NEWD UMP Nuclear Eiergy Waste Disposal Using Massdriver Propulsion The University of Michigan Winter Term 1979 Cover rawn by Dennis Melvin

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PROJECT PERSONNEL Management Kevin Blankinship (manager) John H. Porter (asst. manager) Nuclear Orbital Mechanics Propulsion Ground Support ouglas G. Fortier Todd W. Knowles Robert I. Carlson* Samuel A. Trupiano David T. Rue Bruno P. Cinquepalmi Steve-W. McKinster Lynne M. Wood Rand E. Simberg* James E. Gazur Dennis Melvin Richard Wood Attitude Control Mass Driver Structures obert I. Carlson Douglas G. Fortier Lynne Buben runo P. Cinquepalmi Rand E. Simberg* Alan L. Jones James E. Gazur Samuel A. Trupiano David J. Steigmann* avid T. Rue* Lynne M. Wood Todd W. Knowles Richard D. Wood *Group Leaders

Foreword Project NEWDUMP is the twenty-second in a series of senior design studies carried out by students in Aerospace Engineering 483: "Aerospace System Design. " -Originated in 1965 by Professor Wilbur C. Nelson, this course has been taught regularly since that time. It is offered in parallel with Aerospace Engineering 481: "Airplane Design, " and 482:'Design of Rocket and Air-Borne Remote Sensing Probes, " to accommodate the full spectrum of interest of the aerospace engineering students. The preliminary design study presented here is of a system to affect removal of nuclear waste material into space. The wastes generated in nuclear powerplants are sent to reprocessing facilities to remove less toxic and even desirable raw materials and incidentally to reduce the total mass to manageable amounts. The resulting waste products are transported to a launch site where they are launched by the Space Shuttle to a space station in earth parking orbit. The next phase of the disposal sequence (the earth parking orbit is not considered a suitable permanent depository) was the subject of an intense study in the early phases of the project. Debated were the closely related subjects of the propulsive system to be used and the eventual destination of the wastes. The decision reached was to use a mass-driver as a -propulsive device. A mass-driver, still in the early stages of development, is an electromagnetic gun capable of imparting efficiently large speed increments to payload packages. This concept allowed the team to consider deep space as an attainable destination for the nuclear wastes. The students of the Aerospace System Design Course are organized into a management and several engineering groups, one for each of the main subsystems. Technical assistance is obtained through the cooperation of engineering faculty members as well as in consultation with technical and management staff members in Government and Industry. The one semester's work of each group is integrated into this final report. Professor Harm Buning April 1979 111

TABLE OF CONTENTS Project Personnel Foreword Chapter 1 INTRODUCTION 1 1. 1 Perspectives on the Nuclear Waste Problem 1 1. 2 Study Groundrules 2 1.3 Initial Studies/Conventional Space Disposal 3 1.4 The Mass Driver 3 1.5 Growth Potential 5 1. 6 Conclusions 5 Chapter 2 NUCLEAR 6 2. 1 Introduction 6 2. 2 Radiation Effects 6 2. 3 Considerations for Space Disposal 8 2.4 Reprocessing Procedure 11 2.5 Mix Characteristics 11 2. 6 Shielding 13 2.7 Further Considerations 16 2. 8 References 16 Chapter 3 ORBITAL MECHANICS 18 3. 1 Destination Requirements 18 3. 2 Mass Driver Orbit Options 20 3. 3 Refer ences 22 Chapter 4 MASS DRIVER: LINEAR SYNCHRONOUS MOTOR 27 4.1 Introduction 27 4. 2 System Description 28 4.3 Mass Driver Parameters 29 4.4 Power Supply 29 4.5 Electrical Masses 31 4.6 References 32 Chapter 5 STRUCTURAL DESIGN 34 5. 1 Introduction 34 5.2 Mass Driver Tube Sizing 37 5.3 Shuttle Bay Waste Container Sizing 38 iv

5.4 Sizing of Support Struts for Mass Driver Tubes 43 5.5 Large Space Structure Construction Methods 46 5.6 Suspension Cable System 47 5. 7 Materials 48 5.8 Structural Effects of Firing Failures 52 Chapter 6 ATTITUDE CONTROL 55 6. 1 Introduction 55 6. 2 Definition of Axes 55 6.3 Requirements 55 6.4 Reboost Problem Formulation 57 6.5 Pitch Dynamics and Control System 58 6. 6 Guidance 65 6.7 Attitude Sensing 68 6.8 Flight Computer 69 6.9 Thruster Sizing 74 6.10 References 78 Chapter 7 GROUND SUPPORT 79 7. 1 Introduction 79 7.2 Launch Site Selection 79 7.3 Location of Power and Reprocessing Plants 82 7.4 Transportation and Handling: From Powerplant to Launch Site 84 7. 5 Handling the Waste Containers at J. F. Kennedy Space Center 89 7.6 Environmental Impact 93 7.7 Communications 95 7.8 Space Station/Life Support 96 7.9 Conclusions and Recommendations 96 7. 10 References 101 Chapter 8 COST ANALYSIS 102 8. 1 Introduction 102 8.2 Summary 102 8.3 Utility Impact 106 8.4 Conclusions 106 8. 5 References 106 Appendix A Nuclear 107 Appendix B Orbital Mechanics 109 Appendix C Mass Driver 112 Appendix D Structures 116 Appendix E Attitude Control 164 Appendix F Ground Support 166 Acknowledgments 174 v

INTROD UCTION 1.1 PERSPECTIVES ON THE NUCLEAR WASTE PROBLEM With the recent incident at the Three-Mile Island nuclear plant, the public debate over the future of nuclear energy is expected to heat up, resulting in new, more stringent requirements for nuclear reactor construction and the handling of nuclear waste. The Interagency Review Group (IRG), consisting of representatives from 15 government agencies, is presently evaluating possible methods of waste disposal in an attempt to resolve differences in previous studies and present a solution acceptable to the public. The IRG is expected to produce several options as to the best solution to the nuclear waste problem. These options will include storage/disposal methods such as underground storage, sea bed storage, and reprocessing methods. The effectiveness of each method is reflected in their philosophies regarding what level of safety is desired by the public. Evaluation of the different methods is contingent upon what can be regarded a safe level of toxicity and the capability of maintaining stability of storage over the consequential time periods. Views as to the minimun tolerable level of toxicity differ widely and are reflected in a variety of comparative criteria. These criteria include considerations such as the relation to the toxicity of natural ores, radiation effects on people, ecological considerations, etc. Most methods consequently shoot for target periods of safe storage on the order of 100,000 years. Stability of storage is an equally debatable issue. Most assessments developed rely on a mix of empirical evidence and statistical modeling. An experimental test site for assessing the stability of salt-mine storage in Asse, West Germany, where experiments in waste placement are currently underway. Although the Asse facility offers first-hand information regarding effectiveness of deep-underground disposal, it will require a substantial time baseline before the reliability of this method is accurately ascertained. Viewing the problem of disposal from an economics standpoint, social costs can be associated with alternative activities and the possible hazards. By enumerating the social costs, a perspective can be developed by which an optimum solution is found. Social costs can be categorized as follows: 1. Cost of diverting resources from other uses for handling and storage of nuclear waste. 2. Cost of provision of facilities for work storage/disposal. 1

3. Social cost of system failure (real costs in terms of property damage, radiation-related illnesses, etc. ). Although the first category cannot easily be quantified, it is recognized that the rate of nuclear waste production (dependent upon the number of reactors in operation) and the required storage duration constitute the major cost drivers. The second cost is more accountable, reflecting the R&D, construction, and operating costs. The third category, since it reflects the real costs of failure is a subject of values and the degree of risk-aversity of the public. From these considerations, it is evident tradeoffs between long-run cost and safety result for each method of storage/disposal. In the context of this study, the goal is to provide a disposal system offering an improved tradeoff of long-run costs with safety providing growth potential and allowing for more risk-averse disposal practices. 1. 2 STUDY GROUNDRULES The groundrules developed followed from a respect for safety in transporting and handing nuclear waste and a consciousness of costs. The following groundrules were followed throughout the study: 1. Disposal of only Light Water Reactor (LWR) waste. 2. Disposal system should be capable of transporting all LWR waste currently produced and through to the year 2000. 3. Present state-of-the-art technology should be used wherever possible. 4. Shuttle to be used as the baseline transportation system to earth orbit. 5. Nuclear waste mix disposed of should consist of materials which have little or no industrial usage and are hazardous to man and the environmen 6. Waste mix should be processable by current means. 7. System simplicity preferred for high reliability. 8. Prime concern is safety. Slight reductions in safety are acceptable when resulting in large cost reduction. 2

1.3 INITIAL STUDIES/CONVENTIONAL SPACE DISPOSAL Initially, conventional methods of space disposal were examined in an effort to produce a design concept representing the optimum mix of destination, nuclear waste mix, shielding, and spacecraft configuration for producing a safe, cost-effective method of disposal. The initial studies included: 1. Destination 2. Nuclear waste mix for disposal 3. Reprocessing methods 4. Ground transportation/launch site selection 5. Packaging for space transportation 6. Shuttle bay cooling 7. Environmental impact study 8. Reliability of space disposal operations 9. Long-term disposal safety. The conventional study represented the achievable using current technology. The results of this effort is summarized in Table I. The conventional study served as a baseline for comparison with the mass driver concept. Results are presented in their appropriate sections. Table I. Conventional Space Disposal Study Results Destination: Circular solar orbit at. 86 AU. Waste Mix: Mix 4A (see Nuclear report for description). Weight Waste /Flight: 4000 lbs Orbital Long-Term Stability:102 earth reentries per 106 year Deployment: Shuttle to low earth orbit with two nuclear waste spacecraft. Two shuttle flights for upper stages. Upper stage required for earth escape. Requires kick motor for circularization. 1.4 THE MASS DRIVER In this application, the mass-driver constitutes the primary element in an orbiting nuclear waste disposal facility where canisters, containing high-level radioactive waste are transported to the facility in low earth orbit and accelerated by the mass -driver to speeds on the order of 12 km/sec for solar system escape. 3

Use of an orbiting station using a mass-driver for nuclear waste disposal was first proposed jointly by Alan Friedlander of Science Applications, Inc. and Rand Simberg of the NEWDUMP project team. The mass-driver first appeared in the early 1970's as a device called the'Magneplane,' a joint project conducted by MIT and the Raytheon Corporati, Later, the device gained notoriety as a propulsion system in the space manufacturing/space colony studies conducted at the NASA Ames Research Center. During this stage, the mass driver evolved from on-paper studies to laboratory test models. Research is presently underway at the Francis K. Bitter National Laboratories at MIT and at the Physics Department at Princeton. A comprehensive report on this research will be released in late April of which preliminary copies were procured for the NEWDUMP project. The NEWDUMP orbiting facility was made possible via several technological advances in the following areas: 1. Large Space Structure Technology: Construction techniques have been developed at NASA Marshal Space Flight Center including extravehicular activity simulations at the water tank facility. A'Beam Builder' machine has been constructed by Grumman Aerospace Corporation for construction of beams from aluminum sheets fed into the machine. Structural testing of different aluminum beams has been performed at the NASA Johnson Space Center (JSC). Research into the development of beam builders for large composite structures is presently underway at NASA JSC, Grumman, McDonnell-Douglas, and General Dynamics. 2. Mass-Driver Technology: Much theoretical work has been accomplished during the NASA Ames Research Center studies, and at MIT and Princeton. This work proceeded in parallel with the development of two laboratory test models. 3. Economical Space Transportation: The Space Shuttle has substantially reduced the cost of space transportation since the Apollo project, with possible improvements for even greater economy. The mass driver promises numerous advantages over both conventiona' space disposal and burial/reprocessing methods. The primary advantage of the mass-driver is that it allows for permanent disposal of nuclear waste. Once the radioactive waste container attains the minimum velocity required for escape, it will never return. This eliminates the plethora of long-term storage problems with their associated costs. 4

This does not necessarily conflict with the present frontrunner for nuclear disposal —salt-mine storage. Salt-mine storage would be appropriate as a temporary storage until an orbiting nuclear waste disposal facility is developed. 1. 5 GROWTH POTENTIAL Another advantage of the mass-driver accelerated solar system escape system lies in its growth potential. A study by Rockwell International has shown that the payload capability of the shuttle can be increased by 500 and the cost per pound reduced by as much as 40lo by the development of liquid rocket boosters. Heavy Lift Launch Vehicles (HLLV's) offer greater cost effectiveness, eventually cutting the cost/lbm by a factor of 5. Technical growth will also affect the mass -driver systems. The major areas of growth are expected to be in the power system and in the use of computers, where substantial weight savings can be realized. These areas include: semiconductor technology improvements for high-power applications, improved efficiency of solar cells, and lightweight, high frequency power storage devices. The largest savings in cost and weight is expected in the use of composites. The NEWDUMP design, with its associated'weights and costs was performed using aluminum throughout the structure, relying on current technical knowledge.. The use of composites for reducing thermal stresses will result in a secondary impact on weight savings, resulting in a smaller, lighter structure due to reduced stress requirements. 1. 6 CONCLUSIONS The viewpoint taken in the study is to provide a technically feasible alternative offering a low long-run cost with the potential for inexpensive operating costs for nuclear disposal. Although the cost of constructing an orbiting disposal facility is large, the firing rate accommodated by a single mass-driver is sufficient for the disposal need through the year 2000, based on projected growth in the rate of nuclear waste production. Due to the necessarily large scale of an orbiting waste. disposal facility, a national commitment would be required for development. Since the linear-synchronous motor technology of the mass-driver is still at the laboratory test-model stage, further research work, especially in the experimental area with larger test models having higher acceleration capability is mandated. 5

2 NUCLEAR 2. 1 INTROD UC TION Today, nuclear power plants provide 14%o of the entire electrical power produced in the United States. For every pound of Uranium burned in a nuclear plant, it requires 2,700,000 pounds of coal to produce an equivalent amount of electricity in a conventional, coal-burning, power plant. Nuclear plants also put fewer pollutants into the atmosphere than do their counterpart, coal plants. The drawback with nuclear plants, however, lies in the solid waste produced. It is highly radioactive and remains so for many years. This section is devoted to the description of radiation, its effect upon man, and the considerations which must be taken into account in order to make the option of space disposal feasible. 2. 2 RADIATION EFFECTS The effects of radiation on man are dependent upon the strength of radiation, length of exposure, distance from source, and the biological proper of the tissue absorbing radiation. Radiation consists of alpha particles, beta particles, and gamma rays. The alpha particles are fast moving Helium nuclei (4 He) that are non-penetrat[ and are stopped in a fraction of a millimeter in the superficial tissue. Beta particles are electrons and can be stopped within one centimeter of tissue. T1 most penetrating are the gamma rays which can traverse the entire body. All types of radiation have one property in common, the ability to eject electrons orbiting around the nucleus from the atoms of any material through which they pass. The charged particles (alpha and beta) ionize directly and in qualitatively similar ways. Gamma radiation causes ionization by the product: of secondary electrons. The ionization tracks of the particles differ considerably. The ionization tracks of gamma radiation are long and sparsely ionized; beta particle tracks are shorter and more densely ionized: alpha particles are even shorte3 straight, broad and densely ionized. The densely ionizing particles have a greater relative biological effectiveness than the less densely ionizing particle 6

Particles Range Ionizing Power air (ft) Tissue (cm) Alpha.1.01 10,000 Beta 10 1 100 Gammrna 1000 10 1 Table 2. 1 Relative Comparison of Radiation For radiation to be biologically effective, ionization must take place within the cell nucleus. The ionization produced at various depths of the body will depend on the penetrating power of radiation. The biological effects are related to the quantity of ionization produced in the tissue or the dose of radiation absorbed. The energy absorbed in a particular material from a radiation flux, without reference to the type and energy of radiation, is defined as a unit of absorbed dose or rad. Biological effects of equal absorbed doses in rads of different kinds of radiation are not the same. Hence, the unit rem or dose equivalent is defined where: dose in rems = dose in rads x Relative Biological Effectiveness (RBE). The RBE of radiation is the absorbed dose of 250, 000 volts or x-ray radiation which produces the same biological effect as one rad of the radiation in question. For gamma rays and beta particles, RBE's are approximately one. For alpha particles, the RBE can be as high as ten. Biological effects of ionizing radiation depend on the energy absorbed and on various modifying factors. Since the penetration of gamma rays is much greater than that of the alpha and beta particles, the absorbed dose will be primarily dependent upon the gamma rays, whose RBE is equal to one. Therefore, the dose equivalent in rem and the absorbed dose in rads are numerically equal. Radiation affects man by causing ionization within the cell, the main damages being in the reproductive processes due to chromosome disturbances. This affects tissues that require high rates of new cell production, including skin, intestines, spleen, bone marrow, eyes, gonads, and lymph nodes causing lower immunity, blood clotting, reduced oxygen transport, sterility, dermatities, ulcers, and cataracts. The does of a radionuclide is inversely proportional to the square of the distance from the source. Dependent upon the dosage, a person could suffer a slight loss of hair to third degree burns. Fluctuations in the blood count are the result of changes in production and destruction as well as the life span of a particular cell line. One of the first late effects of radiation is increased likelihood of cancer in the affected organs. 7

Very subtle genetic changes are likely to occur. Assuming a dose of 100 rads, the probability of a new mutation in the immediate offspring is one in twenty-five hundred. Dose Effects and Conditions 100,000 rem spastic seizures; death in seconds 10, 000 rem disruption of central nervous and cardiovascular systems; death in minutes to hours 1,000 rem necroses of progenitive tissue; death 30-60 days 100 rem mild irradiation symptoms in few cases 10 rem few or no detectable effects 10 rem/day debilitation 3-6 weeks; death 3-6 months 1 rem/day debilitation 3-6 months; death 3-6 years.1 rem/day permissable dose range; no effect.01 rem/day permissable dose range; no effect.001 rem/day natural radiation; no effect Table 2. 2 The Effects Upon Man Exposed to Various Doses of Radiation 2. 3 CONSIDERATIONS FOR SPACE DISPOSAL Spent fuel, in the form as it is removed from the reactor, has a large mass. In order to fit into our scenario of disposal and meet present economic standards, it is necessary to reduce the mass of this spent fuel and at the same time retrieve the usable fissile material (that which is capable of producing a fission reaction). Without the extraction of the useful material a Uranium shortage would occur by the year 2000 as predicted by current nuclear power projections (Reference 15)(see Table 2. 3). Therefore, it is necessary that these spent fuel elements be reprocessed. Other aspects of the research included shielding considerations, heat generation, as well as magnetic and other physical properties of the reprocess waste. Absorption of neutrons by fission products interferes with the chain reaction to the point where it is necessary to remove the fuel elements from the reactor core, even though they still contain a large amount of unburned fissible material. These spent fuel assemblies, as they are removed from the reactor, are what are referred to as reactor wastes. Reactor wastes, as a whole, are 8

Total Amount Date Power Total Spent Fuel of Mix 4A (Year) (G. W(e)) (Metric Tonnes) (Kg) Backlog 110,5 32. 2 1979 56.3 1.88. x 103 32,010.0 1980 60.1 2. 00 x 103 34,991.4 1981 70.1 2. 34 x 103 38, 092. 0 1982 81.6 2.72 x 103 41, 172.8 1983 92.8 3.09 x 103 45,983.8 1984 109.4 3.65 x 103 52,637.0 1985 126.8 4.25 x 103 60,561.8 1986 140.8 4.69 x 103 70, 357.6 1987 153.7 5.12 x 103 79,665.4 1988 166.3 5.54 x 103 87,604. 6 1989 179.8 5.99 x 103 95,083. 6 1990 194.8 6.49 x 103 102,638.2 1991 210.7 7.02 x 103 110,728.6 1992 227.5 7.58 x 103 119, 367.0 1993 244.3 8.14x 103 128,395.8 1994 263.2 8.77 x 10 137,632.6 1995 283. 0 9.43 x 103 147,409.8 1996 302.8 10.09 x 103 158,051.2 1997 322. 6 10.75 x 103 168.863.2 1998 342.4 11.41 x 103 179,571.2 1999 362.2 12.07 x 103 190,138.8 2000 380. 2 12.67 x 103 200,490.8 Table 2. 3 Yearly Power, Spent Fuel, and Mix 4A Predictions (See Appendix A. 2 for Mix 4A Calculations) 9

further broken down into mixes. Each mix (Reference 2) is numbered with reference to the materials which are chemically extracted. A consideration of prime importance was minimizing total mass while staying within current technical and economic boundaries. The mix that was chosen, termed'"mix 4A", deals with the extraction from the total reactor waste the following elements: uranium, plutonium, xenon, krypton, iodine, bromine, zirconiumn, molybdenum, and niobium. The elements which are removed consist of those which are rare or can be used by industry and those of short half lives which can be stored in existing geological areas and pose little hazard to the populace. The extraction of these elements as well as the cladding hulls constitute a 97. 88% reduction in total mass. The remainder of the reactor waste will make up the payload (21. 2 kilograms from 1 Tonne of reactor waste). Step l: Removal of U Step 2: Removal Step 3: Removal Step 4: and Pu ( 965 kg) from of Xe, Kr, Br, I of Mo, Nb, Zr Mix 4A 1000 kg of spent fuel from waste remain- from waste remain- (23kg) (1000kg) ing after step 1 ing after step 2 (35kg) (30kg) DIAGRAM 2.1: GRAPHIC VIEW OF THE REMOVAL OF CERTAIN ELEMENTS FROM 1000 KILOGRAMS OF SPENT FUEL TO PRODUCE MIX 4A 10

2. 4 REPROCESSING PROCEDURE These spent fuel assemblies are sent to specialized reprocessing plants where they are mechanically chopped into small pieces (so the fuel will no longer be protected by the cladding) and dissolved in a solution of 2-3 molar Nitric acid (Al(N03) ) (see diagram 2. 2). Both uranium and plutonium (the useful fissile material) are extracted (99. 5%) together in a Tributyl Phosphate solution. These two actinides are then separated from each other by either ion exchange or selective oxidation and solvent extraction methods. The plutonium (valued at $5000 a pound) can be used as a reactor fuel by adding it to natural uranium, thereby eliminating the costly and energy intensive enrichment process (Reference 4). Uranium is recycled for reenrichment or blending with other fuel materials. The aqueous solution remaining is termed the high level waste. The next step is to remove some usable materials; zirconium (Zr), niobium (Nb), and molybdenum (Mo) which constitute a 21% further weight reduction of the remaining solution. A 100%o Tributyl Phosphate solution is then used for extraction of Nb and Zr from the aqueous solution. The Mo is separated (99%) using solvent extraction or sublimation technique. Xenon and krypton are effluent gasses and are removed (100%o) by standard gas handling techniques. Iodine and bromine are removed by virtue of their low boiling points, or, as in the case of iodine, by its reaction with silver to form silver iodide. Iodine removal presents a special health hazard in that its radioactive half life is 1.7 x 107 years and is concentrated in the thyroid gland of living organisms. This could be considered as a single payload for disposal (Reference 2). Bromine is not radioactive after a very short time and can be treated as a chemically toxic waste. Krypton is radioactive and has a half life of 10. 6 years. It may be stored or used industrially. Xenon is non-radioactive and chemically inert. It may be stored, used industrially, or dispersed. Zirconium is used extensively in industry in corrosion prevention, refractory material, and in making super conducting magnetics ($5/lb). Molybdenum and niobium are also used extensively in industry ($15 /lb). 2. 5 MIX CHARACTERISTICS The method for disposal dictates the form that the waste should be in either liquid or solid form. For the purpose of space disposal, a solid in the form of an oxide was chosen. 11

Fuel Rods From Reactor Chop Rods Into Small Pieces Zirconium Hulls To Waste Storage Dissolve UO2, Puo Remove Radioactive Gasses lnd Fission Products G Storage (Xe, Kr, Br, I) In Nitric Acid aqueous phase Solvent Extraction o Removal Of containing Tributrl Phosphate Zr, Nb, Mo fission product (TBP) Storage reducing agent.Partition Waste Concentration (Extract Pu From U and Temporary with Nitric Acid) [ Storage aqueous phase solven1 phase r.zutonium Purification Uranium Purification Waste Solidification and Conversion To PuO2 and Conversion To UF6 and Preparation For Space Disposal DIAGRAM 2.2: REPROCESSING FLOW DIAGRAM FOR MLX 4A 12

Melting point 127 3 K Thermal conductivity.6 - 1. 8 W/m K Thermal density.0398 W/ Density 4. 0 g/cm Table 2. 4 Oxide Characteristics (Values from Reference 2) Due to high heat generation, it is suggested that spent fuel assemblies be stored in cooling tanks at power or reprocessing plants for ten years before being prepared for space disposal. This will also decrease the amount of radioactivity and in essence the amount of shielding needed, hence, a reduction in weight for disposal purposes. Looking at the magnetic susceptibility of the mix, (see Appendix A. 1), it was determined that no interaction between the waste mix and the magnetic fields produced by the mass driver would occur. This makes the option of mass driver bucket retrieval possible. 2. 6 SHIELDING The mix is composed of fission products whose sources of radiation are beta and alpha particles, and gamma rays. The beta and alpha particles are simple to stop. The gamma rays are difficult to stop. With beta particles, the absorption of their energy in matter gives rise to the production of electromagnetic radiation known as Bremsstrahlung radiation. This radiation is more penetrating than the beta particles which produce it. Therefore, it is necessary to use shielding material of low atomic number. The gamma radiation is not completely absorbed by any thickness of shielding,however great. Instead, the intensity of the transmitted radiation decreases approximately exponentially with the thickness of material traversed. The shielding must be thick enough to reduce the dose rate to an acceptable level. The weight of the shield is important. It has been determined that a single layer of tungsten (W) followed by a layer of lithium hydride (LiH) gives the best shielding for its weight (Reference 11). The tungsten is for the shielding of the gamma rays and the lithium hydride is for the neutron shielding. Shielding tickness as a function of fission product contamination and mass of actinides for a range of dose rates are shown in Figures 2, 1 and 2. 2. It has been found that the actinides within the container become self shielding (see Figure 2. 2); that is, the shielding thickness becomes nearly a constant value for increased amounts of actinides. 13

12.1% Fission Products Remaining In Actinide Waste 10 _ Tungsten -------- Lithium Hydride 8 6 4 - xJ\ 0 L 1 I 2 102 Dose rate 1 meter from outer surfal8, rem/hr 10 FIGURE 2.1: THICKNESS OF TUNGSTEN AND LITHIIUM HYDRIDE SHIELDING MATERIAL REQUIRED TO REDUCE DOSE RATE 1. METER FROM OUTER SURFACE OF PACKAGE FOR MATRIX CONTAINING 250 KILOGRAMS OF ACTINIDE WASTE. (ref. 9) 14

400 Danei rat. 100 rTO/hr 300 a < t I Ir12 fision prod Io sI. ~ c~iorTM tsIn 200 Doe~ rate 0ac 400.... I t, 1 0...fiss pr..~c_ f200 r'Cinin is. Sc: z:$ 0 2 4 6 8 10 12 5 -Lithium hydride thic-ntse cm (b) LUthir hydride shielding 15 l ~ ~ ~ ~~~~Ltia yrd hcces'O ~ ~ ~ ~ ~ ~ (b ihu y~imsili~

Removal of the shielding package once the waste containers are deposited on board the mass driver is also considered permissable from the nuclear standpoint. Tungsten (W) 186, because of its large cross section (Reference 8), is the one isotope which is affected significantly by radioactive waste. By the absorption of a neutron, it transforms to W 187 which has a half life of approximately 24 hours and decays to rhenium (Re) 187 which is not radioactive. The amount of radiation expelled by the decay of W 187 is very small. (Comparable to the dose from having x-rays taken at the dentist's office (Reference 10). ) The optimum package ratio occurs for a dose rate of 10 rem/hour at one meter from the external surface. This gives the best weight reduction to dose increase. Further increases to higher allowable dose rates are less effective in increasing package ratios (Reference 7). With reference to 10 CFR 71 for transporation of radioactive waste, a base point of 1 rem/hour at one meter from the external surface of the package was suggested in case of accidental exposure to the general public. Hence, this is the suggested dose value to be used for shielding requirements. 2. 7 FtURTHER CONSIDERATIONS Before implementation, further studies and tests must be performed to determine the effects of radiation on the mass driver, shuttle, and waste handling equipment. This information was unavailable to this research group and is beyond the scope of this report. 2. 8 REFERENCES 1. Alexander, C. W., Kee, C. W., Croff, A. G., and Blomeke, J. O., Projections of Spent Fueld to be Discharged by the U. S. Nuclear Power Industry, " Tennessee, Oak Ridge National Lab (Oct. 1977). 2. Burns, R. E., Causey, W. E., Galloway, W. E., and Nelson, R. W., "Nuclear Waste Disposal in-Space, " Alabama, George C. Marshall Space Flight Center (1978) NASA Tech Paper 1225. 3. Chalke, H. D., Williams, K., Smith, C. L., Radiation and Health, Toronto, Longmans LTD, (1962). 4. Deutsch, R. W., "Nuclear Power", Columbia M.ryland, General Physics Corporation (Oct. 1977). 5. Fisher, Arthur, "What Are We Going to do About Nuclear Waste? ", Popular Science, (December 1978). 6. Heckstall, H. W., Atomic Radiation Dangers, London, T. M. Dent and Sons, LTD, (1958). 7.'"High Level Radioactive Waste Management Alternatives, " Richland, Washington, Battelle Pacific Northwest Laboratories, (May 1974), BNL- 1900-4. 16

