Source: https://jmrplens.github.io/phonometry/aircraft/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 $\varphi$ and polar angle $\theta$, measured at a fixed **60 m** reference distance under ICAO reference atmospheric conditions. Placing that source at a receiver adds the propagation adjustment $\Delta L_p = \Delta L_\mathrm{s} + \Delta L_\mathrm{a} + \Delta L_\mathrm{g}$ ($+\ \Delta L_\mathrm{d}$). This page covers the source and propagation primitives, the flight-condition interpolation across a hemisphere database, the hover/idle source derivation of Table 3, the flight-path kinematics, the single-event integration to `SEL`/`LASmax`/`EPNL` and ground-grid contours, and the terrain mean-ground-plane and screening machinery. The EPNL this page computes is the same quantity certification asks for: ICAO Annex 16 Chapter 8 flies the helicopter level at 150 m over a centre microphone, with two more 150 m to each side. ## 1. The noise hemisphere The library implements the method, not the data: **no hemisphere database ships with phonometry, and there is no NORAH file reader**, so the arrays below are assembled by the reader — from a flight-test campaign that de-propagates each emission direction back to the 60 m reference sphere, or from the NORAH2 reference database, which covers eleven rotorcraft types. 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)`**: $\Delta L_\mathrm{s} = -20\log_{10}(r/60)$ (Eq. 24). - **`atmospheric_adjustment(freqs, r)`**: $\Delta L_\mathrm{a} = -\alpha(f)\,(r - 60)$ 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)`. The three adjustments assume straight rays: refraction by atmospheric gradients is outside Doc 32 itself and is not modelled. ## 3. Flight conditions: interpolating between hemispheres A database records one hemisphere per flight condition (airspeed $V$, path angle $\gamma$): 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 $F_\text{fc} = 2$ 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 $(V, \gamma)$ 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, $\varphi \to -\varphi$), and certification-level offsets enter as `level_offset`. ## 4. Hover, idle and taxi (guidance §A.3.5, Table 3) A hovering or idling helicopter is measured differently from a flyover: on a **ring of ground microphones** around the stationary aircraft (the CAEP in-ground hover practice the guidance points at), one band spectrum per ring bearing (0° at the nose, positive to starboard), reduced to the ring's polar distance — commonly 70 m rather than the flyover database's 60 m. The guidance defines four conditions — in-ground hover (HIGE), out-of-ground hover (HOGE), reduced-rpm idle and full-rpm idle — and three approaches in descending priority: measure all four rings (Approach 1), measure the HIGE ring and the other three in the 0° direction only (Approach 2), or measure the HIGE ring alone and apply fixed offsets (Approach 3). `hover_ring_hemisphere` extends the ring to a full `RotorcraftHemisphere` "assuming constant directivity in φ": each bin $(\varphi, \theta)$ reads the ring at the bearing $\pm\theta$ of its own half — port bins from negative bearings, starboard bins from positive ones, and the $\varphi = 0$ column under the aircraft takes the energy mean of the $\pm\theta$ ring values — with periodic interpolation in the energy domain. The NORAH2 reference implementation reads the same ring by the horizontal bearing of the emission direction instead (constant directivity in elevation, `mapping="bearing"`); the two readings coincide on the hemisphere rim and part by several dB at steep emission angles. `hover_derived_hemisphere` derives HOGE and the idles from the HIGE hemisphere by a uniform level offset: a measured 0°-direction difference (Approach 2, passed as `offset_db`), or the published Approach 3 constants — +12 dB for HOGE, −12 dB for reduced-rpm idle and −2.5 dB for full-rpm idle, all from the HIGE disk. The guidance warns that those constants come from measurements with inverted microphones on ground plates and may not hold for other setups, and the reference database actually ships +8/−10/−2 dB (the `Corr_dB` corrections of its per-type interpolation files): pass them as `offset_db` to reproduce the prototype. The Approach 3 prose derives full-rpm idle from HOGE where its own Table 3 derives it from HIGE, 12 dB apart; the table, backed by the database, is what is implemented (see the [errata registry](https://jmrplens.github.io/phonometry/reference/errata/)). ```python import numpy as np from phonometry import aircraft # A hover ring with a real campaign's shape: one 31-band third-octave # spectrum per 30° of bearing, reduced to the 70 m polar distance. freqs = 1000.0 * 10.0 ** (np.arange(-20, 11) / 10.0) # 10 Hz-10 kHz thirds bearings = np.arange(-180.0, 151.0, 30.0) # the ring closes at ±180° ring_levels = (86.0 - 10.0 * np.log10(freqs / 160.0) ** 2 + 3.5 * np.cos(np.radians(bearings))[:, None]) hige = aircraft.hover_ring_hemisphere(freqs, bearings, ring_levels, distance=70.0) hoge = aircraft.hover_derived_hemisphere(hige, "out_of_ground_hover") # +12 dB full_rpm_idle = aircraft.hover_derived_hemisphere(hige, "full_rpm_idle") # -2.5 dB ```

