aircraft.rotorcraft_noise

Rotorcraft noise by the hemisphere method (ECAC Doc 32 / NORAH2).

The ECAC Doc 32 rotorcraft-noise method describes a helicopter’s highly directive source with a noise hemisphere: one-third-octave-band sound pressure levels on a spherical grid of azimuth φ and polar angle θ at a fixed 60 m reference distance (at ICAO reference atmospheric conditions). Placing that source at a receiver adds the propagation adjustment ΔLp = ΔLs + ΔLa + ΔLg (+ ΔLd) (spherical spreading, atmospheric absorption, ground effect and, later, shielding).

This module provides the source and propagation primitives and the single-event method built on them (clean-room, from the NORAH2 guidance SC01.D1.5d, the basis of ECAC Doc 32):

• hemisphere_source_level — the interpolated source level L(fc, φ, θ) from a RotorcraftHemisphere, bilinear over the 10° grid (Eq. 13) with nearest-bin fill outside the measured coverage (Eq. 14/15).
• spherical_spreading_adjustment — ΔLs = −20·log10(r/60) (Eq. 24).
• atmospheric_adjustment — ΔLa = −α(f)·(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.
• flight_condition_weights / interpolated_source_level — the flight-condition interpolation across a hemisphere set: distance-scaled triangulation inside the convex hull of the normalised (V̄, γ̄) database conditions, nearest neighbour outside (Eq. 3-10).
• flight_path_kinematics — track kinematics by central finite differences: ground speed, airspeed, heading, curvature, bank and path angle (Eq. 16-21 / Doc 32 Eq. 8-10).
• rotorcraft_event_level — the received one-third-octave time history of a single event at recorded time (Eq. 1/22/23) and its integrated metrics: LASmax, SEL (Doc 32 Eq. 27) and EPNL (Doc 32 Eq. 28, ICAO Annex 16).
• rotorcraft_noise_contour — the single-event SEL/LASmax ground grid.

Source (clean-room): ECAC Doc 32, 1st ed.; NORAH2 rotorcraft-noise modelling guidance (EASA.2020.FC.06 SC01.D1.5d), §A.3-A.5. The atmospheric term is validated against the guidance Table 4 (one-third-octave attenuation per km at ICAO reference conditions); the event chain is validated end to end against the NORAH2 reference implementation outputs for the ARP verification cases (angles, retarded times, hemisphere selection, per-step levels and event metrics).

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 − rh is corrected: ΔLa = −α(f)·(r − rh) 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 fr,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, <= 0 for r >= rh).

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).

ΔLd = 10·Ch·log10(3 + (40/λ)·C″·δ) where the argument is at least 1 (below it the attenuation is 0), Ch = min(fm·h0/250, 1) (Eq. 43) and C″ accounts for multiple diffraction (Eq. 44: 1 for a single edge or an edge span e ≤ 0.3 m, (1 + (5λ/e)²)/(1/3 + (5λ/e)²) otherwise). A negative path difference (edge below the line of sight) still yields a small attenuation down to (40/λ)·C″·δ = −2; for bands with δ < −λ/20 the screening chain evaluates the clear-path ground effect instead of the diffraction (§A.4.5). At grazing incidence (δ = 0) the attenuation is the classical 10·log10(3) ≈ 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.

flight_condition_weights

flight_condition_weights(
    airspeeds: NDArray[np.float64] | list[float],
    path_angles: NDArray[np.float64] | list[float],
    airspeed: float,
    path_angle: float,
    *,
    scaling_factor: float = 2.0,
    triangles: NDArray[np.int_] | list[list[int]] | None = None,
) -> list[tuple[int, float]]

Hemisphere blending weights for a flight condition (Eq. 3-10).

The database flight conditions and the query are scaled by the database spans, V̄ = V/(V_max − V_min) and γ̄ = F_fc·γ/(γ_max − γ_min) with the empirical flight-condition scaling factor F_fc = 2: the guidance’s normalisation (Eq. 3-6), which subtracts no minima — a shared offset cancels in the distances δ_j (Eq. 7) either way. Inside the convex hull of the database conditions the enveloping Delaunay triangle contributes with inverse-distance weights (1/δ_j)/Σ(1/δ_j), δ_j = √((γ̄−γ̄_j)² + (V̄−V̄_j)²) (Eq. 7/8); outside it (and whenever no triangulation exists, e.g. collinear conditions) the nearest database condition is adopted unblended (Eq. 9/10). A query on a database condition returns that hemisphere alone. ECAC Doc 32, 1st ed., §4.1 defines no interpolation (“select the most appropriate hemisphere”); this is the interpolation of the NORAH2 guidance §A.3.1 on which the NORAH database and reference implementation operate, and it degrades to the Doc 32 behaviour outside the measured envelope.

