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Implementation of International Standard Atmosphere (ISA) formulas as defined in ISO 2533:1975 and ICAO 7488/3 1994"
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rake
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rspec
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measured
>= 0
 Project Readme

Atmospheric for Ruby (International Standard Atmosphere / ICAO Standard Atmosphere (ISA))

Purpose

This repository provides Ruby code for calculating values defined in the following documents:

  • International Standard Atmosphere (ISA) from ISO 2533:1975, ISO 2533:1975/ADD 1:1985 and ISO 2533:1975/ADD 2:1997

  • ICAO Standard Atmosphere (ICAO Doc 7488/3, 1994)

Which are technically identical documents but different in presentation and units (the ICAO document includes ft in addition to m).

Usage

Formulas and calculations

> require 'atmospheric'
> instance = Atmospheric::Isa.method_name
> # method_name is one of the following

The available methods are:

  • geometric_altitude_from_geopotential(geopotential_altitude)

  • geopotential_altitude_from_geometric(geometric_altitude)

  • temperature_at_layer_from_geopotential(geopotential_altitude)

  • temperature_at_layer_celcius(geopotential_altitude)

  • pressure_from_geopotential_mbar(geopotential_altitude)

  • pressure_from_geopotential_mmhg(geopotential_altitude)

  • density_from_geopotential(geopotential_altitude)

  • gravity_at_geopotential(geopotential_altitude)

  • p_p_n_from_geopotential(geopotential_altitude)

  • rho_rho_n_from_geopotential(geopotential_altitude)

  • root_rho_rho_n_from_geopotential(geopotential_altitude)

  • speed_of_sound_from_geopotential(geopotential_altitude)

  • dynamic_viscosity_from_geopotential(geopotential_altitude)

  • kinematic_viscosity_from_geopotential(geopotential_altitude)

  • thermal_conductivity_from_geopotential(geopotential_altitude)

  • pressure_scale_height_from_geopotential(geopotential_altitude)

  • specific_weight_from_geopotential(geopotential_altitude)

  • air_number_density_from_geopotential(geopotential_altitude)

  • mean_air_particle_speed_from_geopotential(geopotential_altitude)

  • air_particle_collision_frequency_from_geopotential(geopotential_altitude)

  • mean_free_path_of_air_particles_from_geopotential(geopotential_altitude)

Generating ISO 2533 tables

ISO 2533:1975

All tables in the 1975 edition are arranged in these steps in meters:

ISO 2533:1975 table range: step 50 from -2k, 100 from 32k, 200 from 51k to 80k
(-2000..31999).step(50) +
(32000..50999).step(100) +
(51000..80000).step(200)

Tables 5 to 7 all have height information of the following keys in the hash:

  • geopotential-altitude-m

  • geopotential-altitude-ft

  • geometrical-altitude-m

  • geometrical-altitude-ft

All YAML tables generated contain these two keys which group altitude values as the ISO 2533 tables are rendered in both types of altitudes:

  • by-geopotential-altitude

  • by-geometric-altitude

Table 5

Title: "Temperature (T and t), Pressure (p), Density (p) and Acceleration of free fall (g) in terms of geometrical altitude (h) and geopotential altitude (H)"

Provides the following values in addition to geopotential and geometric height:

  • temperature-K

  • temperature-C

  • pressure-mbar

  • pressure-mmhg

  • density

  • acceleration

Atmospheric::Export::Iso25331975.table_5      #=> Hash
Atmospheric::Export::Iso25331975.table_5_yaml #=> YAML

Table 6

Title: "Relations of p’pn, p/pn and bar(p/pn), Speed of sound (a), Dynamic viscosity (p), Kinematic viscosity (v) and Thermal conductivity (lambda) in terms of geometrical altitude (h), and geopotential altitude (H)"

Provides the following values in addition to geopotential and geometric height:

