Convex edges and the Wicked Edge

[HeavyHanded]

Hi,
Because that is a thinner shoulder,
thinner than the blue convex
and thinner than the black V-edge
the blue and black are same height, and begin at same width (thickness),
the red convex is much much taller,
If you want to compare the red convex to a v-edge,
you'd have to draw a new one,
one with the same height, example
the green square is the metal you begin with,
the width/height,
convex will always be fatter than v-edge given same starting square

I think the red absolutely belongs, but I guess it all depends on one's definition. If you make a V edge with same shoulders as the red convex, it no longer has the same terminal edge angle.

Based on the argument that the red convex cannot be compared to the original black V bevel due to differences in shoulder height, the new black V bevel cannot be compared to the red convex for differences in final edge angle.

Of edges with the same terminal angle, the convex always has less mass behind the edge.

Without defining the criteria it is not possible to have a conversation on this topic.

This is how CATRA defines it:

Yes the gothic arch edge does have less material behind the edge than both concave and flat ground edge bevels.

The CATRASHARP model has this type of wheel as standard and is 32° at the edge and 30° at 1mm back from the edge.

On a related note, I do convex edges on a 10" wet wheel by having a forward and back stop on the blade clamp. As it slides fore and aft on the tool rest the wheel can cut an arc of known stop and start values. If the amount of play is restricted enough one can cut a dead flat bevel instead of micro concave.

 

[Chris "Anagarika"]

Martin,

Agree. Putting it in different way:

If one has a V, he can convex it, making it thinner by rounding the back bevel and shoulder and not changing the final apex angle. It reduces drag and usually (depends how much being ground off) doesn't significantly reduce the support/strength.
This is the first black to red.

Or,
He can also convex it by making the apex more obtuse, by making not so micro of microbevel and blend the shoulder of this new more obtuse bevel with the original.

If one has a convex and want to make it V, it usually will end up thinner and has more acute angle.
This is the blue to first black from outmost on the diagram.

Changing from V to convex and back to V again is simply wearing away material. Imagine abrading part of a ball flat and then trying to make it round again.

 

[bucketstove]

I think the red absolutely belongs, but I guess it all depends on one's definition. If you make a V edge with same shoulders as the red convex, it no longer has the same terminal edge angle.

Based on the argument that the red convex cannot be compared to the original black V bevel due to differences in shoulder height, the new black V bevel cannot be compared to the red convex for differences in final edge angle.

Of edges with the same terminal angle, the convex always has less mass behind the edge.

Without defining the criteria it is not possible to have a conversation on this topic.

This is how CATRA defines it:..

Hi,
Yeah, of course it belongs on the image as an example of appples and oranges comparison
All it takes to match the angles to add a microbevel a truly "micro" bevel unlike the exaggerated one in this image

Catra is marketing , comparing to some of their competition, commercial single-stage pull through sharpening machines

 

[HeavyHanded]

Ahhh, now that's nice and snug - thin blue line is new convex with same terminal angle as previous yet even more thin behind the edge.

Anywhere you have an area bounded by straight lines intersecting to form an angle, you can join them with an arc and reduce the surface area. It doesn't matter what scale. This holds true right up until the two intersecting lines become a straight line.


Apples/oranges or potāto/potăto...

 

[cbwx34]

But you do realize drawing it inside the V-Edge is not an informative comparison?

Gaston

It's a comparison based on the edge angle, it's not just "drawing it inside the V-Edge". So, it is an "informative comparison".

I wish that eventually users would understand the red lines don't belong in that diagram...

Comparing the red lines and the black lines is pretty much like comparing a folder to a fixed blade, and pronouncing the folder superior in sharpness...

I had a knife professionally converted from the black lines to the red lines, a full height convex, and the 0-1 steel chipped and crumbled with astonishing ease... Even in its thinner condition, it did not really cut as spectacularly as its thinness would imply, because the initial apex aggressivity is always poorer on a convex...

Great for chopping free-hanging manila rope though...

Gaston

Again, it's a valid comparison based on the edge angles. Your example of how the convex edge performed has so many variables... it would be difficult to form a meaningful conclusion. (Also, the red lines are not a "full height convex".)

Hi,
Because that is a thinner shoulder,
thinner than the blue convex
and thinner than the black V-edge
the blue and black are same height, and begin at same width (thickness),
the red convex is much much taller,
If you want to compare the red convex to a v-edge,
you'd have to draw a new one,
one with the same height, example
the green square is the metal you begin with,
the width/height,
convex will always be fatter than v-edge given same starting square

Nice diagram (did you draw the original that I posted?), but it changes the comparison. The original compared the angle of the edge, you're now comparing the height of the bevel.

