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35,000 ft at 250 knots calibrated airspeed: the 1976 standard atmosphere and the airspeed chain of NACA Report 837

Tool	Standard Atmosphere and Airspeeds
Source	National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, and United States Air Force (1976). U.S. Standard Atmosphere, 1976. NOAA-S/T 76-1562 (NASA TM X-74335), U.S. Government Printing Office, Washington, DC. Tables I, III and IV; Aiken, W. S., Jr. (1946). Standard Nomenclature for Airspeeds With Tables and Charts for Use in Calculation of Airspeed. NACA Report 837, eqs. (1), (2), (6), (9)–(14) and Table II.
Level	Undergraduate

Problem

An airplane flies at 35,000 ft geometric altitude on a standard day with 250 knots calibrated airspeed. Find the temperature, pressure, density, speed of sound and viscosity of the air from the 1976 U.S. Standard Atmosphere, then the impact pressure the indicator senses, the Mach number, the true and equivalent airspeeds, the compressibility correction, the dynamic pressure and the Reynolds number per foot.

Inputs to Enter

Altitude 35,000 ft, ISA + 0; airspeed given as CAS = 250 knots; reference length 1 ft

Open the Standard Atmosphere and Airspeeds tool (loaded with this example)

Answers

Geopotential altitude H = r₀h/(r₀ + h) = 34,941 ft (10,650.1 m); troposphere, T = 288.15 − 0.0065 H = 218.924 K (−65.6 °F), the standard's Table IV row 35,000 ft: 218.924 K
p = p₀ (T/T₀)^5.2559 = 23,908.9 Pa = 499.35 lb/ft² (Table IV: 2.3908 × 10² mb, p/p₀ 0.23596); ρ = p/(RT) = 0.38046 kg/m³ = 0.0007382 slug/ft³ (Table IV: 0.38046, ρ/ρ₀ 0.31058)
a = √(γRT) = 296.61 m/s = 576.57 kt; Sutherland μ = 1.4341 × 10⁻⁵ Pa·s, ν = 3.7694 × 10⁻⁵ m²/s
q_c = p₀[(1 + 0.2 (V_c/a₀)²)^3.5 − 1] = 219.26 lb/ft² (Report 837 Table II: 219.6 with its 1925 constants); M = √(5[(q_c/p + 1)^(2/7) − 1]) = 0.7403
TAS = M a = 426.83 kt; EAS = TAS √σ = a₀ M √δ = 237.87 kt; compressibility correction EAS − CAS = −12.13 kt; q = 0.7 p M² = 191.56 lb/ft²
Re/L = TAS/ν = 1.7756 × 10⁶ per foot; total temperature T(1 + 0.2 M²) = 242.92 K

Notes

The tool's default inputs are this case; press Submit. The atmosphere values reproduce every printed digit of the standard's Tables I, III and IV at the rows read (test_standard_atmosphere.php, 218 checks; References/Standard-Atmosphere/checks/atmos_check.py in numpy gives the same chain). Switching to SI gives 10,668 m, 23,908.9 Pa, 0.38046 kg/m³, 296.61 m/s and the same knots.