Source: https://jmrplens.github.io/phonometry/guides/rotorcraft-noise/ # Rotorcraft noise: the hemisphere method (ECAC Doc 32 / NORAH2) Helicopter noise is strongly directive, so the ECAC Doc 32 method describes the source with a **noise hemisphere**: one-third-octave-band sound pressure levels on a spherical grid of azimuth `φ` and polar angle `θ`, measured at a fixed **60 m** reference distance under ICAO reference atmospheric conditions. Placing that source at a receiver adds the propagation adjustment `ΔLp = ΔLs + ΔLa + ΔLg (+ ΔLd)`. This page covers the source and propagation primitives, the flight-condition interpolation across a hemisphere database, the flight-path kinematics, and the single-event integration to `SEL`/`LASmax`/`EPNL` and ground-grid contours; terrain shielding follows in later work. ## 1. The noise hemisphere A `RotorcraftHemisphere` holds the band levels on the azimuth/polar grid (with missing bins marked `NaN`). `hemisphere_source_level` reads the source level at an arbitrary emission direction: the grid is first gap-filled by nearest-bin constant-value extrapolation (Eq. 14/15, equally-near bins energy-averaged; computed once and cached), then the lookup is bilinear in the energy domain over the four neighbouring bins (Doc 32 Eq. 13), so partially-measured cells stay continuous with their measured corners. ```python import numpy as np from phonometry import aircraft # A hemisphere: band levels of shape (azimuth, polar, frequency) at 60 m. h = aircraft.RotorcraftHemisphere(frequencies=freqs, azimuth=phi, polar=theta, levels=levels) h.plot() # fore-aft directivity (needs matplotlib) lv = aircraft.hemisphere_source_level(h, 0.0, 90.0) # level per band abeam-below ``` ## 2. Propagation adjustments The hemisphere level at 60 m is carried to the receiver by three adjustments (Doc 32 §A.4): - **`spherical_spreading_adjustment(r)`**: `ΔLs = −20·log10(r/60)` (Eq. 24). - **`atmospheric_adjustment(freqs, r)`**: `ΔLa = −α(f)·(r − 60)` with the ISO 9613-1 pure-tone coefficient at the exact band centre (Eq. 26/27), reusing the library's `air_attenuation`; this is what the NORAH2 reference implementation computes. The guidance's alternative SAE (Rickley) band mapping, tabulated in its Table 4, coincides below 3.15 kHz and deviates by up to 2.2 dB/km at 8-10 kHz. - **`ground_effect_adjustment(freqs, hs, hr, dp, flow_resistivity=…)`**: the interference between the direct and ground-reflected rays over an impedance plane (Chien-Soroka, Eq. 28-35), with the Delany-Bazley one-parameter impedance and the CNOSSOS flow-resistivity classes `"A"`-`"H"`.

