Source: https://jmrplens.github.io/phonometry/guides/aircraft-noise/ # Aircraft noise: Effective Perceived Noise Level (ICAO Annex 16 / IEC 61265) The **Effective Perceived Noise Level (EPNL)** is the noise-certification metric for transport-category aircraft. It condenses a half-second one-third-octave spectral time history of a flyover into a single number, in EPNdB, through five steps of **ICAO Annex 16, Vol. I, Appendix 2**. This page covers the four primitives that build the metric and the IEC 61265 measurement-system verifier. Each quantity is validated against the worked examples of the ICAO Doc 9501 Environmental Technical Manual (ETM) Vol. I. ## 1. Perceived noisiness and PNL Each of the 24 one-third-octave-band levels (50 Hz–10 kHz) is converted to a perceived **noisiness** in noys by the analytic piecewise law of Table A2-3, then combined into the total noisiness and the perceived noise level: $$ N = 0.85\,n_{\max} + 0.15\sum_i n_i, \qquad \mathrm{PNL} = 40 + \frac{10}{\lg 2}\,\lg N . $$ ```python from phonometry import aircraft noys = aircraft.perceived_noisiness(spl) # per-band noys (spl = 24 band levels, dB) pnl = aircraft.perceived_noise_level(spl) # PNdB ``` ## 2. Tone correction Spectral irregularities (fan/turbine tones) are penalised by a **tone correction** `C`, found with the slope ("encircling") method: slopes are smoothed to a background spectrum `SPL''`, the tone excess `F = SPL − SPL''` above 1.5 dB is mapped to a correction factor (frequency-split at 500 Hz / 5000 Hz, capped at 6⅔ dB), and the maximum over bands is taken. ```python from phonometry import aircraft c = aircraft.tone_correction(spl) # dB; added to PNL to give PNLT ``` The implementation reproduces the ICAO Doc 9501 ETM Vol. I **Table 3-7** turbofan example exactly, including its `SPL''` background column and the resulting `C = 2.0 dB` at 2500 Hz. ## 3. EPNL Over the flyover, the tone-corrected level is `PNLT = PNL + C`; its maximum is `PNLTM`. The metric integrates `PNLT` over the **10 dB-down** window (the records nearest to `PNLTM − 10` on each side) and normalises to 10 s: $$ \mathrm{EPNL} = 10\lg\!\Big(\sum_{k=k_F}^{k_L} 10^{\mathrm{PNLT}(k)/10}\,\Delta t(k)\Big) - 10\lg T_0, \qquad T_0 = 10\ \mathrm{s}, $$ so `EPNL = PNLTM + D` with the duration correction `D`. Aircraft-flyover perceived-noise-level time history: PNL and the tone-corrected PNLT versus time, with the maximum PNLTM marked and the 10 dB-down integration window shaded, annotated with the resulting EPNL and duration correction ```python import numpy as np from phonometry import aircraft # spectra: a (K, 24) array of one-third-octave band levels sampled every dt s res = aircraft.effective_perceived_noise_level(spectra, dt=0.5) print(res.epnl, res.pnltm, res.duration_correction, res.band_limits) res.plot() # PNL/PNLT time history (needs matplotlib) ``` `effective_perceived_noise_level` returns an `EPNLResult` bundling the per-record `pnl`, `tone_correction`, `pnlt`, the peak `pnltm`, the `duration_correction`, the `epnl` and the 10 dB-down `band_limits`. The reference-condition integrated-method example of ETM Vol. I **Table 4-4** (a 31-record `PNLT` history with non-uniform durations) is reproduced as `EPNL = 92.6 EPNdB`. `epnl_from_pnlt` exposes the duration/limit machinery directly from a `PNLT` series.
