Argentinosaurus is believed to be the largest land animal to have ever lived. It was a dinosaur and at maybe 100 tons and 30 m, it was a very big dinosaur. I wanted to know the largest land animal for the lectures on biological physics I am giving this coming semester, and Google and Wikipedia provided. Anyway, in the lectures my question will be: Why was the largest animal 100 tons, not say 10 tons, or 1000 tons?
The precise size of animals is set by evolution, but the laws of physics set limits. The weight, i.e., the pull of gravity, for both us and dinosaurs is supported by our bones. Bone is strong but not infinitely strong, it has a limited strength. This is expressed as the force per cross-sectional unit area of the bone, aka stress, you can load on bone before it snaps. This is a few 10s of MPa (i.e., mega Pascals, which is 1 million Newtons per square metre).
Now, animals are complex shapes but I am a simple physicist so for simplicity I will assume a perfectly cubic animal – to keep the maths simple – with height h. Then its mass is 1000 h3 kg, taking the density of animals to be close to that of water, which is 1000 kg m-3. Taking the acceleration due to gravity g = 10 m s-2, this gives a weight of 10,000 h3 N (Newtons).
If we say 10% of the h2 cross-section of our cubic animal is bone the stress is 10,000 h3/(0.1 h2)=105h. For h larger than 100 m, the stress is too large for bone to support. The problem is that the force of gravity increases as h3, while the area to bear this load increases more slowly, as only h3. And so for large h, i.e., large enough animals, bone is just not strong enough to support their weight.
I guess that Argentinosaurus is probably not far away from this limit. And the fact that the biggest land animal ever was a dinosaur means that I get to have a dinosaur in my lecture notes, and everyone likes dinosaurs.
