Convex Edge Better by What % ?

Ooh interesting topic!

All I know is that on my sujihiki (slicer), the edge lasts MUCH longer after I polish convex as oppose to flat bevel edge. The flat edge is much sharper, but cutting for 8-12 hours a day, durability is more important as I have more slicers for more precise slicing (yanagi).

My outdoor choppers are also mirror convexed, I find that it sinks deep into wood without wedging. Maybe it's a combo of very smooth surface and the curvature pushing material away from blade.
 
Many variables does not render math useless - Does it?

Math did get us to Mars
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I was at a lecture many years ago given by Herb Simon, a Nobel laureate in economics. He was being hectored by some quants on how adding more variables to models could potentially make them more accurate and "optimal".

Herb quoted the numbers involved in modeling games of chess, which computers at that time couldn't handle well, and then said "most of us think life is more complicated than chess".

Math works great when you really understand exactly what you are measuring and modeling. Once you get into applications that clarity of understanding often fuzzies up....
 
For me, outcomes are not always the way we think they should be, and then need to proven or confirmed. The one that made my head hurt was the Mythbuster show called Mythssion Control. This is the one they did the test of two cars hitting head on at 50mph. The math on this defied common sense. Two cars hitting head on at 50mph do not = one car hitting a wall at 100mph. I liked this show because they struggled with this as much as I did. Then when they demonstrated in the shop with an analog model using clay it was a eureka moment. I do apologize as I cannot find this test on uTube. It is on Netflic season 8, Mythssion Control, @ 31:00.

Why do we want answers to suff? "Because its there"


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And to combat the epidemic of BS in the world
 
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allout said:
For me outcomes are not always the way we think they should be and then need to proven or confirmed. The one that made my head hurt was the Mythbuster show called Mythssion Control. This is the one they did the test of two cars hitting head on at 50mph. The math on this defied common sense. Two cars hitting head on at 50mph do not = hitting a wall at 100mph. I liked this show because they struggled with this as much as I did. Then when they demonstrated in the shop with an analog model using clay it was a eureka moment. I do apologize as I cannot find this test on uTube. It is on Netflic season 8, Mythssion Control, @ 31:00.

Why do we want answers to suff? "Because its there"

Energy = 1/2 mass x velocity squared.
50+50 = 100
100 x 100 x .5 = 5,000.
Click to expand...
 
allout said:
The math on this defied common sense. Two cars hitting head on at 50mph do not = one car hitting a wall at 100mph.
Click to expand...

Thomas Linton said:
Energy = 1/2 mass x velocity squared.
50+50 = 100
100 x 100 x .5 = 5,000.
Click to expand...

The problem with this solution is the fact that kinetic energy is not linearly dependent on velocity, but rather quadratically dependent. You have to solve for the KE of each individual car before you can add them together.

1 car, 100mph:
KE=0.5*M*V^2
V=100
KE=5000*M

2 cars, each 50mph:
KE1=0.5*M*V^2
KE2 = 0.5*M*V^2
V=50
KE1=1250*M
KE2=1250*M
Total kinetic energy here is 2500*M, which is not equal to the first solution of 5000*M.
 
"Total kinetic energy here is 2500*M"

My Head My Brain ...lol...

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The point is the edges. If there are two edges one V and one () {convex] that are dropped in to clay which one will get better penetration? By how much?

Keeping in mind this is not the end all solution but the beginning of one.

As an example: If the solution in the analog test is something like a depth of less 5% difference in 5 different hardnesses of clay then move on. If the difference is greater than it is time for some math.

And maybe, using larger shapes of V and () out of some material. Not knives, or not only knives.




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I didn't read the whole thread but it's an interesting conversation.

I would think that a flat grind will have less resistance at an extreme angle and thus require less force to pass through a given medium.

A convex edge, however, will be more resistant against lateral force due to the fact that the grind is terminating at an increasing angle as it approaches zero, creating a more substantial edge.

So the real answer is...






... There is no spoon
 
We may be having a no spoon moment...:)

"So the real answer is...






... There is no spoon "


In Post #1


"OR


Is it Magic ? :eek:".....:thumbup:
 
I don't understand "it" but in ZaZen there is no correct answer...0_0

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Being from Texas it is V or () FTW ;)
 
My Bad, Back on point!

If there are two edges one V and one () {convex] that are dropped in to clay which one will get better penetration? By what % ?
 
allout said:
My Bad, Back on point!

If there are two edges one V and one () {convex] that are dropped in to clay which one will get better penetration? By what % ?
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It's not that easy. You need to know quite a bit more information in order to make a valid calculation. Staring with the angle of the grinds.

And when talking a convex, there is a bit of calculus involved to explain the "angle" that I really don't feel like explaining.
 
neverdie36 said:
And when talking a convex, there is a bit of calculus involved to explain the "angle" that I really don't feel like explaining.
Click to expand...

