Mike Stewart: Convexed blades with convexed edges hold an edge much longer!

Cobalt said:
True, the context would have to be for a blade of the same overall dimensions. Same width. For the same width it is impossible for a flat ground blade to have more metal behind the edge. That was my point.
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But nothing you've said or shown has demonstrated that at all.
 
Cobalt said:
The green is a virtual line not the blade. The black line inside the orange which is the thicker convex. Glad you see it now. :D
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On the left. The green lines are the tangents to the orange curves at the point whereyou those curves meet. Those green lines form an angle. That angle is the angle of that convex grind.

A vee grind with the same angle is represented by the green lines.

And its thicker. More material behind the edge.
 
marcinek said:
Actually my last post is incorrect. The figure on the left demonstrates my point quite clearly. Those are a convex (orange) and vee (green) with the same edge angle. And the vee clearly has more material behind the edge.
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And the picture on the right? (Speaking tersely.:p )
 
Ok. If we ever meet at a knife show I will buy us beers and we can draw it out to compare. I don't know if we are talking about the same comparable design.

So lets take an exact example. 1/4" thick 1.5" wide blades. One convexed and the other flat. You are saying that the convex does not have more metal than the flat and I am saying it does. Is that correct?
 
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marcinek said:
Yeah, maybe 42blades can do it again, I cant! :D Not sure how to "convince" people of definitions from mathematics. Like arguing someone who says a triangle has 4 sides.
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I have not the strength for it. :p

"It's easier to fool people than to convince them that they have been fooled."
~Mark Twain [possibly falsely attributed]

By contrast, as I like to say, "It's true you can lead a horse to water, but can't make it drink. However, you can thoughtfully provide a salt lick." :D

If people want to know the truth, it has already been presented here, and other places, at great length, and is confirmed by even cursory research into the matter. If they do not want to know the truth there's not a crowbar in the world strong enough to pry their hands off their ears.

Heck--even in a non-mathematical sense you can easily find your approximate edge angle on a convex knife by laying the blade flat on a hard surface and slowly tilting the spine upwards until the edge just touches. Similarly, it's the angle at which, on a flat sharpening stone, you're actually abrading the apex. Everything behind that is just a reduction of the geometry from that angle.
 
Given same volume/amount of steel in cutting edge (same height as well)

Now discuss which geometry(V/Convex/Hollow/S/etc) best for what purposes. Perhaps, MikeS made this claim for certain type of knives - such as bushcraft or chopper. There is no one geometry best for every type of edge works!

For example (IMO): V - Meat processing; Convex - wood & hard fiberous splitting works; Hollow - shallow scoring rubber; etc...

Now analyze why convex geometry works better (or just edge retention aspect) for certain tasks than other geometries. Please serves up a few plates full of physics (formal and hand waving) - I'm hungry for some :p
 
Cobalt said:
Ok. If we ever meet at a knife show I will buy us beers and we can draw it out to compare. I don't know if we are talking about the same comparable design.

So lets take an exact example. 1/4" thick 1.5" wide blades. One convexed and the other flat. You are saying that the convex does not have more metal than the flat and I am saying it does. Is that correct?
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If they have the same edge angle, the vee has more material behind the edge. Like IM said, you also have to have the same edge angle to compare apples to apples.

And your figure on the left shows a vee and a convex with the same edge angle, and the vee is thicker.
 
Cobalt said:
Ok. If we ever meet at a knife show I will buy us beers and we can draw it out to compare. I don't know if we are talking about the same comparable design
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And I would enjoy that....hope it happens one day! :thumbup: We'll chat about tangents and convex sharpening....Im a wet/dry on strop leather guy.
 
marcinek said:
And I would enjoy that....hope it happens one day! :thumbup: We'll chat about tangents and convex sharpening....Im a wet/dry on strop leather guy.
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Lol. More likely we'll get drunk and talk about everything else. I concede. I must be thinking in different terms or something.
 
Cobalt said:
So lets take an exact example. 1/4" thick 1.5" wide blades. One convexed and the other flat. You are saying that the convex does not have more metal than the flat and I am saying it does. Is that correct?
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If the edge angle is equal, then the convex bevel will go visually higher on the blade stock than the "V" edge of equal angle. If the visual bevel width is held constant (which would be silly because it's just a cosmetic effect of imposing certain angles or arcs onto a given piece of stock) then the convex would be thicker but also have a thicker edge angle as a result.

If you were to impose a 15° per side bevel onto a 1/4" thick piece of stock it will look wider than that same 15° per side bevel on 1/8" stock. Fun fact: a BK-16 and BK-2 both have the same primary grind angle (unless they've changed something since the last time I measured it.) The BK-16 is a full flat grind merely because it is narrower than the BK-2, which is a saber grind only because it is so broad. And if the BK-16's blade were widened to equal that of the BK-2, that grind would stop much lower on the blade because the stock is thinner. However, at least up to that depth on both knives the cutting performance is equal. Yet most folks will tell you that the BK-16 is a thinner grind because of its stock thickness being lower and it being a full flat grind instead of a saber grind, which people automatically think is thicker. This is similar to the problems revolving around popular concepts of convex edges, or why people think scandi grinds are such good slicers when they're actually the thickest geometry you can have for a given stock thickness and edge angle (it's just thin stock and a really low edge angle.)
 
Thomas Linton said:
And the picture on the right? (Speaking tersely.:p )
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On the right, those green lines are not tangents to the orange curves. The angle isnt obtuse enough.

In my mathy pic t1 is tangent to curve f1 at point P. t1 just kisses f1. In fact they "osculate"..."kiss"! Isnt math romantic!?!
 
Cobalt said:
Lol. More likely we'll get drunk and talk about everything else. I concede. I must be thinking in different terms or something.
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No! No! Its a counterintuitive concept. In fact for the same edge angle, HOLLOW has the most material behind the edge...

AND...I feel convex is "better" than vee too, but only because it is easier to maintain.
 
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