You may have heard the legend of how in 212 BC, Archimedes defended the port city of Syracuse against the invading Romans by setting their ships afire with the help of mirrors that concentrated the sun’s light. It sounds a bit implausible…

However, maybe you’ve heard of Comte Buffon — the guy who figured out how to compute the number pi by dropping needles on the floor. According to Michael Lahans, Buffon also did an experiment to see if Archmedes’ idea was practical. He got a lot of mirrors, each 8 × 10 inches in size, adjusted to focus their light at a distance of 150 feet. And according to Lahans:

The array turned out to be a formidable weapon. At 66 feet 40 mirrors ignited a creosoted plank and at 150 feet, 128 mirrors ignited a pine plank instantly. In another experiment 45 mirrors melted six pounds of tin at 20 feet.

Should we believe this? I don’t know. Some calculations could probably settle it. Or you could try the experiment yourself. If you do, tell us how it goes.

But there are also non-military uses of concentrated solar power. For example, the new power plant named after Archimedes, located in Sicily, fairly near Syracuse:

Archimede website.

Archimede solar power plant, Wikipedia.

It started operations on July 14th of this year. It produces 5 megawatts of electricity, enough for 4,500 families. That’s not much compared to the 1 gigawatt from a typical coal- or gas-powered plant. But it’s an interesting experiment.

It consists of about 50 parabolic trough mirrors, each 100 meters long, with a total area of around 30,000 square meters. They concentrate sunlight onto 5,400 metres of pipe. This pipe carries molten salts — potassium nitrate and sodium nitrate — at a temperature of up to 550 °C. This goes on to produce steam, which powers an electrical generator.

The news is the use of molten salt instead of oil to carry the heat. Molten salt works at higher temperatures than oils, which only go up to about 390° C. So, the system is more efficient. The higher temperature also lets you use steam turbines of the sort already common in gas-fired power plants. That could make it easier to replace conventional power plants with solar ones.

The project is being run by Enel, Europe’s third-largest energy provider. It was developed with the help of ENEA, an Italian agency that deals with new technologies, energy and sustainable economic development. At the Guardian, Carlo Ombello writes:

So why hasn’t this technology come before? There are both political and technical issues behind this. Let’s start with politics. The concept dates back to 2001, when Italian nuclear physicist and Nobel prize winner Carlo Rubbia, ENEA’s President at the time, first started Research & Development on molten salt technology in Italy. Rubbia has been a preminent CSP [concentrated solar power] advocate for a long time, and was forced to leave ENEA in 2005 after strong disagreements with the Italian Government and its lack of convincing R&D policies. He then moved to CIEMAT, the Spanish equivalent of ENEA. Under his guidance, Spain has now become world leader in the CSP industry. Luckily for the Italian industry, the Archimede project was not abandoned and ENEA continued its development till completion.

There are also various technical reasons that have prevented an earlier development of this new technology. Salts tend to solidify at temperatures around 220°C, which is a serious issue for the continuous operation of a plant. ENEA and Archimede Solar Energy, a private company focusing on receiver pipes, developed several patents in order to improve the pipes’ ability to absorbe heat, and the parabolic mirrors’ reflectivity, therefore maximising the heat transfer to the fluid carrier. The result of these and several other technological improvements is a top-notch world’s first power plant with a price tag of around 60 million euros. It’s a hefty price for a 5 MW power plant, even compared to other CSP plants, but there is overwhelming scope for a massive roll-out of this new technology at utility scale in sunny regions like Northern Africa, the Middle East, Australia, the US.

The last sentence is probably a reference to DESERTEC. We’ll have to talk about that sometime, too.

If you know anything about Archimede, or DESERTEC, or concentrated solar power, or you have any questions, let us know!

26 Responses to Archimede

  1. Nathan Urban says:

    For some reason this post appears in the “Latest Posts” box in the upper right corner, but (at least in my browser) the text doesn’t appear on the main Azimuth page: the Solèr’s Theorem post is still on top.

