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Systems engineering and mission design of a lunar South Pole rover mission: a novel approach to the multidisciplinary design problem within a spacecraft systems engineering paradigm

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Systems engineering and mission design of a lunar South Pole rover mission: a novel approach to the multidisciplinary design problem within a spacecraft systems engineering paradigm

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Content SYSTEMS ENGINEERING AND MISSION DESIGN OF A LUNAR SOUTH POLE ROVER MISSION: A NOVEL APPROACH TO THE MULTIDISCIPLINARY DESIGN PROBLEM WITHIN A SPACECRAFT SYSTEMS ENGINEERING PARADIGM by Michael Edward Luna A Dissertation Presented to the FACULTY OF THE USC VITERBI SCHOOL OF ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ASTRONAUTICS) December 2016 Copyright 2016 Michael Edward Luna ii DEDICATION I would like to dedicate this research to my parents. iii ACKNOWLEDGEMENTS I would like to thank my parents and siblings for encouraging me throughout my PhD studies. Their words and advice provided much needed support in the final stages of my research. I would also like to thank Dr. Theodore Sweetser of the Jet Propulsion Laboratory, who agreed to support my research endeavors as a co-advisor several years ago. He has been a constant source of advice and feedback on my research, guiding me toward a comprehensive project in the very beginning, helping me to view the research from a system’s perspective, and having been willing to meet weekly to discuss my progress and latest results. I would also like to thank Professor Azad Madni, who I had a brief conversation with that helped me to frame the research as a systems problem. I am also thankful to all of my Committee members: Professors Joseph Kunc, Mike Gruntman, Theodore Sweetser, and Najmedin Meshkati. iv TABLE OF CONTENTS Dedication ........................................................................................................................................ ii Acknowledgements......................................................................................................................... iii List of Tables .................................................................................................................................. vii List of Figures .................................................................................................................................. xi Abstract .......................................................................................................................................... xv 1 Introduction ............................................................................................................................. 1 2 Research Problem .................................................................................................................... 5 3 State of the Art ......................................................................................................................... 7 3.1 Lunar Science Missions ........................................................................................ 7 3.1.1 Scientific Evidence of Lunar Polar Water-Ice .................................................. 7 3.1.2 Lunar Polar Volatiles Science .......................................................................... 9 3.1.3 Robotic Lunar Exploration and Planned Missions ........................................ 13 3.1.4 Current Lunar Polar Mission Concepts ......................................................... 17 3.2 System Design Approaches ................................................................................ 19 3.2.1 System Engineering & Design ....................................................................... 19 3.2.2 Example Design Tools ................................................................................... 22 3.3 Science Instruments ........................................................................................... 25 3.4 Subsystem Technologies .................................................................................... 36 3.4.1 Telecommunications..................................................................................... 36 3.4.2 CDS ................................................................................................................ 45 3.4.3 ADCS.............................................................................................................. 46 3.4.4 Propulsion ..................................................................................................... 62 3.4.5 Thermal ......................................................................................................... 63 3.4.6 Structures...................................................................................................... 64 3.4.7 Power ............................................................................................................ 64 4 Technical Approach ................................................................................................................ 70 4.1 Overview ............................................................................................................ 70 v 4.2 Mission Science Objectives ................................................................................ 72 4.3 Requirements ..................................................................................................... 74 4.3.1 Mission Requirements .................................................................................. 75 4.3.2 Design Tool Requirements ............................................................................ 76 4.4 Systems Engineering .......................................................................................... 77 4.5 Design Tool Development .................................................................................. 80 4.5.1 Programming Language Selection ................................................................ 80 4.5.2 Serial vs. Parallel Subsystem Design ............................................................. 82 4.5.3 Trade Studies ................................................................................................ 84 4.6 Science Payload .................................................................................................. 85 4.7 Landing Site Selection ........................................................................................ 94 5 Methods and Tools .............................................................................................................. 100 5.1 Overall Mission and System Design Process .................................................... 100 5.1.1 Trajectory Definition ................................................................................... 101 5.1.2 Definition of System Parameters ................................................................ 107 5.1.3 Generation of System Configuration Inputs ............................................... 128 5.2 Mission and Spacecraft Sizing Tool (MASS) ..................................................... 138 5.2.1 Mission Design Module .............................................................................. 141 5.2.2 System Design Module ............................................................................... 143 5.2.3 Spacecraft Design Module .......................................................................... 145 5.3 Subsystem Design Modules ............................................................................. 150 5.3.1 Telecommunications Design Module ......................................................... 150 5.3.2 CDS Design Module..................................................................................... 160 5.3.3 ADCS Design Module .................................................................................. 170 5.3.4 Propulsion Design Module .......................................................................... 205 5.3.5 Thermal Design Module.............................................................................. 216 5.3.6 Structures Design Module .......................................................................... 222 5.3.7 Power Design Module ................................................................................. 241 5.3.8 Lunar Descent & Landing Design Module ................................................... 258 5.4 Generating Design Data ................................................................................... 276 5.4.1 Selecting Configurations to Run ................................................................. 277 5.4.2 Design Runs................................................................................................. 281 vi 6 Analysis of Results ................................................................................................................ 283 6.1 Configuration Design Feasibility ...................................................................... 283 6.2 Feasible Design Configurations ........................................................................ 285 6.2.1 Design Results ............................................................................................. 285 6.2.2 Selected Designs ......................................................................................... 304 6.2.3 Launch Vehicle ............................................................................................ 318 6.3 Infeasible Design Configurations ..................................................................... 320 7 Conclusions .......................................................................................................................... 328 8 Future Work ......................................................................................................................... 334 8.1 Design Approach .............................................................................................. 334 8.2 Lunar Polar Volatiles Mission ........................................................................... 337 9 Bibliography ......................................................................................................................... 339 10 Appendices ........................................................................................................................... 345 Appendix A: Characteristics of the Moon ................................................................... 345 Appendix A1: Lunar Orbital Characteristics ............................................................ 345 Appendix A2: Lunar Surface Environment .............................................................. 348 Appendix B: Subsystems ............................................................................................. 353 Appendix B1: Telecommunications ........................................................................ 353 Appendix B2: Power................................................................................................ 359 vii LIST OF TABLES Table 3-1. Descent Imagers on Planetary Landers/Probes ............................................................ 27 Table 3-2. Surface Imagers/Cameras on Planetary Landers .......................................................... 27 Table 3-3. Microscopic Imagers on Planetary Landers .................................................................. 28 Table 3-4. Ground penetrating radar on Planetary Landers .......................................................... 28 Table 3-5. IR spectrometers on Planetary Missions ...................................................................... 28 Table 3-6. Mass spectrometers on Planetary Missions ................................................................. 29 Table 3-7. Neutron spectrometers on Planetary Missions ............................................................ 30 Table 3-8. Robotic arms on Planetary Missions ............................................................................. 30 Table 3-9. Sample Acquisition & Processing instruments on Planetary Missions ......................... 32 Table 3-10. DSN Near-Earth Frequency Capability ........................................................................ 39 Table 3-11. DSN Deep Space Frequency Capability ....................................................................... 39 Table 3-12. Summary of Attitude Control Methods ...................................................................... 54 Table 3-13. Spacecraft Power System Technology Options .......................................................... 66 Table 3-14. Power system options considered in this research .................................................... 69 Table 4-1. Lunar Polar Vehicle Science Objectives (42) ................................................................. 73 Table 4-2. Requirements for Lunar Polar Volatiles Mission and Spacecraft .................................. 75 Table 4-3. Requirements for Spacecraft Design Tool .................................................................... 76 Table 4-4. Comparison of C, C++, MATLAB Attributes ................................................................... 80 Table 4-5. Science Traceability Matrix (Science Objective 1) ........................................................ 87 Table 4-6. Science Traceability Matrix (Science Objective 2) ........................................................ 88 Table 4-7. Science Traceability Matrix (Science Objective 3) ........................................................ 89 Table 4-8. Science Traceability Matrix (Science Objectives 4 and 5) ............................................. 90 Table 4-9. Science Instrument Mass and Power Summary ........................................................... 91 Table 4-10. Example Science Modes .............................................................................................. 92 Table 4-11. Comparison of JHUAPL LPVE mission instruments vs. this research .......................... 93 viii Table 4-12. Candidate Lunar South Pole Landing Site Characteristics .......................................... 97 Table 5-1. GMAT Satellite Key Parameters .................................................................................. 102 Table 5-2. Solved GMAT LEO conditions, TLI/LOI Delta-V components, and time of flight ........ 105 Table 5-3. “Mission & System” sheet in Mission and Spacecraft Definition (MASD) tool ........... 110 Table 5-4. “Trajectory” input sheet in Mission and Spacecraft Definition (MASD) tool ............. 112 Table 5-5. “Ground System” input sheet in Mission and Spacecraft Definition (MASD) tool ..... 113 Table 5-6. Payload inputs sheet in Mission and Spacecraft Definition (MASD) tool ................... 114 Table 5-7. “CDS” inputs sheet in Mission and Spacecraft Definition (MASD) tool ...................... 116 Table 5-8. “Telecom” inputs sheet in Mission and Spacecraft Definition (MASD) tool ............... 118 Table 5-9. ADCS inputs sheet in Mission and Spacecraft Definition (MASD) tool ....................... 120 Table 5-10. Propulsion inputs sheet (part 1) in Mission and Spacecraft Definition (MASD) tool 123 Table 5-11. Propulsion inputs sheet (part 2) in Mission and Spacecraft Definition (MASD) tool 123 Table 5-12. Thermal inputs sheet in Mission and Spacecraft Definition (MASD) tool ................ 125 Table 5-13. Structures subsystem inputs sheet in Mission and Spacecraft Definition (MASD) tool ............................................................................................................................................... 127 Table 5-14. Power inputs sheet in Mission and Spacecraft Definition (MASD) tool ................... 128 Table 5-15. Subsystem “Trade” Parameters ................................................................................ 133 Table 5-16. Example set of first 9 System Configuration combinations ...................................... 138 Table 5-17. Transponder Database .............................................................................................. 153 Table 5-18. Antenna Database ..................................................................................................... 154 Table 5-19. RF Amplifier Mass/Power/Efficiency Database ........................................................ 155 Table 5-20. Estimates of CDS Hardware Mass, Power, and Volume based on complexity level 165 Table 5-21. Modern Spacecraft Attitude Control Methods ......................................................... 174 Table 5-22. Star Tracker Database ............................................................................................... 177 Table 5-23. Sun Sensor Database ................................................................................................. 178 Table 5-24. IMU/IRU Database .................................................................................................... 178 Table 5-25. Reaction Wheel Database Subset ............................................................................. 191 ix Table 5-26. RCS Thruster Pairs to Rotate About S/C Body Axes .................................................. 195 Table 5-27. RCS Thruster Database Subset (5 -100 N thrust) ...................................................... 197 Table 5-28. Propulsion Engine Database Subset ......................................................................... 208 Table 5-29. Historical Rover mass and power data ..................................................................... 224 Table 5-30. Historical Rover dimensional data ............................................................................ 224 Table 5-31. Secondary Battery Database ..................................................................................... 243 Table 5-32. Solar Cell Database ................................................................................................... 246 Table 5-33. Power Path Efficiencies by Power Control Method .................................................. 250 Table 5-34. Solar array specific power options ............................................................................ 250 Table 5-35. Radioisotope Power System Database ..................................................................... 251 Table 5-36. Available Bi-propellant Engines for Lander Propulsion System ................................ 279 Table 5-37. Filtering System Configurations into Runnable Set .................................................. 280 Table 6-1. System Configuration Design Feasibility Results ........................................................ 284 Table 6-2. Feasible design total launch masses (min and max) for each Rover power configuration ................................................................................................................................ 288 Table 6-3. Feasible design Rover total mass summary ................................................................ 290 Table 6-4. Minimum mass solar-powered Rover mass breakdown (config ID = 342) ................. 306 Table 6-5. Minimum mass RPS-powered Rover mass breakdown (config ID = 6102) ................. 306 Table 6-6. Minimum mass Fuel cell-powered Rover mass breakdown (config ID = 6822) .......... 306 Table 6-7. Rover subsystem characteristics of minimum total launch mass solar-powered Rover configuration 342 .............................................................................................................. 307 Table 6-8. Lander subsystem characteristics of minimum total launch mass solar-powered Rover configuration 342 .............................................................................................................. 307 Table 6-9. Rover subsystem characteristics of minimum total launch mass RPS-powered Rover configuration 6102 ............................................................................................................ 309 Table 6-10. Lander subsystem characteristics of minimum total launch mass RPS-powered Rover configuration 6102 ............................................................................................................ 310 Table 6-11. Rover subsystem characteristics of minimum total launch mass fuel cell-powered Rover configuration 6822 ............................................................................................................ 311 x Table 6-12. Lander subsystem characteristics of minimum total launch mass fuel cell- powered Rover configuration 6822 ............................................................................................. 312 Table 6-13. Comparison of Selected System Configurations ....................................................... 314 Table 6-14. Comparison of 3 Selected Configurations and Other Lunar Polar Mission Concepts ...................................................................................................................................... 317 Table 6-15. Descent & Landing design for system configuration 342 ......................................... 318 Table 6-16. Descent & Landing design for system configuration 6102 ....................................... 318 Table 6-17. Descent & Landing design for system configuration 6822 ....................................... 318 Table 10-1. Fuel Cell Types (56) ................................................................................................... 362 xi LIST OF FIGURES Figure 3-1. Left: Chang’e 3 lander on the lunar surface. Right: Yutu rover on the lunar surface. Source: CASC/China Ministry of Defense ......................................................................... 15 Figure 3-2. NASA’s prototype Resource Prospector rover searching for a sample at the Johnson Space Center rock yard (August 2015). Source: NASA .................................................... 17 Figure 3-3. Generic Telecommunications Subsystem Block Diagram ............................................ 40 Figure 3-4. Classes of Rocket Propulsion Techniques. Source: (34) .............................................. 62 Figure 3-5. Components of a Space Power System (41) ................................................................ 65 Figure 4-1. “Vee” Systems Engineering Process Model ................................................................. 78 Figure 4-2. Lunar South Pole craters and temperature map from LRO Diviner thermal mapper data (NASA) ...................................................................................................................... 95 Figure 4-3. LRO LEND maps of epithermal neutron flux at North and South lunar poles (47) ...... 96 Figure 4-4. Epithermal neutron flux map at Cabeus crater from LRO LEND data (48) .................. 98 Figure 4-5. Epithermal neutron flux map at Shoemaker crater from LRO LEND data (47) ........... 98 Figure 5-1. Overall Mission and System Design Process .............................................................. 101 Figure 5-2. Solved GMAT lunar transfer trajectory (Earth inertial view) ..................................... 106 Figure 5-3. Solved GMAT low lunar orbit (Moon inertial view) ................................................... 107 Figure 5-4. Overall Process to Define System Design Parameters and Create System Configurations in MASD tool........................................................................................................ 108 Figure 5-5. Trajectory and Ground Systems design parameter organization in MATLAB input files ............................................................................................................................................... 130 Figure 5-6. Payload and subsystem design parameter organization in MATLAB input files ....... 132 Figure 5-7. Overall Architecture of the Mission and Spacecraft Sizing (MASS) Tool ................... 139 Figure 5-8. Algorithm for System Design Module ........................................................................ 144 Figure 5-9. Algorithm for Spacecraft Design Module .................................................................. 147 Figure 5-10. Modeling of Subsystem Design Module Inputs and Outputs .................................. 149 Figure 5-11. Telecom Design Module Top-level Architecture ..................................................... 151 Figure 5-12. Algorithm for designing DTE architecture ............................................................... 153 xii Figure 5-13. Array of Uplink Margins ........................................................................................... 155 Figure 5-14. Array of Downlink Margins ...................................................................................... 156 Figure 5-15. Algorithm for designing the Relay architecture ...................................................... 159 Figure 5-16. CDS Design Module Top-Level Architecture ............................................................ 161 Figure 5-17. ADCS Design Module Top-level Architecture .......................................................... 171 Figure 5-18. Modeled ADCS Slew Profile ..................................................................................... 182 Figure 5-19. Pyramid configuration for 4 reaction wheels (51) ................................................... 186 Figure 5-20. Tetrahedron configuration for 4 reaction wheels (51) ............................................ 187 Figure 5-21. RCS Thruster Configuration (16 thrusters, 2 strings of 8) ........................................ 195 Figure 5-22. RCS Pressurization Systems ..................................................................................... 202 Figure 5-23. Propulsion Design Module Top-Level Architecture ................................................. 206 Figure 5-24. Chemical propulsion module sizing algorithm ........................................................ 211 Figure 5-25. Thermal Design Module Top-Level Architecture ..................................................... 216 Figure 5-26. Rover Structures Design Module Top-Level Architecture ....................................... 222 Figure 5-27. Historical rover mobility system mass vs. remaining rover mass ............................ 225 Figure 5-28. Historical rover wheel diameter vs. total rover mass .............................................. 225 Figure 5-29. Historical rover wheel width vs. total rover mass ................................................... 226 Figure 5-30. Historical rover width vs. total rover mass .............................................................. 227 Figure 5-31. Historical rover length vs. total rover mass ............................................................. 227 Figure 5-32. Historical rover height vs. total rover mass ............................................................. 228 Figure 5-33. Lander Structures Design Module Top-level Architecture ...................................... 229 Figure 5-34. Modeled RCS tank support structure ...................................................................... 231 Figure 5-35. Lander top deck support beams .............................................................................. 234 Figure 5-36. Engine mounting structure (shown in gray) ............................................................ 237 Figure 5-37. 3-member landing leg structure .............................................................................. 239 Figure 5-38. Power Design Module Top-level Architecture ......................................................... 241 Figure 5-39. Descent & Landing phases ....................................................................................... 258 xiii Figure 5-40. Descent & Landing Algorithm .................................................................................. 262 Figure 5-41. Geometry of the Lunar Braking Burn 1 De-orbit and Descent Problem (58) .......... 270 Figure 6-1. Feasible design total launch mass vs. combination run order .................................. 285 Figure 6-2. Feasible design total launch mass vs. final landed mass (by engine family) ............. 286 Figure 6-3. Feasible design total launch mass vs. final landed mass (by Prop tank material type) ............................................................................................................................................. 287 Figure 6-4. Feasible design total launch mass vs. final landed mass (by Rover power source) .. 288 Figure 6-5. Feasible design total loaded propellant mass vs. total launch mass (by engine family) .......................................................................................................................................... 289 Figure 6-6. Feasible design propellant mass fraction vs. total launch mass (by engine family) .. 290 Figure 6-7. Feasible design total propellant mass vs. total Rover mass ...................................... 291 Figure 6-8. Feasible design solved h0 required vs. final landed mass (by engine family) ........... 292 Figure 6-9. Feasible design solved # D&L engines required vs. combination run order ............. 293 Figure 6-10. Feasible design solved Descent & Landing total duration vs. final landed mass (by engine family) ........................................................................................................................ 294 Figure 6-11. Feasible design solved Descent & Landing sub-phase durations vs final landed mass ............................................................................................................................................. 295 Figure 6-12. Zoom of Feasible design solved Descent & Landing FF, BB2, Approach, and Terminal Descent durations vs. final landed mass ...................................................................... 295 Figure 6-13. Feasible design solved Descent & Landing required propellant mass breakdown vs final landed mass ..................................................................................................................... 296 Figure 6-14. Zoom of Feasible design solved Descent & Landing required propellant mass breakdown vs. final landed mass ................................................................................................. 297 Figure 6-15. Feasible design total configuration run time vs. total launch mass ........................ 298 Figure 6-16. Feasible design total # convergence iterations vs. total launch mass ..................... 299 Figure 6-17. Feasible design average iteration run time vs. total launch mass ........................... 300 Figure 6-18. Feasible design rover average subsystem run time vs. combination run order ..... 301 Figure 6-19. Feasible design lander average subsystem run time vs. combination run order .... 302 Figure 6-20. Feasible design average Descent & Landing module run time vs. combination order ............................................................................................................................................ 303 xiv Figure 6-21. Feasible design average Descent & Landing module run time vs. final landed mass (grouped by engine family) ................................................................................................. 304 Figure 6-22. Feasible Rover Design Subsystem Mass Comparison .............................................. 305 Figure 6-23. Feasible Lander Design Subsystem Mass Comparison ............................................ 305 Figure 6-24. MASS GUI for feasible system configuration 342 .................................................... 315 Figure 6-25. MASS GUI for feasible system configuration 6102 .................................................. 315 Figure 6-26. MASS GUI for feasible system configuration 6822 .................................................. 316 Figure 6-27. Atlas V payload mass vs. Apogee altitude ............................................................... 320 Figure 6-28. Infeasible design total launch mass vs combination run order ............................... 321 Figure 6-29. Infeasible designs solved h 0 vs. total launch mass .................................................. 322 Figure 6-30. Infeasible design # engines vs. combination run order ........................................... 322 Figure 6-31. Infeasible design total configuration run time vs. combination run order ............. 323 Figure 6-32. Infeasible design total configuration run time vs. total launch mass ...................... 324 Figure 6-33. Infeasible design total # convergence iterations (until infeasibility) vs. total launch mass ................................................................................................................................. 324 Figure 6-34. MASS GUI for infeasible system configuration 5967 ............................................... 325 Figure 6-35. MASS GUI for infeasible system configuration 6111 ............................................... 325 Figure 6-36. Infeasible design total launch mass vs. final landed mass (by engine family) ......... 326 Figure 6-37. Infeasible design total launch mass vs. final landed mass (by Prop tank material family) .......................................................................................................................................... 327 Figure 6-38. Infeasible design total launch mass vs. final landed mass (by Rover power source) ......................................................................................................................................... 327 Figure 6-39. MASS GUI for infeasible system configuration 5782 ............................................... 328 Figure 10-1. Moon Orbital and Equatorial Inclination (69) .......................................................... 346 Figure 10-2. Lunar Libration in Latitude (70) ............................................................................... 347 Figure 10-3. Lunar Libration in Longitude (70) ............................................................................ 348 Figure 10-4. Physical diurnal libration of Moon as a result of Earth’s rotation (70) ................... 348 Figure 10-5. Example H 2/O 2 fuel cell voltage polarization curve ................................................. 374 Figure 10-6. Example H 2/O 2 fuel cell system mass vs. current density ........................................ 375 xv ABSTRACT Recent lunar missions have provided evidence of the presence of hydrogen and other volatiles at both lunar poles. This evidence has led to several questions regarding the form of the hydrogen (potentially as water-ice), its distribution, and its origin. In addition, the presence of volatiles at the lunar poles provides a potential source of oxygen and water for future crewed lunar missions, as well as propellant for future lunar launches and orbiting lunar fuel depots. To answer the scientific questions and evaluate the potential for resource utilization, scientists have suggested that in-situ exploration of the lunar poles is a next logical step. Several space agencies, including NASA, the Russian Space Agency, and the Indian Space Research Organization (ISRO), are developing missions to explore a sunlit region at one of the lunar poles. Several lunar polar volatiles concept studies have also been conducted within the past several years by industry, academia, and government agencies. While informative, these studies and planned missions have only considered limited options in term of the design trade space for a lunar polar volatiles mission (e.g. sunlight-only operation in some cases, as well as use of specific heritage hardware and subsystem technology options). As such, a more thorough evaluation of the trade space for a lunar polar volatiles mission is needed. To achieve this, a MATLAB-based tool was developed to design multiple candidate lunar polar volatiles system concepts based on traded subsystem technologies. Such a tool also encounters the multidisciplinary design problem, in which the design of the whole system is determined by the design of the inter- dependent subsystems. Thus, this research aimed to accomplish two goals: to develop an automated design tool approach to generate multiple candidate designs of a space mission, and to use this tool to generate numerous designs of a lunar polar volatiles mission. Overall, this xvi research has demonstrated that it is possible to develop an automated multidisciplinary design tool, using a sequential-iterative approach, that produces feasible (converged mass) designs. In addition, the design results show that feasible low-mass designs exist for 3 lunar polar volatiles mission concepts: a solar-powered rover, a radioisotope-powered rover, and a fuel cell-powered rover. These 3 concepts represent viable options to explore either a permanently-shadowed region or a sunlit region at the lunar South Pole for volatiles, a key step for both future robotic and human exploration of the Moon. 1 1 INTRODUCTION Remote sensing of the Moon by spacecraft on missions such as the U.S. Air Force’s Clementine and NASA’s Lunar Prospector has provided evidence of hydrogen deposits within permanently-shadowed regions near the lunar poles. Although the exact form of these hydrogen deposits is currently unknown, many scientists suspect that they exist in the form of water-ice. Several spacecraft, such as NASA’s LRO, Deep Impact, and Cassini, as well as India’s Chandrayaan-1 lunar orbiter have identified global distributions of near-surface water (or hydroxyl) on the Moon. NASA’s LCROSS impactor mission recently detected many volatiles, including water vapor, within one lunar South Pole crater. In addition, detailed study of Apollo lunar mare basalt samples has revealed the presence of hydrogen-bearing minerals suggesting early lunar magma had water content similar to Earth’s mantle. Overall, the evidence for water- ice at the lunar poles, as well as global hydration, is mounting, thereby leading planetary scientists to pose intriguing questions regarding the origin of this water. The National Research Council (NRC) recently addressed research into lunar polar volatiles as a top priority in its 2011 Planetary Science Decadal Survey. According to this report, the study of lunar polar volatiles is an essential component in understanding the formation and evolution of terrestrial planetary bodies and habitable worlds. For example, the presence of lunar polar volatiles such as water-ice would provide crucial information on the early asteroid and cometary bombardment period of the inner solar system and the formation of the Earth- Moon system, including the origin of life on Earth. In essence, obtaining an inventory of the volatile compounds at the lunar poles would provide key insights into the sources, and 2 prevalence within the early inner solar system, of water and chemicals that are the basis of life as we know it. The scientific data returned from these recent lunar missions have raised several questions regarding the processes behind the origin and deposition of water and other volatiles on the Moon globally and at the poles. While various mechanisms have been theorized to explain the lunar polar hydrogen deposits, no firm answers have been found. These questions reveal a gap in scientific knowledge of the Moon that directly address larger scientific questions. Although recent robotic remote sensing missions have investigated volatile deposits at the lunar poles, the NRC report clearly states that “the form, extent, and origin of such deposits are not fully understood” (1). As a result, key questions exist regarding the “compositions, distributions, and sources” of lunar polar volatile deposits. While lunar remote sensing and impact missions can identify regions with hydrogen-rich compounds and other potential volatiles, in-situ missions are necessary to ascertain the chemical and isotopic compositions of these volatiles. According to scientists at the 42 nd Lunar and Planetary Science Conference in 2011, in-situ exploration is considered the “next logical scientific step” in confirming the species of lunar volatiles and hydrogen-bearing compounds and how they are distributed within the regolith. One possible way to address the NRC’s lunar polar volatiles science questions is to deploy a semi-autonomous robotic rover at either lunar pole. Such a science rover would have the benefit of operating its science instruments at multiple locations within a suitable polar area and could obtain samples at depth within the lunar regolith—directly addressing the NRC’s lunar polar volatiles science objectives. The robotic science mission would also be historic and inspirational, as no spacecraft have ever been landed at either lunar pole. 3 In addition to answering science questions, the identification and confirmation of water- ice at the lunar poles would reveal a critical resource for future crewed lunar exploration: lunar water-ice could be extracted as purified drinking water for human crews, and chemically processed into rocket propellants (liquid oxygen and liquid hydrogen) for future lunar surface launches and potential fuel depots (re-fueling stations for spacecraft). As such, it is clear that there is both a current scientific and future exploration need for in-situ robotic lunar science missions. The design of such a lunar polar volatiles rover mission is subject to many trades and options, which could be overwhelming and costly to design using traditional team-based concurrent engineering approaches. In addition, the tool to achieve these designs itself runs into the multi-disciplinary problem (MDP), in which the design of the overall system depends on the design of the inter-related subsystems. Thus, the design tool must be able to address the MDP as well as provide an automated way to design numerous different system configurations and perform subsystem trades. To enable the design of multiple unique system (lander and rover) configurations, a tool named the Mission and Spacecraft Sizing (MASS) tool was developed. The MASS tool can design a multitude of system configurations for a given instrument payload suite, trajectory and general design parameter inputs. The multiple unique system configurations are defined in a separate Excel-based Mission and Spacecraft Definition (MASD) tool. The core engine of the MASS tool is a spacecraft design module that designs each subsystem of each system element in series. This design process is repeated for multiple iterations until the total design mass converges (or not). Using the MASD tool, thousands of unique system configurations were generated. However, the total estimated time (between 20 to 41 days, depending on the average 4 convergence time per design) to run these thousands of configurations presented a research limitation. To avoid these time-intensive runs, the system configurations were filtered down to a few hundred options that could be run in a few hours. These options were obtained by bounding the key performance parameters of the major subsystem design options (for example, lowest and highest efficiency solar cells, rather than all available options). The design results were analyzed to identify 3 candidate system designs: a solar-powered rover mission, a radioisotope-powered rover mission, and a fuel cell-powered rover mission. The minimum total launch mass designs for these 3 options were selected. In terms of future work, the results of this research would provide the planetary science community with multiple candidate conceptual designs, based on a more expansive technical approach than was previously conducted, for a rover mission to explore the lunar South Pole for volatiles and water-ice. These conceptual designs can be starting points for more detailed design of the mission, as well as providing design data for simulation of subsystems and evaluation of their performance. The Excel/MATLAB design tools, as a central element of the system engineering approach in this research, also represent a unique, integrated way to perform a conceptual design of a system of spacecraft and such a method could be adopted for other spacecraft designs. In this regard, the subsystem technology databases used in this research could be expanded to include more options as new technologies develop. The subsystem design modules could also be enhanced with more accurate or detailed models for higher-fidelity design studies. Lastly, it is hoped that the results of this research may promote development of a mission to explore lunar polar volatiles and water-ice to commercial space companies and/or government space agencies, highlighting it as an endeavor both scientifically interesting and technically feasible in the near future. 