How To: Absurd Scientific Advice for Common Real-World Problems

by Randall Munroe

Given how much time modern physics spends on deep and abstract mysteries like searching for gravitational waves or the Higgs boson, it can be surprising how many basic everyday phenomena aren’t well understood. In addition to ice skates, physicists don’t really understand what causes electric charges to build up in thunderstorms, why sand in an hourglass flows at the speed it does, or why your hair gets a static charge when you rub it with a balloon.

If you’ve taken some physics classes and you stare at this diagram long enough, you might start to wonder what the ½ is doing in the drag equation. Since the drag coefficient is a unitless, arbitrary scale factor, the ½ could be eliminated just by doubling all the drag coefficients. Sports physicist John Eric Goff has pointed out that if you derive the equation by thinking about the momentum carried by the incoming air molecules, it seems like a factor of 1—or possibly 2—would be more natural than ½. However, if you think of drag in terms of the kinetic energy of the incoming air, then carrying over the ½ from the kinetic energy equation makes more sense. Physicists tend to explain it this way—by saying the drag equation represents the “dynamic pressure” of the incoming air—but not every authority agrees. Frank White’s Fluid Mechanics textbook simply calls the factor of ½ a “traditional tribute to Euler and Bernoulli.”

This is so arbitrary and bananas.