The Azimuth Project
The Double-Cylindrical PointFocus

The idea that nobody has wanted - so far

The parabola has the well-known property of reflecting axis-parallel rays to a point, as can be seen in this video clip. If we rotate the parabola around its axis, we create a parabolic disc. It has the well-known property of reflecting parallel rays (= planar wave fronts) to a point - if they are incident along the axis direction of the disc - which can be seen in this video clip.

Now, it is a beautiful (and little known) geometrical fact of great practical consequence that we can avoid the astronomical costs associated with creating a large parabolic disc, and harness the work-power of the sun in a more efficient way by bending two flat mirror sheets into the shape of two parabolic cylinders. If these parabolic cylinders are properly configured, the incoming parallel light rays (= planar wave fronts) will create an exact point focus after two successive reflections. This is due to

The Double Cylindrical Point Focus Principle:

If the focal line of the first cylinder is identical to the generating line of the parabola that is the intersection of the second cylinder with a plane perpendicular to its axis, then the incoming rays will be reflected to a perfect point.


The basic ray trace of the Double-Cylindrical Point Focus


The DCPF principle was discovered on 16 November 1976 by Ambjörn Naeve while working with Lloyd Cross, a well-known physicist and holographer who co-founded the School of Holography and the Multiplex Company in San Francisco, California. The original insight was recorded on this piece of paper, and a geometric proof of the DCPF principle can be found here.

Between 9-12 December 1976, Lloyd Cross and Ambjörn Naeve built the first point-focusing mirrors based on the DCPF principle. A short description of this intense event, including some pictures, can be found here.


Lloyd and Ambjörn with the first DCPF mirror


A sketched ray-trace of the first DCPF mirror


A computer-based animation of the double-cylindrical point-focusing mirrors in action, created by Ambjörn Naeve using the Graphing Calculator, can be seen in this video clip, and a live “burning demo” with a DCPF mirror-pair, built by Tomas Elofsson in 1989, can be seen in this video clip.

On 1 July 1989, in Gusum, Sweden, the DCPF mirror-pair shown in the latter video clip (1.5 m^2 primary mirror) was used in an experiment by Ambjörn Naeve and Tomas Elofsson that succeeded in melting limestone (2560 ˚C) in free air. In the pictures below, Tomas Elofsson is shown tuning the mirrors and melting the limestone sample:


Tomas Elofsson tuning the primary mirror


Tomas Elofsson tuning the secondary mirror


Tomas Elofsson melting the limestone sample in a open carbon crucible


A collection of video clips on the double-cylindrical point focus

The DC pointfocus videos by MathRehab on YouTube


Four major advantages of the double-cylindrical point focus

in comparison with the classical parabolic disc point focus

1) It is easier to build in large sizes, since cylindrical surfaces are curved in only one direction and therefore can be BENT into shape from a flat sheet, hence avoiding the “astronomical costs” that occur when a doubly-curved mirror has to be CAST into a fixed shape.

2) The focal point can be positioned outside of the solar influx area between the mirrors, where it is freely available to perform work, as in the DCPF wheelbarrel design.

3) The focal point can be moved by rotating the second cylinder around the focal line of the first cylinder. This fact can be used to create various forms of solid-state heat engines, for example by successively heating and cooling a series of bi-metal coils.

4) The mirror configuration can be approximated with planar strips, the number of which grows LINEARLY with the overall size of the construction – as opposed to the parabolic disc, where the number of planar approximators grows QUADRATICALLY with construction size.


Possible applications of the double-cylindrical point focus

As has been demonstrated above, the DCPF provides a cheap and efficient way to create “a huge burning glass”, which can achieve very high temperatures. Therefore, it enables local (= rural) development of a multitude of technologies that presently require advanced and expensive high-tech labs, such as:

Solar-powered steel plants that recycle scrap metal into a valuable resource for the local community. A discussion and some designs of what a solar steel plant could look like can be found here.

• Cheap and efficient super-heated external combustion engines (steam, sterling, …), whose work-power (like that of all heat engines) is directly proportional to the difference (in ˚K) between input and output temperatures.

• Highly efficient solar electricity generators, which concentrate the energy on high-performance photo-voltaic cells that must be water-cooled to avoid melting.


The idea that nobody wanted (1976 - 2001)

The story (some parts of which are in Swedish) of 25 years of trying to get people interested in the double-cylindrical point focus - from its discovery in 1976 and up until 2001 - can be found here. One of the chapters in this story took place in July 1995 in Gunnarskog in Värmland/Sweden, where Ambjörn Naeve and Tomas Elofsson recorded a video with their daughters acting as solar energy consultants, helping a farmer to melt horse shoes and load batteries by concentrating light on a solar panel.


