Pissing in the Wind, Part 1

When I worked as part of a team made up of nationals of several different European countries, we’d be fond of swapping phrases from different languages (all translated into English). Most would make Hank Paulson blush, and this is a family blog. But one I liked was the equivalent of the English phrase “to make a mountain out of a molehill”. In Holland (or was it Greece?), you’d say instead “to make an elephant out of a mouse”. So, of course, we combined the two and made elephants out of molehills and mountains out of mice. My most notable contribution was the phrase “pissing in the wind“.

What’s bugging me is the question of the potential for generating energy from wind-power. In what’s fast becoming the Bible for such matters, Sustainable Energy Without the Hot Air (SEWTHA), David MacKay asserts that you can only practically generate around 2W of wind power per m2 on or around the UK.

David therefore concludes (page 216) that the UK could feasibly build 35GW of onshore capacity and 29GW of offshore, total capacity 64GW, producing on average 4.2kWh/day/person and 3.5kWh/d/p, 7.7kWh/d/p in total. (Other energy plans for the UK including more or less wind energy are discussed elsewhere in SEWTHA).

Sorting out the units

One man’s sensible units are another man’s bizarre eccentricity. I want to convert David’s units for comparison with other, even more eccentric, sources. Personally I’d like to divide by 24 to get rid of both the hours and the day – David’s wind totals 7.7kWh/day per person, that is 7700/24W per person – call it 300W. Now we’ve got to something I can relate to! And I don’t know, but 300W seems not a lot more than the lights and the TV to me! Maybe we’re going to discover the wind won’t save us…

Anyway, figures are often given in TWh/year for the UK. Strange but true.

I assume MacKay bases his estimates on 60m people. So 7.7kWh/d/p is 7.7*60m*365kWh/yr for the UK or 7.7*60*365GWh/yr = ~170TWh/yr.

How much wind do we need for 1 million jobs?

David MacKay is now an energy advisor to the UK Government, so his view counts. But I keep reading higher figures for the potential for the UK to generate wind energy than 170TWh/yr.

For example, on Saturday I picked up a booklet One million climate jobs NOW! which notes on p45:

“In 2008 the total UK supply of electricity was 401TWh. 7TWh of that came from wind. In 2008 the UK had 3.4GW of installed wind power. So approximately 2TWh of electricity were produced that year for each [G]W of installed capacity. [So far so OK: cf David's 170/64 or a bit over 2.5TWh/yr/GW installed capacity]. 150GW of installed capacity should produce 300TWh, three quarters of current electricity production.”

Obviously, if there is not enough wind for 150GW of capacity and/or for 300TWh/yr, the whole 1 million jobs plan starts to unravel.

Sorting out the units again

One man’s sensible units are another man’s bizarre eccentricity… What does “150GW capacity” mean? Let’s work instead in terms of average output, because we’re going to be considering average wind-speeds (really we should be considering average power in the wind, which is different, but, hey, the modern Principia will have to wait!). Let’s go back to the energy needed of 300TWh/yr. What average power output do we need to achieve this?

What a pretty pass we’ve come to when we’re calculating in Watt-hours per year!! We want Watt-years per year, in other words, simple Watts!! There are roughly 24*365 = 8760 hours in a year, so 300TWh/yr = 300,000/8760GWyears/year = 35GW, rounded up a tad.

To create 1 million jobs we need to build enough wind-turbines to give an average power output of 35GW.

Is there enough wind?

Now we can finally start to make comparisons. How much wind is really out there? And how much of that do we need?

What’s been bothering me for some time now is that MacKay bases his figures (all derived from the 2W/m2 power density) on wind-turbines having to be spaced in a grid 5 times their diameter (5d) apart, as described in his Technical Chapter B, p.265.

This argument seems to apply to current technology only, but is also somewhat counter-intuitive as you would have thought you could simply put taller wind-turbines in between the ones you’ve already got and they wouldn’t interfere. If you only used 2 heights you’d double up to 4W/m2 and we could create our 1 million jobs, moreorless.

In fact, the idea that you can only extract the same amount of energy per unit land area whatever the diameter of the wind turbines is somewhat paradoxical. Surely 1cm turbines spaced 5cm apart is not going to be as good a solution as 100m turbines spaced 500m apart! All very odd: MacKay’s Paradox, perhaps!

Furthermore, it would seem the proximity of other wind turbines is only a problem downwind. Perpendicular to the direction of the wind it might even be better for the turbines to be next to each other as, like New York skyscrapers, the resistance of one would force air towards its neighbour. In many locations useful wind will normally come from one direction (the west near the UK). If only the downwind turbines have to be 5d apart, then you should be able to generate 5 times as much energy, 10W/m2. Now we’re talking!

But I don’t want to stop here. With different designs, e.g. turbines at different heights or funnelling air towards turbines, you might be able to do even better than that. In principle you should be able to capture a proportion of all the energy in the wind up to whatever height you could engineer. How much energy is this?

Problem

MacKay (Chapter B, p.263 ff) only considers the kinetic energy of the wind passing through a single turbine.

But we know that the wind turbines interfere with each other, otherwise we could put them right next to each other and there’d be no 5d rule of thumb. What I’d like to answer are questions such as:
- what proportion of the energy in the air does a large field of wind-turbines extract?
- can we do better than extract 2W/m2 with better technology?
- are we likely to hit any limits, i.e. can we extend a field of wind-turbines indefinitely without weakening the wind?

Obviously this is just a blog (but, hey, what might it lead to?), not a scientific treatise on the subject. Nevertheless, we can take a stab at answering these questions.