8. Hughes, D. J. and Schwartz, R. B., "Neutron Cross Sections" Upton, New York, Brookhaven National Laboratory, (July 1958). 9. Hyland, R. E., Wohl, M. L., and Finnegan, P. M., Study of Extraterrestrial Disposal of Radioactive Wastes. Part 3" NASA TMS-68216 (1973). 10. Kikuchi, C., Nuclear Engineering Professor, Nuclear Engineering Department, University of Michigan, personal communications, Jan-Feb 197 9. 11. Lynche, C. T., CRC Handbook of Materials Sciences, Vol. I, General Properties. 12, "Management of Radioactive Wastes from Fuel Reprocessing," Symposium, OECD-Paris, (1973). 13. McKeon, D. C., Nuclear Engineer, University of Michigan, personal communications, (Jan-Mar 1979). 14. Meek, M. E,, and Rider, B. F., "Complications of Fission Product Yields", Pleasonton, California, Vallecitos Nuclear Center (1972). 15. Pines, David, ed., "Reviews of Modern Physics", New York, American Physical Society, (Jan 1978), Vol. 50, Number 1, Part 2. 16. Summerfield, G., Notes From Nuclear Engineering Course No. 400, University of Michigan, College of Engineering, Ann Arbor. 17. "The Problem of Nuclear Waste-We've Got to Solve it Soon" Changing Times-The Kiplinger Magazine (Feb 1979). 18. Wang, Yen, CRC Handbook of Radioactive Nuclides, The Chemical Rubber Company (1969). 19. Wilson, B. J., The Radiochemical Manual: 2nd ed., Amershan, The Radiochemical Center (1966). 17

3 ORBITAL MECHANICS 3.1 DESTINATION REQUIREMENTS Crucial to any discussion of space disposal of nuclear waste is the question of destination. The answer to this question hinges on many criteria, such as velocity increment (AV) required to achieve the destination, complexi of mission requirements, possibility of later recovery, the chances of eventum return to earth, and possible traffic problems with other vehicles and celestia bodies. Mission complexity invites cost, as do high velocity increments. Therefore, for purposes of economy both of these parameters should be minimized. While it is possible that future generations will find uses for the waste material, (much as gasoline formerly was considered a useless by product of petroleum processing), it was decided that recoverability was to be given low priority compared to the urgency of removing the waste from humanity's immediate environment. There are relatively few places that would provide easy future accessibility; to emphasize the recoverability aspec to any extent would place undue constraints on the problem. Traffic problems were given strong consideration, particularly in those cases where the chance existed of an encounter with a manned vehicle. Finally, the most important parameter of all is long-term stability: long-term in this case meaning on the order of a million years. Obviously, if the waste returns to earth eventually, the purpose of the project is defeated. To summarize, the project requireme: were low tV, minimal mission complexity, no traffic problems, and long-ter: stability, with recoverability considered irrelevant. The first candidate is high earth orbit (HEO). The particular orbit examined was a circular orbit with an altitude of 50, 000 km; safely beyond the projected communications satellite traffic in the geosynchronous region, yet close enough to earth to remain unperturbed by lunar gravity, AV requiremer are not prohibitive, as can be seen from Table 3. 1. Keeping an eye to the futi however, it is not unreasonable to expect traffic to the moon and Lagrange points to increase considerably in the 1980's and 1990's, particularly manned traffic. Putting the payload in a polar orbit at the same altitude would ease this problem somewhat, but only at a large AV cost due to the plane change required. In addition, the long-term stability is questionable in either case. Lunar orbits suffer from the same problems as HEO; possible traffic and orbital instabilities. Placing the waste on the lunar surface was briefly considered. There are two possibilities in this case: hard landing and soft landing. The hard landing option was eliminated mainly for environmental 18

reasons. Each landed payload would create a radioactive crater. Soft landing was ruled out on the basis of complexity; in this case, each landed payload would require the equivalent of an Apollo mission, in terms of both AV and logistics. The only orbits in near-earth space that do exhibit the long-term stability required are the "gravity wells " at the Earth-Moon Lagrange Points L-4 and L-5. Precisely because these orbits are so stable, they will likely be considered valuable'real estate" in the near future. Too valuable, in fact, to be used merely as repositories for nuclear waste materials. It rapidly becomes apparent that the solution to the problem does not lie in near-earth space. Farther out, the options include planetary impacts, planetary orbits, heliocentric orbits, solar impact, and solar system escape. Going to Jupiter's Trojan points or any of the planets is not feasible due to severe launch window constraints. Heliocentric orbits seem to offer more promise. In particular, orbits between Earth and Mars, or between Earth and Venus, display very good stability, at a moderate AV. Another possibility is to place the payload in an orbit about one of the Earth-Sun equilateral points. Because this mission would constitute a rendezvous rather than an orbit change, the velocity change required is very low. The only essential requirement is earth escape, after which a very small boost is sufficient to inject into the proper orbit. So-called'horseshoe" and'tadpole" orbits have been found around these points, and they have been numerically integrated for up to 10, 000 years. There is good reason to believe that they would remain stable much longer than this. There are two problems with heliocentric orbits, one minor, the other major. The minor problem is that while chances of eventual return to earth are extremely low, they are not zero. The major problem is that control of the trajectory must be maintained at long distances from earth for long times after launch. In the case of an equilateral point mission, the injection burn might take place 10 years after launch. This is a long time to expect an unmaintained system to remain reliable, and the consequences of failure would be serious; the waste would remain in an earth-crossing orbit with no easy means of rescue to prevent the eventual return. Bearing this fact in mind, it would clearly be desirable to find some "free" trajectory that required no control once the payload leaves low earth orbit. With such a trajectory, the payload would need only a single boost in the proper direction with the proper velocity to assure that it would eventually reach the desired destination. 19

The study yielded two classes of such trajectories: solar impact and solar system escape. Solar impact was ruled out as a result of the very high (> 20 km/s) velocity increments required. It is possible that such velocities can be reasonably achieved in the near future, but too little researc has been done in this area for the purposes of this project. This leaves only solar system escape. The AV required is moderately high, but this is compensated by several advantages. One of them is that it is a free trajectory, as discussed previously. If a payload in low earth orbit is given ahigh enough velocity in-the right direction at the right time, it is guaranteed to leave the solar system, assuming that it doesn't encounter the moon or planets on the way out. Also, no further propulsive maneuvers are required nor is there a need to track the material for appreciable lenghs of tir Another advantage is that launch windows occur very often; once per orbit or once every 92. 5 minutes in a 400 km circular orbit. The third advantage and perhaps the most important one is that once the waste leaves the solar system it will not return. Despite the high AV required, this option looks more attractive than any other because of its overwhelming virtues in all other respects. Thus, despite the somewhat high velocities required, there is a strong motivation to find or design a device that will provide the requisite velocity to the payload. 3. 2 MASS DRIVER ORBIT OPTIONS 3. 2. 1 Symmetrical Configuration Having chosen a catapult-like device (which a mass-driver is), the first problem to be confronted is Newton's Third Law. Every payload will impart a recoil velocity to the launch vehicle, causing it to behave as a retrofiring engine if the payload is fired forward. In this condition the orbit of the vehicle will decay and the vehicle will eventually burn in the upper atmosphere. The most obvious solution is to fire a payload of mass equal to the nuclear waste payload in the opposite direction. In this manner the two reactions would cancel and no net force would be exerted upon the launchir device. If payloads are to be launched in two directions, there must be an orbital symmetry such that both directions yield a solar system escape trajectory. The only orbit found possessing the necessary properties of symmetry is a circular orbit in the ecliptic plane with the launch vehicle aligned perpendicular to the orbit (Figure 3. 1). In this configuration the mass driver would fire perpendicular to the plane of the ecliptic, launching waste above and below the plane towards system escape (Figure 3. 4). 20

If the long axis of the vehicle lies in the orbital plane, attitude control problems are introduced as a result of the required rotation. By keeping the vehicle always perpendicular to its orbit, attitude control considerations are minimized because the vehicle's attitude remains inertially fixed. In addition, firing out of the ecliptic plane eliminates any concern about hitting planets or objects in geostationary orbit. Unfortunately, the out-of-plane launch also entails a severe disadvantage. It turns out that firing out of the plane requires very high AV's; LV's that are unattainable using a conventional mass driver design. By not launching in the direction of orbital motion, orbital velocity is not used to full advantage. A AV perpendicular to the ecliptic implies a AV perpendicular not only to the orbital velocity about the earth but also to the velocity of the earth about the sun. Because the launch velocity is normal to these two orbital velocities, the velocity must be quite large in order to get a vector sum of solar system escape velocity. The exact amount required at any point in the orbit was calculated with a PET microcomputer. The minimum AV was found to be in excess of 20 km/sec. This velocity would require a mass driver operating at 1000 gravities acceleration to have an accelerating length of over 20 km. While this disadvantage is major, it seems to be the only one, and the configuration displays a great deal of promise in other respects. Its use awaits only the development of more powerful accelerators. 3. 2. 2 In-Plane Configuration The high AV's discussed in the previous section can be reduced considerably by launching payloads in the direction of orbital motion. In this configuration the vehicle lies in the orbital plane, oriented parallel to its orbital velocity about the earth (Figure 3. 3). Unfortunately, this orientation does not possess the symmetry of the perpendicular configuration. Payloads fired forward easily achieve escape velocity, because they utilize to full advantage both the orbital velocity of the launch vehicle and the velocity of the earth about the sun. Compensating payloads must be fired backward to maintain the orbit of the launch vehicle, however, and these packages fired in retrogracdwill not escape the solar system; they will, in fact, fall immediately to earth. This is a disadvantage from the standpoint of lift costs, because each kilogram of nuclear waste requires another kilogram of "dummy" reaction mass. Despite this, it is a more attractive option than the perpendicular configuration because the AV requirements are lowered by a factor of - 2.5. The exact orbit chosen was a posigrade, circular orbit with an altitude of 400 km. This orbit has a local circular velocity of 7670 m/sec with a period of 92.5 min (5550 sec). The orbital plane is coincident with 21

the plane of the ecliptic. 218.440 of the orbit lies in sunlight with 141.560 spent in the shadow of the earth. This gives 56. 12 minutes or 3367 seconds of sunlight per orbit during which energy can be collected with solar panels (Figure 3.4). A AV of 9000 m/sec gives a launch window 250 wide. The window is centered on a point 105. 60 behind the earth velocity vector (Figure 3. 5). The launch window encompasses a time period of 6.42 min (385 sec). The launch window time may be further restricted by the risk of intercepting the moon or objects in geosynchronous orbit. There is also a slight risk of slingshotting off a planet on the way out, causing the payload to return in an earth-crossing trajectory. Conservatively assuming a restriction of 50% due to these factors, the average time per orbit that waste can be launched is 192 seconds. In addition to doubling payload lift costs, one other problem is introduced by launching in the orbital plane. Because the launch vehicle is always aligned parallel to its orbital velocity vector, it rotates at a rate of one revblution per orbit or 1. 13 x 10-3 rad/sec. A consequence of this rotation is that, after release from its launching bucket, the payload is inside a long tube which it "sees, as moving sideways. The payload will strike the inner wall of the launch tube unless some measures are taken to prevent this. One approach is to build a slight curvature into the launch tube to compensate. Another solution is that used in the design of mass driver reaction engines (MDRE). Here, as the payload is released the bucket is snapped away from it and decelerated in a separate launch tube, leaving the payload in free space. A detailed analysis of the payload trajectory is included in the appendix. 3. 3 REFERENCES 1. Friedlander, Alan J. and Feingold, Harvey, "Earth Re-encounter Probabilities for Aborted Space Disposal of Hazardous Nuclear Waste, " Science Applications, Inc., Schaumberg, Ill, AAS/AIAA Astrodynamics Specialists Conference, September 7-9, 1977. 2. Davis, Donald R. and Greenberg, Richard, "Long Term Stability of Solar Storage Orbits, " Planetary Science Institute, presented at the 1977 Astrodynamic Specialists Conference, September 7-9, 1977. 3. Weissman, Paul R. and Wetherill, G. W., "Periodic Trojan-type Orbits in the Earth-Sun System, " The Astronomical Journal, March 1974, Vol. 79, No. 3. 4. Szebehely, Dr. Victor, Theory of Orbits, Academic Press, Inc., New York, N.Y., pp 231-266, 1967. 22

Table 3. 1 Destination Velocity Requirement Destination AV m/s Comments NEAR EARTH SPACE HEO (50,000 km) 4042 traffic problems HEO (polar) 6761 relieves traffic but expensive Lunar Orbit Equatorial 3900 traffic, unstable Polar 3900 unstable traffic L-4, L-5 3900 Lunar Soft Impact 6600 expensive, complexity Hard Impact 3100 environmental BEYOND EARTH GRAVITY FIELD Jupiter, Saturn Trojan Points 8000 expensive Heliocentric (. 86 AU) 4450 throw-away vehicles Earth-Sun Equilateral Points 3400 possible instability, throw-away vehicles Solar Impact 24, 000 EXPENSIVE but free trajectory Solar System Escape 8760 free trajectory, very stable All AV's are calculated from an initial 160 nm shuttle orbit. 23

joV I y Figure 3. 1 Orbital Plane is the X-Y Plane with Payloads Launched in the + Z direction. Figure 3. 2 Payloads Launched Above and. vet~ Below Ecliptic Plane. /nd/ Figure 3. 3 Payload Launched in the Direction of Orbital Motion. 24

/~~~~C( i~~~~~~~~~cr'I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ iI / ~ ~~~~~i ~~~~~~~~~~~~'/.,/ ~~~~~~~~~~~~~~~~i f l;;I:;_:~~~~~ ~il ~ ~ ~~~~~.:.'' /i,~ 1I // //'/'// r.! /: Figure 3.4 cP = Amount o~ Orbit Spent izz $~night = 218.44~.

, /// 3ALCaiH aWt W 9 25 Figure 3. 5 Location and Width of Launch Windoorfor 9000 m/s ~V. 26

4 MASS DRIVER: LINEAR SYNCHRONOUS MOTOR 4. 1 INTRODUC TION In the broadest terms a mass driver is any machine that accelerates a payload of material to a high velocity. This definition would include a cannon, an air rifle, an aircraft carrier catapult, or a child's slingshot. In this report, however, the term "mass driver" will refer specifically to a linear synchronous electric motor. Basic Principles Converting the energy of a magnetic field into mechanical motion is not a new idea; indeed, electric motors have been used in one form or another since electromagnetism was first discbvered, over one hundred fifty years ago. Many people are familiar with the operating principles of the garden-variety electric motors that run elevators, start our cars and blow dry our hair. In a conventional electric motor a rotating electromagnet is attracted by a stationary magnet. As the poles are aligned, the polarity of the electromagnet is reversed, resulting in an unstable configuration. The magnet moves around to become realigned with its new north and south poles and the polarity is switched again. The process continues, resulting in a continuously rotating magnet, or a motor. Both in theory and in practice, such a motor can be "unwound" to impart motion to a magnet in a linear direction. This is the principle that leads to the design of linear induction and linear synchronous motors. In these motors, an electromagnet is placed in a tube lined with stationary electromagnets that are switched on and off in sequence. As the magnet moves through the tube it is pulled by an attractive force from a stationary magnet in front add pushed by another stationary magnet from behind. When the moving magnet reaches the end of the tube, the moving magnet has a high velocity. This velocity is a function of the magnitude of the magnetic forces and the length of the launch tube. In a linear induction motor the sequence of changing magnetic fields is a predetermined function of time. In theory this is a reasonable design, but in practice it leads to inefficiencies because the magnet cannot be relied upon to be in the right place at precisely the right time. A linear synchronous motor, as its name might imply, synchronizes its magnetic fields according to the actual measured position of the magnet. This allows the maximum force to be generated at any given 27

time, and allows very high accelerations, on the order of 102 to 10 g's (1 g = 9. 8 m/s2). Use of either type of linear motor (induction or synchronous gives an additional bonus; the magnetic fields provide a guide force tending to keep the vehicle in the center of the tube, so that the system is mechanically frictionles s. 4. 2 SYSTEM DESCRIPTION The mass driver is essentially a long tube of aluminum. The inside of the tube contains thousands of coaxial, equally spaced aluminum coils. The payload carrier, henceforth referred to as the bucket, is a can with two superconducting coils of square cross section at either end. One coil would be sufficient to propel the device, but two are employed to give stability in pitch and yaw. The spacing between the bucket coils is six times the spacing betwee the aluminum drive coils (Figure 4. 1). The payload to be launched is placed inside the bucket, the front end of which is left uncovered. In general applications, the payload can be loaded at any time previous to launch, but in this particular application, the payload generates a great amount of heat which would likely have an adverse effect on the superconducting coils. For this reason loading occurs immediately prior to launch. The loaded bucket is then placed at one end of the tube. An electric current is pulsed through the two drive coils (stationary magnets) immediately in front of the bucket coils. The current has a direction such that an attractive force acts on the bucket. As the bucket moves forward, a negative pulse is sent through the coils behind it, setting up a repulsive force which also gives forward motion (Figure 4. 2). In addition to forces in the direction of motion, there are forces perpendicular to the motion as the bucket is repelled or attracted by its magnetic image in the tube walls (Figure 4. 3). The "pulling" force from the front coils tends to center the bucket, while the "push" from behind destabilizes the motion. For this reason the "pull" is made slightly greater so as to lend an overall stability to the system (Figure 4. As the bucket moves on to the next set of coils, its position is sensed by the interruption of a light beam. This triggers the next cycle. The next cycle is similar to the first one, except that the frequency of the pulses must be a little higher because the bucket now has a higher velocity and is moving past the coil more quickly. This process continues as the bucket moves down the tube, accelerating the bucket until it reaches the desired velocity. At this point the currents are reversed, pushing from the front and pulling from behind, causing the bucket to decelerate. The payload, being relatively non-magnetic, does not decelerate. It exits the front of the bucket as the bucket is slowed and continues at a constant velocity. The decrease in mass of the bucket as the payload is released causes it to decelerate more rapidly then it was accelerated, because the magnitude of the magnetic forces is the same in both cases. This results in a shorter decelerating section. 28

The bucket is slowed to a stop and removed from the tube. If necessary, its coils are recooled and their-current is readjusted inductively. -' It is then reloaded to be sent back the other way. 4.3 MASS DRIVER PARAMETERS The mass driver launch vehicle consists of four, long parallel mass driver tubes in a square configuration. Four tubes are required to eliminate any net force or torque on the system. If there were only a single tube firing nuclear waste forward, the reaction force backward would result in a rapid orbit decay. Therefore, a "dummy" reaction mass is launched backward to compensate. Only two launch tubes would create a couple which would rotate the structure. Hence, two more tubes are added to give zero moment to the system. The entire vehicle is then kept constantly parallel to its orbital velocity about the earth. Each mass driver tube is 6.4 km long and. 156 meters in diameter. The accelerating section has a length of 4. 13 km. The length of the decelerating section is 2. 19 km. Inside these tubes are circular aluminum drive windings spaced every 2. 89 cm. The buckets which carry the payloads are right circular cylinders, with the forward end open to allow insertion and removal of the payloads. A superconducting coil is wrapped around each end of the bucket. Each coil carries a current of 6. 08 x 104 amps. The total empty bucket mass, including coils, is 1. 123 kg. With a payload of one kilogram, the loaded bucket mass is 2. 123 kg. The payload, also cylindrical, has a length of 14. 43 cm and a diameter of 4. 68 cm. Payload density is assumed 4 x 103 kg/m. To dispose of the 200, 000 kg/year of nuclear waste projected for the year 2000, 40 kg must be launched per orbit. Two kilograms can be launched at once through the two forward tubes, so this works out to 20 launches per orbit. 20 launches in the 192 second launch window gives 9. 63 seconds between launches. The time required to accelerate the loaded bucket to the desired 9000 m/sec is.92 seconds at an acceleration of 1000 gravities or 9800 m/s2 The payload will spend. 24 seconds in the launch tube after release from the bucket. The empty bucket will decelerate to zero velocity at 1890 gravities in.49 seconds. 4.4 POWER SUPPLY A formidable design problem occurs due to orbital mechanical considerations because launches must be made on the night side of the orbit. Since solar power is employed, this means that when power is most needed, it is least available. It becomes clear that some sort of energy collection and storage system is required.

4. 4. 1 Energy Collection The vehicle will spend 61% of its orbit or 56 minutes of each orbit, in sunlight. The amount of energy that must be collected is the sum of the payload kinetic energy plus housekeeping requirements while in the earths shadow. The payload kinetic energy lost per orbit is given by the formula E = V2 (4. 1) To launch an average of 40 kg of nuclear waste per orbit, it may prove necessary to launch 80 kg on some orbits to make up for down-time. Thus the m in Equation (4. 1) is 160 kg (80 kg of nuclear waste plus 80 kg of dummy reaction mass). The V is the AV of 9000 m/s giving E= 6.5 x 109 Joules Assuming housekeeping requirements for cryogenics and life support of 106 watts x 2190 sec (time spent in the dark) gives an additional 2. 2 x 109 Joules or a total energy storage requirement of 8.7 x 109 Joules. To collect this much energy in 56 minutes requires a collection capability of 8.7 x 109 Joules/ (56 min x 60 sec/min) = 2. 6 x 10 watts. Adding housekeeping power of 106 watts gives a total power requirement of 3. 6 x 106 watts. If solar panels are evenly distributed along the length of the structure, there will be two sections of the orbit where the structure will be pointing at the sun, and will not be able to collect energy efficiently due to panels shadowing each other. Therefore, the amount of usable sunlight timte was cut to 40 minutes. This yields a power collection requirement of 4 x 10 watts. Assuming a solar cell efficiency of 17% and a solar constant of 1400 w/m2 gives a total panel area of 1.7 x 104 mz. If at any given time 25% of the panels are shadowed by structure, 2. 3 x 104 m2 are required for the same power capability. There are four panels placed at each of the 628 ring sections, or 2512 panels total, each with an area of 9. 16 m2 or square panels 3. 03 meters on a side. For maximum efficiency the panels should be rotatable to track the sun. This should not present any problems with slip rings, because the panels will never have to make a full revolution. The panels would rotate in the sunlight, transferring power through flexible cables, and could be "unwound" in the dark in preparation for the next orbit. The back sides of the panels, always facing away from the sun, would serve as waste heat radiators. 30

4.4. 2 Energy Storage Storage batteries were chosen to store the collected energy. Although this is not the most economical solution, it is the simplest. The options of homo-polar flywheels, pulsed magneto-hydrodynamics and thermal storage were briefly explored, but the use of such storage systems would require extensive research and development. Certain present state-of-the-art batteries combine the high power densities, high energy densities, and long cycle lives r equired. Lithium-aluminum/iron sulfide batteries were determined to be the most suitable at this time. The 1atteries exhibit a power density of 145 w/kg and an energy density of 5.4 x 10 Joules/kg. Cycle life is on the order of 1000 cycles. The power requirement at any time during the launch phase is housekeeping plus each single launch requirement. The single launch requirement power is mV2 P = 2 At where V = 9000 m/s, m = total loaded bucket mass and At = time between launches = 9. 63 seconds. p = (4) 2. 123 kg (9000 ms). = 3 6 x 107 watts 2 (9.63 sec) with housekeeping the total power is 3.7 x 107 watts or a total battery mass of 3.7 x 107 w/ 145 w/kg = 2. 55 x 105 kg. Note that this much battery mass will store 1.37 x 1011 Joules or 16 times the energy storage requirement. The fact that the batteries will never even approach full discharge should greatly enhance battery life. 4.5 ELEC TRICAL MASSES Except where noted all the equations are taken from the results of the 1977 NASA Ames summer study on space industrialization. v = exit velocity = 9000 m/s mp= specific power plant mass =. 005 kg/watt m = payload mass = 1 kg a = acceleration = 9800 m/s2 fr = launch rate = 1/9. 63 sec-1 but taken conservatively to be 1 hz for the purposes of these calculations 3/2 1/2 1/2 Winding mass = Mw =.122 v mp fr x 4 = 29460 kg 31

Solar panel mass = mp x 4 x 106 watts = 2 x 104 kg Radiator mass = Solar panel mass = 2 x 10 kg Feeder mass = MF = 7.19 x 104 v 5/3a 1/3m /9r 1/3x 4 = 2.4x 105 kg Capacitor mass = Feeder mass = 2.4 x 105 kg Kinetic Power Mass =.0025 fr m V2 x 4 8.1 x 105 kg SCRmass is 1.66x 10-10v3 a m1/3 x4 =4.75 x 10 kg but this equation is based on the weight specifications off-the-shelf 1977 silicon controlled rectifiers. Since that time the specific mass of SCR's has been reduced by a factor of two. Further reduction can be expected in the next decade as solid state devices are developed specifically for use in large-scale space applications. The reason that such reduction has not occurred already can be attributed primarily to a lack of research in the appropriate areas. It was assumed that these devices can be reduced in mass by an order of magnitude by the year 1990. This represents a totaLireduction' of a factor of 20 from the optimized equation yielding an-SCR mass of 2.4 x 105 kg. By summing all of the above masses the total electrical mass is 1.6 x 106 kg. 4. 6 REFERENCES 1. O'Neill, Gerard K., "The Low (Profile) Road to Space Manufacturing," Princeton University, Astronautics and Aeronautics, March 1978, Vol. 16, No. 3. 2. Billtigham, Gilbreath and O'Leary, Space Resources and Space Settlement9 NASA Publication SP-428, August 1979 3. Graham, Robert W., Secondary= Batteries: Recent Advances, Noyes Data CGo~1ot- a —2P3'Ia~rk Ridge, N. J. - 1978. - - 4. NTIS A03/MF A01,'Development of Lithium/Metal SuIfide Batteries'at - Argonne National Laboratory: Summary Report, 1976", March 1977. 32

DRIVE COILS 00, 00 00 0 0 00 0 0 0 BUCKET'COILS * REACDTION MA - AXIS 0.18D P.LL Q1o. PULL Figure 4. 1 Longitudinal Cross-Section of O O O PHASE Axial Drive Coils and Loaded Bucket 1 2I 2 tPHASE 2 13UCK, ET VELOCITY SECOND SNAPSHOT, 45 LATER IN PHASE: CURRENTS 0.707 OF PEAK. Diagrams reprinted from Ref. No.2. O _ 2 THIRD SNAPSHOT. ANOTHER 45~ LATER: O O O O O PHASE 1 2 1 2 1 2 Figure 4. 2 Current in Drive Coils GUIOEWAY 3 _ I',l " SQACEOJJ - E uKE IT SIDE 1 ISPACED NONiSPACED IMAGE CURRENT IMAGE CURRENT Figure 4.3 Bucket and Guideway Geometry 33

STRUC TURAL DESIGN 5. 1 INTROD UCTION The structural design is motivated by three primary considerations: First, it is necessary to insure that the mass driver remains straight while the payloads are being launched. Second, it is important to design the mass driver to be able to withstand the stresses induced by the rapidly accelerating payloads. Third, the containment package for transporting waste material from earth to the orbiting mass driver must meet specified standards for performance while minimizing overall package weight. Due to the extreme slenderness of the mass driver structure, the difficulty of insuring structural integrity becomes great by comparison with'conventional' spacecraft. It is, of vital importance to maintain the'straightness' of the launching tubes so that the payloads will not graze the tubes' inner walls. This problem is not trivial because the structure's extreme slenderness causes it to behave.somewhat like a'string'; that is, it has negligible flexural rigidity on a global scale. Thus any disturbing influences such as the earth's gravity, local perturbations in the gravitational field, thermal irregularities, etc. will have a considerable influence on the mass driver, and will manifest themselves in their tendency to cause the mass driver to deviate from the desired'straight' configuration. In fact, the mass driver is stable in a curved configuration while in earth orbit (Reference 4). The affects of all such disturbing influences will be counteracted by a network of tension cables attached to the mass driver. Materials chosen for the mass driver must meet the requirements of high strength and low weight, and must also retain favorable characteristics in the harsh environment of earth orbit. The package for transporting the nuclear waste material from earth to the orbiting mass driver was designed to make the most efficient use of materials possible. The mission objectives dictated the design of a lightweight system which can withstand the most severe in-flight loadings. No design work was done on a re-entry heat shield or other fail-safe systems. However, approximately 15, 000 lbs of shuttle payload capacity has been allocated for the accommodation of such systems. The total structural mass of the mass driver was found to be 2. 5Z7 x 106 kg (5.559 x 10b lbm). 34

ti~ lr~ ~ ~Tension Cable 10.08 m.8256 / / 1. 1816 m (Length = a 1.2720 m Thickness =.0025 M) Figure 5. 1 Mass Driver Segment Geometry (excluding solar cell arrays) 35

Outer Ring Tension Cable Support Rods,. 256"m/ _ ~~ ~~ INBracing Struts Inner Cylinder (Contains Storage Batteries!.0Sin.5608 -|4. 2748 m AMass Driver Tubes t Figure 5. AdMass Driver Geometry, Cros..Sectional View 36

