And now, Harold Angel will sing …

Since I’m in an edgy mood, it’s time to take another whack at Evan’s questions.

This time we’ll go back to the top:

1. You've talked about different kinds of sharpness -- cutting turkeys vs cutting tomatoes vs wood carving. What do you do for knives you use in the kitchen for multiple purposes? Chopping onions, mincing garlic, slicing tomatoes, slicing cucumbers, etc. I keep a separate knife around specifically for cutting bread, ought I to consider keeping separate knives around for tomatoes?

Good question!

Our stock answer [woo hoo! a kitchen double entendre …] fits pretty well here: it depends.

If you’re a serious cook and you can really feel the difference between these degrees of sharpness/smoothness when you’re cutting up stuff in the kitchen … by all means, prepare specific knives for specific tasks.

If you’re a not so serious cook, well … don’t sweat it.

Certain foodstuffs, like bread, pretty much require a specific knife … unless you like your loaves mashed and torn instead of sliced neatly.

Tomatoes are another item where a specially prepped knife can do wonders … but unless you’re a true fanatic, a highly paid professional or just get your kicks from having a fully loaded knife rack [stop trying to look innocent!], a properly sharpened chef’s knife will probably do the trick quite nicely.

When we move from the prep side of the kitchen to the staging and plating of foods to be served, it’s time to add a knife or two to the equation …

For carving neat slices off large hunks of roasted meats, you can’t beat a good carving knife. Likewise, if you’re doing fancy garnishes or tiny sculpted veggies you’ll probably want something other than your handy-dandy chef’s knife … but those [in my experience, anyway] are the exceptions. Most of the time, the knife I reach for is my tried and true 9 inch chef’s knife.

Until next time, ‘appy ‘olidays!

We digress for a short while ...

It's been waaaaaaaaaaay too long since our last installment
of Sharpenology, and I was recently reminded of this by a
loyal reader and good friend ... who shall remain nameless,
but whose initials are W. Evan Sheehan.

Thanks Evan!

Evan had some questions and I'm pretty sure that he's not
the only one with these questions ... or some that are very
similar ... so I decided to get back in to the writing rhythm
by addressing them.

It all began with this [with minor edits by Yours Truly]:

So many questions...

I am concerned that, at best, I am doing my knives little
good and, at worst, that I am harming them.

I've just finished running my two beloved kitchen knives
over my whetstone; they feel sharper, but not Doc-Sharp (TM).

I also tried helping out [his sweetie's name went here]
knives which have -- to my knowledge -- never been
sharpened before.

I've also got some questions brought on by thinking --
dangerous, I know -- about Sharpenology.

So, in no particular order and without further ado:

1. You've talked about different kinds of sharpness --
cutting turkeys vs cutting tomatoes vs wood carving.

What do you do for knives you use in the kitchen for
multiple purposes? Chopping onions, mincing garlic,
slicing tomatoes, slicing cucumbers, etc.

I keep a separate knife around specifically for cutting
bread, ought I to consider keeping separate knives around
for tomatoes?


2. How does one learn to tell the difference between the
different types of sharpness? (Some of this may already
have been covered on Sharpenology, in which case you'd
not be remiss to smack me in the head and just point.
I should be re-reading that first.)


3. How do you learn to tell when a blade is sharp and
when it needs sharpening?

I've tried looking at the blade, but except to notice
notches it doesn't seem to do me much good. I can
feel that the blade has more bite after I'm done with it,
I've always assumed that meant it was sharper: true,
false? Are there different tests for different types of
sharp (related to #2, I know)?


4. How do I improve my sharpening technique? I haven't
really got anyone around to teach or watch me do it, so
I've got to figure out some way of self checking.


5. Sometimes I feel more of a bite running my finger
right-to-left than the other way, does that mean I did
something wrong?


6. I've noticed a couple of knives with a bevel that is
nigh invisible or maybe not even there, do you have
any tips that will help me not fubar these blades?


7. Where did you learn all this stuff? Maybe I can quit
bothering you and go deal with some of this on my own.

**********

That's a whole lot of questions ... so I'll address the easiest one first:

Where did I learn all this stuff?

[sigh]

Many moons ago ... when the Earth's crust was just beginning
to cool, several years before I met M. Animal MacYoung ...

Oh, sorry! Wrong story ...

