aircraft.atmospheric_absorption

One-third-octave-band atmospheric absorption for aircraft noise (SAE ARP 5534 and 866A).

Aircraft noise certification (14 CFR Part 36, ICAO Annex 16 Vol. I) works with one-third-octave-band spectra, and correcting a measured flyover to reference atmospheric conditions requires the band attenuation over the propagation path. Two SAE practices give it.

sae_band_attenuation — SAE ARP 5534, the current practice. Its pure-tone coefficient (Eqs. 1-6) is the ISO 9613-1 one, Eqs. 1-3 repeating air_attenuation term for term, except for the saturation vapour pressure: Eqs. 5-6 write it in the longer form of ANSI S1.26, which gives a molar concentration of water vapour 4.5 parts in 100 000 below the ISO 9613-1 Annex B formula at 10 °C. The SAE Method (§3.2.2) then turns the pure-tone mid-band path-length attenuation into the one-third-octave-band attenuation and stays consistent with the ISO/ANSI Exact Method well beyond the 50 dB limit of the older Approximate Method. The result is an AircraftBandAttenuation with a .plot().
arp866a_attenuation — SAE ARP 866A (1975), the legacy practice that ECAC Doc 29 Vol. 2 Appendix D still offers for recalculating NPD data, in the form ISO 3891:1978 Annex A gives it: an attenuation coefficient per band, in decibels per 100 m, independent of pressure and of path length, evaluated at the band centre up to 4 kHz and at the lower band edge above. The result is an Arp866aAttenuation with a .plot().

Sources (clean-room, implemented from the documents): SAE ARP 5534 (2021), Application of Pure-Tone Atmospheric Absorption Losses to One-Third-Octave-Band Data, Eqs. 1-10; ISO 3891:1978, Acoustics — Procedure for describing aircraft noise heard on the ground, Annex A (A.1, A.2, Tables 1 and 2), which transcribes SAE ARP 866A. Both are checked against ECAC Doc 29 5th ed. Vol. 2 Appendix D, Tables D-3b and D-3c, and ARP 866A against ISO 3891 Table 10 as well.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

AircraftBandAttenuation

AircraftBandAttenuation(
    frequencies: NDArray[np.float64],
    band_attenuation: NDArray[np.float64],
    midband_attenuation: NDArray[np.float64],
    coefficient: NDArray[np.float64],
    path_length: float,
    temperature_c: float,
    relative_humidity_percent: float,
    atmospheric_pressure_kpa: float,
)

One-third-octave-band atmospheric attenuation over a path (SAE ARP 5534).

Attributes

Name	Description
`frequencies`	Nominal one-third-octave-band centre frequencies, in Hz.
`band_attenuation`	SAE-Method band attenuation `δ_B` per band, in dB.
`midband_attenuation`	Pure-tone mid-band path-length attenuation $δ_{t} = α \cdot s$ per band, in dB (ARP 5534 Eqs. 1-6 coefficient).
`coefficient`	Pure-tone mid-band attenuation coefficient `α` per band, in dB/m.
`path_length`	Propagation path length `s`, in metres.
`temperature_c`	Air temperature, in degrees Celsius.
`relative_humidity_percent`	Relative humidity, in percent.
`atmospheric_pressure_kpa`	Ambient atmospheric pressure, in kPa.

AircraftBandAttenuation.plot()

AircraftBandAttenuation.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the band and pure-tone mid-band attenuation versus frequency.

arp866a_attenuation

arp866a_attenuation(
    frequencies_hz: ArrayLike,
    *,
    temperature_c: float,
    relative_humidity_percent: float,
    eta_interpolation: str = 'quadratic',
) -> Arp866aAttenuation

One-third-octave-band attenuation coefficient by SAE ARP 866A (ISO 3891 Annex A).

The formula of ISO 3891:1978 A.2, in decibels per 100 m:

α = 1 0^{2.05 l o g_{10} (f_{0} /1000) + 1.1394 \times 1 0^{- 3} θ - 1.916984} + η (δ) \times 1 0^{l o g_{10} f_{0} + 8.42994 \times 1 0^{- 3} θ - 2.755624}

δ = \frac{1010}{f _{0}} \times 1 0^{l o g_{10} R H - 1.328924 + 3.179768 \times 1 0^{- 2} θ - 2.173716 \times 1 0^{- 4} θ^{2} + 1.7496 \times 1 0^{- 6} θ^{3}}

with θ in degrees Celsius, RH in percent and f0 from Table 2.

η(δ) comes from Table 1, whose note says “A form of quadratic interpolation shall be used where necessary” without saying which, and the two documents that print this attenuation read it differently. "quadratic" (the default) is the parabola through three neighbouring entries of Table 1 that reproduces every cell of ISO 3891 Table 10 (80 %, -10 °C to 40 °C) to the printed digit, where linear interpolation misses 11 of the 264. "linear" reproduces ECAC Doc 29 Vol. 2 Table D-3b (10 °C, 80 %, over the ten NPD distances): 208 of its 240 cells to the printed digit and all 240 within half a unit of that digit plus 7 parts per million, where the quadratic leaves up to 1.2 dB at 25000 ft; it is the form npd_atmosphere_increment uses. The two part only where δ falls in the curved part of Table 1, below 6.50; from there on both hold η at 0.200. ISO 3891 Table 9 (70 %) is not reproduced as closely as Table 10: the quadratic misses 15 of its 264 cells by one printed unit, seven where it contradicts Table 10 (both humidities give the same value there; see the errata register) and eight more, each within 0.014 dB/100 m of a rounding boundary.

