Air Density and Performance
(Courtesy: Roger Copeland)

The Standard Day (SAE test standard J1349):
100% Air Density Temperature: 60 deg. F
Humidity: 0%
Barometer: 29.92

Barometer

Barometer readings have a linear effect on air density. If the barometer goes up or down 1% from the standard reading, so will air density.

Example:

30.22 (New) 29.92 (Std.Day) = 1.01 or 101%
29.62 (New) 29.92 (Std.Day) = .989 or 98.9% (Round up to 99%)
A barometer of 30.22" gets you to 101% air density, 29.62" nets to 99%, etc.

Each 5 deg. F change in temperature (away from 60 deg. F), you get about a 1% change in air density.
An 80 deg. F day means 96% air density, and a 40 deg. F day means 104% air density.

Temperature goes up... The air gets thinner. Temperature goes down...Air gets thicker. (Air Density) This is not linear, but it's close enough for racing considerations.

Ever notice how much better an engine runs on a cool damp day?

At 60 degrees, jumping from zero to 50% humidity will cost you roughly 1% in air density. That same 50% humidity at 90 degrees will cost you more than 2% in air density. The reason for this is that it requires much more water vapor to get you to 50% humidity at 90 degrees than it does at 60 degrees, since air can hold more water as it's heated.

"Relative humidity" is expressed as a percentage of water in the air compared to how much it can hold at a given temperature. All 3 figures need to be considered. A 50 degree day with 50% humidity and a 29.62" barometer nets you to just about 100% air density, since the 2% you pick up in temperature is offset by the losses from the barometer drop of 1% and the humidity loss of 1%.

Power

Figure around 75-80% power change compared to the air density change. An 8% drop in air density will cost you about 6% in power.

Barometric changes give you about a 1.2:1 change in power.
Temperature changes give you about .7:1 change in power.
Humidity is about 1-1 change in power.

Formulas in different formats can be found on http://www.nwlink.com/~koryg/airdensity.html. The numbers produced from these formulas come within 1% to 2% of the numbers produced by Stephen Bowline's Altalab Instrument Delta-Ace air density gauge (about $450 US!).