PV Shade-Free Sun Angle from Row Pitch
The inverse of the row-spacing tile: with the row pitch fixed by the roof or lot, the lowest solar profile (elevation) angle the layout stays shade-free to, prof = atan(L sin tilt / (pitch - L cos tilt)). A 6.5 ft module at 30 deg tilt with 12 ft of pitch is clear down to a 27 deg sun. Compare it to the winter-design sun elevation. Assumes due-south rows and a level field.
Formula and source
profile_angle = atan( L x sin(tilt) / (row_pitch - L x cos(tilt)) ) (the inverse of pitch = L cos(tilt) + L sin(tilt)/tan(profile_angle)); valid when pitch exceeds the footprint L cos(tilt).
NREL / Sandia PV array row-spacing geometry solved for the profile angle, by name; the relations are first-principles trigonometry.
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