Bishop Hill David Mackay at Oxford
May 16, 2010 Climate: WG3 Energy This is another guest post by DR. David Mackay is Professor of Physics at Cambridge, a Fellow of the Royal Society and a member of the World Economic Forum Global Agenda Council on Climate Change.
Another talk from Oxford. This is my report of David MacKay’s talk on Sustainable Energy – without the Hot Air in the Department of Engineering Science on 13 May 2010.
David MacKay said that he likes back-of-the-envelope calculations such as: if we were to grow biofuel crops alongside roads, how wide a band of crops would be needed to power the traffic on that road? Answer – about 8 km – which shows that changing away from fossil fuels will not be easy. We (the developed world) have an addiction to fossil fuels which is not sustainable, for three reasons: 1. Fossil fuels are a finite resource; 2. They produce CO2 which goes into the atmosphere and oceans, and which the scientists tell us is a massive geoengineering experiment that we would do well to stop; and 3. we should be concerned with security of supply.
Ice core data tells us that CO2 levels started to increase about 1769, the year that James Watt invented the steam engine and the industrial revolution began. We should reduce CO2 emissions to zero eventually, and aim to reach 1 – 2 tonnes per person per year by 2050. The world average is currently 5–6 t and only Congo and Bangladesh meet the 1–2 t target.
MacKay then noted the units that he uses. He quotes energy in kWh and power consumption in kWh per day per person. They may not be physicists’ units, but they relate to personal experience and allow us to deal in small numbers, not billions and trillions. So a UK house runs on about 80 kWh/day, a 100km car journey is 80 KWh, and a plane trip London to LA and back is 10,000 kWh. A phone charger left on for one day uses the same energy as driving a car for one second – so it’s important to realise what matters and what doesn’t. In the UK we use roughly one third of our energy on transport and one third on heating and the rest can be largely supplied by electricity, so it makes sense to look at the areas of transport, heating and power supply first. Total energy use in Europe is about 125 kWh/day/person – in the US or Australia it’s twice this amount.
Considering whether renewables can meet this energy demand, MacKay considered the power available per unit area of land – since renewables generally require land (or sea) area – what sort of areas are we talking about?
For instance biofuels only generate 0.5 W/m2 (somewhat more in the tropics), while wind can give 2-3 W/m2 and up to 20 W/m2 is available from solar PV. Superimposing these data on a graph of per capita energy consumption against population density (see versions here on his blog) the amount of land needed to meet countries’ energy needs by different renewables can be calculated. For instance, the UK consumes about 1.5 W/m2 so to gain all our energy needs from wind power, half of the country would have to be covered with wind farms. MacKay has checked these figures for wind farms in the UK, and finds that they do generate about 3 W/m2. But could technological advances push these numbers up? He thinks not – larger windmills need more space, so the energy/ area does not go up by much. There are promising designs, such as kite-based windmills, but they are not expected to use less space. But put another way, to generate 17 kWh /person /day (14% of energy needs), one 2 MW windmill would be needed per 700 people. This would need about 7% of the UK’s area, or half the area of Wales.
Solar panels would be worth fitting to south-facing roofs in the UK. They have been installed on a large scale in Bavaria, on fields as well as roofs (though they use land that would otherwise be usable for farming) and generate about 5 W/m2. Solar PV efficiencies are near their theoretical limit but of course depend on the amount of sunshine. Concentrating solar power in deserts is likely to be the most effective and can reach 20 W/m2. But large areas of panels are needed and they are expensive.
He also considered tide power, undersea ‘windfarms’ using North Sea tidal currents, and offshore wind power – regardless of the type of renewable energy they all need ‘country-sized’(or ‘sea-sized’) areas to generate a significant proportion of a country’s needs. And each scheme, whether land or sea based, attracts protest. Even a 15-fold increase in UK’s renewables could only meet about 20% of our energy needs. But we have room to install a range of different renewable technologies where they are practical, that would reach the total we need.
Can we reduce demand? The country is unlikely to wish to reduce population, and lifestyle changes are unpopular, so can we increase efficiency? For instance in transport, electricity is far more efficient way of powering a car than a petrol engine (current electric models consume about 21 kWh/100km compared to 80 kWh/100km for a typical petrol car – though inefficiencies in electricity generation are not taken into account). But prototypes suggest this could be improved to about 6 kWh/100km, and renewables could be used to generate the electricity.
