Cross-sectional thickness, convexity, asymmetry, and impact on cutting behavior

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I'm new to kitchen knives, and I'm quickly realizing that how a knife cuts is determined not only by the secondary bevel, but by what's behind it. Different knives have varying thickness behind the edge, but also varying levels of convexity at different distances from the edge. And then there's asymmetric knives. When you cut with a new knife and say "wow that's awesome" it's a combination of all of those things working together.

And yet you hear very little talk about this when it comes to sharpening. Some videos talk about thinning your knife, but it's often described as "lay the primary bevel flat on the stone and rub until it's thinner." Ugh, no! A perfect V shape is not a particulary great cutter and you probably don't want to turn your knife into one. Thinning should be because either (a) my knife has changed and I want to recreate what it was previously (not a V), or (b) I know better than the knife maker and I want to create a new profile that I like better (still not a V!).

So I would like to learn more about knife cross-sectional thickness, and do experiments on how they impact cutting.

1. Is there any good reading material on this topic?

2. Is there an easy way to measure the cross-sectional thickness of a knife? I'd like to measure all the knives I have now to see how the compare. Is the only way to use calipers and measure at 1mm, 2mm, 3mm, etc? This seems pretty tedius. Is there a cool device that you run along the knife and it shows you the cross section in your computer? :-D

3. Are there any known techniques for creating creating these varying-radius convex primary bevels? Is it all done by hand and up to the skill of the sharpener? It seems a little tedius to perfectly recreate the same convexity by hand in one spot on a blade, let alone along the entire length of the blade. I see the videos of Japanese knife makers lying over a large sharpening wheel and periodically glancing at the blade, but I don't see how they can know when it's the perfect thickness by glancing at it.

Looking to learn... pointers to resources welcome. So far searching hasn't turned up much.
 
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That is a fantastic thread. Thank you!

One topic it doesn't cover is the varying radius of the convexity. Below is a picture of two lines that are both convex and come to the same point.. but they are clearly different. They flip flop in terms of which is widest at various parts along the way up.



1667345238293.png


Is there any strategy on where to put the bumps out. I doubt they are all constant radius convex shapes. Note that the red line is thinner behind the edge, which sounds good in theroy, but would likely actually cause more wedging in certain foods.
 
That is a fantastic thread. Thank you!

One topic it doesn't cover is the varying radius of the convexity. Below is a picture of two lines that are both convex and come to the same point.. but they are clearly different. They flip flop in terms of which is widest at various parts along the way up.



View attachment 206318

Is there any strategy on where to put the bumps out. I doubt they are all constant radius convex shapes. Note that the red line is thinner behind the edge, which sounds good in theroy, but would likely actually cause more wedging in certain foods.
With the blue line the bevel is forming a continuous arc with the face. That's what I aiming for when sharpening the dominant side.
 
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Two more related threads:
Understanding Distal Taper
Convexity, flatness, stiction, and food release

I'm actually a little surprised at how little research seems to have been done on this. It seems that it should be well within the reach of existing (probably existing twenty plus years ago) technology to use lasers to map the knife surface and then recreate it with CNC with machines. It seems like Zwilling or Kai certainly should be able to afford this? Given the tech you could make a series of semi-finished blanks needing only final sharpening and compare slight variations in geometry. You could also laser etch the blade in various ways to study stiction. Obviously, there are some level of subjective preferences you're not going to get past but it could reduce the amount of "noise" when thinking or taking about these questions.
 
On a belt system you end up with a certain amount of convexing unless you keep the belts really tight or use a pad.
 
Two more related threads:
Understanding Distal Taper
Convexity, flatness, stiction, and food release

I'm actually a little surprised at how little research seems to have been done on this. It seems that it should be well within the reach of existing (probably existing twenty plus years ago) technology to use lasers to map the knife surface and then recreate it with CNC with machines. It seems like Zwilling or Kai certainly should be able to afford this? Given the tech you could make a series of semi-finished blanks needing only final sharpening and compare slight variations in geometry. You could also laser etch the blade in various ways to study stiction. Obviously, there are some level of subjective preferences you're not going to get past but it could reduce the amount of "noise" when thinking or taking about these questions.
I have zero expertise in this area but from 5 minutes on Google it seems there's 0.05mm accuracy 3D scanners on the market for sub-$1k, and more accurate commercial grade systems for substantially more. Not sure if 0.05mm is enough to capture the relevant range of variation between minor variations in grinds though. Regardless, the tech to scan and model an outstanding grind is definitely there. Maybe the cnc tech to reproduce it at scale isn't cost effective relative to what big manufacturers think the potential market is.
 
