View source for Density altitude

{{Short description|Altitude relative to standard atmospheric conditions}}
{{unreliable sources|date=July 2013}}
[[Image:Density Altitude.png|thumb|right|375px|Density Altitude Computation Chart<ref>{{cite web |url=https://www.faa.gov/regulations_policies/advisory_circulars/index.cfm/go/document.information/documentID/1030235 |url-status=dead |archive-url=https://web.archive.org/web/20161223040752/https://www.faa.gov/regulations_policies/advisory_circulars/index.cfm/go/document.information/documentID/1030235 |archive-date=2016-12-23 |title=AC 00-45H - Aviation Weather Services – Document Information}}</ref>]]

The '''density altitude''' is the [[altitude]] relative to [[International Standard Atmosphere|standard atmospheric conditions]] at which the [[density of air|air density]] would be equal to the indicated air density at the place of observation. In other words, the density altitude is the air density given as a height [[above mean sea level]]. The density altitude can also be considered to be the [[pressure altitude]] adjusted for a non-standard temperature.

Both an increase in the [[temperature]] and a decrease in the [[atmospheric pressure]], and, to a much lesser degree, an increase in the [[humidity]], will cause an increase in the 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 an aircraft's aerodynamic performance under certain weather conditions. The [[Lift (force)|lift]] generated by the aircraft's [[airfoil]]s, and the relation between its [[indicated airspeed]] (IAS) and its [[true airspeed]] (TAS), are also subject to air-density changes. Furthermore, the power delivered by the aircraft's engine is affected by the density and composition of the atmosphere.

==Aircraft safety==

Air density is perhaps the single most important factor affecting aircraft performance. It has a direct bearing on:<ref name="A">AOPA Flight Training, Volume 19, Number 4; April 2007; Aircraft Owners and Pilots Association; {{ISSN|1047-6415}}</ref>
* The efficiency of a propeller or rotor – which for a propeller (effectively an [[airfoil]]) behaves similarly to lift on a wing.
* The power output of a normally-aspirated engine – the power output depends on the oxygen intake, so the engine output is reduced as the equivalent dry-air density decreases, and it produces even less power as moisture displaces oxygen in more humid conditions.

Aircraft taking off from a “[[hot and high]]” airport, such as the [[Mariscal Sucre International Airport|Quito Airport]] or [[Mexico City International Airport|Mexico City]], are at a significant [[aerodynamic]] disadvantage. The following effects result from a density altitude that is higher than the actual physical altitude:<ref name="A" />
* An aircraft will accelerate more slowly on takeoff as a result of its reduced power production.
* An aircraft will climb more slowly as a result of its reduced power production.

Due to these performance issues, an aircraft's takeoff weight may need to be lowered, or takeoffs may need to be scheduled for cooler times of the day. The wind direction and the [[runway]] slope may need to be taken into account.

==Skydiving==

The density altitude is an important factor in skydiving, and one that can be difficult to judge properly, even for experienced skydivers.<ref name=antarctica>{{cite web|last1=Farnsworth|first1=Musika|title=Tragedy in Antarctica|url=http://parachutistonline.com/feature/tragedy-in-antarctica%E2%80%94-lessons-from-the-south-pole|website=Parachutist Online|access-date=14 January 2015|archive-date=15 January 2015|archive-url=https://web.archive.org/web/20150115135028/http://parachutistonline.com/feature/tragedy-in-antarctica%E2%80%94-lessons-from-the-south-pole|url-status=dead}}</ref> In addition to the general change in wing efficiency that is common to all aviation, skydiving has additional considerations. There is an increased risk due to the high mobility of jumpers (who will often travel to a [[Parachuting#Drop zones|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 [[QNH]]/[[Atmospheric pressure#Mean sea-level pressure|QFE]]).<ref name=highfast>{{cite web|last1=Walker-Radtke|first1=Megan|title=High and Fast: Understanding Density Altitude|url=http://parachutistonline.com/feature/understanding-density-altitude|website=Parachutist Online|access-date=14 January 2015|archive-date=15 January 2015|archive-url=https://web.archive.org/web/20150115134536/http://parachutistonline.com/feature/understanding-density-altitude|url-status=dead}}</ref> Another factor is the higher susceptibility to [[Hypoxia (medical)|hypoxia]] at high density altitudes, which, combined especially with the unexpected higher [[free fall|free-fall]] rate, can create dangerous situations and accidents.<ref name=antarctica/> Parachutes at higher altitudes fly more aggressively, making their effective area smaller, which is more demanding for a 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.<ref name=highfast/>

==Calculation==

The density altitude can be calculated from the atmospheric pressure and the outside air temperature (assuming dry air) using the following formula:
:<math>
\text{DA} \approx \frac{T_\text{SL}}{\Gamma} \left[ 1 - \left( \frac{P / P_\text{SL}}{T / T_\text{SL}} \right)^{\left(\frac{g M}{\Gamma R} - 1\right)^{-1}} \right].
</math>