Domestic heating is another huge area – here MacKay suggested improving insulation, and adopting air source heat pumps, which are popular in Europe but have not been widely introduced in the UK – he’s not sure why. Pilot projects in the UK have not shown the coefficients of performance found elsewhere (300-400% in Germany and Japan based on the electricity used) – again he’s not sure why. And for a simple idea – read your meters and see what makes a difference. But, efficiency gains can lead to increased consumption in other areas from the money saved.
So, in summary, his suggestions on the demand side are to electrify transport, insulate houses and improve heating efficiency particularly using heat pumps. And Britain should generate electricity from a wide range of sources: mainly nuclear, wind and imported solar (from north Africa), with the rest from UK solar, clean coal, hydro, tidal, biomass and so on. A combination of these would more than supply the UK’s energy needs.
Answers to audience questions:
Fluctuations in wind energy are real, and need to be compensated, but this does not need fossil fuel. Wind + nuclear + hydroelectric storage such as Dinorwig would meet much of the needs. If integrated with smart meters, the electricity used to heat water and charge cars overnight could be adjusted to match supply (provided consumers were guaranteed that they would have charged cars and hot water by the morning).
Micro CHP is unattractive as it locks the country into using gas or biomass, and compared to efficient large power stations and condensing boilers saves only about 12%. Would prefer to move to heat pumps.
The supply of many rare metals (e.g. Li for batteries) is about 40 years – but this is probably only an apparent limit since mining companies will explore for more when the supply starts to run out.
How well do other countries do? Denmark is often held up as a role model but has higher GHG emissions per person than the UK, as does Germany. See graph of GHG emissions vs energy use – but note how far away we are from 1 tonne per person: http://www.inference.phy.cam.ac.uk/withouthotair/cI/page_337.shtml
Reader Comments (39)
Prof. Mackay states in his original article that "Concentrating solar power stations in deserts, for example, can produce 15 or 20 watts per square meter, on average year-round, day and night."
Solar cells that are capable of producing electricity at night have been demonstrated in Germany and Spain so I suppose that we can accept Prof. Mackay's claim at face value. What a remarkable breakthrough. If verified, it will surely lead to a Nobel Prize in physics, not one of the peace variety.
RayG
The solar plants simply store excess energy during the day by melting salt/heating water. This heat is then used to produce electricity at night. It is not a new idea.
I'm afraid MacKay's reported comments are simple not credible. Again, I can only suggest readers go to:-
http://www.raeng.org.uk/news/releases/shownews.htm?NewsID=553
and download "Generating the Future". So far as I am aware this is the only serious study which has been carried out into the practical implications of reducing CO2 emissions by 80% by 2050 (let alone BuffHuhne's LibDem manifesto target of 100% reduction - not using nuclear.)
And don't forget that the RAE's working group that produced the "Generating the Future" report are 100% true believer AGW alarmists, not a bunch of awkward skeptics.
MacKay's comment "Wind + nuclear + hydroelectric storage such as Dinorwig would meet much of the needs" is either ignorant or dishonest.
Wind managed an average of 0.8% of total electricity demand (not even considering domestic heating and transport) during the recent "mild" winter December - February. There are two pumped storage schemes in the UK, Dinorwig and Ffestiniog. They are capable of producing a modest amount of peak demand electricity, but enough to balance 3,000 becalmed wind generators? Or the projected 6,000 offshore generators? Not a maiden's prayer. How many more sites are there suitable for pumped storage in the UK? One or two maybe? Would they get planning consent? Would the Greenies support them?
As for nuclear, this is capable of producing base load only. Completely impossible to balance Big Wind. And it is clear that the current CONDEM crew have no serious intention of giving any political support to nuclear, so it is extremely unlikely that any new stations will be built until people in the UK tire of shivering in the dark.
Prof. Mackay entire plan depends on Europeans willingly giving the North Africans control over their electrical energy supply - a notion is which to so absurd I wonder why he bothers to suggests it.
Tim
"The solar plants simply store excess energy during the day by melting salt/heating water. This heat is then used to produce electricity at night. It is not a new idea."
There are many new - and old - ideas for storing electricity. Perhaps, Tim, you could come up with one which just might, possibly, be technically feasible even at enormous cost?
Pumped storage is one and intermittently pumping water is one of the few things for which wind generators are quite appropriate. But the scope for this is very limited. Melting salt and heating water and then using it to produce useful amounts of electricity? Yeah. Right. Go on, where is this being done on a meaningful scale? Do say!
Many thanks for posting my report, Bishop. A minor correction to your introduction, David MacKay is at Cambridge, not Oxford. And it's worth noting that he is Chief Scientific Advisor to the UK's Department of Energy and Climate Change.
