Synthetic PLSS: a meter-based land system approximating the PLSS of the western U.S.

Land units in a synthetic meter-based system proximate to the PLSS.

Though it is based on legacy units, the Public Land Survey System that guides property lines in the western half of the United States can be well approximated by the quadruplings of a 25-meter square (a land area equal to a quarter-quarter hectare.) The advantage of using this Synthetic PLSS for solar furnaces is that the basic units are truly international (meter and hectare) while the field sizes are also nearly commensurate with the unalterable grid of property lines the Desert Southwest. It also extends the binary, or quartering-based, range of the PLSS (which only extends from one section down to 10 acres) by three more quarterings.

Scaled generations of all-glass, glass-making solar furnaces

Specifications for scaled generations of all-glass, glass-making solar furnaces.

A classic science-kid's demonstration is making glass from sand with a solar furnace, and, in fact, the glass-making capacity of a solar furnace is prodigious. A solar furnace of any size, even if it is 100% glass, can make all the glass needed to replicate itself in a matter of weeks. The glass replication time of a small backyard solar furnace may be only a matter of days. More likely at large scale, the glass for a furnace would be produced by a smaller solar furnace that produces at a rate that does not outstrip the capacity to fabricate and assemble glass parts. That smaller furnace, in turn, may have been made by an still smaller furnace; and so on, through multiple generations of scale.

Starting at a very big scale (a solar furnace on 9 square miles of land) and working for the most part within areal units of the Public Land Survey System of the western United States, the table above shows specifications for six scaled generations. If these calculations can be taken seriously, the time from the completion of the room-sized 9-square meter furnace to the completion of its descendant quarter-township furnace is 6.3 years.

Reproduction times and mass flows for all-glass, glass-making solar furnaces

All-glass, glass-making solar furnaces can be built up starting from a small seed.

When we tap power from a solar furnace (which is really what CSP power towers are,) we are tapping power from a thing that can make other things. When the day comes that solar furnace energy is cost competitive with coal for boiler-temperature heat, it will already be a factor of two or three times cheaper than any other source of high-temperature heat for making things. The economics of certain materials will be revolutionized by the availability of cheaper high-temperature heat, none more so than glass.

Laurent Pilon et al. studied thermal transfer in a glass-making furnace that produced 3.35 kg/s of soda-lime glass, with a heat transfer from the combustion space to the melt of 8.3 MW. Thus the energy intensity of this portion of the glass making process is (8,300,000 J/s) / (3.35 kg/s) = 2.5 E6 J/kg. The room temperature density of soda-lime glass is 2600 kg/m3, so, ignoring additional heat requirements in the annealing, the energy intensity of finished glass is 6.4 E9 J/m3.

The solar generating unit Ivanpah 1, produces 126 MWe at a 32% capacity factor, thus averaging 40 MWe over the course of 24 hours. At a conversion efficiency of 0.40, Ivanpah 1 must be producing thermal power of 40 MWe / (0.40 MWe/MWth) = 100 MWth = 1.0 E8 J/s .

Therefore, Ivanpah 1, relieved of its power-generating duties, could make glass at the rate of (1.0 E8 J/s) / (6.4 E9 J/m3) = 0.016 m3/s or 16 liter/s.

Ivanpah 1 has 53,527 heliostats each with a mirror area of 15 m2, giving a total mirror area of 803,000 m2.

Now comes the guessing part: if a solar furnace is made entirely of glass, and the total volume of glass is pro-rated to the heliostat mirror area, how thick will the layer be? I'm going to say 5 cm (0.05 m.) On that basis, in making the glass for an Ivanpah 2, Ivanpah 1 must make (.05 m) * (803,000 m2) = 40,000 m3 of glass.

At 16 liter/s (0.016 m3/s), that task will occupy Ivanpah 1 for (40,000 m3) / (0.016 m3/s) = 2.5 E6 s = 700 h = 29 days.