The scaling is span-based, so the weights do not depend on the units of airspeeds or path_angles as long as the query uses the same units as the database conditions.

Parameters

Name	Description
airspeeds	Database hemisphere airspeeds V_j, shape (J,).
path_angles	Database hemisphere path angles γ_j, in degrees, shape (J,) (negative for descent).
airspeed	Query airspeed V_A (the airspeed, not the ground speed, selects the hemisphere; guidance §A.3.3).
path_angle	Query path angle γ, in degrees.
scaling_factor	Flight-condition scaling factor F_fc applied to the normalised path angle (default 2, the guidance’s empirical value).
triangles	Optional precomputed triangulation, shape (T, 3) 0-based indices into the database conditions (guidance §A.3.1 step 4 admits a lookup table; the NORAH database ships one per type). Default None computes the Delaunay triangulation of the normalised conditions. The shipped NORAH lookup tables triangulate the raw (V, γ) plane instead of the normalised one, so passing them reproduces the reference implementation bin for bin.

Returns: The (index, weight) pairs, weights summing to 1.

Raises

Exception	When
ValueError	If the inputs are invalid.

flight_path_kinematics

flight_path_kinematics(
    times: NDArray[np.float64] | list[float],
    positions: NDArray[np.float64] | list[list[float]],
    *,
    gravity: float = 9.80665,
) -> FlightPathKinematics

Track kinematics by central finite differences (Eq. 16-21 / Doc 32 Eq. 8-10).

Computes, at every point of a time-stamped track, the ground speed V_g (Eq. 16), the zero-wind airspeed V_A (Eq. 17), the heading Θ = atan2(ΔX, ΔY) (Eq. 19), the curvature K = ΔΘ/ΔS (Eq. 18), the bank angle Φ = atan(K·V_g²/g) (Eq. 20) and the path angle γ = atan(ΔZ/ΔS) (Doc 32 Eq. 10). The airspeed, not the ground speed, selects the hemisphere (guidance §A.3.3); the guidance recommends smoothing radar tracks (e.g. spline resampling) before differentiating.

Parameters

Name	Description
times	Track times, in s, strictly increasing, shape (N,), N ≥ 2.
positions	Track positions (x, y, z), in metres, shape (N, 3) (x east, y north, z up; any consistent right-handed ground frame works, headings are then relative to its y axis).
gravity	Acceleration of gravity g in m/s² (default 9.80665).

Returns: A FlightPathKinematics.

Raises

Exception	When
ValueError	If the inputs are invalid.

FlightPathKinematics

FlightPathKinematics(
    times: NDArray[np.float64],
    positions: NDArray[np.float64],
    ground_speed: NDArray[np.float64],
    airspeed: NDArray[np.float64],
    heading: NDArray[np.float64],
    curvature: NDArray[np.float64],
    bank_angle: NDArray[np.float64],
    path_angle: NDArray[np.float64],
)

Kinematics of a rotorcraft track (guidance Eq. 16-21 / Doc 32 Eq. 8-10).

All rates come from central finite differences around each track point.

Attributes

Name	Description
times	Track times, in s, shape (N,).
positions	Track positions (x, y, z), in metres, shape (N, 3).
ground_speed	Ground speed V_g (Eq. 16), in m/s, shape (N,).
airspeed	Airspeed V_A (Eq. 17, zero-wind), in m/s, shape (N,).
heading	Heading Θ = atan2(ΔX, ΔY) (Eq. 19), in degrees, shape (N,).
curvature	Track curvature K = ΔΘ/ΔS (Eq. 18), in rad/m, shape (N,) (zero where the ground speed vanishes).
bank_angle	Bank angle Φ = atan(K·V_g²/g) (Eq. 20), in degrees, positive starboard down, shape (N,).
path_angle	Path angle γ = atan(ΔZ/ΔS) (Doc 32 Eq. 10), in degrees, positive climbing, shape (N,).

