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Disclaimer:

On my IV-P I designed the Lycoming engine installation including the
turbocharger system and the cabin air valve. My experience is limited to
this configuration and I am not intimate with the comparable systems on the
Continental engine. I am also taking some liberties with the finer points so
as not to come across as a total dweeb (lost cause). Also, please read my
post from yesterday on this topic.

Lets follow a chunk of air as it passes through the airplanes systems.

Our air chunk is minding it's own business at 10,000 MSL (20" pressure and
23 deg.F) when it is scooped up by our airplane and accelerated to about 250
Kts and crammed together with a bunch of other chunks of air. Its pressure
rises to about 20.75" and its temperature rises to about 27 degrees. Next
comes the air cleaner where it looses about 0.1" of pressure. The
turbocharger compressor (carousel from hell) is the next stop.

As the air chunk passes through the compressor its temperature rises for two
reasons; one is that it is being compressed and the other is that the
thrashing about of the turbocharger imparts motion to the air and motion is
heat. In techno babble, the adiabatic compression raises the absolute
temperature of the gas as a function of the ratio of the outlet pressure
over the inlet pressure (pressure ratio) raised to the 0.283 power times the
inlet absolute temperature. The result change (finale temp - start temp)
must then be divided by the Adiabatic Efficiency (thrashing about heating)
which on most turbos is about 70% (or .7) to get the total temperature rise.

How hot the air gets is therefore a function of the pressure ratio and how
hot it was when it started. So what is the pressure ratio? Well, say you are
flying at 25" MAP, the deck pressure (depending on the system) runs a few
inches over that, so about 28". Divide 28 by 20.65, raise to the .283 power
and multiply by 487 degrees Rankine (deg. F + 460= absolute temperature) and
you get about 530 degrees or a 43 degree rise. Divide this by .7 and we can
estimate the air chunk is now at about 88 degrees (given standard day
conditions). This is assuming that the air is tapped BEFORE the
intercoolers.

Our chunk of air at 28" and 88 degrees is now diverted to the cabin. It is
admitted into the cabin from the deck pressure of the engine through a sonic
venturi. A sonic venturi is nothing more than a nozzle (hole). It regulates
flow by the principle that air cannot flow through a hole faster than the
speed of sound (the sonic part). This is true in the pressure range we are
interested in. The FAA mandated that each passenger receives 10 CFM of fresh
air. A single sonic venturi with a 0.51 inch ID will flow about 50 CFM.

An interesting thing happens when the air expands through the sonic venturi.
It cools because it is expanding but it is also being heated as the
potential energy in the pressure has to go somewhere and heat is the only
option since no work is being done. If half the temperature drop is made up
in heating than the air discharged into the cabin will be 73 degrees.

If you run the equations at FL250 and a 28" MAP you get a discharge
temperature of 117 degrees F.

At 5,000 feet and 18" MAP you don't get any temperature rise at all. !?!?!?!
Wadyamean no heat!

Well, a turbo compressor is not positive displacement so air is free to move
through it. The deck pressure cannot fall significantly below the ambient
pressure. In low altitude, low power flight the turbo isn't doing any work
to compress the air. No compression, no heat amigo.

If you plan to fly low and slow in a IV on a cold day you better bring a
blanket. Especially if you are flying a non-pressurized version. Air leaks
around the gear and baggage doors are many times the flow from the sonic
venturies.

Thermodynamics, not just some good ideas, its the law.

Further reading:
Turbochargers by Hugh MacInnes (HP Books)
Heat Engines by John F. Sandfort (Doubleday)

LML website:   http://www.olsusa.com/Users/Mkaye/maillist.html
LML Builders' Bookstore:   http://www.buildersbooks.com/lancair

Please send your photos and drawings to marvkaye@olsusa.com.