Thought experiment

Let’s work out the kinetic energy of the entire mass of air up to the top of the atmosphere passing between two imaginary poles a metre apart across the 6m/s wind direction. A quick calculation shows that this column of air – 15psi (sorry, pounds – 2.2/kg – per square inch – ~2.5cm2 – you can do the calculation yourself – OK, the conversion is 15psi = ~15/2.2*40*40kg/m2) in old units – weighs ~10000kg. Wow!

If the wind speed all the way to the top of the atmosphere is an even 6m/s (a conservative assumption as it moves faster higher up, we’ll try to come back to this), then the kinetic energy of the air passing between the poles every second is, by the formula 1/2mv2, with 6m of air passing every second, 1/2*6m*10000kg*(6m/s)^2 = ~1 million Joules, that is, (1 Joule per second =1 Watt) we have 1MW of power every metre across that there gentle breeze. Wow, again!!

This is rather different to the figure of 140W/m2 (note the different units) David MacKay calculates because he only considers the energy in a cross-section of the air, the 1.3kg/m3 that actually passes through a 1 m2 cross-section of wind-turbine. The wind goes up a long way and (by these back of an envelope calculations) only 140/1 million = 0.00014 or ~1/7000th of it passes through a 1 m2 cross-section near the ground! (The calculation by mass of air considered, i.e. 1.3/10000, gives roughly the same answer).

But the wind comes from somewhere. If you had many rows of wind turbines, part of the energy will be extracted by each row. The wind for the later rows will have to come from somewhere or we’d be becalmed. The answer is it comes from the other 9998.7kg of air above the wind turbines!

This rather explains MacKay’s Paradox, since we have to suppose air can only fill the lee (downwind) side of the wind turbine from above or below or even from the sides (so perhaps we can’t put our turbines right next to each other after all) at a limited rate (mostly from above). When a wind turbine creates a partial vacuum, the engineers’ rule of thumb used by MacKay is that a “hole” 1m in diameter is filled in 5m, 100m in 500m and so on.

OK, not all the air will necessarily be moving in the same direction (otherwise the weather system we know & love wouldn’t operate as observed), but if even half the mass (remember the air is less dense the higher you go) is, we have 5000kg of air and 500kW/m2 to play with.

Even if we can only extract 1% of this energy, that works out at 5kW/m2.

We can’t keep extracting 1% of the energy, though, from row after row of wind turbines, so maybe we should consider the air-mass to be a wall of wind, from which we could extract, say, 10% of the energy in total, that is, 50kW per metre length of the wall. This is equivalent to funnelling all the air through 100% efficient wind-turbines, that is, extracting all the energy in the wind, up to a height of 50,000/140 = ~350m (the 140W/m2 is David MacKay’s power per unit area of wind-turbine at a wind speed of 6m/s).

Or, perhaps more practically, we could extract around 1/3 of the energy (MacKay suggests 50%, but I’m going to be a bit less optimistic) in the air up to 1000m, one kilometre. (Note that this doesn’t allow for air density decreasing with height, but then again I’m not yet making any allowance for the fact that the wind-speed increases with height).

To obtain the 35GW average power output we need for our 1 million jobs would therefore need a wall of such wind-turbines 35GW/50kW = 700,000m or 700km long. Ouch!

Or perhaps, since we’re talking about the UK, we could have a 1400km wall of wind turbines 500m high, which sounds a bit more practical.

Implications

My 1400km wall of wind-turbines 500m high is very roughly equivalent to (say) a field of large wind-turbines (100m+ diameter) 1400km, that is, 14,000 wind-turbines long (i.e. around the whole length of the UK), right next to each other, but only 5 wind-turbines, that is, with 5d spacing, 2 km across.

The “wall of wind” is therefore equivalent to ~14,000*5 = ~70,000 wind-turbines in total, implying an average output of of 35GW/70,000 or 0.5MW at a wind-speed of 6m/s. Wind turbines are normally quoted in capacity. The 35GW average output was based on a capacity of 150GW and empirical rather than theoretical figures relating average output to capacity. Anyway, my calculations suggest the wind-turbines each have a capacity of 150GW/70,000 = ~2MW, which is a little bit low for such large devices, but in the right ballpark. In particular, I’ve estimated cautiously for the efficiency of the turbines and have made no allowance for a higher wind speed at a higher altitude.

This higher wind-speed is absolutely crucial, because what I hope I’ve demonstrated is that a field of wind-turbines actually extracts energy from higher up in the atmosphere. A field deep enough would actually slow the entire air flow. What happens is that the first row of wind-turbines slows the air, creating a partial vacuum downwind. This is filled mostly from above, slowing the air higher up.

Consider the graphs of wind-speed against height and power density of wind against height David gives here. They’re astonishing. The wind power at a 10m height is around 100W/m2 for a 6m/s wind at that level, but at 100m where the air flows faster it’s nearly 250W/m2 and at 200m where it flows faster still we’ve got over 300W/m2 to play with!

What’s actually happening, of course, is that all the other things on the ground – water, trees and so on – are already capturing the energy in the lowest part of the atmosphere, which fills from above.

Or, to look at it another way, the wind is created by a high pressure mass of air essentially collapsing into a low pressure area, which literally fills, as the weather-men say.

Bearing all this in mind, it seems to me that we’re pissing in the wind in the first place building wind turbines near ground level. We should start 100m or 200m or even 300m up.

Conclusion

There is (significantly) more than 500kW/m or 500MW/km of kinetic energy in a flow of air – 100s of kms across – moving towards the British Isles at an average speed of 6m/s, creating what we call a (west) wind. If we could extract all this energy we’d “only” need a 70km wall of wind turbines for an average output of 35GW.

