Hyperboloid Solar Concentrator Literature Review

Hyperboloid Solar Concentrator

Following is a review of the literature associated with an analysis of hyperboloid solar concentrators. The structure of said review begins with a broad look at both the topics of water desalination and solar power, a more focused discussion of solar concentrators in general, and, finally, a look at the literature regarding hyperboloid solar concentrators.

Condensed History

The history of solar use goes back the “7th century B.C.” (DOE). At that time ancient people used glass and crystals to concentrate the sun’s rays and start fires. From the first to the fourth century, Romans used large windows to heat the baths and warm the rooms that people bathed in. From those beginnings the modern usage of solar power followed.

Moving forward to the Second World War, people did not have enough electricity for the basic functions in their houses because of restrictions imposed by the war department. Because of this people looked to solar energy generation as a way to both heat and electrify their houses. Throughout the next few decades the efficiency of the solar cells used for many applications was increasing at a slow rate, but the technologies being developed meant that smaller cells were able to generate more power (DOE).

As the past decade has progressed there have been astronomical advances in both the use, availability, and affordability of solar technologies. In the past ten years, solar concentrators have gone from large scale operations to the point where they are becoming more feasible for residential homes.

Flat Plate Solar Collectors

The flat plate solar design has become the most popular of collection designs since they are “permanently fixed in position, have simple construction, and require little maintenance” (Koo). This system generally consists of the collectors themselves and some type of conversion medium. The use of the solar power is the main concern at this stage. For residential applications the solar rays are converted to electricity for various uses around the house. The problem in the past had been the financial viability of the technology, but that is not as much of a problem now as it once was. With the advent of new material technologies and the fact that demand has increased, the cost of owning such a system has decreased, and made it easier to afford. The flat panel design made it affordable for the average consumer, but further technologies are making solar collection and concentration even more affordable and feasible for the average consumer.

Solar Concentrators

The technology associated with solar concentration is not new. However, since the cost of creating a solar concentrator is relatively high and the energy transfer has not always been the most efficient (Pitz-Paal), the technology has not always been utilized to its full capacity. Researchers have tried to determine the most effective generation methods for the technology, and have traditionally have had to work with one of three methods: a parabolic trough, a parabolic dish, or a central tower receiver (Cobble, et al.).

The concept of a central receiver for solar concentration has long been used in situations that require a large power output. Engineers realized that “to design a large-capacity (multimegawatt) plant, it is clear that a large scale with >1 MW power requirements can only be delivered by some kind of central receiver” (O’Gallagher 99). The use of these concentrators also requires large available land space to support the cells which feed the concentrator. The extremely temperatures that are generated with this type of concentrator also enhance its efficiency (Pitz-Paal). As in any ideal (such as a Carnot engine) a higher heat sources along with a low heat sink will yield the most efficient production (O’Gallagher 101). Unfortunately, there are problems with this design. The tower can only generate collect reflected solar energy, and concentrate it, if it can see the relaying field (O’Gallagher 101). This means that either the tower has to be placed on a plain that does not in any way impede its access to the reflected light, or it must be made taller to account for variations in the field (Chavez 13). The receiver inside the tower is generally a compound parabolic receiver (CPC) which was one of the first concentrator types devised and though non-complex is also relatively inefficient (Chavez 3). That is another reason for using them on large applications only. Due to lower efficiency they have to have a large enough field to generate from to make them feasible.

Both a parabolic trough and a parabolic disk use the same principle of design to accomplish the task of focusing the solar rays to a single point. “It is not necessary to use the whole part of the parabola curve to construct the concentrator. Most of the parabolic concentrator employs only a truncated portion of the parabola” (Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive 3). This design has advantages because of the concentration properties that it able to employ, but it also has many faults that can make it undesirable in many applications (Krewitt & Trieb). A parabolic concentrator can either be used “by rotating the two dimensional design along the x-axis to produce a parabolic dish (Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive 5), or by simply using the 2D trough without rotation (Ali, et al.). The disadvantages of the design come from the fact that;

“although this concentrator could provide a high concentration, it requires larger field of view to maximize the sun energy collection. To obtain maximum efficiency, it needs a good tracking system, which is quite expensive. That is why this type of concentrator is not preferred in a small residential house”

(Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive).

