International Standard Atmosphere

The International Standard Atmosphere (ISA) is a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes or elevations. It has been established to provide a common reference for temperature and pressure and consists of tables of values at various altitudes, plus some formulas by which those values were derived. The International Organization for Standardization (ISO) publishes the ISA as an international standard, ISO 2533:1975.[1] Other standards organizations, such as the International Civil Aviation Organization (ICAO) and the United States Government, publish extensions or subsets of the same atmospheric model under their own standards-making authority.

Comparison International Standard Atmosphere space diving
Comparison of a graph of International Standard Atmosphere temperature and pressure and approximate altitudes of various objects and successful stratospheric jumps


The ISA mathematical model divides the atmosphere into layers with an assumed linear distribution of absolute temperature T against geopotential altitude h.[2] The other two values (pressure P and density ρ) are computed by simultaneously solving the equations resulting from:

  • the vertical pressure gradient resulting from hydrostatic balance, which relates the rate of change of pressure with geopotential altitude:
, and

at each geopotential altitude, where g is the standard acceleration of gravity, and Rspecific is the specific gas constant for dry air.

Air density must be calculated in order to solve for the pressure, and is used in calculating dynamic pressure for moving vehicles. Dynamic viscosity is an empirical function of temperature, and kinematic viscosity is calculated by dividing dynamic viscosity by the density.

Thus the standard consists of a tabulation of values at various altitudes, plus some formulas by which those values were derived. To accommodate the lowest points on Earth, the model starts at a base geopotential altitude of 610 meters (2,000 ft) below sea level, with standard temperature set at 19 °C. With a temperature lapse rate of −6.5 °C (-11.7 °F) per km (roughly −2 °C (-3.6 °F) per 1,000 ft), the table interpolates to the standard mean sea level values of 15 °C (59 °F) temperature, 101,325 pascals (14.6959 psi) (1 atm) pressure, and a density of 1.2250 kilograms per cubic meter (0.07647 lb/cu ft). The tropospheric tabulation continues to 11,000 meters (36,089 ft), where the temperature has fallen to −56.5 °C (−69.7 °F), the pressure to 22,632 pascals (3.2825 psi), and the density to 0.3639 kilograms per cubic meter (0.02272 lb/cu ft). Between 11 km and 20 km, the temperature remains constant.[3][4]

Layers in the ISA Standard Atmosphere 1976
Layer Level
Altitude above MSL[5]
h (m)
Altitude above MSL[5]
z (m)

( °C/km)[a]

T (°C)
p (Pa)
ρ (kg/m3)
0 Troposphere -610 -611 +6.5 +19.0 108,900 (1.075 bar) 1.2985
1 Tropopause 11,000 11,019 0.0 −56.5 22,632 0.3639
2 Stratosphere 20,000 20,063 -1.0 −56.5 5474.9 0.0880
3 Stratosphere 32,000 32,162 -2.8 −44.5 868.02 0.0132
4 Stratopause 47,000 47,350 0.0 −2.5 110.91 0.0020
5 Mesosphere 51,000 51,413 +2.8 −2.5 66.939
6 Mesosphere 71,000 71,802 +2.0 −58.5 3.9564
7 Mesopause 84,852 86,000 −86.28 0.3734
a lapse rate given per kilometer of geopotential altitude

In the above table, geopotential altitude is calculated from a mathematical model that adjusts the altitude to include the variation of gravity with height, while geometric altitude is the standard direct vertical distance above mean sea level (MSL).[2] Note that the Lapse Rates cited in the table are given as °C per kilometer of geopotential altitude, not geometric altitude.

The ISA model is based on average conditions at mid latitudes, as determined by the ISO's TC 20/SC 6 technical committee. It has been revised from time to time since the middle of the 20th century.