A.2 states the range the formula was measured over: from 2 °C to 30 °C (on the print the mark before the 2 is unclear and may be a minus sign) and from 30 % to 90 %. Its Tables 3 to 12 print the formula from -10 °C to 40 °C and from 10 % to 100 %.

Parameters

Name	Description
`frequencies_hz`	One-third-octave bands, by nominal or exact centre frequency in Hz, from 50 Hz to 10 kHz.
`temperature_c`	Air temperature `θ`, in degrees Celsius.
`relative_humidity_percent`	Relative humidity `RH`, in percent (0 to 100).
`eta_interpolation`	`"quadratic"` (default, ISO 3891) or `"linear"` (ECAC Doc 29 Appendix D).

Returns: An Arp866aAttenuation.

Raises

Exception	When
ValueError	for a band outside Table 2, a temperature at or below absolute zero, a humidity outside 0 % to 100 %, or an unknown interpolation.

Arp866aAttenuation

Arp866aAttenuation(
    frequencies_hz: NDArray[np.float64],
    evaluation_frequencies_hz: NDArray[np.float64],
    delta: NDArray[np.float64],
    eta: NDArray[np.float64],
    coefficient_db_per_100m: NDArray[np.float64],
    temperature_c: float,
    relative_humidity_percent: float,
    eta_interpolation: str,
)

Atmospheric attenuation coefficient per band by SAE ARP 866A (ISO 3891 Annex A).

Attributes

Name	Description
`frequencies_hz`	Nominal one-third-octave-band centre frequencies, in Hz, one per band.
`evaluation_frequencies_hz`	The frequency `f0` of ISO 3891 Table 2 at which each band is evaluated, in Hz: the centre up to 4 kHz, the rounded lower band edge above.
`delta`	The humidity-and-temperature argument `δ` of A.2 per band, dimensionless.
`eta`	`η(δ)` per band, interpolated in Table 1.
`coefficient_db_per_100m`	The attenuation coefficient `α` per band, in decibels per 100 m.
`temperature_c`	Air temperature `θ`, in degrees Celsius.
`relative_humidity_percent`	Relative humidity `RH`, in percent.
`eta_interpolation`	How `η` was read between the entries of Table 1, `"quadratic"` or `"linear"` (see `arp866a_attenuation`).

Arp866aAttenuation.path_attenuation_db()

Arp866aAttenuation.path_attenuation_db(
    path_length_m: float | ArrayLike,
) -> NDArray[np.float64]

Attenuation over a path, $α \cdot s /100$ , in dB.

ARP 866A gives a rate, so the attenuation is proportional to the path length and does not depend on the pressure, unlike SAE ARP 5534.

Parameters

Name	Description
`path_length_m`	Path length `s`, in metres: one length, or a 1-D sequence of them.

Returns: One value per band for a single length, or an array of shape (bands, lengths).

Raises

Exception	When
ValueError	if a length is negative or not finite.

Arp866aAttenuation.plot()

Arp866aAttenuation.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the attenuation coefficient versus frequency.

sae_band_attenuation

sae_band_attenuation(
    frequencies: NDArray[np.float64] | list[float],
    path_length: float,
    *,
    temperature_c: float = 25.0,
    relative_humidity_percent: float = 70.0,
    atmospheric_pressure_kpa: float = 101.325,
) -> AircraftBandAttenuation

One-third-octave-band atmospheric attenuation (SAE ARP 5534, SAE Method).

Computes the pure-tone attenuation coefficient at each band’s exact mid-band frequency (Eqs. 1-6 and 10, $f_{m, i} = 1 0^{i /10}$ ), forms the mid-band path-length attenuation $δ_{t} = α \cdot s$ and maps it to the band attenuation δ_B with the SAE-Method regression (Eqs. 7-8). The coefficient is ISO 9613-1’s with the saturation vapour pressure of Eqs. 5-6, which is what reproduces ECAC Doc 29 Vol. 2 Table D-3c to the last printed digit in all 240 of its cells; the ISO 9613-1 Annex B form leaves 57 of them up to 0.036 dB off.

Parameters

Name	Description
`frequencies`	Nominal one-third-octave-band centre frequencies, in Hz (standard range 50 Hz-10 kHz; the method extends to 25 Hz-20 kHz).
`path_length`	Propagation path length `s`, in metres (`>= 0`).
`temperature_c`	Air temperature, in degrees Celsius (SAE window ~6-32 °C; default 25 °C, the ARP 5534 reference point).
`relative_humidity_percent`	Relative humidity, in percent (SAE window ~20-95 %; default 70 %).
`atmospheric_pressure_kpa`	Ambient atmospheric pressure, in kPa (default 101.325).

Returns: An AircraftBandAttenuation.

Raises

Exception	When
ValueError	If the inputs are invalid.

Created and maintained by José Manuel Requena Plens ORCID All projects