Convex grinds

[Krissig12]

There is no misinformation here. Just mathematics. Mathematics you are ignoring to make the claim that convex edges have more steel behind the edge.

In an apples to apples comparison....they don't. If one wants to pretend that is not the case because one doesn't like math and doesn't want it ruining the "fun,", or one doesn't believe anyone here understands math or is an expert, or because the knife maker one idolizes told them so....that's fine. Whatever makes one happy.

But happy does not mean right. Really, I'm sorry I'm spoiling the fun by dragging observable and quantifiable science in.

So I will let you enjoy your beliefs about convex edges unquestioned from here out.

I don't think I've seen you take a thread in general seriously in quite some time, Marci

Good for you! Teach these guys some maths:thumbup:

 

[harkamus]

All the diagrams posted in this thread do a good job of explaining the math involved, and I think only a fool would contend that a convex edge has more steel behind it than a v-ground edge WITH IDENTICAL TERMINAL EDGE ANGLES. The disconnect, for me at least, is that it can kind of become apples to oranges. Imagine a point "B" along the blue line to the right of point A, and the slope of its tangent will be greater (its resulting edge angle more acute), as well as for "C", "D", etc., causing the resulting slope of our hypothetical convex edge, creating a blade with suitable cutting geometry. Meanwhile, the angle of the red line (our hypothetical v edge) remains constant, until it reaches a primary bevel (not pictured, obviously).



Granted, these diagrams are just illustrative examples and not necessarily to scale, but in the one above, it looks like a knife is being compared to a splitting maul. Even though the terminal edge angles are the same, the convex is the better slicer. To obtain a v edge blade of, say, 1/8" stock that has the same slicing ability as a convex-ground blade of the same thickness, its edge geometry will have to be finer, and the resulting edge angle smaller, resulting in less steel behind the edge for that particular application.

I guess it all comes down to application really, because even in the above diagram, if the bevel/primary grind of the v-edged blade were implemented close enough to the green line, its "slice-itude" wouldn't be far diminished from that of the convex in the example, though still less, albeit with a hardier edge spine.

Meh. I'm rambling now....hope I made some sense....it made sense in my head while typing it out.

You're right. Theoretically, I mean, you could have the dullest apex as the edge, which would be 180 degrees - a straight line -, provided that the apex is sufficiently thin. We're talking on the scope of microns where if you used high power magnification, you could see a straight line as the dull edge.

...which is fine provided that the primary bevel is also thin enough to separate the medium you're trying to cut through.

I think we all went off on a tangent. <---pun intended.

 

[Twindog]

A convex edge can certainly have more steel behind the apex than a V edge -- although a V edge can also have more metal behind the edge. It all depends on the geometry of the edges.

As the example that I showed, if you compare a V edge to a convex edge and the edges retain the same height and width, the convex edge will always have more metal behind the apex. (Don't say behind the edge because that is the blade.)

Just look at the figure on the left. Both edge width (w1) and height (h1) are held constant for both the V edge and the convex edge. You can clearly see that the convex edge has more steel behind the apex.

 

[harkamus]

A convex edge can certainly have more steel behind the apex than a V edge -- although a V edge can also have more metal behind the edge. It all depends on the geometry of the edges.

As the example that I showed, if you compare a V edge to a convex edge and the edges retain the same height and width, the convex edge will always have more metal behind the apex. (Don't say behind the edge because that is the blade.)

Just look at the figure on the left. Both edge width (w1) and height (h1) are held constant for both the V edge and the convex edge. You can clearly see that the convex edge has more steel behind the apex.

But your edge angle is not the same comparing the two.

 

[Twindog]

But your edge angle is not the same comparing the two.

Yes, there is no edge angle with a convex edge. The only angle that people have shown with a convex edge is the "angle of intersection," but that is not the edge angle. But even at that, people are saying that a convex edge can't have more steel behind the apex and that is not true.

 

[Twindog]

Ok...this pic taken friom the interwebs is a little busy, but it is EXACTLY what is going on here.

F1 and F2 are curves that meet at at P. t1 is the tangent to F1 at P. t2 is the tangent to F2 at P. phi (the little curly-que thing) is the angle at which F1 and F2 meet at P. The angle at the bottom is phi also. (They are vertical angles.)

There is nothing more to it. Its math. You have to either live with it, or ignore it. Its just that ignoring it doesn't make it go away and allow one to make false statements. I mena one can make false statements if one wants, of course.

t1 and t2 meet at the same angle as F1 and F2. And F1 and F2 are inside t1 and t2. Less distance between them at a given distance from P.

Less metal behind the edge.

This is Marcinek's idea of how to measure the angle of a convex edge. What you see is a fairly normal profile for a convex edge. That angle is computed to be 90 degrees, which would be the comparable angle of a V edge. Who uses a 90-degree inclusive edge? So of course, a 90-degree V edge will have more metal behind the apex than that convex edge in the diagram. But that angle is not the edge angle, but the angle of intersection, which if you look is found by measuring the angle of two straight lines (the tangent lines).

