Urban Solar Shading: Rooftop PV Yield Simulator

City Layout

Grid size 6 × 6

Street canyon width 14 m

Building height variance 55%

Sun

Time of day 12:00

Readouts

Solar altitude

0.0°

Solar azimuth

0.0°

City PV output

0.0 kW

Shaded rooftops

How it works

Each rooftop carries a flat photovoltaic array. Instantaneous output of an unshaded panel follows the standard PV power equation:

P = η · I₀ · sin(alt) · A
η  = panel efficiency (20%)
I₀ = 1000 W/m² (peak solar irradiance)
alt = solar altitude angle
A  = usable rooftop area

sin(alt) plays the role of cosθ for a horizontal panel: when the sun is overhead (alt = 90°) the panel faces it directly; near the horizon (alt → 0°) the same light spreads over a much larger area and yield collapses.

Solar position comes from the standard hour-angle formula for a mid-latitude city (φ = 45°N) with a fixed early-summer declination δ ≈ 18°:

H = 15° · (hour − 12)
sin(alt) = sin δ·sin φ + cos δ·cos φ·cos H
cos(Az)  = (sin δ − sin(alt)·sin φ) / (cos(alt)·cos φ)

Every frame a ray is cast from each rooftop back toward the sun. If that ray is blocked by a taller neighbour before it clears the block, the rooftop sits in shadow and contributes zero output for that instant — exactly how a real street canyon clips morning and evening yield on shorter buildings squeezed between taller ones. Narrower streets and taller, more uneven skylines increase mutual shading; a wide, uniform low-rise block keeps almost every panel in daylight.

Grid size / street width / height variance rebuild the city. Time of day and Run day cycle sweep the sun from sunrise to sunset. New city layout re-rolls the random building heights for the current settings.

Rooftop generating power Rooftop in shadow

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