I learned about the importance of maintaining ones tools from
my grandfather ... who was the most brilliant natural engineer
I've ever met. He could build anything out of practically
nothing, and could repair any mechanical [or electro-mechanical]
device he ever laid hands on ...

When I began collecting knives at the tender age of 8 or 9,
I figured that I'd better learn to take care of them so that
they'd always be ready to take care of me.

In those days, about the only information around came from
books ... either about knives or knifemakers, and these were
few and far between.

Somewhere in those early years I came across a brief essay
on knife sharpening by A. G. Russell ... who was also selling
arkansas whetstones ... and I saved my pennies to buy one
of these stones & followed A. G.'s minimal instructions on
how to use it.

After many hours of trial & mostly error, I was able to
leave knives in better condition than when I found them.

I kept at this as my collection of knives grew and over
time discovered more books & articles on knife maintenance
which I cheerfully devoured ... gradually accumulating a
collection of sharpening stones and devices equaling my
collection of knives.

As I worked my way through all of these wonderous devices
and 'new' methods of sharpening my beloved knives [and by
this time, the knives of many of my friends and neighbors]
I realized that my grandfather had been right [again] when
he told me that I should learn to work with the simplest
tools, because they would always be available to me.

In this case, the simplest tools were [and are] my hands
and a nice, flat whetstone.

Since that realization, I've used a wide variety of
whetstones ... and am still testing and comparing as
'new' ones are available ... but it still comes back
to the fundamental tools: my hands and a nice, flat
whetstone.

So ... the short & sweet conclusion of that long-winded
answer is: practice.

Probably not the answer that Evan [or any other
folks who might actually read this] wanted to hear,
but that's just how it is.

Next time, more answers to Evan's questions ...

Further dimensions of Sharpenology ...

Ok folks, it's been a while since my last edgy monologue on things sharp.

More precisely, on things which should be sharp ... and I hope it's worth the wait. It's got more words than my earlier posts cuz it's on a topic that's got a lot more dimensions to it ... [pun cheerfully intended].

As promised some time ago [yes, Ted ... a looooooooong time ago], I'll begin looking at some of the qualities and design features which can make a knife more [or less] useful in a variety of situations.

The three most basic of these are blade length, width and thickness [thinness?].

We'll also begin looking at blade shape ... and that is an area which will probably require several return visits in future installments of this little slice of heaven.

Back in some of our earlier examples, we looked at edge geometry & grinds with an eye toward what *sharp* really means ... and we saw that a particular grind could be very good for one purpose [like shaving] and very bad for other purposes [like carving a roast or chopping wood].

Now we're going to take a step back and look at blade geometry and see how that can enhance the usefulness of a knife in both specialized [like skinning, boning or filleting] and more ... um ... general situations.

Let's begin with an activity that can benefit from a fairly specialized design and see how we can tailor a blade to make it just a bit easier to get the job done ...

Say you're a hunter, and you've just bagged a nice elk. The easy part is now done and it's time to haul it home and turn it in to dinner ... well, quite afew dinners, but I digress ...

After you've wrangled the carcass home and got it hanging up, you need to work on breaking this rather large and complex hunk of meat, bones, skin and other goodies in to manageable chunks that will fit in your freezer, look good on your trophy room wall and perhaps get turned in to a pair of moccasins or a nice bag for you or a friend.

Without going in to gory detail ... ahem ... this means that you've got to open up your prize & clean out the internal organs without getting any nasty fluids [or solids] on the meat you plan to eat, separate the parts you want to put up on your wall from the rest of the hide and separate the hide from the parts you want to eat ... cuz it's easier to do a good job of butchering when you don't have skin in the way.

For the moment, we'll assume you've taken care of the innards ... and we'll move to the skin removal portion of the show.

To do this with minimal damage to the skin you need a blade that is sharp [what a surprise!] and won't get in your way when you're working in tight areas ... that way you'll maximize the amount of usable hide and minimize waste.

Remember our earlier examples of the razor and the axe ?

It's time to apply those principles again ... and to add another couple of dimensions to the mix just for good measure.

You need a blade that is sharp, but won't bind ... so a razor-like profile is out, and you need to be able to make reasonably precise cuts and change direction easily [quickly, too if you're not being careful] ... so a thick blade isn't a great idea, and depending on your level of skill at this kind of thing ... it probably wouldn't hurt to keep the length of the blade on the shorter side so that you've got better control over where the tip is in relation to the handle.

