From this badscience thread and particularly this post, a quick set of rough calculations to see if solar power (wind, solar panels, wave, biofuels, etc) is sufficient to supply our energy needs.
Total radiation arriving outside the atmosphere (ie, at all wavelengths) is 1368Watts/m2 (Refs: NASA).
Assume (?) that only radiation reaching the ground is useful (as I understand it... winds etc are caused by ground heat rather than direct heating).
Radiation at ground (refs squ1.org, Wikipedia, Encyclopedia of Earth) appears to be less than half of this (reflected by atmosphere, clouds) but it's not entirely clear.
So:
Approx 500W/m2 (after weather) on the flat plane facing the sun
x Total area facing sun = pi * radius2 = ~100 million sq km = 1014 m2
-> 5x1016 Watts total supply of solar energy at ground facing sun.
As the radiation gathered is on a flat plane, we need wider surfaces on the ground where the sun arrives at an angle in order to cover the same area in that plane.
Multiply by the amount of surface on the globe (~5x1014 m2) vs the surface of the plane (~1014 m2) = x5. Allows for night time.
Allow for inefficiency in gathering and moving the energy: solar photoelectric cells are currently between 12-40% (wikipedia).
Assume 50% overall (including transport) for future technologies - assuming direct collection. Wind and wave may be different.
Allowing for incidence and efficiency, actual total energy harvestable is
5x1016 Watts x 50% x 1/5and requires
= 5x1015 Watts total global harvestable solar energy
@ 500W/m2 x 50% x 5
> 50W/m2 average harvestable solar energy across globe and over a day
Current use in rich countries is ~4-5 Tonnes of oil equivelent per person per year (BERR and Economist's "Pocket World in Figures")
= 200 GJ per person per year
-> 200 x109 J/30 x107 seconds/year (Joules = watts x time)
-> 700 Watts per person.
-> 14 m2 per person.
Naively assuming 10 billion people world population using only the current 'rich country' scaling (ie ignoring air conditioning, etc in emerging warmer countries):
1010 people x 700 Watts
= 7 x 1012 watts total global demand
From a BBC article demand by 2030 (ie not 'final demand') will be 15,000 million tons of oil equivelant per year global total
-> 1.5 x1010 toe @ (40GJ/toe = 4 x1010 J/toe)
-> 6 x1020 J/year / 30 x107 seconds/year
-> 2 x 1012 watts total global demand in 2030
This article, from UNDP data, predicts 102 TW demand by 2050:
= 1014 watts total global demand.
Naive = 7x1012 watts / 50 W/m2 = ~ 1011 m2 = 105 km2
Predicted = 1014 watts / 50 W/m2 = 2 x 1012 m2 = 2x106 km2
Total earth's surface = ~5x1014 m2
-> 0.02% to 0.4% of the earth's surface.
Sahara desert is about 9 million square kilometers.
Theoretically possible; living space can be beneath (use roofs etc) and related infrastructure (power conversions, transport, etc) as well. Food crops need sunlight too. Could do with working out how much material and equipment that coverage needs.
It seems to be on the edge of significant where - ignoring manufacturing the gathering equipment - just the presence of it may have an environmental impact. Perhaps a good one - Sahara desert is about 9 million square kilometers. [an error occurred while processing this directive]