The Physics of the Cut
It is a truth universally acknowledged, by swordfighters at least, that a curved sword is superior at cutting. But why? Why should the curvature of a blade have such an effect on the effectiveness of its cut? Today I'd like to delve into the physics of swordplay, and examine why cutting swords have the form that they do.
First and foremost, I begin from the following assumptions:
That historical swords, made for the singular purpose of life-and-death swordplay, were effective weapons.
That form follows function.
I usually start from this in all things sword-related, but it's worth stating it again. These days, we do swordplay for leisure. We have the luxury of making/owning fanciful swords and armor suited to our preference. Back in medieval times, when a sword was a tool to be used in the defense of one's life, I'm sure swordfighters had a different perspective! So I want to emphasize this point as much as I can: we must assume that swords were made in whatever shape they are because that was what worked at the time.
For example, if you were to imagine the kind of sword that would work best in a large, massed formation of men with heavy shields, you'd probably arrive at a gladius sooner or later. It's short and thick (very maneuverable), has no hilt (easy to strike around a shield without getting caught on anything), and straight (good for thrusts and stabs).
This is what I mean about form following function. It stands to reason that, if a historical sword consistently displayed some particular feature, it was representative of its function in some way.
The Cutting Sword
So what does this mean for a cutting sword? Well, let's look at some examples of curved swords.
There's the katana, of course, as it's the quintessential cutting sword. Then there's the tulwar or talwar, from India; the sabre, from Europe and just about anywhere; the German langes-messer, which is used very much like a longsword; the scimitar from the Middle East; and the slightly more modern cavalry sword from various Western countries.
Having a curve means that the sword is less effective at thrust attacks (which is a subject for another day) but it doesn't follow that being less effective at thrusting equals better at cutting. So let's look at the mechanics of the cut itself.
The Science of a Cut
When you strike and draw with a sword, so that the blade slides across the target, you're making a cut. This is in comparison to the thrust, where you strike with the intention of driving the point into the target instead of drawing across it. If you're a swordfighter, you already know this and you've done both a thousand times.
The actual physics of a cut, at a molecular level, does not resemble cutting as you know it. The blade acts more like a wedge that opens up a fracture in the material. When the blade is drawn against a material, friction between it and the edge causes the initial tear through shearing force. More friction = more tearing = more cutting. (If you're interested in the science, check out this paper.)
This is also the reason why sharp blades are better than dull ones. A sharper blade will concentrate the energy of the cut into a smaller area, and it generates more friction between it and the material than a dull blade.
At this point, I think it's clear that the major factor influencing the cut is that of friction. A sword that can generate more friction between it and the target is a better cutting sword.
The Importance of the Curve
At this point, we need to ask: what generates friction? The answer, if you've ever taken a physics class, is movement - specifically, moving two objects against each other in opposite directions. In a sword cut, it is therefore important to make sure that our strike creates the maximum amount of movement of the blade across the target.
And here is where the curve suddenly becomes very important.
Any strike with a sword involves the edge of the sword impacting the target and doing damage. (Remember, a sword must be rigid enough to deliver its stored energy effectively, and elastic enough that it doesn't shatter.) When you cut with a sword, the sword itself must be angled across the target in order to draw it through, which keeps the edge against the target, generates friction, and cuts it.
With any sword, you will need to angle it at the hilt in order to draw it through. What I mean by this is that the point of the sword doesn't travel exactly in line with the hilt as you swing it; it naturally lags behind a little because it's the most efficient way to move a big steel bar through the air. The cut consists of the swing, the impact with the target, and the draw where the cutting edge is kept in contact with the target.
Do this with a straight sword and with a curved sword, and you'll notice two major differences:
You will need to angle the straight sword more in order to maintain the same cutting surface as a curved sword.
The draw is less effective at the end of the cut with a straight sword, because it becomes progressively harder to keep the edge against the target.
The curve increases the amount of movement of the blade across the target, and thus the amount of friction between the blade and the target. It's possible to cut well with a straight sword, but a curved sword makes it much easier. This is why a curved sword is a better cutting sword.
The Amount of Curvature
So you may be asking yourself now - why isn't a katana as curved as a talwar? If more curve equals a better cut, why wouldn't all cutting swords be more curved?
Form follows function, of course. The curve is a trade-off between cutting and thrusting. The Japanese swordsmiths who created the katana did not intend it to be entirely used for cutting, though its form does lean towards that more than thrusting. The talwar, with its greater curve, leans more heavily towards cutting, and I've heard it mentioned that very heavily curved, single-edged swords may be used with one hand on the sword spine, in techniques involving push cuts.
I hope that this has been informative and interesting, whether you're a swordfighter or whether you're just curious about the mechanics of swordplay. The most important thing to note is that there is no real 'best type of sword', in general - there's only the most appropriate sword for your chosen technique.
It's also worth noting that whether you prefer to cut, thrust, or a combination of both, or anything in between, you must still be able to mount an effective defense with your sword, or you won't last long enough to know if your attacks are effective!