The lift coefficient is a number that engineers use to model
all of the complex dependencies of shape,
inclination, and some
flow conditions on lift. This equation is simply a rearrangement
of the lift equation where we solve for the
lift coefficient in terms of the other variables.
The lift coefficient Cl
is equal to the lift L divided by the quantity:
density r times
half the velocity V squared times the wing area A.
Cl = L / (A * .5 * r * V^2)
The quantity one half the density times the velocity squared is
called the
dynamic pressure q.
So
Cl = L / (q * A)
The lift coefficient then expresses the
ratio
of the lift force to the force produced by the dynamic pressure times the area.
Engineers usually determine the value of the lift coefficient
by using models in a
wind tunnel.
Within the tunnel
we can set the velocity, density, and area of the model and measure
the lift produced. Through division, we arrive at a value for the
lift coefficient. We can then predict the lift that will be produced
under a different set of velocity, density
(altitude), and area conditions using the lift
equation.
The lift coefficient contains the complex dependencies of
object shape on lift.
The lift coefficient also contains the effects of
air viscosity and compressibility. To
correctly use the lift coefficient, we must be sure that the
viscosity and compressibility effects are the same between our
measured case and the predicted case. Otherwise, the prediction will
be inaccurate.
For very low speeds (< 200 mph) the compressibility effects are
negligible. At higher speeds, it becomes important to match Mach
numbers between the two cases.
Mach number
is the ratio of the
velocity to the speed of sound. So it is completely incorrect to
measure a lift coefficient at some low speed (say 200 mph) and apply
that lift coefficient at twice the speed of sound (approximately
1,400 mph, Mach = 2.0). The compressibility of the air will alter the
important physics between these two cases.
Similarly, we must match air viscosity effects, which becomes very
difficult. The important matching parameter for viscosity is the
Reynolds number. The
Reynolds number
expresses the ratio of
inertial forces to viscous forces. If the Reynolds number of the
experiment and flight are close, then we properly model the effects
of the viscous forces relative to the inertial forces. If they are
very different, we do not correctly model the physics of the real
problem and will predict an incorrect lift.
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