# Q & A: How do airplanes fly?

Q:
If gravity makes things fall to the ground, then why do airplanes don't fall to the ground?
- Laura (age 16)
laredo, Texas
A:

Hi Laura,

I've heard a lot of arguments about exactly how airplanes fly... you can find a lot of material online, but I'm not sure you should trust any of it. (Aerodynamics is a very complicated subject, and a lot of the problems can't be solved exactly. Most engineers and physicists study these problems by making complicated computer models.)

However, there are some things which we can say for sure. For starters, we know that the airplane doesn't fall out of the sky, so there must be a force upwards on the plane to balance the force of gravity. What is pushing up on the airplane? It must be air: there is nothing else around.

Specifically, the airplane's wings push the air downward, and (by Newton's second law) the air pushes back upward (the so-called reaction force) on the wing. It is this reaction force from pushing air downwards that keeps the airplane up.

But airplanes are often very heavy... how can air keep them up? I've always wanted to calculate this, so your question motivated me to finally do an estimation. The exact numbers I used are rough, but should give you some idea of how it works.

Let's consider a fully-loaded, 500 ton Boeing 747 at take-off (I got these numbers from wikipedia). The surface area of a Boeing 747 is about 550 square meters. Since the air hits the wings at an angle, the effective area is less; let's estimate this as 200 square meters. The take-off speed is about 300 meters per second, so the wings intersect 1.7 * 10^4 cubic meters (over 20 tons!) of air in one second. To lift the 500 ton jet, the air must be forced downwards so that the rate of change in momentum is equal to the force of gravity. This fairly simple calculation shows that the 20 tons of air are forced downwards by the wings at over 200 meters per second, almost 2/3 the speed of sound!

The moral of the story? Don't stand underneath a 747's wings during takeoff!

Cheers,

David Schmid

(published on 10/01/2013)