Archimedes’ Burning Mirror Problem Solved


 By Christopher Jordan

The ”Secrets of the Sun Sects” makes the case for the extensive use of solar technology by ancient civilizations. There are two strands of evidence, parabolic solar concentrators and heating large black stones. Through two simple devices, it is shown that the successful societies of antiquity were using the sun to underpin their industry, art and science. The solar relics are surprisingly common and are all tied together with the rediscovery of lost techniques that are proving useful today. The implications are explored in some re-framed histories of the important sun cultures.

The focus of this article is the parabolic solar mirrors that are supposed to have existed in antiquity. The majority of comparable proposals fall down primarily because there is no method to make the elusive devices. For centuries, the prevailing view has been that spherical reflectors make poor parabolas, ”The Math behind Burning Mirrors” refutes this completely. With this change of perspective, Christopher Jordan not only shows how they built and used these tools, but also explains many anomalies from the artifacts. These curved mirrors turn out to be the most powerful devices up until the twentieth century with amazing capabilities.

Parabolic concentrators

 The problem of how to make powerful solar concentrators has plagued historians and scientists from Archimedes’ time to Newton’s. The reasons for this interest are not abstract, but the practical uses of the ideal curve. A perfect parabola will concentrate sunlight almost infinitely, which can be very useful, alas, perfection is impossible to engineer.

A hemisphere is easy to make, but it is thought that it proves a poor parabola. The paper above shows explicitly that if smaller and smaller sections of a sphere are used, the approximation to a parabola increases exponentially. If a twentieth of a hemispherical surface is used, it is accurate to within one percent. If a hundredth of the surface is used, it is near perfect. Depending on the focal length chosen, these dishes can have incredible concentration ratios of hundreds of thousands. See the math paper for the calculations.

Concentration ratio as the pendulum length increases for a 1m Sun dish (Point source approximation)

The table above is calculated using the sun as a point source. When the size of the sun is taken into account the intensities range from hundreds of kilowatts to hundreds of megawatts per square meter. The math that underpins the idea is indisputable, but it is the physical proof that persuades most people. There is also the matter of whether the ancients had the technology to build such devices. To address these issues, the mirrors have to be made, tested, found in the archaeological record along with explicit evidence of ancient use.

Dish Construction

The construction task becomes much easier when only a small spherical section is required. To make a seven-degree spherical arc requires only a pendulum, grinder and patience. This can be combined with a potter’s wheel to speed up the process and guarantee the surface. No one argues that pendulums and potters wheels were unknown in the old world.

Pendulum & Potters Wheel Construction Method

With this set up, ancient craftsmen could make mirrors so powerful they could vaporize virtually anything at their maximum power. Beneath the upper limit, there are points where materials can be melted or just warmed. This is the solution to the ‘Burning Mirror Problem’ associated with Archimedes. These dishes have an intense beam focused at a distance equal to half the length of the pendulum. If the pendulum is 10m and the dish is 2m wide, there will be a point of light with just under 2MW/Sqm intensity created at 5m when the dish is pointed at the sun. This is powerful compared to the majority of these weapons, which were shield sized and designed to blind the enemy on the battlefields.

Historical Context

Weaponry is only a small field, in ”Secrets of the Sun Sects”, many of the other uses are demonstrated and then placed in their historical context. Some of the methods have been displaced by better ones, but others lost to time still have utility. The roles played in old stonework, fine art, jewelry, science and chemistry are explored in detail.

It becomes clear that many anomalous artifacts can only be explained by these devices. The most compelling are the huge vitrified stones found across the globe. Some experts deny that the finishes are glazes, primarily because they cannot be applied even today. These finishes cannot be created by any method other than an intense beam of light. This is adequate proof to most that the dishes were used in some cultures.

Alternatively, there are the countless references in texts that mention the devices in use. Prior to the rediscovery of the construction method, sun dish descriptions were considered fanciful exaggerations, now they can be fully appreciated. From the Iliad to the Bible, the Vedas to Conquistador accounts, the Greek and Muslim scientific tracts, each clearly describe mirrors in use. Intriguing references to long-range burning mirrors in Muslim papers, the blazing shields of the Greek wars, Incan sun dish competitions and the intense blinding light of Siva poetically attest to these ”divine” tools in key historical settings. Indeed this anecdotal evidence is the root of the persistent rumors of ancient burning mirrors.

