Airspeed Conversion

Airspeed Conversion (cross-cutting/units-atmos/airspeed-conversion)

Use when the task is converting airspeeds through the compressibility-corrected air-data chain of a subsonic aircraft: calibrated airspeed from impact pressure, calibrated airspeed from true airspeed at altitude, true airspeed from calibrated airspeed at altitude (the compressible inversion through the local static pressure), equivalent airspeed from true airspeed and the density ratio, Mach number from calibrated or true airspeed, and impact pressure from Mach number or calibrated airspeed. This leaf implements the full qc -> CAS, CAS -> M -> TAS -> EAS chain in all directions, subsonic, in pure Python, stdlib only, with the ISA state leg computed internally. It pairs with cross-cutting/units-atmos/unit-conversion for unit factor handling and cross-cutting/units-atmos/isa-atmosphere for the standalone ISA state leaf.

Domain quick reference

• ISA state leg at altitude h (internal, same numbers as isa-atmosphere): troposphere below 11000 m: T = T0 - LAPSEh with T0 = 288.15 K, LAPSE = 0.0065 K/m; p = P0(T/T0)^(G0/(LAPSER)); rho = p/(RT); a = sqrt(GAMMART). Above the tropopause T = 216.65 K constant and p decays exponentially with the scale height R*T/G0. Sea level: P0 = 101325 Pa, rho0 = 1.225 kg/m3, A0 = 340.294 m/s, GAMMA = 1.4, R = 287.05287.
• Impact pressure from Mach: qc = p*((1 + 0.2*M^2)^3.5 - 1), the isentropic pitot relation, subsonic.
• Calibrated airspeed from qc: CAS = A0sqrt(5((qc/P0 + 1)^(2/7) - 1)), the airspeed-indicator compressibility correction evaluated at sea level.
• Mach from qc at altitude: M = sqrt(5*((qc/p + 1)^(1/3.5) - 1)). The inversion is non-unique past M = 1, so qc/p >= 0.8929 is rejected.
• True airspeed: TAS = M*a with the local speed of sound.
• Equivalent airspeed: EAS = TAS*sqrt(rho/rho0). At sea level the density ratio is 1 and 1/3.5 equals 2/7, so the whole chain collapses to the identity CAS = EAS = TAS.
• Knots: 1 kt = 0.514444 m/s (module constant KT_TO_MS).

Workflow

1. Fix the flight condition: pressure altitude in m and exactly one speed input among calibrated airspeed in kt, true airspeed in m/s, equivalent airspeed in kt, or Mach number.
2. Get the whole air-data set with airspeed_chain(altitude_m, cas_kt=..., tas_ms=..., eas_kt=..., mach=...): it returns the dict {altitude_m, p, rho, a, mach, cas_kt, eas_kt, tas_ms, qc_Pa} with every quantity filled by the appropriate chain leg. Exactly one speed input is required.
3. For a single leg, call the scalar functions directly: calibrated airspeed from measured qc with calibrated_from_impact_pressure(qc).
4. Calibrated from a true airspeed at altitude (the step no unit table owns): calibrated_from_true_airspeed(tas_ms, altitude_m) runs the two-step chain M = TAS/a, qc = p*((1 + 0.2*M^2)^3.5 - 1), then the CAS calibration.
5. Inverse leg: true_from_calibrated(cas_ms, altitude_m) inverts the CAS formula algebraically to qc, then applies the subsonic qc inversion at the local static pressure and multiplies by the local speed of sound.
6. Density legs: equivalent_from_true(tas_ms, rho) and true_from_equivalent(eas_ms, rho) carry the sqrt(rho/rho0) factor; mach_from_true_airspeed(tas_ms, a) exposes the M = TAS/a arithmetic.
7. Confirm the deterministic checks with the contract test scripts/test_airspeed_conversion.py.

