Convex grinds

[TLoFP]

Convex edges have less steel behind them but are still tougher.

Toughness is not simply about the amount of steel. To assert this is to over-simplify the dynamics in play as the blade moves through the medium being cut.

A convex edge has stability for the same reason that a stone arch has stability.

https://www.youtube.com/watch?v=XA5AM2Lb0iY


I also reject the assertion that we should only consider edges with the same exact apex angle.

My contention is that a convex edge cuts just as well as a v edge, even if the apex angle (as measured by tangents) of hte convex edge is wider. The absolute apex only matters for a very short time during the cut and slicing has as much or more to do with what is happening at the shoulder of the edge, or just behind it. Putting this another way, I think the angle to compare to is the shoulder angle, not the apex angle.

Compare the following:
1) Pure 17 DPS v-edge
2) Angular compound edge with 17 DPS back bevel and 20 DPS apex
3) Convex edge with effective 17 DPS final back bevel and 20 DPS apex

My contention/experience is that the latter will slice just as well as the first due to the 17 DPS back bevel while being stronger due to the rounded and wider cutting apex.

FWIW, a slight bend in a Lansky rod will reliably produce a 20/17 convex edge.

WoW. I don't think it can be said better. You just added a really important point. I hope this gets laid to rest with your post.

- T

 

[REK Knives]

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EDIT: Note: convex edges do not and cannot have more steel behind the edge. It's not physically possible without changing the apex to make it more obtuse.

This is THE issue... But the problem is that twindog doesn't want to admit that convex apexes do have angles.

 

[mainaman]

This is THE issue... But the problem is that twindog doesn't want to admit that convex apexes do have angles.

Just draw two tangent lines on the each side of the apex and that is the apex angle. If some people do not understand geometry that is their problem.

 

[Twindog]

Just draw two tangent lines on the each side of the apex and that is the apex angle. If some people do not understand geometry that is their problem.

The angle that is measured is the angle of the tangents, which are two straight lines that share a vertex. You can get multiple tangents along the entire length of a convex edge. The angle of intersecting tangents is much greater near the apex of the convex edge than it is further up the edge. Which tangent intersections are you going to use?

You can't compare the angle of intersecting tangents on a convex edge to the edge angle on a V edge -- that is apples and oranges. It's an unfair comparison, which is why the posted drawing of a relatively normal convex edge is compared to a wildly obtuse 90-degree inclusive V edge. Basically, you're comparing a convex edge to a hammer.

 

[pinnah]

The closer to the edge you get the greater the order of magnitude of influence the geometry has on cutting performance, so actually while the shoulder has a strong influence on performance due to its proximity to the edge, it has FAR less influence than the form of the very apex itself. Like really truly massive amounts less. Also, unless I'm way off base here, the comparison to an arched bridge isn't appropriate because of the direction of loading. Using the bridge analogy, the loads being experienced during cutting would actually be squeezing the bridge like an accordion, where it's not going to be as strong as it would be when resisting forces directly on top of the arch.

You're right. I shouldn't have compared this to an arched bridge. Bad mistake on my part.

This said, we that the action is at the apex but we end up with different conclusions.

If all that mattered was pure slicing in material that never ever produced any lateral stress on the edge, then yes, a pure 'V' apex wins.

But in material and in cutting situations that produce lateral stress on the blade then edge performance is a bigger issue than just cutting performance. One also needs edge stability - the ability to resist chipping or folding.

Two things....

1) I find a 17/20 convex to be a winning compromise compared to either a 20 DPS or 17 DPS 'V' edge. It out slices a 20 DPS V edge (same apex but thinner shoulder) and is more durable than a pure 17 DPS V (less rolling).

2) In mediums like wood and in applicatichons like whittling and carving where I'm constantly adjusting the angle of the cut, I find that pure V edges dig in and resist angle adjustments. This is because the sharp pointed apex of the 'V' is out there in the medium fully engaged. With a convexed edge, the medium is slightly wedged open due to the convexed shoulder, thus relieving the pressure on the apex. My sense is that this allows a convexed edge to be corrected for cutting angle during the cut more easily. Sharpening a blade from a plane is one thing. The plane will hold the edge with no movement and a pure chisel apex (essentially a 'V') will work because the edge angle never changes. Carving wood by hand though is entirely different. I'm constantly adjusting the angle of attack and this is much easier with a convexed edge than a pure V edge.

So yes, what heppens at the apex matters. Depends on what you're cutting. When cutting stuff on cutting boards or when working with wood, I find a convex edge much more durable than a pure V edge with very minimal loss of pure slicing abiilty. Well worth that trade-off for me. YMMV obviously.

 

[ToddS]

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EDIT: Note: convex edges do not and cannot have more steel behind the edge. It's not physically possible without changing the apex to make it more obtuse.

This is THE issue... But the problem is that twindog doesn't want to admit that convex apexes do have angles.

Depends on whether you are considering a bevel that has actually been convexed, or the trivial case of knocking the shoulders off of a V-bevel. If you convex an edge, the apex angle will increase and there will be more metal behind the apex. The images I posted earlier show this.

 

[B34NS]

I got what you meant pinnah, and agree with 42, that's why I went with the axe analogy as it's just a little more of an exaggerated model.

With chef's knives in my experience convex edges have been more or less used for protiens in butchery, whereas flat/"v" grinds excel at slicing through fibrous vegetables. More to the effect there just isn't one perfect grind that does it all.

 

[marcinek]

This drawing shows three convex edges overlaid on a V edge.

