Our Roof Systems app undertakes thermal resistance calculations inline with J 1.5 - Total System R-value for walls, roofs and floors based on:

- AS/NZ 4859.2: Thermal insulation materials for buildings
- NZS 4214:2006: 2006: Methods of Determining the Total Thermal Resistance of Parts of Buildings

As there are two references within NCC 2019, a primary (AS/NZS 4859.2:2018) and a secondary (NZS 4214:2006: 2006:2006) reference, Speckel must undertake both as appropriate.

The primary reference document outlines a calculation requirement not undertaken in any market, as it is new and an amalgamation of other Standards. Requirements for roof thermal performance are set forth in J1.2 Thermal construction — general (roof and floors).

Where a roof system is modelled, and it has no structural thermal bridging, Speckel uses AS/NZS 4859.2:2018 only. For Roof Systems with structural thermal bridging to consider, Speckel calculates both AS/NZS 4859.2:2018 and NZS 4214:2006: 2006:2006 to meet the Performance Requirements for roofs, floors and walls, as both the primary and secondary reference are required for Deemed-to-Satisfy and Performance Solutions.

**Speckel Procedure**

To achieve a calculated outcome, Speckel uses the following steps. Please note, this is not a linear calculation and is not defined within a single equation:

- Temperature corrections are performed to any airspaces and insulation layers in the system.

o Equidistant temperature values are given to each layer in the system.

o Insulation declared R-Value is corrected for AS/NZS temperatures.

o Airspace R-Value is calculated, as well as any derating performed.

- Temperature is recalculated now with corrections applied.

o Total System R-Value is calculated.

o NZS 4214:2006: 2006:2006 thermal bridging calculation is performed as necessary on any insulation layers with framing.

o Temperature values are calculated by how much the layer contributes to the Total System R-Value.

- The above steps are repeated iteratively until layer R-Values stabilise to three significant figures.
- Final Total System R-Value results are calculated.

o Full NZS 4214:2006: 2006:2006 thermal bridging calculation is performed as necessary.

**Equidistant Temperature Values**

Two calculations must be performed before the Total System R-Value: Insulation value correction and cavity R-Value calculation (with possible derating).

To calculate the insulation value correction, the mean temperature across that insulation must be known (this is also needed for the air cavity calculation). This mean temperature is calculated by the percentage the layer contributes to the Total System R-Value. The Total System R-Value cannot be undertaken without these two initial calculations, so an impasse is reached.

An iterative process is then used to level out the final Total System R-Value result, so we can take need to make some assumptions with the initial mean temperatures to kick start the calculations. The mean temperatures across each layer are taken as an equal portion of the total temperature change across the system.

**Temperature Values Recalculated**

As per AS/NZS 4859.2:2018 5.2(1) we need FT; the calculated conversion coefficient, to calculate the insulation R-Value adjustment. This value is calculated using the mean temperature we inferred; the declared mean at which the insulation was tested (23⁰C), and a conversion coefficient (fT).

This conversion coefficient is determined using a series of tables which are chosen using insulation material type (i.e. Mineral Wool, Expanded Polystyrene, etc.). And then each of those materials has further requirements (such as density or thickness) which allow us to determine the coefficient, with linear interpolation.

**Airspace R-Value**

As per AS/NZS 4859.2:2018, there are three possible air cavity types: Unventilated, Slightly Ventilated and Well Ventilated. The type is determined by the area of ventilation per metre of length of the wall.

- For Well Ventilated airspace (6.3.2), the air cavity R-Value is 0, and a derate of 100% is given to all layers between the cavity and external air.
- For Unventilated airspaces, the R-Value is calculated using two calculated coefficients; ha and hr. The conduction/convection coefficient (ha) is determined by the mean temperature change and thickness of layer using Table 12 and 13. The radiative coefficient (hr) is calculated using the emissivity of bounding layers and the temperature change across the layer; as per 6.2(2). The emissivity of bounding layers is given an uplift of 1.36 if they are lower than e0.15 as per 6.2(4). No derating is applied with this airspace type.
- The Slightly Ventilated airspace is a mixture between Unventilated and Well Ventilated. The calculation for this type (6.3.1) only results in the Total System R-Value; however, since individual layer R-Values are important for the temperature correction calculations, we cannot use this result. The calculation is simply the linear interpolation of two systems; one with Unventilated and one with Well Ventilated airspace. Using this logic, we then simply do the same to instead calculate the individual airspace R-Value (between 0 and calculated Unventilated R-Value) and the derating amount (between 0% and 100%).

**NZS 4214:2006: 2006 Thermal bridging**

Now that we have performed our corrections, we calculate the actual temperature values as per 10.3. The only usable values are the mean temperature and temperature change across each layer. These values are calculated by the percentage the layer contributes to the Total System R-Value. However, due to the inclusion of clause 10.2, which cites NZS 4214:2006: 2006 for calculation of thermal bridging (which impacts Total System R-Value), we must first perform a simplified thermal bridge calculation.

As per NZS 4214:2006: 2006, we are required to combine any adjacent air cavity and insulation layers into one unified thermally-bridged layer, however, since we need to know individual layer R-Values, we must simplify this. The conjoining of airspace and insulation is omitted for the sake of individual layer calculations, but it will be applied later after results are stabilised through iteration. Only the insulation layer is subject to NZS 4214:2006: 2006 for thermal bridging in this initial processing. The Total System R-Value can now be calculated by simply adding all layer R-Values together (including any thermally-bridged insulation layers).

**R-Values Stabilisation**

The temperature values for the next iteration of corrections can then be calculated. The above process is performed until values have stabilised to three significant values (as per 10.1).

**Full NZS 4214:2006: 2006 Thermal Bridging Calculation**

After determining individual layer R-Values, the Total System R-Value can be calculated. As per NZS 4214:2006: 2006, the proper (adjacent airspace and insulation layers are combined) thermal bridge calculation is performed as necessary.