Source: https://jmrplens.github.io/phonometry/aircraft/airport-noise/ # Airport noise (ECAC Doc 29) Certification measures one aeroplane at one reference point on one flight; an airport study asks a different question: how loud is it *there*, on that street, for that departure. The ECAC Doc 29 method answers it without re-measuring anything. The aeroplane arrives as a **noise-power-distance (NPD)** table, a measured event level against slant distance for a handful of engine power settings; the flight arrives as a path of segments; and the method corrects the NPD baseline segment by segment for everything the tables could not know: the atmosphere on the day, the finite length of each segment, how far off to the side the receiver sits, where the engines are mounted, and the rearward lobe of a jet still on the runway. This page covers that chain end to end, from the NPD interpolation to the ground-grid contour, and it is validated against the reference workbook of Doc 29 5th ed. Vol. 3. The certification metric these tables ultimately come from, the EPNL of ICAO Annex 16, is [Aircraft noise](https://jmrplens.github.io/phonometry/aircraft/aircraft-noise/); the physical propagation ingredients (ground effect, atmospheric absorption, barriers) are [Outdoor sound propagation](https://jmrplens.github.io/phonometry/environment/propagation/outdoor-propagation/). ## 1. The noise-power-distance engine The ECAC Doc 29 airport-noise method describes an aircraft with **noise-power- distance (NPD)** tables that give the event level ($L_\mathrm{Amax}$ or `SEL`) of steady straight flight versus engine power and slant distance. `npd_level` reads an event level for an arbitrary power and distance, interpolating **linearly in power** (Eq. 4-3) and **log-linearly in distance** (Eq. 4-4), extrapolating from the terminal segments beyond the tabulated envelope.

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```python import matplotlib.pyplot as plt from phonometry import aircraft # A schematic NPD table: SEL vs slant distance for two thrust settings. powers = [12000.0, 20000.0] distances = [200.0, 400.0, 630.0, 1000.0, 2000.0, 4000.0, 6300.0, 10000.0] levels = [[98.5, 92.0, 88.2, 83.6, 76.8, 69.4, 63.9, 56.8], [107.2, 100.9, 97.2, 92.7, 86.0, 78.5, 72.9, 65.6]] fig, ax = plt.subplots() for p in (20000.0, 12000.0): curve = aircraft.npd_curve(powers, distances, levels, power=p) line, = ax.semilogx(curve.distance, curve.level, label=f"P = {p:.0f} N") ax.semilogx(curve.table_distances, curve.table_levels, "o", markersize=4, color=line.get_color()) ax.set(xlabel="Slant distance [m]", ylabel="Event level [dB]", title="Noise-power-distance curves (ECAC Doc 29)") ax.grid(True, which="both", alpha=0.3) ax.legend() plt.show() ```

```python from phonometry import aircraft powers = [12000.0, 20000.0] # e.g. net thrust, N distances = [200.0, 400.0, 1000.0, 2000.0, 6300.0, 10000.0] levels = [[98.5, 92.0, 83.6, 76.8, 63.9, 56.8], [107.2, 100.9, 92.7, 86.0, 72.9, 65.6]] aircraft.npd_level(powers, distances, levels, power=16000.0, distance=1500.0) curve = aircraft.npd_curve(powers, distances, levels, power=20000.0) curve.plot() # NPD curve with the tabulated nodes (needs matplotlib) ``` The tables may be used as tabulated while the aerodrome's average conditions stay inside the Doc 29 §2.5 envelope: air temperature below 30 °C, the product of temperature (°C) and relative humidity (%) above 500, and wind below 8 m/s. Outside it the *tables themselves* have to be converted by the Appendix D procedure, which this chain does not implement — `impedance_adjustment` takes only temperature and pressure, and no humidity argument enters the chain anywhere. One restriction runs under all of it: the SAE AIR 5662 lateral attenuation, and with it the whole single-event chain that uses it, is derived for acoustically soft, grassy ground, so a contour drawn over water, an apron or dense hard surfaces is outside the method as published. ## 2. The single-event calculation The full ECAC Doc 29 single-event calculation places a flight path's noise at a receiver by breaking the path into segments and, for each, correcting the NPD baseline level (§4.3-4.5): - **`impedance_adjustment`** ($T$, $p$): corrects the NPD data from their reference air impedance (409.81 N·s/m³) to the aerodrome's temperature and pressure (Eq. 4-6/4-7; +0.074 dB under the standard atmosphere). - **`lateral_attenuation`** ($\beta$, $\ell$): excess lateral attenuation over soft ground (Eq. 4-18/4-19, AIR-5662). - **`engine_installation_correction`** ($\varphi$, mounting): lateral- directivity term for wing/fuselage/propeller installations (Eq. 4-15/4-16). - **`duration_correction`** ($V_{\text{ref}}$, $V_{\text{seg}}$): the speed/duration adjustment for exposure levels (Eq. 4-14). - **`noise_fraction`** ($q$, $\lambda$, $d_\lambda$): the finite-segment energy fraction (Eq. 4-20). - **`start_of_roll_directivity`** ($\psi$, $d_{\text{SOR}}$, engine): the rearward jet/turboprop directivity behind takeoff ground-roll segments (Eq. 4-22/4-24/4-25). Pass a boolean `ground_roll` mask to `event_level`/`noise_contour` to flag the takeoff ground-roll segments; behind them the reduced ($q = 0$) noise fraction and $\Delta_{\text{SOR}}$ are applied (Eq. 4-9).

