Linear Thermal Bridge Coefficient (Psi-value)
Extra heat loss per meter of junction, W/(m.K), quantifying thermal performance at construction details that U-value calculations miss.
What is Psi and how does it fit into thermal calculations?
The linear thermal bridge coefficient, Psi (Ψ), measured in W/(m.K), quantifies extra heat loss through a junction between building elements that one-dimensional U-value calculations miss. When you calculate wall heat loss using U-value, you treat the wall as an infinite plane. In reality, at corners where wall meets roof, floor, or adjacent wall, heat flow becomes two-dimensional. Psi represents this additional flow per meter of junction.
This distinction is critical: planar U-values assume heat flows perpendicular to the wall surface. At a junction, geometry forces heat to flow laterally along the junction, creating localized intense outward flow. Engineers call this the thermal bridge effect. Psi quantifies the penalty in extra watts per meter.
In poorly insulated buildings, thermal bridges contribute 5-10% of total loss. In modern insulated buildings with continuous insulation, the supplement for thermal bridges can represent 15-30% of total heat loss coefficient. In passive-house design, ignoring Psi is a serious error, leading to underestimated heating demand and failed certification.
Why does Psi depend on how dimensions are measured?
This is the crucial and widely misunderstood issue: Psi value depends on the reference dimension system. Three conventions exist, each measuring from a different plane.
| Dimension System | Measurement Plane | Common Use |
|---|---|---|
| External | Outer edges of exterior finishes | European atlases and detailed simulations |
| Internal | Inner surfaces of interior finishes | Energy certificates and code compliance |
| Overall-internal | Interior perimeter plus unheated element exterior | EN 12831 heating design calculations |
A wall-roof junction with Psi of 0.1 W/(m.K) measured externally might be 0.05 W/(m.K) measured internally. The physical behavior is identical, but the numerical value changes because the perimeter itself changes. Entering a Psi value from one system into a calculation using another produces meaningless results. Always verify dimension convention before using tabulated data.
What do negative Psi values mean?
A negative Psi occurs when actual two-dimensional heat flow at a junction is less than adjacent planar U-value elements predict. This happens with geometry improvements, such as an insulated lintel at a window sill. A negative Psi is physically valid, not an error, and should be used as calculated. It does not mean heat flows inward; it simply means the detailed geometry is more efficient than the one-dimensional assumption. Discard negative Psi in favor of zero only when you want a deliberately conservative calculation.
How do Psi, Chi, and fRsi differ?
Psi (Linear coefficient): Heat loss per meter of edge, such as wall-roof junction, W/(m.K). Answers: how much extra heat at this 1-meter junction?
Chi (Point coefficient): Heat loss at a point source, like a balcony anchor through insulation, W/K per point. Answers: how much extra heat at this single point?
fRsi (Surface temperature factor): Dimensionless ratio predicting whether interior surface gets cold enough for mould. Answers: will condensation and mould occur? A junction can pass Psi and Chi yet fail fRsi.
A room corner behind a wardrobe illustrates this: modest Psi (acceptable heat loss) but poor fRsi (condensation risk). The corner is energy-efficient yet develops mould, the failure pattern clients experience in Slovak winters.
Where are thermal bridges in a Slovak family house, and how are they handled?
Thermal junctions occur at predictable locations, each with specific design solutions.
| Location | Risk | Solution |
|---|---|---|
| Window reveals and sills | Mould risk at sill corners from large temperature gradient | Insulated reveals, insulated sill trays with thermal breaks, continuous caulking |
| Floor-wall junction (plinth) | Ground contact causes low surface temperature, condensation and mould at base | Continuous insulation on wall and slab edge, thermal break at edge, insulated foundation strip |
| Slab-edge junction | Two-dimensional flow at intermediate floor slab connection; extra loss if slab is uninsulated | Thermal-break balcony with insulated brackets, recessed insulation pocket, continuous exterior wrapping |
| Wall-to-roof eaves | Heat loss along top plate or beam; condensation if roof interior lacks insulation | Continuous eaves insulation, thermal break at roof-wall, insulated fascia and soffit |
| Balcony junction | Concrete or steel bearing through insulation creates direct thermal path; significant loss and condensation | Thermal-break balcony system with insulated brackets, recessed insulation, decoupled structure |
Most critical in Slovak practice: window sill (mould behind radiators), balcony connection (heat loss underestimated), plinth (damp plus low surface temperature).
