Solar Array Row Spacing Formulas
Solar row spacing formulas: the solar altitude at the winter solstice, the shadow length, the row pitch for no shading and the ground coverage ratio.
The formulas
| To find | Formula |
|---|---|
| Solar altitude at noon on the winter solstice | α = 90° − latitude − 23.45° |
| Height of the top edge | h = L × sin β |
| Footprint of a row | F = L × cos β |
| Shadow length | d = h / tan α |
| Row pitch | P = F + d = L × sin(α + β) / sin α |
| Ground coverage ratio | GCR = L / P |
L is the length of the module row along the slope, β the tilt, α the solar altitude and latitude the site latitude in degrees for the northern hemisphere with the rows facing south. The design is for no shading at solar noon on the shortest day. Many designers choose a longer window, such as 9:00 to 15:00, which needs a larger pitch, and a site with trackers or a slope has its own rules. A smaller spacing is a trade of land against some shading loss that a yield study can price. The latitude, the tilt and the module size here are examples.
Worked example: a row of length 2.28 m at a tilt of 25° at latitude 30°
- α = 90° − 30° − 23.45° = 36.55°
- h = 2.28 × sin 25° = 0.9636 m, and F = 2.28 × cos 25° = 2.066 m
- d = 0.9636 / tan 36.55° = 1.3 m
- P = 2.066 + 1.3 = 3.366 m
- GCR = 2.28 / 3.366 = 0.6773
Pitch by latitude for the same row and a tilt of 25°
| Latitude | Solar altitude | Row pitch | GCR |
|---|---|---|---|
| 10° | 56.55° | 2.703 m | 0.8435 |
| 20° | 46.55° | 2.979 m | 0.7653 |
| 30° | 36.55° | 3.366 m | 0.6773 |
| 40° | 26.55° | 3.995 m | 0.5707 |
Frequently asked questions
Why use the winter solstice?
The sun is lowest then, so the shadows are longest. A spacing that clears the shadow at noon on that day clears it on every other day at noon.
What changes in the southern hemisphere?
The rows face north and the shortest day is in June. The formula then uses the latitude as a positive number with the same 23.45° term.
What happens if the rows are closer?
The back row is shaded in the early and late hours of the winter days. The loss depends on the bypass diodes and the string layout, so a yield study should price it.
Does a lower tilt help?
Yes. A lower tilt gives a lower top edge and a shorter shadow, so the rows can sit closer, at the cost of some yield per module.
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