Differences between Straight and Curved Swords

It seems like a straightforward question, but in fact it turns out to be not. The internet is full of theories and ideas - curved blades cut better, easier, are superior against unarmoured targets... A curved blade brings more edge into a cut than a straight one, curved blades excel at slashing cuts,...

The following is an attempt to sort through the matter based on physics and biomechanics of cutting, historical fencing manuscripts and actual sparring and riding experience.

The reasoning is largely based on the idea that weapons undergo evolution - if the enemy has weapons that are superior, lots of people on the own side get wounded and killed. No one likes that, so rather than trying the same inferior weapon again and again, warriors usually adopt the better weapon. This kind of evolution isn't the only force at play, and contrary to what people appear to sometimes believe doesn't necessarily end with the best solution, but it does sort out inferior solutions pretty efficiently.

Thus, given the historical warfare context, a change in the shape of a sword needs to offer some advantage over the previous design or at least a tradeoff that doesn't make things worse.

To my mind then, the curved sword requires an explanation, because it abandons the tactical possibilities of attacks with both the true and the false endge of the blade (this is coming from someone who really likes the feints, threats and master cuts that require the false edge in sparring). And such an advantage would not just be thrown away. Yet when the e.g. Japanese tachi and ultimately the katana replaced the straight chokutō in the 9th century, this is what happened - so there must have been some comparable advantage to be had.

Some terminology - cutting, slicing and thrusting

• cut: If the edge of the blade moves vertically into the target, the sword cuts into the target. This is the motion of an axe splitting wood or a meat cleaver. In addition to what the edge might or might not part, a cut delivers a significant amount of kinetic energy to the target that can shatter or damage hard, unyielding material.
• slice: If the edge of the blade moves chiefly horizontally across the target while being pressed lower with a small amount of force, the sword slices the target. This is the motion of a kitchen knife cutting a cucumber. A slice has low kinetic energy distributed over a large edge and is only able to part soft material (one cannot slice a coconut open with a kitchen knife).
• thrust: If the point of the blade moves into the target (usually with the weight of the swordsman behind), the sword is used for thrusting. This is a bit different from stabbing where e.g. a dagger is punched with a hand motion into the target. A thrust delivers a lot of energy to a very small area, and so the point can penetrate quite a bit of armour material (like chain mail).

Various other sources use the term chop for what is here denoted as cut and slash for what is here referred to as slice, but these terms will not be widely used in this article.

The ultimate cutting weapon

A good energy transfer requires a lot of mass behind the impact point, but most of the mass of the sword is near the hands, far away from where the cutting edge hits the target. The ultimate cutting weapon fixes this by bringing most of the mass at the impact point - the resulting design is an axe.

For the same effort, axes are much more armor penetrating and devastating than any sword could ever be. A good axe can chop down a Viking shield in a few blows, something a sword really takes some time to do.

In fact, it is possible to design swords that are quite good at cutting. The idea is the same as with the axe - shape the blade such that more weight is near the tip where the edge should impact. Examples are the Iberian falcata or the Greek kopis.

The falcata is optimized for cutting with lots of weight behind the impact point

These weapons have a curved blade for the simple purpose of making them more tip-heavy (again, just like an axe), which improves their transfer function - more kinetic energy ends up damaging the target.

Note however that this is not how a katana is designed.

The ultimate thrusting weapon

Just as it is possible to design a sword that has the properties of an axe, a sword with the property of the spear can be made. A possible outcome is the estoc, a weapon with a thin, narrow blade that has no room for sharp edges and exists for the sole purpose of being thrust through armour.

The estoc is uniquely designed for thrusting and can't cut or slice

Also, the design of the Estoc is fairly outside of the norm for swords.

The ultimate slicing weapon?

If that is so - are there tangible benefits to designing a slicing weapon with a curved blade? In that case, one could understand the design choices as straight weapons emphasizing thrusting attacks somewhat more, curved weapons emphasizing slicing attacks.

In order to investigate that idea, let's look at the role of slicing in actual combat situations.

Slash or draw cuts

The problem with that idea is that it doesn't work in real fencing.

The cut is done as a rotational motion of the sword, it swings in an arc. If a slice is to be superimposed, this means a linear motion of hand (or body) is required in addition.