However, that is not an issue because they have been used successfully on large applications such as the Euclides-Thermie Plant at Tenerife, Canary Islands.

Other designs have also had varying amounts of success and can be used in different applications than either the central tower or parabolic designs. A Fresnel concentrator utilizes a flat upper surface and a back surface that employs canted facets” (Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive 6). This type has the advantage of being able to be employed in smaller applications (Townsend & Fung), it also “requires a lesser amount of material to fabricate” (Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive, 6). A dielectric totally internally reflecting concentrator (DTIRC) was designed to “have concentration capability close to the theoretical limit” (Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive 8). By increasing the efficiency of the operation, it is also possible to minimize the size to the greatest extent possible (Garcia-Botella, Fernandez-Balbuena, Vazquez, & Bernabeu). This makes it possible to use this module in more than just extreme commercial applications as long as the cost per unit can be brought to a reasonable level (Schwabach).

The final type of solar concentrator is the hyperboloid. A hyperboloid solar concentrator “produces energy by rotating the two dimensional design along its symmetrical axis. The diameters of the entrance and exit aperture are labeled as d1 and d2 respectively. If the inside wall of the hyperbolic profile is considered as a mirror, the sun rays entering the concentrator from AA’ will be reflected and focused to the exit aperture BB'” (Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive). The major advantage of this design is that it is a very compacted relation of the original paraboloid design.

Hyperboloid Concentrators

Hyperbolic concentrators have been in use for several years and they have direct application for many different needs. However, they have not been used to their greatest efficiency because solar generation has not been able to produce as much power as a typical power plant at a similar cost (Townsend & Fung). This is a significant issue when the primary areas of the world that need clean water and the other benefits that can be provided by solar power concentration and generation are also among the poorest regions in the world (Krewitt & Trieb). Of course, the focus of researchers and engineers is not necessarily to help these regions, but to find more cost effective ways to generate power because of the present demand for sustainable technologies (Krewitt & Trieb). Due to both of these factors the hyperboloid design has become one which is discussed more and more as an option that can translate a viable energy source that can be used anywhere at a relatively low cost to the company installing the generation platform.

This technology takes the best aspects of the parabolic design and further concentrates the solar rays to make collection even more efficient (Chavez 13). According to research conducted by Garcia-Botella, et al., “By its geometric design, it is easy to prove that the 2D HPC is an ideal concentrator. All the rays incident on the entry aperture of a 2D HPC at angles minor or equal to ? will be redirected, by the parabolic section of the concentrator, to the segment F ? F0, and their second and successive reflections will cause them to emerge from the concentrator.” The fact that it can utilize most, if not all of the solar rays that are collected by the array means helps to minimize the actual size of the array also.

But the of the efficiency of the design requires further proof. It is necessary to ensure that the all of the rays “directed to the virtual elliptic receiver at the exit aperture are reflected by the concentrator to some point on this receiver” (Garcia-Botella, et al.). The explanation of the math for this process is explained in a long section of the report from Garcia-Botella, et al.;

“Three properties of one-sheet hyperbolic concentrator geometry are useful: (1)

