Tuesday, March 26, 2013

How much solar capacity would be required to replace the energy output we get from oil?

A while ago I was watching a talk by Elon Musk, founder of PayPal, SpaceX and Tesla, he was talking about a bunch of things but something he said struck me;

I think it is helpful to use the analytical approach in physics, which is to try boil things down to first principles and reason from there, instead of trying to reason by analogy. The way this applied to rocketry was to say, okay, well, what are the materials that go into a rocket, how much does each material constituent weigh, what's the cost of that raw material, and that's going to set some floor as to the cost of the rocket. That actually turns out to be a relatively small number. Certainly well under 5% of the cost of a rocket and, in some cases, closer to 1% or 2%. You can call it, maybe, the magic wand number. If you had piles of the raw materials on the floor and you just waved a magic wand and rearranged them, then that would be the best case scenario for a rocket. So, I was able to say, okay, there's obviously a great deal of room for improvement. Even if you consider rockets to be expendable.” - transcript

At the end of the talk he spoke a little about how he thought that the only way away from fossil fuels is solar.

In order to test my ability to use his ‘back to physics’ model, I decided to work out if going all solar was possible or obviously ridiculous.

Is there enough solar energy falling on earth to replace the ‘banked solar’ of fossil fuels?

Start with Sci-fi. Is there enough energy?

If we imagine a large solar array, floating outside the atmosphere, in the same orbit around the Sun as earth. How large would this array need to be to capture the equivalent amount of energy to that which we release by burning oil every day?

First off, How much oil do we produce?
How much energy is contained in a barrel of oil?
About  6.12×109 J

This gives us a world output of 6.12 ×109 x 85.64 ×106 J/day = 5.241168e+17 J/day

If we simplify from day to second we get: 5.241168e+17/86400 J/s = 6.0661667e+12 J/s

Luckily J/s is also known as Watt (W) making the next bit easier.

How much energy does the Sun give off?
That value is known as the Solar Constant and is about 1,367 Watts per square meter

Do the division and you get an array 4,437,576,225.31 square meters in size.

Convert from square meters to square kilometers and you get, 4,438 km^2.
An array slightly larger than Rhode Island.

That’s not as bad as I expected.

What happens when we move to Earth?

From a convenient web page:
Missouri has more than 200 sunny days per year, for an average of 4.5 to 5.0 kWh per square meter per day”

That translates to ≈1000 kWh per square meter per year.

One barrel of oil contains 1.7 MWh.
Convert to kWh (x1000), 1700 kWh
We use the same ‘barrels per day’ number as earlier, we assume a 365 day year.

Oil produces 5.313962e+13 kWh per year.

Divide by that neat 1000 kWh per square meter, per year and you get : 53,139,620,000 (m^2)

That’s 53,140 square km. or 76% of Missouri’s area, or less than 20% of the area currently farmed for corn in the US.

What I learned?

40% of US corn is used to make Ethanol for fuel, replace that with solar and you can replace the all world’s oil and get 20% of the land back.

Solar’s practical and corn is a really inefficient way to farm sunshine.