More Logic on Real Sword Weight

[John_Clements]

EDIT: After the following mathematical reasoning by Latham was shown by our members to be faulty (even though his final statement itself is essentialy true) we've discontinued including it in the article. (I'm not at all surprised a liberal arts major like myself did not catch his error. "Me likr swords")

We’ve added the following material to our extensive article on real sword weight. I think it’s very enlightening, if not obvious, but intriguingly reflects almost a "D&D"-like approach to things. It’s by John Latham of Wilkinson Swords writing in 1863 on the shape of sword blades:

“To estimate the effect of a sword-cut we will take the formula generally in use for expressing the vis viva or force of a moving body, which is, the weight multiplied by the square of the velocity. Assuming this formula (which, however, requires considerable qualification) we will suppose a strong man, cutting with a sword of 4 lbs. in weight, to which he is able to give a velocity which we will call 1. This effect produced we will therefore call 4 [4x1 ~2]. We next suppose a weaker man who takes a sword 2 lbs. in weight and able to give it a velocity double that of the first, the effect produced will be equal to 8, or twice that which can be exerted by the stronger man using the heavier sword [2x2 ~2]. But let us supposed that the strong man takes the lighter sword; he will be able to give it a higher velocity, which we will assume to be equal to 3, in which case the effect produced, squaring the velocity, will be 18, or three times the effect which he himself could produce with the heavier sword [2x3 ~2]. I merely take this illustration as showing that the force of a blow is enormously increased by velocity, but much less by increased weight…”

Latham also added that, “The nature of the body cut at, however, affects the result very much.” He then concluded by commenting that the common mistake is to believe a strong man would take a heavier sword so he could do more damage with it. “The weight a man can move with the greatest velocity is that with which he will produce the greatest effect, but the lightest sword is not necessarily the one he can move the quickest. It is possible for a sword to be so light that we feel the resistance of the air in making a cut with it, and this is what we express when we say a sword feels ‘whippy’ in the hand. Such a sword is worse than one too heavy.” He goes on to comment more about the problem of such weapons being impressive to the uninformed or unskilled and even how many manufactures were simply clueless about proper military weapons.

Interesting that even back then they were already having problems with unenlightened individuals selecting poorly-made whippy ineffectual blades to practice with. Funny that.

Sorry I can't do superscripts for the added equations.
See the full article here:

JC
What Did Historical Swords Weigh?

[david welch]

“The weight a man can move with the greatest velocity is that with which he will produce the greatest effect, but the lightest sword is not necessarily the one he can move the quickest."

It just seems to me that you can go too far in either direction. If that was completely true, why aren't axes and sledgehammers made as light as possible within the limit of being able to withstand a blow?

John, you have done more test cutting that anyone with the largest variety of swords. Do you feel there is a middleground of what cuts/works best. I mean, don't you want to use a sword that is as heavy as you can possibly use quickly? Or am I just reading more into this than intended?

[John_Clements]

Hi

I'm pretty sure Hank R. has cut with more swords than me.

The sword you want depends upon how you fight and who you fight.
But yes, neither too heavy nor too light for the job is logical.

JC

[JeanryChandler]

I've noticed since last year I used to prefer very light longswords around 2.5 lbs and a close to the hilt balance because they seemed more agile, then I started to prefer heavier swords around 3.5 and maybe a 6 inch balance point which seemed swifter in mastercuts for example, and now I'm finding best results with weapons more in the middle range, just under 3 lbs with a 4" balance point... (given that there is much more to balance than the balance point)

Of course, blunts tend to be heavier just because of the edge geometry. With real swords in the day desirable weight also had a lot to do with whether or not you were contending against armor etc.

I was at a LARP event once to try to sell some sparring swords, and I couldn't hold a candle to those kids with their feather light car arial boffers which wiegh like three ounces. I was "owned" by a 15 year old kid with a kite stick sword.. even if metal and sharpend somehow those couldnt cause anything more than 'cat scratches' IRL

There does seem to be a general trend that the ancient swords of the medieval and renaissance period seem to be 10%-20% lighter than most replicas across the board though, don't you think?

