SSI Low Mass SPSs Built from Lunar Material

OPENING THE HIGH FRONTIERTOR A BETTER FUTURE SPACE STUDIES INSTITUTE Low Mass Solar Power Satellites Built from Lunar or Terrestrial Materials: Final Report April 7, 1994 Seth D. Potter New York University Department of Earth System Science 34 Stuyvesant Street New York, NY 10003-7599 Telephone: FAX: Internet: potter@ Study sponsored by Space Studies Institute P.O. Box 82 Princeton, NJ 08542 Copyright © 1994, by Seth D. Potter and the Space Studies Institute PRINCETON, NEW JERSEY

l.-Iniroduction The SSI-sponsored study of low-mass solar power satellites has been completed. The following is a report on results. Information from the progress report dated October 15, 1993 is included. The report was written by Seth Potter, except for Sections 8 through 8.5 (including Table 3 and Figures 1 through 5), which were based on reports submitted by Dr. Gregory Matloff. 2, Goals and Ground Rules for Study As stated in the Proposal on September 9,1993, the primary goal of this study is to design a lightweight solar power satellite (SPS) which makes use of thin-film photovoltaic materials and solid state microwave transmitters deposited on lightweight substrates. The SPS is then to be redesigned to use lunar materials, if possible. The desirability of using lunar materials will then be assessed. Throughout the study, "traditional" requirements on SPS's will be adhered to whenever possible (e.g., geostationary orbit, microwave power transmission, etc.), but will be altered if necessary to facilitate the design of a simple, easily launched SPS (e.g., new materials; integrated, rather than gimbaled, antennas; etc.). The study is a “first order” design. Future designers may need to alter such things as frequency (depending on federal and international frequency allocations) and total mass (depending on an eventual selection of type of thrusters). 3. Power Transmission One of the major constraints on SPS design is the need to transmit power from geostationary orbit to the Earth. The NASA/US Department of Energy reference design1 utilized microwaves at a frequency of 2.45 GHz. This is a well-understood frequency, with equipment such as magnetron tubes readily available. Since the physics of power transmission causes the beam to spread out into a 10 x 13 km area on Earth (for a 1 km transmitting antenna), the reference SPS had to transmit large amounts of power (5 gigawatts) in order to be economical. One of the advantages of a thin-film SPS is that with

solid state microwave transmitters and solar cells integrated onto the same substrate, larger transmitting antennas are possible. If each transmitter element is powered only by the solar cells in its immediate vicinity, then losses along power buses from the solar cells to the antenna are minimized. Furthermore, the design is simple, consisting of the same element repeated many times, as well as durable (since few single parts are critical to the overall operation of the SPS). For the study, the entire surface of the SPS is assumed to contain both solar cells and integrated transmitters. Thus, as the SPS diameter is increased, more power is squeezed into a tighter microwave beam. The SPS was sized so that the peak beam intensity at the Earth's surface is 30 mW/cm2. This figure is the same as that used in the previous SSI-sponsored study on SPS's built of lunar materials2, and is similar to that from the NASA/US DOE study (i.e., 23 mW/cm2). It has been suggested that higher values, such as 40 to 50 mW/cm2 may be acceptable3. Thus, a value of 30 mW/cm2 is in keeping with previously accepted intensities, while still allowing for some leeway in the design. Frequencies higher than 2.45 GHz lead to smaller, more feasible SPS's. However, frequencies higher than about 10 or 15 GHz are subject to attenuation in rain as well as clear air (although there are "windows" in clear air at 35 and 94 GHz)4>5’6. In addition, the efficiency of solid state microwave transmitters decreases with frequency. Therefore, 10 GHz was chosen as the baseline frequency for the study, although other frequencies were considered for comparison purposes. The nominal latitude for the study is 35°, in keeping with the NASA/US DOE reference design. The intensity of the power beam is dependent on the latitude, although it is not highly sensitive to it (at least, for latitudes below about 60"). Thirty-five degrees is not far removed from most of the world's population centers, so the resulting design will be practical for many regions. If the same design is mass produced to power many areas, the peak intensity at higher latitudes will be less than 30 mW/cm2, while the peak at the equator will be just under 40 mW/cm2. Alternatively, the design can be customized for each latitude. In the calculations for this study, the SPS-to-rectenna distance and the beam angle from vertical at the Earth's surface were corrected for latitude. Distances were thus somewhat greater than the geostationary altitude of 35,786 km. Beam angles from the vertical were slightly greater than the latitude. The energy distribution of a microwave beam consists of a central main lobe, where most of the energy is concentrated, as well as sidelobes. Sidelobes can be minimized by the proper choice of beam taper (i.e., a variation in the intensity of the beam across the face of the transmitting antenna), although the main lobe then becomes broader. Beam tapering

