What's tougher a scandi or convex edge?

Ankerson said:
The edge geometries are different in that example, the flat and hollow are the same while the convex is increased.

Or more like 15 DPS (Hollow), 15 DPS (Flat) 20 DPS (Convex)
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Nope. ALL 15 dps, because the 15 dps is measured from angle of incidence, i.e. at what angle the apex intersects the hone, and it keeps the same bevel height and bevel thickness which define the edge geometry.

When you measure thickness within the bevel (i.e. a lower height), you note that the convex is thicker than the flat, as it must be by definition. One can then assert that, measured from THAT bevel-height, the convex is thicker and so not comparable to the flat, which is true. To achieve the comparable convex grind at THAT bevel height, you must grind it down to match the thickness of the flat, whereupon it will STILL be thicker at every point below that! It MUST be. That is the meaning of the word.

Again keeping "the angle the same" means angle of incidence, and that is all.
 
chiral.grolim said:
Nope. ALL 15 dps, because the 15 dps is measured from angle of incidence, i.e. at what angle the apex intersects the hone, and it keeps the same bevel height and bevel thickness which define the edge geometry.

When you measure thickness within the bevel (i.e. a lower height), you note that the convex is thicker than the flat, as it must be by definition. One can then assert that, measured from THAT bevel-height, the convex is thicker and so not comparable to the flat, which is true. To achieve the comparable convex grind at THAT bevel height, you must grind it down to match the thickness of the flat, whereupon it will STILL be thicker at every point below that! It MUST be. That is the meaning of the word.

Again keeping "the angle the same" means angle of incidence, and that is all.
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If they are both at 15 DPS then the convex would have to be thinner behind the edge than the flat.
 
marcinek said:
convex2.jpg
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The first thing that pops into my mind when I see this picture is: These are two different knives. If each box represented .5 mm, the non-convex blade is a full 2 mm thinner overall than the blade with a regular bevel. If the convexed edge started as wide as the regular bevel, you would see the material bulging outside of the regular bevel.

I guess it's all in what you would consider a convex edge. I don't start my convex very far from the edge, and this almost resembles a normal bevel, the only difference being the way light reflects off of the edge. The unfortunate side to this, is my "cutting edge" isn't as acute as a regular bevel and slicing performance is reduced. My convexed knives are generally hard-use choppers.
 
Ankerson said:
Because the if the angles are the same the convex would have to be thinner...

To result in having the Convex being thicker the angle would have to increased for that to be possible.
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EXACTLY the OPPOSITE. At the same held angle, which is the only angle being measured, the convex-grind will always be thicker UNLESS you reduce the angle and thereby raise the bevel height, whereupon it is no longer comparable to the previous bevel-grind.
 
Alright, re-posting from the older thread:

convex.jpg


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.

convex%25202.jpg


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).
 
Chiral--it IS possible to measure the *effective* edge angle of a knife with a convex edge, and it's very easy to approximate. Your edge angle is the threshold at or below which the knife will no longer cut.

You need to abandon your insistence on maintaining equal visual bevel width--that's not something that's practical to hold as a constant from a real-world standpoint. Using stock thickness and effective edge angle as constants (among a few others, like profile) makes much more practical sense.

The "curving outward" aspect of a convex should be taken as curving outward from the centerline of the cross section of blade stock--not the original edge bevel.
 
FortyTwoBlades said:
Chiral--it IS possible to measure the *effective* edge angle of a knife with a convex edge, and it's very easy to approximate. Your edge angle is the threshold at or below which the knife will no longer cut.

You need to abandon your insistence on maintaining equal visual bevel width--that's not something that's practical to hold as a constant from a real-world standpoint. Using stock thickness and effective edge angle as constants (among a few others, like profile) makes much more practical sense.

