Lift is created by deflecting a moving fluid
(liquid or gas), and drag is generated on a body in a
wide variety of ways. From Newton's second law
of motion, the aerodynamic forces on the body (lift and
drag) are directly related to the change in
momentum of the fluid with time. The fluid momentum is equal to
the mass times the velocity of the fluid. Since the fluid is moving,
defining the mass gets a little tricky. If the mass of fluid were
brought to a halt, it would occupy some
volume
in space; and we could
define its density to be the mass divided
by the volume. With a little math which is described on the
fluid momentum page, we can show that the aerodynamic forces are
directly proportional to the density of the fluid that flows by the
airfoil.

Lift and drag depend linearly on the density of the fluid. Halving
the density halves the lift, halving the density halves the drag.
The fluid density depends on the type of fluid and the depth of the fluid.
In the atmosphere, air density decreases as altitude increases.
This explains why
airplanes have a flight ceiling, an altitude above which it
cannot fly. As an airplane ascends, a point is eventually reached
where there just isn't enough air mass to generate enough lift to
overcome the airplane's weight. The relation
between altitude and density is a fairly complex exponential
that has been determined by measurements in the atmosphere.

Let's investigate the dependence of lift on density using a Java
simulator.

Due to IT
security concerns, many users are currently experiencing problems running NASA Glenn
educational applets. The applets are slowly being updated, but it is a lengthy process.
If you are familiar with Java Runtime Environments (JRE), you may want to try downloading
the applet and running it on an Integrated Development Environment (IDE) such as Netbeans or Eclipse.
The following are tutorials for running Java applets on either IDE:
Netbeans Eclipse

As an experiment, set the altitude to 5300 feet and note the
value of the density and the amount of lift.
Now change the altitude to 26,500 feet. What is the new value of the
density? What is the value of the lift? How
do these compare to the previous measurement? Notice that the altitude
did not double. Now take this airplane to Mars. How does the density and
lift compare to Earth at the same altitude? Move the altitude up to
37000 feet. How does the density and lift compare to the original
measurements on Earth?

You can download your own copy of the program to run off-line by clicking on this button:

You can further investigate the effect of density and the other
factors affecting lift by using the
FoilSim III Java Applet.
You can also
download
your own copy of FoilSim to play with
for free.