The limit of 2W/m2 only applies to the technology we are using just now to extract energy from the wind. At this stage in the development of the industry, there are plenty of sites and it’s the technology that’s expensive. This will change over time, and there will be an incentive to design machines to extract more of the energy from the wind, particularly higher in the atmosphere.

It may be possible to extract significantly more than 2W/m2 by building turbines closer together across the wind direction and (as, to be fair, David MacKay points out), much taller.

However, maybe we have to bear in mind that we might not be able to build row after row of giant wind-turbines indefinitely. From a British Isles (UK and Republic of Ireland) point of view this might not be too much of a problem, since we are on the western seaboard of Europe. But eventually if we build turbines along the west coast, perhaps along the spine of the country and in the North Sea, we could just conceivably start to affect the very wind itself – the Danes and Germans might not be so pleased!

To determine whether this hypothesis is true, we have to look at other aspects of the energy in the wind. The kinetic energy arises from the potential energy of different pressures of different air-masses. And we need to look at how that potential energy itself is generated.

In other words: how renewable is the wind?

Another time, maybe.

Some Contrarian Climate Change Ideas

I had a day (well afternoon and evening) out of the home-office yesterday. I took the train to Cambridge and caught the first hour or so of a Cambridge Energy Forum on UK buildings before heading to the Guildhall for a well-attended public meeting on “what Copenhagen means for you”.

Maybe I’m an unreconstructed contrarian, but I find myself disagreeing with much of what I’m being told on the topic of global warming. Here are my latest musings.

What’s the target?

The Guildhall meeting started with a very competent whirlwind summary of the science of climate change by Emily Schuckburgh of the British Antarctic Survey. In particular she showed a rather longer graph than I’d seen before of historic temperatures and CO2 concentrations derived from ice-core analysis: around 800,000 years worth. During all this time the level of atmospheric CO2 had varied only between 180 and 280ppm, in close correlation with the temperature.

Furthermore, when temperatures have briefly spiked up during inter-glacials they have reached levels somewhat higher than at present (or in the entirety of recorded human history for that matter). Schuckburgh suggested temperatures may have been 4C higher than her baseline (presumably the pre-industrial average temperature, 0.8C lower than at present) for brief periods (and -8C lower during ice ages). Scary stuff.

Why then, do we think we’ll manage to keep temperatures within 2C of pre-industrial levels – and they’ve already risen 0.8C – at the sort of CO2 concentrations implied by the discussions at Copenhagen? We’re at around 390ppm right now and it doesn’t look like the proposed policies have much chance of keeping us below, at best, 450ppm.

And on top of that, CO2 isn’t the only greenhouse gas. Some have only just been invented! If we can’t get all the methane (CH4) and nitrous oxide (N2O) down to natural levels and the anthropogenic alphabet soup of CFCs, HFCs and so on down to negligible levels, then we’ll be even warmer.

Here’s my contrarian position (1): we need to get CO2 levels back down to the natural range of 180-280ppm. Presumably we’d aim for 280ppm, since 180 implies an ice age!

At present the strongest mainstream position – supported by reputable scientists and prompted by James Hansen’s landmark paper – is that we should aim for 350ppm.

The theory – perhaps I should say hope – is that we can “stabilise” levels at 350ppm and a 2C temperature rise. This is wishful thinking poppycock. In fact, the climate system is not a stable one. In particular, it will not be stable at 350ppm and a 2C temperature increase. It will have a tendency to warm further, for example, as ice melts, darkening the planet’s surface; as CO2 levels rise further as forests burn in the occasional much hotter summers we’d experience; as wetlands dry out and release their carbon too; and as the ocean circulation gradually slows due to the reduced temperature differential between the poles and the equator, removing less and less carbon from the atmosphere as time goes on.

We’ve opened Pandora’s box – we have to put all the demons back in, not just some of them.

Will the Gulf Stream slow and keep Britain cool?

This was meant to be a post about policy, but I’ll get the other science point out of the way, since this old chestnut came up in the Q&A at the Guildhall.

The point is that the Gulf Stream (as the North Atlantic branch of the ocean’s circulation is popularly known) can be disrupted by lots of fresh water flowing into the North Atlantic. Such water floats (because it’s fresh which makes it lighter, even though it’s cold which tends to make it heavier) and would prevent the circulation whereby (salty) cold water sinks as it approaches the pole, drawing more warm surface water up from equatorial regions, keeping Northern Europe, including the UK, a lot warmer than other regions at such a high latitude.

As the world emerged from the last ice age (and previous ones), it seems vast quantities of meltwater from the North American ice-sheet poured into the North Atlantic as ice-dams gave way. This disrupted the oceanic circulation and caused warming to reverse for a while, at least in the North Atlantic region.

It’s possible that meltwater from Greenland could have a similar effect to that from Canada, but unless someone’s asleep on the job, this isn’t imminent, since we’d see the water pooling in Greenland.

So, what will happen to the Gulf Stream in the absence of disruption from a sudden flood of meltwaters?

Here’s my contrarian position (2): the ocean circulation will strengthen in the short-term (which, depending largely on future greenhouse gas emissions, is likely to be a century or two), then gradually weaken as the ice-caps disappear. There’s no get out of jail free card for the UK, certainly not in our life-times.

The point is that the circulation is ultimately driven by the temperature difference between polar and equatorial regions.

More heat is captured by the atmosphere in the tropics than at the poles, that’s why you have a circulation in the first place. With the presence of greenhouse gases, even more heat is captured in equatorial regions and tends to be transported poleward either in the oceans or the atmosphere. More warm water stays near the surface until it cools as it approaches the poles. The result is a stronger circulation.

The presence of ice (Antarctica, Greenland, permafrost) keeps the polar regions from warming. Until this ice melts, more heat will be transported poleward. Indeed, the heat uptake by ice melt that drives the circulation.

