How much error is tolerable in the sharpening angle?

Good questions.

How consistent does an angle need to be to get the best possible edge? How much tolerance is there for slop in maintaining angle while sharpening? A degree either way? A tiny fraction of a degree?

Acceptable slop is probably in the area of 10 - 20%.  More acute angles are less tolerant than more obtuse.  While I know you're looking for exact answers, I used the term "acceptable" because it's very soft.  In other words, a lot depends on the user and the intended use. 

The way to check for angle variance along the length of the blade is by using "the Magic Marker trick."  It will show you the high and low spots.  An uneven shoulder bevel is the consequence of angle bobbles, and the Magic Marker trick makes it very visible.  So does "the glint test."  But let's start with the MM trick.

Short rod tool and jig gags like the Lasky are okay for pocket knives, but something of a pain for long kitchen cutlery.  There are better tool and jigs.  But -- of course -- they cost more.

How much can the edge deviate from its line down the center of the blade (assuming a 50/50 edge) and not lose any sharpness?

I'm not exactly sure what you're asking.  Any deviation from absolutely true will be experienced as lessened sharpness.  But the assumption that 50/50 symmetry is or will be experienced as the sharpest is not only false, it's backward.  Everything else being equal, the more lopsided the symmetry, the closer to "single edge," the sharper the blade will feel.  

However, there's always a degree of tension between absolute sharpness and durability.  If the angle is too steep, or if the geometry too asymmetric for the knife's combination of profile, alloy, hardening, and the tasks for which it is used, the edge will not hold up long enough to be useful.  Similarly, if you sharpen a very high quality chefs knife to the same symmetry and angles as you would a heavy cleaver, you're not going to get anything like what the chefs can give.

The great thing about doing your own sharpening with a flexible system, is that you're in control.

There IS a definite learning curve to free handing, but it's hardly insurmountable.  You can become quite good without making a hobby out of it.  Ask a lot of questions, and stick with it. 

There are some good books -- Edge in the Kitchen by Chad Ward; some good videos -- Chef Knives To Go has a good, beginner's level, free series; several good web sites including Chat Ward's E-Gullet FAQ and Steve Bottoroff's site; forums devoted to knives and sharpening where you can get lots of help -- Fred's Cutlery Forum, the Knife Forum; not to mention several very competent people here.

Many of the people who teach sharpening will leave you with the idea that whatever system they use is the best.  Actually, there are a lot of good ways and a lot of mix and match, too.  Don't feel like you have to lock in on one, but don't be afraid either.  If it works great, if you find something better down the line you can change.

I've been sharpening for close to 50 years, have been pretty good for almost 40 of them, and am still trying and learning new things.

The questions you're asking indicate an intelligent approach, I'm confident in your eventual competence. 

BDL

Quote Nicholas; How consistent does an angle need to be to get the best possible edge?

Nicholas, I cannot emphasize more; sharpening knives is all about maintaining angle consistently. The better you are at it, the better the result will be!

But, when performing manual sharpening on stones, there will always be a systematic deviation in the consistency no matter how hard you try not to. Your body does it, simply watch your hands when sharpening, you will see how difficult -read impossible- it is to keep the exact angle. I would dare say there's not one handsharpened knife that doesn't have more or less convexed bevels, unless it's done by a robotarm.

The best way to maintain angle consistency when sharpening is to forget about "the rules" that say you have to sharpen at a so-and-so angle. The very truth is that most people who sharpen regularly don't even know at what angle they sharpen! Why? The best angle to sharpen at, is to let your handpositions be taken over automatically into a "natural" position without trying to force them into what feels like an unnatural angle dictated by "the rules". Just always obey to what angle your hands go to automatically and you will simply perform the best sharpening ever ànd have less work to resharpen them using the same natural angle.

Just to indicate how unsignificant a strict sharpening angle is, take a look at this chart I made a long time ago. It's made to check the angle you actually sharpen at. It's very simple to use. Measure the height of the blade of your knife (measure at the heel). Look that up in the left column. Measure how high you lift the spine of your knife above the sharpening stone (measure at the same spot, this time straight above the heel). Look that up in the row to the right. At the top of that column is the exact angle.

Now, compare two adjacent values in a row. There's so little difference, which indicates how insignificant a strict sharpening angle is. Unless someone is able to make changes in spine position less than 1 mm... 

(Click on the image to enlarge)

I thought long and hard before posting again because I neither want to be in nor be seen to be in competition with Chris.  But, I think the following, as written, is terrible advice, and didn't want to let it stand without comment.

The best way to maintain angle consistency when sharpening is to forget about "the rules" that say you have to sharpen at a so-and-so angle. The very truth is that most people who sharpen regularly don't even know at what angle they sharpen! Why? The best angle to sharpen at, is to let your handpositions be taken over automatically into a "natural" position without trying to force them into what feels like an unnatural angle dictated by "the rules". Just always obey to what angle your hands go to automatically and you will simply perform the best sharpening ever ànd have less work to resharpen them using the same natural angle.

