aircraft.rotorcraft_propagation

Rotorcraft propagation, ground effect and screening (ECAC Doc 32 / NORAH2).

Between the noise hemisphere that describes a helicopter and the receiver on the ground lies the path, and the path knows nothing about rotorcraft. The ECAC Doc 32 propagation chain $\Delta L_p=\Delta L_{\mathrm{s}}+\Delta L_{\mathrm{a}}+\Delta L_{\mathrm{g}}$ adds spherical spreading, atmospheric absorption and the ground effect of a point source over an impedance plane; the NORAH2 guidance extends that last term to real terrain, where a fitted mean ground plane replaces the flat ground and a blocked line of sight becomes diffraction. Every function here takes a geometry and a spectrum; rotorcraft_noise holds the hemisphere source and the event chain that call them.

This module provides the propagation primitives of the method (clean-room, from the NORAH2 guidance SC01.D1.5d, the basis of ECAC Doc 32):

• spherical_spreading_adjustment — $\Delta L_{\mathrm{s}}=-20\cdot {\log }_{10}(r/60)$ (Eq. 24).
• atmospheric_adjustment — $\Delta L_{\mathrm{a}}=-\alpha (f)\cdot (r-60)$ with the ISO 9613-1 pure-tone coefficient (Eq. 26/27), reusing air_attenuation.
• ground_effect_adjustment — ΔLg for a point source over an impedance plane (Chien-Soroka, Eq. 28-35) with the Delany-Bazley one-parameter impedance and the CNOSSOS flow-resistivity classes.
• mean_ground_plane — the least-squares plane through a terrain section (Eq. 36-40), whose equivalent orthogonal heights carry a varying profile into the flat-ground equations.
• mean_flow_resistivity — the log-mean flow resistivity of a path that crosses several ground types (Eq. 41).
• diffraction_attenuation — the pure diffraction attenuation ΔLd of a path difference (Eq. 42-44).
• terrain_screening_adjustment — the combined ground-and-screening adjustment over a vertical section (§A.4.4-A.4.5, Eq. 45-47): the mean-ground-plane ground effect while the line of sight is clear, the rubber-band diffraction over the terrain once it is blocked.

ECAC Doc 32, 1st ed., defines no topography or screening at all: its Eq. 12 chain ends at the flat-ground ΔLg. The mean ground plane, the log-mean flow resistivity and the diffraction of §A.4.4-A.4.5 come from the guidance, whose diffraction equations follow CNOSSOS-EU.

Source (clean-room): ECAC Doc 32, 1st ed.; NORAH2 rotorcraft-noise modelling guidance (EASA.2020.FC.06 SC01.D1.5d), §A.4. The atmospheric term is validated against the guidance Table 4 (one-third-octave attenuation per km at ICAO reference conditions); the ground and screening chain is validated end to end, inside the event chain, against the NORAH2 reference implementation outputs for the ARP verification cases.

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

atmospheric_adjustment

atmospheric_adjustment(
    frequencies: NDArray[np.float64] | list[float],
    distance: float,
    *,
    temperature: float = 25.0,
    relative_humidity: float = 70.0,
    pressure: float = 101.325,
    reference_distance: float = 60.0,
) -> NDArray[np.float64]

Atmospheric-absorption adjustment ΔLa of the hemisphere level (Eq. 26/27).

The hemisphere already includes absorption out to the reference distance rh, so only the excess path $r-r_{\mathrm{h}}$ is corrected: $\Delta L_{\mathrm{a}}=-\alpha (f)\cdot (r-r_{\mathrm{h}})$ with the ISO 9613-1 pure-tone coefficient α evaluated at the exact band centre (Eq. 26/27, ICAO reference atmosphere by default). This matches the guidance Eq. 27 to 0.02 dB/km and the NORAH2 reference implementation. The guidance’s alternative per-band mapping (SAE method by Rickley et al., its Table 4) coincides below 3.15 kHz and deviates by up to 2.2 dB/km at 8-10 kHz; for a path-dependent band mapping use sae_band_attenuation.

Note

The printed guidance Eq. 27 pairs the coefficient 6.6928e-6 with $f_{\mathrm{r},\mathrm{O}}=630.7$ Hz, which evaluates to nonsense (14.3 dB/km at 500 Hz against Table 4’s 3.1). The physically correct pairing (6.6928e-6 with the oxygen relaxation frequency, 1.3415e-6 with 630.7 Hz) reproduces Table 4 and this implementation to 0.02 dB/km; do not “fix” the code by transcribing the typo.

