Lift depends on the
density
of the air, the square of the velocity, the
air's viscosity and compressibility, the
surface area over which the air flows, the
shape of the body,
and the body's inclination
to the flow. In general, the dependence on body shape, inclination,
air viscosity, and compressibility is very complex.
One way to deal with complex dependencies is to characterize the
dependence by a single variable. For lift, this variable is called
the lift coefficient, designated "Cl." This
allows us to collect all the effects, simple and complex, into a
single equation. The lift equation states that lift L is equal to the
lift coefficient Cl times the density r times half of the
velocity V squared times the wing area A.
L = Cl * A * .5 * r * V^2
For given air conditions, shape, and
inclination of the object, we have to determine a value for Cl to
determine the lift. For some simple flow
conditions, geometries, and low inclinations, engineers
can determine the value of Cl mathematically. But, in general, this
parameter is determined experimentally.
In the equation given above, the density is designated by the
letter "r." We do not use "d" for density, since "d" is often used to
specify distance. In many textbooks on aerodynamics, the density is
given by the Greek symbol "rho" (Greek for "r") as used in the
figure. The combination of
terms "density times the square of the velocity divided by two" is
called the
dynamic pressure
and appears in Bernoulli's
pressure equation.
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