NUMBERS COUNT
excerpt of editorial by Cliff Swartz in THE PHYSICS TEACHER, p536, Vol34,
Dec 1996
...Can airplanes really fly? If you looked at one of the big jets at the
terminal, and hadn't already bought your ticket, you might think that
something that big could never get off the ground. From the booklet
(Magnitudes of Physics) we find that the mass of an empty 747 is 1.6e5
kilograms. Let's assume that the weight at takeoff is about 200tons --
2.0e6 Newtons. The only way to get a holding force upwards of 2e6 Newtons,
is to provide a downward thrust of 2.0e6 Newtons. Short of a skyhook, the
only thing we have to throw down is air. The momentum flow of that air
must be at least 2.0e6 kg(m/s)/s. That's what the wings are for. They
divert the air they reach and deflect it downwards. (Sure, sure,
Bernoulli, but if that much air doesn't go down, the plane doesn't stay
up.) The volume of air deflected per second must be about the length of
the wings times the speed times the vertical thickness of the layer, which
we will assume is about the same as the horizontal width of the wing. For
our big passenger jet at takeoff that's about 50m x 60m/s x 5m = 1.8e4m^3/s.
Since the density of air is 1.2kg/m^3, there must be about 2.1e4 kg of air
being shot partially downward every second, with a speed of about 70m/s.
That yields a thrust (v*dm/dt) of 1.5e6 Newtons, which, considering my
sloppy approximations, is just about enough to get that plane off the
ground. Note how chancy the explanation would be without numbers...