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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(-20, 11) / 10.0) # 10 Hz-10 kHz thirds bearings = np.arange(-180.0, 151.0, 30.0) spectrum = 86.0 - 10.0 * np.log10(freqs / 160.0) ** 2 directivity = (3.5 * np.cos(np.radians(bearings)) + 3.0 * np.exp(-((bearings - 120.0) ** 2) / (2.0 * 40.0**2))) ring = spectrum[None, :] + directivity[:, None] hige = aircraft.hover_ring_hemisphere(freqs, bearings, ring, distance=70.0) k = int(np.argmin(np.abs(freqs - 315.0))) theta = np.linspace(0.0, 180.0, 361) fig, (ax, ax2) = plt.subplots(1, 2, figsize=(12, 5.2)) ax.plot(np.append(bearings, 180.0), np.append(ring[:, k], ring[0, k]), marker="o") ax.set(xlabel="Ring bearing [°] (0° nose, +90° starboard)", ylabel="Band level at 70 m [dB]") for condition, label in ((None, "HIGE (from the ring)"), ("out_of_ground_hover", "HOGE (+12 dB)"), ("full_rpm_idle", "Full-rpm idle (-2.5 dB)"), ("reduced_rpm_idle", "Reduced-rpm idle (-12 dB)")): h = hige if condition is None else aircraft.hover_derived_hemisphere(hige, condition) ax2.plot(theta, [aircraft.hemisphere_source_level(h, 0.0, t)[k] for t in theta], label=label) ax2.set(xlabel="Polar angle θ [°] (0° forward → 180° rearward)", ylabel="Source level at 70 m [dB]") ax2.legend() plt.show() ```

**Taxi** is a selection between two of these sources, not a new one: a helicopter without wheels taxis hovering in ground effect (the HIGE hemisphere), and a wheeled one ground-taxis on its wheels with the rotor at idle (the full-rpm-idle hemisphere). The guidance's sentence pairs them the other way around ("… in-ground hover and full-rpm idle respectively"); the pairing here follows the physics of the two operations (see the errata registry). ```python wheeled = False # skid gear: taxi is a hover taxi = full_rpm_idle if wheeled else hige # guidance p. 19 (see caveat) ``` A hover or idle **event** is the standard single event with a stationary track: one hemisphere, a fixed position, the receiver of interest. The derived hemisphere carries the ring's `distance`, which the whole chain honours as the reference distance; hover and flyover hemispheres recorded at different distances run as separate events, which is also how the reference implementation switches source by operating mode. ```python t = np.arange(0.0, 30.5, 0.5) # 30 s of hover at 3 m track = np.column_stack([np.zeros_like(t), np.zeros_like(t), np.full_like(t, 3.0)]) res = aircraft.rotorcraft_event_level([hige], [0.0], [0.0], t, track, (100.0, 0.0)) ``` What stays outside the implementation is §A.3.5's last resort when no hover data exists at all: correcting two side-line level-flight microphones to the 150 m hover circle by the ICAO Annex 16 integrated method, a measurement-correction chain this module (which consumes already-reduced hemispheres) does not model. ## 5. 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 $V_\mathrm{g}$, airspeed $V_\mathrm{A}$ (zero wind), heading $\Theta = \operatorname{atan2}(\Delta X, \Delta Y)$, curvature $K = \Delta\Theta/\Delta S$, bank angle $\Phi = \arctan(K V_\mathrm{g}^2 / g)$ and path angle $\gamma = \arctan(\Delta Z / \Delta S)$. 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 ``` ## 6. 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 $t_\mathrm{r} = t_\mathrm{e} + r/c$ (Eq. 22, $c = 346.1\ \text{m/s}$) 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 ground=aircraft.RotorcraftGround(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), ground=aircraft.RotorcraftGround(flow_resistivity="D")) event.plot() plt.show() ```

