Physics of Biological Size in Movies

Physics can be found everywhere including vertebrate zoology. Body size and morphology typically have some evolutionary or physical purpose. Elephants, for instance, have large legs to support their body weight. However, movies often manipulate body sizes- the shrinking or growing of people, Godzilla, King Kong, etc. But could these size transformations ever happen in real-life? The answer is almost certainly no, for a multitude of metabolic, physical, and morphological reasons.

But here, I will consider one beneficial physical change that occurs if humans could be shrunk.

One important understanding prior to entering this discussion is the general influence of area vs. volume. As size increases or decreases, the volume changes more relative to the area:

Now let’s discuss falling objects:

Terminal velocity is the point at which a constant velocity is reached by a falling object due to drag force equaling the gravitational force.

where m=mass, g=9.8 m/s², p=density of medium (air), A= area of object, C_d= coefficient of drag.

Gravitational force is dependent on the mass (or volume) of the object. Drag force is dependent on the cross-sectional area of the object (area). As the size of the object changes, gravitational force will be more subject to change than the drag force. This means that terminal velocity is not constant, but changes as the proportion of gravity and drag force changes.

If a human were considering how to get down from some high place, they would have to carefully consider the impacts of just falling. Its why fire escapes are so important. Humans reach a terminal velocity of about 120mph, dependent on mass and cross sectional area. This would most certainly result in injury or death.

However, if a human were shrunk ( a few centimeters), there would be many more options to get down from a proportionally high place. The decrease in size leads to a decrease in gravitational force (mass) and to a lesser extent a decrease in drag force (area). Therefore, the terminal velocity is smaller and much less deadly.

The “less deadly” factor points to the hit of the fall. Kinetic energy at the bottom of the fall will be much less for the miniature human as both its mass and velocity are smaller than the normal sized human. Because the velocity is a squared term, the larger velocity of the normal human will have a much bigger effect on its kinetic energy.

In a non-movie context, this is why from the same height fall, a human might be injured but a mouse will be unharmed.

Source: Vertebrate Zoology/Body Size article- http://fathom.lib.uchicago.edu/2/21701757/