    • John Baez says:

      I’m not having that problem. Is anyone else having that problem?

      • Tim van Beek says:

        At the office I had the same problem, now that I’m home everything is okay.

      • DavidTweed says:

        FWIW, I had a very weird experience. The RSS reader said the new post was there so I came to read the whole thing and it wasn’t there (but Nathan’s comment was as a way to get at it). A while later I refreshed the main page and it appeared on the main page. Later on I refreshed and it disappeared. Finally it seems to be there permanently.

  2. Ali Moharrer says:

    Nine units of SEGS (Solar Electricity Generating) plants built mid eighties through early nineties, in the Southern California deserts having been quietly and reliably generating a total of ~350 MW for a long time. With the recent permitting of other large scale CSP power plants also in California, more upgraded parabolic mirrors collector arrays will be used with a projected optical efficiency of 83%. See for example Blythe solar power project recently approved by California Energy Commission that will consist of four identical units of 250 MW power plants. Blythe Plant will be the largest solar power plant ever to be built at a single location though First Solar Agua Caliente PV power plant, with 290 MW AC rating continues to be the single largest solar generating plant in the world when completed and as things stand. The annual average solar to electric efficiency of these power plants is still lower than the conventional power plants but as technology improves, this efficiency figure may also change.

    • John Baez says:

      Thanks, Ali! I spent the morning learning about solar power. I added your information to

      Concentrated solar power, Azimuth.

      and also a long-needed new page:

      Photovoltaic solar power, Azimuth.

      Here’s what I wrote:

      As of 2009, photovoltaic solar power generated 21 gigawatts of power, a very small fraction of the roughly 4500 GW total global power-generating capacity from all sources (need exact figure!). However, between 2004 and 2009, the amount of photovoltaic solar power being generated increased at an annual average rate of 60 percent:

      • REN21, Renewables 2010 Global Status Report, page 29

      Quoting from this report:

      Cumulative global PV installations are now nearly six times what they were at the end of 2004. Analysts expect even higher growth in the next four to five years. Thin film’s share of the global market increased from 14 percent in 2008 to 19 percent in 2009 for cells, and from 16 to 22 percent for modules.

      Germany again became the primary driver of PV installations, more than making up for the Spanish gap with 3.8 GW added — about 54 percent of the global market. This was far above Spain’s prior record-breaking addition of 2.4 GW in 2008, and brought Germany’s capacity to 9.8 GW by the end of 2009, amounting to 47 percent of existing global solar PV capacity. While Germany has played a major role in advancing PV and driving down costs, its importance will decline as other countries step up their demand and reduce the industry’s reliance on a single market.

      After its record-breaking year in 2008, the Spanish PV market plummeted to an estimated 70 MW added in 2009, due to a cap on subsidies after the national solar target was exceeded. But there were other sunny spots in Europe. Italy came in a distant second after Germany, installing 710 MW and more than doubling its 2008 additions due to high feed-in tariffs and a good national solar resource; such strong growth is expected to continue. Japan reemerged as a serious player, coming in third with 485 MW installed after reinstating residential rebates and introducing a buyback program for residential rooftop systems.

      The United States added an estimated 470 MW of solar PV in 2009, including 40 MW of off-grid PV, bringing cumulative capacity above the 1 GW mark. California accounted for about half of the total, followed by New Jersey with 57 MW added; several other states are expected to pass the 50 MW per year mark in the near future. Residential installations came to 156 MW, a doubling from 2008 thanks in part to removal of the $2,000 cap on the federal Investment Tax Credit and to a 10 percent drop in installed costs relative to 2008.


      The First Solar Agua Caliente photovoltaic power plant, with an 290 megawatt alternating current rating, is slated to be the single largest solar generating plant in the world when it starts up in 2013. Located 65 miles east of the city of Yuma on the former White Wing Ranch, the Agua Caliente Solar Project will produce sufficient electricity to power about 100,000 average homes per year, displacing approximately 220,000 metric tons of carbon dioxide per year — the equivalent of taking about 40,000 cars off the road.

