Total R-value Calculations (ISO 6946:2017)

Better Building performs thermal resistance calculations for walls, roofs, and floors in accordance with international standards. These calculations are based on:

ISO 6946:2017: Building components and building elements — Thermal resistance and thermal transmittance — Calculation methods

ISO 6946:2017 provides comprehensive methods for calculating the thermal transmittance and thermal resistance of building components, excluding doors, windows, and glazed units. The standard offers both detailed and simplified calculation methods for components consisting of thermally homogeneous and inhomogeneous layers.

Better Building Procedure

To achieve a calculated outcome, Better Building follows these steps using the ISO 6946 methodology. This process is iterative when dealing with components containing inhomogeneous layers:

1

Initial Assessment

• Determine if the component consists of thermally homogeneous layers only, or includes inhomogeneous layers

• Identify all layers, including air layers and surface resistances

• For homogeneous components, use the simplified method (Section 6.7.1)

• For inhomogeneous components, use the upper/lower limits method (Section 6.7.2)

2

Thermal Resistance Calculation for Homogeneous Layers

For each homogeneous layer, calculate the thermal resistance:

R = d / λ

Where:

• R is the thermal resistance (m²·K/W)

• d is the thickness of the layer (m)

• λ is the design thermal conductivity (W/(m·K))

Design thermal conductivity values must be obtained in accordance with ISO 10456, accounting for the specific temperature and moisture conditions.

3

Surface Resistances

Apply surface resistances according to Section 6.8 and Annex C:

Standard Values (Table 7):

• Internal surface resistance (Rsi): 0.10 to 0.17 m²·K/W (depending on heat flow direction)

• External surface resistance (Rse): 0.04 m²·K/W

For specific boundary conditions, low emissivity surfaces, or non-planar surfaces, use the detailed procedures in Annex C.

4

Airspace R-Value Calculation

For unventilated air layers (Section 6.9.2 and Annex D):

Ra = 1 / (ha + hr)

Where:

• ha is the conduction/convection coefficient (W/(m²·K))

• hr is the radiative coefficient (W/(m²·K))

Convection Coefficient (ha): The larger of 0.025/d or values from Tables D.1 or D.2 based on:

• Heat flow direction (upward, horizontal, downward)

• Temperature difference across the airspace (ΔT)

• Thickness of airspace (d)

For ΔT ≤ 5 K (Table D.1):

• Horizontal: ha = 1.25 W/(m²·K)

• Upwards: ha = 1.95 W/(m²·K)

• Downwards: ha = 0.12 × d^-0.44 W/(m²·K)

For ΔT > 5 K (Table D.2):

• Horizontal: ha = 0.73 × (ΔT)^1/3 W/(m²·K)

• Upwards: ha = 1.14 × (ΔT)^1/3 W/(m²·K)

• Downwards: ha = 0.09 × (ΔT)^0.187 × d^-0.44 W/(m²·K)

Radiative Coefficient (hr):

hr = E · hr0

Where:

• E is the intersurface emittance

• hr0 = 4σTmn³ (radiative coefficient for black-body surface)

• σ = 5.67 × 10^-8 W/(m²·K⁴) (Stefan-Boltzmann constant)

• Tmn is the mean thermodynamic temperature (K)

E = 1 / (1/ε₁ + 1/ε₂ - 1)

Where ε₁ and ε₂ are the hemispherical emissivities of the bounding surfaces (typically 0.9 for building materials).

Ventilated Air Layers:

• Slightly ventilated (500-1500 mm² openings per metre): Linear interpolation between unventilated and well-ventilated values (Section 6.9.3)

• Well-ventilated (≥1500 mm² openings per metre): Disregard airspace thermal resistance and all layers between airspace and external environment (Section 6.9.4)

5

Total Thermal Resistance - Homogeneous Components

For components with only thermally homogeneous layers (Section 6.7.1.2):

Rtot = Rsi + R₁ + R₂ + ... + Rn + Rse

Where:

• Rtot is the total thermal resistance (m²·K/W)

• Rsi is the internal surface resistance (m²·K/W)

• R₁, R₂, ..., Rn are the thermal resistances of each layer (m²·K/W)

• Rse is the external surface resistance (m²·K/W)

6

Total Thermal Resistance - Inhomogeneous Components

For components containing inhomogeneous layers (Section 6.7.2), use the upper and lower limits method:

Step 1: Divide the component Split the component into:

• Sections (perpendicular to the surfaces)

• Layers (parallel to the surfaces)

Each section should be thermally homogeneous.

