Parachutes and Public Radio

I'm a relatively light sleeper. The ear-piercing klaxons that are most alarm clock buzzers are way more than necessary to get me out of bed, and even most music stations are more than I want to deal with abruptly when I'm trying to work up the will to leave warm comfort to go to a day's work. So it's usually the dulcet tones of NPR that start when the clock alarm reaches the specified time.

This morning the programming included a short "Everyday Science" piece about how parachutes work. Their explanation went more or less like this: when you open the parachute, the chute pushes the air down which in turn pushes you up. This upward force balances the force of gravity, slowing you down.

That's true as far as it goes, but it's not quite complete. After all, exactly the same thing happens when you don't deploy the parachute. Your body pushes the air, the air pushes you, and that force and the force of gravity cancel out, bringing your acceleration to zero. But all zero acceleration means is that your velocity is constant. In this case that constant velocity is very large and things will end badly for you when that high-speed trajectory intersects the ground. Why is a parachute an improvement on this? That's the question the segment didn't answer.

We can answer it. I think the easiest way to do so is by looking at the energy exchanges rather than forces. Once we have the energy situation squared away, we can look at the forces with greater understanding.

Start with energy. Unlike the federal budget, the energy budget is required by the laws of physics to stay perfectly balanced. For a falling skydiver, energy in is a result of falling down the gravitational potential of the earth's field. Each distance h fallen results in an energy of m*g*h added to the balance sheet of the skydiver. However, not all of that energy ends up being converted to his kinetic energy. Energy is required to move the air just below him out of the way. If he's moving slowly, the air doesn't have to be moved quickly, and so only a little of that potential energy is used to increase the kinetic energy of the air below him. The rest goes into kinetic energy and the falling skydiver speeds up. As he speeds up, the air just below him has to be pushed out of the way faster, using more kinetic energy. Less energy is left to go into the speed of the skydiver, and his velocity increases more slowly. Eventually equilibrium is reached and the energy required to shove that h length column of air out of the way fast enough is exactly equal to the potential energy from falling that distance. None is left to make the skydiver move faster.

Now pull the parachute cord. The chute deploys and suddenly every meter of distance fallen requires a much larger volume of air to be displaced. All the air under the chute has to be moved, not just the air right under the skydiver's body. As such the equilibrium between energy gained by falling and energy lost by moving the air occurs at a much lower speed. With a good parachute, this speed is low enough to land safely.

Looking at things in terms of forces (as the radio segment did) is now a little easier conceptually. The force required to move the air is proportional to the amount of air moved and the speed with which is has to be moved. More parachute, more air. More air, more force at a given speed. Gravity's force on the skydiver is constant, and so the equilibrium speed is much lower. And that's that.

I'm not criticizing the radio too much, by the way. What I've written at some length isn't going to fit in a 60 second time slot. Good on them for doing as well as they did.