Of course, the heat transport itself progressively melts the ice. When it’s eventually all gone, temperatures will tend to equalise between the poles and the equator, weakening the circulation. We’re not there yet, though.

I should remind readers that the ocean circulation is one of the major ways in which carbon dioxide is removed from the atmosphere.
[5/11/09 Afterthought: Oops, this throwaway comment could be a bit misleading. In fact, the ocean circulation returns CO2 to the atmosphere, so, if the circulation increases in strength, as I'm suggesting it will over the next century or two, the net effect will be for the ocean to take up less CO2 (net, the oceans are currently absorbing CO2 because the ocean and atmosphere are out of equilibrium because of the "extra" anthropogenic CO2 in the atmosphere). This mechanism represents a positive feedback during deglaciation warming phases, and, if my hypothesis is correct, during the current phase of global warming. When the ocean circulation is interrupted, then there is a positive cooling feedback as the ocean releases less CO2 due to the reduced circulation, taking up more net. This could explain the persistence of cooling phases during deglaciations (warming periods after ice ages), such as the 1000 year long Younger Dryas event.].

Therefore, as I said in my first heresy, we’d better get temperatures and CO2 levels back down before the ocean circulation strengthens too much. [5/11/09: Amended this sentence, see previous note in square brackets].

Burning wood is not a good idea

Everyone loves Julian Alwood! (He taught on my MBA programme). He told an amusing anecdote yesterday about how some well-meaning foreigners had tried to introduce a more efficient stove in Malawi. The problem was Malawians bash the meat while its cooking, apparently, and the new stoves didn’t last very long.

But the main point is that the big problem in Africa is burning wood. It releases carbon (and, almost as important, retains moisture). “Reducing deforestation” (George Orwell would have loved the double negative!) was mentioned by Chris Hope, among others, yesterday as the cheapest way to avoid deforestation. What’s really needed in Africa is a robust solar stove design, but more about that another time.

So why then was a picture shown at the Cambridge Energy Forum of a supposedly virtuous Briton carrying some logs to put on his fire?

I’ve harped on about the biofuel topic on this blog previously and will no doubt do so again (see the Biofuel category in the box on the right), but here’s my contrarian position (3): Everyone should avoid the use of all forms of biomass as fuel.

Here’s something you may have missed. A radio programme a day or two ago was discussing a satellite that has just been launched to detect moisture levels from space. The point was made that if forecasters had realised that European soil moisture levels were so low in 2003 they would have been able to forecast that year’s heatwave much more accurately.

Interesting factoid. I don’t know about you, but it suggests to me that one way we could adapt to global warming here in Europe is to increase soil moisture levels. How do we do that? More trees (including decaying ones), less arable farming, that’s how. And how do we achieve that change? We ban agrofuels (the right-on term for biofuels) and discourage biomass burning. Simple isn’t it, when you think things through?

Trying to reduce UK (or other comparable country’s) energy consumption is a waste of time, effort and money

I have to say I was stunned by the facts and figures thrown at me by the Cambridge Energy Forum (and in Michael Kelly’s talk on a similar topic in the Guildhall). I think they’ll put up a report of the meeting and slides on their site, in due course, so I won’t try to cover everything that was said.

Let it suffice for me to report that improving the energy efficiency of the UK’s housing stock turns out to be a Sisyphean task. (And even if we succeeded, energy consumption would tend to rebound as we spent the money saved! I won’t go into all this again – my most recent post on the topic is here). After you’ve insulated the loft and put in the low-energy lightbulbs – and anyone who doesn’t take the simple steps is an idiot – it starts to get really expensive.

And you can’t wait for new low-energy houses to be built to replace the existing housing stock because that would take 20,000 years. Or something.

The UK will not reduce its energy consumption by 50%. It won’t happen. The effort is futile. It’s a dead parrot of a policy.

The reason is economics. Importing solar-generated electricity can be achieved at a fraction of the cost per kWh. Promoting that sort of scheme is what everyone should be putting their effort into. And the Desertec plan was only mentioned once, en passant, in the Guildhall.

And then there are the economic reasons. People want to be richer, not poorer. They don’t want to be turning their thermostats down. And what’s more, people are tending to get richer over time – despite a raft of policies promoted by governments round the world designed by a secret global committee with the objective of halting this process – ultimately because technological (and learning) advances mean productivity tends to steadily increase (especially when regular economic recessions purge the least efficient).

The fact that more people are getting richer all the time suggests that policies based on changing people’s behaviour through taxation have had their day. We need to think again about behavioural taxes on everything from alcohol to carbon.

The main advantage (probably the only one, at least in this contrarian’s view) of a carbon tax (championed by the even more lovable Chris Hope last night), or any other way of pricing carbon, is that it makes dirty energy more expensive than clean energy, encouraging companies to invest in renewable energy production. This presupposes, though, that the main reason companies aren’t investing in renewable energy projects is price. And when I read in New Scientist magazine on the train home that “over 5 gigawatts of [UK] wind power are currently stalled by aviators’ objections” to possible radar interference alone, I really wonder whether price rather than the planning system really is the problem.

Nevertheless, internalising the carbon cost must be part of the solution. The problem with introducing a UK tax on carbon is that it will use up an enormous amount of political capital. To be effective there would have to be a huge shift to carbon taxes. And I can see the headlines already. “Driving is just for the rich in Cameron’s Britain”! Not going to happen, is it?

People certainly don’t like being morally preached at (as Chris Hope pointed out), but they like being taxed, and changes to how they’re taxed, even less.

The problem with a tax on carbon in general is that it sets no limit on emissions – so, since a tax simply redistributes spending power, could turn out to be ineffective.

