Source: https://jmrplens.github.io/phonometry/buildings/insulation/spanish-building-code/ # Spanish Building Code (CTE DB-HR) The *Documento Básico HR* "Protección frente al ruido" of the Spanish building code states its requirements in A-weighted global quantities that are close relatives of, but not identical to, the ISO 717-1 weighted ratings: $R_\mathrm{A}$, $R_\mathrm{A,tr}$, $D_\mathrm{nT,A}$ and $D_{2\mathrm{m,nT,Atr}}$. This page implements the direct Annex A route, which is the normative one for DB-HR, the requirement tables of clause 2, and the two design calculations most often used with them: the window-size correction and the insulation of a composite facade. The band spectra it consumes come from field measurement or from prediction; the ISO 717 reference-curve engine, which it is worth not confusing this with, is in [Insulation Ratings (ISO 717)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-ratings/). ## The global index of Annex A Instead of shifting a reference curve, DB-HR weights the measured band insulation with a normalised source spectrum and sums it energetically (Formulae A.5 to A.7): $$ I_x = -10 \log_{10} \sum_i 10^{(L_{x,i} - X_i)/10} \quad \text{[dBA]} $$ where $X_i$ is the band insulation (the sound reduction index $R$ or $R'$, the standardized level difference $D_\mathrm{nT}$, $D_{2\mathrm{m,nT}}$ and so on) and $L_{x,i}$ the normalised source spectrum. The sum runs over **eighteen** one-third-octave bands, 100 Hz to 5 kHz, two more than the sixteen of ISO 717-1 (100 Hz to 3150 Hz): the 4 kHz and 5 kHz bands, which are the first reason the two routes do not always agree. The band centres are in `DB_HR_FREQUENCIES`. | Normalised spectrum | Annex A table | Quantity it defines | Formula | | :--- | :--- | :--- | :--- | | A-weighted pink noise, $L_{\mathrm{Ar},i}$ | Table A.5 | $R_\mathrm{A}$, $D_\mathrm{nT,A}$, $D_{2\mathrm{m,nT,A}}$ | (A.5), (A.7) | | Road traffic, $L_{\mathrm{Atr},i}$ | Table A.3 | $R_\mathrm{A,tr}$, $D_{2\mathrm{m,nT,Atr}}$ | (A.6) | | Railway noise, $L_{\mathrm{Aef},i}$ | Table A.4 (numerically identical to A.3) | $D_{2\mathrm{m,nT,A}}$ | (A.5) | | Aircraft noise, $L_{\mathrm{Aav},i}$ | Table A.2 | $D_{2\mathrm{m,nT,Atr}}$ | (A.6) | The railway row is the one worth reading twice. Clause 3.1.3.4 point 1 says that where railway noise dominates the facade is assessed in $D_{2\mathrm{m,nT,A}}$ through formula (A.5), and only road traffic and aircraft give $D_{2\mathrm{m,nT,Atr}}$ through (A.6); Table H.1 prints the same split. Because Table A.4 is digit for digit Table A.3, a rail-dominant facade comes out at the same *number* as a road one, but the quantity the requirement and the report are stated in is not the same. That is why `d2m_nt_a()` and `d2m_nt_atr()` are separate entry points and each refuses the other's spectra, rather than one function with a spectrum switch that would silently put the wrong name on the result. All four are in `DB_HR_NORMALISED_SPECTRA` under the keys `"pink"`, `"traffic"`, `"railway"` and `"aircraft"`. The calculation below reproduces Ejemplo 7.2 of the *Manual*, the apparent sound reduction index $R'$ of a party wall taken from a real field test report: ```python from phonometry import building r_prime = [36.2, 41.5, 36.9, 40.4, 44.7, 42.4, 45.7, 46.1, 47.1, 52.3, 54.3, 57.5, 57.8, 57.3, 59.0, 62.8, 64.7, 65.3] index = building.ra(r_prime) index.value # 51.44 dBA index.intermediate # 51.4 dBA, the one-decimal intermediate index.reported # 51 dBA, the integer that defines the requirement ```

Show the code for this figure

```python import matplotlib.pyplot as plt from phonometry import building r_prime = [36.2, 41.5, 36.9, 40.4, 44.7, 42.4, 45.7, 46.1, 47.1, 52.3, 54.3, 57.5, 57.8, 57.3, 59.0, 62.8, 64.7, 65.3] building.ra(r_prime).plot() plt.show() ```

