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Intake Air Temp

All,
 
I've been reading some of the recent threads about proper location for the 
air intake, and want to offer some thoughts.  Specifically, I recall some 
posts that say the intake should not be located inside the engine compartment 
(as with some of the K&N devices?) because the air temperature will be much 
higher.  I get the sense that the posters think that air temp will be much 
higher.  I presume the concern is that air density will therefore be lower, and 
that power output will be significantly reduced.
 
Let's consider a case where the intake is located inside the engine 
compartment.  Even though the engine compartment is _d***_ hot when we stop 
the car and open the hood on a hot day, I don't think that temp should be 
anywhere close to the temp of the intake air.  This is because the engine has 
to pull air from _outside_ the car, otherwise it would quickly use up all the 
(hot) air inside the engine compartment.  While the car is moving, it seems 
that as a worst case the intake air would be no warmer than the thermostat 
temp.  This would be the case if _all_ the air that gets into the engine 
compartment were forced to come through the radiator.  I'm guessing there are 
lots of pathways by which intake air can bypass the radiator, so the intake 
air temp should actually be cooler than the thermostat temp.
 
Another important factor is that air density is not inversely related to air 
temp in degrees F.  It's proportional to degrees F _plus_ 460.  (For example, 
the ratio of the density of air at 180 vs. 80 degrees F is (80 + 460)/(180 + 
460) or 0.84.)  Smaller temp changes have even smaller effects on air density. 
 Granted that in a real race situation, racers are looking for any slight 
advantage they can get.  It's just that I wonder if the intake location is all 
that important in non-race setups.  Any other thoughts?
 
 Regards,
 Jerry
 Arlington, TX (18-Sep-96, 18:43)
 '95 540i-6 spd