If Chris means "don't sweat the difference in a narrow range, like that between 14* and 16*, if you can hold one easily and not the other, that's not only true it's good advice.  But if he meant that you should sharpen all your knives at whatever angle is most comfortable and "natural," that's bad advice.

Bevel angles can be too acute or too obtuse for a given knife and/or a given task.  "Natural angle" notwithstanding, you don't want to sharpen a "lobster cracker" to 10* or a "laser" suji to 25*.   There are ways to set your own angles with relative precision, and an excellent way of finding the factory angle on a new knife ("clicking in") which is usually very close to what you want anyway.  After sharpening that angle carefully for a little while, your wrist will automatically lock in.  Furthermore, whatever angle seems "natural" to you, can and will be altered by minor changes in posture and how you use your shoulders, hands and arms during the sharpening stroke, not mention tempo and pressure.

I'm not saying it's the be all end all of angles, but "clicking in" is usually a very good place to start.  Do this by laying the knife flat on your stone, and with a very soft grip, rotate it up so the edge stays on the stone.  You'll feel it as you pass the angle the to which the knife was already set.  Then, rotate the knife so it goes back flat, and again you'll feel it as you pass the set.  Do this a few times, and you'll quickly be able to feel the set itself.  Stop rotating at the set, and the knife is "clicked in."  For what it's worth, that's how most carpenters sharpen.

Probably the most common method of determining an angle is iterative guesstimation.  Hold the knife straight up on the stone and say, "that's 90*."  Halve that and call it 45*.  Half of 45* is 22.5* (although you'll never hit it that exactly), an excellent and common angle for most older Euro stainless, knives intended for heavy duty work, etc.  A third of 45* is 15* -- your basic Japanese knife, while half of 22.5* is a skosh more than 11*, close enough to 10* for high performance Japanese knives.  It's not exactly perfect, but more than likely "close enough" for kitchen purposes. 

Another method, is to use a protractor and/or graph paper to draw large examples of the desired angle, place a few of them around your stones, and compare frequently as you slowly and gently sharpen.  I know it sounds stupid, but it's how I taught myself to profile given angles with fair accuracy.  The fact that I am stupid doesn't mean it won't  work for you.

Once you've started to sharpen at a given angle, the Magic Marker trick will show you any deviations and allow you to repair them by "sectioning" (working on one part of the edge at a time), and grinding out the low spots.  Changes in the width of the bevel shoulder (which you can clearly see against the marker's black) is a very sensitive gauge of angle variation.  I can't over-emphasize how helpful the MM trick is, nor how much I wish I'd been taught that way.  (I learned from the Boy Scout Manual in the early sixties). 

Most of us tend to "click in" unconsciously with just a little extra obtuseness to feel the edge on the stone.  Consequently, after each sharpening the angles become increasingly obtuse; and after a few sharpenings we have to "thin" our edges.  

As you gain some experience, I think you'll find that motion, posture, pressure and speed are more important to consistency than a "natural" sensation  for your wrist.  If you sharpen with too much forearm, and not enough shoulder, or too fast or too hard for your skill level, you'll be inconsistent with any angle -- no matter how good it felt.

I suggest taking a look at Chris Ward's sharpening FAQ posted on E-Gullet, who will explain a lot of this.  Better still, watch the (free!) sharpening video tutorials at Chef Knives To Go.  In addition, you may want to read some of the sharpening posts on my site, CoodFoodGood.

It sounds complicated, but becomes automatic very quickly. 

BDL

Quote Nicholas; ...With the amount of hand-wavering that happens when a reasonably competent sharpener sharpens freehand, assuming that they don't push the angle at the edge more obtuse than the intended edge angle, the variations in angle won't negatively affect the edge, but instead introduce a slight convexity...

The convexing effect cannot be avoided when handsharpening! But, there's a more important effect! When making lower angles than intended, the edge will not drag over the stone surface. However, when making a number of higher angles than intended, the edge will drag over the stone at another angle too. When making too many of these movements especially when using high grit polishing stones, you could notice that your knife gets duller instead of sharper... you just have been "rounding" the edge again!

That's why I suggested in my previous post to use a more controlable natural angle. Of course it's not free of making deviating angles, you just will make less of them. I'm talking about reasonable natural angles. Here's an example, not one of my preferred VG10 knives but on one of my still most used knives, the no-nonsense Fujiwara FKM210. I have no idea what angle it is. It has just been tweaked a little on a coticule natural stone.

Also, I cook a lot but I'm not a professional cook, so I don't do daily sharpening like you will probably do. I perform occasional complete sessions starting with a 1k King synthetic stone or an 800, never lower than that, except when I have damage to repair. After using the 1k, I go to non-synthetic stones; a 4k Belgian Bleu and a 6-8k coticule.

Between these occasional "complete" sharpening sessions, I only tweak edges with the 4k Belgian Bleu and/or the coticule.

