building.prediction.linings

Prediction of wall and ceiling linings: the weighted improvement an additional layer gives the element behind it (ISO 12354-1:2017 Annex D).

A lining is not a floor covering. It is added to a wall or a ceiling, not laid under a tapping machine, and what it changes is the airborne sound reduction index of the basic element it is fixed to. Annex D therefore rates it as a shift of a single number rather than as a spectrum, and it reads that shift off one quantity: the mass-spring resonance of the lining against the element. That single frequency is what makes the annex one subject and this module one file.

A lining improves or degrades the sound insulation depending on where its resonance falls, so Annex D predicts the weighted improvement from fo alone: Formula (D.1) for a layer bonded directly to the wall, Formula (D.2) for one on studs over a filled cavity, then Table D.1 for interior linings (weighted_lining_improvement), Formulae (D.3) to (D.6) for exterior thermal systems and (D.7) for stud systems (lining_improvement), and Formula (D.8) to carry a laboratory rating to the field (lining_improvement_in_situ).

Citations are to ISO 12354-1:2017. One printed defect is relevant here and is recorded in docs/ERRATA.md: the overlap of the last two rows of Table D.1 at 1 600 Hz.

Several relations used here carry no published worked example, so they are implemented as printed and checked only for self-consistency: the cavity stiffness $0.111/ d$ of Formula (D.2) and the exterior-system and stud fits of Formulae (D.3) to (D.8). The guide “Predicting Resilient-Layer Performance” says which pieces have an oracle and which do not.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

lining_improvement

lining_improvement(
    resonance_frequency: float,
    *,
    system: LiningSystem = 'mineral_wool',
    anchors: bool = False,
    glued_area: float | None = None,
) -> LiningImprovementResult

Single-number ratings of an additional layer (Formulae D.3 to D.7).

For the reference situation of ISO 12354-1:2017 Annex D, a system applied to a heavy basic wall of about 350 kg/m²:

system="mineral_wool" (Formula D.3), an exterior thermal system on mineral wool with 40 % glued area and no anchors: $Δ R_{w} = - 36 lo g_{10} (f_{o}) + 82.5$ , $Δ R_{A} = - 42 lo g_{10} (f_{o}) + 92.0$ , $Δ R_{A, t r} = - 39 lo g_{10} (f_{o}) + 87.7$ , each floored at −4 dB.
system="foam" (Formula D.4), the same on PS, EPS or EEPS foams: $- 33 lo g_{10} (f_{o}) + 76.0$ , $- 33 lo g_{10} (f_{o}) + 74.0$ , $- 36 lo g_{10} (f_{o}) + 77.0$ , floored at −3 dB.
system="studs" (Formula D.7), a layer on studs not directly fixed to the basic wall: $- 20 lo g_{10} (f_{o}) + 48$ , $- 22 lo g_{10} (f_{o}) + 51$ , $- 24 lo g_{10} (f_{o}) + 54$ , floored at −4 dB.

anchors=True applies Formula (D.5) for 4 to 10 anchors or battens per m² ( $0.66Δ R_{w, r e f} - 1.2$ and its two companions), and glued_area applies Formula (D.6), $Δ R - 0.05 % S_{o} + 2.0$ , for a glued area other than the 40 % reference. Both corrections are applied after the floor of the reference formula, in the order the annex states them.

The annex places the $\geq - 4$ dB (or $\geq - 3$ dB) floor inside Formulae (D.3) and (D.4) and says nothing about re-applying it after (D.5) and (D.6), so this function does not: a fully glued system on anchors can return about −6.8 dB, below the reference floor. That is the annex read literally, and the reason the two corrections are exposed as flags rather than folded into the fit.

Parameters

Name	Description
`resonance_frequency`	Resonance frequency `fo`, in Hz (`lining_resonance_frequency`).
`system`	`"mineral_wool"`, `"foam"` or `"studs"`.
`anchors`	Apply the Formula (D.5) anchor/batten correction.
`glued_area`	Glued area `%So` as a percentage of the element area, greater than 0 and at most 100, or `None` to keep the 40 % reference. Formula (D.6) divides by the glued area, so a wholly unglued system is not a case of it: use `anchors` for a mechanically fixed lining. It corrects the glued exterior systems only, so it is rejected for `system="studs"`.

Returns: A LiningImprovementResult.

Raises

Exception	When
ValueError	If an input is not positive and finite, `system` is unknown, or `glued_area` is out of range or combined with `system="studs"`.

lining_improvement_in_situ

lining_improvement_in_situ(
    laboratory_improvement: float,
    resonance_frequency: float,
    base_rating_in_situ: float,
) -> float

Transfer a weighted lining improvement to the field (Formula D.8).

Even when the per-band improvement is invariant, its single-number rating still depends on the basic element it sits on, so ISO 12354-1:2017 Formula (D.8) shifts the laboratory rating by $a X$ with

$a = 1.35 lo g_{10} (f_{o}) - 3.5$ , capped at 0, and $X = R_{w, s i t u} - 53$ , clamped to [−10, +7].

