Science of Anime: Scale

A lot of anime like to have things big.

The very first super robot, Tetsujin 28, is 18 meters tall, big enough that it’s English name was Gigantor. Of course, a lot of other mecha (especially the less realistic ones) are even bigger; Zearth from Bokurano is 500 meters tall. But it’s not just mecha; Dragon Ball, One Piece, Naruto, and Attack on Titan are just some of the more obvious examples of anime with giant creatures of one kind or another.

Goku_VS_Gohan_(great_ape)

All of the ones I’m talking about are able to walk around on land under normal gravity. (I’ll have something to say about certain even bigger ones that are only seen in space in a later post.)

Most of the mecha are more or less human-shaped, and of course so are the humanoid giants. The giant animals tend to have the same proportions as the small or medium-sized animals they resemble.

But you can’t just scale something up (or down) and expect it to still work at any size. The main issue is the square/cube law. For the same shape, area increases with the square of the height/length, but volume increases with the cube. And assuming the density also stays the same, mass increases the same as the volume. In other words, if you make something twice as tall, it weights 8 times as much, but the area supporting it is only 4 times as much.

In real life, the largest land animals to have ever lived were the largest dinosaurs (Brachiosaurus, Dreadnoughtus, etc.), and likewise the largest animals to walk on two legs were the largest of the bipedal dinosaurs (Tyrannosaurus, Spinosaurus, etc.). But a lot of these anime giants are much larger than any dinosaur.

But the square-cube law doesn’t merely limit size below some maximum. It’s also the reason why real large animals aren’t proportioned the same as small ones. The more weight legs have to support, the thicker they need to be; and also straighter. Occasionally an attempt to make a giant robot look a little less human includes giving it always-bent digitigrade legs like a bird or a cat; but there’s a reason that elephants don’t have legs like that. (Elephant legs actually are closer to digitigrade than ours are, but they are kept straight and they don’t really have the actual advantages of digitigrade structure.)

Speaking of elephants, they can’t jump. Not even a little. They’re just too heavy. But fictonal creatures a lot bigger than elephants often can; in Naruto, the kaiju-sized frog Gamabunta can leap many times his own length, as if jumping abilty scaled up in a linear way. (This is the same fallacy behind Spider-Man’s “proportional strength of a spider”.)

And one other thing. All those giant bipedal dinosaurs used their tails for balance, something that a humanoid mecha obviously can’t do.

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