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Physics, Maths & Compliance

A detailed breakdown of the calculations driving the Buildup engine, aligned with NZBC standards and BRANZ research.

1. Thermal Performance & NZBC H1

Calculations for total thermal resistance follow NZS 4214:2006. This standard is cited by NZBC Clause H1 as the primary method for calculating the R-value of building elements containing thermal bridging (e.g., timber or steel framing).

The Averaging Method

For any layer containing framing, the tool calculates the resistance using two distinct paths and then takes the arithmetic mean, as required by the standard:

R_{total} = \frac{R_{isothermal} + R_{parallel}}{2}

Where:

Isothermal Plane Method ($R_{iso}$): Assumes heat flows laterally to equalize temperature at the interface of each layer. $$R_{iso} = R_{si} + \sum \left( \frac{1}{\frac{f}{R_f} + \frac{1-f}{R_i}} \right) + R_{se}$$
Parallel Path Method ($R_{par}$): Assumes heat flows in straight lines from the inside to the outside, either through the frame or the insulation. $$R_{par} = \frac{1}{\frac{f}{R_{path, f}} + \frac{1-f}{R_{path, i}}}$$

NZBC H1 Requirement: When a building element contains a ventilated cavity (e.g., a drained cavity behind cladding), the thermal resistance of all layers located to the exterior of that cavity is halved ($0.5 \times R$) to account for the cooling effect of the circulating air.

2. Hygrothermal Analysis & NZBC E3

To demonstrate compliance with NZBC Clause E3 (Internal Moisture), the tool employs the Glaser Method (ISO 13788). This steady-state calculation checks for interstitial condensation by comparing actual vapor pressure to saturation levels.

Saturated Vapor Pressure ($P_{sat}$)

The maximum amount of water vapor air can hold is temperature-dependent. The engine uses the Magnus-Tetens approximation:

P_{sat}(T) = 610.78 \times \exp\left( \frac{17.27 \times T}{T + 237.3} \right)

Vapor Diffusion and $S_d$ Values

The resistance to vapor flow is defined by the Equivalent Air Layer Thickness ($S_d$), calculated from the material's vapor resistivity ($\mu$) and its thickness ($d$ in meters):

S_d = \mu \times d$$ $$P_{v, interface} = P_{in} - (P_{in} - P_{out}) \times \frac{\sum S_{d, internal}}{\sum S_{d, total}}

3. The BRANZ SR344 Context

Research Grounding: The logic for flagging "Risk" vs "Managed Risk" in this tool is informed by BRANZ Study Report SR344 (2015): Hygrothermal Performance of Common New Zealand Wall Assemblies.

SR344 highlights that while the Glaser Method is a simplified tool, it is highly effective for identifying "red flag" assemblies in New Zealand's unique climates. Key findings from SR344 integrated into this tool include:

The 60% Depth Heuristic: Research shows that condensation occurring in the outer layers of a wall (closer to a ventilated cavity) is significantly less likely to cause structural damage than condensation occurring behind the internal lining.
Buildup Logic: If the intersection point ($c_x$) is beyond 60% of the assembly's depth, it is flagged as Managed, assuming a functional drained cavity is present.
Climate Sensitivity: SR344 demonstrates that New Zealand's high outdoor humidity means that "breathable" outer layers are often more critical than high-performance vapor barriers in temperate zones (like Auckland).
Vented Cavity Performance: The study validates the NZBC assumption that a 20mm cavity provides enough air movement to mitigate minor amounts of interstitial moisture, provided the dew point does not occur deep within the structural framing.