Step 2: Calculate upper limit (Rtot,upper)

Assuming one-dimensional heat flow perpendicular to surfaces:

1/Rtot,upper = fa/Rtot,a + fb/Rtot,b + ... + fq/Rtot,q

Where:

• fa, fb, ..., fq are the fractional areas of each section

• Rtot,a, Rtot,b, ..., Rtot,q are the total thermal resistances of each section

Step 3: Calculate lower limit (Rtot,lower)

Assuming all planes parallel to surfaces are isothermal. For each inhomogeneous layer:

1/Rj = fa/Raj + fb/Rbj + ... + fq/Rqj

Then use Formula (4) to sum all layers including Rsi and Rse.

Step 4: Calculate total thermal resistance

Rtot = (Rtot,upper + Rtot,lower) / 2

Limitation: The method is valid only when Rtot,upper / Rtot,lower ≤ 1.5. If this ratio exceeds 1.5, use the detailed calculation method (ISO 10211).

7

Thermal Transmittance Calculation

Calculate the thermal transmittance (Section 6.5):

U = 1 / Rtot

Where:

• U is the thermal transmittance (W/(m²·K))

• Rtot is the total thermal resistance (m²·K/W)

8

Corrections to Thermal Transmittance

Apply corrections according to Annex F where relevant:

Uc = U + ΔU

ΔU = ΔUg + ΔUf + ΔUr

Where:

• ΔUg = correction for air voids in insulation (Annex F.2)

• ΔUf = correction for mechanical fasteners (Annex F.3)

• ΔUr = correction for precipitation on inverted roofs (Annex F.4)

Correction for Air Voids (ΔUg):

Based on installation quality (Table F.1):

• Level 0: ΔU'' = 0.00 W/(m²·K) (no significant air voids)

• Level 1: ΔU'' = 0.01 W/(m²·K) (air gaps bridging insulation, no circulation)

• Level 2: ΔU'' = 0.04 W/(m²·K) (gaps with free air circulation)

ΔUg = ΔU'' × (R₁/Rtot)²

Correction for Mechanical Fasteners (ΔUf):

For fasteners penetrating insulation (Annex F.3.2):

ΔUf = α × (λf × Af × nf / d₁) × (R₁/Rtot)²

Where:

• α = 0.8 for fully penetrating fasteners; α = 0.8 × (d₁/d₀) for recessed fasteners

• λf is the thermal conductivity of fastener (W/(m·K))

• Af is the cross-sectional area of one fastener (m²)

• nf is the number of fasteners per m²

• d₁ is the length of fastener in insulation (m)

• d₀ is the thickness of insulation layer (m)

Correction for Inverted Roofs (ΔUr):

For insulation above waterproofing membrane (Annex F.4):

ΔUr = p × f × x × (R₁/Rtot)²

Where:

• p is average precipitation rate during heating season (mm/day)

• f × x is the drainage factor (typically 0.04 for single layer with butt joints)

• R₁ is the thermal resistance of insulation above membrane (m²·K/W)

Apply corrections only if total ΔU > 3% of U

Key Differences from AS/NZS Standards

1. Temperature Corrections: ISO 6946 does not include the iterative temperature correction procedure found in AS/NZS 4859.2. Temperature dependencies are handled through appropriate selection of design thermal conductivity values per ISO 10456.

2. Thermal Bridging: ISO 6946 uses correction factors (Annex F) rather than the NZS 4214 combined layer method. For significant thermal bridging, ISO 10211 detailed calculations are required.

3. Airspace Calculations: ISO 6946 provides more detailed procedures in Annex D, including different coefficients for various temperature differences and heat flow directions.

4. Accuracy Criteria: ISO 6946 includes error estimation for the simplified method (Rtot,upper / Rtot,lower ratio) and specifies when detailed methods are necessary.

5. Surface Resistances: ISO 6946 provides standard values with detailed calculation procedures in Annex C for specific conditions.

By following these steps, Better Building ensures accurate and internationally-compliant thermal resistance calculations for building components using the ISO 6946:2017 methodology.