  • ppn

  • rhorhon

  • sqrt-rhorhon

  • speed-of-sound

  • dynamic-viscosity

  • kinematic-viscosity

  • thermal-conductivity

Atmospheric::Export::Iso25331975.table_6      #=> Hash
Atmospheric::Export::Iso25331975.table_6_yaml #=> YAML

Table 7

Title: "Pressure scale height (H_p) Specific weight (gamma), Air number density (n), Mean air-particle speed (v), Air-particle collision frequency (omega) and Mean free path of air particles (l) in terms of geometrical altitude (h) and geopotential altitude (H)"

  • pressure-scale-height

  • specific-weight

  • air-number-density

  • mean-speed

  • frequency

  • mean-free-path

Atmospheric::Export::Iso25331975.table_7      #=> Hash
Atmospheric::Export::Iso25331975.table_7_yaml #=> YAML

ISO 2533 ADD 1:1985

Addendum 1 adds "Hypsometrical tables".

Table 1 (hPa)

Title: "Geopotential altitude as a function of barometric pressure for 5 ⇐ p < 20 hPa at intervals of 0.01 hPa"

For the range of (5.0..19.99).step(0.01) in hPa.

Provides:

  • pressure-mbar

  • geopotential-altitude

Atmospheric::Export::Iso25331985.table_1      #=> Hash
Atmospheric::Export::Iso25331985.table_1_yaml #=> YAML

Table 2 (hPa)

Title: "Geopotential altitude as a function of barometric pressure for 20 ⇐ p < 1200 hPa at intervals of 0.1 hPa"

Same as Table 1 but for the range of (20.0..1199.9).step(0.1) in hPa.

Atmospheric::Export::Iso25331985.table_2      #=> Hash
Atmospheric::Export::Iso25331985.table_2_yaml #=> YAML

Table 3 (mmHg)

Title: "Geopotential altitude as a function of barometric pressure for 4 ⇐ p < 10 mmHg at intervals of 0.01 mmHg"

Same as Table 1 but for the range of (4.0..9.99).step(0.01) and results in mmhg.

Provides:

  • pressure-mmhg

  • geopotential-altitude

Atmospheric::Export::Iso25331985.table_3      #=> Hash
Atmospheric::Export::Iso25331985.table_3_yaml #=> YAML

Table 4 (mmHg)

Title: "Geopotential altitude as a function of barometric pressure for 10 ⇐ p < 900 mmHg at intervals of 0.1 mmHg"

Same as Table 3 but for the range of (10.0..899.9).step(0.1) and results in mmhg.

Atmospheric::Export::Iso25331985.table_4      #=> Hash
Atmospheric::Export::Iso25331985.table_4_yaml #=> YAML

Table 5 (hPa) and Table 6 (mmHg)

The difference is Table 5 is in hPa while Table 6 is in mmHg.

Title: "Barometric pressure, in hectopascals, as a function of geopotential altitude for -1000 ⇐ H < +4600 m at intervals of 1m"

Provides:

  • geopotential-altitude

  • pressure-mbar

  • pressure-mmhg

Range of (-1000..4599).step(1).

Atmospheric::Export::Iso25331985.table_56      #=> Hash
Atmospheric::Export::Iso25331985.table_56_yaml #=> YAML

ISO 2533 ADD 2:1997

Addendum 2 is exactly like ISO 2533:1975 with the tables but extended the tables:

  • 1975’s range is -2km to 80km. 1997 provides -5km to 2km (yes -2km to 2km overlaps…​)

  • 1975 tables only provide H and h in meters. 1997 adds a lookup table of H and h in feet.

ISO 2533 ADD 2:1997 Tables 1 to 3 have height range in meters
(-5000..2000).step(50)
ISO 2533 ADD 2:1997 Tables 4 to 6 have height range in feet
(-16500..-13999).step(250) +
(-14000..104999).step(200) +
(105000..262500).step(500)

Table 1 (-5km to 2km)

Title: "Temperature (T and t), pressure (p), density (p) and acceleration of free fall (g) in terms of geometrical altitude (h) and geopotential altitude (H) — Altitudes in metres"

Exactly same as ISO 2533:1975 Table 5, but with a different height range.

