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

Purpose

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

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 standards but different in presentation and units (the ICAO document includes ft in addition to m).

This library serves as a reference implementation for the values defined in ISO CD 2533:2025.

Usage

General

This library contains code for two separate, but related, purposes.

Calculating atmospheric properties at different altitudes. The algorithms are based on ISO 2533.
Generating tables of atmospheric properties at different altitudes. This library is used to data tables provided by the full ISO 2533 series:
- ISO 2533:1975
- ISO 2533:1975/ADD 1:1985
- ISO 2533:1975/ADD 2:1997
- ISO CD 2533:2025

For the typical user who wishes to calculate atmospheric properties, there is no need to worry about how the tables work.

To calculate atmospheric properties, either use the formulas directly or use the Atmospheric::Export::AltitudeAttrs class to bulk obtain the values needed.

Prerequisites

Include the atmospheric gem in your Gemfile:

gem 'atmospheric'

Then use require in code:

require 'atmospheric'

Atmospheric attributes by altitude

The Atmospheric::Export::AltitudeAttrs class provides a way to obtain the atmospheric properties at a particular given altitude, geopotential or geometric.

The resulting object can also be easily serialized, courtesy of the lutaml-model library.

Syntax:

require 'atmospheric'

Atmospheric::Export::AltitudeAttrs.new.set_altitude(
  value: {altitude-value} (1)
  type: {altitude-type} (2)
  unit: {altitude-unit} <3>,
  precision: {precision-mode} (4)
)

Value of the altitude desired. Integer.
Type of altitude. Symbol. One of :geometric, :geopotential.
Unit of the altitude. Symbol. One of :meters, :feet.
Precision mode. Symbol. One of :normal, :high, :reduced. Default is :normal.

Each attribute of the AltitudeAttrs object is wrapped in a defined data class which is associated with a UnitsML unit.

Behavior of the precision mode:

:reduced: (default) Uses Isa::NormalPrecision for calculations with signficant digits rounding according to the original ISO 2533 specification.
:normal: Uses Isa::NormalPrecision for calculations without value modification.
:high: Uses Isa::HighPrecision for calculations without value modifications. This mode uses BigDecimal.

Depending on the type of the value, it is in one of the following classes:

Integer. Class: UnitValueInteger
Float. Class: UnitValueFloat

The AltitudeAttrs object provides the following attributes:

All attributes are represented as collections (arrays) to support multiple units:

geometric_altitudes: Array of geometric altitude values. Units: m, ft.
geopotential_altitudes: Array of geopotential altitude values. Units: m, ft.
temperatures: Array of temperature values. Units: K, degC.
pressures: Array of pressure values. Units: mbar, mm_Hg.
densities: Array of density values. Units: kg*m^-3.
accelerations: Array of acceleration values. Units: m*s^-2.
ppns: Array of pressure ratio values (unitless).
rhorhons: Array of density ratio values (unitless).
sqrt_rhorhons: Array of sqrt of density ratio values (unitless).
speeds_of_sound: Array of speed of sound values. Units: m*s^-1.
dynamic_viscosities: Array of dynamic viscosity values. Units: Pa*s.
kinematic_viscosities: Array of kinematic viscosity values. Units: m^2*s-1.
thermal_conductivities: Array of thermal conductivity values. Units: W*m^-1*K-1.
pressure_scale_heights: Array of pressure scale height values. Units: m.
specific_weights: Array of specific weight values. Units: N*m^-3.
air_number_densities: Array of air number density values. Units: m^-3.
mean_speeds: Array of mean speed values. Units: m*s^-1.
frequencies: Array of frequency values. Units: s^-1.
mean_free_paths: Array of mean free path values. Units: m.

Each attribute value is wrapped in UnitValueFloat or UnitValueInteger with UnitsML unit metadata.

require 'atmospheric'
attrs = Atmospheric::Export::AltitudeAttrs.new.set_altitude(
  value: -2000,
  type: :geopotential,
  unit: :meters
)

# Access collection values
attrs.geometric_altitudes[0].value  #=> -1999 (meters)
attrs.geometric_altitudes[1].value  #=> -6560 (feet)
attrs.geopotential_altitudes[0].value #=> -2000 (meters)
attrs.geopotential_altitudes[1].value #=> -6562 (feet)
attrs.temperatures[0].value           #=> 301.15 (Kelvin)
attrs.temperatures[1].value           #=> 28.0 (Celsius)
attrs.pressures[0].value             #=> 1277.74 (mbar)
attrs.pressures[1].value             #=> 958.382 (mm_Hg)

The object can be serialized into YAML or XML.