5. 2 MASS DRIVER TUBE SIZING It so happens that the analysis of the mass driver tubes presents considerable difficulty for the following reasons: The nuclear waste payload is accelerating from rest in the mass driver tubes. The interaction of the magnetic fields associated with the payload bucket coils and the mass driver's drive coils causes stress waves to be propagated from each drive coil as the bucket passes that drive coil. These stress waves are propagated through the tube in two directions from each drive coil. The stress waves in one direction are tensile while those in the opposite direction are compressive (Figure 5. 3). When the velocity of the bucket is substantially subsonic (i. e., less than the speed of sound in aluminum, which is approximately 5000 m/sec or 16, 390 ft/sec), the waves propagated as a result of the passage of the bucket will arrive at the. following drive coil considerably in advance of the traveling bucket. Thus, the instantaneous force between two drive coils will give the transient stress which the tube must tolerate. This force is found to have a maximum tensile value of 800 newtons (180 lbf) and a maximum compressive value of 500 N 9112. 5 lbf) (Reference 4). These forces are found by numerically solving a series of non-linear simultaneous equations involving drive coil current, bucket coil current, and'gradients of mutual inductance' (Reference 4). However, the complete description of the stresses in the mass driver tubes requires a more rigorous analysis. When the accelerating bucket attains a velocity which is supersonic, the magnetic field interaction will cause stress waves to be propagated (again, at the speed of sound) which travel at a slower rate than the bucket. Thus, the bucket will reach the next drive coil in advance of the stress wave generated by the previous drive coil. If our bucket were traveling at a constant velocity, the stress waves generated by each coil would be identical in amplitude and waveform. The magnitude of the transient stress which the tubes must endure would be given by the superposition of these waveforms where they undergo constructive interference. This is not a difficult problem to analyze but the result has little relevance because our payload is accelerating. Due to this acceleration, stress waveforms will be generated which have successively shorter wavelengths because the bucket is in the vicinity of a drive coil for successively shorter periods of time. The constructive and destructive interference patterns of these waves are very difficult to ascertain. Thus, the ultimate transient stress which the tubes must tolerate is very difficult to arrive at. This analysis is beyond the present capabilities of the authors and must await further re sea r ch. 37

To further compound the problem, the effects of shock stress waves produced by the accelerating bucket must also be considered. The fact that the wave source (bucket) is accelerating complicates this problem considerably This analysis must also await further research. Thus, for design purposes, it was decided to use the maximum tensile and compressive forces which are encountered in the subsonic region outlined previously. This analysis includes a very considerable safety margin which should account for the aforementioned effects of the accelerating payload. A major concern in this project is to insure that no stresses occur in the mass driver as a result of attitude control maneuvers. It was decided that a linear distribution of thrust, which passes through zero at the mass driver's center of mass, provided the desired effect. Section II of the appendix includes a verification of this fact. It is also important to prevent dynamic resonance of the mass driver during such maneuvers. Accordingly, the flexural vibrations of the mass driver which would arise from attitude control thrusting are discussed in Section III of the appendix. 5. 3 SHUTTLE BAY WASTE CONTAINER SIZING 5. 3. 1 Design Criteria The nuclear waste containment package was designed using the following criteria: 1. Radiation shielding sufficient to insure that a radiation level of one rem/hour at a distance of one meter (3. 28 ft) from the package is not exceededed. 2. Package integrity must be maintained during launch. 3. The package must be thermally and chemically stable so that it may resist the heat and corrosive agents produced by the nuclear waste material. 4. The package weight must be minimized to permit a maximum payload (nuclear waste) carrying capacity. 5. 3. 2 Summary of Container Properties I. Small, cylindrical waste containers: 38

Dimensions: r (-outer radius) = 2. 34 cm (. 921 in) 1 (-length) = 14.43 cm (5. 68 in) m(-mass) = 1 kg (2.2 Ibm) These dimensions were determined from an optimization formula which i's includ.d. in- the Mass Driver report. The containers are made of stainless steel for thermal and chemical stability. II. Large cannister for containment of nuclear packages: A. Materials - Tungsten layer - Lithium Hydride layer - Stainless steel load-bearing outer shell (cylindrical) 1. Tungsten layer (closest to nuclear waste containers) is 5 cm in thickness (1. 97 in). Justification for this specification is given in the materials specification Section 5:. 5. Z.' Lithium Hydride layer (surrounding tungsten layer) is 12 cm (4. 72 in) thick. Again, see Section 5. 5. 3. Stainless steel load-bearing layer (surrounding Lithium Hydride Layer) is. 5 cm (. 197 in) thick (see Section 9 of the appendix for an explanation of the specifications). B. Shape Right circular cylinder with length to diameter ratio equal to one for efficient packaging and high strength. C. Procedure for Optimization of Package Dimensions 1. The small cylindrical nuclear waste containers have the dimensions given in Part I of this section. Also, the density of the waste material is know to be 4 gms/cm3. In addition, the shielding and load-bearing materials in the containment cannister are as given in "A", above. Material densities are: a) steel (8. 0 gms/cm3 b) Lithium Hydride (. 77 59 kms /cm3 ) c) Tungsten (19. 3 gms/cm ). 2. Procedure (as shown in Figure 5.4) 39

Accelerating Bucket (Accelerating to the Right) Compressive Wave K End View of Drive Coil Side View of a Longitudinal Cut of a Mass Driver Tube Figure 5. 3 Schematic Representation of Mass Driver - Bucket Interaction. Estimate Find Ro Solve Calculat Pkg/W.t Find for forl #Cans Real.... 0Optimal Pkg/Wt Compare Real &Est. Pkg/Wt Figure 5.4 Method for Package Size Optimization 40

a) Estimate a ratio of package weight (loaded) to contents weight. b) Using the maximum total weight limit, find the weight of the nuclear material for the estimated ratio. Each small container has a known mass (1 kg), so solve for the number of small containers in each large cannister. c) Assuming 100% packaging efficiency, find the inside radius of the cannister to contain the computed amount of nuclear material. (This radius corresponds to the radius required to contain'loose' (unpackaged) nuclear material. d) Assume a packing efficiency for the small containers in the large cannister. Find a new cannister radius corresponding to the decreased (previously 100%) efficiency, and determine the number of cans possible for the new radius. Since the total number of small containers is known, and the number of cans per layer (shelf) has been determined (see Section 8 of the appendix), one can solve for the number of layers needed to contain all the cans. Again, the cannister has a ratio of length to diameter equal to one, so the length of the cannister for the radius computed (a function of packing efficiency) can be determined. This package length can then be compared to the internal container length (:umber of layers times the length of each small container). One may now calculate the thickness of each shelf (see Section 8 of the appendix). Reiterate, using a smaller packing efficiency (=-) if the shelf thickness is less than that required for structural purposes (again, see Section 8). e) Calculate the true weight of the package using the radius (a function of A) needed for the best efficiency with acceptable shelf thickness. f) Compute'real' ratio of package weight to contents weight for the real weight, and the number of containers for the estimated ratio of package weight to total weight. This will be greater than or equal to the actual ratio if it is less than the estimated value because the number of cans will be greater. g) Reiterate, using an estimated value of the ratio of package weight to contents weight equal to the'real' value found from the previous iteration. The error will decrease to zero using this method (when the estimated and'real' ratios are equal). The result is the optimum ratio of package weight to contents weight. h) A numerical example is given in Section 8 of the appendix. III. Conclusion The small cylindrical waste containers are contained in the large cylindrical cannister. A. Small containers (see Figure 5.5) 1 ) Dimensions: 41

14.43 cm Figure 5.5 Small Nuclear Container 42

r = 2.34 cm 1 14.43 cmrn t (thickness) = 1. 66 x 10 cm, from Section 8 of the appendix. 2) Mass a) nuclear material contained:,9997 kg (2. 199 ibm) b) stainless steel container: 3. 27 x 10-4 kg (7. 19 x 10-4 lbm) c) total mass of each package: 1 kg (2. 2 ibm). B. Large cannister (see Figure 5. 6) 1) Dimensions: a) outer radius = 95.83 cm (37.73 in) b) inner radius = 78. 33 cm (31. 04 in) c) outer length = 191. 66 cm (75.46 in) d) thickness = 17.5 cm 1) tungsten layer: 5 cm 2) Lithium Hydride layer: 12 cm 3) stainless steel shell:.5 cm 2) Internal shelving: a) number of shelves = 7 b) thickness of each shelf =. 507 cm c) mass of each shelf = 77.5 kg d) maximum shelf deflection during launch = 3. 18 cm b) & d) were determined in Section 8 of the appendix. 3) Packaging: a) packing efficiency (by shelf area) = 78.7% b) number of containers per shelf = 882 c) number of concentric rings of containers per shelf = 17. 4) Mass a) ratio of package weight to contents weight = 1. 90 b) mass of nuclear material = 6, 174 kg (13, 583 lbm) c) mass of package = 11,730 kg (25,807 lbm) d) total mass = 17,904 kg (39,389. 8 Ibm) 5.4 SIZING OF SUPPORT STRUTS FOR MASS DRIVER TUBES 5. 4. 1 Design Criteria The support struts for the mass driver tubes were designed using the following criteria: 1. The struts should withstand a conservative model of the applied forces, with a safety factor equal to 1. Z. 43

Shelf - Layer of Cans - Steel Lithium Hydride Tong sten [ Figure 5. 6 Large Cannister for Shuttle Transport 44

2. The mass of the struts should be minimized. 3. The struts must not interfer with the mass driver's inner structure. The applied force may be conservatively modelled as the mass of the payload inside the mass driver multiplied by its acceleration. The largest applied force on a strut will occur when the payloads are traveling (in adjacent tubes) in opposite directions and are located at the ends of a single strut. One might suppose that the entire mass driver would buckle when the applied forces are directed towards one another and are applied at opposite ends of the mass driver. However, due to the fact that the payloads are traveling at supersonic velocities for the majority of the launch time, the axial applied force will not be'felt' by the entire mass driver instantaneously. Buckling is a quasi-static phenomenon and will not occur unless the applied force is'felt' globally by the entire structure. 5. 4. 2 Conclusion (see Section 10 of the appendix for calculations) The support struts are welded to the mass driver tubes at an angle of 450 to the tubes longitudinal axis (see Figure 5.7). Dimension: a) length of strut =.4435 meters (17.48 in) b) height, width = 1.854 x 10-2 m (. 73 in) c) cross-section area = 3.437 x 10-4 m2 (.533 inZ) d) mass of each strut = 4. 116 x 10-1 kg (9. 055 x 10-1 lbm) e) number of struts = 8.063 x 104 f) total strut mass = 3. 318 x 104 kg (7. 3 x 104 lbm).. 313 6m Support Beam 450 Mass Driver Tube Figure 5.7 Side View of Mass Driver Support Bracing 45

5. 5 LARGE SPACE STRUCTURE CONSTRUCTION METHODS The'beam-builder' is a realistic and efficient method for large scale space construction. The space shuttle serves as an ideal launch vehicle and construction base for the unit. Following the boost to orbit, the unit is deployed from the stowed configuration in the shuttle bay. Beam builders are now capable of fabricating an interconnected skeleton of four triangular beams 200 meters long. The unit can turn out a triangularly shaped cap structure of thin aluminum or other desirable material at a rate of 5 ft/min. This is the equivalent of fabricating a one mile long structure in a period of 24 hours. Longitudinal members and cross-beams are made up of elements referre to as caps. The cross-beams serve to interconnect the four longitudinal members, and are otherwise identical to the longitudinal structure. Pre-formec cross-members are located at intervals along the caps and provide rigidity. Continuous cord is installed diagonally across opposite corners of each cap section. The two principal parts of the unit are the beam-builder and the assembly jig. The beam building process occurs in the following sequence: Pre-consolidated flat strip material is rolled out of a storage cannister by a drive mechanism. Next, the material is heated, fabricated into the desired shape, and rapidly cooled. As the cyclic process continues, cross-members are discharged from their storage clips and are ultrasonically spot welded to the caps. At the same time, constant-force tension mechanisms are installing the diagonal cord, which is being unwound from the storage spool. The assembly jig serves to retain and transport the completed structure across the face of the unit so that the following section can be fabricated. Once the longitudinal structure has been constructed, caps are fabricated into nine (9) cross beams which connect the four (4) longitudinal beams. The completed assembly takes on the appearance of a ladder. The process just described is best utilized in the manufacturing of long, continuous structures. For instance, the process would be well-suited to the construction of solar power satellites. The beam-builder concept, with certain modifications, can be employed in two ways for the construction of the mass driver. First, the diagonal bracing struts (discussed in the previous section) could be fabricated using this system. Second, thousands of rods are necessary in the tension cable system mentioned previously. Beam builder concepts provide a means of extruding these structures in space. Thus, the employment of a beam-builder(s) would accelerate the construction of the mass driver and its related structure. 46

5. 6 SUSPENSION CABLE SYSTEM The center of the mass driver is orbiting the earth at an altitude of 400 km (216 nautical miles). Assuming that the mass driver is in a straight configuration, the radius of the orbit will increase as the mass driver is traversed from the midpoint to the ends. In other words, individual elements of the mass driver travel at different orbital altitudes. Each elemental part tends to seek an orbit at a certain altitude with respect to the center of the earth. The result is a moment distribution along the mass driver structure which tends to displace the ends of the mass driver towards the center of the earth (see Section 11 of the appendix). In order to counteract this moment, a system of supporting rods and tension cables has been developed (see Figure 5. 1). The principle behind this system is as follows: when the mass driver begins to bend, forces would be applied to the cables in order to restore the mass driver to the aligned configuration. The first consideration was to determine the spacing between individual supporting rods. In an effort to achieve maximum effectiveness and maximum weight, it was decided that the supporting rods would be installed on alternating outer rings of the mass driver (see Section 4 of the appendix for details). Since the moment on the mass driver due to gravity is continuous with respect to the longitudinal axis (see Section 1 1 of the appendix), it is desirable to counteract this moment by a continuous applied moment. Spacing the supporting rods on alternating rings gives a good approximation. To minimize thermal stresses, it is desirable to rotate the mass driver about its longitudinal axis. In this event, it would be necessary to install supporting rods symmetrically around the cross-section. Accordingly, four supporting rods are installed at equidistant points on the outer rings to compensate for the gravitational bending moment regardless of the mass driver's orientation. The distance between supporting rods is 20. 16 m (66. 14 ft). The angle between the cables and the mass driver's longitudinal axis is 450. Thus, the length of each rod is 10. 08 meters (the distance between adjacent outer rings). Deciding on the rod's cross-sectional shape was the next consideration. It was determined that a square section was superior to a circular section because the former has a greater moment of inertia for a given cross-sectional area. The'I'-section proved to be yet more attractive due to a 40% savings in mass for a given strength. 47

Aluminum (7075-T6) was chosen for use in I-beam construction due to its high strength and low density. The material chosen for the cable is stainless steel (347) due to its high yield strength. Due to cyclic loadings, the tension cables will experience metal fatigue over a period of time. As a result, cables will require periodic replacement. A series of equations were used to relate cable and beam crosssectional areas to cable tension (see Section 7 of the Appendix). The cables and beams were designed to sustain a load of 4448 N (1000 lbf), which, it is believed, will be sufficient to generate a bending moment to counteract that which is produced by gravity. Conclusions: a) The rods will have an "I"-shaped cross-section with an area of 3. 7 x 10-3m2. b) Mass of each rod = 106. 01 kg c) The cables have a cross-sectional area of 1.84 x 10'5 m an( each has a mass of 2. 09 kg. The complete system will consist of 12. 62 km of I-beam support rods having a total mass of 132,725 kg. The cables will have a total length of 35.7 km and a total mass of 5. 233 kg. The total system therefore has a mass of 137,958 kg. Rotating the mass driver requires that the tensions in the cables be varied continually so that the gravitational bending moment will be counteracted. This gives rise to the metal fatigue discussed previously. This continuous adjustment necessitates the use of a computer. The cables are threaded through teflon-coated holes at the tops of the support rods to minimize friction. Tension in the cables is controlled by electromechanical actuators (linked to the computer by a feedback control system) which are installed on alternate outer rings. Laser-beam sights will be used as an auxiliary system for detecting deviations in the mass driver's alignment. 5. 7 MATERIALS 5. 7. 1 Space Environment Considerations The mass driver will experience varying temperatures once the 400 km altitude is attained. These temperatures are determined by direct solar radiation, reflected solar radiation (albedo), and planetary radiation (Figure 5.8). 48

Poatr'-orA 4. SW4oPoro Vo /// sUm R^*-tIjO"C O"X ta/ t4Ab DAtYVS Figure 5. 8 Radiation Zones Zone 1. solar, Albedo Planetary Zone 2. Solar, Planetary Zone. Planetary

The solar radiation received depends upon the distance from the sun. The greater the distance, the smaller the radiation flux. This value is assumed approximately constant since the earth's orbit varies by only 3. 4% during the year. The reflected radiation, or albedo, is dependent upon the fraction of solar radiation which is reflected and backscattered from the clouds, atmosphere, earth's surface, and the moon. Since albedo varies continually according to the position of the moon and atmospheric conditions, an average albedo of.36 was used in the calculations (see Section 8 of the Appendix). Planetary radiation depends upon the mass driver's altitude. The high the orbit, the lower the heat transfer to the mass driver caused by planetary radiation. If the orbital altitude remains nearly constant, the planetary radiation may be considered to be approximately constant also. The combination of these three types of radiation determines the surface temperature of the mass driver. These surface temperatures were calculated for various points in the mass driver's orbit. Stainless steel and aluminum were chosen for the construction of the mass driver because of their excellent strength, weight, and thermal characteristics. 5. 7. 2 Waste Containment Materials Since transportation of the nuclear waste from processing plants to orbit consumes a significant amount of time, waste containment packages mus1 resist corrosion to avoid radioactive contamination. The container must also have good strength and heat transfer properties. Accordingly, stainless steel 347 was selected as the material for the small cylindrical containers. It may be necessary to incorporate an active cooling system to ensure package integrity during launch, though stainless steel's extremely high milting temperature is an advantage here. 5. 7. 3 Radiation Shielding The thickness of the tungsten layer (which shields gamma radiation) and lithium hydride (neutron radiation) was determined from the graph in Figure 5. 10 (which may be found in Reference 2). Accordingly, thicknesses of 12 cm and 5 cm for lithium hydride and tungsten respectively were chosen to ensure that a radiation level of 1 rem/hour at one meter from the package is not exceeded (see Figure 5.9). 50

Figure 5. 9_ Nuclear Waste Containment Package Stainless steel.5 cm (. 2") -Z /.Tungstun.5 cm (2") = ~ Lithium Hydride 12 cm (4. 73 ") 12 10 | \^ \ Fission products remaining in actinide waste, percent E 8 -'~ ~ 1\& Tungsten c 6- Lithium hydride L. ~~,05 ae rue nt~ meter from outer surface, temlhr Figure 5. 10 Thic kness of Tungstun and Lithium Hydride Shielding Material Reqtired to Reduce Radiation Dose Rate 1 Meter from Outer Surface. 51

5.8 STRUCTURAL EFFECTS OF FIRING FAILURES Launch failures were investigated to determine the magnitudes of the resulting torques on the mass driver. There are two fundamental cases to consider: 1. one- or three-tube failure 2. adjacent-tube failure Case 1: When there is a one or three tube failure, a torque is developed about the y' or z' axes (Figure 5. 12). Case 2: When adjacent tubes fail, torques are developed about the y1 and z' axes (Figure 5. 12). 52

3 Yt. a,~ Y 45~ + k Tube3 T ube 2 5696- - m Figure 5. 11 Mass Driver Cross Section t — Force in * Force out -+ vl Mass Driver Cross Section 53

Failure Tube I Failure Tube 2 Failure Tube 3 Failure Tube 4 in'~'K~ 3"5, 45>, Z 4 Failure Tubes 1 and 2 Failure Tubes 2 and 3 Failure Tubes I and 4 Failure Tubes 4 and 3 Figure 5. 12 Torques Acting on Mass Driver Due to Launch Failure.

6 ATTITUDE CONTROL 6. 1 INTROD UC TION The primary objective of the attitude control system (ACS) is to maintain a suitable orientation in space for operation of the overall system. it is essential to closely monitor and actively control the mass driver due to instability in pitch due to the gravity gradient. It was figured that the mass driver would realign itself to vertical attitude from 0. 10 of the horizontal in 6 hrs. The proposed attitude control system incorporates a series of thrusters, evenly spaced along the length of the mass-driver. Attitude sensing is accomplished by a system of horizon sensors and rate gyros. Control is accomplished by a high-throughput digital control system. Pitch control laws were developed for maintaining longitudinal stability in the presence of the gravity gradient. Guidance laws were also developed for rotation of the mass driver from an initial vertical attitude (assumed by the mass-driver during construction operations) to the horizontal attitude for firing without exceeding structural limits. 6.2 DEFINITION OF AXES It is useful to define three sets of reference coordinates to describe the motion of the mass -driver. One coordinate system is an earth-centered system used to describe the orbital motion of the mass -driver in formulating the reboost problem. Another system is a right-handed stability axis system with the +x-direction corresponding to the direction of motion in the circular orbit, and the + z -direction toward the center of the earth. This stability axis system was used to develop guidance and control laws. A third system is a right-handed body-fixed system with the x-axis as the long axis of the mass driver. The pitch angle is defined as the angle between the stability x-axis and the body-fixed x-axis. 6. 3 REQUIREMENTS The ACS/guidance system requirements in pitch were based on the following considerations 1. Must be highly accurate, 2. Must take into account instability in pitch due to gravity gradient, 55

center of mass reference direction Earth Centered Axis System Earth Stability and Body-fixed Axis Systems Figure 6.1 Axis Systems 56

3. Must dampen to a tolerably small pitch displacement in a minimum amount of time, 4. Must not exceed structural limits, 5. Must possess a high degree of system reliability for maintaining steady operation and minimum of repair, 6. Must be capable of remaining on station, in the desired orbit. The following specifications were developed in accordance with the above guidelines: 1. Accuracy of alignment: =.l (pitch) 0=.1~ (yaw) 2. Dampens from a + 100 perturbation in 0 to within. 1~ within 250 seconds. 3. Structural limits: iX ='. 6680/sec max 4. Meantime between failures (MTBF) per thruster assumed to be 10 years in accordance with present reliability capability. 6.4 REBOOST PROBLEM FORMULATION The Project NEWDUMP vehicle is subject to orbit decay due primarily to aerodynamic drag. This drag results in a change of altitude for orbit given by: Ah = -2 go p r where CD = drag coefficient = 2 for A = frontal area = n/m2 w = vehicle weight = - 2 x 106 kg p = density = 4.67 x 10-15 kg/m3 r = orbit radius = 677 5 km The result is an altitude loss on the order of.07 meters per day, or a 1 km drop in 37 years, approximately. 57

The most convenient way to counteract this force is to occasionally re-boost the satellite by accelerating more reaction mass from the aftfacing mass-driver than waste payload from the foreward-facing mass-drivers, resulting in a net positive thrust. The AV produced in this manner is found from the mass driver group report. Even though the atmospheric density is a function of solar activity. The orbit decay problem is not especially critical. The orbit altitude can simply be monitored so that when it falls to a certain level a AV will be applied to raise the vehicle to a higher orbit. To avoid transferring the vehicle into an elliptical orbit, if part of the required AV is applied when the mass-drivers fire payload, then a similar AV must be applied 1800 past this point to re-circularize the orbit. As an example, if the orbit is allowed to decay 1 km a re-boost AV of. 6 m/sec will be required (Hohman transfer). This can be accomplished by accelerating an additional 40 kg of reaction mass from the aft-facing mass drivers every orbit for 7 orbits. 6. 5 PITCH DYNAMICS AND CONTROL SYSTEM 6. 5. 1 Assumptions Since the attitude displacement 9 was defined with respect to the local horizontal (Figure 6. 1) the frame of reference will be noninertial and must reflect the constant angular rate due to the motion in the circular orbit (Figure 6. 2). The mass driver will rotate with a steady-state pitch rate O', where Q = To orbital period (92 min) =. 065 /sec. (6. 1) For the attitude control design, this angular rate is assumed negligible. The ACS provides for maintenance of 9 = 0 along the flight path due to the use of horizon sensors, providing a direct measure of 9 locally. There are four kinds of forces acting on the satellite: magnetic, radiation, aerodynamic, and gravitational. Magnetic effect are assumed to be negligible over'long' time periods ( 1 min). Magnetic disturbances will arise due to the local, but powerful magnetic field generated by the mass-driver coils. Since these magnetic disturbances are of short duration ( -, 3 sec) they can be neglected as a biasing torque and treated stochastically. 58

Q = Steady State Pitch Rate I \ \ /' \ \ —7\ \ / Earth / / /~~~~~~~~ /u62tyt i Mi I~ ~ ~ ~ Figure 6. Z Steady-State Mass-Driver Motion.

Due to the small frontal area and high altitude (400 km) aerodynamic forces can be neglected relative to the gravity gradient moment. Solar radiation pressure on the solar panels can be neglected since the panels are distributed symmetrically with respect to the center of mass of the mass driver, giving a center of radiation pressure coincident with the center of mass (i. e. no moment arm). The fourth force, gravity gradient is modeled as a perturbing torque due to its large magnitude (19, 200, 000 nm at 450 pitch attitude). The mass driver is assumed sufficiently straight allowing the products of inertia to be considered negligible, with respect to the principal moments of inertia. This follows from the structures requirement that the mass drivez be maintained straight for acceptable bucket clearances during firing. This also allows the longitudinal mode to be uncoupled from the lateral and directional modes, resulting in a simple, rigid-body model. 6. 5. 2 Equation of Motion The rigid-body assumption allows the pitch dynamics to be modeled as in Equation 6. 2: LYe' = Mc +Mgg + Md. (6. 2 where iW = y-principal moment of inertia Mc = moment commanded by thruster firing (control moment) Mgg = gravity gradient moment ~Md = disturbing torques. The gravity gradient moment, assuming a high structural fineness ratio and constant longitudinal mass distribution is: M =8 m (1)2 sin 20 = sinin 2z. (6. 3 gg 8 r r c c where -= _ gravitational constant for earth rc orbital radius mn mass of mass-driver I -mass driver length. Equation (6. 2) becomes. Iyy = + k sin 2 + Md (6.4) 60

6. 5.3 Maximum Required Control Moment The control moment must be large enough so that the maximum gravity gradient moment can be overcome. This requirement follows from the need to attain a horizontal attitude when initially aligned vertically. The max moment will occur at e = + 450 and is found to be: Mc = k = 19, 200, 000 N. M. (6. 5) 6. 5. 4 Perturbation Equations of Motion Lower case of 0 was used in the above since the trim value of pitch attitude is 00. Since a is taken to be sufficiently small (I 1 I 0O), the sine term is approximately proportional to the argument, yielding the equation: Iy 0 - Zk0 = Mcs + Mcmd = Mc (6. 6) where Mcs = contribution to moment due to control system Mcmd = contribution to control moment due to attitude commard. The equation may be written in state-matrix form as (letting q 0): 2k 1 1 I yy Cyy tyy yy 0=q This allows the dynamics to be stated in the following state form: x =Ax + Bu + Bicmd + Cw (6.8) where ucmd M d W = Md J 61

Iv can easily be ascertained that the dynamic system (6.7) is completely controllable via the control moment Mcs. 6. 5. 5 Natural Dynamic Characteristics To obtain the roots of the natural motion, the characteristic equation of the perturbation equation must be solved. This involves finding the eigenvalues for the matrix 0 a2] A = (6.10 This gives the-characteristic equation, s2 _ az = 0 (6.11 with natural roots s=+a This represents an exponential growth of time constant To -? = 2 — (6. 12Z For an orbital period of 92 min, this gives a time constant (time to increase amplitude by a factor of e) of 8. 45 min. From the time constant, it can be estimated that from a. -10 misalignment from the horizontal, it will take approximately 2 hr to achieve vertical attitude orientation. 6. 5. 6 Control Law Synthesis An optimal control law was developed for attaining a damping to a minimal attitude perturbation in a minimal amount of time. The controller gains follow from the solution K of the algebraic matrix Riccati equation: 2 + KA +ATK- KB R1 BTK = 0 (6. 131 where K1 K2 K= Kz K3J and A, B are the state and control matrices defined previously. R is a fx control weighting matrix set equal to 1. Q is a diagonal weighting matrix penalizing large excursions in q2, 8. 62

Solution of the Riccati equation gives a control law minimizing the *cost* functional: co _T T J x 2x +u R1 dt (6. 14) 0 2 = 1 21 R=l 0 22 The controller gains are computed from the Riccati matrix K by: G=R BT K. (6. 15) G [g1 g2] where, gl apitch rate feedback to moment command (rate gyro) g2 = pitch attitude feedback to moment command (horizon sensors) (Figure 6. 3). Solution of the optimal regulator problem gives the following relations. K>-2+Zza2 2 K a2 2 b n V= 1 b a K1 b 1 -2 K1 g= bK1 g2 = -bK2 where w, C are the desired natural frequency and damping ratio, respectively, of the atmitude controlled mass driver. Critical damping (. = 1) is desired since it allows for faster damping compared with overdamped modes and allows no overshoot (maintaining small 2 at all times). 63

r —......I..- Mc ~++1, M! g 1d 9t~ ~ q k = 19,200, 000 N. M. g2 -4. 199 x7109 N. M/g 2 F = 2.23 x 10 kg. m2/radin Figure 6. 3 Control System Block Diagram

