Source: https://jmrplens.github.io/phonometry/buildings/insulation/facade-insulation/ # Façade Sound Insulation A façade is the one element of a building that faces the noise everybody complains about: the road, the railway, the flight path. It is also the element whose insulation gets asked for twice, once predicted and once measured, which is why both halves live on this page. ISO 16283-3 measures the finished envelope, referencing the receiving-room level to the level 2 m in front of the façade under a 45° loudspeaker or under the road traffic itself. EN 12354-3 predicts the same standardized level difference from the sound reduction indices of the wall, the glazing and the air inlet before any of them is installed, and EN 12354-4 turns the envelope round to radiate an indoor source outwards. A closing section puts the measured and the predicted $D_{2\mathrm{m,nT}}$ side by side and shows what does, and does not, separate them. The reference curves behind every single number live in [Insulation Ratings (ISO 717)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-ratings/); the internal partitions of the same building in [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/) and [Predicting Sound Insulation (EN 12354)](https://jmrplens.github.io/phonometry/buildings/design/insulation-prediction/). ## Field measurement (ISO 16283-3) The same source/receiver logic reaches the building **façade**, but now the source is *outdoors*: a loudspeaker at 45° or the road traffic itself. Rather than a level difference across an internal partition, ISO 16283-3 references the receiving-room level $L_2$ to the level **2 m in front of the façade** $L_{1,2\mathrm{m}}$, giving the level difference $D_{2\mathrm{m}}$ and, exactly as in the airborne case, its standardized and normalized forms: $$ D_{2\mathrm{m}} = L_{1,2\mathrm{m}} - L_2, \quad D_{2\mathrm{m,nT}} = D_{2\mathrm{m}} + 10 \log_{10}\frac{T}{T_0}, \quad D_{2\mathrm{m,n}} = D_{2\mathrm{m}} - 10 \log_{10}\frac{A}{A_0}, $$ with $T_0 = 0.5$ s, $A_0 = 10$ m² and $A = 0.16\ V/T$ (dwellings). When the microphone sits **on the test element** (surface level $L_{1,\mathrm{s}}$) the *element* method also yields an apparent sound reduction index, carrying a fixed angle-of-incidence correction: $-1.5$ dB for the 45° loudspeaker method, $-3$ dB for the all-angle road-traffic method: $$ R'_{45°} = L_{1,\mathrm{s}} - L_2 + 10 \log_{10}\frac{S}{A} - 1.5, \qquad R'_\mathrm{tr,s} = L_{1,\mathrm{s}} - L_2 + 10 \log_{10}\frac{S}{A} - 3. $$ The façade quantity is airborne, so its single-number rating uses the **ISO 717-1** reference curve through `weighted_rating` unchanged (Annex F). ```python import numpy as np from phonometry import building # Outdoor level 2 m in front of the façade, receiving-room level and T per # one-third-octave band; surface_level is the microphone on the test element. l1_2m = np.full(16, 75.0) # L1,2m outdoors l2 = np.full(16, 33.0) # receiving-room L2 t2 = np.full(16, 0.5) # receiving-room T (s) fac = building.facade_insulation(l1_2m, l2, t2, volume=50.0, area=11.5, surface_level=np.full(16, 78.0), method="loudspeaker") print(round(float(fac.d_2m[0]), 1)) # 42.0 D2m = L1,2m - L2 print(round(float(fac.d_2m_nt[0]), 1)) # 42.0 (= D2m since T = T0) print(round(float(fac.d_2m_n[0]), 1)) # 40.0 normalized to A0 = 10 m^2 print(round(float(fac.r_prime[0]), 1)) # 42.1 R'45deg (loudspeaker, -1.5 dB) # The road-traffic element method carries the -3 dB all-angle correction instead tr = building.facade_insulation(l1_2m, l2, t2, volume=50.0, area=11.5, surface_level=np.full(16, 78.0), method="road_traffic") print(round(float(tr.r_prime[0]), 1)) # 40.6 R'tr,s (traffic, -3 dB) # The façade quantity is airborne: rate D2m,nT with the ISO 717-1 engine print(building.weighted_rating(fac.d_2m_nt).rating) # 42 Dls,2m,nT,w fac.plot() # per-band D2m,nT with D2m, D2m,n and R' overlaid (needs matplotlib) ``` *The four façade quantities of one measurement: the raw $D_{2\mathrm{m}}$, its standardized and normalized forms, and the element $R'_{45°}$ carrying the −1.5 dB angle-of-incidence correction. The rating box reads the single number $D_{\mathrm{ls},2\mathrm{m,nT,w}}$ obtained by feeding $D_{2\mathrm{m,nT}}$ to the ISO 717-1 engine.