involves redistributing the power across the face of the integrated SPS, which complicates the design, and may lead to power distribution losses in the SPS. Therefore, this study emphasizes untapered microwave beams. However, a commonly used family of tapers will be considered in the initial analysis of the peak beam intensity.

This equation applies to a beam that is perpendicular to the ground. The beam from a satellite orbiting over the equator transmitting power to a latitude of 4>0 will have an angle of 0 from the vertical, where: and an altitude of 35,785 km (geostationary orbit),

4. Choice of Materials Researchers7-8 have investigated several different thin-film photovoltaic materials. Amorphous silicon (a-Si) compares favorably with other materials, such as CdS, Cu2S, and CuInSe2 in terms of efficiency. All of these materials are radiation-tolerant, thereby eliminating the need for a protective cover glass. They are also low in mass, and therefore, inexpensive for the quantities that will be needed. Amorphous silicon is at a slight disadvantage in terms of light degradation (10 to 15% after two years, compared to, say, where h and 4> are given in Equations 4 and 3, respectively. Thus, for a given altitude, rectenna latitude, and power beam frequency, the allowable peak beam intensity determines the SPS diameter.

CuInSe2, which has none8), but it is believed that this can be improved upon. Because of its favorable characteristics, and the fact that it is the only thin-film photovoltaic material available on the Moon, amorphous silicon will serve as the basis for this study. If SPS designers wish to substitute a different material for the SPS built of terrestrial materials, the results of this study are still applicable, since the efficiencies are similar. Literature on photovoltaics often contains present-day, near-term future, and long-term future figures on efficiencies. The near term-future figures will be used in this study. For a-Si, the efficiency used is 11.5%718, with a degradation of 4% (Ref. 9, page 164), so that the overall cell efficiency is 0.115 x 0.96 x 100% or 11.04%. The materials for the substrate are Kapton polyimide for an SPS built of terrestrial materials (25|1 thick in the near-term; 7 g thick in the long term) and steel foil for an SPS built of lunar materials (25|1 thick in the near-term; 7.5g thick in the long term)10. The long-term figures were used in this study. For array mass calculations (cells plus substrate), specific powers (watts per kilogram) given in the literature7’10 were based on cell efficiencies of 5, 10, or 15%, so they were rescaled for an efficiency of 11.5%. Support structures for a bicycle wheel-type SPS should consist of lightweight materials, in order to take advantage of the mass savings available from thin-film solar cells and substrates. The materials to be considered are silicon carbide (SiC), for an SPS built of terrestrial materials) and glasses such as basalt fiber, glass ceramic, and fiberglass, for an SPS built of lunar materials)11’16. Densities and tensile strengths of these materials are given in Table 3 (Section 8 of this report). 5. Bicycle Wheel Versus Inflatable Sphere SPS Two different SPS designs were considered, based on Reference 7: bicycle wheel and inflatable sphere. The inflatable sphere has the advantage of needing no support structure, other than a low-pressure gas to inflate it. In addition, it always has an entire hemisphere facing both the sun and the Earth. However, its effective area for both the solar cells and the transmitting antenna array is equal to its cross-sectional area, not its total surface area. Thus, the array is four times more massive than if it were a flat disk. Power from the sun-facing part of the array must be redistributed to the Earth-facing part. The power must be redistributed still further, since the limb of the Earth-facing side will have more transmitting elements per cross-sectional area than will the center, due to the fact that the limb is seen edge on. This may not greatly increase the mass or complicate the design;