By specifying the time to damp from 0 = 100 to 0 =. 10 as initially O, wn can be found. This time was chosen to be 250 sec where M = F O (6.21) cmd cmd where F can be found by expanding the matrix A + BG: a2 + b g2 b (6. 22) F was computed to be 108. 0 nm/deg. This gives the following state/controller description of the system'] [b a +b g2 L 9 F L'Ii L 0 0 cmd This description is realized in Figure 6. 3. 6. 6 GUIDANCE 6. 6. 1 Introduction During construction the mass driver is oriented vertically with respect to the horizon. The stability of this orientation is maintained by the gravity gradient effect. The mass driver must be oriented to a horizontal attitude after construction is completed. The mass driver must be aligned without exceeding allowable pitch rates and accelerations specified by the structural limits. The maximum allowable pitch rate was given as.6680/sec. The maximum angular acceleration was harder to discern with the conservative figure of. 10/sec decided upon. In order to maneuver the mass driver within these constraints, feedback guidance laws were developed. Implementing guidance laws requires a separate guidance computer, operating in conjunction with the back-up attitude control processor. The guidance computer/back-up ACS is responsible for acquiring horizontal attitude and maintaining dynamic stability until the mass driver is within 10~ of horizontal attitude where the primary ACS horizon sensors acquire the horizon. Control is then transferred to the primary ACS, which trims the mass driver to horizontal attitude. 65

* I I max / -. I ii, I \ C Critically Damped Decay Iti t t2 t 0 i 2 I 8=-10 i - - Critically Damped Switch Control Decay [ /I From Guidance Backup ACS to Primary ACS i I Linear (constant 0) I#~~~~~~ / ~~Figure 6. 4 o = -90~~/. Parabolic Acceleratlion (consttari 6) 66

_ tcs _____ e'(/' (6camt TOAL to o 9qo~.5 0 t, 5 88.75'.5 0 5 t, I~~.s ~o~.5 0 107.5 I62.5 160.5 0 167.5 tL t2.1..001.- 01209.6 _..._.......Table 65 Table 6. 5

6. 6. 2 Feedback Guidance Laws for Initial Orientation Maneuver The guidance mode chosen was to implement a constant angular acceleration guidance until a pitch rate of. 50/sec was attained. The guidance computer then switches to a constant pitch rate guidance mode to limit the pitch rate to below the structural limit. When the attitude reaches the interval -10~< 0 < 100, attitude control is transferred from the guidance/ backup ACS to the primary ACS. Referring to Figure 624, the guidance is initially scheduled for a constant pitch acceleration of. 10/sec. At time tl when a pitch rate of. 50/sec is realized the guidance switches to a constant pitch rate control of. 50~/sec and maintained until the pitch attitude is 100 at t2 where control is transferred from the guidance/backup ACS system to the primary ACS. The mass driver is then critically damped to an attitude of. 1~, the resolution limit of the horizon sensors. The feedback guidance laws, corresponding to the appropriate time intervals are: [to., tl); constant 8: Mmd = - k sin 2e + IO where eo = 1~0/sec2 and [tl, t2); constant 8: Mcmd -k sin 2). From the feedback guidance laws, the vehicle states at the critical times to, t1, etc are given in Table 5. 6.7 ATTITUDE SENSING The attitude sensing system is a highly accurate system that incorporates two Horizon Edge Trackers (HET) and six rate gyros. The HET's generate pitch data in the range of pitch angles from e = + 100~. This is the range wherein the output remains linear. Each HET has three heads to have a three-edge tracking field of view. The HET's are mounted on the ends of the mass driver. Roll, pitch, and yaw rates and displacement data are generated from a system of six rate gyros mounted on the crew station at the center of the mass driver. The sensor specifications can be assumed to be as accurate or more accurate than those listed below. Horizon Edge Trackers Accuracy: with. 10 Full scale: + 100 Output: pulse amplitude modulated (PAM) Converter: pulse amplitude modulated (digital) Number: 2 sensors (3 head per sensor) 68

Rate Gyros Accuracy: within. 010/sec Full scale: 60/sec -1200~/sec Output: analog Converter: analog/digital Number: six 6. 8 FLIGHT COMPUTER 6. 8. 1 Processor Requirements Hardware architecture requirements are difficult to quantity, requiring knowledge of the number of sensors and control devices, stability margins of the flight control system, control processes to be implemented, and the complexity of the guidance and control laws. From these considerations, a set of specifications were developed: 1) The processor arrangement must allow for a high throughput in a minimum amount of time. This requirement follows from the need to control a large number of thrusters and from the large volume of data from the structural mode control (SMC) sensors. 2) The architecture must reflect the different control functions to be realized and the associated complexity of the models implmented in the software. This architecture must not affect substantially the high throughput and minimum time specification above. 6. 8. 2 Hardware Architecture The requirements above were realized in the diagram in Figure 6. 6. Data for attitude control is converted into digital form from the horizon sensors and the rate gyros. For the horizon sensors, since the output is in the form of a pulse-amplitude modulated (PAM) signal, PAM/digital converters are required. The output from the rate gyros is in analog form and requires appropriate A/D converters. Two computers are used for attitude control. First is the primary ACS processor, which utilizes horizon sensor and rate gyro information for state estimation. The ACS, from the control laws program residing in the read-only-memory (ROM) computer the required roll, yaw, and pitching moment commands. Due to the complexity of such computations, a random access ('scratchpad') memory (RAM) is used to store intermediate results of calculations. The RAM is also used to store input data before processing. 69

The backup ACS is used to provide stability during the initial rotational maneuver from vertical attitude to horizontal attitude, and is driven by the guidance processor. It also serves as the backup to the primary ACS during normal operation. Since the horizon sensors become ineffective at large pitch attitudes and since their linearity range in pitch is + 100, the backup ACS estimates e from the rate gyros. Associated RAM's and ROM's are implicit in Figure 6. 6 for the backup ACS, guidance, SMC and input/output processors. Since the rate gyros are skewed for high reliability, the ACS processors decode the measured angular rates into the appropriate roll, yaw and pitch components. Data busing is used to provide a pipeline for data from the sensors to the processors, from processor to processor, and to the output device drivers. Data busing is necessary due to the large number of sensors and actuators and from the need for high reliability. Since large numbers of thrusters need to be controlled and due to the need for reducing computational time delays, separate output processors are used to drive the roll, yaw and pitch thrusters. Individual thruster thrusts are gain-scheduled as shown in Figure 6. 8. The thrustor valve drivers are disabled for unused backup thrusters or for inoperational thrusters. This function may be performed by either a self-test monitoring processor or by the flight crew. The gain schedules are stored in the ROM's with thruster enable/disable commands stored in the associated RAM's. Since speed is desired, most output processor functions are hardwired. 6. 8. 3 Structural Mode Control Processor Since the mass driver is subject to thermal loads and has a low elasticity associated with a high slenderness ratio ( / d > 1000), active stabilization is used to maintain structural rigidity and to dampen structural vibration. The control laws may be formulated as a regulator problem, using deflections and slopes of segments along the mass-driver as state variables. Due to the complexity of the problem, including the large number of states and the dynamics of each segment, these control laws were not formulated and are treated as a key item for further development. Displacements are measured via accelerometers and slopes by rate integrating gyroscopes placed at equal lengths along the mass-driver. Due to the large number of sensors required, an input processor is necessary for computing the slopes and deflections from sensor data. The input processor receives structural sensor data and attitude data for computing the difference in deflection and slope perturbations from the desired rigid-body slopes and deflections. 70

Rate Integrating O - - - - SMC ~Gy-ros.........PInput r"Processor Output AccelerometerZ- Bus anics Cable SMC Input Data Bus ACS A Bus 4/ -- | Guidance Drivers ROM M Horizon Sensors Processor npu In!Output - - __ Rate Gyros Pr ocesso Figure 6. 6 ACS/SMC Hardware Architecture - Processor ACS Output ACS Input Data Bus Rate Gyros

Output 3q 2q 9 39 59 79Input 2 2 2 2 q =.1 - Horizon Sensor q =.060/sec - Rate Gyro A/D Converter - Quantizer Data Word Parity Bit Sign Bit ACP Computer Word Figure 6. 7 Attitude Control Processor (ACP) Word Length 72

i3 Kt m 3T Kt { T M Center of Mass Driver T _ Kt ZT 2 Kt 3 T 3 Kt Figure 6. 8 Pitch Thruster Scheduling + 0 Thruster Control 73

The structural mode control processor then computes the static commands which are transmitted to the SMC output processor and the dynamic commands, transmitted to the ACS output processors. To maintain alignment in the presence of thermal stresses, a network of cables, controlled by electromechanical actuators is used to maintain static alignment. For damping structural vibrations, the ACS thrusters are used since they allow greater control power and give a faster response. Structural static commands are converted into the appropriate electromechanical actuator commands by the SMC output processor. Structural dynamic commands are thrust commands which are added to the appropriate rigid-body thrust commands to permit rigid body maneuvers and structural damping to be initiated simultaneously. 6.9 THRUSTER SIZING 6. 9. 1 Design Approach Given the thruster layout shown in Figure 6. 1 1, the individual thrust supplied by each thruster is then obtained. Ideally, it is desirable to have a linear distribution of thrust along the length of the mass driver (Figure 6. 9) when rotating the mass driver. The linear distribution results in a zero shear force distribution along the massdriver. In practice, since there are a finite number of thrusters with finite thrust, the actual distribution can better be modeled with a linear distribution of impulse thrusts along the mass-driver (Figure 6. 10). 6. 9. 2 Thruster Placement Thruster placement, AX, was found from the following considerations. 1. Placement on the outer collars connecting the mass-driver tubes for good structural support. 2. Providing a sufficiently wide spacing between thruster quads in order to reduce the number of thrusters required for acceptable reliability. 3. Maintaining sufficiently close separation between thruster quads for prevention of structural mode excitation during attitude maneuvers. 74

From these considerations, a thruster separation of AX = 30. 24 m was chosen from the approach that AX should be minimized as much as reliability will permit. Thruster quads would actually be placed every 10. 08 m, giving triple modular redundancy to the attitude control system. Assuming a mean time between failures (MTBP) per individual thruster of 10 yrs, an MTBF for the entire system was computed to be 108 days. System reliability can be improved further by modular construction of the ACS thruster assemblies for case of replacement and active repair practices by the flight crew. The thruster arrangement per collar was developed with the purpose of surviving two failures in + pitch, - pitch, + yaw, etc and still being operative, yet maintaining a minimum of thrusters. The thruster arrangement is given in Figure 6. 11). 6. 9. 3 Thruster Sizing The thrusters are sized for having idential thrusts for translational maneuvers. Thus, since the end thrust is the maximum thrust, the thrust of the end thrusters at maximum pitching moment Mcmax, gives the required thrust of each thruster. There are two possibilities for sizing the thrust at maximum moment. First is the use of four thrusters at maximum gravity gradient moment (8 = + 450) for basing thrust calculations. Second is the use of the primary pitch ACS thruster at maximum 0 for the primary ACS (0 = + 100). The second criterion proved the more conservative, requiring a higher moment per thruster. The moment supplied by the thrust distribution p(x) is given by Mc(P)= f xp(x)dx where p(x) = P Evaluating the integral ( ) gives Mc to be Pi 2 Mc(P) =The thrust of the end thruster, Te is related to the moment Mc and the spacing between thruster, AX, by T 2 M(T) = 12 75

x P[ Figure 6. 9 Linear Loading Distribution Figure 6. 10 Impulse Loading Distribution 76

ol Thruster nozzles Figure 6. 11 Thruster Configuration at a Thruster Station 77

Since Mc must be great enough to counteract the gravity gradient moment at m = 100, the above equation can give a thrust requirement for T e Mc(T) = Mgg(Om) = k sin 2 m Te 12 k sin 2 0m. 12 m Substituting the appropriate values in the above, yields a thrust Te = 58. 3 n. The best type of RCM (Reaction Control Motor) with the thrust capability required by this application is the hydrazine monopropellant RCM. Although no motors of this type are presently available which can be throttle in the range (0-60 n) required by this particular application, it should be practical to assign motors with this capability as this type of motor is throttleable in other force ranges, and thrust is a function of inlet pressure. Thrust is a function of inlet pressure. This dictates that the primary fuel supply be located at the ends of the vehicle so that where the supply pressure has dropped off due to friction in the supply line less thrust and therefore inlet pressure will be required. Progressively smaller fuel supplies can be stationed closer to the vehicle's center. Hydrazine RCM's have a specific impulse on the order of 225 seconds. Fuel consumption is a function of the perturbations on the orbit and how quickly deviations in pitch attitude can be detected and corrected before the gravity gradient force becomes large. The number of perturbations encountered and their affect on fuel consumption is an area requiring further study. 6. 10 REFERENCES 1. Athans, Michael and Falb, Peter L. Optimal Control, McGraw-Hill, New York, 1966. 2. AFFDL TR-66-68 Section IX,'Quantization Errors of Numerical Integrations," Air Force Flight Dynamics Laboratory, Wright-Patterson AFB, Ohio 1968. 3. Bhat, U. Narayan, Elements of Applied Stochastic Processes, John Wiley and Sons, N.Y. 1972. 4. Greenwood, Donald T., Principles of Dynamics, Prentice Hall, Englewood Cliffs, New Jersey, 1965. 5. Hayes, John P., Computer Architecture and Organization, McGraw Hill, N.Y., 1978. 6. Seltzer, S. M. and Shelton, H. "Specification of Spacecraft Flexible Appendage Rigidity, " AIAA Journal of Guidance and Control, Nov-Dec 1978. 7. Slafer, L. and Oberly, P., "Hughes Satellites: Control Systems and Their Electronics," presentation at The University of Michigan, Feb 1979. 78

7 GROUND SUPPORT 7. 1 INTRODUCTION The idea of disposing nuclear waste in space is exotic by nature. It requires many new ideas and technologies. The other side of the project is to use existing technology as much as possible. The main concern has been the use of existing technology to solve many of the ground operations problems. The main portion of the work was with ground operations and in life support systems in space. The areas of investigation are: 1. Launch site selection 2. Location of power and reprocessing plants 3. Transportation and handling a,. Power plants to reprocessing plants b. Reprocessing plants to the launch facility c. Handling interior to the launch site 4. Environmental impact study 5. Communications 6. Space station design concept 7. 2 LAUNCH SITE SELECTION In selecting a possible launch site to use in transporting the nuclear waste containers into space, three alternatives were considered: use of facilities at the Kennedy Space Center (KSC) in Florida, use of planned facilities at Vandenburg Air Force Base (AFB) in California, and the construction of a new launch facility dedicated exclusively to the disposal of nuclear waste. For the reasons outlined below, it was decided that the facilities.at Cape Kennedy would be the best to use for this purpose. For several reasons, the construction of a new facility dedicated solely to nuclear waste disposal is a very attractive option. The building of a dedicated launch facility in an isolated area greatly reduces the danger presented to the general public by an accident that would release nuclear waste into the biosphere. A dedicated facility also offers greater safety in the handling of waste. Handling and transportation equipment used should be designed exclusively for the handling of radioactive materials. Problems that could occur in handling could easily be taken into consideration in the design of the launch and handling facilities. As attractive as these factors are, they are outweighed by two other considerations. The first of these is cost. To construction from the ground up the facilities required for the launch, control, recovery, and maintenance 79

of the Space Shuttles that are to be used to haul the waste into orbit would require the expenditure of several hundred million dollars. Add to this the cost incurred in the designing of the new facility and the procurement of the necessary land, which for maximum isolation from the general public would be a virtually uninhabited island. This would require several billion dollars to be spent constructing a new facility. Its isolation also means that the site's operating expenses would be higher than those at KSC since supplies and fuel necessary would have to be transported farther. In short, the construction of a new, dedicated facility is not cost-effective when compared to the cost of operating from launch sites already in existence. The second factor which argues against the construction of a new isolated facility is the additional risk that is involved in transporting the waste through a greater distance. This factor is most important when considering the transportation of waste across several thousand miles of ocean to an island facility. This journey would be subject to the possibility of a storm or maritime disaster, each of which could result in contamination by released nuclear waste. Although this risk is lessened if the facility is located somewhere in the North American continent, there is still an additional risk that is created by the transportation of waste through additional miles that would not be present if facilities at KSC are used. The second launch site considered was the Shuttle launch facilities currently under construction at Vandenburg AFB near Lompoc, California. Although the facilities, when completed in 1982 will not be as extensive as those at Cape Kennedy, they would be adequate for the required operations. However, due to its location on the West Coast, the launching site at Vandenburg AFB is less desirable than at Kennedy for two reasons. First, Vandenburg is located on the West Coast, while the majority of the nuclear power plants and all of the existing and proposed processing facilities are located east of the Mississippi River. The additional cost that would be incurred by shipping the waste to the West Coast makes Vandenburg AFB an unfavorable choice when compared to Kennedy. The other reason is that because of its location with respect to the continental United States, all launches from there must be directed either to the west or the south away from populated areas so that a rocket which does not launch properly will not come down in any densely populated areas. To place a payload in an equatorial orbit by a Shuttle launched from Vandenburg AFB would require the expenditure of more fuel in order to cancel out the adverse effects of the Earth's rotational velocity. The extra cost and difficulty that would be entailed by conducting such operations from Vandenburg AFB make it less desirable than the Kennedy Space Center. As a result of the above analyiss, it was decided that the facilities at Kennedy were the logical ones to be used to handle the launching of nuclear 80

O ORBITER PROCESSING PURISlMA OINT POEA W id i~V _ _aLOMPOC, POINT LA ~,., GUNCHI AREA Do ARGUELLO HOATH 3 (Facilities are projected for completion in 198) 81 NASA~~~~~~~~r ~/ FACILITIES-~~~~~~~a Fig~ ~~~~SUTH7 a f adnugAi oc a (Fciiie reprjctdfo omlein n/92 VAB

waste containers into orbit. Kennedy provides the best location with respect to the reprocessing centers. The facilities there are extensive with large amounts of available land suitable for the construction of the handling facilities that would be needed to unload, service, and store the waste containers prior to loading them into a Space Shuttle for launch. Kennedy is located close to several large population centers, but the danger presented to these areas can easily be minimized by proper design and planning. 7. 3 LOCATIONS OF POWER AND REPROCESSING PLANTS Irradiated fuel must be transported from the nuclear power plants to the launch site by way of reprocessing plants. Because of limited knowledge of existing facilities, a study of locations of power plant and reprocessing plant locations was necessary. It was found that at the present time there are approximately 70 nuclear power plants operating in the United States. There are about 120 plants projected for operation within the next ten years (Reference 1). The majority of the plants are located in the eastern half of the United States, with a few locations on the west coast. A complete listing as of June 30, 1978, is included in the appendix (Reference 2). In the United States today there are three plants which were constructed for reprocessing nuclear waste. None of the three are presently in operation due to government restrictions and only one of the plants has ever been in operation (Reference 3). The Nuclear Fuel Service Reprocessing plant is located in West Valley, New York. Of the three reprocessing plants, this plant was the only operating plant. When it was shut down in 1971 its facilities had the capacity to reprocess 1000 kg per day and were being expanded to handle 3000 kg per day. It is located on 3300 acres of land owned by the State of New York, approximately 26 miles south of the city of Buffalo. Dairy farms are located relatively near this plant so it is constantly being monitored. In Morris, Illinois, another reprocessing plant is located. This plant is known as the Morris Operation but was formerly known as the Midwest Fuel Recovery Plant. It is located on private land and is on the same site as a nuclear power plant owned by the General Electric Company. This plant could handle 1000 kg waste per day but was never operational due to cold checkout operation problems. The closest city to this plant is Joliet, which is 14 miles away, and is a suburb of Chicago. The plant site is located near a population center and has facilities for holding fuel along with three reactors. 82

V Sites with'Operating Plants Sites with Plants Under m Construction or Planned Figure 7. 2 Nuclear Power Sites in the United States 83

In Barnwell County, South Carolina, the Barnwell Nuclear Fuel Plant is under construction. It is located on private property next to the Savannah River Laboratories. It was designed to handle approximately 500 kg of waste per day. The closest city is Augusta, Georgia, which is 31 miles away. It is not in a large population area like the Morris Operation. Plans are underway for another reprocessing plant. The Exxon Corporation has applied to construct another facility in Oak Ridge, Tennessee. There are several good reasons why so few plants have been constructed. To reprocess this waste requires a complex chemical process. Add on to the complex process, the effects that everything which is being worked on is radioactive. Also, licensing of a reprocessing facility takes several years and is very restrictive. These complexities make the costs and standards very high. Because of these factors, reprocessing plants are not often constructed. The present capacity of the three reprocessing plants is about 9000 kg per day. This works out to a total of approximately 3. 3 million kg per year. The capacity needed by the year 2000 will be 12.7 million kg per year. This means that by the year 2000, reprocessing plant capacity will have to be four times the present capacity to prevent backlogs. This must be achieved either by building more plants or increasing capacity of the existing plants. 7.4 TRANSPORTATION AND HANDLING: FROM POWER PLANT TO LAUNCH SITE This analysis was made to assess the best means of transporting the waste from the nuclear power plants to the reprocessing facilities and then on to the Nuclear Payload Preparation Facilities at the Kennedy Space Center in Florida. Presently, it is estimated that 1. 6 million packages per year carry a quantity of radioactive material whose shipping, packaging, and labeling are regulated by the Department of Transportation (Reference 9). The railway system is the best mode of transportation chosen to transport the waste, since, 1. Most nuclear power plants have a rail system at the reactor site, 2. Railways can transport larger volumes per shipment. It would take 455 truckloads at an average of 22 tons per truck to carry 10, 010 tons of waste, where as it takes a typical unit train of 100 tons per 100 cars to equal 10, 000 tons. 3. Safety of handling and transportation. Irradiated shipping fuel casks are already in existence, have been tested for severe accidents, and used in operation (Reference 8), and 4. Low environmental risk. If a major accident were to occur the clean up operations would be more confined and isolated on a rail system in the country, than for a truck on a congested highway. 84

PCR OROITAL DEPLOYMENT REENTRY VI IIr:rI ASk f MIWkY PUUlIN"I NUCLEA1r PAYLOAD PKEPARlATIOW IACIUITY ~jr (NVPPF LAUNCI COMPLEX 39 IBON1lONtAL LANDING 00 SPECIAL, PU'RPOSEI TRANSPORTER 9 WASTE TREATMENTA RAILROAD SIUPPING CAR NUCLEAR WASIE PAYLOAD AR WASTE FABRICATION lACIITY STORAGE SITES Figure 7. 3 Ground Operations

,~~~0, CO1L L~f SOO~p O Figure 7.4 Cutaway Diagram of a Shipping Cask Showing the Principal Components 86~ e 11

Approximate: Length 5.3 meters Diameter 1.6 meter Weight VALVE box empty 55 tons loaded 67 tons STAINLESS STEEL SHELLS' VALVE BOX IM PACT FINS.7:-.~~~~~~~~~~~~~~~~~~~~: ~45~~~~~~~~~~~~~~~~~~~~~ b.]., REMOVABLE FUEL BE Fgi IMPACT FINS CLOSURE HEAD Figure 7.5 Irradiated Fuel Cask

TIPPINO CRADLE Approximate wcight of cask and shipping assembly: CASK empFty 70 tons Irradite FeCsko Ral a loaded 82 tons )WOVIABLE COOLING DUCT FIXED ENCLOSURE1 00 FIXEDr COOLIA uc IGUNYDANT ENGINE/8LOW14~ COOLINYG SVSTIEMII 100 TOM CAP)ACITtf FLAT CARr Figure 7. 6 Irradiated Fuel Cask on Rail Car

The cask used to transport the irradiated fuel is housed in a thermal cooling unit in transit to deal with the continued large heat generation. Also, the containers are provided with radiation shielding and are able to withstand the impact of any transportation accident (Reference 14). Safety in transportation does not require special routing, although special routing is used at some bridges and tunnels to avoid possible interference with the flow of traffic, should an accident occur. These shipments are therefore subject to the same transportation environment and rules as already stated. Protection of the public and transport workers from radiation during the shipment of radioactive materials is achieved by a combination of limitations on the contents according to the quantities and types of radioactivity, standards, and criteria for package design and control (Reference 10). At the reprocessing plants the fuel is converted into an oxide powder for long-term storage and also to extract specific elements from the fuel. An extension of the reprocessing facility should be constructed to handle the oxide powder and its packaging into 1 kg modules. These modules are then placed inside the containment vessel which will be shipped by rail to the Nuclear Payload Preparation Facilities at Kennedy Space Center. 7.5 HANDLING OF THE WASTE CONTAINERS AT J. F. KENNEDY SPACE CENTER Upon arrival at the Nuclear Payload Preparation Facility (NPPF), the cask containing the waste canister is unloaded from the railroad car. The canister is removed from the shipping cask, checked carefully for any faults, and is then transported to the holding section of the facility where it is placed in a shielded and cooled room. It will remain there, under constant surveillance, until the time comes to prepare it for loading into the Shuttle. Approximately 80 hours before scheduled launch, the canister is removed from the holding area and moved to the preparation portion of the NPPF. Here the canister is again checked for any package faults or failures. After passing this check-out, the canister is then mated with a monitoring module which will monitor the surface temperature of the canister to insure that any irregular behavior within the canister does not go unnoticed. The information gathered will be relayed both to the ground and to the crew of the Shuttle. After installation and check-out of the temperature monitoring system, the waste container is hooked up to a cooling system which will keep the waste canister cooled to simplify handling and protect the surroundings from the heat given off by the waste. This cooling system will be used during the handling of the handling container and canister on the ground. The handling container, with the canister 89

inside, will be attached to the Shuttle's interior cooling system at the time of loading. After completing check-out of this portion of the package assembly operation, a parachute recovery system is attached to the package. With this system, the canister can be brought safely back to earth in the event that the canister is jettisoned by the Shuttle orbiter in an in-flight emergency. With the completion of the final check-out of this installation, the waste canister package is now ready for loading onto a special transporter for transportation to the launch pad where it will be installed in the Shuttle orbiter. To transport the waste canister package to the launch pad, a special transporter will be required. The waste canister package weighs in excess of 20 tons. The transporter will require a primary and secondary cooling system to insure that the package will be continually cooled, as failure to do so could cause the canister to overheat and endanger the transporter and crew due to the heat generated by the nuclear waste. The assembly will also be transported in a vertical position to assist in loading the package into the orbiter bay. By carrying the load vertically, it also removes the necessity of using equipment at the launch pad to move the package from a horizontal to a vertical position. By minimizing the amount of handling of the package at the pad, it is possible to minimize the risk of an accident occuring at the launch pad and contaminating the immediate area with released waste. These requirements necessitate the use of a special transporter dedicated entirely to the transporting of waste canister packages. This will make the monitoring, detection, and containment of any radioactive contamination much easier. The nuclear waste package will arrive at the launch pad approximately 53 hours before scheduled launch time. At this point, the package will be loaded in the payload Changeout Room (PCR), the facility at the pad used to load payloads into the Shuttle orbiter when the orbiter is in the vertical position. This operation takes 13 hours. At the end of this time the Shuttle is moved to the pad and the PCR is moved into position next to the orbiter. Starting at approximately 21 hours before launch, the waste package is transferred from the PCR into the Shuttle cargo bay. This process takes 9 hours and involves transferring the cooling of the waste package to the orbiter's internal cooling system, connecting the temperature monitoring system to the Shuttle, and securing the package in the Shuttle. A careful check-out of all systems is completed, and when all requirements are satisfied, the Shuttle bay doors are closed and the waste is ready for launch into orbit. In the total process of handling the nuclear waste at the Kennedy Space Center, the most important link in the chain is the NPPF. This facility will need to be constructed, and there are several factors which need to be considered in its design and construction. The facility will need to have a holding area where several nuclear waste canisters could be stored for short 90

ORBITER:^t*AVERAL _o~n~ n s s UTY LYA NUNf PROC9W~N FACIIT COMPLEX 41 HEADOUARTERS~ OPE~RATIONSU ANO~WI 049CKOUT SLOG EX4 ~~M~ i,_ ~14YPEROO LIC~#Lt *-.9SA FLUX -N01~ ~ ~ ~~~9 nO~~~r s~~'i~~T~~c~~ /-ANQA AO.SAF HANGAR ANAI A: F1 HANG"MI AG CC.~ OCIBAN OP LIGHTH~~L~nnOUSE DELTA SOLUD COMPLEXK MOTOR FSACILITY CAPE CANAVER)AL TEStE T FACILITY 9LTALAUNC Figure 7.7 Map of J. F. Kennedy Space Center (showing major buildings that are used by the Shuttle Transport System)