Hi,
Yeah, of course it belongs on the image as an example of appples and oranges comparison
All it takes to match the angles to add a microbevel a truly "micro" bevel unlike the exaggerated one in this image

Changing parameters no longer makes the comparison valid. That becomes an "apples and oranges comparison".

Personally, I think it's better to simply understand the relationship between 'V' or 'flat' edges vs. convex edges, then it is to try and compare the parameters... (I'm betting if an actual study was done without bias and controlling the various variables, there would be little actual difference in use... especially on most EDC blades). For example, knowing that if I sharpen a knife at an approx. 20° convex angle, and want to maintain it with a Sharpmaker, how would the two match up?

 

[HeavyHanded]

Personally, I think it's better to simply understand the relationship between 'V' or 'flat' edges vs. convex edges, then it is to try and compare the parameters... (I'm betting if an actual study was done without bias and controlling the various variables, there would be little actual difference in use... especially on most EDC blades). For example, knowing that if I sharpen a knife at an approx. 20° convex angle, and want to maintain it with a Sharpmaker, how would the two match up?

My 2¢, if one were to do a rigorous study they'd likely find that once the difference in degrees between the primary and cutting bevel falls below a certain threshold the differences between a convex and V bevel would be nil or within the margin of error of whatever cut test one has devised.

Only where there is a pronounced angle change and projecting shoulder will you see a real difference, or possibly when cutting very specific materials.

Now that my wet wheel is set to do larger blades I should use it on a machete and compare to my convexed varieties. I actually have a pair of Tram 14" bolos I could do this with...if I were more interested...

 

[bucketstove]

Nice diagram (did you draw the original that I posted?), but it changes the comparison. The original compared the angle of the edge, you're now comparing the height of the bevel.
Changing parameters no longer makes the comparison valid. That becomes an "apples and oranges comparison".

Hi,
I copy/edit the original image posted in this thread
to point out the critical issue
of the starting point/box/rectangle/square
not being equivalent

The original red convex
already changed the critical parameter (width/thickness)
thus invalidating the comparison between convex/vedge.

Comparing the red convex , a thinner edge,
to a thicker edge (either black convex, or v-edge ),
is unfair comparison for deciding if convex
has performance advantage over v-edge,
thinner edge is always thinner than thicker edge.

The important difference is that it is thinner,
not that it is convex.
Both thinner convex and thicker convex are convex,
the thinner one will have performance advantage over thicker one

Yeah, you can always draw a thinner convex inside a v-edge,
but then its a thinner convex, not equivalent starting point,
you can just as easily draw a thinner v-edge inside that ,
keep changing starting point to infinity and beyond...


Which is easier to dunk in water? Easier to push through water ?
A 12 inch box or 6 inch ball?
A 12 inch ball or 6 inch ball?
A 12 inch ball or a 6 inch box?

Smaller has advantage right? Less water to move out of the way, basic geometry

 

[cbwx34]

Hi,
I copy/edit the original image posted in this thread
to point out the critical issue
of the starting point/box/rectangle/square
not being equivalent

The original red convex
already changed the critical parameter (width/thickness)
thus invalidating the comparison between convex/vedge.

Comparing the red convex , a thinner edge,
to a thicker edge (either black convex, or v-edge ),
is unfair comparison for deciding if convex
has performance advantage over v-edge,
thinner edge is always thinner than thicker edge.

The important difference is that it is thinner,
not that it is convex.
Both thinner convex and thicker convex are convex,
the thinner one will have performance advantage over thicker one

Yeah, you can always draw a thinner convex inside a v-edge,
but then its a thinner convex, not equivalent starting point,
you can just as easily draw a thinner v-edge inside that ,
keep changing starting point to infinity and beyond...


Which is easier to dunk in water? Easier to push through water ?
A 12 inch box or 6 inch ball?
A 12 inch ball or 6 inch ball?
A 12 inch ball or a 6 inch box?

Smaller has advantage right? Less water to move out of the way, basic geometry

It's not 'invalidating the comparison'... that is the comparison. Given an edge sharpened at the same (approx.) angle... this is what the comparison is: (convex is thinner, larger bevel, etc.).

If you want to say 'Given an edge sharpened at the same bevel height', which is what your box shows, then you have a new comparison: (flat grind is thinner, etc.)

It doesn't invalidate the comparison just because one or the other is 'thinner'... otherwise both would be invalid. It's simply a comparison based on a given parameter. In the case of the red line, it's the angle sharpened at. You could make a third comparison... What would the differences be, if both types were as close as possible to the same thickness?... and you'd have a new set of differences.

 

[bgentry]

Isn't this all a bit pointless to try to compare? Convex and V are two different shapes with two different performance characteristics.

The main performance difference between Convex and V is that Convex has a rounded transition to the next part of the blade grind. In other words, the "corner" between edge bevel and blade has been smoothed out. So a convex will (mostly) cut more easily due to less drag in that area.

