Source: https://jmrplens.github.io/phonometry/environment/sources/cnossos-road-emission/ # CNOSSOS-EU road traffic source emission Every strategic noise map drawn in the European Union since 2021 starts from the same two numbers per octave band: how loud a vehicle is, and how many of them go past per hour. **Annex II of Directive 2002/49/EC**, as replaced by the CNOSSOS-EU methods, turns those into a **directional sound power per metre of source line**, which the propagation stage then carries to the receiver. This guide covers the road source, section 2.2 of Annex II with the coefficient database of Appendix F. The railway source (2.3, Appendix G) and the CNOSSOS-EU propagation model (2.5) are separate. ## 1. Which text is implemented Annex II is a moving target and getting the layering wrong is the easiest way to ship a wrong table. Three instruments are in play: | Instrument | What it does to the road source | | :--- | :--- | | Commission Directive (EU) **2015/996** | Replaces the whole of Annex II. Supplies formulae 2.2.1 to 2.2.20 and Tables F-1 to F-4. | | **Corrigendum** of OJ L 5, 10.1.2018 | Corrects 2.2.1: the sound powers are calculated "for each octave band from **63 Hz to 8 kHz**", not the 125 Hz to 4 kHz the original text printed. Appendix F always covered 63 Hz to 8 kHz, so the uncorrected text contradicted its own tables. | | Commission Delegated Directive (EU) **2021/1226** | Replaces **Table F-1** and **Table F-4** in their entirety, merges the former 4a and 4b rows of Table F-4 into one, and prints the octave-band A-weighting to be used in 2.5.5. | The library implements the consolidated result. Tables F-2 (studded tyres) and F-3 (junctions) have never been amended. The 2021 amendment is not cosmetic: the current road source is about **2,5 to 3,5 dB(A) louder** than the one published in 2015, so any comparison with pre-2021 literature carries that offset. ## 2. The source and the source line Each vehicle is one **point source 0,05 m above the road surface**, radiating uniformly; the first reflection on the pavement is already inside the sound power, which is why the method calls it a semi-free-field quantity. A traffic flow is an incoherent **source line**, ideally one line per lane at the lane centre. For each vehicle category $m$ and octave band $i$, formula (2.2.1) turns a single-vehicle sound power into a power per metre of line: $$ L'_{W,\mathrm{eq,line},i,m} = L_{W,i,m} + 10\,\log_{10}\!\left(\frac{Q_m}{1000\,v_m}\right), $$ with $Q_m$ in vehicles per hour and $v_m$ in km/h. The vehicle power itself is the energy sum of a **rolling** and a **propulsion** term (2.2.2), except for the powered two-wheelers of category 4, which have no rolling noise at all and take the propulsion term alone (2.2.3): $$ L_{W,i,m} = 10\,\log_{10}\!\left(10^{L_{W\mathrm{R},i,m}/10} + 10^{L_{W\mathrm{P},i,m}/10}\right). $$ Table [2.2.a] fixes five modelled categories: **1** light motor vehicles, **2** medium heavy vehicles, **3** heavy vehicles, **4a** mopeds and **4b** motorcycles. (A sixth "open" category exists in the text but carries no coefficients.) *Light vehicles carry the flow, but 45 heavy vehicles per hour still take over the mid frequencies: the per-metre spectrum shows exactly where each category governs.*

Show the code for this figure

```python import matplotlib.pyplot as plt from phonometry import ( JunctionType, RoadSurface, RoadTraffic, RoadVehicleCategory, road_source_power, ) traffic = [ RoadTraffic(RoadVehicleCategory.LIGHT, 1200.0, 50.0), RoadTraffic(RoadVehicleCategory.MEDIUM_HEAVY, 90.0, 50.0), RoadTraffic(RoadVehicleCategory.HEAVY, 45.0, 50.0), RoadTraffic(RoadVehicleCategory.MOTORCYCLES, 60.0, 50.0), ] result = road_source_power( traffic, surface=RoadSurface.THIN_LAYER_A, temperature=12.0, gradient=3.0, junction_distance=60.0, junction_type=JunctionType.CROSSING, ) result.plot() plt.show() ```

## 3. Rolling noise (2.2.4 to 2.2.10) Rolling noise is tyre-road noise. It grows logarithmically with speed from the reference speed $v_\mathrm{ref} = 70\ \text{km/h}$: $$ L_{W\mathrm{R},i,m} = A_{\mathrm{R},i,m} + B_{\mathrm{R},i,m}\,\log_{10}\!\left(\frac{v_m}{v_\mathrm{ref}}\right) + \Delta L_{W\mathrm{R},i,m}, $$ where the correction collects four independent effects (2.2.5): the road surface, the studded tyres, the junction and the air temperature. **Air temperature** (2.2.10) is a straight line, applied equally to all eight bands: $\Delta L_{W,\mathrm{temp}} = K_m\,(20\ \text{°C} - \tau)$, with $K_1 = 0{,}08\ \text{dB/°C}$ for light vehicles and $K_2 = K_3 = 0{,}04\ \text{dB/°C}$ for the two heavy categories. Cold air makes tyres harder and the road louder, so the correction is *positive* below 20 °C. **Studded tyres** (2.2.6 to 2.2.9) apply to category 1 only. The per-tyre excess $D_{\mathrm{stud},i}(v)$ saturates below 50 km/h and above 90 km/h, and the fleet-level correction weights it by the share of the year that studded tyres are on the road, $p_\mathrm{s} = Q_{\mathrm{stud,ratio}} \cdot T_\mathrm{s}/12$: $$ \Delta L_{\mathrm{studded},i} = 10\,\log_{10}\!