# Density altitude

Density Altitude Computation Chart[1]

Density altitude is the altitude relative to the standard atmosphere conditions (ISA) at which the air density would be equal to the indicated air density at the place of observation. In other words, density altitude is air density given as a height above mean sea level. "Density altitude" can also be considered to be the pressure altitude adjusted for non-standard temperature.

Both an increase in temperature, decrease in atmospheric pressure, and, to a much lesser degree, increase in humidity will cause an increase in density altitude. In hot and humid conditions, the density altitude at a particular location may be significantly higher than the true altitude.

In aviation the density altitude is used to assess the aircraft's aerodynamic performance under certain weather conditions. The lift generated by the aircraft's airfoils and the relation between indicated and true airspeed are also subject to air density changes. Furthermore, the power delivered by the aircraft's engine is affected by the air density and air composition.

## Aircraft safety

Air density is perhaps the single most important factor affecting aircraft performance. It has a direct bearing on:[2]

• The lift generated by the wings — reduction in air density reduces the wing's lift.
• The efficiency of the propeller or rotor — which for a propeller (effectively an airfoil) behaves similarly to lift on wings.
• The power output of the engine — power output depends on oxygen intake, so the engine output is reduced as the equivalent "dry air" density decreases and produces even less power as moisture displaces oxygen in more humid conditions.

Aircraft taking off from a "hot and high" airport such as the Quito Airport or Mexico City are at a significant aerodynamic disadvantage. The following effects result from a density altitude which is higher than the actual physical altitude:[2]

• The aircraft will accelerate slower on takeoff as a result of reduced power production.
• The aircraft will need to achieve a higher true airspeed to attain the same lift - this implies both a longer takeoff roll and a higher true airspeed which must be maintained when airborne to avoid stalling.
• The aircraft will climb slower as the result of reduced power production and lift.

Due to these performance issues, a plane's takeoff weight may need to be lowered or takeoffs may need to be scheduled for cooler times of the day. Wind direction and runway slope may need to be taken into account.

## Calculation

Density altitude can be calculated from atmospheric pressure and temperature (assuming dry air).

$\mathrm{DA} = \frac{T_\text{SL}}{\gamma} \left[1-\left(\frac{P/P_{SL}}{\mathrm{T}/T_{SL}}\right)^\frac{\Gamma R}{gM-\Gamma R}\right]$

where

$\mathrm{DA}=$ density altitude in feet
$P=$ atmospheric (static) pressure
$P_{SL}=$ standard sea level atmospheric pressure (1013.25 hPa ISA or 29.92126 inHg US))
$\mathrm{T}=$ true (static) air temperature in kelvins (K) [add 273.15 to the Celsius (°C)] figure
$T_{SL}=$ ISA standard sea level air temperature in kelvins (K) (288.15 K)
$\gamma=$ lapse rate (0.0019812 K/ft)
$\Gamma=$ lapse rate (0.0065 K/m)
$R=$ gas constant (8.31432 J/mol·K)
$g=$ gravity (9.80665 m/s²)
$M=$ molar mass of dry air (0.0289644 kg/mol)

National Weather Service Equation

The National Weather Service uses the following dry-air approximation of the above equation in their standards.

$\mathrm{DA} = 145442.16 \left[1-\left(\frac{17.326 P}{459.67+T}\right)^{0.235}\right]$

where

$\mathrm{DA}=$ density altitude in feet
$P=$ Is the station pressure (atmospheric static pressure) in inches of mercury (inHg)
$T=$ T is the station temperature (atmospheric temperature) in Fahrenheit (F)

Note that the NWS standard specifies that the density altitude should be rounded to the nearest 100 feet.

Easy formula to calculate density altitude from pressure altitude

This is an easier formula to calculate (with great approximation) density altitude from pressure altitude ..and International Standard Atmosphere temperature deviation

Density altitude in feet = pressure altitude in feet + 118.8 x (OAT - ISA_temperature)

Where:

OAT = Outside air temperature in °C
ISA_temperature = 15 °C - 1.98ºC / 1000ft x PA

considering that temperature drops at the rate of 1.98 °C each 1000 ft of altitude until the Tropopause (36000ft), usually rounded to 2ºC

Or simply:

DA=PA+118.8([PA/500]+OAT-15)

Or even simpler

DA=1.24 PA + 118.8 OAT - 1782

where DA=density altitude and PA=pressure altitude where PA=Hgt+30(1013-QNH)

## Notes

1. ^
2. ^ a b AOPA Flight Training, Volume 19, Number 4; April 2007; Aircraft Owners and Pilots Association; ISSN 1047-6415

## References

This article incorporates public domain material from the United States Government document "Pilot's Handbook of Aeronautical Knowledge".