A lot of intellectual effort seems to be going into working out what is the “right” price for carbon. The Kyoto idea of carbon trading may have had a lot of problems, but the principle of letting the market determine the carbon price (by squeezing supply) was the right one.

So what’s my contrarian position? OK (4): Right now energy policy should focus entirely on removing all obstacles to the development and roll-out of renewable forms of energy. Let’s see how far that gets us.

Guilt is not an appropriate emotion for dealing with this problem

Chris Hope was the only one last night who explicitly mentioned that the West caused the problem and should pay to fix it.

Well, I’m sure that “from each according to their abilities”, despite its connotations, might be a principle that could reasonably be applied in the context of international climate change negotiations. But what appears to be happening in the Copenhagen negotiations (I was hoping to find out more last night) is that the aid agenda has taken over the global warming agenda.

For starters, I don’t see a lot of evidence of binding emission targets being linked to these large transfers of money. But for the main course, we’ve brought some more presuppositions with us. There are serious doubts that aid is what’s needed to promote development. Yeap, for decades we’ve been following a seriously flawed policy. For example, Paul Kagame, President of Rwanda, wrote in yesterday’s Guardian, that “Africa must attract broad investment, not rely on handouts, if we are to sustain development”.

What’s needed is trade, not just aid.

Aah, you say, the Copenhagen largesse is investment. Well, maybe some of it will be spent wisely. But there is plenty of money in the world – too much in fact (that’s what caused the credit crisis) – looking for investment opportunities. Why do we need billions more?

A cynic, and I am one, so I’ll carry on, might even conclude that the $100bn or whatever comes out of the wash in Copenhagen, is in fact a further Keynesian stimulus for sluggish western economies. Think about it. Many of those pounds, dollars and euros are going to be spent on – to hazard a guess, as the details are not very clear – engineering projects that will be carried out by western companies. And I would have thought Gordon Brown (who’s driving this handout) is savvy enough to know this. Watch shares in Aggreko and Balfour Beatty when this deal is done!

And what happens when the money runs out? When we eventually decide we don’t need to pay developing countries for a climate deal, or decide that they’re not keeping their side of the bargain (whatever that is)? The money will be like aid, creating dependency.

On the other hand, and let’s call this my final contrarian position (5): paying for ecosystem services – and here’s some good news that could come out of Copenhagen – and/or energy, such as desert solar, will (if executed properly) provide countries with sustainable income streams which will support their further development.

Deserts vs Roofs, Round 2

Following Scientific American’s foray into the arena of grand, green projects, which I looked at a couple of days ago, I see that, in New Scientist, Fred Pearce has been looking at the Desertec plan to bring solar electricity from the Sahara to Europe.

Fred’s article compares Desertec with the feed-in tariff fueled PV roofing of Germany.  My immediate observation is that it’s hardly a case of either one or the other.  The Desertec plan, which is backed by “20 major German corporations” aims to raise €400 billion to meet (only) “15% of Europe’s electricity needs by 2050″.  And unless I was asleep when I read the relevant chapter in David MacKay’s book, PV panels on roofs alone can’t provide all our electricity. The quote from Germany’s rooftop PV champion is therefore rather puzzling:

“Some of the opposition to Desertec comes from an unexpected quarter. Hermann Scheer, the German member of parliament who masterminded the programme that has put solar panels on 100,000 of the country’s roofs, declared Desertec to be an unnecessary and expensive distraction that would divert investment from projects in Germany itself. Europe could generate as much solar energy as it needs domestically with more rooftop PV panels, Scheer says.”

Maybe he’s joking.

Pearce rather confusingly compares PV in Germany with solar thermal in the Sahara. That’s one two many dimensions for me. The argument is confused by the need, for example, to use water for the solar thermal. If we do a quick thought-experiment comparing PV in Germany and the Sahara the economics becomes obvious. PV in the Sahara would generate at least twice as much electricity per area of PV panel on German roofs, because of the lack of cloud in the Sahara, more overhead sun (reducing losses in the atmosphere) and lack of any tracking ability whatsoever and much greater possibility of being shaded at the ends of the day of fixed panels on roofs (I could say 3 times as much electricity – though I would then have to check my facts more thoroughly, since 3x might be per area of land, which is a slightly different matter – but don’t need to). So if we give a €400bn budget to each location we would have to spend only €200bn on panels in the Sahara.

But we have to allow for transmission losses – let’s say 20% (the article gives 10% for the high-voltage direct current (HVDC) links from Africa to Europe but let’s be pessimistic). So for the equivalent of €400bn of rooftop PV we need to spend €240bn in the Sahara.

HVDC is a proven technology and the article says we need 20 links from Africa to Europe. Let’s be pessimistic again and price these at €5bn a pop [Postscript: I've now found that David MacKay gives £1bn for 2000km of HVDC + £1bn for the cost of the land it uses (p.216), so my guesstimate implies he's a hopeless optimist!]. That’s $340bn we have to spend on our Sahara project.

And maybe another wodge – say €10 billion (I’m basing this on a rather generous €1000 per rooftop worth, estimating rough equivalence with Desertec – and market saturation of suitably angled roofs – at 10 million chunky 1kW average output rooftop systems, 100 times as many as at present) – to enable tracking of the sun to ensure we achieve at least double the output of the German rooftop PVs. I’ve managed to get us up to €350bn.

OK, let’s add on 10% extra capacity to allow for the accidental disruption of supply, political risk, bribes, earthquakes cutting the cables, outages caused by sandstorms and so on. That gets us to €385bn.

I’m really trying to push up the cost here. I’m not even making an allowance for ease of installation and maintenance, the ability to standardise and optimise panel dimensions, the lower labour costs and so on, of arrays in the desert compared to on German roofs.