Making the glass for two copies of itself, an all-glass Ivanpah 1 solar furnace would be offline for just two months! (Of course there's a lot more to it than just making glass, but that other stuff is not Ivanpah 1's responsibility.)

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Suppose each solar furnace makes the glass for two copies of itself and only afterwards gets about the business of full-time power generation. The glass for two units can be made in 2 months, but completing them will take longer, let's say it takes an additional 10 months. Setting the year clock to n = 0 when the first solar furnace starts making glass, and taking a census of solar furnaces annually, the census series will be:

1, 3, 7, 15, 31, 63, 127, 255, 511…  =  2ⁿ⁺¹ - 1

Replicating to 300 units takes less than 8 years.

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That said, it might make more sense to do things the old-fashioned way, using a special-purpose solar furnace sited near the best raw materials. An individual glass-making unit would need 300 months (25 years) to make glass for 300 units, so 3 specialized glass-making furnaces would be needed to make 300 units in about 8 years.

The quarter-township units proposed in an earlier post are considerably larger than Ivanpah 1, their thermal power is

(1000 MWe) * ( 0.75 capacity factor) / (0.40 MWe/MWth) = 1875 MWth,

which is comparable to the thermal power of a 1 GWe coal-fired plant.

That is 1875 / 100 = 19 times more thermal energy than Ivanpah 1 produces, so it yields 19 * 16 l/s  =  300 liters of glass per second. If the glass layer thickness (0.05 m) is the same, the reproduction time will be the same as calculated above (4 weeks), but the mass flows are huge: 2,800 tons of glass per hour, 24/7. Put in terms of the 120-ton capacity of one railroad coal car, that would be 570 cars—or about five, 120-car unit trains per day. That is a mass flux is needed in two directions, carrying materials in and glass parts out.

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Such big mass flows need to be as short as possible. A "growing from an acorn" motto seems more appropriate than "dividing like yeast." Since a small unit can make in three years the glass for a unit 36 times larger than itself; and, since solar resource quality varies gradually over wide areas; it makes sense to site a relatively small, specialized glass-making unit where raw material resources are excellent, and let it slowly build the larger specialized power-generating unit. When the local area is considered built-out, the glass-making unit might be disassembled and relocated, or retired in-place to making spares.

To make a quarter-township solar generating unit, a one-section (one square mile) solar glass-making unit would need 9 months to make the glass; a quarter-section solar glass-making unit would need 36 months. Since it usually takes 3 to 4 years to build a conventional power plant, a quarter-section glass-making unit is probably about right.

The quarter-section glass-making unit could itself be built in 16 months by a 10-acre glass-making unit. If fabrication and assembly proceed just-in-time with the glass production, a quarter-township generating unit would be completed in 16 + 16 + 36 = 68 months (5.7 years) after the 10-acre unit starts producing glass.

In this way, the maximum mass flow, which occurs during the 36 months when the quarter-section glass-making unit is making parts for the quarter-township generating unit, amounts to 570/36 = 16 rail cars per day, but these trips are from local quarries and out to the adjoining, under-construction, heliostat field.

If the 10-acre (40,470 m2) unit can be slimmed down to a 2.5 cm glass layer—say, by using half-scale heliostats—then its mass is

40,470 m2 * (0.70 mirror/land ratio) * (0.025 m) * (2600 kg/m3) = 1800 tons

amounting to 15 rail cars to deliver it ready-to-assemble.

As a check: the trucked-in plant would make that much glass (15 rail cars) in just 2 weeks (being a slimmed-down, half-thickness design), so it can make about 1 rail car per day of glass. After successive multiplications of 16x (going up to a quarter-section, or 160 acres) and 36x (going up to a quarter-township, or 9 sections) the yield of the quarter-township unit should be (1 railcar/day) * 576 = 576 railcars/day, which checks against 570 rail-cars calculated above.

