Reference dimensions, linear and point thermal transmittance, and calculation procedures in Rhino.
On this page
Thermal bridge definitions
One-dimensional heat transfer represents the undisturbed, or clear-field, portion of a layered wall or roof. Junctions such as balconies, corners and structural penetrations introduce geometric or material variations that require two- or three-dimensional analysis.
At a junction, geometry and material conductivity affect the direction and distribution of heat flux. A calculation based only on clear-field U-values does not account for these local effects.
As illustrated in the figure above, one can view the influence of the thermal bridge as an additional heat loss (the yellow area under the curve) that is added to the uniform planar heat loss of the wall without the slab (the blue area).
Linear thermal transmittance (Ψ) and point thermal transmittance (χ) describe the difference between the calculated thermal coupling coefficient and the reference contributions. These quantities express the junction contribution rather than the total heat flow. For χ, any specified linear-bridge contributions are also subtracted.
Dimension conventions and reference area (A_total)
The reference heat-flow terms in Ψ and χ depend on the U-values, lengths and areas used in the calculation. Apply a consistent dimension convention to the junction calculation and the building energy model.
For Point Bridges (χ)
For the rectangular planar assembly illustrated below, the reference area is its width multiplied by its height. Use the modelled reference face and the stated dimension convention when determining this area.
For Linear Bridges (Ψ)
At junctions such as corners, internal and external reference dimensions differ. State whether the calculation uses internal dimensions or external dimensions, consistent with the building energy model.
External Dimensions: You measure the length of the element along the extreme outer face of the building envelope.
Internal Dimensions: You measure the length of the element along the inner face of the room.
For the corner shown, external dimensions give larger reference lengths and therefore larger one-dimensional reference heat-flow terms. The corresponding Ψ is lower and may be negative. Both conventions can describe the same total heat flow when applied consistently.
Calculating the Effective U-Value (\(U_{eff}\))
The effective U-value (\(U_{eff}\)) combines clear-field heat transfer with the contributions of linear and point thermal bridges over a specified envelope area, as described in the BC Hydro Building Envelope Thermal Bridging (BETB) Guide.
The formula to calculate the overall effective U-value of a building assembly is:
\(\sum (U_{clear} \cdot A)\) [Clear Field]: The sum of the planar heat flows through the basic wall/roof assemblies (\(U\)-value \(\times\) Area).
\(\sum (\Psi \cdot L)\) [Linear Bridges]: The sum of all linear thermal bridges (e.g., slab edges, window perimeters, parapets) multiplied by their continuous Length (\(L\)).
\(\sum (\chi \cdot n)\) [Point Bridges]: The sum of all point thermal bridges (e.g., canopy structural beams, pipe penetrations, anchors) multiplied by their Quantity (\(n\)).
\(A_{total}\): The total opaque surface area of the building envelope being calculated.
Using the Koala Thermal Bridges Form
The Rhino plugin calculates Ψ and χ after ISO 10211 and writes the calculation report. Assign materials and indoor/outdoor boundary conditions to your layers, then click Bridge Analysis… above the layer table in the KOALA panel. The form stays open while you pick points and distances in the model.
Review the current study in Bridge Analysis.
For frame Uf, glazing-edge Ψg, installation Ψ or whole-window Uw, use the adjacent Window Analysis… control. Follow the window analysis workflow for its reference measurements. Both forms use the same study and report.
Calculation procedure:
Add a calculation: a linear bridge (Ψ) or a point bridge (χ), and choose whether it is reported in external or internal dimensions.
Describe the flanking elements: for each undisturbed wall, roof or floor next to the bridge, either pick a point on it so Koala detects the axis and traces its layers and surface resistances from the model, or enter a U-value with its source.
Give the dimensions: the length (Ψ) or area (χ) of each element inside the model, to internal and to external surfaces, and the distance from the bridge to its cut-off plane. Lengths can be measured between two points in the model.
For a point bridge: add the linear bridges that are inside the model, with their Ψ and length, so they are not counted as part of χ.
Calculate: Koala solves the model once: heat flow, and surface temperatures with the surface resistances you assigned. The ISO 13788 surface check (a second solve with an indoor resistance of 0.25 m²K/W) is an option of the report window. With Verify on in the panel it also solves at half the cell size.
Export report: open Report… to enter project information, review figures and export PDF, CSV tables or JSON in the document’s units. The report lists the declarations and checks still needed.
A model that is one uniform extrusion is solved as a 2D section and gives \(L^{2D}\) directly. A 3D model gives \(L^{3D}\): use it for χ, or give its length along the bridge to read it as Ψ. The result shows every term of the subtraction, the value in both dimension systems where both sets of lengths are given, the change at half the cell size, and the lowest indoor surface temperature with its \(f_{Rsi}\) and location.
The shared calculation report
Window and bridge assessments use the same report window. Project details, named views, section drawings, surface-temperature checks and PDF, CSV and JSON export are described in Results and reporting.
Understanding the Underlying Math
The following sections detail the mathematical procedures defined in ISO 10211. These principles form the basis of the Koala calculator's internal logic and serve as a reference for verifying calculations or performing manual analysis.
1. Calculating Psi (Ψ) for Linear Bridges
Subtract the reference contributions of the flanking constructions from the calculated two-dimensional thermal coupling coefficient (\(L^{2D}\)).
\(L^{2D}\) is derived from the 3D simulation: \(L^{2D} = \frac{Q_{total}}{\Delta T \cdot L_{extruded}}\). It represents the thermal coupling coefficient per meter of length.
\(U_i\) is the 1D clear-field U-value of the flanking element \(i\).
\(l_i\) is the measured cross-sectional length (Internal or External) of the flanking element \(i\).
2. Calculating Chi (χ) for Point Bridges
Subtract the planar reference contributions from the calculated three-dimensional thermal coupling coefficient (\(L^{3D}\)). Subtract any specified linear-bridge contributions within the model to isolate the point-bridge contribution.
