Saturday, January 31, 2009

Power per unit land area of windfarms

As I've said in SEWTHA (the book), the average power per unit land area of a typical well-located onshore windfarm in Britain is about 2 watts per square metre. (Or 2 MW per square km.) This number is my estimate of the best that can be done in Britain, and, as I explained in the appendix, the theoretical power per unit land area doesn't depend very much on the size of the turbines used, because bigger turbines are spaced further apart.

I'm always keen to check my numbers and update them if necessary. Today the the New Scientist interview with James Lovelock prompted me to write a blog article giving explicit data from a real windfarm. James Lovelock says "to spoil all the decent countryside in the UK with wind farms is driving me mad. It's absolutely unnecessary, and it takes 2500 square kilometres to produce a gigawatt - that's an awful lot of countryside." That's a power per unit area of 0.4 W/m2, which is 5 times smaller than my 'best possible' 2 W/m2 estimate.

Let's look at some data. I picked a random windfarm in Britain with ten 27m-diameter turbines: Blood Hill windfarm. The helpful REF website gives exact energy-generation statistics for several years. The collage at the top of this page shows the data, and a map of the site, which is very close to the sea in Norfolk. What's the area of this site? The blue grid lines are 1km squares. I'd say the ten turbines 'occupy' about 0.3 km2 (including an appropriate strip of land around the turbines, where similar size turbines could not be placed). The average output of the ten turbines is 420 kW. So that is a power per unit area of 1.4 W/m2.

If anyone would like to repeat this calculation for real data from other windfarms around Britain or the world, we could collate the answers in the open-source wiki for Sustainable Energy - without the hot air.

Monday, January 12, 2009

Google searches, energy cost, carbon footprint, and cups of tea

A friend asked me to confirm or deny the assertion (Harvard/BBC) that two Google searches on a desktop computer produces 14g of CO2, which is the roughly the equivalent of boiling an electric kettle.
  • ``US physicist Alex Wissner-Gross claims that a typical Google search on a desktop computer produces about 7g CO2.
  • ``However, these figures were disputed by Google, who say a typical search produced only 0.2g of carbon dioxide.''

My own rough back of envelope guess came out in between Wissner-Gross's assertion and Google's...

Here's how I worked it out:
  1. according to a google search(!), google has about 700,000 servers.
  2. let's guesstimate the power to run a server and all its plumbing: 250 W.
  3. google received 90 million searches per day in 2006
    and 1200 million per day in 2007...
  4. Hmm, this growth rate is big enough that it is going to be hard to get a trustworthy answer!
  5. Well, let's multiply 700,000 servers * 0.250 kW * 24 hours per day / 1200 M searches per day -
    that is 0.0035 kWh per search; 0.007 kWh for a pair of searches; and 3.5g of CO2 for a pair of searches. (Assuming that electricity has a footprint of 500 g per kWh.) [In fact I think I heard that google has lots of servers in Iceland, where the electricity footprint is much smaller.] Meanwhile, boiling a 250 ml cup of water uses about 0.028 kWh. So my estimate is that the energy cost of two google searches (measured at the googleplex alone) is about one quarter of the energy cost of boiling a cup.

This calculation has not included the energy cost of running your own desktop computer, wireless, and modem for the duration of the search too; nor the cost of running the internet twixt you and google. If it takes you one minute of computer time to do the search, and if your computer and peripherals use 120 W, then the cost of your computer's power in that duration is 0.120 kW * (1/60) hour, which is an extra 0.002 kWh.
Here's the bottom line from my rough guesses: the total energy cost of the pair of searches seems to be about 0.01 kWh. That's exactly the same as the energy used by leaving a phone charger plugged in for one day. Which is also the same as the energy used by driving an average car for one second.

Saturday, January 3, 2009

Would electric freight vehicles be possible?

energy consumption versus range
In Sustainable Energy - without the hot air, one of my main conclusions is "electrify everything" - in particular, I recommend electric vehicles. At a recent talk, someone in the audience said, yes, maybe electric cars are now viable. But surely you couldn't electrify freight? Leaving aside two possible answers (namely 1: for local freight deliveries, electric trucks are already genuinely in use, and are manufactured by a couple of companies in the UK; 2: we could make electric freight like eletric trolley buses, using overhead lines), I thought it would be interesting to investigate, using the same model I used for cars in my book, the possibility of making long-distance freight vehicles with on-board batteries.
The model assumes that energy goes into air resistance, into rolling resistance, and into brakes. The model includes regenerative brakes (assumed to be 50% efficient, round-trip), and includes energy inefficiency in the energy-conversion chains (from grid to battery and from battery to wheels). The frontal area is assumed to be 8.6 m2 and the freight carried is 26 tons. The other main assumptions are the distance between stops (500m? 5000m?) and the typical speed (50km/h? 100km/h?).
energy consumption versus range
The figures above and below show the theoretical energy consumption (in kWh per ton-km) for two different batteries' energy densities (corresponding to lead acid and lithium), compared with a fossil fuel truck with the same frontal area and load, versus the range (ie the distance between refuelling stops). The top figure is for the case of 500 m distance twixt stops and 50 km/h speed. The bottom figure (just above) is for the case of 5000 m twixt stops and 100 km/h speed.
The bigger the battery, the bigger the range and the bigger the energy consumption. The main conclusion of these figures is that, on energy grounds, trucks with big batteries are viable. They are superior in energy consumption to the fossil fuel truck. (The point at the top, by the way, is the fossil fuel truck benchmark from the book, which is obtained from government statistics; the lower point is the theoretical performance of a fossil fuel truck according to the model. The latter is presumably lower because the former includes a load of empty-running journeys.)
Of course many other factors need to be borne in mind - could a truck stop provide a 120-kW outlet for charging each truck parked at the truck stop, for example? And what is the capital cost of the batteries? And could they be recycled?
But I find it interesting that in principle, long-distance electric trucks would be more energy-efficient than fossil-fuel trucks. As usual, I have declared one unit of grid electricity to have the same value as one unit of chemical energy. Yes, yes, with today's electricity mix in Britain, blah blah blah, inefficiencies in conversion, ... a factor of 2.4 or some such... But as usual I am focussing attention on the future energy system we should be building, not the details of today's obsolete fossil-fuel electricity system. We want to electrify transport in order to get the whole energy system off fossil fuels as much as possible.