Any remaining doubts as to the existence of sun dishes in the old world can be quelled by a museum trip. There are thousands of these devices on display. After creating and using a sun dish, it is obvious that the curve is almost as imperceptible as a shaving mirror. The once active items are cataloged as less interesting oxidized metal objects such as shields, helmets, trays, gongs and ritual garb. However, once the shallow curves are identified, the utility becomes clear. Dishes from the cultures of the Mediterranean, Egypt, Asia, the Americas and Neoliths are all to be found. Links for Ancient Mirrors

The definitive presence of these devices raises other questions about the development and decline of several disciplines and cultures for that matter. Alchemy and the lead to gold transform has left little doubt that these men had a poor grasp of chemistry and lacked the tools for most of the procedures. The more thoughtful look beyond the gold and recognize the origins of chemistry. With these powerful solar devices on hand, the alchemist had the ability not only to create certain materials, but also to readily experiment with others.

The history of ceramics helps illustrates the point. It is believed that ceramics evolved with the evolution of the wood kiln and complex firing techniques. Most stones when placed in a normal fire will not alter their composition in anyway at all, yet this leap in process was made throughout the ancient world. There is no doubt that kilns were eventually used to produce large quantities of potteries. However, Jordan contends that the first experimental work was carried out with these mirrors.

After some ceramists suggested it was impossible to make ceramics with sunlight, the technique was demonstrated at an International Ceramics conference. Despite the production of glazes in minutes as opposed to hours, the historical concept gained little traction. However, it was shown that it is easy for craftsmen to expose a range of materials to very high heats using parabolic dishes.

Solar concentrator creating high temperatures

Parabolic Solar Concentrator melting rocks & metals

Recent mirror research followed a similar path to the speculative alchemist. Metals, rocks, gems, bricks and ceramic paints were just left in the beam for a few minutes to see what happened. The solar device was made and techniques were devised to anneal gems, cut stones, fire pottery, produce ceramics, vaporize, cut and smelt metals in less time than it takes to fire up a wood kiln. Even kids today appear to be treading the same path with homemade reflective dishes. This is not beyond the scope of an ancient craftsman, whose normal methods involved elaborate kilns and would mostly result in failure. The inference is that the development of many fields owes a great deal to the use of this solar technology.

Conclusion

Jordan shows techniques that delight artisans and scientists alike, with a tool that is a little cumbersome, but delivers a very high power to cost ratio. Uniquely historians find the knowledge useful in reframing the past. The lost tract ”On Burning Mirrors” has effectively been reconstructed and shows why ancient scholars obsessed over spherical surfaces. Despite doubts over the most famous Burning Mirror of Archimedes used at Syracuse, it is certain that these tools were utilized in the ancient world. Understanding the operation of sun dishes will surely lead to some famous historical texts being rewritten or at least reinterpreted.

Scientists can use dishes to reduce the costs of high temperature research. The solar concentrators have already been used to make unique new types of crystals for photovoltaic cells. It is expected that similar techniques will be developed for industrial production. Meanwhile artisans can recreate those revered finishes of the past. The sun cultures produced some of the finest stonework, it is only fair that artists trying to mimic it should at least have the same power at their fingertips.

In the present age when we are looking for ways to solve our current energy issues, it seems that the ancients can still teach us a thing or two.

Non-fiction Books & Research by Christopher Jordan

Secrets of the Sects

The Sun Devices

The Math Behind Burning Mirrors

Website: Secrets of the sun Sects Blog

Novels by Philip Newman

With research by Christopher Jordan

Meira and the Language Stone

Meira and the Seahorse

Website: Sothic Press

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  1. #1 by Murray on January 18, 2013 - 11:57 pm

    whoah this blog- is excellent i really like studying your articles.

    Stay inside good work! You are aware of, many persons
    are hunting around for this purpose information, you might help them greatly.

    • #2 by secretsofthesunsects on January 19, 2013 - 7:54 am

      Thanks for the support Murray

      I try to help where I can,

      Share the info with whoever you think can use it. The paper on the mirrors is free from Smashwords for any one wanting to do some back yard high temp or light flux work. Why should it only be the ancient alchemist that have all the fun :)

      Chris

  2. #3 by Pamela on March 4, 2013 - 5:39 am

    I’m not sure where you’re getting your information, but great topic.
    I needs to spend some time learning much more or understanding more.

    Thanks for fantastic information I was looking for this information for my mission.