I have zero expertise in this area but from 5 minutes on Google it seems there's 0.05mm accuracy 3D scanners on the market for sub-$1k, and more accurate commercial grade systems for substantially more. Not sure if 0.05mm is enough to capture the relevant range of variation between minor variations in grinds though. Regardless, the tech to scan and model an outstanding grind is definitely there. Maybe the cnc tech to reproduce it at scale isn't cost effective relative to what big manufacturers think the potential market is.
Oh nooooooo..... you may have just cost me $1000. :-D

But seriously, I'm going to have to read a bit to see if this would actually help me evaluate knives or not. If it could produce a series of cross sections along the length of the blade, with pictures and estimated measurements, that would be pretty fantastic. But it seems like it's unlikely to actually be able to do that.
 
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I have zero expertise in this area but from 5 minutes on Google it seems there's 0.05mm accuracy 3D scanners on the market for sub-$1k, and more accurate commercial grade systems for substantially more. Not sure if 0.05mm is enough to capture the relevant range of variation between minor variations in grinds though. Regardless, the tech to scan and model an outstanding grind is definitely there. Maybe the cnc tech to reproduce it at scale isn't cost effective relative to what big manufacturers think the potential market is.
I've been wondering this too; to what extent is grind thicnkess behind the edge determined by CNC limitations, or is it maybe just a conscious choice because they want the knives to stand up to abuse better.
 
If it could produce a series of cross sections along the length of the blade, with pictures and estimated measurements, that would be pretty fantastic
I’ve been playing with a cheap laser goniometer from Gritomatic. The reflections at a given point tell you a lot about the shape of the edge at that point.

I was thinking: in an MRI or CAT scan, some clever mathematics – involving the “Radon transform” – makes it possible to reconstruct a 3D model from scans that shoot light through an object. 3D scanners use triangulation and structured light methods to build the model by bouncing light off the object.

Intuitively, reconstruction of a knife’s edge should be possible using methods that are similar in spirit and probably simpler in practice. The goniometer’s graph of intensity vs angle paints a pretty clear picture of your edge: sharp bright spots means flat bevels, dim smearing means convexing.

Reflections appearing “off the perpendicular” suggest grinding grooves, but then we start getting into interferometry and begin to desire pricey lasers of different colours.

(If we assume the edge forms a convex hull we can exclude the special cases of concavity and preserve monotonicity in the transform. Sorry, no S grinds!)

If one could rig a mechanism to run the knife through the goniometer at a calibrated speed, one could build an “axial” model of the whole object, using little more than a webcam or phone camera to take intensity readings across the range of the goniometer. Then it becomes a video extraction problem, I think I’ve seen a Raspberry Pi tutorial for that.

As for edge thickness, a “bullet time” array of multiple laser sources aimed at the edge would produce a composite through the usual triangulation scanning method. Or a single source, we just have to move it laterally in relation to the knife.

A bit of Googling doesn’t show anyone having done this yet though. I suppose it would amount to a very specialized version of a 3D scanner.

Anyone have physics undergrads available for an independent study project? 🤪 Or a bright preteen doing science fair.
 
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I’ve worked with systems that can measure metal thickness (not surface shape) of a 3D part and generate a an image of thickness of the entire object. $$$$, not for home use!

Next time I have access to one I’ll have to scan some knives.
 
I think the ticket is structured light, which can be done with a consumer projector and camera. You just need the right software. Brown University has an open-source option, which I haven't tried yet. TBH as long as you're looking for visual representation, a single image showing the curvature in a linear pattern as projected on a curved surface would give a lot of info without having to do any 3d mesh reconstruction. I've previously considered using a line laser, but this does a single slice at a time.
 
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