in fact, the power redistribution network can be deposited on the interior of the sphere12. The curvature of the array causes a transmitter phase difference across the Earth-facing side, which can easily be compensated for. When designing a bicycle wheel-type SPS, an allowance must be made for the tracking loss, since the array cannot simultaneously point at both the sun and the Earth, except at midnight (and at noon, if both sides of the SPS are covered with solar cells and microwave transmitters). A tracking loss of 30% was assumed, based on Landis and Cull's (Ref. 7) figure for an SPS in orbit around the Moon. Calculations were also done for a bicycle wheel SPS with no tracking loss. This can be achieved if the array points toward the Earth and a mirror orbiting with the array reflects sunlight toward it. Such a mirror might consist of aluminum on Kapton13, plus an appropriate support structure and might weigh as much as the SPS; the increase in system mass is thus 40% over a system with a tracking loss (in which the size or number of SPS's is increased to compensate for the lost power). Such an increase in mass may be deemed worthwhile, since the power level of a non-tracking array may fluctuate throughout the day as it orbits the Earth. 6. System Efficiencies The microwave power level incident on the rectenna is considerably different from the power level of sunlight incident on the SPS. Furthermore, the power available to consumers is somewhat less than that incident on the rectenna. In addition to the inefficiency of the solar cells and tracking losses, other inefficiencies must be accounted for. The efficiencies used in this study are based on Table 1 from Vondrak (Ref. 3), but with modifications. They are shown here in Table 1.

TabkJ. Solar Power Satellite System Efficiencies Note that atmospheric transparency had to be adjusted for latitude (since an oblique beam cuts through more atmosphere than a beam at the equator) and for frequency. It is significant mainly at higher frequencies, such as 35 GHz and 94 GHz.

7, SPS Size and Power Level When the first nine efficiencies in Table 1 are multiplied together and the result substituted for T| in Equation 7c, the size of an SPS whose peak beam intensity (Inc) is 30 mW/cm2 at the Earth's surface can be computed. For a non-tracking bicycle wheel SPS beaming power to a latitude of 35’ at a frequency of 10 GHz, the diameter is 2021 meters and the power incident on the Earth's surface (Equation 6) is 153 megawatts. When the last three efficiencies in Table 1 are accounted for, it is seen that 109 megawatts is available to consumers. The rectenna energy collection efficiency is based on the percent of the power of an untapered beam that falls within the main lobe5-14. The mass of the solar cell/transmitter array is 51 metric tonnes. This does not include the mass of the support structure, which is quite low, and will be assessed in Section 8. Results were also obtained for a bicycle wheel design with a mirror, an inflatable sphere, as well as SPS's with other frequencies and latitudes. A peak beam intensity of 30 mW/cm2 at the Earth's surface was assumed in all cases. The results are summarized in Table 2. The types of SPS referred to in Table 2 are non-tracking bicycle wheel (b.w.), bicycle wheel with mirror (b.w.m.), and inflatable sphere (i.s.). The first three rows of the table can be thought of a reference designs, with the rest of the table included for comparison. Note that rows 9 through 11 show that the design is only mildly sensitive to latitude (at least, for latitudes in which an SPS is practical). Rows 4, 7, and 8 show that the design is highly sensitive to power beam frequency. The 10 GHz SPS’s shown in the first (b.w.) and third (i.s.) rows served as the basis for calculations of structural design and total mass seen in Section 8 (for the inflatable sphere, there is no support structure, except for a low pressure gas whose mass was assessed in Section 8.5). The masses in parentheses for the bicycle wheel with mirror are simply double the array masses (since the mirror is assumed to have the same design as the bicycle wheel SPS, except that the substrate is coated with reflective material such as aluminum, instead of amorphous silicon and solid state transmitters), and are included for comparison. The masses of the inflatable sphere design were obtained by considering a flat array with no tracking loss and multiplying the mass by 4 (since the surface area of a sphere is 4 times its cross-sectional area). The specific power levels (power per unit mass) were computed by dividing the power delivered to consumers by the masses of the arrays (including a mirror where appropriate) built from tetrestrial materials. Results indicate that frequencies of 10 GHz and below have the highest specific power, due to the higher microwave transmitter efficiencies and lesser atmospheric absorption than at higher frequencies. The non-tracking