      • First Solar, Agua Caliente Solar Project

  3. Blake Stacey says:

    Greg Gbur has a nice summary of investigations into the Archimedes death ray, here.

    • Phil Henshaw says:

      Hi, I’m curious if any of you would concur with my calculation of the size of a 19% efficiency PV array with 7500 Wh/sq meter radiation, to generate the average amount of energy to deliver $1 of GDP?

      What I get is 1300sf for a day on average. So for your $6 glass of wine as average spending you’d need the equivalent of 7800sf of PV array?, and for your $50k income, the use of a 180,000sf array every day.

      • John Baez says:

        I find it a bit tough to follow these calculations. Let me try to redo some of them, sticking to metric as much as possible.

        The earth receives about 150 watts/m2 of solar radiation, averaging over location and time of day (including night!).

        You use a different figure…

        But following you, I’ll multiply by figure by 0.19 since solar cells aren’t perfectly efficient, and by 0.5 assuming only half the ground gets covered, and by 5/6 assuming an energy return on energy invested of 6.

        This brings it down to about 12 watts/m2.

        Then you do a conversion from energy to GDP, which people might argue about: you say that in 2008, the world GDP was about 64 trillion dollars, and the world energy consumption was about 512,000 quadrillion BTU. I like metric, so I’ll convert that to 5.4 × 1023 joules.

        Hmm, Wikipedia says the world used 4.7 × 1020 joules in 2008. That’s 3 orders of magnitude off!

        Where are you getting your figure of 512285 quadrillion BTU? Your table 3 doesn’t go up to 2008, but it seems to say that in 2007 the total energy use was about 477 quadrillion BTU. Again, that’s about 3 orders of magnitude off.

        Did you perhaps mean 512.285 quadrillion BTU? If I use that figure I get about 8000 BTU per dollar of GDP, which matches your figure.

        Okay, so you left out the decimal point in your table but it didn’t really affect the next step in your calculation.

        Let me redo it my way. Wikipedia gives a world GDP of $57 trillion in 2009, which is at least roughly consistent with your $64 trillion in 2008. (Did it go down due to the financial crisis?)

        So, I’ll use your figure of $64 trillion GDP and the Wikipedia figure of 4.7 × 1020 joules in 2008, and get 7.3 million joules per dollar GDP.

        Before I proceed, I have to ask, what does this figure of “7.3 million joules per dollar GDP” really mean? Surely it doesn’t take this much energy for me to produce a dollar of goods or services!

        But I guess you’re claiming it does?

        Anyway, to finish off the calculation, if one dollar GDP equals 7.3 million joules in some mysterious sense, and solar power brings in 12 watts/m2, then in some mysterious sense solar power brings in “one dollar per second per 6 million square meters.”

        But surely people building solar power plants earn a lot more than that from the power they sell!

        So I guess I’ll ask you again: what does “7.3 million joules per dollar GDP” really mean?

        • Phil Henshaw says:

          Yea, with complicated things I can never check figures unless I start over with the concept too. I’m using IEA World indicators time series data. My copy is linked from the references noted on that page, at:

          The GDP difference seems due to my using PPP dollars which effectively corrects the currency fluctuations for physical productivity, and gives that nice smooth GDP curve and matching smooth Energy use curve (fig 1).

          As to your question, “What does it mean… Surely it doesn’t take this much energy for me to produce a dollar of goods or services!”. I got: 8000 btu/sec = 8443528 joules/sec, so 8.4 million in 2008. So yes, that is exactly what it means, the total purchased energy the world was using in 2008, on average, to produce $1 of GDP.

          I’m not sure about your last calculation, but the rest seems OK except that I’m using 7500 Watts per sq meter per month from the charts of measured solar radiation at the ground referred to. I don’t know if the world average for mid-latitudes is somewhat above or below, to that’s just a sample number.