All meridional sections of a one-sheet hyperbolic concentrator are hyperbolas, (2)

all cross sections of a onesheet hyperbolic concentrator are ellipses and (3) the tangent plane, at any point P. Of a one-sheet hyperbolic concentrator, is defined by the bisector of the angle FPF0, where F. And F0 are the foci of the hyperbola in the meridional plane (Fig. 2), and the tangent line to the elliptic cross section at P. All the skew rays incident at point P. directed to the virtual elliptic receiver generate an oblique elliptical cone, or incident cone. Then, the reflected cone will be the mirror image of the incident cone, through the tangent plane at point P. by

the geometry of this particular problem, the cross section of the incident cone, normal to the bisector of the angle FPF0, is an ellipse (Fig. 3). One of the principal axes of this ellipse lies in the tangent plane of the one-sheet hyperboloid and, by definition, the bisector of the incident cone too; therefore, the tangent plane coincides with a symmetry plane of the incident cone. This produces that the reflected cone coincides with the incident cone (Fig. 4), which means that all rays incident at point P. aimed to the virtual elliptic receiver, are reflected by the concentrator to some point on this receiver. This proves that a one-sheet hyperbolic concentrator is an ideal 3D asymmetric concentrator. ”

The concentration of all of the rays collected can also be explained in the superior non-imaging optics that are used in the array (Chavez). Non-imaging optics have the ability to transfer light at a greater efficiency level that traditional optics (Cobble, et al.) and this further increases the efficiency of this type of array.

The application of this technology is also one of its beneficial features. Water desalination was discussed earlier as a principle need in many areas of the world. However, there is great controversy as to whether employing current desalination methods is so detrimental for the environment that the benefits cannot override the negative consequences (Schwabach). Environmental groups have begun filing lawsuits against the continued utilization of desalination techniques because they are harming the environment more than they are helping the people in these areas. Due to the need that these people have for clean water sources that are not naturally available, solar concentration is seen as a viable alternative. Also, the low impact that hyperboloid concentrators have as compared to other concentrators with the power to generate large amounts of energy (Muhammad-Suki, Ramirez-Iniguez, McMeekin, Stewart, & Clive) (which is required in the desalination process) (Rolla), makes it an ideal method for generating the power and desalination capabilities that are needed.

Water Desalination

Research shows that clean water sources around the world are becoming scarcer (Matare; Rolla). Due to the increase in world population, there is more need for water in places that typically have low rainfall and no clear source of clean water. This has led to an increased use of desalination to gain the margins that these arid populations need. In the southwestern United States, the deserts in northern Africa and the Middle East large desalination projects have been implemented that have yielded tens of thousands of gallons of water every day (Matare). Finding the water has not been an issue, even removing the salt content is not technologically difficult, but producing pure water efficiently is a difficulty.

Since the process requires large amounts of energy, it has traditionally been a process that requires a region where two factors, cheap energy and expensive water, exist. As one researcher said;

“Using energy solely for the purpose of distilling water is prohibitively expensive except in a few areas-notably the Arabian peninsula-where energy is cheap and water is extremely expensive. However, many industrial processes, especially the generation of electricity, produce large amounts of waste heat. Typically the facilities producing this heat are cooled by dissipating the heat into water. This heat can also be used to distill fresh water from saline water used for cooling”


Therefore, finding a way to use common distilling processes more efficiently is the problem that scientists most want to solve. Also, when the process is completed if the water is not too brackish it can be returned to the sea. This is an added advantage of the solar distillation process (Rolla).

Solar distillation can only occur in a very few regions though because of the need for consistent and intensely focused solar rays. One of these issues has been solved through better technology such as paraboloid and now hyperboloid solar concentrators (McConnell and Thompson). Solar concentrators are more energy efficient because they track the sun (Kribus) and produce a great amount of thermal energy which can be used in applications other than just desalination, heating or energy production (Ali, et al.).


The need for energy in the world is greater now that more nations are increasing their industrial capabilities. This industrialization has also focused the world’s attention on the fact that fossil fuels are an unsustainable method for future power generation. Because of this fact, engineers continue to try and devise more efficient means for using the sustainable fuel sources available such as solar power.

Since the sun is presently able to direct unquenchable amounts of power toward the earth, it makes since to try and tap these resources. The only problem has been that the means for gathering this energy have been costly, taken large amounts of space, and have been inefficient in gathering the available rays. This is becoming less and less of an issue the more engineers tweak the materials and designs.

