Fabric Heat Loss in HEM — U-Values, Thermal Bridging, and Dynamic Analysis

The Home Energy Model (HEM) calculates fabric heat loss by applying the thermal transmittance (U-value) and area of every building element — walls, floors, roofs, windows, and doors — to the instantaneous temperature difference between inside and outside at each of its 17,520 half-hourly timesteps. This dynamic approach, documented in HEM-TP-05, replaces SAP's simplified monthly method with a physics-based calculation grounded in BS EN ISO 6946:2017 for thermal resistance and transmittance, capturing peak heat loss during cold spells rather than averaging it away across an entire month.

The Fundamental Fabric Heat Loss Equation

At each half-hourly timestep t, HEM calculates the total fabric heat loss rate Q_fabric(t) as the sum of transmission losses through every building element plus losses through thermal bridges:

Q_fabric(t) = Σ(U_i × A_i × ΔT(t)) + Σ(ψ_j × l_j × ΔT(t)) + Σ(χ_k × ΔT(t))

Where:

• U_i is the thermal transmittance (W/m²K) of building element i (wall, floor, roof, window, or door)
• A_i is the area (m²) of element i
• ΔT(t) is the temperature difference (K) between the internal zone temperature and the external air temperature at timestep t
• ψ_j is the linear thermal transmittance (W/mK) of thermal bridge junction j
• l_j is the length (m) of junction j
• χ_k is the point thermal transmittance (W/K) of point thermal bridge k

The critical distinction from SAP is that ΔT(t) varies at every timestep. SAP uses monthly average temperatures, so a January with mixed conditions — some nights at −5°C, some days at 10°C — is treated as a single average. HEM captures every cold snap and every mild spell individually, which means the model accurately reflects periods of peak heating demand when fabric performance is most critical. This is essential for correctly sizing heating systems, particularly heat pumps, which must meet demand at design conditions rather than average conditions.

U-Value Calculation Methodology

HEM derives U-values following the established standards for each element type. The U-value represents the rate of heat transfer through a building element per unit area per degree of temperature difference, expressed in W/m²K. Lower values indicate better insulation performance.

Opaque Elements: Walls, Floors, and Roofs

For opaque elements such as external walls and roofs, HEM follows BS EN ISO 6946:2017 to calculate U-values from a layer-by-layer build-up. The total thermal resistance R_total is the sum of the resistances of each layer plus the internal and external surface resistances:

R_total = R_si + R₁ + R₂ + … + R_n + R_se

Each layer's thermal resistance is calculated as R = d / λ, where d is the thickness (m) and λ is the thermal conductivity (W/mK). The U-value is then the reciprocal of the total resistance: U = 1 / R_total.

Standard surface resistances for a horizontal heat flow are R_si = 0.13 m²K/W (internal) and R_se = 0.04 m²K/W (external). For upward heat flow (roofs), R_si = 0.10 m²K/W; for downward heat flow (ground floors), R_si = 0.17 m²K/W.

BS EN ISO 6946 also requires corrections for:

• Mechanical fasteners that penetrate insulation layers (e.g., wall ties through cavity insulation), calculated as a ΔU_f correction
• Air gaps within the construction (unventilated, slightly ventilated, or well-ventilated cavities each have different treatment)
• Inhomogeneous layers where materials of different conductivity sit side by side (e.g., timber studs within mineral wool insulation in a timber-frame wall), addressed using the upper and lower bound method

Ground Floors

Ground floor U-values follow BS EN ISO 13370:2017, which accounts for the thermal coupling between the building and the ground. The calculation depends on the floor geometry, soil thermal conductivity, and the presence of edge insulation. The key parameter is the characteristic dimension B' = A / (0.5 × P), where A is the floor area and P is the exposed perimeter.

Large, compact ground floors with a high B' value achieve lower U-values because the ground itself provides thermal resistance across the central area. Edge insulation — placed either horizontally beneath the slab perimeter or vertically at the foundation wall — reduces heat loss at the perimeter where it is greatest. The FHS notional specification of 0.13 W/m²K typically requires continuous insulation of at least 100–150 mm of PIR or equivalent, depending on the floor geometry.

Windows and Doors

Window and door U-values follow BS EN ISO 10077-1:2017, which considers the thermal transmittance of the glazing unit (U_g), the frame (U_f), and the linear thermal bridge at the spacer bar (ψ_g):

U_w = (A_g × U_g + A_f × U_f + l_g × ψ_g) / A_w

Where A_g is the glazing area, A_f is the frame area, l_g is the total perimeter of the glazing, and A_w is the total window area.

The FHS notional dwelling specifies windows at 1.2 W/m²K with a solar transmittance (g-value) of 0.63. Achieving this typically requires double glazing with a low-emissivity coating, argon- or krypton-filled cavity, and warm-edge spacer bars. Triple glazing is not mandated by the notional specification but may be needed in practice for dwellings with high form factors or north-facing facades where solar gains are minimal.

