If You Were the Size of…
Shrink yourself to an ant or grow into a giant, keeping your shape. Weight grows with length cubed but muscle strength only squared — which is why insects can lift many times their own weight and giants would collapse.
On Being the Right Size
Double your height and keep your shape: you become 2×2×2 = 8 times as heavy, but your muscles and bones only get 2×2 = 4 times as thick. Relative to your weight you are half as strong, and your leg bones carry twice the stress.
Shrink instead and the effect reverses: an ant-sized human could lift dozens of times their own weight and would hardly notice a fall — air resistance matters more and more as things get small. Biologist J.B.S. Haldane wrote a famous essay about it in 1926: a giant ten times our height would break his thighs with every step.
What Scales How
scale factorKey Relations
Every length gets s times bigger, every area s², every volume (and so the mass) s³.
Muscle force grows with the cross-section of the muscle; the weight it must lift grows with volume.
Kleiber’s law and the heart-rate rule from the other tabs, written with the scale factor.
Terminal speed depends on weight over drag area, so small creatures fall slowly; a human in free fall reaches about 55 m/s.
Sources & Verification
- K. Schmidt-Nielsen, Scaling: Why Is Animal Size So Important?, Cambridge University Press, 1984 — Ch. 2 (Problems of Size and Scale) and Ch. 5 (The Strength of Bones and Skeletons).
- M. Kleiber, “Body size and metabolism”, Hilgardia 6(11), 315–353 (1932).