True flatness of diamond hones.

Edgepal,

The apex is the cutting point, EVERYTHING behind the apex is friction. The apex angle also does not need to be the complete bevel angle.... And edge geometry + hardness = the edges ability to withstand your uses. The angle itself is not the sole factor.

The angle wobble again is throwing you for a loop. When I sharpen and have 5 degrees of play I still end up with a 40 degree inclusive bevel apex with a 30 degree inclusive shoulder angle. My wobble is from the center of the knife not the sides so its rare my angles at the apex are different. In the past several months I have checked my edges with a CATRA edge protractor, out of the 300 or so times I used it I was only off by 1-1.5 degrees with maybe half a dozen knives. Not bragging just stating evidence in what I have discovered with my own sharpening.

Lagrangian,

You can grind a groove in a blade in a few short passes just by having your fingers in the wrong place applying pressure. Not a groove that's all to visible but enough to severely distort the edge if you sharpen below say 10 microns in abrasive size. So, if you touch the work piece in any way while grinding you must know how to "map out" the pressure points needed or you end up with high and low spots.

It's not the flex of the blade that changes the contact point its the opposing pressure. The work piece could be a few inches thick and I would be able to pinpoint where the grinding took place on the opposing side.

About the edges, edge 1) would be a noticeably better cutter and slide through material smoother with less possible micro chipping at the apex, its a total of 6 degrees thinner again geometry wins. Edge 2) would have wedging problems on thick materials as the Sharp shoulders would create a high load of friction before the transfer to the blade grind. Sharp angles don't flow.
 
Knifenut1013, things who are involved is, as you say, friction, steel quality, edge angle ,blade profile, and so on. All those things are involved. We have only, so far, discussed edge angles.

No, I am not looping. If you grind a flat edge, the sharpener will take away more material on the flat edges both sides (across the edge) – and minor material from its center, this because of the wobbling.

You have find out that you are wobbling 1-1,5 degrees on the edge. But, on the backend of the edge, have you measure that angle? You will see that you wobble 1,5 degree also there = total about 3 degrees – on one side of the edge – and half of that is on the side of the cutting edge.

If you sharpen a convex edge you have the same “problem”, both ends of the edge will be grinded more than the center of the edge. You understand this – and I respect that. When you understand this, you can also try to compensate this by wobble more on the backend of the edge – and minor wobble on the side of the cutting edge. In that way the edge will change minor – but – it will change the degrees on the angle – slightly. All those small changes add up to a point where you must regrind the complete edge. I think everybody recognize this “phenomenon”. Right?

Sharpening tools is nothing new, they are, at least 1000 years old. Already the old Vikings use sharpening tools to get good edges because they also understood this – and they work a lot in wood.

Stone age people for 6000 years also understand this. Their problem was not to get edges sharp, their edges was sharper then our edges are today – their problems was the retention of the sharp edges, they was very thin and very sensitive for “bending” and for side forces. So, they start to grind their edges, not to make them sharper, to make them stronger and so that they get more material in, and behind, the cutting edge.

So, this problem is more than 6000 years old. The goal is still the same (in my kind) to get an edge as sharp as possible – in combination with a very good retention – and we still struggle with this.

Most people, in my experiences, try to get their edges as sharp as possible, to shave with, make the arm hair pop – and so on. But, have that edge a good retention when you work with the knife? No, it have not. It is a stone age problem – in a new version, now people struggle to make the edges really sharp – and for 6000 years ago that understood that really sharp edges do not work properly…

Development?

(I am sorry, my English is limited as you can se. I would like to write things, but I have no words for it in English – and I know that my English can be seen as rude because I translate from Swedish directly – it is not my meaning at all to be rude, I just argue from my experiences.)

Regards
Thomas
 
knifenut1013 said:
Edgepal,
Lagrangian,

You can grind a groove in a blade in a few short passes just by having your fingers in the wrong place applying pressure. Not a groove that's all to visible but enough to severely distort the edge if you sharpen below say 10 microns in abrasive size. So, if you touch the work piece in any way while grinding you must know how to "map out" the pressure points needed or you end up with high and low spots.

