Why the 40° edge will not score as well as the 20°

[KnifeGrinders]

Differentiation between keenness and sharpness has been best done by Todd Simpson:
Keenness is measured at the very apex of the edge, while Sharpness is determined by thinness of the edge behind the apex, and depends on the edge angle.
https://scienceofsharp.wordpress.com/201...-and-keen/
https://scienceofsharp.wordpress.com/201...en-part-2/

The BESS test line is severed in the test by combination of a cut and tear.
The test line is about 200 micron in diameter; to cut it the edge has to go through at least a quarter of that, i.e. at least 50 micron, where the tear starts developing, and the test line eventually gets severed.
Owing to this, the BESS score that we see on the instrument reflects both the keenness and sharpness of the edge.

We know by experience that a higher angle edge, e.g. 40 degrees included, scores worse on the BESS Edge Sharpness Tester than a lower edge angle, e.g. 20 degrees included, even when the edge apex in both splits hair, i.e. the keenness is the same. This difference in the BESS score is due to the "sharpness" component of the testing.

There are 3 testers in the world that quantify sharpness: the US BESS Edge Sharpness Tester for $179-259, the New Zealand Anago for approx. $20,000, and the UK CATRA for approx. $50,000 - 80,000. For a small-scale sharpener the BESS Edge Sharpness Tester is the only feasible. Only a few of the larger knife making factories use the CATRA testing, while the Anago is used by some makers of the industrial knife sharpening equipment.

Of all 3, only the BESS Edge Sharpness Tester tests both the keenness and sharpness, and can tell about sharpness in the razor range.

CATRA can not be used to evaluate the edge sharpness, because the edge is abraded beyond shaving sharp in its 1st cycle, the edge gets practically dull by the 4th cycle (can't cut print paper), and the full test includes 60 cycles. CATRA best evaluates role of the blade geometry and the steel wear resistance in the cutting ability.
The NZ Anago evaluates the edge sharpness, but not the keenness.

[EOU]

Holy smokes, we didn't know that the other guy's stuff was that costly! Thank you for the post KG!

EOU's and BESS's measurement philosophy is based on calculating how much force it takes to cut something. It's the same philosophy employed  millions of times each day, worldwide, by sharpened edge users. When you have to get up on the balls of your feet in order to apply enough force to push the knife edge through what you used to cut easily - even the cutlery neophyte knows that the edge is dull and needs to be sharpened. We simply borrow from that well established precedent with our edge testers and BESS test media.

Please don't forget about the value of BESS test media and the BESS scale here though. When an instrumentation user tells the Exchange that an edge measured 90 - we understand immediately just how sharp that edge is. This ability to communicate sharpness levels accurately is of huge benefit to sharpeners everywhere.

We've  shipped three times as many edge testers in the first six months of  2019 as we did in the same period of 2018. If we can maintain that growth into the future - most knife sharpeners will, one day, be talking BESS numbers and all for just, as KG reports with his usual precision; 179.00 - 259.00 dollars.

[Jan]

Todd Simpson quantifies the edge sharpness by the edge width at 3 microns from the apex. This definition is suitable to describe cutting during beard shaving.

Todd admits that for other applications, such as food cutting, it is better to measure the sharpness by the edge width at several millimetres behind the edge. The type of the blade grind is much more important in this case.

Jan

[grepper]

Mr. Jan uttered, "Todd admits that for other applications, such as food cutting, it is better to measure the sharpness by the edge width at several millimetres behind the edge."

Millimeters?  That far away from the apex his edge sharpness tester need only be a ruler.  

To my feeble mind the whole keenness vs sharpness thing and measuring sharpness at some arbitrary distance behind the apex shrouds the simple concept of edge sharpness in a superfluous veil of speculative ambiguity, thus relegating understanding of it to the ethereal realms of the ancient Chinese Zen masters of sharpening or maybe God. 

From a less convoluted perspective, I empirically understand that a more acute bevel and thinner blade cleaves material more easily.  That seems like a different issue, differentiated from apex sharpness.

[Mike Brubacher]

Your thoughts are well taken Jan. I take a little different view of the whole sharp versus keen theory  and my intransigence  has little to do with measuring the sharpness of edges or sharpening. It has to do with the English language and distinguishing, clearly, a new thought, method or process from the old. As an aside, it would be interesting to know if a parallel exists in the Czech language for the English terms, sharp and keen. If there is no parallel, then non-English speakers can't play this game. Clearly, in English dictionaries, the terms are synonymous and can be used interchangeably and even outside of descriptions for cutting edges i.e. " He has a keen mind " . Substitute "sharp" for keen and the statement's meaning remains unchanged. 

For all that Todd has done to clarify things for knife sharpeners (and that list is extensive), for me, this one, in trying to establish a difference between the terms sharp and keen, has muddied the water. I'm not commenting on the theory here, I'm just wishing that he had picked a different term to distinguish his theory; the "Todd Factor" would have suited me just fine. As it is, I find myself trying to remember which one is which when the subject arises. Is sharp what we used to describe an edge as and keen is the new factor or is it the other way around? I've been exposed to this theory off and on for years now and I can't keep it straight. It's difficult to imagine that newcomers to this sport would fare much better but perhaps they can; perhaps I'm just an old dog.

