Convex grinds

[marcinek]

I think one of the stumbling blocks here is thinking that straight lines and curves are different things.

In fact a straight line is just a special example of a curve. Straight lines form a subset of curves.

Extra credit for a Venn Diagram.

 

[Rhinoknives1]

To the OP in plain Speak!

I make knives & sharpen them for a living and I find a convex edge to last longer and cut circles or curves better than a vee grind on the same knife.

The one exception is on a straight razor. A vee grind will shave your face better better than a convex grind so how long they last doesn't matter.

See! No math involved!

 

[TLoFP]

I think one of the stumbling blocks here is thinking that straight lines and curves are different things.

In fact a straight line is just a special example of a curve. Straight lines form a subset of curves.

Extra credit for a Venn Diagram.

I am surprised we are assuming Euclidean Geometry! What if the space-time continuum is curved? I think if we were to calculate the geodesics of the space-time continuum then we would find the perfect edge geometry. A geometry so keen that it has the ability to cut into space-time itself, thus releasing a blast of tachyons and propelling you into the future.

- T

 

[REK Knives]

Actually, in the most technical sense - the mathematical one - he's wrong. Curves meet at angles.

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=curves%20meet%20at%20angles

thanks for that i was just saying that even IF he stuck to that line of reasoning then logically it follows that v edges don't truly have an angle either hehe

 

[LEGION 12]

I am surprised we are assuming Euclidean Geometry! What if the space-time continuum is curved? I think if we were to calculate the geodesics of the space-time continuum then we would find the perfect edge geometry. A geometry so keen that it has the ability to cut into space-time itself, thus releasing a blast of tachyons and propelling you into the future.

- T

Whaaat

 

[marcinek]

To the OP in plain Speak!

I make knives & sharpen them for a living and I find a convex edge to last longer and cut circles or curves better than a vee grind on the same knife.

The one exception is on a straight razor. A vee grind will shave your face better better than a convex grind so how long they last doesn't matter.

See! No math involved!

Its always better with math involved!

That said... I take my full "flat" blades with vee grinds and convex the edge. And they cut better and are, for me, easier to maintain. In addition to knocking off the shoulders giving you a thinner and better slicer....the ease of maintenance ALSO makes a better slicer. The edge is in better shape.

 

[marcinek]

thanks for that i was just saying that even IF he stuck to that line of reasoning then logically it follows that v edges don't truly have an angle either hehe

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.

 

[rustyrazor]

that's a half hour i won't get back

 

[marcinek]

that's a half hour i won't get back

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

 

[Whitedog]

To the original poster, go ahead and try that convex blade you might really like it. If not sell it or put a V grind on it. Convex is really easy to maintain.
Looks like all the internet PHDs came out with the charts and graphs makes me want to run get some rubber waders so nothing splashes on me.

 

[Rhinoknives1]

To the original poster, go ahead and try that convex blade you might really like it. If not sell it or put a V grind on it. Convex is really easy to maintain.
Looks like all the internet PHDs came out with the charts and graphs makes me want to run get some rubber waders so nothing splashes on me.

Waders? Hell! I had my shop apron, Face shield, Respirator, and fingers skins on for full protection in a blast area!

 

[harkamus]

Freaking math. Thank goodness I teach a physics based science.

Oh wait, that involves math.

For the life of me, I cannot even begin to understand how people cannot see that two arcs intersect to form an angle that terminates at the apex by two straight lines. Where is Spock when you need him? (RIP Leonard Nimoy)

 

[Shotgun]

To the original poster, go ahead and try that convex blade you might really like it. If not sell it or put a V grind on it. Convex is really easy to maintain.
Looks like all the internet PHDs came out with the charts and graphs makes me want to run get some rubber waders so nothing splashes on me.

Wait. What was the original OP about?

Yeah OP. Try the convex. Life's too short not to try all the grinds. Some people have been known to put a convex edge on a sharpener system and make them into v's.

 

[Mecha]

Well, in a way. I also agree with this statement: "A v edge can be more or less acute than another v edge. And a convex edge can have more steel behind the apex of a v if it has a more obtuse edge angle than the v. "


Again, it's like saying a 2000 pound block of concrete can be heavier than a 500 pound block of velveeta cheese.

Now we're talkin' my kind of math!

 

[Rhinoknives1]

Freaking math. Thank goodness I teach a physics based science.

Oh wait, that involves math.

For the life of me, I cannot even begin to understand how people cannot see that two arcs intersect to form an angle that terminates at the apex by two straight lines. Where is Spock when you need him? (RIP Leonard Nimoy)

And your point is?

 

[Twindog]

Convex edges don't have angles. The intersection of curved lines have an "angle of intersection," which, as the formulas show, are represented by straight lines.

I think most of the misinformation in this thread comes from people converting V edges to hybrid convex edges that basically knock off the shoulders of the V edge, improving slicing ability.

But you can convert a convex edge to a V edge and that V edge will be more acute and slice better.

The geometry of convex edges and V edges are infinite. Anything that one particular V edge can do a particular convex edge can also do equally well, and vice versa.

 

[FortyTwoBlades]

Convex edges don't have angles. The intersection of curved lines have an "angle of intersection," which, as the formulas show, are represented by straight lines.

I think most of the misinformation in this thread comes from people converting V edges to hybrid convex edges that basically knock off the shoulders of the V edge, improving slicing ability.

But you can convert a convex edge to a V edge and that V edge will be more acute and slice better.

The geometry of convex edges and V edges are infinite. Anything that one particular V edge can do a particular convex edge can also do equally well, and vice versa.

You're about 90% correct. Indeed, the possible geometries are limitless, but there can be constraints imposed in order to make apples-to-apples comparisons. You cannot convert a V edge to a V edge of equal edge angle and improve cutting ability, because it already is that angle. You can maintain the equal effective edge angle and convert a V edge to a convex without reducing blade height, and it will have increased cutting performance for only a minor drop in edge durability. You cannot convert a convex to a V of equal effective edge angle without reducing the height of the blade.

Note that I say effective edge angle not just edge angle. That is to say, the angle above which the edge will be able to engage the cutting medium. Regardless of your argument regarding a lack of angles with convex edges there is still an effective edge angle and approaching a flat cutting medium at or below this angle will not allow the edge to engage the target.

 

[marcinek]

Convex edges don't have angles. The intersection of curved lines have an "angle of intersection," which, as the formulas show, are represented by straight lines.

I think most of the misinformation in this thread comes from people converting V edges to hybrid convex edges that basically knock off the shoulders of the V edge, improving slicing ability.

But you can convert a convex edge to a V edge and that V edge will be more acute and slice better.

The geometry of convex edges and V edges are infinite. Anything that one particular V edge can do a particular convex edge can also do equally well, and vice versa.

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.

 

[harkamus]

And your point is?

My point is that it is not that difficult to understand that two arcs that are joined together to form a point, will form a point that is created by two lines, that is an angle created by two lines. As I mentioned, the only condition for this to be untrue is if one were to take a perfect circle, chop of an arc, and have that arc be the apex. Only then is the angle not created by two lines.

BUT, if you were to draw two tangential lines from that arc that you cut out of a circle, place them in such a way as to create as little of a change in angle as possible, you'd still end up with an angle created by two lines.

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.


Quick paint explanation.

 

[bladesandbrews]

The red line it tangent to the blue curve at point A.

Imagine you draw a vertical line though A and reflect the blue curve and red line across that vertical line.

Then you have a vee grind (the red lines) and a convex grind (the blue curves) that have the same edge angle. And the convex is inside the vee. And thinner.

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.