          The price energy is sold at is a quite different thing, and solar is generally subsidized to compete with oil, etc, so may be hard to gage. The $1 price the GDP value of using the 8000btu’s at the efficiency of the world economy. What I’m saying is that the value to the economy of using 8000btu or 8.4Mjoules, on average, is 1$.

          What happens is when you compare these figures (shares of global energy implied) with traceable energy uses for businesses to operate, the averages are generally greater than the traceable energy uses, often a difference of 500% or more. So, some untraced energy use seem to go uncounted.

          fyi – I have a long paper on the subject that’ll be in an upcoming issue of Sustainability (MDPI) fyi: There appears to be a fascinating cognitive error in the ISO standards used for designing measures business environmental impacts! Read the abstract and a couple pages and see what you think.


  4. John F says:

    The competitor for Desertec is the Sahara Solar Breeder Project.

    No extra-Google knowledge about the project, sorry.

    As a funny aside, I’m sitting here reviewing a climate related proposal from a good PI with PhD in environmental statistics. A prior/preliminary data table has an entry for the average of outliers!

    • John Baez says:

      A solar breeder project! Cool! The Azimuth Project has a page on solar breeders. I’ll have to add this information there.

      The idea of a ‘solar breeder’ is to make a solar power plant that makes solar power plants. The Sahara Solar Breeder Project wants to make photovoltaic panels out of Sahara sand! I’m not sure it’s a practical idea, but you gotta admit it’s got charm.

    • John Baez says:

      I added information about the Sahara Solar Breeder Project to our Solar breeder page. Here’s what I wrote:

      More recently, the following institutions in Japan:

      • University of Tokyo

      • Hirosaki University

      • National Institute for Material Science

      • Tokyo Institute of Technology

      • Chubu University

      • National Institute of Informatics

      have teamed up with the Université des Sciences et la Technologie d’Oran (USTO) in Algeria, and launched a joint initiative called the Sahara Solar Energy Research Center (SSERC). Commonly called the Sahara Solar Breeder Project, its self-proclaimed incredibly ambitious goal is to “build enough solar power stations by 2050 to supply 50 per cent of the energy used by humanity”. The plan is to build a solar breeder in the Sahara desert, and convert sand there to silicon wafers used in solar panels:

      • Michael Fitzpatrick, Sun and sand breed Sahara solar power, New Scientist, 30 November 2010.

      • Diginfo, The Sahara Solar Breeder Project, YouTube.

      The project appears to be led by Hideomi Koinuma from the Science Council of Japan, who proposed the idea at the 2009 G8+5 Academies’ Meeting in Rome:

      • G8+5 Academies’ Meeting; Rome, 26 – 27 March 2009, Programme, Accademia Nazionale de Lincei.

      Despite many news reports on this project, details seem hard to find, so it is difficult to tell how seriously to take it.

      Does anyone here know more?

  5. Tom Leinster says:

    Want to see concentrated sunshine melt rock?

    • streamfortyseven says:

      I’d be more interested in seeing concentrated sunshine melt iron and steel and aluminum… Do that, especially the last one, and we’ve got something to talk about.

      Here’s a patent application for a solar smelter (and a link to a database where you can search and get pdf files of patents for free):

      Here’s a web site, incidentally by the same guy who has the patent app above, about solar smelters. He’s apparently got a working model:

      Appropriately enough, it’s on a wiki devoted to the art of solar cooking:

      Two articles in Russian by the same author on large solar smelting furnaces, behind a Springer paywall:
      “Applied Solar Energy
      Volume 44, Number 1, 24-27, DOI:
      Analysis of operating characteristics of various
      smelting furnaces on a Large Solar Furnace, A. A.
      Abdurakhmanov et al.”

      “Applied Solar Energy
      Volume 44, Number 4, 284-287, DOI:
      Creating melting furnaces based on the large solar
      furnace, A. A. Abdurakhmanov et al.”

      Solar cookers can be used to solve the problem of deforestation (as in Haiti, where all of the woodbearing plants get burned for charcoal) and indoor air pollution from wood-fueled cooking fires:

      • John Baez says:

        Thanks for all the info! It will be duly transcribed into the Azimuth Project.