David Mackay richly deserves to be a fellow of the Royal Society, renowned as it has been since Newton for rejecting real science (Harrison on longitude, Ross on malaria, Wrights on aeroplanes). His comments above are in that rich vein: "We (the developed world) have an addiction to fossil fuels which is not sustainable, for three reasons: 1. Fossil fuels are a finite resource [they are not, see Thomas Gold on the Myth of Fossil Fuels, first of which is that oil is a fossil fuel when it is not, next time you do some petrol sniffing see if you can spot the fossils, but nobody at the RS has the foggiest notion of what a fossil fuel is, and especially not any of its present (Rees) or immediate past (Lord May) or next President, Paul Nurse];" "2. They produce CO2 which goes into the atmosphere and oceans, and which the [pseudo-] scientists tell us is a massive geoengineering experiment that we would do well to stop" [why, when ALL our food is dependent on atmosphreric CO2]; and "3. we should be concerned with security of supply". Why, so long as there are people out there with oil to sell? Even the wretched BP admits that the world's Proven (One P) oil reserves are now as they have always been since 1950, even earlier, at least 30 years of CURRENT consumption.
FInally, Mackay's initial comment about biofuels needing vast amounts of farmland if they are to replace petroleum, ignores that burning biomass, palm oil, ethanol or any of the others releases just as much CO2 as burning petroleum. Truly, only an FRS like Mackay could be so ignorant as not to be aware that burning anything needs O2 before it releases CO2.
Is there any evidence that science is even taught anymore in Britain? I will send £10 to the first who sends me an A-Level chemistry examination that shows any requirement to know that burning carbon needs O2 and produces CO2. Certainly it seems all too easy for Mackay to be FRS without knowing that.
Martin,
I don't know how efficient the heat storage mechanism are and I suspect you are right to be sceptical. I was only pointing out that the claim of being able to produce power from a solar power plant at night is technically plausible.
"The country is unlikely to wish to reduce population"
I wouldn't take this for granted. For several decades the lifetime fertility rate in the UK has been below 2 per women, the level necessary to maintain the population in the long term. If this rate continued, and in the absence of net immigration, the population would eventually begin to decline. Many would welcome this, as the UK (and especially England) has one of the densest and most urbanised populations on the world. It also seems consistent with individual choices, as women, on average, do not seem to want a lot of children. However, there are signs that the fertility rate is picking up again, so this may not last.
"Concentrating solar power in deserts is likely to be the most effective and can reach 20 W/m2"
It is rather along way from North Africa to the UK. Can an electrical engineer tell me what transmission losses would be involved?
Tim Curtin - burning biomass releases carbon dioxide that was recently in the atmosphere, so makes no net change to atmospheric CO2 concentration (on a timescale of months or years). Fossil fuel burning is exactly the same chemical process, but that CO2 was last in the atmosphere millions of years ago, and releasing it now does increase atmospheric CO2 concentrations.
I'm not sure what your point about oxygen is, but last June's AQA paper includes the question
- the £10 can go in the blog tipjar of your choice :-)I am becoming increasing sceptical about the quality of the senior scientists we have in this country. Given all the variables involved in moving to renewable energy on a massive scale, it is clear to me that it's not only unlikely that we'll get an 80% reduction by 2050, it's impossible to do so without deliberately taking our society back to the middle ages. While I quite understand that this is the fervent wish of the environmentalists, it's unlikely to happen. And if it did we represent less than 2% of all GHG emissions, and will have no affect on the world's total output.
I continue with the theme, that the scientists, and environmentalists are totally naive about our ability to shift from fossil fuels to renewables on a scale large enough to replace the fossil fuels. Not only will it require massive long term engineering projects to design the renewables, build them and test them, but even then there won't be enough energy to support us without massive changes in our lifestyles.
Envrionmentalism is a religion, it has the main characteristic of both Islam and Christianity, the central belief that humans are sinners and unless they change their ways the world will be destroyed. All three have core characteristics that any reasonable person wouldn't shy away from: loving they neighbour, peace, charity, helping the poor, conserving our natural surroundings. All three have extremists who would cheerfully put to death those who don't agree with their remedies for the salvation of mankind. You only have to look at this week's New Scientist to see the environmentalist taliban unleashed on the sceptics to see an example of how far they are prepared to go to deal with people they see as heretics.
