How Would the Square-Cube Law change Medieval/Ancient Warfare Between Tiny Humanoids

Question

My story has a battle between two tiny races of humanoids. Assume that both of these races have developed in relative isolation from one another so they have not had a lot of time to develop specialized weapons and tactics against each other's strengths and weakness or steal each other's technology.

Gnomes average 20-30cm (8-12in) tall. They basically look like your average variety garden gnomes. They are rather strong for their size, but are limited by their proportionally shorter appendages. Their level of technology is roughly comparable to 12th century Europe.

Their opponents are the Gremlins which average 30-40cm (12-16in) tall. They weigh about the same as the gnomes, but are faster and have longer appendages. Their level of technology is much more comparable to the Late Bronze Age. They are no less clever than gnomes or humans, their civilization is just not as far along.

My original concept was to basically make it a stereotypical dwarves vs orcs kind of conflict, but then it occurred to me that these guys are much smaller than orcs or dwarves. Thanks to the square-cube law, this makes them proportionally stronger and tougher than you would expect out of humanoids. The gremlins would reasonably be able to jump like cats and climb like squirrels and the gnomes would be able to wield weapons and armor that are much thicker and heavier for their body size than you would expect. It also means both sides have much shorter acceleration arcs when swinging/throwing/shooting weapons. So with all of these factors in play, it seems to me that the very nature of weapons, armor, and tactics would have to have to change to make since for these tiny humanoids.

What kinds of armaments and tactics would each side most likely use the first time they meet in battle?

In case it matters, the battlefield is the inside of a 16th century human barn and neither side wants the barn to be destroyed.

Also, neither side has access to magic or explosives of any kind.

Answer 1

1. Blunt force / "bludgeoning" damage will be less effective than points and blades.

Consider an ant, flicked off a table to the floor. Usually, it just walks around as if nothing has happened, even though it has just, within the space of one second, been:

• Accelerated to a high velocity
• Launched over a distance several hundred times its own body length
• Come to a sudden stop on impact with the floor.

If a human body were subjected to the same treatment, it would be chunky salsa. This is a direct consequence of the square-cube law: a human body impacting a surface has so much more inertia/kinetic energy to dissipate than an ant.

Your gnomes and gremlins are somewhere in between. If you swing a gnome-sized club down on a gnome's head, it will take more damage than an ant-sized club to an ant's head, and less damage than a human-sized club to a human head. So blades and points that concentrate force will, by proportion, be more effective than blunt weapons.

2. Sustained muscle effort will be more damaging than a weapon's inertia.

This is another consequence of the square-cube law, and goes hand-in-hand with the previous point. When humans hit each other with medieval weapons, inertia usually does the main job. You usually wind up, take a huge swing, and accelerate the weapon to as high a speed as possible before it hits.

Let's go back to the insect world for a moment. How do insects fight? They don't ram each other or throw punches. They grapple each other and kill with muscle exertion. They bite legs or heads off, hold their target while they thrust a stinger in, or even cooperate to literally pull their target apart.

So again, your gnomes and gremlins are in between. A blow, especially with a blade or point, can still slice or puncture, but I would expect that more deathblows would be dealt by getting a hold of your opponent and using your own muscle strength to crush or stab or slice into a weak spot. Perhaps there would be an increased use of weapons designed to immobilize or entangle.

3. Missile weapons may still be useful, but probably less so.

Following directly from point 2: medieval missile weapons are entirely dependent upon their inertia for damage (barring the use of poison). Square-cubed down to gnome/gremlin size, they simply won't pack anywhere near the same punch they do at human scale. Again, with points and blades, one can perhaps mitigate this to some extent, but even so, they will be much more easily stopped by armor than at human scale. (Thickness of armor decreases proportionally to length; inertia of missile decreases with cube of length...how fast would you need to fire a sewing needle in order to puncture a ping-pong ball?)

The emerging picture...

As other answers have been added and comments have been made, some additional thoughts have come to mind. I would like to stress that, while my above points are sound scientific consequences of the square-cube law, the ideas below are closer to guesswork. But I'm hoping they're helpful!