Bands below the 50 Hz floor of the ISO 9613-1 tabulation (the NORAH grid starts at 10 Hz) use the same analytic formulas; the advisory out-of-range warning is suppressed because α is negligible there (Table 4 lists 0.0 dB/km for every band up to 50 Hz). The suppression only applies while every band stays within the 10 kHz top of the NORAH grid; above that the advisory warning propagates, since α is large and extrapolated.

Parameters

Name	Description
frequencies	One-third-octave-band centre frequencies, in Hz.
distance	Slant distance r, in metres (> 0; below rh the adjustment is a small positive value, i.e. less absorption than the reference path).
temperature	Air temperature, in °C (default 25 °C, ICAO reference).
relative_humidity	Relative humidity, in % (default 70 %).
pressure	Ambient pressure, in kPa (default 101.325).
reference_distance	Hemisphere reference distance rh, in metres (default 60). Pass RotorcraftHemisphere.distance when the data uses a non-standard polar distance.

Returns: The adjustment ΔLa per band, in dB (added to the level, $\le 0$ for $r\ge r_{\mathrm{h}}$).

Raises

Exception	When
ValueError	If a distance is not strictly positive.

diffraction_attenuation

diffraction_attenuation(
    frequencies: NDArray[np.float64] | list[float],
    path_difference: float,
    *,
    edge_height: float,
    edge_span: float = 0.0,
    capped: bool = True,
) -> NDArray[np.float64]

Pure diffraction attenuation ΔLd per band (guidance Eq. 42-44).

$\Delta L_{\mathrm{d}}=10\cdot C_h\cdot {\log }_{10}(3+(40/\lambda )\cdot C^{\prime \prime }\cdot \delta )$ where the argument is at least 1 (below it the attenuation is 0), $C_h=\min (f_m\cdot h_0/250,1)$ (Eq. 43) and $C^{\prime \prime }$ accounts for multiple diffraction (Eq. 44: 1 for a single edge or an edge span $e\le 0.3$ m, $(1+(5\lambda /e{)}^2)/(1/3+(5\lambda /e{)}^2)$ otherwise). A negative path difference (edge below the line of sight) still yields a small attenuation down to $(40/\lambda )\cdot C^{\prime \prime }\cdot \delta =-2$; for bands with $\delta <-\lambda /20$ the screening chain evaluates the clear-path ground effect instead of the diffraction (§A.4.5). At grazing incidence ($\delta =0$) the attenuation is the classical $10\cdot {\log }_{10}(3)\approx 4.8$ dB.

The attenuation is returned positive (a loss); in the Doc 32 Eq. 23 chain, whose adjustments are added to the level, it enters with a minus sign. The wavelength uses the Doc 32 reference speed of sound $c=346.1$ m/s.

Parameters

Name	Description
frequencies	One-third-octave-band centre frequencies, in Hz.
path_difference	Path difference δ between the diffracted and the direct path, in metres (negative when the edge lies below the line of sight).
edge_height	Edge height h0 above the mean ground plane(s), in metres (the greatest of the two side values for a terrain edge; ≥ 0).
edge_span	Distance e between the first and last diffraction edges, in metres (default 0: single diffraction).
capped	Apply the 25 dB upper bound of §A.4.5 (default). The image-path terms inside the ground-diffraction weighting (Eq. 46/47) are evaluated unbounded.

Returns: The attenuation ΔLd per band, in dB (≥ 0).

Raises

Exception	When
ValueError	If the inputs are invalid.

ground_effect_adjustment

ground_effect_adjustment(
    frequencies: NDArray[np.float64] | list[float],
    source_height: float,
    receiver_height: float,
    horizontal_distance: float,
    *,
    flow_resistivity: float | str = 'G',
) -> NDArray[np.float64]

Ground-effect adjustment ΔLg over an impedance plane (Eq. 28-35).

A point source over a locally-reacting impedance ground produces interference between the direct and reflected rays. With the spherical reflection coefficient Q (Chien-Soroka) and the Delany-Bazley impedance, $\Delta L_{\mathrm{g}}=10\cdot {\log }_{10}\{1+(r_1/r_2{)}^2|Q{|}^2+2(r_1/r_2)|Q|\cdot I\}$ (Eq. 29), where I (Eq. 30) is the in-band interference factor.