If it is necessary to reduce the freight still more, another factor of 16, down to a 2500 m2 land area (50 m x 50 m,) would just add 8 more months (since slimmed-down units replicate in just half a month.) The trucked-in weight now down to 110 tons. Another factor of 16, down to a 160 m2 land area (13 m x 13 m,) would add 8 months and reduce freight down to one load for a medium duty truck, 7 tons.

The Veselago lens, transflection, and negative-one refractive index (nori) optics

Optical diagram of a single-interface Veselago lens. Image quoted from Yee Sin Ang et al., "Retro reflection of electrons at the interface of bilayer graphene and superconductor."

I just learned of the Veselago lens, an imaging application of negative-one refractive index. The diagram above shows the simplest case, a single refractive index interface producing a real image: in fact, every object in n_i will have a real image in -n_i, and vice-versa. Uses of the Veselago lens (typically with two interfaces, as shown below) are being actively investigated by nano-materials scientists interested in genuinely propagating waves in a negative index medium. As we have seen, such is not necessary in solar power optics, if the divergence pattern has the right symmetry, a Fresnel mirror with its facets tilted 90° has optics identical to an n_i/-n_i interface.

Optical diagram of a two-interface Veselago lens. Image quoted from Lukas Novotny, "Principles of Nano-Optics."

It is helpful to look at the Veselago lens from all four perspectives: retroflection, transmission, reflection, and transflection. If a room has a retro-reflective plane instead of a window, light will be returned directly back to each object in the room, forming a real image that happens to coincide in every case with the object itself, and thus has the same handedness. If there is indeed a transmissive plane where the window should be, an observer on the outside perceives a virtual image that happens to coincide in every case with the object itself, and thus has the same handedness. If there is a mirror (reflective plane) where the window should be, there is virtual image of the room (turned inside-out) in the space outside, and thus handedness is reversed. If there is a transflective plane (or equivalently, the n_i/-n_i interface of a Veselago lens) there is a real image of the room (turned inside-out) in the space outside, and thus handedness is reversed.

Life after Coal

Life after coal: what 300 GW of solar might look like.

Above, I envision 300 quarter-township solar generating units dispersed in the southwestern United States. Each unit would be rated about 1 GW at 75% capacity factor—effectively retiring the country's entire 300 GW of coal-fired generating capacity. The underlying solar resource map is quoted from the National Renewable Energy Laboratory.

We would rather not build these solar generating units disturbing some 3,000 miles of the Southwest's beautiful, living deserts—but, would we drastically and irreversibly alter the earth's climate rather than build them?

Solar Highbeams Open Hardware Project

The Solar Highbeams Project will initiate and sustain a forum for a collaborative international effort to conceive, research, and develop a supply chain for next-generation concentrated solar power (CSP) plants, energized by the new possibilities of telescopic heliostats. The Project will leverage the success and toolset of Creative-Commons-based collaboration in open source software projects. Funding is sought for administration of a GitHub project page and sponsorship of token cash prizes for best relevant work presented at a designated solar conference.

Concentrated Solar Power (CSP) power tower demonstrations have shown high efficiency and the ability, when combined with sufficient thermal storage, to operate at capacity factors typical of conventional fossil-fueled plants. However, these technology demonstrations are based on Vant-Hull and Hildebrandt's power tower concept, an idea now forty years old and consigned (by conservation of extendue, an optical statement of the Second Law of Thermodynamics) to poor utilization of land. The land utilization problem of CSP's is starkly evident in a satellite view of any of the CSP demonstrations: most of the available sunlight falls to the ground between heliostats.

Redirecting light from a high sun toward a low target is implicitly an attempt to increase solar flux density—the Second Law of Thermodynamics requires either a compensating loss of energy (sunlight hits the ground) or an increase in beam divergence. An optical instrument that increases beam divergence while keeping the beam as collimated as possible (parallel rays are mapped to parallel rays) is called a telescope. Therefore, we must either resign ourselves to the wasteful land appetite of current CSP demonstrations, or begin investigation of telescopic heliostats and explore what their consequences will be for the rest of the system.

