same overall dimensions. So my angle would in fact be different but the blades would be the same size. Chiral grolim explained it well in this thread here is his post:

http://www.bladeforums.com/forums/s...ck-vs-thin-comparison?p=11852440#post11852440

this is also a pretty good explanation

There are a couple of important reasons why this is inaccurate.

1) the image you present is a false representation. The left image suggests that material can be added to the edge by abrasion, a physically impossible absurdity that needn't even be mentioned. The image should instead show the reality in which the apex is brought back. The right image is ALSO misleading because it implies THREE false things: a) that the bevels are being sharpened at the same angle of incidence (or held angle) - they are NOT; b) that the presented convex and flat grind apex angles are identical - they are NOT; and c) that the geometries of these bevels correspond as similar - they do NOT. The flat bevel which corresponds to the green convex bevel would be drawn from apex to bevel shoulder (the blue dot). Draw that bevel and tell me which is thinner.

I went into this in another thread, but i will resubmit my explanations here.



Cross-section (A) shows convex- (violet) and flat-ground (gray) bevels with corresponding (i.e. similar) geometries = equal height and shoulder width. One can imagine each profile being ground from identical billets. Note which profile leaves more metal behind the edge.

Cross-section (B) demonstrates how one would grind a comparable convex bevel (violet) out of an original flat-grind (pink). Again, the gray represents reducing the convex bevel back to flat while matching the geometry (height and thickness) of the original (pink) bevel. The gray and pink profiles are identical, the violet profile is comparable... and it is thicker than the gray profile from apex to shoulder, requires less removal of material from the original pink profile.

Cross-section (C) shows the original convex grind (white, violet-outline), reduction to flat-grind (pink), and further reduction to a thinner convex grind (violet). The violet edge is indeed thinner than the pink at the pink shoulder. However, 1) from apex until the orange line denoting tangential separation (~1/2 the height of the pink bevel), the violet convex grind is STILL thicker than the pink flat-grind (pushing the apex of the violet grind to match the pink would obviate this fact), and 2) the pink and violet bevels do not have similar geometries - the pink is as different from the violet as it is from the gray. As before, the true comparison is between the violet and the gray - bevels of equal height and shoulder thickness. If the pink and violet shoulders where at the same height, the entire violet blade would be thinner as well (assuming the same primary bevel angle and total blade height)!

The crux of the confusion about supposed "thinner" convex grinds is the angle being measured, or rather NOT measured.



In practice (sharpening, and other practices as well, like aerodynamics), the angle being measured is the "held angle" or "angle of incidence" between hone surface (flat gray in the above diagram) and spine-center (red line).
NOTE: If this is NOT the angle you are using to grind your bevel, then you are very likely not using ANY angle measurement at all but instead merely extrapolating after-the-fact. For example, the violet-line in the diagram is presumed tangential to the precise apex-angle of the green convex... but the precise apex-angle of the green convex cannot be measured without precision instruments or precise knowledge of the geometry of the curve(s) at the point of bevel intersection (the true apical angle of incidence of a curved shape). Such measurements are unnecessary for the purpose of this discussion as the measured apex and tangent bevel do not produce a triangle of similar geometry beyond an infinitesimally short shoulder height (i.e. at the point of bevel intersection).

Sharpening angle is measured by width of the blade and distance from spine-center to hone. Draw a chord perpendicular to the hone surface that meets the spine-center line to form a triangle. This triangle is geometrically "similar" to the smaller triangle formed by drawing a chord perpendicular to spine-center that intersects the bevel shoulder (light blue triangle). These triangles are similar because their dimensions are directly proportional, their angles equal - these triangles even share an apex!
Altering the shape of the triangle by increasing or decreasing the height of the bevel along the spine-center WITHOUT a proportional change in shoulder thickness (which necessarily changes the angle of incidence) produces NON-similar triangles. Insistence on correlating non-similar geometric shapes produces this idea of "thinner" convex grinds that contradict geometric and mathematical definitions.

To be clear, the definition of "convex" is as follows: curved or rounded outward; (math) a continuous function with the property that a line joining any two points on its graph lies on or above the graph; from Latin convexus = carried out/away from.
"Convex" is defined as away from flat, an alteration of shape that can ONLY be accomplished by an increase in angle, i.e. more obtuse, to a form which lies outside or above the corresponding flat plane. To make a convex bevel thinner than a flat bevel, one MUST change the angle of incidence, but the result is still thicker than the flat bevel ground at that new angle and it is the flat bevel at that angle which informs the use of the term "convex" to describe the rounded out bevel. Again, "out". "Out" from what? "Convex" is defined as out from the correlated flat. "Out" cannot be "in" at the same time in the same context. If your convex is thinner than your flat grind, then they were produced at different angles of incidence and do not correlate. You might as well correlate a thinner flat grind with a thicker one and then state: "Look, this one is thinner!" Of course it is thinner, you sharpened it at a lower angle.

However, you can alter the shape of the bevel without changing the angle of incidence, shoulder width, or bevel height by using a curved or flexible hone instead of a solid hone. How much the shape is altered is controlled by the amount of deformation and curvature (again, away from flat) of the hone. The result is a thicker bevel, one with more metal that it would have if ground flat at the same angle of incidence. Returning to the first diagram (C), the convex apex (violet) will always be more obtuse than the correlated flat apex (gray), which is the entire point (pun intended) - a more robust edge for a given bevel height & thickness. One CANNOT thin from a flat bevel to a convex bevel without widening the bevel, i.e. establishing an entirely different bevel. Conversely, one CAN thin from a convex edge to a flat-edge while maintaining the same bevel dimensions, reducing the apex angle.


