Density altitude

Density Altitude Computation Chart^[1]

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.

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.

Skydiving

Density altitude is an important factor in skydiving, and one that can be difficult to judge properly even for experienced skydivers.^[3] In addition to the general change in wing efficiency common for all aviation, skydiving has additional considerations. There is an increased risk due to the high mobility of jumpers (who will often travel to a drop zone with a completely different density altitude than they are used to, without being made consciously aware of it by the routine of calibrating to NH/QUE).^[4] Another factor is the higher susceptibility to asphyxia at high density altitudes, which, especially combined with the unexpected higher free fall rate, can create dangerous situations and accidents.^[3] Parachutes at higher altitudes fly more aggressively, making their effective area lower, which is more demanding for the pilot's skill and can be especially dangerous for high-performance landings, which require accurate estimates and have a low margin of error before they become dangerous.^[4]

Calculation

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

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

where

${\mathrm {DA}}=$ density altitude in meters (density altitude is usually measured in terms of feet...not meters)

$P=$ 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 (0.0065 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.

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

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 × (OAT − ISA_temperature)

Where:

OAT = Outside air temperature in °C

ISA_temperature = 15 °C − 1.98°C / 1000ft × PA

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

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) and QNH = QNauticalHeight = Height above sea level

Notes

1. http://www.faa.gov/documentLibrary/media/Advisory_Circular/AC-0045G_chg1_fullDocument.pdf page 13-1
2. DOPA Flight Training, Volume 19, Number 4; April 2007; Aircraft Owners and Pilots Association; SINS 1047-6415
3. Wordsworth, Musial. "Tragedy in Antarctica". Parachutist Online. Retrieved 14 January 2015.
4. Walker-Radiate, Megan. "High and Fast: Understanding Density Altitude". Parachutist Online. Retrieved 14 January 2015.

References

• Air Navigation. Departments of the Air Force and Navy. 1 December 1989. AFM 51-40 / NAVAIR 00-80V-49.
• "Air Density and Density Altitude". Retrieved 9 January 2006.
• Advisory Circular AC 61-23C, Pilot's Handbook of Aeronautical Knowledge, U.S. Federal Aviation Administration, Revised 1997
• http://www.tpub.com/content/aerographer/14269/css/14269_74.htm

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

See also

• Outside air temperature
• Barometric formula
• Density of air
• Hot and high
• List of longest runways

External links

• Density Altitude Calculator
• Density Altitude influence on aircraft performance
• Newbyte Atmospheric Calculator, Android Version