In addition, pressure at mmHg is no longer produced, but the implementation still provides it for completeness.

Atmospheric::Export::Iso25331997.table_1      #=> Hash
Atmospheric::Export::Iso25331997.table_1_yaml #=> YAML

Table 2 (-5km to 2km)

Title: "Relations of p’pn, p/pn and bar(p/pn), Speed of sound (a), Dynamic viscosity (p), Kinematic viscosity (v) and Thermal conductivity (lambda) in terms of geometrical altitude (h), and geopotential altitude (H) — Altitudes in metres"

Exactly same as ISO 2533:1975 Table 6, but with a different height range.

Atmospheric::Export::Iso25331997.table_2      #=> Hash
Atmospheric::Export::Iso25331997.table_2_yaml #=> YAML

Table 3 (-5km to 2km)

Title: "Pressure scale height (H_p) Specific weight (gamma), Air number density (n), Mean air-particle speed (v), Air-particle collision frequency (omega) and Mean free path of air particles (l) in terms of geometrical altitude (h) and geopotential altitude (H) — Altitudes in metres"

Exactly same as ISO 2533:1975 Table 7, but with a different height range.

Atmospheric::Export::Iso25331997.table_3      #=> Hash
Atmospheric::Export::Iso25331997.table_3_yaml #=> YAML

Table 4 (-16.5kft to 262.5kft)

Title: "Temperature (T and t), pressure (p), density (p) and acceleration of free fall (g) in terms of geometrical altitude (h) and geopotential altitude (H) — Altitudes in feet"

Exactly same as ISO 2533:1975 Table 5, but in feet and different range.

Pressure at mmHg is not produced, but the implementation still provides it for completeness.

Atmospheric::Export::Iso25331997.table_4      #=> Hash
Atmospheric::Export::Iso25331997.table_4_yaml #=> YAML

Table 5 (-16.5kft to 262.5kft)

Title: "Relations of p’pn, p/pn and bar(p/pn), Speed of sound (a), Dynamic viscosity (p), Kinematic viscosity (v) and Thermal conductivity (lambda) in terms of geometrical altitude (h), and geopotential altitude (H) — Altitudes in feet"

Exactly same as ISO 2533:1975 Table 6, but in feet and different range.

Atmospheric::Export::Iso25331997.table_5      #=> Hash
Atmospheric::Export::Iso25331997.table_5_yaml #=> YAML

Table 6 (-16.5kft to 262.5kft)

Title: "Pressure scale height (H_p) Specific weight (gamma), Air number density (n), Mean air-particle speed (v), Air-particle collision frequency (omega) and Mean free path of air particles (l) in terms of geometrical altitude (h) and geopotential altitude (H) — Altitudes in feet"

Exactly same as ISO 2533:1975 Table 7, but in feet and different range.

Atmospheric::Export::Iso25331997.table_6      #=> Hash
Atmospheric::Export::Iso25331997.table_6_yaml #=> YAML

ISO NP 2533:2024

General

ISO 2533 is now proposed to be revised for a 2024/2025 version, 49 years since the last edition (1975) and 27 years since it was last updated (1997).

ISO NP 2533:2024 will likely include all content in the previously published Addenda, including:

  • Standard atmosphere values from altitude -5km to 80km (geometric and geopotential)

    Note
    		 The 1975 edition provided values from -2km to 80km (even though it said 32km in the title).
    Note
    		 The 1997 ADD 2 provided values from -5km to 2km.

  • Standard atmosphere values from altitude -16,500ft to 262,500ft (geometric and geopotential)

    Note
    		 The 1997 ADD 2 provided these values.

  • Hypsometrical tables (altitude as a function of barometric pressure) (geometric and geopotential; hPa/mbar)

    Note
    		 The 1985 ADD 1 provided these hypsometrical tables in hPa/mbar and mmHg. In the 2024 edition only hPa/mbar is provided.

