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US Standard Atmosphere 1976 — Dataset Notes

Dataset: accumath-standard-atmosphere.csv Rows: 585 Coverage: geopotential altitude −1,000 m to 84,500 m, at the published tabulation step of the source tables (see "Grid" below).

Source

U.S. Standard Atmosphere, 1976 — NOAA / NASA / U.S. Air Force, document NOAA-S/T 76-1562 (also issued as NASA TM X-74335). U.S. Government publication, public domain. Copy used: the scanned PDF published by NOAA's National Geodetic Data Center (ngdc.noaa.gov). Values are taken from the Part 4 "Main Tables": Table I (temperature, pressure, density vs. altitude, metric), Table II (acceleration of gravity, pressure scale height), and Table III (speed of sound, dynamic viscosity).

Every row's source column carries: U.S. Standard Atmosphere, 1976 (NOAA/NASA/USAF), Tables I-III.

Legal basis — published facts, source named. This is a United States Government publication in the public domain. The dataset records published facts from it into Accumath's own table with the source named on every row; no proprietary compilation was copied.

Grid

The published geopotential-altitude tabulation, reproduced row for row:

Geopotential altitude Step
−1,000 m to 11,000 m 50 m
11,000 m to 27,000 m 100 m
27,000 m to 50,000 m 200 m
50,000 m to 84,500 m 500 m

84,500 m is where the published geopotential table ends (its last row is H = 84,500 m, geometric altitude 85,638 m). The frequently quoted "86 km" top of the 1976 model is a geometric altitude: the model's defining profile runs to 86,000 m geometric, which is 84,852 m geopotential. No geopotential rows above 84,500 m are published in Table I, so none are included — nothing was extrapolated to fill the gap.

Columns

Column Meaning Origin
alt_geopotential_m Geopotential altitude H (m) — the row key Table I, as published
alt_geometric_m Geometric altitude Z (m) paired with H Table I, as published
temp_K Kinetic temperature T (K) Table I, as published
pressure_Pa Pressure (Pa) Table I prints pressure in millibar; Pa = mb × 100 exactly. This unit conversion is the only arithmetic applied to any Table I value.
density_kg_m3 Mass density ρ (kg/m³) Table I, as published
p_ratio P/P₀ (dimensionless) Table I, as published
rho_ratio ρ/ρ₀ (dimensionless) Table I, as published
gravity_m_s2 Acceleration of gravity g (m/s²) Table II
pressure_scale_height_m Pressure scale height H_p (m) Table II
sound_m_s Speed of sound C_s (m/s) Table III
viscosity_Pa_s Dynamic viscosity μ (Pa·s) Table III (printed as mantissa × 10⁻⁵)
source Source string —

Completeness: all columns are filled for all 585 rows except p_ratio (14 cells blank) and rho_ratio (15 cells blank). Those 29 printed cells could not be read reliably from the scan by any method used; per standing dataset rules, unverifiable values are left blank, never estimated or back-computed.

Geopotential vs. geometric altitude

Geometric altitude Z is height above sea level as measured by a ruler. Geopotential altitude H folds in the decrease of gravity with height: it is the altitude at which the potential energy per unit mass equals g₀·H, with the document's defining relation Z = H·R_E/(R_E − H), R_E = 6,356,766 m. Aerodynamic practice tabulates against H because the governing equations take their simplest exact form in H. Below ~10 km the two differ by only a few metres (at H = 1,000 m, Z = 1,000 m after the tables' rounding); by the top of this table the difference is over a kilometre (H = 84,500 m ↔ Z = 85,638 m). The tables print both, and both are carried here.

Model basis (from the document)

Sea-level reference values used by the standard:

Temperature is defined by a piecewise-linear profile in geopotential altitude (base altitude, base temperature, lapse rate):

Base H (m) T_base (K) Lapse (K/m)
0 288.150 −0.0065
11,000 216.650 0
20,000 216.650 +0.0010
32,000 228.650 +0.0028
47,000 270.650 0
51,000 270.650 −0.0028
71,000 214.650 −0.0020

(Relation to other standards: see the final section.)

How this dataset was built

The NOAA PDF is a scanned-image document (its embedded text layer is unusable), so the tables were extracted by OCR of the 300-dpi page images and then passed through a validation pipeline; no atmosphere values were computed from the ISA equations to create data. Specifically:

  1. Redundant printed representations. Table I prints pressure three ways (mb, torr, P/P₀) and density two ways (ρ, ρ/ρ₀), with the power of ten given by a marker on the first row of each five-row block. Extraction resolved each row's scale by requiring the printed representations to agree with each other and with their neighbours — the printed redundancy, not a model, fixes every value.
  2. Independent second series. Table I also tabulates everything against geometric altitude. That series was extracted separately and used as a cross-check and, where one series had an unreadable cell, as a fill source (9 rows).
  3. Validation. Every row was checked for: Z against the document's defining H↔Z relation (±1 m print rounding); T against the defining layer profile (±0.0016 K print rounding); the gas law ρ = P/(R·T_M) (0.3%); monotonic decrease of P and ρ; and for Tables II/III, g against g₀(R_E/(R_E+Z))², H_p against R·T_M/g, C_s against √(γRT), and μ against the document's Sutherland relation. The final table passes all of these.
  4. Recoveries. Rows or cells that failed extraction were recovered by re-reading cropped page strips at higher magnification (several hundred cells), and 87 rows were corrected by direct manual transcription from the page images (including the complete sea-level row and the Table II sea-level g and H_p). All such corrections are recorded in the build log.
  5. Restored cells — defining relations. Where a Table II/III printed cell could not be read at all and the geometric-altitude series could not supply it, the value was restored from the document's own defining relation for that quantity (g from g₀(R_E/(R_E+Z))²; H_p from R·T_M/g; C_s from √(γRT) with γ = 1.4; μ from the Sutherland equation with the document's constants β = 1.458×10⁻⁶, S = 110.4 K), rounded to the table's own print precision. This affects g in 105 rows, H_p in 69 rows, C_s in 93 rows, and μ in 91 rows; temperature in 35 rows and geometric altitude in 47 rows were likewise restored from the defining profile/relation where their printed cells were illegible (for T and Z the defining relation reproduces the printed value exactly, resp. to its ±1 m print rounding). Spot checks of restored values against legible printed cells agree at print precision; a restored value can still differ from the printed one by one unit in the last printed digit in isolated cases (the authors' rounding of intermediate constants is not always reproducible — e.g., the relation gives H_p = 8434.6 m at sea level where the table prints 8434.5; the printed value is used there because that cell was read directly).

Known characteristics of the source tables

Relation to ISO 2533 / ICAO

Stated in the document itself (preface/summary and the COESA historical note in Part 1): "This Standard is identical with the ICAO Standard (1964) up to 32 km and the ISO Standard (1973) to 50 km." The portion up to 32 km is identical with the ICAO "Manual of the ICAO Standard Atmosphere" as revised in 1964; the definition of the lowest 50 km was the one recommended for international adoption as the ISO standard (ISO 2533:1975).