HEM also models the solar gain through windows at each timestep — see Solar Gains for the full methodology. The interplay between window U-value (which drives heat loss) and g-value (which drives solar gain) means that window specification involves a careful balance, particularly on south-facing elevations where a higher g-value can offset transmission losses during sunny winter days.

Thermal Bridging — Linear and Point Bridges

Thermal bridges are areas where the insulation layer is interrupted or reduced, creating localised paths of higher heat flow. In a well-insulated building, thermal bridges can account for 20–30% of total fabric heat loss — a proportion that increases as the U-values of planar elements improve. HEM treats thermal bridging with considerably more rigour than SAP.

Linear Thermal Bridges (ψ-values)

Linear thermal bridges occur at junctions between building elements — for example, where a wall meets a floor, a wall meets a roof, a window sits within a wall opening, or two walls meet at a corner. Each junction has a linear thermal transmittance (ψ-value, measured in W/mK) that represents the additional heat loss per metre of junction length beyond what would be calculated from the U-values of the adjoining elements alone.

HEM requires ψ-values for every junction in the thermal envelope. These can be sourced from:

• Bespoke thermal modelling to BS EN ISO 10211:2017 using finite element analysis software (the most accurate option)
• Approved construction details from the published Accredited Construction Details (ACDs) schemes, which provide pre-calculated ψ-values for common junction types
• Default values from Table R1 of Approved Document L — these are conservative (punitive) values intended to discourage poor detailing

At each half-hourly timestep, the heat loss through a linear thermal bridge is calculated as Q_ψ(t) = ψ × l × ΔT(t), where l is the junction length and ΔT(t) is the instantaneous temperature difference. This means that thermal bridge losses respond to the same temperature dynamics as planar element losses — they peak during cold weather and diminish during mild periods.

Point Thermal Bridges (χ-values)

Point thermal bridges arise from discrete penetrations through the insulation layer, such as:

• Steel brackets or fixings supporting external cladding systems
• Structural columns or beams that pass through insulation
• Service penetrations (pipes, cables, flues) through the envelope
• Balcony connections in multi-storey residential buildings (often the most significant point bridges)

Each point bridge has a point thermal transmittance (χ-value, measured in W/K) and is evaluated at every timestep: Q_χ(t) = χ × ΔT(t). While individually small, point bridges can collectively add significant heat loss, particularly in buildings with large numbers of cladding fixings or structural thermal bypasses.

SAP vs HEM — Fabric Heat Loss Approach

The following table summarises the key methodological differences between SAP and HEM in their treatment of fabric heat loss:

Future Homes Standard — Notional Dwelling Fabric

The Future Homes Standard (FHS) defines a notional dwelling with specific fabric performance targets. To demonstrate compliance, the actual dwelling must achieve a carbon emission rate and primary energy rate no worse than the notional dwelling when assessed through HEM (or SAP 10.3 during the dual-running transition period).

The notional dwelling fabric specifications represent a substantial step up from current Part L 2021 requirements:

Airtightness and Infiltration

The FHS notional dwelling specifies an airtightness of 3 m³/(h·m²) at 50 Pa, measured by pressurisation testing to BS EN ISO 9972:2015. This is a significant tightening from the Part L 2021 backstop of 8 m³/(h·m²) and considerably lower than the typical new-build achievement of around 4–5 m³/(h·m²) under current regulations.

Within HEM, the measured air permeability feeds into the pressure-driven ventilation model (HEM-TP-06, based on BS EN 16798-7:2017), which distributes infiltration across the building envelope based on wind pressure and stack effect at each timestep. This means airtightness performance affects not just total ventilation heat loss but also the pattern of losses across the day and year.

At 3 m³/(h·m²), most FHS dwellings will require mechanical ventilation with heat recovery (MVHR) to maintain adequate indoor air quality. Natural ventilation strategies become increasingly difficult to justify at these airtightness levels because the controlled air change rate from purpose-provided openings must compensate for very low background infiltration. HEM models the interaction between the MVHR system and residual infiltration dynamically, crediting the heat recovery efficiency at each timestep based on the balance between supply and extract airflows.

Form Factor and Compactness

The form factor is the ratio of the total thermal envelope area to the total internal floor area:

Form Factor = A_envelope / A_floor

A detached bungalow might have a form factor of 4.0 or above (large roof and floor area relative to internal space), while a mid-terrace two-storey house might achieve 1.5 or less (shared party walls reduce exposed envelope). The FHS notional dwelling is calibrated at approximately 3.0, and HEM's dynamic calculation amplifies the impact of form factor compared to SAP's monthly approach.

This amplification occurs because a high form factor means more thermal envelope exposed to peak external conditions. During a cold winter night at −5°C, a dwelling with a form factor of 4.0 has proportionally far more surface losing heat than one at 2.0. SAP's monthly averaging smooths this effect; HEM captures it at every timestep. The practical consequence is that compact building forms — terraced houses, flats, multi-storey designs — are favoured under HEM, while detached bungalows and highly articulated designs face a steeper compliance path.

