Source: https://jmrplens.github.io/phonometry/environment/sources/cnossos-rail-emission/ # CNOSSOS-EU railway source emission A road is one source line 5 cm above the pavement. A railway track is **two**, one at the axles and one at the roof, because a train radiates from places that are four metres apart and shield each other differently. Section 2.3 of **Annex II of Directive 2002/49/EC**, as replaced by the CNOSSOS-EU methods, builds both of them from a roughness spectrum, a handful of transfer functions and the traffic flow. This guide covers the railway source, section 2.3 of Annex II with the coefficient database of Appendix G. The road source (2.2, Appendix F) and the CNOSSOS-EU propagation model (2.5) are separate. ## 1. Which text is implemented Annex II is a moving target, and on the railway side the layering is worse than on the road side: the corrigendum replaced the **whole** of Appendix G, and the 2021 amendment then replaced five of its seven tables again and rewrote three pieces of the method. | Instrument | What it does to the railway source | | :--- | :--- | | Commission Directive (EU) **2015/996** | Replaces the whole of Annex II. Supplies formulae 2.3.1 to 2.3.18 and Tables G-1 to G-7. | | **Corrigendum** of OJ L 5, 10.1.2018 | Replaces the **whole of Appendix G** (dropping its Min/Max validity columns and adding the descriptor codes to the column headers) and corrects the roughness conversion `f = v/lambda`, where the published text says the speed is in km/h. It is in **metres per second**: read literally, the printed formula is wrong by a factor 3,6. | | Commission Delegated Directive (EU) **2021/1226** | Replaces Tables **G-1b, G-2, G-3a, G-4 and G-7** in their entirety; substitutes a **new curve-squeal rule**; makes bridge noise a **separate source** built on a transfer function instead of a constant; rewrites the **vertical directivity** of source A; corrects three band labels and one pair of values in Table G-5. | The library implements the consolidated result, and every shipped table records in its comment which instrument it came from. Three of the 2021 changes are behavioural, not cosmetic, so a comparison with a pre-2021 study has to account for them: the rail roughness of an average network is now much higher at long wavelengths, the bridge correction has a spectrum instead of a flat 1 dB or 4 dB, and the vertical directivity is identically zero below the horizon where the old form gave a positive correction. ## 2. Two source lines, and what sits on each The method places **two** incoherent source lines at the centre of the track, referred to the plane tangent to the two upper rail surfaces: | Height | Index | Physical sources allocated to it | | :--- | :--- | :--- | | **0,5 m** (source A) | $h = 1$ | Rolling noise (rail, wheel and freight superstructure), impact noise, curve squeal, bridge noise, and the traction and aerodynamic components that sit low: gears, motors, shrouds and screens. | | **4,0 m** (source B) | $h = 2$ | The traction and aerodynamic components that sit high: diesel exhausts, roof apparatus, the pantograph recess. | Nothing in the method decides the traction split for you. Table G-5 tabulates the traction sound power **separately for the two heights**, so the split is read from the database rather than assumed; the Directive only adds that where a real component sits between the two model heights, its energy is distributed proportionately over them. For each 1/3-octave band the flow equation turns a single-vehicle sound power into a power per metre of line (2.3.2), or, for a stationary vehicle, into the idling equivalent over the reference period (2.3.4): $$ L'_{W,\mathrm{eq,line},i}(\psi,\varphi) = L_{W,0,\mathrm{dir},i}(\psi,\varphi) + 10\,\log_{10}\!\left(\frac{Q}{1000\,v}\right), \qquad +\,10\,\log_{10}\!\left(\frac{T_\mathrm{idle}}{T_\mathrm{ref}\,L}\right). $$ $Q$ is in vehicles per hour, $v$ in km/h, $L$ the length of the track section in metres. Note the unit: the flow term uses km/h, while the roughness conversion two sections down uses m/s. Both are correct, and mixing them up is the single most expensive mistake available in this model. *At 160 km/h the track is source A almost everywhere: the 4,0 m line only carries the traction noise of the unit, some twenty-five decibels below. It is above 200 km/h, when aerodynamic noise appears at the pantograph, that source B starts to matter.*

