Shading, Setbacks, and Capacity on a Two-Plane Roof
At 38.5° N, a homeowner wants 8 kW of PV. The house has a 5/12 south plane measuring 34 ft along the ridge by 14 ft from eave to ridge, and a similar west plane. The AHJ enforces fire-service setbacks of 3 ft at the ridge and 18 in. at both gable ends and the eave. A 40 ft tall deciduous maple stands 45 ft south of the south eave; the array's collector height will be about 12 ft above grade. The client's site report, generated from satellite imagery with a modeled tree and horizon, predicts a 9% annual shading loss on the south plane. On a December site visit, a handheld shade measurement at 9:30 a.m. shows the south plane at roughly 40% of the irradiance of an unshaded reference cell. Modules are 400 W, 78 × 39 in. The client wants 8 kW with the shortest possible payback; the utility tariff nets monthly, so every annual kWh is worth the same, but winter kWh are not worth more than summer kWh.
1. Reconcile the 9% annual shading figure with the 40% December reading, and explain what that means for equipment selection.
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Both numbers can be correct because they answer different questions. The annual figure is an irradiance-weighted integral: December mornings are a small share of annual energy, and a 40% loss in a low-sun, low-irradiance hour barely moves the annual total. The 40% reading is a snapshot of an hour that matters for string behavior, not for annual yield.
That distinction drives the equipment choice. The shade event hits the whole south plane at the same time, so a dual-MPPT string inverter does not help - two MPPTs only pay off when strings see different orientations or persistent, dissimilar shade. The relevant options are:
- Module-level power electronics on the south plane so shaded modules do not drag string current down, which matters disproportionately in the morning hours when the string would otherwise operate below its MPPT window.
- String architecture with the shaded modules grouped, if partial array - the shaded group on its own MPPT and the clear group on another.
- Move capacity to the west plane, which carries no tree shade, and accept the lower plane-of-array irradiance.
Also check the DC/AC ratio: on an unshaded plane, oversized DC clips at midday, but a shaded south plane rarely clips, so a higher ratio is tolerable there. The annual 9% is the number for the payback spreadsheet; the December snapshot is the number for deciding hardware.
2. Determine how many modules actually fit on the south plane after setbacks, and compare that to the 8 kW target.
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Work along the slope first. The plane is 14 ft from eave to ridge. Remove 3 ft at the ridge and 18 in. (1.5 ft) at the eave: 14 − 3 − 1.5 = 9.5 ft = 114 in. of usable slope length.
Along the ridge: 34 ft minus 18 in. at each gable = 34 − 3 = 31 ft = 372 in.
Orientation choice:
- Landscape (39 in. up-slope, 78 in. along ridge): 114 ÷ 39 = 2 rows, with 78 in. used and 36 in. left over; 372 ÷ 78 = 4 modules per row. 2 × 4 = 8 modules = 3.2 kW.
- Portrait (78 in. up-slope, 39 in. along ridge): only one row fits in 114 in.; 372 ÷ 39 = 9 modules = 3.6 kW.
So the south plane tops out near 3.2–3.6 kW, well under the 8 kW target, and portrait leaves a 36 in. band of unusable roof at the ridge that also complicates rail layout. The realistic layout puts about 9 modules on the south plane and the rest - roughly 11 modules - on the west plane, with a separate string and MPPT for each plane. Tell the client this before the contract is signed; an 8 kW promise based on gross roof area is a promise the setbacks will not keep.
3. The client asks whether the tree can simply be removed later. What growth and site factors should be documented in the site assessment?
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The assessment should record the species, current height, trunk position relative to the array, and a growth projection. A 40 ft maple can add roughly 1 ft per year in height on a good site, so in 20 years the top is at 60 ft and the shadow elevation angle grows correspondingly. Current geometry: tree top 40 ft, array collector at 12 ft, horizontal separation 45 ft, giving a shadow angle of arctan(28 ÷ 45) ≈ 32°. Winter solstice noon sun altitude at 38.5° N is 90° − 38.5° − 23.5° = 28°, so the shadow already reaches the array at the most valuable winter hour - and it will get worse regardless of leaf drop, because the deciduous canopy is bare in exactly the months the geometry is worst.
Document ownership. If the tree is on the neighbor's lot, removal is not the client's decision and local tree ordinances may protect it; if it is on the client's lot, record an estimated removal cost and permit requirement in the proposal. Either way, do not model future production on an assumed removal. Note interfering structures or future construction on adjacent parcels, and state the shade assumption explicitly in the production estimate so the client sees the basis for the number rather than a single annual kWh figure.