First of all, the amount of relative linear motion in an actual fight is difficult to control - usually the target doesn't stand just still and waits to be cut up - the target is a moving opponent who does not want to be hit and threatens to counter-attack. Typically a fencer needs to move forward to attack with a cut - the opponent might step backward to get away, thus cancelling out any linear motion. He might also sidestep, introducing a motion perpendicular to the direction of an intended slice - or he might step forward, changing the impact point on the blade. Drawing the blade in during the cut can easily mean that the opponent is not hit at all when he steps backward. None of this can really be controlled by the attacker.

But second, it really doesn't matter much. As evident from analyzing slow-motion captures of cuts (see my article on Cutting mechanics), in a good cut the sword moves an angular speeds of 1000-2000 deg/s when it hits the target. The part of the blade that impacts thus travels at a good 20-30 m/s due to the angular motion. At the same time, even a vigorous forward-motion doesn't create more than 2-3 m/s linear motion of the sword. So in fact any motion during a cut is something like a ten percent correction to the impact motion, to first approximation the blade always impacts vertically and hence cuts and doesn't slice.

Or, put the other way round: a cut in which the vertical motion into the target is as important as the horizontal motion across the target is so slow that it is tactically meaningless.

In a real swordfight, cuts have to be reasonably fast, and then they predominantly are cuts. A slashing cut doesn't occur.

Slice attacks

The quick answer to that is an unconditional 'no'.

First, note that practically any form of armour makes slicing attacks meaningless. If you can't part it easily with a kitchen knife, you can't slice through it with a sword. Any form of metal between blade and skin will prevent a slice - chain mal will certainly do, but even a metal buckle of a belt can't simply be sliced through. Hardened leather will prevent a slice just as well, and so will wood.

Thus, slicing the opponent is completely useless on a battlefield where opponents are typically in the habit of wearing armour. The Fiore manuscript (2), our historical battlefield survival guide, doesn't even mention slices as a suitable mode of attack, it just lists colpi (cuts) and punte (thrusts). The Zettels of the Liechtenauer system are more geared towards duels and do mention slicing - but mainly as an attack of opportunity.

From practical sparring experience, it is surprisingly hard to formulate a plan of attack that ends with the opponent being sliced. Usually it is done when an opportunity presents itself - a thrust to the head missed, but the sword is not placed right for pressing it against the neck and pulling back. Or both are in a high bind, with a short shove the blade can be pressed to the opponent's wrists and pushed down while retreating and slicing. So in practice slice attacks depend on factors which a fencer can't really control too well.

It would be weird to design weapons chiefly for a task that the swordsman can't even reliably perform.

What swords are usually for

Depressingly many internet discussions and sword type comparisons narrow things down to 'how much damage does the weapon do when it hits'. In reality, the question really is more if the weapon hits before the wielder is dead or incapacitated.

An axe hit is much more dangerous than a longsword hit, yet in a life and death situation, I'd rather have the longsword, because by the time the axe-fighter gets even halfway close, he is unlikely to be able to still use his arms because I've hit him two or three times on the hands with my fast and nimble weapon.

So, the real reason that normal swords aren't as top-heavy as an axe or a falcata is not that they are superior slicers that way, it is that a center of gravity close to the crossguard makes the sword more nimble and allows to feint, parry and quickly counter. An axe is a single-purpose weapon designed to deliver a lot of kinetic energy, it is easy to use and self-explaining. A sword is a multi-purpose weapon with lots of tactical applications that isn't really great for cutting, which is why the use of a sword needs to be learned and trained - there's a reason there's a concept of swordsmanship but none of axemanship.

Swords like the estoc do break that concept, they are single-purpose tools, but that is of necessity. The estoc is a response to full plate armour on the battlefield - and that is impervious to cuts, slices and even most thrusts. Armoured fencing thus allows to ignore feints and tactical niceties, it is focused solely on thrusting into gaps and chinks in the armour while preventing the opponent from doing the same.

But once we start from the realization that normal swords are primarily shaped the way they are because they are supposed to be versatile fencing weapons, the question of curved vs. straight blade boils down to something else than optimizing damage - does a curved blade have maybe seconary benefits over a straight blade? In this case, the tradeoff would be between tactical versatility (two edges allow backhand cuts that aren't possible with a curved blade) and these benefits?

Let us thus look into what curved blades do for cutting (rather than slicing).

