Rows of trackers turn from east to west to face the sun. Packed tightly, the rows shade each other at dawn and dusk unless they back off ("backtracking"). Change the row spacing and watch the yield per panel and per hectare of land trade off against fixed-tilt panels.
Rows seen from the south end. Yellow lines: sun rays; red parts of a panel: shaded by the neighbouring row (found by ray tracing, not by the formula).
Each button integrates whole years with the current latitude and cloud cover (12 representative days, 6-minute steps).
The science
Sun position. With declination δ = 23.45° sin(2π(284+n)/365), hour angle h = 15°(t − 12) and latitude φ the unit sun vector (east, north, up) is (−cos δ sin h, sin δ cos φ − cos δ sin φ cos h, sin δ sin φ + cos δ cos φ cos h). Solar time is used (no equation of time or longitude correction).
Tracking angle. A horizontal north-south axis lets the panel normal tilt east or west, n = (sin θ, 0, cos θ). The incidence is smallest when tan θ = seast/sup, giving cos(AOI) = √(1 − snorth²). Rotation is limited to ± the maximum angle.
Row shading. In the east-west plane the sunlight arrives at angle ψ from vertical. A panel of width w stops a beam of width w cos(θ − ψ), while the next row is P cos ψ away across the beam, with P = w/GCR (ground cover ratio). The shaded fraction is 1 − cos ψ / (GCR cos(θ − ψ)), floored at zero. Perfect sun-following (θ = ψ) is shade-free only while cos ψ ≥ GCR.
Backtracking. When cos ψ < GCR the tracker turns away from the sun just enough that the shadow edge touches the neighbour's lower edge: θ = ψ − sign(ψ)·arccos(cos ψ / GCR). The panel loses a little cosine in return for no shadow; the net gain is largest at high GCR.
Irradiance. Direct beam from the Hottel clear-sky transmittance, diffuse from the Liu-Jordan relation, both reduced for clouds so that the global total follows the Kasten-Czeplak factor 1 − 0.75 c3.4; this is a simple textbook model with illustrative cloud behaviour, not a weather file. On the panel: G = DNI cos(AOI)(1 − shade) + DHI (1+cos β)/2 + ρ GHI (1−cos β)/2. Neighbouring-row shading of the diffuse light and of the ground-reflected light is ignored.
What is simplified. Rows are infinitely long and flat ground is assumed (no terrain-following), solar time is used, the cell temperature and electrical model are left out (the numbers are sunlight on the panel, in kWh/m², which divided by 1 kW/m² gives peak-sun hours or kWh per kWp before system losses), and the fixed-tilt array is shaded with the same GCR, facing the equator at the chosen tilt. Numbers are for a clear-to-partly-cloudy idealised site, not a forecast for any real plant.