bicycle wheel design appears to have the highest specific power of the three designs considered. Its mass savings over the bicycle wheel with mirror will remain when support structures are included. The inflatable sphere does not require a support structure and the mass of the inflation gas is negligible compared with that of the array (see Section 8.5). The last two rows in Table 2 show that for a bicycle wheel in equatorial low Earth orbit (here, 1200 km), array masses on the order of one-half to 1^ tonnes are possible (the support structure will increase this slightly). (Lunar masses are shown for comparison, but may not be applicable to low Earth orbit SPS's.) These SPS's can be lofted in one launch with existing vehicles. The power levels shown are not continuous, but are only for times when the satellite "sees" both the sun and the rectenna. Continuous power can be provided through a combination of energy storage at the rectenna site and the deployment of many such SPS's and rectenna sites to maximize the power transmission duty cycle.

Table 2 Summary of SPS Sizes and Power Levels

8. Structural Analysis We start by tabulating relevant aspects of these spacecraft and reference sources for this information. Table 3 Structural Materials 8J-. Calculation of Gravity Gradient Stresses and Radiation Pressure Stresses On Bicycle Wheel SPS

8J Calculation of Gravity Gradient/Radiation Pressure Compensating Structural Mass Requirements for Bicycle Wheel SPS It is easy to demonstrate that structural mass requirements to compensate for gravity gradient and radiation pressure forces are greater for a tensile (or compressive) situation than for forces perpendicular to the SPS surface. Thus, we conservatively assume the situation illustrated by Figure 1, where a cylindrical structural fiber is assumed to support the entire worst case force, calculated above, here symbolized by Fpeak- From Ref. 22,

8.3 A Structural Design to Increase Rigidity of a Bicycle Wheel SPS Consider the bicycle wheel SPS structural design presented in Figure 3. In this end-on representation, a hub is constructed at the geometrical center of the SPS. Loadbearing fibers run from the top (and bottom) of the hub to the rim. This arrangement can minimize warping of the array. From the top (or bottom), the arrangement of fibers is identical to that in Figure 2. Assuming 8 fibers on top and 8 on the bottom, fiber mass can be calculated by simply multiplying the values in Section 8.2 by 2: for terrestrial material, fiber mass = 0.056 kg; for lunar basalt or fiberglass, fiber mass = 0.38 kg; for lunar glass ceramic, fiber mass = 3.8 kg. We assume that the rim thickness is 4 times the fiber thickness. Since there are 16 fibers,