Example 1. AltitudeAttrs in YAML

attrs = Atmospheric::Export::AltitudeAttrs.new.set_altitude(
  value: -2000,
  type: :geopotential,
  unit: :meters
)

attrs.to_yaml

geometric-altitude:
- value: -1999
  unitsml: m
  type: integer
- value: -6560
  unitsml: ft
  type: integer
geopotential-altitude:
- value: -2000
  unitsml: m
  type: integer
- value: -6562
  unitsml: ft
  type: integer
temperature:
- value: 301.15
  unitsml: K
  type: float
- value: 28.0
  unitsml: degC
  type: float
pressure:
- value: 1277.74
  unitsml: mbar
  type: float
- value: 958.382
  unitsml: mm_Hg
  type: float
density:
- value: 1.47808
  unitsml: kg*m^-3
  type: float
acceleration:
- value: 9.8128
  unitsml: m*s^-2
  type: float
ppn:
- value: 1.26103
  type: float
rhorhon:
- value: 1.20659
  type: float
sqrt-rhorhon:
- value: 1.09845
  type: float
speed-of-sound:
- value: 347.886
  unitsml: m*s^-1
  type: float
dynamic-viscosity:
- value: 1.8514e-05
  unitsml: Pa*s
  type: float
kinematic-viscosity:
- value: 1.2526e-05
  unitsml: m^2*s^-1
  type: float
thermal-conductivity:
- value: 0.026359
  unitsml: W*m^-1*K^-1
  type: float
pressure-scale-height:
- value: 8809.5
  unitsml: m
  type: float
specific-weight:
- value: 14.504
  unitsml: N*m^-3
  type: float
air-number-density:
- value: 3.0734e+25
  unitsml: m^-3
  type: float
mean-speed:
- value: 469.18
  unitsml: m*s^-1
  type: float
frequency:
- value: 8535100000.0
  unitsml: s^-1
  type: float
mean-free-path:
- value: 5.4971e-08
  unitsml: m
  type: float
precision: reduced

Example 2. AltitudeAttrs in XML

attrs = Atmospheric::Export::AltitudeAttrs.new.set_altitude(
  value: -2000,
  type: :geopotential,
  unit: :meters
)

attrs.to_xml

<atmosphere-attributes>
  <geometric-altitude unitsml="m" type="integer">-1999</geometric-altitude>
  <geometric-altitude unitsml="ft" type="integer">-6560</geometric-altitude>
  <geopotential-altitude unitsml="m" type="integer">-2000</geopotential-altitude>
  <geopotential-altitude unitsml="ft" type="integer">-6562</geopotential-altitude>
  <temperature unitsml="K" type="float">301.15</temperature>
  <temperature unitsml="degC" type="float">28.0</temperature>
  <pressure unitsml="mbar" type="float">1277.74</pressure>
  <pressure unitsml="mm_Hg" type="float">958.382</pressure>
  <density unitsml="kg*m^-3" type="float">1.47808</density>
  <acceleration unitsml="m*s^-2" type="float">9.8128</acceleration>
  <ppn type="float">1.26103</ppn>
  <rhorhon type="float">1.20659</rhorhon>
  <sqrt-rhorhon type="float">1.09845</sqrt-rhorhon>
  <speed-of-sound unitsml="m*s^-1" type="float">347.886</speed-of-sound>
  <dynamic-viscosity unitsml="Pa*s" type="float">1.8514e-05</dynamic-viscosity>
  <kinematic-viscosity unitsml="m^2*s^-1" type="float">1.2526e-05</kinematic-viscosity>
  <thermal-conductivity unitsml="W*m^-1*K^-1" type="float">0.026359</thermal-conductivity>
  <pressure-scale-height unitsml="m" type="float">8809.5</pressure-scale-height>
  <specific-weight unitsml="N*m^-3" type="float">14.504</specific-weight>
  <air-number-density unitsml="m^-3" type="float">3.0734e+25</air-number-density>
  <mean-speed unitsml="m*s^-1" type="float">469.18</mean-speed>
  <frequency unitsml="s^-1" type="float">8535100000.0</frequency>
  <mean-free-path unitsml="m" type="float">5.4971e-08</mean-free-path>
  <precision>reduced</precision>
</atmosphere-attributes>

Altitude by pressure

The Atmospheric::Export::PressureAttrs class provides a way to obtain the altitude at a given pressure value (mbar, mmhg).