1. Since it seems likely that grappling and thrusting is the name of the game, I would expect that, one-on-one, a gremlin would have an advantage over a gnome since it is "faster and has longer appendages". This, coupled with the earlier state of their civilization, inclines me to believe that the winning strategy for the gremlins is to get in close, fast, and try to take on the gnomes in general melee.
2. Building on point 1, gremlins would be likely to employ ambushes, and use tactics that create confusion and chaos to prevent coordinated defense.
3. Also building on point 1, gremlins would probably use daggers.
4. Conversely, gnomes would want to mitigate the gremlins' one-on-one advantage with coordinated defense. One might expect to see small groups of gnomes that operate as a single unit, fighting almost back-to-back, or perhaps larger units analogous to a phalanx.
5. Based on point 4, I would expect gnomes to use weapons like spears to hold gremlins at bay, and as a deterrent to make gremlins less inclined to jump at/on/into the middle of them. (Even a squirrel-sized creature could injure itself grievously by jumping right onto a grounded spike...)
6. I would also expect gnomes to use weapons intended to immobilize gremlins, so that their unit can move in together to make the kill.
7. Perhaps an innovative immobilizing weapon for use at their scale would be something made of loops of wire--something like a whisk? With the idea being to swing it down on a target's head or sword-arm. The inertia of the blow may to sufficient for it to wrap itself around the body part or weapon and ensnare it; but requiring the target to (stop what it's doing and) use its arms to free itself.
8. Given the relative impotence of missile weapons, I would expect a phalanx-like formation to be a strong unit. However, gremlins would undoubtedly find their own ways to attack them (throw large nets over parts of it? Have several gremlins jump onto it all at once, all holding wooden shields in front of them to prevent impaling themselves?)
9. The ability to physically throw an opponent is also more readily available to creatures at gnome/gremlin scale. If there is a clash of two large bodies of fighters, it may be a viable tactic for fighters at the front line to grab an opponent an hurl it to behind one's own line, where others wait to dispatch them where they fall.
10. A corollary to this is that there may be circumstances where throwing/springboarding an ally (or a horde of allies...) is a useful tactic. I've heard it said that "nobody tosses a dwarf", but gnomes and gremlins may have gone to a different school...

Answer 2

Other users have discussed actual combat, but I'd like to mention some points about logistics and broader tactics

Topography and geography would be a bigger deal

In general, the rule of thumb is that the smaller you get, the more uneven the landscape becomes from your perspective and the more difficult it is to get around anywhere. As an example of this, consider a river. For a an army of human-sized beings a river is easily fordable or it may even be possible to wade across, whereas for your miniature humanoids even a small river might be unfordable for a standing army and would require specialized bridges or boats to cross. Figuring out how to get from point A to point B as well as avoiding rough terrain to keep an army from getting boxed in would be a big deal.

Similarly, because a landscape is more complex at a smaller size, this opens the door for new tactics that wouldn't be possible for humans. A good example of this would be setting up an ambush where one side rappels down from the trees. A large number of humans could not easily hide in a tree unless that tree were very, very large, but to a 12-inch-tall being this kind of ambush could be set up in almost any forest.

Local wildlife is a bigger deal

As you get smaller, the number of potential predators or other dangerous wildlife dramatically increases. Additionally, while humans have pretty much wiped out anything large enough to cause a threat to us (aside from other humans), this would be a lot harder at smaller scales because dangerous megafauna can more easily hide and survive.

For a second, let us compare a human army with an army of ants. A human army is large enough that any tiger or elephant is liable to get out of their way, and it would be very unlikely that a standing army would have anything to fear from either. A column of army ants, on the other hand, has issues where workers and soldiers get picked off by other predators such as mantises. Yes, in the link shown the ants eventually won, but at the same time they had to deviate from their plan and waste time and troops fighting and killing a much larger predator. Imagine a world where a standing army has to worry about one animal having a bad day and deciding to ruin all of their pre-laid plans by taking out half their army. Imagine a world where instead of just having to worry about one enemy forcing marching around the landscape, armies have to deal with constant guerilla warfare fighting off predators that have no allegiance, no organization, and no supply chain. At least with another army you have a vague idea of where they are.

For a fictional example, check out Amphibia. Despite the fighting between the main factions of amphibians, half of the threats in the series come from the local wildlife as much as other sophonts. Indeed, two plot points early in the series come from a standing army being wiped out by a pair of herons and the largest, most-developed city in the world being under siege by a bunch of non-sentient ants.