It's not the flex of the blade that changes the contact point its the opposing pressure. The work piece could be a few inches thick and I would be able to pinpoint where the grinding took place on the opposing side.

About the edges, edge 1) would be a noticeably better cutter and slide through material smoother with less possible micro chipping at the apex, its a total of 6 degrees thinner again geometry wins. Edge 2) would have wedging problems on thick materials as the Sharp shoulders would create a high load of friction before the transfer to the blade grind. Sharp angles don't flow.
Click to expand...

Hi knifenut1013,

Thanks for your post! :)

----------------------------------------------------------------------------------------------------------
The part I think I understand:

I understand that the edge with 3 degrees of convexing (6 degrees if you count both sides) will have better geometry for cutting, and is less likely to microchip. I think you are saying that in practical, real-world cutting, these 6 degrees of convexing will be noticable. This is quite interesting to me, and I'm surprised enough to be unsure. But honestly, I have no reason to second guess your opinion; I have almost zero experience with convex edges. So thanks for your input.

btw, In my setup, where I compare [1] to [2], I have the v-grind set up so that the angle at the apex is the same as for the convex edge. So if you were to zoom into the edge with a microscope, at higher and higher magnification, they would look more and more identical. I understand that away from the edge there is additional friction in the V-edge from the "shoulder" of the bevel. So in the case of [1], the "shoulder" has been reduced only by 3 degrees per side, and the two sides of the convex edge only bulge out slightly (If the convexing were circular, then they are 3-degree arc of a circle on both sides).

I understand the idea that convex edges "flow" better in terms of wedging and friction behind the apex. I'm kind of curious at what point the convexing is so slight, that in practice, it becomes unnoticable to the user.

----------------------------------------------------------------------------------------------------------
The part where I'm confused:

It seems I'm misunderstanding your point about applying pressure while sharpening. I'm confused about the "groove" you mention. When hear the word groove, I think of something like a trench in a flat field (like a WWI trench the the middle of a flat meadow). I'm not sure how I would accidently put a groove... Unless I accidently hit the blade edge with the side (corner) of the sharpening stone. Probably you don't mean that, since that's obviously a very bad thing to do.

But this is very easy to make this mistake, if you are sharpening a straight edge which is much longer than the width of the sharpening stone. And this error is easily caused by misapplied pressure and/or misalignment so that the edge of the blade is not in the plane of the sharpening stone. You then cut a tiny trench in the knife which is parallel to the sharpening stroke, and is at most, a millimeter wide or so (depends how much the edge of your sharpening stone gouges into the knife). To reduce the damage of doing this, some sharpeners "round off" the four edges of their waterstones before using them. This is a lot like chamfering/beveling or deburring the edges of the sharpening stone itself. I know you know this; I'm only explaining because it might be what you're trying to tell me. If it is, then we're on the same page. If not, then I'm still confused.

I think I must be missing your point. Would you be willing to draw and post a diagram? That would probably be the fastest way to explain. Suppose I first magic-marker the knife bevel (ie: the Sharpie test), and then I make a stroke that cuts the groove you mention. What would that look like? Maybe you could just make a diagram with a long thin rectangle, and shade in the parts where there there is still Sharpie marker remaining. A quick camera photo of a pencil-sketch on paper, that would be good enough.

Sincerely,
--Lagrangian
 
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I demonstrate focusing pressure in my video sharpening a BK9, the methods and techniques used for the long flat sections of that large blade are the same as I speak of here. I don't know if you can put a size limit on it, the finer the stone becomes the smaller the point of contact becomes. If you take a blade such as a mora and place your fingers in the exact same spot for each pass the opposing side will show this to a trained eye. From here it becomes difficult to not be blade specific, maker, steel, hardness, grind, and so on.

As for the angle look at my video on the Les George, video 5. I show the use of the protractor.
 
Hi knifenut1013,

You're a veteran of the forums with a lot of posts and some very very long threads. It's a lot to search through. Could you please post a URL link to the threads (and/or specific posts), and/or videos you're referring to?

Sincerely,
--Lagrangian

P.S. I once asked richard j three very specific questions about paper wheels, and he told me to go read a super-long thread. That took me over two hours, and in there, I did not find the answer to my questions. I kind of don't want to do that again. Richard J, after that, though, did answer my quetions directly. But I wish he did that first; it's way more efficient.

