This is what happens with looooong conference calls: you’re sitting in front of your speakerphone, on mute so other participants can’t hear your typing or other asocial activities; your PC displays the PowerPoint under discussion.  You get bored, distracted, or, in the best cases, antsy.

So, as I was listening to one more paean to the electric car, I decided to do a little bit of math and googling. Specifically, I wanted to get an idea of the electric power required to recharge electric cars instead of pumping gas into today’s tanks.  This because, for years, I have harbored a vague, undocumented feeling that electric cars would create interesting problems for today’s antiquated, frail electric grid. (Europeans might not realize how often we experience brownouts or outright outages, even here, in the Vatican of high-tech – I used to write Mecca but, you know...)

Off to googling, I type “joules in gasoline” and the first hit comes from the Syracuse University Physics department.  It is a very complete set of really helpful data, which I’ll use several times in this column.
The physics page tells us 1 gallon of gasoline contains 1.3 x 10^8 joules or, not using the ^ sign, 130 million joules.  (The joule is the unit of energy.) 20 gallons get us 2.6 x 10ˆ9 joules, 2.6 billion joules a.k.a gigajoules.

Now, power: 1 watt, the unit of power, is 1 joule per second. I just went to the gas station to check how fast the gasoline flowed at the pump: 9.5 gallons per minute.  We’ll generously allocate 3 minutes for the 20 gallons fill up.  That’s 2.6 gigajoules divided into 180 seconds: 14.4 megawatts.

In electric terms, filling up a 20-gallon tank of gas is equivalent to applying 14 megawatts of power for 3 minutes.

Assuming the 220V supply our washers and dryers use at home, divide 14 megawatts into 220V and you get about 63,000 amps. (watts = amps x volts.) For perspective, a home dryer needs about 5 amps (amperes is the more correct unit name). If, instead of 3 minutes, you allow 4 hours, that is a felicitous 14,400 seconds, the 14.4 megawatts of our 20-gallon tank need “only” 1,000 amps of current.

There many ways to criticize this comparison between gasoline and electricity, starting with the fact an electric motor converts joules into motion more efficiently than today’s gasoline engines, but the problem remains: gasoline stores energy very efficiently and replacing it on a large scale with electric power won’t be easy, even if/when we solve the battery problem.

In 2007 the US had 241 million registered cars.  Let’s say less than half of these, 100 million, fill up once a week, evenly spread over eight working hours to account for the country’s fours time zones.  The formula becomes: 100 million cars x 20 gallons or 10ˆ8 cars x 2.6 x 10ˆ9 joules = 2.6 x 10^17 joules

Let’s google “powers of ten prefixes, we get telling us we need 260 petajoules for the 100 million cars.
Now, for the total duration: 8 hours x 3600 seconds per hour x 7 days = 201,600 seconds, approx. 2 x 10ˆ5 s. We divide the joules into the seconds: 2.6 x 10ˆ17 / (2 x 10^5) = 1.3 x 10ˆ12 watts.

Filling up the cars as described represents 1.3 terawatts coming through the grid to the electric filling stations. As it happens the Syracuse University page pegs the entire US electric supply at about 1 terawatt.  Again, I’m not vouching for exact numbers, just the orders of magnitude. Now, add an uncomfortable twist to those numbers: transmission losses in the electric grid, more than 7%, this compares to a less than .1% for the transportation and evaporation of gasoline.

The result is we have more than the science problem of replacing gasoline with electric energy storage.  We also face an infrastructure challenge to, first, generate the electricity and, second, transport it to the filling stations at home or on roadsides.  It will take a very long time, huge amounts of money and interesting politics to solve these two problems.  And, while I’m not a diehard GM fan, it should (but won’t) kill the “General Motors killed the electric car” myth.

But that’s not a reason to give up.

Shai Agassi if the founder of a company called Better Place. See his is a “simple” but grand idea: let’s solve the battery-charging problem in two steps.  First, a standard interchangeable, snap in/snap out battery for electric cars.  Second, let’s place battery exchange lanes into conventional gas stations.  You need more “juice” pull in, swap batteries and you’re on your way.  Actually, as you’ll see, this is more ambitious, you just pay for energy.  The following piece is an interview with David Pogue, the New York Times’ über-geek, a friendly, witty and knowledgeable tech columnis. A careful reading will let one see a no less careful handling of the power grid management question: how do we channel all the required electric power at the right time and place?  Nonetheless a fascinating read.

Let’s do more math, for solar energy now.

Back to the Energy Content page, we see 1 square meter of US soil receives 100W (when lit, of course), that is 100 joules per second.  Let’s go back to our tank of gas and its 2.6 gigajoules and assume (optimistically) a 20% conversion of photons to electrons and 8 hours of (averaged) sunlight:
(2.6 x 10ˆ9 / 100) / 20%  = 1.3 x 10ˆ8

The 20-gallon tank needs 130 million square meters of solar cells for one second.

Turning to days and years: 24 hours x 3600 seconds x 365 days, divided by 3 to account for the average 8 hours of sun per day = 10.5 million seconds of sunlight in a year, which you divide into the previous result and get 12.4 years. You’d need about 12 years for one square meter to produce the electric equivalent of one thankful.  Moving to a 100 m2 solar panel: it would need more than 40 days (12.4 years divided by 100) to do the same.

Now, imagine 100 million cars...

This leads us to renewable energies, the plural being questioned by some, getting us into Talmudic of Byzantine disquisitions of what exactly is renewable. Geothermal takes heat away from the Earth’s molten core, tidal slows our planet’s rotation down, wind takes a combination of solar heat and Earth rotation and nuclear (fission) uses non-renewable uranium.  Solar is the only truly renewable energy, unless you assume the Sun will someday shut down, in a distant future...

The more interesting thought is this: the fossil fuels we use today are stored solar energy. Coal, natural gas and oil all result from photosynthesis storing carbon in plants to be buried in the ground for eons.  If you believe Wikipedia, photosynthesis converts between 3% and 6% of sunlight into biomass, with an apparent maximum of 8% for sugar cane – what Brazil uses for ethanol.

What we are facing is this: undisturbed by humankind, the planet stored solar energy in the ground over geological eras, millions of years.  Now, we consume energy at a rate that will deplete that stored solar energy in about two centuries, the twentieth and the twenty-first.  Even if we dedicated the entire Earth’s surface to solar energy collection and conversion, either photovoltaic or photosynthetic, electronics or plants, we couldn’t possibly match our consumption.

This isn’t saying current efforts at using electronics, or the biomass, or moderating consumption and CO2 emissions are useless, they give us more time to face really difficult energy decisions – unless the miracle of controlled nuclear fusion happens.

All these unpleasant thoughts because of a conference call. —JLG

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