Info on these natural stones; http://www.ardennes-coticule.com/index.asp?ID=358

I can't give information nor on the stones you mention, nor on the knives. I only know them by name and reputation on the knife forums. I prefer to talk about my own experiences only.

Originally Posted by Nicholas Beebe 

There's a lot of discussion, passion and controversy about "convexing," on the Knife Forum.  It's pretty much a tempest in a tea pot.  Some convexing is probably inevitable.  It doesn't do a lot of harm or good. 

Edges with significant, intentional convexing are more robust than perfectly flat bevels, more resistant to the kinds of deformation called rolling and waving.  Everything else being equal, they lack the same feel of absolute sharpness, as they're thicker and have more of a tendency to wedge -- even at the micro level.

Trueness is the technical term for straightness.  A true edge will always seem sharper than one which is out of true.

As a practical matter, multiple bevels and convexity are very much the same thing -- that is, they feel and work the same in the cut.  In most cases, it's easier to control intentional double or triple bevels than to create an edge with the same degrees of convexity on both sides.

The Rika is a very easy stone to learn, low cost, and pleasant to use.  In most ways it's more like a 3K than a 5K, and should be considered on the fine end of medium.  The Arashiyama is more of a finishing stone, which cuts as fast as a 6K but finishes more like an 8K.  In fact, it was often sold as an 8K.  Either stone would be fine following the Bester 1200.  The Rika's edge will be toothier, the Arashiyama more polished.  The Rika's will hold up slightly better through a service or two -- but only slightly.  You can feel the difference between the two edges when cutting, the Arashiyama's feels smother.  It's not worth sharpening a line knife any finer an Arashiyama.

I'd probably go with the Arashiyama, but it's very much a matter of taste.

They're very different knives.  The problem with plastic boards is that a sharp knife cuts into them, and can chip if there's any torque (and there always is) when the knife is lifted out of the cut.  My HD hasn't shown any propensity for chipping, and my experience with Shiroko is that it's also pretty chip resistant.  However... plastic boards on the line is not an easy environment for a knife.  If those are the only three choices, I'd go for the Kikuichi.

Also, plastic boards tend to deform edges.  If you're planning on using a rod hone (aka "steel") on the line to true them up, don't even think about a laser -- any laser -- as they don't true well on a rod.  My guess is there's so much pressure at the contact point, and the knives are so flexible, they edges deform on the rod itself.  And frankly, steeling anything harder than 60RCH is kind of iffy in terms of chipping. 

If you're seriously invested in using a wa-gyuto on the line, you might want to talk to Jon at Japanese Knife Imports who has a very interesting selection and knows as much about this stuff as anyone else; and you should definitely talk to Mark at Chef Knives To Go.  Given your current selections, it seems you're probably planning on ordering from CKTG anyway.  Let me add in passing that Jon's had his stock of HDs rehandled to a stabilized and more "normal" ocatagonal wa handle; while Mark sells them with the "prestigious" half-round bottom.  Mine has Mark's handle.  I love it, but the feeling isn't universal.

BDL

KS is a great wa-gyuto.  Very few as good, and none better.  I've used a 270 KS a lot, but can't say whether or not it's really appropriate for lots of work on a plastic board.  My feeling is not.  FWIW, it's just fantastic.  If you can live with a western handle you might consider the Masamoto HC which has the same basic profile but along with the western handle has a full tang.  Masamoto and other Japanese manufacturers make the yo knives a little thicker and heavier than the "wa" models which have a transitional machi instead of just going blade/tang.

The HC isn't shiroko, but V2C which is very special in its own right.  It has the same Masamoto gyuto profile -- very Sabatier-like and very wonderful.  On the one hand, there's nothing really exciting about it, but on the other there's nothing at all wrong with it either; comme il faut in my opinion.  Over the years I've had the chance to spend a lot of hours with an HC, and for a long time it was on the top of my list. My tastes changed a little, but I still think it's a great knife. 

If you want a wa-gyuto let's start over from the beginning instead of concentrating on a couple of knives that have so far struck your fancy,

BDL

I'm going to add a caveat to BDL's statement.
 

Quote:

Originally Posted by boar_d_laze 
As a practical matter, multiple bevels and convexity are very much the same thing -- that is, they feel and work the same in the cut.  In most cases, it's easier to control intentional double or triple bevels than to create an edge with the same degrees of convexity on both sides.

...with stones.

Once you learn stropping, equal convexity happens quite naturally. But it's a rather different technique than anything on a stone as you're relying on a somewhat deforming substrate rather than a rigid stone. You can do it on a stone. You still use an edge trailing stroke, and roll the wrist/blade into the stone to match the convexity. I find that difficult compared to a leather strop on a board or a suitably stiff-but-giving mouse pad and sandpaper.

The perils of this sort of convex edge is that it's often difficult to restore from dull. It's much easier to maintain frequently than restore it occasionally.