This is why, generally in my own posts, I like to include links to videos and references.
 
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Hi Knifenut,

Thanks for the links! I haven't had a chance to see them yet, but I will, hopefully soon, be able to set aside time to watch them carefully. I look forward to continuing our conversation then.

Sincerely,
--Lagrangian
 
knifenut1013 said:
I demonstrate focusing pressure in my video sharpening a BK9, the methods and techniques used for the long flat sections of that large blade are the same as I speak of here. I don't know if you can put a size limit on it, the finer the stone becomes the smaller the point of contact becomes. If you take a blade such as a mora and place your fingers in the exact same spot for each pass the opposing side will show this to a trained eye. From here it becomes difficult to not be blade specific, maker, steel, hardness, grind, and so on.

As for the angle look at my video on the Les George, video 5. I show the use of the protractor.
Click to expand...

Hi knifenut1013,

Thanks! :) I re-read your previous post and watched your videos. I understand your points now.

About pressure on the blade causing uneven grind:
I see what you mean; if you were to push hard, and only at specific spots on the blade when sharpening, the stone would grind more underneath those specific spots, which leads to an uneven grind. It would be interesting to see if this can be quantified and measured.

It's a minor point, but technically, this is due to the knife (and possibly the stone) not being infinitely rigid. In theory (like from mechanics class, or theoretical robotics), if the knife were infinitely rigid, then the sharpening stone would not be able to feel where your finger was pressing. What's happening is that the knife is bending very very slightly, and is pushed down more where the pressure-points are. An analogy would be grinding a "cardboard knife" on "the sidewalk." Because the cardboard is not very rigid, it will grind more where there are pressure-points. The mechanical details are that the side-walk pushes back of course, and where there is no finger behind it, the pressure from the sidewalk makes the knife bend. These regions will be ground less. In the regions where there is a finger to press into the knife, the back-pressure from the stone is countered by the finger, and so grinds more. It is unrealistic, but in an undergraduate class on mechanics, we usually assume all objects are infinitely rigid. Although unrealistic, it's still a reasonable first approximation; afterwards, small amounts of bending can be calculated as a correction factor. (Large amounts of bending is another story; if there is huge bending, that has to be calculated from the start.)

I very much like your point about pressure-points and slight-bending, and will be thinking about it. Thanks! :)

Also, I see you're also using a CATRA laser goniometer. Very cool! :) I'm hoping to build one myself, using a laser pointer and some other stuff. Not sure how accurate I can get it, but I wish I could do better than 0.1 degrees. There are many problems for getting higher accuracy, one of which is that the surface-scratches on the bevel will scatter the light-beam, and several other minor issues and imperfections from real life. I bought a set of angle gauge blocks, so hopefully I can test and calibrate it properly. The blocks claim to be accurate to +/-20 arc-seconds, which is about +/-0.006 degrees. But they are cheap angle-blocks made in China, so who knows if they really are that accurate. But I doubt I'll get anywhere near that level of accuracy anyway, so probably they are good enough. If I get to make it, I'll try to post about it later.
http://www.amazon.com/gp/product/B005PH7AP6/ref=oh_details_o02_s00_i00

Sincerely,
--Lagrangian
 
Regarding pressure points/bending of the blade, resulting in uneven grinding:

Uneven factory grinds and blade warp account for more of the variation in contact between the hone and the blade. Rarely is a blade perfectly flat/straight anyway; there's always a little bit of bend/warp in them, more so with thin blades (I see this an awful lot on traditional pocketknives). A thin, warped blade with a straight edge, like a sheepsfoot or wharncliffe blade, will not be able to hide a tiny bit of warp after re-bevelling on a flat hone. Then, throw in a wavy grind from the factory, and this creates variation in thickness of the steel. If you hold a blade to the light, with one of the flat sides up, you can usually see the 'waves' in the grind. At more acute sharpening angles, the variation is more easily seen in the varying width of the bevel produced on the hones.