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import aircraft freqs = 1000.0 * 10.0 ** (np.arange(-13, 11) / 10.0) # 50 Hz-10 kHz thirds hs, hr, dp = 150.0, 1.5, 500.0 # overflight geometry grass = aircraft.ground_effect_adjustment(freqs, hs, hr, dp, flow_resistivity="D") asphalt = aircraft.ground_effect_adjustment(freqs, hs, hr, dp, flow_resistivity="G") fig, ax = plt.subplots() ax.axhline(0.0, color="0.5", linewidth=1.0) ax.semilogx(freqs, asphalt, marker="o", markersize=3, label="Hard (asphalt/concrete, class G)") ax.semilogx(freqs, grass, marker="s", markersize=3, label="Soft (grass/pasture, class D)") ax.set(xlabel="One-third-octave-band centre frequency [Hz]", ylabel="Ground-effect adjustment ΔLg [dB]", title="Rotorcraft ground effect (ECAC Doc 32, Chien-Soroka)") ax.grid(True, which="both", alpha=0.3) ax.legend() plt.show() ```

```python import numpy as np from phonometry import aircraft freqs = 1000.0 * 10.0 ** (np.arange(-13, 11) / 10.0) # 50 Hz-10 kHz thirds r = 500.0 received = (lv + aircraft.spherical_spreading_adjustment(r) + aircraft.atmospheric_adjustment(freqs, r) + aircraft.ground_effect_adjustment(freqs, 150.0, 1.5, 500.0, flow_resistivity="D")) ``` The standard database is recorded at 60 m, the default. If a hemisphere uses a different polar distance (`h.distance`, e.g. 70 m hover rings), pass it to both distance-dependent adjustments: `spherical_spreading_adjustment(r, reference_distance=h.distance)` and `atmospheric_adjustment(freqs, r, reference_distance=h.distance)`. ## 3. Flight conditions: interpolating between hemispheres A database records one hemisphere per flight condition (airspeed `V`, path angle `γ`): approaches at several descent angles, level flyovers at several speeds, take-off climbs. Real flight conditions rarely coincide with a measured one, so the NORAH2 guidance interpolates (Eq. 3-10): both axes are normalised by their database spans (with the empirical scaling factor `Ffc = 2` on the path angle), a Delaunay triangulation covers the normalised conditions, and a query inside the convex hull blends the three hemispheres of its enveloping triangle with inverse-distance weights in the energy domain. Outside the hull the nearest condition is adopted unblended, which is also the behaviour ECAC Doc 32, 1st ed. prescribes for its whole envelope (it defines no interpolation yet). `flight_condition_weights` returns the `(index, weight)` pairs; `interpolated_source_level` applies them to the hemisphere lookups: ```python import numpy as np from phonometry import aircraft # One hemisphere per measured flight condition (speeds in kt, angles in deg). speeds = [50.0, 70.0, 60.0] angles = [0.0, 0.0, 10.0] weights = aircraft.flight_condition_weights(speeds, angles, 60.0, 2.5) lv = aircraft.interpolated_source_level( [h_50_level, h_70_level, h_60_climb], speeds, angles, 60.0, 2.5, 0.0, 90.0) # blended level per band, abeam-below ``` The airspeed, not the ground speed, selects the hemisphere. The weights are unit-invariant (knots or m/s, as long as the query matches the database), and a database lookup triangulation can be passed as `triangles` (the NORAH database ships one per type; its shipped tables triangulate the raw `(V, γ)` plane, so passing them reproduces the reference implementation bin for bin). Types whose rotor configuration is mirrored with respect to their class reference substitute `h.mirrored()` (Eq. 2, `φ → −φ`), and certification-level offsets enter as `level_offset`. ## 4. Flight-path kinematics `flight_path_kinematics` derives, from a time-stamped track by central finite differences, everything the event needs (Eq. 16-21 / Doc 32 Eq. 8-10): ground speed `Vg`, airspeed `VA` (zero wind), heading `Θ = atan2(ΔX, ΔY)`, curvature `K = ΔΘ/ΔS`, bank angle `Φ = atan(K·Vg²/g)` and path angle `γ = atan(ΔZ/ΔS)`. The guidance recommends smoothing radar tracks (e.g. spline resampling