Monday, April 16, 2007

The Mathematics of Free Energy

The Mathematics of Free Energy

Some would note that I am a bit idealist about getting off the grid and Green energy. Some might say it's impossible and rather impractical. However, I believe that the mathematics behind it really "adds up". Here's a look at the arithmetic behind it all.

First the energy usage of the world per year: from ecoworld.com we have the following estimated energy usage in 1995:

316,000,000,000,000,000 BTU = 92,614,302,461,899 KW hrs

The math: The sun pumps out 1.3 KW hrs/m^2 of energy in outer space. The actual sunlight hitting the earth's surface varies throughout the year but let's say it averages 40% of the outer space value (which is a little on the low end). The earth has a land area of about 148,939,100 km^2. If we can harness that energy at 50% efficiency (high for existing technologies), then the following tells us how much energy we can catch in one hour on average.

1.3 (kW hrs/m^2)*1000000 (m^2/km^2)*148,939,100 (km^2) * .50 (efficiency) * .4 (amount reaching earth) = 38,724,166,000,000 kW hrs

More simple math shows that in only 2 hours the earth receives enough energy to power it for the rest of the year.

However let's say that we wished to avoid covering the whole earth in solar panels (after all I do like the green grass and nice trees...the minimum land area that we would need to produce to catch the energy required in one year would be:

Lmin = 92,614,302,461,899 KW hrs/(1.3 (KW hrs/m^2)*1000000 (m^2/km^2)* .50 (efficiency) * .4 (amount reaching earth) *24 (hrs/day)*365 (days/year)) = 40663 km^2

Thus with only .02 % of the earth's available land (or presumably oceanic) surface we could generate enough energy to totally power the earth for a year. Even if you factor in an extra 50% energy usage growth since 1995 and another 50% for future usage we would still only need to cover less than .05% of the earth in solar panels.

To put this in perspective, covering the otherwise unused Sahara desert (86,000,000 km^2) with solar panels would generate enough power each year to power 211 earths.

The proof is in the numbers, there is absolutely no reason to keep paying for oil, nuclear or anything else. Let's put up some solar panels, or windmills or invent something even better!

4 comments:

Ray said...

Yo Theo!

I did read your little article. As you know, I am in China. I think a lot people in US would think China is backwards when it comes to tech and being green. But consider these shocking points:

1. Majority of the houses in my small town has solar panels to heat water for shower, save for a week or two combined time in the year where no solar is available (one can remedy this with a backup electric heater), I have not paid a dime for hot water last year.

2. Most of the toilets here have two buttons, one for full tank and the other one for half tank. The reason is obvious, you don't need 1 liter of water if you just going #1. WHY HAVE I NEVER EVER HEARD OF SUCH THING IN USA??? If this becomes popular in USA, think of the amount of water we can save?

3. In a small town like mine, almost 1/4 of the vehicles on the road is electric bike/motorcycles, the rest are gas powered motorcycles and cars. Electric bikes are not allowed in bigger cities for various reasons but for getting around a small town, it is a beauty.

As far as solar panel goes, I am all for cover my entire lawn in Colorado with solar panels, just to show the HOA!

Unknown said...

Theo, I would point out what you omitted if I could only understand it. I respect your intellect. Grampa VR

Another_viewpoint said...

Theo:

The oil companies have now purchased most, if not all, of the solar panel manufacturing companies. The recently-developed high-efficiency, radically-lower-cost solar panel disappeared from the market almost as soon as it was announced, never to be heard of again, much like highly-efficient carburetors did when they were developed... All forms of alternative energy, when they would in any way cut into oil ("energy mega-conglomerate") company profits, are either suppressed, ignored or face such onerous governmental regulatory hurdles as to make them unworkable.

In other words, it's all about the money! As long as the monopolistic mega-money boys continue to get fabulously richer and more powerful from whatever energy sources that we invent or choose, those new energy sources and ideas will find favor, including government support and regulatory favor. But if there's any threat whatsoever to the income stream of Big Energy, those are ideas which will never find a viable market.

This is precisely analogous to how the obscenely-wealthy pharmaceutical companies first bought the FDA, then bought up all of the vitamin and herbal supplement manufacturers, and are right now on the verge of passing legislation that will give them total control over every type of health-stimulating product or service so that they alone will profit from EVERYONE that gets sick. The energy companies, already fully in control of all usable forms of government, including our military machine, can, already have, and will continue to do exactly the same.

(We could open up a fascinating can of worms here by looking at our President's past and present financial ties to the international oil industry - from whence he, and his personal fortunes, came - and how that affects our internal and external government policies, including our fascistic military intervention in other oil-rich countries under thinly-disguised false pretexts, but that topic is perhaps far too big for this forum...)

Even if we were to ignore those issues, we would still have the issues of distributing the electricity generated by that desert full of solar power cells. A single concentration of cells would mainly benefit those in the immediate proximity of the cell bank. Then as soon as we tie into the major energy-distribution grid to get that power somewhere other than a local area -- and that grid is an exceedingly fragile, notoriously hodgepodge network that poses great dangers to those who live near them, from the carcinogenic electromagnetic radiation hazards amongst others -- we're once again back into the monopolistic hands of the Big Energy boys, who control that network.

Perhaps what needs to be looked at instead is a realistic view of whether or not all of this enormous appetite that we have developed for energy is actually necessary and good. I for one am not the least bit impressed by anything that I see in the American energy-glutton lifestyle that has any redeeming value to it, from our insistence of never for a moment being in silence (Muzak in stores and elevators, iPods in our pockets) to our obscenely selfish needs to have "newer" and "different-looking" vehicles every year. Again, this is a topic that is far bigger than this forum would probably encompass comfortably, so I won't pursue it more fully right now.

The main point is that whenever we operate on untested foundational assumptions, our conclusions will inevitably be wrong. I would suggest that to try to find a "fix" for our energy problems while not sufficiently exploring the fundamental issues of whether or not we truly need "more energy" and what kind(s) of energy is (are) best (I would challenge most uses of electricity as being at very best unwise, if not downright foolish and, yes, even outright destructive) and other easily-missed foundational assumptions will be but to sew yet another arm onto a Frankenstein Monster in a frantic attempt to fix the unfixable, to prop up the unsupportable, to defend the indefensible, to feed the insatiable.

Theo V. said...

another_viewpoint:

yes, these are interesting points you bring up. I myself do like the conspiracy theory about the oil companies. I don't really disbelieve it. However, given that some forms of solar energy methods are so simple and easy to manufactur at home...why not dream about it :-) Perhaps there could be a sort of energy insurgency similar to the insurgency in Iraq. We could even have IED's...improvised energy devices! The most basic ones are merely pipes painted black. Stick a few on your roof, run some water thorugh them...and voila you've got free hot water!

But aside from all the possible conspiracies you are right in that this world is fading away. We don't live in a permanent world and so in reality working on Solar Energy is in the end a bit of a wash. However if we Glorify God along the way and are responsible stewards of the resources He gave us then I fail to see why we shouldn't give renewable a try.

As Thoreau said (in summary) we don't really need much to live. We surely don't need ipods and computers and cars. But sadly they are an artifact of our technology world. Perhaps they are contributing to the world's decay in many ways. I don't propose renewable energy as a way to feed our habits, I propose it as a way to be responsible with our resources and Glorify God.