Heat-Pump Cold-Temperature Capacity and Auxiliary Heat
Whether a heat-pump conversion holds on the design day: a heat pump's capacity falls as it gets colder, so interpolating the AHRI 47 F and 17 F rating points down to the design temperature gives the delivered capacity, and the shortfall below the Manual J design load is the auxiliary strip heat (kW) the installer must add. A unit sized on its 47 F nameplate is badly undersized at 5 F - the classic cold-climate conversion failure. Prefer a published low-temperature data point over extrapolation when a conversion hinges on it. A sizing check, not a performance guarantee.
Formula and source
slope = (cap_47_btuh - cap_17_btuh) / (47 - 17); cap_design = max(0, cap_17_btuh + slope x (design_temp_f - 17)); shortfall = max(0, design_load_btuh - cap_design); aux_kw = shortfall / 3412.
The AHRI 210/240 low-temperature rating points (the 47 F and 17 F integrated heating capacities) and a linear capacity-versus-temperature interpolation, by name; 3,412 Btu/h per kW is a named constant.
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