\left[(1 - p_\mathrm{s}) + p_\mathrm{s}\,10^{D_{\mathrm{stud},i}/10}\right]. $$ **Junctions** (2.2.17) add $C_{\mathrm{R},m,k} \cdot \max(1 - |x|/100,\ 0)$, with $x$ the distance in metres to the nearest junction and $k$ the junction type: 1 for a crossing with traffic lights, 2 for a roundabout. The rolling coefficients $C_\mathrm{R}$ are *negative* (traffic near a junction is slower), the propulsion coefficients $C_\mathrm{P}$ positive (it is accelerating). Both vanish from 100 m out. ## 4. Propulsion noise (2.2.11 to 2.2.16) Propulsion noise is the power train: engine, exhaust, transmission, intake. It is **linear** in speed, not logarithmic, because at low speed the engine is working hardest relative to the distance covered: $$ L_{W\mathrm{P},i,m} = A_{\mathrm{P},i,m} + B_{\mathrm{P},i,m}\,\frac{v_m - v_\mathrm{ref}}{v_\mathrm{ref}} + \Delta L_{W\mathrm{P},i,m}. $$ Where the two speed laws cross is what makes the road source behave the way it does: below the crossover the source is an engine, above it a tyre. *A light vehicle is tyre-dominated from about 25 km/h; a heavy vehicle only from about 60 km/h, which is why a lorry is still an engine at urban speeds.*

Show the code for this figure

```python import matplotlib.pyplot as plt import numpy as np from phonometry import ( CNOSSOS_A_WEIGHTING, road_propulsion_noise, road_rolling_noise, road_vehicle_sound_power, ) weights = np.asarray(CNOSSOS_A_WEIGHTING) a_weighted = lambda bands: 10.0 * np.log10(np.sum(10.0 ** ((bands + weights) / 10.0))) speeds = np.linspace(20.0, 130.0, 221) fig, ax = plt.subplots() for category, name in [("1", "Light vehicles (1)"), ("3", "Heavy vehicles (3)")]: rolling = [a_weighted(road_rolling_noise(category, v)) for v in speeds] propulsion = [a_weighted(road_propulsion_noise(category, v)) for v in speeds] total = [a_weighted(road_vehicle_sound_power(category, v)) for v in speeds] ax.plot(speeds, total, lw=2.4, label=f"{name} - total") ax.plot(speeds, rolling, ls="--", lw=1.2, label=f"{name} - rolling") ax.plot(speeds, propulsion, ls=":", lw=1.2, label=f"{name} - propulsion") ax.set_xlabel("Speed v [km/h]") ax.set_ylabel("A-weighted sound power [dB(A) re 1 pW]") ax.legend(fontsize="small") plt.show() ```

**Road gradient** (2.2.13 to 2.2.16) is the one correction whose published form is genuinely asymmetric, and the asymmetry is not a transcription slip. For light vehicles the downhill branch has **no speed factor**, while the two heavy categories do and use different speed offsets: | Category | Downhill ($s$ below the breakpoint) | Flat band | Uphill | | :--- | :--- | :--- | :--- | | 1 | $(\min(12\ \%, -s) - 6\ \%)/1\ \%$ | −6 % to 2 % | $(\min(12\ \%, s) - 2\ \%)/1{,}5\ \% \cdot v/100$ | | 2 | $(\min(12\ \%, -s) - 4\ \%)/0{,}7\ \% \cdot (v - 20)/100$ | −4 % to 0 % | $\min(12\ \%, s)/1\ \% \cdot v/100$ | | 3 | $(\min(12\ \%, -s) - 4\ \%)/0{,}5\ \% \cdot (v - 10)/100$ | −4 % to 0 % | $\min(12\ \%, s)/0{,}8\ \% \cdot v/100$ | Category 4 takes no gradient correction. The slope saturates at 12 % in both directions. Downhill noise comes from engine braking, uphill noise from load, so both branches are positive. For a bidirectional flow, split the flow in two and correct one half uphill and the other downhill. ## 5. The road surface (2.2.19, 2.2.20 and Table F-4) Table F-4 gives, for the reference surface and each of fourteen named pavements, an octave-band coefficient $\alpha$ and a speed coefficient $\beta$, per vehicle category, with the speed range over which the row is declared valid. The surface enters the two terms differently: $$ \Delta L_{W\mathrm{R,road},i,m} = \alpha_{i,m} + \beta_m\,\log_{10}\!\left(\frac{v_m}{v_\mathrm{ref}}\right), \qquad \Delta L_{W\mathrm{P,road},i,m} = \min\{\alpha_{i,m};\,0\}. $$ An absorbing surface reduces propulsion noise; a noisy one does not increase it. That asymmetry is deliberate: the pavement can absorb the engine sound radiated down onto it, but a rough texture only generates tyre noise, and tyre noise is already the rolling term. ```python from phonometry import RoadSurface, road_surface_coefficients row = road_surface_coefficients(RoadSurface.TWO_LAYER_ZOAB_FINE) row.speed_range # (80.0, 130.0) km/h, the printed validity range row.alpha["1"] # alpha per octave band for light vehicles row.beta["1"] # -0.1, the speed coefficient ``` The reference surface of the first row is all zeros: it