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```python import matplotlib.pyplot as plt from phonometry import ( BrakeType, ContactFilter, RailRoughnessClass, RailwayTrack, RailwayVehicle, RollingStock, TrackTransferClass, TractionVehicle, WheelDiameter, aerodynamic_sound_power, contact_filter, impact_roughness_single, rail_roughness, railway_source_power, track_transfer, traction_sound_power, wheel_roughness, wheel_transfer, ) stock = RollingStock( axles=4, wheel_roughness=wheel_roughness(BrakeType.NON_TREAD), contact_filter=contact_filter(ContactFilter.LOAD_50_DIAMETER_920), wheel_transfer=wheel_transfer(WheelDiameter.MM_920), traction=traction_sound_power(TractionVehicle.ELECTRIC_MULTIPLE_UNIT), aerodynamic=aerodynamic_sound_power(), ) track = RailwayTrack( rail_roughness=rail_roughness(RailRoughnessClass.NORMAL), track_transfer=track_transfer(TrackTransferClass.MONOBLOCK_MEDIUM), impact_roughness=impact_roughness_single(), ) result = railway_source_power( RailwayVehicle(stock, flow_rate=96.0, speed=160.0), track, phi=90.0, psi=10.0, ) result.plot() plt.show() ```

## 3. Rolling noise: roughness in, sound power out Rolling noise is the wheel and the rail exciting each other through the roughness of the two running surfaces. The method separates the cause from the radiation: - **cause**: the rail roughness $L_\mathrm{r,TR}$ (Table G-1b, selected by digit 2 of the track descriptor) and the wheel roughness $L_\mathrm{r,VEH}$ (Table G-1a, selected by the brake type, digit 3 of the vehicle descriptor), energy-summed and then filtered by the **contact filter** $A_3$ (Table G-2), which accounts for the finite size of the contact patch: $$ L_{\mathrm{R,TOT},i} = 10\,\log_{10}\!\left(10^{L_{\mathrm{r,TR},i}/10} + 10^{L_{\mathrm{r,VEH},i}/10}\right) + A_{3,i}; $$ - **radiation**: three speed-independent transfer functions turn that roughness into sound power per axle, one for the track (Table G-3a, selected by the sleeper and rail-pad codes), one for the wheel (Table G-3b, selected by the wheel diameter) and one for the superstructure of a freight wagon (Table G-3c, which is 0,0 dB in every band): $$ L_{W,0,\mathrm{TR},i} = L_{\mathrm{R,TOT},i} + L_{H,\mathrm{TR},i} + 10\,\log_{10} N_\mathrm{a}, $$ and the same addition for the wheel and the superstructure. The three components are then energy-summed, and all three sit at source A. The superstructure term applies to vehicle type `a` (freight) only. A minimum speed of **50 km/h**, or 30 km/h for trams and light metro, is used to determine the roughness, which freezes the source spectrum below it; the flow term still uses the true speed. While a vehicle idles, rolling noise is excluded altogether. ## 4. The wavelength-to-frequency conversion Roughness is tabulated against **wavelength**, and read at $\lambda = v/f$, so the whole roughness spectrum slides along the frequency axis as the train speeds up. That is the reason a fast train is bright and a slow one is not: the same millimetre-scale roughness excites a higher band. *The same track and the same wheel at three speeds. The curve does not change shape, it slides: multiplying the speed by 2,7 moves it by rather more than an octave and lifts it, because the long wavelengths of an average network are the rough ones.*

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```python import matplotlib.pyplot as plt from phonometry import ( RAILWAY_THIRD_OCTAVE_BANDS, BrakeType, ContactFilter, RailRoughnessClass, contact_filter, rail_roughness, roughness_to_frequency, total_effective_roughness, wheel_roughness, ) rail = rail_roughness(RailRoughnessClass.NORMAL) wheel = wheel_roughness(BrakeType.NON_TREAD) filt = contact_filter(ContactFilter.LOAD_50_DIAMETER_920) fig, ax = plt.subplots() for speed in (60.0, 160.0, 300.0): total = total_effective_roughness( roughness_to_frequency(rail[1], rail[0], speed), roughness_to_frequency(wheel[1], wheel[0], speed), roughness_to_frequency(filt[1], filt[0], speed), ) ax.semilogx(RAILWAY_THIRD_OCTAVE_BANDS, total, label=f"v = {speed:g} km/h") ax.legend() plt.show() ```

