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#1
07-17-2012, 04:11 PM
 PhantomPholly Senior Member Join Date: Aug 2008 Location: Atlanta Posts: 2,249
Solar calcualtions - is this right?

Had a curious thought the other day about exactly how much surface area it would take to power the U.S. with solar (assuming trivial things like grid storage were solved, etc.), and was wondering if someone would check my math.

Assumptions (almost everything "rounded" to make math easier):
U.S. Electric Consumption - just a bit over 10,000,000 MW*hrs/day
A typical cheap solar panel - if you round the size up, it looks like 18 square feet would be about 250 watts; doubling that to 36 square feet would therefore be about 500 watts
Average insolation about 2 hrs / day
SWAG (pure assumption) - the sum of all rooftop surface area including homes, offices, warehouses, factories, etc. averages about 1,000' sq. per capita
300 million residents * 1,000' sq. = 600,000,000,000' sq total roof area

Calculations:
36 square feet = 500 watts * 2 hrs/day = 1KW*hr/day
36 * 1,000 = 36,000 square feet = 1MW*hr/day
If we covered all 60,000,000,000' sq we could generate (theoretically/approximately):
60,000,000,000' sq / (36,000' sq/MW*hr/day) = 16,666,666 MW*hr/day, or roughly about 60% more power than we use.

Is that correct? Yes, I know that insolation is less up north but am really just looking for order-of-magnitude of land use needed. If this is right, we (theoretically) wouldn't need to set aside ANY land just for solar; it could all (or nearly all) be done on existing rooftops without even improving efficiency.
#2
07-17-2012, 04:44 PM
 Ziggythewiz Senior Member Join Date: May 2010 Location: Houston Posts: 3,747
Re: Solar calcualtions - is this right?

2 hrs per day is rather low. 4 is typically used. I think anything but major cities could easily be powered by rooftop PV. You'd run into transmission issues getting it to all the skyrises, but maybe no worse than now.

My house would only need to cover 1/3 of the southish face to meet my needs, and that's with the old 6% panels. With the ~20%ers prevalent now I could power half my block.

I know at one time it required ~100 sq miles, but that was for solar collectors, not PV. I don't know why most are hung up on low efficiency molten salt rigs now instead of that.
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#3
07-17-2012, 11:03 PM
 Salty9 Senior Member Join Date: Jul 2009 Location: 42.596N 122.688W Posts: 747
Re: Solar calcualtions - is this right?

As a SWAG(Thanks Phantom), if we cut our energy waste in half, we could probably export oil. No one since Carter talks conservation. Energy companies are playing potlatch with 300,000,000 years of carbon.
#4
07-17-2012, 11:11 PM
 Ziggythewiz Senior Member Join Date: May 2010 Location: Houston Posts: 3,747
Re: Solar calcualtions - is this right?

You call it waste, most call it use. Americans aren't that interested in cutting usage. We like our way of life. What Phantom shows is that even using PV we could renewably power everything we want without 'wasting' land to power generation.
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#5
07-18-2012, 02:33 AM
 Jan Senior Member Join Date: Oct 2009 Posts: 863
Re: Solar calcualtions - is this right?

You can very easliy calculate the nett. energy with this website:

http://re.jrc.ec.europa.eu/pvgis/apps4/pvest.php#

It's only for Europe and Africa, but maybe you can find a prety similar place. It takes the avarage solar radiation per month into its calculation. Including latitude, cloudcoverage and altitude. And you can position the panels as you wish. Even with a tracking option, and see the gain.
#6
07-18-2012, 08:01 AM
 ricklearned Senior Member Join Date: Mar 2012 Location: Southern California Posts: 301
Re: Solar calcualtions - is this right?