Parameters

Name	Description
frequencies	One-third-octave-band centre frequencies, in Hz.
source_height	Source height above the ground hs, in metres (clamped to >= 0.1).
receiver_height	Receiver height above the ground hr, in metres (clamped to >= 0.1).
horizontal_distance	Horizontal source-receiver distance dp, in metres (> 0).
flow_resistivity	Ground flow resistivity σ in Pa·s/m², or a CNOSSOS class letter "A"-"H". The default "G" (20e6, hard surfaces) is the CNOSSOS class covering the paved surroundings typical of heliports; the guidance’s own suggestions, concrete $\sigma =65\times 10^6$ for city areas and grass $\sigma =200\times 10^3$ for rural areas (§A.4.3), can be passed as numeric values.

Returns: The adjustment ΔLg per band, in dB (added to the level).

Raises

Exception	When
ValueError	If the inputs are invalid.

mean_flow_resistivity

mean_flow_resistivity(
    lengths: NDArray[np.float64] | list[float],
    resistivities: NDArray[np.float64] | list[float],
) -> float

Logarithmic mean flow resistivity along a path (guidance Eq. 41).

When the ground type changes along a terrain profile, the guidance averages the flow resistivity by the logarithm, weighted by the length of each ground segment: $\bar{\sigma }=10^{\sum d_i\cdot {\log }_{10}({\sigma }_i)/\sum d_i}$.

Parameters

Name	Description
lengths	Segment lengths dᵢ, in metres (> 0), shape (n,).
resistivities	Segment flow resistivities σᵢ, in Pa·s/m² (> 0), shape (n,).

Returns: The mean flow resistivity σ̄, in Pa·s/m².

Raises

Exception	When
ValueError	If the inputs are invalid.

mean_ground_plane

mean_ground_plane(
    distances: NDArray[np.float64] | list[float],
    heights: NDArray[np.float64] | list[float],
) -> MeanGroundPlaneResult

The mean ground plane of a terrain section (guidance Eq. 36-40).

Fits $z=a\cdot d+b$ to the polyline of straight segments that form the terrain profile by continuous least squares (the residual is integrated along d, not summed over the vertices), using the closed forms of Eq. 37/38 with the segment integrals A and B of Eq. 39/40.

Parameters

Name	Description
distances	Section distances d, in metres, strictly increasing, shape (M,) with $M\ge 2$ (arbitrary spacing).
heights	Terrain heights z(d), in metres, shape (M,).

Returns: A MeanGroundPlaneResult.

Raises

Exception	When
ValueError	If the inputs are invalid.

MeanGroundPlaneResult

MeanGroundPlaneResult(
    slope: float,
    intercept: float,
    distances: NDArray[np.float64],
    heights: NDArray[np.float64],
)

A mean ground plane fitted to a terrain section (guidance Eq. 36-40).

ECAC Doc 32, 1st ed., assumes flat terrain; its guidance (§A.4.4) represents a varying vertical section by the least-squares line $z=a\cdot d+b$ through the terrain polyline, evaluated in closed form from the per-segment integrals (Eq. 37-40). Equivalent source and receiver heights are then measured orthogonally to this plane and substituted into the flat-ground equations.

Attributes

Name	Description
slope	The fitted slope a (Eq. 37).
intercept	The fitted intercept b, in metres (Eq. 38).
distances	The section distances d, in metres, shape (M,).
heights	The terrain heights z(d), in metres, shape (M,).

MeanGroundPlaneResult.equivalent_height()

MeanGroundPlaneResult.equivalent_height(
    distance: float,
    height: float,
) -> float

The orthogonal (equivalent) height of a point above the plane.

Positive above the plane; the guidance substitutes these equivalent heights, floored at 0.1 m for source and receiver, into the flat-ground equations (§A.4.4).

MeanGroundPlaneResult.height()

MeanGroundPlaneResult.height(
    distance: float | NDArray[np.float64],
) -> NDArray[np.float64]

The plane height $ad+b$ at distance, in metres.

MeanGroundPlaneResult.plot()

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

Plot the terrain section and the fitted mean ground plane.

spherical_spreading_adjustment

spherical_spreading_adjustment(
    distance: float,
    *,
    reference_distance: float = 60.0,
) -> float

Spherical-spreading adjustment ΔLs of the hemisphere level (Eq. 24).

The hemisphere levels are defined at the reference distance rh (60 m in the standard database), so at slant distance r the geometric spreading adjustment is $\Delta L_{\mathrm{s}}=-20\cdot {\log }_{10}(r/r_{\mathrm{h}})$.