Syntax:

require 'atmospheric'

Atmospheric::Export::PressureAttrs.new.set_pressure(
  value: {pressure-value}, (1)
  unit: {pressure-unit}, (2)
  precision: {precision-mode} (3)
)

Value of the pressure desired. Float.
Unit of the pressure. Symbol. One of :mbar, :mmhg.

Note	The `set_pressure` method does not yet support high-precision mode.

Behavior of the precision mode:

:reduced: (default) Uses Isa::NormalPrecision for calculations with signficant digits rounding according to the original ISO 2533/ADD 2 specification.
:normal: Uses Isa::NormalPrecision for calculations without value modification.
:high: Uses Isa::HighPrecision for calculations without value modifications. This mode uses BigDecimal.

Each attribute of the PressureAttrs object is wrapped in a defined data class which is associated with a UnitsML unit.

Depending on the type of the value, it is in one of the following classes:

Integer. Class: UnitValueInteger
Float. Class: UnitValueFloat

The PressureAttrs object provides the following attributes:

All attributes are represented as collections (arrays) to support multiple units:

pressures: Array of pressure values. Units: mbar, mm_Hg.
geometric_altitudes: Array of geometric altitude values. Units: m, ft.
geopotential_altitudes: Array of geopotential altitude values. Units: m, ft.

attrs = Atmospheric::Export::PressureAttrs.new.set_pressure(
  value: 5.0,
  unit: :mbar
)

# Access collection values
attrs.pressures[0].value           #=> 5.0 (mbar)
attrs.pressures[1].value           #=> 3.7503084135 (mm_Hg)
attrs.geopotential_altitudes[0].value #=> 35776.5 (meters)
attrs.geopotential_altitudes[1].value #=> 117377.0 (feet)
attrs.geometric_altitudes[0].value #=> 35979.0 (meters)
attrs.geometric_altitudes[1].value #=> 118041.0 (feet)

The object can be serialized into YAML or XML.

Example 3. PressureAttrs in YAML

attrs = Atmospheric::Export::PressureAttrs.new.set_pressure(
  value: 5.0,
  unit: :mbar
)

attrs.to_yaml

pressure:
- value: 5.0
  unitsml: mbar
  type: float
- value: 3.7503084135
  unitsml: mm_Hg
  type: float
geopotential-altitude:
- value: 35776.5
  unitsml: m
  type: float
- value: 117377.0
  unitsml: ft
  type: float
geometric-altitude:
- value: 35979.0
  unitsml: m
  type: float
- value: 118041.0
  unitsml: ft
  type: float

Example 4. PressureAttrs in XML

attrs = Atmospheric::Export::PressureAttrs.new.set_pressure(
  value: 5.0,
  unit: :mbar
)

attrs.to_xml

<hypsometrical-attributes>
  <pressure unitsml="mbar" type="float">5.0</pressure>
  <pressure unitsml="mm_Hg" type="float">3.7503084135</pressure>
  <geometric-altitude unitsml="m" type="float">35979</geometric-altitude>
  <geometric-altitude unitsml="ft" type="float">118041</geometric-altitude>
  <geopotential-altitude unitsml="m" type="float">35776</geopotential-altitude>
  <geopotential-altitude unitsml="ft" type="float">117377</geopotential-altitude>
</hypsometrical-attributes>

Algorithms

General

For users who wish to access the algorithms directly, the Atmospheric::Isa::Algorithms class provides a set of methods for calculating atmospheric properties at different altitudes.

ISO 2533 specifies a number of formulas for the calculation of atmospheric properties at different altitudes.

These algorithms are implemented in the Atmospheric::Isa::Algorithms class.

There are two ways to use the Atmospheric::Isa::Algorithms class:

as a singleton class, using one of the precision modes (see below)
as a class instance

require 'atmospheric'
# Singleton class
instance = Atmospheric::Isa::NormalPrecision.instance.instance
instance.geometric_altitude_from_geopotential(100).to_f
=> 100.00157315171192

# Class instance
instance = Atmospheric::Isa::Algorithms.new(precision: :high)
instance.geometric_altitude_from_geopotential(100).to_f
=> 100.00157315171192

Formulas and calculations

The Algorithms class supports the following methods for calculating atmospheric properties.