Quote:
 Originally Posted by PhantomPholly ........SWAG (pure assumption) - the sum of all rooftop surface area including homes, offices, warehouses, factories, etc. averages about 1,000' sq. per capita 300 million residents * 1,000' sq. = 600,000,000,000' sq total roof area Calculations: 36 square feet = 500 watts * 2 hrs/day = 1KW*hr/day 36 * 1,000 = 36,000 square feet = 1MW*hr/day If we covered all 60,000,000,000' sq we could generate (theoretically/approximately): 60,000,000,000' sq / (36,000' sq/MW*hr/day) = 16,666,666 MW*hr/day, or roughly about 60% more power than we use.......
I think the SWAG of 1000 sq ft per capita could be off. It doesn't account for how many people live or work in a multistory building. Although your calculations suggest that it would take about 500 sq ft per parson to generate enough electricity to power the US.

Also I don't know what the current cost is per sq ft but 8 years ago it would have cost \$30.000 for that amount of solar per person. ( 10 watts/sq ft. panel cost \$6/sq ft)
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Last edited by ricklearned; 07-18-2012 at 08:08 AM.
#7
07-18-2012, 08:30 AM
 Ziggythewiz Senior Member Join Date: May 2010 Location: Houston Posts: 3,747
Re: Solar calcualtions - is this right?

All this should be done in meters. 1 m^2 = 10.76 ft^2

1 m^2 gets an average of 1 kW of sunlight. Average hours of full sun for US is 4, so a typical 20% efficient panel of 1 m^2 (most are 1-1.5 m^2) would make .8 kWh / day.

Per capita consumption ~ 13 MWh / year = 44.5 m^2 (1/4 of Phantom's estimate)

Would cost around \$9,000 per person (for the PV)
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#8
07-18-2012, 08:38 AM
 PhantomPholly Senior Member Join Date: Aug 2008 Location: Atlanta Posts: 2,249
Re: Solar calcualtions - is this right?

Quote:
 Originally Posted by ricklearned I think the SWAG of 1000 sq ft per capita could be off. It doesn't account for how many people live or work in a multistory building. Although your calculations suggest that it would take about 500 sq ft per parson to generate enough electricity to power the US.
Yeah, I picked it moderately arbitrarily. 1,000' sq. is 20x50, or a typical double-wide trailer. Many share, or live in multis like you mentioned, but then there are also enormous warehouses, factories, etc. Just as an example, I once worked in a steel mill that was 3/4 mile long by 1/2 mile wide - and it was one of the smaller mills in the area. There's probably been a government study somewhere that gives the total coverage of the ground by buildings.

In any event, this was just a back-of-the-napkin attempt simply to determine the scale of the project.

Quote:
 Also I don't know what the current cost is per sq ft but 8 years ago it would have cost \$30.000 for that amount of solar per person. ( 10 watts/sq ft. panel cost \$6/sq ft)
Definitely not economical today. Cutting the area in half as you suggest and then cutting it in half again per the poster who pointed out we get 4 hrs rather than 2 of insolation per day, using my example cells it would cost around \$15 trillion for the panels alone (using the panels I linked above @\$250/panel full retail price).

Sayyyyyyyy.... If we'd spent our \$15 trillion in debt on solar panels instead of programs that simply teach more people to be government-dependent, we could all be enjoying free energy now! The jerks...
#9
07-18-2012, 08:44 AM
 PhantomPholly Senior Member Join Date: Aug 2008 Location: Atlanta Posts: 2,249
Re: Solar calcualtions - is this right?

Quote:
 Originally Posted by Ziggythewiz All this should be done in meters. 1 m^2 = 10.76 ft^2 1 m^2 gets an average of 1 kW of sunlight. Average hours of full sun for US is 4, so a typical 20% efficient panel of 1 m^2 (most are 1-1.5 m^2) would make .8 kWh / day. Per capita consumption ~ 13 MWh / year = 44.5 m^2 (1/4 of Phantom's estimate)
I was doing it based on the panels in the link, which probably aren't that efficient. Idea was to pick cheapest price per watt and figure out how many square feet would be needed to cover.

But thanks everyone for their help - it seems to bear out my conjecture that it is likely that we could power the country just using existing rooftops.
#10
07-18-2012, 09:02 AM
 ricklearned Senior Member Join Date: Mar 2012 Location: Southern California Posts: 301

It was a good WAG, and I agree if we spent a little more on renewable sources of energy we would be further ahead.
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