Dear Straight Dope:
I want to know why a person falling from a 6 story window is killed, but a bug is dropped from a proportional height — say, 6 feet — gets up and walks away. Why isn't it dead?
SDStaff Hawk replies:
Bugs have more air resistance.
Next, we must consider the surface area of the falling object. The surface area is the amount of the exposed surface the object has, and, generally speaking, the bigger an object is, the more surface area it has. When an object falls, it displaces the air beneath it. Since the air tends to resist displacement, it produces a force opposite to that of gravity in the phenomenon known as “air resistance.” Note that the amount of air displaced is dependent on the size of the object and not its mass, so the bigger the object, the more air it displaces, the higher the air resistance. However, if an object is large without a lot of mass or substance (e.g., a sponge or Rush Limbaugh), we usually describe it as “light” (OK, scratch the Limbaugh analogy). So, when an object falls, it falls because of gravity but the amount of force it has is determined by its mass. At the same time, air resistance produces a force opposite to gravity but the amount of that force is dependent on its surface area.
Now, let’s get back to our test subjects. Our human test subject is 2 meters tall, 0.6 meters wide, and 0.4 meters deep and weighs 90.7 kilograms. He therefore has a surface area of 4.48 square meters. If we divide the mass by the surface area, we get 20.3 kilograms/square meter. On the other hand, our ant test subject is 0.002 meters tall, 0.002 meters wide, and 0.006 meters long and weighs 0.00002 kilograms. He therefore has a surface area of 0.000056 square meters and a mass:surface area ratio of 0.36.
From these rather crude figures (they’re rather crude test subjects, especially the human) we see that the human’s mass:surface area ratio is several times greater than that of the ant. Hence, there is a significant disproportionality between the two species when they hit the pavement. Another contributing factor is biology. Humans and most other animals have an internal skeleton. Insects and other arthropods (like spiders, crabs, etc.) have an external skeleton (a.k.a. “exoskeleton”). This no doubt contributes another measure of safety to the poor hapless ants that got thrown off of a building in the interest of science.
SDStaff Hawk, Straight Dope Science Advisory Board
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