The drag coefficient is a number which
engineers use to model all of the complex dependencies of
drag on shape
and flow conditions.
The drag coefficient Cd is equal to the
drag D
divided by the
quantity:
density r
times
reference area A
times one half of the
velocity V
squared.
Cd = D / (.5 * r * V^2 * A)
This slide shows
some typical values of the drag coefficient for a variety of shapes.
The values shown here were determined experimentally by placing
models in a
wind tunnel
and measuring the
amount of drag, the tunnel conditions of velocity and density, and
the reference area of the model. The
drag equation
given above was then used to calculate the drag coefficient.
The projected frontal
area of each object was used as the reference area.
A flat plate has Cd = 1.28, a wedge shaped prism with the wedge facing
downstream has Cd = 1.14, a sphere has a Cd that varies from .07 to .5,
a bullet Cd = .295, and a typical airfoil Cd = .045.
We can study the effect of shape on drag by comparing the values
of drag coefficient for any two objects as long as the same reference
area is used and the
Mach number
and
Reynolds number
are matched.
All of the drag coefficients on this slide were produced in low speed
(subsonic) wind tunnels and at similar Reynolds number, except
for the sphere. A quick comparison shows that a flat plate gives the highest
drag and a streamlined symmetric airfoil gives the lowest drag, by a
factor of almost 30! Shape has a very large effect on the amount of
drag produced. The drag coefficient for a sphere is given with a
range of values because the drag on a sphere is highly dependent on
Reynolds number. Flow past a sphere, or cylinder, goes through a
number of transitions with velocity. At very low velocity, a stable
pair of vortices are formed on the downwind side. As velocity
increases, the vortices become unstable and are alternately shed
downstream. As velocity is increased even more, the
boundary layer
transitions to chaotic turbulent flow with vortices of many different
scales being shed in a turbulent wake from the body. Each of these
flow regimes produce a different amount of drag on the sphere.
Comparing the flat plate and the prism, and the sphere and the
bullet, we see that the downstream shape can be modified to reduce
drag.
A typical value for the drag coefficient of a model rocket is .75, based
on the crosssectional area of the rocket. As shown above, this value
can be reduced slightly by adding a fairing, or small cone, to the rear
of the rocket between the body and the nozzle exit. Long thin rockets have
less drag than short thick rockets.
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