## Lilliputian Physiology

To appreciate the effects of scaling and shrinking on an organism we understand better than insects, let's now perform the thought experiment of shrinking a woman until she is about an inch tall. Remember, her body circulation won't circulate at these dimensions, but let's imagine we got around this problem and we can keep her alive. At this point her linear dimensions have shrunk by a factor of about seventy. Thus, the surface area of her body (through which she loses heat) has decreased by a factor of 70 x 70 or about 5000, but her body's mass (that produces heat) has decreased by 70 x 70 x 70 or 350,000 times. As a Lilliputian she now has great difficulty maintaining her temperature. When her environment cools in winter she dies, unless her metabolic rate or heat producing capacity increases drastically.

The relative importance of physical forces working on and in her body depends on her size because of scaling again. How does she breathe? The surface area of her lung has only decreased by five thousand-fold, so she can still acquire the increased oxygen she needs perhaps by breathing more rapidly, but taking more breaths each minute challenges her musculature and requires more energy each minute to contract her muscles. Being so small, now like a shrew, she must eat her own weight in food each day just to stay alive and even more calories to support her increased activity.

Because our Lilliputan's surface area is now relatively larger after shrinking (she now has an increased surface to volume ratio), she looses water at a faster rate, so she must drink more. But now water's surface tension has become a major force in her life. When she was larger, surface tension was less than gravity. But drinking is now very difficult. The surface film tends to pull her into itself when she tries to drink. As a small 'machine' now living in the realm of microphysics, it would behoove her to develop long mechanically advantageous jointed stilt-like legs as well as a straw-like proboscis she could unroll like a mosquito's to poke a hole in the water surface. Her muscles must now attach differently than when she was bigger.

Consider the problems of a recluse spider. The spider's jaws clamp as it bites with its chelicerae at a force that is proportional to the cross-sectional areas of its jaw muscles. However, the spider's weight is proportional to its volume. So to bite and puncture human skin is difficult for the spider. Our Lilliputian would be at similar mechanical disadvantages, but she has also gained an advantage. Being so small, like a little spider now, she falls gracefully through the air.

A falling Lilliputian accelerates until the drag force imposed by the air on her body equals the gravity acting on her mass. When these forces are equal to each other and from this point on, her falling velocity is constant. Her now constant falling speed is her terminal velocity, and for an adult person, terminal velocity is close to one hundred and twenty miles per hour. Air's drag on a moving object is proportional to the object's cross-sectional area, but the force of gravity is proportional to the object's mass (and thus volume, if the density is constant). As objects shrink, gravity's pull decreases more rapidly than drag, so terminal velocities of small objects decrease.

A falling object acquires kinetic energy proportional to its velocity of falling squared. Kinetic energy dissipates rapidly when the object hits something and stops falling. A falling spider's health is potentially better than a falling person's. Smaller objects fall more slowly, but because of the squared velocity term in the kinetic energy relationship, much less energy dissipates when these objects impact, so injuries are less. An elephant falling out a window will be hurt or die, a squirrel may not be hurt, but our Lilliputian runs away unharmed, that is if her heart is up to it.

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