Is Solar Enough?

(c) 2015 by Barton Paul Levenson

All human energy use--expressed in terms of power, energy per unit time--is about 18 terawatts. That's 1.8 x 10¹³ watts, 18 trillion Joules per second. Can we get all that from the Sun?

Let's find out. The Solar constant out where we are is about 1,360 watts per square meter (Kopp and Lean 2011). Earth gets sunlight on its cross-sectional area (π R²). The Earth's mean radius is 6,371,010 m² (Lodders and Fegley 1998, p. 128), so its cross-section is 1.27517 x 10¹⁴ m², and we take in 1.734 x 10¹⁷ Watts. Nice! But that's not the whole story.

Earth's surface area is that of a sphere--4 π R². That amounts to 5.10066 x 10¹⁴ m², so we're getting 340 W m^-2. But that's at the top of the atmosphere. Earth's albedo is about 0.3, so we reflect 30% of that right back out into space, leaving us with 238 m^-2. And not all that gets through to the ground, because the air absorbs some. Mean annual ground surface illumination is 161 Watts per square meter (Trenberth et al. 2009).

And putting solar panels or mirror/boiler farms on the ocean would be difficult. Only 29.2% of Earth's land surface is actually land! And some of that we need for other things, like cities, agriculture, forests, rangeland, etc. Only 30% or so is unliveable.

And Solar panels aren't perfectly efficient, and neither are mirror/boiler farms. Average efficiency nowadays is only 15% or so.

So in the end, all we can get from Solar power is about 161 x 5.1066 x 10¹⁴ x 0.292 x 0.3 x 0.15. And that only amounts to only 1.079 x 10¹⁵ Watts. That's only sixty times world human energy use. Darn!

Wait a minute. That means if we only used 1.7% of the Earth's bare rock and sand for Solar power, we'd get all the energy humanity needs. Hey, that's a good idea!

References

Kopp G, Lean JL 2011. A new, lower value of total solar irradiance: Evidence and climate significance. Geophys. Res. Lett. 38, L01706-L01712.

Lodders K, Fegley B Jr. 1998. The Planetary Scientist's Companion. NY: Oxford Univ. Press.

Trenberth KE, Fasullo JT, Kiehl J 2009. Earth's Global Energy Budget. Bull. Am. Meteorol. Soc. 90, 311-324.