I have one particular pocketknife with an obvious, distinct deeper grind in a section from the plunge line (ricasso) to about 3/8" from the tip. The width of that section is exactly 2-1/2", which also happens to be a standard width of belts used on grinders. I have no doubt, the operator 'leaned into' the belt a little bit with this one, digging a little too deeply into the blade with the full width of the belt. This translated into a little 'hitch' in the bevel width at the transition in grind, 3/8" from the tip, where the steel becomes immediately thicker.
 
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I like that explanation, infinitely rigid is what we like to believe the knife is but its more like the cardboard knife. Changes in stock/grind thickness, hardness, and even the abrasive size of the stone all start to change the contact area on the edge and the methods needed to grind the object. I sometimes think of it as trying to follow one piece of grit with the next.
 
P(pressure)=F(force)/A(area). If Fc & Ac are uniform constant, P is constant(Pc), thus a constant/grail pressure.

1) Per Knifenut - uneven F => ununiform P => uneven grind (lead to 2 below).

2) Per knifenut - A(area) delta due to change in stock thickness, hardness, abrasive => Pnew = Pc*(1+delta). If stock thickness, hardness are constant for the entire bevel + perfect stone, Pnew is constant too =>no problem for this case. Ununiform P otherwise. I use 'delta' because this value normally inside of +-1.0 range.

3) Geometric intersection - A(area) factor change due to geometry, e.g. flat vs belly of edge. Pnew = Pc*factor. Normalize 'flat.factor' to 1, so 'belly.factor' = order of magnitude greater than 1 (in a pure geometry, a pt vs a line).

How flat is good enough? As long as stone high spots not exceed taller than 1/2 edge thickness, I also think (agree with Knifenut) that pressure is more important.

How constant the angle need be? Try keep within +- 5 deg wobble (:grumpy: - I wish my hands & eyes are that steady), it will mostly avg itself out. Again, pressure is more important.
 
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Hi bluntcut,

I agree with your points, including the one about wobble mostly averaging out. I have no idea how to quantify it, but I'm curious about how much it will average out. For example, if you sharpen a knife with some wobble, then the knife edge will be slightly convex. For a given amount of wobble how uniform and smooth is this convex edge in practice? Of course it will vary for different with different hands and sharpening technique, etc. But it would be interesting to have some understanding or example data for it.

In statistics, this is similar to asking how big is the variance (or standard deviation) around the mean (average).

Sincerely,
--Lagrangian
 
Let me see if I can describe this in English…

I have use a CAD program that can measure down to 0,001 mm. I have drawn an edge, the first 0,02 mm of the edge, (two hundred parts of 1 mm).
I have measure what’s happen to the edge if I add 1 degree. I marked out 10 degree and 11 degree and measure it.

When I change the edge from 10 to 11 degree, I add material to the edge = the edge gets thicker. 0,055 mm behind the cutting edge I added 0,001 mm more material to the edge. (1 thousand part of 1 mm).

• That is the practical result of changing an edge from 10 to 11 degrees – on the tip of the edge – or correct: 0,055 mm behind the cutting edge.

• In 10 degree, the edge have 0,010 mm material in the edge in this point, I went up to 11 degree and added 0,001 mm more material = 10% more material was added.

When I sharpen a knife by freehand, 34 joints in my both arms are involved, I have weights in my both hands(a knife and a sharpener) – and my hands, and 34 joints moves, all at the same time = it is totally impossible to hold a consistent angle. After years of training, it is possible to come down to only 3 degrees wobbling. Less than 3 degrees wobbling is impossible to perform for human beings.

When I wobble, where will the sharpener take away most material? On two points, on the side of the cutting edge – and on the other side of the edge –in the center of the edge it will grind away less material.

Why? It is a flat edge and the sharpener have a sort of supply from the flat edge. When it has this supply the surface of the sharpener grinds a big surface under a short time. When the sharpener starts to wobble, this support will disappear , and now the sharpener grinds a much smaller surface and on the cutting edge the sharpener have contact with just the side cutting edge – and the surface it grinds are just a thin “line” – and the pressure is the same = the sharpener grids away more material just here.

The edge is very thin. I cannot measure the cutting edge – but 0,006 mm behind the cutting edge, it is, in 10 degree angle, 0,001 mm thick = 1 thousand part of 1 mm thick.

