Desert Solar Calc

Whups, Terrestrial Solar Will Suffice

Ted Bagg

[Originally posted Sat 25 Sep '04 on PeakOil.com: http://peakoil.com/fortopic1698-0-asc-15.html.  This calculation was suggested to me by the inventor Alvin Marks, ca. 1991.]

After looking up a few values and doing some calculations I find that we don't really need to develop extraterrestrial solar collectors, ground-based ones can completely replace the power presently supplied by petroleum, many times over. (This is almost a shame; I had a nifty scheme sketched out for reflecting sunlight from a squad of robot-assembled archimedean-spiral parabolic mirrors above the Sun's polar regions to Earth's Lagrangian points, thence beaming power to the Moon along an unstable chain of stations in the Earth's orbit and connecting to Earth via geosynchronous satellites...)

A. World Demand for Oil Expressed in Watts

The average barrel of crude is less directly related to the energy it contributes to humanity than its directly-combustible retail products, gasoline and kerosene. Conservatively rounding up the value I've come across, 5.8 million British Thermal Units per barrel [1,2], to one digit in condideration of this difficulty yields a fuzzy 6.0e6 BTU/bbl ~ 6.3 GJ/bbl (a BTU is 1054.35 joules [3 p F-308]). The imprecision will prove unimportant as the planet's potential solar power generating capacity so greatly outstrips projected demand.

In 2002, a respected oil administrator, Dr. Adnan Shihab-Eldin, reported and projected [4] worldwide demand for crude to be 76, 89, and 106 million barrels per day in 2000, 2010, and 2020. The foregoing equivalence then gives us the table (a watt is one joule per second; remember to convert days to seconds; a terawatt (TW) is a trillion watts):

2000: 5.6 TW
2010: 6.5 TW
2020: 7.8 TW.

B. Solar Power on the Moon

One of the nice things about putting solar collectors on the Moon would be no biosphere underfoot there to be killed by the shade (although darkening its brilliance would be another kind of crime). The lunar disk is a radiation aperture (ignoring the occasional lunar eclipse) of 3.14159 times the square of the 1738.3 km lunar radius [3 p F-137], or 9,492,909 square kilometers. And without an atmosphere, the sun's full intensity of more than 135 milliwatts per square centimeter [5] would fall on whatever collector we can devise. If we devise a collector covering the Moon's entire surface, we can multiply the two (remembering to convert kilometers to centimeters) and get an incident solar power of more than 12.8 PW (a petawatt is a thousand terawatts). Three orders of magnitude is a lot of leeway for supporting infrastructure.

C. Solar Power in Earth's Deserts

However, most of this infrastructure (geosynchronous satellites or skyhooks above deserts and oceans, permanent lunar bases, &c.) is unnecessary as we don't have to coat the Moon just yet. Comparison of terrestrial desert areas with solar irradiance values at corresponding latitudes shows that solar collectors in deserts would completely satisfy the projected demand listed above for energy from oil, with power to spare.
The CRC Handbook [3 p F-162] provides monthly surface solar irradiance values at various lattitudes, under the normative condition that clouds are absent. Here are the values for 45, 35, and 25 degrees of latitude, in kilocalories per square centimeter (per month):

Lat. / Month (Jan ... Dec)

45:	6.7	10.3	14.8	19.5	22.6	23.9	23.2	20.1	15.8	11.5	7.8	5.9
35:	10.7	14.0	17.6	21.0	23.0	24.0	23.4	20.9	17.0	13.2	9.7	7.7
25:	14.1	16.8	19.5	21.6	23.0	23.4	23.1	21.8	19.8	17.4	14.6	13.1

Adding up the rows gives the annual values at each latitude, in kcal / sq.cm. / year:

45 : 182.1
35 : 202.2
25 : 228.2

Three representative deserts at these latitudes are the Gobi, the Mojave, and the Sahara, with respective areas [6] in thousands of square kilometers:

Gobi:	1,040
Mojave:	35
Sahara:	8,420

There are 4184 joules in a kilocalorie. Converting likewise from years to seconds and multiplying each desert's area by the corresponding annual irradiance gives the total solar power it receives under the ideal condition (for power engineers, not desert life) that it never rains:

Gobi:	251 TW
Mojave:	9 TW
Sahara:	2,547 TW

There are about 15 million square kilometers of desert on our planet. The Australian and Arabian deserts alone are respectively 1.5 and 1.3 million [6]. Comparison of these figures with the table of projected demand for oil energy shows that we can retire oil as an energy source by converting a small fraction of desert sunshine into power.

References

1. http://www.eia.doe.gov/neic/infosheets/apples.htm  (I'd obtained a larger value of 6.2 million BTU / BBL from one of these two references when I wrote this originally and split the difference.  Now that both references give 5.8 million, 6 million is a conservative value for my purposes as it leads to a possible overstatement of the demand.)

2. http://www.uwsp.edu/cnr/wcee/keep/Mod1/Whatis/energyresourcetables.htm

3. CRC Handbook of Chemistry and Physics, 63rd Edition, The Chemical Rubber Company, Boca Raton, 1982.

4. http://www.fromthewilderness.com/free/ww3/042204_mazur_morgan_oil.html

5. [3 p F-161 (Corrected 19 Jun 2022)] Measured in the upper atmosphere. Later, more accurate meaurements made in space were slighly greater:  http://trs-new.jpl.nasa.gov/dspace/handle/2014/36577 p.7

6. http://home.alltel.net/bsundquist1/la6.html or McWhirter, ed., Guinness Illustrated Encyclopedia of Facts, Bantam Books 1981