How do Psi values enter energy calculations?
Numerical simulation: Two-dimensional modeling to EN ISO 10211 using software like Therm or Psi-Therm. Input material properties, geometry, boundary conditions; software calculates actual heat flux and reports Psi. Mandatory for passive-house certification, recommended for custom details. Highest accuracy but requires skill and time.
Tabulated defaults: Organizations publish Psi tables for standard details. Slovak practice references national guidance or European passive-house atlases. Values are deliberately conservative, representing midpoint or upper-bound performance. Actual site performance may be better (lower Psi). Appropriate for preliminary design; if certification is at risk, simulation is safer.
Practical difference: a tabulated 0.1 W/(m.K) may be median, but your specific detail might achieve 0.07 or 0.12 W/(m.K). For retrofit with tight energy budget, simulation of 2-3 critical details justifies the cost. For new single-family house, tabled values suffice with good site supervision.
What role does Psi play in Slovak building standards?
Psi appears in Slovak energy calculations under STN 73 0540 series, implementing the Energy Performance of Buildings Directive. Every junction requires either a simulated or tabled Psi value. In passive-house design, the sum of all linear bridge losses must not exceed a specific fraction of total heat loss. Because passive-house heating loads are tiny (often <10 W per square meter), small Psi oversights break certification. This is why Slovak passive-house practitioners simulate every junction detail and iterate design to minimize Psi before construction.
Frequently asked questions
- What is Psi and why does it matter if I already know the U-value?
- Psi quantifies heat loss at construction junctions that U-values treat as one-dimensional planar elements. When a wall meets a roof or floor, the heat flow becomes two-dimensional at that corner, and this extra flow is missed by planar U-values alone. In modern well-insulated buildings, these junctions contribute 15-30% of total heat loss, making Psi essential for accurate energy calculations.
- Why does the same junction have different Psi values in different standards?
- Psi depends on where you measure the dimensions: from the outer edge of finishes (external), the inner surface (internal), or an overall-internal hybrid dimension. A junction with a Psi of 0.1 W/(m.K) measured to external dimensions will have a different (usually lower) value when measured to internal dimensions. Mixing conventions in a calculation is simply wrong and produces misleading results.
- Can Psi be negative, and does that mean there is a thermal benefit?
- Yes, Psi can be negative. This occurs when the geometry and materials at a junction reduce heat loss below what would be expected from the adjacent planar elements alone. A negative Psi is not an error or sign of a data mistake; it is physically valid and should be used as calculated. It does not mean the junction generates heat, only that the detailed geometry is more efficient than the simplified planar assumption.
- How is Psi different from Chi and fRsi?
- Psi quantifies heat loss per meter of edge (linear thermal bridge, such as a wall-roof junction). Chi measures heat loss at a point source (a balcony anchor or fixing that penetrates insulation), expressed in W/K per point. fRsi is the surface temperature factor at a junction, answering whether the interior surface will get cold enough for mould, not how much total heat is lost. All three are independent; a junction may pass Psi and Chi limits but still fail fRsi.
- Can a room corner pass on heat loss (Psi) but still get mould?
- Absolutely. This is a common failure mode in Slovak residential buildings. A corner behind a wardrobe may have a modest Psi value and acceptable heat loss, but its low surface temperature (poor fRsi) drops below the dew point in winter, causing moisture to condense and mould to grow. The two metrics measure different risks.
- Do tabulated Psi values from design atlases apply to my building?
- Tabulated values are conservative defaults, designed to cover typical construction methods and material combinations. They may be more pessimistic than actual performance if your detail differs in materials or geometry. For a final energy certificate or passive-house certification, you should verify critical junctions by numerical simulation to EN ISO 10211 or EN ISO 13370 standards rather than relying entirely on tabulated defaults.