Where is the official definition of pressure altitude?

Question

I know that pressure altitude for a certain pressure is defined to be the altitude in the standard atmosphere which has that pressure.

But I can't find whatever standard, regulation, or glossary officially defines it to be so. I tried to look in the AIM, the P/CG, a search of the FARs for "pressure altitude" wading through a ton of results, and what searchable partial copies of the US Standard Atmosphere of 1976 I could find. I don't have access to a copy of the ISO standard that defines the International Standard Atmosphere.

Does anyone know of an FAA, ICAO, or ISO document providing this definition?

Answer 1

Pressure Altitude

As defined by FAA in the Pilot's Handbook of Aeronautical Knowledge:

Pressure altitude is the height above a standard datum plane (SDP), which is a theoretical level where the weight of the atmosphere is 29.92 "Hg (1,013.2 mb) as measured by a barometer. An altimeter is essentially a sensitive barometer calibrated to indicate altitude in the standard atmosphere. If the altimeter is set for 29.92 "Hg SDP, the altitude indicated is the pressure altitude. As atmospheric pressure changes, the SDP may be below, at, or above sea level. Pressure altitude is important as a basis for determining airplane performance, as well as for assigning flight levels to airplanes operating at or above 18,000 feet.

The pressure altitude can be determined by either of two methods: 1. Setting the barometric scale of the altimeter to 29.92 and reading the indicated altitude. 2. Applying a correction factor to the indicated altitude according to the reported altimeter setting.

More info from the FAA here.

From Docket No. 18334, 54 FR 34304, Aug. 18, 1989, as amended by Amdt. 91-314, 75 FR 30193, May 28, 2010

§91.217 Data correspondence between automatically reported pressure altitude data and the pilot's altitude reference.

(a) No person may operate any automatic pressure altitude reporting equipment associated with a radar beacon transponder—

(1) When deactivation of that equipment is directed by ATC;

(2) Unless, as installed, that equipment was tested and calibrated to transmit altitude data corresponding within 125 feet (on a 95 percent probability basis) of the indicated or calibrated datum of the altimeter normally used to maintain flight altitude, with that altimeter referenced to 29.92 inches of mercury for altitudes from sea level to the maximum operating altitude of the aircraft; or

(3) Unless the altimeters and digitizers in that equipment meet the standards of TSO-C10b and TSO-C88, respectively.

(b) No person may operate any automatic pressure altitude reporting equipment associated with a radar beacon transponder or with ADS-B Out equipment unless the pressure altitude reported for ADS-B Out and Mode C/S is derived from the same source for aircraft equipped with both a transponder and ADS-B Out.

ICAO has described how they calculate Pressure Altitude

Source

In relation to QNE:

When the ISA mean sea level standard pressure of 1013.2 hPa is set on an aircraft altimeter subscale, the height so indicated upon landing at an airfield is known as the QNE reading. More widely, this is also the PRESSURE ALTITUDE, which is alternatively defined as the height of any level in the international standard atmosphere (ISA-see above), above the level corresponding to a pressure of 1013.2 hPa.

Here is a free tool to calculate standard atmospheric conditions (ISA) at a given geometric or pressure altitude and ambient temperature.

Answer 2

The notion of pressure-altitude, used in aviation and displayed on barometric altimeters, is set by ICAO. It is derived from a model elaborated by WMO and ICAO, two agencies of the United Nations, building on previous work done in the US and in Europe.

ICAO defines pressure-altitude in distinct documents:

• ICAO Annex 2 of the Chicago Convention (Rules of the Air)
• ICAO Annex 8 of the Chicago Convention (Airworthiness of Aircraft)
• ICAO Doc 4788 (Manual of the ICAO Standard Atmosphere)

In addition, ICAO atmosphere model has been published as ISO 2533 standard, subtitled "identical with the ICAO and WMO Standard Atmospheres from -2 to 32 km", hence compatible with ICAO model. ISO is interlocked with ICAO for updates.

Annex 2 - Rules of the Air

Annex 2 introduces the notion of pressure-altitude and where it is defined:

Pressure-altitude. An atmospheric pressure expressed in terms of altitude which corresponds to that pressure in the Standard Atmosphere. As defined in Annex 8.

This is a pressure measurement converted into an equivalent height above mean see level, according to the model used by ICAO.

Annex 8 - Airworthiness of Aircraft

This document provides a description of what is the standard atmosphere to be used when designing and certifying aircraft performances, e.g. for takeoff and landing at high altitude airports.

Some constant and gradients are provided:

The model and various formulas are fully detailed in the last document.

Doc 7488 - Manual of the ICAO Standard Atmosphere

Details and precomputed tables are provided in ICAO Doc 7488 for various parameters. In particular:

Assuming a linear variation of the temperature with geopotential altitude, the simultaneous solution of the hydrostatic equation (equation (1)) and the perfect gas law (equation (2)) yields the following expression for pressure: [...] $$p = p_b \; exp \bigg [ \frac {g_0} {RT}(H-H_b) \bigg ] \quad (13)$$

From in this formula we can derive the relationship pressure-to-altitude. For altitudes below 11km (p in hPa, h in m):

$$h = 44301.59796 \times (1 - (\frac {p} {1013.25})^{0.190284})$$

or equivalent (formula from ISO 2533):

$$h = \frac {3.731444 - p^{0.1902631}} {0.841728 \times 10^{-4}}$$

This gives this curve:

The formulas constants change at 11, 20 and 32 km, following the different temperature gradients in the different atmosphere layers.

Coefficient and exponent values reflect the different factors taken into account to determine the Standard Atmosphere model, including sea level pressure, temperature, density and gravity gradients (see this answer from @fab for details). However this model is simplified, e.g. air is always dry.