Fixed offset Carnot model:

T_condensing = T_flow + {{ condensing_fixed_offset }}°C

T_evaporating = T_ambient + {{ evaporating_fixed_offset }}°C

COP = {{ practical_cop_factor }} × (T_condensing + 273.15) / (T_condensing - T_evaporating)

Variable offset Carnot model (speed dependent):

T_condensing = T_flow + (speed/120) × {{ condensing_scale }}°C

T_evaporating = T_ambient + (speed/120) × {{ evaporating_scale }}°C

COP = {{ practical_cop_factor }} × (T_condensing + 273.15) / (T_condensing - T_evaporating)

Variable offset Carnot model (output dependent):

T_condensing = T_flow + (output/{{ max_output }}) × {{ condensing_scale }}°C

T_evaporating = T_ambient + (output/{{ max_output }}) × {{ evaporating_scale }}°C

COP = {{ practical_cop_factor }} × (T_condensing + 273.15) / (T_condensing - T_evaporating)

Carnot with a fitted second-law efficiency curve, from vaillant_cop_fit.js. Unlike the other Carnot models it has no adjustable inputs: its 12 coefficients per unit were least-squares fitted to these same datasheet tables, so this is a measure of how well the structure can fit, not an independent validation.

q̂ = output / Q_nom   (Q_nom = {{ vaillant_cop_fit_params[selected_model][11] }} kW)

T_condensing = T_flow + 4 q̂    T_evaporating = T_ambient − 7 q̂    L = T_c − T_e

η = (e₀ + e₁q̂ + e₂q̂² + e_xzq̂z) × (1 + a₁z + a₂z² + a₃z³) × (1 + b₁w),   z = (L−45)/45,   w = (T_flow−50)/15

frost = 1 − f_A exp(−½((T_ambient − f_μ)/f_σ)²)

COP = η × frost × (T_condensing + 273.15) / L

Same structure as the unit-specific fit, but with a single pooled parameter set fitted jointly to both units in normalised load space, so the only unit dependent inputs are the nominal capacity and an optional efficiency scale. It reproduces both tables at about 7% MAPE, compared with 5.6 to 6.5% for the unit-specific fits. That is the price of generalising, though it is still better than applying one unit's own parameters to the other, which gives 8.7 to 10.2%.

q̂ = output / Q_nom

T_condensing = T_flow + 4 q̂    T_evaporating = T_ambient − 7 q̂    L = T_c − T_e

η = scale × (e₀ + e₁q̂ + e₂q̂² + e_xzq̂z) × (1 + a₁z + a₂z² + a₃z³) × (1 + b₁w)

COP = η × frost × (T_condensing + 273.15) / L

For a different unit, set Q_nom to its nominal capacity and leave the scale at 1.0 for other Arotherm+ sizes; for other inverter-driven air-source monoblocs, derive the scale from a few datasheet rating points using calibrateEtaScale().

Same pooled approach as the generic fit, but the efficiency polynomial is written in inferred compressor speed rather than load fraction. Normalised volumetric capacity c = Q/(rps·Q_nom) collapses onto one curve for both units, so speed can be back-calculated from the operating point and nominal capacity alone. This fixes most of the cold high-speed corner error of the load-fraction version. Fitted with the frost amplitude free, the pooled fit chose f_A = 0, so v2 is a pre-defrost surface by construction and has no defrost option here; the remaining error against these tables is therefore partly the datasheet's embedded defrost penalty. Its other known weakness is underprediction at mild ambient (+10 to +20°C) for the 5 kW unit, the flip side of fitting across the EN 14511 wet/dry coil boundary at about +7°C.

c = (c₀ + c₁T_ambient + c₂T_ambient²) × (1 + c₃(T_flow − 50))    rps = output / (Q_nom c), clamped to 30–120

q̂ = output / Q_nom    s = rps / 100

T_condensing = T_flow + 4 q̂    T_evaporating = T_ambient − 7 q̂    L = T_c − T_e

η = scale × (e₀ + e₁s + e₂s² + e_xzsz) × (1 + a₁z + a₂z² + a₃z³) × (1 + b₁w),   z = (L−45)/45,   w = (T_flow−50)/15

COP = η × (T_condensing + 273.15) / L

The same capacity model gives the modulation envelope at a condition via outputRange(), and raw (unclamped) speed via estimateSpeed() to detect demand below the minimum modulation, i.e. on/off cycling.