Cohort residual slice 11: Simplified Type 1 RR geometry — _part_geometry + heat_transmission

Implements RdSAP10 §3.9.1 Simplified Type 1 (True Room-in-Roof, no
common walls):

  A_RR = 12.5 × √(A_RR_floor / 1.5)

When the cert lodges only a `SapRoomInRoof(floor_area, construction_
age_band)` (no gable / party / sheltered / connected wall lengths),
ΣA_RR_gable/other = 0 → A_RR_final = A_RR, treated as timber-framed
roof structure with U from Table 18 col (4) "Room-in-roof, all elements".
The storey-below roof area (§3.8) is deducted by A_RR_floor per §3.9.

Changes:
  - `_part_geometry`: returns new keys `rr_floor_area_m2` and
    `rr_simplified_a_rr_m2`; existing `top_floor_area_m2` now subtracts
    `rr_floor_area_m2` (the §3.9 deduction).
  - Main loop: `roof += U_RR × A_RR` where U_RR is from
    `u_rr_default_all_elements(country, rir.construction_age_band)`.
    A_RR also joins the (31) external-area total for thermal-bridging.

Test: synthetic 2-storey + RR (15 m² floor) at age B → roof_w_per_k
math closes at abs=0.001 vs hand-computed 100.92 W/K.

Cohort impact (post-slice-11 vs post-slice-8):
  - 000474, 000490 unchanged at Δ=0 ✓
  - 000480: Δ=+12 → +4   (RR Simplified resolved most of the gap)
  - 000487: Δ=+11 → +3   (same)
  - 000516: Δ=+12 → +4   (same)
  - 000477: Δ=+2  → −6   (overshoot — the U985 PDF uses detailed §3.10
    per-surface RR lodgement; Simplified Type 1 at U=2.30 is too high
    for an RR with measured retrofit insulation. Closes once Detailed
    lands + 000477 fixture upgrades to detailed lodgement, slice 14.)

Reference: RdSAP 10 (10-06-2025) §3.9.1 page 21-22; Table 18 page 45.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

packages/domain/src/domain/sap/worksheet/heat_transmission.py

@@ -56,9 +56,11 @@ from domain.ml.rdsap_uvalues import (
     u_floor,
     u_party_wall,
     u_roof,
+    u_rr_default_all_elements,
     u_wall,
     u_window,
 )
+from math import sqrt
 
 
 _WALL_INSULATION_NONE: Final[int] = 4
@@ -147,6 +149,8 @@ def _part_geometry(part: SapBuildingPart) -> dict[str, float]:
             "top_floor_area_m2": 0.0,
             "gross_wall_area_m2": 0.0,
             "party_wall_area_m2": 0.0,
+            "rr_floor_area_m2": 0.0,
+            "rr_simplified_a_rr_m2": 0.0,
         }
     fds = list(part.sap_floor_dimensions)
     ground = next((fd for fd in fds if fd.floor == 0), fds[0])
@@ -165,11 +169,28 @@ def _part_geometry(part: SapBuildingPart) -> dict[str, float]:
         (fd.party_wall_length_m or 0.0) * (fd.room_height_m or _DEFAULT_STOREY_HEIGHT_M)
         for fd in fds
     )
+    # RdSAP10 §3.9.1 Simplified Type 1 (True Room-in-Roof): when an RR is
+    # lodged with only its floor area (no gable/party/sheltered/connected
+    # wall lengths), the spec's empirical formula treats it as one chunk
+    # of timber-framed roof structure of area A_RR = 12.5 × √(A_RR_floor
+    # / 1.5). The storey-below roof area (§3.8) is deducted by A_RR_floor
+    # — the regular roof "becomes" the residual footprint not under the
+    # RR. Type 2 (common walls < 1.8m) and the Detailed §3.10 path are
+    # additive on top — they decompose A_RR into per-surface areas with
+    # their own U-values, deducted from A_RR_final per step e.
+    rr_floor_area = 0.0
+    rr_a_rr = 0.0
+    rir = part.sap_room_in_roof
+    if rir is not None and rir.floor_area > 0:
+        rr_floor_area = float(rir.floor_area)
+        rr_a_rr = 12.5 * sqrt(rr_floor_area / 1.5)
     return {
         "ground_floor_area_m2": ground.total_floor_area_m2 or 0.0,
-        "top_floor_area_m2": top.total_floor_area_m2 or 0.0,
+        "top_floor_area_m2": max(0.0, (top.total_floor_area_m2 or 0.0) - rr_floor_area),
         "gross_wall_area_m2": gross_wall,
         "party_wall_area_m2": party_wall,
+        "rr_floor_area_m2": rr_floor_area,
+        "rr_simplified_a_rr_m2": rr_a_rr,
     }
 
