This article is written for Passive House designers who are calculating thermal bridges themselves using thermal bridge modelling software like Flixo or THERM. We explain the puzzling question of why U-values of mixed materials can be different between PHPP and Flixo (and also why the PHPP U-values worksheet can produce an error message).

It’s not always necessary to calculate thermal bridges yourself; a lot of standard details have been modelled already in the *High-Performance Construction Details Handbook*. Or designers may be re-using a detail that has already been used in their practice. In such instances, the psi value is simply entered into the Areas sheet in PHPP (or ECCHO from NZGBC).

Simple cases aside, some thermal bridges will need to be calculated and this is when Passive House design gets more technical and interesting. There are several different standards and depending on which method of calculation you use, results may differ for the same mixed material. In the example below, ISO 6946’s result is U0.261 W/(m2K) and a hand calculation produces a result of U0.265 W/(m2K). This small difference can nonetheless impact psi calculations.

**Different methods of calculating U-values**

PHPP follows ISO 6946 and calculates upper and lower limits of the R-value. These are calculated using two different methods: the upper by way of the parallel path and the lower by way of the isothermal planes methods. The latter calculation produces a lower R-value; it’s better than that parallel path method at taking into account more of the actual heat loss from the stud to the insulation but it errs on the other side and *over-*estimates the heat loss. This is why ISO 6946 automatically averages the two values.

You can see this formula in the U-values sheet in PHPP if you unhide column Y. This is why an error can be generated in this worksheet. The average is deemed to be unreliable when the difference between the average, and the two R-values it is averaging, goes over 10%. The error won’t prevent you from saving or submitting the file but it’s not acceptable and will result in a ‘please explain’ from the certifiers.

A designer won’t encounter this error when working with a sensible combination of materials, like a standard wall assembly involving timber studs and insulation infill. But replace the timber stud with a steel frame and the difference in conductivity between the framing and the infill is great enough to start triggering this error message. We’ve seen it arise when a design has the odd steel column for some structural purpose and also in the case of a building that was not high-performance but was targeting Homestar certification. That required an energy model, which graphically illustrated the thermal cost of steel framing.

Anyway, should you encounter such a roadblock, what do you do? (Short of amending your design to use less conductive materials, which from a big picture point of view is clearly the best option.) Do not homogenise the wall in the way we explained for a timber-framed wall. Instead, model the framing element in your thermal bridge modelling software and calculate its psi value. Enter a U-value in PHPP’s U-values worksheet as if the conductive framing material does not exist in this wall. FInally, enter the total length of the framing in the PHPP *Areas* sheet along with the corresponding psi value calculated in your thermal bridge modelling software.

It’s also worth noting that NZBC R-value calculations according to NZS 4214 produce only the R-value lower limit (see a previous article we’ve written on this topic here). This standard is not suitable in any case for generating values that can be used in an energy simulation tool, as the standard itself explicitly notes.

As an aside, NZS 4214 also uses different surface resistances to ISO 6946. Sustainable Engineering’s team has worked on projects where this has made quite a difference to outcomes. For example, in calculating the U-value of a door panel, the conservative option (NZS 4214) saw the product fall short of the manufacturer’s target value. Calculating the value using ISO6946 saw the door panel exceed the targeted performance. A small difference in numbers made a big commercial impact.

**Be consistent**

Perceptive designers will have noticed that when they create a construction that includes a mixed material element in Flixo or THERM, the U-value generated in that software is not the same as the PHPP U-value. This is because the hand calculation done to calculate the mixed material thermal conductivity doesn’t use both methods from ISO 6946.

Different programs use different methods to calculate their results. You can’t subtract a U-value calculated by PHPP from the heat flux in a THERM model and expect a correct result. Consistency rules. Psi values are very small numbers. If the inputs are even slightly out, the psi value could be out by a lot.

The important rule of thumb is **use the same software for sourcing all the values needed to calculate your thermal bridge.**

Take a corner: there’s extra timber framing that means additional heat loss and it needs to be thermally modelled. If using THERM to do this, do *not* take the U-value for the *wall* from PHPP. Calculate the U-value for the wall in THERM too because you’ll need this number for a hand calculation to produce the psi value for the whole assembly. Flixo saves you this step because it automatically runs the calculation to produce the psi value. But THERM is free, so we understand why some people use it.

If you’re excited about thermal bridge modelling and want to keep developing your Passive House design skills and confidence, Sustainable Engineering has self-paced online courses available. You can enrol at any time.

**Appendix: Example calculation of mixed materials**

The example we’ll use is a timber framed wall with insulation infill: 140mm studs at 600mm centres with 10mm of gypsum wallboard. The timber in the wall is more conductive than the insulation. By understanding the conductivity of each of the different materials in the wall, we can calculate a psi value for the whole wall. This is what’s meant by homogenising mixed materials.

Let’s look in turn at how the different software programs calculate their values. That way we can understand why they differ.

**ISO 6946: the PHPP method**

PHPP calculates U-values following the methodology in ISO 6946. This is what the standard says about the methodology for calculating the total thermal resistance of a component:

*The total thermal resistance, RT, of a component consisting of thermally homogeneous and thermally inhomogeneous layers parallel to the surface is calculated as the arithmetic mean of the upper and lower limits of the resistance.*

Let’s assume building paper and a ventilated cavity externally, so that the external surface resistance is the same as the internal surface resistance: 0.13m2/K.W.

The insulation layer is made up of both insulation and timber, which has far lower insulative value. It’s necessary to calculate the timber percentage, which in this case is as follows:

**0.045/0.6 x100 = 7.5% timber content**

Here it is modelled first in PHPP and then Flixo:

*To calculate the R-value according to the ISO6946 R-value **upper** limit:*

Here’s the same thing done in Flixo (which shows U-values instead of R-values):

To calculate the Upper U-value using the isothermal planes method you first need to manually calculate the mixed materials thermal conductivity for each layer. For this single layer with 7.5% timber and 92.5% insulation:

Timber: 7.5% x lambda value of timber = 0.075 x 0.13 W/(mK) = 0.00975

Insulation: 92.5% x lambda value of insulation = 0.925 x 0.033 W/(mK) = 0.030530.033 x 0.925 =

Mixed material thermal conductivity = 0.00975+ 0.03053 = 0.0403 W/(mK)

U_Lower= 0.075 x 0.726 + 0.925 x 0.220 = 0.258

(U_Lower + U_Upper) / 2 = **0.261 W/(m2K), which is the same result as PHPP. **

The error that designers could make in THERM is to hand calculate the thermal conductivity of the mixed material (0.0403 W/(mK) in this example), use this in the thermal bridge calculation and then subtract out the U-value from PHPP. Because the psi value is often the small difference between large numbers, the difference between U_Lower and U_Upper can easily make the psi value result very wrong.