The "curving outward" aspect of a convex should be taken as curving outward from the centerline of the cross section of blade stock--not the original edge bevel.
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It isn't "visual" bevel, and you last sentence has no meaning :confused: Look at the diagrams again and imagine that they are magnifications ;) Does that solve the "visual" issue? If you are measuring ANY angle, you require 3 points which define bevel height and thickness. Comparing convex vs flat vs concave bevels requires that they share all three of these points, i.e. same bevel height and thickness, regardless of how tiny those dimensions are. THAT is what MATH and GEOMETRY insist upon. It isn't me, it's you ;)

The problem is with misuse of the term "convex", as I detail above. Is it really so hard for people to understand the definition of the word??? "OUT" In this context, "out" means "thicker". It CANNOT mean "THINNER" at the same time in the same context. Please speak in context.

When you approximate the apex angle on a convex grind, you are not measuring "edge angle" as it relates to the bevel. And when you make that approximation, what angle do you declare it to be at? "Hmm, this cuts at about 20 degrees," i.e. it cuts like a 20-degree FLAT bevel, i.e. the bevel that shares approximately that height and thickness, NOT the flat bevel that shares the actual grind height. Look at the sharpening diagram above. That purple line in the hone is the "approximate" apex angle of the convex bevel. Look at how short that bevel would have to be to match the thickness!
 
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Excellent pictures, chiral. They prove the point. Your convex edge in A does have more metal behind the edge...because it has a larger edge angle. As you say....simple geometry doesn't lie.
 
marcinek said:
Excellent pictures, chiral. They prove the point. Your convex edge in A does have more metal behind the edge...because it has a larger edge angle. As you say....simple geometry doesn't lie.
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Define "edge angle" please. I have defined it above. Where are you confused?
 
chiral.grolim said:
It isn't "visual" bevel, and you last sentence has no meaning :confused: Look at the diagrams again and imagine that they are magnifications ;) Does that solve the "visual" issue? If you are measuring ANY angle, you require 3 points which define bevel height and thickness. Comparing convex vs flat vs concave bevels requires that they share all three of these points, i.e. same bevel height and thickness, regardless of how tiny those dimensions are. THAT is what MATH and GEOMETRY insist upon. It isn't me, it's you ;)

The problem is with misuse of the term "convex", as I detail above. Is it really so hard for people to understand the definition of the word??? "OUT" In this context, "out" means "thicker". It CANNOT mean "THINNER" at the same time in the same context. Please speak in context.

When you approximate the apex angle on a convex grind, you are not measuring "edge angle" as it relates to the bevel. And when you make that approximation, what angle do you declare it to be at? "Hmm, this cuts at about 20 degrees," i.e. it cuts like a 20-degree FLAT bevel, i.e. the bevel that shares approximately that height and thickness, NOT the flat bevel that shares the actual grind height. Look at the sharpening diagram above. That purple line in the hone is the "approximate" apex angle of the convex bevel. Look at how short that bevel would have to be to match the thickness!
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OUT means that it bulges outward away from the central vertical plane that you refer to as the center spine. Pretty simple. The problem with your terminology is that it seemingly presumes that you can somehow add metal to the geometry, when the knife would have to have been made that way in the first place. There's no set frame of geometrical reference for wear. Once you start with given stock you can only go thinner, regardless of what grind you use to do so. You can't use mathematical/geometric terminology that's completely void of specific context to describe a specific class of object that has its own set of conventions... The whole problem with the geometry debate is that you can confuse the conversation depending which side of the fence you're viewing it from. The simple act of use and sharpening alters the overall sectional geometry even if it was able to be kept mathematically exact. If you were to maintain equal edge angle on a linear edge configuration your bevel height is going to be raised, and the height of the primary grind bevel reduced. Thus it makes more sense to view the bevel height as variable.

Ultimately almost any reduction in the slope of the wedge that forms the blade and/or overall sectional volume improves cutting performance while the opposite yields greater strength.
 
