Re: [math-fun] Physically intuitive?
Brad Klee <bradklee@gmail.com> wrote:
The same day I found three species of Onthophagus, I also found an Alaus oculatus (the largest Elateridae I have seen in situ) near a rather large gallery of Bess beetles. While I was handling it, it snapped at me, and the power of it surprised me completely!
Latch mechanisms aside, small creatures tend to produce more power per unit mass and per unit volume. Power is limited by the ability to take in oxygen and to eliminate carbon dioxide and heat. And, over the longer term, also by the ability to take in food and eliminate waste. This is done through their surfaces, and is used or generated through their volumes, so creatures with a small ratio of volume to surface area can produce more power per mass. A small ratio of volume to surface area goes with a creature that is small in one, two, or all three dimensions (i.e. flat, long and skinny, or just overall small). This applies to things other than animals. For instance the sun, which has an astonishingly low power output per kilogram -- four or five orders of magnitude less than a person! The sun's surface is hot only because there's so much volume behind every square meter of its surface. The sun's fuel has far more energy per kilogram than human fuel, but the sun's (primordial) breakfast has to fuel it for billions of years, while your breakfast only need fuel you until lunch. It's been pointed out that if the Star Wars Death Star generates heat at the same rate per volume as an average office building, it would have to be white hot to radiate away all the waste heat. (There's no convective or conductive heat loss in the vacuum of space, only radiative.) No wonder it blew up. It's also been pointed out that whole world's human population could fit into a cubical building about two kilometers on a side. True, but there's only one place in the solar system with enough cooling capacity to keep everyone from soon dying of heatstroke. The building would have to be situated in the mouth of the Amazon River. Plenty of places, on and off Earth, are much colder than that tropical river, but none of them have that much moving fluid with that high a specific heat. According to my calculations, the river would be heated by just one degree Celsius, not counting waste heat from whatever machinery in the building keeps everyone fed, entertained, etc. Getting back to the subject line, one of my hobbies is collecting un-intutive facts.
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Keith F. Lynch