This document will also align to the values provided in ICAO Doc 7488/3.

All tables in the new edition are arranged in these steps.

ISO 2533:2024 atmosphere values (m): step 50 from -5k, 100 from 32k, 200 from 51k to 80k
(-5000..31950).step(50) +
(32000..50900).step(100) +
(51000..80000).step(200)
ISO 2533:2024 atmosphere values (ft): step 250 from -16500, 200 from -14000, 500 from 105000 to 262500
(-16500..-13750).step(250) +
(-14000..104800).step(200) +
(105000..262500).step(500)

Tables 5 to 10 all have height information of the following keys in the hash:

  • geopotential-altitude-m

  • geopotential-altitude-ft

  • geometrical-altitude-m

  • geometrical-altitude-ft

All YAML tables generated contain these two keys which group altitude values as the ISO 2533 tables are rendered in both types of altitudes:

  • by-geopotential-altitude

  • by-geometric-altitude

Table 5 (meters)

Note
 This corresponds to ISO 2533:1975 Table 5 combined with ISO 2533:1975/ADD 1:1997 Table 1.

Title: "Temperature (T and t), Pressure (p), Density (p) and Acceleration of free fall (g) in terms of geometrical altitude (h) and geopotential altitude (H)"

Provides the following values in addition to geopotential and geometric height:

  • temperature-K

  • temperature-C

  • pressure-mbar

  • pressure-mmhg

  • density

  • acceleration

Atmospheric::Export::Iso25332024.table_5      #=> Hash
Atmospheric::Export::Iso25332024.table_5_yaml #=> YAML

Table 6 (meters)

Note
 This corresponds to ISO 2533:1975 Table 6 combined with ISO 2533:1975/ADD 1:1997 Table 2.

Title: "Relations of p’pn, p/pn and bar(p/pn), Speed of sound (a), Dynamic viscosity (p), Kinematic viscosity (v) and Thermal conductivity (lambda) in terms of geometrical altitude (h), and geopotential altitude (H)"

Provides the following values in addition to geopotential and geometric height:

  • ppn

  • rhorhon

  • sqrt-rhorhon

  • speed-of-sound

  • dynamic-viscosity

  • kinematic-viscosity

  • thermal-conductivity

Atmospheric::Export::Iso25332024.table_6      #=> Hash
Atmospheric::Export::Iso25332024.table_6_yaml #=> YAML

Table 7 (meters)

Note
 This corresponds to ISO 2533:1975 Table 7 combined with ISO 2533:1975/ADD 1:1997 Table 3.

Title: "Pressure scale height (H_p) Specific weight (gamma), Air number density (n), Mean air-particle speed (v), Air-particle collision frequency (omega) and Mean free path of air particles (l) in terms of geometrical altitude (h) and geopotential altitude (H)"

  • pressure-scale-height

  • specific-weight

  • air-number-density

  • mean-speed

  • frequency

  • mean-free-path

Atmospheric::Export::Iso25332024.table_7      #=> Hash
Atmospheric::Export::Iso25332024.table_7_yaml #=> YAML

Table 8 (-16.5kft to 262.5kft)

Note
 This corresponds to ISO 2533:1975/ADD 2:1997 Table 4.

Title: "Temperature (T and t), pressure (p), density (p) and acceleration of free fall (g) in terms of geometrical altitude (h) and geopotential altitude (H) — Altitudes in feet"

Exactly same as ISO 2533:1975 Table 5, but in feet and different range.

Pressure at mmHg is not produced, but the implementation still provides it for completeness.

Atmospheric::Export::Iso25332024.table_8      #=> Hash
Atmospheric::Export::Iso25332024.table_8_yaml #=> YAML

Table 9 (-16.5kft to 262.5kft)

Note
 This corresponds to ISO 2533:1975/ADD 2:1997 Table 5.

