Equations for Building Performance

Equations for Building Physics R-value calculation

1

R=d/λ R = Thermal resistance (m2K/W) d = Thickness of material (m) λ = Thermal conductivity of material (W/mK)

U-value calculation

2

U = 1/(Rsi + R1 + R2 +....+ Rse) U Rsi Rse R1 R2

= U-value of building element (W/m2K) = Internal surface resistance (m2K/W) = External surface resistance (m2K/W) = Thermal resistance of building component 1 (m2K/W) = Thermal resistance of building component 2 etc... (m2K/W)

Heat loss through a building element

3

Heat loss (Q) = U x A x (Te-Ti) U A Te Ti

= U-value of building element (W/m2K) = Area of building element (m2) = External temperature (K) = Internal temperature (K)

Heat loss through a thermal bridge

4

Heat loss = Ψ x L x (Te – Ti) Ψ L Te Ti

= Psi-value (thermal bridge) (W/mK) = Length of thermal bridge (m) = External temperature (K) = Internal temperature (K)

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Equations for Building Physics U-value of a window from its components

5

Uwindow = (Ag x Ug + Af x Uf + Lg x ψg ) / (Ag + Af) Ag Ug Af Uf Lg Ψg

= Area of window glazing (m2) = U-value of window glazing (W/m2K) = Area of window frame (m2) = U-value of window frame (W/m2K) = Length of thermal bridge between glazing and frame (m) = Psi-value (thermal bridge) between glazing and frame (W/mK)

Ventilation heat loss

6

Ventilation heat loss = Cv x N x V x (Te-Ti) Cv N V Ti

= Specific heat capacity of air – usually given as 1210 J/m3K = Number of air changes per second (ach/s) = Volume of the building that is heated (m3) = Internal temperature and Te = external temperature

Heat gain via solar transmittance

7

Qs = A x g x Irr A = Area of glazing (m2) g = Solar transmittance of glazing Irr = Solar irradiation (W/m2)

Sd value for vapour permeability

8

Sd = µ x d Sd = Equivalent air layer thickness (m) μ = Mu-value or water vapour resistance factor d = Thickness of material (membrane)

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