5 2 RESEARCH PROBLEM Evidence provided by recent lunar missions suggests the presence of hydrogen-rich volatiles, possibly including water-ice, at certain locations at the lunar poles. These recent missions, however, have not been able to conclusively determine whether there is indeed widespread water-ice present at the lunar poles. In other words, there is a gap in scientific knowledge in this area. In addition, while there have been several recent conceptual studies of a lunar polar volatiles rover mission, these studies have been limited in terms of proposed technologies and consideration of alternative subsystem designs. Current approaches to a lunar polar volatiles rover mission, as published by industry, academic institutes, and government agencies, have not incorporated extensive systems engineering or trade space studies, having imposed instead severe design and operational constraints: e.g. sun-light only operation at the lunar poles, direct ballistic-only trajectories, specific heritage hardware, and limited exploration of alternative subsystem designs. Thus, there is a gap in the evaluation of a wider range of designs for such a rover mission. A solution to the scientific knowledge gap is to design, build, launch, and operate a suitable spacecraft (such as a landed rover) to conduct in-situ prospecting for lunar polar volatiles. In this regard, to go beyond the traditional point designs that have been proposed for such a mission, a method must be devised to generate numerous candidate rover mission designs. Identifying a reasonable design method in itself presents another problem, which is the process of designing the overall mission, spacecraft, and subsystems. Thus, the research problem identified here is two-fold: 6 1. To evaluate numerous candidate designs for a lunar polar volatiles rover mission, and 2. To develop a spacecraft design tool to generate these numerous candidate designs. In the effort to design a lunar polar volatiles rover mission, the development of the spacecraft design tool encounters what is known as the multi-disciplinary design problem (MDP). In this problem, the design of an overall system depends on the design of the system’s component elements (or subsystems), where the design of one subsystem typically affects the design of the other subsystems (2). To be able to design multiple candidate designs for the rover mission, a tool must be developed that takes a reasonable approach to addressing the MDP. In the case of the rover mission, both a lander and rover must be designed, and this includes designing their respective subsystems, which are all inter-dependent. The central goal of the research presented here is then to advance the state of the art in concept development of a lunar polar volatiles rover mission by applying a more thorough systems approach than has heretofore been conducted by industry, government or academia. To achieve this goal, the current research aims to perform system and subsystem trade studies and total spacecraft system design to identify multiple candidate system designs that meet the fundamental set of science requirements. In general, this research serves as a unique and new addition to the body of knowledge of spacecraft design (for a mission with a scientific need) by demonstrating a more thorough evaluation of the design trade space and selecting candidate designs based on that evaluation. 7 3 STATE OF THE ART In this section, the state of the art in lunar polar volatiles science, the spacecraft system design process, and spacecraft subsystem technologies is discussed. This provides background information on which a technical approach and solution to the research problem described earlier can be identified. 3.1 LUNAR SCIENCE MISSIONS 3.1.1 Scientific Evidence of Lunar Polar Water-Ice In 1961, California Institute of Technology researchers Kenneth Watson, Bruce Murray, and Harrison Brown first proposed the existence of water ice and other volatiles trapped within the permanently shadowed regions (PSR) at the lunar poles (3). Although the crewed Apollo lunar missions (from 1969 to 1972) brought back samples of lunar rocks and regolith, they were all found deplete of water, except for possible contaminants. As such, the prospect of lunar water ice lingered until 1991, when ground-based radar observations provided initial evidence for hydrogen deposits at the poles of Mercury. This discovery bolstered expectations of finding similar deposits in the polar regions of the Moon. Later ground-based observations by the Arecibo radio observatory in Puerto Rico in 1997 and 2003, however, did not reveal any significant areas at the lunar poles within the upper meter of regolith having the signature of water-ice (4). Additional evidence arrived in 1994, however, when the U.S. Department of Defense’s (DoD) Clementine lunar robotic spacecraft, using its bi-static radar instrument, measured radar backscatter signals with circular polarization ratios (CPR) greater than 1.0 at the lunar South 8 Pole. In 1996, a Science magazine article suggested that the high CPR was representative of ice crystals. This evidence was considered inconclusive, however, as high CPR can also result from rough, rocky surfaces. Despite this, more evidence of water-ice came again in 1999, when NASA’s Lunar Prospector spacecraft detected high concentrations of hydrogen near the lunar poles. In 2009, the journal Science reported that four spacecraft 1 had detected the signature of trace amounts of water or hydroxyl (OH - ) globally in the upper few millimeters of the lunar surface, particularly near the poles. In October of 2009, NASA’s LCROSS (Lunar Crater Observation & Sensing Satellite) spacecraft, a secondary payload launched with the Lunar Reconnaissance Orbiter (LRO) in June of 2009, jettisoned its Centaur upper stage to impact the partially-shadowed lunar South Pole crater Cabeus A. This impact generated a plume that was observed by the LCROSS shepherding spacecraft (which shortly thereafter also impacted the Moon), LRO and several Earth-based observatories. Both LRO and LCROSS instruments detected that up to 20% of the material ejected by the impact were volatiles, including 100 kg of water in the impact crater and ejecta blanket (5) (6). In 2010 the Indian Chandrayaan-1 lunar spacecraft’s mini-SAR (synthetic aperture radar) instrument found evidence for up to 600 million metric tons of water at the lunar North Pole. Although measurements from the aforementioned robotic spacecraft indicate the presence of hydrogen deposits in the form of water-ice at the lunar poles, the evidence is not yet final. It is clear that orbital missions to the Moon have not been able to determine the exact 1 NASA’s Lunar Reconnaissance Orbiter, Cassini and Deep Impact spacecraft, and India’s Chandrayaan-1 lunar orbiter 9 form of the widespread hydrogen deposits. While the LCROSS mission did find evidence for water from the Cabeus crater impact, it is not the equivalent of analyzing samples on site. In addition, it is known that the lunar polar hydrogen deposits exist within permanently-shadowed craters (and also in some polar sunlit regions), which have yet to be investigated by any landed robotic vehicles. 3.1.2 Lunar Polar Volatiles Science Additional details on the scientific basis to suspect the presence of volatiles at the lunar poles is presented in this section. Early analysis of lunar samples suggested the Moon was totally dry. Water was detected in lunar glass beads but it was thought initially to be the result of terrestrial contamination. However, terrestrial contamination would have shown increased ppm (parts per million) of H 2O outward from the center of the glass beads. Instead, the water content was shown to increase toward the center of the glass beads. The permanently-shadowed regions (PSRs) on the Moon are regions where water-ice may be present on the surface. These PSRs, also known as cold traps, are expected to be surround by a permafrost layer of water-ice on average up to 10 cm depth. The PSRs, or cold traps, are characterized by little or no sunlight and, as a result, low temperature. Temperature is the key variable regarding the survivability of water captured at the lunar poles, as temperature controls the sublimation rate. According to data from the LRO’s lunar radiometer experiment, the annual average temperature of lunar polar cold traps is < 100 K, although there are some cold traps that have a minimum temperature as low as 20 K (7). 10 Recent laser reflectivity results from LRO’s Lunar Orbiter Laser Altimeter (LOLA) are also in line with the water-ice interpretation. The LOLA instrument is a low power transmitter that emits laser light for only a few nanoseconds. The laser light reflects off the lunar surface and is received by the LOLA instrument. Using the LOLA instrument, scientists have reported anomalously high reflectivity in the Shackleton crater floor at the lunar South Pole. This crater is an interesting site, because it receives very little direct sunlight and as such remains a cold trap throughout much of the year. In addition, past orbital and Earth-based radar mapping and orbital imaging campaigns have shown conflicting evidence regarding volatiles at Shackleton crater. One alternative explanation of the high LOLA laser reflectivity results within Shackleton crater is space weathering. This is the alteration of chemicals from micro-meteoroid bombardment and solar wind sputtering. These processes result in vapor depositing of iron grains on the crater rims. As a result, mass wasting (shedding material) can result in the appearance of un-weathered material, which seems to have a bright reflectivity signature. However, recent results indicate that the increased reflectivity observed in the PSRs appears to be independent of mass wasting and space weathering. This leaves two remaining hypotheses: either the PSR surface are less susceptible to space weathering (resulting in high reflectivity), or there are volatiles within these PSRs (8). Another key line of evidence for water-ice at the lunar poles comes from neutron detectors aboard orbital missions (see Lunar Prospector and LRO). Neutron detectors make use of neutron scattering, in which neutrons from some source (cosmic rays in the case of planetary science applications) scatter off a surface. The high-speed neutrons lose energy as they collide with atomic nuclei—the lighter the element, the more energy the neutron loses. Since hydrogen is the lightest element (consisting of a single proton), it is very effective at slowing down 11 neutrons. Thus, if a surface is composed of hydrogen-rich material, then a neutron spectrometer can detect that as a larger number of slow-moving neutrons, or as a reduction in the detected amount of high-energy neutrons (9). LRO’s LEND instrument (Lunar Epithermal Neutron Detector), in observations over 4 years from July 2009 to July 2013, of the lunar South Pole has shown low neutron count rates in several prominent craters such as Faustini, Haworth, and Shoemaker. Low neutron count rates indicate the presence of hydrogen. It has also been observed that the global lunar hydrogen concentration increases as a function of lunar latitude (> ± 65 degrees). In addition, the polar facing slopes appear to have higher hydrogen concentration than equator facing slopes. Scientists currently estimate that ~1.5% of the polar deposits are water-ice by mass. Based on this, the expected deposits of water ice must be at least 1 m below the lunar surface. This minimum depth represents the sensitivity level of epithermal neutrons, which penetrate regolith deeper than fast neutrons (10). Radar imaging of the lunar poles represents another good tool for detecting lunar volatiles. Radar is capable of “seeing in the dark” and can observe the PSRs. Since water-ice has unique radar properties, radar can be used to detect the presence of water-ice within the PSRs. Radars are active instruments that provide their own energy source to illuminate the surface being observed. Radar instruments make use of the reflected beam’s circular polarization ratio (CPR), defined as 𝜇 = 𝑆 /𝑂 , where S represents polarization the same as the transmitted beam, and C is the opposite polarization. In general, a rough surface causes multiple bounce backscattering and shows moderate CPR from 0.5 to 1. In the case of ice, however, an interesting property is that there is no backscatter. Instead, there is forward scattering off surface material voids, which preserves polarization. In the intervening surface material matrix, 12 the polarization adds coherently so that the resulting CPR > 1. CPR greater than 1 has been observed on the moons of Jupiter, one reason why they are called the “icy moons”. The first observations of the lunar poles in radar were taken by ground-based radar observatories. Since the polar regions of the Moon have an increasing number of radar- shadowed regions, orbital radar is really needed to image these regions. Two prominent lunar orbital missions that included radar instruments are India’s Chandrayaan-1 (operated from November 2008 to August 2009) and NASA’s LRO. The Chandrayaan-1 spacecraft carried an onboard miniature synthetic aperture radar (min-SAR) that imaged almost 90 % of the lunar poles. The LRO spacecraft had a more sophisticated radar named min-RF, which obtained full coverage of the lunar poles at S-band, including the first radar views of the lunar far side. High CPR signals (typically associated with water-ice) can be misleading, however. High CPR can also be explained by extremely rough, blocky surfaces that cause corner reflections which change the CPR. For example, a surface feature in Arizona shows high CPR (as observed by the AIRSAR mission), but this feature does not have water-ice. To overcome this limitation in standard radars, a bi-static radar instrument can be used to distinguish between radar returns caused by thick ice deposits vs. those caused by rocky surfaces. Previous bi-static radar measurements have come from the Clementine mission in April 1994 (these results were controversial), and both the Chandrayaan-1 and LRO missions (11). In general, low radar return results suggest that there are no near-surface, thick deposits of ice in Cabeus crater (the impact site of the LCROSS mission). Any water there must therefore be interspersed in the regolith in small grains less than 10 cm in size. At the lunar North Pole, radar observations have indicated that there are many anomalous craters that are good candidates for water-ice. 13 Given the previous indications of water-ice at the lunar poles, NASA launched the LCROSS spacecraft (co-manifested with LRO) to impact the Moon in September 2009. In this mission, both the Centaur upper stage and the LCROSS spacecraft impacted the Moon. The impact site, the Cabeus A crater, was selected because it is in persistent shadow, is extremely cold (with an average temperature around 70 K), has significantly low-neutron count (one of the strongest signals of hydrogen at the lunar South Pole), and was expected to be 20-40% ice-rich by area. The Centaur impact produced a 20-30m crater. The LCROSS spacecraft observed this impact, and later itself impacted the Moon about 3 km from the Centaur impact site. LCROSS observed a strengthening cloud of dust and water (ice and vapor), suggesting a persistent water cloud. The water detection suggests water ice grains > 1 µm in size that are relatively pure (ice- to-dust ratio). This data suggests that there is a persistent surface source of water, such as sublimation from exposed ice (12). Scientists theorize that the water at the lunar poles may have come from several sources: asteroids, Jupiter-family comets and Halley-type comets, micrometeoroids, outgassing from the Moon’s interior, and the solar wind (13). Recent models of water deposition from these various sources at the lunar poles, however, cannot account for the observed distribution of elemental hydrogen and OH/H 2O. 3.1.3 Robotic Lunar Exploration and Planned Missions Having identified a gap in the scientific knowledge of lunar polar water-ice (i.e. the questions on lunar polar volatiles posed by the National Research Council in its Decadal Survey), and the possibility of filling that gap with a robotic mission, a literature survey was performed to explore suitable enabling technologies and initial concepts (14). First, a historical survey of lunar 14 missions was done to provide a context for the lunar science that has been performed, so as not to duplicate the effort of any prior mission. This survey revealed that of all robotic missions to the Moon, only 12 were landers: 5 Soviet Luna landers and 7 American Surveyor landers that all landed in mid-latitude regions on the lunar near side between 1965 and 1968. Of the 6 Soviet lunar sample return missions attempted from 1969 to 1976, only 3 were successful and they only retrieved samples from the lunar equatorial regions. For rovers, only 2 were landed in mid- latitude regions of the Moon by the Soviet Union in 1970 (Lunokhod 1) and 1973 (Lunokhod 2). Apart from these landed missions, the only one designed specifically to explore the lunar South Pole was LCROSS (2009), and this was an impactor rather than a landed vehicle. Thus, this survey reveals that no robotic missions have been landed at either lunar pole. Next, future lunar missions currently in the planning and development stages were investigated. The Indian Space Research Organization (ISRO) plans to launch the Chandrayaan-2 mission, consisting of an orbiter, lander, and 20 kg solar-powered mini-rover, to the Moon by 2018 (15). This rover, whose mission life is just 14-15 days, is designed only to explore sun-lit areas near a shadowed South Pole crater, as LRO data suggest the presence of some near- surface ice in sun-lit polar areas. On December 14, 2013, the China National Space Agency (CNSA) successfully landed the Chang’e 3 vehicle at Sinus Iridum (44 degrees N latitude) on the lunar near side. This landed mission represented the first time since 1976 (the Soviet Union’s Luna 24 sample return lander) that a robotic craft was safely landed on the Moon. The Chang’e 3 mission consisted of a lander and 140 kg six-wheeled rover named Yutu (“Jade Rabbit”) that was powered by solar arrays. The rover ceased mobile operations in early 2014 as a result of a mechanical failure. The lander employed a hazard detection system to image the lunar surface prior to landing to identify 15 landing hazards. The CNSA also plans to launch a sample return mission to the Moon in 2017 to obtain 1-2 kg of lunar material. Figure 3-1. Left: Chang’e 3 lander on the lunar surface. Right: Yutu rover on the lunar surface. Source: CASC/China Ministry of Defense In 2013, NASA launched the LADEE (Lunar Atmosphere and Dust Environment Explorer) orbiter to the Moon. NASA is also planning to participate in the international lunar network (ILN) in 2018, which is to be a geophysical network of landers in cooperation with other spacefaring nations. The Russian Space Agency (RSA) is planning several robotic lunar missions. The Luna- Glob 1 mission, repeatedly delayed but now to be launched between 2017 at the earliest to 2019, consists of an orbiter and lunar North Pole lander (Luna-25). The Luna-Resurs lander (Luna-27) was to be provided by Russia on the Indian Chandrayaan-2 mission; however, the failure of the Fobos-Grunt spacecraft in 2011 resulted in Russian withdrawing from the mission due to an inability to provide the lander within the proposed timeline. Additional planned Russian lunar missions include the Luna-Grunt orbiter, lander, and a 400 kg rover capable of in- situ soil analysis, followed by another Luna-Grunt lunar sample return mission. Ultimately, Russia is planning the Luna-Poligon (Lunar Range) fully operational robotic base after 2025 (to be completed by 2037) for resource prospecting and lunar mining (16). 16 The University of Surrey in the UK has proposed two lunar missions: the Moonraker lander to date basalts on the near side, and the MoonLITE orbiter equipped with 4 penetrators for a 1-year mission (17). The Google Lunar X-Prize is also sponsoring an international competition to award $30 million to the first private team to land a rover on the Moon, traverse 500 m, and transmit high-definition video, images, and data (18). Currently, 16 privately-funded teams are registered in the competition. NASA’s Human Exploration and Operations Mission Directorate (HEOMD) is also planning a lunar rover mission known as Resource Prospector (formerly known as RESOLVE, or Regolith & Environmental Science, and Oxygen & Lunar Volatile Extraction). Currently in formulation, if approved this mission could launch in the early 2020s. This proposed mission represents an attempt to close one of NASA’s identified “strategic knowledge gaps” regarding potential future human exploration destinations, particularly the ability to live off of local resources. The 243 kg solar-powered rover is planned to operate for 10 days on the lunar surface at the lunar South Pole’s Cabeus A crater. Carrying a 72 kg science instrumentation package that includes a drill (to obtain 5 samples at up to 1m depth), an in-situ resource utilization (ISRU) high-temperature chemical reactor unit (to heat samples up to 150 C to extract volatiles, or up to 900 C to extract oxygen and water production by means of hydrogen reduction), a gas chromatograph and mass spectrometer (to test volatiles produced by the reactor), neutron spectrometer (to detect sub-surface hydrogen), and near-IR spectrometer (to detect surface volatiles). One of the goals of this proposed mission is to prospect for lunar water, extract it, process it and store it. A limited number of alternative designs were considered, characterized by the active surface spacecraft and the lunar sites visited: a lander to one site; a “hopper” lander capable to visiting multiple sites; a rover powered by batteries only, 17 solar arrays only, solar arrays + batteries, or a radioisotope power system; and lastly, a lander and rover both equipped with science instruments. The solar array + batteries rover option was ultimately selected for additional study, given its ability to explore the boundary between a sunlit and shadowed region (19). Figure 3-2. NASA’s prototype Resource Prospector rover searching for a sample at the Johnson Space Center rock yard (August 2015). Source: NASA Thus, of all the robotic lunar missions currently in development, only 3 are planned for the lunar poles: the lunar South Pole mini-rover aboard the Indian Chandrayaan-2 mission, the Russian Luna-Glob 1 lunar North Pole lander, and NASA’s not-yet-approved Resource Prospector rover mission. However, all 3 are planned for sunlit regions, which may not harbor the highest concentrations of potential water-ice deposits. 3.1.4 Current Lunar Polar Mission Concepts Lastly, proposed lunar mission concepts were researched to determine whether any landers or rovers are being studied by any organization to operate in permanently shadowed craters at either lunar pole. In 2005, Ball Aerospace performed a concept study for a lander with a 50-100 kg science payload to land at Shackleton crater at the lunar South Pole. The Ball team 18 came up with two point designs: one using a dual-mode 2 bi-propellant propulsion system, and another (selected as the final design) using a solid rocket motor (SRM) for a direct landing from trans-lunar cruise. The lander design was also constrained for sunlight only operation; single- string Ball heritage hardware; and a standard ballistic trajectory (borrowed from the Surveyor 1 mission). In 2011, the Johns Hopkins University Applied Physics Laboratory (JHUAPL) performed a concept study on behalf of the NRC’s Planetary Science Decadal Survey for a lunar polar volatiles explorer. The JHUAPL team designed a lander/rover to land in a permanently shadowed region using an SRM for direct descent from the cruise trajectory. The design team compared two power-driven point design options: an Advanced Stirling Radioisotope Generator (ASRG) powered rover versus a batteries-only rover. The lander/rover design had the following constraints: landing in a permanently shadowed region under Earthshine, cruising to the Moon on a standard 5-day ballistic trajectory, and employing a DoD-heritage main propulsion system. The European Space Agency (ESA) recently performed a Phase B1 study in 2012 to deliver a lander to a crater rim or mountain peak at the lunar South Pole in 2018. Constraints for this mission concept study included: continuous sunlight due to the limited availability of radioisotope heater units or RTGs in Europe; heritage hardware from the ESA ATV (automated transfer vehicle for the International Space Station, ISS); direct-to-Earth (DTE) communications for 14 days (followed by radio darkness during the lunar night); and a ballistic trajectory from a high Earth orbit (20). The project, however, was put on hold in 2012. 2 Used for attitude control as well as orbital maneuvers 19 Overall, a literature survey of planned and studied missions has shown three important results: 1) recent lunar missions (particularly orbiters) have not definitively proven the existence of lunar polar water-ice; 2) no robotic vehicles have been landed at the lunar South Pole to study its volatile resources; and 3) recent lunar polar volatiles mission concept studies are limited by very restrictive operational constraints (e.g. sunlight-only operation, direct ballistic trajectories, specific heritage hardware) and subsystem design options explored. Thus, a more thorough system engineering effort at the conceptual stage is needed to establish science needs and mission requirements, to evaluate feasible concepts by trading suitable subsystem technologies, and to identify a feasible mission concept. 3.2 SYSTEM DESIGN APPROACHES 3.2.1 System Engineering & Design The early formulation phase represents a key step in the project life cycle of a space mission or any system. In this regard, applying a thorough systems engineering process at the early concept level phase is a primary enabler of mission success, since it 1) promotes the discovery of critical design issues early in the life-cycle that might affect the development or operation of the system, and 2) reduces the risk of costly design changes being required later on. In general, systems engineering is a formal process by which engineers can decompose and allocate requirements to elements of the system, define its physical characteristics and configuration, perform trade studies of alternative design options, and identify design drivers. All of these activities enable the systems engineer to identify viable designs that meet the customer requirements and stakeholder needs. 20 There are various systems engineering processes, such as water-fall (a sequential development process), spiral (a risk-driven iterative process), and the standard “Vee” process (which consists of the Decomposition & Definition branch, and the Integration & Verification branch). Another related approach is the NASA Systems Engineering Engine process, which consists of three parallel processes: System Design Processes, Product Realization Processes, and Technical Management Processes. The System Design Processes consists of Requirements Definition and Technical Solution Definition processes, which are similar to the “Vee” Process’s Decomposition & Definition Branch. The selection of a suitable systems engineering process typically depends on the application or type of system involved. In addition to the systems engineering process, which is useful for managing the technical design, development, and operation of the system itself, is the design methodology. A methodology consists of guidelines or techniques for solving a particular problem. Three general design methodologies available to design engineers are sequential, centralized, and concurrent. The sequential methodology is a classical approach in which each technical domain/discipline specialist performs their design work in isolation one at a time, and communicates their design to the next specialist in series. This can result in design inconsistencies due to a given specialist using incorrect assumptions, and so this method usually requires several iterations to converge on a design, resulting in a very lengthy process on the order of several months. This is incompatible with the current drive toward reduced product development times. The centralized approach operates by having all the technical domain specialists provide their design data to a central team of system engineers, who manage the design, analyze it and ensure consistency by means of enhanced communication. Then there is the concurrent engineering method. First implemented in the aeronautics industry, concurrent 21 engineering is an approach in which all the technical domain specialists begin working on the system design in parallel, using interconnected design tools in a common design environment in real-time. In this approach, the specialists can directly communicate with each other and exchange data using modern information technology methods. Iteration is still needed for the design to converge, since some of the specialists may be using assumptions out of synch with the rest of the design. The concurrent engineering approach dramatically reduces the time needed to produce a product from several months to several weeks. For space systems, the preferred method to produce a set of architectures or feasible designs is concurrent engineering. Some notable examples of concurrent engineering centers include TeamX at the Jet Propulsion Laboratory, the Integrated Design Center (IDC) at NASA’s Goddard Spaceflight Center, and the European Space Agency’s Concurrent Design Facility (CDF) at the European Space Research and Technology Centre (ESTEC) in the Netherlands. Team X, for example, can achieve a space mission concept design in as little as one 3-hour design session. More sessions, however, are usually required depending on the trade space exploration desired or the complexity of the mission. Some challenges of the current implementations of concurrent engineering include efficient communication between engineers due to many simultaneous conversations, synchronization of the baseline design among the various subsystem engineers, consistency in design documentation, and efficient capture of design decisions and risks. In addition, due to cost constraints, there is usually insufficient time to thoroughly explore the design trade space in the available concurrent engineering design sessions, resulting in a need to properly select the relevant trades before or during a typical study. For deep space science missions, in particular, the variety of destinations and uniqueness of the science objectives renders it time-consuming and costly to explore many 22 alternative concept designs, even under the concurrent engineering paradigm. Thus, there remains a design challenge in executing an effective trade space evaluation. 3.2.2 Example Design Tools Some tools have been developed in an attempt to address the problem of effective trade space evaluation. In general, existing tools to explore the spacecraft design trade space have relied on studying slight variations of existing spacecraft designs, i.e. heritage spacecraft, or require a baseline design of some sort. The tool referenced in (21), for example, requires a space mission design team (such as TeamX) to arrive at a baseline point design specified at the component level before being able to run multiple trade studies. Perhaps up to 80% of the total cost of large aerospace projects depends on decisions made during the early project design phase. As a project develops and matures, it becomes increasingly difficult to make design changes to improve the design or enact cost-saving measures. This indicates a need to provide a thorough exploration of the design trade space. For deep space missions, given the wide range of destinations and uniqueness of each potential mission, it is time-consuming (as therefore costly) to produce a set of alternative designs. Typically, to avoid this cost, mission designers have employed their design intuition and judgment in making design decisions for the mission. However, the result can be final design concepts that differ significantly from the originally envisioned concept. Thus, as implied earlier in this research, there is in general a need within the spacecraft design process to “rapidly” develop the mission concept’s trade space. Each of the alternative design options must be evaluated at the subsystem level. 23 The approach described in (21) is to combine team-generated point designs with model- driven parametric designs to rapidly explore the trade space. To explore the trade space, an Excel-based Systems Trade Model (STM) tool was developed. In this approach, a preliminary baseline design concept (down to the subsystem level) for a particular science mission is first generated by a spacecraft design team (such as JPL’s Team X). In Team X, which uses the concurrent engineering approach, a design team of between 5 to 30 engineers with varying flight experience meets to turn an overall sketch of the mission (including trajectory and science payload requirements) into a final design concept. Each subsystem engineer produces their own design to meet the stated requirements, and the systems engineer collects the resultant subsystem inputs (mass, power, data rates, etc.), to produce a general snapshot of the design. This interaction is iterated on numerous times within a given design session (usually 3 hours each). The overall design process can take up to 3 or 4 design sessions to produce a feasible design. Given the time-critical nature of this concurrent engineering process, there is often little time to evaluate all design possibilities. The result is that only a limited set of design trades are explored, or that these trades must be identified in advance. Once a baseline design is generated, the STM tool itself can be populated. The tool maintains key system and subsystem design relationships to generate an array of trade space options. Another recent method, as outlined in (22), involves the use of a “declarative modeling” approach. In this approach, which requires its own modeling language, the use of interval math arithmetic is applied to the satellite design problem, where each design parameter has an upper and lower bound. The union of all intervals of all variables in the system composes a complete trade space. In this approach, rules and constraints are applied to enforce the mathematical relationships between parameters and then shrinks the interval until a point solution is found. 24 The platform on which the declarative modeling approach was tested is known as SPiDR, or System Platform for Integrated Design in Real-Time. This tool is a procedural web-based design portal for real-time system level, component-based satellite design. The platform has evolved into a graphical user interface environment for rapid modeling of spacecraft. The SPiDR platform uses a procedural and unidirectional, water-fall method for subsystem sizing. Some early procedural approach options considered were: 1) an iterative approach to achieve design convergence, and 2) following some scheme that sets the flow of the design. A problem with the first approach is the possibility of the snowball effect, where the design mass grows and does not converge. A problem with the second approach is that it prioritizes the design of some subsystems above others. To avoid these problems, the interval math-based declarative approach was investigated in a later version of the SPiDR platform. A potential drawback of the declarative approach is that the modeling language is not intuitive. Elegant code can be produced but may be problematic for an average engineer to use. An attempt to alleviate this problem was made with the use of a graphical user interface (GUI) to help build the design program. This GUI interface still itself has a challenge in that a lengthy process is required for manual input specification. In addition, another potential challenge is the ability to capture increasing levels of design fidelity and detail in a rule and constraint network. In addition to the above system design tools, there are also some standalone tools to conduct architecture-level studies and trade space evaluations. For example, the EXAMINE (Exploration Architecture Model for In-space and Earth-to-orbit tool), developed by NASA’s Langley Research Center, is an Excel-based tool that allows a user to graphically define a space system architecture by manually defining waypoints and specifying vehicles at each one (23). The tool operates on the specified architecture by use of sophisticated vehicle sizing algorithms. 25 However, it is limited by the need for extensive user input to define each architecture, which renders the approach not conducive to rapid, automated exploration of the trade space. Another approach that has been investigated is the use of the Object Process Network modeling language applied to Moon-Mars architecture generation. The limitation of this method is that vehicles are specified by destination and travel on predetermined paths (24). Overall, the above architecture-level and system-level design methodologies and tools reveal challenges in the generation of point designs and limitations in the evaluation of the trade space of alternative design options. The rapid concurrent engineering methods are challenged with consistency in communication, synchronization, and documentation of the baseline design among the various engineering disciplines, and limited to exploration of a handful of down-selected trade options. Several of the discussed design tools are also challenged with the amount of manual specification of user inputs, limited by the need for baseline or heritage designs, or are not intuitive in terms of the programming language. 3.3 SCIENCE INSTRUMENTS A unique set of science instruments is required to properly detect and characterize the volatiles (including potential water-ice) at the lunar poles. As an aid in identifying the proper set of science instrumentation (to estimate mass and power requirements), a survey of instruments flown or planned on landers, rovers, or other probes was conducted. In general, the instruments flown on past in-situ missions or planned on future missions can be categorized as follows:  Descent Imagers  Surface Imagers and Cameras  Ground penetrating radars 26  Spectrometers o Infrared (IR) spectrometers: A technique that measures the infrared spectrum of a given sample material (solid, liquid, or gas) to observe the absorption lines as a way to identify the chemical constituents. o Mass spectrometers: a technique that ionizes chemical species within a sample and analyzes dispersions of ions within an electromagnetic field, measuring the elemental mass-to-charge ratio (m/z). o Mossbauer spectrometers: a technique in which a gamma-ray beam bombards a sample and a detector measures the intensity of the beam transmitted through the sample. The resulting spectra can be used to deduce the chemical composition of the sample. o Neutron spectrometers: A technique in which the energy of neutrons scattering off a sample of material are measured. In planetary science applications, these neutrons typically come from cosmic rays. o Raman spectrometers: Uses Raman scattering of laser light to measure molecular vibrations of a sample of material, useful in identifying the chemical constituents.  Atmospheric/meteorology packages  Robotic arms  Sampling acquisition and processing devices The following tables summarize the characteristics of different types of instruments flown or proposed on landers, rovers, and atmospheric probes to the other planets. 27 Table 3-1. Descent Imagers on Planetary Landers/Probes First, descent imagers, as shown in Table 3-1 above, have flown on 3 Mars missions: the Phoenix lander, Mars Science Laboratory (MSL), and the ill-fated Mars Polar Lander (MPL), and on the Huygens probe that investigated Titan as part of the Cassini-Huygens mission. The Mars mission descent imagers have been less than 1 kg in mass and required up to 10 W of power. The Huygens probe descent imager was much more massive, as it also included a spectral radiometer. Table 3-2. Surface Imagers/Cameras on Planetary Landers Surface imagers (or surface cameras mounted on masts) have flown on 4 Mars missions: both Mars Exploration Rovers (MER), Phoenix, MSL, and MPL. Of the landers, the lightest mass Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose Phoenix Mars Descent Imager MARDI 0.453 3 Descent Camera Camera to provide geographic context of landing site during descent. Data-handling problem lead to non-use of the camera. Hugyens Probe Descent Imager/Spectral Radiometer DISR 11.7 13 Descent Camera MSL Mars Descent Imager MARDI 0.6 10 Descent Camera Color camera to take images during 2min period beteween heatshield separation and touchdown. Will help determine vehicle landing location and geologic context. MPL Mars Descent Imager MARDI 0.42 2 Descent Camera Bottom-mounted camera to image terran as lander descends. Will take 10 images, first 10 sec after parachute deploys & before heat shield jettison (at 8km alt), and last at 6m alt. Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose MER Panoramic Camera Pancam 0.34 3 Surface Camera Panoramic multispectral imaging Phoenix Surface Stereo Imager SSI 5.37 51.2 Surface Camera Camera to provide hi-res stereo panoramic images of Martian landscape, from optical thru IR wavelengths. Camera head and mechanical design derived froom Imager for Mars Pathfinder and MPL SSI. MSL Mast Camera Mastcam 2 13 Surface Camera Visual & multi-spectral imaging of landscape mounted on mast 2m above ground. Uses Bayer Pattern Filter CCD to obtain natural color images (w/ need for three images thru red, green, blue filters) MPL Stereo Surface Imager SSI 5.85 n/a Surface Camera Part of MVACS (Mars Volatiles and Climate Surveyor) instrument package. Mast-mounted multi-spectral imager to provide stereo panoramic & close-up imaging. Same imager as Mars Pathfinder. ExoMars Panoramic Camera (Wide-angle camera + High resolution camera) WAC + HRC 1.56 n/a Surface Camera Consists of a wide angle camera and a high resolution camera. 