The same formula applies to ΔRw, ΔRA and ΔRA,tr.

Parameters

Name	Description
`laboratory_improvement`	Laboratory rating `ΔRlab` measured to ISO 10140-1:2016 Annex G for the heavy basic element, in dB.
`resonance_frequency`	Resonance frequency `fo` of the system, in Hz.
`base_rating_in_situ`	Weighted sound reduction index `Rw,situ` of the basic element in the field situation, in dB.

Returns: The field rating ΔRsitu, in dB.

Raises

Exception	When
ValueError	If an input is not finite, or `fo` is not positive.

lining_resonance_frequency

lining_resonance_frequency(
    base_mass_per_area: float,
    lining_mass_per_area: float,
    *,
    dynamic_stiffness: float | None = None,
    cavity_depth: float | None = None,
) -> float

Resonance fo of a lining on a basic element (Formulae D.1/D.2).

Exactly one of the two branches applies:

dynamic_stiffness (Formula D.1), for an insulation layer fixed directly to the basic construction, without studs or battens: $f_{o} = s^{'} (1/ m_{1}^{'} + 1/ m_{2}^{'}) / (2 π)$ .
cavity_depth (Formula D.2), for a layer built on metal or wooden studs not connected to the basic element, with the cavity filled by a porous layer of airflow resistivity $r \geq 5$ kPa·s/m²: $f_{o} = (0.111/ d) (1/ m_{1}^{'} + 1/ m_{2}^{'}) / (2 π)$ , i.e. the near-isothermal stiffness of the filled cavity replaces s'.

Parameters

Name	Description
`base_mass_per_area`	Mass per unit area `m'1` of the basic structural element, in kg/m².
`lining_mass_per_area`	Mass per unit area `m'2` of the additional layer, in kg/m².
`dynamic_stiffness`	Dynamic stiffness per unit area `s'` of the insulation layer (EN 29052-1), in N/m³.
`cavity_depth`	Depth `d` of the stud cavity, in m.

Returns: The resonance frequency fo, in Hz.

Raises

Exception	When
ValueError	If an input is not positive and finite, or if the two branches are both given or both omitted.

LiningImprovementResult

LiningImprovementResult(
    resonance_frequency: float,
    system: LiningSystem,
    delta_rw: float,
    delta_ra: float,
    delta_ratr: float,
    anchors: bool = False,
    glued_area: float | None = None,
)

Single-number ratings of an additional layer (ISO 12354-1 Annex D).

Attributes

Name	Description
`resonance_frequency`	Resonance frequency `fo` of the system, in Hz.
`system`	`"mineral_wool"`, `"foam"` (exterior systems glued to the wall, Formulae D.3/D.4) or `"studs"` (Formula D.7).
`delta_rw`	Improvement of the weighted sound reduction index `ΔRw`, in dB.
`delta_ra`	Improvement of the A-weighted rating `ΔRA`, in dB.
`delta_ratr`	Improvement of the traffic-weighted rating `ΔRA,tr`, in dB.
`anchors`	`True` when the Formula (D.5) anchor correction was applied.
`glued_area`	Glued area as a percentage of the element area, or `None` when the 40 % reference was kept.

LiningImprovementResult.plot()

LiningImprovementResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the Annex D ratings against the resonance frequency.

Draws the three Annex D curves over the tabulated range with this system’s own resonance marked, the analogue of Figures D.2 and D.3. Requires matplotlib (pip install phonometry[plot]); returns the Axes.

LiningImprovementResult.ratings

property

(ΔRw, ΔRA, ΔRA,tr) as a tuple, in dB.

weighted_lining_improvement

weighted_lining_improvement(
    resonance_frequency: float,
    base_rating: float,
) -> float

Weighted improvement ΔRw of an interior lining (Table D.1).

ISO 12354-1:2017 Table D.1 reads ΔRw off the lining’s resonance frequency, rounded to the centre of the one-third-octave band in which it falls. Below 200 Hz the improvement also depends on the bare element: $Δ R_{w} = 74.4 - 20 lo g_{10} (f_{o}) - R_{w} /2$ , never below 0 dB (NOTE 1). At and above 200 Hz the lining degrades the insulation, by 1 dB at 200 Hz down to 10 dB from 630 Hz to 1 600 Hz, recovering to 5 dB from 1 600 Hz to 5 000 Hz.

Table D.1 is stated for basic elements with $20 \leq R_{w} \leq 60$ dB. Its last two rows both cover 1 600 Hz with different values; this function takes the more conservative −10 dB there (see docs/ERRATA.md).

Parameters

Name	Description
`resonance_frequency`	Resonance frequency `fo` of the lining, in Hz (`lining_resonance_frequency`); must fall in the 30 Hz to 5 000 Hz range Table D.1 covers.
`base_rating`	Weighted sound reduction index `Rw` of the bare wall or floor, in dB.

Returns: The weighted improvement ΔRw, in dB.

Raises

Exception	When
ValueError	If `fo` is outside the tabulated range or an input is not finite.

Created and maintained by José Manuel Requena Plens ORCID All projects