WORKING TIME BEFORE LAUNCH. HR 160 150 140 130 120 110 100 90 sO 70 60 50 40 30 20 10 0 iORBITERTO OF SAFING, DESERVICING, AND PREPARATION FOR PAYLOAD REMOVAL (REFERENCE) AYLOD REltVAL 0) I ORBITSER /! I~1I ~MISSION-UNIUE PAYLOAD ACCOMMODATION EQUIPMENT REMOVAL 48.0) FAOCESSIIT N I ~ MI=SION-UNIQUE PAYLOAD ACCOMMODATION EQUIPMENT INSTALLATION (16.0) FACILITY..,. 1OPF) ORBITER SCHEDULED MAINTENANCE AND PREPARATION (REF) IC!! PREPARATION FOR MIATING (REFERENCE) ORBITER I I,VEHICLE!ORBITER REMATE. MATE. I ORBITER TO VAB ASUIMLD Y. AIN ERFA CE ERIFICATION (REFIERENCE) BUILDING I ( REFERENC_) (VAB) SHUTTLE INTEGRATED OPERATIONS (REFERENCE),III~.1 ~ l SHUtTLE TO PAD A i I,.... LAUNCH PAD OPERATIONS (30.0) PAYLOAD INSTALLATION IN PCR (13.0) FUEL CELL DEWAR LOADING - HAZARDOUS OPERATION (REFERENCE)I I I I CAGO BAY OORS CLOSED A CA1ji i POWER ON SHUTTLE LAUNCH READINESS VERIFICATION (REFERENCE)I IAICHI I I I I I I LAUNCH / /! I PAYLOAD INSTALLATION AND LAUNCH READINESS VERIFICATION (9.01 PAD I I I I I CABIN CLOSEOUT OPERATIONS (REFERENCE) HAZARDOUS SERVICING (REFERENCE SERVICE DISCONNECTS (REFERENCE) CARGO BAY DOORS LATEST CLOSURE (CONTINGENCY)!I iI I I! ~ STANDBY LAUNCH FROM STANDBY (220)1 j jj. FTOFFA Figure 7. 8 Payload Processing Schedule and Shuttle Operation Ground Flow 92

periods of time. This area would need to be shielded so that in the event of a canister rupture, the waste will not contaminate the surrounding area. This shielding would also protect the surroundings against the radiation given off by the waste canisters. This holding area would also need to provide individual cooling units for each waste canister and a backup system capable of switching on automatically and running continuously. Both of these would have to be capable of operating independent of outside power sources. The building should be equipped to handle a wide variety of possible accidents and circumstances. The cargo handling areas should be constructed to minimize the amount of direct human contact with the waste canisters by maximum use of remote handling equipment. The facility should also be built sturdily enough to withstand a wide range of possible weather situations. This facility should also have a wide range of mobile equipment for handling spills outside of the facility. The handling of waste within the confines of Kennedy Space Center would also require the establishment of certain new operating procedures. Procedure for dealing with several different types of accidents should be established and the necessary personnel trained to handle them. Surveys of the transportation routes to the launch pad from the NPPF should be performed regularly to guard against the spillage of small amounts of radioactive waste. All operations involving the handling of the waste canisters should be carried out with maximum emphasis on safety and system redundancy. The canisters should be handled as little as possible and during this handling the area should be cleared of as many sharp objects and unnecessary personnel as to minimize the danger of accident and contamination. With proper planning and training of personnel, the danger to the general public will be minimized and the effect of a spillage of waste localized quickly and effectively. 7. 6 ENVIRONMENTAL IMPACT Throughout the transportation route from nuclear power plants to space, it is possible for the containment vessel to break and thus effect the environment. Several key areas of environmental impact are, transportation from the power plant to the launch pad, on or near launch pad explosions, and the possible encounter of a waste package with other space objects. All these environmental problems must be considered in the design. In the rail link between the power plant and launch site, the possibility of a severe accident occuring is very small. In the past 25 years in the U. S., there have only been 300 reportable accidents and only 30%o of these have had released radiation. None of these accidents have had related deaths. A 93

container would be involved in a transportation accident only once in 10 years and only one accident out of 100 will be severe. These statistics show that a rail accident is very unlikely (Reference 8). Studies have been made about on or near launch pad explosions and have shown that the possibility of an accident occuring which would release nuclear waste is almost nonexistent. Several types of accidents were studied and showed that with a 1%o release of a 5500 waste package there would be no health hazard within 100 km. This study concluded that there were no problems but much more work must be done for more conclusive results (Reference 13). To show how devastating a waste spillage would be some examples of the previously mentioned problems are included. They readily show how important it is to make every effort to put safeguards on transportation, as already exists with the rail system. If a severe accident were to happen (possible but not probable) enroute to the reprocessing centers, it would have devastating effects upon the surrounding areas. The water system could be affected if the waste were not cleaned up within a time limit of 10 hours. Also in this time frame (using seven irradiated fuel elements) the radiation level at 100 feet could be as much as 104 rem/hr (industrial limits are 5 rem/year). Approximately 30,000 persons within a mile radius (based on 104 persons/square mile) might receive a cumulative dose of about 1000 rem. If a person remained unshielded at an average distance of 100 feet from the fuel elements for 6 minutes, he might receive a dose of as much as 1000 rem. The land around the spillage would be uninhabitable for approximately 150 years. Even then, a cautious approach to the land is warranted, since a steady dose of radiation would be emitted from the ground level every hour (References 9, 14). Another major concern is the assessment of the environmental impact of on or near-pad shuttle failure with the release of the nuclear waste payload, either before or after liftoff. Taking the most severe case is where the Shuttle orbiter explodes fully loaded (fuel, waste package) on the launch pad. Taking into account the meteorological circumstances (spring, fall and sea breezes) the waste dispersion would reach a radius of 100 km (62. 5 miles). Assuming there are 55 kg of waste that would be released, the population would be exposed to 1000 rem. Although these are the most severe cases, when the probability of these mishaps occuring and the extent of the consequences are taken into account, the risk to the environment due to the radiological effects of transportation accidents is small. Accidents to packages more severe than design accidents (see Figure 6) can occur but the probability is very low (Reference 13). 94

One final environmental consideration is the possibility of contaminating either the other heavenly bodies in the solar system or the planets in some other solar system. In the latter case, the possibility of contaiminating another solar system is non-existent. The nearest star is 4 light-years away and it would take a waste package about 60 million years to reach it. After this time, the package would simply be 1 kg of dust and would not present a danger to anyone. The other consideration, the contamination of our own solar system, is more important. The amount of waste in any one load is very small and would be incinerated in the upper atmosphere of any of the outer planets. The smaller moons have no such protective shield, but the extent of the contamination from an inpact would be localized due to the small amount of waste involved and the absence of an atmosphere which would spread the waste across the face of the body. Therefore, the contaimination of the outer planets with nuclear waste is not a serious worry. However, it is also a problem that can easily be avoided. It is possible to launch the waste packages into orbits that will avoid all the outer planets. This is a complicated problem in celestial mechanics but it is one that can be solved today. Therefore, there is no real danger of contaminating the rest of the universe with nuclear waste. 7.7 COMMUNICATIONS The present tracking system used by the United States is the Spaceflight and Tracking Data Network (STDN). The system consists of 14 ground based stations in the United States and throughout the world. This system has become too costly to operate for several reasons. The present system has several stations in foreign countries and the land which the stations are located on must be leased from each country. These costs have increased significantly. Also, many of these stations have data storage and handling facilities which are very expensive. These reasons have boosted the cost of operation significantly (Reference 4). The communication network projected for the 1980's is the Tracking and Data Relay Satellite Systems (TDRSS). This system incorporates the use of two satellites placed in geosynchronous orbit. These satellites will relay messages from spacecrafts to earth based stations in the United States in real time. There will still be some foreign stations for highly eliptical, lunar, and interplanetary space flight missions. Also, this system's data handling equipment is operated and paid for by the particular user. This reduces the cost of communications. This system has a wider bandwidth for communication, and one channel could be routed via a domestic satellite. This tracking network is also planned on being used on Space Shuttle flights and for Spacelab experiments. 95

7.8 SPACE STATION - LIFE SUPPORT In the existing space shuttle program, the European Space Agency has developed a program of Spacelabs. There are several configurations of module and pallet configurations which allow many scientific experiments to be conducted from the Space Shuttle. A possible life support system could be constructed of certain elements of these existing Spacelabs. There are several reasons for using the Spacelab configuration for a life support system. Most of the experimental work has already been done resulting in low cost. The communication system used on these experiments is the TDRSS which is compatible to the tracking system for NEWDUMP. Only a slight amount of modification is necessary for application to the project. Because these space labs were designed for experimental purposes, it would be possible to add on extra modules for experiments. The configuration chosen is shown in Figure 11. This system is approximately 18 m (59 ft) long on a side and approximately 4 m (13. 3 ft) in diameter. The total system is 20 canisters with 5 per side. Each side'bottle-necks' because airlocks will be placed in each narrow section in case a separation occurs. The facility contains the following: 1) power storage, 2) control room, 3) life support section (air conditioning, water, and food storage), 4) repair center, 5) sleeping area for 12 people, 6) latrines, and 7) galley, sick bay, recreation area. The total interior volume is 444 m3 (15, 680 ft3), excluding the connecting tunnels. The total weight is approximately 70, 000 kg (150, 000 lbs). The life support system would be connected in some manner, exterior of the tension cables. The total weight of the life support structure is several orders of magnitude lower than the total mass driver weight, and because it is located at the half way point of the mass driver, it will not contribute significantly to moments or inertial effects. 7. 9 CONCLUSIONS AND RECOMMENDATIONS The following conclusions and recommendations were arrived at by the Ground Support investigations. 96

ISA NE DUMP 1igure7.SchmatiD SpECTofi Vri Figure 7. 9 Schematic of Double Module Space Lab Configuration of Canisters

%O 00 VENT AN ARELIEF SELL * P cm ASjPAcm FITTINGS STR _C b / E hh WT ENDSCONS Figure 7. 10 Present Space Lab Configurations Showing Pallets and Canisters

1) The best launch facility would be Kennedy Space Center, due to launch considerations and its location. 2) There are approximately 70 nuclear power plants now producing and 120 projected plants. Also 3 reprocessing plants have been built and 1 permit to build a plant has been requested. 3) A facility must be constructed at the present reprocessing plants to package the waste in containers which will be sent in space. This will minimize contact with containers. 4) Waste will be transported by way of the rail system. Interior to the launch facility, the package will be handled in a special manner. 5) A handling system at KSC must be constructed for holding and checkout of waste packages. 6) The environmental impact if a breech in containment occurs would be directly related to the severity of the accident. 7) The tracking system used will be the Tracking and Data Relay Satellite System because it is projected to be used on Space Shuttle and Spacelabs. 8) A preliminary design of Spacelab modules could be constructed to house a life support system. 9) More research must be done on adapting the Spacelab modules to use for a life support system, and adapting it for use on a mass driver. 99

W'ASTE FLOW/ ROJEC TED FOR /TH YEAR 2000 0 I A?,4g./ 120szea -I - )j'71I KCN/AeAR1S TIER Y~A~.. 2 oo, oo0 K\/% -1 r'!EL RE PROCESSING RLLANTS N-LA _~Ot It-. A..V Figure 7. 11 Overall View of Waste Flow in Project NEWDUMP AUCLEAR POWER PLAVTS',OM~~71c,)

7. 10 REFERENCES 1. Deutsch, R. W., Nuclear Power, General Physics Corporation, Columbia, Maryland, 197 6, p. 7. 2. Environmental Information Center, Inc., "The Energy Index'78", Energy Reference Department, New York, N. Y., 1978. 3. Gilmore, William R., Editor, "Radioactive Waste Disposal, " Noyes Data Corporation, Park Ridge, N. J., 1977. 4. Dickinson, W. B., "The Spaceflight and Tracking Data Network Data Handling System in the 1980's, " EASCON'75; Electronics and Aerospace Systems Convention, NASA Goddard Space Flight Center; Electronics and Aerospace Systems Convention, Washington, D. C. September 29-October 1, 1975, Record. 5. Deerkoski, L. F., "Tracking and Data Relay Satellite System (TDRSS) Telecommunication Services, " EASCON'75; Electronics and Aerospace Systems Convention, NASA Goddard Space Flight Center; Washington, D. C., September 29-October 1, 1975, Record. 6. National Aeronautics and Space Administration, Space Transortation System Users Handbook, June 1977. 7. Aviation Week and Space Technology, January 29, 1979 8. U. S. Atomic Energy Commission, "Environmental Survey of Transportation of Radioactive Materials to and from Nuclear Power Plants, " December 1972. 9. Bodansky, A and Schmidt, F. H., The Nuclear Power Controversy, Prentice, Hall. 10. National Ener" Transportation Vol. 1, Current Systems and Movements Committee of Commerce, Science, and Transportation, No. 95-15. 1 1. Nuclear Safety; Transport of Radioactive Materials in the United States, Vol. 18, No. 3, May-June 1977. 12. Battelle Columbus Laboratories, Prelrimiary Evaluation of the Space Disposal of Nuclear Waste; Contract No. NAS8-32391, August 30, 1977. 13. Battelle Columbus Laboratories, Evaluation of Space Disposal of Defense Nuclear Waste, Final Review, NASA Marshall Space Flight Center, January 29, 1979, Columbus, Ohio. 14. United States Atomic Energy Commission, "Shipping Radioactive Material at the National Reactor Testing Station, " Washington, D. C., AEC Headquarters Bld., Germantown, Maryland, October 1960. 101

8 COST ANALYSIS 8. 1 INTRODUCTION This chapter is devoted to a cost estimate of Project NEWDUMP and its impact on the electric utility and the consumer industry. 8. 2 SUMMARY The total cost is broken down into three categories; construction of the mass driver in space, operating costs of Project NEWDUMP, and a storage facility at Cape Kennedy. The cost of constructing the mass driver is 11. 567 billion dollars. This includes research and development work still to come and Space Shuttle transportation to orbit. The operating costs are 2. 974 billion dollars per year. This includes reprocessing of the waste, ground transportation to Cape Kennedy, and thirtysix Space Shuttle flights each year. All figures are in 1980 dollars. Cost Percent Item $ x 10~ of Total Cost Cape Handling Facility 123 0.8 Mass Driver 11,444 78.7 Waste Disposal Operations (yearly) 2,974 20. 5 14, 541 100.0 Table 8, 2. 1 8. Z. 1 Mass Driver The mass driver costs were figured by extrapolation of other predictions made on smaller mass drivers. These predictions were then related to large space satellites. They are listed in Table 8. 2. Z. 8. 2. 2 Handling Facility An estimate of a wast facility at Cape Kennedy was assessed as a nuclear waste storage site meeting NRC safety reuglations. This facility was estimated at 123 million dollars. 102

Handling Facility 0.8% $123 Yearly Mass Driver Operations 78. 7%o 20. 5% $11,444 $, 974 $14,541 = 100% FIGURE 8. 2.1 TOTAL PROJECT COST (MILLIONS) Transportation Construction and to Orbit / Fabrication of Materials 32. 5% / 37. 0% $3,700 $4, z25 Research and \ Development 30. 5% $3,519 $11,444 = 100% FIGURE 8. 2. 2 TOTAL MASS DRIVER COST (MILLIONS) 103

, / \ ~Mass Driver Yearly Finance Charge Operations 28. 3 83% 71.7%?, $1,174 $2, 974 $4, 148 = 100 % FIGURE 8.3.1 FINANCES (MILLIONS) Space Shuttle / \ m 31. 1%o 7 \\ $924 Nuclear Plant to Launch Pad Mass Driver 58. 9% 10.oo $1,754 \ $296 $2, 974.6 = 100% FIGURE 8.2. 3 YEARLY OPERATIONS COST (MILLIONS) 104

Cost Percent $ x 106 of Total Research and Development Mass driver 3,270 28.6 Batteries 205 1.8 Attitude Control Engines 44 0. 1 Subtotal 3,519 30. 5 Construction and Fabrication of Materials Electronics 1,699 14. 8 Structures 2, 021 17.7 Batteries 223 1. 9 Solar Cells 117 1. 0 Attitude Control Engines 5.1 Computers 5.1 Crew Station 155 1.4 Subtotal 4, 225 37.0 Transportation to Orbit Space Shuttle 1,940 17.0 Developmental Testing 1,760 15. 5 Subtotal 3,700 32.5 Total 11,444 100. 0 Table 8. 2. 2 8. 2. 3 Yearly Operations The yearly operations were estimated based on a yearly waste disposal of two hundred thousand kilograms after reprocessing. These are broken down in Table 8. 2. 3. Cost Percent $ x 106 of Total Nuclear Plant to Launch Pad Reprocessing 1,305 43.9 Transporting Spent Fuel 95 3. 2 High Level Waste Transportation Z5 0. 8 High Level Waste Management 253 8. 5 Safeguards 76 2. 5 Subtotal 1,754 58. 9 Space Shuttle Transportation 874 29. 4 Waste Packages 50 1.7 Subtotal 9Z4 31.1 Mass Driver Maintenance and Operations 296 10.0 Total 2,974 100.0 105 Table 8.2.3

8- 3 UTILITY IMPACT The yearly cost of 2. 974 billion dollars can be covered by an increase of 5. 12% to the electric utilities annual revenue. In order to keep the program operating and pay for the mass driver in a twenty-five year nine percent loan the increase in annual revenue would be 7. 15%. This constitutes 4. 148 billion dollars per year to remove nuclear waste into space. After the first year 71.4% of the utility bill increases go directly to nuclear waste disposal. The yearly costs are outlined in Table 8. 3. 1 Cost Percent $x106 of Total Mass IDriver and I-ndling Facility Finance Charge 1,174 28.3 Yearly Operations 2, 974 71.7 Total 4,148 100.0 Table.3.1 The consumer will receive an increase in rates of only 0. 4i per 5 kw-hr. This translates to $4. 37 per month per family in America. 8.4 CONCLUSIONS The cost of nuclear waste disposal into space is not prohibitive. The cost to remove 1 kg permanently is $20, 074 which is in the realm of ground disposal ($9427 /lb). 8. 5 REFERENCES 1. Space Planner Guide, USAF, Air Force System Commands, July 1965, pp. VII 1 - VII 27. 2. Project OASIS, The University of Michigan 1978 Senior Aerospace Design Project. 3. Edison Electric Institute, "Statistical Year Book of the Utility Industry," for 1975 published Oct'76 No. 43, No. 76-51. 4. Environment; Volume 17, No. 5, July-Aug'75, "Expensive Enrichment," Marvin Resnikoff. 5. Astronautics and Aeronautics, March 1978, "The Low (Profile) to Space Manufacturing" Gerard O'Neill. 6. Space Transportation System User Handbook NASA June 1977. 7. Steven Rasch, Bechtel Corporation, personal communication. 106

APPENDIX A NUCLEAR A. 1 MAGNETIC SUSCEPTIBILITIES -6 -6 Element 10 cgs Element 10 cgs Hydrogen (H) -22 Bismuth (Bi) -83. 0 Lithium (Li) 14. 2 Polomium (Po) ---- Iron (Fe) 7200. 0 Astatine (At) --- Carbon (C) -6. 0 Radon (Ra) ---- Cobalt (Co) 4900. 0 Francina (Fr) — _ Nickel (Ni) 660. 0 Radium (Ra) ---- Copper (Cu) Z67. 3 Actinium (Ac) -.-0 Zinc (Zn) -46. 0 Thorium (Th) -16.0 Gallium (Ga) -34.0 Protactinium (Pa).0 Germanium (Ge) -28.8 Uranium (U) 2360. 0 Arsenic (As) -5.5 Neptunium (Np). Selenium (Se) -27. Z2 Plutonium (Pu) 730. 0 Bromine (Br) -56.4 Americium (Am) -48.1 Krypton (Kr) -28. 8 Curium (Cm) ---- Rhenium (Re) 50. 2 Berkelium (Bk) -__ Strontium (Sr) -106. 0 Californium (Cf) - Vttrium (Y) 44.4 Einsteinium (Es) Zitconium (Zs) -13.8 Idium (In) -47. 0 Niobium (Nb) -10.0 Molybdenum (Mo) 41.0 Technetium (Tc) 244. 0 Ruthenium (Ru) 162. 0 Rhodium (Rh) 104. 0 Palladium (Pd) 567.4 Silver (Ag) -24. 0 Cadium (Cd) -159. 0 Tin (Sn) -41.0 Antimony (Sb) -69.4 Tellurium (Te) - 39. 5 Iodine (I) -79.4 Xenon (Xe) -42. 9 Cesium (Cs) 1534. 0 Basium (Ba) -29. 1 Lanthanum (La) -78. 0 Cerium (Ce) 26. 0 Psaseodymium (Ps) 8994. 0 Helium (He) -1.88 Thallium (T1) -32.0 Lead (Pb) -42. 0 107

A. 2 NUCLEAR WASTE MASS Total Mass BPW Total Mass BsPW 1.8 3299 x 10 g 4. 6141 x 10 g Mass of Removed Mass of Removed Elements BRW Elements BRW U = 1.765 x 105 g U = 4.412 x 105 g Pu = 1.482 x 103 g Pu = 4 016 x 103 g Br = 3. 311 g Br = 9. 984 g Kr = 5. 429 g Kr = 1. 650 x 102 g 2 3 Zr = 5.528 x 10 g Zr = 1. 672 x 10 g -3 -3 Nb = 1.051 x 10 g Nb = 3.096x 10 g 2 3 Mo = 5. 084 x 10 g Mo = 1. 535 x 10 g 1 2 I 3594 x 10 g I= 1 083 x 10 g 2 3 Xe = 8. 017 x 10 g Xe = 2.446 x 10 g Total = 1.798895811 x 10 g Total= 4. 511522871 g Percent of weight Percent of weight removed removed 98. 14% 97.77% Total Weight Reduction 97.88%o 108

APPENDDC B ORBITAL MECHANICS AV requirements for solar system escape for perpendicular launch. B. 1 TEXT AND RESULTS The following program computes the AVmd to be provided by the mass driver to escape from the solar system. The mass driver is placed in a circular parking orbit around the earth at an altitude h; the parking orbit plane coincides with the ecliptic plane. The local circular speed in the parking orbit is found from VI C R +h (1) 0'' where Vc is the characteristic speed of the earth, Ro its radius. At an arbitrary point P in the parking orbit the mass driver imparts a AVmd to the payload. The AVmd is perpendicular to the orbital plane and since the payload at least must escape the earth's gravity AVmd > Vlc. After this velocity change the payload is in an escape trajectory plane which makes an angle ~ with the parking orbit plane (Figure l(a)) ( AV = arctan VC (2) The hinge line between these two planes is the line OP. where O is the center of the earth. In the escape trajectory plane the payload is initially at the perigee (point P) of the hyperbolic escape trajectory. The perigee velocity, Vp, is Vp md) + (Vic)2 (3) and the residual velocity the payload has when having escaped the earth's field is found from the energy equation* to be (Figure 1(b)) VW =7o2 2(Vlc)2 (4) At that time the payload is at a true anomaly O. given by *. 2. *V 2 V V~ V2 2 2 Ro + h 2 Ic 109

o =arccos (-, (5) 0o e where e is the eccentricity of the escape hyperbola. The eccentricity can be expressed in terms of Vp and h via the energy, E, and angular momentum, H p 2EH" e = +1, (6) e where 2 V0 E= — H= V(R +h) (7) The following transformations serve to find the components of V in the ecliptic plane coordinate system, where x is along Vs, the orbital speed of the earth around the sun, y is in the ecliptic plane radially outward from the sun, and z completes the right-handed axis system. All axis systems have their origin at 0. Consider first the xl, y 1, z system. x i along the extension of the line 1S, y, is parallel to V (Figure l(b), (cl)) p V1 = V cos (a - 0 ), (8) Vy= V sin (r- 0 ), (9) V =0; (10) system by rotation through the angle + about the xl axis (Figure 1(d)) V = Vx (11) X2 1 VY= V cos, (12) Y1 V2 y1sin. (13) The x2 - y2 plane already is the ecliptic plane and to move the x2, y2 z2 system to coincide with the final x, y, z system it must be rotated about the z2 axis through the angle (-(3) according to the r. h. rule. Now the payload velocity relative to earth is (Figure 1 (e), see Figure 1(a) for definition of A) Vx = Vx2 cos - VY2 sin 3, (14) 110

Vy V, sin3 + Vcos3 (15) + z2 Vz = Vz (16) The magnitude of the payload velocity relative to the sun is VT + Vs) + (Vy)2 + (V)2 (17) and this is to be compared to Vesc = J Vs (18) the escape speed from the solar system. The excess speed Vex, Vex = VT - Vesc (19) is computed. If it is negative, the mass driver AV d is increased by 1 km/sec and the process is repeated, for each value of j3. Once lowest AVmd (to the nearest. 1 km/s) is determined to give a positive Vex, the program calculated the inclination of the escape plane to the ecliptic plane is = arctan V, (20) and the initial flight path angle relative to the sun ys = arctan ( V y) (21) The program finally prints out 3, AVmdd Ves, is and YsResults 1) Figure 2 gives AVmd vs ( 2) The minimum inclination is 280 = is min 3) The minimum flight path angle is -10. 10 = YS nin 111

APPENDIX C C. 1 MASS DRIVER The following mass driver parameters are based on the equations developed for the optimized Mass Driver Reaction Engine (MDRE) from the 1977 NASA Ames summer study on space colonization. The caliber or "bore", D, is computed from the equation D=(13 6 538 x 10- p P p where ml is the payload mass in kg and p is the payload density in kg/m3 With ml = 1 kg and pp = 4x 103 kg/m3 D was found to equal.156 meters Payload Geometry payload length =.925D =. 144 meters payload diameter =. 3D.047 meters payload volume = 2. 5 x 10- m3 Drive Coil Geometry im = inductance length = drive coil spacing =. 185D =. 0289 meters (p = phase length of drive coil oscillation = 41 m =. 1156 meters bucket coil spacing = 6.tm =.1734 meters Bucket Coil Weight and Geometry WB = bucket coil width =. 1D =.0156 meters r = effective radius of bucket coil =. 26D =. 0407 meters VBC = volume of individual bucket coil vWBWB2 WB -6.2x105 m B r + 2 - r 6.2 x 105 P s = density of bucket coil = 4. 53 x 103 kg/m3 (niobium tin) mBc = mass of bucket coil = VBc s=.281 kg msuper = total coil mass per bucket = 2 mBc = 562 kg mB = empty bucket mass = 2 msu er 1. 123 kg mBL = loaded bucket mass = mB mB 2. 123 kg mB ratio of tuoaded to loaded bucket mass =. 529 mBL iB= current in each bucket coil = 2. 5 x 106 D = 6. 084 x 104 ampere 112

Mass Driver Geometry Sa = acceleration length = V /2a = 4. 133 x 103 meters Sd = deceleration length = V /Za = 2.186 x 10 meters total length = Sa + Sd = 6. 319 x 10 meters 113

C. 2 PAYLOAD TRAJECTORY After the payload has been released from the bucket the magnetic guide forces will no longer be acting on it. It will be in free fall inside a moving container and an analysis was done to determine the trajectory. Call the mass driver acceleration length "a" and the deceleration length "b". The rotation rate is h and time of flight t... e..- _ _ b _ Ina time t the end of the mass driver will have moved a distance Act wher e I = a + The payload will shift in the same time a distance b sin 0 where 0 is the angle of the velocity vector with respect to the structure orientation at t = 0 V tan 0 = — V = AV V = OC where -b where = tan or 0 = tan-l c AV in addition to this the payload will fall a distance 1/2 g t under the influence of gravity d1 =t 1 2 d2= b sin 0+ gt The difference between these distances is the amount of clearance required in the tubes. 114

For a =4.2km b= 2. 1 km = 1/92.5 min x 1 min/60 sec x 2w rad = 1. 13 x 10 rad/sec t =.24 sec g = 867 cm/sec gives I = 3. 15 km c = 1.05 km = 1. 3 x 104 rad dl - d2 = 85.43 -52.65 = 32.77 cm This distance is clearly much larger than the launch tube, therefore some means must be found to assure adequate clearance. Probably the best solution is the method used in the design of Mass IDiver Reaction Engines (MDRE). Here, the payload is released from the launch tube at the same time as release from the bucket; the bucket is snapped away from the payload magnetically and decelerated in a separate, but parallel tube. 115

APPENDIX D STRUCTURES D. 1 MASS DRIVER TUBES From Reference 4, the maximum tension in the subsonic range is 800 N. Thus, the axial stress, ar, will be given by (assuming that the tubes may be modeled as thin-walled pressure vessels): Ft t (5. 1. 1) where Ft = maximum tensile force (= 800N) r = 1/2 the bore of the mass driver's drive coils t = tube thickness (meters) We wish to hold a'_ s' where o- is the yield stress of the tube material (Al 7075-T6). For Afr7075-T6, j,, = 4.4814 x 108 N/m. Therefore, from (5. 1. 1),. Ft 3. 6425 x 10-6 m (. 0001434") Zwr (ys) The maximum compression in the mass driver tubes is 500 N. In this compressive state, we may model the tubing section between adjacent drive coils as a thin-walled shell. We wish to prevent buckling of this shell. From Reference 5, the buckling stress of such a shell depends upon the magnitudes of the terms: ra z Za A) () and B) t 3(1-vz) If A) and greater than B), we may use the "Euler-strip" formula. If vice versa, we may use Donnell's empirical relation: Tr2 Et2 "Euler-strip" formula: acr 1(1-) Z cr 112(1 - vZ) 12 Donnell's relation: cr = E 6 (t/a) - 10 (a/t) cr 1 +.004(E/-ys) where Ocr = critical buckling stress (of shell) t = tube thickness v = Poisson's ratio 116

I = shell length (distance between drive coils) E = Young's modulus ys 8= yield strength a = 1/Z bore of mass driver coils (radius of shell). We have, a =.078 meters I =.02892 meters as determined from an optimization relation included in the Mass Driver report. na )' 71.8 Thus, to use Donnell's relation, we require that 2t J3( v~)' 71.8 which implies that t s. 35 cm. For handling and construction purposes, it is desirable to have t somewhat larger than. 35 cm. To yield a conservative design (and also to account for the effects of the accelerating payload), t = 5. 0 cm will be used. Thus, we use the "Euler-strip" formula: ~r Et O'cr -.70-78 2 (Note: for longer cylinders, crI- l;1 (It~ V %cr is independent of I ) where E' 10,000 psi (= 6. 8944 x 10 N/m2) t =.05 m v =.33 I =.02892 m We obtain r= 1.9021 x 1011 N/m2. cr The actual compressive stress experienced in the subsonic range is: 500 N 500 N4 c= [(a+t( 128) - (. 078)2]mz = 1.55 x 1 N/. 117