Syntax:

require 'atmospheric'
instance = Atmospheric::Isa::Algorithms.new.{method_name} (1)

method_name is one of the methods listed below.

The available methods are:

Converting between geometric and geopotential altitudes:

geometric_altitude_from_geopotential(geopotential_altitude)
geopotential_altitude_from_geometric(geometric_altitude)

Obtaining the temperature value from an altitude:

temperature_at_layer_from_geopotential(geopotential_altitude) (Kelvin)
temperature_at_layer_celcius(geopotential_altitude) (Celcius)

Obtaining the pressure value from an altitude:

pressure_from_geopotential_mbar(geopotential_altitude) (mbar/hPa)
pressure_from_geopotential_mmhg(geopotential_altitude) (mmHg)

Obtaining other atmospheric properties from an 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)

Obtaining thermal conductivity from temperature:

thermal_conductivity_from_temp(temp)

Obtaining geopotential altitude from a given pressure:

geopotential_altitude_from_pressure_mbar(mbar)
geopotential_altitude_from_pressure_mmhg(mmhg)

Precision modes

There are two precision modes available for calculations.

High precision mode: Uses more accurate constants and number calculations through Ruby’s BigDecimal to provide results with higher precision. Suitable for applications where the utmost accuracy is required.
Normal precision mode (default): Uses standard constants and number calculations to provide results with sufficient accuracy for most applications.

To use the high precision mode, you can either:

use the Atmospheric::Isa::HighPrecision class
use the Atmospheric::Isa::Algorithms class then call the set_precision(:high) method

require 'atmospheric'

# High precision mode
high_precision_instance = Atmospheric::Isa::HighPrecision.instance

speed_h = Atmospheric::Isa::HighPrecision.instance.speed_of_sound_from_temp(100)
=> 0.200467958523516054299360531511514627125051490111885121917578012786288944852326625441743718038552367514555018117e3

speed_h.class
=> BigDecimal

# Normal precision mode (default)
normal_precision_instance = Atmospheric::Isa::NormalPrecision.instance.instance

speed_n = Atmospheric::Isa::NormalPrecision.instance.instance.speed_of_sound_from_temp(100)
=> 200.46795852351607

speed_n.class
=> Float

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 as collections (arrays) with UnitsML unit metadata:

geometric-altitude (collection: m, ft)
geopotential-altitude (collection: m, 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 geometric altitude (h) and geopotential altitude (H)"

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

temperature (collection: K, degC)
pressure (collection: mbar, mm_Hg)
density
acceleration

Atmospheric::Export::Iso25331975.table_5         #=> Lutaml::Model
Atmospheric::Export::Iso25331975.table_5.to_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 geometric 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         #=> Lutaml::Model
Atmospheric::Export::Iso25331975.table_6.to_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 geometric 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         #=> Lutaml::Model
Atmospheric::Export::Iso25331975.table_7.to_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 (collection: mbar, mm_Hg)
geopotential-altitude

Atmospheric::Export::Iso25331985.table_1         #=> Lutaml::Model
Atmospheric::Export::Iso25331985.table_1.to_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         #=> Lutaml::Model
Atmospheric::Export::Iso25331985.table_2.to_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 (collection: mbar, mm_Hg)
geopotential-altitude

Atmospheric::Export::Iso25331985.table_3         #=> Lutaml::Model
Atmospheric::Export::Iso25331985.table_3.to_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         #=> Lutaml::Model
Atmospheric::Export::Iso25331985.table_4.to_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 (collection: mbar, mm_Hg)

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

Atmospheric::Export::Iso25331985.table_56         #=> Lutaml::Model
Atmospheric::Export::Iso25331985.table_56.to_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 geometric 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         #=> Lutaml::Model
Atmospheric::Export::Iso25331997.table_1.to_yaml #=> YAML

Table 2 (-5km to 2km)

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

Atmospheric::Export::Iso25331997.table_2         #=> Lutaml::Model
Atmospheric::Export::Iso25331997.table_2.to_yaml #=> YAML

Table 3 (-5km to 2km)

