Old post for geeks getting into the facts of ram air
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Page 415 of the Bosch Automotive Handbook, 5th edition

has the two equations you need
to see how horsepower and torque change
when either temperature or pressure change.

For temperature the offical equation
used by Americans (SAE) Europeans (ISO) and Japanese (JIN)
is:

{ Temperature Before + 460/Temperature After +460} raised to exponent 0.6

you need a scientific calculator to do this
but there is one built into every Windows computer
under Start...Accessories

As an example,
say that your re-locate your air inlet to a spot where the air temperature
drops to 80 degrees
when before the air coming in had been 100 degrees.

{100 +460 divided by 80 + 460} raised to exponent 0.6

={560/540} raised to exponent 0.6

= {1.037} raised to exponent 0.6

= 1.022

You mulitply this number times your horsepower or torque
so if your engine.
If your engine makes 230 hp at peak
1.022 times 230 = 235 horsepower with the 20 degree lower air temperature.

You may have heard the 'Rule of Thumb' that each 10 degree F reduction in air
temperature improves horsepower by 'about' 1% and the equation above is where
that comes from, but is more accurate

For corrections when the pressure changes
the following equation is used:

{absolute pressure after/absolute pressure before} raised to exponent 1.2

As an example
say that the weather is changing where you live
and one day the weatherman says the pressure is
29.5 inches of Mercury as a stormy "Low" passes over
then the next day a clear sky "High Pressure Area" passes over
and the pressure rises to 30 inches of Mercury

{30/29.5} raised to exponent 1.2
{1.0169} raised to exponent 1.2
= 1.0204

It is important to realize
that built right into your engine
are IAT (intake air temperature)
and MAP (manifold air pressure)
sensors.

Your IAT and MAP sensor outputs can tell you whether an aftermarket air intake
has helped or hurt your power output. You can read these sensors
yourself by using an OBD-II scanner, or a cheap electrical multimeter.

You are correct to suspect that most CAI's
only make more noise and have flashy colored parts.

Want confirmation about this from a CAI manufacturer?

Well right now KN Filters is running an advertisement in the various hot rod
magazine saying that a typical paper air filter from the factory creates a
restriction of about 2.8 inches of water....and when this filter gets really
dirty the restriction rises to about 12 inches of water restriction. The KN
advertisement has a dyno graph showing that this can cause about 11 hp power
loss on a high horsepower engine.

The pressure of the air around us is about 404 inches of water
so KN Filter is saying that the pressure is changing from
404 - 2.8 = 401.2
to a new pressure of
404 - 12 = 392 inches of water

Play around with the equations above
and you can find out what the actual horsepower of the engine KN was using
was....and then confirm it by looking at the dyno graph in the advertisement.
=======
Heard of the 'Ram Air' effect where the speed of the air hitting the vehicle
builds up pressure in a forward facing air duct and helps 'supercharge' your
engine a bit. ?

Well, at 'typical' street speeds the effect is very very small.

The formula for that is:

Inches of water pressure from Ram Air = (mph) times (mph) divided by 2025.

So at 70 mph the ram air effect is:
(70 mph) times (70 mph) divided by 2025 = 2.4 inches of water.

So the very best possible air inlet tube designed for Ram Air would actually
have a positive pressure of 2.4 inches of water.

How much pressure is an inch of water ?

One psi of pressure is equal to about 28 inches of water.

You can get this by dividing the cubic inches in one cubic foot ( 12 x 12 x
12 ) by the weight of one cubic foot of water ( 62.4 lbs).

The air pressure around us is averages about 14.5 psi at typical heights above
sea level.

So another way of looking at it is that the air pressure around us is about
400 inches of water. ( 14.5 x 28).

So the best Ram Air system at 70 mph gives you a boost of about 2/400 or one
half of one percent. Small.

Ram air started in airplanes where it means more. An airplane going 300 mph
gets a boost of:

300 x 300 divided by 2025 = 44 inches

This is a percentage boost of 44/400 or about 11%

Want a challenge?
Consider your tires.
Some strange facts:
At 70 mph the center of your tire is moving 70 mph.
The bottom of your tire where it 'grabs' the pavement is moving at 0.1 mph
The top of your tire is moving forward at 140 mph.
If you could put a 'Ram Air' inlet right at the top of the tires (where it is
horribly dirty and wet) you could get a significant air pressure boost.....