Contrary to statements above and popular belief, nuclear power stations can do more than just baseload. Because of the high capital costs, it makes economic sense to run them in baseload. However, with economic incentives, they can do load follow and limited AFRO (automatic frequency responsive operation). It needs different fuel design and management and a revised safety case, but it can be done.
I thought the way that solar power plants could generate electricity at night was by the simple expedient of criminals playing arc lights onto to them powered by the grid. When you get 4 times the rate it's a splendid return. I doubt that any of the green bureaucrats thought to limit the feed in tariff for solar to the daytime.
Mackay cannot be a real scientist but of course he is feted by amongst other the BBC.
Paul
"MacKay suggested improving insulation, and adopting air source heat pumps, which are popular in Europe but have not been widely introduced in the UK – he’s not sure why."
The main selling point for air source heat pumps in France is that 15% of the cost is tax deductible. The salesmen are less forthcoming on their poor performance in frosty weather when the heat exchanger ices up and the pump has to go into reverse to thaw it out.
Power consumption is high at start up and in cold weather. There are already stories of neighbours suffering voltage drops if the farm up the lane has its heat pump and its milking machine on at the same time. I don't know whether EDF is considering the cost of upgrading rural power lines, but they ought to be doing so.
The efficiency of HVDC cables is a loss of about 3% per 1000 km.
Have a look:
http://www.tennet.org/english/tennet/news/Langste_onderzeese_hoogspanningskabel_ter_wereld_geopend.aspx
"Solar PV efficiencies are near their theoretical limit but of course depend on the amount of sunshine."
Nonsense. You can get to 45% with multi-junction cells. Even higher than that with the addition of a fresnel lens. compare that to the 22% of conventional silicon or 18% with thin film technologies.
These are currently made in small scale and mass production is just beginning....prices will come down dramatically, just as the other two have (those two currently falling in price by 4% a qyarter...20% a year(.
The line loss would be approx. 17% from Libya to the Midlands unless, of course, you used superconducting transmission lines.
Tim Worstall,
The efficiency of solar cells is 20%, some come to 24%. Using a fresnel lens does not increase the efficiency of the cell, it only concentrates more light on a smaller area. It heats up the solar cell, which means that it actually decreases efficiency (try to read the specs of a modern solar cell and tell me that I am wrong!). The major problem with fresnel lenses is to avoid heating and burning the cells and they cause the need for active solar tracking to be really effective (a fresnel decreases the part of the sky that is projected on the PV cell) . The other cells (ThinFilm) you mention suffer from lower effiency, limited life time, due to sensitivity to moisture and temperatures (You can get them very cheap on Ebay). If the cells are not properly balanced, ie they all have more or less the same specs, then they will wear out very rapidly This can be prevented by bypass diodes (which are present in most good quality panels), but they actually short circuit the less effective cells, giving rise to a lower efficiency of the entire panel. Especially when one does not clean them regularly and allow for some cells to become covered by dirt or leaves. (I will have a dramatic video on my blog in the near future). Efficiency will drop drastically. Multi junctions are prohibitively expensive.
"There are promising designs, such as kite-based windmills"
They are not promising if the generator is in the air, connected to the ground by a conducting cable. As John Brignell asks, "What is the weight of the cable?"
http://www.numberwatch.co.uk/2006%20February.htm#enginasters
DR. David Mackay is Professor of Physics at Cambridge, a Fellow of the Royal Society and a member of the World Economic Forum Global Agenda Council on Climate Change.
Did this man learn nothing from the absolutely dismall performance of the UK's "Windmills" during the last 2 winters?
How can someone with so much education come across as so stupid?
Or is it of course just religous dogma?
A Little Off Topic, but have you noticed that since the change of Government in the UK the "Lets cut CO2" adverts are back with a vengance?
re: Gas in the UK - this Jan09 report from National Grid is interesting:
http://www.nationalgrid.com/corporate/Media+Centre/Press+Releases/Global+Press+Releases/020209.htm
Sorry, shorter URL here:
http://www.nationalgrid.com/uk/Media+Centre/Documents/biogas.htm
Possibly dumb question, but what about syngas process like Fischer-Tropsch or Sabatier to turn gas into 'fossil' fuel? Sabatier is CO2 + 4H2 → CH4 + 2H2O, we supposedly have an excess of CO2 and people get excited about the potential of a hydrogen economy. At least till the infrastructure costs are pointed out.
I'm assuming it's a cost/efficiency issue, especially if the process energy costs are high. If 'green' energy is unreliable then may be this could be a way of using surplus energy. Doesn't meet 'green' objectives of reducing the numbers of cars on the roads though.