42 presented an interesting way he finds the "effective angle" of a convex edge. That method would come up with a much different answer than the equation above.

Angles are measured by the turn of two straight lines joined at a vertex. Convex edges are not straight lines.

 

[Rhinoknives1]

Does anyone have any Valium? We need to put some into the inter webs tangent line flow in a circular motion!

To the OP, Stay Safe and have fun with your new convex edges!

 

[FortyTwoBlades]

This is Marcinek's idea of how to measure the angle of a convex edge. What you see is a fairly normal profile for a convex edge. That angle is computed to be 90 degrees, which would be the comparable angle of a V edge. Who uses a 90-degree inclusive edge? So of course, a 90-degree V edge will have more metal behind the apex than that convex edge in the diagram. But that angle is not the edge angle, but the angle of intersection, which if you look is found by measuring the angle of two straight lines (the tangent lines).

42 presented an interesting way he finds the "effective angle" of a convex edge. That method would come up with a much different answer than the equation above.

No it wouldn't. Presuming equal effective edge angle per side with a calculated included angle of 90° then the method I described would yield the revelation that the edge would engage the target medium at any angle of presentation greater than 45°, and thusly a total angle of 90°.

 

[rustyrazor]

But now you know what a tangent is, and you are richer for it.

I do forward air control and surveying; I know what a tangent is... just know what an argument about one looks like now, lol. and a little richer for it no doubt.

 

[marcinek]

This is Marcinek's idea of how to measure the angle of a convex edge. What you see is a fairly normal profile for a convex edge. That angle is computed to be 90 degrees, which would be the comparable angle of a V edge. Who uses a 90-degree inclusive edge? So of course, a 90-degree V edge will have more metal behind the apex than that convex edge in the diagram. But that angle is not the edge angle, but the angle of intersection, which if you look is found by measuring the angle of two straight lines (the tangent lines).

42 presented an interesting way he finds the "effective angle" of a convex edge. That method would come up with a much different answer than the equation above.

Angles are measured by the turn of two straight lines joined at a vertex. Convex edges are not straight lines.

And the edges of a convex grind aren't red....thats another reason why the picture doesn't work by your argument.

You ever see Zoolander? There is a scene in it where he is presented a scale model of a school or something he is funding. And he rejects it because does not understand how the kids are going to fit inside such a tiny building.

 

[LEGION 12]

This is Marcinek's idea of how to measure the angle of a convex edge. What you see is a fairly normal profile for a convex edge. That angle is computed to be 90 degrees, which would be the comparable angle of a V edge. Who uses a 90-degree inclusive edge? So of course, a 90-degree V edge will have more metal behind the apex than that convex edge in the diagram. But that angle is not the edge angle, but the angle of intersection, which if you look is found by measuring the angle of two straight lines (the tangent lines).

42 presented an interesting way he finds the "effective angle" of a convex edge. That method would come up with a much different answer than the equation above.

Angles are measured by the turn of two straight lines joined at a vertex. Convex edges are not straight lines.

Convex edges are straight lines with a slight curve. I feel a little richer from reading this thread.

 

[Twindog]

And the edges of a convex grind aren't red....thats another reason why the picture doesn't work by your argument.

You ever see Zoolander? There is a scene in it where he is presented a scale model of a school or something he is funding. And he rejects it because does not understand how the kids are going to fit inside such a tiny building.

The red shows the extra steel that is contained within the convex edge that is behind the apex and is not contained in the V edge. Under conditions where the edge height and width are held constant, the convex edge will always have more metal being the apex, although the amount of extra steel will vary considerably depending on the amount of curvature in the arcs that form the convex edge.

On the drawing on the right, the convex edge is contained within the V edge, and with this geometry (where the edge height is lengthened for the convex edge but not the V edge), the red shows the amount of steel behind the apex of the V edge that is not contained in the convex edge. By changing edge height and width, you will change the geometry, and this characteristic holds true for both convex and V edges. Because changing the edge height and width affects geometry, you can't compare a convex edge to a V edge when they have different edge heights and widths.

You think that by making a convex edge taller respective to a V edge that you are showing something about the differences between convex and V edges. All you are showing is the effect of making the edge height taller.

The convex edge has no angle, but it does have varying amounts of acuity. The acuity changes at various points along the convex edge but is constant along the V edge. As you approach the apex of a convex edge, the edge becomes less acute -- how much less acute depends on the amount of curvature in the arcs that create the convex edge.

You're trying to compare an edge geometry that is measured as an angle with fixed acuity along the entire edge bevel to a different geometry that is not measured in angles and which has varying levels of acuity along the entire edge bevel. Classic apples and oranges.

 

[pinnah]

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.