      • Tom Leinster says:

        streamfortyseven says “I’d be more interested in seeing concentrated sunshine melt iron and steel and aluminum…”

        Then you’re in luck: the video does show concentrated sunshine melt steel. It also says that the hot spot reaches 3500C, and that there is no known substance on earth that can resist that. The melting point of iron is 1500C, and aluminium a mere 660.

      • John Baez says:

        I started a page on solar energy based on what streamfortyseven told us:

        Solar energy, Azimuth Project.

        It’s just a stub so far, and I bet streamfortyseven could easily make it ten times better in half an hour. (Don’t worry about getting the formatting right; the elves will take care of that.)

        I’m sure it’s obvious to all of you, but converting bauxite ore into aluminum takes a lot more energy than melting aluminum cans to recycle them. Aluminum is highly reactive. This is why the pure metal form was isolated so late — 1825. And this is why Napoleon let his guests use gold forks and knives, while reserving the more precious aluminum cutlery for himself! Little did he know how tacky this would later seem.

        So, I’d like to see a solar-powered system melt rock and make aluminum!

  6. Tony Vladusich says:

    The Syracuse experiment was done by an MIT group and Mythbusters. My recollection from the episode was that the myth was busted.


    • john e gray says:

      Mythbusters is going to revisit the problem on Wednesday night (December 8) at the request of President Obama who appears on the show.

      • John Baez says:

        I thought for sure you were trolling us, John, but apparently not!

        Clearly Obama has been reading Azimuth.

        NEAL CONAN, host:

        This is TALK OF THE NATION. I’m Neal Conan in Washington.

        Over almost eight years now, Adam Savage and Jamie Hyneman have tested rumors, urban myths and tall tales. You’ve probably seen the “MythBusters” probe the mysteries of Christmas lights to see if they can actually set a tree ablaze, fire guns at each other to see if bullets really fuse together when they collide and combine Diet Coke and Mentos to see if that can really make your stomach explode – a very cool job that’s involved the detonation of tons of explosives over the years.

        And for this week’s episode, they got an invitation to the White House.

        (Soundbite of TV show, “MythBusters”:)

        President BARACK OBAMA: Now, I do know that science requires a lot of trial and error. Part of what “MythBusters” is about is testing out various hypotheses, and I think that we’ve got a big one that hasn’t been thoroughly tested.

        Mr. ADAM SAVAGE (Host, “MythBusters”): Which one is that?

        Pres. OBAMA: Well, it is Archimedes’ solar ray.

        Mr. JAMIE HYNEMAN (Host, “MythBusters”): Well, that is a classic.

        Pres. OBAMA: It is a classic, and so I’m hoping that we can take one more crack at it.

        Mr. SAVAGE: OK.

        CONAN: Using only mirrors and the sun, the Greek scientist Archimedes supposedly set fire to Roman ships during the siege of Syracuse. The MythBusters will join us in just a moment.

        Adam Savage and Jamie Hyneman are with us from our bureau in New York. Nice to have you with us on the program today.

        Mr. SAVAGE: Nice to be on.

        Mr. HYNEMAN: Hi.

        CONAN: And while you were at the White House, did you find out whether, in fact, you can still in places see the scorch marks from the fire the British set in 1812?

        (Soundbite of laughter)

        Mr. SAVAGE: Given that the entire interior was replaced sometime in the ’40s, I don’t think so.

        CONAN: OK, so that would be busted then?

        Mr. SAVAGE: I think so.

        CONAN: OK, without too much experiment. It must have been quite a thrill to be invited to the White House.

        Mr. SAVAGE: It is, absolutely. You know, on a day-to-day basis, our job is fairly blue-collar. We get beaten up and bruised, and our crew is pretty small. So, you know, getting invited to get kids interested in science with the president is pretty heady stuff.

        CONAN: But you had done the Archimedes story, I guess, a couple of times before.

