Seasonal window and shading worked analysis
Reference example: Berlin, south-facing façade, room 4 m wide × 5 m deep. The clear window sill is 0.8 m high and head is 2.4 m high, giving a 1.6 m opening. A horizontal overhang projects 1 m, with its underside 0.2 m above the head.
Compare one centered 2.4 m window with two 1.2 m windows separated by a 0.4 m pier. Both have 2.4 m total clear width, or 60% of room width. This is a comparison, not an optimum window count or width ratio.
At rounded winter-solstice noon altitude 14°, a ray to the rear floor enters at 5 × tan 14° ≈ 1.25 m, within the opening. At rounded summer-solstice noon altitude 61°, the overhang shadow extends 1 × tan 61° − 0.2 ≈ 1.60 m down from the head, approximately shading to the sill. Allow a design margin and check more hours.
Window-head height controls maximum penetration; sill height controls where floor sunlight begins. Width and spacing redistribute lateral ray coverage. At 15° to either side of the façade normal, the projected rear shift is 5 × tan 15° ≈ 1.34 m. These are illustrative directions, not computed morning/evening times.
Report illustrations use strong yellow for straight-on rays and 30%-opacity bands for other directions. Overlap shows coverage at different times, not added physical intensity or diffuse light. The section determines actual floor penetration.
Choose heating, mixed or cooling priorities using local climate and occupancy. Check eaves, overhangs, side fins, recessed openings and adjustable screens against the desired winter access and critical hot-season hours. Neither the example nor the ideal thin-opening equations account fully for frames, finite shading edges, furniture, terrain, glare or thermal performance.