In practice, if you want a thinner edge, widen the bevel - lowering the spine-to-hone distance accomplishes this (creating a lower apex-angle). If you want a more robust edge, EITHER reduce the bevel height (raising the spine-to-hone distance to a more obtuse sharpening angle) OR use a flexible hone to sharpen convex and maintain the same bevel height (same spine-to-hone distance).

 

[FortyTwoBlades]

from: https://www.easycalculation.com/analytical/learn-angle-between-two-curves.php

There are plenty of youtube videos and sites explaining how to calculate the angle of intersection between two curves.

CATRA site shows that if the angle is equal, the convex edge has less material than the V edge.

http://www.catra.org/pages/products/kniveslevel1/faq.htm.

Yup. This. And yet it won't convince anyone who chooses to willfully ignore it despite how easy it is to verify the truth of this without even needing to do any calculation.

 

[Revolverrodger]

The two curves that form a convex grind meet at a point. The angle formed by the tangents to the curves at that point is the angle between the curves. More basic geometry.

Lol... it is a single curve.... no angle

 

[Jens Schuetz]

Convex =duller?
I've got a few thick knives which are good choppers and shaved with their V edge but where horrible at cutting vegetables. They just broke through instead if cutting requiring a lot of effort.

Then I "convexed" them knocking or the shoulders and things improved drastically.

Less material makes it thinner and improves cutting while keeping the apex angle the same.
Thus you actually get a blade which cuts better and stays robust because you are not sacrificing too much steel arround apex.

 

[Cobalt]

Lol... it is a single curve.... no angle

lol....Yeah, he is right. I was thinking he was talking the transition curves not where they intersect at the tip. My bad. He is also right about there being more metal if you turn a v-grind into a convex. And I understand that. But as I posted above if you grind from a flat bar stock, there should be more metal left with a convex grind. The numbers in weight and lateral strength show that from Ed Fowlers post above.

 

[Hevy Devy]

Lol... it is a single curve.... no angle

So your 'convex edge' looks like this then..

Would make a great slicer I suspect..

 

[trevitrace]

Lol... it is a single curve.... no angle

Lol... right... curve... no cut

 

[marcinek]

Convex edges are a perfectly normal V edge badly sharpened so that it is duller.

By far, head over heels, no contest, that is the most nonsensical claim made in this thread.

"Sharp" has to do with edge refinement only. What do you do when you sharpen? You refine the edge.

Flat, convex, hollow has nothing to do with sharpness at all.

 

[arty]

A convex edge works well for selected applications:
An Axe edge - chopping
Kukri
And a Western Deba - a heavy chef's knife designed to cut through tough stuff in the kitchen, like quartering chickens, slicing through the shells of lobster tails, etc. Mine came with a heavy convex edge.
For everything else, I like a normal V edge.

 

[marcinek]

Lol... it is a single curve.... no angle

No it isn't. A single curved is a dulled edge. When you sharpen, you "unround" the edge and put a point on it, by forming two curves that meet at a point.

(Or straight lines, but they are just curves whose tangents have the same slope at each point on them.)

Again, as I posted before even the Bark River Collectors Assn says that a convex edge is not one rounded curve...

http://brkca.com/convex.htm

Press too hard and the abrasive will actually be coming back up in the wake of the blade and remove the edge, dulling the knife rather than sharpening it.

 

[marcinek]

So your 'convex edge' looks like this then..

Would make a great slicer I suspect..

And to do that you would have to hold the knife perpendicular to the abrasive surface when sharpening/creating it. Do any of you "one curve theorists" do that?

The spine of the knife is lifted slightly from the paper until the edge is contacting the paper; usually this is about a 13° angle.

 

[bob7]

Conman Conveniently Converses about Convex Edges

 

[Fanglekai]

Lol... it is a single curve.... no angle

No. This is wrong. See my above post.

 

[shqxk]

Technically, more metal behind edge bevel will resist major deformation better but not always translate into better edge holding since the thicker edge will require more force to make the cut and excessive force when cutting may lead to higher lateral stress and resulting in losing very edge faster.

 

[me2]

this is also a pretty good explanation

Jerry and Ed could both be right or wrong. Without some cross sectional measurements is not possible to compare knives from different makers. I have never used a strider knife, but it doesn't take too much to imagine their hollow grinds removing less material than one of Ed's light convex grinds. It could also be stronger for that reason. What is the stock thickness and width? What is the primary grind angle/wheel diameter/radius of curvature of the primary grind for flat/hollow/convex grind? How thick is the edge left prior to sharpening? These are questions that will tell you which will be thicker/stronger/heavier.

 

[Jason B.]

Convex edge threads are funny.

Convex edges are THINNER for the given apex angle than a V edge of the same APEX angle. End of story.

Convex edges are not stronger but they do have superior cutting geometry. They SEEM stronger because they have less drag/resistance while cutting which translates to less force exerted on the edge apex and less edge damage.

Full convex blades are stronger because they are two or three times as thick as normal blades. So, in these cases there really IS more metal behind the edge BUT! It becomes a completely unfair comparison at that point.

 

[Jason B.]

Double post