# Calculating U-Values of Reflective Foils in a Pitched Roof

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This article follows on from a previous contribution to the NES Insights blog: ‘Calculating U-Values with Reflective Foil Insulation’, which provided an overview of how thermal transmittance through an external wall should be calculated using the BRE U-Value Calculator software, when the wall was insulated using Thermal Economics Alreflex 2L2 FR foil insulation. In this article, the thermal transmittance will be considered for a pitched roof, insulated along the slope with Thermal Economics Raftertherm insulation board. The Raftertherm board is a graphite-enhanced, expanded polystyrene board that has been laminated with a 3mm Alreflex bubble and foil membrane; more information on the Raftertherm board can be found on the Thermal Economics website.

For the purposes of this example, it will be assumed that the pitched roof is constructed and insulated using the LABC Registered Detail EWW37, which includes both the Raftertherm Board Type S and Board Type A. The important difference between the boards from the OCDEA’s perspective is that the Board Type A has the Alreflex layer laminated to one side, whereas the Board Type S does not. This will have to be shown in the U-Value calculation, because the different surface emissivities will have an effect on the thermal resistance of the adjacent air cavity.

### LABC Registered Detail EWW37

An LABC Registered Detail is a product, system or house type that has been certified by the LABC as having demonstrated compliance with building regulations and standards across England, Wales and Scotland; as such a Registered Detail will automatically be accepted as satisfactory evidence by all local building authorities in the UK. Thermal Economics have registered the Raftertherm non-ventilated roof insulation system with the LABC; this means that the sloping ceiling will have a U-Value of 0∙16Wm^{-2}K^{-1} without further calculation, provided that the pitched roof is constructed as per the Thermal Economics installation guide. This article will calculate the U-Value for LABC Registered Detail EWW37 to demonstrate the U-Value calculation for reflective foils in a pitched roof.

The construction of LABC Registered Detail EWW37 is shown in Figure 1. It consists of the Tyvek Enercor roofing underlay installed over rafters (min. depth 150mm); which are insulated between the rafters with 115mm Raftertherm Board Type S, and underneath with 50mm Raftertherm Board Type A on Raftertherm fixing brackets; with plasterboard finish on battens. The Raftertherm Board Type A is installed with the foil facing towards the inside; all joints and penetrations are taped and sealed with Alu Tape to preserve the vapour control barrier.

Fig. 1

Before the U-Value can be calculated, it is necessary to obtain the following manufacturer’s data:

· Thermal Conductivity (λ) of Raftertherm Board (0∙030Wm^{-1}K^{-1});

· Thermal Resistance (R) of Alreflex foil surface (0∙100m^{2}KW^{-1});

· Emissivity (ε) of Alreflex foil surface (0∙03);

· Emissivity (ε) of Tyvek Enercor (0∙15).

The rest of the material properties can either be deduced using the four values above, or BR 443 default values used.

### Understanding the U-Value Calculation

The pitched roof construction can be modelled in six layers as shown in Figure 2, using the BRE U-Value Calculator software. These will include four ‘solid’ layers, and two unventilated, ‘still air’ layers with an assumed temperature of 10°C. All except two of the layers are inhomogeneous, and include the bridging effect of the timber rafters and battens with thermal conductivity of 0∙13Wm^{-1}K^{-1} at 8∙33% fraction.

Fig. 2

Although shown in Figure 2, the fixings correction for the Raftertherm fixing brackets is ignored in the U-Value calculation because it is less than 3% of the uncorrected U-Value; further information on this can be found in Section 4.9 of BR 443. This rule can be enabled within the BRE U-Value calculator by ticking ‘Omit Delta-U when < 3%’ from the ‘Options’ menu.

### R-Values for Still Air Layers

The R-Value of the first still air layer (TE Alreflex cavity/ battens) can be deduced using the formula in BS EN ISO 6946, with surface emissivity of 0∙03 for the Alreflex foil to give a value of 0∙48m^{2}KW^{-1}. However, it is convenient to include the material R-Value of the Alreflex foil in this same layer, so a specified R-Value of 0∙58m^{2}KW^{-1} (0∙48 + 0∙10 = 0∙58) is used in the calculation.

There is a stated value for a cavity ≥ 25mm in the BBA Agrément Certificate 08/4548 (0∙37m^{2}KW^{-1}); which can be used for the R-Value of the second still air layer (Tyvek Enercor cavity/ rafters). Alternatively, the R-Value can be calculated using the emissivity of the Tyvek Enercor.

### Non-Standard External Surface Resistance

The cavity between the roofing underlay and the tiles is considered to be a well-ventilated cavity with a temperature of 0°C. This is the same temperature as the assumed outside air temperature, hence there is no heat transfer through the cavity or the tiles and anything above the roofing underlay can be omitted from the calculation. However, the low-emissivity of the Tyvek Enercor roofing underlay will have a significant effect on the U-Value and should be included by using a non-standard surface resistance for the Rse-value.

The equations for finding the surface resistance are given in Annex A of BS EN ISO 6946, and the surface resistance is a function of the convective and the radiative coefficients. The two variables required when calculating the radiative coefficient are the surface emissivity, and the mean thermodynamic temperature. For the external surface resistance, the mean thermodynamic temperature is 273∙15K. The R_{se}-value is calculated using the same convective coefficient as for the R_{si}-value because the external surface of the Tyvek Enercor is sheltered by the roof tiles.

The correct R_{se}-value for a sheltered surface with an emissivity of 0∙15 is 0∙18m^{2}KW^{-1}. This is input into the BRE U-Value Calculator software by selecting ‘Surface Resistance’ from the ‘Data’ menu, and unticking the box that says “Use standard surface resistance values”. The R_{se}-value can then be manually typed over, and input as 0∙18m^{2}KW^{-1}.

### About the Author

John Hefford is the Senior Technical Consultant at Thermal Economics, and is a qualified OCDEA accredited by National Energy Services. In addition to carrying out thermal calculations, Mr. Hefford also leads the Fair Regulation working group at TIMSA. Thermal Economics provide free-of-charge U-Value calculations using our products. OCDEA’s and other persons calculating U-Values can obtain help with modelling Thermal Economics products by telephoning the Thermal Economics Technical Office on 01582 544255, or by e-mailing info@thermal-economics.co.uk.

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