Even being really pessimistic, we’re €15bn up on the deal. I’ll take that. Plus we have the option of expanding the project further, exploiting economies of scale, after 2050 – whereas in comparison we’re running out of roofs in Germany.

The reason why the Desertec guys have gone for CSP, of course, is it’s even cheaper than PV [something like 8 times cheaper on an average power delivered basis according to David MacKay, p.216]. As Fred himself says: “The clincher is cost. Building a power-station-scale solar thermal installation costs only a fraction of PV generators with the same output.”  And it comes with integral energy storage (read the article) whereas the German rooftop panels will generate most energy when it’s not needed (OK they can sell it to parts of Europe where they have a daily air-conditioning peak, but Desertec can do that too).

Look, feed-in tariffs to roof-owning Germans was a way of funding the early development of PV technology. It’s just not a sensible financial mechanism for rolling out PV. And German rooftops are not a sensible place to put the things.

CSP in the desert wins hands-down over PV on German roofs. If there really is a choice between the two, I don’t know why we’re even discussing cost.

But Fred’s article raises some other strange objections to Desertec:

• “…it could make Europe’s energy supply a hostage to politically unstable countries” say critics.  Nein, nein, nein!  It’s trade.  And trade cements peaceful international relationships.  It’s when trade breaks down – like in the 1930s – that wars start.  Compare the relationship of the West over the last 30 years with, I don’t know, Afghanistan (little trade) and Saudi Arabia; or North Korea and South Korea.  I find it rather strange that a global problem – climate change – is spawning a retreat to local solutions.  Maybe it’s some kind of innate human response – akin to cowering in Mother’s skirts – when bad things happen.  We need collaborative, mutually beneficial solutions if we’re going to crack this one.  Any doubters should just pretend we’re facing some other kind of common threat – a 1km asteroid hurtling towards us at 40,000kph, say.  We’d need to work together on that, wouldn’t we?  Same difference with global warming. In any case, building Desertec diversifies Europe’s energy supplies compared to where they are now, reducing reliance on any one regime. The theoretical problem of supplier-power will be lessened for at least 30 years, until we switch off the gas, by which time we might have come up with other energy sources. Even in the worst case, it’s difficult to imagine reliance on renewables being worse than reliance on dwindling fossil-fuel supplies. So why don’t we just get on with it?

• “Europe should not be exploiting Africa in this way”.  What?  Make your mind up.  How is it exploitation?  You help us make some electricity, we give you some euros and you can buy stuff.  What exactly is the problem with that? This “argument” is hand-wringing liberalism gone mad.

• “But capital cost is not the end of the story. While a solar thermal power plant requires a round-the-clock crew, PV installations pretty much run themselves.”  I seriously doubt this.  Think about it.  You’ll have a few maintenance teams in the desert each looking after a vast amount of output.  Compare that with the army of bureaucrats alone needed to manage millions of rooftop PVs and the owners’ accounts, sort out disputes, investigate fraud (what if they just sell normal electricity back to the grid and put a piece of cheap plastic on the roof?) und so weiter, together with the thousands of small businesses fixing the things when – like any domestic appliance – something goes wrong.  Not to mention the army needed to get up on people’s roofs every now and then to clean the birdshit off the things.  Someone’s in fantasy-land, and it’s not me.

• “What’s more, PV power plants can grow piecemeal: they can start generating power for the grid from the day the first panel is installed, while solar thermal mirrors are useless until the entire power station is completed.”  So?

I’m sold on Desertec. How can I invest?

Scientific American’s Sustainable Future

Scientific American’s customer management is appalling. When I first subscribed to the print edition, the magazine’s online presence was trumpeted as one of the benefits. I therefore understood I would also obtain access to the Scientific American Digital (how quaint!). Nope. I got no more online access than I had previously and ended up paying a Scientific American Digital subscription on top of the print subscription. Someone should call the Advertising Standards Authority! (Annoyingly my online subscription has now expired, and, I see from the correspondence page – which publishes letters on topics in the edition, I kid you not, 4 months earlier, like we’re still in the 1950s – that I appear not to have received the July issue at all).

Just lately – in the midst of a UK postal strike – I can find no way to notify my address change or even log on at www.scientificamerican.com. The site recognises none of the several numbers on the address labels of the magazines I’m sent. The contact email address intl@scientificamerican.com simply doesn’t work. Mind-blowing. Scientists, eh? Hardly surprising there were dodgy solder-joints at the LHC, was it?

Nevertheless, I persist with Scientific American. It’s worth it for the quality of the articles. And, I have to say, its old-fashioned feel.

The lead article in the November issue is titled: “A Plan for a Sustainable Future”, by Mark Z Jacobson and Mark A Delucchi . It discusses how the entire world could be powered by wind, water and solar power by 2030. And it’s well worth a read.

The authors note that building “millions of wind turbines, water machines and solar installations” is not without precedent. For example, “during WWII the US retooled automobile factories to produce 300,000 aircraft”. For clean energy the numbers are feasible: the list includes 490,000 tidal turbines, 3,800,000 5MW wind turbines, 49,000 concentrated solar power (CSP) plants and 40,000 solar PV plants.

I’m afraid I have some quibbles:

• The authors quote a US Energy Information Administration projection of 16.9TW of global energy demand in 2030, compared to 12.5TW now.  I suspect 16.9TW will prove to be a massive underestimate.  As well as a greater population and higher living standards, there’ll be new sources of demand in 20 years, for example, for large numbers of desalination plants to produce fresh water.  I’d be amazed if we aren’t using twice as much energy by 2030 as we are now.