But again, they are DIFFERENT. You can't compare them unless you really nail down exactly what you are trying to compare. Do you want the same bevel height? Or the same width at the top of the bevel? These are two different things and you can't have both with these two different shapes. Do you want to compare mass in the bevel area?

What about actual cutting comparisons? You can see how this quickly gets way too complicated to make any kind of simple comparisons.

So I'm going to say this:

Convex edges have a rounded shape that reduces drag. Convex edges promote the person grinding to make the overall edge thinner due to the geometry. I.E., making the bevel height larger in order to produce the same terminal angle. This is why they are perceived as having higher performance. I think it's as simple as that.

Brian.

 

[cbwx34]

Isn't this all a bit pointless to try to compare? Convex and V are two different shapes with two different performance characteristics.

The main performance difference between Convex and V is that Convex has a rounded transition to the next part of the blade grind. In other words, the "corner" between edge bevel and blade has been smoothed out. So a convex will (mostly) cut more easily due to less drag in that area.

But again, they are DIFFERENT. You can't compare them unless you really nail down exactly what you are trying to compare. Do you want the same bevel height? Or the same width at the top of the bevel? These are two different things and you can't have both with these two different shapes. Do you want to compare mass in the bevel area?

What about actual cutting comparisons? You can see how this quickly gets way too complicated to make any kind of simple comparisons.

So I'm going to say this:

Convex edges have a rounded shape that reduces drag. Convex edges promote the person grinding to make the overall edge thinner due to the geometry. I.E., making the bevel height larger in order to produce the same terminal angle. This is why they are perceived as having higher performance. I think it's as simple as that.

Brian.

Yup... that's basically what I said a couple of posts up. :thumbup:

 

[bucketstove]

It's not 'invalidating the comparison'... that is the comparison. Given an edge sharpened at the same (approx.) angle... this is what the comparison is: (convex is thinner, larger bevel, etc.).

If you want to say 'Given an edge sharpened at the same bevel height', which is what your box shows, then you have a new comparison: (flat grind is thinner, etc.)

It doesn't invalidate the comparison just because one or the other is 'thinner'... otherwise both would be invalid. It's simply a comparison based on a given parameter. In the case of the red line, it's the angle sharpened at. You could make a third comparison... What would the differences be, if both types were as close as possible to the same thickness?... and you'd have a new set of differences.

Hehe, ok, here is analogy of this comparison,
its a 100 meter race ,
mr v-edge and mr convex are at starting line (0 meters),
then mr convex moves up to 10 meter mark,
this is a fair race to show how mr convex is the best shape

 

[bucketstove]

Isn't this all a bit pointless to try to compare? Convex and V are two different shapes with two different performance characteristics.

The main performance difference between Convex and V is that Convex has a rounded transition to the next part of the blade grind. In other words, the "corner" between edge bevel and blade has been smoothed out. So a convex will (mostly) cut more easily due to less drag in that area.

But again, they are DIFFERENT. You can't compare them unless you really nail down exactly what you are trying to compare. Do you want the same bevel height? Or the same width at the top of the bevel? These are two different things and you can't have both with these two different shapes. Do you want to compare mass in the bevel area?

What about actual cutting comparisons? You can see how this quickly gets way too complicated to make any kind of simple comparisons.

So I'm going to say this:

Convex edges have a rounded shape that reduces drag. Convex edges promote the person grinding to make the overall edge thinner due to the geometry. I.E., making the bevel height larger in order to produce the same terminal angle. This is why they are perceived as having higher performance. I think it's as simple as that.

Brian.

When you're making a knife,
there is only so much metal,
ie starting box,
if you remove metal from behind the box
or cut the box in half
to say convex shape is thinner
that is nonsense comparison ,
and its exactly what these images have been used to argue,
that somehow because its convex its thinner, not because its thinner


yeah, perceptions are easily deceptive,
if you're focusing on making blade round/convex ,
and you forget about making it thin, you end up with fat convex

 

[bgentry]

if you remove metal from behind the box
or cut the box in half
to say convex shape is thinner
that is nonsense comparison ,

You seem to not want to acknowledge that the "high" convex in the picture has the same terminal edge angle as the "low" V grind. This is ONE way of comparing edges. Another way of comparing the edges is the edge bevel height. You are focusing entirely upon that measure.

This is why this whole comparison is kind of a waste of time. There isn't a right or wrong answer. These are DIFFERENT grinds.

Brian.

 

[cbwx34]

You seem to not want to acknowledge that the "high" convex in the picture has the same terminal edge angle as the "low" V grind. This is ONE way of comparing edges. Another way of comparing the edges is the edge bevel height. You are focusing entirely upon that measure.

This is why this whole comparison is kind of a waste of time. There isn't a right or wrong answer. These are DIFFERENT grinds.

