Originally posted by: silverpig
11450 KW of power = 11450 KJ/s
Let's assume that this particulary area is pretty sunny, so it gets direct sunlight 65% of it's days and 12 hrs a day.
Even if you have your arrays tracking the sun, you won't get anywhere near 100% for 12 hours a day, even at the equator. At mid latitudes, even less, especially in the winter. And mechanical trackers will add considerably to your up front & recurring costs.
365 x .65 = 237.25 days/yr of direct sunlight
327.25 days/yr x 12 sunlit hours/day = 2847 hr/yr of good sunlight
2847 hr/yr x 3600 sec/hr = 10 249 200 sec/yr of good sunlight
10 249 000 sec/yr x 11450 KJ/s = 117 353 340 000 KJ/year from one acre of sunlit land
Ok, I must be missing something here. what is you conversion factor between "seconds of good sunlight/acre" and Kilojoules/year???
A decent estimate of solar irradiance on orbit is about 1358 W/m^2 (
Space Mission Analysis & Design, 2nd Ed.). Of this, IIRC, roughly 50% is available @ sea level at noon (need to confirm this). So, a plate perpendicular to the sun at noon at sea level would bring in about 679 W/m^2 or 679 J/m^2/s If you don't track the sun, this number is proportional to the cosine of the angle between teh collector normal on the sun.
1 acre = 4046.8726 m^2
So, 1 acre receives roughly 2748 KJ/s
Now, apply a reasonable figure for PV efficiency, say 24%
2748 KJ/acre/s * 0.24 = 660 KJ/acre/s
Efficiency of electrolysis of water is roughly 60% IIRC from previous ATOT debates on this subject. So the energy content of the hydrogen that this acre could produce is roughly:
660 KJ/acre/s * 0.6 = 396 KJ/acre/s
Let's use you highly optomistic time numbers above:
396 KJ/acre/s*10249000s = 4,100,000,000 KJ/acre/yr Still considerably better better then the ethanol numbers, but not nearly what you had come up with.
Now, 1 gallon of gas has an energy content of
115,000 btu/hr
1 btu = 1.0551 KJ
1 gallon gas = 121,331 KJ
So, 1 acre could potentially produce the energy equivalent of 33450 gallons of gas per year.
I found a consumer price for PV arrays of roughly $500/m^2, so 1 acre of PV arrays would be about $2.1 million + cost for tracking mounts, electrolysis system, & all the other infrastructure. Economies of scale will bring the PV cost down, so lets be optomistic and call it $2.1 million total capital investment/acre + some ongoing operating & maintenance cost.
So, not counting the ongoing cost, it would have to produce the equivalent of 1.25 million gallons of gas @ $2/gallon to recoup the capital costs. At 33450 gallons/year that would take roughly 31 years to recoup the capital investment, if you could turn it on and walk away ... ie. no operating costs at all. Of course this is a complete WAG, but it's probably in the ballpark.
Good luck finding investors.
By contrast, the infrastructure cost for ethanol is likely to be quite a bit lower, particularly because you don't need to replace all the infrastructure we didn't even consider here ... vehicles, distribution system, etc.