When the sharpener are moving on just the cutting edge directly –in a higher angle – how many strokes will eat up the complete edge?
This small amounts of material I talk about here are not visible for the naked eye. You cannot see them or feel them with your fingertips (fingertips can feel a difference in 0,01 mm, not less than that).

But, the convex edge have started. For every sharpening you do, this small changes adds up to each other – and in the end, the edge will have an edge who do not penetrate material, it is too steep. You still can’t see it – but what this wobble have created is a very steep convex edge – on a very small part of the cutting edge – invisible for the naked eye.

To practical see what I talking about. If you have a carpenter axe (flat edge) and a felling axe (convex edge). Take the carpenter axe and find its angle in degrees when you slice wood, in what angle starts the edge to slice wood. Now, do the same thing with the feeling axe, in what angle starts the felling axe edge to slice the wood.

If we use the same angles on our axes, the carpenter axe will start to slice wood in about 10-12 degrees. The felling axe will starts to slice wood in about 20 -25 degrees because of its convex edge.

This is the result of what I have tried to write above – but minimize the result of the axe-edges down to a knife edge – and minimize that down to some hundred parts of 1 mm – and there you have the result of the wobble of, in best case, 3 degrees.

Was this possible to understand in my Swenglish?

Thomas
 
Hi EdgePal,

I believe I understand everything you are saying. I think it can be summarized as:
(1) High school geometry and trigonometry.
(2) If you wobble 3 degrees, then the bevel of your knife will be a convex curve where the surface tangent ranges over 3 degrees.

I could be wrong, but I don't think I need (1) or (2) explained to me... It seems straightfoward to someone with an undergraduate degree in physics, like myself, and probably is elementary to any engineer.

That's fine, but it doesn't answer my question. I'm curious about measuring real-world data on how much variance there is in the edge geometry for a given amount of wobble. It's possible to theorize as much as you want about ideal geometry, and how you want to model the wobbling (should it be a Gaussian wobble? Non-Gaussian?). But theory alone, without data, is virtually meaningless. I'm curious about what the variance is (standard devaition) for real knifes. I wish to see real experimental data.

Sincerely,
--Lagrangian
 
Lagragian, me too.

But how shall this be visible in reality? We are discussing some few thousand parts of a millimeter because it starts there.

It will be visible first after that the edge have been sharpened perhaps 10-15 times – but still hard to se.

Then, I don’t write it to you personally, I wrote this in a public forum - and I tried to write it so everybody can understand it…:)

Regards
Thomas
 
I believe you would see it using a microscope. Phil Wilson, and others, have mentioned a technique where the knife is sprayed with a mold-release agent (or just WD-40 if that's all you have), and then epoxy putty (such as JB-Weld putty) is put onto the blade to make a mold. After the putty cures, it is hard and unlikely to significantly change shape when removed from the knife.

At this point, the epoxy putty can be cut along a cross section and polished. It can then be put into a high-magnification microscope and photographed. Using a ruler, or measurement software in a computer, the angles and convexing of the edge can be measured. A high-end microscope can resolve features down to 0.2 microns, which is half the wavelength of visible light (visible light is around 0.4 to 0.7 microns). Lesser microscopes may be able to resolve down to 0.5 or 1.0 microns. So my guess is, probably, we can see it, so long as our equipment and experimental technique are good enough. Maybe? Maybe not? Depends on whether other unanticipated real-world effects get in the way.

I have not tried this myself, but to me it sounds like a very usable procedure. From what I've read, I have great respect for Phil Wilson, so if he has used this himself, I figure it must be a reasonable method.

Sincerely,
--Lagrangian

P.S. If the knife bevel has a really good mirror-polish, then it may be possible to use a laser-goniometer plus some additional optics, to see it. CATRA sells a laser gonoiometer for measuring blade angles, however it is only rated to an accuracy of 0.5 degrees. I'm wondering if it is possible to add additional optics to increase the accuracy by an order of magnitude or more.
http://www.catra.org/pages/products/kniveslevel1/lglm.htm

CATRA also sells an optical goniometer, but I have no idea how accurate it's angular control is.
http://www.catra.org/pages/products/kniveslevel1/og.htm