Youv'e got to admire the 'thinking': peak oil is a trigger for panic - but peak lithium is a trigger for complacency. ;-)
Just a correction to the statemnent above that "There are two pumped storage schemes in the UK, Dinorwig and Ffestiniog."
There is also Cruachan and Sloy in Scotland.
The original post is unnecessarily difficult to skim correctly.
Perhaps you could rearrange the first sentence so that folks like me can't accidentally parse it as (fading into the second sentence and thus) referring to "Doctor David Mackay"? I had to do some backtracking to figure out what was going on. An easy quick fix would be to add a paragraph break after the first sentence, perhaps also enclosing the first sentence in parentheses.
Also, it would be helpful to label the without-the-hot-air hyperlink as "his freely-downloadable book": i.e., "...talk on his freely-downloadable book *URL*, in the Department...".
Having just skimmed the first 15 pages or so of that online book, it seems to me that Mackay is guilty of flaky preaching to the choir about the underlying AGW problem. He spends pages in a lovingly detailed victory dance over the counterargument that CO2 concentration hasn't increased. Then he spends less time on the counterarguments about CO2 sensitivity --- disposing of them by uncritically endorsing IPCCish results as a scientific consensus and thus a reasonable estimate of CO2 sensitivity. I don't see any nonpartisan way to justify that. As far as I can tell, disputes about the existence of a rise of CO2 level are almost inaudible compared to disputes about temperature sensitivity. (CO2 level disputes seem to be a distant fourth behind at least three other disputes, about 1. temperature sensitivity, 2. temperature measurements, and 3. credibility of current-generation climate models.) And the question of how we judge a valid consensus is an interesting one from the point of inference and statistics; note that Wegman took a swing at it. Mackay has plenty of expertise in the fundamentals of statistical reasoning, and it would be nice if he'd write even a third as much about back-of-the-envelope/quantitative-elevator-pitch cross-checks of his confidence in the IPCC temperature sensitivity and consensus as he spent on such cross-checks of CO2 level rise.
Yikes, I see this already an awfully long comment, and I still have ever so much more to say! (How can I be bankrupt? I still have checks left!) Fortunately I still have the password to my long-dormant blog, so I've written it up there.
one last remark here: Mackay's other downloadable book, _Information Theory..._, is impressive. (I downloaded it five years ago in order to study several sections of it.) Hence my particular interest in seeing what Mackay had to say about AGW.
A nuclear plant on about one sq km can produce more than a gigawatt. This works out to on the order of a kilowatt per sq meter, 24/7.
"... we have room to install a range of different renewable technologies where they are practical, that would reach the total we need."
Yes, indeed. And surely Britain can do without those silly peaceful countryside vistas and unspoiled Scottish highlands. Wouldn't everybody really rather look at phalanxes of enormous grotesque industrial wind turbines? Who cares if they generate nothing but tax breaks and subsidies for financiers; they must be wonderful -- all the bureaucrats in Brussels say so...
Atomic Hairdryer,
Not a dumb question at all, a very good one. Such processes work wonderfully well. e.g. South Africa currently produces huge quantities of her fuel requirements from coal in exactly that way.
Peak oil and similar are attractive to a certain mindset, but they forget the implications of Hotellings Rule - The price of an exhaustible commodity will converge towards the price of a substitute resource.
If the donkey engines are not pumping anything and the shale is dry, but there is a demand for liquids to come out at the pumps downtown, people will start processing natural gas, coal or whatever. Equally, if the prie of crude goes to 300/barrel, I think it becomes very attractive to start processing natural gas etc?
Professor at Cambridge and Chief scientific advisor to the Ministry: who was the lecturer ? just a question of conflict of interest !
David Mackay is a coward who promotes the AGW scare but is too afraid to debate Christopher Monckton. Ask Lord Monckton, he can confirm this.
Re Chuckles
"Not a dumb question at all, a very good one. Such processes work wonderfully well. e.g. South Africa currently produces huge quantities of her fuel requirements from coal in exactly that way."
That's what got me wondering, plus it's development during the 2nd world war out of necessity, which should be the mother of invention after all. We've had a few decades to refine the processes and it seems economical in South Africa and a few other places.
As an engineer, proposed mitigation solutions don't seem fit for purpose in addressing supposed problems. We have a CO2 problem apparently, so we propose to spend billions sequestering it and burying it in the ground, which seems very wasteful. We have a supposed 'peak oil' problem, but then CO2 could help with that using enhanced recovery using liquid CO2. Or if we had an impending 'peak gas' problem, could use it for enhanced gas recovery.
