Writing Blog Number 2 (continued)

20251102 Square-Cube Law

Square-Cube Law

This is a little thing for people writing about oversized creatures, in a horror, fantasy or even science-fiction setting, especially on Earth.

The square-cube law is how things change as they grow larger.
         To be really nerd-tastic: When a thing is increased by a certain degree or magnitude (call it x), the surface area and cross-section area are the square of this multiplier (x²) and the mass is the cube (x³) of the multiplier.

So, let’s say we have a thing that triples in size. The surface area and cross-section area are 3² or 9 times the original, and the weight is 3³, or 27 times original. So… let’s take a practical example.

We have a 6’ tall man who weights 200lb. Through magic, he grows to three times his size – 18’ tall. But that means his surface area would be 9 times what it was, the cross sectional area of his musculature would have to be 9 times what it was in order to carry the new mass… and this new weight would be 200*27 or 5400lbs.

So what? you might ask?

The problem is that in living creatures, strength is pretty close to being related to area of support, likewise the power that can be exerted; that means the strength of a muscle or bone is proportional to the area of the cross-section of the muscle or bone, not the volume. This means, simply, if you triple the size of a creature but it maintains its same shape or dimensions, you end up with a being that does not have the 9 times the muscle cross-section, and hence strength, it needs in order to move 27 times the mass or weight! In fact, the legs probably couldn’t carry it if they maintained the same proportions, and the creature would collapse in agony on broken limbs. By the way, this also applies to mechanical machinery.
         It is worse for flying creatures. Triple the size again and we get an increase in the power of the wings of 9 times based on the same crass-sectional area increase, but now it is carrying 27 times the mass. In fact, at this sort of level, the creature would probably no longer be able to fly.

Now, look, of course stories can have larger creatures, but they would have to change shape. A giant human would need a body that was much stockier and thicker, looking very out of proportion when compared to a normal human. A flyer would need very hollow bones to reduce the amount of excess mass suddenly thrown onto the being, and that would make the body’s structure weaker. That would also mean it could not carry x times the amount of weight. Or maybe not carry a person, for example.

However, there is a bonus. If something is shrunk in size, say to a third of their original size, then they will have proportionally 9 times the strength.

Now, this is all well and good when looking purely at biomechanics. But biochemistry is an issue as well. The change in size means metabolism also changes, how much heat is given off in relation to body changes, the amount of food needed to maintain heat or energy changes, the amount of oxygen needed to supply energy changes. These are deeply scientific concepts and make giant animals just seem insane.

Hang on! you cry, interrupting me. What about whales? Well, see buoyancy is related to density not mass, and so animals that live in the water can grow much larger because there is not the stress on supporting limbs. But they still need to eat a lot.

This is why skyscrapers could not be built without mass-produced steel. Double the size of a building and you have 8 times the mass, and wood and brick cannot hold that sort of stress. There needed to be a stronger material. Not only that, but the ground supporting them has to be able to handle something 8 times the weight! This would also apply to kaiju (like Godzilla) or even giant robots fighting them (like in Pacific Rim).
         So, yeah, this is something ignored all too often but draws people with some knowledge occasionally out of the story.

Physics be damned, I guess, when a story is there to be told.