Note

The guidance prints Eq. 21 as γ = acos(ΔZ/ΔS), which returns the complement of the path angle (90° in level flight) and is dimensionally inconsistent with its use; ECAC Doc 32 Eq. 10 states the correct atan form, which this implementation follows.

FlightPathKinematics.plot()

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

Plot the speed and angle profiles along the track.

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, ΔLg = 10·log10{1 + (r1/r2)²|Q|² + 2(r1/r2)|Q|·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 σ = 65e6 for city areas and grass σ = 200e3 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.

hemisphere_source_level

hemisphere_source_level(
    hemisphere: RotorcraftHemisphere,
    azimuth_deg: float,
    polar_deg: float,
) -> NDArray[np.float64]

Interpolated source level L(fc, φ, θ) from a hemisphere (Eq. 13-15).

The grid is first gap-filled by nearest-bin constant-value extrapolation (Eq. 14/15, computed once per hemisphere and cached), then the query is a bilinear interpolation in the energy domain over the four neighbouring azimuth/polar bins (Eq. 13). Filling the grid before interpolating keeps partially-measured cells continuous with their fully-measured neighbours (the valid corners still contribute) instead of snapping to a single bin.

Queries outside the grid clamp to the boundary node and edge-interpolate; Eq. 14/15 taken literally would return the single nearest node, which coincides on the boundary nodes but is discontinuous alongside them, so the smoother clamp is intentional. Bands with no filled bin anywhere in the grid return NaN.

Parameters

Name	Description
hemisphere	The RotorcraftHemisphere source description.
azimuth_deg	Emission azimuth φ, in degrees.
polar_deg	Emission polar angle θ, in degrees.

Returns: Band levels at (φ, θ), in dB, shape (F,).

interpolated_source_level

interpolated_source_level(
    hemispheres: Sequence[RotorcraftHemisphere],
    airspeeds: NDArray[np.float64] | list[float],
    path_angles: NDArray[np.float64] | list[float],
    airspeed: float,
    path_angle: float,
    azimuth_deg: float,
    polar_deg: float,
    *,
    scaling_factor: float = 2.0,
    triangles: NDArray[np.int_] | list[list[int]] | None = None,
) -> NDArray[np.float64]

Source level at a flight condition between hemispheres (Eq. 8/10 over Eq. 13).

Blends hemisphere_source_level lookups of the hemispheres selected by flight_condition_weights in the energy domain (Eq. 8).

Parameters

Name	Description
hemispheres	The database hemispheres, one per flight condition.
airspeeds	Database airspeeds V_j, shape (J,).
path_angles	Database path angles γ_j, in degrees, shape (J,).
airspeed	Query airspeed V_A (same units as airspeeds).
path_angle	Query path angle γ, in degrees.
azimuth_deg	Emission azimuth φ, in degrees.
polar_deg	Emission polar angle θ, in degrees.
scaling_factor	Flight-condition scaling factor F_fc (default 2).
triangles	Optional precomputed triangulation (see flight_condition_weights).

Returns: Band levels at the reference distance, in dB, shape (F,).

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: σ̄ = 10^(Σ dᵢ·log10(σᵢ) / Σ dᵢ).

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·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 ≥ 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·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 a·d + 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.

rotorcraft_event_level

rotorcraft_event_level(
    hemispheres: Sequence[RotorcraftHemisphere],
    airspeeds: NDArray[np.float64] | list[float],
    path_angles: NDArray[np.float64] | list[float],
    times: NDArray[np.float64] | list[float],
    positions: NDArray[np.float64] | list[list[float]],
    receiver: tuple[float, float] | NDArray[np.float64] | list[float],
    *,
    receiver_height: float = 1.2,
    ground_elevation: float = 0.0,
    airspeed: float | NDArray[np.float64] | list[float] | None = None,
    path_angle: float | NDArray[np.float64] | list[float] | None = None,
    heading: float | NDArray[np.float64] | list[float] | None = None,
    bank_angle: float | NDArray[np.float64] | list[float] | None = None,
    flow_resistivity: float | str = 'G',
    temperature: float = 25.0,
    relative_humidity: float = 70.0,
    pressure: float = 101.325,
    level_offset: float | NDArray[np.float64] | list[float] = 0.0,
    scaling_factor: float = 2.0,
    triangles: NDArray[np.int_] | list[list[int]] | None = None,
    atmospheric_method: str = 'iso9613',
    terrain: tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.float64]] | Sequence[NDArray[np.float64]] | None = None,
    terrain_resolution: float | None = None,
) -> RotorcraftEventResult

Rotorcraft single-event level at a receiver (Doc 32 §6.1 / guidance §A.5.1).