        Mr. HYNEMAN: Yes, we have. But the difference with those was that they all involved stationary mirrors. We used one-foot-square mirror tiles like you can buy in a hardware store and precisely focused those at wood. And, I mean, yes you can set things on fire with mirrors. We know this, and that’s not what we were testing. In general, it’s: Would you be able to do that to an actual ship?

        And what you know, that’s where the episode with Obama in it came into play because we the big question was: Could you have shields from soldiers polished to a mirror finish and get them to set something on fire? And that’s a whole different thing.

        Mr. SAVAGE: And that was the one thing that we hadn’t done in the I guess two or three other times we’ve actually tested this story is we’ve never gotten the resources together to wrangle 500 soldiers on the shore.

        (Soundbite of laughter)

        Mr. SAVAGE: And in this case, it worked out perfectly serendipitously because not only was the perfect shoreline right across the bay in Alameda, but it was right next door to the school where Jamie’s wife has been teaching science for the last 20 years. And we used 500 of their students, middle and high school students, as our soldiers.

        CONAN: So your hoplites were provided by school.

        Mr. SAVAGE: Exactly.

        CONAN: Besides, if you’re getting an order from the president of the United States to try something out, you can’t sit there in the White House library and say: Mr. President, we’ve tried it. It’s busted. It doesn’t work.

        Mr. SAVAGE: You know, actually one of my favorite things that we do on the show is go back and retest things once we’ve got new data or new resources.

        I can’t think of another television show that would tell you, admit to you, that hey, last season, we wasted an hour or your time stirring something up.

        (Soundbite of laughter)

        • john e gray says:

          what is trolling? you don’t need to post, just curious.

        • John Baez says:

          The current definition of trolling seems to focus on quite nasty ways that people use the internet to make other people upset.

          But back when the internet was young, before the web was invented, trolling was often more benign. On so-called usenet newsgroups, people would make absurd claims with a straight face, just for the pleasure of tricking people into taking them seriously and arguing with them.

          For example, I once claimed (in some usenet newsgroup where nobody knew me) that just as the Egyptians had secretly built the golden ratio into the dimensions of the pyramids (a controversial claim), the Babylonians had secretly built the number pi into their architecture: a Babylonian column had been unearthed where the ratio of the circumference to the diameter was almost equal to pi! I was roundly denounced as an idiot until somebody pointed out that I was a mathematician and must have been kidding.. That was precisely what I wanted. That’s “trolling”.

          Similarly, I can imagine someone reading this blog article and posting an absurd comment claiming that Mythbusters was about to test whether Archimedes could have set those ships on fire…. at the insistence of President Obama!

          So, I thought you were trolling. But it turned out you were serious.

          By the way, I haven’t watched the show. What happened?

    • John Baez says:

      Tony wrote:

      My recollection from the episode was that the myth was busted.

      If you read Greg Gbur’s account, pointed out here by Blake Stacey, you’ll get a very interesting analysis of this question. Whether they busted the myth depends in part on what the myth was!

      • Tony Vladusich says:

        Yeah, as I wrote that comment I did a search to check the facts and noticed that the whole story was somewhat more complicated than I thought. Sounds like real science!

      • john e gray says:

        Pres.O was amusing asking them to reexamine the myth, but the Mythbusters did not choose poor approach to resolving it. Flat mirrors are almost impossible to focus to the point where they would burn cloth or wood, so where would Arch get the idea. Greek shields were concave not flat like the Roman shields, which is how a polished shield might have accidentally set something on fire, which is the mostly likely way he might have made an observation that might of lead it to try this. I was disappointed that the M people didn’t spend some time thinking like a bright high school students and tried to use a mirror might burn wood up close, and then determine if it were possible to try to accomplish the myth at a distance. Pres.O seems to be trying to hard to promote science in junior high school and higher in the USA now. By the way, he gave a very nice talk five min talk about the importance of science to the future before he handed out the National Medal of Science. You can find videos of both appearances on the white house website.

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