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

Atmospheric::Export::Iso25331997.table_3         #=> Lutaml::Model
Atmospheric::Export::Iso25331997.table_3.to_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 geometric 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         #=> Lutaml::Model
Atmospheric::Export::Iso25331997.table_4.to_yaml #=> YAML

Table 5 (-16.5kft to 262.5kft)

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

Atmospheric::Export::Iso25331997.table_5         #=> Lutaml::Model
Atmospheric::Export::Iso25331997.table_5.to_yaml #=> YAML

Table 6 (-16.5kft to 262.5kft)

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

Atmospheric::Export::Iso25331997.table_6         #=> Lutaml::Model
Atmospheric::Export::Iso25331997.table_6.to_yaml #=> YAML

ISO 2533:2025

General

ISO 2533 is now being revised targeting a 2025 publication, which will be 50 years since the last edition (1975) and 28 years since it was last updated (1997).

It is currently in the CD stage (Committee Draft) and is expected to be published in 2025.

ISO NP 2533:2024. approved in 2024.
ISO WD 2533:2024. launched: 2024-11-22, closed: 2025-02-17.
ISO CD 2533:2024. pending.

ISO 2533:2025 covers 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 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

The Iso25332025 class provides the following methods to generate tables:

table_atmosphere_meters

Atmosphere attributes by altitude (m). Grouped by by-geopotential-altitude and by-geometric-altitude. Each entry underneath is an AltitudeAttrs object. The altitude interval values follow these steps:

Step 50 from -5k, 100 from 32k, 200 from 51k to 80k.

(-5000..31950).step(50) +
(32000..50900).step(100) +
(51000..80000).step(200)

table_atmosphere_feet

Atmosphere attributes by altitude (ft). Grouped by by-geopotential-altitude and by-geometric-altitude. Each entry underneath is an AltitudeAttrs object. The altitude interval values follow these steps:

Step 250 from -16500, 200 from -14000, 500 from 105000 to 262500

(-16500..-13750).step(250) +
(-14000..104800).step(200) +
(105000..262500).step(500)

table_hypsometrical_altitude

Atmosphere attributes by altitude (m). This is the same as table_atmosphere_meters except with a modified step.

Step 1 from -1000 to 4599

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

table_hypsometrical_mbar

Hypsometrical table by pressure (mbar). This is a table that provides altitude values per unit of pressure. Each entry underneath is a PressureAttrs object. It follows this step schedule:

Step 0.01 from 5 to 20, 0.1 from 20 to 1770.9

(5.0..19.99).step(0.01) +
(20.0..1770.9).step(0.1)

Example 5. Generating the ISO 2533:2025 tables

# Defaults to precision mode `:reduced`
Atmospheric::Export::Iso25332025.table_atmosphere_meters #=> Lutaml::Model
Atmospheric::Export::Iso25332025.table_atmosphere_meters.to_yaml #=> YAML

# To use precision mode `:high`
x = Atmospheric::Export::Iso25332025.table_atmosphere_meters(precision: :high)
x.to_yaml #=> YAML

The above table methods are used as the data sources for the data tables in ISO 2533:2025:

table_atmosphere_meters: Table 5 (meters), Table 6 (meters), Table 7 (meters). This data table is split into 3 tables for readability reasons.
table_atmosphere_feet: Table 8 (feet), Table 9 (feet), Table 10 (feet). Similarly, this data table is split into 3 tables for readability reasons.
table_hypsometrical_altitude: Table 11 (mbar).
table_hypsometrical_mbar: Table 12 (geopotential), Table 13 (geometric).

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 geometric altitude (h) and geopotential altitude (H)"

This table is a subset of the table_atmosphere_meters method.

Table 6 (meters)

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

This table is a subset of the table_atmosphere_meters method.

Table 7 (meters)

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

This table is a subset of the table_atmosphere_meters method.

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 geometric 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.

This table is a subset of the table_atmosphere_feet method.

Table 9 (-16.5kft to 262.5kft)

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

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

This table is a subset of the table_atmosphere_feet method.

Table 10 (-16.5kft to 262.5kft)

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

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

This table is a subset of the table_atmosphere_feet method.