Brian.

That pretty much sums it up.

 

[bucketstove]

You seem to not want to acknowledge that the "high" convex in the picture has the same terminal edge angle as the "low" V grind. This is ONE way of comparing edges. Another way of comparing the edges is the edge bevel height. You are focusing entirely upon that measure.

This is why this whole comparison is kind of a waste of time. There isn't a right or wrong answer. These are DIFFERENT grinds.

Brian.

That pretty much sums it up.

Hehe,
see post #23
equal angle with microbevel

 

[Gaston444]

Because of the theoretical curvature of a convex line, a true convex edge has a quite an open final angle (relative to its overall edge thinness), that final angle being defined as the first angle at which the actual edge apex actually touches the surface of a flat hone .

If that apex on a convex edge touches the hone surface at the same knife spine angle/elevation (from the hone) as a true V-Edge, then the curvature of that edge makes this "equivalent" convex edge far, far more fragile and more delicate compared to the "matching" V-Edge, because that curvature is material removed from where the V-edge would build extra strength, despite a similar final edge angle.

The V-edge always has the maximum initial apex sharpness for a given amount of lateral strength.

In profile, this same principle makes the initial tip profile sharpness of American Tanto tips a bit more aggressive for a given profile strength. But the strength/sharpness ratio is not quite as critical in profile as in the cross-section...

Convex edges that I had done to match my V-edges, in initial edge aggressivity at least, where always much thinner and much more fragile, and they chipped out easily: The contrary of what is usually argued...

The reason convex edges where used in Japanese swords was due to the way the swords were made with a high polish (with tiny polishing stones), which polish was not so much for sharpness as to prevent corrosion: True V-edges ground separately could not be polished along with the main flats, so for the Japanese combining the main flats and the edge polish made sense as a polishing shortcut...

The main reason convex edges were re-introduced in US custom knives, by Bill Moran, was for cutting the ubiquitous one inch free-hanging manillla rope bundles: Having a hard outer layer of fibers, with a flexible inner core, meant the best edge for that unsupported rope was one where the shoulders were "washed-out" to reduce drag, and so reduce rope movement as the rope is pushed: The less the rope is pushed around by edge shoulders, the more it will get cut...

With a few rare exceptions like this in mind, to say convex edges have inherent advantages in efficiency over equivalent V-edges is the same as saying that the shortest path between two points is NOT a straight line... At same final edge angles, the Convex is weaker, at same shoulder strengths, the V-edge is sharper: The V-Edge wins on both counts regardless of criteria.

Gaston

 

[cbwx34]

With a few rare exceptions like this in mind, to say convex edges have inherent advantages in efficiency over equivalent V-edges is the same as saying that the shortest path between two points is NOT a straight line... At same final edge angles, the Convex is weaker, at same shoulder strengths, the V-edge is sharper: The V-Edge wins on both counts regardless of criteria.
Gaston

Good post, and while I have no 'side', (I just posted the diagram for reference), I gotta ask... from your summary, wouldn't the opposite also be true? Could you not say, "At the same final edge angles, the convex is sharper (since geometry behind the edge also matters), and at the same shoulder, the convex is stronger"? If no, why not? Seems like all your saying is: thinner is sharper but weaker, thicker is stronger but less sharp.

 

[bgentry]

Hehe,
see post #23
equal angle with microbevel

You are exceptionally difficult to have a conversation with, because of comments like this. You don't acknowledge any points. You just reference your own posts with "hehe" and smiley faces all the time. Do you want to engage in conversation? From my perspective, you don't seem to.

Brian.

 

[lutejones]

Good post, and while I have no 'side', (I just posted the diagram for reference), I gotta ask... from your summary, wouldn't the opposite also be true? Could you not say, "At the same final edge angles, the convex is sharper (since geometry behind the edge also matters), and at the same shoulder, the convex is stronger"? If no, why not? Seems like all your saying is: thinner is sharper but weaker, thicker is stronger but less sharp.

Nicely put,
I've been following the thread with great interest.
I think that convexing the back bevel is a great way to improve cutting performance once you achieve an initial angle that hold up well your uses. And more important very easy to do freehand on a not so flat stone (oils tones of old for example).
Although I have to agree with bucketstove in that you can also achieve this with a micro bevel, thinning the grind and then raising the microbevel in small amounts until it holds up. but it seems to my a little more difficult to get there empirically because you can get too thin and chip the edge.
Regards
Mateo
If something is not clear feel free to ask since English is not my mother language


Enviado desde mi iPhone utilizando Tapatalk

 

[Chris "Anagarika"]

Mateo,

Thinning and testing is exactly what Carter recommends. Thin it as much as one can, and micro it if it chips. That way one has the thinnest and thus most cutting performance the steel & blade can take.

Your English is fine, I can understand what you're saying.