Title: "Relations of p’pn, p/pn and bar(p/pn), Speed of sound (a), Dynamic viscosity (p), Kinematic viscosity (v) and Thermal conductivity (lambda) in terms of geometrical altitude (h), and geopotential altitude (H) — Altitudes in feet"

Exactly same as ISO 2533:1975 Table 6, but in feet and different range.

Atmospheric::Export::Iso25332024.table_9      #=> Hash
Atmospheric::Export::Iso25332024.table_9_yaml #=> YAML

Table 10 (-16.5kft to 262.5kft)

Note
 This corresponds to ISO 2533:1975/ADD 2:1997 Table 6.

Title: "Pressure scale height (H_p) Specific weight (gamma), Air number density (n), Mean air-particle speed (v), Air-particle collision frequency (omega) and Mean free path of air particles (l) in terms of geometrical altitude (h) and geopotential altitude (H) — Altitudes in feet"

Exactly same as ISO 2533:1975 Table 7, but in feet and different range.

Atmospheric::Export::Iso25332024.table_10      #=> Hash
Atmospheric::Export::Iso25332024.table_10_yaml #=> YAML

Table 11 (hPa)

Note
 This corresponds to ISO 2533:1975/ADD 1:1985 Table 1 combined with Table 2.

Title: "Geometric and geopotential altitude as a function of barometric pressure for 5 ⇐ p < 20 hPa at intervals of 0.01 hPa and 20 ⇐ p < 1200 hPa at intervals of 0.1 hPa_"

For the range of (5.0..19.99).step(0.01) + (20.0..1199.9).step(0.1) in hPa.

Provides:

  • pressure-mbar

  • geopotential-altitude-m

  • geopotential-altitude-ft

  • geometric-altitude-m

  • geometric-altitude-ft

Atmospheric::Export::Iso25332024.table_11      #=> Hash
Atmospheric::Export::Iso25332024.table_11_yaml #=> YAML

Table 12 (hPa)

Note
 This corresponds to ISO 2533:1975/ADD 1:1985 Table 5 but in geometric altitude.

Title: "Barometric pressure, in hectopascals, as a function of geometric altitude for -1000 ⇐ H < +4600 m at intervals of 1m"

Provides:

  • geometric-altitude-m

  • pressure-mbar

  • pressure-mmhg

Range of (-1000..4599).step(1).

Atmospheric::Export::Iso25332024.table_12      #=> Hash
Atmospheric::Export::Iso25332024.table_12_yaml #=> YAML

Table 13 (hPa)

Note
 This corresponds to ISO 2533:1975/ADD 1:1985 Table 5, in geopotential altitude.

Title: "Barometric pressure, in hectopascals, as a function of geopotential altitude for -1000 ⇐ H < +4600 m at intervals of 1m"

Provides:

  • geopotential-altitude-m

  • pressure-mbar

  • pressure-mmhg

Range of (-1000..4599).step(1).

Atmospheric::Export::Iso25332024.table_13      #=> Hash
Atmospheric::Export::Iso25332024.table_13_yaml #=> YAML

Testing

$ rspec

Tests are encoded in spec/fixtures/tests.yml in the following format:

- H: -2000.0
  h: -1999.0
  TK: 301.15
  TC: 28.0
  p_mbar: 1277.74
  p_mmhg: 958.382
  rho: 1.47808
  g: 9.8128
  p_p_n: 1.26103
  rho_rho_n: 1.20659
  root_rho_rho_n: 1.09845
  a: 347.886
  mu: 1.8514e-05
  v: 1.2526e-05
  lambda: 0.026359
  H_p: 8809.5
  gamma: 14.504
  n: 3.0734e+25
  v_bar: 469.18
  omega: 8535100000.0
  l: 549710000.0

Each of these values are associated with a cell in the tables of the source documents.

The only defining value in a tests is H (geopotential altitude). It is used to generate all the other values.

License

Copyright Ribose.

TODO

  • expose this as a plugin to LutaML / Metanorma YAML2text