I would like to correct one or two mistaken statements that have been made in prior entries here.
Quote: That's a pretty good description of it except you toss in the other problem that part of an edged sword's benefit comes from the momentum of the swing. Low mass means lower momentum.
FALSE. That is true of a baseball bat, not an effective sword. The cut comes from the energy of the swing, not the momentum. A cut should swing rapidly across the target, not straight into it like an axe. (Which is why katanas and many other swords are curved. In fact this is the whole point of the existence of swords... otherwise you might as well just use an axe.)
Velocity is key. Momentum is mass times velocity, energy is mass times the square of the velocity. Reducing the mass allows one to swing the blade faster, increasing the velocity of the swing, resulting in much more energy in proportion.
Further, if you have had instruction in the use of the katana, you would know that momentum is your enemy. The reason that you are taught to pull back to limit your swing is to combat the momentum of the sword, which could otherwise become stuck in tough parts like bone and cartilage. You pull back so that you can swing again rapidly, without getting stuck. So momentum actually detracts from the usefulness of the blade, and students spend a great deal of time learning to counter it.
A lighter blade can move more swiftly and thus do more damage in a short period of time, which is why a light sword, and even sometimes a foil, have been proven to consistently beat a Claymore in one-on-one, unarmored combat. It is the presence of armor that dictates heavier swords, which have the momentum to batter through the armor. Those are doing more bashing than cutting, and so the different design.
Also, sword experts will tell you that even with the ability to cut with the length of the sword, the decisive action (again in unarmored combat) is usually made by the tip of the sword... which again argues for speed and light weight versus momentum.
Most of the time, you will not face armored opponents.
The main problem here is that a good sharp edge tends to be brittle, and once a blade is chipped, its structure may be compromised. But solutions are possible, if one is willing to think outside the box.
The ultimate in unarmored-combat sword technology would probably be something like a (least brittle as possible) titanium-alloy backbone, with a large number of small, replaceable, bolt-on edge pieces of either titanium nitride or silicon nitride.
For the price there is not much better than nitride, but for utmost hardness, diamond is the king. And that is doable, too, for a price: not long ago, a major manufacturer of razor blades in the United States offered a diamond-coated blade. (No joke... they gave it a microscopically-thin coat of diamond, using a sputtering technique often used for microchip manufacturing.) These were the finest razor blades ever made. I know, because I used them. A single blade would last months. But after about 2 years, they were pulled from the market because not enough of them were being sold... buyers were only using a few, and word was not getting out to others. Too bad. If they would have stuck it out... or advertised more... they would have eventually owned the whole market!!! They WERE that good. And the diamond coat was thin enough that the blade remained flexible.
The same thing could be done with a sword... but it would probably not be practical to coat the whole blade, and even if you did you could, you would still have the chipping issue.
Swords have traditionally been made of one piece of steel. But this is what I mean by thinking out of the box. Samurais may have glamor and respect, but again it has been said many times that modern steel technology has stepped far beyond the old hand-folded steel forgings. (I should mention here, too, that despite what one poster said, when folding the steel a "flux" of charcoal dust and sometimes borax was sprinkled on the surface before the fold, which assisted the weld and did indeed improve the carbon content beyond what was otherwise lost.) In any case, why not up the ante, and take it beyond "modern steel" to even newer materials? Plain steel today is for wusses with no imagination.
For many years now, industrial machinists have used bolt-on Nitride blades for cutting and shaving even the hardest steels. (For those of you who are not already familiar with the idea, nitride inserts are a lot like "carbide" inserts in saw blades, but even better.) Why not borrow the same technology? Seems to me it would be a pretty easy thing to do.
Replaceable edge segments with a hard coat (nitride or even diamond) solve the major problems, and would make for a truly magnificent piece of cutting engineering. A world-class edge that would be maintainable as long as sections could be replaced. But it would demand quite a price at first, and it would probably look more like engineering than art.
But on the other hand, to me, good engineering IS art.