There may also be other ways of measuring the knife angle, some of which I'm thinking about. For example, it may be possible to rig a dial test indicator to a micrometer: Lay the knife on it's side so that it is flat and in the plane of the table (ideally a machinist's surface granite plate, or a 1-2-3 block). The dial test indicator would be set up with a tiny spherical tip (ideally, a tiny high-precision tungsten-carbide ball, or maybe a sapphire/ruby ball), and would measure the height of the blade above a specific point. The micrometer would be set up to push the knife at the spine, and would push the knife in the plane of the table surface. As the knife moved a precisely known distance (based on the micrometer), the dial test indicator would measure the height. Because the tip of the dial test indicator is a small sphere, the center of the sphere travels on an offset surface of the knife. This offset surface is the offset surface of the knife edge, where the offset is the radius of the sphere. The test dial indicator is really measuring the height of the offset surface, not the knife surface. So you would need a computer to do some math and reconstruct the original knife surface from the offset surface. Below is a brief diagram of how this might be done. Dial test indicators are easily available that are accurate to approximately 2.54 microns (ie: 0.0001" inches) or 2.0 microns. This may or may not be a high enough accuracy and resolution to see what we want, but I think it is worth a try.
69FPg.png


Of course, if you have access to a super-high-resolution CMM (coordinate measuring machine), or a super-high-resolution dial test indicator, test indicator, etc. then you can probably reach 1.0 micron resolution and accuracy. But that may require fairly high-end equipment. I don't know what the resolution is for super-high resolution laser scanners, but they might be in range. Mitutoyo sells some optical micrometers with incredibly high resolution and accuracy.

One might consider replacing the dial test indicator with a micromter that brings a spherical probe tip down. This is a possibility. However, one must carefully see if the downward force of the micrometer screw-mechanism is too big and actually deforms the knife edge which is very thin. Too much contact force is possible with a dial test indicator too, however, typically a dial test indicator has a fairly light contact force by design. Perhaps this could be overcome by backing the otherside of the knife with either hard stacking wax, or epoxy.

If contact pressure is a critical issue, then I suppose one could use electrical conductance, which is used in some CMM machines. The machine detects contact between the probe tip and the workpiece because touching them completes an electrical circuit. Of course, this requires that the workpiece and the contact-probe be electrical conductors.
 
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My English are limited as you know, I think I understand the principles you talk about – and it is a nice idea (as I understand it). Nice drawing by the way! They was helpful.

I measured from a point 0,006 mm behind the cutting edge, there is the edge 0,001 mm thick. To find out what’s really happened on the tip of the edge, we must be able to measure finer than 0,001 mm. We must come down to 0,0001 mm.

I somewhere read that today it is possible to get an edge down to 6 molecules wide. I do not know how big a steel-molecule is, but molecules’ are 1 step above atoms I think. Stone age people who use obsidian use edges 1 molecule wide (Obsidian molecule). So, their edges was then 6 times sharpener then our sharpest edge. Their problem was retention of the edge. Our problem, 6000 years later, is the same.

In think that polishing an edge, use light and study color of the light (spectra) can be possible to use because the convex sphere should (?) spread the different colors in the spectra like this \/ and it should be very accurate and readable…I think…perhaps…

I use a 3d drawing program: emachinshop, you can download it here: http://www.emachineshop.com/ and it is free. It is easy to learn how to use for drawings like this because you work with figures and type down length of lines and angles and so on – and this program can measure down to 0,001 mm, (it also works in thumbs). I can send you the drawing I did.

In my mind, the fact that the wobble forms a convex edge very fast is the impotent thing to accept and understand for all people who grind edges. I have discuss this for many years – and I have meet sometimes very strong resistance from people who clime that I am wrong in this – and that they can, by freehand, grind an edge perfectly flat. In my mind, when people understand what’s really happens to the edge – first then can they act against it. If they do not understand it – they cannot act against it.

I have say, many times, that this is both not a problem at all – and it is a very big problem. It depends on how much you use the knife = how much you sharpen the edge. I lived long times in the wilderness far from civilization, 6 month at the time. I very soon find out this during the sixties. First I did not understand what’s happened, later I did – and I could act about it. For me, and all the people around me, this was a big problem because we use our knifes hard every day. In the same time, people who do not use their knifes often, this happens very slowly, some never even notice it – and for them, this is not a problem at all. = this is a knife user’s problem.