Use at non-standard day conditions

The ISA models a hypothetical standard day to allow a reproducible engineering reference for calculation and testing of engine and vehicle performance at various altitudes. It does not provide a rigorous meteorological model of actual atmospheric conditions (for example, changes in barometric pressure due to wind conditions). Neither does it account for humidity effects; air is assumed to be dry and clean and of constant composition. Humidity effects are accounted for in vehicle or engine analysis by adding water vapor to the thermodynamic state of the air after obtaining the pressure and density from the standard atmosphere model.

Non-standard (hot or cold) days are modeled by adding a specified temperature delta to the standard temperature at altitude, but pressure, density, and viscosity are not recalculated at the resultant non-standard temperature. (Thus the temperature effects on them are considered to be much less important than the effect of altitude.) Hot day, Cold day, Tropical, and Polar temperature profiles with altitude have been defined for use as performance references, such as United States Department of Defense MIL-STD-210C, and its successor MIL-HDBK-310.[6]

ICAO Standard Atmosphere

The International Civil Aviation Organization (ICAO) published their "ICAO Standard Atmosphere" as Doc 7488-CD in 1993. It has the same model as the ISA, but extends the altitude coverage to 80 kilometers (262,500 feet).[7]

The ICAO Standard Atmosphere, like the ISA, does not contain water vapor.

Some of the values defined by ICAO are:

ICAO Standard Atmosphere
Height km & ft Temperature °C Pressure hPa Lapse Rate °C/1000 ft
0 km MSL 15.0 1013.25 −1.98 (Tropospheric)
11 km 36 000 ft −56.5 226.00 0.00 (Stratospheric)
20 km 65 000 ft −56.5 54.70 +0.3 (Stratospheric)
32 km 105 000 ft −44.5 8.68

Aviation standards and flying rules are based on the International Standard Atmosphere. Airspeed indicators are calibrated on the assumption that they are operating at sea level in the International Standard Atmosphere where the air density is 1.225 kg/m3.

Other standard atmospheres

The U.S. Standard Atmosphere is a set of models that define values for atmospheric temperature, density, pressure and other properties over a wide range of altitudes. The first model, based on an existing international standard, was published in 1958 by the U.S. Committee on Extension to the Standard Atmosphere,[8] and was updated in 1962,[5] 1966,[9] and 1976.[10] The U.S. Standard Atmosphere, International Standard Atmosphere and WMO (World Meteorological Organization) standard atmospheres are the same as the ISO International Standard Atmosphere for altitudes up to 32 km.[11][12]

NRLMSISE-00 is a newer model of the Earth's atmosphere from ground to space, developed by the US Naval Research Laboratory taking actual satellite drag data into account. A primary use of this model is to aid predictions of satellite orbital decay due to atmospheric drag. The COSPAR International Reference Atmosphere (CIRA) 2012 and the ISO 14222 Earth Atmosphere Density standard both recommend NRLMSISE-00 for composition uses.

JB2008 is a newer model of the Earth’s atmosphere from 120 to 2000 km, developed by the US Air Force Space Command and Space Environment Technologies taking into account realistic solar irradiances and time evolution of geomagnetic storms. It is most useful for calculating satellite orbital decay due to atmospheric drag. The COSPAR International Reference Atmosphere (CIRA) 2012 and the ISO 14222 Earth Atmosphere Density standard both recommend JB2008 for mass density in drag uses.

The standard conditions for temperature and pressure are a model of gas temperature and pressure used in chemistry.