Thanks, as that would have likely been painful. But is it possible that in an attempt to break ground on an answer it is being over thought? What I mean is, on the analog Mythbuster car clay model there were numinous variables at play that I would think were "ball parked" to just get thoughts into action. Of course "ball park" math would get astronauts killed.

@ neverdie you sound like a math guy, what side of the fence do you come down on, V or () ?
 
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allout said:
Thanks, as that would have likely been painful. But is it possible that in an attempt to break ground on an answer it is being over thought? What I mean is, on the analog Mythbuster car clay model there were numinous variables at play that I would thing were "ball parked" to just get thoughts into action. Of course "ball park" math would get astronauts killed.

@ neverdie you sound like a math guy, what side of the fence do you come down on, V or () ?
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Well I'm no mathematician. I have limited experience in physics and engineering. I currently work for a manufacturing company where I do some in house engineering.

I prefer a convex for long term sustainability and strength.

If the most extreme slicer is what your after then a low angle flat grind might be preferred.
 
V versus Convex


I hope this does not end up as another one of those nightmare porn math / spooky physics phenomenon things. Hahaha that might not be so funny…


Warning: If you have not seen the “Double Slit Experiment” stay away! (XXX). Seeing this “spooky physics experiment” or not seeing it may well alter who or what you are.:yawn:
[video=youtube;DfPeprQ7oGc]http://www.youtube.com/watch?v=DfPeprQ7oGc[/video]




@ nerverdie Well Said



I wonder if V vs () in chopping it is more of terminal ballistics math and in slicing it is more an aerodynamics math? Or maybe math is just math like people are just people...








[video]http://tinyurl.com/ofzd5w9[/video] RIP:thumbup:
 
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Most comparisons like this start out with "all other things being equal..."

The trouble is all other things aren't equal.

Given knives of equal hardness, etc. etc. the narrowest angle hollow grind will cut best, then flat, then convex -- because flat is wider than hollow, and convex is wider than flat.... and the width produces some resistance going through the material.

But we don't all carry hollow ground razors for everything. Because that thickness produces some durability and some maintainability.

A well done convex grind is very user friendly and holds up well. But a hollow-ground purpose-built kitchen knife will slice tomatoes better. So what, unless you are slicing tomatoes?
 
42 is the unified answer for both double-slit & convex vs V :p

allout said:
V versus Convex


I hope this does not end up as another one of those nightmare porn math / spooky physics phenomenon things. Hahaha that might not be so funny…


Warning: If you have not seen the “Double Slit Experiment” stay away! (XXX). Seeing this “spooky physics experiment” or not seeing it may well alter who or what you are.:yawn:
[video=youtube;DfPeprQ7oGc]http://www.youtube.com/watch?v=DfPeprQ7oGc[/video]




@ nerverdie Well Said



I wonder if V vs () in cutting it is more of terminal ballistics math and it slicing it is more an aerodynamics math? Or maybe math is just math like people are just people...








[video]http://tinyurl.com/ofzd5w9[/video] RIP:thumbup:
Click to expand...
 
@pmeisel
I think I understand what you are saying. Could that fall into the exaggerating to prove a point type of thing? In other words a factory flat ground razor will cut newspaper better than a convex big blade but the razor will not cut wood as well. This is poorly stated, please work with what I am trying to say.




Case in point: My D2 Kershaw Outcast. It has a flat DMT guided edge of unknown degrees (probably about 22 per side) that was finished to hair popping by hand. I was not happy with how it cut wood; small pencil sizes oak branches to 6” oak branches (green and deadwood). "All things being equal” ( I could not resist) if I regrind with a convex what would happen?

A. Nothing - as stated they are the same.
B. You will perceive it to cut better.
C. I teach math, and the result is an 8.25% increase
D. You are talking apples and tomatoes
E. Move to Colorado and learn it don’t really matter, dude.
F. It will cut the same and the edge will last longer.









"To achieve the maximum cutting efficiency a precise angle of 42 is required." - Deep Thought
 
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How you grind the convex bevel will affect the outcome. From a cross sectional of a V edge bevel - let's call this area X. When convexing - are you?
1. Keep same area X and bevel height (i.e. convert line to Bezier curve, while keep same integral area)
2. Keep same area X but with +- bevel height
3. Decrease area X and keep same bevel height
4. Decrease area X and increase bevel height
5. Increase area X and keep same bevel height
6. Increase area X and +- bevel height

In addition, convex/curve control points also has major performance impact.

IME (BM Pardue D2 & high rc D2 knives made by me) - high likeliness that a super sharp D2 with 44* inclusive edge bevel against dry oak = bunch of large chips. A micro-bevel of 54+* inclusive may alleviate/mitigate chipping problem. OTOH, D2 Outcast low RC may has enough toughness for chopping impact.
 
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