History teaches that solar power has been available in some manner for close to three millennia now, and the ability to use the sun gets better with each new technology. With the advent of new hyperboloid technologies, it is now possible to gather nearly all of the rays that enter the collector. With this ability power generation, water desalination and cooling abilities are now available to more regions of the world. Just like when flat plate collectors were fist conceived, these new types of concentrators are making commercial and residential application more realizable. Now, like in ancient times, the use of solar power has become more of a reality because people have reached a point in which they look for all possible means of energy production. These new technologies make humans just a little less reliant on a fuel source that is quickly being depleted, and more open to an energy source which is permanent and unquenchable.

Works Cited

Ali, Imhamed M. Saleh, Tapas K. Mallick, Peter a. Kew, Tadhg S. O’Donovan, and K.S.

Reddy. “Optical Performance Evaluation of a 2-D and 3-D Novel Hyperboloid

Solar Concentrator.” World Renewable Energy Congress, 2010. Print.

Chaves, Julio. Introduction to Non-Imaging Optics. New York: CRC Press, 2008. Print.

Cobble, et al. “Omni-directional Compound Paraboloid-Hyperboloid Radiation Device.”

United State Patent. 1981. Print.

Garcia-Botella, Angel, Antonio Alvarez Fernandez-Balbuena, Daniel Vazquez, Eusebio

Bernabeu, and Augustin Gonzalez-Cano. “Hyperbolic Concentrators.” Applied

Optics, 48.4 (2009): 712-715. Print.

Garcia-Botella, Angel, Antonio Alvarez Fernandez-Balbuena, Daniel Vazquez, and Eusebio Bernabeu. “Ideal 3D asymmetric Concentrator.” Solar Energy, 83

(2009): 113-117. Print.

Jones, Richard a.L. “Nanotechnology and Visions of the Future.” Soundings 36 (2007):

85-97. Print.

Koo, Jae-Mo. “Development of a Flat Plate Solar Collector Design Program.” University

of Wisconsin, 1999. Web.

Krewitt, Wolfram, and Franz Trieb. “Perspectives for a Global Sustainable Energy

Supply.” The Whitehead Journal of Diplomacy and International Relations, 10.2

(2009). 115-129. Print.

Kribus, Abraham. “A High-Efficiency Triple Cycle for Solar Power Generation.” Solar

Energy 72.1 (2002). 1-11. Print.

Matare, Herbert F. “Energy Independence for the U.S.A.” The Journal of Social, Political,

and Economic Studies 34.1 (2009): 15-21.

McConnell, R.D., and J. Thompson. “A Hybrid Solar Concentrator for the Electrolytic

Production of Hydrogen.” United States Department of Energy: Energy Efficiency

and Renewable Energy. 2004. Print.

Muhammad-Suki, F., R. Ramirez-Iniguez, S.G. McMeekin, B.G. Stewart, and B.

Clive.”Solar Concentrators.” International Journal of Applied Sciences (IJAS), 1.1

(2009). 1-15. Print.

O’Gallagher, Joseph J. Nonimaging Optics in Solar Energy. San Rafael, CA: Morgan & Claypool Publishers, 2008. Print.

Pit-Paal, Robert. “High Temperature Solar Concentrators.” In Solar Energy Conversion

and Photoenergy Systems. 2007. Print.

Rolla, Tracy C. “Sun and Water: An Overview of Solar Water Treatment Devices.”

Journal of Environmental Health 60.10 (1998). 30-42. Print.

Schwabach, Aarron. “Using International Law to Prevent Increased Harm from Increased Use of Desalination.” Texas International Law Journal 34.2 (1999):

187-213. Print.

Townsend, James C., and Francis C.W. Fung. “Combined Thin Film Potovoltaic and Reflective 3D Parabolic Panels for Utility-Scale Solar Dishes.” Web.

US Department of Energy (DOE). “The History of Solar.” U.S. Department of Energy:

Energy Efficiency and Renewable Energy, 2010. Web.

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