See also


  1. ^ International Organization for Standardization, Standard Atmosphere, ISO 2533:1975, 1975.
  2. ^ a b Gyatt, Graham (2006-01-14): "The Standard Atmosphere" Archived 2007-03-10 at the Wayback Machine. A mathematical model of the 1976 U.S. Standard Atmosphere.
  3. ^ Auld, D.J.; Srinivas, K. (2008). "Properties of the Atmosphere". Retrieved 2008-03-13.
  4. ^ Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge Univ. Press, 1967.
  5. ^ a b c U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962
  6. ^ Mathworks atmosnonstd
  7. ^ Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet)) (Third ed.). International Civil Aviation Organization. 1993. ISBN 92-9194-004-6. Doc 7488-CD.
  8. ^ U.S. Extension to the ICAO Standard Atmosphere, U.S. Government Printing Office, Washington, D.C., 1958
  9. ^ U.S. Standard Atmosphere Supplements, 1966, U.S. Government Printing Office, Washington, D.C., 1966
  10. ^ U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MB)
  11. ^ NASA, "U.S. Standard Atmosphere 1976" Archived 2006-05-13 at the Wayback Machine
  12. ^ Tomasi, C.; Vitake, V.; De Santis, L.V. (1998). "Relative optical mass functions for air, water vapour, ozone and nitrogen dioxide in atmospheric models presenting different latitudinal and seasonal conditions" (PDF). Meteorology and Atmospheric Physics. 65 (1): 11–30. Bibcode:1998MAP....65...11T. doi:10.1007/BF01030266. Retrieved 2007-12-31. …the ISO (International Organisation for Standardisation) Standard Atmosphere, 1972. This model is identical to the present Standard Atmospheres of ICAO (International Civil Aviation Organization) and WMO (World Meteorological Organization) up to a height of 32 km
  • Davies, Mark (2003). The Standard Handbook for Aeronautical and Astronautical Engineers. New York: McGraw-Hill. ISBN 0-07-136229-0.
  • NASA JPL Reference Notes
  • ICAO, Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet)), Doc 7488-CD, Third Edition, 1993, ISBN 92-9194-004-6.

External links

.338 Lapua Magnum

The .338 Lapua Magnum (8.6×70mm or 8.58×70mm) is a rimless, bottlenecked, centerfire rifle cartridge. It was developed during the 1980s as a high-powered, long-range cartridge for military snipers. It was used in the Afghanistan War and the Iraq War. As a result of this, it became more widely available. The loaded cartridge is 14.93 mm (0.588 in) in diameter (rim) and 93.5 mm (3.68 in) long. It can penetrate better-than-standard military body armor at ranges up to 1,000 metres (1,090 yd) and has a maximum effective range of about 1,750 metres (1,910 yd). Muzzle velocity is dependent on barrel length, seating depth, and powder charge, and varies from 880 to 915 m/s (2,890 to 3,000 ft/s) for commercial loads with 16.2-gram (250 gr) bullets, which corresponds to about 6,525 J (4,813 ft⋅lbf) of muzzle energy.

British military issue overpressure .338 Lapua Magnum cartridges with a 91.4 mm (3.60 in) overall length, loaded with 16.2-gram (250 gr) LockBase B408 very-low-drag bullets fired at 936 m/s (3,071 ft/s) muzzle velocity. This round, fired from a L115A3 Long Range Rifle, was used in November 2009 by British sniper Corporal of Horse (CoH) Craig Harrison to establish the then-new record for the longest confirmed sniper kill in combat, at a range of 2,475 m (2,707 yd).In addition to its military role, it is increasingly used by hunters and civilian long-range shooting enthusiasts. The .338 Lapua Magnum is capable of taking down any game animal, though its suitability for some dangerous game (Cape buffalo, hippopotamus, white rhinoceros, and elephant) is arguable, unless accompanied by a larger "backup" calibre: "There is a huge difference between calibres that will kill an elephant and those that can be relied upon to stop one." In Namibia the .338 Lapua Magnum is legal for hunting Africa's Big five game if the loads have ≥ 5,400 J (3,983 ft⋅lbf) muzzle energy.


Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are indicated airspeed ("IAS"), calibrated airspeed ("CAS"), equivalent airspeed ("EAS"), true airspeed ("TAS"), and density airspeed.

Indicated airspeed is simply what is read off of an airspeed gauge connected to a pitot static system, calibrated airspeed is indicated airspeed adjusted for pitot system position and installation error, and equivalent airspeed is calibrated airspeed adjusted for compressibility effects. True airspeed is equivalent airspeed adjusted for air density, and is also the speed of the aircraft through the air in which it is flying. Calibrated airspeed is typically within a few knots of indicated airspeed, while equivalent airspeed decreases slightly from CAS as aircraft altitude increases or at high speeds.