Supply lines might be more vulnerable

In general, smaller animals have higher metabolisms than larger ones. An elephant eats more food than a mouse, but if you have a number of mice equal in weight to an elephant, they will actually eat more than the elephant. This is especially pertinent for smaller endotherms as the higher surface area means they lose heat faster and have to eat more to maintain their body temperature. Terrestrial sophonts pretty much have to be endothermic in order to keep their brain fed and warm. Consider the most intelligence modern animals: primates, cetaceans, elephants, pigs, crows, parrots, and octopodes. Of those only octopodes are really cold-blooded, and they're in the water.

This means your small humanoids will require more food than a human army of similar mass, and hence will be very vulnerable to starving if their supply lines are disrupted. In fact, they might also be more vulnerable to death by exposure in desert or winter conditions as they have a harder time staying warm or cold.

Another major hurdle is fire. Fire requires the same amount of fuel no matter what size. This is one reason it is thought that ants don't use fire, it consumes more fuel than the ants can feasibly gather to keep it going and can easily cook them if they aren't careful. Your species might be big enough to use fire, but they would have to carry around proportionally more fuel than humans would to keep the fires going, which means they would be more vulnerable to not having fires around to cook food or keep warm at night.

Answer 3

Most weapons rely on momentum to pierce armour or batter through it. However momentum is greatly reduced, and armour has increased relative strength, so normal weapons won't work against armor. Even without armour their effectiveness will be less.

Instead, the strength of the weapon-bearer, and the amount of force they can bring to bear without pushing themselves away from their opponent will be what allows them to stab or crush.

This might lead to a prevalence of armoured dagger grappling. Grappling and wrestling would have strong martial traditions.

Also consider how small animals fight or break open sturdy food like a walnut:

• Biting with teeth or beak, which is simple and powerful, but very short ranged
• Scratching, though this would be fairly ineffective given armour
• Barbed quills or stingers, often poisonous
• Trapping, with webs or sticky fluid
• Strangling
• Squirting nasty fluids like acid or venom
• Spring-loaded 'fists' (mantis shrimp) or jaws (trap jaw ants)

To me that suggests:

• Chemical warfare
• Adhesives, nets and lassos, especially for negating the gremlins' mobility
• Spring-loaded hand-weapons might be useful. Think a spear with a gin-trap on the end. This might combine with shield formations

Also dog cavalry.

Answer 4

This is a really interesting question, and I'll do my best to answer!

Gnomes

The gnomes are interesting. They're small, but they don't have the long arms or legs to get the rapid mobility like a gremlin would. Because of this, I think their tactics and armaments would rely heavily on brute force attacks. I assume something like plate armor would be relatively common for protection. Then, the more typical weapon for armament would be assumed to be something like a sword and shield, but taking into account that they've been fighting against themselves and that'd be how they developed their weapons, I think brute force style weapons would be common, such as warhammers. The reason for this is that When your enemy is wearing very thick armor, sometimes it's hard to penetrate, so instead a viable tactic is just to hit them with enough force to cause internal bleeding or break bones and not necessarily penetrate armor.

Plate armor is expensive though, but due to their larger size, they would be able to make more of it than typical soldiers in the medieval ages could. Regardless of this fact, I think there still likely would be a large force of less armored soldiers, using primarily cloth and leather based armors, with maybe some chainmail thrown into the mix. These soldiers I think would try and use their greater mobility due to not wearing heavy armor, and try to use knives and swords to stab in the slits and weakpoints of armor. They would utilize tactics like ambushes, but would primarily just help the ones in plate armor and scout about.

I think they would also make use of things such as trebuchets, catapults, or ballistae, as these could help to provide more punch to their brute force attacks and defeat well armored foes. Meanwhile, things such as bows wouldn't be as utilized, just since their short arms couldn't pull as far back, leading to the bows being much weaker, not too suitable for warfare.

Overall, for the gnomes, they'd operate similarly to real life knights did, using soldiers with heavy plate armor to spearhead assaults, supported with siege weapons. In the case of the barn, they likely wouldn't use siege weapons, instead simply just storming in their with heavily armored soldiers, supported with the lighter ones. Alternatively, they could simply just camp around the barn like it's a siege and just wait for the gremlins to surrender if they get there second.