Table 11 (mbar)

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 (collection: mbar, mm_Hg)
geopotential-altitude (collection: m, ft)
geometric-altitude (collection: m, ft)

# Defaults to precision mode `:reduced`
Atmospheric::Export::Iso25332025.table_hypsometrical_mbar         #=> Lutaml::Model
Atmospheric::Export::Iso25332025.table_hypsometrical_mbar.to_yaml #=> YAML

# To use precision mode `:high`
x = Atmospheric::Export::Iso25332025.table_hypsometrical_mbar(precision: :high)
x.to_yaml #=> YAML

Table 12 (geopotential altitude, m)

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

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

This table is a subset of the table_atmosphere_meters method.

Table 13 (geometric altitude, m)

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

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

This table is a subset of the table_atmosphere_meters method.

XML Schema

An XSD schema for the XML serialization format is provided at schema/atmospheric.xsd.

The schema defines the following root elements:

atmospheric

Polymorphic root element. Two variants:

Hypsometrical table: contains <hypsometrical-attributes> records (pressure → altitude lookup).
ISO 2533:2025 table: contains <by-geometric-altitude> and <by-geopotential-altitude> sections, each with <atmospheric-attributes> records.

<!-- Hypsometrical table variant -->
<atmospheric>
  <hypsometrical-attributes>
    <pressure unitsml="mbar" type="float">1013.25</pressure>
    <pressure unitsml="mm_Hg" type="float">760.0</pressure>
    <geometric-altitude unitsml="m" type="float">0.0</geometric-altitude>
    <geometric-altitude unitsml="ft" type="float">0.0</geometric-altitude>
    <geopotential-altitude unitsml="m" type="float">0.0</geopotential-altitude>
    <geopotential-altitude unitsml="ft" type="float">0.0</geopotential-altitude>
  </hypsometrical-attributes>
</atmospheric>

<!-- ISO 2533:2025 table variant -->
<atmospheric>
  <by-geometric-altitude>
    <atmospheric-attributes>...</atmospheric-attributes>
  </by-geometric-altitude>
  <by-geopotential-altitude>
    <atmospheric-attributes>...</atmospheric-attributes>
  </by-geopotential-altitude>
</atmospheric>

atmosphere-attributes

Full atmospheric property record (ISO 2533:2025). Contains all altitude, temperature, pressure, density, and derived properties.

hypsometrical-attributes

Pressure-to-altitude record. Contains pressure and altitude values.

group-one-attrs

ISO 2533:1975 Group One record (temperature, pressure, density, acceleration). Temperature values use integer type (scaled by 1000).

attributes-group

Wrapper for a collection of <atmospheric-attributes>.

All value elements share a common pattern:

Text content: the numeric value
unitsml attribute (optional): the UnitsML unit identifier (e.g., m, ft, K, mbar)
type attribute (required): either "float" or "integer"

<temperature unitsml="K" type="float">288.15</temperature>
<geometric-altitude unitsml="m" type="integer">5000</geometric-altitude>
<ppn type="float">0.53338</ppn>  <!-- dimensionless, no unitsml -->

Testing

General

$ bundle exec rake

Re-generate fixture tables

The spec/fixtures/iso* directories contains YAML files that are used to generate the ISO 2533 tables.

To re-generate the tables, run:

$ bundle exec rake clean generate

These tasks are defined in the Rakefile.

Algorithms

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.

atmospheric

Runtime

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

Purpose

Usage

General

Prerequisites

Atmospheric attributes by altitude

Altitude by pressure

Algorithms

General

Formulas and calculations

Precision modes

Generating ISO 2533 tables

ISO 2533:1975

Table 5

Table 6

Table 7

ISO 2533 ADD 1:1985

Table 1 (hPa)

Table 2 (hPa)

Table 3 (mmHg)

Table 4 (mmHg)

Table 5 (hPa) and Table 6 (mmHg)

ISO 2533 ADD 2:1997

Table 1 (-5km to 2km)

Table 2 (-5km to 2km)

Table 3 (-5km to 2km)

Table 4 (-16.5kft to 262.5kft)

Table 5 (-16.5kft to 262.5kft)

Table 6 (-16.5kft to 262.5kft)

ISO 2533:2025

General

Table 5 (meters)

Table 6 (meters)

Table 7 (meters)

Table 8 (-16.5kft to 262.5kft)

Table 9 (-16.5kft to 262.5kft)

Table 10 (-16.5kft to 262.5kft)

Table 11 (mbar)

Table 12 (geopotential altitude, m)

Table 13 (geometric altitude, m)

XML Schema

Testing

General

Re-generate fixture tables

Algorithms

Copyright and license