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Assuming the plate is fixed and perpendicular to the wind
what you would like to know is the force against it. Since force =
Pressure/Area we first need to find the pressure.
The dynamic pressure energy of the airstream at 200 mph is
found by 1/2pV^2 where p is air density and V is velocity. I am going to
assume sea level air density even though we know it will be less at
altitude. So that is one square foot of air = 0.00234 slugs (sorry I'm an
old English units guy). Velocity (ft/sec) = 200mph *5280/3600 =
293.3 ft/sec
That gives us a dynamic Pressure =
1/2(0.00234*(293.3)^2 = 0.5*(0.00234)*(86034) = 100.66 lbs/ft^2 or 100 lbs per
square foot. Dividing by 144 gives us lbs per square inch. So
pressure = 100.66/144 = .699 lbs/sq inch or about 19 inches of H20.
But, sticking with psi we have
That pressure is acting on 15 sq inches so the total force
on that plate = 0.699*15 = 10.485 lbs of force.
That is assuming all the energy in the air is converted to
dynamic pressure which would probably only happens at the very center of the
plate, the air near the edges would tend to flow (at least partially)
around the plate, so the velocity/pressure distribution would not be even
across the plate. It would be maximum in the center and taper off near the
edges. So this means the actually force would undoubtedly be less
than 10 lbs because of that and the fact that the air at altitude will be
considerably less dense, depending of course on your
altitude.
Then there is the fact the plate is moving through
the air means that the pressure in back of the plate is going to be less than if
it were standing still. But I am not going to even
attempt to get into quantifying those factors. But, the force
will still likely be less than 10 lb
You might try searching the web for things like - air
resistance, plate plate, dynamic pressure, etc
Hope this helps
Ed
----- Original Message -----
Sent: Thursday, October 18, 2007 2:35
PM
Subject: [FlyRotary] Math Help
Not being much of a math or engineering whiz, can anyone help
me calculate the force the relative wind would put on a device that hangs in
the breeze on my airplane? Assuming a 200 MPH airspeed, and a flat plate
of 15 sq. inches, what would be the amount of force on the plate in
pounds?
Best Regards,
Steve
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