PV Shade-Free Sun Angle from Row Pitch
With the row pitch fixed by the roof or lot, the lowest solar profile (elevation) angle the layout stays shade-free to.
Example
You enter
- Module slope length (ft) 6.5
- Array tilt (degrees) 30
- Available row pitch (ft) 12
You get
- Shade-free down to (profile angle) 27.0278
- Ground-coverage ratio 0.541667
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Scopeprof = 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 or tableprofile_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).
Source and editionNREL / Sandia PV array row-spacing geometry solved for the profile angle, by name; the relations are first-principles trigonometry.
Free accessThe row-spacing geometry and the ground-coverage-ratio definition are public NREL / Sandia relations and first-principles trigonometry.
What governsEstimate. AHJ and licensed professional govern.
API field namesmodule_length_ft, tilt_deg, row_pitch_ft, profile_angle_deg, gcr
- Shade angle the sun elevation at which adjacent rows just begin to shade; below it the array self-shadesNREL / Sandia
- Pitch constraint the pitch must exceed the module footprint L cos(tilt) or the rows overlapfirst principles
- Assumptions due-south rows and a level field; azimuth or slope is a separate correctionscope of this tile