to a 0.5 s cadence) before differentiating. ```python kin = aircraft.flight_path_kinematics(times, positions) # positions (N, 3), m kin.plot() # speed and angle profiles kin.airspeed, kin.path_angle # select the hemisphere per point kin.bank_angle # tilts the hemisphere in turns ``` ## 5. The single event: `SEL`, `LASmax` and `EPNL` `rotorcraft_event_level` runs the whole chain for one flyover at one receiver. Per track point, the flight condition selects (or blends) the hemispheres and the emission angles address the source level; the hemisphere frame is oriented by the heading and tilted by the bank angle in turns (pitch attitude is implicit in the hemispheres). The received one-third-octave history is expressed at recorded time `tr = te + r/c` (Eq. 22, `c = 346.1 m/s`) and integrated: `LASmax`, `SEL` over the full history and over the certification 10 dB-down window (Doc 32 Eq. 27), and `EPNL` per ICAO Annex 16 (Doc 32 Eq. 28), reusing the library's `epnl_from_pnlt`. ```python res = aircraft.rotorcraft_event_level( hemispheres, speeds, angles, # the database times, positions, # the track (m, z up) receiver=(120.0, 0.0), # ground position of the microphone flow_resistivity="D") # grass site res.la_max, res.sel, res.epnl # LASmax, SEL, EPNL res.plot() # the LA(t) time history ```

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import aircraft # A synthetic helicopter-like hemisphere on the standard 31-band, 10° grid. freqs = 1000.0 * 10.0 ** (np.arange(-20, 11) / 10.0) # 10 Hz-10 kHz thirds az = np.arange(-90.0, 91.0, 10.0) po = np.arange(0.0, 181.0, 10.0) spectrum = 88.0 - 12.0 * np.log10(freqs / 100.0) ** 2 # broad low-mid hump levels = (spectrum[None, None, :] - 0.045 * np.abs(po - 80.0)[None, :, None] - 0.02 * np.abs(az)[:, None, None]) h = aircraft.RotorcraftHemisphere(freqs, az, po, levels) speed = 30.87 # 60 kt, in m/s t = np.arange(0.0, 130.01, 0.5) track = np.column_stack([np.zeros_like(t), speed * (t - 65.0), np.full_like(t, 150.0)]) event = aircraft.rotorcraft_event_level( [h], [speed], [0.0], t, track, (120.0, 0.0), flow_resistivity="D") event.plot() plt.show() ```

Radar-track workflows can hand the smoothed per-point `airspeed`, `path_angle`, `heading` and `bank_angle` directly instead of deriving them from the positions; when they are derived, the track is in metres and seconds, so the database airspeeds must then be in m/s. ## 6. Ground-grid contours `rotorcraft_noise_contour` evaluates the same event over a whole grid in one vectorised pass per emission step and reduces each receiver's history to the `SEL` (`metric="exposure"`) or `LASmax` (`metric="maximum"`) footprint: ```python res = aircraft.rotorcraft_noise_contour( hemispheres, speeds, angles, times, positions, x=np.linspace(-2000.0, 2000.0, 81), y=np.linspace(-3000.0, 3000.0, 121), metric="exposure", flow_resistivity="D") res.plot() # filled SEL contours ``` The ground may vary across the receivers without a full elevation model: `flow_resistivity` and `ground_elevation` accept one value per grid point (shape `(len(y), len(x))`), and each receiver's two-ray model then uses its local values. ## 7. Terrain: the mean ground plane and screening Doc 32, 1st ed., assumes flat terrain; its guidance adds the machinery for real sites. A varying vertical section is represented by its **mean ground plane** (Eq. 36-40), the least-squares line through the terrain polyline computed in closed form; source and receiver enter the flat-ground equations with their **equivalent heights**, measured orthogonally to that plane and floored at 0.1 m. Ground that changes type along the path averages its flow resistivity by the logarithm, weighted by segment length (Eq. 41). When terrain blocks the line of sight, the sound follows the shortest convex path over it (the guidance's rubber band) and every touched vertex is a **diffraction edge**. The attenuation