Long ago, in a distant movie theater, there was a really bad movie called The Sword and the Sorcerer.
On the other hand, it was a fantasy-adventure movie that was around in the early days of fantasy role-playing – so quite a few gamers at the time promptly tried to lift things from it for their own characters.
One of the big favorites was the triple-bladed sword. After all, with three blades on one hilt, it should do three times as much damage, right?
Well no, that’s not right. It doesn’t even do slightly more damage.
Damage is work – tearing apart, crushing, or splitting open flesh and bone, all takes energy. In the case of a physical weapon it takes kinetic energy.
The kinetic energy carried by a moving object – including a weapon – is 1/2 Mass x Velocity x Velocity.
If your weapon – whether it’s a tri-bladed sword, or just a massive four-by-four, fencepost, or iron staff instead of a normal quarterstaff – is, let us say, three times as massive as a normal one, you can only swing it at one-third the acceleration, A, since the force exerted by your muscles is fairly constant over such a short term.
The distance, D, over which it’s being accelerated remains the same.
The time to travel that distance is the square root of (2D/A). That is, at one-third the acceleration, the time taken to cover the distance to the target will be increased by the square root of three. This does give a heavier weapon more time to build up speed than a lighter one.
In comparison to the original weapon, the actual impact velocity of our triple-mass weapon will thus be one-third the impact velocity of the original weapon multiplied by the square root of three.
The total kinetic energy in comparison with the original weapon will thus be (3 x the Original Weapon’s Mass) x ([the square root of three]/ three) x ([the square root of three]/three) = the same amount.
That kinetic energy will be spread out over a slightly larger area
It will be coming in at just under 60% of the speed of the original weapon, and so will be far easier to block, deflect, or evade.
The extra-massive weapon will be far less controllable and harder to swing back again than the original.
The kinetic energy will be less effectively transferred to the target, thanks to the conservation of momentum: more kinetic energy will be transferred into moving the target struck and more will remain in the weapon than was the case with the original weapon. It’s the same basic principle behind a bullet getting the lions share of the kinetic energy when fired but only carrying 50% of the momentum. Momentum is shared equally; kinetic energy is not.
OK, that quick analysis suggests that our triple-mass weapon is a great deal less effective than the original – but we must be missing something, because that would suggest that the lighter the weapon, the more effective it is, and that’s not always true either. Lighter weapons are easier to maneuver, and strike more quickly, but they often do seem to do less overall damage.
To account for that, we have to take a quick look at biomechanics.
There are distinct limits on both how quickly a muscle can contract and on how much force it can exert. These vary from organism to organism, both within and outside of any given species – but the overall limits are pretty similar within any given species.
Ergo, any given weapon will have an ideal mass for any given wielder – the greatest mass for which it will still reach the maximum possible velocity towards the very end of it’s average arc. Within a given species, that will usually mean that any given weapon will have a fairly narrow range of ideal masses. Using a heavier weapon is more effective until that ideal value is reached, at which point it’s effectiveness will begin falling off again.
Yes, that’s basically another bell curve. Life is like that.
Things get a bit more complicated when you start factoring in other factors – but the basic math doesn’t change.
If you bring in gravity, it’s important to remember that everything you get from gravity you have to put into potential energy in the first place. Gravity is most useful when your target is holding still, which is why executioner’s axes and digging picks are heavier than those designed for battle.
For thrusting weapons you’re best off with the mass concentrated towards the part you hold if you want to move it around readily. If you want to block with it as well, you’ll want a somewhat more equal distribution. If you just want to block, broad and flat is the way to go – and you’ve basically got a shield.
For swinging weapons, like axes, you can maximize the kinetic energy transfer by putting most of the mass at the far end, where the weapon will be moving most rapidly. To maximize it’s maneuverability, you’ll want the weight on the end closest to you. If you want to block and strike with it, you’ll want a more equal distribution.
For weapons designed to pierce and be twisted or pulled through flesh, kinetic energy is less important than maneuverability, since much of the damage is from yanking on them after the initial impact. They tend to be lighter and shorter, so that the user is not at such a leverage disadvantage when pulling or pushing the weapon through the target’s tissues.
For cutting weapons that are drawn across flesh to slice or tear it, you’ll want a slightly uneven curve so that weapon continues to be drawn across the same place as the weapon as the user turns to pull it across his or her target.
Swung lever-assisted weapons need to be lighter, so that the user can exert enough force to maximize their acceleration despite the extra lever length. This covers everything from slings to flails and morning stars.
I could go on a good deal longer here, but I think that’s enough. It should be no surprise to anyone that most traditional weapons are already pretty well optimized. That’s why people use things which are especially made to be weapons rather than simply using whatever implement is ready to hand – and why most armies have always been armed with a relatively few simple weapons selected to balance effectiveness, ease of training, and costs. Fortunately, when it comes to basic melee weapons, it’s not that hard to rack up a decent “score” on all three counts.
For some quick, practical rules?
Make an improvised weapon roughly half as effective as whatever actual weapon you’re comparing it to.
A bizarre low-tech weapon is very unlikely to be any better than one of the old historical standards unless the user is given a LOT of special training in some special trick – and even then it’s probably limited.
If it sounds impractical, it probably is.
If it could have been made long ago, but no one’s ever equipped their army with it, it’s probably not very good.
If it’s simple, cheap, low-tech, nonmagical, sounds effective, and has never been in wide historical use, there’s probably something about it that you’re missing.