FortyTwoBlades said:
OUT means that it bulges outward away from the central vertical plane that you refer to as the center spine. Pretty simple. The problem with your terminology is that it presumes that you can somehow add metal to the geometry, when the knife would have to have been made that way in the first place. You can't use mathematical/geometric terminology that's completely void of specific context to describe a specific class of object that has its own set of conventions... The whole problem with the geometry debate is that you can confuse the conversation depending which side of the fence you're viewing it from. You're looking from convex working in while community convention is to look at flat and work in since flat is a more conventional factory geometrical configuration. The simple act of use and sharpening alters the overall sectional geometry even if it was able to be kept mathematically exact. If you were to maintain equal edge angle on a linear edge configuration your bevel height is going to be raised, and the height of the primary grind bevel reduced. Thus it makes more sense to view the bevel height as variable.

Ultimately almost any reduction in the slope of the wedge that forms the blade and/or overall sectional volume improves cutting performance while the opposite yields greater strength.
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Look at A, B, C in the diagram above. You are grinding metal, i.e. removing it. There is no confusion there. You are also grinding to establish the flat bevel, but you must remove MORE material to do so despite grinding at the same angle, and that is regardless of how tiny the bevel is. YOU are the one asserting the addition of metal.

It does NOT depend on "side of fence", and please review the definition of the words "convex" and "concave" as they relate to geometry and math, as you are very much confused. The words mean the same thing in this context as others.
 
FortyTwoBlades said:
If you were to maintain equal edge angle on a linear edge configuration your bevel height is going to be raised, and the height of the primary grind bevel reduced. Thus it makes more sense to view the bevel height as variable.
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When sharpening at the same angle, and please note that is held angle or angle of incidence, you establish a new bevel height & thickness if there is a back-bevel - to keep that same sharpening angle, the triangle changes size but remains proportionally identical. This changes nothing about the relationship between convex, flat, and concave. When you sharpen back the edge, you can do so convex (removes the least metal, is thickest), flat, or concave (removes the most metal, thinnest) while maintaining the same bevel height and thickness!!! If you want to create another bevel of equal thickness within the new bevel, you can so, but the previous principle stands, and so forth until you cannot grid any more bevels because the edge can only get so thin/short.
 
A convex edge is formed where two curves meet at a point. Each of those curves has a tangent at that point. The angle between those two tangents is the edge angle. The same is true for a flat grind....the tangent happens to coincide with the grind.
That is what is happening in my pic. Two identical, reflected curves meet at a point, and the tangents to those curves at that point are shown, and form the vee.
Simple geometry.
What you are demonstrating is that a more-obtuse convex edge has more steel behind the edge than a less-obtuse flat edge. And I agree with that. But that convex edge has less steel behind the edge than an equally-obtuse flat grind.
Unless you make up some new definition of what an angle is...which you seem to be trying to do.
 
I'll whip up a few diagrams. If you were to continue to maintain the same bevel height when resharpening you will be making the overall geometry more obtuse, regardless of the edge grind style you choose.

In terms of measuring the effective edge angle of a convex, imagine that the apex of the bevel is a hinge with a flat plate attached. The effective edge angle would be measured between the center plane and the furthest that the flat plate could be pushed.
 
I hate to even mention it, but as one who has gone from grinding Hollow, to grinding Flat, to now mostly grinding Convex;

...the shape of a Convex bevel can vary in shape depending on the intended use.


This thread seems tied up in semantics, and both side are easily argued.


The point of my intrusion is that the shape and nature of a Convex grind is another variable that adds to how an edge performs at a given task.


You can have a fat bottomed Convex edge that can be as tough as an axe, or thin the point of that Appleseed to where it's slicie-slicie, or, of course, anywhere in between.


Hollow grinds (defined my wheel diameter) and Flat grinds (flat by definition) offer limited options to the maker, and are popular because of there ease of manufacture. But a Convex edge offers much more flexibility in how the finished product can performing different intended uses.


There's no doubt that a super slim, flat ground blade, hand made and heat treated for max performance by an expert knife maker, can be a great performer. But this thread is about Convex Vs. Scandi, and I think the OP has figured out what he wanted to know.


