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 $\Delta L_p=\Delta L_{\mathrm{s}}+\Delta L_{\mathrm{a}}+\Delta L_{\mathrm{g}}$ (plus $\Delta L_{\mathrm{d}}$ with shielding): spherical spreading, atmospheric absorption, ground effect and, later, shielding. Those adjustments depend on the path and not on the rotorcraft, and live in rotorcraft_propagation; this module is the source that emits and the event that receives.

This module provides the source 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).
• hover_ring_hemisphere / hover_derived_hemisphere — the hover/idle source derivation of guidance §A.3.5 (Table 3): the ground-ring measurement of in-ground hover extended to a hemisphere assuming constant directivity in φ, and the out-of-ground-hover and idle hemispheres derived from it by the published offsets or a measured 0°-direction difference.
• 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 and §A.5. 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.

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, $\bar{V}=V/(V_{\max }-V_{\min })$ and $\bar{\gamma }=F_{\mathrm{fc}}\cdot \gamma /({\gamma }_{\max }-{\gamma }_{\min })$ with the empirical flight-condition scaling factor $F_{\mathrm{fc}}=2$: 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 $(1/{\delta }_j)/\sum (1/{\delta }_j)$, ${\delta }_j=\sqrt{(\bar{\gamma }-{\bar{\gamma }}_j{)}^2+(\bar{V}-{\bar{V}}_j{)}^2}$ (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 $\Theta =atan2(\Delta X,\Delta Y)$ (Eq. 19), the curvature $K=\Delta \Theta /\Delta S$ (Eq. 18), the bank angle $\Phi =\arctan (K\cdot V_{\mathrm{g}}^2/g)$ (Eq. 20) and the path angle $\gamma =\arctan (\Delta Z/\Delta S)$ (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,), $N\ge 2$.
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.

FlightConditionInterpolation

FlightConditionInterpolation(
    scaling_factor: float = 2.0,
    triangles: NDArray[np.int_] | list[list[int]] | None = None,
)

How a flight condition blends the database hemispheres (Eq. 3-10).

The two settings of flight_condition_weights, which the event and contour entry points hand it per track point.

Attributes

Name	Description
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 (default None: the Delaunay triangulation of the normalised conditions). See flight_condition_weights.

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 $\Theta =atan2(\Delta X,\Delta Y)$ (Eq. 19), in degrees, shape (N,).
curvature	Track curvature $K=\Delta \Theta /\Delta S$ (Eq. 18), in rad/m, shape (N,) (zero where the ground speed vanishes).
bank_angle	Bank angle $\Phi =\arctan (K\cdot V_{\mathrm{g}}^2/g)$ (Eq. 20), in degrees, positive starboard down, shape (N,).
path_angle	Path angle $\gamma =\arctan (\Delta Z/\Delta S)$ (Doc 32 Eq. 10), in degrees, positive climbing, shape (N,).

Note

The guidance prints Eq. 21 as $\gamma =\arccos (\Delta Z/\Delta S)$, 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.

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,).

hover_derived_hemisphere

hover_derived_hemisphere(
    hemisphere: RotorcraftHemisphere,
    condition: str,
    *,
    offset_db: float | None = None,
) -> RotorcraftHemisphere

HOGE/idle hemisphere derived from in-ground hover (guidance Table 3).

Table 3 derives the out-of-ground-hover and idle sources from the in-ground-hover directivity pattern by a level offset, applied here uniformly to every band and bin: the table is stated on LA levels, and a constant spectral shift moves the LA by exactly that value (which is also how the NORAH2 reference database applies its corrections). With offset_db the offset is the measured 0°-direction difference of Approach 2, LA_cond(0°) − LA_HIGE(0°); without it the Approach 3 constants apply (+12 / −12 / −2.5 dB for "out_of_ground_hover" / "reduced_rpm_idle" / "full_rpm_idle", with the guidance’s caveat that they come from inverted microphones on ground plates). The corrections shipped with the NORAH2 public database differ from the published constants (+8 / −10 / −2 dB in every type’s interpolation file); pass them as offset_db to reproduce the reference implementation.