Please feel free to comment on this post.  Did you find it impartial or was it unbiased?  Oh wait, those  two terms  have the same meaning don't they?

[Jan]

Mike, in the Czech language we use only one word to describe sharpness. We do not have another word to describe similar properties of a thin edge that is able to cut things easily. I am sorry I cannot play the game sharp vs. keen with you because it may be English language specific.

On web I have found the following explanation:
The adjective "keen" comes from the Old English word "cene" that translates to "bold and brave" and while the spelling is now really different, the sounds are similar. Variations of keen as being "bold" and "strong" show up in other languages like Old Norse, German, Dutch, but apparently only English has the meaning of "sharp" — relating to "an edge or blade." Keen has a lot of close — and brutal — synonyms, such as caustic, cutting, piercing, and penetrating!

Jan

[Mike Brubacher]

Thanks for providing a response to my question Jan. I think that I may have to sit on the sidelines along side you. I haven't even gotten to sharp yet.

[Jan]

Mr. Jan uttered, "Todd admits that for other applications, such as food cutting, it is better to measure the sharpness by the edge width at several millimetres behind the edge."

Millimeters?  That far away from the apex his edge sharpness tester need only be a ruler.  

To my feeble mind the whole keenness vs sharpness thing and measuring sharpness at some arbitrary distance behind the apex shrouds the simple concept of edge sharpness in a superfluous veil of speculative ambiguity, thus relegating understanding of it to the ethereal realms of the ancient Chinese Zen masters of sharpening or maybe God. 

Mr. Grepper, Todd is focused on shaving, what is a very shallow cutting process characterised by dimensions in microns and first dozens of microns. During food cutting we have to penetrate and displace large volume of material whose characteristic dimensions are millimetres. That is the reason why the edge width measured e.g. 2 mm behind the edge may describe the kitchen knife behaviour better than the edge width measured 3 microns behind the edge.

Mr. Grepper, I have a question concerning keen and toothy edge. Can toothy edge be keen? It seems to me that keen edge is polished edge without teeth. But as a non-native English speaker I easily may be wrong.

Jan

[KnifeGrinders]

We are talking about cutting the BESS test line of 0.2 mm in diameter, and since during the test we actually have a combination of cut (initial nick) and tear, we actually are talking about cutting into the first 0.05 - 0.1 mm of the test line.

Thinking of an explanation for "Why the 40° edge will not score as well as the 20°" when the apex width is the same, I conclude that there is more than the apex width that gives the score we see.

You've seen a Big Brown Bear YouTube video that shows a knife scoring 4 BESS - that's how score his knives he intentionally sharpens at an edge angle lower than the straight cutthroat razors.
Well sharpened and properly deburred straight razors of 7-8 dps score in the vicinity of 20 BESS;
Quality knife steel properly sharpened at 10 dps scores 30-50 BESS;
The same knife steel at 15 dps scores 70-90 BESS;
and at 20 dps over 100 BESS.

Looking at this regression in the BESS score, at this drop in edge sharpness with the increase in edge angle, we inevitably think that the BESS score depends on more than only the edge apex width/diameter. The score comes from both the apex width and the edge width behind the apex, and the latter comes from the edge angle.

Practically, in actual sharpening challenges, it is futile to expect a 20 dps edge score under 100 BESS, and a 15 dps score under 50 BESS, even when in the hanging hair test both split it.

[grepper]

Mr. Grepper, I have a question concerning keen and toothy edge. Can toothy edge be keen? It seems to me that keen edge is polished edge without teeth. But as a non-native English speaker I easily may be wrong.

To be honest Mr. Jan, and while I could very likely be laboring under a delusion, I find this whole keen vs sharp thing to be extraneous fluff that only serves to further complicate and propagate the invented idea that sharpening is somehow mysterious and can only be understood by the most perspicacious of deep thinkers.

First the terminology, i.e., keen vs sharp is confusing.  The dictionary definition is sharp = keen, and therefore keen = sharp.  It is confusing even to a native English speaker.  But, just for grins, I will no longer use the word sharp to mean sharp or keen, instead I'll call sharp "sausage".  Additionally, I'll refer to bevel angle as "orange" and blade thickness as "kumquat", keen as "blunt", toothy as "nose" and polished as "elbow".

Maybe I'm just slow of mind and unable to fathom the intricacies in the pearls of wisdom presented, but this whole blunt vs sausage thing makes my brain hurt and only serves to muddle concepts easily understood and already extremely well defined, i.e., sausage of the edge apex, orange of the bevel and the kumquat of the blade.   Secondarily, is the edge finish nose or elbow.

I don't grasp the propensity in the knife sausaging world to confound and over complicate the beautiful simplicity of grinding an edge.  At least to me, sausaging need not be, and is not enhanced by making it complicated and, especially for someone just learning about it, appearing to be difficult to understand.  This stuff ain't rocket science.
 
"An ancient pond.  A frog jumps in.  Oh!  The sound of water!" 

Ooops!  Almost forgot to answer your question:  I believe a blunt edge can be either nose or elbow and both can be extremely sausage.