Two things about this conversion deserve to be stated plainly, because neither is settled by the Directive. **The speed is in metres per second.** The published 2015 text says km/h in both places where the conversion appears, which would put the spectrum 3,6 times too low in frequency. The corrigendum of 2018 corrected both. This library implements the corrected form. **The interpolation rule is prose, not a formula.** All the Directive says is that "the two corresponding 1/3 octave bands defined in the wavelength domain shall be averaged energetically and proportionally", with no formula and no worked example. Two readings are shipped, and the default is the one that reproduces the Commission's own reference source module: ```python from phonometry import RoughnessInterpolation RoughnessInterpolation.PROPORTIONAL # levels interpolated linearly in lambda RoughnessInterpolation.ENERGY # energies interpolated linearly in lambda ``` They differ by up to about 1 dB on a steep part of a spectrum. This is the single largest interpretation risk in the railway model, and any implementation that does not say which rule it uses is not comparable with another one. A third, smaller ambiguity is handled without a switch. The 2021 amendment put the tables it replaced on the standard 1/3-octave wavelength series but left Table G-1a alone, so the wheel roughness is still printed at 120, 12, 3,2 and 1,2 mm where every other table now reads 125, 12,5, 3,15 and 1,25 mm. Rather than forcing the two onto a common grid, each table is resampled on the grid the Directive prints for it. ## 5. Impact noise, and curve squeal **Impact noise** from joints, switches and crossings is added as a fictitious extra roughness, energy-summed into the total before the transfer functions are applied (2.3.11). Table G-4 is given for one joint per 100 m, and any other density scales it (2.3.12): $$ L_{\mathrm{R,IMPACT},i} = L_{\mathrm{R,IMPACT-SINGLE},i} + 10\,\log_{10}\!\left(\frac{n_l}{0{,}01}\right). $$ For jointed track a default $n_l = 0{,}01\ \text{m}^{-1}$ is prescribed. Impact noise is not modelled below the minimum speed, nor while idling. The increment applies from 50 m before the joint to 50 m after it, which is a **segmentation** instruction: the model gives the source strength, and it is up to the track segmentation to place it over the right 100 m. **Curve squeal** is an excess added to the rolling-noise sound power at all frequencies. The rule is the one the 2021 amendment substituted, and it is not the 2015 one: | Vehicle | Condition | Excess | | :--- | :--- | :--- | | Train | $300\ \text{m} < R \le 500\ \text{m}$ over at least 50 m of curve | 5 dB | | Train | $R \le 300\ \text{m}$ over at least 50 m of curve | 8 dB | | Train | switch turnout with $R \le 300\ \text{m}$ | 8 dB | | Tram | curve or switch turnout with $R \le 200\ \text{m}$ | 5 dB | ```python from phonometry import curve_squeal_excess curve_squeal_excess(280.0) # 8.0 dB curve_squeal_excess(450.0) # 5.0 dB curve_squeal_excess(280.0, tram=True) # 0.0 dB, trams need R <= 200 m curve_squeal_excess(280.0, track_length=20.0) # 0.0 dB, the curve is too short ``` The 2015 text read "8 dB for R < 300 m and 5 dB for 300 m < R < 500 m", which left the two endpoints with no rule at all even though the same paragraph scoped the effect to "curves with radius below **or equal to** 500 m". The 2021 wording closes both intervals. ## 6. Traction and aerodynamic noise **Traction noise** is tabulated per vehicle and per source height (Table G-5). The Directive models only two running conditions, constant speed (which it says is valid as well when the train accelerates or decelerates) and idling, and takes the source strength at maximum load, so $L_{W,0,\mathrm{const},i} = L_{W,0,\mathrm{idling},i}$ and the one table serves both. Idling is only considered if trains idle for more than half an hour. **Aerodynamic noise** is relevant only above **200 km/h** and follows a logarithmic speed law about $v_0 = 300\ \text{km/h}$ (2.3.13, 2.3.14): $$ L_{W,0,i} = L_{W,0,h,i}(v_0) + \alpha_{h,i}\,\log_{10}\!\left(\frac{v}{v_0}\right), $$ with $\alpha_1 = \alpha_2 = 50$ in every band, so a doubling of speed adds 15,05 dB. Table G-6 is the reference spectrum of a 20 m vehicle at $v_0$: at the lower height it is broadband, at the upper one it is essentially silent except for a 1,6 kHz to 3,15 kHz plateau at 105 to 110 dB, which is the pantograph. ## 7. Source directivity Each source is corrected in the two planes before the flow term is added (2.3.5). The **horizontal** correction is a dipole (2.3.15), 0 dB broadside and $10\log_{10} 0{,}01 = -20\ \text{dB}$ along the track: $$ \Delta L_{W,\mathrm{dir,hor},i} = 10\,\log_{10}\!