We have an impending electricity problem and we're suggesting electric cars as a replacement for oil burners, increasing electricity demands and potentially creating a 'peak rare earth' problem. Or, we could try hydrogen, but then enormous distribution and conversion costs, plus need to make the hydrogen as well.
A more sensible approach would seem to me to optimise what we already have. Wean people off domestic gas, use that more efficiently. Electricity is more flexible but we're running out, and we're trying to replace generating capacity we have with the most expensive and least efficient alternatives. Yet if we had plentiful electricity at reasonable prices, we could potentially synthesise gas, petrol and oil and increase our energy and fuel security,
Current policy doesn't really seem to make any sense.
Atomic H, You'e correct, the process has been fine tuned and SASOL makes a fortune out of it. Your problem is that you ARE an engineer, and don't buy into the artificial political constraints placed on the solutions -
e.g. you are never allowed to use nuclear; if rivers are plentiful, hydro is out; tidal is disallowed, and weak diffuse energy sources like solar and wind are mandatory.
A focus on completely impractical methodologies like hydrogen is also useful.
A useful rule of thumb is to do the inverse of what the politicians select. And of course, the developing countries will not implement any of it, and will cheer heartily as the west hamstrings itself and commits economic suicide.
How do these people get to be Professors?
"He also considered tide power, undersea ‘windfarms’ using North Sea tidal currents, and offshore wind power – regardless of the type of renewable energy they all need ‘country-sized’(or ‘sea-sized’) areas to generate a significant proportion of a country’s needs."
Ok, where exactly are any working designs that use tidal currents and undersea currents? There aren't any. Why would you consider something that doesn't exist?
Air source heat pumps are more efficient, than what? I live in an area that doesn't have natural gas hook ups, and my heat pump doesn't give off much heat below 25 F. It is supplemented by a simple set of resistant heater coils (like a toaster) to get luke warm air on those chilly nights.
In reality, ground coupled heat pumps are about 30% more efficient than air sourced. They are not practical for cities, as you need a big surface area, or deep well to run the exchanger through.
Import solar from North Africa? Has he ever looked at the engery loss per km in a high power line? Obvuiously not, or he wouldn't be suggesting this. Plus, you would have an infastructure vulnerable to terroists attacks.
More lithuim will be found. Where? Most of it is in China and Bolivia, in dry lakebed deserts. I think we probably have a good handle on how many of them are in the world. Plus processing large amounts of lithium, a heavy metal, has pollution and medical concerns. And no country has the grid to start supplying even 5% of their cars with electric power. OK, I guessed at the 5% value, but I'm probably closer to correct than this babbling baffoon.
"Multi junctions are prohibitively expensive."
So were chips with a million transistors on them only two decades ago. Come along now, you cannot possibly be insisting that a technology won't work based purely upon current costs of that technology.
If we accept Moore's Law as being even partially valid (which I most certainly do) then the cost constraint in the medium term for multi-junction cells is the price of the gallium and germanium (both currently at many hundreds of $ per kg) to make them. But then that cost itself is easy enough to reduce. (Hint, I work in the extraction of weird metals and yes, I do know what I'm talking about here).
@Tim Worstall
You may know what you're talking about wrt weird metal extraction but Moore's Law for million transistor chips works because of what the industry calls 'geometry'. The million transistors do not occupy any more 'silicon real estate' than the single transistor of 50 years ago (I may be exagerrating a bit). You're not going to generate much power with a 'reduced geometry' solar cell (simply because you can't intercept much power).
I'm also dubious that the cost of the materials will fall radically. Extracting a metal from its ore does not equal producing a high purity, low defect single crystal ingot.
"I'm also dubious that the cost of the materials will fall radically. Extracting a metal from its ore does not equal producing a high purity, low defect single crystal ingot."
Sure, but that's manufacturing. That is something that gets better. Si ingot has fallen from some $450 a kg to around $50 a kg over the past 5 or 6 years. An order of magnitude improvement in price.
BTW, the number of transistors on a PV cell doesn't increase the amount of sunlight that falls on it, this is true. But it does increase the percentage of such that becomes electricity.
It is arguable whether David Mackay is actually a physicist. His expertise seems to be in writing computer software.
Many of his back of the envelope calculations seem rather dubious.
ps There is no net energy return from biofuels because it uses more fuel to grow them than you obtain at the end,