On the Existence of Dragons, Part 1.5

Just a bit more explanation, since I don't like making big changes to previous posts...

The Square-Cube Law is based on the fact that a cubic function (based on x³) will always overtake a quadratic (based on x²) function. No matter what. Even if you compare 0.01x³ and 999x², the cubic will always "win". And they'll keep getting further and further apart the higher you go. There's no way to make them stay close together for very long.

The Square-Cube Law, then, brings this from algebra to geometry. It says that, as you scale something up, its volume increases by a cube, and its surface area by a square.

I just took this from Google Images for now, I'll make a better version of it later. Sorry.

This is relevant in all sorts of different fields. For example, let's say you are designing a ship. If you take, say, a small sailboat and scale it up to the right size, it won't work at all. It might not even float, and it certainly won't be able to sail. The mass of the boat increased by the cube of the scaling factor, but the size of the sails only increased by the square.

And, as the previous post stated, this is why an elephant looks nothing like a scaled-up mouse. Strength is based on the cross-section of the muscle, which increases by a square. But mass and weight are based on the volume, which increases by a cube. As an animal is scaled up, its muscles need to be larger and larger compared to its size.

Another biological problem with this that I didn't mention is overheating. Small animals have a lot of surface area compared to volume, so they can lose heat easily through their skin. But large animals have a harder and harder time doing this. (Especially if they breathe fire.) Our dragon would at the very least have to be able to sweat to remove heat, bringing in yet another non-reptilian characteristic. But I suppose it's more likely than fire breathing at any rate.