In this formula,
: <math> \text{DA} </math>, density altitude in [[meters]] (m);
: <math> P </math>, (static) atmospheric pressure;
: <math> P_\text{SL} </math>, [[standard sea level|standard sea-level]] atmospheric pressure, International Standard Atmosphere (ISA): 1013.25 [[pascal (unit)|hectopascals]] (hPa), or [[U.S. Standard Atmosphere]]: 29.92 [[inches of mercury]] (inHg);
: <math> T </math>, [[outside air temperature]] in [[kelvin]]s (K);
: <math> T_\text{SL} </math> = 288.15{{nbsp}}K, ISA sea-level air temperature;
: <math> \Gamma </math> = 0.0065{{nbsp}}K/m, ISA [[lapse rate|temperature lapse rate]] (below 11{{nbsp}}km);
: <math> R </math> ≈ 8.3144598{{nbsp}}J/mol·K, [[gas constant|ideal gas constant]];
: <math> g </math> ≈ 9.80665{{nbsp}}m/s{{sup|2}}, [[gravitational acceleration]];
: <math> M </math> ≈ 0.028964{{nbsp}}kg/mol, [[mole (unit)|molar mass]] of dry air.

===The National Weather Service (NWS) formula===

The [[National Weather Service]] uses the following dry-air approximation to the formula for the density altitude above in its standard:
:<math>
\text{DA}_\text{NWS} = 145442.16 ~ \text{ft} \left( 1 - \left[ 17.326 ~ \frac{^\circ \text{F}}{\text{inHg}} \ \frac{P}{459.67 ~ {{}^\circ \text{F}} + T} \right]^{0.235} \right).
</math>

In this formula,
: <math> \text{DA}_\text{NWS} </math>, National Weather Service density altitude in [[foot (unit)|feet]] (<math> \text{ft} </math>);
: <math> P </math>, station pressure (static atmospheric pressure) in inches of mercury (inHg);
: <math> T </math>, station temperature (outside air temperature) in [[degrees Fahrenheit]] (°F).

Note that the NWS standard specifies that the density altitude should be rounded to the nearest 100{{nbsp}}ft.

===Approximation formula for calculating the density altitude from the pressure altitude===
<!-- This section's formula uses mixed units and should be converted to SI or US, but not both. (I intend to provide such an edit as soon as I have time.)
-->This is an easier formula to calculate (with great approximation) the ''density altitude'' from the ''pressure altitude'' and the ''ISA temperature deviation'':{{Citation needed|date=February 2021}}
:<math>
\text{DA} \approx \text{PA} + 118.8 ~ \frac{\text{ft}}{{^\circ \text{C}}} \left(T_\text{OA} - T_\text{ISA}\right).
</math>

In this formula,
: <math> \text{PA} </math>, pressure altitude in feet (ft) <math display="inline"> \approx \text{station elevation in feet} + 27 ~ \frac{\text{ft}}{\text{mb}} (1013 ~ \text{mb} - \text{QNH}) </math>;
: <math> \text{QNH} </math>, atmospheric pressure in [[bar (unit)|millibars]] (mb) adjusted to [[sea level|mean sea level]];
: <math> T_\text{OA}</math>, outside air temperature in degrees Celsius (°C);
: <math display="inline"> T_\text{ISA} \approx 15 ~ {{}^\circ \text{C}} - 1.98 ~ {{}^\circ \text{C}} \, \frac{\text{PA}}{1000 ~ \text{ft}} </math>, assuming that the outside air temperature falls at the rate of 1.98{{nbsp}}°C per 1,000{{nbsp}}ft of altitude until the [[tropopause]] (at {{val|36000|u=ft|fmt=commas}}) is reached.

Rounding up 1.98{{nbsp}}°C to 2{{nbsp}}°C, this approximation simplifies to become
:<math>\begin{align}
            \text{DA}
  & \approx \text{PA} + 118.8 ~ \frac{\text{ft}}{^\circ \text{C}} \left[ T_\text{OA} + \frac{\text{PA}}{500 ~ \text{ft}} {^\circ \text{C}} - 15 ~ {^\circ \text{C}} \right] \\[3pt]
  & =       1.2376 \, \text{PA} + 118.8 ~ \frac{\text{ft}}{{}^\circ \text{C}} \, T_\text{OA} - 1782 ~ \text{ft}.
\end{align}</math>

==See also==
*[[Outside air temperature]]
*[[Barometric formula]]
*[[Density of air]]
*[[Hot and high]]
*[[List of longest runways]]

== Notes ==
{{Reflist|2}}

==References==
{{refbegin}}
*{{cite book |id= AFM 51-40 / NAVAIR 00-80V-49| date=1 December 1989 | title=Air Navigation | publisher=Departments of the Air Force and Navy }}
*{{cite web | title=Air Density and Density Altitude | url=http://wahiduddin.net/calc/density_altitude.htm | access-date=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 {{Webarchive|url=https://web.archive.org/web/20080919003959/http://www.tpub.com/content/aerographer/14269/css/14269_74.htm |date=2008-09-19 }}
{{refend}}
*{{USGovernment|url=https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak/|title=Pilot's Handbook of Aeronautical Knowledge}}

==External links==
*{{usurped|1=[https://web.archive.org/web/20090120190403/http://www.pilotoutlook.com/calculators/density-altitude-calculator Density Altitude Calculator]}}
*[http://www.experimentalaircraft.info/flight-planning/aircraft-performance-3.php Density Altitude influence on aircraft performance]
*[http://www.newbyte.co.il/calculator/index.php NewByte Atmospheric Calculator]

{{DEFAULTSORT:Density Altitude}}
[[Category:Altitudes in aviation]]
[[Category:Atmospheric thermodynamics]]