Curvature and cutting performance

The issue with thiis argument is that the curvature of many swords isn't all that large. Here is an example of katana-blades:

katana blades with rather modest curvature

In particular, the curvature is small when comparing it to typical curvature radii on the target side. The human body has lots of curved parts and e.g. the wrist has a very small curvature radius that renders the much larger of the katana practcally meaningless. Since it is the combination of blade and target that matters, cutting through a wrist is practically the same for straight and curved sword.

Moreover, the above argument actually requires that the edge is curved, not the blade. It is however quite possible to construct swords that have a straight blade and are double-edged, yet the edge is curved. The depicted spatha has even a stronger edge curvature near the tip than the katana above.

A Roman spatha with straight blade but curved edge near the tip.

So, if improved cutting power due to edge curvature is an issue - why not solve it like this and keep the advantage of two edges?

The whole idea of constructing swords such that they have more cutting power against unarmoured opponents becomes faintly absurd when one considers that a straight longsword has no real lack of cutting power. It is possible to find demonstrations in the internet where someone cuts a deer carcass into two halfes with a single strike of a longsword. Improving upon that is certainly possible, but likely an overkill - should we assume that nobles were no longer content to merely kill rebellious peasants so that they asked swordsmiths for weapons that would cut those rebels in half reliably every time?

For a battlefield, that is clearly pointless - the Fiore manuscript (2) is not at all concerned with inflicting the most gory wounds on the opponent, it teaches how to incapacitate him as quickly as possible - which is reasonable, because there may be other armed and hostile people on the field that need to be dealt with.

Yet, fairly consistently, people who cut e.g. tatami report that a katana does this easier than a longsword - so if it is not curvature, what is it?

Single-edged vs. double-edged swords

Below is a schematic picture of the blade cross section of single and double-edged swords.

Comparison of double edged (left) and single edged (right) blade cross section

Having a single edge allows to make the edge finer while giving the tapering more space - and put somewhat more mass behind the impact point. All of these properties improve cutting performance. In particular, the single edged blade has less issues with edge alignment.

What this means is the following: As a blade passes through the target in a cut, the edge must face with good precision into the direction the blade is traveling. If there is an angle between blade movement and edge, the blade gets a tendency to turn sideways and get stuck in the target - as a result the cut remains shallow. Good edge alignment during a cut generally requires training - but the issue is less severe for the single edge profile. In other words, a single edge sword tolerates more cutting mistakes.

So, a katana is indeed better for cutting than a longsword - but that isn't really related to curvature, the blade profile is responsible.

And here at last a plausible tradeoff for abandoning the tactical possibilities of two edges becomes visible: A swordfight is a messy and chaotic environment (this is becoming a theme in this article) in which it is hard or even impossible to control some factors. A sword design that simplifies matters, for instance that makes it easier to get a proper cut in the case a hit is achieved, brings a tangible advantage to the field.

The logic might then go like this - the katana is single-edged because that makes cutting more reliable in an actual fight, and once we have a single edged sword, we might as well have it curved, this doesn't take away any extra important property - but it does add a few nice perks.

Ease of handling - carrying and drawing a sword

Even so. That 1.4 m oversized longsword in its sheath on your back is a devastating weapon in any swordfight - but if you take ten seconds to get it out of there and into your hands in fighting position, you're dead if the guy with the short sword pulls it out in a surprise move and thrusts it through your chest.

The point being - there is enormous use in having a weapon that you can easily carry around wherever you're going and that you can draw in a hurry if needed.

These are actual historical issues - for instance the Fiore manuscript shows how one can use the sheath of the sword while drawing it as a defense against an attack by a dagger. Japanese swordsmanship knows iaijutsu, the art of striking out of the motion of drawing the sword.

Using the sheath of the sword as protection - Fiore manuscript (2)

As far as handling the weapon goes, curved swords offer quite some advantages. They are easier to carry, because the curvature brings the tip up, so the sheath isn't so close to the ground all the time. And if you try to draw a straight sword beyond a certain length, your hand needs to go far from the body, the position is quickly becoming awkward (if you have a long sword on your back, drawing it is so awkward, it makes the sword useless) - this is not so for a curved sword where the drawing hand goes more around the body than away from it.

Here, the katana beats the longsword flat-out - it is better to carry as well as easier to draw.