P.O. Åhlander driving the DCPF solar horse cart


Ylva Naeve and Amanda Elofsson as solar energy consultants


These activities created a big stir in the community, with the local newspaper Värmlandsbygden publishing a cover story on the DCPF with a frontpage headline stating: “They have the solar power that melts mountains” (“De har solkraften som smälter berg”). Some local politicians got involved, interested in creating jobs for the local community, and it looked like things would start moving when an application for funding was sent to the Swedish Innovation and Industry Development Agency (NUTEK), which at that time was responsible for strengthening regional growth by furthering industrial applications of innovations. However, the application was dismissed on grounds that included the following reasons (translated from Swedish):

“A problem with the suggested design is that the temperature becomes very high. This means that the heat losses are increased, which makes the [DCPF] technique less interesting in energy applications. Moreover, concentration of light by mirrors is part of the research that is already carried out within the solar energy domain - although with different configurations than the DCPF, which lead to lower temperature levels and lower heat losses.”

By that time it had become painfully obvious - from this response as well as from other responses similar to it - that we were facing a serious pedagogical problem, and that there was a lot of learning of basic physics that needed to happen in several places in society for things to move forward.


Towards a global learning environment for solar energy

What problems or issues does the DCPF address?

The DCPF can contribute to the design of a more decentralized and sustainable energy technology that will be necessary as our technology must evolve beyond its present oil-burning stage.

The DCPF enables a more simple and less expensive approach to high-temperature solar energy applications that makes it possible to apply and maintain them in “low-tech” rural areas that are facing increasing difficulties of raising capital for development. For example, using the DCPF, low cost, medium temperature “scrap-mirror-strips” (that are “left-overs” from ordinary mirror production) can be used to create effective solar cookers, water-purifiers, and sea-water-desalination systems.

Who would benefit the most from the DCPF and how?

The DCPF is not a traditional “product” but a piece of globally important information for the sustainable survival of humanity in the rapidly emerging “post-oil-burning” age. If a big corporation wants to market solar energy concentrators, it can afford the large investments (“astronomical costs”) involved in creating a big parabolic disc reflector. However, this does not apply to smaller operators in poorer communities (such as rural areas in developing countries), who cannot afford these kinds of investments. About half of the people on this planet live under such conditions, and they are the principal beneficiaries of the DCPF. But we all benefit from a global increase of energy-independence, which can enable the Big Switch that humanity is facing for sustainable survival: Decreasing our dependence on globalized production processes, supported by localized information (secrets, patents, …) and increasing our dependence on more localized production processes supported by globalized (= globally relevant) information.

What are the initial steps required to get the DCPF off the ground?

1) Create an online Interactive Learning Environment around the DCPF principle, where “solar engineer wannabes” from across the globe can learn how to apply this technique to solve local production problems. The beginnings of such an online ILE can be found here.

2) Start an “ethical branding” movement among technical universities, that can work in partnerships with rural communities and developing countries in order to field-test various materials and designs. Such testing will be crucially important in order to optimize the DCPF constructions for a variety of different local conditions.

3) Create a pool of globally relevant and open ideas that can be contributed to under clear licensing conditions. Such licensing can build on Creative Commons. The default license should be: “Free to use, with proper accreditation to the source.“

Basic Properties of Conics and Quadrics

Optical properties of Concis and Quadrics

Caustics involving conic reflectors
Point-focusing properties of Conics
Point-focusing properties of Quadrics
Practical burning demos of the DCPF mirrors

Tracking the sun - as it is seen from the surface of the earth


Hibernating the DCPF mirrors

In February of 2004, Tomas Elofsson tragically and unexpectedly died from a heart failure, and in August of 2005 the large mirrors were moved from his home in Krokek, Kolmården to Ektorp, Södertörn. Some pictures from this move can be found here.

At Ektorp the large mirrors were stored for about two years. Some pictures from this period can be found here.

In May 2007, the large mirrors were moved from Ektorp to my father’s house in Stureby, Stockholm where they have been stored since then. Some pictures from this period can be found here.

It is impossible to predict when the applications of the DCPF principle will start to appear. However, I am convinced that this will happen sooner or later. And when it does, the material that I have created to explain the workings and advantages of the DCPF principle will be useful. In fact, I believe that it can make an important contribution towards improving the organizational performance of Humanity Inc., an improvement that is of vital importance if we are going to survive on this planet. Please use the information that I have assembled for this overall purpose.

I close this page by quoting a few words from a famous speech by Thomas Jefferson. To me, these words represent the attitude that once contributed to making the US a great nation and a role model for others throughout the world.

“If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of everyone, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.

That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density at any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement or exclusive appropriation. Inventions then cannot, in nature, be a subject of property.“

Stockholm, Sweden
31 December 2010
Ambjörn Naeve

category: energy