    • #4 by secretsofthesunsects on March 4, 2013 - 7:41 am

      Pamela

      I pick up the bits and pieces of history that seemingly do not fit into the current paradigms, then try and link it all together. It is a standard approach in the domain of science. Look for thing that do not fit, the new theory will emerge from these tidbits.

      Thanks for the interest.

      Chris

  3. #5 by Ginger on April 9, 2013 - 11:34 pm

    Would die to perpetually get updated great website!
    .

  4. #6 by Itenion on May 4, 2013 - 1:55 pm

    While taking a smaller section of a sphere does give a better approximation of paraboloid, it also means the focal length increases dramatically for a constant surface area of your dish.
    For example, if you want a 1° of your sphere (for high approximation) and 1 m2 surface area, the focal length would be almost 65m and “depth” of your dish about 2.5mm at the diameter of 1,12m.

    With such shallow depth, any slight imperfection in construction of the dish would result in major loss of efficiency. And even if by some miracle anyone in ancient times could construct such dish, the physical properties of material used – no matter how finely polished, at a focal length of 65m the difusion would be still a lot bigger factor than the difference between true paraboloid and spherical approximation.

    On the other hand, using a paraboloid with 1m focal length and 1 m2 surface area, regardless of some imperfections would be much more efficient.

  5. #7 by Itenion on May 4, 2013 - 1:59 pm

    MODERATOR NOTE: in second paragraph, can you fix my number either to:
    – diameter of 1,12m
    or
    – radius of 0,56m

    and delete this post afterwards, thx

  6. #8 by secretsofthesunsects on May 4, 2013 - 5:49 pm

    Itenion

    That is exactly the case. I show that the use of a sphere has a maximum power of about 3-4MW per Sqm in the free (pay what you like) paper. It drops when the FL is zero and infinity. The biggest problem with using long focal length mirrors is the arc of the sun increases the diameter of the spot (regardless of what method is used). Even a perfect parabolic mirror with a 50m focal length will have a large focal point. This limits the potential as a solar concentrator.

    The two factors are calculated in the paper. It lays waste to the Burning Mirrors of Syracuse story. The maximum practical focal length is about 15m (or 30 cubits as the Ancient Greeks and Islamic scholars complained). At that range fires can be set or combatants blinded.

    It does however show that long focal length mirrors can be made and they have a myriad of uses apart from burning or melting stuff. To get to very high temps or energy intensities, relatively deep focal length mirrors need to be used, much like the one in the photo. That hit10-15Mw per Sqm when measured. These were within the capabilities of an ancient craftsman. All he needed was a parabolic template and a big Potter’s wheel. Even higher intensities can be gained with very deep dishes, even if they are relatively small. The intriguing thing for me is that a 10cm dish with the same curve to FL ratio will have the same intensity as a 1000cm dish.

    It seems the long focal length mirror was possible, but a red herring when it comes to Syracuse. The variety of uses of shield sized/shaped dish are outlined in the books. I have used them to melt stones, metals, make glass, ceramics, vaporize metals, anneal gems etc.. They are the ancient alchemists tool of choice if high temps are needed.

    For the battlefield a reflector will temporarily blind an attacker long enough to finish the job with a short sword. Seems these types of events are related under the blazing shields of Homer’s Ilyad.

    Regards

    Chris

  7. #9 by Itenion on May 6, 2013 - 1:07 pm

    The part I don’t understand is what does arc of the sun have to do with it?
    I assume you’re talking about the fact that sun’s rays aren’t really perfectly parallel?

    Granted the focal point wouldn’t really be a point but rather a small circle if you observe it at mathematical focal point of the perfect parabola.
    If that’s the case, doesn’t it just mean that the focal point would simply move a tiny bit further away from the mirror along it’s axis compared to mathematical focal point of perfectly parallel rays of light? Which would be (for example) at 50.01m instead of 50.00m ?

    • #10 by secretsofthesunsects on May 6, 2013 - 5:43 pm

      Itenion

      You’ve got it, the sun is not a point source so a circle is at the focal point rather than a point in the ideal case. The numbers above ignore the arc, which means the intensity of the FP goes to infinity as it approaches a perfect parabola.
      In reality no perfect parabola has an infinite intensity, it is reduced by the size of the sun in radians. As the focal point gets further from the dish the sun image in the FP gets bigger and bigger. Just like projecting onto a screen further and further away. It is about 1cm for every meter of focal length.

      Hope that helps

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