`ra()`, `ra_tr()`, `dnt_a()`, `d2m_nt_a()` and `d2m_nt_atr()` are named shortcuts over `db_hr_global_index()`, which accepts any spectrum and, given the `frequencies` argument, selects the eighteen DB-HR bands out of a longer series. ## Rounding and the relationship with the ISO 717 route Clause 3.1.3.1 point 4 of DB-HR requires the final values of the quantities that define the requirements to be expressed rounded to an integer, while intermediate values are carried with one decimal. The result object therefore exposes all three forms: `.value` (unrounded), `.intermediate` (one decimal) and `.reported` (the integer used in the check). DB-HR and ISO 717-1 reach the same place by different routes, and Annex H of the document itself accepts three approximations as long as the two routes differ by less than 1 dB: $$ D_\mathrm{nT,A} \approx D_\mathrm{nT,w} + C \quad (H.1), \qquad D_{2\mathrm{m,nT,A}} \approx D_{2\mathrm{m,nT,w}} + C \quad (H.2), \qquad D_{2\mathrm{m,nT,Atr}} \approx D_{2\mathrm{m,nT,w}} + C_\mathrm{tr} \quad (H.3) $$ with (H.2) covering the rail-dominant case of the previous section. On the two published spectra this page reproduces, the agreement is exact to the integer: | Case | Direct route (Annex A) | ISO 717-1 route | Published? | | :--- | :--- | :--- | :--- | | Separating wall of Ejemplo 7.2 | $R'_\mathrm{A} = 51.4$ dBA, rounded to 51 | $R'_\mathrm{w} = 52$ with $C_{100-5000} = -1$, i.e. 51 | yes, Ejemplo 7.1 prints $R'_\mathrm{w} = 52$, $C = -1$ and the 51 dBA | | Facade of Ejercicio 7.1 | $D_{2\mathrm{m,nT,Atr}} = 32.8$ dBA, rounded to 33 | $D_{2\mathrm{m,nT,w}} = 38$ with $C_{\mathrm{tr},100-5000} = -5$, i.e. 33 | no, the book prints neither 38 nor $-5$ | The two rows are not equally strong evidence. The wall row is a genuine external check, because the *Manual* prints the ISO 717-1 numbers as well as the direct one. For the facade the book publishes only the 32,8 dBA; the 38 and the $-5$ come from this library's own ISO 717-1 engine, so that row shows the two routes agreeing with each other rather than agreeing with a source. The real trap is the name of the spectrum adaptation terms. Annex H writes them as plain $C$ and $C_\mathrm{tr}$ and refers their definition to UNE-EN ISO 717-1 without narrowing the frequency range. Since the DB-HR indices run to 5 kHz while the ISO 717-1 core range stops at 3150 Hz, the terms that make (H.1) to (H.3) come out right are the **enlarged-range** $C_{100-5000}$ and $C_{\mathrm{tr},100-5000}$; that reading is not in Annex H itself but in the *Manual*, in the note to expressions [7.15] and [7.16]. It matters: on the facade of Ejercicio 7.1 the core-range $C$ is $-2$ while $C_{100-5000}$ is $-1$, so taking the wrong one gives 36 dBA instead of 37 for the $D_{2\mathrm{m,nT,A}}$ of that facade. On the same specimen $C_\mathrm{tr}$ and $C_{\mathrm{tr},100-5000}$ are both $-5$, so the $D_{2\mathrm{m,nT,Atr}}$ that DB-HR actually requires happens not to discriminate between the two readings at all. ```python from phonometry import building, weighted_rating_extended d2m_nt = [28.5, 28.5, 18.9, 23.7, 30.7, 31.3, 37.8, 35.2, 34.7, 38.5, 37.7, 43.1, 42.3, 44.2, 41.9, 37.5, 39.4, 41.5] direct = building.d2m_nt_atr(d2m_nt) direct.intermediate, direct.reported # 32.8 dBA -> 33 dBA iso = weighted_rating_extended(d2m_nt, building.DB_HR_FREQUENCIES) iso.rating, iso.ctr_100_5000 # 38 dB, -5 dB -> 33 dBA, the same figure iso.c, iso.c_100_5000 # -2 and -1: core range versus enlarged range ``` ## The requirements of clause 2 DB-HR states its requirements on two kinds of room: the **protected room** (*recinto protegido*, a habitable room with reinforced acoustic protection: bedrooms, living areas, classrooms, operating theatres, professional offices) and the **habitable room** (*recinto habitable*) in general. **Facades (Table 2.1).** The requirement on $D_{2\mathrm{m,nT,Atr}}$ is read by bands of the site's day noise index $L_\mathrm{d}$ ($L_\mathrm{d} \le 60$, $60 < L_\mathrm{d} \le 65$, $65 < L_\mathrm{d} \le 70$, $70 < L_\mathrm{d} \le 75$ and $L_\mathrm{d} > 75$ dBA): | Use and room | $\le 60$ | 60-65 | 65-70 | 70-75 | $> 75$ | | :--- | ---: | ---: | ---: | ---: | ---: | | Residential and hospital, bedrooms; cultural, health, educational and administrative, living areas | 30 | 32 | 37 | 42 | 47 | | Residential and hospital, living areas; cultural, health, educational and administrative, classrooms | 30 | 30 | 32 | 37 | 42 | Three rules modify the reading: a facade not directly exposed to the dominant noise (an enclosed courtyard, a quiet surrounding) is assessed with $L_\mathrm{d}$ reduced by 10 dBA, where aircraft noise dominates the table value is increased by 4 dBA, and where no official $L_\mathrm{d}$ exists for the site, 60 dBA is assumed for residential acoustic areas. **Airborne insulation between rooms (clause 2.1.1).