Swords as cavalry weapons

A Turkish kilij cavalry sword (above) and an early 19th century cavalry saber.

Why would that be?

Let's start with the realization that the environment of a fight on horseback is very different from a fight on foot. When bearing down on a foot soldier, the rider might move easily with speeds of 10-15 m/s, when meeting another mounted soldier head-on, the relative speed might rather be 20-30 m/s, a full charge in gallop can reach nearly 20 m/s. Fighters on horseback do not exchange a series of strikes and parries with their opponents, they pass each other and pretty much one quick action happens before they separate again. The tactical environment is thus very different, there is no possibility to wear the opponent down (as Meyer would advise longsword or dusack-fencers to do) and no time for elaborate feints.

The author riding a cavalry charge.

There also is the issue of controlling the horse. Horses have their own mind do things like paying attention to where they step or avoiding obstacles without involvement of the rider, but they're not on any sort of auto-pilot - and as a rule they do not like loud noises, sharp edges, the smell of blood or smoke - in other words they don't really like to run into a battle. The horse needs to be controlled while the weapon is being used - here is a clear case for simplicity. A weapon that handles in a straightforward way is superior to a complicated one. Also note a rather obvious point - one cannot use a two-handed sword from horseback, so cavalry-swords are single-handed weapons.

The whole situation - a single short pass, no time for tactical finesse, simplicity - actually seems to call for an axe. This would deliver maximal kinetic energy to the target.

Why didn't they use axes?

The kinematics of a cavalry attack

The question is - is it necessary at all to optimize doing damage?

A good cut with a sword corresponds to something like 150 J of kinetic energy in the sword. If the rider charges at a foot soldier and cuts in a way to maximize impact energy (i.e. such that sword motion and horse motion add up at the impact), the motion of the horse can add another 200 J of kinetic energy to the sword. In other words, the impact energy doubles.

Now, as has been said above, a straight sword has no real lack of cutting power, it can kill an unarmoured human just fine. From horseback, the sword can deliver twice the energy. So why on earth would someone want a weapon optimized to slice that is even better at killing unarmoured people from horseback? What is the military advantage in cutting rebelling peasants into small bits rather than just killing them and be done with it?

The geometry of a cavalry attack when the rider maximizes impact energy.

Of course when dealing with other horsemen, the problem is different - the enemy may be wearing armour. Knights had to deal with opponents clad in steel plating - but even so, when two riders are charging each other, a lance might eliver some 300+ J of kinetic energy - with 100 J concentrated in a thrust of a tip enough to pierce steel plating (3). So there is maybe a case to be made also for shorter weapons to be armour-penetrating - but that leads right back to the axe. An axe would go a long way in maximizing impact energy.

So why did cavalry not use axes as a rule?

After the attack

Say the rider passes a foot soldier during an attack, the axehead is then solidly embedded in the target by the large kinetic energy of the weapon - what then? The rider of course doesn't stop, the horse keeps going on, but the axe of course is stopped.

So, the rider cannot hold on to his weapon, it slips from his grip as the wounded foot soldier falls and the horse continues running. And this is a very bad outcome on a battlefield - having a somewhat poor weapon is always better than losing the weapon and having none at all.

I'm guessing this is the reason axes never made popular cavalry weapons.

What about a sword then?

Generally, a sword blade doesn't embed itself in the target as deep as an axehead would do - so it likely can be pulled out as the rider continues. The following illustration depicts the situation for a straight sword and a curved cavalry weapon, a Turkish kilij:

The geometry of weapon movement after an attack from horseback.

The last position of the swords is when the weapon slides across the shoulder of the footman and gets free. What is apparent is that the angle of the handle turns quite a bit less between impact and getting free for the curved sword than for the straight sword. Essentially that means that it is easier to hold on to the the curved sword, the forces that are acting to drag it out of the hand are reduced by the curvature.

Now, loss of a weapon that got stuck in an opponent was a genuine issue on medieval battlefields - we know that for instance because Philippo di Vadi advises in his fencing manual (4) not to thrust in a one-vs-many situation as the weapon might get stuck, leaving the fencer no weapon against the rest of the opponents. And the issue is magnified when riding because the horse moves away rapidly - basically anything that makes a weapon get stuck in the target is bad.