With EAS constant, true airspeed increases as aircraft altitude increases. This is because air density decreases with higher altitude, but an aircraft's wing requires the same amount of air particles (i.e., mass of air) flowing around it to produce the same amount of lift for a given AOA; thus, a wing must move faster through thinner air than thicker air to obtain the same amount of lift.

The measurement and indication of airspeed is ordinarily accomplished on board an aircraft by an airspeed indicator ("ASI") connected to a pitot-static system. The pitot-static system comprises one or more pitot probes (or tubes) facing the on-coming air flow to measure pitot pressure (also called stagnation, total or ram pressure) and one or more static ports to measure the static pressure in the air flow. These two pressures are compared by the ASI to give an IAS reading.

Alcohol by volume

Alcohol by volume (abbreviated as ABV, abv, or alc/vol) is a standard measure of how much alcohol (ethanol) is contained in a given volume of an alcoholic beverage (expressed as a volume percent). It is defined as the number of millilitres (mL) of pure ethanol present in 100 mL (3.4 fl. oz) of solution at 20 °C (68 °F). The number of millilitres of pure ethanol is the mass of the ethanol divided by its density at 20 °C, which is 0.78924 g/mL (105.3 fl oz/gallon). The ABV standard is used worldwide. The International Organization of Legal Metrology has tables of density of water–ethanol mixtures at different concentrations and temperatures.

In some countries, e.g. France, alcohol by volume is often referred to as degrees Gay-Lussac (after the French chemist Joseph Louis Gay-Lussac), although there is a slight difference since the Gay-Lussac convention uses the International Standard Atmosphere value for temperature, 15 °C (59 °F).


Altitude or height (sometimes known as 'depth') is defined based on the context in which it is used (aviation, geometry, geographical survey, sport, atmospheric pressure, and many more). As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context. Although the term altitude is commonly used to mean the height above sea level of a location, in geography the term elevation is often preferred for this usage.

Vertical distance measurements in the "down" direction are commonly referred to as depth.

Atmosphere (unit)

The standard atmosphere (symbol: atm) is a unit of pressure defined as 101325 Pa (1.01325 bar). It is sometimes used as a reference or standard pressure.

Calibrated airspeed

Calibrated airspeed (CAS) is indicated airspeed corrected for instrument and position error.

When flying at sea level under International Standard Atmosphere conditions (15 °C, 1013 hPa, 0% humidity) calibrated airspeed is the same as equivalent airspeed (EAS) and true airspeed (TAS). If there is no wind it is also the same as ground speed (GS). Under any other conditions, CAS may differ from the aircraft's TAS and GS.

Calibrated airspeed in knots is usually abbreviated as KCAS, while indicated airspeed is abbreviated as KIAS.

In some applications, notably British usage, the expression rectified airspeed is used instead of calibrated airspeed.

Density of air

The density of air or atmospheric density, denoted ρ (Greek: rho), is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 15°C, air has a density of approximately 1.225 kg/m³ (0.001225 g/cm³, 0.0023769 slug/(cu ft), 0.0765 lb/(cu ft)) according to ISA (International Standard Atmosphere).Air density is a property used in many branches of science, engineering, and industry, including aeronautics; gravimetric analysis; the air-conditioning industry; atmospheric research and meteorology; agricultural engineering (modeling and tracking of Soil-Vegetation-Atmosphere-Transfer (SVAT) models); and the engineering community that deals with compressed air.Depending on the measuring instruments used, different sets of equations for the calculation of the density of air can be applied. Air is a mixture of gases and the calculations always simplify, to a greater or lesser extent, the properties of the mixture.