\left(0{,}01 + 0{,}99\,\sin^2\varphi\right). $$ The **vertical** correction of source A (2.3.16) depends on the band, and it is one of the pieces the 2021 amendment rewrote. The current text drops the absolute-value bars of the 2015 form and makes the correction identically zero for $\psi \le 0$: $$ \Delta L_{W,\mathrm{dir,ver},i} = \frac{40}{3} \left[\tfrac{2}{3}\sin 2\psi - \sin\psi\right] \log_{10}\!\left(\frac{f_{\mathrm{c},i} + 600}{200}\right), \quad 0 < \psi < \pi/2, $$ and zero elsewhere. The two editions disagree over the whole lower half space, and also above about 41,4 degrees, where the bracket turns negative. Both are available, because comparing with a study computed before 2021 needs the old one: ```python from phonometry import DirectivityEdition, vertical_directivity vertical_directivity(-30.0) # zeros vertical_directivity(-30.0, edition=DirectivityEdition.ORIGINAL_2015) # positive ``` At source B, only the aerodynamic source is directional, $10\log_{10}(\cos^2\psi)$ for $\psi < 0$ (2.3.17); everything else at 4,0 m is omni-directional, and so is bridge noise at 0,5 m. One point of interpretation: 2.3.15 offers the dipole "by default ... for rolling, impact, squeal, braking, fans and aerodynamic effects". Traction noise other than the fans is not in that list, and the Directive gives no other horizontal directivity for it. This library applies the dipole to every source, which is what the Commission's reference source module does. ## 8. Bridges On a bridge the deck radiates too. The 2015 text added a constant to the rolling noise, 1 dB for concrete or masonry and 4 dB for steel with ballasted track. The 2021 amendment replaced that with a **separate source**, built exactly like a rolling-noise component but with the bridge transfer function of Table G-7 (2.3.18): $$ L_{W,0,\mathrm{bridge},i} = L_{\mathrm{R,TOT},i} + L_{H,\mathrm{bridge},i} + 10\,\log_{10} N_\mathrm{a}. $$ The rolling noise of the vehicle on the bridge is still computed normally, with the transfer function of the track system that is actually on the bridge; the bridge term is added to it. It sits at source A and is omni-directional, which the amendment states explicitly. ```python from phonometry import BridgeType, RailwayTrack, bridge_transfer RailwayTrack( rail_roughness=..., track_transfer=..., bridge_transfer=bridge_transfer(BridgeType.PLUS_10_DBA), ) ``` ## 9. Handing the source to a propagation model The railway source is derived in **1/3 octave bands** and then energy-summed into octave bands for propagation, which is what 2.3.2 requires and what (EU) 2021/1226 point (1) made explicit. The result object carries both: ```python result.third_octave_line_power # (2, 24), the two heights in 1/3 octaves result.line_power # (2, 8), the same in octave bands result.total_line_power # (8,), the two heights energy-summed result.components["rolling"] # the per-source breakdown, before directivity ``` Splitting a source line into equivalent point sources is, in the words of section 2.5.3, "outside the scope of the current methodology": a point source standing for a segment of length $dL$ simply carries $L'_{W,\mathrm{eq,line},i} + 10\log_{10}(dL)$, which is arithmetic. CNOSSOS-EU has **its own** propagation method in section 2.5 of Annex II, and it is not ISO 9613-2. Chaining a CNOSSOS emission onto the ISO 9613-2 propagation of this library is a legitimate engineering estimate, but it is not the normative CNOSSOS chain and must not be reported as one. ## 10. What is pinned against digits, and what is not Annex II prints **no worked example and no check value** anywhere in 2.3 or Appendix G, so it is worth being explicit about what the agreement in the test suite measures. **Verified against published digits.** Every Appendix G table, against the Official Journal text of the instrument that enacted it. And the whole chain of equations end to end, against the emission test workbook the European Commission published with its reference source module: feeding the shipped equations the **2015** coefficient database that workbook was computed with reproduces **all 34 560 published rows of the twenty vehicles whose catalogue entries are well formed**, that is 17 280 cases at both source heights, to 0,0055 dB, inside the two decimals it prints. A hundred and twenty-three of those cases are committed to the repository and run in CI. The three vehicles left out are described in `tests/data/cnossos/README.md`: their rows record defects of the reference program, not of the method. That agreement resolves the loud parts of the database and not the quiet ones: a coefficient twenty decibels below its neighbour does not move the total, so the placeholder rows of the reference catalogue and the source-A traction column, which rolling noise always covers, are carried by the test set without being constrained by it. `tests/data/cnossos/README.md` reports the measurement. **Verified as equations times transcribed tables, not end to end.