Gremlins

For the gremlins, they would likely use their long arms and legs to adapt a very mobile form of warfare, which actually better fits the technology they have available to them.

Any sort of armor they had would be light at best. The heaviest armor would likely be made from overlapping bronze plates that allowed some amount of flexibility and mobility. I think most soldiers would adopt armors made from cloths or leathers though, as it restricts movement less and is lighter.

As for weapons, they'd always use things that suit maneuverability and whatnot. I imagine you'd see things like swords, daggers, and spears. They would also likely use bows, as their arms are long enough to have them be effective, and they're mobile enough to get into good firing positions before moving away.

So, the gremlins will use highly mobile tactics and light armor. Imagine hiding in the trees and dropping down on unsuspecting dwarves, stabbing through the holes in their armor and using speed to evade their attacks. While soldiers with knives or swords may go to the grounds, soldiers with bows or spears might just stay in the trees where they can't be hit. In this case in a barn, they might hide in the rafters, or climb on the walls. If they get there first, they'd probably try and set an ambush, hiding inside or outside to jump on the gnomes when they enter.

Answer 5

I'm late to the party. I won't bother reiterating all the things other answers got right. Instead, I hope to complement them by filling in what I see as gaps in their coverage.

I think it's a mistake to downplay the effectiveness of missiles. Based on their respective levels of technology, both gnomes and gremlins would have bows and I should think they would be approximately as effective as human bows. The square-cube law cuts both ways. Compared to a human using a human-sized bow, both races would be able to draw a bow with greater force relative to their body weight. This means they could either shoot relatively larger arrows, or shoot smaller arrows with more force. Either way, I think this would cancel out any negative effects of the square-cube law on a missile's effectiveness.

Furthermore, with 12C technology, the gnomes would have crossbows. I don't know how closely you're sticking to traditional notions of gnomes, but they're generally considered to be mechanically inclined so I would imagine their weaponry would be top notch. In general, crossbows can deliver just as much force as a regular bow. Because they are mechanical devices, they could be engineered to deliver even greater force at the expense of making them more difficult to load. For example, they could be cocked using a crank system or by multiple gnomes pulling together. Point is, gnomes would have very effective missile weapons which would be effective against the gremlins as well as larger races such as humans. I would not fear a gnome's crossbow any less than a human's.

Gnomes would also have a plethora of seige weapons at their disposal, such as catapults, trebuchets, balistas, battering rams, and so on. Some, like the balista, would also be effective anti-personnel weapons similar to how cannons were used in the Napoleonic era. A balista could fire a variety of missiles including large bolts (larger than the arrow from a human's bow) or hefty rocks. Rocks, like cannon balls could be fired into the gremlin ranks and cause considerable damage, smashing and maiming as they tumble. Remember that killing isn't always the goal. Breaking an arm or leg is almost as good. Such weapons can also have considerable effect on the enemy's morale. Again, thanks to their ingenuity and mechanical aptitute, gnomish balistas would be of excellent design and quality. They could utilize gears so that they could be loaded with tremendous force for devastating effect.

Bolas, another type of missile, could be used for hunting or warfare. They would be effective against creatures both big and small. They're essentially just a couple rocks connected with rope. They're thrown at the legs and trip the target by wrapping around the legs. Gnomes or gremlins could even bring down humans this way. Once downed, they could swarm the human to finish them off.

Poison darts, another type of missile, could be potentially very effective. The darts themselves don't need to be big or cause damage to the victim. The poison does the heavy lifting. The dart is just a means of delivery. Blow guns (such as is used in the Amazon) can be remarkably accurate, and are nearly silent to boot. Poison darts in combination with stealthy ambush tactics would be very effective.

Another point: You mention that gnomes and gremlins don't have a history of warfare against each other. Who do they have experience fighting? Whoever it is, big or small, they each would have developed weapons and tactics to be effective against their respective traditional foes. Likewise, if they hunt, what do they hunt? They would have weapons and tools tailored to their usual foes and quarries. If this battle in the barn is the result of a chance encounter, then these are the weapons they would most likely be carrying.