Jeanry

[JeanryChandler]

Ten years ago most people I met thought that medieval swords weighed between ten and twenty pounds. In the last few years the common misconception gradually seems to have dropped to around five pounds, a figure I still hear mentioned on TV. As recently as a couple of years ago, many of the better replicas of medieval swords commercially available still weighed as much as 4 lbs or more.

In contrast, the 200 or so medieval or renaissance era swords I have seen advertised in online antiques auctions and the four I have handled physically were all less than three and a half pounds in weight, many including two handed types less than three lbs.

Personally, I'm interested in knowing the historical truth, nothing more or less. The issue of weight in particular remains a key point of argument raised against WMA by for example some less informed EMA practitioners. I'm interested in seeing the historical record become more widely known. Period.

Jeanry

[Mike Habib]

"'The weight a man can move with the greatest velocity is that with which he will produce the greatest effect, but the lightest sword is not necessarily the one he can move the quickest.'

It just seems to me that you can go too far in either direction. If that was completely true, why aren't axes and sledgehammers made as light as possible within the limit of being able to withstand a blow?"

There are a few reasons why having some weight is helpful (others can think of more I am certain)

* As mentioned in the article, especially light weapons actually do not move as quickly as those with some limited weight.

* Especially light swords are also prone to chaotic movement. If a blade is especially light and thin, it will actually produce significant lift (perpendicular to the blade) when is swung at any angle that isn't perfectly level, which will pull it towards one of the flats. It will feel like it is being pushed on and may actually vibrate oddly.

* I don't think resistance to deflection is exactly the same as momentum. In fact, it seems that very small fast objects should be especially prone to deflection.

* Overall, however, I think the main reason that lighter is not always better is that the relationship between the weight of an object and the speed at which a person can swing it (ie. the velocity and mass terms are related). If it takes a fair bit of weight reduction to get a lot of speed gain, then some interesting things happen. This seems pretty likely, because as things get very light, the difference in how fast you can swing the object should be pretty small (I can throw a .5kg object and a .6kg object at near the same speed, for example, because neither is heavy).

For those that like math: if you assume that speed and mass are related linearly (which they probably are not, in which case the following effect is even more pronounced) you can model the whole thing as Momentum=mass(-a*mass+b)^2. In this case, 'a' would be the weight/speed tradeoff, and 'b' would be the maximum weight a person could swing.

When you plot that out, you get an intermediate optimum for momentum versus mass...it's at a low mass (ie. light weapon), but not ultrasmall.

Just a thought, sorry for the long post.

Cheers,
--Mike Habib

[Mike Habib]

One other quick note: all else being equal, making a sword longer will make it heavier, obviously. Increasing the length can increase the tip velocity greatly, since it will travel so much faster than the wielder's hands. Thus, weapon length should be in the overall momentum equations as well, and this will also be related to mass. In some cases, increased the mass somewhat to get extra length can be highly advantageous.

Cheers,
--Mike Habib

[JeanryChandler]

It just seems to me that you can go too far in either direction. If that was completely true, why aren't axes and sledgehammers made as light as possible within the limit of being able to withstand a blow?"

Actually hammers and axes used for combat are MUCH lighter and thinner than those used for work. The axe heads on war hammers aren't much bigger than that of a typical claw hammer even when mounted on a 5' shaft... the cross sections of Viking axe heads shows that they are very thin compared to equivalent farm tools.

Jeanry

[Stacy Clifford]

I was going to say basically the same thing. The mass distribution in axes and hammers is different because they are designed primarily for penetration/crushing/shock with little regard for maneuverability. A farm tool doesn't need maneuverability for defense, it just needs mass to attack a target that is hard all the way through, like a log or a rock. An armored knight isn't hard all the way through, so you can sacrifice some weight for speed and maneuverability and still achieve a useful effect from the mass distribution.

[Benjamin Abbott]

Interesting. I would really like to see a similar article (or multiple articles) setting the record straight for other types of weapons. I guess that's not too likely, though.

What exactly did warhammers weigh, for example? Reproduction weights are easy enough to find, but records from originals are hard to come by. I'm especially interested in polearms myself. Pikes are particularly hard to pin down: I've seen figures ranging from 6 to 10 lbs. An TV shows on the history channel still claim poleaxes weighed 15lbs - it would be good to dispell such myths.