Rim Mass = 16 (fiber mass/16) 2n , where the multiplicative factor of 16 is due to the fact that the rim thickness is 4 times the fiber thickness and the rim mass/length is consequently 16 times greater than the fiber mass/length. The divisor of 16 is due to the fact that the rim is 2tc times the length of one fiber, not 16 fibers. The rim mass is therefore about 6.3 times the total fiber mass, or 0.35 kg for terrestrial, 2.4 kg for lunar basalt or fiberglass, and 24 kg for lunar glass ceramic. To calculate hub mass, we assume that the hub projects L/2 below the SPS and L/2 above the SPS. Assuming that the hub is constructed of material similar to lunar glass ceramic, and is a cylinder with a radius of 1 m, hub mass = 2000 k (I)2 L, where the factor 2000 is the (MKS) density of this material from Table 3. We next assume a hub length (L) of 10 cm. (This is justified below.) For such a hub length, the hub mass is about 630 kg. 8.3,1 Justification of a 10-cm Hub Length One source of SPS flex can be evaluated using Figure 4. Here, an SPS of radius (Rad) 1 km is in orbit R (42,000 km) from the Earth’s center (36,000 km above the Earth's surface). In this figure, the SPS is oriented directly towards the Earth. Parameter "h" represents the maximum flex caused as the SPS adjusts to the Earth's geodetic. We use a scientific calculator to first estimate length Z from R and Rad using the Pythagorean relationship. Parameter h is the difference between R and Z. A maximum length of h = 1.2 cm is obtained. Since L = 2h = 2.4 cm, a value of L = 10 cm is conservative by a factor of about 4. But for part of every orbital cycle, the SPS will be in darkness and its temperature may plummet from 245 K to near absolute zero. The coefficient of linear expansion of commercial glass is about 11 x 10‘6/K [Ref. 23]. Therefore, the maximum change in length of a 10-cm glass hub will be 0.03 cm. 8.4 Thruster Support for Bicycle Wheel SPS A bicycle wheel SPS will have to be slewed during the course of the day in order to track either the Earth or the sun (or both). Rotation about three axes (with a bit of

redundancy) can be achieved by placing four thrusters around the rim at 90-degree intervals. Consider the "pin-wheel" arrangement in Figure 5. The SPS mass is supported against thruster action by the four-strut arrangement shown. These struts are at right angles to each other, meet at the SPS Center of Mass (CM) and each has a gimbaled thruster on the end farthest from the CM. Each thruster can apply thrust perpendicular to the local strut (Tt) and parallel to that strut (Tl). SPS rotation is modeled using the moment of inertia (I) for a thin bar rotating about a perpendicular through its center: Furthermore, Table 2 shows that a 2000-meter diameter bicycle wheel has an array mass of roughly 50 tonnes. However, due to the light weight of the structural material, it was considered worthwhile to "overengineer" the support struts to support additional weight.) If all SPS mass must (in worst-case scenario) be supported by each leg of the structure, I Previous calculations have implicitly assumed Tt, thrust applied perpendicular to the strut. Maximum strut mass can be estimated by assuming that this maximum thruster force Conservatively assume that the specific gravity of the strut material is 10 (density = 10,000 kg/m3). Because each strut has a length of 1000 m and there are 4 struts, the total structural mass required to support thruster-caused rotations of the SPS is about 0.12 kg.

Of course, peak thrusts might be 10 times the average value. If structural strength of materials degrade in space during a 30-year life time, tensile strength might be reduced by a factor of 10. Still, a structural mass budget of 1000 kg is conservative by a factor of more than an order of magnitude. Finally, what is the magnitude of thruster linear accelerations? Assuming a 1 N force on a 600,000 kg mass, the peak linear acceleration is of the order 2 x 10’6 m/sec2. This is equivalent to about 2 X 10'7 g, where "g" is one Earth surface gravity. 8.5 Calculation of Required Gas Masses for Inflatable Sphere SPS’s We begin by first estimating the amount of gas required to be within an inflatable sphere SPS at any time, and then estimate the amount of gas necessary to counteract leakage through the SPS walls. Gas mass within SPS: We begin with the Ideal Gas Law24: The minimum gas pressure within the sphere that is required to maintain inflation is here defined as twice the amount required to compensate for the algebraic sum of maximum gravity gradient and radiation pressure stresses. We estimate the absolute value of the gravity gradient acceleration, following the formalism in Section 8.1, as 2.5 x 10’5 m/sec2. Multiplying by the tabulated values for mass for both the terrestrial material and lunar material inflatable sphere SPS, we find that the gravity gradient forces are 4.3 N for the terrestrial materials case and 16.1 N for the lunar materials case. The temperature T is taken to be 245 K and V is calculated, for the sphere radius in the above table:

Next, we scale the solar radiation pressure results (from the bicycle-wheel SPS calculations in Section 8.1 and the area projected to the sun by an inflatable sphere SPS). The maximum radiation-pressure force on an inflatable sphere SPS is about 17.7 N. The maximum combined forces on an inflatable sphere SPS are therefore about 22 N for terrestrial materials and 34 N for lunar materials. The total surface area of the inflatable sphere is 4k (925)2 — 1.1 x 107 m2. This means that the maximum combined stresses for terrestrial and lunar inflatables respectively are about 2 x IO*6 N/m2 and 3 x 10*6 N/m2. The required gas pressures to support terrestrial material and lunar material inflatable SPS’s respectively, are therefore about 4 x IO*6 N/m2 and 6 x IO-6 N/m2. These pressures are next substituted into the above equation m — 45,000 P. The inflatable sphere SPS constructed of terrestrial materials requires an interior gas mass of about 0.2 kg. An identical SPS constructed from lunar materials requires an interior gas mass of about 0.3 kg. Total gas mass required to compensate for diffusion through SPS walls: As discussed in Refs. 25 and 26, gas diffusion through an inflatable spacecraft's walls is a complicated function of wall and gas materials, temperature, and pressure. Rather than attempting here to solve this complex problem analytically, we argue by analogy with Quasat, a European proposal for an inflatable radio telescope in a 20,000 km orbit19. Quasat was designed to carry 1.6 kg of nitrogen gas to maintain inflation at a pressure of 10 Pa (1 Pa = 1 N/m2 — 10"5 atm). This high pressure is required to maintain the observatory-grade optical figure of the Quasat radio antenna. Quasat can be approximated by a sphere with a diameter of 10 m. The approximate volume of the Quasat inflatable orbiting radio antenna is therefore about 500 m3. Substituting into the Ideal Gas Law for the Quasat volume, 245 degrees Kelvin, and nitrogen gas, we find that about 0.069 kg of nitrogen is within Quasat at any one time. Therefore, the ratio of total gas mass to the mass of gas within the inflatable structure at any one time is 23. But Quasat has a design lifetime of 5 years and a SPS must operate for about 30 years. Thus, the minimum ratio of total gas mass to mass within the inflatable structure for our inflatable SPS is about 140. The inflatable SPS constructed from terrestrial materials must carry at least 30 kg of nitrogen gas. If constructed of lunar materials, this SPS must carry at least 42 kg of nitrogen gas.

Figure 1. Worst Case Force Situation fora Sunsat Figure 2. Vertical Illustration of Bicycle-Wheel Sunsat Structural Spokes Figure 3. Side View of Bicycle-Wheel Sunsat Structure Figure 4. Geometry for Determination of Sunsat Flex due to Earth Geodetic

Figure 5. Thruster Support for Bicycle Wheel SPS. 9. Comparison of Old and New Reference Designs For the bicycle wheel SPS, the total of the rim plus fiber mass for the most massive case is about 28 kg. Since the hub weighs 600 kg and the struts that support the thrusters weigh 1000 kg, the rim plus fiber mass is negligible. Total mass is therefore approximately equal to the array mass plus 1.6 metric tonnes for a terrestrial or lunar bicycle wheel whose diameter is approximately 2 km. For an inflatable sphere, the mass of the inflation gas (even enough for 30 years) is negligible compared to the array. The 10 GHz designs from Table 2 can be viewed as new reference designs and compared to the NASA/US DOE reference designs1. This comparison is presented in Table 4. Note that the figure of merit shown here is specific mass (kg/kW), rather than specific power (kW/kg), since the former more easily lends itself toward the discussion of global energy requirements in Section 10. By examining the specific masses in Table 4, it is seen that thin-film SPS’s allow for a substantial improvement over conventional designs. The best case scenario is the terrestrial bicycle wheel (without mirror), which is better than the NASA/US DOE Type 1 by a factor of more than 20 (i.e., a 95% savings in mass per unit of power delivered). For the terrestrial bicycle wheel with mirror, this factor is only 15, but, as stated earlier, this may be an acceptable price to pay for a more steady supply of power. The inflatable sphere