• On the other hand, ruling out wind and solar power production “in the open seas” is suspect: I would have thought there was a lot of scope to generate power there, e.g. on floating islands, which I’ve seen proposed, probably in Scientific American itself.

• Nuclear power is dismissed because of the “carbon emissions” caused by “reactor construction and uranium mining and transport”, but no explanation is given as to why these activities couldn’t be powered by clean energy.

• Interestingly, the authors are concerned about all forms of pollution, so rule out carbon capture and sequestration (CCS) and biofuels on the grounds of air pollution other than CO2. I’d have liked to see at least a nod to the other problems with these primitive technologies: principally the difficulty of capturing all the CO2 in a coal-fired plant, the cost of burying the carbon and the risks; and, for biofuels, the land use problems – not just food vs fuel, but that the land would store carbon quicker if left alone!

• I doubt that geothermal energy is “renewable”.  There may be a lot of it, but the rocks will reheat only very slowly.

• The authors suggest that we deploy 1,700,000,000 – yeap, 1.7 billion – “rooftop photovoltaic systems”.  I think this is nuts.  First off, I’m really struggling with the numbers – the 0.003MW – or 3kW – size of each system must refer to average (mean) output to be consistent with the rest of the article.  But, according to my mate David MacKay (print edition, p.40), 20W/m2 is going some for solar PV in the sort of countries where there are a lot of roofs. So these systems would have to be 150m2 each. They have big roofs in America, I guess. But my more fundamental objection is that the output of 100,000 of these babies only adds up to 1, yes one, of the 40,000 PV power plants. What’s easier, do you think, fit solar panels on every roof in a medium-sized town, such as Southampton where I come from, or stick them all in a big field outside of town (perhaps a long way outside, like in North Africa, where funnily enough you need far fewer panels)? I’ll give you a clue: let’s be pessimistic and say it takes 1/2 hour to put a panel in a standardised array in a field and optimistically 2 days to put the scaffolding up so you can get on the roof without a health and safety violation – before you start the pretty much bespoke installation process. Barmy idea, isn’t it? I worry that the inclusion of the rooftop PVs owes more to some kind of philosophical belief in the virtues of localism than to sound scientific (or economic) reasoning. And of course the article concludes by advocating the dreaded feed-in tariffs. What better way of transferring money to those with big roofs from those, um, without big roofs?

Nevertheless, notwithstanding a few hints that it may be informed by countercultural ideology, I recommend taking a look at “A Path to Sustainability by 2030″.

But the November 2009 Scientific American is worth buying for another article alone. No, not more minute analysis of the “Hobbits of Indonesia” (not read that one yet, but – to go all Iain M Banks for a moment – does the obsessive human interest in the details of our family tree perhaps represent some kind of species-level insecurity?), but “The Rise of Vertical Farms” by Dickson Despommier. The author should perhaps have credited “The World Without Us“, but he makes the point that we should farm indoors and leave nature to absorb the excess carbon we’ve been stuffing into the atmosphere.

The key argument is that you can grow so much – so much less riskily too – in controlled climate conditions indoors: “4 growing seasons, double the plant density, and 2 [or more, surely, of many crops - judging by a photo I once saw in the Guardian of a hydroponic indoor vegetable farm in Tokyo] per floor”, so that, excusing the quaint American units, a “30-story building covering one city block [5 of these 'acre' things] could … produce 2,400 acres of food”!

Despommier worries about how his vision can be made to happen, but in fact it’s simple. As soon as a realistic price is put on ecosystem services, there’ll be a huge economic incentive to invest in “vertical farms”.

The Electro-Kinetic Bandwagon

My first reaction on reading an interesting Guardian CiF piece by Professor David MacKay discussing a method of scavenging kinetic energy from motor vehicles was that the energy belongs not to the scavenger but to the owner or user of the vehicle who, rather than have it scavenged without permission, may want to scavenge it themselves. They can do this by, for example, employing a KERS (kinetic energy recovery system), or “regenerative braking”, as is being done now by some F1 teams, as well as so-called “hybrid” cars, and as is likely to be standard on motor vehicles within a decade or so.

I was therefore somewhat bemused to read that Sainsbury’s intends to install a system to capture kinetic energy from cars using its supermarkets. It seems Ealing Council is also about to shell out large sums on the deployment of “electro-kinetic” technology in place of traditional speed-bumps. And I happen to have an indirect interest in how Ealing Council spends public money!

My second observation was that speed bumps don’t actually slow vehicles down by making them drive up a little hill. We’ll see later that simple physics demonstrates that this couldn’t possibly be the case. No, you slow down because driving fast over speedbumps is bad news for your car and could even harm the people inside it, let alone any fragile objects in the boot.

Still, I suppose it’s possible that a different kind of speed-bump could slow you down by extracting energy. As the inventor’s website points out , in FAQ number 1, the only sitings of the electro-kinetic device that won’t steal energy from the vehicle are those where the car is braking anyway. Let’s hope potential customers have thought this through. If the car isn’t braking anyway, stealing its energy and converting it to electricity is incredibly inefficient. Most of the energy in the fuel has already been lost through inefficiencies in turning hydrocarbons into carbon dioxide, water, trace pollutants and kinetic energy. Most of that kinetic energy will be lost converting it to electricity.

But could the “electro-kinetic” technology even extract enough energy from cars? Will it provide the electrical power output that is claimed?

Now, the term “electro-kinetic” seems more 1909 than 2009. In fact, the technology is 19th century as well, as YouTube shows. Rocket science this isn’t. Nevertheless, we can apply the same laws of physics to “electro-kinesis” as to rocketry.