Another consideration here is that there aren't many straight lines in this kind of work ... and since you want to maximize the amount of usable hide you get out of this, you'll want to be following the natural curves closely.

Ok ... now we've got the requirements, let's look at how to meet them ...

Thin enough for good cutting, thick enough to support edge geometry that won't bind while you're working, short enough to give you tight control over where the blade is going and curved enough to help you follow the curves that are already there ...

Where do we go from here ?

Let's start with length and profile, since those are features we haven't discussed in our other examples ...

For my own use [and discussion here], I've got a set of working criteria that I apply to blade length ... those of you who have spent time around horses will should pick up on this very quickly, cuz it's what you folks already use to measure those lovely critters ... it's the hand.

When I think of a small knife, I'm usually picturing one with a blade of 5 inches or less [12.7cm, give or take, for the metric folks] and that's 1.1 hands ... a shade more than the width of my own hand. Very convenient for measuring, since I take them with me everywhere ...

By that same roundabout process, I think of a large knife as having a blade of 2 [or more] hands in length ... which leaves a reasonable middle ground and gives us some starting points for more discussion later on.

So ... let's take a length of 5 inches and move on to width.

Just as length can help or hinder, the width of the blade will also have effects on the ease &/or precision of the cuts we'll be making ... so we should be looking at enough width for strength [just like blade thickness,blade width is a factor in both durability and flexibility of a knife], but not so much that it prevents us from working in tight areas.

For a knife with a 5 inch blade, let's begin with a width of 2 inches ... a bit under half of the length of the blade. At this point it's an arbitrary decision but a reasonable one, and we'll check back on this from time to time to see if this width is still reasonable as we add in the other features and dimensions of the knife.

The next dimension is a little tricky ... blade thickness.

Blade thickness could be pretty much anything from as thin as a razor blade [with the obvious drawback of not being very durable] to as thick as an axe which would tend to limit the precision of our cuts & overall 'handling' ofthe knife, especially in tight areas.

For fixed blade knives, blade thickness [measured at the spine] typically ranges from about 1/8 of an inch [approx. 3.175mm] to 3/8 of an inch for 'heavy duty' blades which may be expected to double as lightweight hand axes in an emergency situation.

Back to our current design problem ... we want something that's thin enough to allow the blade to move easily as it's separating skin from meat & bone, and thick enough to take a little punishment if we accidently run in to some-thing tougher than skin or meat [like a bone].

Let's start at 3/16 of an inch [approx. 4.763mm] as a good compromise for giving us a relatively thin profile, but still having enough substance to take some punishment without causing severe damage.

Our theoretical skinning knife is now made from 3/16 inch stock, is 5 inches long [not including the guard & handle] and 2 inches wide ... but what shape [or profile, if you prefer] is it ?

Back again to what it will be doing and how it will be used to do it ...

Most likely, the cuts you'll be making with this knife will be gently curved, cuz there don't seem to be too many straight lines in this kind of work ... [at least at this early stage] ... and since human arms & hands tend to work in arcs, a blade that is too straight will probably wind up getting in your way sooner or later.

A common gentle curve for this type of knife gives us something called a trailing point, which means that the point of the blade follows [or trails after] an imaginary line drawn from the base of the blade's spine [where it would meet the guard] forward past the end of the blade and off in to space.

Contrast this with a drop point [or leading point] design, in which the point of the blade is forward of this same imaginary line.

Why a trailing point instead of a leading one ... ?

Imagine you're peeling something apart ... and to help things along, you're running your index finger along the line of separation ... it's kinda tough to see exactly where the very tip of your finger is, but it's not too hard to see where it was ... right?

Now replace the tip of your finger with the point of a knife ... and give that knife a curve which allows you to work in an arc [say, pivoting from your elbow] ... if the point is leading, you don't really know where it is and this may increase your risk of poking a hole [or holes] in one or both of the layers of stuff you're trying to peel apart.

If that point were trailing, you'd still be able to maximize the work you're doing by taking advantage of the arc of movement from your elbow, but you'd also have the ability to see where the point of the knife was while you were working ... and that would tend to minimize the risk of poking a hole in it while you were working.