Trying to argue about knives without using them is pretty silly to start with.

Any well made knife can work well.

My advice would be to spend more time using knives, and form you own opinions.




Big Mike
 
Big Mike said:
I hate to even mention it, but as one who has gone from grinding Hollow, to grinding Flat, to now mostly grinding Convex;

...the shape of a Convex bevel can vary in shape depending on the intended use.


This thread seems tied up in semantics, and both side are easily argued.


The point of my intrusion is that the shape and nature of a Convex grind is another variable that adds to how an edge performs at a given task.


You can have a fat bottomed Convex edge that can be as tough as an axe, or thin the point of that Appleseed to where it's slicie-slicie, or, of course, anywhere in between.


Hollow grinds (defined my wheel diameter) and Flat grinds (flat by definition) offer limited options to the maker, and are popular because of there ease of manufacture. But a Convex edge offers much more flexibility in how the finished product can performing different intended uses.


There's no doubt that a super slim, flat ground blade, hand made and heat treated for max performance by an expert knife maker, can be a great performer. But this thread is about Convex Vs. Scandi, and I think the OP has figured out what he wanted to know.


Trying to argue about knives without using them is pretty silly to start with.

Any well made knife can work well.

My advice would be to spend more time using knives, and form you own opinions.




Big Mike
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Pretty spot on, man! SOOOOO many potential variables, and it all comes down to (in grossly simplified terms) that thinner = cuts better/more fragile, thicker = tougher/cuts worse.
 
marcinek said:
A convex edge is formed where two curves meet at a point. Each of those curves has a tangent at that point. The angle between those two tangents is the edge angle. The same is true for a flat grind....the tangent happens to coincide with the grind.
That is what is happening in my pic. Two identical, reflected curves meet at a point, and the tangents to those curves at that point are shown, and form the vee.
Simple geometry.
What you are demonstrating is that a more-obtuse convex edge has more steel behind the edge than a less-obtuse flat edge. And I agree with that. But that convex edge has less steel behind the edge than an equally-obtuse flat grind.
Unless you make up some new definition of what an angle is...which you seem to be trying to do.
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1) The flat grind has NO tangent, it is mathematically impossible.
2) Asserting that a "convex" grind is thinner than a flat grind is the same as asserting that the bevel formed by those tangents is thinner than the sharpened bevel. It is ridiculous and clearly out of context, context being the bevel.

Edge angle is established as I have stated, by measuring bevel height and width. These dimensions provide the angle of incidence, the sharpening angle, in this context the "edge angle".

I have not changed the definition of "angle" which is a measure of the space between two intersecting lines (NOTE, the definition does not specify the lines as flat). YOU have changed the definition of "convex".

Convex = curved out. Out from what? From the tangents? No. From the line drawn between the two points that establish the bevel. THAT flat line, and the angle of intersection with another such line to form a triangle is the ONLY geometry that matters here. THAT is the context, and THAT ANGLE is the angle of incidence, the sharpening angle, the "edge angle". A convex bevel ground to match that thickness at that height, which is the only context in which the term "convex" applies, is necessarily THICKER than the flat bevel despite sharing the same angle of incidence. Is the apex angle of the tangents of the convex curve more obtuse? OF COURSE. But that is IRRELEVANT in context. The tangents form a more obtuse angle because the shape has been altered by the hone without changing the angle of incidence. A Concave grind would have a more acute apex formed by the tangents, but that is IRRELEVANT in context because, again, one does not compare the apeces, one compares the bevels which are the same height and shoulder thickness.

Again, the key point: Convex edge is thicker than flat edge is thicker than concave edge without changing the sharpening angle. The "effective edge" at the apex only matters AT THAT POINT which is awful small ;)


Now, please, show me that you all understand the meaning of the term "convex".
 
The effective edge angle is incredibly important. To trivialize that fact is to prove ignorance of the practical application of edged tools.
 
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