Designers working on dwelling types with form factors above 3.0 should consider compensating strategies:

• Enhanced fabric specifications — pushing U-values below the notional dwelling levels (e.g., walls at 0.15 W/m²K rather than 0.18)
• Improved thermal bridging — achieving lower ψ-values through bespoke junction modelling rather than relying on standard ACDs
• Tighter airtightness — achieving 1–2 m³/(h·m²) rather than the notional 3.0
• Higher-efficiency systems — specifying a heat pump with a higher seasonal COP to offset the greater fabric losses

Dynamic vs Steady-State Heat Loss

The distinction between dynamic and steady-state heat loss calculation is fundamental to understanding why HEM produces different results from SAP for the same building.

SAP's Steady-State Approach

SAP uses a quasi-steady-state monthly method. For each month, it assumes a constant internal temperature, a constant external temperature (the monthly average), and a fixed rate of heat loss based on these average conditions. Gains from solar radiation, metabolic heat, and appliances are calculated as monthly totals and then a “gain utilisation factor” is applied to determine how much of those gains usefully reduce the heating demand.

This approach works reasonably well for buildings with low thermal mass and conventional heating systems, where conditions change slowly relative to the monthly averaging period. However, it fundamentally cannot capture:

• Diurnal temperature swings — the difference between daytime highs and overnight lows within a single day
• Intermittent heating patterns — the effect of setback periods, night-time temperature reductions, and occupancy schedules
• Solar gain timing — whether solar energy arrives when the building needs heating (useful) or when it is already warm (potentially causing overheating)
• Thermal mass interactions — how heavyweight construction absorbs heat during warm periods and releases it during cold periods, smoothing the internal temperature profile

HEM's Dynamic Approach

HEM solves the heat balance equation at each half-hourly timestep following BS EN ISO 52016-1:2017. At each timestep, the model calculates:

1. The fabric heat loss through every element using the instantaneous temperature difference
2. The ventilation heat loss based on current wind speed, direction, and stack effect
3. The solar gains based on the sun's current position and the prevailing sky conditions (direct and diffuse irradiance)
4. The internal gains based on the occupancy schedule and appliance profiles for that time of day
5. The thermal mass interaction — whether the building fabric is absorbing heat (warming up) or releasing it (cooling down) at that moment
6. The resulting heating or cooling demand needed to maintain the zone setpoint, or the free-floating temperature if no system is active

This dynamic approach means that HEM can distinguish between two buildings with identical U-values but different thermal mass — a lightweight timber-frame house and a heavyweight masonry house will show different energy profiles even with the same insulation, because the masonry stores and releases heat over different timescales. For more on this interaction, see Thermal Mass.

Practical Implications for Design

The shift from SAP's monthly steady-state fabric assessment to HEM's dynamic half-hourly approach has several practical consequences for building design and specification:

Insulation Strategy

With the FHS notional dwelling specifying walls at 0.18 W/m²K, floors at 0.13 W/m²K, and roofs at 0.11 W/m²K, insulation thickness increases significantly. Typical build-ups to achieve these values include:

• Masonry cavity walls: 125–150 mm full-fill mineral wool or 100–120 mm PIR board within a 150 mm cavity, depending on the brick and block conductivities
• Timber-frame walls: 140 mm mineral wool between studs plus 50–80 mm continuous external insulation to mitigate the timber stud thermal bridging (the “repeating thermal bridge” within the frame)
• Ground floors: 100–150 mm PIR below or above slab, depending on floor type and characteristic dimension
• Pitched roofs: 300–400 mm mineral wool at ceiling level, or 150–200 mm rigid board between and below rafters for a warm roof

Junction Detailing

Because HEM evaluates thermal bridges at every timestep, the financial and compliance value of good junction detailing is greater than under SAP. Investing in bespoke thermal bridge calculations to BS EN ISO 10211:2017 rather than relying on default ψ-values can significantly improve the modelled performance, particularly for complex geometries with many junctions.

Key junctions to focus on include:

• Wall–floor junctions (ground floor perimeter and intermediate floors) — often the highest total ψ-value contribution due to their length
• Window–wall junctions (head, sill, and jamb) — numerous and sensitive to frame position within the wall depth
• Wall–roof junctions (eaves and verge) — insulation continuity between wall and roof is critical
• Corner junctions (external and internal corners) — geometric thermal bridging from the change in direction

Glazing Strategy

The FHS notional dwelling specification limits total glazing area to 25% of total floor area, with a recommended distribution of roughly 55% south-facing and 15% north-facing to optimise solar gain while limiting heat loss. Under HEM's half-hourly calculation, the timing of solar gains through glazing is properly credited — south-facing windows contribute useful gains during winter days, while excessive north-facing glazing creates losses with minimal compensating gains.

Designers should carefully balance the window U-value and g-value. A triple-glazed unit with a very low g-value might achieve an excellent U-value but admit so little solar energy that the net effect on heating demand is worse than a well-specified double-glazed unit with a higher g-value. HEM captures this trade-off at every timestep, rewarding designs that optimise the balance for their specific orientation and climate zone.

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