Tilt, Shade, and the Winter Sun
A school at 34°N plans a 100 kW solar array and has one year of data from a test array: fixed tilt 34°, facing due south, 1,420 kWh per kW. A vendor proposes a 20° tilt, claiming an 8% gain because "the panels will face the sun more directly." The only nearby comparison is a neighbor's 20° array that produced 1,390 kWh/kW, but that site loses its first two morning hours to a 12 m building. A 2 m fence runs along the south edge of the proposed field, and the facilities manager wants row spacing that avoids shade at winter-solstice noon, when the noon Sun altitude is 32.5°.
1. Calculate the noon shadow length of the 2 m fence at winter solstice and at equinox, and use the results to recommend row spacing. Explain why winter rather than summer controls the design.
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Noon shadow length = height ÷ tan(altitude).
- Winter solstice, altitude 32.5°: 2 ÷ tan 32.5° = 2 ÷ 0.637 ≈ 3.14 m.
- Equinox, altitude 90° − 34° = 56°: 2 ÷ tan 56° = 2 ÷ 1.483 ≈ 1.35 m.
- Summer solstice, altitude 79.5°: 2 ÷ tan 79.5° ≈ 0.37 m.
Design consequence: winter solstice sets the spacing. At solar noon the shadow points due north, so rows should be separated north–south by at least 3.2 m for 2 m-tall rows, plus a margin for the fence and for mid-morning shading, when the Sun is lower and off-axis. Using equinox spacing (1.4 m) would leave the first row shaded for weeks around December. The fence should be placed so its 3.1 m noon shadow falls outside the first row, or the first row should be set back.
2. Evaluate the vendor's 8% claim. Identify the confound in the comparison and describe a fair test.
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The vendor's 8% claim is not supported by the evidence given.
The comparison is confounded: the neighbor's 20° array loses its first two morning hours to a 12 m building. Morning hours are lower-yield but not worthless, and a 15% shading loss could easily exceed the difference between 1,390 and 1,420 kWh/kW (about 2%). So the neighbor's lower output may reflect shade, not tilt.
There is also a physical reason to doubt a large gain. At 34°N, a fixed tilt near the latitude (roughly 30–35°) is close to the year-round optimum. A 20° tilt favors summer, when the Sun is high, and sacrifices winter, when the Sun is low and days are short. Annual totals often change by only a few percent over that range, and the direction depends on local cloudiness.
Fair test: two strings at the same site with identical modules and inverter, alternating tilt by season, or an hourly simulation using typical meteorological year data plus the actual horizon profile.
3. Predict the seasonal output pattern for the proposed array and explain why annual kWh alone is an incomplete basis for choosing a tilt.
Read the worked answer
Seasonal pattern: output should peak around late spring through summer and bottom in December–January. Sun altitude runs from 32.5° at winter solstice to 79.5° at summer solstice, and day length changes from about 10 to 14.5 hours at 34°. Clear-sky noon irradiance on a 34° tilt is relatively strong in winter because the panel faces the low Sun nearly head-on, but total daily energy is still lowest in winter because of short days and more cloud cover.
Why annual kWh alone is insufficient: a design optimized only for annual total may produce very little in winter, when grid demand or heating loads can peak. It also ignores summer heat derating, soiling, and the value of generation at peak times.
Recommendation: keep the tilt near 30–35°, use winter-solstice row spacing, and evaluate the design on monthly output and capacity factor, not just the yearly sum.