The actual tensile stress experienced in the subsonic range is: 800N 2.472x104 2 t: + z:.472 x 1o N/mr ft [(a + t)- a2] Thus rcr 7 I= 1. 23 x 10 0'C and c =7.695 x 106 crt and ys = 1.813 x 104 nt and s = 2. 89 x 104 erc Thus, we see that both plastic yielding and buckling are avoided within very considerable safety margins for t =. 05 m. This thickness yields a tube mass (4 tubes), m, equal to: m = 4 p rr [(a+t)2] 1 (5. 1.2) where p = density of Al 7075-T6 (= 2800 kg/m3) I = length of mass driver (= 6320 m) Therefore, the total tube mass (from (5. 1.2)) is: m = 2.29 x 106 kg = 5. 04 x 106 Ibm. 118

F t:,,1 -—'a -....., - X L~ Figure D. 1 Thrust Distribution on Mass Driver -~1 d --- x Figure D. 2 Geometry of Rotating Mass Driver 119

D. 2 VERIFICTION OF ZERO MOMENT AND SHEAR FORCE DISTRIBUTIONS IN THE MASS DRIVER DUE TO ATTITUDE CONTROL THRUSTING A linear distribution of thrust per unit length is used for attitude control thrusting as shown in Figure 5. 2. 1. It is assumed, for this analysis, that this distribution is perfectly continuous. From Figure 5. 2. 1, F F dT = () x dx; (-) is the slope of the thrust distribution. T =1 F x2 2 L where T = thrust, F = thrust per unit length at x = L. Therefore, thrust per unit length is proportional to x. That is, the thrust distribution is linear in x. The resultant thrust acting over one-half of the mass driver is given by L 1 T dT: 2 FL. Alternate derivation of resultant thrust' L (F/L)x L 1 T ffdy dx= dy dx = fx dx FL. Now, consider the inertial loading on an infinitesimal element of the mass driver, as shown in Figure 5. 2. 2. We see that, for small 4, y/s = cos ( - 1. Thus, y s=x.. y=x The D'Alembert inertial force (FD) on the element is given by mas s d(FD) = mij dx, where m unit length But, y xO 120

a | (m X L s1. - — v x L -' Figure D. 3 Loading on Mass Driver Due to Attitude Control Maneuvers (F~Z A ~~-M, |I- l2....'l.. m L./3.M(x) o Figure D. 4 Equivalent Loading on One-Half of the Mass Driver 121

Thus, y =x 6= x X) Therefore, d(FD) m X x dx, for small f where, X aangular velocity (') time derivative (")= second time derivative. Thus, the resultant inertial force on the mass driver is given by 2 FD f= d(FD): f m & xdx:= 2 m Xx. Therefore, the D'Alembert reaction per unit length is proportional to x (linear with respect to x). The total reaction over one-half the mass driver's length is L LL FD = Id(FD) = m x dx 2I mi X L. 0 0 Thus, attitude control firing exposes the mass driver to the loading shown in Figure 5. 2. 3. This loading is equivalent to that shown in Figure 5. 2. 4 over one-half the mass driver's length, where: M = (m L3 _ FL) and Xo 2 (m w L - FL) From equilibriu, we have (at section A-A) 1 F. 3 1 2 M(x)= (- mWX + 2(m -L FL)x ~L 21 21 +- (F L m L3) (5. 2. 1) and S(x)=(m FL )x + (FL - m4L ) (5.2.2) 122

F I L F Figure D. 4 Rotation of Mass Driver 123

where m(x), S(x) are the moment and shear respectively. From Figure 5. 2. 4, we see that the applied tangential force (due to thrusting), f, on the element located at x = + L is given by f = F dx = (m dx) aT, where a T = tangential acceleration. But, aT = X L F dx = (m dx) 4 L' F = m L (5.2.3) From Eq. 5.2.3 it is seen that the coefficients of Eqs. 5, Z, 1, 5.2.2 vanish identically. Thus, there are no stresses in the mass driver due to attitude control firing. D. 3 FLEXURAL VIBRATIONAL MODES AND FREQUENCIES OF THE MASS DRIVER STRUCTURE Since the attitude control thrusters are very closely spaced (10. 08 meters) and all fire simultaneously, the mass driver will experience a global force. That is, the mass driver will be induced to vibrate flexurally on a global scale. Thus, it may be modeled as a free beam of small stiffness. The following assumptions are made in this analysis: 1) The entire mass driver can be modeled as a continuous beam (i. e. no concentrated masses) 2) No nuclear waste (or other) payload is launched during attitude control maneuvers. The governing differential equation for the motion of the mass driver is (from Reference 7) 34, 2 EI + m = 0 (5. 3. 1) 124

where E = Young's modulus I = moment of inertia of cross section m= mass/length of mass driver w = transverse (flexural) displacement x = distance from end of mass driver t = time To solve this partial differential equation, the technique of "Separation of Variables" is employed... (x, t) = W(x) T(t), from which are obtained the following equations. 1 * 2 T + w T=0 (53. Z) fill EIW -mw W=O (5.3.3) where o = "natural" vibrational frequencies (') = second time derivation ()"" = 4th x-derivative The solution of Eq. 5. 3. 3 yields the fundamental and harmonic mode shapes. Eq. 5. 3. 3 can be written as: W'l' - 4 W = 0 (5.3.4) where 2 X = mI (5. 3. 4a) The solution to this equation is W(x) = C sinh x + D cosh Xx + E sin x + F cos ax (5. 3. 5) Upon substitution of the boundary conditions into Eq. 5. 3. 5, and the expansion of the determinant of the coefficients of the resulting set of simultaneous equations, we obtain f(Xl )= cos Xt - h, (5. 3. 6) cosh Xi where I = mass driver's length from which the values of M (roots of [f(M ) = 0] are obtained). A plot of f(\t ) = O is shown in Figure 5. 3. 1, from which it is observed that the roots are 125

f(X ) +1 *..1 ~ ~ ~ ~ ~ ~ ~2 2.5w O /1. 5 r 2z Figure D. 3. 1 f(Xi ) vs. Xi 4l (x) Fz (S) L Figure D. 3 2 First and Second Vibrational Modes 126

1 = O, 1. i5r, 2. 5,.... The first root (XI = 0) corresponds to co = 0 (rigid body translation and rotation) and is not of interest here. Thus, the fundamental vibrational frequency is given by X1 = 1. 5Sr 4 (1.5)4 (4= mfrom 5. 3. 4a ~ =(1.5) () E * (15~2I2 2 EI,t)2~ Thus, the fundamental frequency is W1 =22. Zml (5. 3.7) The first harmonic is given by Xi = Z. 5S 2 X- (2. 5)4 ()4= o; = 61.69 E'4 (5.3.8) The mode shapes corresponding to these frequencies are given by x) = [(-. 205)(sinh1. 5 + sin 1.. x + c. and 2,Sirx. 5Snx 2. Six +. c s (X) = [-(sinh 5 + sin ) +cosh 2 + coW Z ] Plots of l1(x), +2(s) appear in Figure 5. 3. 2. In general, the ends of the mass driver will contain nuclear waste payloads while the attitude control thrusters are firing. Thus, the vibrational frequencies and modes must be recalculated in the case of concentrated masses at the ends. The resulting equation for finding the values of XI (roots of f(M1 ) is 127

___ M+M2 Ml ] -(XE ) sin X coshX [-. f(U ):f (),,inh C ~os, Xi[- m l...]ml -Z (X)Zsin sinh [( +cos X coshXl - (5. 39) (mll) where M1, M are the masses of the payloads at the two ends of the mass driver respec'tively. Note that Eq. 5. 3. 9 reduces to the continuous mass (Eq. 5. 3. 6) case when M1, M2= 0. Eq. 5. 3. 9 must be solved graphically with M1, M2 specified. The crew living quarters located at x = I /2 represents another concentrated mass. An exact solution to this problem involves the expansion of an 8 x 8 determinant. It is therefore desirable to use an energy method to obtain an approximate solution in this case. However, none of these concentrated masses will alter the fact that the bivrational frequencies are very small (large periods) due to the influence of 12 in the denominator of the frequency expressions. Thus, attitude control thrusting frequencies and tension cable forcing frequencies will not cause the mass driver to resonate. D. 4 ANALYSIS OF OUTER RINGS (see Reference 3) It is assumed that the outer rings may be modeled as four separate circular arcs, each built-in at the points where they are welded to the mass driver tubes, as shown in Figure 5. 4. 1. From Reference 3, the slope of the arc at the point of the applied load is given by jZ Wsr 1 - sin- TA d= E- cos[ I r+ r tan) a co a + sin a'O ZEI xcCos J, +r -(2 ~Wr/) aCosJ ZCI [Wr co -sin s-n + cos tan sin a - co (5. 4. 128

a b,,,-/#g, IIr A \ B / /A~~.TA Cross Section W of Arc: j 1.06 m k.l. 5m T Figure D4.1 Representation of Circular Arc Section of Outer Ring 129

Eq. 5. 4. 1 accounts for the reaction forces at the supports. Also, W = applied force (related to cable tension) y = deflection of arc r = radius of arc 8 = coordinate location on arc 4 = (or - angle subtended)/2 a = (r - 20/2 TA= reaction moment at arc support C = shear modulus of elasticity J = polar moment of inertia of cross-section (rectangular) E = Young's modulus I = moment of inertia (2nd moment of area) or (rectangular) cross 8 -section In this case, 4. 448 N W = z (1000 lbf) ( ) cos 45 6290.4N ZUt l 1 16f 2 cables per design limit angle between cables attachment point for cable tension and mass driver Also, r, 5308 m = 450 =.785 rad a =450 =.785rad E = 10,400,000 psi = 7. 171 x 1010 N/m2 (Al 7075-T6) C E/2(1 +v) where v = Poisson's ratio =.33 (Al 7075-T6).', C 3,910, 000 psi = 2. 696 x 1010 N/m2 From symmetry, the reaction forces at A, B are given by RA = RB = W/2 (5. 4.2) The moment about A, B is given by MA = MB = Z cos W (1 - sin ))+ TA tan (5.4.3) From symmetry, dy/dO (Eq. 5. 4. 1) must be zero. Therefore, for a given arc thickness, TA can be found. Thus, MA is known and the displacement at the point of applied load is given by 130

2 Y= 2EI [MA asina- (RAr - TA) (sina- acosa)] 2 + 2rCJ [(TA - RAr)(sin a- a cos a)+ 2RAr (a - sin a) + MA (atsin a+ 2 cos a - 2)] (5.4.4) Now, a rectangular cross-section arc is used (Figure 5. 4. 1) bt3. I(= Iy)= where b = width of cross-section t = thickness of cross-section and J=bt3 tb3 1 3 b3 J —Iy + Iz =- (bt +tb These values of I, J are substituted into Eq. 5. 4. 1 for b =. 15 meters. This yields TA as a function of t. From Eq. 5. 4. 3, we have MA as a function of t. Substitution into Eq. 5. 4. 4 yields y (displacement) as a function of t. The following FORTRAN program computer this displacement for various values of t. It was decided to use t =. 06 meters because this results in a very small displacement (y =. 2025 millimeters) for cable tension of 1000 lbf (4448 N). Also, it is desirable to use this value of t to provide a firm support to resist twisting induced by perturbations of the tension cable support rods. The cross-sectional area of each ring is therefore )2 2 rr(.5308 m +.06 m) - i(. 5308 m) =.2114 m. The mass of each ring is (2800 kg/m3)(. 2114 m ( 15 m) = 88. 8 kg. Now, there are 628 rings.,. total outer ring mass = 55,758.9 kg =1.2267 x 105 lbm. 131

The inner cylinders (which contain the storage batteries, as indicated in Figure 5. 1) are welded to the mass driver tubes and thus impart extra torsional rigidity to the mass driver. The cylinders have an outer radius of.2748 meters, a thickness of. 0025 meters, and a length of 1. 272 meters. Therefore, the solid cylinder volume is = 2n (. 2748 m)(. 0025 m)(l. 272 m) =.0055 m3. The cylinders are constructed of 7075-T6 Aluminum (density 2800 kg/m3)... each cylinder has a mass of 15. 37 kg. There are 628 cylinders.,', the total cylinder mass = 9,655 kg = 21,240.5 1bm. D. 5 MAXIMUM PITCH RATE ALLOWED FOR ATTITUDE CONTROL MANEUVERS From Figure 5. 2. 4, the outward radial force which is "felt" by an element dx is given by df = mwZ x dx (5.5.1) This follows from the centripetal force relation (velocity)2 f = (mass (radius) and velocity = (angular rate) (radius) Thus, the total outward radial force exerted by one-half of the mass driver is given by f= m x dx= mA x 1 (5. 5.2) o (m = mass/unit length, X = angular velocity, I = mass driver's length). 132

Therefore, the total tension, T, felt at the mass driver's midpoint is 2 2 T =f=m 212 (5.5.3) We wish to ensure that T does not exceed the limit of elastic proportionality (the mass driver does not undergo permanent deformation) with an imposed safety factor of 1. 2. Thus, 1. 2T= as A (5. 5. 4) where a'y = yield strength A = total solid cross-sectional area of mass driver tubes (assumed to withstand all tension). From Section. 1: A = 4ir [(a + t)2 - a] =.1294 mZ. Also, - 4. 4814 x 108 N/m (7075-T6 Al) ys and I = 6320 m. from Eq. 5. 5..4, 2 2 y A. max 1.2m12 * X = 1. 0/Io [i] a: kmax meter D. 6 THERMAL EFFECTS If the mass driver structure is not rotated about its longitudinal axis, thermal gradients will induce a bending moment which acts over the mass driver's length. To determine this moment it is necessary to obtain the temperature distribution over the mass driver's cross-section. Due to the rather complex geometry of the mass driver's cross-section (Figure 5. 2), the problem of obtaining this temperature distribution becomes a very involved exercise in heat transfer. The problem is of such complexity that a meaningful analytical result is virtually impossible to obtain. 133

Even if an accurate model of this temperature distribution were available, it would need to be continually revised for each sunlit point in the mass driver's orbit because of the constantly changing angle between the mass driver's longitudinal axis and the incoming solar radiation. In view of these difficulties, no quantitative result was obtained for this time dependent temperature distribution. However, the equations which lead to the thermally induced bending moment are developed below. It is assumed that the tension cables described elsewhere (5. 6) in this report will counteract the bending moment (as well as the moment resulting from gravitational effects) and maintain the mass driver in a straight configuration. (It should be noted that the same thermal irregularities will incude bending moments in the tension cable support rods. This would have an adverse effect on the stability analysis used in the design of these rods. However, it is assumed that this effect is sufficiently small to justify its exclusion in design calculations. ) If the deflection components are w, v, we have d x2 E ( Iy z I- Zyz ) thermally induced curvatures d2 I I Tz I\z ~dxz v rz - Iz vZ Since the mass driver cross-section has an axis of symmetry (Figure 5. 2), the product of inertia (Iyz) vanishes. d. dw _ dx2 EI y and dZ v MTz dx2 IE where I = moments of inertia about the cross-sections bending axes y,z MT = thermally induced moments about the bending axes E = Young's modulus 134

MTz - EI x d2w MTy -Y dxZ From Reference 10, MTy = ff [a (E T) z] dy dz where a = coefficient of thermal expansion T (= T(y, z)) = temperature distribution over the cross-section y, z = centroidal axes of the cross-section and MTz ff [(a (Ty)] dy dz. To find MT MTz it is necessary to determined T(y, z). Furthermore, aE Ty, aE Tz must be integrable functions if one is to obtain an analytical solution. Otherwise, one must resort to numerical methods. Following this procedure, the bending moments MTy and MTz are known functions of x (longitudinal mass driver coordinate). These moments can be superimposed on the gravitational moment (see Apppendix Section 11) to give the total moment (which must be exerted by the tension cable-support rod assembly in the opposite direction) acting on the mass driver. D. 7 OPTIMIZATION OF PACKAGE SIZE I. Small nuclear waste containers Dimensions r (= radius) = 2. 34 cm (. 921 in) I (= length) = 14. 43 cm (5. 68 in) m (= loaded mass) = 1 kg (2.2 lbm) Material Stainless steel, p (= density) = 8. 0 grms/cm3 135

A. To determine the thickness, t, of the container, it is assumed that the container may be modeled as a thin-walled pressure vessel. From Figure 5.7. 1, the sume of the forces in the vertical direction is given by iTr F = - tl + r rPi sin 0dO= O 0 where P is the interval pressure arising from the acceleration of the nuclear material during launch. It is assumed that the pressure is uniform and equal to that which occurs at the bottom of the container during launch. Thus, the design will be conservative, since this pressure actually decreases elsewhere in the container. Zo 2 tl = f r (Ma/wrr) 1 sin O dO 0 where M = mass of waste in each container (= 1 kg) and a = space shuttle's maximum acceleration ('Z29. 4 m/sec ) Mai 2 2- ti =f -M sin 0dO c' rr = _ Ma1 [cos 0] rr 0 2Mal rr ~ Ma I andc r and Ma c wrt From Reference 1, c = Zo1 (see Figure 5.7. 1) Tc will be the largest stress in the container we wish to ensure that a-c does not exceed the yield strength of stainless steel. 136

Figure D. 7. 1 Stresses on Small Cylindrical Container 137

For a safety factor of 1. 2, we have 1. 2 c = Ty8 (c(rys yield strength of sttinlesi steel 28957 x 10 N/m ). Ma,, 1. -' = w rrt ys 1.2 Ma ys -6 t = 1.66x 10 meters. B. To find the mass of each container, 2 m = p {(2Zrr + irrl )t}.327 grams = 3. 27 x 104 kg (see Figure 5. 5) II. Numerical example of package size optimization for the large cannisters. We know that the mass (loaded) of each small container is 1 kg. Now, we assume a ratio of package weight to the weight of the contents for the large cannister: OT package assume, contents - oT contents Now, the total (cannister + waste) payload is conservatively] restricted to weight 40, 000 lbs (18181. 818 kg)., total weight = wT pkg + wT contents = 4 (wT contents) w OT contents = 4545. 45 kg and each container weighs 1 kg, so there are 4545 containers. A. Assuming 100%o packing efficiency (n = 1), 4545 kg = p V = (4 gmns/cm3) (wRi L) where p = density of nuclear material V = interior volume of cannister I = inner radius of cannister) (4 gmins/cm3)()(ZRI3?), for L = ZR 138

RI = 56. 55 cm (for wT package/wT contents = 3). B. Assuming 801% packing efficiency (n =. 8), (n) w (R1)= w(RI) R= (n) /2 (5.7.1)', for n = 8, R1 = 63. 225 cm where R1 = the new estimate of the cannister's inner radius. Now, the containers are packaged in concentric rings, as shown in Figure 5.7. 2. From the figure, R1 - rc is the radial distance to the center of the outermost ring, and circumference = 2w (R1 - rc) and circumference circuferenc = number of containers in each ring. Zrc Thus, for n =.8, number containers in outer ring 2w(63. 275 cm - 2. 34 cm) 2 (2. 34 cm) = 81.742 = 81 containers in the outer ring. number containers in the next innermost ring = 2r [63. 225 cm - 3(2. 34 cm)] 2 (2. 34 cm) = 75. 459 = 75 containers. So, in general (for a given n); number containers w (Ri rIr C) = --'...rounded down to (5.7. 2) per ring r c an integer value 139

where R. = inner radius of cannister (a function of n); i = 1, 2, 3,... r = radius of small container C = (2N - 1), for the Nth ring, I = 3 for the 2nd ring, etc.) Now, for n =.8, wT package/cT contents = 3, we have (from Eq. 5.7.2); I No. containers 1 81 3 75 5 69 7 62 9 56 11 50 13 44 15 37 17 31 19 25 21 18 23 12 25 6 566 containers per shelf There are (wT package/w contents = 3) 4545 containers and 566 containers per shelf. Therefore, wehave 8. 03 = 9 shelves requires. Now, to determine whether or not n =.8 is realistic, we compare the total container height [= (No. of shelves) (height of each container)] with the total inner height of the large cannister:,', total container height = (9) (14. 43 cm) = 129. 87 cm cannister height (L = 2R) = (2) (63. 275 cm) = 126.45 cm. We see that it is not possible to fit all the containers in the cannister for n =.8. Indeed, we cannot fit the shelves either (see Section 8 of Appendix). C. So, we will now assume a decreased packing efficiency. Assume X T package (T contents again) from Eq. 5.7.1, R2 = inner radius of cannister = 65. 298 cm. 140

from Eq. 5.7.2, I No. container s 1 84 3 78 5 71 7 65 9 59 11 53 13 46 15 40 17 34 19 27 21 21 23 15 25 9 27 2 there are 603 containers per shelf' there are 8 shelves.,', total container height = (8 shelves) (14.43 cm/shelf) = 115. 44 cm cannister height = 2 (65. 298 cm) = 130. 596 cm. This allows a clearance of 1. 89 cm per shelf, which is insufficient (see Section 8 of the Appendix). D. For the 5th iteration, we obtain (for n =. 68, and (w package/c contents 3); from Eq. 5.7.1, R5 = 68.58 cm and from Eq. 5.7.2 I No. container s 1 88 3 82 5 76 7 70 9 63 11 57 13 51 15 44 17 38 19 32 21 26 23 19 25 13 27 7' there are 666 containers per shelf. 141

Again, there are (for 4T package/w contents = 3) 4545 containers.. there are 4666 7 shelves 666 and, total container height = (7 shelves) (14. 43 cm/shelf) = 101. 01 cm cannister height = 2 (68. 58 cm) = 137. 16 cm which gives 5.16 cm/shelf (which is sufficient). E. Calculation of actual package weight for R = 68. 58 cm. 1) Tungsten layer (5 cm thick) R ( radius) ~ 68.58 cm + 2.5 cm = 71.08 cm surface area = 2w R L + 2 vR2 (but L = 2R) =6irR2 2 9. 523x 10 cm2 0 4 2 mass = (p)(V) = (19.3 gms/cm3)(9. 523 x 10 cm2)(5 cm) 9.19 x 10~ gms 2) Lithium hydride layer (12 cm thick) R = (68. 58 + 5 + 6) cm = 79. 58 cm mass = (.775 gm/cm3)(6i)(79. 58 cm)2(12 cm) = 1. 110 x 106 gns. 3) Stainless steel shell (. 5 cm thick, from Section 9) R = 68.58 + 5 + 12 +.25 = 85.83 cm mass = (8. 0 gms/cm3) (6Tr)(85. 83 cm)2(. 5 cm) = 5. 554 x 105 ginms. 4).'. total cannister (package) mass (excluding shelves) = 1.086x 10 gms = l.086x 104 kg. Again, the mass of the contents is (4545 containers) (1 kg/container) = 4545 kg. the ratio of package weight to contents weight is 1. 086 x 104 A.... = 2.39. 4545 142

F. Now, reiterate the entire process, using an estimated weight ratio of 2. 39. This gives a smaller'true' weight ratio, so continue the iterations using each preceding iteration's'true' ratio, until: G. OT package/wT contents = 1. 88' T package + WT contents = 2. 88 OT contents * 2. 88 wT contents = 18181.81kg T contents = 6313 kg. Again, each container weighs 1 kg, so there are 6313 containers. H. Assuming n = 1. 0, the inside volume of the cannister is V = R~3 = mass 6.13 x 10 ms density 4. 0 gms/cm RI. Rt (first estimate of cannister's inner radius) = 63. 15 cm. I. For n =.65, RI = 78. 33 cm, and from Eq. 5. 7.2, I No. containers 1 102 3 95.. there are 882 containers/shelf. 5 89 7 83 for this efficiency, there are 6174 9 76 containers in total. 11 70 6174 13 64.. we have 8 = 7 shelves 15 58 17 51 17 45 and, total container height = 21 39 (7 shelves)(14. 43 cm/shelf) = 100. 38 cm 21 39 23 32 25 26 cannister height = 2RI = 156. 66 cm. 27 20 29 14 This gives 8. 04 cm/shelf. 31 7 33 1 143

J. Real package weight (for R = 78. 33 cm) 1) Tungsten: mass = (19.3 gms/cm3)(6r)(80. 83 cm)2(5 cm) = 1. 188 x 107 ginms. 2) Lithium hydride: mass = (.775 gms/cm3 )(6w)(89. 33 cm)2(12 cm) = 1. 399 x 106 gins. 3) Stainless steel shell: mass = (8. 0 gms/cm )(6a)(95. 58 cm)2(. 5 cm) = 6.888 x 105 gms. 4),'. total package mass = 1. 397 x 107 gms. 5) The shelves (see Section 8) have the following dimensions: - R (= radius) = 78.33 cm - mass resting on each shelf = 882 kg (882 containers) - thickness (Section 8) =. 507 cm - mass of each shelf = 77.5 kg - total mass of shelves = (7 shelves) (77. 5 kg/shelf) =5.425 x 105 gms = 542. 5 kg. 6) Ibtal mass inside package = oT contents + wcT shelves 6. 174 x 106 g + 5. 424 x 105 g =6.717 x 10 gmins Therefore, the weight ratio = 1. 90, which is very close to the estimated value of 1. 88. So, this is the optimum design. D. 8 ANALYSIS OF THE SHELVES IN THE NUCLEAR WASTE CANNISTER (see Reference 8) The small payload containers will be resting on shelves in the large cannister. We may assume that these shelves can be modeled as thin circular plates which are'built-in' at their edges, as shown in Figure 5. 8. 1. 144

We also assume that the weight of the cans can be modeled as a uniformly distributed load, as shown in Figure 5. 8. 1. Thus, the load per unit area (a function of radial distance for circularly symmetric plate and loading) is given by (r) = ~Z [M(y'max )] = qo, a constant (5. 8. 1) where M = total mass on plate (mass of containers which are resting on it) Y max = maximum shuttle acceleration along its longitudinal axis max (= 3g's, or 29.4 in/sec2) The governing differential equation for the transverse deflection of the plate is: D V4 w(r) = q(r) (5.8.2) where D = flexural rigidity of the plate = Eh3/12(1 -v2) E = Young's modulus h = plate thickness V = Pois88son' ratio p4 ( ) = biharmonic operator X (r) = plate deflection (a function of radial distance) q(r) = applied load/unit area. For axisymmetric geometry and loading, and statically determinate plates, Eq. 5. 8. 2 reduces to (in polar coordinates) d 1 d dw Dr [r dr (r )] = - Q(r) where r ( 1 I q(r) g dt 0 where = variable of integration. The solution is (r) = D I3(r) + Br + r + e (5. 8. 3) 0 (c must be zero due to the singularity at r = O. This is the'regularity condition' ). 145

90;r Walls of Tungsten r = 0 r = R Layer Figure D. 8. 1 Model of Cannister Shelves (Edge View) Mr? Me Mr(r) (l+v)R2 R/2 k~ 8 q R 8 Me(r) Figure D. 8. 2 Moment Distribution in Shelf as a Function of Radius 146

~.(r)= -I 3(r)+ Br2 + E I3(r) is determined from the following sequence: r rrqo o' o O r 2 b) Il(r)-f Q(4)dt = - o ~ ] qoIr= o oq o d) I(r) f Id () )d4 4 16 o 0 0 0 O O (r)= 64D r4 +Br2 +E (5.8. 3a) We have two unknowns (B, E). Therefore, we need two boundary conditions to completely specify the problem. In this case, the boundary conditions are w(r)l = dw =0 R dr r= - R Thus, Eq. 5.8.3a becomes w(r)= 64D (r4 - 2R r + R) (5. 8. 4) We wish to limit the stress on the plate so that it will deform elastically (no permanent deformation). To establish the appropriate design, the Von Mises yield criterion is used (Reference 9) which states (for plane stress): 2 2 2 1' + 2 2 = a+ 2 for yield (5. 8. 5) 2 y W1' Og are the principal stresses and ays is the yield stress. In this case, crl = r (stress in radial direction) r2 = "0 (stress in circumferential direction). 147

Thus Eq. 5. 8. 5 becomes 2 2 2 r r e ys (5. 8.5a) Thus r, must be determined: Mr zrax r I where Mr = moment in the radial direction Zmax = h/2 I = h3/12. 6 Mr' 0r h Now Mr = Dd' + -r _qo 2 qo z 16 (3 + v)r + - (1 + v)R2 from Eq. 5. 8. 4. 6 M16 2. e= - Me = moment in circumferential direction and 2 r dr = 16 (1 + v)R -(1 + 3v)r2], from Eq. 5. 8. 4 Mr. M0 are plotted in Figure 5. 8. 2. From the figure, we see that the maximum biaxial (r, 0) stress state occurs either at r = 0 or at r = R because Mr, M0 have their extreme values atr = 0, r = R. Consider r = 0: 6 (1 + v)Rz /h2 =. 375 qo (1 + v)R2/h2 = -6 [ G(1+ v)R2 ]/hZ -.375 qo (1 + v)R/h. Thus, at r = O, ar = o' Consider r = R: 0*1, = (...~S ) =.....) 75R2/h2 6 qo vR2 R2 2 e= -'(- 8 )=.75%0v /hZ Thus, at r = R, 0r f c0 (they differ by a factor of v). 148

