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Atmostropic · US76

US76 implementation verification

First, verify the Dart reference against published NASA US76 data. Then compare each language port with that reference. AtmostropicRef denotes the executed Dart reference in both sections.

Verification data

U.S. Standard Atmosphere, 1976, jointly published by NASA, NOAA and the United States Air Force in October 1976. Report identifiers: NASA-TM-X-74335 and NOAA-S/T-76-1562; NASA NTRS record 19770009539.

The source CSV retains 85 independently published model rows from sea level to 84,000 m, at 1,000 m geometric-altitude intervals. Table I supplies temperature, pressure, density and geopotential altitude; Table III supplies sound speed and both viscosities. Published rounding is retained.

Verification source data (CSV)Original NASA source

Publication edition: US76 · October 1976
PDF retrieval / CSV extraction: 8 September 2026
Report assembled (UTC): 2026-09-09 18:03:05 UTC

Table I: printed pp. 53–67, odd-numbered pages. Table III: printed pp. 101–115, odd-numbered pages. Exact page references are retained in the CSV. NASA data are held fixed and are not downloaded or updated during report generation.

Calculation timestamps, fingerprints and retained data

AtmostropicRef computed 2026-09-09T11:40:27Z · retained calculation data
Dependency fingerprint: a0cb226cda433fcf463750099f907b9a8a243b4e7769a16dc49bbb9637494003

JavaScript computed 2026-09-09T18:00:35Z · retained calculation data
Dependency fingerprint: 32fae51429ade0b816db5a641eff2da1eeec1dfc1e6071228a535372fb9e4d74

Java computed 2026-09-09T18:02:33Z · retained calculation data
Dependency fingerprint: 470bb05f0279b3f0189c218da72b3fefa5bfd93432811f66f1842c16f0df0a05

C# computed 2026-09-09T18:03:04Z · retained calculation data
Dependency fingerprint: 24eefeb0ffdc5e03512a15bf386c057b5cfbe9546180e56ba064f6dbe23a573b

Python computed 2026-09-09T18:03:04Z · retained calculation data
Dependency fingerprint: 7b5fabdc6353a995846964d7ab9af5d9f80b32c9d27f7d85803221c3066d4c3c

TypeScript computed 2026-09-09T18:03:04Z · retained calculation data
Dependency fingerprint: 14b3a68675047d6e3e1c8fb00ea1e020af76bfc2f2531ea7c0b4b4d520ddcab6

CSV SHA-256: 87046a41fc10f29391ba192c2eefc3eb0557b7cf2025bd900337797a2f01bb5b
NASA PDF SHA-256: 23eb6b68346d4abc6071fc598872d51c40cf8c613d1a5d1006c6261bcd09dcea

Retained differences and summary metrics · Canonical verification method

Comparison method

The blue curve in every chart connects actual Dart reference calculations every 100 m. Open markers show values at the 85 source altitudes, with no interpolation. Reference-versus-NASA statistics use those 85 altitudes. Port-versus-reference statistics use all 841 calculated altitudes, including points between NASA samples.

Axes retain the original tables’ metric units: m, K, mbar, kg/m³, m/s, N·s/m² and m²/s. Calculated pressure is converted from Pa to mbar by dividing by 100; N·s/m² equals Pa·s. Geometric altitude is the common input, so it is not plotted against itself.

Differences are Dart minus NASA in the first section and each port minus Dart in the second. Relative differences divide by the comparison reference; the zero-altitude geopotential relative difference is undefined (n/a). No acceptance tolerance is assigned. Pressure, density and kinematic viscosity offer logarithmic and linear scales.

Reference verification: AtmostropicRef vs NASA

Dart reference: blue curve. NASA verification data: orange open circles.

Ambient temperature

Linear axes

AtmostropicRefNASA US76

Ambient temperature, linear vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **0.00519988 K** at 83,000 m; max relative difference **0.00269717%** at 83,000 m.

Ambient pressure

Y-axis scale

AtmostropicRefNASA US76

Ambient pressure, log vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **0.00615474 mbar** at 16,000 m; max relative difference **0.0632909%** at 72,000 m.

Ambient pressure, linear vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **0.00615474 mbar** at 16,000 m; max relative difference **0.0632909%** at 72,000 m.

Air density

Y-axis scale

AtmostropicRefNASA US76

Air density, log vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **3.87659e-05 kg/m³** at 2,000 m; max relative difference **0.0634381%** at 72,000 m.

Air density, linear vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **3.87659e-05 kg/m³** at 2,000 m; max relative difference **0.0634381%** at 72,000 m.

Speed of sound

Linear axes

AtmostropicRefNASA US76

Speed of sound, linear vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **0.00897785 m/s** at 68,000 m; max relative difference **0.00298516%** at 68,000 m.

Dynamic viscosity

Linear axes

AtmostropicRefNASA US76

Dynamic viscosity, linear vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **6.90533e-09 N·s/m²** at 43,000 m; max relative difference **0.0420211%** at 43,000 m.

Kinematic viscosity

Y-axis scale

AtmostropicRefNASA US76

Kinematic viscosity, log vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **0.000172133 m²/s** at 83,000 m; max relative difference **0.0636492%** at 70,000 m.

Kinematic viscosity, linear vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **0.000172133 m²/s** at 83,000 m; max relative difference **0.0636492%** at 70,000 m.

Geopotential altitude

Linear axes

AtmostropicRefNASA US76

Geopotential altitude, linear vertical axis. AtmostropicRef is the blue curve; scatter overlays: NASA US76. — **AtmostropicRef − NASA**: max absolute difference **2.89388 m** at 84,000 m; max relative difference **0.0186269%** at 2,000 m.

Language verification: ports vs AtmostropicRef

The blue curve remains the Dart reference. Each included port has a distinct open marker and color. Currently included: JavaScript, Java, C#, Python, TypeScript. Overlapping markers indicate close agreement; the numerical summaries expose differences too small to see at this scale.

Partial language coverage. Not executed or plotted in this report: C++, C, Ruby, Rust, Go. Local toolchains unavailable; execution remains pending. Verification for these ports remains pending.