Equivalent airspeed

Equivalent airspeed (EAS) is calibrated airspeed (CAS) corrected for the compressibility of air at a non-trivial Mach number. It is also the airspeed at sea level in the International Standard Atmosphere at which the dynamic pressure is the same as the dynamic pressure at the true airspeed (TAS) and altitude at which the aircraft is flying. In low-speed flight, it is the speed which would be shown by an airspeed indicator with zero error. It is useful for predicting aircraft handling, aerodynamic loads, stalling etc.


is actual air density.

is standard sea level density (1.225 kg/m3 or 0.00237 slug/ft3).

EAS is a function of dynamic pressure.


is dynamic pressure

EAS can also be obtained from the aircraft Mach number and static pressure.


is the standard speed of sound at 15 °C (661.47 knots)

is Mach number

is static pressure

is standard sea level pressure (1013.25 hPa)

Combining the above with the expression for Mach number gives EAS as a function of impact pressure and static pressure (valid for subsonic flow):


is impact pressure.

At standard sea level, EAS is the same as calibrated airspeed (CAS) and true airspeed (TAS). At any other altitude, EAS may be obtained from CAS by correcting for compressibility error.

The following simplified formula allows calculation of CAS from EAS:


pressure ratio:

and are airspeeds and can be measured in knots, km/h, mph or any other appropriate unit.

The above formula is accurate within 1% up to Mach 1.2 and useful with acceptable error up to Mach 1.5. The 4th order Mach term can be neglected for speeds below Mach 0.85.

Flight level

In aviation and aviation meteorology, flight level (FL) is an aircraft's altitude at standard air pressure, expressed in hundreds of feet. The air pressure is computed assuming an International Standard Atmosphere pressure of 1013.25 hPa (29.92 inHg), and therefore is not necessarily the same as the aircraft's actual altitude either above sea level or above ground level.

Hypsometric equation

The hypsometric equation, also known as the thickness equation, relates an atmospheric pressure ratio to the equivalent thickness of an atmospheric layer under the assumptions of constant temperature and gravity. It is derived from the hydrostatic equation and the ideal gas law.

Pressure altitude

Pressure altitude within the atmosphere is the altitude in the International Standard Atmosphere (ISA) with the same atmospheric pressure as that of the part of the atmosphere in question.

The National Oceanic and Atmospheric Administration (NOAA) has published the following formula for directly converting atmospheric pressure in millibars () to pressure altitude in feet ():

In aviation, the pressure altitude is the indicated 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 readout of the altitude. Examples would be landing at a very 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 and . Standard pressure, the baseline used universally, is hectopascals (), which is equivalent to or inches of mercury (). 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 transition altitude).

QNE is an aeronautical code Q code. The term QNE refers to the indicated altitude at the landing runway threshold when or is set in the altimeter’s Kollsman window. In other words, it is the pressure altitude at the landing runway threshold.

Most aviation texts for PPL and CPL exams describe a process for finding the pressure altitude (in feet) using the following formula:

For example, if the airfield elevation is and the altimeter setting is , then


For example, if the airfield elevation is and the QNH is , then

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.

Pressure reference system

Pressure reference system (PRS) is an enhancement of the inertial reference system and attitude and heading reference system designed to provide position angles measurements which are stable in time and do not suffer from long term drift caused by the sensor imperfections. The measurement system uses behavior of the International Standard Atmosphere where atmospheric pressure descends with increasing altitude and two pairs of measurement units. Each pair measures pressure at two different positions that are mechanically connected with known distance between units, e.g. the units are mounted at the tips of the wing. In horizontal flight, there is no pressure difference measured by the measurement system which means the position angle is zero. In case the airplane turns, the tips of the wings mutually change their positions, one is going up and the second one is going down, and the pressure sensors in every unit measure different values which are translated into a position angle.