The difficulty in advancing a fundamentally new concept of CSP is that ultimate success depends on an ecology of new ideas and things, ideas and things that will never come into being unless a community of people endorse a common goal and individually see how their own possible contribution would fit. The same problem is faced by open source software projects, and a number of new tools and practices have fostered their successes. GitHub is a website for opensource software projects beginning to be used for open source hardware as well. The site provides a public and permanent record of incremental contributions—encouraging maximum openess from contributors—but also allows hive dispersal through forking, a facility that permits an independent-minded faction of contributors to take things in their own direction if their ideas do not find acceptance in the community as a whole.

Preliminary investigation of telescopic heliostats indicates that they improve mirror/land ratios from 0.21 to 0.70. Central, beam-down optics are unavoidable, but the necessary central optics, which look something like an overturned apple, need only 60% the height of a power tower on the same field. That makes larger heliostat fields practical.

Calculations indicate that a solar generating unit harvesting a quarter-township, a Public Land Survey System unit which is nine square miles (23,000,000 m2,) would need central optics 190 m high—that is just 15% taller than the current generation of power towers (the Crescent Dunes tower is 165 m.) Based on the performance of Ivanpah Unit 1, which is rated 126 MW at 32% capacity factor, with no storage, and harvests a land area of 3,800,000 square meters, the increased field area, and the improved mirror/land ratio (0.70 vs. 0.21,) a quarter-township solar generating unit in the Desert Southwest should be rated about 1 GW at 75% exploiting a half-day of thermal storage.

126 MW * (0.32/0.75) * (0.70/0.21) * (23,000,000 m2 / 3,800,000 m2)  = 1.08 GW

Ten things we know about telescopic heliostats

They're necessary. Ground loss—the quantity of sunlight falling between heliostats—is atrocious in current generation CSP's. Obvious in a satellite view is the fact that far more sunlight is reaching the ground than the mirrors. Land requirements are being tripled! The Second Law of Thermodynamics decrees that a heliostat without ground loss must act like a telescope, i.e., it must increase the divergence of the reflected beam while maintaining collimation (parallel rays map to parallel rays.)

Telescopic heliostats must have two mirrors. No fewer than two lenses (objective and eyepiece) compose a telescope.

Optimum power is about 6X. Magnifying the sun's disk, which is 0.5° in diameter, six times makes an intensified, but still collimated beam (or highbeam) that can be aimed at an elevation angle as small as its own diameter, 3.0°. That condition minimizes the height of the central, beam-down optics or lamp.

Central, beam-down optics are necessary. At 3.0° divergence, the highbeams are simply too spread to form a high quality focus without another optical stage.

The lamp (central beam-down optics)—shaped something like an overturned apple—will be only 60% as tall as a power tower on the same field. Larger heliostat fields are thus made practical.

The objective needs to move, the eyepiece doesn't. The objective (primary) mirror can redirect sunlight vertically to a fixed focus: the much smaller eyepiece (secondary) mirror gets to sit right there.

The objective needs to have its optical profile continuously fine-tuned to the sun's changing zenith distance. To first order, the adaptation needed is simply a thin-shell bending of the mirror.

Telescopic heliostats move in concert. The only real difference between two telescopic heliostats in a field is the azimuth aiming of their eyepieces. All the objectives could be mechanically ganged.

At at 0.70 mirror/land ratio, telescopic heliostats can be sited with negligible blocking. Surprisingly, the presence of the eyepieces adds no complication at all to heliostat siting when a phyllotaxis-based algorithm is used. The packing density achieved is more than three times that of a conventional heliostat field.

These improvements in field size and field packing make it practical to design a replicable 1 GW, 75% capacity-factor, standard solar plant covering one quarter-township (9 square miles) in the southwest U.S. The central lamp, about 190 m high, would be only 20% taller than current-generation power towers. Goodbye coal!