For every track point the flight condition selects (or blends, Eq. 3-10) the hemispheres, the emission angles address the source level (Eq. 13-15) and the propagation adjustment ΔLp = ΔLs + ΔLa + ΔLg (Eq. 23-35) places it at the receiver. The received one-third-octave history is expressed at recorded time t_r = t_e + r/c (Eq. 22) and integrated into LASmax, SEL (Doc 32 Eq. 27) and EPNL (Doc 32 Eq. 28, ICAO Annex 16 App. 2, reusing epnl_from_pnlt).

The flight condition per point comes from the airspeed/path_angle overrides when given (e.g. the smoothed values of a radar-track workflow), otherwise from flight_path_kinematics on the track itself, in which case the database airspeeds must be in m/s. The hemisphere frame is oriented by the heading and tilted by the bank angle in turns (guidance §A.3.4); pitch attitude is implicit in the hemispheres.

Parameters

Name	Description
hemispheres	The database hemispheres, one per flight condition.
airspeeds	Database airspeeds V_j, shape (J,) (same units as the airspeed values used for selection).
path_angles	Database path angles γ_j, in degrees, shape (J,).
times	Track times, in s, strictly increasing, shape (N,).
positions	Track positions (x, y, z), in metres, shape (N, 3) (z up, above the ground elevation datum).
receiver	Receiver ground position (x, y), in metres.
receiver_height	Microphone height above local ground, in metres (default 1.2).
ground_elevation	Ground elevation z at the site, in metres on the track datum (default 0); source and receiver heights above ground follow from it.
airspeed	Per-point airspeed override, scalar or shape (N,).
path_angle	Per-point path-angle override, in degrees.
heading	Per-point heading override, in degrees.
bank_angle	Per-point bank-angle override, in degrees (positive starboard down).
flow_resistivity	Ground flow resistivity σ in Pa·s/m², or a CNOSSOS class letter (see ground_effect_adjustment).
temperature	Air temperature, in °C (default 25, ICAO reference).
relative_humidity	Relative humidity, in % (default 70).
pressure	Ambient pressure, in kPa (default 101.325).
level_offset	Source-level offset ΔEPNL added to the hemisphere levels (Eq. 2 class substitution), in dB (default 0). Scalar or per track point, shape (N,): Chapter-8 substitutions correct climb, level and descent conditions with different certification levels.
scaling_factor	Flight-condition scaling factor F_fc (default 2).
triangles	Optional precomputed flight-condition triangulation (see flight_condition_weights).
atmospheric_method	"iso9613" for the pure-tone Eq. 26/27 term (the guidance text), or "sae" for the SAE ARP 5534 band-integrated mapping used by the NORAH2 reference implementation (they agree to ~0.05 dB below 3.15 kHz).
terrain	Optional digital elevation model (x, y, z) on the track frame (x and y strictly increasing, z of shape (len(y), len(x)), all in metres on the track datum). When given, every emission-receiver pair is evaluated over its sampled vertical section (guidance §A.4.4/A.4.5): mean-ground-plane ground effect with equivalent heights, and rubber-band diffraction where terrain blocks the line of sight; ground_elevation is then taken from the model. The model must cover the whole track and the receiver (fabricating terrain beyond its edges is refused).
terrain_resolution	Section sampling step along the path, in metres (default: the elevation model’s cell size; sections are capped at 20000 sampling intervals).

Returns: A RotorcraftEventResult.