 

[B34NS]

all the geometry is great but what I'm really wanting to know is why a convex edge instead of a V edge? does it hold an edge better or worse than other grinds? any info on convex blades and bark rivers convex blades other than the geometry behind them is what I'm really interested in hearing about.

On the ghost 2, I would see the convex edge being an advantage when it comes to sharpening as karambits take a little getting used to. Other than that, it's a fighting knife, not much versatility to be described by the edge alone on a knife with so many other features. Plus to use those things properly takes some real training. Have fun if you pick it up!

 

[Shotgun]

A convex edge can certainly have more steel behind the apex than a V edge -- although a V edge can also have more metal behind the edge. It all depends on the geometry of the edges.

As the example that I showed, if you compare a V edge to a convex edge and the edges retain the same height and width, the convex edge will always have more metal behind the apex. (Don't say behind the edge because that is the blade.)

Just look at the figure on the left. Both edge width (w1) and height (h1) are held constant for both the V edge and the convex edge. You can clearly see that the convex edge has more steel behind the apex.

I don't know what to say really man. Your drawing clearly proves what we're talking about. I'm not sure why you can't see that.

 

[Twindog]

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

The first two convex edges on the left share the same edge height and width as the V edge. When convex edges are compared to a V edge with the same edge height and width, the convex edge is always more robust because it has more steel behind the apex. However, how much more robust depends on the amount of curvature in the arcs that form the convex edge. The far left convex edge is much more robust than the middle convex edge because is has more curvature.

So even when the edge height and width are held constant, a convex edge can have a wide range of performance that will affect both edge slicing ability and edge robustness. With a V edge, those performance characteristics don’t change as long as the edge height and width are held constant.

The third convex edge shows that a convex edge can be made more acute by raising the edge height and keeping the V-edge height constant. Raising the edge height has a powerful effect on edge geometry and performance.

Edge width (width of the edge at the shoulders) also has a powerful effect. You can see this effect in Ankerson’s epic thread on steel performance. Even when the edge angle is held constant, an edge with narrow shoulders will outperform a wider edge, even when the steel and edge angle are held constant.

Because edge width and height have a powerful influence on edge performance, you have to keep them constant if you want to compare the relative characteristics of convex, V and concave edges.

With a V edge: The more narrow the edge shoulders and the more acute the edge angle (which is made more acute by raising the edge height), the greater the slicing ability and the less its robustness.

With a convex edge, the more narrow the shoulders, the greater the edge height and the less curvatures in the arcs that define its edge, the greater its slicing ability and the less its robustness.

 

[TLoFP]

Angles are measured by the turn of two straight lines joined at a vertex. Convex edges are not straight lines.

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.

 

[FortyTwoBlades]

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.

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.

 

[FortyTwoBlades]

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

The first two convex edges on the left share the same edge height and width as the V edge. When convex edges are compared to a V edge with the same edge height and width, the convex edge is always more robust because it has more steel behind the apex. However, how much more robust depends on the amount of curvature in the arcs that form the convex edge. The far left convex edge is much more robust than the middle convex edge because is has more curvature.

So even when the edge height and width are held constant, a convex edge can have a wide range of performance that will affect both edge slicing ability and edge robustness. With a V edge, those performance characteristics don’t change as long as the edge height and width are held constant.

The third convex edge shows that a convex edge can be made more acute by raising the edge height and keeping the V-edge height constant. Raising the edge height has a powerful effect on edge geometry and performance.

Edge width (width of the edge at the shoulders) also has a powerful effect. You can see this effect in Ankerson’s epic thread on steel performance. Even when the edge angle is held constant, an edge with narrow shoulders will outperform a wider edge, even when the steel and edge angle are held constant.

Because edge width and height have a powerful influence on edge performance, you have to keep them constant if you want to compare the relative characteristics of convex, V and concave edges.

With a V edge: The more narrow the edge shoulders and the more acute the edge angle (which is made more acute by raising the edge height), the greater the slicing ability and the less its robustness.

With a convex edge, the more narrow the shoulders, the greater the edge height and the less curvatures in the arcs that define its edge, the greater its slicing ability and the less its robustness.

But the effective edge angle of the overlays are greater than that of the V. How are you adding this metal back to the blade? Welding it on???

 

[REK Knives]

Well...that's an excellent point too. Unless you are sharpening with some type of jig that allows you to maintain the excat same angle at every stroke, then you are creating a series of microbevels. Create enough of those microbevels and...whammo...now you got a convex edge.

That's one of the beauty parts of it...it takes advantage on people like me who are not consistent in their angles when they hand sharpen.

So you don't have to freak out and grit your teeth while hand sharpening. You just relax and let the sexy, curvy geometries run the show, man. Groovy.

That was, in essence, on a jig.. It was a straight razor where the spine is the jig and rides flat on the stone during the sharpening process &#128522;