*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import building # A dwelling façade, 45° loudspeaker method: outdoor level 2 m in front, # receiving-room level and T per one-third-octave band. bands = np.array([100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150], float) l1_2m = np.array([76.0, 77.0, 78.0, 78.5, 79.0, 79.0, 79.0, 79.0, 78.5, 78.0, 77.5, 77.0, 76.5, 76.0, 75.0, 74.0]) d2m = np.array([24.0, 25.5, 27.0, 28.5, 30.0, 31.5, 33.0, 34.5, 36.0, 37.0, 38.0, 38.5, 39.0, 39.0, 38.5, 38.0]) t2 = np.array([0.65, 0.62, 0.58, 0.55, 0.52, 0.50, 0.49, 0.48, 0.47, 0.46, 0.45, 0.44, 0.43, 0.43, 0.42, 0.42]) fac = building.facade_insulation(l1_2m, l1_2m - d2m, t2, volume=32.0, area=10.8, surface_level=l1_2m + 3.0, method="loudspeaker", frequencies=bands) # One line — D2m,nT with D2m, D2m,n and R' overlaid per band: fac.plot() plt.show() # By hand, from the result's fields: w = building.weighted_rating(fac.d_2m_nt) fig, ax = plt.subplots() ax.semilogx(bands, fac.d_2m_nt, "-s", label="D2m,nT (standardized)") ax.semilogx(bands, fac.d_2m, "--o", label="D2m") ax.semilogx(bands, fac.d_2m_n, ":", label="D2m,n (normalized)") ax.semilogx(bands, fac.r_prime, "-.", label="R'45°") ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Level difference / reduction index [dB]") ax.set_title(f"Dls,2m,nT,w = {w.rating} dB (C={w.c:+d}; Ctr={w.ctr:+d})") ax.legend() plt.show() ```

`surface_level`, `area` and `volume` are all optional: with only `l1_2m`, `l2` and `t2` the function returns `d_2m` and `d_2m_nt`; add `volume` for `d_2m_n`; add `surface_level` **and** `area` **and** `volume` for `r_prime`. Positions are energy-averaged with the surface-level formula (Clause 9.5.1); band levels are assumed already corrected for background noise. ### `facade_insulation()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `l1_2m` | 1D or 2D array | dB | one/band, or `(positions, bands)` | Level 2 m in front of the façade $L_{1,2\mathrm{m}}$ | | `l2` | 1D or 2D array | dB | same band count | Receiving-room levels | | `t2` | 1D array | s | > 0, one per band | Receiving-room reverberation time | | `area` | float, optional | m² | > 0, with `surface_level`, `volume` | Test-element area $S$ (enables $R'$) | | `volume` | float, optional | m³ | > 0 | Receiving-room $V$ (enables $D_{2\mathrm{m,n}}$; required for $R'$) | | `surface_level` | 1D/2D array, optional | dB | same band count | Surface level $L_{1,\mathrm{s}}$ on the element (enables $R'$) | | `method` | str | — | `'loudspeaker'` (−1.5 dB) / `'road_traffic'` (−3 dB) | Angle-of-incidence correction of $R'$ | | `t0` | float | s | default `0.5` | Reference reverberation time $T_0$ | | `frequencies` | 1D array, optional | Hz | — | Band centres carried on the result for plotting | `facade_insulation()` returns a `FacadeInsulationResult` (`d_2m`, `d_2m_nt`, `d_2m_n` or `None`, `r_prime` or `None`, `frequencies`); feed any 16-band façade quantity to `weighted_rating` for its ISO 717-1 single number. ### ISO 16283-3 field façade report (`.report()`) `FacadeInsulationResult.report(path)` writes the one-page ISO 16283-3 field façade test report: the standard-basis line, an optional metadata header, the one-third-octave table beside the measured-versus-shifted-reference curve, the boxed field rating $D_{2\mathrm{m,nT,w}}\ (C;\ C_\mathrm{tr})$, the engineering-method statement, an optional requirement verdict (a level difference passes at or above it) and a footer. `quantity="d_2m_nt"` (default) reports the standardized level difference; `"d_2m_n"` the normalized one; `"r_prime"` the apparent sound reduction index $R'_{45}$. `verbose=True`, `metadata`, `language="es"` and the `phonometry[report]` extra behave exactly as in the fiches above. ```python fac.report("D2mnTw_facade.pdf") # D2m,nT,w (C; Ctr) fac.report("Rp45_facade.pdf", quantity="r_prime") # R'45,w (C; Ctr) ``` [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso16283_facade_example.pdf) *Field façade fiche (`FacadeInsulationResult.report`), $D_{2\mathrm{m,nT,w}}\ (C;\ C_\mathrm{tr})$.* ## Prediction from the elements (EN 12354-3) Parts 3 and 4 predict the two directions across the building envelope, both from the same energy summation of the element **transmission factors** $\tau = 10^{-R/10}$, area-weighted by $S_i/S$ (a small element or air path enters through its element-normalized level difference $D_\mathrm{n,e}$ with the reference area $A_0 = 10\ \text{m}^2$): $$ R' = -10 \log_{10}\!\Big( \sum_i \tfrac{S_i}{S}\,10^{-R_i/10} + \sum_k \tfrac{A_0}{S}\,10^{-D_{\mathrm{n,e},k}/10} \Big). $$ **Part 3: outdoor → indoor.** From $R'$ (Formula 10) follow the loudspeaker- and traffic-referenced indices $R_{45} = R'+1$ and $R_\mathrm{tr,s} = R'$, and the primary output, the standardized level difference at 2 m (Formula 13) $$ D_{2\mathrm{m,nT}} = R' + \Delta L_\mathrm{fs} + 10 \log_{10}\frac{V}{6\,T_0\,S}, \qquad T_0 = 0.5\ \text{s}, $$ with the façade-shape term $\Delta L_\mathrm{fs}$ (Annex C; 0 dB for a flat reflecting façade; `facade_shape_level_difference` looks it up from the Figure C.2 table for galleries, balconies and terraces, interpolating over the underside absorption $\alpha_\mathrm{w}$). Single-number ratings reuse EN ISO 717-1 (`weighted_rating`). ```python from phonometry import building # EN 12354-3 Annex F: an 11.3 m² façade (V = 50 m³, flat so ΔLfs = 0) of a double # wall, a window, a small skylight and an acoustically-treated air inlet (a Dn,e # element). elements = [ building.FacadeElement("wall", area=6.0, r=[41, 46, 52, 58, 64]), # octave 125-2000 building.FacadeElement("window", area=4.5, r=[23, 22, 30, 36, 37]), building.FacadeElement("skylight", area=0.5, r=[24, 27, 30, 33, 30]), building.FacadeElement("air inlet", dn_e=[28, 23, 25, 38, 44]), # small element ] fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0, frequencies=[125, 250, 500, 1000, 2000], bands="octave") print(fac.r_tr_s_w, fac.c_tr, fac.d_2m_nt_w) # 31 -3 33 (R'tr,s,w / Ctr / D2m,nT,w) fac.plot() # per-element partial indices with R' and D2m,nT overlaid (needs matplotlib) ```

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```python import numpy as np import matplotlib.pyplot as plt from phonometry import building # EN 12354-3 Annex F: an 11.3 m² façade (V = 50 m³, flat so ΔLfs = 0) of a double # wall, a window, a small skylight and an acoustically-treated air inlet (a Dn,e # element). elements = [ building.FacadeElement("wall", area=6.0, r=[41, 46, 52, 58, 64]), # octave 125-2000 building.FacadeElement("window", area=4.5, r=[23, 22, 30, 36, 37]), building.FacadeElement("skylight", area=0.5, r=[24, 27, 30, 33, 30]), building.FacadeElement("air inlet", dn_e=[28, 23, 25, 38, 44]), # small element ] fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0, frequencies=[125, 250, 500, 1000, 2000], bands="octave") x = np.arange(5) fig, ax = plt.subplots(figsize=(9, 5.5)) for name, rp in fac.element_r.items(): ax.plot(x, rp, "--", alpha=0.6, marker=".", label=f"Rp — {name}") ax.plot(x, fac.r_prime, "k-", lw=2.5, marker="o", label="R′ (façade)") ax.plot(x, fac.d_2m_nt, lw=2, marker="s", label="D2m,nT") ax.set_xticks(x); ax.set_xticklabels([125, 250, 500, 1000, 2000]) ax.set_xlabel("Frequency [Hz]"); ax.set_ylabel("Index / level difference [dB]") ax.set_title("EN 12354-3 façade sound insulation (Annex F)") ax.legend(ncol=2); ax.grid(alpha=0.4) fig.tight_layout(); plt.show() ```