Like any good MBA, I started out by looking at the financials. The Guardian reported back in February that:

“The ramps – which cost between £20,000 and £55,000, depending on size – consist of a series of panels set in a pad virtually flush to the road. As the traffic passes over it, the panels go up and down, setting a cog in motion under the road. This then turns a motor, which produces mechanical energy. A steady stream of traffic passing over the bump can generate 10-36kW of power.

The bumps can each produce between £1 and £3.60 of energy an hour for up to 16 hours a day, or between £5,840 and £21,024 a year. Energy not used immediately can be stored or fed into the national grid.”

I wondered how much power you’d have to extract from each vehicle to achieve even 10kW for 16 hours a day. Let’s assume one vehicle passes every 10 seconds on average, that is 360 per hour. We have to extract 10kWh/360 of energy from each vehicle to make the projected return, that is around 28Wh of energy. Is that feasible?

Maybe we ought to turn things round and see how many vehicles we’d need. Back to Professor MacKay’s article where he writes:

“Let’s guess that the kinetic road plates extract one fifth of the kinetic energy of the arriving car. For a car weighing one tonne travelling at 20mph when it hits the road plates, the extracted energy comes to 0.002 kilowatt-hours (kWh).”

It appears we have a slight order of magnitude problem. If we only extract 2Wh of energy from each vehicle, we need 14 times (my 28Wh/David’s 2Wh) the 360 vehicles per hour that I assumed. That is, 1.4 cars per second for 16 hours a day. This seems a big ask. Remember the old “2 second (from the car in front) rule” of road safety campaigns? And we can do some more arithmetic: 20mph (let’s be generous and call it 36kph), is equivalent to 36000m/3600s, that is 10mps (metres per second). That is, we have to have one car every 10 metres all day.

Let’s carry on, though. David has guessed “that the kinetic road plates extract one fifth of the kinetic energy of the arriving car”. Now, that seems a lot me. I’m not a physicist, undergraduate level maths for biologists is as far as I ever got, but I do recollect that kinetic energy is a square function (1/2 mv^2 if I remember rightly). So to lose 1/5th of my energy is equivalent to losing around 10% of my velocity. As a driver I imagine I’d have to hit a rather large kangaroo to be slowed by 10% from 20mph. And a little thought about the other term in the kinetic energy equation – mass – suggests that in fact I’ve underestimated. Applying conservation of energy, a car weighing 1 tonne would have to collide with a very large kangaroo, in fact one of 1/5th the combined mass of the car and the kangaroo – 250kg – to lose the energy required, assuming the car and the kangaroo end up travelling with the same velocity after the collision. Hey, who says physics can’t be fun?

How much is 2Wh anyway?  Remember, we’re generating this every second when a car passes over the “electro-kinetic” device, so our power output is 7.2kW (note we’re already a bit less than the 10kW claimed).   In other words, the energy scavenged from a car should be able light 72 100W lightbulbs – the kind that are so extravagent they’ve now been banned – or 7.2 single-bar electric heaters.  Suspicious?  I am – it may not be Hiroshima, but it’s a spectacular energy conversion nonetheless.

The description of the “electro-kinetic” device tells us that the principle is in fact to extract potential energy from the car, rather than kinetic energy directly. The car’s kinetic energy is used to drive up a ramp, which falls, driving the mechanism in a pit below. This is most clearly seen in the YouTube video. The picture illustrating David MacKay’s CiF piece doesn’t really tell you much. In fact, I’m beginning to wonder if that picture actually shows the final product – it may just be one of those metal plates that are often used to stop people and cars falling into holes in the ground!

How far, then, would a 1 tonne car have to fall to release 2Wh of energy? The relevant equation is that for potential energy:

PE = mgh

where energy is in Joules, m is in kg and h in metres.  g is the gravitational constant, approx 10ms^-2.

As every Cambridge physics professor knows, 1Wh = 3600J.

Therefore we have:

7200J = 1000kg * 10 ms^-2 * h

h = 7200/10000m = 0.72m or 72 centimetres.

Yeap, if my arithmetic is correct, with perfect efficiency your car would need to drop 72 centimetres to provide 2Wh of energy to an electro-kinetic device. Or to slow down by 10% from 20mph – this calculation explains my hunch about how speed-bumps actually work!

Now, if I was going to assemble the best engineers to design such an “electro-kinetic” device, I wouldn’t promise more than around 30% efficiency.  But even if the electro-kinetic engineers can exceed that dramatically, your car would have to drop at least 1 metre to provide 2Wh of energy.  You should experience a short period of freefall on the way to Sainsburys.  But don’t worry, it’s all in a good cause!

Have another look at the YouTube video. It looks to me like the car drops more like 10 centimetres. And the prototype is not driving 72 100W lightbulbs, but 10 of what look like 12W halogen lamps, which only light up when a car is actually passing over the ramp. At least the video only claims “500-800W” output. It’s not clear whether this is the peak or average – which rather matters. Even if we’re talking about continual output, how could the prototype be scaled up to “5 to 10kW”? The only way I can imagine is – rather than dropping cars through 1m – to drop them through 10cm 10 times, i.e. to bump along a series of electro-kinetic ramps. Pack your eggs carefully!

I have to say that my conclusion is to suspect a similar mix of well-meaning, but naive public procurement crashing into commercial interests to that which has led to the biofuel disaster. Garnished with the hopeless optimism that accompanies new technologies, of course. During the dotcom boom I saw at least one sales estimate that was overoptimistic by 2 orders of magnitude (100 times), so I wouldn’t be entirely surprised to find a similar phenomenon affecting “green” technology. I hope Sainsburys and Ealing Council have validated the claims for “electro-kinesis” – and only deploy it where cars have to brake, providing an escape route, of course, for vehicles with KERS!