There is a lot more to blade geometry ... but I think that's enough to chew on for now, so I'm going to wrap this up and save a little bit for our next installment.

As always, all y'all can post specific questions &/or suggestions for new topics ... and I'll see about answering them directly or maybe including them [with answers &/or comments of my own] in a future installment.

Y'all come back now, y'hear ...

... and the bleat goes on ...

In the first installment of Sharpenology, I bored all y'all with my observations about what constitutes sharpness and a brief overview of tools that can be used to get things sharp.

This time, I'll be blathering on about grinding & edge geometry,
so be prepared for some more of my silly ranting and observations on what makes sharp things useful ... and perhaps even a little bit on how to keep them in a state of readiness.

If yer eyes are already rolling back in their sockets, just move
along to some gardening blog or other such nonesense ... or continue reading and kwitcherbitchin.

Ahem ...

As I was finishing up my last posting on things sharp, I was
beginning to think about some of the factors that make a sharp
thing useful for a particular task ... and while sharpness is
certainly an important factor, it isn't the only factor to be
considered when looking at an edged tool.

Take, for example, the humble wood-chopper's axe.

While a good axe can be made shaving-sharp [and a sharpening
tool manufacturer uses this as a marketing pitch for their
brand of gadget], the edge geometry of an axe isn't what you
would call ideal for cutting hair.

Why not ... ?

I'm glad you asked ... <grin> ...

The typical axe is ground to a convex cross-section, coming
down to a fairly thick edge ... while a typical razor is ground to a concave [or hollow] cross-section and comes down to a very thin edge.

What does this mean to the wood cutter &/or the barber ?

Imagine using a straight razor [open razor or cut-throat for
the Brits out there ... you know who you are ...<grin> ...]
to cut wood ... <shudder> ... you'd take a chop at the wood
and there you'd find your blade.  Stuck ... and probably
missing [or about to be missing] a chunk of that lovely, fine
edge you spent hours perfecting & polishing.

But it's sharp as a ... razor ... I hear you say, how can it
get stuck ?

It gets stuck because it is designed to cut without pushing
what it is cutting away from itself.

Huh ?

Think about it for a moment ... now remember those fancy ads
on teevee that show a razor gliding down a shave cream covered
face ?  Remember how that fine edge sliced through the thick
[relatively speaking] beard hair and pulled it along just a
bit ... so that the second [or third, or fourth ...] blade
could cut the hair off under the level of the skin surface
and create the perfect start for a painful ingrown whisker ?

That same effect will demonstrate itself on a much larger
scale in the wood you've tried to chop with that razor ...

The fibers of the wood will close back up against the blade
and trap it ... at best ... or break it ... and you won't have any firewood or any way to shave the next morning.

Ahem ...

So what happens when you cut wood with an axe ... ?

Basically, the edge is sharp enough to cut the fibers of the
wood ... and the convex shape of the blade behind the edge
pushes these cut fibers away from the blade, thus releasing
the axe for another swing ... instead of allowing them to
stay close and trap the blade.

Ok, but I'm not using a straight razor or an axe ... so what
does this all mean to me ?

The straight razor and the axe are two extremes of grinding
types used in modern cutting tools ... and as such, are good
examples of single or limited purpose tool construction.

Another example of this is the chisel [hi Kevin!], which
any sufficiently fanatical woodworker will polish to a level
that will bring tears to the eyes of the village barber.

Yes, like our friend the axe ... you could shave with a chisel.

<shudder>

But that isn't what it was designed to do, so we'll skip that
particular demonstration.

The chisel's grind, however is useful because it is very strong.

Unlike the hollow grind used for our straight razor, the chisel's
flat grind has left us lots of material behind the edge ... which
gives the chisel the rigidity and strength to push through tough
wood fibers, while the angle of the grind pushes those same tough
fibers out of the way to they don't impede the next cut.

Pretty good design, eh ?

But what has it got to do with knives ... ?

Ok, I guess it's time to bring all of this together and get on to
the more practical aspects of grinds & edge geometry.

All of the examples I've given so far have been at the extremes of
their respective geometries ... what you find in a typical modern
knife is usually a combination of one or more of these design ideals executed to a less extreme degree in order to make it more broadly useful in a variety of circumstances.

Here's an example ...

