The Ergosphere
Monday, October 11, 2004
 

And now a word from the janitor

Clicking the "comments" link on a post should now take you to the first comment, rather than the top of the entire post.  If this doesn't work properly, e-mail me. 
Friday, October 08, 2004
 

The Oswalds get it partly right

The Oswald brothers of England (hat tip: PhysOrg.com) did something important and long overdue; they co-wrote a short analysis of the requirements for running Britain's transport systems on wind energy.  And they got a very large number, approximately 100,000 turbines of 3 MW capacity each, making a strip 10 km deep around the entire island nation.

Unfortunately (for them), they were not terribly clear in their assumptions; as a result, they have made several mistakes which call their conclusions into question.  I shall begin where they end, with their technical calculation.

It all comes down to the numbers

The Oswalds' calculation is stated in their paper thusly:

Annual consumption:  54 million tons of oil equivalent (MTOE)     (1)
Efficiency of electrolyzer/fuel cell chain:  50%     (2)
Annual renewable energy required:  108 MTOE     (3)
Converting units to average daily MW[1]:
108*1000*11.63[2]*1000/(365*24) = 143,000 MW   
  (4)

[1] The lack of units in the calculation is in the original.  This is an omission, not an error; if filled in, they would be:
108 MTOE/yr * 1000 kt/mt * 11.63 GWH/kt * 1000 MWH/GWH / (365 days/yr * 24 hr/day) = 143,000 MW
[2] The conversion factor 11.63 GWH/kt (equivalent to 11.63 KWH/kg) appears to be a bit high, but not unreasonably so.  They got it from a fact sheet available here.

What's wrong with that?

There are several minor errors and two major errors in this calculation.  The major errors dwarf the others into irrelevance:
  1. In (2), they assume that conversion to hydrogen is the best, or only, way to make renewable energy available to power transport.
  2. Throughout, they assume that the conversion of oil to work is 100% efficient.

The first assumption is debatable, the second is absurd.  The efficiency of typical diesel truck engines peaks out around 40% and averages considerably less; the efficiency of automobiles is much lower still, around 17% in the USA.

Trying to get it right

If we make an effort to correct their assumptions by: we get much more attractive numbers:

Annual consumption:  54 million tons of oil equivalent (MTOE)     (a)
Efficiency of current vehicles:  25%     (b)
Annual energy applied as motive power:  13.5 MTOE     (c)
Efficiency of battery storage:  70%     (d)
Annual renewable energy required:  19.3 MTOE     (e)
Converting units to average daily MW:
19.3*1000*11.63*1000/(365*24) = 25,600 MW   
  (f)

This reduces the requirements from a 10 km strip of wind plants around Britain to 2 km (assuming no improvements there either; the news just came of a 126-meter wind turbine capable of 5 MW peak, which would cut the number and depth still more) or 24 nuclear plants at 1100 MW each instead of 100.

That's still a hell of a lot.  Nobody said it was going to be a trivial job, but it's nowhere near as big as the Oswalds make it out to be.

There are better scenarios.  If you assume that rainy, foggy Britain gets 300 W/m^2 of sunlight for 6 hours on the average day and you've got solar panels at 15% efficiency, that 25,600 MW of average power could be met with a bit over 2,200 km2 of area; if you can get to 50% efficiency using ballistic-electron quantum dot cells, the requirement is a mere 683 km^2.  Do roofs and pavement on the island cover 3.4% of the area of Wales yet?  If they do, the impenetrable wall of wind turbines turns into faux slate tiles and the problem literally vanishes into the background.   Such are the tradeoffs.  

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