28 was the Mast Camera on MSL, at 2 kg and consuming 13 W of power. An even lighter panoramic camera is planned on the European ExoMars rover (25). Table 3-3. Microscopic Imagers on Planetary Landers Microscopic imagers to study surface samples have also been flown. These imagers have been very light (less than 1 kg) and required less than 3 W of power. Table 3-4. Ground penetrating radar on Planetary Landers A ground penetrating radar is useful for collecting subsurface stratigraphy data. Such an instrument is planned for the European Space Agency’s ExoMars rover. It is expected to have a mass of about 1.38 kg (25). Table 3-5. IR spectrometers on Planetary Missions Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose MER Microscopic Imager MI 0.21 2.15 Microscopic Imager Visible microscopic imaging of target rocks MSL Chemistry & Camera: *Laser-Induced Breakdown Spectrometer *Remote micro-imager ChemCam *LIBS *RMI n/a 3 *Laser Spectrometer *Microscopic Imager *Laser spectrometer: uses powerful laser pulses on small targets w/in 7m of rover, which ablates atoms in an excited state, emitting light. Spectrograph identifies elemental composition of targets. *Microimager: Context imaging for laser spectrometer MSL Mars Hand Lens Imager MAHLI 0.63 n/a Microscopic Imager Focusable color imager on robotic arm turret. Includes 2 white light LEDs for nighttime imaging Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose Future Mission Ground Penetrating Radar 0.5 3 Ground-penetrating radar Identify radar stratigraphy at a depth of 10-20m ExoMars Ground Penetrating Radar WISDOM 1.38 n/a Ground-penetrating radar Shallow ground-penetrating radar Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose MER Miniature Thermal Emission Spectrometer mini-TES 2.4 5.6 IR Spectrometer Infrared emission spectrometry ExoMars Infrared imaging Spectrometer MicrOmega IR 0.96 n/a IR Spectrometer ExoMars Mars Multispectral Imager for Subsurface Studies MaMiss 0.65 n/a IR Spectrometer Located on drill to obtain IR images down borehole. 29 An infrared spectrometer has flown on the both MERs (at 2.4 kg) and is planned on the ExoMars rover (at 0.65 kg) (25) (26). In terms of mass spectrometers, several have flown on past or current Mars missions (MPL, Phoenix, and MSL). The thermal evolved gas analyzer mass spectrometer (TEGA) instrument on Phoenix was 5.7 kg and required 100 W of power, higher in mass than the one flown on MPL (at 3.4 kg). Both examples represent a large reduction in mass compared to the atmospheric probes on the Galileo mission (12.3 kg) and the Huygens probe (17.2 kg). The ExoMars mission is planning a Mars Organic Mass Analyzer (MOMA) instrument at a mass of 6.1 kg. Table 3-6. Mass spectrometers on Planetary Missions Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose Phoenix Thermal Evolved Gas Analyzer mass spectrometer TEGA 5.7 100 Mass Spectrometer Has 8 small ovens to heat samples. Magnetic sector mass spectrometer analyzes composition and isotopic ratios of volatile gases. Galileo Probe Neutral mass spectrometer NMS 12.3 29.3 Mass Spectrometer Hugyens Probe Gas chromatograph mass spectrometer GCMS 17.2 28 Mass Spectrometer MSL Sample Analysis at Mars: *Quadrupole Mass Spectrometer *Gas Chromatograph *Tunable Laser Spectrometer SAM *QMS *GC *TLS 40 600 Mass Spectrometer Addresses past and present habitability of Mars by detecting organic (carbon-based) compounds, chemical state of light elements, isotopic tracers. Supported by Sample Manipulation System (SMS) and Chemical Separation and Processing Laboratory (CSPL). Atmosphere sampled by CSPL valve. Solid material sampled by transferring sieved material to sample cup (74 available) inserted into SAM oven. GC uses He to separate organic compounds into molecular components for QMS and GC MPL Thermal Evolved Gas Analyzer mass spectrometer TEGA 3.4 n/a Mass Spectrometer Device to measure abundances of water ice, CO2, O2, H2O in samples collected by robotic arm. Consists of a tunable diode laser spectrometer, amperometric electrochemical cell, differential scanning calorimeter, 8 sample ovens, 8 reference ovens. ExoMars Mars Organic Mass Analyzer MOMA 6.1 n/a Mass Spectrometer 30 A neutron spectrometer has flown on only one rover mission: MSL (at 4.68 kg and 13W power). Neutron spectrometers have flown on orbital missions to the Moon (and other planets). Two lunar mission examples are the neutron spectrometer on the Lunar Prospector (at 3.9 kg, 2.5 W) and the Lunar Exploration Neutron Detector (LEND) on NASA’s LRO (developed by the Russian Space Research Institute, IKI). Table 3-7. Neutron spectrometers on Planetary Missions Table 3-8. Robotic arms on Planetary Missions Robotic arms on recent landers and rovers have functioned primarily to position science instruments near interesting rock and soil targets for spectroscopy and imaging, as well as to Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose MSL Dynamic Albedo of Neutrons DAN 4.68 13 Neutron Spectrometer Active/passive neutron spectrometer measuring H- and OH-bearing compounds in upper 1-m of surface w/ surface resolution of 1m. Can be used during rover traverses and while rover is parked. Consists of a detector/electronics module and a pulsed neutron generator (PNG). The detector is filled with 3He. The source of neutrons in PNG is a vacuum neutron tube containing tritium-enriched target and deuterium ion source. Deutrons are accelerated toward tritium-enriched target, generating neutrons. Lunar Prospector Neutron spectrometer NS 3.9 2.5 Neutron Spectrometer Instrument designed to detect water ice on Moon to levels less than 0.01 %. Also detects solar wind implanted hydrogen. Consists of two canisters containing He-3 and an energy counter, to count neutrons colliding with helium. One canister is wrapped in cadmium (to screen out thermal, or low-energy, neutrons), the other in tin. Thermal neutrons are cosmic ray generated neutrons that have lost energy due to collisions with hydrogen atoms. Differences in counts between the two canisters signify thermal neutrons, which indicates hydrogen. LRO Lunar Exploration Neutron Detector LEND n/a n/a Neutron Spectrometer Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose Phoenix Robotic Arm w/ scoop RA 9.6 33 Robotic Arm Digs trenches, scoops up soil and water ice samples, and delivers samples to TEGA and MECA instruments MPL Robotic Arm RA 6.12 n/a Robotic Arm Part of MVACS (Mars Volatiles and Climate Surveyor) instrument package. 2-m long with elbow joint and scoop at the end. Has a small camera attached above the scoop, an elbow temp sensor, a soil temperature probe at the arm end. Acquires surface samples and digs trenches. The camera provides close-up images of surface, scooped samples, and trench. 31 provide sample acquisition. Within the past 20 years, robotic arms have flown on the Phoenix and MPL lander missions to Mars, as well as the two MERs and MSL. The robotic arm mass on Phoenix was 9.6 kg, whereas on MPL it was 6.12 kg. The robotic arm, also known as the Instrument Deployment Device (IDD) on the two MERs housed 4 science instruments: the Microscopic Imager (MI), Rock Abrasion Tool (RAT), Alpha Particle X-Ray Spectrometer (APXS), and the Mossbauer Spectrometer (MB). The combined mass of these instruments on the robotic arm turret is ~2 kg. In terms of sample acquisition, processing and analysis, only two flown missions have included such an instrument (see Table 3-9 below): MSL and ESA’s Rosetta comet mission. The MSL rover’s Sample Acquisition, Processing, and Handling subsystem, at a mass of ~70 kg, consists of a robotic arm with a turret at the end housing 5 devices: 2 science instruments—the Alpha Proton X-ray Spectrometer (APXS), and the Mars Hand Lens Imager (MAHLI)—and 3 sample acquisition and preparation tools—the Power Acquisition Drill System (PADS), Dust Removal Tool (DRT), and Collection and Handling for Interior Martian Rock Analysis (CHIMRA). The turret structure has a mass of 30 kg. The Rosetta mission’s Philae lander has a Sample Drill and Distribution System (SD2), which can penetrate 20-30 cm to obtain a 3mm x 6mm sample from comet Churyumov-Gerasimenko. The SD2 instrument has a mass of 5 kg and requires 15W of power (27). 32 Table 3-9. Sample Acquisition & Processing instruments on Planetary Missions In terms of planned or future missions, ESA is expected to house a robotic drill on the ExoMars rover. This drill can sample possible organic material up to 2m depth on Mars. The instrument mass is expected to be 12 kg with power consumption of 70 W. Honeybee Robotics, headquartered in New York, NY, has proposed two drills to operate on the Moon and Mars. The Sample Acquisition Drill on the proposed LunarVader mission is designed to drill down to 1m depth on the Moon (28). It is planned to have a mass of 10 kg and requires up to 100 W of power (29). Honeybee has also proposed several variants of a Mars subsurface drill on their proposed Mars Icebreaker mission. The rotary-percussive drill variants can obtain samples between 1 to 2.5m depth, have mass of 10 kg each, and require between 70 to 120 W power. Mission Instrument Acronym Mass (kg) Power (W) Instrument Type Purpose MSL Sample Acquisition, Processing, and Handling subsystem SA/SPaH 70 n/a Sample Acquisition, Processing & Transfer Acquires and processes rock and soil samples and delivers to SAM and CheMin instruments. Consists of robotic arm, turret on the end of the arm housing drill, brush, scoop, sample processing device, mech & electrical interfaces. Places APXS and MAHLI on selected targets. The remaining three devices on the turret are associated with sample acquisition and sample preparation function: the Powder Acquisition Drill System (PADS), Dust Removal Tool (DRT), and the Collection and Handling for Interior Martian Rock Analysis (CHIMRA). LunarVader Sample Acquisition Drill 10 100 Sample Acquisition, Processing & Transfer Based on Honeybee LunarVader drill to drill down to 1m in lunar regolith. LunarVader Sample Transfer Mechanism 3 12 Sample Transfer The rotary-percussive drill is mounted on a 3-DOF robotic arm that rotates the drill bit end of the drill above the particular sample analysis instrument. A brush is mounted near the drill bit. The drill is rotated so the brush acts against the drill flutes, causing the cuttings to fall into the sample cup or inlet port. Mars Icebreaker Sample Acquisition and Transfer Drill 10 70 Sample Acquisition, Processing & Transfer 1 m rotary-percussive drill on a mission to return to Phoenix or Viking 2 landing site. Drill to acquire and analyze icy samples. Mars Icebreaker Sample Acquisition and Transfer Drill 10 120 Sample Acquisition, Processing & Transfer 2.5 m rotary-percussive drill on a mission to return to Phoenix or Viking 2 landing site. Drill to acquire and analyze icy samples. Mars Icebreaker Sample Acquisition and Transfer Drill 10 100 Sample Acquisition, Processing & Transfer 1 m rotary-percussive drill on a mission to return to Phoenix or Viking 2 landing site. Drill to acquire and analyze icy samples. ExoMars Robotic Drill 12 70 Sample Acquisition, Processing & Transfer To sample possible organic material to a depth of 2m, where degradation from UV (up to 1mm depth), oxidant reaction (up to 1m depth), and ionizing radiation (up to 1.5m depth) is not prevalent. Sample size is 10mm x 30 mm. Rosetta Sample Drill and Distribution System SD2 5 15 Sample Acquisition, Processing & Transfer Penetrates 20-30 cm to obtain a 3mm x 6mm sample in 2014 on Rosetta comet Churyumov- Gerasimenko lander. 33 Note that all the planned sample acquisition and handling technologies are currently at low technology readiness level 3 (TRL), and so would require additional technology development to be flight qualified. For the proposed lunar polar volatiles mission, a robotic drill may be required to obtain samples at depth. The robotic drill is envisioned to be a rotary-percussive drill, similar to those previously mentioned. This is a type of drill that rotates about the drill axis—the “rotary” motion—as well as hammers into the surface—the “percussive” motion. The drill is expected to house a small thermal sensor near the drill bit, to monitor temperatures as the drill digs into the regolith. The drill should be expected to operate at temperatures < 100 K within the permanently-shadowed craters. This just requires using actuators that can survive at those temperatures or suitably placing heaters near the actuators. Honeybee’s lunar robotic drill is expected to drill down to 1 m in 1 hour using 100 W of power and 100 N of weight-on-bit (WOB). Various losses and inefficiencies are expected that will increase the power requirements into the drill actuators. Assuming losses up to 30%, the main actuators will require 150 W or more. Since this power level must be sustained for at most 1 hour, an energy level of 150W-hr is required. Thus, the onboard battery should be sized for this larger energy requirement. Although the Honeybee drill is expected to drill down to 1 m within an hour, the drill operations may actually be somewhat slower. For example, to collect samples at various depths, the drill could be operated in a “biting” mode. In this scenario, the drill is advanced a small 3 TRL is a NASA method of estimating the maturity of critical technology elements of a project. 34 distance into the lunar regolith, followed by drill pull-out, sample collection and transfer. This is repeated several times until the ultimate drilling depth is reached. In terms of sample format, a system that acquires a powder during drill is preferred over one that obtains a solid core. The extra complexity of a solid core processing system renders the solid core acquisition option less attractive. There are several downsides to solid core sampling option. One downside is that, after acquisition is initiated, the core must be broken off at some point. Another drawback is that the solid core must then be crushed into a fine material. Existing rock crushers are assumed to be highly inefficient; it is not known how well lunar regolith from a permanently-shadowed crater could be crushed given that scientists cannot reliably model the consistency or hardness of the material. In addition, an onboard mass spectrometer would likely require a powdered sample—as typically is found in soil-type material. As a result, it might be better to obtain a sample already in powdered form while drilling. This can be achieved by using the drill cuttings as the sample material. As the drill progresses, the cuttings will adhere to the drill flutes. Cuttings at a particular depth can be collected within a tube near the drill bit. A sample possibly containing water ice can be collected by assessing the hardness of the material as its being drilled. That is, ice-bound material will be harder to drill. Once the robotic drill acquires drill cuttings on the auger flutes, a mechanism is needed to transfer them to the sample analysis instruments. One of two options could be emplaced for this:  The first option involves mounting the drill on a 3 degree-of-freedom (DOF) robotic arm. The arm rotates the drill from a stowed position on the rover, to a drill-ready position. The arm then drills and acquires cuttings on the drill flutes, captured within a sample 35 holding tube near the drill bit. The arm then rotates to a sample transfer position above the inlet port of a sample analysis instrument on the deck of the rover. A metal brush near the drill-bit end of the drill can then brush off the drill cuttings from the flutes into the inlet port. The drill is rotated and then advanced along the drill axis so that the brush encounters the cuttings. The cuttings then fall into the inlet port.  The second option involves a drill rigidly attached in a vertical position relative to the rover deck. The cuttings are first obtained on the drill flutes, say in a drill-some-small- depth and pull out procedure. If the sample cuttings are in the form of a fine powder, a pneumatic system can be used to pump the sample through a flexible tube. The exit end of the tube, using a boom or arm, can then be positioned above the appropriate sample analysis instrument inlet port. For the purposes of this research, the first option is chosen, as it is currently being designed by Honeybee Robotics on one of many test robotic drills. Such a sample transfer mechanism, as planned by Honeybee, is expected to have a mass of 3-5 kg, in addition to the drill mass itself, and require 10-12 W of power during sample transfer. The full drill system, including sample transfer, is assumed to require a mass of ~12 kg (per the researcher’s visit to Honeybee Robotics in Pasadena, CA in Spring 2012). While the drill is operating, data would be collected at a rate of 4 Hz on all drill actuators, temperature near the drill bit, and weight-on-bit. The drill will also require a “Z- stage”, which is a mechanism that moves the drill head up and down along the drill axis, providing a 4 th degree of freedom. 36 3.4 SUBSYSTEM TECHNOLOGIES The following sections describe general background information on various spacecraft subsystems, and in some cases the latest available and planned technologies for spacecraft subsystems. In general, this information provided a basis on which to architect the subsystem sizing tools in order to generate system designs for the lunar polar volatiles mission discussed in this research. 3.4.1 Telecommunications The telecommunications subsystem consists of hardware onboard the spacecraft that provides a communications interface between the spacecraft and the ground. Using this subsystem, data from the onboard payload (usually science instruments) and spacecraft engineering and housekeeping data are formatted and transmitted to ground station operators and other users. In addition, spacecraft commands can be transmitted from the ground station to the telecommunications subsystem onboard the spacecraft. These commands then get disseminated to the desired spacecraft subsystem or payload to provide control of activities (30). Primary functions of this subsystem are:  Carrier Tracking: o 2-way coherent: The downlink signal is transmitted at a frequency offset by a fixed, pre-determined ratio from the uplink carrier signal using the receiver’s voltage-controlled oscillator o 2-way non-coherent: The lock onto the uplink signal is lost. As such, the downlink signal is thereafter controlled by the master oscillator, so that the transmit frequency is independent of the uplink signal. 37 o 1-way links: only uplink or downlink  Command Reception and Processing: receive uplink signal direct-from-Earth or from relay satellite, process it into commands, and route the command(s) to the desired subsystem  Spacecraft and Science Telemetry Processing and Transmission: downlink payload and spacecraft engineering and housekeeping (E&H) data direct-to-Earth or to relay spacecraft. The E&H data is received from the Command and Data Subsystem (CDS) either as real-time subsystem data streams or stored data in memory, and then modulated onto a downlink carrier signal.  Ranging: The spacecraft re-transmits a ranging signal received from the ground either coherently or non-coherently. This turnaround provides tracking data to ground navigators so they can determine the spacecraft’s range (position) and range rate (line- of-sight velocity). A 2-way coherent return signal permits the ground to measure the signal’s Doppler shift, and hence, the range rate from the ground station to the spacecraft.  General subsystem operations: Aside from transmission/reception of data, this subsystem must also process received commands, provide engineering telemetry on its own health & safety to CDS, provide antenna pointing (auto-tracking for mechanically steerable antennas or electronically steerable beams), and provide fault detection and recovery in case of a fault in its own or other subsystem (e.g. autonomously transition to the omni-directional antenna if antenna pointing capability is lost due to loss of attitude control). 38 The telecommunications subsystem must be designed to meet requirements, constraints, and regulations. The requirements are mission-specific specifications as to how the subsystem must function and what capabilities it must have. Constraints are typically on subsystem mass, power, and volume given limits on the design of the spacecraft; launch vehicle vibrational severity; electromagnetic interference levels; and cost. Finally, institutional regulations must be met to avoid frequency conflicts and ensure that received radiated power levels at the ground are within limitations. 3.4.1.1 Communications Architecture In order to transmit and receive data between the spacecraft and ground stations, a suitable communications architecture must be selected. The communications architecture consists of a network of spacecraft and ground stations, connected by communications links. For the purposes of this research, the communications architecture can be defined by the functions that must be provided. Three general communications architecture functions are (30): 1. Tracking, Telemetry and Command 2. Data Collection 3. Data Relay These functions can be provided either through a point-to-point architecture or a broadcast architecture. In the point-to-point network, data is transmitted between the ground and spacecraft, or between the ground and a relay satellite and the relay satellite and the spacecraft, via single, direct links. In the broadcast network, data is transmitted between the spacecraft and multiple ground stations located at different positions. 39 For the purposes of this research, given that the complete spacecraft stack travels from low Earth orbit to the Moon, and that the rover lands and solely operates on the lunar surface, a point-to-point architecture can be chosen. To simplify the telecommunications architecture and subsystem design, it is desired to utilize NASA’s Deep Space Network (DSN) of ground stations. This imposes specific restrictions on available communications frequencies and supportable data rates for uplink and downlink, as shown in Table 3-10 and Table 3-11 (31) (30) (32). In these table, the frequencies allocated by the International Telecommunications Union (ITU) for DSN uplink and downlink, for both near-Earth and deep-space applications are shown. Typical frequency bands for deep space missions are S-band, X-band and Ka-band. NASA deep space missions thus far have used downlink/uplink frequencies up to 32 and 34 GHz (Ka-band). Note that the cut-off distance from the Earth for use of the Deep Space table is 2 million kilometers and beyond (33) (30) (34). Table 3-10. DSN Near-Earth Frequency Capability Parameter Unit S-band X-band Ka-band Uplink Lower Freq GHz 2.025 7.19 n/a Uplink Upper Freq GHz 2.11 7.235 n/a Downlink Lower Freq GHz 2.2 8.45 n/a Downlink Upper Freq GHz 2.29 8.5 n/a Uplink Lower Data Rate bps 1 1 n/a Uplink Upper Data Rate bps 2000 2000 n/a Downlink Lower Data Rate bps 8 8 n/a Downlink Upper Data Rate bps 6.60E+06 6.60E+06 n/a Table 3-11. DSN Deep Space Frequency Capability Parameter Unit S-band X-band Ka-band Uplink Lower Freq GHz 2.11 7.145 34.2 Uplink Upper Freq GHz 2.12 7.19 34.7 Downlink Lower Freq GHz 2.29 8.4 31.8 Downlink Upper Freq GHz 2.3 8.45 32.3 40 Parameter Unit S-band X-band Ka-band Uplink Lower Data Rate bps 1 1 1 Uplink Upper Data Rate bps 2000 2000 2000 Downlink Lower Data Rate bps 8 8 8 Downlink Upper Data Rate bps 6.60E+06 6.60E+06 1.00E+07 3.4.1.2 Subsystem Components A block diagram of a generic spacecraft telecommunications subsystem is shown in below in Figure 3-3 (30). This example system includes two transponders for redundancy and two antennas. The basic components of the system are: a transponder, low-pass filters, band- reject filters, RF switches (separate receive and transmit units), diplexer to a given antenna, and the antenna. Figure 3-3. Generic Telecommunications Subsystem Block Diagram In a representative downlink, a transponder receives data simultaneously from two digital bit streams: 1) payload data, either from data storage or real-time data, and 2) spacecraft engineering and housekeeping data from all subsystems. The transponder then modulates the two streams onto subcarriers, followed by modulation into the main carrier signal. The Transmitter Receiver Transponder A Transmitter Receiver Transponder B Low- pass Filter Band Reject Filter Transmit RF switch Diplexer Antenna A Receive RF switch Low- pass Filter Band Reject Filter Low- pass Filter Low- pass Filter Antenna B Diplexer 41 composite signal exits the transponder and passes through a low-pass filter, which reduces interference from other frequency sources. The low-pass filter, when processing a transmitter signal, reduces high frequency content and intermodulation coming from the receiver. The low- pass filter, when processing a received signal, reduces high frequency content above the diplexer stop-band. The signal then passes through a band reject filter, which reduces erroneous signals coming from the transmitter at the receiver’s center frequency. This is done in order to help the diplexer isolate the receiver from the transmitter. Next, the signal is routed to an RF transfer switch, which selects the primary transmitter and antenna. The diplexer allows the same antenna to be used for both transmitting and receiving. In a representative uplink to the spacecraft, one of the antennas receives a composite uplink signal from the ground. The signal travels to the diplexer, which sends it to the receiver RF switch. This switch selects the receiving antenna and receiver within the active transponder. The signal next goes to a low-pass filter and then onto the receiver in the selected transponder. The receiver demodulates the signal and sends commands on to the Command and Data Subsystem (CDS). The following sections describe the key telecommunications hardware components in more detail. 3.4.1.3 Antenna The primary function of the antenna is to receive an incident signal or transmit a signal to another receiver on the ground or onboard another spacecraft. A real antenna neither receives nor transmits radiation with equal sensitivity in all directions—that is, a truly isotropic antenna does not exist. Plotting the radiation intensity of a given antenna in a polar plot reveals 42 its radiation pattern. For a highly directional antenna, this pattern shows that most of the radiation is emitted within a main beam, while lower levels of radiation emerge in the side lobes. The half-power beam-width of a directional antenna can then be defined as the angle of the main beam within which the antenna gain is within 50% (3 decibels) of the peak gain. The 3 dB beam-width for an aperture-type antenna is related to the signal wavelength (or frequency) and antenna diameter according to the following rule of thumb: 𝜃 = 70𝜆 𝐷 = 21 𝑓 𝐺𝐻𝑧 𝐷 Equation 3-1 where 𝜆 is the wavelength and 𝐷 is the antenna diameter. In the second form of the formula, 𝑓 𝐺𝐻𝑧 is the signal frequency in GHz and the diameter is in meters. Other beam-width formulas exist for other types of antennas. Since a directional antenna focuses most of the signal power in a specific direction, the radiation is amplified by a power gain. This is defined as the ratio of the actual power flux density to that from a lossless isotropic antenna, or, alternatively, the ratio of the effective aperture area to that of an isotropic antenna, as shown in the following formula. 𝐺 = 𝐴 𝑒 𝜆 2 4𝜋 = 4𝜋 𝐴 𝑒 𝜆 2 = 4𝜋𝜂𝐴 𝜆 2 Equation 3-2 where 𝜂 = 𝐴 𝑒 /𝐴 is the aperture efficiency, 𝐴 is the physical antenna area, and 𝜆 is the signal wavelength. The ground coverage area determines the required beam-width, which in turn determines the required antenna size. The antenna size in turn contributes to the antenna gain. In a typical spacecraft telecommunications design, the antenna gain and beam-width are traded. 43 There are several types of antennas, as described below (35):  Horn antennas: A low-gain, wide beam antenna, typically used at frequencies above 4 GHz. The antenna is either a section of a rectangular or circular waveguide that flares out at the end to the required aperture size. The beam is conical.  Biconical Horn: Similar to a horn antenna except that the beam is toroidal. This is useful for spinning spacecraft, to provide omnidirectional coverage.  Helical antennas: Below frequencies of 4 GHz, helical antennas provide a low-mass solution. They consist of conducting wires wound about a pole in the form of a helix. The beam is conical.  Reflector antennas: For narrow-beam, high gain requirements, the reflector antenna is the satisfactory solution. In this configuration, a horn illuminates a paraboloid reflector. The beam is conical. There are three basic arrangements for the horn feed: 1. Front-fed, in which a waveguide is routed to the focus of the paraboloid. This is a simple, lightweight structure. However, the aperture blockage raises the side- lobe levels and the feed is exposed to the environment 2. Offset feed, in which half a paraboloid is used and the feed is located along the paraboloid axis and is mounted rigidly on a spacecraft surface. Low aperture blockage reduces side-lobe interference and increases antenna efficiency. 3. Cassegrain, most commonly used on ground stations, in which a sub-reflector is placed along the axis of the paraboloid and reflects the signal to the feed equipment, which is located behind the main reflector. Since the sub-reflector blocks part of the aperture, this reflector type is not usually used onboard spacecraft. 44 2. Phased-array antennas: the aperture consists of many separate radiating elements arranged in an array, which is mounted on a convenient spacecraft surface. Each individual element has weak directive properties, but the combination produces a narrow beam due to constructive and destructive interference. The collective beam can be steered electronically over a large angular range. This antenna type, however has high complexity, cost and mass. 3.4.1.4 Transponder The transponder itself is an electronics box that consists of many components (35). For a received uplink signal, a low-noise amplifier (LNA) amplifies a weak signal to levels that can be processed digitally without degradation induced by electronic circuit noise. The down-converter reduces the signal to a lower, intermediate frequency (IF). The IF processor divides the down- converter output into multiple channels and then uses a switching matrix to route the channels to their respective destinations. On the downlink path, the up-converter amplifies the IF signals to the higher frequency at which they will be transmitted. In both down- and up-converters, filtering is often necessary to reject unwanted frequencies produced in the process. Finally, there is the high-power amplifier (HPA), or transmitter, which increase the signal power to the desired level for radiation to space. This transmitter must perform the power increase efficiently, to reduce the load on the spacecraft power subsystem. There are two ways to amplify the signal to be radiated: using either a traveling wave-tube amplifier (TWTA) or a solid state power amplifier (SSPA). The TWTA operates by having an electron beam interact with an electromagnetic signal that travels along a guiding structure. Both the beam and signal must travel at similar velocities. 45 To reduce the signal speeds, the guiding structure is typically a wire helix. Currently, TWTAs are the only choice for high-power, high-frequency applications. TWTAs with helix tubes can output up to 200W power output, with efficiencies of 55 to 60%. The primary disadvantage of the TWTA, however, is the high-voltage (several kilovolts) which must be supplied. Typically, 28V is supplied to the transponder, with DC-to-DC converters providing the required voltage changes. In addition, TWTAs suffer from degradation as a result of a reduction in cathode emission. The SSPA, is essentially a power transistor that outputs up to 2W at Ka-band (24-40 GHz) and 60W at L-band (1-2 GHz). The advantage is that the SSPA is lower mass, lower cost, and higher reliability than a TWTA, eliminating the need for a complex voltage supply. The main disadvantage, however, is the low power efficiency, typically 25 to 30%. Other components of the transponder may include the local oscillator, which provides a continuous sine wave to the down- and up-converters. It is usually good practice to include a single, master oscillator. 3.4.2 CDS The Command and Data Subsystem (CDS) provides processing of commands, spacecraft and payload telemetry, and houses the spacecraft’s central computing processor. For command processing, the CDS receives commands from the ground, decodes them, and distributes them to the proper subsystem or payload. For telemetry processing, the CDS packages the telemetry streams into a format useful for transmitting back to the ground, and monitors telemetry for performance and fault conditions. The mass and power of the CDS hardware can be determined by assessing the complexity of the spacecraft (30). That is, the more functions the spacecraft as a whole has to 46 perform, the more complex the CDS design. Since the CDS hardware on most modern spacecraft are based on designs with flight heritage, this complexity-based sizing approach can be employed in this research. See Section 5.3.2 for more detail on the architecture of the CDS design tool developed in this research. 3.4.3 ADCS The attitude determination and control subsystem (ADCS) of a spacecraft places the spacecraft body axes in a desired orientation (or attitude) under the influence of external and internal disturbance torques. This requires onboard sensors to determine the attitude, and actuators to impart control torques to change or maintain the attitude. The ADCS provides attitude control that enables other spacecraft subsystems to perform their functions, such as communications, propulsion, solar array pointing for power generation, etc. In general, ADCS provides two functions (36): 1) attitude determination, defined as estimation of the orientation of one or more spacecraft axes in inertial space; and 2) attitude control, which consists of attitude stabilization (maintaining the spacecraft attitude) and attitude maneuvering (re-orienting, or slewing, the spacecraft from one attitude to another). The first function requires attitude sensors to provide attitude measurements. The second function requires a control method (either passive or active) to provide a torque that either maintains the attitude or slews the spacecraft. Passive attitude control requires no control actuators (environmental torques are typically used to achieve control), whereas active attitude control does require actuator hardware. The control method can sometimes include both active and passive techniques. 47 The spacecraft must achieve certain attitudes to perform critical functions—i.e. pointing key instruments to particular targets within some allowable pointing accuracy. The pointing accuracy requirement is defined as the total pointing error between the achieved instrument pointing direction 4 and the actual or true pointing direction. Pointing accuracy can be divided into two derived requirements: pointing knowledge accuracy and pointing control accuracy. Pointing knowledge accuracy is defined as the maximum allowable error of the estimated pointing direction from the true pointing direction. That is, pointing knowledge accuracy is a requirement on how well the spacecraft’s attitude must be known with respect to an absolute reference frame. It is a requirement on attitude determination. Pointing control accuracy is defined as the maximum allowable error between the achieved pointing direction and the commanded pointing direction (as estimated by the attitude determination function). In other words, pointing control accuracy is how well the spacecraft’s attitude must be controlled. It is a requirement on the attitude stabilization aspect of attitude control. There are various sources of error that contribute to pointing knowledge error and pointing control error, such as instrument mounting misalignments and thermal effects on instrument boresight axis alignment (30). There are typically two other requirements on attitude stabilization. The first is pointing stability, which is defined as a limit on low-frequency spacecraft attitude drift while pointed at a target, and is typically expressed as a rate (deg/hr). The second is jitter, which is defined as a limit on high-frequency attitude motion while the spacecraft is pointed at a target, and is also 4 Defined as a vector in some convenient reference frame such as spacecraft body frame or instrument frame 48 expressed as a rate or frequency. Jitter beyond the capability, or bandwidth, of the spacecraft’s controller can lead to blurring of instrument data (e.g. images). The jitter requirement is intended to avoid this blurring. In addition to providing the attitude determination and control functions, the ADCS must also be designed to meet both mission-level and subsystem-level requirements. Mission- level requirements on ADCS derive from the mission profile (orbit, degree of autonomy, lifetime) and science profile (instrument payloads). The design of the ADCS is also coupled to requirements and design aspects of other spacecraft subsystems (thermal, propulsion, power, communications, and structures) (30). 3.4.3.1 Sensors In order to control the spacecraft’s attitude, the spacecraft must first be able to measure and estimate its attitude. Typically, a suite of sensors is used to measure attitude and the measurements are provided to an attitude estimation algorithm, such as a Kalman filter, in onboard software that combines the measurements into an attitude estimate. Attitude determination sensors come in two categories (35):  Reference sensors: this type of sensor measures the direction of a fixed object such as the Earth, Sun or star, or a planet’s magnetic field direction. The measurement rate is at low frequency. Examples of reference sensors include: star scanners, star trackers, star mappers, sun sensors, Earth horizon sensors, and magnetometers.  Inertial sensors: this type of sensor continuously measures attitude changes or angular velocity of the spacecraft. Gyroscopes provide these measurements in one or two axes at high frequency. A rate gyro is an inexpensive sensor that provides very low noise 49 measurements of the spacecraft angular velocity about its output axis. A rate- integrating gyro (RIG) provides the integral of the angular velocity over some time period. The RIG is most commonly used on spacecraft since it provides high accuracy measurements with low drift. Three mutually orthogonal gyros can be combined into an inertial reference unit (IRU). When 3 accelerometers are included for position and velocity measurements, the package then becomes an inertial measurement unit (IMU). Most spacecraft attitude control laws use measurements of the spacecraft angular velocity, so such sensors are typically required. The inherent bias in an inertial rate sensor is a constant offset in the rate measurement. When the measured rates are integrated using spacecraft kinematics, the predicted attitude can drift. The attitude estimates must therefore by corrected using measurements from reference sensors. Typically, both reference sensors and inertial sensors are used to provide attitude measurements to an Extended Kalman Filter, which outputs an optimal estimate of the spacecraft attitude. The reference sensor can be used to acquire the spacecraft’s initial attitude once in orbit and also to provide periodic attitude updates. This requires that the reference object can be measured by the reference sensor: e.g. the Sun, Earth or stars are within the sensor’s field of view. During periods of eclipse or occultation, the inertial sensor provides the attitude measurements; however, the accuracy of the attitude estimate will degrade until the reference sensor measurement is next available. During nominal operations, both types of sensors are providing measurements: the reference sensor with a reference attitude at some update rate and the inertial sensor with the changes in attitude in between the attitude updates. In between attitude updates, the attitude estimation error grows as a result of random drifts in the inertial 50 sensor. A Kalman filter can be used to minimize the attitude estimation error, and hence the attitude knowledge error. In general, to provide the necessary pointing accuracy in a given attitude control mode, high accuracy is required of the reference sensors and low drift rate (or bias) is required of the inertial sensors. 3.4.3.1.1 Sun Sensors A sun sensor is a detector that is sensitive to visible light from the Sun. There are three types: an analog sun sensor, a sun presence detector, and the digital sun sensor. The sensor field of view can range from several square arc-minutes to 128x128 degrees (37). Multiple sun sensors with an unobstructed view are usually required to achieve the desired coverage. The analog sensor is basically a solar cell with a current output proportional to the cosine of the angle between the sensor normal vector and the incident solar radiation. A minimum of three analog sun sensors are required to determine a measured sun vector (38). The sun presence detector simply indicates when the Sun is within the sensor’s field of view. The digital sensor provides an encoded, discrete output that depends on the Sun angle, and is more accurate than the analog sensor. In the two-axis configuration, the digital sun sensor can provide a sun vector measurement in sensor frame, which can be converted to body frame given knowledge of the sun sensor frame orientation with respect to the body frame. Digital sun sensors may also be limited by a maximum spacecraft rate and are sometimes used for spinning spacecraft (39). 3.4.3.1.2 Star Sensors A star sensor is a device that measures the position of a star within the star sensor frame and compares those coordinates with known stars from a star catalogue onboard the 51 spacecraft. Star sensors provide the most accuracy in measuring the spacecraft attitude (capable of achieving better than 1 arc-second accuracy). Since the star sensor relies on viewing, identifying, and tracking one or more stars, complex techniques to do so are required. The onboard software requirements are also extensive. Interference from bright sources, such as the Sun, Earth, and Moon, can affect performance. Occultation can also interfere with the ability to track stars. A star sensor usually consists of a Sun shade, an optical system, the detector, and an electronics box. The Sun shade is very important, since it blocks out stray light from the Sun and other sources (40). Star sensors were once massive, required lots of power, and were very costly. Recent advancements in CCD 5 (charge-coupled device) and APS (active pixel sensor) technologies have reduced the mass, size, and power consumption of star sensors. There are 3 classes of star sensors, described below (35):  Star scanners: These sensors operate on a spinning spacecraft, which provides a method to scan the sky. The spacecraft attitude is determined by comparing the observed stars to those in the star directory.  Star trackers: These sensors operate on a 3-axis stabilized spacecraft. A single star in the field of view can be used to determine the spacecraft attitude coarsely. Usually more than a single star tracker is required to achieve the desired knowledge accuracy. 5 This consists of an array of photo-sensitive elements that are digitally scanned and whose output is passed onto a microprocessor. 52  Star mappers: These sensors also operate on a 3-axis stabilized spacecraft. The field of view of a star mapper is typically large enough to include several stars. From this field of stars, the spacecraft attitude about the sensor’s optical axis can be determined. 3.4.3.1.3 Gyroscopes As previously mentioned, gyroscopes are categorized as inertial sensors, typically included in inertial measurement units (IMUs). There are several types of gyroscopes: mechanical (spinning-wheel) gyroscopes, ring laser gyros (RLGs), hemispherical resonator gyros (HRGs), and fiber optic gyros (FOGs) (35). The operating principle behind each type of gyro is described below.  