The drag coefficient is a number that engineers use to model
all of the complex dependencies of shape
and
flow conditions on rocket
drag.
This equation is simply a
rearrangement of the drag equation where we
solve for the drag coefficient in terms of the other variables.
The drag coefficient Cd
is equal to the drag D divided by the quantity: density r times
half the velocity V squared times the reference area A.
Cd = D / (A * .5 * r * V^2)
The quantity one half the density times the velocity squared is called the
dynamic pressure q. So
Cd = D / (q * A)
The drag coefficient then expresses the
ratio
of the drag force to the force produced by the dynamic pressure times the area.
This equation gives us a way to determine a value for the drag
coefficient. In a controlled environment like a
wind tunnel
we can set the velocity, density, and area and measure
the drag produced. Through division we arrive at a value for the drag
coefficient. As pointed out on the drag
equation slide, the choice of reference
area (frontal area or surface area) will affect the
numerical value of the drag coefficient that is calculated.
When reporting drag coefficient values, it is important to specify
the reference area that is used to determine the coefficient. We can
predict the drag that will be produced under a different set of
velocity, density
(altitude), and area conditions using the drag equation.
The drag coefficient contains not only the complex dependencies of
object shape, but also the effects of air
viscosity and compressibility. To correctly use the drag
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.
At supersonic speeds,
shock waves
will be present in
the flow field and we must be sure to account for the wave drag in
the drag coefficient. So it is completely incorrect to measure a drag
coefficient at some low speed (say 200 mph) and apply that drag
coefficient at twice the speed of sound (approximately 1,400 mph,
Mach = 2.0). It is even more important to match air viscosity
effects. The important matching parameter for viscosity is the
Reynolds number
that expresses the ratio of inertial forces to
viscous forces.
In our discussions on the sources of drag,
recall that skin friction drag depends directly on the viscous
interaction of the object and the flow. 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 drag.
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