 
@@ -328,6 +349,21 @@ def heat_transmission_from_cert(
 
         walls += uw * main_wall_area + alt_walls_contribution
         roof += ur * roof_area
+        # RdSAP10 §3.9.1 Simplified RR contribution. A_RR is treated as
+        # timber-framed roof structure with U from Table 18 column (4)
+        # "Room-in-roof, all elements" (the as-built / unknown default
+        # per footnote (1)). The age band lives on the SapRoomInRoof, not
+        # the SapBuildingPart, so we read it from there. Lines under (30)
+        # in the U985 worksheet — same line ref as the regular roof, so
+        # we fold the contribution into roof_w_per_k.
+        rr_a_rr = geom["rr_simplified_a_rr_m2"]
+        if rr_a_rr > 0:
+            rir = part.sap_room_in_roof
+            assert rir is not None  # rr_a_rr > 0 ⇒ rir present per _part_geometry
+            u_rr = u_rr_default_all_elements(
+                country=country, age_band=rir.construction_age_band,
+            )
+            roof += u_rr * rr_a_rr
         floor += uf * floor_area_total
         party += upw * party_area
         windows += window_u * w_area
@@ -335,9 +371,11 @@ def heat_transmission_from_cert(
         # (31) — total external element area used by both the worksheet
         # readout and the (36) thermal-bridging multiplier. Excludes the
         # party wall (party walls have their own line (32)) per RdSAP
-        # §5.15: bridging applies to *exposed* area only.
+        # §5.15: bridging applies to *exposed* area only. RR area joins
+        # the external surfaces per the spec — A_RR contributes to (31)
+        # alongside walls + roof + floor + openings.
         part_external_area = (
-            main_wall_area + alt_walls_total_area + roof_area + floor_area_total + w_area + d_area
+            main_wall_area + alt_walls_total_area + roof_area + floor_area_total + w_area + d_area + rr_a_rr
         )
         total_external_area += part_external_area
         bridging += y * part_external_area

packages/domain/src/domain/sap/worksheet/tests/test_heat_transmission.py

@@ -21,6 +21,7 @@ from datatypes.epc.domain.epc_property_data import (
     BuildingPartIdentifier,
     EnergyElement,
     SapAlternativeWall,
+    SapRoomInRoof,
 )
 
 from domain.ml.tests._fixtures import (
@@ -1306,3 +1307,64 @@ def test_section_3_partial_match_against_elmhurst_worksheet(fixture: ModuleType)
     # (gap #1). Non-RR fixtures get exact (31) + (36) asserted by the
     # dedicated `test_section_3_non_rr_line_31_and_36_match_elmhurst_worksheet`.
     assert result.total_external_element_area_m2 > 0
+
+
+def test_room_in_roof_simplified_type_1_adds_a_rr_timber_framed_area_to_roof_w_per_k() -> None:
+    """RdSAP10 §3.9.1 Simplified Type 1 (True Room-in-Roof, no common
+    walls). Formula (page 22 step d): A_RR = 12.5 × √(A_RR_floor / 1.5);
+    this area is treated as timber-framed construction and assigned a
+    U-value from Table 18 column (4) "Room-in-roof, all elements" by age
+    band when no gable / party / sheltered / connected wall lengths are
+    lodged (ΣA_RR_gable/other = 0 → A_RR_final = A_RR).
+
+    Also (§3.9 page 21): A_RR_floor is deducted from the storey-below
+    roof area determined by §3.8 (which takes the greatest floor area
+    across levels).
+
+    Synthetic dwelling for arithmetic clarity:
+      - 2 storeys × 40 m² each → §3.8 roof area = 40
+      - RR floor area = 15 m²
+      - §3.9 deducted top-floor roof area = 40 − 15 = 25 m²
+      - A_RR = 12.5 × √(15 / 1.5) = 12.5 × √10 ≈ 39.5285 m²
+      - Age band B → U_roof (Table 18 col 1) = 0.40; U_RR (Table 18
+        col 4 "as built") = 2.30.
+      - roof_w_per_k = 25 × 0.40 + 39.5285 × 2.30 = 10.00 + 90.9156
+                     = 100.9156 W/K.
+    """
+    # Arrange
+    import math
+    main = make_building_part(
+        identifier=BuildingPartIdentifier.MAIN,
+        construction_age_band="B",
+        wall_construction=3,
+        wall_insulation_type=4,
+        party_wall_construction=1,
+        roof_construction=4,
+        floor_dimensions=[
+            make_floor_dimension(
+                total_floor_area_m2=40.0, room_height_m=2.5,
+                heat_loss_perimeter_m=20.0, party_wall_length_m=0.0, floor=0,
+            ),
+            make_floor_dimension(
+                total_floor_area_m2=40.0, room_height_m=2.5,
+                heat_loss_perimeter_m=20.0, party_wall_length_m=0.0, floor=1,
+            ),
+        ],
+        sap_room_in_roof=SapRoomInRoof(floor_area=15.0, construction_age_band="B"),
+    )
+    epc = make_minimal_sap10_epc(
+        total_floor_area_m2=95.0,  # 40 + 40 + 15
+        habitable_rooms_count=5,
+        country_code="ENG",
+        sap_building_parts=[main],
+    )
+
+    # Act
+    result = heat_transmission_from_cert(
+        epc, window_total_area_m2=0.0, window_avg_u_value=None, door_count=0,
+    )
+
+    # Assert
+    a_rr = 12.5 * math.sqrt(15.0 / 1.5)
+    expected_roof_w_per_k = (40.0 - 15.0) * 0.40 + a_rr * 2.30
+    assert result.roof_w_per_k == pytest.approx(expected_roof_w_per_k, abs=0.001)