The mechanical gyro employs a spinning wheel mounted on a gimbal. The wheel’s spin axis changes direction in response to spacecraft angular motion. The spinning wheel, or rotor, has a constant magnitude angular momentum vector that is parallel to the gyro’s spin axis. Any spacecraft motion about the input axis causes the gimbal that supports the spin axis to precess about the output axis. When only one gimbal supports the spin axis, the device is a single-degree of freedom gyro. A two-degree of freedom gyro uses a second gimbal to support the spin axis.  The RLG utilizes a laser whose light is split through a small triangular ceramic glass prism. Rotating the prism about an axis normal to the triangle results in a longer path length than the oppositely reflected beam. The interference between the two beams can be used to measure angular rate. 53  The HRG detects the response of a mechanical resonator (fused silica or quartz shell) to the Coriolis force. When the shell resonates, a standing wave is generated on the surface. Rotation about the sensitive axis cause the nodes of the wave to precess at a rate proportional to the angular velocity. The Cassini spacecraft is equipped with such a set of gyros. NOTE: Inexpensive piezoelectric vibratory gyros (PVGs) based on similar operating principles are also being developed using micro-fabrication techniques. The PVG functions by using piezoelectric transducers to actuate a small steel bar with triangular cross-section. The response to Coriolis effects can be detected, thereby serving as a measure of the angular rate. Currently the performance of PVGs is inadequate for spacecraft.  The FOG feeds a laser beam into both ends of a long fiber optic coil. Rotation of the coil about its axis causes counter-rotating beams to traverse different distances. The phase difference at the detector is a measure of angular rate. 3.4.3.2 Attitude Control Methods To re-orient or maintain the spacecraft’s attitude requires an attitude control method (also called an attitude control technique). Several methods have been developed, each with a known pointing control accuracy capability. Pointing control accuracy represents the difference between the commanded pointing direction and the true desired pointing direction. The fineness of pointing control usually determines the attitude control method. For example, if a specific mission requires coarse pointing control, one control method might be suitable, whereas another might be more useful for fine pointing. 54 Attitude control methods can be organized into two categories: passive and active. Passive techniques do not require control torque actuators to stabilize the spacecraft attitude. Typically, an environmental torque can be used to provide this function. This type of attitude control is simple and cost effective. Examples include gravity gradient, magnetic stabilization, and spin-stabilization. Active control methods, however, are more complex and expensive, requiring actuators to impart control torque and controller logic to command the actuators given feedback estimates of the spacecraft attitude. Examples are dual-spin stabilization, bias momentum stabilization, and zero momentum stabilization. Passive and active control methods can sometimes be combined to provide full 3-axis attitude control (for example, gravity gradient with pitch momentum bias to provide stiffness in yaw). The following table summarizes the characteristics of passive and active attitude control methods, along with the actuators (30). The attitude control methods are described in more detail in the following sections. Table 3-12. Summary of Attitude Control Methods Control Method Type Control Method Actuator Wheel Desaturation Actuators Pointing Constraint Typical Control Accuracy (deg) # Axes Controlled Passive Gravity Gradient None n/a Nadir- pointed > 5 2 Passive Magnetic Permanent magnets n/a Planet north-south pointed > 5 2 Passive Spin- stabilization None (except for mechanism to spin up) n/a Inertially pointed 0.1 to 1 1 Active Dual-spin stabilization None (except for mechanism to spin up) n/a Inertially pointed spun section; 0.1 to 1 1 55 Control Method Type Control Method Actuator Wheel Desaturation Actuators Pointing Constraint Typical Control Accuracy (deg) # Axes Controlled instruments on de-spun platform constrained by geometry Active Pitch Momentum Bias Momentum wheel Thrusters or Magnetic Torque Rods Nadir- pointed w/ pitch wheel normal to orbit plane 0.1 to 1 1 Active Mass Expulsion Thrusters n/a None 0.1 to 5 3 Active Zero Momentum Reaction Wheels Thrusters or Magnetic Torque Rods None 0.001 to 1 3 Active Zero Momentum Control Moment Gyro Thrusters or Magnetic Torque Rods None 0.001 to 1 3 Although several control methods are available to the spacecraft for this mission, some can be ruled out from the beginning. The mission does not require operations in a nadir-pointed orientation, so gravity gradient control is not needed. In general, an inertially fixed axis is not required in normal operations and so spin and dual spin-stabilization control are also not needed. An exception can be made for the use of a solid rocket motor for large Delta-V maneuvers, such as lunar orbit insertion. In that case, spin-stabilization is typically employed to keep the thrust vector aligned with the desired Delta-V direction. Since the pitch momentum bias control method is typically used with gravity gradient control, this control method is not considered in the trade space. Thus, of all the control methods discussed here, only the mass 56 expulsion (thrusters) and zero momentum (reaction wheels with thrusters) control methods are considered for the mission in this research. 3.4.3.3 Attitude Control Actuators There are two types of attitude control actuators: reaction actuators and momentum exchange devices. Reaction actuators generate torques external to the spacecraft and as such can change the spacecraft angular momentum vector. Examples include thrusters and magnetic torque rods (typically used for desaturation of momentum exchange devices). Momentum exchange devices, in contrast, generate torques internal to the spacecraft and as such do not change the net angular momentum vector. Examples are reaction wheels, momentum wheels, and control moment gyros (38). Each of these actuators is described in more detail in the following sections. Since only mass expulsion and zero momentum control are considered for this mission, as discussed in the previous section, the only applicable actuators are thrusters and reaction wheels. Reaction wheels can be used for fine pointing control and reaction control thrusters can be used to coarser pointing control. 3.4.3.3.1 Thrusters Thrusters are reaction actuators that generate torque by expelling mass. They typically use chemical propellants, in either bi-propellant or mono-propellant systems, to generate thrust that imparts torque to the spacecraft. They are used for attitude control, nutation control in spinning spacecraft, spin rate control, and angular momentum dumping from momentum wheels, reaction wheels, or control moment gyros. The desired torque is obtained by suitably 57 selecting the thrust and location of thrusters. Two thrusters with the same momentum arm and thrust can be positioned to provide a pure couple about a desired axis. In general, a reaction control system requires a minimum of 6 suitably-placed thrusters. If the thrusters are angled such that they each produce a force along more than one axis, then a minimum of four thrusters can sometimes be configured. In each of those cases, however, the thrusters produce both translation and rotation. If pure rotation is required, then typically 8 thrusters can be configured in a single string. If both pure rotation and redundancy are required, two strings can be designed for a total of 16 thrusters. Thrusters operate by pulsing on and off, which generates a constant torque for the pulse duration. Control algorithms that employ thrusters typically use pulse width modulation (PWM), in which a suitable pulse duration is commanded so that the average torque imparted during the pulse is equal to the commanded control torque. A limitation on this is minimum impulse bit (MIB), which is the impulse imparted during the minimum achievable thruster pulse (the shortest time that the thruster can be commanded on and then off). To avoid excess propellant usage, the attitude control algorithm can use a dead-zone, which is a region in which no thruster firings are allowed. That is, when the commanded control torque is below a specific level, or when the rate error and attitude error fall within the dead-zone, the thrusters are commanded closed. As such, only coarse pointing accuracy can be achieved by attitude control thrusters (38). 58 3.4.3.3.2 Magnetic Torque Rods Magnetic torque rods are reaction-type devices that pass current through wire coils to generate magnetic dipole moments. The coil dipole moment 𝒎⃑⃑⃑ interacts with a planet’s magnetic field 𝑩 ⃑⃑ to generate a torque on the spacecraft according to the following equation. 𝑻 ⃑ ⃑ = 𝒎⃑⃑⃑ ×𝑩 ⃑⃑ Equation 3-3 Note that the resulting torque is perpendicular to the instantaneous planet magnetic field, so that torque rods alone cannot generate a torque about any arbitrary body axis. In addition, torque rods have limited control authority, since the magnetic torque generated is small under weak planetary magnetic fields (such as the Earth’s). For these reasons, magnetic torque rods are typically not used alone for attitude control. They are usually accompanied by reaction wheels. Torque rods can also be used to unload momentum built up in the reaction wheels. Torque rods are also accompanied by magnetometers, which measure the local magnetic field. Since torque rods, when active, generate a magnetic field, they cannot be operated while magnetometer measurements are being taken. Since the mission being researched here does not require a spacecraft that operates in low Earth orbit, magnetic torque rods are not considered in the trade space. 3.4.3.3.3 Reaction Wheels A reaction wheel is a momentum exchange device. Mechanically, it is a high-inertia rotor whose spin (in either direction) is controlled by a torque motor. Spinning the wheel in one direction about its spin axis applies a torque to the spacecraft. As a result of conservation of angular momentum, the spacecraft platform responds to the torque (the change in angular momentum) by turning about the wheel spin-axis in the opposite direction. In essence, angular 59 momentum is exchanged between the wheel and the spacecraft. Typically, three reaction wheels are mounted with their axes not coplanar (e.g. an orthogonal arrangement) so that a torque can be generated about any desired platform body axis. A fourth wheel, not orthogonal to the others, can be supplied to provide redundancy (38). Since varying torque, up to the motor’s capability, can be commanded to reaction wheels, fine pointing can be achieved. In a zero disturbance torque environment, the spacecraft’s total angular momentum remains constant. However, spacecraft typically experience external disturbance torques, which change the spacecraft angular momentum. When reaction wheels are employed, they change speed to absorb the change in angular momentum. Since the wheels have a maximum angular momentum storage capability (a maximum spin rate), the angular momentum buildup must be removed by reaction type actuators, such as thrusters or magnetic torque rods. These actuators de-saturate the wheels by allowing them to reduce their wheel speeds. Normally wheel speed changes would impart a torque on the spacecraft, causing it to turn about the torque axis. However, these de-saturation actuators apply reaction torque that absorbs the change in angular momentum induced by the wheel speed change. As a result, the spacecraft attitude can be maintained while also dumping the accumulated momentum. The simplest configuration for reaction wheel attitude control consists of three orthogonal wheels, with each wheel’s spin axis parallel to a spacecraft body axis. This configuration permits the independent sizing of each wheel. While three wheels at a minimum can control the spacecraft’s attitude, if one fails then control is lost. To avoid this and increase the system’s reliability, a fourth wheel can be added. The spin axis of this fourth wheel can be oriented off of the three spacecraft axes to reduce the torque required by that wheel (41). A 60 more general 4-wheel orientation can also be considered: for example, the four wheels can be mounted in a tetrahedron configuration. For a 4-wheel configuration, a steering law is needed to distribute momentum between the wheels. The steering law is a function of the mounting angles of the wheels. At any given time, the momentum stored in the wheels can be mapped into the total angular momentum in spacecraft body coordinates according to the following equation (41). 𝒉 ⃑ ⃑ 𝑡𝑜𝑡 ,𝑏 = 𝐴 [ℎ 𝑤 1 ℎ 𝑤 2 ℎ 𝑤 3 ℎ 𝑤 4 ] 𝑇 Equation 3-4 where 𝐴 is the mounting transformation matrix into spacecraft body frame and ℎ 𝑤𝑖 = 𝐼 𝑤𝑖 𝜔 𝑤𝑖 is the angular momentum of each wheel about its spin axis. The same relationship can also be used to transform the four wheel torques into spacecraft body torques. 𝑻 ⃑ ⃑ 𝑐 ,𝑏 = 𝐴 [𝑇 𝑤 1 𝑇 𝑤 2 𝑇 𝑤 3 𝑇 𝑤 4 ] 𝑇 Equation 3-5 Given a commanded control torque in body frame, the corresponding torques to each wheel can be derived using the pseudo-inverse as: [𝑇 𝑤 1 𝑇 𝑤 2 𝑇 𝑤 3 𝑇 𝑤 4 ] 𝑇 = 𝐴 𝑅 𝑻 ⃑ ⃑ 𝑐 ,𝑏 Equation 3-6 where 𝐴 𝑅 = 𝐴 𝑇 ( 𝐴 𝐴 𝑇 ) −1 is the Moore-Penrose pseudo-inverse of A. This pseudo-inverse gives the same result as minimizing the Hamiltonian 𝐻 = ∑ 𝑇 𝑤𝑖 2 4 𝑖 =1 of the wheel torques. Angular momentum can also be minimized. That is, instead of commanding wheel torques directly, wheel angular momentum can be commanded. The problem then is minimization of 𝐻 = ∑ ℎ 𝑤𝑖 2 4 𝑖 =1 . Note that minimizing the wheel torque commands also minimizes the power consumption, as the torque is proportional to motor current, and power is proportional to the square of the current. 61 3.4.3.3.4 Momentum Wheels A momentum wheel is a similar to a reaction wheel except that it has a large non-zero nominal speed. The wheel spin provides a nearly constant angular momentum that provides gyroscopic stiffness to the spacecraft in two axes. That is, the angular momentum allows the spacecraft to resist external torques about those axes and keeps the spacecraft axis inertially fixed that is parallel to the wheel spin axis. Applying motor torque to change the wheel speed allows pointing control about the third axis (the spin axis). The wheel momentum accumulated as a result of external torques must be periodically removed, using thrusters or torque rods. As an example, a momentum wheel with its spin axis aligned with the orbit normal (the spacecraft pitch axis in the standard orbit reference frame) can resist disturbances about the roll and yaw axes, and can control the attitude about the pitch axis. Such a system is called pitch momentum bias, and can be coupled with gravity gradient to control all three axes and keep the spacecraft nadir pointed. Since there is no long-term need for an inertially fixed spacecraft axis in the lunar mission being researched, use of a momentum wheel is not considered in the attitude control trade space. 3.4.3.3.5 Control Moment Gyros If very high spacecraft turn rates are required, a control moment gyro (CMG) can be employed. A control momentum gyro is a single or double-gimbaled wheel that spins at a constant spin rate. High output torque about a desired axis can be generated by gimbaling the spin axis. While useful for agile attitude maneuvers, they require complex control laws, have 62 high mass and are very costly. For these reasons and overall simplicity, CMGs are not considered in the trade space of control actuators for the mission in this research. 3.4.4 Propulsion The propulsion system onboard a spacecraft provides thrust to alter the spacecraft’s orbit or trajectory. In general, rocket propulsion systems can be classified as depicted in Figure 3-4 below (35). Figure 3-4. Classes of Rocket Propulsion Techniques. Source: (35) There are 3 general categories: Thermal, Electric and Nuclear. The thermal classification can itself be categorized into Chemical, Nuclear Thermal, Solar Thermal, and Laser Thermal propulsion. Most modern spacecraft have employed chemical propulsion for both orbit control and attitude control. Electric propulsion has been used for attitude and orbit control on many commercial satellites. Only recently has electric propulsion been employed for low-thrust Rocket Propulsion Thermal Electric Nuclear Chemical Solid Liquid (mono- prop, bi-prop) Nuclear Solar Laser Electrothermal (resistojet, arcjet) Electromagnetic (Pulsed Plasma) Electrostatic (Ion, Hall Effect) Radioisotope Explosion 63 trajectory control for missions beyond low Earth orbit, e.g. NASA’s Deep Space 1 and Dawn missions (1998 and 2007 launches), and ESA’s SMART-1 lunar orbiter (launched in 2003). In chemical propulsion, a fuel and oxidizer are combusted in a chemical reaction. The hot products of this combustion are expanded through a convergent-divergent nozzle at high velocity. The momentum exchange caused by the discharge of these combustion products exerts a propulsive force on the attached vehicle, which causes translation. Standard chemical propulsion can be classified based on the phase of the propellant used: solid, liquid, and even hybrid (not shown). Since all landers sent to the Moon and Mars to date have used chemical propulsion, and the propulsion system mass accounts for a large part of the overall spacecraft mass, chemical propulsion was the focus of the Propulsion system sizing in this research. Initial research was conducted into sizing an electric propulsion system for a low-thrust trajectory to the Moon; however, the design tool capability was not fully tested in this research. Given the use of a chemical propulsion system for trajectory control and lunar descent and landing, a database of commercially available mono-propellant and bi-propellant engines was assembled. See Section 0 for more details on this database. In general, mono-propellant and bi-propellant engines are advantageous because they can provide high thrust, are throttleable, and re-startable. Hybrid engines were not considered as they have typically been employed in launch vehicles rather than spacecraft. 3.4.5 Thermal Since the architecture of the Thermal subsystem design tool involves use of a simple rule of thumb for mass estimation and a radiator-sizing procedure (see Section 5.3.5 for details), 64 no detailed component selection was performed. As such, the thermal subsystem design is an area for future work to select thermal components for the rover and lander to survive in the cold environment of the lunar South Pole. In general, typical components for a thermal subsystem include passive elements (such as radiators for heat dissipation, multi-layered insulation (MLI), and thermal louvers) and active elements (such as electric heaters to maintain electronics temperatures and propellant tanks within operating temperature limits, heat pipes, and radioisotope heater units, RHUs). 3.4.6 Structures The Structures system on a spacecraft provides the basis of the spacecraft configuration, and is typically sized with minimum mass to support expected loads during launch and spaceflight. No trades were identified in the Structures subsystem for the rover and lander in this research. However, the rover was sized based on historical data, and the lander structure mass was estimated considering the acceleration loads (see Section 5.3.6 for details). 3.4.7 Power The power subsystem for a spacecraft contains the following basic components: primary energy source, energy conversion mechanism, power regulation and control, rechargeable energy storage, and power distribution and protection, and power load. This subsystem organization is depicted in the following diagram (42): 65 Figure 3-5. Components of a Space Power System (42) Options for these power subsystem components are listed below:  Primary Energy Source o Solar radiation: Useful for missions within inner solar system where solar flux is high o Radioisotope: radioactive decay of specific elements o Nuclear reactors: fission (splitting atoms) or fusion (technology not invented yet) o Chemical: energy from a chemical reaction  Energy Conversion o Photovoltaic: photons impinging upon semi-conductor materials generate electricity from sunlight o Thermoelectric: electricity generated from a heat source, which produces a temperature difference between two semiconductor materials, thereby generating an electric potential Energy Conversion Power Regulation & Control Rechargeable Energy Storage Primary Energy Source Distribution & Protection Power Loads 66 o Dynamic alternator: also known as a thermodynamic energy converter; an energy source drives a rotating turbo-generator or reciprocating alternator to generate electricity o Electrochemical: converts chemical energy directly into electricity o Thermionic: thermal energy is converted into electricity using thermionic emission: electrons (working fluid) are emitted from a hot body (cathode) and collected at the anode.  Rechargeable Energy Storage o Electrochemical: converts chemical energy into an electrical potential (voltage) difference o Momentum: kinetic energy in rotating inertia is stored and converted to electricity All the energy conversion methods above are static (no moving parts), except for the thermodynamic alternator. The energy source and energy conversion method together produce individual spacecraft power generation technologies. Characteristics of spacecraft power system options currently available or in development are listed in Table 3-13. Table 3-13. Spacecraft Power System Technology Options Power Technology Energy Source Energy Conversion Method Description Solar arrays Sun Photovoltaic  Widely used on spacecraft  Supports long life spacecraft near inner solar system  Arrays must be pointed toward sun  Cannot operate during eclipse 67 Power Technology Energy Source Energy Conversion Method Description  Power capability degrades over time due to various degradation factors Solar Concentrator Sun Thermodynamic  Solar radiation is concentrated to heat a fluid to generate steam and drive an electric generator or alternator  Can generate up to hundreds of kilowatts of power  Requires large concentrator area  Twice the efficiency of solar arrays Thermo- photovoltaic Radioisotope decay or solar Photovoltaic  Heat is radiated toward IR- sensitive PV cells  Cells must be operated at temperatures < 60 C  Power capability degrades over time due to various degradation factors Primary batteries Electrolyte Electrochemical  Used on earliest spacecraft  Electrolyte creates a potential difference between electrode plates  One-time use (non-reversible) based on charge-capacity (A-hr)  Cell voltage decays with discharge Secondary batteries Electrolyte Electrochemical  Electrolyte creates a potential difference between electrode plates  Usually combined with solar arrays  Provides power during eclipse  Recharged during sunlight  Requires charge/discharge controller Radioisotope Power System Radioisotope decay heat Thermoelectric or thermodynamic  Useful for missions to outer solar system  Suitable for power up to several hundred watts  Uses radioisotope such as Pu-238  Thermoelectric system heats an absorbing material (flight proven)  Thermodynamic system uses Stirling cycle with a reciprocating electrical alternator (not yet flight- proven) 68 Power Technology Energy Source Energy Conversion Method Description Alkaline metal thermal to electric converter (AMTEC)  Direct thermal to electric conversion process (static system) using alkali metal conducting ceramic β-alumina solid electrolyte to conduct sodium ions  Operates at ~1000K hot side, 600 K “cold” side  Suitable for power < 100 W (currently in development for greater power levels)  Low cell voltage Nuclear Power System Nuclear Fission Thermodynamic  Fissile material used to heat a working fluid, whose vapor drives a turbine generator  Useful for missions to outer solar system  Suitable for power in tens to hundreds of kilowatts  Uses fissile material such as uranium-235  Suitable for power up to several megawatts Fuel Cells Fuel + Oxidizer reaction Electrochemical  Longer life than primary batteries  Continuously provides power as long as reactants are supplied  Constant cell voltage  Hydrogen/oxygen fuel cell produces water as the byproduct Thermionic Cell Hot body Thermionic  Electrons released from a hot body (Edison effect), say the cathode, are collected at the anode  No moving parts  Operates at 1800 to 2000 K hot side, and rejects heat at 800 to 1000 K  Low cell voltage Flywheels Rotational kinetic energy (momentum) Electromechanical  High specific energy  potential for twice the life and depth of discharge compared to batteries  no capacity degradation over life  significantly less cost per kW-h than some space-qualified batteries 69 Spacecraft power system technology options that were investigated in this research are listed in the following table. Since the focus of this research is to evaluate spacecraft design for a lunar polar volatiles mission, only four basic power system options were considered: solar arrays, batteries, radioisotope power, and fuel cells. Table 3-14. Power system options considered in this research Power System Option Typical Efficiency (%) Typical Specific Power (W e/kg) Solar arrays ~15-30 ~5-10 Batteries (primary or secondary) ~70-75 n/a Radioisotope Power System ~7-32 ~7-15 Fuel Cells ~10-80 ~100-700 Even though momentum energy conversion technology (the flywheel) was not considered in this research, it does present a possible option for replacement of batteries in future spacecraft. In fact, NASA Glenn Research Center is actively studying it. 6 Although a potential replacement for batteries, the flywheel does have the following disadvantages:  Lower reliability  Safety at rotational speeds > 50,000 rpm  Vibration and transient torque effects on attitude control system 6 The goals of this effort are: specific energy > 200 W-hr/kg; charge/discharge cycles > 75,000; system efficiency > 90 %; cost reduction > 25 % (41). 70 4 TECHNICAL APPROACH 4.1 OVERVIEW The technical approach to designing a lunar polar volatiles mission, as explored in this research, is to automate the engineering design process beyond what present concurrent engineering or other tools can provide. This involves eliminating the need for human interaction during each design cycle and providing a method to conduct a vast array of trade studies. The overall intent is not to replace modern concurrent engineering methods and facilities, but rather to supplement them with a method that can inform the customer and discipline engineers with an early assessment of candidate designs. While some initial user input may be needed to define basic mission/spacecraft requirements and objectives, the approach envisioned here does not require multiple engineers to make design decisions during the design process in real-time. Often, in a concurrent engineering environment, only a few alternative concepts are considered due to the overwhelming trade space of possibilities. By automatically building a table of potential configurations, each one a combination of various subsystem design options, and running them through a system design tool, a more thorough trade space evaluation can be made than might otherwise be possible with humans-in-the-design-loop. In this approach, the need for the expertise of the engineers is not be eliminated, however. Instead, this expertise is still needed for the selection of the spacecraft design parameter inputs. In addition, if this approach were adopted within industry, the expertise of the discipline engineers would also be present in the fidelity of the subsystem design modules 71 that were developed, the component databases utilized, and in the programmable rules the design tool employs for making design decisions. The research presented here, as part of the effort to design a lunar polar volatiles mission, develops an engineering design tool to produce an array of feasible designs. In this prototype tool, an Excel-based user-interface provides a means to define numerous combinations of design options for each subsystem of every spacecraft in the system for a particular mission/trajectory. An individual combination defines a unique “system configuration”, which is defined as an assembly of multiple spacecraft with user-specified subsystem options. For a particular system configuration, the Excel tool then writes MATLAB- formatted design parameter input files for each system element and converts the subsystem component databases stored in the Excel spreadsheets into MATLAB data structures. The inputs for the system configurations are passed onto the main MATLAB tool, along with a trajectory. The main engine of the MATLAB tool functions by sequentially designing each spacecraft subsystem in a pre-determined order. The subsystem design modules size each subsystem in terms of mass, power, heat generation, telemetry data rates, etc. In certain cases, internal trades are performed to decide which component in the applicable database best meets the requirements. The component databases are provided primarily to obtain conceptual-level mass and power estimates based on real hardware. For a given subsystem design module, required inputs from another subsystem may not be yet designed or up-to-date, so the tool uses the latest state of that subsystem in its sizing calculations. The design process automatically repeats, with each subsystem design becoming more mature with each iteration. The end goal is that the total system mass converges. If not, the design process terminates (marking that particular system configuration as infeasible) and 72 then proceeds onto designing the next system configuration. In this way, an automated, sequential-iterative design cycle can permit a complete concept point design to emerge. Alternative designs can be developed by automatically repeating this design process with a different set of design parameter inputs. At the basic level, the lunar polar volatiles mission considered in this research consists of at least a lander and rover equipped with suitable science instruments. As previously mentioned, this mission has the objective of addressing important lunar polar science questions (as identified in the National Research Council’s 2011 Planetary Decadal Survey). Since this mission has not yet been flown, and current studies of such a mission have not thoroughly considered the design trade space, the mission also provides a unique application to test the ability of the proposed approach to generate alternative concept designs. 4.2 MISSION SCIENCE OBJECTIVES Science results from a lunar polar volatiles rover mission should address the following questions, as posed by the National Research Council (NRC) in its 2013-2022 Decadal Survey (35):  “How are volatile elements and compounds distributed, transported, and sequestered in near surface environments on the surfaces of the Moon and Mercury? What fractions of volatiles were out-gassed from those planets’ interiors, and what fractions represent late meteoritic and cometary in-fall?  What are the chemical and isotopic compositions of hydrogen-rich volatiles (possibly water ice) near the Moon’s surface?” 73 It is theorized that volatiles in the lunar polar cold traps were deposited from material out-gassed from the lunar interior, solar wind particles, interplanetary dust, and comets. Studying the lunar polar volatiles would help unlock information on the state of the solar system when life emerged on Earth. In particular, a lunar South Pole rover mission would address the following science objectives, derived from the 2011 Decadal Survey. Table 4-1. Lunar Polar Vehicle Science Objectives (43) # Science Objective 1 Determine the form and species of the volatile compounds at the lunar poles. 2 Determine the vertical distribution/concentration of volatile compounds in the lunar polar regolith. 3 Determine the lateral distribution/concentration of volatile compounds in the lunar regolith. 4 Determine the secondary alteration mineralogy of regolith. 5 Determine the composition and variation in the lunar exosphere adjacent to cold traps. As the above NRC Decadal Survey science objectives indicate, there is still a need to identify the species of volatile compounds at the lunar poles both horizontally (at multiple locations) and vertically (at depth). Science objectives 1, 2, and 3 signify that there is a need for in-situ measurements on a platform capable of obtaining spatial volatile measurements. Such a future mission could involve multiple small impactors at several locations; however, the high cost and complexity of separate impactors might preclude such a mission. Another option would be to send several penetrators to obtain scientific data within the soil, however the technology for such penetrators is still not fully developed and the risk of mission failure is high (JAXA at one point considered such a mission but funding and technical problems led to its cancellation). Another option is to send multiple small landers equipped with drills to land at various locations, however the cost and complexity of that approach might render it untenable. A fourth option is to send a single large mobile vehicle (a rover) equipped with a drill to explore a permanently 74 shadowed crater. This last approach would be simpler in terms of cost and complexity, but would require significant engineering to enable it to function within the harsh environment of a lunar cold trap. To address the aforementioned science objectives, the following mission objectives should be met. A mobile platform (rover) is chosen over a stationary lander because of the potential to better determine the concentration of volatiles spatially (both vertically and laterally).  Successfully land a large rover with a suitable science payload near or within a permanently-shadowed lunar South Pole crater  Confirm the presence and distribution of water-ice and other volatiles inside such a crater  Identify the elemental and mineralogical composition of the regolith within such a crater  Characterize the lunar environment in the vicinity of such a crater  Demonstrate the survivability of a large rover within such a crater 4.3 REQUIREMENTS In order to investigate the design trade space for a lunar polar volatiles mission, a design tool must be developed that can generate numerous rover mission designs. In turn, to develop both the mission and tool, the top-level requirements for both must be identified. These requirements are outlined next. 75 4.3.1 Mission Requirements The top-level requirements for the overall mission and spacecraft system are summarized in the following table. This table requires that a lander and rover be landed at the lunar South Pole, in a region of high-hydrogen concentration. To ensure a safe landing, hazard detection technology must be used, to avoid large rocks, craters, and slopes that are present in the rugged terrain around the lunar South Pole. Since a ballistic trajectory is assumed, the launch vehicle upper stage must provide the Delta-V to transfer to the Moon as well as attitude control during the transfer burn. For the spacecraft themselves, the lander must serve as a relay between the rover and the Earth. NASA’s Deep Space Network is required for communication between the lander and the Earth. The lander itself must provide 3-axis attitude determination and control during all relevant mission phases. The lander must be designed to support all major structural loads throughout the mission. Finally, the lander and rover must have separate, independent power systems. Table 4-2. Requirements for Lunar Polar Volatiles Mission and Spacecraft ID Requirement 1 The system shall consist of a lander and a rover that are delivered to the lunar surface. 2 The rover shall be equipped with a suitable set of science instruments that meet the National Research Council’s 2011 Decadal Survey lunar polar volatiles science objectives. 3 The system shall land at a suitable location with high-hydrogen concentration at the lunar South Pole. 4 The system shall land at a safe, hazard-free site, utilizing hazard detection and avoidance technology. 5 For a ballistic trajectory (employing chemical propulsion), the launch vehicle upper stage shall provide the Delta-V for the initial transfer orbit. 6 For a ballistic trajectory (employing chemical propulsion), the launch vehicle upper stage shall provide attitude control during the transfer orbit insertion Delta-V burn. 7 The system shall use the lander as a relay between the rover and the Earth. 76 ID Requirement 8 The system shall utilize the NASA DSN for communication between the vehicle and Earth. 9 The lander shall require full three-axis attitude knowledge as part of attitude determination during all applicable mission phases. 10 The lander shall provide full three-axis attitude control (pure rotation, no translation) during all applicable mission phases. 11 The system shall be designed to maintain operational temperatures for all internal electronics and instruments for all operational environments. 12 The system shall be designed to support all major structural loads. 13 The lander and rover shall have independent power systems. 4.3.2 Design Tool Requirements To build a tool to design multiple configurations of a lander and rover, a basic set of high-level requirements was established. These requirements are listed in the following table. To summarize these requirements, tool should allow the design of numerous system configurations in an automated manner, designing each subsystem of the lander and rover in terms of mass and power, as well as designing the Descent & Landing phase. Table 4-3. Requirements for Spacecraft Design Tool ID Requirement 1 The tool shall enable the design of numerous configurations of a combined lander/rover system. 2 The tool shall perform the design of each system configuration in an automated manner (without humans-in-the-design-loop). 3 The tool shall operate on a set of design parameter inputs for each system configuration. 4 The tool shall provide a graphical interface for the user to specify design parameter inputs. 5 The tool shall design each subsystem of the lander and rover, outputting at least total subsystem mass and power estimates. 6 The tool shall be able to use a separately-designed trajectory file in the JPL SPICE kernel format (SPK file) for position, velocity, and other relevant trajectory data. 7 The tool shall design the Descent & Landing phase of the mission, including estimating the required propellant mass (i.e. this is not included in the SPK trajectory). 77 4.4 SYSTEMS ENGINEERING To properly perform a concept study for a lunar polar volatiles rover mission, a systems engineering approach is indispensable. As a general principle, applying systems engineering early in the life cycle of any space mission is essential to arriving at a design that is feasible and maximizes the chances of success. In particular, the Concept Phase of a space mission’s life cycle is critical in terms of evaluating multiple candidate concepts and justifying the concept that is ultimately selected (44). Many projects have been tempted to shortcut the Concept Phase and proceed directly to detailed design. According to the International Council on Systems Engineering (INCOSE), many failure review boards have found that insufficient study at the conceptual level was a root cause of failure for the system in question. For this reason, the Concept Phase is considered an essential ingredient of mission success: it lays the foundation for the mission requirements, the resulting overall system design after evaluating many concepts, the integration & testing activities, mission operations, and analysis of failure mechanisms. At a high level, one can conceive of a lunar polar volatiles rover mission consisting of the following elements: the surface science payload, a rover, a lander. The mission architecture must identify the type of trajectory to deliver the lander/rover stack to the Moon, the de-orbit method, and the landing site, all of which affect the design of the subsystems of each vehicle. In terms of system design, the rover’s scientific instrumentation must be selected to meet the science objectives; suitable rover subsystems (power, communications, thermal control, and command & data handling) must be designed for survivability to return science data during surface operations; suitable lander subsystems (propulsion, attitude control, power, communications, thermal control, command & data handling) must be designed to operate throughout the mission. 78 To perform subsystem designs and trade studies, a structured system engineering approach is essential. There are many different systems engineering standards depending on the group developing the system: military (e.g. Department of Defense), civil (e.g. NASA), commercial integrators, commercial manufacturers, etc. There are also many different systems engineering process models based on the type of project: waterfall, spiral, the “Vee” process, agile development, etc. The Vee process was selected for this project as it provides a straightforward representation of systems engineering activities during various stages of the project life cycle. The Vee process is illustrated below (45). Figure 4-1. “Vee” Systems Engineering Process Model This Vee process model can be applied at any stage of a project’s life cycle. A typical project life cycle can consist of the following stages (as described in the INCOSE handbook) (44):  Exploratory Research: identify needs of stakeholders, explore ideas and technologies  Concept: Refine stakeholder’s needs, explore feasible concepts, propose viable solutions  Development: Refine system requirements, build system, verify and validate system 79  Production: Produce, inspect, and verify system  Utilization: Operate system to satisfy user’s needs  Support: Provide sustained system capability  Retirement: Store, archive or dispose of system Since this project consists of research into trade studies (system, subsystem, and mission design), the applicable life cycle stages are: exploratory research and concept. Since this project could be envisioned as a NASA mission, the standard NASA life cycle phases can also be referenced. These NASA life cycle phases (which mirror the above INCOSE stages) are:  Formulation o Pre-phase A: concept studies o Phase A: concept & technology development o Phase B: Preliminary design & technology completion  Implementation o Phase C: Final Design and Fabrication o Phase D: System assembly, integration & test, launch o Phase E: Operations & sustainment o Phase F: Closeout Following the NASA life cycle model, this research project focuses on the pre-phase A concept study phase. The outcome or product deliverable of this phase is a feasible concept, based on trade studies and systems engineering processes. 