A certain American cutlery company, which shall remain nameless ... [but whose initials are Buck], used to advertise that their knives were 'sharp as a razor, strong as an axe' ... and used a graphic which depicted a knife cutting a nail to show this combination of strength and cutting ability.

They also took great pains to tell their customers that the actual performance of the nail cutting trick would void any warranties on their products, but that's another story.

How could they make this claim of sharpness AND strength ?

Better still, how could they back it up ... ?

Simply enough, really ...

They just developed [implemented, really] a grind which gave their knives a thin cutting edge [for excellent sharpness], yet a thick and strong spine for durability.

The semi-hollow grind.  While they didn't invent it, they certainly
put it to good use both in their products and their advertising.

Other effects of this particular grind are to make the blade lighter,
which can make it easier to control in certain applications and to
make the blade less likely to get stuck in whatever it is cutting by
moving the material away from the blade after it is cut.

Other examples of applying different grinds & edge geometries to knife design include such lovelies as Mr. Emerson's chisel ground tanto-like blades, which are superb for punching through tough materials and Mr. Nealy's combination blades which use a chisel type reinforced point, like a tanto, but are semi-hollow ground back from the point to provide a thinner edge for times when slicing cuts are more useful than thrusts.

What does all this mean to me, the general purpose knife user ?

More grist for the mill when you're looking at adding a knife to your collection [or arsenal ...].

Think about how you'll most likely be using the knife ... what materials you'll be cutting ... and what kind of maintenance the blade will need after some use.

Certain grinds are easier to maintain, yet may not be suited to the
type of cutting you'll be doing ... others may be a little more work
to keep in shape, but will require that maintenance less often when used in your particular environment.

These factors will also influence your choice of sharpening tools,
which is a subject near and dear to my heart ... and I know holds
some interest for at least a few other folks out in the ether ...

That's all for now, next time I think I'll blather on about blade shapes ... and what features I think make up a good everyday knife.

-doc

First, a bit of history ...

There's been lots of talk recently about sharpening knives and other toys with edges ... what to use, how to do the deed, etc. ... but we haven't really touched on what sharpness *is*, and how an edge can [for some purposes] be *too sharp* ...

If yer eyes are already rolling back in their sockets, just move along to another blog or continue on and kwitcherbitchin.

Ahem ...

What is sharpness ?

Let's start with this:

Sharpness is the condition of an edged tool which allows it to be used for it's intended purpose.

Vague, huh ? To an extent, it needs to be vague ... because what is sharp to someone using a knife as a utility tool for camping isn't the same as sharp to someone using a chisel or plane to carve or shape wood ... or the same as sharp to a butcher ... or the same as sharp to a barber using a straight razor to give a customer a super smooth shave.

Some folks have referred to 'slicing' sharp and 'pushing' sharp, to distinguish between the two primary types of cutting methods used with edged tools.

Both of these cutting actions test a different kind of sharp on an edged tool ... slicing tests the bevel or grind angle of the edge and pushing tests bevel as well, but adds a focus on smoothness of the edge.

Here's where it becomes really fun: the kind of edge you want for one test is in many ways the opposite of the kind of edge you want for the other test.

Let me illustrate a bit:

Say you're getting ready to carve the Thanksgiving turkey [or any other turkey with whom you have a grudge]. You want an edge with a moderately fine bevel [say 19 to 21 degrees], which will force the slices apart as you're moving the cutting edge through them ... and you want the edge to have just a bit of 'tooth' in order to slice through tissue membranes and not just mash them.

Hold that thought while we look at the other extreme ...

If you're a woodworking fiend [and I mean that in the kindest possible way], you need to have chisels & planes which are sharp ... as defined by the original bevel angle, and smooth as possible so as not to tear out chips or chunks of delicate and EXPENSIVE wood that you're carving or planing down to the correct size for your project.

Now let's look at what would happen if we tried to use a woodworker's dream edge to carve a turkey. The slices would tear and fall apart.

Huh ? Why would that happen ... ?

Because the edge is so polished that it will actually create a bit of suction as it cuts through the meat and that, coupled with the mashing effect it has on membranes because it is 'toothless' will give you terrible results for slicing tissue.

The flip-side situation is equally bad, because the fine toothed edge that serves us well for slicing through tissue will rip the heck out of those very expensive wood fibers, pulling chips & chunks out and causing the woodworker to scream blue murder and begin looking for fresh pieces of wood to finish his/her project.