Parameters

Name	Description
hemisphere	The in-ground-hover RotorcraftHemisphere (typically from hover_ring_hemisphere; a fully measured Approach 1 hemisphere works the same).
condition	"out_of_ground_hover", "reduced_rpm_idle" or "full_rpm_idle".
offset_db	Explicit offset from in-ground hover, in dB (Approach 2 or a database correction). Default None: the Approach 3 constant of condition.

Returns: A new RotorcraftHemisphere at the same grid and reference distance, every measured bin shifted by the offset (NaN bins stay NaN).

Raises

Exception	When
ValueError	If the inputs are invalid.

hover_ring_hemisphere

hover_ring_hemisphere(
    frequencies: NDArray[np.float64] | list[float],
    bearings: NDArray[np.float64] | list[float],
    levels: NDArray[np.float64] | list[list[float]],
    *,
    distance: float = 70.0,
    azimuth_step: float = 10.0,
    polar_step: float = 10.0,
    mapping: str = 'constant_phi',
) -> RotorcraftHemisphere

Noise hemisphere from a ground-ring hover measurement (guidance §A.3.5).

In-ground hover, idle and their derived conditions are measured on a ring of ground microphones around the stationary rotorcraft (the CAEP in-ground hover practice the guidance points at): one band spectrum per ring bearing, 0° at the nose and positive to starboard, reduced to the polar distance of the ring. Table 3 (Approaches 2/3) extends that ring to the full hemisphere “assuming constant directivity in φ”; the guidance prints no formula for the extension, so the two readings the data supports are provided and documented here:

• "constant_phi" (default): the level depends only on the polar angle θ, port bins reading the ring at −θ and starboard bins at +θ (each ring bearing meets the hemisphere rim at φ = ±90°, θ = |bearing|, and slides inward at constant φ from there). The φ = 0 column under the aircraft takes the energy mean of the ±θ ring values. This is the literal reading of the guidance text, and it preserves the port/starboard asymmetry the ring measures.
• "bearing": the level depends only on the horizontal bearing of the emission direction, β = atan2(sin θ sin φ, cos θ) (constant directivity in elevation instead of in azimuth). This is what the NORAH2 reference implementation evaluates — its out-of-ground-hover verification case is reproduced with this mapping (and diverges from "constant_phi" by several dB at steep emission angles, where the two readings part).

Ring lookups interpolate periodically in the energy domain. The returned hemisphere carries distance (hover rings are commonly reduced to 70 m rather than the 60 m of the flyover database), which the event chain and the propagation adjustments honour as the reference distance.

Parameters

Name	Description
frequencies	Band centre frequencies, in Hz, shape (F,).
bearings	Ring bearings, in degrees within [-180, 180], strictly increasing, shape (B,) (0 at the nose, positive starboard). The ring closes periodically; a duplicated ±180° endpoint pair is accepted.
levels	Ring band levels, in dB at the ring’s polar distance, shape (B, F).
distance	Polar distance of the ring, in metres (default 70).
azimuth_step	Azimuth grid step, in degrees; must divide the 180° span (default 10, the NORAH grid).
polar_step	Polar grid step, in degrees; must divide the 180° span (default 10).
mapping	"constant_phi" (guidance text) or "bearing" (NORAH2 reference implementation), see above.

Returns: A RotorcraftHemisphere on the requested grid.

Raises

Exception	When
ValueError	If the inputs are invalid.

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.

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],
    *,
    level_offset: float | NDArray[np.float64] | list[float] = 0.0,
    atmosphere: RotorcraftAtmosphere = ...,
    ground: RotorcraftGround = ...,
    track_state: RotorcraftTrackState = ...,
    interpolation: FlightConditionInterpolation = ...,
) -> 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 $\Delta L_p=\Delta L_{\mathrm{s}}+\Delta L_{\mathrm{a}}+\Delta L_{\mathrm{g}}$ (Eq. 23-35) places it at the receiver. The received one-third-octave history is expressed at recorded time $t_{\mathrm{r}}=t_{\mathrm{e}}+r/c$ (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 track_state 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.
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.
atmosphere	The air the event propagates through, a RotorcraftAtmosphere (default: the ICAO reference conditions of the database).
ground	The ground under the event, a RotorcraftGround (default: flat ground at the track datum, CNOSSOS class "G", a 1.2 m microphone). A single receiver takes its scalar fields only; the per-grid-point arrays are for the contour.
track_state	Per-point airspeed, path angle, heading and bank angle, a RotorcraftTrackState (default: all derived from the track by flight_path_kinematics).
interpolation	How the flight condition blends the database hemispheres, a FlightConditionInterpolation (default: F_fc = 2 over the Delaunay triangulation).