designs do not fare quite as well as the bicycle wheels. However, this may change in the future as researchers arrive at more detailed bicycle wheel designs, since the mass of thrusters and fuel was not included. While both bicycle wheels and inflatable spheres may need thrusters to adjust for orbital perturbations, the bicycle wheels must be slewed throughout the course of the day to track the sun and/or Earth. Inflatable spheres simultaneously present an entire hemisphere toward both the sun and the Earth, eliminating the need for slewing. Designs using lunar materials are substantially heavier than those using terrestrial materials, but still represent an improvement over conventional SPS’s. The decision of whether to use terrestrial or lunar materials will depend on global energy requirements and launch costs.

Table 4 Comparison of Conventional and Thin-Film Solar Power Satellite Designs

IQi-Ihin-Film SPS and Global Energy Requirements If the power level and specific power of an SPS are known, then an assessment of global energy requirements can lead to an estimate of the number of SPS's that need to be deployed and thus the mass of terrestrial or lunar material that needs to be placed in geostationary orbit. An assessment of global energy requirements for the next century is given in Reference 27. The assessment was done by combining the results of a carbon cycle model with an atmospheric carbon dioxide/temperature relationship and an energy/economics model. The latter model analyzed market forces and projected the growth in use in fossil fuel and non-fossil fuel energy sources. The carbon cycle model led to a conclusion that a 1% annual decrease in the use of fossil fuels is necessary to avoid a global greenhouse warming. When this decrease in fossil fuel use is subtracted from the projected increase, an energy shortfall emerges. The results are shown in Figure 6, which is based on Figure 8 from Reference 27. The curves in this figure interpolate between energy values calculated for 25 year intervals. The values for the shortfall curve fall very near a straight line whose slope is 0.45 terawatts (0.45 x 1012 watts) per year, with the rate being slightly less at present and somewhat more in the future. It may be argued that the global warming constraint used was overly strict, leading to a rather pessimistic figure for the shortfall. However, if the SPS’s have a lifetime of a few decades, then future nonfossil fuel production capacity will have to increase at faster and faster rates as the world requires more energy and aging power plants need to be replaced. The total energy demand is from 9 to 35% higher than the fossil fuel energy demand over the time interval shown. Furthermore, the present annual increase in world energy demand is 2.6%; if this continues, then the world will use 192 terawatts, with an additional 5 terawatts of generating capacity needed per year by the year 2100 [based on Ref. 28], Thus, a figure of 0.45 TW of additional non-fossil fuel power generating capacity needed per year may be rather conservative. If half of this capacity consists of SPS’s (with the other half, perhaps, being ground-based solar collectors, wind power, etc.), then 0.23 TW or 230 GW of SPS generating capacity must be added annually. Since the bicycle wheel with mirror appears to be the most promising design, it will serve as the basis for further calculations. The 10 GHz version (Table 2, row 2) supplies 130 MW to consumers, resulting in an annual deployment of:

The total number of units can be decreased by using a larger design, such as the 2.45 GHz bicycle wheel with mirror (Table 2, row 5), which supplies 533 MW to consumers. Thus, the annual deployment becomes: 230 x 103 MW 4- 533 MW/SPS - 430 SPS’s. For the NASA/US DOE reference design, (5 GW), this figure is: 230 GW 4- 5 GW/SPS = 46 SPS’s. The number of thin-film SPS’s needed may seem huge, but to nut them in perspective, 230 GW also corresponds to roughly 230 new nuclear power plants coming on line each year, or about one every day and a half. If constraints on orbital spaces necessitate fewer, larger SPS’s, and lower frequencies are not available, then large thin-film SPS’s can be constructed with only the central area used as the transmitting aperture. The large collector area will capture a great deal of solar energy, while the small transmitting aperture will cause the beam to spread out, keeping it from becoming too intense. Perhaps a more meaningful figure than the number of SPS’s that need to be deployed each year is the amount of material that will have to be launched each year. The 10 GHz bicycle wheel with mirror built of terrestrial materials has a specific mass of 0.68 kg/kW. Thus, the following amount of material will have to be launched annually: 230 x 106 kW x 0.68 kg/kW — 1.6 x 108 kg = 160,000 metric tonnes. For a conventional SPS, the amount of material needed annually would be: 230 x 106 kW x 10.2 kg/kW = 2.3 x IO9 kg = 2.3 x 106 metric tonnes. The reference system called for deploying two SPS’s each year3, for a total of up to 102,000 metric tonnes of material launched per year. Since this led to the suggestion that lunar materials be used, the need for lunar materials is suggested for the thin-film case as well. Although the thin-film SPS’s are much lighter than conventional designs, the higher estimates of global energy needs given here cause an increase in total mass requirements. The lunar bicycle wheel with mirror has a specific mass of 2.5 kg/kW, leading to an annual launching of: 230 x 106 kW x 2.5 kg/kW — 5.8 x 108 kg = 580,000 metric tonnes. Because of the difference in specific mass, the advantage of lunar materials is partly negated. However, while the lunar SPS is 2.5 kg/kW 4- 0.68 kg/kW — 3.7 times heavier per unit power delivered, launching from the Moon to geostationary orbit uses less than 8% of the energy needed from an Earth launch2. Due to the Moon’s lack of a significant atmosphere, as well as other factors, the savings in launch cost per unit mass (Moon versus Earth) may amount to a factor of about 50 [Ref. 2]. Thus, the cost of launching a given amount of power generating capacity is 50/3.7 — 14 times less from the Moon than from

the Earth. In addition, if the structure of the SPS is augmented with thrusters, de-spun docking platforms, etc., the difference between terrestrial and lunar specific masses is likely to decrease. Such structural additions may also tip the balance toward inflatable sphere designs. FIGURE 6. Projected world energy shortfall determined by subtracting allowable fossil fuel energy production (based on a 1% annual decrease in fossil fuel energy production) from the projected annual fossil fuel energy demand. The allowable production was determined by the need to prevent a global greenhouse warming. Adapted from Reference 27.

LL Conclusions The results shown above indicate that the reference designs for a thin-film SPS should be based on a power beaming frequency of approximately 10 GHz. Lower frequencies may be desirable if larger SPS's are desirable, although communications needs may render these frequencies unavailable. Higher frequencies may make possible a "mini- SPS," which can serve as a demonstration project, or be used to supply power to small, remote villages in areas with little rainfall. A non-tracking bicycle wheel design may be the simplest in the short run, and it has the highest array specific power of the three designs considered. However, its variation in delivered power during the course of its orbit may make it more difficult to integrate into existing power grids. Thus, the bicycle wheel with mirror SPS will probably be more feasible in the long run, although future developments may tip tire balance in favor of the inflatable sphere. A major issue in the deployment of thin-film SPS’s is the use of lunar versus terrestrial materials. It is likely that terrestrial designs will prove useful in the short run, allowing thin-film SPS’s to be deployed before a lunar infrastructure is built. Due to the large number of SPS’s that will eventually be needed, combined with the need to replace aging SPS’s, a lunar infrastructure may eventually become necessary. The ultimate decision about SPS deployment strategies will depend upon future global energy needs, launch costs, and the cost of building and operating a lunar infrastructure. To date, thin-film solar cells have been produced in relatively small modules at manufacturing volumes far below that required for SPS construction. The substrates commonly used are not lightweight. Research in depositing thin film solar cells on lightweight substrates is only just beginning. However, the promise of thin-film technology, combined with future world energy needs, suggests that it is worthwhile to develop manufacturing technologies which would allow thin-film solar cells and solid state microwave transmitters to be deposited on lightweight substrates and produced in large quantities. 12. Acknowledgments I would like to thank Geoffrey Landis and Ronald Cull of NASA Lewis Research Center and Brandt Goldsworthy of Goldsworthy and Associates for their discussions and the information they provided, Professor Martin Hoffert of New York University for his

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