combines the pure diffraction of the path difference `δ` (Eq. 42-44, `10·Ch·log10(3 + (40/λ)·C″·δ)`, capped at 25 dB) with the source-side and receiver-side ground effects, each over its own mean ground plane and weighted by its image-path diffraction (Eq. 45-47, the CNOSSOS-EU scheme the guidance adopts). The ground effect is not evaluated separately in that regime. `mean_ground_plane`, `mean_flow_resistivity` and `diffraction_attenuation` expose the pieces; `terrain_screening_adjustment` runs the whole section: ```python import numpy as np from phonometry import aircraft d = [0.0, 150.0, 260.0, 300.0, 340.0, 420.0, 600.0] # section distances z = [0.0, 4.0, 48.0, 62.0, 40.0, 8.0, 2.0] # terrain heights freqs = 1000.0 * 10.0 ** (np.arange(-13, 11) / 10.0) res = aircraft.terrain_screening_adjustment( freqs, source=(0.0, 90.0), receiver=(600.0, 3.2), distances=d, heights=z, flow_resistivity="D") res.screened, res.path_difference # True, the rubber-band delta res.adjustment # per band, replaces the flat-ground ΔLg res.plot() # the section geometry ```

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import aircraft freqs = 1000.0 * 10.0 ** (np.arange(-13, 11) / 10.0) # 50 Hz-10 kHz thirds d = np.array([0.0, 150.0, 260.0, 300.0, 340.0, 420.0, 600.0]) z = np.array([0.0, 4.0, 48.0, 62.0, 40.0, 8.0, 2.0]) res = aircraft.terrain_screening_adjustment( freqs, (0.0, 90.0), (600.0, 3.2), d, z, flow_resistivity="D") flat = aircraft.ground_effect_adjustment(freqs, 90.0, 1.2, 600.0, flow_resistivity="D") fig, (ax, ax2) = plt.subplots(2, 1, figsize=(9, 7)) res.plot(ax=ax) ax2.axhline(0.0, color="0.5", linewidth=1.0) ax2.semilogx(freqs, flat, ls="--", marker="s", markersize=3, label="Flat ground (no hill)") ax2.semilogx(freqs, res.adjustment, marker="o", markersize=3, label="Screened by the hill (Eq. 45-47)") ax2.set(xlabel="One-third-octave-band centre frequency [Hz]", ylabel="Ground and screening adjustment [dB]") ax2.grid(True, which="both", alpha=0.3) ax2.legend() plt.show() ```

The event and contour run over real sites by passing a digital elevation model: `terrain=(x, y, z)` on the track frame. Every emission-receiver pair then samples its own vertical section at `terrain_resolution` (default: the model's cell size) and evaluates it with the machinery above; the receiver ground comes from the model. The cost grows with track points times grid points, so keep contour grids modest with terrain. ```python res = aircraft.rotorcraft_event_level( hemispheres, speeds, angles, times, positions, receiver=(1200.0, 300.0), terrain=(tx, ty, tz), flow_resistivity="D") ``` ## Validation Validated against the NORAH2 guidance Table 4 (all 31 bands, 10 Hz-10 kHz), the closed-form inverse-square spreading, the analytic rigid-ground `+6 dB` and grazing limits of the ground effect, off-node bilinear lookups on the reference hemispheres of all eleven rotorcraft types, hand-checked interpolation simplices, closed-form kinematics and the Lorentzian `SEL − LASmax` flyover integral, and end to end against the NORAH2 prototype's ARP verification cases: emission angles reproduce to 0.01°, retarded times to 0.02 s, every step level of the hard-ground events to 0.08 dB(A) out to 18 km, `LASmax` to 0.03 dB and `SEL` to 0.05 dB over hard ground (0.4 dB over soft ground), the 187-microphone contour grid to 0.7 dB worst-case, `PNLTM` to 0.1 dB and `EPNL` to about 1.3 dB (the prototype's sub-noy-floor perceived-noisiness policy differs from the published Annex 16 law). One documented divergence remains: at far range over soft ground the prototype damps the coherent two-ray interference of guidance Eq. 30 towards the incoherent sum (up to 4.9 dB on individual low-level steps beyond 7 km); neither Doc 32 nor the guidance contains such a term, and this implementation follows the published equations. The terrain machinery is anchored in closed form: the mean