Raises

Exception	When
ValueError	If the inputs are invalid.

rotorcraft_noise_contour

rotorcraft_noise_contour(
    hemispheres: Sequence[RotorcraftHemisphere],
    airspeeds: NDArray[np.float64] | list[float],
    path_angles: NDArray[np.float64] | list[float],
    times: NDArray[np.float64] | list[float],
    positions: NDArray[np.float64] | list[list[float]],
    *,
    x: NDArray[np.float64] | list[float],
    y: NDArray[np.float64] | list[float],
    metric: str = 'exposure',
    receiver_height: float = 1.2,
    ground_elevation: float | NDArray[np.float64] | list[list[float]] = 0.0,
    airspeed: float | NDArray[np.float64] | list[float] | None = None,
    path_angle: float | NDArray[np.float64] | list[float] | None = None,
    heading: float | NDArray[np.float64] | list[float] | None = None,
    bank_angle: float | NDArray[np.float64] | list[float] | None = None,
    flow_resistivity: float | str | NDArray[np.float64] | list[list[float]] = 'G',
    temperature: float = 25.0,
    relative_humidity: float = 70.0,
    pressure: float = 101.325,
    level_offset: float | NDArray[np.float64] | list[float] = 0.0,
    scaling_factor: float = 2.0,
    triangles: NDArray[np.int_] | list[list[int]] | None = None,
    atmospheric_method: str = 'iso9613',
    terrain: tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.float64]] | Sequence[NDArray[np.float64]] | None = None,
    terrain_resolution: float | None = None,
) -> RotorcraftNoiseContourResult

Rotorcraft single-event level over a ground grid (Doc 32 §6.3).

Evaluates the event of rotorcraft_event_level at every grid point (xi, yj) in one vectorised pass per emission step, and reduces the received histories to the exposure (SEL, Doc 32 Eq. 27) or maximum (LASmax) level.

Parameters

Name	Description
hemispheres	The database hemispheres, one per flight condition.
airspeeds	Database airspeeds V_j, shape (J,).
path_angles	Database path angles γ_j, in degrees, shape (J,).
times	Track times, in s, strictly increasing, shape (N,).
positions	Track positions (x, y, z), in metres, shape (N, 3).
x	Grid x coordinates, in metres (at least 2).
y	Grid y coordinates, in metres (at least 2).
metric	"exposure" (SEL) or "maximum" (LASmax).
receiver_height	Microphone height above local ground, in metres.
ground_elevation	Ground elevation, in metres on the track datum: a scalar, or one value per grid point (shape (len(y), len(x))) for receivers on uneven sites without a full elevation model.
airspeed	Per-point airspeed override (see rotorcraft_event_level).
path_angle	Per-point path-angle override, in degrees.
heading	Per-point heading override, in degrees.
bank_angle	Per-point bank-angle override, in degrees.
flow_resistivity	Ground flow resistivity σ in Pa·s/m², a CNOSSOS class letter, or one value per grid point (shape (len(y), len(x))) for heterogeneous ground across the receivers (each receiver’s two-ray model uses its local value).
temperature	Air temperature, in °C.
relative_humidity	Relative humidity, in %.
pressure	Ambient pressure, in kPa.
level_offset	Source-level offset ΔEPNL (Eq. 2), in dB, scalar or per track point.
scaling_factor	Flight-condition scaling factor F_fc (default 2).
triangles	Optional precomputed flight-condition triangulation.
atmospheric_method	"iso9613" or "sae" (see rotorcraft_event_level).
terrain	Optional digital elevation model (x, y, z) (see rotorcraft_event_level); it must cover the whole track and grid. Every emission-receiver pair then samples its own vertical section, so the cost grows with track points times grid points; keep contour grids modest with terrain.
terrain_resolution	Section sampling step, in metres (default: the elevation model’s cell size; sections are capped at 20000 sampling intervals).

Returns: A RotorcraftNoiseContourResult.

Raises

Exception	When
ValueError	If the inputs are invalid.

RotorcraftEventResult

RotorcraftEventResult(
    frequencies: NDArray[np.float64],
    emission_times: NDArray[np.float64],
    times: NDArray[np.float64],
    distance: NDArray[np.float64],
    azimuth: NDArray[np.float64],
    polar: NDArray[np.float64],
    band_levels: NDArray[np.float64],
    a_levels: NDArray[np.float64],
    la_max: float,
    sel: float,
    sel_10db: float,
    pnlt: NDArray[np.float64],
    pnltm: float,
    epnl: float,
)

A rotorcraft single-event time history at a receiver (Doc 32 §6.1).