Worked example

• ISA 30,000 ft (9144 m): module isa_state returns T = 228.71 K, p = 30089.6 Pa (spec band 30089-30100), rho = 0.45831 kg/m3, a = 303.17 m/s.
• 250 KCAS at 30,000 ft: airspeed_chain(9144.0, cas_kt=250.0) returns qc = 10498.2 Pa (bound 10400-10600), M = 0.6681 (bound 0.66-0.68), TAS = 202.55 m/s = 393.73 kt (bound 200-205 m/s, 393-394 kt), EAS = 240.83 kt (bound 239-242 kt).
• M = 0.8 at the tropopause 11000 m (p = 22632.0 Pa, a = 295.07 m/s): qc = 11866.9 Pa (bound 11800-11950), CAS = 265.21 kt (bound 265-266), EAS = 250.10 kt (bound 249-251), TAS = 236.06 m/s = 458.86 kt exactly (M*a).
• Sea level 100 m/s CAS: EAS, TAS and CAS all equal 100.000 m/s to below 1e-6 kt (the density ratio is 1 and 1/3.5 = 2/7, so the chain collapses to identity).
• 10,000 ft (3048 m), sigma = rho/rho0 = 0.73848: TAS 150.0 m/s maps to EAS = 150.0*sqrt(0.73848) = 128.90 m/s.
• Round trips: CAS -> TAS -> CAS and TAS -> CAS -> TAS at 0, 3048 and 9144 m recover the input to below 2e-13 m/s (spec: < 1e-9).

Pitfalls

• Treating a CAS <-> TAS conversion as a plain unit factor: at altitude the leg is a two-step chain through the local static pressure and speed of sound, so no fixed factor exists and TAS at a fixed CAS grows with altitude.
• Feeding zero or multiple speed inputs to airspeed_chain: the exactly-one-input rule raises ValueError instead of picking a leg for you.
• Converting EAS with a sea-level density ratio: the EAS legs carry sqrt(rho/rho0) at the flight condition, and EAS equals CAS and TAS only at sea level where sigma is 1.
• Passing non-physical states to a leg: altitude < 0, M < 0 or M >= 1, qc < 0, p <= 0, rho <= 0, or a subsonic qc inversion with qc/p >= 0.8929 raises ValueError rather than returning an extrapolated number.
• Reaching for the transonic-similarity coefficient: the Prandtl-Glauert correction belongs to the aerodynamics sibling leaf, and the airspeed-indicator compressibility correction owned here is not the same quantity.
• Round-tripping across static conditions: CAS -> TAS -> CAS and TAS -> CAS -> TAS recover the input below 1e-9 m/s only when both directions run at the same altitude and static state.

Verification

• Worked-example outputs sit inside the spec magnitude bounds above; take the module outputs as the contract test targets to 4 significant figures.
• Monotonicity: CAS increases with qc; M increases with qc at fixed p; TAS at fixed CAS increases with altitude (TAS at 250 KCAS and 9144 m exceeds TAS at 250 KCAS and sea level).
• Ordering at altitude: EAS < CAS < TAS for a subsonic cruise point.
• Sea-level identity: CAS == EAS == TAS within 1e-3 kt.
• ValueError rejection: altitude < 0; M < 0 or M >= 1; qc < 0; p <= 0; rho <= 0; tas < 0; cas < 0; eas < 0; qc/p >= 0.8929 in the subsonic qc inversion; zero or multiple speed inputs to airspeed_chain.
• Deterministic: no RNG, bit-identical floats run to run.
• Run the contract test offline: python3 scripts/test_airspeed_conversion.py (35 tests, deterministic, stdlib only).

Related leaves

• cross-cutting/units-atmos/isa-atmosphere: the standalone ISA T/p/rho/a state leaf at altitude; this leaf uses the same leg internally.
• cross-cutting/units-atmos/unit-conversion: unit factor table including knots and Mach from a passed speed of sound.
• cross-cutting/units-atmos/dimensional-analysis: dimensional consistency checks for speed and pressure relations.
• flight-test-operations/planning/position-error-calibration: calibrates measured flight-test channels into calibrated airspeed, upstream of this chain.
• flight-test-operations/performance/level-acceleration-test: embeds one leg of this chain in the acceleration survey.
• aerodynamics/high-speed/transonic-similarity: the coefficient correction sibling (Prandtl-Glauert family); do not confuse it with the airspeed-indicator compressibility correction owned here.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_airspeed_conversion.py

The test covers the worked-example magnitude bounds (250 KCAS at 30,000 ft, M = 0.8 at the tropopause, sea-level identity, 10,000 ft EAS), calibrated airspeed from qc and the algebraic inverse, the CAS <-> TAS chains through the local static pressure, EAS legs, round-trip identities at 0, 3048 and 9144 m below 1e-9 m/s, monotonicity, EAS < CAS < TAS ordering, chain dict shape with the exactly-one-input rule, and ValueError rejection of every non-physical input listed in Verification.

Compliance

• Standards referenced, not reproduced: NACA TR-824 is the historical reference for the airspeed-indicator compressibility correction; the relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.