Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 208
the sky near the equator, so panels there should lie flat. 48 But at high
northern latitudes, the sun is lower toward the southern horizon, so the
panels should tilt up to best face the sun. Tilting at an angle equal to the
latitude is the best compromise, as Figure 13.10 illustrates.
sun view sun view side view
flat panels titled panels titled panels
48: . . . point mostly up
Figure 13.10: The left globe shows the sun’s
view of 21 panels of the same size sitting
flat on the ground at their various sites. In
the middle globe, the panels are all tilted
up toward the equator. Notice the improvement
in how much panel area is visible to
the sun by doing this—especially at higher
latitudes. At right is the side view, from
which it is easier to appreciate why the best
tilt angle is equal to the site latitude.
Figure 13.11: Solar potential for flat panels
tilted to latitude, oriented south—relevant
to PV panel installations. The graphic is presented
in units of kWh/m 2 /day, the breakpoints
between colors running from 3.0 to
6.5 kWh/m 2 /day in steps of 0.5. Annotations
are added once in each color b<strong>and</strong> (in
black or yellow) to indicate the equivalent
measure in W/m 2 [87]. From NREL.
Tilting panels toward the equator at an angle equal to site latitude
optimizes annual yield, <strong>and</strong> the results are shown in Figure 13.11. Note
that the numbers in Figure 13.11 are not strictly insolations, since that’s
defined as what reaches flat ground. In this case, the area (square meters)
is that of the panel, not of the l<strong>and</strong>.
The fact that the numbers in Figure 13.11 are higher than in Figure 13.9 is
not to say that the l<strong>and</strong> offers more solar energy if the panels are tilted:
just that an individual panel can get more light. But in this case, panels
need to be spaced out to avoid shadowing, 49 as Figure 13.12 illustrates.
Some applications need to track the sun, like those that concentrate
solar power, <strong>and</strong> only work when the sun is not blocked by clouds. 50
This brings us to Figure 13.13, showing the potential per square meter of
collector (mirror or lens) used for the concentration (the topic of Section
13.8.2). The same pattern holds, in that the desert southwest dominates.
But a look at the numbers indicates that the cloudier regions are not
much better than just a flat panel facing upward (as is the case for Figure
13.9). In the southwest, where skies are often cloud-free, the boost can
49: . . . which can be more devastating than
just fractional area blocked, due to series
arrangement of cells in panel modules
50: Photovoltaics still produce 10–50% of
full capacity under cloudy skies during daylight
hours, depending on how thick the
clouds are: daylight still means photons.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.