** Everything the 2021 amendment changed. The workbook predates it, so the new curve-squeal rule, the bridge transfer function, the current vertical directivity and the five replaced tables are each pinned individually, by transcription and by closed-form assertion, but their combination has never been checked against an independent published result. **Not anchored on any oracle.** The choice of interpolation rule in section 4; the proportional distribution of traction sound power when a real component sits between the two model heights, for which the Directive gives no formula; and the segmentation of a line into point sources, which the method declares out of scope. ## What this guide covers **Covered.** Section 2.3 of Annex II to Directive 2002/49/EC in the consolidated text: the vehicle and track descriptors of Tables [2.3.a] and [2.3.b], the traffic-flow line power (2.3.1, 2.3.2, 2.3.4), the directional sound power (2.3.5), rolling noise (2.3.6 to 2.3.10), impact noise (2.3.11, 2.3.12), curve squeal, traction noise, aerodynamic noise (2.3.13, 2.3.14), the source directivity (2.3.15 to 2.3.17) and bridge noise (2.3.18), together with the whole Appendix G database, through `railway_source_power` and the component functions around it. **Not covered.** The road source (2.2 and Appendix F), the industrial source (2.4 and Appendix H), the aircraft source (2.6 and 2.7) and the CNOSSOS-EU propagation method of section 2.5, which is a different model from the ISO 9613-2 one implemented in this library. Rail roughness classes `N` (not well maintained) and `B` (bad condition) carry no spectrum in Appendix G and have to be supplied by the Member State. The other railway sources of 2.3.3, such as depots, stations and loudspeakers, are treated by the industrial method. ## See also - [Outdoor Sound Propagation](https://jmrplens.github.io/phonometry/environment/propagation/outdoor-propagation/): the ISO 9613-2 chain that carries a source power to a receiver. - [Environmental noise levels](https://jmrplens.github.io/phonometry/environment/assessment/environmental-levels/): the $L_\mathrm{den}$ and $L_\mathrm{night}$ indicators the resulting maps are drawn for. ## References - 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). The Joint Research Centre reference report the Directive text descends from, with the IMAGINE measurement campaigns behind the Appendix G coefficients. - International Organization for Standardization. (1996). *Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of calculation* (ISO 9613-2:1996). [iso.org catalogue](https://www.iso.org/standard/20649.html). The propagation model this library uses to carry the emission to a receiver. CNOSSOS-EU has its own propagation method in section 2.5 of Annex II, which is not ISO 9613-2. ## Standards Directive 2002/49/EC, Annex II, section 2.3 with the coefficient database of Appendix G, in the consolidated text — three instruments read together: - Commission Directive (EU) 2015/996 ([eur-lex.europa.eu](https://eur-lex.europa.eu/eli/dir/2015/996/oj)), which replaced Annex II with the CNOSSOS-EU methods. The implemented railway source is section 2.3, formulae 2.3.1 to 2.3.18. - Its corrigendum of 10 January 2018, OJ L 5, p. 35 ([eur-lex.europa.eu](https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32015L0996R(01))), which replaces the whole of Appendix G and corrects the roughness conversion, where the published text read km/h for a speed that has to be in metres per second. - Commission Delegated Directive (EU) 2021/1226 ([eur-lex.europa.eu](https://eur-lex.europa.eu/eli/dir_del/2021/1226/oj)), in force since 31 December 2021, which replaces Tables G-1b, G-2, G-3a, G-4 and G-7, substitutes a new curve-squeal rule and a new bridge model, and rewrites the vertical directivity of source A.