ground plane is exact on linear and symmetric profiles, a flat section reproduces the flat-ground model to machine precision and an inclined plane its analytic rotation, the log-mean resistivity recovers the geometric mean, the grazing diffraction gives the classical `10·log10(3)`, and a hand-checked hill fixes the rubber-band path difference. Per-receiver ground handling validates end to end against the prototype's ARP Case 3 (187 microphones, each on its own ground elevation: every step level to 0.08 dB(A), `SEL`/`LASmax` to 0.05 dB, the contour grid to 0.15 dB) and the mixed-ground Case 2 grid reproduces in a single per-receiver-resistivity call. The prototype's public release does not include a reconstructible screening case (the frame of its terrain model could not be pinned to the published outputs), so the diffraction chain itself rests on the closed-form anchors and its CNOSSOS-EU lineage. ## References - European Civil Aviation Conference. (2026). *Report on standard method of computing rotorcraft noise contours* (ECAC.CEAC Doc 32, 1st ed.). [ECAC documents page](https://www.ecac-ceac.org/documents/ecac-documents-and-international-agreements), [free PDF](https://www.ecac-ceac.org/images/documents/ECAC-CEAC-DOC_32-REPORT_ON_STANDARD_METHOD_OF_COMPUTING_ROTORCRAFT_NOISE_CONTOURS.pdf). The standard rotorcraft contour method whose hemisphere source model and propagation adjustments this page implements. - Olsen, H., Tuinstra, M., & van Oosten, N. (2024). *Rotorcraft noise modelling guidance* (Research Project NOISE SC01, deliverable D1.5d, contract EASA.2020.FC.06). European Union Aviation Safety Agency. [EASA project page](https://www.easa.europa.eu/en/research-projects/environmental-research-rotorcraft-noise), [free PDF](https://www.easa.europa.eu/en/downloads/132005/en). The equation-level guidance (Eq. 13-35) behind the implementation, with the Table 4 attenuation values and the reference hemispheres used as oracles. - Chien, C. F., & Soroka, W. W. (1975). Sound propagation along an impedance plane. *Journal of Sound and Vibration*, 43(1), 9-20. [doi:10.1016/0022-460X(75)90200-X](https://doi.org/10.1016/0022-460X(75)90200-X). The two-ray interference solution over an impedance plane behind the section 2 ground-effect adjustment. - Delany, M. E., & Bazley, E. N. (1970). Acoustical properties of fibrous absorbent materials. *Applied Acoustics*, 3(2), 105-116. [doi:10.1016/0003-682X(70)90031-9](https://doi.org/10.1016/0003-682X(70)90031-9). The one-parameter flow-resistivity impedance model the ground effect evaluates. - Kephalopoulos, S., Paviotti, M., & Anfosso-Lédée, F. (2012). *Common noise assessment methods in Europe (CNOSSOS-EU)* (EUR 25379 EN). Publications Office of the European Union. [doi:10.2788/31776](https://doi.org/10.2788/31776), [JRC repository](https://publications.jrc.ec.europa.eu/repository/handle/JRC72550). The flow-resistivity ground classes `"A"`-`"H"` accepted by `ground_effect_adjustment`. ## Standards ECAC Doc 32, 1st ed., *Report on Standard Method of Computing Rotorcraft Noise Contours*; NORAH2 rotorcraft-noise modelling guidance (EASA.2020.FC.06 SC01.D1.5d), §A.3-A.5: the noise hemisphere (§A.3.2), spherical spreading (Eq. 24), atmospheric attenuation (Eq. 26/27, ISO 9613-1 coefficient, Table 4), ground effect (Chien-Soroka, Eq. 28-35, Delany-Bazley impedance, CNOSSOS flow resistivity), flight-condition interpolation (Eq. 3-10), flight-path kinematics (Eq. 16-21 / Doc 32 Eq. 8-10), recorded time (Eq. 22), the single-event metrics `SEL`/`LASmax` and `EPNL` (Doc 32 Eq. 27/28, ICAO Annex 16 App. 2), the mean ground plane and equivalent heights (Eq. 36-40), the log-mean flow resistivity (Eq. 41) and the terrain screening chain (Eq. 42-47 with the guidance's noise-path appendices; CNOSSOS-EU lineage). Hover, idle and taxi source handling (guidance §A.3.5) remains outside the implementation.