Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 209
incoming sun
same input
5 panels, flat
same panels, tilted; shadows
3 panels, tilted; catching all
Figure 13.12: On a fixed piece of l<strong>and</strong> receiving a fixed amount of sunshine at a slant angle, the amount of energy received is independent
of whether the panels are flat or tilted. Just tilting the flat panels up (middle) results in self-shading. It makes the most sense to tilt <strong>and</strong>
separate panels (right), one benefit being that fewer panels are needed to collect the same incident energy.
be about 30% over the flat, upward-facing panel. Concentration schemes
make less sense away from such regions.
Figure 13.13: Solar potential for tracking
panels, facing directly toward the sun’s position
<strong>and</strong> requiring a cloud-free view of the
sun (concentrating collectors). The graphic
is presented in units of kWh/m 2 /day, the
break-points between colors running from
4.0 to 7.5 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.
Stepping back, let’s appreciate a few big-picture facets from these maps.
First, numbers tend to be in the general neighborhood of 150–300 W/m 2 .
Burn this range in—it’s a useful context. Second, the variation from the
most solar-intense places in the contiguous U.S. to the weakest areas 51 is
not more than a factor of two on an annual basis. This is astounding. The
Mojave desert in California <strong>and</strong> the rain-forest Olympic Peninsula in
Washington would seem to be practically day vs. night with respect to
solar illumination. But not so much: only a factor of two. 52 Part of what
this means is that if storage over annual timescales could be realized,
solar power would become practical almost everywhere. 53
51: . . . ignoring Arctic-leaning Alaska
52: The northwest benefits from long summer
days when clouds are also less likely.
53: This would require huge storage capacity:
giant batteries, for instance.
Box 13.2: Hours of Full-Sun Equivalent
A useful take-away comes from the native units used in the three
maps presented here: kWh/m 2 /day, as opposed to our preferred
W/m 2 . Although they look different at a glance, kWh is a unit of
energy, so kWh/day is a power, just like W. Since a kilowatt is 1,000 W
<strong>and</strong> a day is 24 h, 1 kWh/day is 1,000 Wh/24 h = 41.67 W. 54 So we
can multiply 6 kWh/m 2 /day by 41.67 to get 250 W/m 2 .
54: The hours in numerator <strong>and</strong> denominator
cancel, since the kilowatt-hour is kW
times hours.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.