## Why Animals Have a Maximum Size

Relative physical quantities scale in different ways, creatures of similar form eg dog and horse, are not similarly scaled versions of the same shape. Differences in size means that the shape alters. Taken to extremes, larger or smaller versions of the same creatures are not viable.
A person standing up they place a stress on their leg bones equal to weight divided by area. If the size of the persona doubles, so that all the lengths are doubled, then the volume (and the weight) increase by a factor of
$2^3=8$
, but the cross sectional area of the leg bones increase by a factor of
$2^2=4$
. Hence the stress on the leg bones increases by a factor of
$\frac{8}{4}=2$
. The leg bones of a person 10 times as tall would experience 10 times the stress. Obviously, there is a limit to the stress a leg bone can experience without breaking, and this limit imposes a maximum practical size on similarly shaped organisms, and in fact any animal that must support its own weight by standing up.