Bill Freeman wrote:
Many moons ago I, too believed in "flat plate equivalent".
Then I took Aero 301, and was *really* confused by the
textbook. The drag equation is:
Drag = CsubD * q * Area
where q = the dynamic pressure= (rho* vel^2)/2
which is one half of the density times the velocity squared.
So if we take a 12" x 12" flat plate and put it in the wind tunnel,
measuring the drag force, the density and the airspeed, we
can put all the "knowns" on one side and solve for the Coefficient
of Drag (CsubD) for a flat plate. The values will vary somewhat
based on airspeed and the size of the plate, but the generally
accepted CsubD for a flat plate is 1.28. Boy, when I first heard
this I squirmed in my seat! Say it ain't so!
I don't know what books you are reading but that is just not so.
The drag of a Standard flat plate of specified dimensions is
assigned a C sub d of one and is then used to calibrate wind
tunnels world wide.
That is the ONLY possible way in the world to be sure that
the C sub d of any object specified cross sectional area tested
in wind tunnels around the world will give the same C sub d. Read
Hoerner Fluid Dynamic Drag page 3-14 and 3-15. This is the last
word and the bible of the entire aerodynamics world. Been using
it for forty years and it always works for me! The value of one
assigned the C sub d of this one square foot plate is not arbitrary
and it is the ONLY way to make any sense out of drag measurements.
The frontal area in square feet of an object is then multiplied
by a measured C sub d and the drag is accurately predicted.
If you halve the area and keep the C sub d the same the drag will
be half. This has been done millions of times.
Millions upon millions of measurements have been made around the
world for the last 100 years and they can be repeated and verified
at any time. C sub d times the frontal area in square feet gives
the drag when multiplied by roh/2 X Velocity squared.
The correspond number for one square foot of wing surface area is
also one... unity.... uno!!!!! When you see a C sub L of 1.2 it
means that one square foot of wing area will produce 1.2 pounds
of lift at some speed. Pure and simple. Absolutely and fundamentally
not different than one square foot of frontal area on a fuselage
with a Equivalent Flat Plate area of 1.2 producing 1.2 pounds of drag
at some speed. No difference.
Now tell me a C sub L of 1.2 does not produce 1.2 pounds of lift
because the lift on on one square foot of wing area with a C sub L
of one is not one pound at the same speed.
The drag of an airplane is often reported as "equivalent flat plate area",
which is a convenient way to compare drag between different aircraft.
The problem comes when you try to calculate the drag FORCE from
the "equivalent flat plate area" value. The correct way is to multiply
the area times the CsubD, which is 1.28, to get the equation to work
out, as in the example experimental case.
What can be very confusing is that some folks say "equivalent flat plate
area" when they MEAN "equivalent area for a hypothetical object with
a CsubD =1.0".
NO! Absolutely NOT! That is not what they are saying
What they are saying is that the number is the PRODUCT of the
area and the C sub d what ever they may be. No need even to know
how much of each is involved. It absolutely says nothing specific about area.
Somewhere, I (and many others) had gotten the idea the a flat plate has a
CsubD of 1.0. This was an article of faith, but it was incorrect.
So, what is the bottom line? If you are comparing an airplane with 1.6 sq ft
of "equivalent flat plate area" to another with a 2.1 sq ft "equivalent
flat plate
area", be absolutely sure that both are assuming the same CsubD for their
reported area. Many folks say "equivalent flat plate area" when they MEAN
"equivalent flat plate area with a CsubD =1.0". These are NOT the same
thing at all. The answer will be off by 28% (amazing).
Possibly this came about when the Wright Brothers (who invented this whole
science, of course) used a flat plate as the reference drag body for their
wind tunnel experiments. (I think this is correct). This would have given
them a "drag factor" of 2.0 for something that had twice the drag of
a flat plate of equal area. This would be a very useful and perfectly workable
way to do the science, but it unconciously "defines" the "drag factor"of a
flat plate
as 1.0, where everything is referenced to this. Unfortunately, when you do
the actual FORCE measurement and plug in the correct units everywhere, in
the correct equation, the proportionality constant necessary to get the correct
value from the equation is 1.28. This is the correct (modern?) definition of
CsubD, and is absolute, rather than relative.
So, let's be careful using the term "equivalent flat plate area", because it is
widely misused and can lead to serious calculation error.
Let the attacks begin! ;-)
Bill Freeman
Long EZ builder & pilot
BSME, MSME
EAA Technical Counselor
C sub D and C sub L are NOT absolute numbers. They are both ratios referenced
to one square foot. This, I think, is the root of your misunderstanding.
On this news letter equivalent flat plate area will definitely be accepted and used.
Paul Lamar
The AirCraft Rotary Engine NewsLetter. Powered by Linux.
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