Attributes

Name	Description
frequencies	Band centre frequencies, in Hz, shape (F,).
emission_times	Emission times t_e, in s, shape (K,).
times	Recorded times t_r = t_e + r/c (Eq. 22), in s, shape (K,).
distance	Slant distance r per step, in metres, shape (K,).
azimuth	Emission azimuth φ per step, in degrees, shape (K,).
polar	Emission polar angle θ per step, in degrees, shape (K,).
band_levels	Received (unweighted) band levels, in dB, shape (K, F).
a_levels	A-weighted overall level L_A(t) per step, in dB(A), shape (K,).
la_max	Maximum A-weighted level LASmax, in dB(A).
sel	Sound exposure level over the full history (Doc 32 Eq. 27, t_0 = 1 s), in dB(A). The full-history integration is the land-use planning convention of the NORAH2 reference implementation.
sel_10db	Sound exposure level restricted to the 10 dB-down window about LASmax (the certification convention), in dB(A).
pnlt	Tone-corrected perceived noise level per step, in TPNdB, shape (K,); NaN where undefined (zero total noisiness, or the band grid does not cover the 24 noy bands 50 Hz-10 kHz).
pnltm	Maximum PNLT (with the Annex 16 bandsharing adjustment), in TPNdB; NaN if no step has a defined PNLT.
epnl	Effective perceived noise level (Doc 32 Eq. 28 / ICAO Annex 16), in EPNdB; NaN if no step has a defined PNLT.

RotorcraftEventResult.plot()

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

Plot the A-weighted level time history with its event metrics.

RotorcraftHemisphere

RotorcraftHemisphere(
    frequencies: NDArray[np.float64],
    azimuth: NDArray[np.float64],
    polar: NDArray[np.float64],
    levels: NDArray[np.float64],
    distance: float = 60.0,
)

A rotorcraft noise hemisphere (ECAC Doc 32 §A.3.2).

One-third-octave-band sound pressure levels on a regular azimuth/polar grid at the 60 m reference distance (ICAO reference atmosphere). Missing bins (outside the measured coverage) are NaN and filled by nearest-bin extrapolation on lookup.

Attributes

Name	Description
frequencies	Band centre frequencies, in Hz, shape (F,).
azimuth	Azimuth angles φ, in degrees, shape (A,) (-90 port … +90 starboard).
polar	Polar angles θ, in degrees, shape (P,) (0 forward … 180 rearward).
levels	Band levels, in dB, shape (A, P, F).
distance	Reference distance, in metres (default 60). The standard NORAH database uses 60 m; when the data uses another polar distance (e.g. 70 m hover rings), pass this value as reference_distance to spherical_spreading_adjustment and atmospheric_adjustment so the propagation chain honours it.

RotorcraftHemisphere.mirrored()

RotorcraftHemisphere.mirrored() -> RotorcraftHemisphere

The hemisphere with the azimuth axis reversed (φ → −φ).

Doc 32 Eq. 2 substitutes a class member whose main/tail-rotor configuration is mirrored with respect to the class reference (the bracketed types of its Table 2, e.g. [A600] in the R22 class) by reversing the hemisphere azimuth angle.

Returns: A new RotorcraftHemisphere with mirrored azimuth.

RotorcraftHemisphere.plot()

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

Plot the hemisphere directivity for one band (polar section).

RotorcraftNoiseContourResult

RotorcraftNoiseContourResult(
    x: NDArray[np.float64],
    y: NDArray[np.float64],
    level: NDArray[np.float64],
    metric: str,
)

Rotorcraft single-event noise level over a ground grid (Doc 32 §6.3).

Attributes

Name	Description
x	Grid x coordinates, in metres, shape (nx,).
y	Grid y coordinates, in metres, shape (ny,).
level	Event level over the grid, in dB(A), shape (ny, nx).
metric	"exposure" (SEL) or "maximum" (LASmax).

RotorcraftNoiseContourResult.plot()

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

Plot filled noise contours over the 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 ΔLs = −20·log10(r/rh).

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 δ < −λ/20 fall back to the clear-path evaluation (with terrain-only obstacles δ > 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, −(ΔLd + ΔLg) 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.