Standard atmosphere

Standard atmosphere may refer to:

A standard reference value for air pressure:

Atmosphere (unit), an approximation of the value at sea level

Atmospheric pressure, other reference values

One of various static atmospheric models of how atmospheric pressure, density, and temperature vary with altitude, such as:

The U.S. Standard Atmosphere, a series of models that give values for pressure, density, and temperature over a range of altitudes

The International Standard Atmosphere (ISA), an international standard model, defining typical atmospheric properties with altitude, at mid-latitude

Standard conditions for temperature and pressure

Standard conditions for temperature and pressure are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST), although these are not universally accepted standards. Other organizations have established a variety of alternative definitions for their standard reference conditions.

In chemistry, IUPAC changed the definition of standard temperature and pressure (STP) in 1982:

Until 1982, STP was defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly 1 atm (101.325 kPa).

Since 1982, STP is defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly 105 Pa (100 kPa, 1 bar).STP should not be confused with the standard state commonly used in thermodynamic evaluations of the Gibbs energy of a reaction.

NIST uses a temperature of 20 °C (293.15 K, 68 °F) and an absolute pressure of 1 atm (14.696 psi, 101.325 kPa). This standard is also called normal temperature and pressure (abbreviated as NTP).

The International Standard Metric Conditions for natural gas and similar fluids are 288.15 K (15.00 °C; 59.00 °F) and 101.325 kPa.In industry and commerce, standard conditions for temperature and pressure are often necessary to define the standard reference conditions to express the volumes of gases and liquids and related quantities such as the rate of volumetric flow (the volumes of gases vary significantly with temperature and pressure) – standard cubic meters per second (sm3/s), and normal cubic meters per second (nm3/s). However, many technical publications (books, journals, advertisements for equipment and machinery) simply state "standard conditions" without specifying them, often leading to confusion and errors. Good practice always incorporates the reference conditions of temperature and pressure.

Surface weather observation

Surface weather observations are the fundamental data used for safety as well as climatological reasons to forecast weather and issue warnings worldwide. They can be taken manually, by a weather observer, by computer through the use of automated weather stations, or in a hybrid scheme using weather observers to augment the otherwise automated weather station. The ICAO defines the International Standard Atmosphere (ISA), which is the model of the standard variation of pressure, temperature, density, and viscosity with altitude in the Earth's atmosphere, and is used to reduce a station pressure to sea level pressure. Airport observations can be transmitted worldwide through the use of the METAR observing code. Personal weather stations taking automated observations can transmit their data to the United States mesonet through the Citizen Weather Observer Program (CWOP), the UK Met Office through their Weather Observations Website (WOW), or internationally through the Weather Underground Internet site. A thirty-year average of a location's weather observations is traditionally used to determine the station's climate. In the US a network of Cooperative Observers make a daily record of summary weather and sometimes water level information.

True airspeed

The true airspeed (TAS; also KTAS, for knots true airspeed) of an aircraft is the speed of the aircraft relative to the airmass in which it is flying. The true airspeed is important information for accurate navigation of an aircraft. Traditionally it is measured using an analogue TAS indicator, but as the Global Positioning System has become available for civilian use, the importance of such analogue instruments has decreased. Since indicated airspeed is a better indicator of power used and lift available, True airspeed is not used for controlling the aircraft during taxiing, takeoff, climb, descent, approach or landing; for these purposes the Indicated airspeed – IAS or KIAS (knots indicated airspeed) – is used. However, since indicated airspeed only shows true speed through the air at standard sea level pressure and temperature, a TAS meter is necessary for navigation purposes at cruising altitude in less dense air. The IAS meter reads very nearly the TAS at lower altitude and at lower speed. On jet airliners the TAS meter is usually hidden at speeds below 200 knots (370 km/h). Neither provides for accurate speed over the ground, since surface winds or winds aloft are not taken into account.

U.S. Standard Atmosphere

The U.S. Standard Atmosphere is a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes or elevations. The model, based on an existing international standard, was first published in 1958 by the U.S. Committee on Extension to the Standard Atmosphere, and was updated in 1962, 1966, and 1976. It is largely consistent in methodology with the International Standard Atmosphere, differing mainly in the assumed temperature distribution at higher altitudes.

ISO standards by standard number

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