** Partition walls (*tabiquería*) within one use unit must have $R_\mathrm{A} \ge 33$ dBA. Against a room of another use unit, a protected room requires $D_\mathrm{nT,A} \ge 50$ dBA and a habitable room $\ge 45$ dBA; against a services or activity room, a protected room requires $\ge 55$ dBA and a habitable room $\ge 45$ dBA. When the two rooms share a door or a window, the requirement moves to the opening (sound reduction index of 30 dBA for the protected room, 20 dBA for the habitable one) and to the enclosure around it (50 dBA). **Party walls (clause 2.1.1 c).** Against a *medianería* DB-HR offers two **alternative** routes, not cumulative ones: either each of the two leaves reaches $D_{2\mathrm{m,nT,Atr}} \ge 40$ dBA, or the two leaves taken together reach $D_\mathrm{nT,A} \ge 50$ dBA. `db_hr_party_wall_requirement()` returns whichever route is asked for. **Impact sound (clause 2.1.2).** The standardized impact sound pressure level $L'_\mathrm{nT,w}$ must not exceed 65 dB in a protected room against a room of another use unit, nor 60 dB against a services or activity room; that same 60 dB limit applies to the habitable room. **Reverberation and absorption (clause 2.2).** The reverberation time must not exceed 0.7 s in an empty classroom or conference hall under 350 m³, 0.5 s with the fixed seating installed, or 0.9 s in empty restaurants and dining rooms. In common areas sharing doors with protected rooms, the equivalent sound absorption area must be at least 0.2 m² per cubic metre of volume. ```python from phonometry import building facade = building.db_hr_facade_requirement(65.0, "residential", "bedrooms") facade.limit # 32 dBA (Table 2.1) airborne = building.db_hr_airborne_requirement("protected", "other_unit") [(r.quantity, r.limit) for r in airborne] # [("DnT,A", 50.0)] building.db_hr_impact_requirement("protected", "other_unit").limit # 65 dB building.db_hr_party_wall_requirement().limit # 40 dBA per leaf building.db_hr_party_wall_requirement("DnT,A").limit # 50 dBA both together building.db_hr_reverberation_requirement("classroom").limit # 0.7 s check = building.assess_db_hr([(33.0, facade), (51.44, airborne[0])]) check.complies # True ``` `check_db_hr_requirement()` rounds the achieved value the way DB-HR asks before comparing it (to an integer for the dB quantities, to one decimal for the reverberation time) and returns the margin; `assess_db_hr()` does the same over a list of value-requirement pairs. ## Windows and composite facades The tests that determine the sound reduction index of a window are run on specimens of about 1.8 m², and a larger window insulates less. The *Catálogo de Elementos Constructivos* of the building code corrects the catalogue value of $R_\mathrm{A}$ and $R_\mathrm{A,tr}$ by total window area: 0 dB up to 2.7 m², $-1$ dB between 2.7 and 3.6 m², $-2$ dB between 3.6 and 4.6 m² and $-3$ dB above 4.6 m². A 4 m² sliding window with 4-6-4 glazing, catalogued at $R_\mathrm{A} = 26$ dBA, ends up at 24 dBA (Ejemplo 7.4). A real facade is not a homogeneous element: it has a blind part and one or more openings. The sound reduction index of the whole follows from the area-weighted sum of the transmittances, which is what `composite_transmission_loss()` does in [Predicting Panel Sound Insulation](https://jmrplens.github.io/phonometry/buildings/design/panel-sound-insulation/). With the 8 m² facade of Ejemplo 7.5, a blind part of 40 dBA and a 2 m² window of 26 dBA, the whole comes out at 31.5 dBA: ```python from phonometry import building from phonometry.building.prediction.aperture_transmission import composite_transmission_loss building.window_size_correction(4.0) # -2 dB: 26 dBA catalogued -> 24 dBA composite_transmission_loss([6.0, 2.0], [40.0, 26.0]) # 31.53 dBA composite_transmission_loss([6.0, 2.0], [50.0, 26.0]) # 31.97 dBA: +10 dBA on the blind part composite_transmission_loss([6.0, 2.0], [40.0, 31.0]) # 35.63 dBA: +5 dBA on the window ``` Those last three lines hold the most useful rule of thumb in facade design: improving the blind part by 10 dBA raises the overall insulation by 0.4 dBA, practically nothing, whereas improving the window by 5 dBA raises it by 4.1 dBA, almost the full increment. The weak element is where the effort pays. ## Plots `DbHrGlobalIndexResult.plot()` draws the band insulation together with the transmitted level weighted by the normalised spectrum, as in the figure above: it shows at a glance which bands dominate the energy sum, and therefore where the element has to be improved. `DbHrAssessment.plot()` draws the achieved values against their limits, one per checked requirement. ## What this guide covers **Covered.