is the virtual average of a dense asphalt concrete 0/11 and a stone mastic asphalt 0/11, between two and seven years old, in representative maintenance condition, dry, with no studded tyres, at 20 °C, on the flat. Under exactly those conditions every correction in 2.2 vanishes identically, so at the reference speed $v_m = v_\mathrm{ref} = 70\ \text{km/h}$, where the two speed terms vanish as well, the sound powers **are** the Table F-1 coefficients $A_{\mathrm{R},i,m}$ and $A_{\mathrm{P},i,m}$. ## 6. Handing the source to a propagation model The emission stage produces a power per metre. Splitting that 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 and is offered as such. ```python from phonometry import ( PropagationGeometry, RoadTraffic, RoadVehicleCategory, line_source_segment_power, predicted_receiver_level, road_source_power, ) result = road_source_power([ RoadTraffic(RoadVehicleCategory.LIGHT, 1000.0, 90.0), RoadTraffic(RoadVehicleCategory.HEAVY, 120.0, 80.0), ]) segment = line_source_segment_power(result.total_line_power, 20.0) # a 20 m segment levels = predicted_receiver_level( segment, PropagationGeometry(100.0, result.source_height, 4.0), frequencies=result.frequencies, ) ``` Note what this is and is not. CNOSSOS-EU has **its own** propagation method in section 2.5 of Annex II, and it is not ISO 9613-2: the two differ in the ground model, in the diffraction treatment and in the way favourable and homogeneous conditions are combined. 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. For the A-weighted total, use the octave-band weighting the Directive itself prints in 2.5.5 as amended, rather than recomputing it: ```python from phonometry import CNOSSOS_A_WEIGHTING CNOSSOS_A_WEIGHTING # (-26.2, -16.1, -8.6, -3.2, 0.0, 1.2, 1.0, -1.1) result.a_weighted_line_power ``` ## 7. Substituting a national database Appendix F is called a *database*, not a table of constants, because Member States may substitute measured national values, and because the same equations have already been evaluated with two different coefficient sets (the 2015 one and the 2021 one). Both coefficient objects can be replaced: ```python import dataclasses from phonometry import ROAD_COEFFICIENTS # One measured national row for light vehicles, the rest of Appendix F as published. national = dataclasses.replace( ROAD_COEFFICIENTS, rolling_a={ **ROAD_COEFFICIENTS.rolling_a, "1": (83.4, 89.0, 88.1, 93.6, 100.4, 96.9, 87.0, 76.5), }, ) ``` A substituted database has to cover every category of the traffic it is used with: reaching for a category it does not carry raises `ValueError` rather than failing later. That mechanism is also what pins the implementation: the European Commission published a test set of 4 875 road emission cases computed with the 2015 coefficients, and feeding the shipped equations that superseded database (not the 2021 tables the library ships by default) reproduces every published band level to 0,005 dB, inside the two decimals the test set prints. ## What this guide covers **Covered.** Section 2.2 of Annex II to Directive 2002/49/EC in the consolidated text: the traffic-flow line power (2.2.1), the vehicle power (2.2.2, 2.2.3), rolling noise with its studded-tyre and temperature corrections (2.2.4 to 2.2.10), propulsion noise with the road-gradient correction (2.2.11 to 2.2.16), the junction correction (2.2.17, 2.2.18) and the road-surface effect (2.2.19, 2.2.20), together with the whole Appendix F database, through `road_source_power`, `road_vehicle_sound_power`, `road_rolling_noise`, `road_propulsion_noise` and `road_surface_coefficients`. **Not covered.** The railway source (2.3 and Appendix G), 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. The open vehicle category 5 has no coefficients in Appendix F and is therefore not modelled. How a source line is split into point sources is declared out of scope by the method itself. ## 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, and the only place the measurement campaigns behind the Appendix F coefficients are described. - 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 2.2 with the coefficient database of Appendix F, in the consolidated text — which is three instruments read together, and reading only one of them is the easiest way to ship a wrong table: - 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 road source is section 2.2, formulae 2.2.1 to 2.2.20. - 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 sets the octave-band range of the road source to 63 Hz - 8 kHz and replaces the whole of Appendix G. - 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 F-1 and F-4 in their entirety and prints the octave-band A-weighting used to sum the source spectrum.