[JeanryChandler]

I dont know about pikes and the larger pole arms, but for all hand weapons from 3 to up to around 7 feet in length the average range of weight seems to be around 2.5-5 lbs. Much more than that and the reach / weight tradeoff becomes inefficient.

You can see several antique weapons, many listed with their actual wieght at the myarmoury site. You can also look at a lot of online auction sites which deal with antique weapons, they almost always list the weight.

Jeanry

[George Turner]

Latham's reasoning on kinetic energy is unsound. I'll present this in really simplistic (constant force) and linear terms for clarity.

Given: F=ma and velocity_final=sqrt(2*a*s)

where F is your body's force, m is the sword's mass, a is the resulting acceleration, and s is the distance that you apply force, which in our case is limited by our swing length or arm length, etc. The length of our swings isn't a function of sword weight.

KE=1/2*m*vfinal^2
KE=1/2*m*sqrt(2*a*s)^2 = 1/2*m*2*a*s
but a=f/m, so
KE=1/2*m*(2*f/m)*s
and finally
KE=f*s

mass isn't even in the equation for kinetic energy, measured in Joules, which are units of work, which is force times distance. The kinetic energy in your blows would be determined by your body, not your sword, except for one niggling little detail: Your arms have mass and suck up some of the energy, which doesn't end up contributing to the blow.

So now we have
f=(m_sword+m_arm)*a, but KE=1/2*m_sword*2*f*s/(m_sword+m_arm), giving us
KE=f*s*m_sword/(m_sword+m_arm)

The lighter you make the sword the less kinetic energy your blow will have, because your arms possess their own mass.

You can think of this in many other ways. Assume your body has a constant peak power output, and faster blows have less time to tap into it. Less energy tapped means less energy for your blow. This is slightly at odds with the above solution because the above solution wasn't power limited but force limited.

Looked at another way, you can increase the weight of your rifle bullet all over the place without profoundly affecting muzzle energy, because you largely set the muzzle energy when you weigh out the powder for the cartridge. There are efficiency losses here too, though, since smokeless powder has a maximum velocity even with no bullet at all. Human muscles are similar, with a maximum attainable velocity even when stripped from the bone and put in a petri dish. In short, your peak torque or force is at zero velocity, and keeps decreasing as your muscle moves faster.

Anyway, in all real cases sword energy should go up with mass, not down, and the limiting factor is tactical. The 40 lb wall hanger is very energetic if it hits, but it never lands because the wielder is already dead.

What you probably choose is the lightest sword that can still deliver enough energy or momentum to land killing blows. Less is useless and more is too slow, so your optimal sword mass is a function of armor and the mass of the swords you're facing.

[Jeffrey Hull]

SC:

That is a really good point.

JH

[david welch]

Actually Stacy, that was my point. When I said:

It just seems to me that you can go too far in either direction. If that was completely true, why aren't axes and sledgehammers made as light as possible within the limit of being able to withstand a blow?

I meant, if the author was correct why are work axes and sledgehammers not as light as possible. I thought Latham was saying, and I was trying to disagree with, the lighter you make a tool you swing, the more energy it has. Sorry I was not very clear.

Thanks, George. You answered the question I was trying to ask.

[Robert Subiaga]

But let's also not forget a fact that's one of my pet peeves when it comes to firearms ballistics: Kinetic Energy is not what we should be concerning ourselves over with inelastic collisions.

(I know, I know, the ammo makers still insist on putting it in all their tables ... )

A big problem--which some of you have alluded to in many ways already--with too light a blade is that the blade deforms on impact, rather than making sure all the deformation is in the target's body. (The blade may not keep its deformation and spring back to original shape after impact, but it still didn't do what is was supposed to.)

That's why a whip, despite being capable of inflicting some nasty wounds, produces so much less damage than the amount of kinetic energy says it should.

It also argues for why a good cutting sword, despite being reasonably thin and sharp, should have breadth. You don't want it flexing in the direction of the cut.

(The opposite of a flat parry, where you do want that flex.)