** The DB-HR Annex A global index (Formulae A.5 to A.7) over the eighteen bands from 100 Hz to 5 kHz with the four normalised spectra of Tables A.2 to A.5, the rounding of clause 3.1.3.1 point 4, the requirements of clause 2 (Table 2.1 for facades, 2.1.1 airborne and party walls, 2.1.2 impact and 2.2 reverberation and absorption) and the window-size correction of the *Catálogo de Elementos Constructivos*. **Not covered.** The design options of clause 3 (the simplified option with its solution tables, and the general option, which is the EN 12354 prediction) are not implemented here: the calculation route of the general option lives in [Predicting Sound Insulation (EN 12354)](https://jmrplens.github.io/phonometry/buildings/design/insulation-prediction/). The execution conditions of clause 5 and the maintenance conditions of clause 6 are out of scope as well. ## Quick answers ### How does the DB-HR index RA differ from the Rw of ISO 717-1? The $R_\mathrm{w}$ of ISO 717-1 comes from shifting a reference curve over sixteen one-third-octave bands (100 Hz to 3150 Hz). The $R_\mathrm{A}$ of DB-HR comes from weighting the band sound reduction index with a normalised pink-noise spectrum and summing energetically over **eighteen** bands (100 Hz to 5 kHz). DB-HR accepts the equivalence $R_\mathrm{A} \approx R_\mathrm{w} + C$, but that $C$ is the enlarged-range term $C_{100-5000}$, not the core-range one. ## See also - [Insulation Ratings (ISO 717)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-ratings/): the reference-curve route with $R_\mathrm{w}$, $C$, $C_\mathrm{tr}$ and the enlarged-range terms that DB-HR calls simply $C$ and $C_\mathrm{tr}$. - [Spanish Noise Regulation (RD 1367/2007)](https://jmrplens.github.io/phonometry/environment/assessment/spanish-noise-regulation/): where the site's day noise index $L_\mathrm{d}$ that Table 2.1 is entered with comes from. - [Façade Sound Insulation](https://jmrplens.github.io/phonometry/buildings/insulation/facade-insulation/): the ISO 16283-3 measurement of $D_{2\mathrm{m,nT}}$ and its EN 12354-3 prediction, which feed the $D_{2\mathrm{m,nT,Atr}}$ index of this page. - [Predicting Panel Sound Insulation](https://jmrplens.github.io/phonometry/buildings/design/panel-sound-insulation/): the composite-facade calculation and transmission through openings and slits. - [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/): the band spectra of $R'$, $D_\mathrm{nT}$ and $L'_\mathrm{nT}$ that these global quantities summarise. - API reference: [`building.regulation.spain`](https://jmrplens.github.io/phonometry/reference/api/building/spain/). ## References - Avilés López, R., & Perera Martín, R. (2017). *Manual de acústica ambiental y arquitectónica*. Paraninfo. ISBN 978-84-283-3814-1. Ejemplo 7.2 and Ejercicio 7.1 (pp. 394-395) are the numeric oracles of the global index on this page, and Ejemplos 7.4 and 7.5 (pp. 408-410) the window-size correction and the composite-facade calculation. - Ministerio de la Presidencia (Spain). (2007). *Real Decreto 1367/2007, developing Ley 37/2003 del Ruido on acoustic zoning, quality objectives and acoustic emissions* (BOE-A-2007-18397). [BOE consolidated text](https://www.boe.es/buscar/act.php?id=BOE-A-2007-18397). The source of the day noise index $L_\mathrm{d}$ that Table 2.1 of DB-HR is read against. ## Standards CTE Documento Básico HR *Protección frente al ruido*, the noise part of the Spanish building code: [codigotecnico.org](https://www.codigotecnico.org/pdf/Documentos/HR/DBHR.pdf). The Annex A global index (Formulae A.5 to A.7) over the eighteen bands 100 Hz to 5 kHz with the normalised spectra of Tables A.2 to A.5, the rounding rule of clause 3.1.3.1 point 4, and the requirements of clause 2: Table 2.1 for facades, 2.1.1 for airborne insulation and party walls, 2.1.2 for impact sound and 2.2 for reverberation and absorption.