Sizing a South Window Overhang for Summer and Winter Noon
A south-facing studio window is 2.40 m high and 3.00 m wide. The team is testing a single flat horizontal overhang fixed at the window head; its depth is d metres. At solar noon the summer solar altitude is 72° and the winter solar altitude is 34°. The brief requires full direct-sun exclusion at summer noon, but at winter noon the lower 1.80 m of the window must remain in direct sun. Assume the wall is vertical, the overhang is opaque and thin, and the sun's rays lie in a vertical plane perpendicular to the facade. Ignore diffuse radiation and reflections. The client wants the smallest overhang that satisfies both conditions, because a deeper overhang darkens the room and blocks upward views. A fabricator can supply depths in 50 mm increments.
1. Derive the shadow depth on the wall and determine the range of d.
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For a thin horizontal overhang of depth d at the window head, a ray at altitude α drops d tan α over the horizontal depth. The shadow depth on the vertical wall below the head is s = d tan α. Summer full shade requires s ≥ 2.40: d ≥ 2.40 / tan 72° = 2.40 / 3.078 = 0.780 m. Winter lower 1.80 m clear requires s ≤ 2.40 − 1.80 = 0.60 m: d ≤ 0.60 / tan 34° = 0.60 / 0.675 = 0.889 m. So 0.78 m ≤ d ≤ 0.89 m; in 50 mm increments, 0.80 m or 0.85 m. The smallest is 0.80 m, but 0.80 m barely meets summer shade.
2. If d = 0.85 m, compute the shaded fraction at summer and winter noon.
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At d = 0.85 m: summer s = 0.85 × 3.078 = 2.62 m, which exceeds the 2.40 m window height, so the whole window is shaded (shaded fraction 100%). Winter s = 0.85 × 0.675 = 0.574 m; shaded fraction = 0.574 / 2.40 = 24%, and the clear lower portion is 2.40 − 0.574 = 1.83 m, just above the 1.80 m requirement. The design therefore blocks summer noon sun and admits winter noon sun to almost the full lower window.
3. State two limitations of the noon-only calculation for real design.
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Noon-only ignores morning and afternoon sun, when the solar altitude is lower and the azimuth is east or west; a horizontal overhang alone cannot block low east/west sun, so vertical fins or side reveals are needed. It also ignores diffuse sky light, which is a major part of daylight and is reduced by any overhang. Finally, the calculation assumes a thin opaque overhang and a wall exactly perpendicular to the sun's vertical plane; real facades have azimuth deviations, and a 0.80 m overhang may not fully shade at other summer hours.