Now, at r = 0, the Von Mises criterion becomes (from Eq. 5. 8. 5a) r (= ) = )ys R2.375 (1 +v) ( ) =s Now, at r = R, the criterion becomes (from Eq. 5. 8. 5a),.75 qo (R/h)2 (2 v + 1)/2 =ys Stainless steel (347) is used (v =. 31). Therefore, the biaxial stress at r = 0 gives.49125qo (h)2 s' and, at r = R:.589575 qo (y.) = y' Therefore, the plate would yield at r = R. To prevent yielding, a safety factor of 1. 2 is used:.Z 12(.589575)% () =ys For stainless steel, Tys = 33,000 lbf/in2 = 2.275 x 108 N/m2 and p (density) = 7930 kg/m3. h = 1. 2 (. 589575) qo RI/ry But, = M (' max).. h = 1.7059 x 10'4 S/i meters, where [M] = kg. From Section 7, the mass on each shelf is 882 kg.'. h =. 506 cm to avoid yielding. 149

A value of h _. 507 cm is chosen. The corresponding deflection at r = 0 (maximum deflection) is given by Eq. 5. 8. 4 and is found to be only 3. 18 for R = 78. 33 cm. This is compati le with the design developed in Section 7. Thus, each shelf has a mass of wR hp = 77. 5 kg (170. 5 lbs). D. 9 ANALYSIS OF CANNISTER OUTER SHELL (see Reference 5) We wish to prevent elastic buckling of the stainless steel outer cylinder. This structure can be modeled as a unity aspect ratio (length/diameter = 1) circularly cylindrical shell. The appropriate expression for the critical load depends upon the magnitudes of the terms: 1) )2 and 2) 2a 3(1 - where a = mean cylinder radius I = cylinder's length t = wall thickness v Poisson's ratio. If 1) is the greater quantity, we may use the "Euler-strip" expression: 2 2 cr E= t.~2 [Note: for longer shells the buckling cr 12(1 - )1 2 stress is independent of 1.] where E = Young's modulus'cr = critical (buckling) stress. If 2) is larger, Donnell's empirical relation is used:.6(t )-10-7 a cr E 1 +.004 ( ) YP where'yp = yield stress. The outer shell is as shown in Figure 5. 9. 1. 150

The solid volume is: Vol. - Z atl + 2ra2 t = 2rat(l +a) But I = 2a.. Vol. - 6Ta t It is assumed that the shell is rigidly supported at its base, y = 0. Thus, the total applied stress will be rtot = +rc + b where GC = compressive axial stress ob = axial stress due to bending Now, or m(y )/2Zrat Now c max where Y max is the shuttle's maximum acceleration along its longitudinal axis, and m is the mass of the load acting on the shell. (= mass of shell contents) =b = where M = maximum bending moment I = moment of inertia (2nd moment of area) of shell's cross - section and Cb = mg(l /2)a/I, where g = acceleration of gravity. (This corresponds to horizontal flight (which gives the maximum M)). Calculation of I: 2w a+t/2 Ifz dA f r3 sin 0dr dO A o a-t/2 (algebra steps deleted) (4a3t+ at3) 151

f i Figure I) 9. 1 Diagram of Cannister's Outer Shell. (Right Circular Cylder with I /2a= 1) z i t~t LI Fa Figure D. 9. 2 Diagram for Calculating Moment of Inertia of Shell CrossSection. 152

mg (I /2)a - 2mn 1. ~b = /4a3 t+at3 r(4 a2 t+t3 =/m a 2+ mg tot 2wat w(4a2t+t3) m[(=' )(4a2+t2) + 4agl ] Mtot (neglecting the mass of the shell). Now, consider some values of a, t (assume v =.3) IA a t value of value of Appropriate _ _ 1).2) formula 144" 72".5" 2. 47 7 5. 8 Donnell' s Clearly, for typical shell dimensions, Donnell's is the appropriate formula. Again, Donnell's formula is: = E 6(t/a) - 10" (a/t) cr 1+. 004 (E/oyp) A safety factor of 1. 2 is used. Therefore, if the total weight of the shell contents is 40, 000 lbs (18181. 82 kg), we wish to design the shell to withstand the effects caused by, (1. 2)(18181. 82 kg) = 21,818. 2 kg (1495. 4 slugs) Now, r[ (max)(4a2+t2)+ 4agl ~tot 2 a t (4 a2 +t2) and m = 1495. 4 slugs, for design purposes. Our design criterion is given by the equation [(ym )(4a +t )=4agl].6(t/a)- 107(a/t).. m E- (at) 2irat(4a +t ) 1+.004 (E/ryp) 153

AN TERMINAL SYSTEM FORTRAN G(21.8) MAIN 03-24-79 17:11:53 PAGE C THIS PROGRA4 USES DONNELL'S EOUATTON FOR THE BJC(LING STRESS OF A 1.000 C CIRC:JLARLY SY4METRIC CYLINnRICAL SHELL. FRCM THIS THE SHELL THICKNESS 2.000 C CAN BE FWNO FOR GIVEN PARAMETERS. THE OAAPYETERS ARE E(LBS/SQ.oI.), 3.000 C YP(LBS/SQ. IN.), A(INo, T(INo4, H(IN.)I DENS(G4S/CC)I SMASSISLUGS), 4.t0) C HEFT(SLUG) 4t.000 1 READ(5,Il00,EN0D999) EtYPDENSA,T,H, TMAX 5.000 WRITE(6,200 ) EYPtDENS,AH,ITMAX 6. 0O'J r)0 2 I=1,ITMAX 7.000 HEFT=1 t2*E*1.6*T/A-1.E07*A/T )/ ( 1.+*004*E/YP ))/((11 60*(4*4**2 8. 000 1+T**2)+1545. 6*A*H ) 2* 3. 14159*A*T*(4*A ** T*2) I 9.000 IF(HEFToGE.14954o22 13 TD 3 1 0000 T=T+. 001 11000 2 CONTINUE 12*000 3 S MAS S=2*3. 141599 A*T* H+A )*DENS*2 o54**3/ 1030.I / 1 459 13 003 WRITE(6t201) ItHEFTtTSMASS 14.00) GO TO 1 15.000 999 STOP 16. 000 100 FORMAT(FIO. ItFIOO, F5.2tF5S2,F5.2,F5.2,15) 17.9o0) 230 FORMAt (2E, F 10* OI/'YP' =,FO1*/lfDENS =',F5.2/.18000 1'A =. iF5o2/1H =,F5o2/' IlTMX = tI5) 19,000 2'1 FOPMAT('0i1'= 5/'HEFT I',FlO.4/'T r'F5.3/ 20.000 un L'SMASS = t,F10.4) 21.000 END 22. 00:)

from which the shell thickness, t, may be determined for a given material. Note that this expression yields a conservative design because the strengthening effect of the cylinder's end plates has been neglected. Also, the value of wtot is not likely to be realized in service. Also, this analysis assumes that the shell carries the entire load of its contents axially (the axial force is transmitted directly to the shell). This axial force, it is assumed, can be replaced by an applied load at the ends of the shell. This leads to a conservative result because the actual load is distributed over the shell's length and has its maximum at the bottom of the shell (the design point). Once t (thickness) is found from Eq. 5.9. 1, the shell mass can be determined from shell mass = p (6wa2t), p = density of material used. The values of't' and shell mass are computed for various values of'a' (cylinder radius) and for various materials by the following FORTRAN program. To yield a conservative design, a stainless steel shell,. 5 cm thick is used (this value is incorporated into Section 7's design)..10 DESIGN OF SUPPORT STRUTS FOR THE MASS DRIVER TUBES The distance between mass driver tubes is. 3136 meters. From Figure 5. 10.1, the strut length is given by L = (. 3136 m) sin 45~ =.4435 m and F = (mass of accelerating payload) (acceleration of payload) = (2. 13 kg)(9, 800 m/sec ) = 2. 0874 x 104 Newtons and 2. 0874 x 104 N FB (axial force on strut) cos 450 = 2. 9516 x 104 N. 155

The buckling load of the strut, Pcr, is Pcr = El (v/L)2 For a given cross-sectional area (and hence, mass) of the strut, a square cross-section beam is desirable because it results in a relatively high buckling load. For a safety factor = 1. 2, we have Pcr= EI(r2/b2) Eb4 w2 1.2 (12)(1.2)LZ where b = length of a side of the strut's corss section. Thus, for Aluminum 7075-T6 (E = 7.17 x 1010 N/m2 ) struts, b = 1. 854 x 10-2 meters and each strut has a mass of (2.7 x 103 kg/m3)(1. 854 x 10-2 m)2(. 4435 m) =.4116 kg. For stainless steel (E = 2. 086 x 1011 N/m2) struts, b = 1.42 x 10'2 m and each strut has a mass of (8. 0 x 103 kg/m3)(1. 42 x 10'2 ) (. 4435 m) =.7 54 kg. Now, there are four struts for every.3136 meters of mass driver length, and the mass driver is 6,320 meters long. Therefore, there are.3t36 t) (6320 m) = 8. 0612 x 104 struts. Thus, for Aluminurn, the total strut mass is (8. 0612 x 104 struts)(. 4116 kg/strut) = 3. 318 x 104 kg (7.3x104 1bm) For stainless stell, the total strut mass is (8. 0612 x 104 struts)(. 7154 kg/strut) = 5. 767 x 104 kg. Thus, the Aluminum struts result in a more efficient design. 156

Figure D 10. 1 / K,//R+Ar EARTH CENTER Figure D. 11. 1 Geometry of Orbiting Mass Driver.Z L, Figure D. 12.1 I-Beam Cross-Section 157

D. 11 INDUCED BENDING MOMENT ON ORBITING MASS DRIVER The centripetal force, Fc, acting on a body is given by Fa=mv /R where m = mass of body V = tangential velocity of body R = radius of circular trajectory The centripetal force acting on an arbitrary element at a distance x from the mass driver's center of mass is given by (see Figure 5. 11. 1) d F = mdx (V + AV) R + AR where m = mass per unit length Vc = the circular velocity of the mass driver's e. g. = where u = a gravitational constant. dv dr 3 /Z.', AV = --- AR 3/2 R / and R= (R2 + x2 )1/2 r (Pythagorean theorem).. dFc = nmdx R~ i W (R'- + x2)1Z/ 2 -R 2 /R 2 xz}2 2 1/2 c23/2 cdF 221/2 12 21/2 x m Vc +32R [(R + x) R] }/(R +x)5.. Eq. 5. 11. 2 gives the loading distribution on the mass driver and is equal to the 2nd x-derivative off the bending moment distribution, which is the desired quantity. 158

m = mass/length of the mass driver Vc ='local' circular velocity -'7.7134 km/sec u = gravitational parameter - 3. 986032 km3/secZ R = distance from the center of the earth to the mass driver = 6700 kmn x = distance to any section of the mass driver from the mass driver's c. g. If we integrate Eq. 5. 11. 2 twice and apply the "free-beam" boundary conditions to determine the constants of integration, we obtain the bending moment, M(x). M(x) 59. 1168 m x In (x + xZ )- +R=Z +ZR ] 5 X2 +(5.5981 x 10 )m (-) -11 1 +(1.32 x 10 )m[(X2 + R) 2 + 2 [xln (x + xZ + R) -xZ + R - 520. 842 mx + 394438. 157 m (5.11.3) where [M(x)] = kilonewtons - kilometers [x] = kilometers [ R] = kilometers [ml = kilograms/kilometer. This is the induced bending moment which must be counter-acted by the tension-cable support-rod assembly..P12 ANALYSIS OF TENSION CABLE - SUPPORT ROD SYSTEM 1) Tension cables: The axial stress, ax, in the cables is given by T x A where T = tension in cable A = cable's cross sectional area. 159

To prevent yielding of the cable, we wish to ensure that the axial stress does not exceed the yield stress (with a safety factor of 1. 2) 1. Zrx (1.2) T/A = ys where ys = yield stress. A= 1. T/ar (5.12.1) ~ys The length, L, of the cable is given by L = 1 /cos 9 where I = length of support rod 9 = angle between support rod and cable. Thus, the mass, M, of each cable is given by M = (LA) p where p = the density of the cable material (stainless steel). 2) Support rods: The critical (buckling)load of the support rods depends upon cable tension as follows: Pcr = 2 Tcos e (5.12. 2) where Pcr = buckling load T = maximum allowable cable tension From beam theory, we find the general expression for a cantilever beam-colum (support rod) to be Pcr T-'T' EI where E = Young's modulus I = 2nd moment of area (moment.', Pcr - 2.47 El2 of inertia) of cross-section.. Pcr 2. 47 E I /1 Thus, for a safety factor = 1. 2, (5. 12. 3) (E)(2, 47) It was determined that a rod with an I-shaped cross section provides a large moment of inertia in relation to its weight. Thus, the I-section is used for the support rods (see Figure 5. 12. 1). 160

From the parallel axis theorem, we obtain I =.016734 a4 (5. 12.4) z I =.1149 a4 where a is the dimension shown Y in the figure and y, z are the centroidal axes. Since Ik is smaller than IY, it is necessary to use IZ in Eq. 5. 12. 3 to determine'a', because the rod will seek to buckle about the z-axis, as this mode corresponds to a smaller buckling force. Now, it is assumed that a maximum cable tension of 1000 lbf (4448 N) is sufficient to counteract the moment outlined in the previous section. Thus, from Eq. 5. 12. 1 we can determine the cable's cross-sectional area and hence its mass. From Eq. 5. 12. 2 we have the buckling load and from Eqs. 5. 12. 3 and 5. 12. 4 we have the rod's dimensions and hence its mass (the length is known, as explained in Section 5. 6). The following FORTRAN program incorporates these equations to determine, ultimately, the most weight efficient combination of materials, cross-sectional shapes, etc. The results are given in Section 5. 6. D. 13 MASS-DRIVER TEMPERATURE CALCULATIONS Consider the energy-balance equation: rate of energy absorbed + internal power dissipation = rate at which a body radiates energy. or a AsA iq + Fas Aaq ia + F Ae e + P= YE A(surface) (5.13.1) where P = internal power dissipation = 0 by assumption. ai = solar absorption of polished aluminum =. 20 e - emissivity of polished aluminum =. 04 As = mass driver's approximate projected surface area (toward sun) = 3840 mz Ae = mass driver's2estimated projected surface area (toward earth) 3840 m A= estimated surface area of mass driver = 12063.7 m2 (surface) q= rate of solar flux per unit area = 1396 watts/m2 161

SUPPORT ROD AND TENSION CABLE PROGRAM REAL MOD, MOI, LEN DO 500 I = 1, 16 READ (5, 1000) LEN, TEN, BT CBLN = SQRT (2*(LEN**2)) MOD = 71700000000.0 YLDST = 289600000. 0 AREA = 1. 2* TEN/YLDST CBMS = CBLN*AREA*7930 PCR = 2*TEN*LEN/CBLN MOI = PCR*LEN**2 / (2. 96*MOD) IF(BT. EQ. 1)GO TO 2 IF(BT. EQ. 2)GO TO 3 2 STSD=SQRT(SQRT( 1 2*MOI)) STMS=STSD**2 *LEN*2800 GO TO 4 3 SIB=SQRT(SQRT(MOI/. 0167 34)) STMS=. 28*SIB**2*LEN*2800 4 WRITE(6, 2000)BT, STMS, CBMS 1000 FORMAT(F5. 2, F10. 2, 2) 2000 FORMAT(IZ, 2F10. 2) 500 CONTINUE END SUPPORT ROD AND TENSION CABLE PROGRAM PROGRAM TERMINOLOGY MOD= ELASTICITY MODULUS (ALUMINUM) MOI= MOMENT OF INERTIA LEN=DISTANCE BETWEEN STRUTS TEN= TENSION IN CABLES BT=BEAM TYPE 1 = SQUARE, 2 = I-BEAM CBLN=CABLE LENGTH YLDST= YIELD STRENGTH AREA= CROSS-SECTIONAL AREA OF CABLE CBMS=MASS OF CABLE PCR=CRITICAL BUCKLING LOAD STSD=SQUARE STRUT DI MENSION STMS= MASS OF STRUT SIB=I-BEAM DIMENSION 162

4 = rate of planetary flux per unit area = 250 watts//m q frate of albedo flux per unit area = 502. 6 watts/m2 a = average albedo constant for earth =. 36 F = orbit altitude factor =. 8854 Y = Boltzman's constant = 5. 67 x 10-8 watts/m2(~K)4. From Eq. 5.13. 1, the mass driver's surface temperature is: j 1/4 5.13. 2 sDface Y f A (surface) J From Eq. 5. 13. 2, the surface temperatures at positions 1, 2, 3, 4 in Figure 5. 8 are Surface Temp. ~C OF T] 206.35 403.43 T2 161.85 323.33 T3 -85.45 -121.8 T4 161.85 323.33 D. 14 REFERENCES 1. Nash, William A., Strength of Materials, 21 ed. McGraw-Hill, 1972, p. 42. 2. U. S. NASA Technical Memorandum, TMX-2912. 3. Gibson, A. H., and Ritche, E. G., The Circular Arc Bow Girder, D. Van Nostrand Co, New York, 1915, p. 28. 4. NASA Report (unpublished) on Mass Drivers. 5. Timoshenko, Gene, The eor of Elastic Stabiit, McGraw-Hill Book Co., Inc., 1961, Chapter 11. 6. Aerospace Engineering 314 Class Notes (Professor D. L. Sikarskie). 7. Aerospace Engineering 414 Class Notes (Professor J. G. Eisley). 8. Aerospace Engineering 514 Class Notes (Professor D. L. Sikarskie). 9. Applied Mechanics 211 Class Notes, University of Michigan. 10. Boley and Weiner, Theory of Thermal Stress, John Wiley and Sons, Inc. 1960. 11. Space Construction Automated Fabrication Experiment Definition Study (SCAFEDS) Vol. I, General Dynamics, Onvair Division, 1978. 12. Bernstein, I. M., and Pecker, Donald, Handbook of Stainless Steel, McGraw-Hill, 1977. 13. Langton, N. H., Space Research and Technology, Vol. 1: Space Environment American Elsevier Publishing Co., 1969. 14. Mantel, Charles, Engineering Materials Handbook, McGraw-Hill, 1958. 15. Touloukian, Y. S., Thermal Physical Properties of High Temperature Solids Vol. 1, 5 Collier-Macmillian, 1967. 163

APPENDIX E Gravity Gradient Moments 1. General Case Principal axes at the mass center: x, y, z. a, j3, y are direction the force field. Then the gravitational moment is: mg = — 3 [Y(yy( - Izz,)ex + aY(Izz - 1x)ey + ap(g -. )e ] (1) rc 2. Long Slender Spacecraft We consider only pitch rotation about the y-axis so that the structures attitude is in the orbital plane. For this orientation the direction cosines are a= cos (90 + ) = - sin 9 =0 Y = cos (180 - ) = - cos From equation 1): -O. 3u "M 3 (u [sin ~ cos ( (Izz - I )] ey g = 3 xx rc Assuming the mass driver is in the form of a solid homogeneous cylinder of length I and diameter d. I y I ( = I (3 d2 +1t M d2 3 d2 1 2 1 d2 I -I M- +-1 d zz xx 48 12 8 M 2 3 2 12 3 164

This gives us for the moment expression: 3u 2 8in cos M 2 3 2 M 3' " (3 -d) e gr2 12 4 1 Y = u 2 3d W u ( 3 md ) ) sin 2) ey 8 r 4 y or finally 1 u I 2 [ M Mr —) -— )z sin (24,) e g 8 r m r 4 Y Propulsive Restoring- Moment Let the propulsive force be always linearly distributed as shown. P x The propulsive "pressure" is then P(N/m) and let the maximum be P at the end of the structure. Thus 2P p=- X In terms of P the restoring moment is i /2 I/2z 3 2 2/pydy=, z ZP z 4P 2 f py dy = 2 r 7 —y dy = 0 0 4P I 1 2(Nm) -- P1 (Nm) 31 8 6 165

_APPENDIX F GROUND SUPPORT NUCLEAH POWER PLANTS IN THE U.S. June 30. 1978 The reactor types listed are: Pressurized Water Reactor - PWR: Boiling Water Reactor - BWR: High Temperature Gas-cooled Reactor --- HTGR; Liquid Metal Fast Breeder Reactor - LMFBR; Light Water Breeder Reactor - LWBR The reactor manufacturers are: Allis-Chalmers - AC: Babcock & Wlcox - BEW; Combustion Engineering - CE:.General Atomic - GA; Genera Electric - GE; and Westinghouse - W. An asterisk indicates that the plant itas been deterred mndefintely and the new stan-up date has not been announced. A double asterisk indicates that no start-up date has yet been established. Net State and Utility Plant Location MWe Typo/Mfr Operable ALABAMA Alabama Power Co. Joseph M. Farley 1 Houston County 829 PWR/W 1977 Alabama Power Co. Joseph M. Fwrley 2 (C) Houston County 829 PWR W 1980 Tennessee Valley Authority Bellefonte 1 (C) Scottsboro 1.235 PWR'BbW 1980 Tennessee Valey Authority Bellefonte 2 (C) Scottsboro 1.235 PVR B[bW l9F' Tennessee Valley Authority Browns Ferry 1 Decatur 1.065 BWR!GE 1973 Tennessee Valley Authority Browns Ferry 2 Decatur 1.065 BWR GE 1974 Tennessee Valley Authority Browns Ferry 3 Decatur 1.065 BWR/GE 1976 ARIZONA Arizona Public Service Co. Palo Verde 1 (C) Wintersburg 1.270 PWR CE 1982 (Salt Rrver Progect) Arizona Public Service Co. Palo Verde 2 (C) Wintersbuig 1.270 PWR CE 1984 (Salt Rner Proect) Arizona Public Service Co. Palo Verde 3 (C) Wintersburg 1.270 PWR!CE 19b6 (Salt River Proect) Arizona Public Servce Co. Palo Verde 4 (01 Wintersburg 1.270 PWRiCE 1988 Arizona Pubic Service Co. Palo Verde 5 (0) Wntersburg 1.270 PWR CE 199'r ARKANSAS Arkansas Power b Light Co. Arkansas Nuclear One — Russellville 850 PWR i B6W 1974 Arkansas Power & Light Co. Arkansas Nuclear One-2 IC) RusselvillHe 912 PWVVR'CE 1978 CALIFORNIA Pacific Gas and Electnc Co. Diablo Canyon (C) Avla Beach 1.U84 PVR W 1 78 Pacific Gas and Electrinc Co. Diablok Canyon 2 (C) Avila Beach 1. lOt PWR W 1979 Pacific Gas and Electric Co. Humboldt Bay Humboldt Bay 63 BWR/GE 1962 Pacific Gas and Electric Co. ur I 110) 1, 1168 WR GE * Pacific Gas and Electric Co. unit 2 (0) -- 1. 168 B'R,'GE Sacramento Municipal Utility District Rancho Seco 1 Clay Station 918 PWR /8W 1974 Southern Californie Edison Co. San Onotfr I San Clemente 430 PWR/W 1967 (San Diego Gas and Electric Co.) Southern California Edhson Co. San Onofre 2 (C) San Clemente 1.140 PWR CE 19'81 (San Diego Gas and Electric Co.) Southern Californita Edson Co. San Onofre 3 (C) San Clemente 1.140 PVVR'CE 1963 (San Diego Gas and Electric Co.) COLORADO Public Service Company of Colorado Fort St. Vrain Platteville 330 HTGR/GA 1973 CONNECTICUT Connecticut Yankee Atomic Powe Co. Connecticut Yankee Haddam Neck 575 PWR/W 1967 Northeast Nuclear Energy Co. Millstone I Waterforrl 660 BWR/GE 1970 Northeast Nuclear Energy Co. Millstone 2 Waterford 830 PWR/CE 1975 Northeast Nuclear Energy Co. Millstone 3 (C) Wawttord 1.150 PWR,'W 1986 FLORIDOA Florida Power Corp. Crystal River 3 Red Level P25 PWR/BbW 1976 Florida Power 6 Light Co. St. Lucie I St. Lucie County 802 PWR/CE 1976 Florida Power 6 Ic pit Co. St.luce 2 IC) St. Lucie Couity (442 PWR/CE 1981 Florida Power b Light Co. Turkey Point 3 0 Turkey Point 693 PWR/W 1972 Florida Power b Light Co. Turkey Point 4 Turkey Point 693 PWR/W. 1913 GEORGIA Gw'slra POtwr Co. Alvin W Voiltk? I (C) WailuNW) 1100(X) PWR,'W 1984 (Oglethorpe Electric Membership Curp.) Georgia Power Co. Alvin W. Vogtle 2 (C) Waynesboro 1.100 PWR/W 1985 (Oglethorpe Electric Membership Cup.} Soiitce Alutnilc Inrdltslial rmin, i. Jili.1!1 it/t p i.i Ref. 2, Chapter 7. 166

Stter and Utility Ptent LNotioa MW. Type/Mf. Operable GEORGIA (continmed) Georgie Power Co. Edwin I. Hatch I Be t ley 7 BWR/G 1974 O hope Electric Membeship Corp.J) Georgia PowM Co. Edwin I. Hatch 2 Baxley 795 WR/G 197 (Oglethore Electric Memb p Corp.) ILLINOIS Commonwoalth Fdion Co fridwroodt 1 (C) Brai nd 1 PWR/W 191 Commonwaalth Edison Co. Braidwood 2 (C) Braidwood 1.120 PWR/W 1982 Commonwealth Edison Co. Byron I (C) Byron 1.120 PWR/W 1981 Communowalth Edison Co. Byron 2 (C) Byron 1.120 PWR/W 1982 Commonwealth Edison Co. Dresden 1 Morris 200 WR/GE 1989 Conmonwealth Edison Co. Dreasde 2 Morris 794 BWR/GE 1963 Commonwealth Edison Co. Dresden 3 M ims 794 BW/GE 1971 Commonwealth Edison Co. LaSalle 1 (C) Seneca 1.078 BWR/GE 1979 Commonwealth Edison Co. LaSalek 2 (C) Seneca 1.078 BWR/GE 1990 Conmonwealth Edison Co. Zion 1 Zion 1.040 PWR/W 1973 Commonwealth Edison Co. Zion 2 Zion 1.040 PWR/W 1973 Commonwealth Edison Co. Quad Cities 1 Cordao 789 BWR/GE 1971 (lowa. linois Gas and Electric Co.) Commonwealth Edison Co. Quad Cities 2 Cordova 739 BWR/GE 1972 (Iowa Illinois Ga and Electric Co.) linois Power Co. Cinton (C) Clinton 950 BWR/GE 1982 Ilkno1s Power Co. Cnton 2 (C Clinton 950 BWR/GE 1988 INDIANA Northern Indiana Public Sece Co. Bally Ntcer 1 (C) Dunes Acres 660 BWR/GE 1984 Public Service Indiana Marble H I 1(C) Madison A1 130 PWR/W 1982 Public Srvice nda Marble H 2 (C) Madison 1.130 PWR/W 1984 IOWA Iowa Electric Light and Power Co. Duane Arnold Cw FRapids 3 BW/G974 (Centrlf lowa Power Cooperativ") Iowa Power and Light Co. Vandalia (0) Vandeia 1.270 PWR/BbW (Central Iowa Power Cooperatve. Associated Electric Cooperative of Missoui) KANSAS Kansas Gas and Electric Co Wolf Creek (C) Burington 1.150 PVVR/W 1983 (Kansas City Power & Light Co.) LOUISIANA Gulf States Utilities Co. River Bend 1 (C) St. Frncisve 934 BWR/GE 1984 Gulf States Utilities Co. River Bend 2 (C) St. Fracsvoee 934 BWR/GE 1986 Louisiana Power 8 tight Co. Waterford 3 (C) Taft 1.165 PWR/CE 1981 MAINC Maine Yankee Atomic Power Co. Maine Yankee Wiscest 790 PWR/CE 1972 MARYLAND Batimore Gas and Electric Co. Calvert Cliffs I Lusby 84 PWR/CE 1974 Baitimort Gas end Electric Co. Cmvert Cliffs 2 Lusby 348 PWR/CE 1976 MASSACHUSETTS Boston Edison Co. Pilgrim 1 Plymouth 656 BWR/GE 1972 Boston Edison Co. Plgnm 2 (0) Plymouth 1.150 PWR/CE 1985 Northeast Nuclear Energy Co. Montague 1 (0) Montague 1.150 BWR/GE 1988-1990 Northeast Nuclear Energy Co. Montague 2 (0) Montague 1.150 BWR/GE 19q0-1992 Yank"e Atomic Electric Co. Yankee Rowe 175 PWR/W 1960 MICHIGAN Consumers Power Co. Big Rock Point Big Rock Point 72 BWR/GE 1962 Consumers Power Co. Midland I (C) Mdland 492 PWR/BbW 1982 Consumers Power Co. Midland 2 (C) Midlndm 818 PWR/B&W 1981 Consumers Power Co. Palisades South Haven 805 PWR/CE 1971 Detroit Edison Co. Enrico Fermi 2 (C) Lagoonm Beach 1.123 BWR/GE 1980 Detroit Edison Co. Greenwood 2 10) St. Clair County 1.208 PWR/8\W 1987 Detroit Edison Co. Greenwood 3 (0) St. Clar County 1.208 PWR/BEW 1989 Indibn Michigam Eletric Co. Donald C. Cook 1 Bridcgmae 1.054 PWR/W 1974 Indiana I Michigan Electric Co. Donald C. Cook 2 BridgOmn 1.100 fWR/W 1977 MINNESOTA Northe States Power Co. Monticello Monticello 54 BWR/GE 1970 Northern Sttes Power Co. Prire Islnd 1 Red Wng 30 PWR/W 1973 Northern States Power Co. Pririe Iland 2 Red Wing S30 PWR/W 1974 Source Alomrc ldtuSlrfrl Forum. Jlne 30 1978 l 1-6 167