Show the code for this figure ```python import numpy as np from phonometry import aircraft k, dt = 41, 0.5 idx = np.arange(k) shape = 15.0 * np.exp(-((np.log10(aircraft.NOY_BANDS) - np.log10(400.0)) ** 2) / 0.5) gain = 30.0 * np.exp(-((idx - 20.0) ** 2) / (2 * 5.0**2)) - 5.0 spectra = (55.0 + shape)[None, :] + gain[:, None] spectra[:, 17] += 12.0 * np.exp(-((idx - 20.0) ** 2) / (2 * 6.0**2)) # 2500 Hz fan tone aircraft.effective_perceived_noise_level(spectra, dt).plot() ```
### ICAO EPNL report (`.report()`) `EPNLResult.report(path)` renders a one-page PDF fiche laid out like an aircraft-noise-certification data sheet: a standard-basis line (ICAO Annex 16 Vol. I Appendix 2), an optional TCDSN-style metadata header (aircraft, manufacturer / type-certificate holder, applicant, measurement point), a metrics table of the informational intermediate quantities (the peak `PNLTM`, the duration correction `D`, the 10 dB-down record window and, when non-zero, the bandsharing adjustment) above the full-width landscape `PNLT`-versus-time plot (the result's own `.plot()`), the boxed `EPNL = X EPNdB` single number, a Level | Limit | Margin verdict row when a certification limit is supplied, a static reference-conditions strip (25 °C, 70 % RH, sea level, zero wind, ISA) and a footer with the fixed disclaimer. It uses the same `ReportMetadata` container (documented under [Field insulation](https://jmrplens.github.io/phonometry/guides/insulation-field/#report-metadata-reportmetadata)) and rendering engine as the ISO 717 insulation fiche; a supplied `requirement` is read as the certification EPNL limit in EPNdB (the EPNL passes at or below it), and `metadata=None` produces a lightweight prediction fiche with no verdict row. Rendering needs reportlab (`pip install phonometry[report]`); only `engine="reportlab"` is supported. The fiche renders in English by default; pass `language="es"` for a Spanish fiche (translated fixed strings and a comma decimal separator), e.g. `res.report("epnl_fiche_es.pdf", language="es")`. The fiche is a computational EPNL result and is not an official State noise certificate; it does not reproduce any TCDSN. ```python from phonometry import effective_perceived_noise_level, ReportMetadata # spectra: a (K, 24) array of one-third-octave band levels sampled every dt s res = effective_perceived_noise_level(spectra, dt=0.5) res.report( "epnl_fiche.pdf", metadata=ReportMetadata( specimen="Example twin-turbofan transport", manufacturer="Example Aircraft Company", measurement_standard="ICAO Annex 16 Vol I Amendment 14 Chapter 4", laboratory="Phonometry Reference Laboratory", requirement=101.0, # certification EPNL limit (EPNdB) ), ) # EPNL (EPNdB) with PNLTM and D ``` The example fiche is regenerated with `make reports` and kept rendered in the repository:

One-page ICAO Annex 16 EPNL certification fiche: a metadata header, a reference-conditions strip, an intermediate-quantities table (PNLTM, duration correction D, 10 dB-down window), the landscape PNL/PNLT time-history plot, the boxed EPNL = 98.3 EPNdB single-number result and a PASS verdict against a 101 EPNdB limit

## 4. Measurement-system verification (IEC 61265) `verify_aircraft_noise_system` checks a supplied set of measured performance values against the IEC 61265:1995 tolerances for aircraft-noise measurement systems: the microphone directional-response limits (Table 1, with the "intermediate angle uses the greater angle's limit" rule) and the scalar frequency-response, linearity and resolution limits. The one-third-octave filtering itself is covered by the library's IEC 61260 class-2 filter verification (`verify_filter_class`). ```python from phonometry import metrology report = metrology.verify_aircraft_noise_system( directional={4000.0: {30: 0.4, 60: 0.9, 90: 1.9, 120: 2.4, 150: 2.4}}, frequency_response={1000.0: 1.2}, ) print(report["passed"], report["checks"]) ``` ## 5. Atmospheric absorption (SAE ARP 5534) Correcting a measured flyover spectrum to reference atmospheric conditions needs the one-third-octave-band attenuation over the path. The pure-tone coefficient is the ISO 9613-1 one (identical, per ARP 5534 §3.1) already provided by `air_attenuation`; `sae_band_attenuation` adds the **SAE Method** (ARP 5534 §3.2.2), a regression that maps the pure-tone mid-band path-length attenuation `δ_t = α·s` to the band attenuation `δ_B` and stays consistent with the ISO/ANSI Exact Method well beyond the 50 dB limit of the older Approximate Method. Aircraft atmospheric absorption versus frequency for two path lengths: the SAE-Method one-third-octave-band attenuation rises with frequency and stays below the pure-tone mid-band value at high absorption
Show the code for this figure ```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 fig, ax = plt.subplots() # solid: SAE band attenuation, dashed: pure-tone mid-band for s in (1000.0, 7620.0): att = aircraft.sae_band_attenuation(freqs, s, temperature=25.0, relative_humidity=70.0) line, = ax.semilogx(att.frequency, att.band_attenuation, marker="o", markersize=3, label=f"SAE band ({s:.0f} m)") ax.semilogx(att.frequency, att.midband_attenuation, "--", alpha=0.6, color=line.get_color()) ax.set(xlabel="Frequency [Hz]", ylabel="Attenuation [dB]", title="Aircraft atmospheric absorption at 25 °C, 70% RH") 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 att = aircraft.sae_band_attenuation(freqs, path_length=7620.0, temperature=25.0, relative_humidity=70.0) print(att.band_attenuation) # δ_B per band, dB att.plot() # band vs pure-tone mid-band (needs matplotlib) ``` `sae_band_attenuation` returns an `AircraftBandAttenuation` with `band_attenuation` (`δ_B`), `midband_attenuation` (`δ_t = α·s`) and the pure-tone `coefficient` (`α`, dB/m). The SAE Method is valid roughly 6–32 °C and 20–95 % RH (the 14 CFR Part 36 test window), over path lengths to 7620 m, and is reciprocal (source↔receiver). ## 6. Airport noise: the NPD engine (ECAC Doc 29) The ECAC Doc 29 airport-noise method describes an aircraft with **noise-power- distance (NPD)** tables that give the event level (`LAmax` 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. Noise-power-distance curves for two engine power settings: the event level falls log-linearly with slant distance between the tabulated nodes, higher power giving a higher level
