I told you there were going to be puns.
A long time ago, a pretty cool guy called Gallileo described something which would eventually be known as the Square-cube law in mathematics.The square cube law states: When an object undergoes a proportional increase in size, its new volume is proportional to the cube of the multiplier and its new surface area is proportional to the square of the multiplier. Basically, when you increase the size of any dimension of an object, its surface area is increased by the SQUARE of that increase and the volumne (thus mass) is increased by the CUBE of the increase. When applied to real world thermodynamics and biology, the square-cube law explains why elephants have a harder time cooling themselves than smaller animals, why there is a size limit on a sand-castle, and why giant ants would never exist.
You see, if an animal were scaled up, its relative muscular strength would be considerably cut, since the cross section of its muscles would increase by the SQUARE of the scaling factor while its mass (and weight) would increase by the CUBE of the scaling factor. Thus, while a smaller ant can carry 50 times their own body weight, a giant ant couldn’t even move his fat ass and wouldn’t be able to produce enough energy to survive. This works in the reverse way too, big things couldn’t survive being considerably smaller.
This week, I’m going to reference another one of Newton’s laws of motion, the second one (force = mass x acceleration). As tvtropes puts it: “if you double a critter’s height while keeping it the same shape, you end up with four times the muscle power moving eight times the mass, so instead of having the same relative agility as the original, the double-sized creature actually has only half.”
What does this mean for films? Well, most examples completely ignore this law. Godzilla would never have worked, the giant ants in THEM would’ve crushed themselves too. This applies to machines as well, which is why we’ll most likely never see giant war robots. This is averted in at least one show. A while back in my other column, I discussed one of my favorite shows (saga of shows), the classic Anime Mobile Suit Gundam. Mobile Suit Gundam has giant robots of death but the creator, Yoshiyuki Tomino, knew about this and in the original script only had the series take place in space. He also had the robots (Mobile Suits) powered by fusion reactors in order to have the power to move. When he decided to set part of the series on earth, he added that Mobile Suits were made with a high-tech alloy to prevent their weight from crushing themselves.
Now this covers how the square-cube law applies to the machine, but not to its surroundings. Contrary to popular belief, solid ground isn’t exactly solid. An 18-meter tall Mobile Suit weighs 60 metric tons and would crush any earth it stood upon.
What does this mean for the Jaegers and Monsters of Pacific Rim? Well, it depends. The Jaegers could easily be powered by a generator sophisticated enough to put out the energy needed to move the behemoths, and the same future technology could be used to justify not crushing themselves under their own weight. But like the aforementioned Gundam example, the ground beneath the machine would crumple and break. The Monsters, depending on their origins might break this rule. Based upon their shape, their muscles would not be strong enough to move them. And barring their skeleton being made of some super-strong foreign material or developed to withstand the extreme pressures of the super-deep ocean, they could never support their own weight. Now since the movie hasn’t come out yet I can’t exactly say for sure yet.
Oddly enough, Airships (see: blimps) are helped by the Square-Cube law. You see, as the size of the airship increases, the amount of gas inside increases, and thus the buoyancy increases.
Join me next week as I deconstruct Hollywood tropes and delve into the magical world of science.
Also, be sure to read my other column: Mindless Action Mondays
And as the good Bill Nye put it: “SCIENCE RULES”