80 4.5 DESIGN TOOL DEVELOPMENT Given the high-level design tool requirements outlined in Table 4-3, a brief discussion of the assumptions and decisions made, regarding tool development and implementation, are provided next. 4.5.1 Programming Language Selection First, a decision had to be made as to what programming language to use to develop the tool. Three programming languages were considered: C, C++ vs. MATLAB. A comparison of the of the options is provided in Table 4-4. Overall, the flexibility and ease-of-use of MATLAB made it the option to select. Table 4-4. Comparison of C, C++, MATLAB Attributes Attribute C or C++ MATLAB Portability Y Y Need to compile Y N Parallel Execution Y N Need for variable declaration Y N Built-in matrix-based math functions N Y Built-in “structure” data type Y Y Built-in optimization or search functions N Y Ease of writing code Medium Easy Built-in error detection and warning N (user must print warning) Y Built-in graphical plotting tools N Y Ease of building a graphical user interface Medium Medium At first, the C or C++ programming languages were considered. The pros to this are:  The potential portability of the final code (compiled for the proper operating system)  The ability to code and compile separate programs and run them in parallel. 81 However, there were several cons to consider:  The need to declare and initialize every variable in use was considered a negative, given the hundreds of parameters potentially required.  Specialized functions for any matrix-based linear algebra calculations would have to be developed from scratch, as the researcher was not aware of any validated free libraries to perform such calculations.  Any optimization or search functions would have to also be developed from scratch.  The difficulty in compiling and debugging code written in these languages was considered a drawback.  The lack of any easy-to-use graphical plotting tools.  Given the requirement to have a user interface to input design parameters, the added effort of having to build an entire graphical user interface (GUI), say in Visual C++, would have been extremely time-consuming and tedious. The other option considered was MATLAB, a high-performance language geared toward matrix-based technical computing. The advantages of MATLAB are:  Variable declaration by data type is not required. Variable initialization is based on the as-needed use of the variable and the algorithm being coded.  The ability to perform matrix-based calculations, so no special set of libraries must be developed.  Built-in error detection to identify the module and line of code where an error occurred.  Availability of built-in optimization and search functions.  No compilation of code is required, since MATLAB is an interpretive language. MATLAB also comes with its own IDE (Integrated Development Environment) that has smart 82 coding features to assist the user in writing error free code, as well as stepping through code while it’s running.  MATLAB has a built-in “structure” data type that can be used to house collections of parameters. C and C++ have this ability also, but the data structures must be declared before use.  Availability of graphical plotting tools.  The ability to develop graphical user interfaces (although it has some limitations and can be somewhat cumbersome to use in practice)  With the right license type, more than one MATLAB instance can be called to distribute the load in running planned lander/rover system configurations. Some disadvantages of MATLAB are:  Functions within a single instance of MATLAB can only be called in series, not in parallel. That is, there are no executables as in C/C++ that can run in parallel and communicate with one another in real-time.  The entire MATLAB engine must be loaded into memory. This could be an issue if numerous instances of MATLAB are required to distribute the load of designing numerous system configurations. 4.5.2 Serial vs. Parallel Subsystem Design Another aspect of the design tool development is how to approach the design of the required spacecraft subsystems. Two approaches were immediately obvious: a serial approach in which each subsystem is sized in a specific order, or a parallel approach in which the subsystems are designed concurrently. The choice of programming language determined which 83 approach could be used. If C or C++ was chosen, then either a serial or parallel approach could be taken. The C/C++ code could be written as one executable with each subsystem designed in series, or as separate executables where each subsystem is designed at the same time as other subsystems (in parallel). With MATLAB selected, however, only the serial approach could be taken. This required the researcher to assume a pre-determined order for the subsystem design module calls (see Section 5.2.3 for details). This order was determined based on the researcher’s judgment, rather than an investigation of which order made the most sense. For example, the Structures module is the second-to-last subsystem that is designed within the sequential ordering. The rationale for this is that, for the very first call of the Structures module, if no other subsystems have been sized, there are no load requirements on the spacecraft. Similarly, the Power module was specified last since it was assumed that the power requirements from all other subsystems must be known first. In either the serial or parallel subsystem design cases, iteration of some type is required to achieve design convergence. The serial subsystem design case requires a straightforward iteration process. Since the subsystems are all interdependent, the inputs into each subsystem become more mature, reflecting the latest state from the previous iteration. In this manner, the design of each subsystem matures with each “system iteration.” A key assumption is that this maturation process leads to convergence of the overall system design in terms of mass. In the parallel design case, however, the iteration process is expected to be a little more complex. The run-time for each subsystem design module can be different, and depends on the complexity of the sizing algorithm implemented. That is, each subsystem design module would not take the same amount of time to run once, so synchronizing the inputs to obtain design convergence would be a little more involved. 84 4.5.3 Trade Studies Lastly, the method used to conduct trade studies in the design tool was considered. Two options became apparent: conducting trade systems at the system level vs. performing internal trade studies within the selected subsystem design modules. Performing all trades at the system level meant that the user would have to somehow specify each trade option for each subsystem as an input. The result would be a unique set of design parameter inputs encapsulating each system configuration. Each system configuration constitutes a trade of the overall system to be compared with the other system configurations. This would have potentially led to an overwhelming number of system configurations to design and evaluate (leading to a total run- time problem). The other option, performing all trades internal to each subsystem, would have required more complex subsystem design algorithms, thereby increasing the time to code and also the run time per subsystem module. Given these two extremes, a decision was made to conduct some trades at the system level, and some internally. The design tool was written to conduct the following trades at the system level:  Telecom architecture (relay or direct-to-Earth)  Propulsion engine selection  Power system type selection and specific technology within that power system category The design tool was written to conduct the following trades internally:  Telecom hardware selection (based on a searching for antenna dimensions and RF power required to provide > 3dB link budget for all communication events)  ADCS sensors and actuators selection The CDS, Thermal, and Structures design modules did not explicitly involve any design trades. The goal for those modules was simply to estimate mass and power based on system 85 complexity (CDS), spacecraft system dry mass (Thermal), or structural loads and assumed material properties (Structures). 4.6 SCIENCE PAYLOAD Given the survey of past and planned science instruments on recent landers, rovers, and atmospheric probes (see Section 3.3), the science payload for the lunar polar volatiles was selected. To properly study the potential volatiles within the lunar regolith at depth and at multiple sites (per the NRC’s 2011 Decadal Survey lunar polar volatiles science objectives), this science payload should be housed on the rover. NASA science mission concepts and proposals typically follow a formal process to select science instrumentation. One of the required elements of NASA science mission proposals is the Science Traceability Matrix (STM). This is a table that links high-level science objectives down to the selected instrumentation and to the associated mission and spacecraft requirements. A typical STM consists of the high-level Science Objectives, followed by the Measurement Objectives, the measurement requirements, the selected instruments, the instrument requirements, and science data products. This information can also be linked to mission requirements and technology development needs. An STM was created to aid in the identification of science instruments for this research. The final STM generated for this research is shown in Table 4-5 through Table 4-8. In this STM, the Science Objectives begin with the 5 objectives outlined in the NRC’s 2011 Decadal Survey for lunar polar volatiles science. The first part of the STM, in Table 4-5, traces the selection of 3 instruments to the first science objective: determining the form and species of the volatile 86 compounds at the lunar poles. The 3 selected instruments are a Sample Pyrolysis Quadrupole Mass Spectrometer, a Regolith Conductivity Analyzer, and a Downhole Microscopic Imager. To determine the composition of the lunar regolith in a polar cold trap, a mass spectrometer of some sort is needed. The type of mass spectrometer selected uses vacuum pyrolysis—heating a sample to elevated temperatures in a vacuum to release the trapped volatiles (e.g. temperatures greater than 1400 degrees C are required to release trapped oxygen and other noble gases). For comparison, the Viking lander gas chromatograph mass spectrometer (GCMS) was capable of heating samples to 500 C, the Phoenix Thermal Evolved Gas Analyzer (TEGA) instrument was able to heat samples up to 950 C, and the MSL rover’s SAM instrument (Sample Analysis at Mars) can heat samples between 950-1100 C. This type of mass spectrometer has been shown to be an efficient way to release trapped volatiles within a sample of material. Since no flight proven mass spectrometer yet operates up to 1400 C, the technology is being developed by NASA as a part of its Desert Research and Technology Studies (Desert RATS) program. In this regard, this program has been testing the Volatile Analysis by Pyrolysis of Regolith (VAPoR) instrument, which is a simplified version of the MSL rover’s SAM instrument (46). 87 Table 4-5. Science Traceability Matrix (Science Objective 1) Science Objective Measurement Objective Measurement Requirement Instrument 1. Determine the form and species of the volatile compounds at the lunar poles. Determine the composition of volatile compounds (isotopes, elements, molecules, minerology) in the regolith in-situ. Obtain spectral data at sufficient resolution and atomic mass range to determine chemical composition of volatile compounds (H 2O, hydroxyl OH, CO 2, CO, methane CH 4, ammonia NH 3, N 2, H 2) from 10 regolith samples (5 at depth and 5 at the surface). Sample Pyrolysis Quadrupole Mass Spectrometer Determine the soil characteristics of the lunar regolith both from an undisturbed (in-situ) and disturbed sample. Measure temperature, thermal conductivity (heat flow), electrical conductivity of 5 regolith surface samples. Regolith Conductivity Analyzer Observe the size and texture of regolith at microscopic levels. Downhole Microscopic Imager The second science objective is to determine the vertical distribution/concentration of volatile compounds in the lunar polar regolith, as shown in Table 4-6. One measurement objective this implies is the ability to detect the presence of layered volatile deposits in the subsurface regolith. To achieve this, a ground penetrating radar was selected to detect the change in dielectric constant due to layering with back-scattered radar. A second measurement objective is to obtain the concentration (or abundances) of volatiles compounds at depths up to 2 m (data from LRO’s LEND instrument suggest that hydrogen deposits exist within the upper 1m of the regolith). This implies the presence of a sample acquisition drill to extract vertical 88 samples. One challenge of drill design and operations would be to ensure it can operate in the less than 100 K temperatures of a lunar polar cold trap. A sample transfer mechanism will also be needed to deliver the acquired samples to the sample analysis instruments (such as the mass spectrometer). To measure hydrogen concentration at depth, a neutron spectrometer can be mounted near the drill head. Honeybee Robotics has implemented drill systems with an embedded neutron spectrometer detector at a mass of 0.5 kg and 1 W. Table 4-6. Science Traceability Matrix (Science Objective 2) Science Objective Measurement Objective Measurement Requirement Instrument 2. Determine the vertical distribution/concentration of volatile compounds in the lunar polar regolith. Determine the presence of layered volatile (specifically water ice) deposits within the regolith to a depth of N m. Detect the change in dielectric constant due to layering with backscattered radar. Ground Penetrating Radar Measure the concentration (abundances) of volatile compounds to a depth of 2m in situ. Acquire samples of regolith at depth for sample chemical analysis Sample Acquisition Drill Deliver regolith samples acquired at depth to sample analysis instruments Sample Transfer Mechanism Measure hydrogen concentration (2 ppm) with sufficient resolution beyond orbital remote sensing capabilities, within each hole drilled into the regolith. Downhole neutron spectrometer 89 The third science objective is to determine the lateral distribution/concentration of volatile compounds in the lunar regolith (see Table 4-7 below). This can be achieved by imaging the terrain with cameras (both visible light and infrared). If the rover operates within a permanently-shadowed region (PSR), artificial lighting can be used to illuminate the local terrain. Otherwise, sunlight can provide the illumination source. In addition, to determine the lateral distribution of hydrogen, the downhole neutron spectrometer mentioned earlier can be used to measure samples at depth at multiple locations. Instead of requiring 2 neutron spectrometers, the downhole neutron spectrometer (mounted on the drill head) can also be used when it is in a stowed position. Table 4-7. Science Traceability Matrix (Science Objective 3) Science Objective Measurement Objective Measurement Requirement Instrument 3. Determine the lateral distribution/concentration of volatile compounds in the lunar regolith. Obtain visible images of surface geology. *Obtain monochrome visible imaging spatial data under illuminated conditions *Provide lighting to generate shadows on rocks within field of view Visual Imaging Camera Measure the temperature of surface regolith in context to local geology Obtain thermal maps at a minimum of 5 surface locations separated by at least 1 m Thermal IR Camera Measure the concentration (abundances) of volatile compounds horizontally at various surface locations in-situ. Measure hydrogen concentration (2 ppm) at 5 surface targets. Downhole neutron spectrometer 90 The fourth and fifth science objectives and their associated instruments are listed in Table 4-8. The fourth science objective is to determine the secondary alternation minerology of the regolith—that is, determining the minerals formed from low-temperature geochemical and gas phase diffusion processes operating on primary minerals. To achieve this, an X-ray diffractometer can be used to analyze the structure of the regolith using the backscatter signal from an X-ray source onto a surface or sub-surface sample. The fifth science objective is to determine the composition and variation of the lunar exosphere adjacent to a cold trap. The measurement objective corresponding to this is to determine the chemical compounds in the lunar exosphere to understand how volatiles are transported and how they are retained within the cold traps. To achieve this, spectral data of the ambient exospheric gases (such as Neon 20, He, H 2, and Argon 40) can be obtained. Since a mass spectrometer is already included in the set of science instruments, an exosphere inlet can be used to sample the exospheric gases. Table 4-8. Science Traceability Matrix (Science Objectives 4 and 5) Science Objectives Measurement Objectives Measurement Requirements Instruments 4. Determine the secondary alteration mineralogy of regolith. Determine minerals formed by secondary alteration (from low- temperature geochemical and gas phase diffusion processes operating on primary minerals). Measure backscatter signal from an X-ray source onto at least 1 surface sample and 1 subsurface sample. Soil Sample X- ray diffractometer 91 Science Objectives Measurement Objectives Measurement Requirements Instruments 5. Determine the composition and variation of the lunar exosphere adjacent to cold traps. Determine the chemical compounds present in the lunar exosphere within a cold trap to understand volatiles transport & retention processes. Obtain in-situ spectral data of ambient exosphere gases (Neon 20, He, H2, Argon 40) at a minimum of 5 separate horizontal locations. Sample Pyrolysis Quadrupole Mass Spectrometer Using some of the data in the science instrument database identified in Section 3.3, along with a literature search on planned advancements in instrument technology, the following table of instrument masses and power required was assembled. This table represents a lower bound on the total instrument masses, assuming instrument technology development. The instruments selected were categorized into two groups based on the importance of their measurements: those of Priority 1, which are considered essential to the science data return, and those of Priority 2, which are not essential but would provide “bonus” science. According to this categorization, the Priority 1 instruments (including the mass spectrometer, imaging camera, drill, sample transfer mechanism, and downhole neutron spectrometer) sum up to a mass of 24 kg. The Priority 2 instruments sum up to a mass of ~5.1 kg. So, if all instruments were included on the lunar polar volatiles rover, the total mass would be 29.1 kg. Table 4-9. Science Instrument Mass and Power Summary Instrument Priority Mass (kg) Peak Power (W) 1. Sample Pyrolysis Quadrupole Mass Spectrometer 1 4 80 2. Visual Imaging Camera 1 3 15 3. Sample Acquisition Drill 1 10 100 4. Sample Transfer Mechanism 1 3 35 5. Downhole Neutron Spectrometer 1 4 3 92 Instrument Priority Mass (kg) Peak Power (W) 6. Regolith Conductivity Analyzer 2 0.1 0.6 7. Ground Penetrating Radar 2 0.5 3 8. Thermal IR Camera 2 2 5 9. Soil Sample X-ray diffractometer 2 2 12 10. Downhole Microscopic Imager 2 0.5 2 Total (Priority 1) 24 Total (Priority 2) 5.1 Total (All) 29.1 In terms of power, the instruments requiring the most power are the mass spectrometer (80 W), the sample acquisition drill (100 W), and the sample transfer mechanism (35 W). To simplify the payload power modes and reduce the required power from the rover, it is assumed that the instruments are each operating at different times. The following table illustrates an example list of power modes for the science payload. Note that the imaging mode includes use of all cameras. However, it may be desirable to image while drilling and transferring the sample, so that the drill mode total power could increase. Table 4-10. Example Science Modes Mode Power (W) Drilling 100 Sample Transfer 35 Sample Analysis 80 Imaging 25 Neutron Spectrometry 3 Radar Sounding 3 Conductivity 0.6 X-ray Diffractometry 12 Overall, for the purposes of this research, a total science instrument payload mass of 30 kg with a peak power of 100 W was assumed. These instrument mass and power estimates 93 assume advancement in development of the sample acquisition drill, the sample transfer mechanism, the mass spectrometer, and ground penetrating radar. As an example of the assumption of further technology development, the instrument masses for this research are compared with the Johns Hopkins Applied Physics Lab’s (JHUAPL) study report on a lunar polar volatiles explorer (LPVE) mission (47). A total instrument suite mass of ~69 kg was assumed for the JHUAPL concept, more than twice the estimate assumed in this research. The large reductions in assumed mass are highlighted in Table 4-11. The mass spectrometer assumed in this research is almost 10 kg lighter than that assumed in the JHUAPL study, while the power estimate is nearly twice as much in this research as the JHUAPL study. The sample acquisition drill, based on Honeybee Robotics plans, has a mass of 10 kg vs. ~42 kg in the JHUAPL study. However, the power estimate is nearly the same. The sample transfer mechanism is assumed to be 3 kg in this research vs. 8.5 kg in the JHUAPL study. Lastly, the ground penetrating radar is assumed to be extremely miniaturized in this research (at 0.5 kg) compared to 3.5 kg in the JHUAPL study. Table 4-11. Comparison of JHUAPL LPVE mission instruments vs. this research Instrument Mass (kg) (This research) Mass (kg) (JHUAPL study) Power (W) (This research) Power (W) (JHUAPL study) Sample Pyrolysis Quadrupole Mass Spectrometer 4 13 80 47 Visual Imaging Camera 3 n/a 15 n/a Sample Acquisition Drill 10 41.6 100 98 Sample Transfer Mechanism 3 8.5 35 34 Downhole Neutron Spectrometer 4 0.8 3 2.9 Regolith Conductivity Analyzer 0.1 n/a 0.6 n/a Ground Penetrating Radar 0.5 3.5 3 8 94 Instrument Mass (kg) (This research) Mass (kg) (JHUAPL study) Power (W) (This research) Power (W) (JHUAPL study) Thermal IR Camera 2 n/a 5 n/a Soil Sample X-ray diffractometer 2 0.9 12 12 Downhole Microscopic Imager 0.5 0.3 2 1 Total 29.1 68.6 4.7 LANDING SITE SELECTION For the purposes of this research, the landing site for the lunar science rover is designated to be near the lunar South Pole. While the lunar North Pole is equally as valid, the lunar South Pole was a general area of interest in NASA’s recent crewed lunar return efforts (canceled in 2009). The specific landing site should be an area with a high concentration of hydrogen, as revealed by recent spacecraft observations of the lunar poles. Such a high hydrogen concentration site at the lunar South Pole is likely to be within a permanently- shadowed region but could also be within a sunlit region, as both regions appear to have signatures of hydrogen. In addition, the landing site determination can be affected by architecture-level decisions such as the type of communications and power system. For a vehicle that must maintain direct communications with Earth, the landing site must be in an area with visibility to the Earth. For vehicles dependent on solar power generation, the landing site must clearly be within a sunlit region or with nearby accessibility to a sunlit region. Also, the landing site environment has an effect on the thermal design of the rover, which must operate in the cold temperatures of shadowed regions or warmer temperatures of sunlight regions. Figure 4-2 shows a temperature map with craters named for context. 95 Figure 4-2. Lunar South Pole craters and temperature map from LRO Diviner thermal mapper data (NASA) The first step in identifying a potential landing site for this research is to obtain a map of areas in the lunar South Pole with high hydrogen concentration. Figure 4-3 below shows a map of epithermal neutron flux (count rate, or counts per second) as detected by the Lunar Exploration Neutron Detector (LEND) instrument onboard NASA’s Lunar Reconnaissance Orbiter (LRO) spacecraft, launched in 2009 and currently orbiting the Moon. The Russian-made LEND instrument consists of nine detectors that operate by measuring the flux of neutrons (thermal, epithermal, and fast) that are produced from molecules and atoms near the lunar surface when bombarded with high-energy cosmic rays. The neutrons can interact with other elements in the lunar regolith, which can slow them down. The neutrons can also be absorbed by some of these elements, such as hydrogen. As a result, neutron speeds can be used to deduce elemental composition. The map in Figure 4-3 depicts LEND neutron count rate data for both the North and South lunar polar regions above +80 and -80 degrees latitude, respectively. The dark blue and purple regions indicate areas with low neutron count rates, which are called neutron 96 suppression regions (NSR). The NSRs are indicative of areas with increased hydrogen content. In the case of the lunar South Pole epithermal neutron map (right projection), two distinct dark patches are seen (48): 1. One on the right half of the projection South Pole projection, within a Shoemaker crater, with up to ~0.2 % water by weight. 2. One on the left half of the South Pole projection, within Cabeus crater, with even higher estimated water-ice levels of ~0.4 % water by weight. Figure 4-3. LRO LEND maps of epithermal neutron flux at North and South lunar poles (48) From this LEND data, the Cabeus and Shoemaker craters appear to be interesting initial candidate sites for a lunar polar volatiles rover mission. Characteristics of these craters are summarized in Table 4-12. The Cabeus crater region has the largest diameter and depth, with maximum crater floor slope of 15 degrees. 97 Table 4-12. Candidate Lunar South Pole Landing Site Characteristics Crater Name Width (km) Depth (km) Floor max slope (deg) Latitude (deg South) Longitude (deg) Cabeus 98 4 15 84.9 35.5 West Shoemaker 50 3-4 13 88.1 44.9 East Zoomed maps of both these craters are shown in the following two figures. Figure 4-4 shows the epithermal neutron flux at Cabeus crater with an inset on the upper right containing a temperature map. In the larger neutron flux map, the white outlines indicate permanently- shadowed regions, while the pink contours denote neutron suppression regions. It can be seen that the neutron suppression region extends beyond the bounds of the permanently-shadowed region by up to 20 km. The thermal map inset indicates that the region with strongest neutron suppression has a temperature of about 40 K (-233 degrees C), while the outer region has a temperature of about 80 K (-193 degrees C). Thus, within Cabeus crater there is hydrogen both within shadow and in sunlight. The estimated hydrogen content in the deepest neutron suppression region is 500 ppm, while in all of Cabeus crater it is 300 ppm (49). 98 Figure 4-4. Epithermal neutron flux map at Cabeus crater from LRO LEND data (49) Figure 4-5 below shows the epithermal neutron flux at Shoemaker crater. In this case, the neutron suppression region contains an entire permanently-shadowed region as well as a ring outside it. Figure 4-5. Epithermal neutron flux map at Shoemaker crater from LRO LEND data (48) 99 The above two results are in agreement with other studies. According to (49), in which 9 permanently-shadowed regions were studied for neutron suppression, Cabeus crater has the strongest neutron suppression, followed by Shoemaker crater, and then Haworth crater. The enhanced hydrogen content suggested at Cabeus crater was the reason that the LCROSS spacecraft was directed to impact it in September 2009. The discovery that the lunar poles have some neutron suppression regions outside of permanently-shadowed regions (within sunlight) is an interesting result. It is expected that in sunlit areas near the poles, the upper few centimeters of regolith could be heated to 200 K (-73 degrees C). At this temperature, any hydrogen-rich volatiles, such as water ice, should evaporate. Thus, the hydrogen content in these sunlit areas should be much less than the underlying soil. That is, hydrogen content is expected to increase with soil depth. For example, if the upper 60 cm thick hydrogen-poor layer is assumed to have a concentration of 100 ppm, the buried hydrogen could be between 600 to 4500 ppm. This represents buried water-ice content of up to 4% by weight. Note that LCROSS detected about 5.6 +/- 2.9 % water content by weight. A more complex model of volatile accumulation is needed to explain the suggestion of a shallow subsurface hydrogen layer (49). From a science perspective, then, the desired landing site for this research is selected to be the floor of Cabeus crater. As previously stated, there are both shadowed and sunlit regions within Cabeus crater that could accommodate either a non-solar powered rover or a solar powered one. 100 5 METHODS AND TOOLS 5.1 OVERALL MISSION AND SYSTEM DESIGN PROCESS In this research, the overall process for designing a space system to meet the requirements of a specific mission involves a few steps, as depicted in Figure 5-1 below. The first step is to conceptually define the objective of the mission, based on customer requirements and stakeholder needs. In the case of this research, the objective of the mission being designed is to prospect for lunar polar volatiles in order to answer scientific questions as posed by the National Research Council’s most recent 2011 Decadal Survey. Once these objectives are defined, the next step is to brainstorm how to deliver the spacecraft to its destination (the trajectory) and what instrumentation (payload, in terms of mass, peak power, and peak data rate) is required to meet the mission objectives. Once these high-level requirements are determined, the next step is to design the mission and spacecraft to meet these requirements. 101 Figure 5-1. Overall Mission and System Design Process 5.1.1 Trajectory Definition The first step in the mission and spacecraft design process is to design and build a trajectory to transport the spacecraft to its ultimate destination (in the case of this research, the Moon). This trajectory can be designed using a suitable trajectory design software package. In this research, the General Mission Analysis Tool (GMAT, version 2013) designed by the NASA Goddard Space Flight Center (GSFC) was used. Regardless of what tool is used, the trajectory must be converted into two data files: 1) the SPK (spice kernel) format for use by the JPL SPICE toolkit (provided by JPL’s NAIF—Navigation and Ancillary Information Facility—to provide space geometry and event data for mission design, science planning and science data analysis), and 2) a time-based simulation data file containing spacecraft position and velocity data relative to Define high-level requirements:  mission objectives based on stakeholder needs  applicable trajectory type(s)  payload instruments (mass, power, etc.) Design and build trajectory SPK and simulation data files Define spacecraft design parameters and build system configuration .m parameter files using Mission and Spacecraft Definition (MASD) tool Run specific system configuration .m files in Mission and Spacecraft Sizing (MASS) tool to produce a point design for each configuration .m file MASD Tool MASS Tool Rank system configuration point designs by desired criteria (mass, etc.) and identify minimum mass design solutions Analysis Tool 102 both the Earth and the destination central body (e.g. the Moon), along with a spacecraft mass estimate. 5.1.1.1 GMAT Resources The trajectory in GMAT can be designed either using the graphical user interface (GUI) or a GMAT script. In any case, the procedure in GMAT requires the user to specify the “resources” to be used in designing the trajectory. The essential resources include a satellite object, a fuel tank (to model propellant consumption), 2 impulsive burns (translunar injection or TLI, and lunar orbit insertion or LOI), 2 propagators (one Earth-centered and the other Moon- centered), and a differential corrector boundary value solver. The key satellite parameters (epoch and a subset of the orbital elements) are summarized in Table 5-1. As this table shows, the satellite object has a starting epoch of July 13, 2018 03:00:00 UTC. The initial parking low Earth orbit (LEO) is given as a 150 km circular orbit. This altitude was selected as the optimal Earth departure altitude to minimize the total Delta-V to reach a 15 km low lunar orbit (from an early patched conic study done by the researcher as part of the USC Ph.D. Qualification Exam). Thus, the orbit semi-major axis is set as 6528.137 km (6378.137 km Earth equatorial radius + 150 km) and the eccentricity is set as 0. Since the argument of perigee is undefined for a circular orbit, a value of zero is assumed. The values of the other orbital elements (inclination, right ascension of the ascending node or RAAN, and true anomaly) are not known a priori and are solved for by GMAT. Table 5-1. GMAT Satellite Key Parameters Parameter Value Epoch July 13, 2018 03:00:00 UTC Semi-major axis (km) 6528.137 LEO altitude (km) 150.0 Eccentricity 0.0 103 The fuel tank object is set with a total fuel mass of 10,000 kg (a placeholder number), a density of 1260 kg/m 3 , pressure of 1500 kPa, and volume of 9 m 3 . Negative fuel mass was permitted to allow GMAT to reach a trajectory solution without terminating the run in cases where negative fuel mass was encountered. Each of the two impulsive burn objects (TLI and LOI) specify the components of the Delta-V vector in an Earth-centered “VNB” orbital reference frame, where V is along the orbit velocity vector (orbital frame X-axis), N is normal to the orbit plane (Y-axis), and B (Z-axis) completes the triad. The required Delta-V components for both the TLI and LOI burns are solved for by GMAT. For the TLI burn, however, an estimate of the Delta-V component in the X-axis direction is given as 3.146 km/s to assist the solver in finding a trajectory solution. This value was obtained from the researcher’s previously-mentioned patched conic lunar trajectory study. Both impulsive burn objects are allowed to decrement mass using the fuel tank object, with an assumed propulsive I sp of 300 seconds. The 2 propagators both use the Runge-Kutta 89 numerical integrator (provided by GMAT). The Earth-centered propagator uses a 20x20 (degree x order) harmonic Earth gravity field based on the JGM-2 gravity model, assumes no atmospheric drag, includes gravitational perturbation from the Moon only (treated as a point mass), and accounts for solar radiation pressure. The Moon-centered propagator uses a 20x20 harmonic lunar gravity field based on the LP-165 gravity model, includes gravitational perturbation from the Earth (point mass), and accounts for solar radiation pressure. The differential corrector (DC) solver in GMAT is a numerical solver for boundary value problems. According to the GMAT Help, the DC uses a simple shooting method to refine a set of 104 variable parameters to meet a set of goals, where the derivatives are obtained by finite differencing. For this research, the default forward difference method was used. 5.1.1.2 Mission Sequence To allow GMAT to find a trajectory from the Earth to a low lunar orbit starting at the specified satellite epoch and circular low Earth orbit, a mission sequence is specified. This mission sequence includes two “Target” commands. The target command solves for a condition by varying one or more parameters. The objective of the first target command, named “Target Periselene” is to execute the TLI burn to target a periselene at 100 km altitude over either lunar pole. The parameters that the “Target Periselene” command varies are the LEO inclination, RAAN, and true anomaly, as well as all 3 components of the TLI Delta-V vector. The search range for each variation in LEO inclination, RAAN, and true anomaly is from 0 to 360 degrees. The variation in the TLI Delta-V vector components is from -4 to 4 km/s in X, Y, and Z (or VNB) directions. All of these parameter variations uses the differential corrector boundary value solver. Given the varying LEO orbital geometry, satellite true anomaly, and TLI Delta-V components, the TLI impulsive burn is then executed. The trajectory is then propagated using the Earth-centered propagator until lunar periapse (or periselene) is reached. Two “Achieve” commands are then used to specify goals for the final state at the end of the propagation. The first goal is to achieve a 100 km lunar altitude at periselene. The second goal is to achieve a polar position at periselene, by setting the required B-plane component 𝐵 ∙ 𝑇 = 0. Once the desired state at periselene is achieved, the second target command then executes. The goal of this command, named “Target LOI” is to execute the LOI burn to place the 105 satellite into a circular lunar orbit (with altitude of 100 km and a polar inclination from the previous target command). To do this, the LOI Delta-V x-component is varied between -3 to 0.2 km/s. The Δ𝑉 𝑥 parameter variation is seeded with an initial value of -0.776 km/s (as identified in the researcher’s early patched conic study). Note that the Delta-V component has a negative sign since the satellite’s velocity must be reduced in order to be captured into lunar orbit. Given the varying Δ𝑉 𝑥 , the LOI impulsive burn is executed. The orbit is then propagated using the Moon-centered propagator for 1 lunar orbit. To ensure a circular orbit is achieved, an “Achieve” command is used to target a lunar eccentricity of 0. 5.1.1.3 Trajectory Solution The GMAT mission sequence described above converges to a solution very quickly, taking only 15.5 seconds. The periselene targeter converged in 19 iterations (out of the user- specified maximum of 50). The final values of the varied parameters are summarized in the following table. Note that the TLI Delta-V vector has values in all 3 components, indicating that the desired Delta-V direction is not in-plane to the low Earth orbit. Also note that the Delta-V magnitude is 3.654 km/s (compared to the 3.146 km/s from the lunar patched conic trajectory study). The LOI targeter achieved a solution in 3 iterations, requiring an LOI Delta-V x- component of -0.861 km/s (compared to the -0.776 km/s obtained from the lunar patched conic study). Table 5-2. Solved GMAT LEO conditions, TLI/LOI Delta-V components, and time of flight Parameter Value LEO inclination (deg) 20.950 LEO RAAN (deg) 0.440 LEO true anomaly (deg) 4.362 TLI DVx (km/s) 2.933 TLI DVy (km/s) 1.558 TLI DVz (km/s) 1.524 106 Parameter Value TLI DV magnitude (km/s) 3.654 LOI DVx (km/s) -0.861 Trajectory time of flight (days) 3.2 The overall trajectory (from TLI to 1 lunar orbit past LOI) took 76.87 hours (or 3.2 days), which is a relatively fast lunar trajectory. The final epoch is July 13, 2018 07:04:02.7 UTC. From the GMAT simulation data file, the satellite mass after TLI was 3177.8 kg, and the final mass after LOI was 2371.6 kg, suggesting an LOI propellant mass of 806.2 kg. The total propellant mass for this lunar mission, including de-orbit, descent, and landing, is estimated in this research by the MATLAB-based Mission and Spacecraft Sizing (MASS) tool. Visualizations of the solved trajectory are provided in the following figures. In these figures, the satellite’s trajectory is shown in red, and the Moon’s trajectory is shown in gray. In Figure 5-2, note that the trajectory appears to be very elongated, corresponding to the fast lunar transfer time of flight. Figure 5-2. Solved GMAT lunar transfer trajectory (Earth inertial view) 107 The polar low lunar orbit after LOI is shown in Figure 5-3. This provides visual confirmation that the intended final condition was achieved. Figure 5-3. Solved GMAT low lunar orbit (Moon inertial view) 5.1.2 Definition of System Parameters Once the trajectory files are available, the next step is to use an Excel-based tool named the Mission and Spacecraft Definition (MASD) tool to define the overall spacecraft design parameters. The end goal is to create a set of system configuration .m input files that will be used in a separate MATLAB-based Mission and Spacecraft Sizing tool. The overall process for using the MASD tool to define the spacecraft design parameters is depicted in Figure 5-4 below. 108 Figure 5-4. Overall Process to Define System Design Parameters and Create System Configurations in MASD tool The first step in using this tool is to enter high-level information in the “Mission & System” sheet, as depicted in Table 5-3. This high-level information includes:  Trajectory type: the type of trajectory being employed in the mission  Mission Phases: a list of mission phases (as user-input phase names, selecting the phase type from a pre-defined list, and selecting the primary gravitational body influencing the trajectory for each mission phase)  Spacecraft Elements: a list of spacecraft elements required for the mission (as user- input element names, selecting the spacecraft type from a pre-defined list). Multi- element spacecraft are treated like a spacecraft stack, where one spacecraft is the Enter high-level mission & system data:  Trajectory type  Mission Phases  Spacecraft elements  Spacecraft Subsystem Matrix Click on “Pre-populate Subsystem Design Parameters” button to pre-fill the following input sheets with default design parameters  Trajectory  Ground System  Payload  7 Subsystems Customize system by specifying design parameters in all input sheets Click on “Create MATLAB Inputs” button to create MATLAB design parameter input .m files (multiple system configuration combinations). Parameter files are:  Trajectory parameters .m file  Ground system parameters .m file  System configuration .m files containing design parameters for all subsystems in each spacecraft element MASD Tool MASD Tool MASD Tool MASD Tool Subsystem databases 109 payload of another spacecraft. This approach lends itself for delivery systems such as a Lander carrying a rover to the lunar surface.  Spacecraft subsystem matrix: A table specifying “Y” or “N” indicating whether a particular subsystem is present onboard each spacecraft element in the stack. This is useful in case a particular spacecraft element does not contain a particular subsystem, e.g. a Rover typically does not contain a Propulsion system (rather it contains a Mobility system that is book-kept with the Structures & Mechanisms subsystem). Once this high-level information is entered in the “Mission & System” sheet, the first action is to click the button named “Assign Spacecraft & Prefill Subsystem Parameters”. The functions of this button are to: 1) get the list of user-input spacecraft elements; 2) get an array of true/false flags for the subsystems in each spacecraft element, indicating whether the user requires that subsystem to be present onboard the given spacecraft element; 3) going to each subsystem sheet in the Excel workbook and adding a new column for each spacecraft element that the user-defined; 4) and pre-filling the design parameters with default values for each new spacecraft element column in each subsystem sheet. The purpose for pre-populating the design parameters is to save the user time in specifying all the design parameters, since many of the default values will likely be acceptable. The sheets that are pre-populated with default design parameter values are: Payload, CDS, Telecom, ADCS, Propulsion, Thermal, Structures, and Power. 