Seasonal Solar Tilt Optimizer (2D)

Site & Schedule

Latitude φ 40°N

Tilt-adjustment strategy

Manual tilt (fixed mode) 40°

Day of year Day 80 — Mar 21

Live Readout

Solar-noon elevation

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Panel tilt (selected)

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Incidence angle

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Irradiance factor

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How it works

The sun's declination on day n of the year (Cooper's equation) is:

δ(n) = 23.45° · sin( 360°/365 · (284 + n) )

At solar noon, for a site at latitude φ, the sun's elevation angle and the beam-tilt angle that points a panel straight at the sun are:

Elevation  α = 90° − |φ − δ(n)|
Optimal tilt β* = φ − δ(n)   (clamped to 0°–90°)

Any panel actually mounted at tilt β misses the sun by an incidence angle θ = |(φ − δ(n)) − β|, and the fraction of direct beam it collects follows Lambert's cosine law:

Irradiance factor = cos(θ), clipped to 0 when θ ≥ 90°

Fixed — one tilt held all year (the classic "tilt = latitude" rule of thumb, overridable with the manual slider).
Seasonal (4×/year) — re-aimed once per quarter at that quarter's mid-point optimum.
Monthly (12×/year) — re-aimed at the start of every month.
Continuous tracking — re-aimed every single day, so θ = 0 and the factor stays at 1.0 — the theoretical ceiling every other schedule is measured against.

This 2D companion replaces the 3D scene with three linked panels: a side-view sun-elevation diagram (drag it left/right to scrub the day of year, just like rotating the year forward), an annual irradiance-factor curve for all four schedules at once, and a bar chart of each schedule's annual yield relative to continuous tracking — the same trade-off real PV installers weigh between a cheap fixed rack and an expensive tracking mount.

drag the sky diagram ↔ to scrub the day