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import aircraft # NPD tables (SEL and LAmax) for one aircraft, two power settings. powers = [8000.0, 12000.0] distances = [60.0, 120.0, 240.0, 480.0, 960.0, 1920.0, 3840.0, 7680.0] sel = [[98.0, 92.0, 86.0, 80.0, 74.0, 68.0, 62.0, 56.0], [104.0, 98.0, 92.0, 86.0, 80.0, 74.0, 68.0, 62.0]] lmax = [[94.0, 88.0, 82.0, 76.0, 70.0, 64.0, 58.0, 52.0], [100.0, 94.0, 88.0, 82.0, 76.0, 70.0, 64.0, 58.0]] # Departure: ground roll along +x, then a steady climb. xs = np.linspace(0.0, 18000.0, 40) z = np.clip((xs - 1500.0) * 0.11, 0.0, 2500.0) power = np.where(xs < 3000.0, 12000.0, 10000.0) path = np.column_stack([xs, np.zeros_like(xs), z, power, np.full_like(xs, 82.3)]) ground_roll = xs[:-1] < 1500.0 # takeoff roll: segments still on the runway segments = aircraft.FlightSegmentState(ground_roll=ground_roll) contour = aircraft.noise_contour(path, powers, distances, sel, lmax, segments=segments, x=np.linspace(-2500.0, 20000.0, 56), y=np.linspace(-6000.0, 6000.0, 44)) contour.plot() # single-event SEL footprint (needs matplotlib) plt.show() ```

The mechanism behind these ground corrections is two-path interference: the direct wave and its ground reflection. Below, a 400 Hz source 1.5 m above a rigid plane forms the lobe pattern, with the image source ghosted below the ground and a receiver sitting in an interference dip. [Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_fdtd_ground_effect.webm) $\Delta_{\text{SOR}}$ is what makes the departure footprint bulge rearward behind the runway: jet-exhaust noise radiates a lobed pattern in the rear arc, strongest at an azimuth $\psi \approx 120°$ from the nose and falling away both abeam ($\psi = 90°$) and directly behind ($\psi = 180°$).

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import aircraft az = np.linspace(90.0, 270.0, 361) # rearward semicircle psi = np.where(az <= 180.0, az, 360.0 - az) # ΔSOR is left/right symmetric jet = [aircraft.start_of_roll_directivity(p, 300.0, "jet") for p in psi] prop = [aircraft.start_of_roll_directivity(p, 300.0, "turboprop") for p in psi] ax = plt.subplot(projection="polar") ax.set_theta_zero_location("N") # nose up, azimuth clockwise ax.set_theta_direction(-1) ax.plot(np.radians(az), jet, label="Turbofan jet") ax.plot(np.radians(az), prop, label="Turboprop") ax.set_rlim(-16.0, 0.0) # radial axis: dB re abeam ax.legend(loc="lower center") plt.show() ```

`event_level` assembles these (Eq. 4-8/4-9) and sums the segments into the exposure level `SEL` (Eq. 4-11) or the maximum level $L_\mathrm{Amax}$ (Eq. 4-10); `noise_contour` evaluates `event_level` over a ground grid to produce a noise contour. Mark the takeoff ground-roll segments with the boolean `ground_roll` mask. ```python import numpy as np from phonometry import aircraft # NPD tables (SEL and LAmax) for one aircraft, two power settings. powers = [8000.0, 12000.0] distances = [60.0, 240.0, 960.0, 3840.0] sel = [[98.0, 86.0, 74.0, 62.0], [104.0, 92.0, 80.0, 68.0]] lmax = [[94.0, 82.0, 70.0, 58.0], [100.0, 88.0, 76.0, 64.0]] # A departure flight path: columns x, y, z (m), power, speed (m/s). xs = np.linspace(0.0, 18000.0, 40) path = np.column_stack([xs, np.zeros_like(xs), np.clip((xs - 1500) * 0.11, 0, 2500), np.where(xs < 3000, 12000.0, 10000.0), np.full_like(xs, 82.3)]) ground_roll = xs[:-1] < 1500.0 # takeoff roll: segments still on the runway segments = aircraft.FlightSegmentState(ground_roll=ground_roll) aircraft.event_level(path, [2000.0, 500.0, 0.0], powers, distances, sel, lmax, segments=segments) # SEL at a point