The composite is easier to reason about drawn as areas. `plot_facade_elements` tiles the elevation with every element's drawn area equal to its real area (here a 6 m² masonry wall, a 1.5 m² window and its 0.3 m² roller shutter box), and a prediction that retained its `elements` redraws its own façade with `fac.plot_geometry()`. *The areas the energy sum weighs, to scale: the window holds a quarter of the wall's area but each square metre of it transmits a hundred times more, so the small tiles decide $R'$.*

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```python import matplotlib.pyplot as plt from phonometry import building # The prediction's composite drawn as areas: 6 m2 of wall, a 1.5 m2 window # and its 0.3 m2 roller shutter box. elements = [ building.FacadeElement("Masonry wall", area=6.0, r=[50.0] * 5), building.FacadeElement("Window", area=1.5, r=[30.0] * 5), building.FacadeElement("Roller shutter box", area=0.3, r=[22.0] * 5), ] building.plot_facade_elements(elements) plt.show() # A prediction retains its elements, so it redraws its own elevation: # fac = building.facade_sound_reduction(elements, area=7.8, volume=50.0) # fac.plot_geometry() ```

The façade prediction also writes a one-page **prediction** report through a `report(path)` method, the same layout as the airborne and impact prediction fiches. `FacadePredictionResult.report()` renders the façade-element table (each element's weighted partial index $R_\mathrm{p,w}$) beside the per-element / $R'$ / $D_{2\mathrm{m,nT}}$ plot, the boxed predicted $D_{2\mathrm{m,nT,w}}$ (with $R'_\mathrm{tr,s,w}$ and $C_\mathrm{tr}$), the prediction statement and, when a `requirement` is supplied, a PASS/FAIL verdict (the level difference passes at or above it). `verbose=True` annexes each element's share of the transmitted sound energy, which singles out the limiting element (the air inlet here, not the wall). The report needs the ISO 717-1 single-number ratings, so build the result on the 5 octave or 16 one-third-octave bands. The applicable `ReportMetadata` fields describe the predicted situation: `specimen` (the façade element set), `area` (the exposed façade area), the receiving-room `receiving_volume`, the outdoor/traffic situation in `test_room`, plus the calculator / laboratory identity fields (`client`, `manufacturer`, `measurement_standard`, `laboratory`, `operator`, `report_id`, `test_date`), a free-text façade-shape and model summary in `notes` and the target $D_{2\mathrm{m,nT,w}}$ in `requirement`. Metadata, `language="es"` and the `phonometry[report]` extra behave as in the measurement fiches. ```python from phonometry import building, ReportMetadata # EN 12354-3 Annex F facade -> D2m,nT,w = 33 dB (R'tr,s,w = 31, Ctr = -3). elements = [ building.FacadeElement("Masonry wall", area=6.0, r=[41, 46, 52, 58, 64]), building.FacadeElement("Glazing", area=4.5, r=[23, 22, 30, 36, 37]), building.FacadeElement("Roof light", area=0.5, r=[24, 27, 30, 33, 30]), building.FacadeElement("Air inlet", dn_e=[28, 23, 25, 38, 44]), ] fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0, frequencies=[125, 250, 500, 1000, 2000], bands="octave") fac.report("D2mnT_prediction.pdf", metadata=ReportMetadata( specimen="Masonry wall + window + roof light + air inlet", area=11.3, receiving_volume=50.0, requirement=30.0, notes="Flat facade, ΔLfs = 0 dB (Annex C).")) # D2m,nT,w = 33 dB ``` [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso12354_facade_prediction_example.pdf) ## Indoor sound radiated outdoors (EN 12354-4) **Part 4: indoor → outdoor.