Winter Row Spacing on a Constrained Ground-Mount Site
A ground-mounted array is planned for a 40° latitude site with three rows of 2.0 m-long modules at 25° tilt. The back edge of each row is 1.8 m above grade, including clearance. The designer wants no direct shadow on the row behind between 9:00 and 15:00 on the winter solstice. At 9:00 on that date, the sun’s altitude is 14°; the 15:00 altitude is similar. The available land from the front of the first row to the back of the third row is 18 m. The client wants three rows to maximize capacity, and the installer has already ordered the racking. A simple rule of thumb of two row heights was used in the first layout, giving a pitch of 3.6 m. The designer must determine whether that pitch is adequate and whether three rows fit. Soil conditions and wind loading are not the issue here; shading and land use are.
1. Calculate the minimum row pitch needed to avoid shading at 9:00 on the winter solstice. Define what the pitch includes.
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The horizontal depth of one module row is D = 2.0 × cos 25° = 1.81 m. The shadow cast by the 1.8 m back edge at a 14° solar altitude is S = 1.8 / tan 14° = 1.8 / 0.2493 = 7.22 m.
The minimum front-edge-to-front-edge pitch is P = D + S = 1.81 + 7.22 = 9.03 m. Equivalently, the clear gap from the back of one row to the front of the next must be at least 7.22 m. The two-row-height rule giving 3.6 m is far too small and would cause severe winter shading.
2. Does the three-row layout fit within 18 m? Show the total depth and state what would have to change if it does not.
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For three rows, total depth = 2P + D = 2 × 9.03 + 1.81 = 19.87 m. That exceeds the available 18 m by 1.87 m, so the layout does not fit at the calculated no-shade pitch.
At the 18 m limit, the maximum pitch is P = (18 - 1.81) / 2 = 8.09 m. The allowable shadow length is 8.09 - 1.81 = 6.28 m, so the maximum back-edge height is h = 6.28 × tan 14° = 1.57 m. The current back edge is 1.8 m, so it must be lowered by about 0.23 m, or the design must accept some winter shading.
3. Give two design changes that preserve three rows and state a tradeoff of each.
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Change 1: reduce tilt from 25° to about 15°. The row depth increases slightly to 1.93 m, but the back-edge height drops, so the required pitch falls enough for three rows to fit. Tradeoff: lower tilt generally reduces winter energy yield and can increase soiling accumulation because rain sheds less effectively.
Change 2: lower the rack height or clearance so the back edge is about 1.57 m or less while keeping 25° tilt. This preserves the tilt but may reduce clearance for snow, vegetation, or airflow. A third option is to accept some shading at the December extremes, but that must be modeled and agreed with the client because winter production will drop.