Radar-track workflows can hand the smoothed per-point `airspeed`, `path_angle`, `heading` and `bank_angle` of a `RotorcraftTrackState` 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. ## 7. 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", ground=aircraft.RotorcraftGround(flow_resistivity="D")) res.plot() # filled SEL contours ``` The ground may vary across the receivers without a full elevation model: the `flow_resistivity` and `ground_elevation` of the `RotorcraftGround` accept one value per grid point (shape `(len(y), len(x))`), and each receiver's two-ray model then uses its local values. ## 8. 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 $\delta$ (Eq. 42-44, $10 C_h \log_{10}\bigl(3 + (40/\lambda)\,C''\,\delta\bigr)$, 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. ```python from phonometry import diffraction_attenuation bands = [63.0, 250.0, 1000.0, 4000.0] diffraction_attenuation(bands, 0.0, edge_height=2.5) # grazing incidence diffraction_attenuation(bands, 1.0, edge_height=2.5) # 1 m into the shadow ```

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import diffraction_attenuation bands = np.array([63.0, 250.0, 1000.0, 4000.0]) delta = np.linspace(-0.4, 1.5, 441) ld = np.array([diffraction_attenuation(bands, float(d), edge_height=2.5) for d in delta]) fig, ax = plt.subplots(figsize=(9, 6)) for i, label in enumerate(["63 Hz", "250 Hz", "1 kHz", "4 kHz"]): ax.plot(delta, ld[:, i], label=label) ax.axvline(0.0, color="0.5", linestyle="--") ax.axhline(25.0, color="0.5", linestyle=":", label="25 dB cap") ax.set(xlabel="Path difference δ [m]", ylabel="Diffraction attenuation ΔLd [dB]") ax.legend() plt.show() ```

Every curve is flat at zero left of its own threshold (the guidance's $(40/\lambda)\,C''\,\delta \ge -2$, so a longer wavelength still shows attenuation further below the line of sight). Grazing incidence is $10\,C_h\log_{10}3$, not a fixed value: the three bands whose frequency already saturates $C_h$ at 1 (Eq. 43, $h_0$ = 2.5 m) cross the classical $\approx 4.8$ dB, while 63 Hz, with $C_h = 0.63$ there, crosses at 3.0 dB instead. Only the 4 kHz band is short enough to reach the 25 dB cap within this range, at $\delta \approx 0.68$ m. `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 in the `RotorcraftGround`: `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), ground=aircraft.RotorcraftGround(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 $\mathrm{SEL} - L_\mathrm{ASmax}$ 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 Table 3 hover/idle derivation is anchored in closed form (the ring-to-rim identity, hand-computed constant-φ bins, the exact Approach 3 offsets) and end to end against the prototype's out-of-ground-hover verification case: its eight microphones, spanning bearings, elevations, receiver heights from 0.01 m to 8.2 m and four flow resistivities, reproduce `LASmax`/`SEL` to 0.45 dB worst case with the prototype's own conventions passed explicitly (`mapping="bearing"` and its +8 dB database correction as `offset_db`; the guidance's constant-φ text and published +12 dB are the defaults). The residual peaks on the nadir microphones, where the prototype's damped interference differs most from the published coherent Eq. 30. 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 $10\log_{10} 3$, 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. ## See also - [Aircraft noise: Effective Perceived Noise Level](https://jmrplens.github.io/phonometry/aircraft/aircraft-noise/): the ICAO Annex 16 Appendix 2 chain this page's Doc 32 Eq. 28 term calls, and the measurement practice a hemisphere campaign follows. - [Airport Noise (ECAC Doc 29)](https://jmrplens.github.io/phonometry/aircraft/airport-noise/): the fixed-wing contour method, where a noise-power-distance table plays the role the noise hemisphere plays here. - [Outdoor sound propagation](https://jmrplens.github.io/phonometry/environment/propagation/outdoor-propagation/): the ISO 9613-2 ground effect and the CNOSSOS ground classes this two-ray adjustment shares. - API reference: [`aircraft.rotorcraft_noise`](https://jmrplens.github.io/phonometry/reference/api/aeroacoustics/rotorcraft-noise/). ## 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), the terrain screening chain (Eq. 42-47 with the guidance's noise-path appendices; CNOSSOS-EU lineage) and the hover/idle source derivation of §A.3.5 Table 3 (the ring-to-hemisphere constant-φ extension, the Approach 2/3 offsets and the taxi selection rule). Only §A.3.5's no-hover-data fallback (two side-line microphones corrected to the 150 m hover circle by the ICAO Annex 16 integrated method) remains outside the implementation.