Editing Pressure altitude

{{Short description|Altitude at which atmosphere has a specified pressure}}

Given an [[atmospheric pressure]] measurement, the '''pressure altitude''' is the imputed [[altitude]] that the [[International Standard Atmosphere]] (ISA) model predicts to have the same pressure as the observed value.

The [[National Oceanic and Atmospheric Administration]] (NOAA) published the following formula<ref>{{Cite web|url=https://www.weather.gov/media/epz/wxcalc/pressureAltitude.pdf|title=Pressure Altitude}}</ref> for directly converting atmospheric pressure in [[Bar (unit)|millibars]] (mb) to pressure altitude in [[Foot (unit)|feet]] (ft):
<math display=block>
h = 145366.45 \left[ 1 - \left( \frac{\text{Station pressure in millibars}}{1013.25} \right)^{0.190284} \right].
</math>

In [[aviation]], pressure altitude is the height above a standard datum plane (SDP), which is a theoretical level where the weight of the atmosphere is {{convert|29.921|inHg|mbar psi}} as measured by a barometer.<ref>Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25B), 2016, Chapter 4, p 4-4</ref> It indicates altitude obtained when an [[altimeter]] is set to an agreed baseline pressure under certain circumstances in which the aircraft’s altimeter would be unable to give a useful altitude readout. Examples would be landing at a high altitude or near sea level under conditions of exceptionally high air pressure. Old altimeters were typically limited to displaying the altitude when set between 950&nbsp;mb and 1030&nbsp;mb. Standard pressure, the baseline used universally, is 1013.25&nbsp;[[Pascal (unit)|hectopascals]] (hPa), which is equivalent to 1013.25&nbsp;mb or 29.92&nbsp;[[inches of mercury]] (inHg). This setting is equivalent to the atmospheric pressure at [[mean sea level]] (MSL) in the ISA. Pressure altitude is primarily used in aircraft-performance calculations and in high-altitude flight (i.e., above the [[Flight level#Transition altitude|transition altitude]]).

== Inverse equation ==
Solving the equation for the pressure gives
<math display=block>
p = 1013.25\left(1-\frac{h}{44307.694 \text{ m}}\right)^{5.25530} \text{ hPa}
</math>
where {{math|m}} are meter and {{math|hPa}} refers to hecto-[[Pascal (unit)|Pascal]]. This may be interpreted as the lowest terms of the [[Taylor expansion]] of
<math display=block>
p = 1013.25  \exp\left(\frac{-h}{8431 \text{ m}}\right) \text{ hPa}
</math>
where {{math|exp}} is the [[exponential function]].

== QNE ==
{{Unreferenced section|date=January 2024}}
QNE is an [[Aeronautical Code signals|aeronautical code]] [[Q code]]. The term refers to the indicated altitude at the landing runway threshold when <math> 1013.25 ~ \mathrm{mb} </math> or <math> 29.92 ~ \mathrm{inHg} </math> is set in the [[altimeter#Use in aircraft|altimeter's Kollsman]] window. It is the pressure altitude at the landing runway threshold.

Most aviation texts for [[private pilot licence|PPL]] and [[commercial pilot license|CPL]] exams describe a process for finding the pressure altitude (in feet) using one of the following rule of thumb formulae.

Internationally, pressure altitude is approximated as:
:<math>
\text{Pressure altitude (PA)} = \text{Elevation} + 30 \times (1013 - \text{QNH}).
</math>
For example, if the airfield elevation is <math> 500 ~ \mathrm{ft} </math> and the [[QNH]] is <math> 993 ~ \mathrm{mb} </math>, then
:<math>
\begin{align}
\text{PA} & = 500 + 30 \times (1013 - 993) \\
          & = 500 + 30 \times 20 \\
          & = 500 + 600 \\
          & = 1100.
\end{align}
</math>

If the altimeter uses [[Inch of mercury|inches of mercury]], as common in the United States, Canada, and Japan, the following formula is used:
:<math>
\text{Pressure altitude (PA)} = \text{Elevation} + 1000 \times (29.92 - \text{Altimeter setting}).
</math>
For example, if the airfield elevation is <math> 500 ~ \mathrm{ft} </math> and the altimeter setting is <math> 29.32 ~ \mathrm{inHg} </math>, then
:<math>
\begin{align}
\text{PA} & = 500 + 1000 \times (29.92 - 29.32) \\
          & = 500 + 1000 \times 0.6 \\
          & = 500 + 600 \\
          & = 1100.
\end{align}
</math>

[[Aviation transponder interrogation modes|Aircraft Mode “C” transponders]] report the pressure altitude to air traffic control; corrections for atmospheric pressure variations are applied by the recipient of the data.

The relationship between static pressure and pressure altitude is defined in terms of properties of the ISA.

==See also==
* [[QNH]]
* [[Flight level]]
* [[Cabin altitude]]
* [[Density altitude]]
* [[Standard conditions for temperature and pressure]]
* [[Barometric formula]]

==References==
{{reflist}}

[[Category:Altitudes in aviation]]