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.

Thursday, September 29, 2011

States of mind, and the States in between.

I met a man in New York with Texas on his mind. (If I was a song writer, that'd be a hit.)

We drove to Texas. There are things that we talked about, things we did and places we stayed, but the drive itself is just the paint on the walls, the background. The interstate system just works. It's old, it's creaky, and whoever thought sectional concrete was the correct material for a motorway needs to be brought out back and shot, (Or placed in a special hell where a loud arhythmic thud is piped in.) but the mechanical act of driving 1700 miles isn't hard.

We drove in shifts, switching every half-tank or so. Stopping for lunch, and sleeping in motels. As most of my formative driving trips were in the form "drive all night and get the car back before my mother has to go to work" or, upon landing in France, "I'll see you in Germany", this was positively sedate.

My cohort is a mathematician working in the field of drug development and thanks to a reliance on compute clusters has developed an interest in networking, combining that with my unhealthy addiction to both new knowledge and conversation we weren't sitting in silence for long.

Given that my mathematics is almost as bad as my chemistry I enjoyed almost understanding some of what he does, while he asked me intelligent and complicated questions about what I do.

As we were talking about networking and I constantly needed examples we ended up designing the network for a small company with a branch office and a VPN. Getting to explain and teach to an engaged (and in this case trapped) audience is something I really enjoy and after 5 months of not thinking about this stuff it was a great way to knock the rust off my memory.

We live in exciting times, and while a lot of the twentieth century's progress was achieved by applying engineering rigor and reproducibility to electronics and computer science the twenty-first will be brought to us by applying the same broad principals to biology and medicine.

This is awesome, mind bending stuff, and my man in the opposite seat is in the thick of it. Aids is chronic, in the first world. We can cure some cancers. We are not done but there are reasons to believe that one day we will be. We discovered penicillin, 83 years ago this month. Someone born in Japan today will live that long. What the hell will she see?

An artifact of discussing health and exercise for hours is that this may have been the least unhealthy road trip on record. We stopped and ate real food, admittedly some of this food was gravy, and we went for a run. A RUN on a ROAD TRIP! I'll be thrown out of the union.

At one point, not far from Delaware Water Gap, we crossed the Appalachian Trail. We'd been driving only a few hours from New York, and we were back where it had taken me two months to walk from. This world used to be a big place.

After Jersey and Pennsylvania, America flattens out. Ohio, Indiana, Illinois, Missouri, Oklahoma, Texas. Each flatter than the one before, wheat and corn fields stretching for ever. With dead straight roads and dead flat earth you can see the horizon curve away in a way that I've only ever associated with the sea.

As we left Oklahoma, we climbed up onto an area called the 'caprock' and as we climbed so did the mercury. Big rig trucks were pulling in under bridges looking for shelter, that shimmer they use in movies to denote heat is real, and somewhere along here, the air-conditioning failed. It didn't break, it just couldn't materially affect the temperature of the air. Sitting in a small glass domed metal box, with air, hot as a hair-dryer blowing in your face. Welcome to Texas.

The panhandle of Texas is flatter than an iron and hotter than hell. Between you and me, I think it's named after the wrong bit of the pan.

On the evening of the third day we got to Amarillo. (You, in the back, stop singing that damn song.) It's a classic American sprawl. The center of the town was based around the railway rather than a river, and when the interstates came people moved to the suburbs. Combine this with the billiard table terrain and I couldn't tell where I was, anywhere in town, for the duration of my trip.

As I've come to expect the Amarillians(?) were lovely and welcoming, treating me to a spectacular angus rib-eye steak for dinner on arrival. I'm an enthusiastic eater of sirloin but clearly, on this evidence I need to spend some more time exploring the rest of the cow.

When Texans are complaining about the heat, worry. So clearly we went on a hike.

Palo Duro canyon is the second largest canyon in the US, and the largest in Texas. It's beautiful, the colours are fantastic, and the scenery looks like something pre-historic.  We went on a 5.5 mile hike (walk?) across the canyon floor to a stone pillar called Lighthouse Peak. It was a nice stroll, flat elevation, the only real issue being the 115F (46C) temperature. The views were spectacular, but we made a bee line home when we started running low on water.

Another local attraction is Cadillac Ranch. Ten Cadillacs, standing in a field, constantly spray painted by visitors. It's pretty damn cool. I tagged it with my trail name, and got some pics. Again the heat drove us off pretty quickly. 

I had a great time getting to and being in Texas, but was looking forward to coming home.
It was nice to go from deep in the US to Dublin as it put the similarities and differences between the places in relief, but more on that next time.

Talk soon.