Parameters

Name	Description
distance	Slant distance r from the rotorcraft to the observer, in metres (> 0).
reference_distance	Hemisphere reference distance rh, in metres (default 60). Pass RotorcraftHemisphere.distance when the data uses a non-standard polar distance (e.g. 70 m hover rings).

Returns: The spreading adjustment ΔLs, in dB (added to the level).

Raises

Exception	When
ValueError	If a distance is not strictly positive.

terrain_screening_adjustment

terrain_screening_adjustment(
    frequencies: NDArray[np.float64] | list[float],
    source: tuple[float, float],
    receiver: tuple[float, float],
    distances: NDArray[np.float64] | list[float],
    heights: NDArray[np.float64] | list[float],
    *,
    flow_resistivity: float | str | NDArray[np.float64] | list[float] = 'G',
) -> TerrainScreeningResult

Ground effect and terrain screening over a vertical section (§A.4.4-A.4.5).

The terrain profile between the source and the receiver decides the propagation regime:

• Line of sight clear (no profile point strictly above it): the section’s mean ground plane (Eq. 36-40) supplies equivalent orthogonal heights (floored at 0.1 m) and the flat-ground two-ray model of §A.4.3 evaluates on the plane, with the log-mean flow resistivity (Eq. 41) when it varies along the path. Terrain points below the line of sight are never treated as diffracting obstacles (the guidance’s topography rule, which avoids accidental screening in flat terrain).
• Blocked: the sound follows the shortest convex path over the terrain (the guidance’s rubber band); its vertices are the diffraction edges. The attenuation combines the pure diffraction of the path difference δ (Eq. 42-44, capped at 25 dB) with the source-side and receiver-side ground effects weighted by their image-path diffractions (Eq. 45-47), each side using its own mean ground plane, equivalent heights and log-mean flow resistivity. The ground effect is not evaluated separately in this regime; bands with $\delta <-\lambda /20$ fall back to the clear-path evaluation (with terrain-only obstacles $\delta >0$, so the rule engages for constructed screens below the line of sight rather than for terrain).

ECAC Doc 32, 1st ed., defines no screening or topography (its Eq. 12 propagation chain ends at the flat-ground ΔLg); this implements the NORAH2 guidance sections A.4.4/A.4.5 and its noise-path appendices, whose diffraction equations follow CNOSSOS-EU.

Parameters

Name	Description
frequencies	One-third-octave-band centre frequencies, in Hz.
source	Source (d, z) in the section, in metres.
receiver	Receiver (d, z) in the section, in metres (the microphone point, i.e. ground plus microphone height).
distances	Terrain section distances d, in metres, strictly increasing, covering [source d, receiver d].
heights	Terrain heights z(d), in metres.
flow_resistivity	Ground flow resistivity: a value in Pa·s/m², a CNOSSOS class letter, or one value per profile segment (shape (M−1,)) averaged per sub-path by Eq. 41.

Returns: A TerrainScreeningResult.

Raises

Exception	When
ValueError	If the inputs are invalid.

TerrainScreeningResult

TerrainScreeningResult(
    frequencies: NDArray[np.float64],
    adjustment: NDArray[np.float64],
    screened: bool,
    path_difference: float,
    diffraction_points: NDArray[np.float64],
    source: tuple[float, float],
    receiver: tuple[float, float],
    distances: NDArray[np.float64],
    heights: NDArray[np.float64],
)

Ground and screening over a terrain section (guidance §A.4.4-A.4.5).

Attributes

Name	Description
frequencies	Band centre frequencies, in Hz, shape (F,).
adjustment	The combined ground-and-screening adjustment per band, in dB, added to the received level in the Doc 32 Eq. 23 chain (it replaces the flat-ground ΔLg): the mean-ground-plane ground effect when the line of sight is clear, $-(\Delta L_{\mathrm{d}}+\Delta L_{\mathrm{g}})$ of Eq. 45 when terrain blocks it.
screened	Whether terrain blocks the line of sight (any profile point strictly above it).
path_difference	The rubber-band path difference δ, in metres (NaN when unscreened).
diffraction_points	The diffracting edges (d, z) on the convex propagation path, shape (n, 2) (empty when unscreened).
source	The source (d, z), in metres.
receiver	The receiver (d, z), in metres.
distances	The section distances, in metres, shape (M,).
heights	The section terrain heights, in metres, shape (M,).

TerrainScreeningResult.plot()

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

Plot the section geometry: terrain, line of sight and sound path.