Energy and Human Ambitions on a Finite Planet, 2021a

10 Renewable Overview 168
Treating Earth as a sphere of radius R, it has surface area 4πR 2 , but
the sun doesn’t “see” the whole surface at once. In fact, from the
vantage point of the rays of sunlight intercepting Earth, what matters
is the projection of Earth, 14 which just looks like a disk of area πR 2 .
Averaging the solar input across the entire planet therefore reduces
the 1,360 W/m 2 by a factor of 4 to 340 W/m 2 .
Not all the sunlight arriving at the top of the atmosphere makes it to
the surface, so in practice, a typical location will receive an average 15
of about 200 W/m 2 . This is a number that comes up often as a typical
insolation, so is worth remembering.
14: Imagine taking a picture of a sphere situated
across the room. The area the sphere
takes up on the photo is πR 2 ,notthetotal
curved surface area of 4πR 2 . See also
Fig. 9.6 (p. 144).
15: ...averaging over day, night, sun angles,
<strong>and</strong> weather conditions.
Clouds <strong>and</strong> ice (mostly) reflect almost 30% of incoming sunlight, leaving
123,000 TW to be absorbed by l<strong>and</strong>, water, <strong>and</strong> atmosphere in various
forms (see Table 10.2). Virtually all of the energy hitting the surface
goes to direct thermal absorption, 16 much of which then flows into 16: That is, heating (see Example 10.3.2);
evaporation of water—the starting point of the hydrological cycle. A
tiny portion of the absorbed energy gives rise to wind, some of which
will drive waves. An even smaller portion contributes to photosynthesis
<strong>and</strong> supports essentially all life (biology) on the planet. And finally, a
tiny fragment of the absorbed energy drives ocean currents. Table 10.2
tracks where the incoming solar energy goes, in several stages, also
listing non-solar geothermal <strong>and</strong> tidal contributions. For comparison,
the current energy scale of human activity is approximately 18 TW, while
human metabolism, 17 is about 0.8 TW.
note that solar panels could intercept part
of this energy flow.
17: Recall Ex. 5.5.2 (p. 74). 100 W per person
times 8 billion people is 800 GW, or 0.8 TW.
Table 10.2: Earth’s energy input budget. Symbols ⊙, ⊕, <strong>and</strong> ☾represent Sun, Earth, <strong>and</strong> Moon, respectively. The second group breaks out
the solar input into three pieces that add to the total in the row above. The third group all comes from absorbed energy—mostly at Earth’s
surface. The last group is not from radiant solar energy, so that percentages are in parentheses as they do not belong to the solar budget
[63–65].
Category Power (TW) % solar source Comments
total solar input 174,000 100 ⊙ the next 3 inputs come from here
surface absorption 83,000 47.9 ⊙ heats surface; evaporates H 2 O, powers life, wind, etc.
reflection to space 51,000 29.3 ⊙ from clouds, ice; uncaptured energy
atmos. absorption 40,000 22.6 ⊙ heats atmosphere, some to wind
evaporation 44,000 25.4 ⊙→⊕surf. from surface absorption; hydrological cycle
wind 900 0.5 ⊙ absorp. from absorptions above, also makes waves
photosynthesis 100 0.06 ⊙→⊕surf. fuels biology (life) on the planet
ocean currents 5 0.003 ⊙→⊕surf. moves water around
geothermal 44 (0.025) ⊕ half original heat, half radioactive decays
tides 3 (0.0018) ☾, ⊙ gravitational; mostly from Moon, some from Sun
Example 10.3.2 Solar Heating: How much would a black table 18
warm up sitting in full sun for ten minutes?
18: . . . parameters defined below
A nice round-number approximation of full overhead sunlight is that
it delivers 1,000 W/m 2 to the ground. If we situate a table whose top
surface area is 1 m 2 , has a mass of 20 kg, <strong>and</strong> a specific heat capacity
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.