The other part of blade design that really affects how it works is the cross-section. How thick, how tapered, and so forth.
I'm going to try to put some drawings or pictures in to illustrate this, until I can scan or save some I'll just have to describe them.
Generally speaking, a thick edge is tougher, but harder to cut with. A thin edge much less tough, but cuts more easily. There are a lot of ways to work this, but they break down fairly simply. For a thin edge on a blade that should not see heavy cutting work, many companies and makers use a hollow-grind. The body of the blade, down to where the bevel starts, is flat or parellel sides. Then the bevel is ground on a round grinding wheel or belt wheel, so the bevel is convex, thus hollow-ground. Advantages, it cuts easily, even when it's getting dull, which is why so many inexpensive /and many cheap/ kitchen knives use it. Unless used with really good steel and heat treatment, it dulls quickly, and the edge can be bent or chipped fairly easily if used for heavy work.
Next up is flat grind. From the point the bevel begins to the edge, it is flat. This can start as little as 1/4 of the way back from the edge, or be flat all the way to the back of the blade. Many, maybe most, commercial hunting knives, and some kitchen knives, are made this way; most of the good kitchen knives are. This is, generally speaking, not as heavy as a hollow-ground, but much tougher, and it cuts fairly easily. Remember, the wider the blade just behind the edge itself, the harder it is for it to cut smoothly. This is the way I do most of my blades.
I've done some hollow-ground. The trick for a working blade is to start the grind a fair ways back from the edge, and not grind it too thin. Done right, this works quite well. Long ago Buck Knives started semi-hollow grinding; the hollow cut out metal from a little behind the edge up to the flats. This left a thicker, stronger edge with enough relief behind it to make cutting easier.
Last is convex. In this the bevel is ground in a smooth curve from the back to the edge; think of a properly made & sharpened axe. Not for delicate work generally, but a very strong edge profile. Cleavers, heavy chopping knives, etc.
Personally, for general-use blades, I like to flat-grind, but use a convex edge; instead of sharpening at a flat angle, use give it a convex profile. Done right, it will be wonderfully sharp and yet tough enough for most all use. I've used this on almost everything, always on the big dirks, bowies, etc. Small knives for precise cutting I'll often use a thin flat grind.
Swords use variations of all the above, with the edge best shaped convex. One of the only truly flat-to-the-edge swords I know of is the Japanese styles; as someone once pointed out they had to go through armor much more rarely than European blades, so could get away with it.
So there are the basic blade cross-sections. And yes, you can combine them in a single blade if you have need.
Which leads to some wierd shapes, but that's for another day.
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