** The sound power level radiated by a segment (Formula 2) is $L_W = L_{p,\mathrm{in}} + C_\mathrm{d} - R' + 10 \log_{10}(S/S_0)$ with $S_0 = 1$ m² and the inside-field diffusivity term $C_\mathrm{d}$ (Annex B; −6 dB ideal diffuse, −5 dB average industrial). Openings are elements whose "R" is the silencer insertion loss (a bare opening is 0 dB). The exterior level follows from the simplified Annex E attenuation $A_\mathrm{tot}$ of a finite radiating side, $L_p = L_W - A_\mathrm{tot}$. ```python from phonometry import building # EN 12354-4 Annex G, side 1: a 10×20 m concrete wall segment with a 6×4 m # industrial door, inside level Lp,in, Cd = -5 dB. The 40 dB cap on R' is an # Annex G example footnote (field leaks), not part of Formula (2)/(3): pass it # explicitly to reproduce Annex G; by default no cap is applied. bands = [63, 125, 250, 500, 1000, 2000, 4000, 8000] seg = building.radiated_sound_power( [building.FacadeElement("wall", area=176.0, r=[32, 36, 36, 33, 39, 49, 57, 63]), building.FacadeElement("door", area=24.0, r=[21, 23, 28, 30, 30, 30, 30, 30])], lp_in=[70, 74, 76, 72, 70, 67, 62, 57], area=200.0, c_d=-5.0, r_prime_cap=40.0, octave_bands=bands) print(round(seg.l_w[0], 1), round(seg.l_w[1], 1)) # 59.8 61.2 (LW at 63/125 Hz) # Exterior level 5 m in front of the centre of the 60×10 m side (LWA = 62.9 dB(A)). a_tot = building.outdoor_attenuation(width=60.0, height=10.0, distance=5.0) print(round(a_tot, 1), round(building.outdoor_level(62.9, a_tot), 1)) # 26.3 36.6 seg.plot() # radiated LW per octave with the A-weighted LWA line (needs matplotlib) ``` *The Annex G side-1 segment: the wall dominates the area but the door's weaker $R$ carries the radiated power, so the octave spectrum stays flat where the wall alone would fall. The dashed line is the A-weighted single number $L_{W\mathrm{A}}$ formed from the octave bands.*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import building # EN 12354-4 Annex G, side 1: a 10×20 m concrete wall segment with a 6×4 m # industrial door, inside level Lp,in, Cd = -5 dB. bands = [63, 125, 250, 500, 1000, 2000, 4000, 8000] seg = building.radiated_sound_power( [building.FacadeElement("wall", area=176.0, r=[32, 36, 36, 33, 39, 49, 57, 63]), building.FacadeElement("door", area=24.0, r=[21, 23, 28, 30, 30, 30, 30, 30])], lp_in=[70, 74, 76, 72, 70, 67, 62, 57], area=200.0, c_d=-5.0, r_prime_cap=40.0, octave_bands=bands) # One line — LW per octave with the A-weighted LWA line: seg.plot() plt.show() # By hand, from the result's fields: x = np.arange(len(bands)) fig, ax = plt.subplots() ax.bar(x, seg.l_w, label="radiated LW per octave") ax.axhline(seg.l_w_dba, ls="--", color="tab:red", label=f"LWA = {seg.l_w_dba:.1f} dB(A)") ax.set_xticks(x, [str(b) for b in bands]) ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Radiated sound power level [dB re 1 pW]") ax.set_title("EN 12354-4 radiated sound power (Annex G)") ax.legend() plt.show() ```

> **Worked-example note.** The 2000 worked examples carry small internal rounding > inconsistencies at the higher octave bands (Part 3's printed $R'$ disagrees with > its own per-element partial indices at 1 k/2 k; Part 4's $R'$ rows above 500 Hz > disagree with its Table G.2 inputs). The implementation is faithful to the > formulas: it reproduces the low bands, every single-number rating and the whole > Annex E propagation exactly. ### `FacadeElement` / `facade_sound_reduction()` / `radiated_sound_power()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `FacadeElement.area` | float | m² | > 0 for `r` / `insertion_loss` | Element area $S_i$ (ignored for `dn_e`) | | `FacadeElement.r` / `dn_e` / `insertion_loss` | float or seq | dB | give exactly one | Area element $R_i$ / small-element $D_\mathrm{n,e}$ / opening insertion loss | | `facade_sound_reduction(area)` | float | m² | > 0 | Total façade area $S$ | | `facade_sound_reduction(volume)` | float | m³ | > 0 | Receiving-room volume $V$ (Formula 13) | | `facade_sound_reduction(delta_l_fs)` | float | dB | default `0` | Façade-shape term $\Delta L_\mathrm{fs}$ (Annex C; look it up with `facade_shape_level_difference`) | | `radiated_sound_power(lp_in)` | float or seq | dB | — | Inside level $L_{p,\mathrm{in}}$ per band | | `radiated_sound_power(c_d)` | float | dB | default `-6` | Diffusivity term $C_\mathrm{d}$ (Annex B) | | `radiated_sound_power(r_prime_cap)` | float | dB | default `None` (off) | Optional field cap on $R'$, an Annex G example footnote (it uses 40 dB), not part of Formula (2)/(3) | | `radiated_sound_power(octave_bands)` | seq of int | Hz | default `None` | Octave centres matching the bands; enables the A-weighted $L_{W\mathrm{A}}$ | | `facade_sound_reduction(frequencies)` | seq | Hz | default `None`; length = band count | Band centres carried on the result for plotting | | `outdoor_attenuation(width, height, distance)` | float | m | > 0 | Finite radiating side and reception distance (Annex E) | | `outdoor_level(l_w, attenuation)` | float or seq | dB | broadcast-compatible | Exterior $L_p$ from one or more sides (Formula E.1) | `facade_sound_reduction()` returns a `FacadePredictionResult` (`r_prime`, `r_45`, `r_tr_s`, `d_2m_nt`, `element_r`, and the `r_tr_s_w` / `d_2m_nt_w` / `c_tr` single numbers); `radiated_sound_power()` a `RadiatedPowerResult` (`l_w`, `r_prime`, `l_w_dba`). Both expose `.plot()`. ## Measurement against prediction The two halves of this guide describe the same wall from opposite ends of its life: EN 12354-3 before it exists, ISO 16283-3 once it does. They are worth comparing because they end on the same quantity, the standardized level difference at 2 m, and because the geometry term that carries the prediction from an index to a level difference is the measurement's own normalisation written another way. Start from the measured definition, replace $D_{2\mathrm{m}}$ by the apparent index it implies and substitute the Sabine absorption area $A = 0.16\ V/T$: $$ D_{2\mathrm{m,nT}} = D_{2\mathrm{m}} + 10 \log_{10}\frac{T}{T_0} = R' + 10 \log_{10}\frac{A}{S} + 10 \log_{10}\frac{T}{T_0} = R' + 10 \log_{10}\frac{0.16\ V}{S\ T_0}. $$ The reverberation time cancels: what survives is the room volume against the façade area. EN 12354-3 Formula (13) writes that same term as $10 \log_{10} V/(6\,T_0\,S)$, which is the Sabine constant carried as $1/6 = 0.167$ instead of the $0.16$ of the measurement standard. The two therefore differ by a fixed $10 \log_{10}(0.167/0.16) = 0.18$ dB in every band, of any room, and by nothing else. (The 2017 revision of the prediction standard harmonised its constant to 0.16, so the gap is specific to the EN 12354-3:2000 edition the module implements.) That is small enough to check numerically. Take the Annex F façade predicted above, put it in a receiving room of 50 m³ with $T = T_0$, and reconstruct the receiving-room level a measurement would have found: ```python import numpy as np from phonometry import building # The Annex F façade predicted above, now "measured" in a receiving room of # 50 m3 whose reverberation time is exactly T0 = 0.5 s. elements = [ building.FacadeElement("wall", area=6.0, r=[41, 46, 52, 58, 64]), building.FacadeElement("window", area=4.5, r=[23, 22, 30, 36, 37]), building.FacadeElement("skylight", area=0.5, r=[24, 27, 30, 33, 30]), building.FacadeElement("air inlet", dn_e=[28, 23, 25, 38, 44]), ] volume, area = 50.0, 11.3 fac = building.facade_sound_reduction(elements, area=area, volume=volume, frequencies=[125, 250, 500, 1000, 2000], bands="octave") # What the field measurement would read: A = 0.16 V / T is the Sabine area of # ISO 16283-3, and R' - 10 lg(S/A) is the level difference it implies. t2 = np.full(5, 0.5) l1_2m = np.full(5, 75.0) l2 = l1_2m - (fac.r_prime - 10 * np.log10(area / (0.16 * volume / t2))) meas = building.facade_insulation(l1_2m, l2, t2, volume=volume) print(np.round(meas.d_2m_nt - fac.d_2m_nt, 2)) # [-0.18 -0.18 -0.18 -0.18 -0.18] print(building.weighted_rating(meas.d_2m_nt).rating, fac.d_2m_nt_w) # 33 33 ``` The two curves run parallel to the second decimal and both rate at $D_{2\mathrm{m,nT,w}} = 33$ dB. Everything that separates a real prediction from a real measurement therefore sits in the inputs, not in the formulas: * **The element indices.** The prediction consumes laboratory $R$ values measured with flanking suppressed and with the element mounted as the laboratory mounts it. The built façade adds its perimeter seals, its roller-shutter box, the joint between frame and reveal and whatever the site did to them. * **The shape term.** $\Delta L_\mathrm{fs}$ is 0 dB only for a flat reflecting façade. A balcony, a gallery or a terrace changes the field at the 2 m position, and a measurement takes that change as it is while a prediction has to look it up in Annex C. * **The source.** ISO 16283-3 labels the loudspeaker result $D_{\mathrm{ls},2\mathrm{m,nT}}$ precisely because a loudspeaker at 45° is not road traffic; its element index carries a −1.5 dB angle correction where the all-angle traffic method carries −3 dB. EN 12354-3 predicts the traffic-referenced $R_\mathrm{tr,s} = R'$ directly and offers $R_{45} = R' + 1$ for the loudspeaker comparison. * **The receiving room.** The prediction assumes the design volume and a diffuse receiving field. The measurement takes the room furnished, and the diffuse assumption behind $A = 0.16\ V/T$ weakens exactly in the small rooms and low bands where façade requirements bite. The practical reading: size the glazing and the air inlets with the prediction, accept the finished façade with the measurement, and do not treat a couple of decibels between the two as an error in either. A prediction built on laboratory indices and a field measurement of the finished envelope each carry an uncertainty of that order on their own; the [ISO 12999-1 uncertainty section](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/#measurement-uncertainty-iso-12999-1) puts a number on the measurement half. And when the two disagree by much more than that, the per-element share of the transmitted energy in the prediction report is the place to look first: on this façade it is the air inlet, not the wall, that decides the result. ## References - Hopkins, C. (2007). *Sound insulation*. Butterworth-Heinemann. ISBN 978-0-7506-6526-1. [doi:10.4324/9780080550473](https://doi.org/10.4324/9780080550473). The transmission physics of the envelope behind both the measured and the predicted façade quantities. - International Organization for Standardization. (2016). *Acoustics — Field measurement of sound insulation in buildings and of building elements — Part 3: Façade sound insulation* (ISO 16283-3:2016). [iso.org catalogue](https://www.iso.org/standard/59748.html). The field façade element and global methods, with the angle-of-incidence corrections. - European Committee for Standardization. (2000). *Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 3: Airborne sound insulation against outdoor sound* (EN 12354-3:2000). [BSI Knowledge catalogue](https://knowledge.bsigroup.com/products/building-acoustics-estimation-of-acoustic-performance-in-buildings-from-the-performance-of-elements-airborne-sound-insulation-against-outdoor-sound). The