Show the code for this figure ```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) ``` ## 7. Airport noise contours (single event) 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(β, ℓ)`**: excess lateral attenuation over soft ground (Eq. 4-18/4-19, AIR-5662). - **`engine_installation_correction(φ, mounting)`**: lateral-directivity term for wing/fuselage/propeller installations (Eq. 4-15/4-16). - **`duration_correction(Vref, Vseg)`**: the speed/duration adjustment for exposure levels (Eq. 4-14). - **`noise_fraction(q, λ, dλ)`**: the finite-segment energy fraction (Eq. 4-20). - **`start_of_roll_directivity(ψ, dSOR, 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 `ΔSOR` are applied (Eq. 4-9). Single-event SEL contour of a departure: an elongated footprint along the flight track, loudest near the ground roll and decaying as the aircraft climbs away
Show the code for this figure ```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)]) contour = aircraft.noise_contour(path, powers, distances, sel, lmax, 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. Animation: a 2D FDTD simulation of a 400 Hz point source 1.5 metres above rigid ground; the direct and ground-reflected wavefronts interfere and a lobe pattern forms, the ghosted image source below the ground explains the geometry, and the level on an 8 metre arc converges to the two-path image-source model with its predicted nulls [Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_fdtd_ground_effect.webm) `ΔSOR` 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 `ψ ≈ 120°` from the nose and falling away both abeam (`ψ = 90°`) and directly behind (`ψ = 180°`). Polar diagram of the start-of-roll directivity ΔSOR over the rearward semicircle for turbofan-jet and turboprop aircraft: both show a lobe near 120° from the nose and fall off directly behind the aircraft
Show the code for this figure ```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 `LAmax` (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)]) aircraft.event_level(path, [2000.0, 500.0, 0.0], powers, distances, sel, lmax) # SEL at a point contour = aircraft.noise_contour(path, powers, distances, sel, lmax, 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 (β, φ), lateral attenuation, engine installation, noise fraction and the start-of-roll directivity `ΔSOR` (turbofan and turboprop, all 124 ground-roll reference rows to < 0.01 dB) reproduce the reference values, and the segment energy sum matches the reference `SEL`. The model also covers the landing rollout (`landing_roll` mask: reduced noise fraction Eq. 4-21b, nearest-end geometry, no directivity term), per-segment bank angle (`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. ## References - International Civil Aviation Organization. (2017). *Annex 16 to the Convention on International Civil Aviation: Environmental protection — Volume I: Aircraft noise* (8th ed.). [ICAO store](https://store.icao.int/en/annex-16-environmental-protection-volume-i-aircraft-noise). The normative Appendix 2 EPNL procedure implemented in sections 1-3. - International Civil Aviation Organization. (2018). *Environmental technical manual — Volume I: Procedures for the noise certification of aircraft* (Doc 9501, 3rd ed.). [ICAO store](https://store.icao.int/en/environmental-technical-manual-volume-1-procedures-for-the-noise-certification-of-aircraft-doc-9501-1). The worked examples (Table 3-7 tone correction, Table 4-4 integrated-method EPNL) used as the numeric oracles of sections 2-3. - International Electrotechnical Commission. (1995). *Electroacoustics — Instruments for measurement of aircraft noise — Performance requirements for systems to measure one-third-octave-band sound pressure levels in noise certification of transport-category aeroplanes* (IEC 61265:1995; since revised as [IEC 61265:2018](https://webstore.iec.ch/en/publication/32635), the 1995 edition is the implemented one). [IEC webstore](https://webstore.iec.ch/en/publication/5076). The measurement-system tolerances checked by the section 4 verifier. - SAE International. (2013). *Application of pure-tone atmospheric absorption losses to one-third octave-band data* (SAE ARP 5534, reaffirmed 2021). [sae.org](https://www.sae.org/standards/content/arp5534/). The SAE-Method band attenuation of section 5. - SAE International. (2012). *Standard values of atmospheric absorption as a function of temperature and humidity* (SAE ARP 866B, stabilized 2012). [sae.org](https://www.sae.org/standards/content/arp866b/). The predecessor SAE atmospheric-absorption practice, source of the 50 dB-limited Approximate Method that section 5 contrasts with the SAE Method. - 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 7. - 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 and the single-event segment chain of sections 6-7. - 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 7 single-event chain is validated against. ## Standards ICAO Annex 16, *Environmental Protection*, Vol. I, *Aircraft Noise*, Appendix 2: the analytic EPNL procedure (perceived noisiness Table A2-3, tone correction Table A2-2, duration correction). ICAO Doc 9501, *Environmental Technical Manual*, Vol. I: the worked examples (Table 3-7 tone correction, Table 4-4 integrated-method EPNL) used as numeric oracles. IEC 61265:1995, *Instruments for the measurement of aircraft noise*: the measurement-system performance tolerances. SAE ARP 5534:2021, *Application of Pure-Tone Atmospheric Absorption Losses to One-Third-Octave-Band Data*: the SAE-Method band attenuation (Eqs. 7–10), with the pure-tone coefficient from ISO 9613-1. 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.