Energy per kW of panels: the shading cost of closer rows.
Energy per acre of rows: more panels on the same land.
Energy per kW of panels.
Energy per acre of rows.
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Rows of panels on the ground or a flat roof cast shadows on the rows behind them, most of all on winter mornings and afternoons when the sun is low. Spacing them farther apart avoids that, but uses more land. This page finds the spacing for no shade through the middle of the shortest day, and shows what closer rows or a lower tilt do to the energy from each panel and from each acre.
SolarPlan is a free, independent project, developed by enginerds from the University of Southern California and the University of Pennsylvania.
The common rule spaces rows so that none shades the next from 9 am to 3 pm solar time on the winter solstice. What sets the spacing is the sun’s angle measured across the rows (its profile angle), which is lowest at the ends of that window. A row of slant length L at tilt β, with the sun at profile angle ψ, casts a shadow reaching L·sin β / tan ψ behind its top edge; the rows sit that far apart plus their own depth, L·cos β. The ground coverage ratio is the slant length over the pitch.
| City | Latitude | Sun across rows | Coverage at 20° | at 25° | at 30° | Pitch at 25° |
|---|---|---|---|---|---|---|
| Seattle | 47.6° | 11° | 0.37 | 0.32 | 0.29 | 35.2 ft |
| San Francisco | 37.8° | 21° | 0.54 | 0.49 | 0.46 | 23.0 ft |
| Los Angeles | 34.1° | 24° | 0.59 | 0.54 | 0.51 | 20.8 ft |
| Phoenix | 33.4° | 25° | 0.60 | 0.55 | 0.52 | 20.6 ft |
| Denver | 39.7° | 19° | 0.51 | 0.46 | 0.43 | 24.4 ft |
| Dallas | 32.8° | 26° | 0.61 | 0.56 | 0.53 | 20.2 ft |
| Minneapolis | 45.0° | 14° | 0.42 | 0.38 | 0.34 | 30.3 ft |
| Chicago | 41.9° | 17° | 0.48 | 0.43 | 0.39 | 26.4 ft |
| Atlanta | 33.7° | 25° | 0.59 | 0.55 | 0.51 | 20.7 ft |
| Miami | 25.8° | 33° | 0.68 | 0.64 | 0.61 | 17.8 ft |
| New York | 40.7° | 18° | 0.50 | 0.45 | 0.41 | 25.2 ft |
| Boston | 42.4° | 16° | 0.47 | 0.42 | 0.39 | 26.9 ft |
Rows closer than the winter rule lose some energy to shading, mostly in winter, and some sky light at every hour, but put more panels on each acre. Where land is the limit, closer rows usually win; where panels are the limit, the winter rule or wider is better. A lower tilt does both: each panel gives up some energy, but its shorter shadow lets the rows close up. Large US plants typically use coverage ratios of 0.40 to 0.50 for fixed tilt and 0.25 to 0.40 for single-axis trackers (Berkeley Lab, 2022).
Energy is computed hour by hour over a typical year with the model PVWatts version 8 uses (National Laboratory of the Rockies), including its row-shading model: the shadow of each row on the next, with the strings wired along the rows, and the sky and ground light the rows block. The field stands for a large array of 20 rows. Energy per acre counts only the rows: modules at their rated efficiency times the coverage ratio. Roads between blocks, inverter pads, fences and setbacks add land. For comparison, Berkeley Lab measured US plants built through 2019 at a median 0.35 MW DC per acre of array area for fixed tilt and 0.24 for trackers. Level ground is assumed: rows on a slope facing the sun can sit closer, and on a slope facing away need more room.
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