Limits on Size of Land Animal

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Limits on Size of Land Animal

May 13 2011 4:48:36 pm EST

Topics: Morphology,

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In the first chapter of On Growth and Form, we learn the effects of magnitude on the shape of an animal.

In essence, magnitude is governed by basic physics. Mass is proportional to the cube of the linear dimensions of an animal. An animal must overcome its own mass with musculature. However, the strength of the muscle varies with the cross-section, or the square of the linear dimensions. Here are some examples:

Chapter II, On Magnitude. Page 23:

“...A fish, in doubling its length, multiplies its weight no less than eight times; and it all but doubles its weight in growing from four inches long to five.”

Page 25-26

“...The strength of an iron girder obviously varies with the cross-section of its members, and each cross-section varies as the square of a linear dimension; but the weight of the whole structure varies as the cube of its linear dimensions. It follows at once that, if we build two bridges geometrically similar, the larger is the weaker of the two*, and is so in the ratio of their linear dimensions.”

Page 28

“We learn in elementary mechanics the simple case of two similar beams, supported at both ends and carrying no other weight than their own. Within the limits of their elasticity they tend to be deflected, or to sag downwards, in proportion to the squares of their linear dimensions ; if a match-stick be two inches long and a similar beam six feet (or 36 times as long), the latter will sag under its own weight thirteen hundred times as much as the other. To counteract this tendency, as the size of an animal increases, the limbs tend to become thicker and shorter and the whole skeleton bulkier and heavier; bones make up some 8 per cent, of the body of mouse or wren, 13 or 14 per cent, of goose or dog, and 17 or 18 per cent, of the body of a man. Elephant and hippopotamus have grown clumsy as well as big, and the elk is of necessity less graceful than the gazelle.”

And finally, page 30:

“The strength of a muscle, like that of a rope or girder, varies with its cross-section; and the resistance of a bone to a crushing stress varies, again like our girder, with its cross-section. But in a terrestrial animal the weight which tends to crush its limbs, or which its muscles have to move, varies as the cube of its linear dimensions; and so, to the possible magnitude of an animal, living under the direct action of gravity, there is a definite limit set.”

Dates:

2011

2010