It was because of just this I started to construct sharpening tools, first for just me; later people around me like to have one also. Knife users, woodworkers, whittlers, butchers, and so on, knows this problem and understand it. People who do not use knifes a lot – don’t. In my mind, this is important knowledge; a sort of base knowledge in knifes sharpening.

It is all about how many degrees you must angle out the neck of the knife before the cutting edge starts to slice wood (as my example with the axes) and also about the edge penetration skill. If the tip of the edge is to “dull” (have to steep angle) – you must use more force. More force makes the edge duller faster. If I don’t understand what’s happen to the edge – I do not act against it and sharpen my edge – and in that process the convex cutting edge will be steeper convex = it is a circle.

Thomas
 
Hi EdgePal,

Thanks for you link to http://www.emachineshop.com/ That looks very useful :)

As for sharpness length-scales, here's what I have so far (I'm copying a post I made to the spyderco.com forums). For me, the entire length-scale is anchored at 0.4 microns. This is because Prof. Verhoeven showed 0.4 microns is the approximate sharpness of a modern razor, and because 0.4 microns is the shortest wavelength of visible light.

180 - 7 Microns: Diameter of human hair. https://en.wikipedia.org/wiki/Hair
100 Microns: Approximate thickness of paper (copier paper of weight 24 lbs; 500 sheets is about 2 inches thick).
16 Microns: Thickness of household aluminum foil. https://en.wikipedia.org/wiki/Aluminium_foil
25.4 Microns: = 0.001 inches (1.0 mil). Standard resolution for an imperial caliper.
2.54 Microns: = 0.0001 inches (0.1 mil). Standard resolution for an imperial micrometer.
0.75 - 0.38 Microns: Wavelength of visible light. https://en.wikipedia.org/wiki/Visible_spectrum
0.4 Microns: Sharpness of a modern razor blade. http://www-archive.mse.iastate.edu/...te.edu/static/files/verhoeven/KnifeShExps.pdf
0.2 Microns: Resolution limit of optical microscopes. http://www.microscopyu.com/tutorials/flash/pixelcalc/index.html
0.05 Microns: Sharpness of diamond coated razor blades. http://www.technologyreview.com/computing/25988/
0.005 Microns: Sharpness of a diamond microtome knife. http://www.tedpella.com/diamond_html/diamondk.htm
0.003 Microns: Sharpness of concoidally fractured obsidian. http://en.wikipedia.org/wiki/Obsidian
0.00034 Microns: Van Der Waals diameter of a single carbon atom. https://en.wikipedia.org/wiki/Van_der_Waals_radius

This is also fairly interesting when combined with Komitadjie's Grand Unified Grit Chart, which is an approximate conversion between sharpening stone grits and microns. The graph below is made by Mr. Wizard who used the data compiled by Komitadjie.
http://www.knifeforums.com/forums/showtopic.php?tid/904090/tp/7/
e8mLQ.jpg


Finally, you should note that the sharp needle probes used in scanning-tunneling-electron-microscopes (STEM) and atomic-force-microscopes (AFM) are litterally so sharp they have a single atom at their tips. For a conventional needle, you cannot get sharper than that!

Sincerely,
--Lagrangian

P.S. btw, you should have a look at Clip's amazing microscope photos of knive edges in this thread:
http://www.spyderco.com/forums/showthread.php?54864-Under-the-microscope
 
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Langrangian

Yes, it is useful – and I think you will be amazed by the zoom function :) in this program.

Nice pictures – and it give me an idea, I hope a good one. The wobble would be possible to see in the scratches from the sharpener on the edge because it is possible to see where the scratches starts and ends – don’t you think?

Thomas
 
Hi EdgePal,

Don't expect me to be too amazed; I worked for one year as a programmer at Parametric Technology Corporation, which makes the CAD program Pro Engineer. Every few days, or weeks, they literally sell millions of dollars worth of CAD software, upgrades, training programs, or service contracts. Although the job wasn't a good fit for me, and I left after a year, I was extremely impressed with their software.

Sincerely,
--Lagrangian
 
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