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',
    level_offset: float | NDArray[np.float64] | list[float] = 0.0,
    atmosphere: RotorcraftAtmosphere = ...,
    ground: RotorcraftGround = ...,
    track_state: RotorcraftTrackState = ...,
    interpolation: FlightConditionInterpolation = ...,
) -> 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).
level_offset	Source-level offset ΔEPNL (Eq. 2), in dB, scalar or per track point.
atmosphere	The air the event propagates through, a RotorcraftAtmosphere.
ground	The ground under the grid, a RotorcraftGround. Its ground_elevation and flow_resistivity also accept one value per grid point (shape (len(y), len(x))), and its terrain model 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.
track_state	Per-point airspeed, path angle, heading and bank angle (see rotorcraft_event_level).
interpolation	How the flight condition blends the database hemispheres, a FlightConditionInterpolation.

Returns: A RotorcraftNoiseContourResult.

Raises

Exception	When
ValueError	If the inputs are invalid.

RotorcraftAtmosphere

RotorcraftAtmosphere(
    temperature: float = 25.0,
    relative_humidity: float = 70.0,
    pressure: float = 101.325,
    atmospheric_method: str = 'iso9613',
)

The air a rotorcraft event propagates through (Eq. 26/27).

The ICAO reference conditions of the hemisphere database are the defaults, so an event flown at those conditions needs no atmosphere at all. The Doc 29 airport chain keeps its own AerodromeAtmosphere instead of sharing this one: it corrects a broadband NPD level with the impedance of Eq. 4-7 alone, with no band-by-band absorption to ask the humidity or the method about, and at a different reference temperature.

Attributes

Name	Description
temperature	Air temperature, in °C (default 25, ICAO reference).
relative_humidity	Relative humidity, in % (default 70).
pressure	Ambient pressure, in kPa (default 101.325).
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).

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 $t_{\mathrm{r}}=t_{\mathrm{e}}+r/c$ (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.

RotorcraftGround

RotorcraftGround(
    receiver_height: float = 1.2,
    ground_elevation: float | NDArray[np.float64] | list[float] | list[list[float]] = 0.0,
    flow_resistivity: float | str | np.floating[Any] | np.integer[Any] | NDArray[np.float64] | list[float] | list[list[float]] = 'G',
    terrain: tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.float64]] | Sequence[NDArray[np.float64]] | None = None,
    terrain_resolution: float | None = None,
)

The ground a rotorcraft event stands on (guidance §A.4.3-A.4.5).

Flat ground at the track datum by default: the microphone height, the elevation of the site and the ground type feed the two-ray ground effect, and an optional elevation model replaces the flat plane with real terrain.

Attributes

Name	Description
receiver_height	Microphone height above local ground, in metres (default 1.2).
ground_elevation	Ground elevation z at the receivers, in metres on the track datum (default 0); source and receiver heights above ground follow from it. A contour grid also accepts one value per grid point (shape (len(y), len(x))) for receivers on uneven sites without a full elevation model.
flow_resistivity	Ground flow resistivity σ in Pa·s/m², or a CNOSSOS class letter (see ground_effect_adjustment). A contour grid also accepts 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).
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 every 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).

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.

RotorcraftTrackState

RotorcraftTrackState(
    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,
)

Per-point flight state of a rotorcraft track (Eq. 16-21).

Every field left unset is derived from the track itself by flight_path_kinematics; a radar-track workflow that has already smoothed these quantities hands them over instead. Each is a scalar (broadcast over the track) or an array of shape (N,).

Attributes

Name	Description
airspeed	Airspeed V_A, in the units of the database airspeeds (the derived values are in m/s).
path_angle	Path angle γ, in degrees (negative descending).
heading	Heading Θ, in degrees.
bank_angle	Bank angle Φ, in degrees (positive starboard down).