110 Table 5-3. “Mission & System” sheet in Mission and Spacecraft Definition (MASD) tool Once the design parameters in the individual subsystem sheets are pre-populated, the next step is for the user to customize the design parameters themselves. This is the most interactive portion of the design definition process, as the user must go through the various input sheets and specify desired values for the various design parameters. In addition to the payload and various subsystem sheets, two additional inputs sheets are the “Trajectory” and “Ground System” input sheets. Additional ancillary data sheets are the “Defaults” sheet containing the default value of all design parameters for each input sheet, the “Definitions” sheet containing lists of the available options for specific design parameters present throughout the various input sheets, and an “External Data” sheet containing tables connected to tables existing within external workbooks (using the Microsoft Excel Query tools). Screenshots of the various input sheets are shown in the following sections along with a brief summary of the design parameters included within each sheet. In each screenshot, it is assumed that a Rover and Lander are the two user-input spacecraft elements. Also, note that the second MISSION AND SPACECRAFT DEFINITION (MASD) tool MISSION Trajectory Options Value Trajectory Type Ballistic Mission Phase Name Phase Type Primary Gravitational Body Cruise Cruise Earth Lunar Orbit Orbital Operations Moon Descent and Landing Entry, Descent, and Landing Moon Surface Operations Surface Operations Moon Spacecraft Elements Spacecraft Element Name Spacecraft Type Rover Rover Lander Lander Spacecraft Subsystem Matrix Set has_XYZ_flag = true or false depending on S/C element type Spacecraft Element CDS Telecom ADCS Propulsion Thermal Structures Power Rover Y Y Y N Y Y Y Lander Y Y Y Y Y Y Y 1) Pre-populate Subsystem Design Parameters 2) Create MATLAB Inputs 111 column, labeled “MATLAB Parameter Name” contains the parameter name as a variable that is recognized by the MATLAB-based Mission and Spacecraft Sizing tool (MASS), which is described in Section 5.2 in more detail. 5.1.2.1 Trajectory Inputs Sheet The trajectory inputs sheet contains a single column to define trajectory-specific inputs such as:  General trajectory inputs: o The path to the trajectory SPK file o The path to the trajectory simulation data text file o The spacecraft SPK ID (for querying spacecraft position and velocity in the trajectory SPK file) o Target body: The destination of the mission o Landing site latitude and longitude (for surface missions)  Descent & Landing inputs: See section 5.3.8 for details of the Descent & Landing simulation o # of integration steps for braking burn 1 (BB1) phase o Initial (or lower bound on) starting altitude for the BB1 de-orbit phase o Maximum starting altitude for the BB1 de-orbit phase o BB1 de-orbit altitude search step size o Approach phase velocity magnitude o Approach phase slant angle o Approach phase starting slant range 112 o Approach phase final slant range o Hazard avoidance divert distance o Maximum allowable # of descent engines for D&L algorithm to assume An example input sheet is shown in Table 5-4. Table 5-4. “Trajectory” input sheet in Mission and Spacecraft Definition (MASD) tool 5.1.2.2 Ground System Inputs Sheet The “Ground System” inputs sheet contains design parameters for the ground network antenna system that communicates with the spacecraft. For this research, NASA’s Deep Space Network is assumed for the lunar mission, although other ground networks could conceivable be used as well. The design parameters included in the “Ground System” inputs sheet include: Trajectory MATLAB Parameter Name Value General Trajectory Type type Ballistic Trajectory ID traj_ID 1 SPK File Path spk_filepath C:\Users\Michael\OneDrive\Documents\Education\PhD\Thesis\GMAT\BallisticLunarTransfer_h0_150km_TLI_targ_90deg_inc_LOI_100km.bsp Sim Data Path traj_data_filepath C:\Users\Michael\OneDrive\Documents\Education\PhD\Thesis\GMAT\BallisticLunarTransfer_h0_150km_TLI_targ_90deg_inc_LOI_100km.txt Spacecraft SPK ID sc_spk_id -123456789 Target Body target_body Moon Landing Site Latitude (deg) landing_site_latitude_deg -89 Landing Site Longitude (deg) landing_site_longitude_deg 0 Descent & Landing # integration steps for Braking Burn 1 descent_landing.N_steps_bb1 500 Plot BB1 mass data per D&L iteration descent_landing.plot_mass_iter_flag FALSE Starting altitude for BB1 de-orbit burn search (km) descent_landing.h0_initial_km 15 Maximum altitude for BB1 de-orbit burn search (km) descent_landing.h0_max_km 100 BB1 de-orbit altitude search step size (km) descent_landing.dh0_km 1 Initial uprange distance at BB1 start descent_landing.S0_initial_km 700 Approach phase velocity magnitude (m/s) descent_landing.v0_approach_mps 10 Approach phase slant angle (deg) descent_landing.slant_angle_approach_deg 30 Approach phase starting slant range (m) descent_landing.r0_approach_m 1000 Approach phase final slant range (m) descent_landing.rf_approach_m 150 Hazard avoidance divert distance (m) descent_landing.D_term_m 100 Initial # descent engines descent_landing.num_engines_initial 1 Maximum # descent engines descent_landing.max_num_engines 6 113  The antenna system being used (assumed use of 34m DSN antennas since the 70m systems are very expensive to use)  The desired frequency band for the antenna (this depends on the frequency band capability of each antenna system)  Miscellaneous link parameters such as ground antenna pointing error (assumed to be 6 milli-degrees per pg. 243 of (33)), antenna efficiency, antenna noise temperature, transmission line loss, receiver line loss, Earth atmospheric zenith loss, maximum elevation angle (assumed to be 6 degrees per Ted Sweetser recommendation), system implementation losses, receiver noise figure, modulation scheme, required receiver signal-to-noise ratio, and uplink data rate An example input sheet is shown in Table 5-5. Table 5-5. “Ground System” input sheet in Mission and Spacecraft Definition (MASD) tool Ground System MATLAB Parameter Name Value Ground Antenna Network Type type DSN Antenna System antenna_system DSN 34m Desired frequency band desired_freq_band X-band Pointing Error (deg) pointing_err_deg 0.006 Antenna Efficiency antenna_efficiency 0.55 Antenna noise temperature Tant_K 68.75 Transmission Line Loss (dB) Lt_line_loss_dB -1 Receiver Line Loss (dB) Lr_line_loss_dB -0.5 Polarization Loss (dB) L_polariz_loss_dB -0.3 Earth atmospheric zenith absorption loss (dB) L_absorp_loss_zenith_dB -0.04447 Minimum elevation angle (deg) min_elev_angle_deg 6 System Implementation Loss (dB) L_implement_dB -2 Receiver Noise Figure (dB) receiver_noise_figure_dB 1 Modulation Scheme modulation_scheme BPSK/QPSK + R-1/2 Viterbi Decoding Required receiver signal-to- noise ratio (Eb/N0) (dB) receiver_Eb_N0_req_dB 5 Uplink Data Rate (bps) R_uplink_datarate_bps 4000 114 5.1.2.3 Payload Inputs Sheet The Payload inputs sheet contains the fewest number of design parameters. The payload mass (for all instrumentation) and peak power (of all payload operation modes) are entered in this sheet. An example Payload inputs sheet is shown in Table 5-6 below. Note the presence of the “Science Payload” and the “Other Payload” rows. The science payload entries indicate the mass, power, and data rate estimates for the payload instrument suite onboard the spacecraft element. The other payload entries indicate any other instrument packages that are not used for science but nevertheless required onboard the spacecraft. Note that the “other payload” mass and power design parameters have entries of 20 kg and 20 W, respectively, for the Lander. These design values represent estimates for an onboard Hazard Detection and Avoidance (HDA) system, similar to that flown on NASA’s ALHAT (Autonomous Landing and Hazard Avoidance Technology) project (50), and assumed to be present on the Lander to aid in safe landing site identification. The mass and power estimates currently just represent placeholder numbers. Table 5-6. Payload inputs sheet in Mission and Spacecraft Definition (MASD) tool 5.1.2.4 CDS Inputs Sheet The CDS inputs sheet contains several parameters specifying that subsystem’s functionality, capability and operation. The list of inputs includes: Science Payload Definition MATLAB Parameter Name Rover Lander Another spacecraft is payload? has_spacecraft_payload_flag N Y Science Payload Mass (kg) m_instr_payload_kg 30 0 Science Payload Peak Power (W) P_instr_payload_peak_W 100 0 Science Payload Peak Data Rate (kbps) R_instr_payload_peak_kpbs 50,000 0 Other Payload Mass (kg) m_other_payload_kg 0 20 Other Payload Peak Power (W) P_other_payload_peak_W 0 20 Other Payload Peak Data Rate (kbps) R_other_payload_peak_kbps 0 1000 Other Payload Operations Phase other_payload_ops_phase n/a Descent and Landing 115  System type: command only, telemetry only, or combined command & telemetry  Autonomy o Software autonomy complexity level: simple or complex o Presence of fault monitoring o Presence of fault detection  Command Processing o Command processing rate (# commands per second) o Total # of command channels for subsystem control o Computer bus constraints (single, multiple, or integrated units)  Environmental: low and high operating temperature limits for CDS electronics in a warm electronics box (WEB), and the radiation environment level  Telemetry o Standard telemetry sampling frequencies (Hz) for voltage, current, temperature, data storage; telemetry margin; and total # of telemetry channels An example CDS inputs sheet is shown in Table 5-7 below. 116 Table 5-7. “CDS” inputs sheet in Mission and Spacecraft Definition (MASD) tool 5.1.2.5 Telecom Inputs Sheet The Telecom inputs sheet contains the most design parameters of all the input sheets. The telecom design parameters are grouped into the following categories:  General: Telecom architecture type (e.g. DTE or Relay), and whether the spacecraft element serves as a relay node to Earth.  Uplink/Downlink Parameters: List of link parameters such as spacecraft receiver noise figure, link polarization loss, system implementation loss, Earth atmospheric zenith absorption loss, link modulation scheme (should be the same as that input in the “Ground System” inputs), minimum elevation angle (if the spacecraft operated on a planetary surface or surface of a moon with an atmosphere), and the required spacecraft receiver signal-to-noise ratio CDS MATLAB Parameter Name Rover Lander System Type system_type Combined Command and Telemetry Combined Command and Telemetry Autonomy Software level of autonomy software_autonomy Complex Complex Has fault monitors? has_fault_monitors_flag Y Y Has fault correction? has_fault_correction_flag Y Y Command Processing Onboard Command Rate (cmds/sec) cmd_rate_cmds_per_sec 50 50 # Command Channels for Subsystem Control num_cmd_channels 200 200 Computer Bus Constraint bus_constraint Integrated Integrated Environmental Low Operating Temperature (deg C) T_low_op_C -10 -10 High Operating Temperature (deg C) T_high_op_C 50 50 Radiation Environment (krad) radiation_environment_krad 10 10 Telemetry Voltage telemetry rate (Hz) fs_generic_voltage_rate_Hz 10 10 Current telemetry rate (Hz) fs_generic_current_rate_Hz 10 10 Temperature telemetry rate (Hz) fs_generic_temp_rate_Hz 1 1 Data storage telemetry rate (Hz) fs_data_storage_Hz 1 1 Telemetry data rate margin factor f_tlm_margin 0.1 0.1 # telemetry channels num_tlm_channels 500 500 117  Hardware parameters: RF amplifier cut-off power above which to select a TWTA (traveling wave tube amplifier) vs. an SSPA (solid state power amplifier)  Primary Antenna parameters: the antenna type, presence of a gimbal, pointing error, efficiency, range of dimensions (minimum, maximum and step size) for the antenna diameter and length (if applicable), range of RF transmission power (minimum, maximum, and step size), antenna noise temperature, and line loss  The same set of design parameters for the Backup antenna  The same set of design parameters for the Relay antenna (if present)  Telemetry: Standard telemetry sampling frequencies (Hz) for voltage, current, temperature; and telemetry compression ratio. An example of the Telecom inputs sheet is shown in Table 5-8. 118 Table 5-8. “Telecom” inputs sheet in Mission and Spacecraft Definition (MASD) tool 5.1.2.6 ADCS Inputs Sheet The ADCS inputs sheet contains the second most numerous list of design parameters. These parameters are grouped into the following categories:  General o Is an inertial sensor (e.g. IMU) required? o Does the spacecraft element have attitude control (e.g. for a free flying spacecraft that can slew)? o Include a reaction control subsystem (RCS) in the internal design trade space? TELECOM MATLAB Parameter Name Rover Lander General Telecom Architecture Type telecom_arch_type Relay (w/ DTE in loop) Relay (w/ DTE in loop) Does this spacecraft relay data directly to Earth? is_relay_node_flag N Y Uplink/Downlink Parameters Spacecraft receiver noise figure (dB) receiver_noise_figure_dB 1 1 Link polarization loss (dB) L_polariz_loss_dB 0 0 System implementation loss (dB) L_implement_dB -2 -2 Earth atmospheric zenith absorption loss (dB) L_absorp_loss_zenith_dB 0 0 Link modulation scheme modulation_scheme BPSK/QPSK + R-1/2 Viterbi Decoding BPSK/QPSK + R-1/2 Viterbi Decoding Minimum elevation angle (deg) min_elev_angle_deg 0 0 Required spacecraft receiver signal-to- noise ratio (Eb/N0) (dB) receiver_Eb_N0_req_dB 5 5 Hardware Parameters RF amplifier cut-off power above which to select TWTA (W) RF_power_TWTA_cutoff_W 15 15 Cabling mass fraction cabling_mass_fraction 0.1 0.1 Primary Antenna (for DTE) Primary antenna type primary_antenna.antenna_type Parabolic Parabolic Is antenna gimballed? primary_antenna.gimbaled_flag N N Primary antenna pointing error (deg) primary_antenna.pointing_err_deg 0 0 Primary antenna efficiency factor primary_antenna.antenna_efficiency 0.55 0.55 Primary antenna min diameter (m) primary_antenna.D_antenna_min_m 0.1 0.1 Primary antenna max diameter (m) primary_antenna.D_antenna_max_m 0.5 0.5 Primary antenna diameter step size (m) primary_antenna.D_antenna_step_m 0.05 0.05 Primary antenna min length (m) primary_antenna.L_antenna_min_m n/a n/a Primary antenna max length (m) primary_antenna.L_antena_max_m n/a n/a Primary antenna length step size (m) primary_antenna.L_antenna_step_m n/a n/a Primary antenna min RF transmission power (W) primary_antenna.Pt_min_W 5 5 Primary antenna max RF transmission power (W) primary_antenna.Pt_max_W 80 80 Primary antenna RF transmission power step size (W) primary_antenna.Pt_step_W 1 1 Primary antenna temperature from environmental noise (K) Tant_K 84.56 84.56 Primary antenna line loss (dB) L_line_loss_dB -0.5 -0.5 119  Telemetry: standard voltage, current, and temperature telemetry sampling frequencies, along with RWA speed sampling frequency  Software o Cycle time for ADCS software o Software functionality flags for items such as kinematic integration, attitude error determination, ephemeris propagation, orbit propagation, and Kalman filter presence  RCS inputs (if applicable): If an RCS is included in the trade space, parameters such as: o # thrusters firing per control axis (typically 2) o # single string thrusters o # thruster strings (typically 2) o RCS propulsion system type (typically mono-prop) o Pressurant o Pressurant feed system type (e.g. tank pressure fed) and subtype (blowdown) o RCS propellant mass margin, residual mass margin, loading uncertainty factor o Minimum impulse specific impulse (Isp) fraction  RCS tank parameters: parameters such as fuel tank maximum pressure, fuel tank material, composite tank liner material (if fuel tank is composite), tank pressure factor of safety, propellant control device type, etc.  Body vectors: Definition of standard body vectors used for specifying the spacecraft attitude  Pointing: Parameters such as default pointing accuracy, knowledge accuracy fraction, slew coasting time fraction, and default slew coasting rate 120 An example of the ADCS inputs sheet is shown below. Table 5-9. ADCS inputs sheet in Mission and Spacecraft Definition (MASD) tool 5.1.2.7 Propulsion Inputs Sheet The Propulsion inputs sheet contains the following categories of design parameters: ADCS MATLAB Parameter Name Rover Lander General Inertial reference sensor required? inertial_sensor_required_flag Y Y Has attitude control functionality? has_attitude_control_flag N Y Include reaction control system in design trade space? rcs_possible_flag N Y Telemetry Voltage telemetry rate (Hz) fs_generic_voltage_rate_Hz 10 10 Current telemetry rate (Hz) fs_generic_current_rate_Hz 10 10 Temperature telemetry rate (Hz) fs_generic_temp_rate_Hz 1 1 RWA speeds telemetry rate (Hz) fs_rwa_speeds_Hz 10 10 Software Cycle time (sec) t_software_cycle_sec 0.05 0.05 Has kinematic integration? has_kinematic_integration_flag Y Y Has attitude error determination? has_error_determination_flag Y Y Has ephemeris propagation? has_ephemeris_propagation_flag Y Y Has complex ephemeris? has_complex_ephemeris_flag N N Has orbit propagation? has_orbit_propagation_flag Y Y Has Kalman filter? has_kalman_filter_flag Y Y RCS inputs (if applicable) Assumed thruster valve current (A) rcs.I_assumed_current_thruster_valve_A n/a 1 RCS torque margin (%) rcs.f_rcs_torque_margin_percent n/a 100 # thrusters firing per control axis rcs.N_thrusters_firing_per_axis n/a 2 # single string thrusters rcs.num_single_string_thrusters n/a 8 # thruster strings rcs.num_thruster_strings n/a 2 RCS propulsion system type rcs.type n/a Mono-prop Pressurant rcs.pressurant n/a All Pressurant Phase rcs.press_phase n/a gas Pressurant Feed Type rcs.press_type n/a Tank Pressure Fed Pressurant Feed Subtype rcs.press_subtype n/a Blowdown Regulator pressure drop (if applicable) (MPa) rcs.dP_regulator_MPa n/a n/a Mixture ratio (if applicable) rcs.mixture_ratio n/a n/a RCS propellant mass margin rcs.f_margin n/a 0.25 RCS propellant residual mass margin rcs.f_residual n/a 0.03 RCS propellant loading uncertainty rcs.f_load_unc n/a 0.005 Minimum impulse Isp fraction rcs.f_Isp_min_pulse n/a 0.85 Nominal Fuel Temperature (deg C) rcs.T_fuel_C n/a 25 Nominal Pressurant Temperature (deg C) rcs.T_press_C n/a 25 RCS tank parameters (if applicable) Fuel tank maximum pressure (MPa) rcs.P_fuel_tank_max_MPa n/a 15 Fuel tank material type rcs.tank_material_type n/a All Metal fuel tank material alloy/product rcs.tank_material_type_metal_alloy_product n/a Al 7075-T73 Composite fuel tank material alloy/product rcs.tank_material_type_composite_alloy_product n/a Torayca T1000G Composite tank liner material product rcs.tank_liner_material_product n/a Al 7075-T73 Tank liner thickness (m) rcs.tank_liner_thickness_m n/a 0.000254 Tank pressure factor of safety rcs.tank_pressure_factor_of_safety n/a 1.25 Propellant control device type rcs.prop_control_type n/a bladder Propellant control material rcs.prop_control_material_name n/a Elastomer Propellant control material thickness (m) rcs.prop_control_material_thickness_m n/a 0.002 Body Vectors Definition Primary Antenna Boresight body_vec(1) X axis X axis Solar Array Normal body_vec(2) Y axis Y axis Primary Thrust body_vec(3) Z axis Z axis Pointing Attitude Pointing Constraint attitude_constraint none none Default pointing accuracy (deg) pointing_accuracy_mag_deg 1 1 Knowledge Error Fraction f_knowledge_accuracy 0.1 0.1 Slew coasting time fraction f_coasting_time 0.4 0.4 Default slew coasting rate (deg/s) w_coasting_default_deg_per_sec 0.1 0.1 121  Telemetry: Standard voltage, current, temperature telemetry sampling frequencies, and the primary engine control cycle frequency.  Propulsion system inputs: for the primary propulsion system o Propulsion system type: Based on the type of trajectory  Chemical ballistic and Weak Stability Boundary: Mono-prop, bi-prop, and solid rocket motor  Low thrust: electric propulsion (ion, hall thruster, pulsed plasma thruster) o Pressurant Feed type: only tank pressure fed supported in MASS tool (i.e. pump fed not supported) o Pressurant Feed subtype: Regulated and Blowdown supported for tank pressure fed type o Pressurant o Fuel ullage factor: determines amount of pressurant ullage gas within fuel tank o Oxidizer ullage factor: determines amount of pressurant ullage gas within oxidizer tank o Contingency propellant factor: determines additional propellant for contingency Delta-V o Residual propellant factor: determines amount of residual propellant in the lines and valves o Propellant loading uncertainty factor: determines amount of additional propellant filled due to loading uncertainty 122 o Fuel operating temperature (used only if fuel is a gas, so not used since fuel is typically a liquid) o Oxidizer operating temperature (used only if oxidizer is a gas, so not used since oxidizer is typically a liquid) o Pressurant operating temperature (used only if pressurant is a gas)  Engine inputs o # active thrusters per trajectory control Delta-V: usually 1, even if multiple engines are present for the Descent & Landing portion of lunar mission o Minimum nozzle separation distance: the separation distance between nozzles at the exit plane  Tank parameters o Fuel tank maximum pressure o Oxidizer tank maximum pressure o Pressurant tank maximum pressure o Fuel tank material type: metal, composite, or all (if “all” selected, two separate configurations are created in separate runs of the MASS tool) o Metal fuel tank material alloy/product (if metal is selected as the tank material type) o Composite fuel tank material alloy/product (if composite if selected as the tank material type) o Composite tank liner material product (used if a composite tank is selected) o Tank pressure factor of safety o Propellant control device type and material 123 An example of the Propulsion inputs sheet is shown below in Table 5-10 and Table 5-11. Table 5-10. Propulsion inputs sheet (part 1) in Mission and Spacecraft Definition (MASD) tool Table 5-11. Propulsion inputs sheet (part 2) in Mission and Spacecraft Definition (MASD) tool The Thermal inputs sheet contains the following categories of inputs:  General PROPULSION MATLAB Parameter Name Rover Lander Telemetry Voltage telemetry rate (Hz) fs_generic_voltage_rate_Hz n/a 10 Current telemetry rate (Hz) fs_generic_current_rate_Hz n/a 10 Temperature telemetry rate (Hz) fs_generic_temp_rate_Hz n/a 1 Engine control cycle (Hz) fs_engine_control_cycle_Hz n/a 5 Propulsion system inputs Prop Sys Type type n/a Bi-prop Pressurant Feed Type press_type n/a Tank Pressure Fed Pressurant Feed Subtype press_subtype n/a Blowdown Pressurant pressurant n/a All Pressurant Phase press_phase n/a gas Fuel Ullage factor f_ullage_fuel n/a 0.05 Oxidizer Ullage factor f_ullage_ox n/a 0.05 Contingency Propellant factor f_margin n/a 0.05 Residual Propellant factor f_residual n/a 0.03 Propellant Loading Uncertainty factor f_load_unc n/a 0.005 Fuel Operating Temperature (deg C) T_fuel_C n/a 25 Oxidizer Operating Temperature (deg C) T_ox_C n/a 25 Pressurant Operating Temperature (deg C) T_press_C n/a 25 PROPULSION MATLAB Parameter Name Rover Lander Engine inputs # active thrusters per trajectory control DeltaV num_active_thrusters n/a 1 Min nozzle exit separation distance (m) min_nozzle_exit_separation_distance_m n/a 0.05 Tank parameters Fuel tank maximum pressure (MPa) P_fuel_tank_max_MPa n/a 15 Oxidizer tank maximum pressure (MPa) P_ox_tank_max_MPa n/a 15 Pressurant tank maximum pressure (MPa) P_press_tank_max_MPa n/a 56 Fuel tank material type tank_material_type n/a All Metal fuel tank material alloy/product tank_material_type_metal_alloy_product n/a Al 7075-T73 Composite fuel tank material alloy/product tank_material_type_composite_alloy_product n/a Torayca T1000G Composite tank liner material product tank_liner_material_product n/a Ti-6Al-4V Tank liner thickness (mm) tank_liner_thickness_m n/a 0.5 Tank pressure factor of safety tank_pressure_factor_of_safety n/a 4 Propellant control device type prop_control_type n/a bladder Propellant control material prop_control_material_name n/a Elastomer Propellant control material thickness (m) prop_control_material_thickness_m n/a 0.002 124 o Thermal subsystem mass fraction: typically, between 2-4% of the spacecraft dry mass  Telemetry: standard voltage, current, and temperature telemetry sampling frequencies  Operational temperatures o Spacecraft internal units’ lower temperature limit o Spacecraft internal unit’s upper temperature limit o Temperature margin: additional degrees Celsius below or above lower/upper temperature limits  Surface Properties o Electronics surface material: representative surface material for most electronics within spacecraft warm electronics box (WEB) o Spacecraft surface material: representative surface material for spacecraft thermal equilibrium calculations An example Thermal inputs sheet is shown in Table 5-12 below. 125 Table 5-12. Thermal inputs sheet in Mission and Spacecraft Definition (MASD) tool 5.1.2.8 Structures Inputs Sheet The Structures subsystem inputs sheet contains the following categories of inputs:  General o Spacecraft reflectance factor (for solar radiation pressure calculations) o # Rover wheels (applies to Rover only)  Telemetry: standard voltage, current, and telemetry sampling frequencies  Warm Electronics Box inputs o WEB structure material alloy/product o WEB sheet thickness  Lander structural parameters (applies to Lander only) o Material type: metal or composite o Material alloy/product: specific metal or composite name o Yield safety factor THERMAL MATLAB Parameter Name Rover Lander General Thermal mass fraction f_thermal_mass 0.04 0.04 Telemetry Voltage telemetry rate (Hz) fs_generic_voltage_rate_Hz 10 10 Current telemetry rate (Hz) fs_generic_current_rate_Hz 10 10 Temperature telemetry rate (Hz) fs_generic_temp_rate_Hz 1 1 Operational Temperatures S/C internal units lower temperature limit (deg C) T_sc_internal_units_lower_C 0 0 S/C internal units upper temperature limit (deg C) T_sc_internal_units_upper_C 40 40 Temperature margin (deg C) T_margin_C 5 5 Surface Properties Electronics surface material electronics_surface_material Al 6061-T6 polished Al 6061-T6 polished S/C surface material sc_surface_material White paint (silicate) White paint (silicate) 126 o Buckling safety factor o Bending safety factor o Yield margin of safety o # thrust structure columns: 4 are assumed and supported in MASS o Separation distance between tank and thrust structure o # engine mounting struts: 4 are assumed and supported in MASS tool o Max load factor: acceleration in Earth g’s due to launch and/or Delta-V maneuver thrusting o # landing legs: 4 are assumed and supported in MASS o Rock hazard height: height of a rock before it hits the landing engine nozzles o Nominal leg strut spacing: distance between the top of each leg at the base of the Lander o Leg theta elevation angle: elevation angle of leg with respect to X-Y lander plane (parallel to ground) o Leg phi azimuth angle: clock angle of leg with respect to Y-axis of lander. Assumed to be 45 deg. An example of the Structures subsystem inputs sheet is shown in Table 5-13. 127 Table 5-13. Structures subsystem inputs sheet in Mission and Spacecraft Definition (MASD) tool The Power inputs sheet contains the following categories of inputs:  General: o Power system type: currently can be solar arrays + batteries, radioisotope + batteries, and fuel cells + batteries o Secondary battery chemistry: used to select which battery technology option to use in the above power system type o Solar array structure type (if applicable): can be rigid panel, flexible fold-up panels, or flexible roll-up panels o Fuel cell sizing method (if applicable): can be either to minimize fuel cell system mass or minimize fuel cell system power density o Power Control method: either Peak Power Tracking or Direct Energy Transfer STRUCTURES MATLAB Parameter Name Rover Lander General S/C reflectance factor reflectance_factor 0.7 0.7 # Rover Wheels num_wheels 4 n/a Telemetry Voltage telemetry rate (Hz) fs_generic_voltage_rate_Hz 10 10 Current telemetry rate (Hz) fs_generic_current_rate_Hz 10 10 Temperature telemetry rate (Hz) fs_generic_temp_rate_Hz 1 1 Warm Electronics Box inputs WEB structure material alloy/product web.alloy_product Al 7075-T73 Al 7075-T73 WEB sheet thickness (m) web.thickness_m 0.0025 0.0025 Lander Structural Parameters Material Type material_type n/a Metal Material Alloy/Product alloy_product n/a Al 7075-T73 Yield Safety Factor fs_yield n/a 2 Buckling Safety Factor fs_buckling n/a 2 Bending Safety Factor fs_bending n/a 2 Yield Margin of Safety (%) fms_yield n/a 200 Thrust structure minimimum height (m) h_thrust_struct_min_m n/a 0.25 # thrust structure columns num_thrust_struct_columns n/a 4 Separation distance between tank and thrust structure (m) d_sep_tank2thrust_struct_m n/a 0.05 # engine mounting struts num_engine_mounting_struts n/a 4 Max load factor n_max_load_factor n/a 4 # Landing legs num_legs n/a 4 Rock hazard height (m) h_rock_hazard_m n/a 0.35 Nominal leg strut spacing (m) b_leg_strut_spacing_m n/a 0.25 Leg theta elevation angle (deg) theta_AB_el_leg_deg n/a 70 Leg phi azimuth angle (deg) phi_AB_az_leg_deg n/a 45 128 o Spacecraft Bus Voltage  Telemetry: standard voltage, current, temperature telemetry sampling frequencies, and power subsystem telemetry sampling frequency An example Power inputs sheet is shown in Table 5-14 below. Table 5-14. Power inputs sheet in Mission and Spacecraft Definition (MASD) tool 5.1.3 Generation of System Configuration Inputs 5.1.3.1 Parameter File Generation Once the user has specified desired parameters in each design sheet of the Mission and Spacecraft Definition (MASD) tool, as described in Section 5.1.2, the next step is to generate combinations of system configurations based on the parameter values and selections. This is done by clicking on the “Create MATLAB Inputs” button on the Mission & System sheet of the MASD tool. This button executes VBA code that reads in the design parameters in each Excel Table from each input sheet. First the design parameters in the Trajectory Inputs and Ground System input sheets are read in and then printed out to separate MATLAB .m files named POWER MATLAB Parameter Name Rover Lander General Power system type type All Solar Array + Battery Secondary battery chemistry battery_chem Li-ion Li-ion Solar array structure type (if applicable) solar_array_structure_type Flexible Fold-up Blankets Flexible Fold-up Blankets Fuel cell sizing method (if applicable) fuel_cell.sizing_method Minimize mass Minimize mass Power Control Method power_control_method Peak Power Tracking Peak Power Tracking S/C Bus Voltage (V) bus_voltage 100 100 Telemetry Voltage telemetry rate (Hz) fs_generic_voltage_rate_Hz 10 10 Current telemetry rate (Hz) fs_generic_current_rate_Hz 10 10 Temperature telemetry rate (Hz) fs_generic_temp_rate_Hz 1 1 Power telemetry rate (Hz) fs_power_Hz 5 5 129 “traj_params.m” and “ground_params.m”. These input files are written to a folder on the Desktop of the computer on which the designs will be run. The parameters in these files are written, one per line, using the MATLAB “structure” data type. According to the MATLAB documentation (release R2013a), a “structure” data type is an “array with named fields that can contain data of various types and sizes”. This provides an easy way to encapsulate related parameters and other data under a common data grouping. It also enables parameter groups to be sent as arguments to specific top-level custom MATLAB functions. For example, the design parameters are all grouped under the “mission” structure. Within this structure is another structure field named “traj” that houses all the trajectory- related parameters, mostly those that control the Descent & Landing sizing module. The Descent & Landing parameters are themselves housed within a “descent_landing” field within the “traj” structure. The same situation applies to the “ground_params.m” input file: all ground network related parameters are grouped under the “mission” structure, within the “ground_network” sub-structure. The ground parameters input file also contains a database of parameters for NASA’s Deep Space Network. These parameters are grouped by frequency band (the DSN supports S-band, X-band, and Ka-band, depending on the antenna ground station in use) for both near-Earth and deep space applications. The following chart in Figure 5-5 depicts the organization of the trajectory and ground system parameters. Each blue box represents a MATLAB data structure, whereas each green box represents a parameter = value setting. So, for example, the design parameter that sets the starting value of the descent de-orbit altitude h 0 (used as part of the Descent & Landing 130 module’s braking burn 1 initial conditions search algorithm) can be found according to the following syntax: “mission.traj.descent_landing.h0_initial_km = <value>;”. Note that each parameter input line is terminated with a semicolon, as this is the MATLAB syntax that suppresses output of the parameter value in the MATLAB Command Window. The name of each MATLAB parameter is specified in the “MATLAB Parameter Name” column of each design parameter input sheet (see various examples in Section 5.1.2). This column was made visible in order to allow the name of the parameter to be changed easily while developing the MASD tool. Once the tool development was complete, however, it was NOT desirable to change the MATLAB parameter name, since the MATLAB tool that generates the system designs expects parameters according to pre-defined names (and would require editing the MATLAB design tool to use the new parameter names). Figure 5-5. Trajectory and Ground Systems design parameter organization in MATLAB input files mission traj descent_landing <param> = <value> mission ground_network <param> = <value> freq_band(i) near_Earth deep_space <param> = <value> <param> = <value> 131 After the trajectory and ground systems input MATLAB files are generated, the VBA code executes the following logic for each of the user-specified spacecraft element in the mission: it goes through each of the payload and subsystem parameter input sheets, extracts the design parameters and writes their parameter = value lines to a separate MATLAB parameter input file containing all the “general” parameters for that spacecraft element. The term “general” refers to parameters that are intended to be fixed, or constant, across all system configuration combinations. As an example, if a Rover and Lander are specified in that order, the VBA code first outputs Rover-related parameters to a “rover_general_params.m” file and then proceeds to output Lander-related parameters to a “lander_general_params.m” file. The design parameters for each spacecraft element are organized using the same MATLAB structure organization that was employed for the trajectory and ground system parameters. This is depicted in below. In this figure, the spacecraft element design parameters are organized by the “mission” structure, following by a sub-structure field for the “system_config”, followed by a sub-structure for the “element”, followed by a sub-structure for the subsystem (either “payload” or one of the general spacecraft subsystems), and then the parameter field itself. For example, the Lander telecommunications architecture type parameter is specified as: “mission.system_config.element(2).telecom.telecom_arch_type = ‘<string value>’;”. This parameter organization is depicted in below. 132 Figure 5-6. Payload and subsystem design parameter organization in MATLAB input files Once the general parameters are created for a given spacecraft element, the next step is to generate the “trade” parameters input files containing the set of parameters for each “tradeable” parameter option for each subsystem for each spacecraft element. As previously mentioned, some of the design parameters in a given input sheet consist of fixed values, whereas others (the “trade” parameters) consist of more than one applicable option or an option that itself expands into a set of unique design parameters that are obtained from a database. For a subsystem that has a set of “trade” parameters, the unique design parameters mission system_config <param> = <value> element(i) payload cds telecom adcs prop thermal structures power … … 133 are output to a .m file according to the following naming convention: <element name>_<subsystem>_<trade parameter name>_trade<trade number>.m. The trade number designator can be either a single number or in the form “N_M”, where N represents the primary trade option and M represents a trade sub-option. These “trade” parameter input files are placed in the data generation folder, within a “trade_params” folder and subsystem subfolder. The list of “trade” parameters or parameters with expandable parameter sets per subsystem, as used in this research, is given below. Table 5-15. Subsystem “Trade” Parameters Subsystem Parameter Available Options # Unique Options ADCS RCS pressurant Nitrogen, Helium, or All 2 ADCS RCS fuel tank material type Metal, Composite, or All 2 ADCS Composite tank liner material product Single user-specified option 1 ADCS Propellant control device material Single user-specified option 1 Propulsion Propulsion system type Bi-prop (several engine sub-options available in Thruster/Engine database) 9 (Bi-prop engines > 200 N max thrust) Propulsion Propulsion system pressurant Nitrogen, Helium, or All 2 Propulsion Fuel tank material type Metal, Composite, or All 2 Propulsion Composite tank liner material product Single user-specified option 1 Propulsion Propellant control device material Single user-specified option 1 Thermal Electronics surface material Single user-specified option 1 Thermal Spacecraft surface material Single user-specified option 1 Structures Warm electronics box (WEB) structure material alloy/product Single user-specified option 1 Structures General structure material alloy/product Single user-specified option 1 134 Subsystem Parameter Available Options # Unique Options Power Power system type Solar array + battery, Radioisotope + battery, Fuel cell + battery, or All 5 solar cell types, 4 RPS types, 2 fuel cell types Power Secondary (re-chargeable) battery chemistry Single user-specified option 1 Power Solar array structure type (if applicable) Single user-specified option (Rigid Panel, Flexible Fold-up Blankets, Flexible Roll-up Blankets) 1 Power Power control method Single user-specified option (Peak Power Tracking, Direct Energy Transfer) 1 For example, the power system type parameter in the Power input sheet has a list of choices that the user can select from: All, Solar array + Battery, Radioisotope + Battery, and Fuel Cell + Battery. Say the user selects the “Solar array + Battery” option for the Lander. Since multiple solar cell options are available in the solar cell database, each of these options can be used as a potential solution. So, the VBA code extracts each solar cell entry from the solar array database and prints out the associated set of parameters (or “properties”) to a unique file for each entry. For the solar cell trade parameter, the output files are named as “lander_power_type_trade1_<N>.m”, where the “1” indicates the only power type selected (solar array + battery) and N represents a numeric designator for the solar cell option. Note that the battery chemistry selection in this research is limited to one battery option (e.g. Li-ion) for both the Rover and Lander, in order to reduce the number of possible power type combinations (e.g. several solar cell options + one battery cell selection). 135 5.1.3.2 Spacecraft Subsystem Combinations Generation Once all the spacecraft element subsystem trade parameter files have been created, the next step is to combine them ultimately into a set of unique system configurations. The first step in this process is to get all the unique subsystem trade parameter file prefixes for each spacecraft element from the .m file names and identify the number of options for each trade parameter. A 2D array containing this information is generated for each spacecraft element and passed to a VBA function named RecursiveCombinations. This function uses a recursive call to itself to parse through the 2D array of options by subsystem trade parameter and generate a list of .m file combinations, printing one combination line to a row in the “Subsys Combos” sheet. In other words, each trade parameter option .m file in each subsystem is combined with every other trade parameter option .m file for that subsystem. Once this list of subsystem combinations is created for each spacecraft element, another VBA function is called to concatenate the contents of each trade parameter .m file listed within each combination row into a subsystem configuration .m file for that spacecraft element. The subsystem configuration files are named as <element>_<subsystem>_config<N> and placed within a subsystem subfolder within a “subsys_configs” folder. For example, the 2 Lander ADCS trade parameters (RCS pressurant and RCS fuel tank material type), each containing 2 trade options, are combined into 4 Lander ADCS configurations (e.g. lander_adcs_config1.m through lander_adcs_config4.m). 5.1.3.3 Spacecraft Element Combinations Generation Once the set of unique spacecraft element subsystem configuration .m files are created, the next step is to combine them into a set of spacecraft element configuration .m files. This is 136 done using the same VBA functions that were used in generating the subsystem configuration .m files. That is, the RecursiveCombinations VBA functions is again called given a 2D array of subsystem options (a list of config .m files per subsystem) for each spacecraft element to generate a list of combinations. In other words, each subsystem configuration .m file is combined with every other subsystem configuration .m file and output to a row in the “Elem Combos” sheet in the MASD Excel tool. The individual subsystem configuration .m files are combined in numerical order (rather than the standard file system order that places “lander_prop_config10.m” and “lander_prop_config11.m”, etc. after “lander_prop_config1.m”). This preserves a logical order for the combination sequences, since the numerical ID of the element combinations will represent a consistent grouping of the various subsystem configurations. For example, Lander configurations 1 through 180 will combine Lander ADCS configuration 1 with Lander Power configurations 1 through 5, with Lander Propulsion configurations 1 through 36, with the single Lander Structures and Thermal configurations. The number of spacecraft element combinations generated can be large, depending on the number of options available per trade parameter. Using the data in the fourth column of Table 5-15 above (the number of unique combinations available per trade parameter), the number of spacecraft element configurations can be determined. In this research, the Rover is traded only on power system type (5 solar cell options + 4 RPS options + 2 fuel cell options). That results in 11 rover power configurations. For the Lander, there are 2 ADCS RCS pressurant gas options, 2 ADCS RCS tank material options, 9 Propulsion bi-propellant system options, 2 Propulsion pressurant gas options, 2 Propulsion tank material options, and 5 Power solar cell options. Multiplying all these together 137 results in 720 unique Lander configurations. Generating this many .m files takes a couple minutes. 5.1.3.4 System Configuration Combinations Generation The final step is to combine all the individual spacecraft element configuration .m files into a set of complete system configuration .m files. This again involves making use of the RecursiveCombinations VBA function to generate a list of combinations of each spacecraft element configuration .m file with every other element configuration .m file. This list is output, one combination per row, to a “Sys Combos” sheet in the MASD tool. Given that 11 Rover configurations and 720 Lander configurations were generated in the previous step, the result is 11*720 = 7920 unique system configuration combinations. This number of combinations can easily be stored in Excel, as it is below the maximum number of rows that can exist (over 1 million rows). Since each unique system configuration must be combined with the set of “general” parameter inputs per spacecraft element described earlier, the additional “general” parameter input files are also included in each combination row (although they are the same set of files in each system configuration combination row). Once the list of system combinations is generated, the final step is to concatenate the .m files listed in each combination into a unique system configuration .m file. The system configuration .m files are named as “sys_configN.m” and placed within a “sys_configs” subfolder. An example listing of the first 9 system configuration combinations is shown below in Table 5-16, where the first combination would be named “sys_config1.m”. 