Net State and Utility Plnt Location MWe Type/Mfr. Operab MISSISSIPPI MIssspp, Power 6 Light Co. Grand Gulf I (C) Prat Gibson 1.250 BWR/GE 1981 M sisip Power 6 Light Co. Grand Gull 2 (C) Port Gibson 1.250 BWR'/GE 1984 Tennessee Valley Authority Yellow Creek I (LWAI Tishirmngo County 1,285 PWR/CE 1985 Tennessee Valley Authority Yellow Creek 2 (LWA) TshmiVngo County 1.285 PWR/CE 1986 MISSOURI Union Electric Co. Callaway 1 IC) Callaway County 1,150 PWR/W 1982 Unon Electric Co. Calway 2 (C) Callaway County 1.150 PWR/W 1987 NEBRASKA Nebraska Public Power District Cooper Brownville 778 BWR/GE 1974 Omaha Public Power DOitrict Fort Calhoun I Fort Calhoun 461 PWR/CE 1973 NEW HAMPSHIRE Public Sevice Co. of New Hampshire Seabrook 1 (C) Seabrook 1.194 PWR/W 1982 (United Illuminetirng Co.) Pubic Service Co. of New Hampshire Seabrook 2 (C) Seabrook 1.194 PWR/W 194 (United Illuminating Co.) NEW JERSEY Jersey Central Power 6 Light Co. Forked River 1 (C} Lacey Township 1.070 PWR/CE 1983 Jersey Central Power b Light Co. Oyste Creek Tont River 660 BWR/GE 1969 Publc Service Electric and Gas Co. Atlantic 1 (0) Lttle Egg Inlet 1.150 PWR/W 1988 (offshore) Public Service Electric and Gas Co. Atlantic 2 (0) Little Egg Inlet 1.150 PWR/W 1990 (offshore) Public Servce Electric and Gas Co. unit 1 (0) -- (offshore) 1.150 PWR/W 1993 Public Service Electric and Gas Co. unot 2 (0) -- (offshore) 1.150 PWR/W 1995 Public Service Electric and Gas Co. Hope Creek 1 (C) Salem County 1,067 BWR/GE 1984 Public Service Electric and Gas Co. Hope Creek 2 (C) Salem County 1.067 BWR/GE 1986 Public Service Electric and Gs Co. Salem I Salem 1.090 PWR/W 1976 (Philedelphia Electric Co.) Public Service Electc and Gas Co. Salem 2 (C) Salem 1.115 PWR/W 1979 (Phildeldph Electnc Co.) NEW YORK Consolidated Edison Co. of N.Y.. Inc. Indian Point I Buchanan 265 PWR/BsW 1962 Consolidated Edison Co. of N.Y.. Inc. Indan Point 2 Buchanan 873 PWR/W 1971 Power Authority of the State of New York Indian Point 3 Buchanan 873 PWR/W 1975 Power Authority of the State of New York James A. FitzPatrick Scribe 821 BWR/GE 1974 Power Authority of the State of New York Greene County (0) Cementon 1.200 PWR/BbW 1986 Long Island Lightmg Co. Jamesport 1 (O) Rwverhead 1,150 PWR/W 1988 (New York State Electric 6 Gas Corp.) Long Island Lighting Co. Jamesport 2 (O) Riverhead 1.150 PWR/W 1990 (New York State Electnc 6 Gas Corp.) Long Islend Lijhtrin Co. SlHwrehtm (C) Brookhaven 854 IWR/GE 1.J14(' New York State Electnc 6 Gas Corp. unit I () - 1.250 PWR/CE 1991 (Long Island Lighting Co.) New York State Electric b Gas Corp unit 2 (O) - 1.250 PWR/CE 1993 (Long Island Lighting Co.) Nigeara Mohawk Power Corp. Nine Mile Point 1 Oswego 610 BWR/GE 1969 Nagara Mohawk Power Corp. New Mile Pmnt 2 (C) Owegu 1.080 RWR/GL 1983 Rochester Gas end Electric Corp. Robert E. Ginno Rochester 410 PWR/W 1969 Rochester Gas and Electric Corp. Sterking (C) Sterling 1.150 PWR/W 1986 (Orange 6 Rockland Utilities. NigaW Mohawk Power Corp.. Central Hudson) NORTH CAROLUNA Carolina Powenr Light Co. Brunswir 1I Southport 821 BWR/GE 1976 Carolina Power 6 ight Co. Bnsmwck 2 Southport 621 BWR/GE 1974 Carolna Power 6 Light Co. Sheaon Harns 1 (C) New Hil 915 PWR/W 1984 Caroina Power 6 Light Co. Shearon Harrs 2 (C) New Hill 915 PWR/W 1986 Caroin Power 6 Light Co. Sheeron Harrs 3 (C) New HMI 915 PWR/W 1990 Carolna Power 6 Light Co. Shearon Hatns 4 (C). New Hidl 915 PWR/W 1988 Carolin Power 6 Light Co. S.R. 1 1(0) - 1150 PWR/BOW 1989 Crol Powerb 6 Light Co. S.R. 2 (0) - 1.150 PWR/BbW 1991 Duke Power Co. Thomas L. Perkins 1 10) Davie County 1.280 PWR/CE 1988 Duke Power Co. Thomas L. Perkins 2 (0) Davie County 1.280 PWR/CE 1991 Duke Power Co. Thomas L. Perkws 3 (0) Davi County 1,280 PWR/CE 1993 Duke Power Co. William McGure 1 IC) Cown Ford ODamn 1.180 PWR/W 1979 Duke Power Co. William McGure 2 (C) Cownsn Ford Oem 1.180 PWR/W 1981 OHIO Cmncmtat Gas 6 Electrc Cn Wm. H. Zrnmner 1 (C) Moscow 810 BWR/GE 1979 (Cugtkurdu waft',,utheln OtWo FleCti; Co., Deyton Po and Light Co.) Souc! Alomic Illthi.dia Firim. JJu.:.):1/r,i 1-.6 1 b6

Net State and Utility Plant Location MWe Tye/Mtr eble OHIO(continued) Cincinnati Gas Electric Co. Wn.. H. Zimmr 2(0) Moscow 1,150 WA/GE (Columbus and Southemrn Oho Electnc Co.. Dayton Power and Light Co-) Central Area Power Coordinrtion Group (CAPCO Perry 1 (C) Noth Perry 1,205 BWR/GE 1981 (Cleveland Electnc Iluminatng Co. (operating ut*ty). Duquesne Light Co.. Oho Edsown Co.. Pennsylvana Powe Co. Toledo Edison Co.I Central Area Power Coordination Group (CAPCO) Perr 2 (C) Nnrth Perry 1.205 BWR/('~ 1983 ICleveland Electnc Illumnating Co. (ooeratng utility), Duquesne Light Co., Ohio Edson Co.. Pennsylvania Power Co.. Toledo Edison Co.l Central Area Power Coordination Grou ((CAPCO) Ene 1 (0) Blwn Heights 1.267 PNR/BbW 1986 COhio Edison Co. (operatng utility). Cleveland Etlectm Illumnating Co.. Dtquesne Light Co.. Pennsylvanla Power Co., Toledo Edison Co.1 Central Area Power Cuordlation GrCoup (CAPCO) Ene 2 (0) Berin Heights 1.267 PWR/B&W 1988 101co Edison Co. (opratmg utility). Cleveland Electric ll1uminatmg Co.. Dquesrne Light Co.. Penisylvania Power Co. Toledo Ecdison Co.l Central Area Power Coordination Group (CAPCOI ODvis-eBs tI Oak Harbor 906 PWR/8bbW 1977 (Toledo Edison Co. (operating utility). Cleveland Electric lilumnating Co.l Cential Area Power Cowornatin Group (CAPCO) Davis-Besse 2 (LWA) Oak Harbor 906 PWR/8hW 1985 (T(ledn Edswon Co. (oerating utility). Cleveland Electric Illuminating Co.. Duquesne Light Co., Oltno Edicurt Co.. fenitylvInara Power Co.l Central Area )'uwer Cordwiatton Group (CAPCO) Davis.-Bese 3 (LWA) Oak Hartor 906 PWR/BbW 1987 Toledo Edison Co. (opeating utility). Cleveland Elkctric Illkjrrmlati) Co,. Ouqtwsne Light Co. Ohio Edjson Co.. Pennsylvania Power Co.? OKLAHOMA Puhblic Service Co. of Oklahoma Black Fox 1 10) Inola 1.150 BWR/GE 1984 (Associated Electric Coopemative) Puitmi Service Co. of Oklahoma Black Fox 2 (O) Inola 1,150 BWR/GE 1986 (Associated Electric Cooperattve) OREGON Portland General Electric Co. Troan 1ainier 1.130 PWR/W 1975 (Eugene Water &t Electric Board) Portland General Electric Co. Pebble Spnngs 1 (0) Arlington 1.260 PWR/B&W 1986 (Pacitic Power & Light Co.. Puget Sound Power b Lgjht Co.) Portland General Electric Co. Pebble Sprmgs 2 (0) Arlington 1.260 PWR/BbW 1989 (Pacific Power b Light Co. uqget Solund Power t Light Co) PENNSYLVANIA fDepaerment of Energy Shippingport Shippingport 60 LWBR/W 1977* (Power distributed by Duquesne Light Co) Central Area Power Coordination Group (CAPCO) Beaver Valley 1 Shippingport 52 PWR/W 1976 IDuquesne Light Co. (operating utility). Ohio Edison Co.. Pennsylvania Power Co.l Central Atea Power Coordination Group (CAPCO) Beaver Valley 2 (C) Shippingpor 852 PWVR/W 1982 IDuquesne Light Co. (operating utility Cleveland Electnc Illuminatng Co.. Ohio Edison Co.. Pennsvlvania Power Co. Toledo Edison Co.l Metropolitan Edison Co. Three Mile Island 1 Londndonder Township 819 PWR/8SW 1974 (Jersey Central Power f Light Co.. Pennsylvania Electric Co.) Metropolitan Edison Co. Three Mile Island 2 Londonderry Township 906 PWR/BEW 1978 (Jeey Central Power & Light Co.. Pennsylvania Electric Co.) Pennsylvania Power E Light Co. Susquehanna 1 (C) Berwick 1,05 BWR/GE 1981 Pennsylvania Power Et Light Co. Suscuehanna 2 (C) Berwick 1,050 BWR/GE 1982 Pthladelphia Electric Co. Limeck I (C) Limerick Township 1.065 BWR/GE 1985 Philadelphia Electnc Co Lrwerick 2 (C) Limerick Township 1.065 BWR/GE 1987 Philadeiphia Electric Co. Peach Bottom 2 Peach Bottom 1,065 BWRtGE 1973 tPublic Service Electric and Gas Co.) Township Philadelphia Electric Co. Pech Bottom 3 Peach Bottom 1.0S5 8WR/GE 1974 (Public Service Electric and Gas Co.) Township aAlthough the original Shippingport core first began to produce power in 1957. the LWBFt core went into operation in 1977. S.irce Atomt'ndlustlal Foumrn Jure 30. 1978. 1-G; 169

Net State ad Utility Planrt Loamon MW. Type/M Oerak le RHOODE ISLAND New England Power Co NEP- I (0) Charmestown I 150 PWR/W New Englae Power Co NEP - (O) Charlestown 1150 PWVR/W 1968 SOUTH CAROLINA Carolin, Power 6 Light Co. H. Robite. 2 Hartsville 700 PWR/W 1970 Dulke o CoP Cu caObe 1 (CI) York County 1145 PWA/W 191i Duke Powe Co Catavt 2 (C) York County- 1.145 PWRI/W'3983 Duke Power Co Cherokee I (C) Cherokm County 1.2980 PWRA'/CE 1985S Duke Power Co Cherkee 2 (C) Cherokee County 1.280 PWR/CE 1987 Duke Powe~ Co Cherokee 3 (C) Cherokee County 1.290 PWIRCE 1989 Duke Power Co Oconee 1 Lake owee 887 PWII/Bb6W 1973 uk Power Co. Oconee 2 Lake Keowee 87 PWR/OW 1973 ukeM Power CO Oconee 3 Lake Kaowee 87 PWRI/BW 1974 South Carolina Electri Gas Co Vg C Summer 1 (CI Parr 900 PWRI/W 19U (South Caokln Pubic Service Authwraiy) TEINNESSEE Tennessee Valtl Authorlv HMwisviile A. tI C) Ma'tsvle 1.205 BWR'GE 1983 Tefmnnessee Vev Authrtyv lartvdle A.2 (C) Hartsvdle 1.205 SWAR/GE 1984 Tennessee Vally Authrity Hrtsvlle 8-1 (Cl aHtisvie 205 BIWRGE 19B3 Terfiessee Vefyv Authority 4irtsvoIl 8.2 (C) Hartlvie 1.205 BWR/'GL 19(4 Tennessee Valey Authority Phcap Bend 1 (C) Surgoinvdle 1.220 SWR/GE 1914 lertnewte Vadlv Authoityv Phii Boend 2 IC) Surgonusvil 1.220 BWR GE 19b etnessee Valle Aulhmrity Sequovey 1 (C) Ocisv I1140 PW W 9197 lemrNessee Valley Authority Sequoyah 2 (C) kivsy 1.140 PWR W I.Q8 Tlrrewse ValWy Authrity Wtts, Bar 1 (C) Spring CItvy 115 PWR'W 91':i Imnrwsse VallV Authority Wetlls a 2 IC) Spr"L City 1. tt PW'W I'tl! IerN!*s'ee Valfe Authority Clioch Rver Breeler Oak Pioe 350 LMIBR W 19J4 (Cfinmonwralth Edison C'a. I Reactot Plant (01 U.S Deprtmentm of Enrgy) TEXAS Gull States Utiities Cc, 8u Hills 1 (0) Jaser %A PWR CF 1989 Gu States Utilitie Co Bu (tra 2 (01 Ja41r il ti'l PwR c.r rI 1l HoustmIn Liplqtli t1 Prwwe Co Allen, Cteek I ii) Wealk I,,( I11(I ((t I!1h',.loulh lTeranis I'rIi t Iltrnrislj I wti bniuf tfi,teme Pr.iit I ILl Meltawrt Crurilv I.54) PWV W 1'M rg 6 PowM Co ttj tCl tmanwIe Central Power and Llght Co.. Ctv Pubti Service Board of Sn Antonio City of Austrrij SKuth Texas Pr opct IHouston Light Soulth Yeses PfreCt 2 (Cl Matsgorda Countyv 1 250 pWR W 8 ret 6 Power Co (prouect inanamm. Central Power an Light Co. City Pubk Srwce Board of Sar Antonio. City of Auseml Teias Utiktws CGeneratig Co Cirariche PaolL 1 (Cl Somerve County I 150 PWA W 1981 iates Pouvv 6 Ltht Co.. Texas EtItrit. Srvmce Co, 7elvs Power & LPht Co I Te.ms Utikt (wnefat-ql Co Crrianche Pak 2 (C2C) Smrf vell Cnurv I 150 PWR W It l"I I).41is Prwov 6 tiht Ci. teats Lk(.rt.. Serice Co. Yenrs Powe b Light C) I VERMONT Vermmonl Yankee Nuclear Pow Corp Vermmot Yank Vernon 514 WR/GE 1972 VIRGINIA V#irgi Electric and Power Co North Anne 1 Mineral 907 PWI/w 19177 Virlmie Electric.r.) Prwr Co North Anna 2 (C) Minral 907 PWR/W 1919 Vininia Electric arWId PWer Co North Annm 3 IC) Minral 907 FPWR/8&W 193 Vegmni Electric an Povwr Ca Nortrh Anna 4 (C) Mi~rl 907 PWR/SbW 1984 Virgini Electric ma Power Co. Str 1 Grvel Neck 822 PWR/W 1972 VWrgtni Elektric andm Pow Co Stay 2 Grevy Neck 822 PWR/W 1973 WASHINGTON Ptirit Sound Powe and tight Co Skag I (0) S4edo Worv e1.268 BWRa/G 1985I (Poritanit C"are Lctric Co. Pacifi Piwer Er LkM Co.) Poqt Sound Ponwer rd Ltht Co. Ski 2(0) Sadno Woolev 1.288 BWR/GE 1987 (Portlan Gwar IFlectric Co. rPific Power b (ight Co.) ODepartment Qf Emnergy Hanord - N Richlend W00 Grapite 138 (Power distributed by Weelnois (NRC) Public Powe Supply SVtermn) Wastwrgttir Pulk. Pwmerm:;upqi System WI"S. I (C) R'hrMrdl 1 267 PV R/BbW 19t2 Washwrwuori Puilic Per Supply ~ VVPPSS 2 (C) Ilchland 1.103 9WR/GE 1990O WVVstnlqtonhlc Prower Swlv Systrm WPPSS 3 (C) Sato" 1.242 PVRn'CL 1q4 Wahin"ton Pitkl. Powe Supl Systlemn WPIMS 4i(C) iChlei, 1,267 MRlt'ltW' OM4 Weshiton Puilc Power Sup System WPS (C):tts.r 1242 Pwn/CL 195 WISCONSIN Dirn Power Coperaive LaCrosse Genoe 60 OWR/AC 19A7 NkthWrt Stems Power Co. Tyrwe 1 (C) Duranni 1 If) PWnI'W 1985 Wmaconn Elefctic Pmowe Co. Haven I (0) Haven 9(i) PWR'W 1967 W1#orrtm t~wlas obrm Ca ~ ucm 3 K)I )t~v~r ~ yll) Pnfi/W 1987! Wiaconsin Eliectic Pwe Co Haven 2 10) Ifav4v 9'1 PWII1,W 19RA~ W19acn:in Mchgan Power Co. Poinmt ech 1 Iwo Creeks 41 PWR/W 19710 W'emamin I Electric Poqwe C) I ICOnI Michiga Powe Co. Poirt sead 2 Two Creeka 417 PWR/W 1971 (Wimmnit Elctric Pmwr Co.) %MWeenwim P Serwe Corp Keweunm Cartton Townahip PWR/W 1973 (wmeanern Poer and Light Co) PUERTO RICO P Ierto ico Water Renra Autority llhotea c53 PR,'W!,~Lilift't At~)lltlt4' Itllllt.%111.if I sillli.JIf~:~) l't l i' I 1; 170

US. Nuoiar Powerplant Opmetions' Proren* of Teel Deueab Ieagemw Eearl Thousands of nt bloweurs 1972 AVERAGE 1./26 0.L14 31 111 Jn,,y ".31 114 t I FebruatrV 44.289 29.138 12 0 153 AVERAGE 130 5.76g0 4.S March 44.289 2. 785 12 2 April 45.131 27.631 12 1 1974 AVERAGE 29.921 13.011 &. May 45.222 27.687 1'2 June 45.991 29.885 11 9 1905 AVERAGE 35.061 115.21.0 July 45.984 29.335 1 0 August 45.982 30.571 11 6 1916 January 36.750 21.638 90 SeOtemier 46.051 27.26 11 1 Feruarv 36.879 20.657 92 Octobe 46.088 25,593 11 4 March 38,.012 18.80 8.5 Novemhr 46.0688 27 025 11 6 April 39.763 15.142 7 2 Dcember 4.133 31,350 12 9 May 39.902 16.034 7 6 June 39.791 21.885 91 AVERAGE 4LS64 25.640 11.5 July 40. 168 23.002 9 5 August 42.067 24.681 9.8 1975 January 41.16/ 34.122 131 September 42.896 24.014 105 Fruary 48.080 32.440 R12 6 Octorw 42.877 23.327 10.6 March 46.067:0. 113 13 0 November 43.613 22.406 9.5 April 48.926 24.451 11 0 December 42.877 28.390 115 bw 48.924 21.441 R11 6 June 49.714 H110.813 Rll 8 AVWAGE 40.82 21.76 9.4 July 49.119 R11.612 12 3 August 49.815.4.r9/ 12 7 AVEUAG 46.60S 31.056 12 3 (8 monthfit'Includs all units authoried to genrte commercial electricity. ncludin units in stalrtup tlesti and those owted by the Government. "*Prflminavy dta H Revised dlat Source. Capacity data tof units in commrncia operation or sartup testing and Average Power for August 1918 from Nuclear Regulatory Commisson. Remamni Gata from FPC Form 4. "Monr y PowerplmI Arepoo " Source: Dep of Energy Monthly Energy Review. Oct. 1978. p. 54 FORECAST OF DOMESTIC URANIUM REQUIREMENTS Tom U30e - No Redle DOM. Comem Tal* Imwimet PFed Ctewre' Yea AnnM"d Cenwleotive 1978 19.600 1.60 19,9 21.200 39.800 19S 26.100 t 6'IO 1961 33 200 9. 100 1912 33.300 132.400 1I6I 31,qm0 161 300 1t4 40.300 2U.6iOO 196"% 41 100 744.100 19,6 43000 21. 100 It11 44.,00 336.300 196l 44.6(8) 360.600 19 44.I MIU 42,. )10 1990 45.640 411.1w0'O 2t% tios to Octor. 1. 1980. 0.26% Itils thefeltW ret 1is the moun o U-235,n ihe r1 tlletd wumn str1Eisum slter niWcmes Sourew SMrrIaNI 0rd of 1r' Mtklarm ItdurtrY., GJ. 1004 78). U.S. eer1tmlen o trserqy. Jlnirv 1. 19176,toc;i INtO NpwS Flhlrpariqr Aiqt 198It p DOMESTIC URANIUM RESOURCE ESTIMATES AS OF 1/11'78 Tom U30O Predetien Cast ereeee Pem.dot S00,.leur TeM Sl5 30.000 Q540.000 4U.o W)00 16S (VjO 1.56.000 St.I30 Incrvreni 370.0 4.000 64.000 2 0.000 1.690.000 5.O3 t*.(JOO 0 1. 0S.oW 1.135 00 4 1.f 3.75%.000 $306 b1 in- re.OIit:W)t.W30110). nlM i/ i l.((]' I1.110.000 S.3 i90.000 1.395.000 t1 16.000 b66.000 4.365.000 W? P 2,,1.-0t 19171 21"00 140.W.1 1 04.001) 1.0300 5t 39 000 1 636.0 1 5) 60(3) 4.505.000'By Itwutuct *d Ihmw14la t Coni copp ptuot1oCn Soece Srrrw elOar ef roe L/eniw Indwar, GJlOOt71., U.S. De:atnwrmen oE!nergy. Juwry 1. g197..Soice INFO Ntws f nt.Iir Aurnl 191119/. p 5 171

ATTAINABLE WORLD URANIUM PRODUCTION CAPABILITIES Tont U30. 1977 1980 1985 North Amefi 24,0.30 3/7,450 56.460 United States 16,100 26,900 39.500 Canala 7,930 10.330 16.250 Mexico 0 220 710 Attfrica 11.840 22.100 30.810 South Africa — 8.-71 6 15,210 16 Niqer 2.090 5.330 11.700 Gabon 1.,040 1.560 1.560 Central African Emuie 0 0 1,300 Australia 520 650 15,340 Europe 3,350 4.990 7,460 France 2.860 3.700 4.810 Spain 250 180 1,650 Portugdl 110 120 350 Itly 0 160 160 Gemany. F.R. 130 130 260 Yugoslavia 0 0 230 Asia 300 480 430 Ihdia 260 260 260 Japan 40 40 40 Tuwkey 0 130 130 Phillppilrie O 50 0 South Americ 170 970 1.80 Arglentina 170 4/0 780 B aiil 0 500 500 Total (rounded) 40.000 67,000 112.000 Source: Uraium Resources Production end DOmand, OECD Nuclear Energy Agency and the International Atomic EnerWy Agency, December 1977. United States statistics from DOE.';4It.t i t NF'O Ne*w. AwlhaA# I(tWH 6 WORLD URANIUM REQUIREMENTS' Thousand Tons U301 Without Recycle With RacycleZ "Accelerlted"' "Present Trend"4 "Accelerated" "Present Trend" owr Growth Power Growth Power Growth Power Growth Yew Annual Cumulative Annual Cumulative Annual Cumulative Annual Cumulative 1978 38 68 J8 68 38 68 38 68 1979 45 113 45 113 45 113 45 113 1980 56 169 53 166 56 169 53 166 1981 66 235 61 227 66 235 61 227 1982 78 313 69 296 78 313 69 296 1983 90 403 77 373 87 400 74 370 1984 103 506 84 458 96 497 79 450 1t35 114 620. 92 550 107 603 84 534 1986 127 747 101 651 117 /20 90 624 1987 144 892 109 160 127 848 95 119 1988 162 1.U4i 117 877 138!185 100 819 1989 182 1.236 125 1.007 149 1.135 10o 924 1990 203 1.43! 133 1.135 164 1.299 110 1.035 Bsed on 0.25% U-235 enrichment plant tails assay. Tils is Ithe amount of U-235 in the depleted uranium stream after enrichment. 2Beginning in 1985. 3Assumes the oels of ambitous nucear power programs, planned in response to the oil embargo, risingl costs, and the possibl unavailability of conventional fuels. Perceives current patterns of energy utilization supply as well as pwesnt delays in the construction of new reactors and generally assumes a continuation of these trends. Source: kraium Reources, Production end Demnd, OECD Nuclear Energy Agency and the International Atomic Enwgy Agency, cemb t977. f.nz.( lN () I'qksq Ihk~k b;* Al I'1/ll I1 ti

WORLD URANIUM RESOURCES (As of January 1. 1977) Thousand Tons U30I Resonablv Arered Estimatued Additional <$30/lb. U3 0 $30.b. Total <$30lb. U306 $3050/b. Total Noth Americ 913 227 1140 1633 684 2,317 United States 690 200 890 1.120 330 1,450 Canada 217 19 236 510 343 863 Mexico 6 0 6 3 0 3 Denmark 0 8 8 0 11 11 Lrire...~...,_ 743 196 62 258 South Al ca 398 55 453 44 49 93 Niger 208 0 208 69 0 69 Algwia 36 0 36 65 0 65 Gabon 26 0 26 6 6 12 Central African Empire 10 0 10 10 0 10 7airce 2 0 2 2 0 2 Somalla 0 8 8 0 4 4 Malagascar 0 0 0 0 3 3 Australia 376 9 38S 57 6 63.Europe 81 417 498 58 _57 115 France 48 19 67 31 26 57 Spain 9 0 9 11 0 11 Portugal 9 2 11 1 0 1 Yugoslavia 6 3 9 6 20 26 United Kingdom 0 0 0 0 10 10 Ge many, F.R. 2 1 3 4 1 5 Italy 2 0 2 1 0 1 Austria 2 0 2 0 0 0 Sweden 1 390 391 4 0 4 Finland 2 2 4 0 0 0 Asia 54 4 58 31 0 31:ilaa 39 0 39 31 0 31 Japan tO 0 10 0 0 0 Turkey 5 0 5 0 0 0 Korea' 0 4 4 0 0 0 Philippines *0 0 0 0 Cetral & South Amnica 47 31 78 18 1 19 o8rail 24 0 24 11 0 11 Ai.qetiina 23 31 54 0 0 0 Chile 0 0 0 7 0 7 Bulivia 0 0 0 0 1 1 GfanwJ Total (rounded) 2.200 700 2,900 2.000 800 2.800 *Les thin 1.000 Tons of U308. Source: Uranium Resources, Production and Demand, OECD Nuclear Energy Agency and the Intemrnational Atomic Energy Agency, December 1977. United States statistics from DOE..t fc' INo I) INt ws fi.hti!', Atg 19111. p) 7 173

ACKNOWLEDGEMENTS Prof. Harm Buning, Aerospace Engineering, University of Michigan Prof. J. Eisley, Aerospace Engineering, University of Michigan Mr. Kevin Fine, Francis Bitter National Magnet Laboratory, MIT Mr. William Gilbrath, NASA, Ames Mr. Keith Henson, Analog Precision, Inc. Mr. Lyle Jenkins, NASA Johnson Space Center Mr. B. R. Klein, Bechtel Associates Professional Corp. Dr. Henry Kolm, Francis Bitter National Magnet Laboratory, MIT Mr. Don Kopinski, Bechtel Associates Professional Corp. Mr. Don McKeon, University of Michigan Mr. Walter K. Muench, Grumman Aerospace Corp. Dr. B. E. Schutz, University of Texas Prof. R. A. Scott, Applied Mechanics, University of Michigan Prof. David L. Sikarskie, Aerospace Engineering, University of Michigan Dr. F. J. Stebbins, NASA Johnson Space Center Dr. Victor Szebehely, Aerospace Engineering, University of Texas Prof. John E. Taylor, Applied Mechanics, University of Michigan Mr. Thomas Van Flandern, U. S. Naval Observatory Mr. Fred Williams, MIT A special thank you is extended to the following persons for taking the time to lecture to the team and assisting us in our efforts: Mr. Alan L. Friedlander, Science Applications, Inc. Prof. Robert M. Howe, Aerospace Engineering, University of Michigan Prof. C. Kikuchi, Nuclear Engineering, University of Michigan Most of all we extend a very special thanks to Professor Harm Buning for his guidance throughout the project. We would also like to thank Ann Gee for her typing throughout the term and Caroline Rehberg for her efforts in typing this report. 174