So how do we solve these problems ?

By asking what the intended purpose of the tool is before we begin sharpening ... and using the appropriate sharpening tools &/or methods to do the job ... and by knowing when to quit sharpening the tool.

Assuming the your edged tools are in reasonable shape [MacYoung, this is NOT a safe assumption for you to make. EVER!], you won't need power tools or extremely coarse hones to begin the job. For kitchen knives, utility camping / outdoor use you'll want to start around 500 grit and finish at about 2000 to 2400 grit.

If your knives need a lot of work, you might start at 200 grit ... but be careful, grits that coarse take off A LOT OF METAL VERY QUICKLY. Let me repeat that, just in case it didn't come through clearly the first time:

... you might start at 200 grit ... but be careful, grits that
coarse take off A LOT OF METAL VERY QUICKLY.

Another factor which may come in to play with modern knives is the hardness of the steel. This isn't as big a factor as some folks would like to make it, but it can have an effect on how quickly you'll get the results you want.

Typical abrasives [hones, sharpening stones, etc.] are made from things like silicon carbide, aluminum oxide and various ceramic or clay binders with these [or similar] abrasive materials mixed in and fused with them.

These are great for steels hardened to about 60 on the Rockwell scale, but will be less effective on steels much harder than about 65 or so.

For steels hardened to those rarified levels [you won't find many, and in my not-so-humble-opinion, they're not worth the trouble] you'll want a different type of abrasive material: industrial diamond or cubic boron nitride.

Don't worry about these for now, just be aware that the folks who want to sell sharpening gear to you will push these little darlings at you because they can ... and because they're EXPENSIVE.

Ok, back to the real world. Good quality silicon carbide [Norton Crystollon stones] or aluminum oxide [Norton India stones] are fine for most applications ... and if you want to get fancy, you can use waterstones [ceramic or clay binders with these same abrasives] in the appropriate grit ranges to do the work.

How to choose ?

How much sharpening do you do ?

How much fussing are you willing to do to get ready for sharpening ?

Norton [or similar] stones should be used with light mineral oil as a lubricant while sharpening ... and gently rinsed & lightly re-oiled after use before you put them away.

Waterstones need to be soaked in water before use, and use water as a lubricant during sharpening. They also required gentle rinsing before they are air dried and put away ... AND they will require periodic re-flattening of their surfaces in order to maintain a useful working area.

The reason for this is that the binding materials which hold the abrasives in these stones wears away during the sharpening process.

This wear is responsible for two of the better qualities of waterstones: they cut quickly, because fresh abrasive is constantly being exposed; and they polish the edge while they are sharpening, because the binder material which is wearing off during the sharpening process mixes with water and forms a paste which lubricates and also contains small amounts of the abrasives which are being released by the wearing of the binder.

Which one is right for you ?

If you just want sharp edges and don't want to spend too much time maintaining your hones, go for oilstones.

If you feel the need to become somewhat fanatical about your sharpening gear, try waterstones ...

Either way, you'll have the basic tools required to get edged things sharp.

But what about other tools ... ? Ceramic hones, diamond hones, strops, ScarySharp, etc. ... ?

Ceramic hones can be very good, and I've recently been told about some which sound excellent ... but they won't do a 'better' job than the oil or waterstones I've already talked about.

Some folks like them because they've been told they can be used dry. True enough, but they work better with water as a lubricant ... and they still need periodic gentle cleaning to get the ground off metal out of their surfaces, so it all balances out in the end.

Diamond hones are lovely, and I own and use several for specialized tasks [like fixing serrations] ... but unless you're working on this kind of stuff all the time or have knives / tools made out of the previously mentioned super hard steels, save your money for buying more knives.

Strops are lovely, and are an absolute necessity for putting the final polish on straight razors and some superfine woodworking tools ... but again, save your money unless you use these tools or plan to make a go of sharpening as a business [not something I would try, but you might be able to do it].

ScarySharp ... a great concept, but it's primarily good for woodworkers who have tools with rectilinear edge geometry and large edge bevel area.

It was designed for woodworking tools and not for knives, and when one attempts to apply it to knives ... well, it just seems to fall short.

At least for me ...

Ok, I've spewed long enough ... chew on this and I'll just wait for the questions [and comments] to start coming in.

-doc