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SAP 10.2 Appendix N3.5 Equation N5 (PDF p.107):
T = [N24,9 × Th + N16,9 × T_uni + (Nm − N16,9 − N24,9) × T_bi] / Nm
`extended_zone_mean_temperature_c` is the pure-math leaf: takes
pre-computed bimodal (9-hour heating, two off periods) and unimodal
(16-hour heating, one 8-hour off period per Table N7 footnote b)
zone temperatures and the per-month day allocations, blends across
the three heating patterns (Th for 24-hour days, T_uni for 16-hour,
T_bi for the standard 9-hour SAP schedule).
Pinned against cert 0380's January living-area MIT: Th=21, T_bi
=18.5551 (worksheet "Living" row), T_uni back-solved from (87)
= 19.6153, N24=3, N16=28, Nm=31 → 19.7493 (worksheet (87) Jan).
Collapses cleanly: N24=N16=0 → T_bi (warm months / non-HP certs);
N24=Nm → Th (full 24-hour heating).
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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