From: Fredmoreno@aol.com
Message-ID: <e4eb46b6.25206728@aol.com>
Date: Mon, 27 Sep 1999 02:22:32 EDT
Subject: OAT errors and aerodynamic heating
To: lancair.list@olsusa.com
Mime-Version: 1.0

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A response to the note about OAT reading high due to ram compression.  

The implication is that if you mount you probe in a region where the flow is 
not stopped, this error will not occur.  Not so.  

When the flow if fully stopped as in front of the pitot tube (or the leading 
edge of the wing), the temperature rise is termed the stagnation temperature 
rise.  This temperature rise goes like velocity squared.  Away from regions 
where the flow is stopped (like most of the surface of the wing and the 
fuselage) there is frictional heating in the boundary layer, and the 
resulting temperature rise is called the Recovery Temperature.  It varies 
depending on laminar or turbulent boundary layers, but as a general rule is 
about 80% of the stagnation temperature rise.  Put a probe out in the stream, 
and you get stagnation temperature heating on the front, and recovery 
temperature rise for heating elsewhere.  Net result is the same: you cannot 
accurately measure the OAT from inside the airplane.  You have to "back 
calculate" it based on measurement of pitot pressure, and corrections for 
compressibility, heating, etc. This is what the air data computer does on the 
big jets.  Or you can buy a Jeppesen whiz wheel Model CR computer and the 
associated BW-2 workbook and manual.  This takes all these effects into 
account, and lets you calculate the REAL TAS and OAT from the measurements 
available in the cockpit, the "measured OAT" and IAS (which can also be in 
error due to compressibility effects).  

I recently calculated the various effects for the speeds of interest, and 
here is the result.  Vf is velocity in feet per second, Vk is velocity in 
knots (TAS), M is Mach number (assuming sea level), PE is pressure error due 
to compressibility effects, VE is velocity error in % due to compressibility 
which shows up on the IAS instrument, and Tr is recovery temperature heating 
due to friction assuming a recovery factor of 0.8 which is commonly used for 
most conventional aircraft temperature measurement installations. 

Vf        Vk       M        PE        VE        Tr

110        65       0.1       0.25%   -0.13%  0.8
220      130       0.2       1.0        -0.5       3.2
330      196       0.3       2.5        -1.1       7.3
440       261      0.4       4.0        -2.4       13.0
550       326      0.5       6.25      -3.3        20.3

So at 200 knots TAS the gage in the plane will measure OAT about 7 degrees F 
higher than actual, and at 300 knots, the error is about 18F.  There is no 
escaping it.  It does not depend on where you put the instrument.  If you put 
it in a low pressure region (top of the wing, for example), the pressure 
falls, but the velocity increases and the frictional heating offsets the 
effect of static temperature drop due to pressure drop.  Energy is conserved 
everywhere.  

Note that the combination of compressibility effect (which leads to errors in 
the IAS) and the errors in OAT both conspire in the same direction.  If you 
calculate TAS using your E6B or the ring around the outside of your air speed 
indicator, the resulting "TAS" will be higher than the real TAS.  At 20,000 
feet the error at 200 knots TAS is 5-6 knots.  At 300 knots it is about 15 
knots.  So you are not going as fast as you thought.  Sorry.  By general 
agreement in the industry, the IAS gage assumes incompressible flow.  Bad 
assumption as speeds rise above 200-250 knots.  

The best concealed location for a temperature probe I have seen is in the 
NACA duct for the cabin air inlet.  It is out of the main flow, will not 
collect ice, is generally behind the firewall so engine heating effects are 
eliminated (must usual cause for errors due to conduction, warm air leakage, 
warm boundary layers on cowls, etc.)  And it is a short run from there to the 
gage if your inlet is near your legs. Base of the windshield is not bad 
either since the velocity is low and the drag from a probe sticking up a bit 
is negligible.   I have even seen conventional bimetallic gage and stem 
thermometers with the stainless stem stuck through the wall into the NACA 
duct with the gage facing the pilot.  Works fine.  Subject to the corrections 
noted above, that is.  

Fred
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