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. The wall stress of a pressure vessel is proportional to the pressure times the radius. That stress is accommodated by the tensile strength of the vessel wall material (collagen? muscle?) multiplied by thickness. A shrew and a whale both use the same materials - and the shrew needs a proportionally thinner wall to accommodate the proportionally smaller stress. One to one scaling. A shrew's lifetime is short because its metabolism runs faster; species survival is optimized by devoting resources to fast reproduction, not individual longevity. |
Scale
The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies
Geoffrey West 303.44 WES 2017 Beavertin Library
Great ideas. A fat book that should have been leaner - though it could have been more explicit about unsolved problems and open questions.
A couple of math goofs:
Page 119: ... "our capillaries are only 5 micrometers wide (about a hundredth of an inch), which is somewhat smaller than a hairbreadth"
An inch is 25.4 millimeters, or 25400 micrometers, so capillaries are about 0.2 thousandths of an inch, or 0.2 mils or 200 millionths of an inch. Inches are a weird archaic unit, so it is unsurprising that a particle physicist (trained to work with vastly smaller metric units, not mixed engineering units) doesn't notice this error.
Page 125: "shrew's heart" ... and ... "whale's heart" ... "This is pretty amazing -- just think of the enormous stresses on the walls of the shrew's tiny aorta and arteries compared with the pressures on yours or mine, let alone those on a whale's. No wonder the poor creature dies after only a year or two."
- The wall stress of a pressure vessel is proportional to the pressure times the radius. That stress is accommodated by the tensile strength of the vessel wall material (collagen? muscle?) multiplied by thickness. A shrew and a whale both use the same materials - and the shrew needs a proportionally thinner wall to accommodate the proportionally smaller stress. One to one scaling. A shrew's lifetime is short because its metabolism runs faster; species survival is optimized by devoting resources to fast reproduction, not individual longevity.