Conceptually the same is true when two riders meet each other head-on and exchange a single blow. In this situation, the forces are even larger and anything that makes the blades separate easily helps to hold on to the weapon (it is quite possible to disarm someone by cutting a sword out of his hand on the ground - with the added kinetic energy of the motion of two horses, this outcome becomes more likely).

I believe this property of curved blades - that they pull from the target easily after the hit when the horse moves on - is the most compelling argument that can be made for their use in mounted warfare. Add to that the simplicity of cuts with a single-edge profile and the advantages of drawing (after all, weapons have to be drawn on horseback) - and it becomes clear why curved blades definitely are the weapon of choice for cavalry.

Economy of use

Thus, most interesting fencing swords belong to the nobility.

We've seen above that there are good reasons they would use curved swords when on horseback. But this means they already have curved swords on their belts - would they change weapons when they fight e.g. a duel or are forced to dismount?

Plausibly they might not - they might just conclude that their curved sword is 'good enough' also for other purposes. After all, for instance a duel tends to be a formalized form of combat in which combatants cannot simply bring any weapon they fancy. A duel of a longsword against a saber would be a done deal - most advantages lie with the longsword - but a duel of saber against saber is fair because nobody uses the 'best' weapon.

Cultural significance

The answer is probably that the sword meant something to a knight beyond merely being a weapon - it was a symbol for knighthood and its divine mandate, and it doesn't seem to be a random accident that a straight medieval sword has the shape of a cross. In fact, a knight kneeling to pray in front of a sword that is stuck into the ground is quite an iconic image.

Thus, for a crusader, adopting the curved Saracen sword in battle would have been akin to sacrificing his identity as a knight of God - and that is a concern that plausibly outweighs the battle advantage of the curved sword.

(It is quite certain that other cultures also attach significance to their particular swords and their shape, Japan for instance comes to mind, but I do not have the background knowledge to elaborate other examples).

Summary

While it superficially appears that fencing swords would be optimized for slicing, the main design concern actually are the rotational properties to make the sword swing well and respond fast - the center of gravity is intentionally fairly close to the handle and the moment of inertia for cuts is low (arming swords for instance have a pommel to generate such a mass distribution). This very property makes the sword fairly poor cutting tools because if the center of gravity is far from the impact point, the transfer function of sword kinetic energy to the target is bad.

Swords which deviate from this fencing shape usually make a tradeoff - they have to sacrifice some fencing-related advantage to gain something else.

Curved blades can then plausibly appear due to the following tradeoffs (note that in reality there are no hard and fast limits between the types, this is a schematic consideration):

Top-heavy cutting swords

The same properties - higher moment of inertia and higher kinetic energy - however also inevitably mean that it is harder to change the line of attack (and thus feint) and to bring the sword around fast (e.g. for a block). Also, precise control of the point is difficult with a top-heavy sword.

To achieve top-heaviness, the pommel must be absent and the blade then can be shaped in a way that brings more mass towards the tip. The Iberian falcata or the Greek kopis are good examples for this kind of curved blade (note that while the blade is curved forward, the cutting edge in the impcat region is curved backward):

The Greek kopis, a sword optimized for cutting power.

Because one cannot defend overly well with such swords, typically one would want to use a defensive device like a shield together with them. For instance the Vikings demonstrated that the combination of shield and axe as optimized cutting weapon can be quite powerful.

Single-edged fencing swords

The Japanese katana is a good example for such a curved fencing sword that is usually wielded with both hands), many types of cavalry saber fall also into this group:

A Japanese katana

As their straight counterparts, such swords serve well in a number of roles - they do reasonably well from horseback as well as in fencing on foot, they are easy to carry and easy to draw.

Highly curved cavalry swords

A Persian shamshir cavalry sword.

With such highly curved blades, swords are no longer good fencing weapons. The curved blade makes accurate thrusting difficult and it sacrifices a noticeable amount of reach compared with a straight blade of the same weight. Also, cavalry weapons tend to be top-heavier than fencing swords because they typically see a single short clash of blades, not a longer sequence of contacts, which slows them down.

Because these swords are optimized for use from horseback, they would typically be one-handed.

(2) The Fiore Manuscript on Wiktenauer

(3) An experimental investigation of late medieval combat with the couched lance

(4) Vadi's Fencing Manual on Wiktenauer

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