façade sound insulation prediction (Annex F worked example). - European Committee for Standardization. (2000). *Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 4: Transmission of indoor sound to the outside* (EN 12354-4:2000). [BSI Knowledge catalogue](https://knowledge.bsigroup.com/products/building-acoustics-estimation-of-acoustic-performance-in-buildings-from-the-performance-of-elements-transmission-of-indoor-sound-to-the-outside). The outdoor-radiation prediction (Annex G worked example). ## Standards ISO 16283-3:2016, which defines the field façade quantities $D_{2\mathrm{m}}$, $D_{2\mathrm{m,nT}}$, $D_{2\mathrm{m,n}}$, $R'_{45°}$ and $R'_\mathrm{tr,s}$ of the loudspeaker and road-traffic methods and their test report; EN 12354-3:2000, which predicts the same $D_{2\mathrm{m,nT}}$ from the element indices with the Annex C façade-shape term (Annex F worked example); and EN 12354-4:2000, which predicts the sound power radiated outwards by a building side and its exterior level (Annex G worked example). The single-number ratings come from ISO 717-1 (Annex F of ISO 16283-3 and EN ISO 717-1 for the prediction). **Not covered.** The band levels handed to `facade_insulation` are assumed already corrected for background noise, and ISO 16283-3's procedural requirements are documented but never checked: nothing verifies the 45° ± 5° incidence, the 5 m / 7 m slant distances, the 3 → 10 microphone escalation and its recess special case, the 50 pass-bys and the simultaneity of a traffic measurement, or that the method chosen matches the question asked. The low-frequency corner procedure of Clause 7 — the façade counterpart of the **ISO 16283-1** procedure, triggered by the same 25 m³ receiving-room threshold — is not implemented, and neither are the railway and aircraft methods of Annex E. The EN 12354-3 and EN 12354-4 worked examples of the 2000 editions carry small internal rounding inconsistencies in the higher octave bands; the implementation follows the formulae rather than the printed rows. ## See also - [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/): the airborne and impact field measurements of the internal partitions, and the ISO 12999-1 uncertainty that qualifies every field rating. - [Predicting Sound Insulation (EN 12354)](https://jmrplens.github.io/phonometry/buildings/design/insulation-prediction/): the airborne and impact flanking models of EN 12354-1/2 that share the transmission-factor summation used here. - [Insulation Ratings (ISO 717)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-ratings/): the reference-curve engine behind the $D_{2\mathrm{m,nT,w}}$, $R'_{45,w}$ and $R'_\mathrm{tr,s,w}$ single numbers. - [Sound Insulation Survey Method (ISO 10052)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-survey/): the octave-band façade quantity of the quick survey method. - [Predicting Panel Sound Insulation](https://jmrplens.github.io/phonometry/buildings/design/panel-sound-insulation/): the mass law, coincidence dip and aperture models behind the element $R$ values the prediction consumes. - [Outdoor Sound Propagation](https://jmrplens.github.io/phonometry/environment/propagation/outdoor-propagation/): the propagation from the source to the 2 m position in front of the façade, and onwards from the radiating side of EN 12354-4. - [Theory](https://jmrplens.github.io/phonometry/reference/theory/rooms-buildings/): the reference-curve derivation behind the weighted single-number ratings. - API reference: [`building.prediction.facade`](https://jmrplens.github.io/phonometry/reference/api/building/facade/) and [`building.measurement.insulation`](https://jmrplens.github.io/phonometry/reference/api/building/insulation/).