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I am looking for the most accurate formula to calculate the Density Altitude (DA) to use it for calculating aircraft performances during landing. Now I found the following formula:

DA = PA + [120*(OAT - ISA temperatures at given altitude)]

PA = ((standard pressure - given pressure)*30) + field elevation

My question is: Why is the dew point not included in this formula and what influence does it have on the density altitude? What is the correct formula with dew point included to calculate the DA?

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    $\begingroup$ Short answer: water vapor is less dense than air. Replace air molecules with water vapor and the density goes down. Refer to FAA-H-8083-25, Pilot’s Handbook of Aeronautical Knowledge p 4-5 for details $\endgroup$ – JScarry Oct 26 '17 at 15:27
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    $\begingroup$ Look at the wet versus dry adiabatic lapse rate. $\endgroup$ – GdD Oct 26 '17 at 15:33
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Density altitude is the air density expressed as an altitude above MSL. Both temperature and humidity affect air density; however, temperature has a far greater impact.

Electronic E6Bs account for the effect of humidity by using both temperature and dew point temperature, the latter of which provides a measure of the air's water vapor content (technically it measures the temperature to which the air would need to be cooled for saturation to occur).

In contrast, the simple rule of thumb provided above only addresses the impact of non-standard temperature on density altitude. However, the effect of humidity can be "roughly" approximated by multiplying the dew point temperature (in degrees Celsius) by 20 and reading the results in feet.

This correction is then added to the above temperature correction rule of thumb for density altitude. Note the correction for humidity is highly non-linear and so it provides only a rough approximation. It should only be used in the dew point temperature range of 5-30 degrees Celsius.

Details can be found in Guinn, T. A., & Barry, R. J. (2016). Quantifying the Effects of Humidity on Density Altitude Calculations for Professional Aviation Education. International Journal of Aviation, Aeronautics, and Aerospace, 3(3). http://dx.doi.org/10.15394/ijaaa.2016.1124

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Dew point is a measure of how saturated a given parcel of air. It is the temperature if the air is cooled to it, the air will turn to a liquid state. A simple way to imagine the dew point is the temperature at the base of a cloud.

Dew point isn't used in calculating density altitude because density altitude is pressure altitude, corrected for non-standard temperature. The temperature could remain the same, but pressure will change as fronts move over an airport, thus changing density altitude.

An excellent summary of dewpoint can be found in a 2003 article in AOPA from Thomas Horne, Dew Point Review (Internet Archive link).

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The formula that you have listed is an approximation only. The real formula from Wikipedia is:

Density Altitude Formula

Where the humidity factor comes in is the Molar mass of the air which is M in the equation. Water has a smaller molecular mass then other components of air so it lowers the value of M and increases the density altitude. Humidity is not usually included in density altitude calculations because calculating the Molar mass is difficult for a given humidity level. However certain apps like ForeFlight are able to calculate the humidity effects of Density Altitude and can provide a more accurate density altitude then what you would calculate with pressure altitude and temperature alone. Humidity is not as much a contributing factor than the Temperate and Pressure altitude but it is by no means negligible. For example, in ForeFlight I saw an airport where the pressure altitude and temperature was lower than standard; however, the density altitude ended up being 1000 feet above the airport elevation because the humidity level was 60%.

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