A Niche in the Library of Babel

The consistently interesting magazine “American Scientist” has a good article this month on energy issues and transportation, “The Other Climate Threat” by Andreas Schäfer, Henry D. Jacoby, John B. Heywood, and Ian A. Waitz. It’s behind a pay wall, unfortunately, but can be found at better newstands.  A more technical version of it is also at the National Academy of Engineering site, here.

They note that all over the world people appear to spend about 1.0 to 1.5 hours a day traveling, no matter what the societal level.  In African villages that’s how far people walk, and in more mechanized places it’s how they much time they spend on the train or in the car.   The upper limit makes sense – much more than that and you don’t have time for anything else – but the lower limit is surprising.  Maybe it’s like the radius of your hunting ground; too small and you’ll be missing the big game.  If you’re not traveling that much, you’re missing a better job.

Likewise, transportation occupies a fairly narrow band of GDP, from 5% at the bottom to 12% at the top, which makes sense for the same reason.  However, the range in GDP and technology means that there are enormous differences in the total amount traveled per year, from 200 to 300 km per person  per year in South Asia, to 15 thousand km/p/yr in North America.   The world average is 5500 km/p/yr.   Distance traveled appears to correlate to GDP within about a factor of 2.  The richer you are, the farther you go.  You’re not just hunting the local rabbits, you’re after more valuable but rarer game like elephants.

Since routine supersonic or rocket travel appears impractical, the limit would be 1.2 hours/day in jet aircraft, or 900 km/day and 300K km/year.   That’s not out of the question – some people commute between Washington and New York, and that’s 650 km per day.   That would correspond to a GDP or $300K per capita, which is also conceivable.  The upcoming George Clooney movie “Up In the Air”, is about just such a person, although his situation is portrayed as comically tragic.

Where do I personally fit into this chart?  My commute is about 40 km round-trip, which is on the low side of people I work with.  I drive about 20,000 km per year, so the commute is only 50% of that.  That’s kind of surprising – I would have thought that most of my car’s miles would be in the commute.  I’ve flown about 50,000 km this year, with 3 trips to from the US east to west coasts, and one to Japan.  That puts me at 5X the average distance for an American, but my income is also in that range.

Anyway, what all this means is that as the entire world becomes richer, everyone is going to travel more, and thus emit more CO2.   The desire to travel seems pretty basic.   It’s not something amenable to exhortation to change lifestyle.   It’s going to be critical to shift to the most efficient mode in terms of grams CO2 per km.   Europe is now aiming for car efficiencies of < 100 gm/km (62 miles/gallon).   Planes are not that great, about 20 to 30 mpg, counting that fact that emissions at high altitudes are about 2X worse than those at ground level in terms of global warming.   Trains are best, at 40 to 80 mpg, particularly since electrified trains can get their power from low-carbon sources. Boeing and Airbus are going to have to improve efficiency and find low-carbon power sources if they want to stay in business.

So how can they do that?  Zeppelins!  Hydrogen-powered ones at that.    Over-pressure the gas bags (OK, keep it as a liquid in tanks) and use the extra for fuel.  Trans-Atlantic flights would refuel in Iceland from geothermal electricity.   Trans-Pacifics stop in Hawaii for the same reason.   Yellowstone would have mooring towers just outside the park boundaries.    Trans-American flights would stop at nuclear power parks located in South Dakota, far from human habitation.

I’m sure they’ll ignore this advice and go for something boring like algae-derived diesel, but a steampunk fan like me can dream.

So I was standing in the gas station, hose in hand, idly counting the seconds to fill my tank.   About 80 for 12 gallons, or 9 gallons/min.  I see that gas pumps are limited to 10 gallons/min, so that’s about right.   I see that gasoline holds about 130 megajoules per liter, so what’s the above flow in power terms?

10 gal/min * 4 liters/gal * 130e6 joules/liter / 60 sec/min = 87 megawatts!

That’s enough to power a small city!   That’s the engine power of a modern destroyer.  And there it is, flowing between my fingers.  What would that be in electrical wire terms?  A typical extension cord uses 16 gauge copper wire 1.3 mm in diameter, and can handle 15A at 110V, or 1600 W.  To handle the above power it would need to be:

((1.3 mm)^2 * 87 MW / 1600 W)^0.5 = 300 mm in diameter

That’s a solid copper rod a foot across.   No wonder they’re worried about how long it takes to charge an electric car!  No cable can deliver the power flow that you get from a small gas hose.

OK, so how about a big gas hose?  The Trans-Alaska pipeline is 4 feet in diameter and 800 miles long.  It carried 320,000 cubic meters per day of crude oil at its peak in 1988.  Oil weighs about 0.7 kg/liter and contains ~42 Mjoules/kg.  All together that’s:

320 Km^3/day * 1e3 liter/m^3 * 0.7 kg/liter * 42e6 j/kg / 86,400 sec/day = 110 gigawatts!

That’s a hundred nuclear reactors.  It’s 6X the electrical output of the world’s largest dam, Three Gorges.   It’s twice the power consumption of Great Britain.  It’s about equal to all the wind turbines in the world.  No wonder the oil companies really, really wanted to build that pipeline.  No wonder Alaska basically lives off the taxes collected from it!