contour = aircraft.noise_contour(path, powers, distances, sel, lmax, segments=segments, x=np.linspace(-2500, 20000, 60), y=np.linspace(-6000, 6000, 48)) contour.plot() # SEL contour over the ground (needs matplotlib) ``` Validated against the **ECAC Doc 29 5th ed. Vol 3 Part 1 reference workbook**: the segment geometry ($\beta$, $\varphi$), lateral attenuation, engine installation, noise fraction and the start-of-roll directivity $\Delta_{\text{SOR}}$ (turbofan and turboprop, all 124 ground-roll reference rows to $< 0.01\ \text{dB}$) reproduce the reference values, and the segment energy sum matches the reference `SEL`. The model also covers the landing rollout (the `landing_roll` mask of the `FlightSegmentState`: reduced noise fraction Eq. 4-21b, nearest-end geometry, no directivity term), per-segment bank angle (its `bank`, §4.5.2 sign convention), the §4.5.5 nearest-end lateral geometry behind takeoff roll, the Eq. 4-13b average runway-segment speed and the recommended 30 m floor on NPD lookups. Seven branch-covering receptor events of the reference workbook are reproduced end-to-end in the test suite. ## See also - [Aircraft noise](https://jmrplens.github.io/phonometry/aircraft/aircraft-noise/): the ICAO Annex 16 certification metric behind the aircraft data. - [Outdoor sound propagation](https://jmrplens.github.io/phonometry/environment/propagation/outdoor-propagation/): the ISO 9613-2 attenuation terms and the ground effect the lateral attenuation condenses into one curve. - [Environmental levels](https://jmrplens.github.io/phonometry/environment/assessment/environmental-levels/): the $L_\mathrm{den}$-style long-term indices that a full airport study accumulates from single events. - API reference: [`aircraft.airport_noise`](https://jmrplens.github.io/phonometry/reference/api/aeroacoustics/airport-noise/). ## References - European Civil Aviation Conference. (2016). *Report on standard method of computing noise contours around civil airports* (ECAC.CEAC Doc 29, 4th ed.), Volume 2: Technical guide. [ECAC documents page](https://www.ecac-ceac.org/documents/ecac-documents-and-international-agreements), [free PDF](https://www.ecac-ceac.org/images/documents/ECAC-Doc_29_4th_edition_Dec_2016_Volume_2.pdf). The NPD interpolation of section 1 and the single-event segment chain of section 2. - European Civil Aviation Conference. (2026). *Report on standard method of computing noise contours around civil airports* (ECAC.CEAC Doc 29, 5th ed.), Volume 3: Reference cases and verification framework. [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_29_5th_Edition-REPORT_ON_STANDARD_METHOD_OF_COMPUTING_NOISE_CONTOURS_AROUND_CIVIL_AIRPORTS-Volume_3-REFERENCE_CASES_AND_VERIFICATION_FRAMEWORK.pdf). The reference workbook the section 2 single-event chain is validated against. - SAE International. (2006). *Method for predicting lateral attenuation of airplane noise* (SAE AIR 5662). [sae.org](https://www.sae.org/standards/content/air5662/). The soft-ground lateral-attenuation model that Doc 29 §4.5.4 adopts in section 2. ## Standards ECAC Doc 29, 4th ed., Vol 2 (2016): the NPD event-level interpolation (§4.2) and the single-event segment calculation (duration, §4.5.1; engine installation, §4.5.3; lateral attenuation, §4.5.4, AIR-5662; the finite-segment noise fraction, §4.5.6; the start-of-roll directivity, §4.5.7; and segment summation, §4.3) through to ground-grid noise contours, with the impedance adjustment (§4.2.1). The single-event chain is validated against the ECAC Doc 29 5th ed. Vol 3 Part 1 reference workbook.