Yes. And all three of your convex edges have a more obtuse edge angle than the vee. Thank you for once again giving a picture that illustrates my point so well.

 

[marcinek]

The angle that is measured is the angle of the tangents, which are two straight lines that share a vertex. You can get multiple tangents along the entire length of a convex edge. The angle of intersecting tangents is much greater near the apex of the convex edge than it is further up the edge. Which tangent intersections are you going to use? .

The ones for each edge at the point where they meet.

 

[marcinek]

Just draw two tangent lines on the each side of the apex and that is the apex angle. If some people do not understand geometry that is their problem.

Thank you.

 

[marcinek]

There are pretty close approximations of the tangents to each of the curves in your picture.

 

[B34NS]

There are pretty close approximations of the tangents to each of the curves in your picture.

Great way to show it!:thumbup: In design we use this all the time making vector graphics we refer to them as Bézier curves

 

[marcinek]

That's just misinformation, plain and simple.

"The angle between two curves at a point where they intersect is defined as the angle between their tangent lines at that point." - wiki

The one thing you guys have to stop arguing about is the fact that any two intersecting curves define an angle at the point of intersection.

I'd love to be able to stop arguing about that, my friend. But people aren't following the point.

Its like that stupid black/blue vs white/gold dress thing. Though its not about perception. Its about fact. It's like trying to convince someone that 12 inches makes up a foot.

I really need to walk away.

 

[Shotgun]

Which tangent intersections are you going to use?

The greatest one which is at the apex. All the other angles drawn from the other tangents will be less than the one at the apex because the arcs slope in toward themselves.


If you're not satisfied with that you can step it up to calculus and use all of them if you wish.

 

[Twindog]

There are pretty close approximations of the tangents to each of the curves in your picture.

Those are all tangents taken from the apex, but those angles of intersecting tangents will be different for each point on the convex edge.

Look at your red tangent -- that would be the left side of a V edge that you would compare that convex edge to. So you would be comparing that outside convex edge to a V edge with roughly a 120-degree inclusive angle. Of course the convex edge will have less metal behind the apex than a huge 120-degree V edge.

It's a crazy comparison because you're comparing apples and oranges. The angle of intersection of tangents at the apex of a convex edge cannot be fairly compared to a V edge, which is measured as an angle. You're taking the most obtuse part of the convex edge -- ignoring the more acute parts of the convex edge -- and trying to compare it to a V edge that has constant acuity.

 

[marcinek]

Those are all tangents taken from the apex, but those angles of intersecting tangents will be different for each point on the convex edge.

You measure the edge angle at the point where the edges meet...at the point.

Show me a picture of how you measure the edge angle of a vee grind, please.

 

[marcinek]

So...by your argument, all of the convex edges you drew have the same edge angle, correct?

 

[marcinek]

I'm walking away.

Enjoy your weekend. Don't drink and drive! Good night!

 

[chiral.grolim]

I apologize for not having read through the entire thread, just wanted to throw in a couple more of ToddS's beautiful images from scienceofsharp.

The angle at the apex is always 90-dps, the apex has radius regardless of being sharpened flat or convex or hollow. Here are a couple of images, note the scale:

Do you see how the apex rounds over? What is the apex angle? Well, it depends on how close to the apex you choose to make your measurements, but a tangent-line that doesn't cut into the bevel at any other point can only be made at the very tip were it would be essentially flat, i.e. 90-dps. Are people seriously suggesting that "convex" is thinner than "flat" because the corresponding "flat" is supposed to be the tangent of the apex?? This is NOT a valid way of establishing the angle of a convex edge.

Here is a cut-away cross-section of that same edge but from a bit further back (lower magnification, again note the scale):

Now what is the bevel angle of the blade edge? You can see that the very last 500nm of bevel round-over at the apex (convex), but everything behind that is much more acute AND of much greater relevance to the cutting to which this blade will be subjected, i.e. shaving hairs some 3000nm thick. Understand that "apex angle" is not really relevant nor can it be measured accurately except through such intensive means as ToddS has taken with these images. What IS relevant is the thickness of that last 500nm (is it thin enough to penetrate) and the angle behind it (where the metal acts as a wedge and incurs friction/tugging during the cut).

"Convex" is a word meaning "curved or rounded outward; 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," i.e. the term corresponds to flat geometry beneath it, i.e. a thinner bevel, from which it is rounded outward. When comparing the angle/thickness of a convex bevel to a flat bevel, you must establish the vertices for the angle vectors, and those straight (flat) vectors will always lay beneath (thinner, more acute) the convex curve to which they correspond. Here is another ToddS image where he measures bevel-angle from the apex to a height of 3 microns:

And i see that some posters still bring up the tired line that, "you can't add metal back to the edge!" Of course you cannot, but you can remove less metal from the edge via convex-grinding at the same angle of incidence using a soft-backing (i.e. leaving more metal behind the edge) vs. removing more metal via flat-grinding at that angle of incidence to produce a bevel of equal height and equal base-width but with less material behind the edge.

 

[REK Knives]

. Of course the convex edge will have less metal behind the apex than a huge 120-degree V edge.

It's a crazy comparison because you're comparing apples and oranges. The angle of intersection of tangents at the apex of a convex edge cannot be fairly compared to a V edge, which is measured as an angle. You're taking the most obtuse part of the convex edge -- ignoring the more acute parts of the convex edge -- and trying to compare it to a V edge that has constant acuity.

Aaaaand he sees the light! Lol

That's exactly what we have been doing the whole time... Measuring the APEX angle. This is why a convex edge always has less metal behind the apex IF THE APEX ANGLES ARE THE SAME 😊