Quick Science Facts: BIOMECHANICS

Original article: http://en.wikipedia.org/wiki/Square-cube_law#Biomechanics

If an animal were isometrically scaled up by a considerable amount, its relative muscular strength would be severely reduced, since the cross section of its muscles would increase by the square of the scaling factor while its mass would increase by the cube of the scaling factor. As a result of this, cardiovascular and respiratory functions would be severely burdened.

In the case of flying animals, the wing loading would be increased if they were isometrically scaled up, and they would therefore have to fly faster to gain the same amount of lift. Air resistance per unit mass is also higher for smaller animals, which is why a small animal like an ant cannot be seriously injured from impact with the ground after being dropped from any height.

As was elucidated by J. B. S. Haldane, large animals do not look like small animals: an elephant cannot be mistaken for a mouse scaled up in size. This is due to allometric scaling: the bones of an elephant are necessarily proportionately much larger than the bones of a mouse, because they must carry proportionately higher weight. To quote from Haldane’s seminal essay On Being the Right Size, “…consider a man 60 feet high…Giant Pope and Giant Pagan in the illustrated Pilgrim’s Progress…. These monsters…weighed 1000 times as much as Christian. Every square inch of a giant bone had to support 10 times the weight borne by a square inch of human bone. As the human thigh-bone breaks under about 10 times the human weight, Pope and Pagan would have broken their thighs every time they took a step.” Consequently, most animals show allometric scaling with increased size, both among species and within a species. The giant creatures seen in monster movies (e.g., Godzilla or King Kong) are also unrealistic, as their sheer size would force them to collapse.

However, the buoyancy of water negates to some extent the effects of gravity. Therefore, sea creatures can grow to very large sizes without the same musculoskeletal structures that would be required of similarly sized land creatures, and it is no coincidence that the largest animals to ever exist on earth are aquatic animals.