138 Table 5-16. Example set of first 9 System Configuration combinations Generating 7920 .m files takes a few minutes due to the slow nature of reading from and writing to a text file in VBA. In a typical system configuration .m file, there are between 845 to 865 individual parameters, depending on the subsystem trade parameter options (the fuel cell option has more parameters than the solar array option, for example). 5.2 MISSION AND SPACECRAFT SIZING TOOL (MASS) The objective of the mission described in this research is to deliver a lander and its rover payload to the lunar South Pole to prospect for lunar volatiles. To obtain a conceptual design of both spacecraft, a design tool named the Mission and Spacecraft Sizing (MASS) tool was developed in MATLAB. This primary objective of this tool is to perform spacecraft system design by means of automated trade space exploration. That is, the intent of the tool is to design both the lander and rover given numerous different configurations of each spacecraft. The competing configurations are determined by user inputs specified in the Excel-based Mission and Spacecraft Definition (MASD) tool, as described in Section 5.1.2 (Definition of System Parameters) and 5.1.3 (Generation of System Configuration Inputs). The formal design problem that the MASS tool is intended to solve is known as the multi-disciplinary design problem (MDP). In the MDP, the design of the entire system depends ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config1.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config2.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config3.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config4.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config5.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config6.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config7.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config8.m ..\lander_general_params.m ..\rover_general_params.m rover_config1.m lander_config9.m 139 on the design of each subsystem, and each subsystem design in turn depends on the design of the other subsystems. The method chosen to address this problem as it applies to the lunar science mission of this research is a sequential-iterative approach. That is, each subsystem of each spacecraft is designed in series, passing design outputs from one subsystem to the next. Once all subsystems have been designed, the process then repeats in an iterative manner until either the total system mass converges or not. The overall architecture of the MASS tool is depicted in Figure 5-7. Figure 5-7. Overall Architecture of the Mission and Spacecraft Sizing (MASS) Tool Get list of configuration IDs to run MASS tool For each system configuration in list:  Load ground and trajectory parameters  Load system config parameters  Load subsystem database parameters  Call Mission module  Get list of mission events  Call System design module Mission module  Iterate on design of current system configuration, calling the Spacecraft design module for each system element System design module  Compute additional Delta-V to transfer from lunar capture orbit to low lunar orbit  Terminate system iterations upon total system mass convergence, reaching max # iterations allowed, or for infeasible Descent & Landing design  Design each subsystem of current spacecraft element  Call Descent & Landing design module (if element is Lander) Spacecraft design module 140 The tool first starts by loading in several files required by the JPL SPICE toolkit (a suite of functions to process spacecraft trajectory data and solar system ephemerides and other geometry). These files are the planetary SPICE kernel (de430.bsp, containing solar system body ephemerides), the planetary constants kernel (pck00010.tpc), and the leap seconds file (naif0010.tls). The JPL SPICE toolkit functions are used throughout the MASS tool to find spacecraft position, velocity, and other relevant data (e.g. eclipse periods, etc.). Once the above files are loaded, the user is prompted for a text file containing a list of numbers, corresponding to the ID of each system configuration that the user intends to design. Each of these configurations has a “sys_config<N>.m” file associated with it. These “system configuration” .m files were generated by the process described in Section 5.1.3. The tool has a for-loop to cycle through each of the configuration IDs. Within the for- loop, the “ground_params.m” file (containing ground network parameters) and “traj_params.m” file (containing trajectory and Descent & Landing parameters) are loaded. Then the system configuration .m file associated with the current configuration ID is loaded. Again, this system configuration .m file contains all the design parameters that will be used in designing the system. Next, the following subsystem database .m files are loaded: Telecom, ADCS, Propulsion, CDS, and Structures. The Telecom, ADCS, and Propulsion databases contain mass, power, and other performance parameters for several different components under different technology categories. The Telecom database contains parameters for several different transponders and transceivers, as well as an RF amplifier mass database based on required RF output power. The ADCS database contains parameters for multiple star trackers, sun sensors, IMUs, and reaction wheels. The Propulsion database contains parameters for several mono- propellant and bi-propellant thrusters/engines, as well as a database of physical properties for 141 various propellants and pressurants. The CDS database contains computing throughput parameters for different spacecraft software functions. The Structures database contains properties for various metals and composites, as well as rover sizing parameters (based on historical data). The parameters in each database .m file are categorized under a common MATLAB structure named “database”, followed by a sub-structure for the relevant subsystem. A timer is then started to keep a track of the duration required to design each system configuration. The design process begins by a call to the Mission module given the “mission” structure, “database” structure, and the current system configuration ID. The details of this module are described next. 5.2.1 Mission Design Module The purpose of the Mission module is to load the trajectory file (as a SPICE kernel, or SPK) into memory, to obtain a list of mission events based on that trajectory, and to then call the System design module to execute the spacecraft design process. The event module first finds the set of eclipse periods along the spacecraft trajectory, using a JPL SPICE function. The maximum periods in eclipse and sunlight are then obtained. Next, the list of impulsive Delta-Vs that the spacecraft must provide (i.e. after the translunar injection burn in LEO) is obtained. To obtain this, the GMAT simulation data file is first searched for abrupt changes in the simulated spacecraft mass, which indicates a propulsive Delta-V maneuver was executed. The rough time of this mass change is then used as an input in searching the trajectory SPK file for the exact time of the impulsive Delta-V maneuver. The Delta-V vector (in Earth mean equator of J2000 frame, or EMEJ2000) and magnitude can then be obtained. For the GMAT trajectory designed in this research, there is only one post-TLI Delta-V maneuver: at lunar orbit insertion (LOI). The TLI 142 Delta-V burn is assumed to be provided by the launch vehicle upper stage. The post-TLI Delta-V maneuver(s) are then assigned an event name based on an annotation function that analyzes the pre-impulse and post-impulse spacecraft state to obtain the type of final state orbit and an event type (a Delta-V event). Mission events are then defined for the given trajectory. First, the post-TLI Delta-V maneuver time(s) are used to split the trajectory into segments. For a single post-TLI Delta-V maneuver, the result would be 2 segments. Then, for simplicity, communication events are then added in the middle of each segment and assigned an event name using the previously mentioned annotation function. Next, non-propulsive coasting (or cruise) events are added in between trajectory start and the first “Comm” event, and between Delta-V-to-Comm segments. As an aside, due to a design idiosyncrasy, note that the Telecom design module (Section 5.3.1) checks the link at each mission event, not just those designated “Comm” events. The events are then sorted in time order, and each event (except for Descent & Landing, and Surface Operations events) are assigned a set of vectors to define the initial and final attitude at each event. That is, the spacecraft attitude is defined with a primary body vector being aligned with a primary target vector, and a secondary body vector pointing as close as possible to a secondary target vector. These attitude vectors are used by the ADCS design module to determine slew requirements for the ADCS actuators. Since the trajectory is constant for all system configurations, this results in the following list of 6 mission events: Event # Event Name Event Type Event Phase Event Epoch (UTC) 1 Earth coasting post- orbit transfer (after TLI) Coasting Cruise 2018 JUL 13 22:13:05.84 143 Event # Event Name Event Type Event Phase Event Epoch (UTC) 2 Earth communication post-orbit transfer In-Space Communication Cruise 2018 JUL 14 17:26:11.68 3 Lunar orbit insertion burn targeting (h a x h p) 99.9 x 99.8 km alt orbit Delta-V Lunar Orbit 2018 JUL 16 05:54:30.85 4 Descent & Landing Delta-V Entry, Descent & Landing 2018 JUL 16 07:52:22.361 5 Surface Science Surface Science Surface Operations 2018 JUL 16 07:52:22.361 6 Surface Communication Surface Communication Surface Operations 2018 JUL 16 07:52:22.361 Once the mission events are defined and added to the “traj” data structure, the System design module is called with the following key inputs: trajectory data structure, ground network data structure, and system configuration data structure. 5.2.2 System Design Module The overall architecture of the System design module is depicted in Figure 5-8. The System design module consists of two main for-loops: the inner loop that executes the full spacecraft design module for each spacecraft element in the system (in this case 2 elements, a rover and lander), and the outer loop that controls the number of “system iterations”. A system iteration consists of one complete call to the full spacecraft design module, described in Section 5.2.3, and which designs all of the spacecraft subsystems and the Descent & Landing phase. The system iteration process continues until either total system mass convergence (to within a hard- coded tolerance of 3 kg) or the hard-coded maximum number of iterations (15) is reached. Within the inner loop, a check is done on whether the Descent & Landing design became “infeasible”. If so, a warming message is printed and the code exits the System design module (to proceed onto the design of the next system configuration in the list of configurations to run). 144 The iteration history of each subsystem’s total mass is also stored in arrays for display in a special GUI that plots the total rover and lander mass, the rover and lander subsystem masses, and the run time per iteration. Figure 5-8. Algorithm for System Design Module Lastly, assuming that the code did not exit due to an infeasible Descent & Landing design (i.e. that a required de-orbit altitude h0 was found in the Descent & Landing design module), the System module proceeds to compute the additional Delta-V required to get from the circular lunar capture orbit (100 km in this research) into a circular low lunar orbit (LLO) with an altitude of h 0. This requires two impulsive Delta-Vs based on the standard Hohmann transfer: one to transfer from the circular lunar capture orbit to periselene with an altitude of h 0, and a Get the relay node for current system element (i.e. lander is rover’s relay node) Update mass properties for payload (i.e. rover is lander’s payload) Call the Spacecraft design module for each system element (i.e. rover or lander) Check for feasible Descent & Landing trajectory design. If infeasible, exit System module Compute additional Delta-V to transfer from initial circular lunar capture orbit to circular low lunar orbit at altitude h0 Update MASS GUI with plots of subsystem masses per system element Terminate system iterations upon:  total system mass convergence, OR  reaching max # iterations allowed, OR  if infeasible Descent & Landing design Inputs Outputs 145 second to circularize at the altitude h 0. The Delta-V calculations are done using standard orbital mechanics methods. The two additional Delta-V events are then added to the list of mission events in the “traj” data structure. This is done so that the total Delta-V for all post-TLI maneuvers can be used to estimate the total propellant mass required for orbital maneuvering. Since the Delta-V vectors in EMEJ2000 are also required by other parts of the MASS tool, these must also be computed. For the transfer Delta-V maneuver, the Delta-V direction is the direction of the spacecraft’s velocity vector with respect to the Moon, which can be found from the trajectory SPK file. For the circularization Delta-V maneuver, the Delta-V direction can be found via the universal variables solution to Kepler’s problem, as described in Section 4.3 of reference (51). Using this method, the transfer orbit’s initial position and velocity vectors (in EMEJ2000) are propagated over the predicted time of flight to obtain the final position and velocity vectors at transfer orbit periapse. The circularization Delta-V direction can then be found by obtaining the unit vector of the final periapse velocity vector. 5.2.3 Spacecraft Design Module The spacecraft design module is a MATLAB function in which the various subsystems design modules are called in a sequential order to size the various subsystems for a given spacecraft element. The operation of the spacecraft design module is depicted in Figure 5-9 below. The specific subsystem order shown in the figure was an initial educated guess based on the judgement of the researcher. The sizing functions included are (in the order shown in Figure 5-9): Telecommunications, CDS (Command & Data subsystem), ADCS (Attitude Determination & 146 Control Subsystem), Propulsion, Thermal, Structures, Power, Descent & Landing design (to size descent & landing propellant mass). In the above list there are 7 subsystem sizing modules and one Descent & Landing design module. The landing simulation module uses inputs from all other subsystems, and attempts to model the descent and landing portion of the lander’s trajectory—sizing the propellant mass required to safely execute a soft, propulsive landing on the lunar surface. The Descent & Landing design module outputs an updated Trajectory parameters data structure. Once all subsystem modules and the landing simulation module are called, the total subsystem masses are obtained and added together to get the total spacecraft element launch mass (including any necessary propellant). Finally, the subsystem data structures for the spacecraft element are updated and set as the latest designed subsystem data structures. In other words, all the subsystem design results are captured for the spacecraft element being sized. 147 Figure 5-9. Algorithm for Spacecraft Design Module The inputs required for the spacecraft design module, indicated by the “Inputs” box in Figure 5-9 above, are: current system-level iteration count, ground network parameters (data structure), trajectory parameters (data structure), subsystem databases (data structures), spacecraft element parameters (data structure), and relay element parameters (data structure). The outputs of the spacecraft design module are: updated trajectory parameters (data structure), updated spacecraft element parameters with subsystem parameters updated (data structure), and updated relay element parameters (data structure). In Figure 5-9 above, one of the first steps involved is to obtain the subsystem data structures from the given spacecraft element data structure: Payload, Telecommunications, CDS, ADCS, Propulsion, Thermal, Structures, and Power. These data structures are inputs that are common to all the subsystem design modules. The individual subsystem design modules are Inputs Telecom CDS ADCS Propulsion Thermal Structures Power Landing Simulation Module Get subsystem masses and total mass Update spacecraft element’s subsystem data structures Get the spacecraft element’s subsystem data structures Outputs 148 generally modeled as indicated in Figure 5-10 below. Each subsystem design module outputs an updated set of subsystem data structure parameters. The spacecraft design module is architected such that the outputs of each call to a specific subsystem design module are passed onto the call of the next subsystem design module. So, in the data flow represented in Figure 5-9 above, the Telecom module takes inputs from several subsystems, including Telecom, to provide a telecommunications hardware design for the given spacecraft element, updating the Telecom parameter data structure in the process. The design parameters for each subsystem, including the recently updated Telecom parameters, are next passed onto the CDS design module. The CDS design module computes CDS telemetry data rates and sizes the CDS hardware in terms of mass, power, and volume, outputting updated CDS parameters. Next the ADCS design module is called, passing in all required subsystem design parameters, including the updated Telecom and CDS parameters. The ADCS module selects and sizes ADCS hardware (sensors and control actuators) based on inputs from all subsystems, as appropriate, and outputs an updated set of ADCS parameters. Next the Propulsion design module is called, passing in all required subsystem design parameters, including the previously designed subsystems (Telecom, CDS, and ADCS) in order to size the primary propulsion system propellant and tankage, as well as position the engines, outputting an updated set of Propulsion parameters. Next the Thermal, Structures, and Power subsystems are called, each with an increasing number of recently design subsystems, and each outputting an updated set of its own subsystem parameters. Thus, within a single system-level design iteration for a given spacecraft element, the spacecraft is designed incrementally, in a particular order of subsystem design module calls. 149 Figure 5-10. Modeling of Subsystem Design Module Inputs and Outputs Note that a given spacecraft element may not include all the common spacecraft subsystems shown above in Figure 5-10. For example, a typical rover will not have a propulsion subsystem. To account for the absence or presence of a given spacecraft subsystem, TRUE/FALSE flags for each traditional spacecraft subsystem are obtained from the spacecraft element’s subsystem data structures before any of the subsystem design modules are called. As an example, for the rover, the “has propulsion subsystem” flag will be set to FALSE and the call System iter Spacecraft element type Trajectory parameters Database parameters Ground parameters Payload parameters ADCS parameters Propulsion parameters Telecom parameters CDS parameters Thermal parameters Power parameters Structures parameters Subsystem X Design Module Subsystem X parameters Has subsystem X? Skip Relay element Y N 150 to the Propulsion subsystem design module will be skipped. This avoids errors in the execution of the MATLAB program. 5.3 SUBSYSTEM DESIGN MODULES Descriptions of the algorithms within each subsystem design module, sequentially called in the Spacecraft design module of Section 5.2.3, are described in this section. 5.3.1 Telecommunications Design Module The telecommunications design module is built to size and select telecommunications hardware for the spacecraft element being designed. The architecture of this tool is depicted in Figure 5-11 below. This design tool accepts the following MATLAB inputs: spacecraft element type, ground parameters (data structure), database parameters (data structure), trajectory parameters (data structure), payload parameters (data structure), Individual subsystem parameters (a separate data structure for each subsystem), relay element parameters (spacecraft element that serves as a relay). The tool returns the following MATLAB outputs: updated Telecom parameters (data structure), updated relay element parameters (spacecraft element that serves as a relay). This design tool first initializes several internal variables related to mass and power, antenna dimensions, and hardware selection flags. It then proceeds to perform link budget calculations based on whether the telecom architecture for the specified spacecraft element is “Direct-to-Earth” or “Relay”. As part of the link budget calculations, the tool also determines the antenna dimensions (for both primary and backup antennas), RF power required, and electronics required (transponder or transceiver, and RF amplifier required—either TWTA or 151 SSPA). After the telecom hardware is sized and selected from a database, the cable mass is determined and added to the overall mass. Lastly, all relevant design outputs are passed as MATLAB outputs. Figure 5-11. Telecom Design Module Top-level Architecture The details of each telecom architecture MATLAB design function (Direct-to-Earth or Relay) are described next. 5.3.1.1 Direct-to-Earth Telecom Architecture If the telecommunications architecture of the spacecraft element being designed is designated as “DTE”, then the “Direct-to-Earth” architecture design function is called. The algorithm for the DTE design function is depicted in Figure 5-12 below. In this figure, the steps involved in computing the DTE links are listed under the “Compute DTE links” label. First, the DTE links are computed for the primary antenna onboard the spacecraft element. This is done by defining the uplink and downlink parameters (such as antenna type, pointing error, losses, required receiver signal-to-noise ratio, etc.), and then computing the uplink and downlink Inputs Outputs Direct-to- Earth Arch. Telecom Arch. Type Relay Arch. DTE Arch Design Tool Relay Arch Design Tool DTE Arch Design Tool Has science instr? Assign output s 152 margins for a range of receiver antenna (i.e. on the spacecraft) dimensions for each communication (i.e. comm.) event. This process returns an array of uplink margins, organized as shown in Figure 5-13 below: each array row is a unique antenna dimension, and each array column is a comm. event. The minimum-size antenna case (for reduced mass) that has uplink margins > 3 dB for all comm. events is selected as the desired antenna size. The downlink computation process also returns an array of downlink margins, organized as shown in Figure 5-14 below: again rows represent unique antenna dimensions, columns are comm. events, and the 3 rd dimension represents unique RF transmission power values. Next, for the selected receiver antenna dimension (a specific row in the downlink margins array), the minimum downlink RF power case that has downlink margins > 3 dB for all comm. events is selected as the transmission power level. 153 Figure 5-12. Algorithm for designing DTE architecture This above process is repeated for the backup antenna. After the two antennas’ dimensions and RF transmit power are determined, the required telecommunications electronics hardware is selected as either a transponder (combined transmitter and receiver), or a transceiver (for UHF-links only). An example of the available transponders in the database is shown below in Table 5-17. Table 5-17. Transponder Database Manu- facturer Model Receive Frequency Range (GHz) Transmit Frequency Range (GHz) Mass (kg) Transmitter Power Consumption Receiver Power Consumption L3 Comm. CSX-610 2.025-2.12 2.2-2.3 2.631 35 5.5 L3 Comm. MSX-765 2-2.11 1-2 2.722 35 8 Inputs Outputs  Get uplink and downlink parameters  Compute uplink/downlink margin for each antenna dimension  For a given antenna dimension, compute uplink and downlink margin for each communication event  Get array of all uplink margin cases (for all antenna dimensions and comm. events)  For each spacecraft uplink receiver antenna dimension case, find cases with ALL comm. events with uplink margin > 3 dB.  Select good uplink case with smallest antenna dimension.  Get array of downlink margins (as array of comm. events and RF output power)  For selected spacecraft antenna receiver dimension, find RF power cases with ALL comm. events having downlink margin > 3dB.  Select good downlink case with smallest RF output power. Compute DTE Links: Primary Antenna Compute DTE Links: Backup Antenna Select minimum mass applicable Transponder or Transceiver electronics Compute primary antenna mass Compute backup antenna mass Compute RF amplifier mass (TWTA or SSPA) 154 Manu- facturer Model Receive Frequency Range (GHz) Transmit Frequency Range (GHz) Mass (kg) Transmitter Power Consumption Receiver Power Consumption General Dynamics X-band Small Deep Space Transponder 7.145- 7.235 8.4-8.5 3.175 15.8 12.5 Then, given the antenna dimensions, the antenna masses are computed (for both primary and backup antennas) by calculating the antenna transmission area and multiplying by a sizing factor k (kg/m 2 ). The sizing factor k is read in from the telecommunications database for the specific type of antenna (parabolic, helix, or horn). The antenna database is shown below in Table 5-18 (30). Table 5-18. Antenna Database Antenna Antenna Type Mass (kg) Diameter (m) Length (m) Area (m 2 ) k (kg/m 2 ) Quad Helix Helix 1.8 0.4 0.4 0.16 11.3 Parabola (Fixed) Parabola 3.9 0.7 0 0.49 8.0 Parabola w/ Feed Array Parabola 29.4 2.44 0 5.954 4.9 Parabola w/ Feed Array Parabola 15.2 1.56 0 2.434 6.2 Parabola w/ Feed Array Parabola 47.1 1.7 0 2.89 16.3 Parabola (steerable) Parabola 5.8 1.1 0 1.21 4.8 Horn Horn 3.1 0.3 0.65 0.195 15.9 Finally, the required RF (radio frequency) amplifier mass and DC (direct current) power are determined. The RF amplifiers supported by this tool are either a TWTA (traveling wave-tube amplifier), or SSPA (solid state power assembly). The rule followed in selecting a TWTA vs. an SSPA is that the TWTA is selected at higher power efficiencies (34). That is, if the RF power is greater than or equal to an RF power cut-off value, a suitable TWTA is selected. Otherwise, an 155 SSPA is selected. Either way, the RF amplifier mass, power, and efficiency are interpolated from a telecom database of TWTA or SSPA mass, power, and efficiency as a function of required RF transmission power (as shown below in Table 5-19 (30)). An RF amplifier is selected only when a transponder has been selected. If a transceiver was selected (e.g. for UHF relay), no RF amplifier is selected. Table 5-19. RF Amplifier Mass/Power/Efficiency Database RF Power Output (W) TWTA Mass (kg) SSPA Mass (kg) TWTA DC Power (W) SSPA DC Power (W) TWTA Efficiency (%) SSPA Efficiency (%) 0.2 1.9 1.2 10 10 2.0 2.0 1 2 1.2 10 15 10.0 6.7 5 2.5 1.2 20 20 25.0 25.0 10 3 1.3 30 40 33.3 25.0 20 4 1.35 40 70 50.0 28.6 50 6 2 80 100 62.5 50.0 80 8 3 105 110 76.2 72.7 Figure 5-13. Array of Uplink Margins Rows = Antenna dimension case (diam and length) Columns = Communication event 156 Figure 5-14. Array of Downlink Margins In Figure 5-12, the uplink/downlink margin calculation requires some explanation. For uplink, the radio signal frequency is determined by the selected frequency band of the ground station (a user input) and whether the spacecraft is “near Earth” or in “deep space”. For NASA’s Deep Space Network of antennas, near Earth is considered anywhere within 2 million km of the Earth and deep space is outside of that (33). The actual uplink and downlink frequencies are the middle of the user-selected DSN frequency band (X-band, S-band, or Ka-band, as available per each DSN antenna’s capability). The uplink RF transmission power from the ground station is selected to be the maximum uplink power for the selected frequency band. The uplink data rate is a user-defined value. Given all the uplink parameters, a generic link budget function is called to return uplink design outputs for each comm. event. For downlink, the transmission data rate requirement is read in from the CDS parameters data structure for the particular comm. event in question. The downlink for a Rows = Antenna dimension case (diam and length) Columns = Communication event 3 rd Dim: Downlink RF Power 157 particular spacecraft receiver antenna can be accomplished with a range of RF transmit power levels. Thus, the generic link budget function is called to return downlink design outputs for each comm. event and each RF transmit power level. That is, for a given spacecraft antenna dimension and a particular comm. event, a range of RF transmit power levels are evaluated. 5.3.1.2 Relay Telecom Architecture If the telecommunications architecture of the spacecraft element being designed is designated as “Relay”, then either the “Relay” or “DTE” architecture design function is called, as depicted in Figure 5-11. The reason either one can be called is that there are two parts to the relay architecture: one spacecraft collects valuable data (at the “science node”) that is relayed to another spacecraft (the “relay node”) that in turn transmits the data directly to Earth. The relay architecture design function is called only if the given spacecraft element has science instruments whose data must be relayed to another spacecraft—that is, the spacecraft is considered a “science node”. In this case, the telecommunications hardware for both the science node and relay node are sized and selected (for the forward and return links). Otherwise, the spacecraft is considered a “relay node” and the Direct-to-Earth architecture design function described in the previous section is called. For example, a rover equipped with science instruments with a “Relay” architecture designation should have the relay architecture design tool called to select telecommunications hardware to transmit data to a lander “relay node”. When it is the lander’s turn to have its telecommunications system designed, its “Relay” architecture designation will result in the “DTE” architecture design tool being called so that the relevant hardware for DTE is sized and selected. The algorithm for the relay architecture design tool is depicted in Figure 5-15 below. 158 For the relay architecture design tool, the first step is to call the “Compute relay links” function—that is, to compute the applicable forward and return link margins. Using the resulting link margins, the antenna dimensions and RF transmit power for both the science and relay nodes are determined. The first step involved in computing the relay links is to obtain the required forward link and return link parameters (such as antenna type, pointing error, losses, required receiver signal-to-noise ratio, etc.). Next, several for loops are employed to compute the link margins. The first for-loop is the forward link transmit antenna diameter for the assumed helix antenna. The second nested for-loop is the forward link transmit antenna length for the assumed helix antenna. These first two for-loops define unique relay node helix antenna dimension combination cases. The third nested for-loop is the forward link transmit RF power level. The fourth for-loop is for the various comm. events. Within this fourth for-loop, the function checks whether the comm. event is designated as requiring relay communications. For the selected lunar science rover mission in this research, the only comm. event assumed to require relay communications is during surface science and surface communications. For simplicity and to reduce the number of link parameter combinations being evaluated, the forward link receiver antenna diameter and length (i.e. at the science node) is set to the same diameter and length as the relay node transmit antenna. Then the link budget tool is called with the forward link parameters. The fifth and final nested for-loop is for the return link RF power level. At this point, the link budget tool is called with the return link parameters. After the forward and return link margins are computed, they are extracted into a 1D array of forward and return link margins. The forward and return link margins are added to form a combined 1D array. The indices of the forward link and return link margins >= 3 dB are obtained. These indices are used to find the selected forward and return links with minimum 159 link margin. The selected forward and return links are then used to identify the antenna dimensions and transmit RF power level. Next, the required transponder or transceiver hardware is selected. If the relay frequency is in the UHF band, the minimum mass applicable transceiver is selected from a database. Given the selected science node and relay node antenna dimensions, the antenna mass on the science node spacecraft and antenna mass on the relay node spacecraft are computed. This is done by calculating the antenna transmission area and multiplying by a sizing factor k (kg/m 2 ). The sizing factor k is read in from the telecommunications database for the specific type of antenna (parabolic, helix, or horn). Figure 5-15. Algorithm for designing the Relay architecture Inputs Outputs  Get forward link and return link parameters  For each forward link transmit (relay node) antenna dimension: o For each forward link (relay node) transmit RF power level:  For each comm. event:  Compute forward link margin  Compute return link margin for each return link transmit RF power level  Get array of all forward link margin cases (for all antenna dimensions, transmit RF power levels, and comm. events)  Get array of all return link margin cases (for all antenna dimensions, comm. events, and transmit RF power levels)  Find forward and return links cases link margin > 3 dB each.  Select relay node antenna dimension and RF transmit power with minimum link margin.  Select science node antenna dimension and RF transmit power with minimum link margin. Compute Relay Links: For Science Node Select minimum mass applicable Transponder or Transceiver electronics Compute science node antenna mass Compute relay node antenna mass Compute RF amplifier mass (TWTA or SSPA) 160 Finally, the required science node relay RF amplifier mass and DC power are determined. This is done by linearly interpolating from telecom database curves in the same manner as done for the DTE architecture. That is, the supported amplifiers are either the TWTA or SSPA. The TWTA is chosen if the required RF power is greater than or equal to an RF power cut-off value, otherwise the SSPA is selected. Assuming that the relay architecture employs the UHF band and a transceiver is selected, no RF amplifier is required. 5.3.2 CDS Design Module The overall function of the CDS design module is to compute the CDS telemetry data rates, determine the CDS complexity based on desired CDS functions in order to select CDS hardware, compute CDS hardware heat generation, and size the CDS software. The architecture of the CDS design module is shown in Figure 5-16 below. 161 Figure 5-16. CDS Design Module Top-Level Architecture The inputs required for the CDS design module are: system iteration count, spacecraft element type, trajectory parameters (data structure), database parameters (data structure), payload parameters (data structure), and individual subsystem parameters (a separate data structure for each subsystem). The outputs of the CDS design module are just one: the updated CDS parameters (data structure). 5.3.2.1 Telemetry Data Rates The first step in the CDS design module is to determine CDS data rates for telemetry (from all subsystems) for each comm. event. The CDS telemetry for a given comm. event consists of two parts: housekeeping telemetry (from all subsystems) and payload telemetry. The housekeeping telemetry rates for all engineering subsystems (telecommunications, CDS, ADCS, Propulsion, Thermal, Structures, and Power) are all computed by summing the contributions of telemetry from individual components that have been selected. For example, if an IMU is Input s Outputs Compute CDS telemetry data rates for each comm. event Determine CDS functions & overall CDS complexity Size CDS hardware mass, power, and volume Compute CDS dissipated heat Get existence factors for CDS software functions Estimate CDS software code memory, data storage memory, and throughput 162 present in the ADCS design, the gyro rate telemetry data rate is estimated as the number of separate telemetry signals times the bits per signal measured times the sampling frequency in Hz, as indicated in the equation below. 𝑅 = 𝑁𝑏 𝑓 𝑠 Equation 5-1 where N = # of individual signals, b = the # of bits per sample, and f s = the sampling frequency. So since there are 3 axes of gyro rates to measure, the telemetry rate (in bits per second) for one signal is multiplied by 3. In a similar manner, the IMU accelerometer position and velocity measurement telemetry rates are also estimated. The combined telemetry data rate is then compressed using a compression factor as compressed rate = factor*(full rate). If the spacecraft element is a science node (that is, having science instruments), and the specific comm. event is designated as a relay comm. event, the return link data rate is set as the compressed CDS telemetry rate. 5.3.2.2 CDS Hardware Selection The next step is to determine the CDS complexity level in order to size the CDS hardware in terms of mass, power, and volume. This procedure is outlined in the Chapter 11.3 of Space Mission Analysis & Design (SMAD), reference (30). The CDS complexity level can be divided into three possible levels: simple, typical, and complex. Determining the complexity level involves considering the CDS’s required capability and functions. CDS functional requirements to consider are listed below. Each of these items contributes to the CDS’s complexity score. A single point is added for each complexity level based on the absence or presence of a given CDS requirement, or on the value a particular requirement takes compared to thresholds. 163  Processing commands o Command rate (commands per second): Simple if less than 50 cmds/sec, typical if between 50 and 75, and complex if greater than or equal to 75. o Command computer interface (assumed true if the spacecraft element has a science payload or ADCS). No computer interface is considered part of a simple system, whereas a computer interface is considered typical or complex. o Stored commands (assumed true if the spacecraft element has a telecommunications subsystem and commands must execute when the spacecraft is out of contact with Earth). If there are no stored commands required, the CDS is considered simple. If a computer interface is required, a point is added to the complex category. If not, a point is added to the typical category. o # of command channels: Simple point added if between 0 and 200, typical if between 200 and 500, and complex if greater than or equal to 500.  Processing of Telemetry Data o Housekeeping telemetry data rate: Simple point added if between 0 and 4,000 bps, typical if between 4,000 and 64,000 bps, and complex if greater than or equal to 64,000 bps. o Payload telemetry data rate: Simple point if there is no payload telemetry data rate, typical if between 0 and 200 kbps, and complex if greater than 200 kbps. o Telemetry computer interface: If there is a telecom system required, then a telemetry computer interface is assumed and it gets a complex point added. 164 Otherwise, no telemetry computer interface is assumed and simple and typical points are added. o # of telemetry channels: Simple point added if between 0 and 200 channels, typical if between 200 and 500, and complex if greater than or equal to 500.  General computer functions o Mission time clock: If there is an ADCS or command computer interface required, a mission clock is assumed. In that case, a point is added for typical and complex categories. Otherwise, for no mission clock, a simple point is added. o Computer watchdog timer: This is a timer onboard the spacecraft computer to check that the computer hardware and software are functioning correctly. A watchdog timer is assumed present if there is a command computer interface. If so, then a point gets added for typical and complex categories. Otherwise, no watchdog timer is present and a simple point gets added. o ACS functions: If an attitude control subsystem is present (part of the ADCS), then a complex point gets added. Otherwise, a point gets added for simple and typical categories.  Computer bus constraints: The computer bus architecture can be described as one of three classes: o Single unit: provides one unit for command processing, one unit for telemetry processing, or a single unit that integrates both. A single unit gets a simple score. 165 o Multiple unit: Since the single unit solution can require a large wire harness to route every interface signal to a physical location on the unit, the multiple unit solution allows for a computing interface located remotely from the central processing unit. Multiple unit gets a typical score. o Integrated: This type of unit combines command, telemetry, flight processing and attitude control in one overall system. This system typically requires increased software programming and costs. An integrated unit gets a complex score.  Radiation environment: If the radiation environment is between 0 and 2 krad, a simple point is added. If between 2 and 50 krad, a typical point is added. If greater than or equal to 50 krad, a complex point is added. Once complexity level points are summed for all complexity level categories, the overall CDS complexity is marked as simple, typical, or complex. The CDS mass, power, and volume are then estimated according to Table 5-20 from (30). Note that an overall CDS system type, designated as command only, telemetry only, or combined, also determines the CDS mass, power, and volume. Table 5-20. Estimates of CDS Hardware Mass, Power, and Volume based on complexity level Parameter CDS System Type Simple Typical Complex Volume (cm3) Command only 3,000 4,000 6,000 Telemetry only 3,000 6,000 10,000 Combined system 6,000 9,000 15,000 Mass (kg) Command only 2.5 3 5 Telemetry only 2.5 4 7.5 Combined system 5.5 6.5 10.5 Power (W) Command only 2 2 2 Telemetry only 10 16 20 Combined system 12 18 25 166 Next, the heat dissipated by the CDS electronics at the low and high operating temperature limits is computed. This requires estimating the overall size of the CDS electronics. For simplicity, the estimated CDS volume from Table 5-20 above is assumed to be a cube. A generic waste heat function is used to estimate the dissipation area of the cube (assumed to be all sides) and, given the emissivity of the assumed cube, to compute the low and high heat dissipation according to the Stefan-Boltzmann equation below, where Q is heat dissipation, 𝜎 is the Stefan-Boltzmann constant, 𝜖 is surface emissitivity, T is temperature in Kelvin, and A is surface area. 