The formula

A row of height h = L·sin β casts a shadow of length h / tan α when the sun stands at elevation α. Projected onto the north–south line of the array (for a sun at azimuth difference γ from due south), the distance the next row must start behind the first is

pitch = L·cos β + L·sin β · cos γ / tan α

The calculator evaluates it every half hour from 10:00 to 14:00 solar time on the winter solstice and takes the largest value — the standard design window. Outside those hours the sun is so low that a small amount of row-to-row shading costs very little energy.

Steep off-grid rows need a lot of land

At 50° N and 70° tilt, a 2 m row is 1.9 m tall and needs about 8.6 m between front edges — a ground cover ratio near 23%. The same row at 35° needs roughly 6.5 m. That is why steep off-grid arrays are usually a single row, a wall, or a pole mount.

Ground cover ratio

Ground cover ratio (GCR) is module length divided by pitch. Utility-scale plants in mid-latitudes use 0.3–0.5 and accept some winter shading; a small off-grid system that lives on its winter output should keep rows shade-free, even if the ratio falls below 0.3.

Check the winter sun's real path over your site on the sun map — hills and trees to the south raise the effective horizon and the required spacing.