𝑄 = 𝜎𝜖 𝑇 4 𝐴 Equation 5-2 5.3.2.3 CDS Software Size Estimation Finally, the CDS software size, data storage size, and processing throughput are estimated. Note that in this research, the estimates of CDS software, data storage, and throughput are not used in estimating the mass, power, or volume of the CDS hardware, as these are based on a complexity score. To estimate CDS software characteristics and computing resources, several existence factors (or flags, 1 indicating existence, and 0 not) are defined according to the required CDS functions. This procedure is based off of that described in section 16.3, pg. 673, of SMAD (30). The modeling of the CDS software function existence factors is described in the following bullets.  Communications o Command processing and telemetry processing existence factors are set to 1 if a telecom system is required 167  ADCS: Existence factors are set for the following groups of ADCS processing functions. If an ADCS is not required, all existence factors are set to 0. o Attitude sensor processing  Individual factors are set to 1 for the existence of a rate gyro, sun sensor, Earth sensor, magnetometer, and star tracker o Attitude determination  Individual factors are set to 1 for the presence of onboard kinematic integration, attitude error determination, ephemeris propagation, complex ephemeris propagation, spacecraft orbit propagation, and Kalman filter estimation o Attitude control  Individual factors are set to 1 for the presence of attitude control methods such as precession control, magnetic control, thruster control, reaction wheel control, and control moment gyro control  Autonomy o Simple autonomy o Complex autonomy  Fault Detection o Fault Monitors: If fault monitors are required, fault monitoring is given a factor of 1. o Fault Correction: If fault correction is required, it is given a factor of 1.  Other Functions 168 o Power management: If there is a power subsystem, power management is given a factor of 1. o Thermal control: If there is a thermal subsystem, thermal control is given a factor of 1. The software code size, data memory size, and processing throughput for each of the functions described in the bullets above are then estimated using a common CDS processing function. This CDS processing function takes the existence factor for a particular software function, the software function execution frequency, and type of software function, and returns the software function code size, required data memory size, and required processing throughput in thousands of instructions per second (kips). The code size S (in kwords) is estimated as: 𝑆 = 𝑓 𝑒𝑥𝑖𝑠𝑡𝑒𝑛𝑐𝑒 𝑆 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑓 𝑒𝑥𝑒𝑐 _𝑟𝑎𝑡𝑖𝑜 Equation 5-3 using the existence factor (a 0 or a 1), the default code size S default for a generic spacecraft, and the execution ratio defined as the ratio between the actual function execution frequency divided by the default execution frequency. The data memory size D (in kwords) is estimated as: 𝐷 = 𝑓 𝑒𝑥𝑖𝑠𝑡𝑒𝑛𝑐𝑒 𝐷 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑓 𝑒𝑥𝑒𝑐 _𝑟𝑎𝑡𝑖𝑜 Equation 5-4 using the existence factor (a 0 or a 1), the default data size D default for a generic spacecraft, and the execution ratio just described. The default code size, data storage size, throughput, and execution frequency are stored in the CDS database MATLAB structure for the different software functions. The data in this database is obtained from Table 16-13, pg. 665 of (30). 169 The processing throughput (in kips) is estimated as: 𝑇 = 𝑓 𝑒𝑥𝑖𝑠𝑡𝑒𝑛𝑐𝑒 𝑇 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑓 𝑒𝑥𝑒𝑐 _𝑟𝑎𝑡𝑖𝑜 Equation 5-5 using the existence factor (a 0 or a 1), the default throughput T default for a generic spacecraft, and an execution ratio. The basic operating system (OS) software functions must also be estimated. To do this, the number of tasks per second for communications (commanding and telemetry), attitude sensing, attitude determination & control, autonomy, fault protection, and other functions must be estimated by adding the component function execution frequencies for each category. Then the tasks per second for each category are added together. This total number of tasks per second, n, is used to estimate throughput requirements for a couple OS sub-functions. Typical OS functions are summarized below (30):  Executive: Throughput (in kips) is estimated as 0.3*n  Run-time kernel  Input/Output (I/O) device handlers: Throughput is estimated as 0.05*m, where m is the number of data words handled per second.  Built-in test & diagnostics  Math utilities The number of data words handle per second, m, is estimated by summing the contributions from the sensors (rate gyro, sun sensors, Earth sensors, magnetometers, star trackers), telemetry stream, command stream. This total is used to compute the throughput for the I/O device handlers. The OS total code size, data size, and throughput are also summed from the contributors. 170 The total software application code size, data size, and throughput requirements are then computed from the individual software component estimates computed above (communications, attitude sensing, attitude determination & control, autonomy, fault detection, and other functions). The total code size (in kwords), data size (in kwords), and throughput for both the applications + OS is then summed (without margin). Margin for uncertainty is computed as the total application code size, data size, and throughput + the non-COTS code size, data size, and throughput. The non-COTS contributions are themselves estimated as the OS contribution minus the run-time kernel contribution. Margin for a spare copy of the application and OS is computed as the total code size, data size, and throughput plus the uncertainty margin. The next step is to convert the total software code size and data size from kwords to units of bytes. This is done by assuming there are 4 bytes per word (32-bits) and 1024 words per kword. Thus the total software size in bytes is the total size in kwords times words per kword times bytes per word. The basic outputs of all the above CDS design module computations are then captured in the CDS data structure, e.g. items such as total mass, volume, length, width, height, heat dissipation area and low/high rates, power, and software size in bytes. 5.3.3 ADCS Design Module The purpose of the ADCS design module is to select attitude sensors and control actuators needed to execute the various slews required for the mission, and to control the spacecraft attitude. The mass, power, and size of the sensors and actuators are obtained from 171 an ADCS database of components. The architecture of the ADCS design module is depicted in Figure 5-17 below. Figure 5-17. ADCS Design Module Top-level Architecture For this research project, in order to design the ADCS under a given set of mission and subsystem requirements, the following general design process was used (30): 1. Control Modes: Define the attitude control modes. An attitude control mode is characterized by its own set of requirements on pointing accuracy (both knowledge and control), pointing stability, jitter, and slewing that the spacecraft must meet in order to Inputs Outputs Get list of ADCS events For each ADCS event: 1. Get pointing knowledge & control accuracy 2. Define applicable control methods 3. Select reference and inertial sensors 1. Identify unique control methods over all events 2. Identify unique ref and inertial sensors 3. Select reference sensors with min knowledge accuracy 4. Select inertial sensor with min angular rate For each ADCS event: 1. Compute init/final attitudes, slew angle, and slew duration 2. For each control method: a. Compute total disturbance torque at final attitude b. If RWA+RCS, find required RWA pyramid vs. tetrahedron slew torques c. If RCS-only, find required slew torque Select actuator with max control authority to meet requirements for all slews 1. If RWA+RCS: a. Select either pyramid or tetrahedron config b. Select RW with smallest mass that meets both torque and momentum requirements c. Size RCS thrusters for Delta- V and Descent & Landing attitude control d. Estimate RCS propellant mass e. Size RCS tanks 2. If RCS only: a. Find max slew torque requirement and compare with max external torque b. Find min disturbance torque for limit cycling calcs c. Size RCS thrusters for slews, Delta-V and Descent & Landing attitude control d. Estimate RCS propellant mass e. Size RCS tanks 1. Select smallest mass control system 2. Calculate heat dissipation for all sensors and actuators 172 provide a particular function (e.g. communications, power, propulsive maneuvers, etc.). Each control mode can have multiple instances, or events, requiring attitude control. Find the minimum pointing accuracy from all control modes for all events. Determine the pointing knowledge accuracy and pointing control accuracy requirements from the minimum pointing accuracy requirement. 2. Control Method: Use the minimum pointing control accuracy requirement and any attitude/pointing constraint to determine the applicable attitude control methods (one or more may be applicable). 3. Disturbance Environment: Quantify the disturbance torques (both internal and external) expected during each event of each control mode. These disturbance torques will be used in sizing the actuators for each control mode event. 4. Select and Size ADCS hardware: ADCS sensors should be selected to meet the smallest required pointing knowledge accuracy. a. Given the pointing knowledge accuracy, select the most suitable (lowest mass and power) attitude determination sensors from a database. b. Size the attitude actuators to meet the disturbance torques in each control mode event, selecting the most capable actuator set with the largest control torques as the final desired hardware. Finally, select the actuator hardware that meets the required capability from a database. The inputs required for the ADCS design module are: system iteration count, spacecraft element type, trajectory parameters (data structure), database parameters (data structure), payload parameters (data structure), and individual subsystem parameters (a separate data structure for each subsystem). These inputs contain parameters for pointing requirements, 173 primary propulsion subsystem parameters, reaction wheel and RCS thruster parameters, electronics surface emissivity, a database of ADCS sensors and control actuators, payload parameters, and durations for each sub-phase of the Descent & Landing phase of the mission (in the trajectory parameters), and individual subsystem masses. The output is an update to the single data structure for ADCS. This data structure is updated with the results of the ADCS design. This output includes selected ADCS sensor specifications (both inertial and reference sensors), attitude control actuators (for the two supported control methods, RWA + RCS, and RCS-only), the total ADCS mass and masses of attitude sensors and actuators, and total power for all ADCS sensors. 5.3.3.1 ADCS Events The first major step in the ADCS design module is to copy the list of mission events from the Trajectory data structure to a list of events for ADCS. If the spacecraft element is a Lander, Orbiter, or other generic spacecraft, all events are captured except for any Entry, Descent, and Landing (EDL) events and surface operations events. Otherwise, if the spacecraft element is a Rover, the event is copied if it is a surface operations event. Now that the list of ADCS events for the given spacecraft element has been identified, the pointing accuracy magnitude required for each event is obtained. The pointing accuracy is ultimately a user-provided input. The pointing accuracy consists of two major components: knowledge accuracy and control accuracy. The knowledge accuracy is computed as a fraction of the total pointing accuracy, and the control accuracy is computed given the fact that the total pointing accuracy is the root-sum-squared (RSS) of the knowledge accuracy and control accuracy. 174 5.3.3.2 Control Methods Next a list of suitable control methods for each ADCS event are obtained so that the control accuracy can be met. There are several types of control methods that modern spacecraft can employ. Examples of passive attitude control methods include gravity gradient stabilization, magnetic stabilization, and spin-stabilization. Examples of active attitude control methods include zero momentum and bias momentum. To enable the ADCS design tool to automatically select a control method for a given control mode, the pointing control accuracy requirement can be used to determine which group of control methods is applicable. The attitude constraint and # of axes to be controlled can next be used to further select the applicable control methods. For the purposes of this research, the attitude constraint is defined as a particular attitude that is the only one achievable by the given control method. Table 5-21 below illustrates this method of categorizing the control methods (30). Table 5-21. Modern Spacecraft Attitude Control Methods Required Pointing Control Accuracy Attitude Constraint Control Method Usability Condition # Axes controlled > 5 deg Nadir pointing only Gravity gradient If in low orbit 2 (no yaw) Nadir pointing only Gravity gradient w/ pitch momentum bias If in low orbit 3 North/South Pointing Magnetic stabilization If planet has magnetic field 2 (north/south only) None Mass Expulsion (thrusters) n/a 3 1 – 5 deg Inertial Spin stabilization n/a 1 175 Required Pointing Control Accuracy Attitude Constraint Control Method Usability Condition # Axes controlled Inertial/Platform Dual-spin stabilization If articulated platform is required with inertial pointing 1 None Mass Expulsion (thrusters) 3 0.1 – 1 deg Inertial Spin stabilization n/a 1 Inertial/Platform Dual-spin stabilization n/a 1 Inertial Pitch Momentum bias w/ Desaturation Thrusters or Magnetic Torquers n/a 3 None Mass Expulsion (thrusters) n/a 3 None Zero momentum (reaction wheels) n/a 3 < 0.1 deg None Zero momentum (reaction wheels) n/a 3 None/Articulated Zero momentum (reaction wheels) w/ articulated platform If vibration is a concern for the instrument 3 If the pointing target is inertial, only spin-stabilization and zero-momentum control methods are considered applicable. If the pointing target is non-inertial, then gravity gradient, dual-spin stabilization, momentum bias, and zero momentum, and mass expulsion control methods are applicable. For the purposes of this research, the applicable attitude constraint is considered to be “none” so that for pointing control accuracies between 0.1 and 1 degrees (as shown in Table 5-21 above), zero momentum (reaction wheels) and mass expulsion (thrusters) are assumed 176 applicable. For control accuracies greater than or equal to 1 degree, the applicable control method is assumed to be mass expulsion (RCS thrusters). 5.3.3.3 Sensor Selection Sensor selection depends primarily on the required orientation of the spacecraft (pointing specific instruments or spacecraft axes at specific targets) and the required pointing knowledge accuracy. For example, pointing to an inertial target will benefit from reference sensors. Inertial rate sensors can provide measurements for attitude estimation in between reference sensor updates and during periods of occultation of the celestial reference objects. Other system-level requirements on redundancy, fault tolerance, sensor field of view, and sensor data rates can also influence sensor selection (30). For this research project, both reference sensors (to provide inertial attitude measurements) and inertial sensors (to provide measured spacecraft attitude rates) will be used to provide the required 3-axis attitude estimates. The purpose of an attitude sensor is to provide measurements to determine the spacecraft attitude. Sensors can be selected to determine the orientation of a single spacecraft axis or all three spacecraft axes. Generally, knowledge of the orientation of all three spacecraft axes in inertial space is required. Usually a suite of sensors will be used to provide the attitude measurements for attitude estimation. Once single-axis or three-axis attitude determination is identified, the sensors that provide those measurements can be selected. If the spacecraft element being designed is a Cruise Stage, Lander, Orbiter, or generic spacecraft, and the attitude constraint is “none”, both star trackers and sun sensors are assumed required for attitude sensing. Otherwise, if the spacecraft is a Rover, no reference 177 sensors are assumed. For the supported spacecraft, a generic attitude reference sensor function is called to select both the star tracker and sun sensor, given the ADCS database and the knowledge accuracy requirement. For the star tracker, the set of star trackers from the ADCS database with cross boresight accuracy (at beginning of life, BOL) less than or equal to the required knowledge accuracy is obtained. Then of this set, the minimum mass star tracker is identified and selected as a required reference sensor. The star tracker database is shown in Table 5-22. Table 5-22. Star Tracker Database Manufacturer Model Optical Head (OH) Mass (kg) OH Power (W) Electronics Box Mass (kg) Electronics Box Power (W) Attitude Accuracy Cross- boresight (arcsec, 1 σ) Attitude Accuracy Roll about boresight (arcsec, 1 σ) Ball Aerospace CT- 602 5.49 9 0 0 3 10 Ball Aerospace CT- 633 2.49 9 0 0 4 38 Ball Aerospace FSC- 701 1.6 0.85 5.8 16 2.9 29.733 Sodurn SED26 3.7 13.5 0 0 3.67 11 Selex Galileo A-STR 3.55 13.5 0 0 2.75 3.7 Selex Galileo AA- STR 2.6 12.6 0 0 2.75 3.7 Andrews Space PYXIS 0.93 4.4 0 0 10 40 For the sun sensor, the set of sun sensors from the ADCS database with off-axis accuracy less than or equal to the required knowledge accuracy is obtained. Then for the list of applicable sun sensors, each sensor is configured to provide full coverage about all axes. That is, the number of sun sensors required for full coverage, given the available field of view of the 178 particular sun sensor, is determined. In each sun sensor case, the total mass of the sun sensors, including electronics, is computed. Then the minimum total sun sensor assembly mass, including electronics, is identified and set as the selected sun sensor. Table 5-23. Sun Sensor Database Manufacturer Model # Axes Measured Sensor Head Mass (kg) Electronics Box Mass (kg) Sensor Head Power (W) Electronics Box Power (W) FOV w/ baffle (deg) Bradford Engineering Fine & Coarse SS 1 0.365 0 0.2 0 128 SSBV Space & Ground Fine SS 1 0.035 0 0.728 0 140 Adcole Digital SS 2 0.25 1.1 0 0.6 128 Adcole 2-axis Fine SS 2 0.38 1.2 0 1 64 Adcole A2100 Type Fine SS 1 0.36 1.21 0 0.8 100 Next, the inertial sensor (i.e. IMU) is selected, if one is required. If there is a spin rate requirement (such as when a solid rocket motor is included as part of the propulsion subsystem), the angular rate in degrees per second is obtained; otherwise it is assumed to be zero. In any case, the set of IMUs capable of measuring rates greater than the required angular rate are obtained. Then the minimum mass IMU of this set is identified and selected as the required IMU. The IMU database is shown below in Table 5-24. Table 5-24. IMU/IRU Database Manufacturer Model Gyro Type Mass (kg) Power (W) Angular Velocity Range (deg/s) Honeywell Miniature IMU (MIMU) Ring Laser Gyro 4.7 32 375 179 Manufacturer Model Gyro Type Mass (kg) Power (W) Angular Velocity Range (deg/s) Northrop Grumman Scalable Space Inertial Reference Unit (SSIRU) Hemispherical Resonator Gyro 7.1 43 7 Northrop Grumman LN-200S Fiber Optic Gyro 0.748 12 1000 Kearfott Corporation Space Qualified Kearfott Inertial Reference Unit (SKIRU D-II) not given 12.7 26 8 Note that selection of the reference and inertial sensors is done for each ADCS event. Thus, there may be different ADCS sensors selected for each ADCS event. However, only one set of reference and inertial sensors can be selected for the spacecraft element to support all ADCS events. To identify this final set, a list of unique, individual reference sensors and inertial sensors is obtained. For each unique reference sensor, the sensor with minimum knowledge accuracy is selected. For each unique inertial sensor, the sensor with minimum angular rate is selected. 5.3.3.4 Control Actuator Sizing Actuator sizing depends on the type of actuator, which itself relies on the selected control method. Once a control method has been identified, the corresponding actuator hardware can also be identified. As previously mentioned, some control methods don’t require any actuator hardware, e.g. gravity gradient or passive magnetic. Most control methods, however, do require actuators to impart control torque. For this mission, the control methods 180 being considered are mass expulsion (thrusters) and zero momentum (reaction wheels with thrusters for momentum unloading). A set of thrusters or reaction wheels can be sized to meet two functions: 1) maintaining the spacecraft attitude in the presence of disturbance torques; and 2) Slewing the spacecraft to change from one attitude to another. The following describes the general approach to sizing thrusters and reaction wheels for this mission. If attitude control is required for the spacecraft element, an actuator set is sized for each ADCS control event. Each ADCS event can be one of several control modes or types. The supported event types are listed below:  Delta V  Coasting  In-space Communication  Descent & Landing  Surface Science (only for Rover)  Surface Communication (only for Rover) 5.3.3.4.1 Modeling Slews For each applicable ADCS event, the epoch of the event is obtained. Each event is characterized by an initial attitude and a final attitude. The final attitude is the attitude at which the specific event or activity takes place. For example, the final attitude for a Delta V event will be an attitude that aligns the thrust vector with the inertial Delta V vector, and requires a slew from a prior attitude. In this research, the attitude is defined by a primary body vector on the spacecraft being aligned with a primary target vector, plus a secondary body vector being 181 aligned as close as possible with a secondary target vector. The primary body vector targeting allows two degrees of freedom to be constrained. The third degree of freedom is constrained with the spacecraft rotating about primary body vector until the secondary body vector aligns as close as possible with the secondary target. The attitude quaternion (from the EMEJ2000 frame to the body frame) is computed for the initial and final attitudes given the names of the primary and secondary body and target vectors. The slew angle and slew axis (in body frame) are then computed from these initial and final attitude quaternions. Next the maximum coasting rate for all slews is identified as either the maximum star tracker rate (if a star tracker is present) or a user-provided default coasting rate. Given the maximum slew coasting rate, the fraction of total slew time coasting (another user-provided input), and the computed slew angle, the slew duration is computed per the slew profile depicted in Figure 5-18. In this figure, the control torque applied to the Δt 1 segment and Δt 3 segment are considered equal and opposite. Thus, it can be assumed that Δt 1 = Δt 3. t ω max Δt 1 Δt 2 Δt 3 182 Figure 5-18. Modeled ADCS Slew Profile Using this fact, and the definition of coasting fraction as Δt 2 divided by the total slew time, one can solve for the total slew time as follows: 𝑡 𝑠𝑙𝑒𝑤 = 2𝛥 𝑡 1 + 𝛥 𝑡 2 Equation 5-6 where Δ𝑡 1 = 𝜏 0 𝐹 𝜏 0 = θ slew /𝜔 𝑚𝑎𝑥 𝐹 = 1+ 2𝑓 𝑐𝑜𝑎𝑠𝑡𝑖𝑛𝑔 1− 𝑓 𝑐𝑜𝑎𝑠𝑡𝑖𝑛𝑔 Δ𝑡 2 = 2𝑓 𝑐𝑜𝑎𝑠𝑡𝑖𝑛𝑔 Δ𝑡 1 1 − 𝑓 𝑐𝑜𝑎𝑠𝑡𝑖𝑛𝑔 5.3.3.4.2 Disturbance Torques For each unique control method in the list of control methods per ADCS control event, the disturbance torques are computed both at the initial attitude and at the final attitude. In each case, the disturbance torques computed are gravity gradient, solar radiation pressure, aerodynamic, and engine thrust misalignment disturbance during Delta-V maneuvers. To compute the disturbance torque, the total mass properties (moment of inertia matrix, mass, and center of mass location) of the combined spacecraft and its payload must be computed. The gravity gradient torque is computed using the following gravity gradient equations (see Eqs. 4.8.8 on pg. 109 of (41)). 𝑇 𝑔 𝑔 𝑥 = 𝐶 ( 𝐼 𝑧 − 𝐼 𝑦 )∗ 𝑎 23∗ 𝑎 33 𝑇 𝑔 𝑔 𝑦 = 𝐶 ( 𝐼 𝑧 − 𝐼 𝑥 )∗ 𝑎 13∗ 𝑎 33 𝑇 𝑔 𝑔 𝑧 = 𝐶 ( 𝐼 𝑥 − 𝐼 𝑦 )∗ 𝑎 13∗ 𝑎 23 Equation 5-7 183 𝐶 = 3𝜇 /𝑅 0 3 where 𝜇 = the gravitational parameter of the celestial body being orbited, 𝑅 0 is the radius from the central celestial body to the spacecraft, and a ij are components of the direction cosine matrix (DCM) from the orbit reference frame (ORF) to body frame. The orbit reference frame is defined such that Z orf is in the radial direction, Y orf is in the orbit normal direction, and X orf completes the right-hand system and points toward the velocity direction. The solar radiation pressure torque is calculated next. First the solar intensity flux 𝐽 𝑠𝑜𝑙𝑎𝑟 (in W/m 2 ) at the spacecraft’s heliocentric distance is computed according to the following equation (see Eqn 11.1, pg. 359 of (35)). 𝐽 𝑠𝑜𝑙𝑎𝑟 = 𝑃 𝑠𝑢𝑛 4𝜋 𝑅 2 Equation 5-8 where 𝑃 𝑠𝑢𝑛 = 3.856∗ 10 26 W is the total power output from the Sun and 𝑅 is the spacecraft’s heliocentric distance in meters. Given the solar intensity flux at the spacecraft’s location, the solar pressure force 𝐹 𝑠𝑜𝑙𝑎 𝑟 in Newtons acting on the spacecraft can be determined as follows (see Table 11-9A, pg. 366 of (30)). 𝐹 𝑠𝑜𝑙𝑎𝑟 = 𝐽 𝑠𝑜𝑙𝑎𝑟 𝑐 𝐴 𝑠 ( 1+ 𝑞 ) 𝑐𝑜𝑠𝜃 Equation 5-9 where 𝑐 = the speed of light in m/s, 𝐴 𝑠 = the cross-sectional surface area, 𝑞 = the surface material reflectance factor (between 0 and 1), and 𝜃 = the solar incidence angle. The solar pressure force can be transformed from a scalar to a vector in the spacecraft body frame by multiplying it by the unit vector to the sun in body frame. The solar radiation pressure torque can then be found according to the following equation: 𝑇 ⃑ 𝑠𝑜𝑙𝑎𝑟 = 𝑟 𝑐𝑝 ×𝐹 𝑠𝑜𝑙𝑎𝑟 Equation 5-10 184 where 𝑟 𝑐𝑝 is the moment arm from the spacecraft’s center of mass to the center of pressure where the solar pressure force acts. For this research, the aerodynamic drag force is assumed to be zero for simplicity, although in reality this depends on the spacecraft’s altitude in the LEO parking orbit prior to the launch vehicle upper stage executing the translunar injection (TLI) burn. The last of the disturbance torques to compute is from the engine thrust misalignment. That is, if the engine thrust vector does not point directly to the spacecraft’s center of mass, the misalignment will induce a disturbance torque proportional to the misalignment distance and the thrust magnitude. Since the disturbance torques are calculated for each ADCS control event, the Delta-V torque is computed only during a Delta-V event. First, the applicable Delta-V maneuver for the specific ADCS control event is found from a list in the Trajectory data structure. Next, the parameters of the Delta-V maneuver for the propulsion system in use are found. These include the single-engine thrust, the I sp, the maximum spin rate and (if a solid rocket motor is in use for the particular Delta-V), and the fractional limit on Delta-V loss caused by the engine misalignment. If the engine is gimballed, the Delta-V disturbance torque is assumed to be zero, since the engine can be vectored so the thrust vector points at the spacecraft center of mass. Otherwise, the Delta-V disturbance torque is computed as the cross product of the position vector from the spacecraft’s center of mass to the engine firing, as shown in the equation below. 𝑇 ⃑ 𝐷𝑒𝑙𝑡𝑎𝑉 = 𝑟 𝑐𝑚 2𝑒𝑛𝑔𝑖𝑛𝑒 ×𝐹 𝑡 ℎ𝑟𝑢𝑠𝑡 Equation 5-11 185 If a solid rocket motor is providing the specific Delta-V, the spacecraft will need to spin to provide a gyroscopic torque that counters the Delta-V disturbance torque to prevent a Delta- V loss less than that expected from the Delta-V loss fraction. This required spin rate can be determined using the following equation, per Eq. 6.2.8, pg. 134 of (41). 𝜔 𝑧 = √ 4𝜋 𝑇 𝐷𝑒𝑙𝑡𝑎𝑉 𝜃 𝑛𝑢𝑡 𝐼 𝑧 ( 𝐼 𝑧 𝐼 𝑥 − 1) ⁄ Equation 5-12 where 𝜃 𝑛𝑢𝑡 = acos ( 1− 𝑓 𝐷𝑉 _𝑙𝑜𝑠𝑠 ) is the average nutation angle induced by the disturbing torque. Once all the disturbance torques are computed for each control method, at both the initial and final attitudes, they are summed to get the total spacecraft external disturbance torque vector in body frame at both attitudes. 5.3.3.4.3 Computing Slew Torques Given the disturbance torques at the initial and final attitudes, the torque required to slew the spacecraft from the initial attitude to the final attitude for each ADCS control event is determined. The required torque depends on the control method being employed: in the case of this research, either zero momentum reaction wheels, or mass expulsion (i.e. RCS thrusters). 5.3.3.4.3.1 Reaction Wheel Sizing For the reaction wheels, the maximum per reaction wheel torque and momentum for two reaction wheel configurations, pyramid and tetrahedron, are computed. In both of these configurations, 4 reaction wheels are assumed. The pyramid configuration for 4 reaction wheels is depicted in Figure 5-19 below, reproduced from (52). Notice that the 4 reaction wheels are placed at the base of an inverted 186 pyramid, with reaction wheels 1 and 3 located in the X-Z plane of the spacecraft, and 2 and 4 located in the Y-Z plane. In addition, all 4 wheels are positioned at an angle β above the X-Y plane. The 4 wheels can also be rotated from the nominal positions about the Z axis by an angle θ. Thus, the 3x4 reaction wheel frame to spacecraft body frame torque distribution matrix can be found as: 𝐴 𝑤 _𝑝𝑦𝑟𝑎𝑚𝑖𝑑 = [ 𝑐𝑜𝑠 βcos θ 𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝜃 𝑠𝑖 𝑛𝛽 −𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝛽 −𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝜃 −𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝜃 sin𝛽 𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝜃 −𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝛽 ] Equation 5-13 In the above equation, the angle 𝛽 is needed to maximize momentum storage and the angle 𝜃 provides torque about all axes (52). Figure 5-19. Pyramid configuration for 4 reaction wheels (52) The tetrahedron configuration is shown in Figure 5-20 below. The 3x4 reaction wheel torque distribution matrix is given in the following equation. In this equation, the angle β indicates the angle between the X-Y plane and the axes of reaction wheels 1, 2, and 3. The angle θ represents the rotation about the Z-axis so that reaction wheels 1, 2, and 3 all contribute to torque about all body axes. Note that in this torque distribution matrix the fourth wheel (4 th column) is aligned with the +Z-axis and does not have any torque contribution to other body 187 axes. If all wheels are intended to provide a torque contribution about all axes, the wheel configuration would need to be rotated about the X and Y body axes. 𝐴 𝑤 _𝑡𝑒𝑡𝑟𝑎 = [ 𝑐𝑜𝑠 βcos θ 𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝜃 −𝑠𝑖𝑛𝛽 −𝑐𝑜𝑠𝛽 cos ( 𝜋 6 − 𝜃 ) 𝑐𝑜𝑠𝛽 cos ( 𝜋 3 + 𝜃 ) −𝑠𝑖𝑛𝛽 −𝑐𝑜𝑠𝛽 cos ( 𝜋 6 + 𝜃 ) −𝑐𝑜𝑠𝛽𝑐𝑜𝑠 ( 𝜋 3 − 𝜃 ) −sin𝛽 0 0 1 ] Equation 5-14 Figure 5-20. Tetrahedron configuration for 4 reaction wheels (52) For a given 4-wheel configuration, the next step is to size the reaction wheels for the slew being modeled in each ADCS control event. First, the reaction wheel torque and momentum capability required to execute the control event’s slew are found. This is done using time-optimal control. The spacecraft body torque required to accelerate and decelerate the spacecraft to achieve the desired rotation (slew angle) about the desired slew axis in the desired time is computed according to the following equation (see Eqn. 7.7.5, pg. 207 of (41)). 𝑇 ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 = 4𝐼 𝑠 𝑡 𝑓 2 𝜃 𝑓 Equation 5-15 where 𝐼 𝑠 = the spacecraft inertia matrix, 𝑡 𝑓 = the slew duration, and 𝜃 𝑓 is the slew axis vector in the spacecraft body frame. 188 Next, the torque contributed by the reaction wheels is computed per Equation 5-16 below, assuming there are no external torques. Although in reality there are external torques, this assumption is made to simplify the equations involved. 𝑇 ⃑ 𝑤 _𝑏𝑜𝑑𝑦 = −𝑇 ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 Equation 5-16 since 𝑇 ⃑ 𝑡𝑜𝑡 = 0 = 𝑇 ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 + 𝑇 ⃑ 𝑤 _𝑏𝑜𝑑𝑦 . That is, to achieve a position rotation about a given body axis, a negative torque from the wheels must be provided. Next the spacecraft momentum accumulation during the slew acceleration stage is computed. Since the acceleration time for time-optimal control is 0.5𝑡 𝑓 , the spacecraft body momentum accumulated is 𝐻 ⃑ ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 = 𝑇 ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 𝑡 𝑓 2 . The reaction wheels must provide this same level of momentum, so that: 𝐻 ⃑ ⃑ 𝑤 _𝑏𝑜𝑑𝑦 = −𝐻 ⃑ ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 Equation 5-17 In order to find the required torque and momentum capability per reaction wheel (in wheel frame) to achieve the slew, the pseudo-inverse of the reaction wheel torque distribution matrix must be obtained. That is, the 3x4 wheel torque distribution matrix (transforming from wheel frame to body frame) must be converted to a 4x3 matrix that transforms from body frame to wheel frame. The pseudo-inverse can be found as follows: 𝑃 𝑖𝑛𝑣 = 𝐴 𝑤 𝑇 ( 𝐴 𝑤 𝐴 𝑤 𝑇 ) −1 Equation 5-18 Thus, the per-wheel torque and momentum can be found from the following set of equations: 189 𝑇 ⃑ 𝑤 __𝑤 ℎ𝑒𝑒𝑙 = 𝑃 𝑖𝑛𝑣 𝑇 ⃑ 𝑤 _𝑏𝑜𝑑𝑦 Equation 5-19 𝐻 ⃑ ⃑ 𝑤 __𝑤 ℎ𝑒𝑒𝑙 = 𝑃 𝑖𝑛𝑣 𝐻 ⃑ ⃑ 𝑤 _𝑏𝑜𝑑𝑦 Equation 5-20 Since a 4-wheel configuration offers redundancy against failure of one wheel, the torque and momentum required for a given slew will be distributed differently among the remaining functional wheels. So, the above equations can again be used to determine the new wheel torque and momentum capability given a new wheel torque distribution matrix. This is done for each of four separate cases in which each reaction wheel is assumed to be out of commission. So, the reaction wheel torque distribution matrix is modified by replacing the column of the failed reaction wheel with a 3x1 zero vector. Then the maximum torque and momentum among the all-wheel and failed-wheel cases are found. 5.3.3.4.3.2 Mass Expulsion (RCS Thrusters) Sizing The torque requirement to execute a slew must be found for RCS thrusters in a similar manner as it was found for reaction wheels. Given the slew profile described in Section 5.3.3.4.1, the coasting and acceleration durations of the slew are obtained from the coasting fraction and the total slew duration. The coast rate vector in the body frame is then computed using the slew angle and slew axis (in body frame). The coast angle vector is next obtained by multiplying the coast vector by the coast duration. Next the angles about each axis achieved during acceleration are found as follows: 𝛿 𝜃 𝑎 𝑐 𝑐𝑒𝑙 = 𝜃 𝑠𝑙𝑒𝑤 − 𝛿 𝜃 𝑐𝑜𝑎𝑠𝑡 2 Equation 5-21 The spacecraft body torque to acceleration to the coasting rate is then obtained as: 190 𝑇 ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 = 2𝐼 𝑠 𝑡 𝑓 2 𝛿 𝜃 𝑎𝑐𝑐 𝑒𝑙 Equation 5-22 5.3.3.4.4 Selecting Control Actuator Once the torque (and momentum, if applicable) slew requirements for the reaction wheels or RCS thrusters are determined, the task is next to select the actuator for each control method with the maximum control authority to perform all slews and provide general attitude control. 5.3.3.4.4.1 Reaction Wheels + RCS Thrusters First, the maximum reaction wheel torques over all ADCS control events for both the pyramid and tetrahedron configurations are found. These two maximum wheel torques are compared and the configuration with the smallest torque is selected as the final configuration to meet the slew requirements. Given the desired maximum reaction wheel torque and momentum, the reaction wheel in the ADCS database with the smallest mass, that meets both requirements, is found. That is, the wheels in the ADCS database with torque and momentum capability greater than or equal to the desired torque and momentum are found. Then of this set, the wheel model with the smallest mass (both the reaction wheel itself plus the associated electronics) is identified and selected as the desired reaction wheel. A subset of the reaction wheel database is shown in Table 5-25 below. 191 Table 5-25. Reaction Wheel Database Subset Manufacturer Model Mass (kg) Steady State Power (W) Max Angular Momentum (Nms) Max Torque (Nm) Honeywell HR12-12-0.2 6 22 12 0.2 Honeywell HR12-25-0.2 7 22 25 0.2 Honeywell HR12-50-0.2 9.5 22 15 0.2 Honeywell HR14-25-0.2 7.5 22 25 0.2 Honeywell HR14-50-0.2 8.5 22 50 0.2 Honeywell HR14-75-0.2 10.6 22 75 0.2 Honeywell HR16-50-0.2 9 22 50 0.2 Honeywell HR16-75-0.2 10.4 22 75 0.2 Honeywell HR16-100-0.2 12 22 100 0.2 Since reaction wheels are typically combined with RCS thrusters for activities such as momentum unloading or attitude control during Delta-V burns, the RCS thrusters must be sized along with the reaction wheels. To size the RCS thrusters when reaction wheels are also present, the larger disturbance condition (momentum unloading or Delta-V torque) must be ascertained. The total disturbance torque during momentum unloading can be found from: 𝑇 ⃑ 𝑡𝑜𝑡 _𝑢𝑛𝑙𝑜𝑎𝑑 _𝑏𝑜𝑑𝑦 = ℎ ⃑ ̇ 𝑢𝑛𝑙𝑜𝑎𝑑 _𝑏𝑜𝑑𝑦 + 𝜔⃑ ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 ×ℎ 𝑢𝑛𝑙𝑜𝑎𝑑 _𝑏𝑜𝑑𝑦 − 𝑇 𝑒𝑥𝑡 Equation 5-23 where ℎ ⃑ ̇ 𝑢𝑛𝑙𝑜𝑎𝑑 _𝑏𝑜𝑑𝑦 is the torque state of the wheels in body frame, 𝜔⃑ ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 is the body rate vector during momentum unloading, and ℎ 𝑢𝑛𝑙𝑜𝑎𝑑 _𝑏𝑜𝑑𝑦 is the momentum state of the wheels in body frame. To simplify the calculations, the spacecraft can be assumed to have zero body rates (𝜔⃑ ⃑ 𝑠𝑐 _𝑏𝑜𝑑𝑦 = 0) with zero external torques. In reality, the spacecraft will have non-zero body rates and external disturbance torque during a momentum unloading event. This is one possible 192 area of improvement for the ADCS design module. Thus, the torque on the spacecraft during momentum unloading can be assumed to come entirely from the reaction wheels. The momentum unloading event is characterized by spinning the wheels down to zero while the RCS thrusters counter the wheel disturbance torque acting on the spacecraft (to maintain pointing so the spacecraft does not slew). So the first term in Equation 5-23 must be determined. Each reaction wheel (in either the 4-wheel pyramid or tetrahedron configuration) has the same maximum torque and momentum capability. During any given momentum unloading event, each of the wheels can be spinning at a variety of speeds (momentum) up to the maximum allowed wheel speed. Since this state is unknown, a momentum distribution vector (4x1) is assumed. In the case of the pyramid configuration, the vector is assumed to be 𝑎 = [1 1 1 1] T , with all wheels at the same momentum. In the case of a tetrahedron configuration, the vector is assumed to be 𝑎 =[1 -1 1 -1] T , with odd-numbered wheels having the same momentum and even-numbered wheels having the same momentum. Each wheel is assumed to be at 75% of the maximum momentum capability, since a spacecraft in operation will require some margin against over-speeding the wheels. The momentum state of the wheels can then be found as the limited momentum times the momentum distribution vector. During momentum unloading, the wheels are assumed to spin down to zero rpm at ½ the maximum torque capability. In a similar manner, the torque on the spacecraft as the wheels are spinning down can be computed as the wheel spin-down torque times the momentum distribution vector. The wheel momentum state can then be transformed to body frame by multiplying the momentum vector by the torque distribution matrix. Similarly, the wheel torque 193 during spin-down can be converted to body frame. This is the disturbance torque that the RCS thrusters must overcome during wheel spin-down. Next the set of disturbance torques during each Delta-V burn is obtained. Given this, the overall RCS torque requirement is determined to be either the momentum unloading torque or the Delta-V disturbance torque. To size the RCS thrusters to function for both momentum unloading and Delta-V attitude control, the minimum RCS torque in obtained for each case. This is needed as an input in sizing the RCS thrusters. The procedure for selecting the proper RCS thruster from the ADCS database is described in the following section 5.3.3.4.4.2. Once the RCS thruster is sized and selected, the propellant mass for momentum unloading, attitude control during Delta-V burns can be found, and attitude control during Descent & Landing can be determined. Currently, the ADCS design module assumes zero propellant mass for momentum unloading as the MATLAB function to compute this takes a long time to run. This is an area of possible improvement in the future. To estimate the propellant mass required to perform attitude control during Delta-V burns, a limit cycling approach is taken. This is discussed in section 5.3.3.4.4.2. Finally, since the reaction wheels cannot control the spacecraft under the disturbance torques present during Descent & Landing, the RCS thrusters must do this. The propellant mass for attitude control via RCS thrusters during all Descent & Landing phases is determined. This is discussed in more detail in section 5.3.3.4.4.2. Once the total RCS propellant mass is determined, the RCS tanks are sized. This is discussed in the next section as well. 194 5.3.3.4.4.2 RCS Thrusters Only 5.3.3.4.4.2.1 Sizing the RCS Thrusters To size the thrusters for the mass expulsion control method, the first step is to find the maximum slew torque requirement over all slews. Next, the maximum total disturbance torque (out of the set of all disturbance torques acting on the spacecraft at the final attitude for each ADCS control event) is found. The maximum RCS slew torque magnitude is compared to the maximum external disturbance magnitude. The larger of the two is selected as the RCS torque requirement (without margin). Additional margin (a user-provided value) is added to this torque requirement to determine the RCS torque requirement as a vector in body frame. Next, the minimum disturbance torque at the final attitude of all ADCS control events is found. This minimum disturbance torque vector (in body frame) is used in selecting the minimum impulse of the RCS thrusters. This minimum case is used because using the maximum disturbance torque for limit cycling calculations would result in an RCS thruster with high minimum impulse being selected. This, in turn, would cause 2-sided limit cycling when the spacecraft experiences smaller disturbance torques. Given the RCS slew torque requirement, the minimum disturbance torque vector, the minimum moment arm from the spacecraft center of mass to the RCS thrusters, the number of thrusters firing per axis, among other parameters, the RCS thrusters can be sized. In the RCS thruster sizing function, the following simplifying assumptions are made in finding the required RCS thrust for slews and attitude control: 195  The moment arm for all thrusters is assumed to be the same (i.e. the center of mass is assumed at the origin of the spacecraft structure and equidistance from all thrusters, as depicted in Figure 5-21 below)  There are 2 thruster strings (for redundancy)  There are 8 thrusters per string (for a total of 16 thrusters)  The thrusters fire in pairs (as a couple) to provide a moment/torque that causes the spacecraft to slew about a given body axis (see Table 5-26)  The RCS thruster is assumed to be mono-propellant based Figure 5-21. RCS Thruster Configuration (16 thrusters, 2 strings of 8) Table 5-26. RCS Thruster Pairs to Rotate About S/C Body Axes Axis Rotation A-string (even) B-string (odd) +X 6,16 5,15 -X 8,14 7,13 196 Axis Rotation A-string (even) B-string (odd) +Y 4,10 3,9 -Y 2,12 1,11 +Z 2,10 or 6,14 3,11 or 7,15 -Z 4,12 or 8,16 5,13 or 1,9 The required RCS thruster force can then be found from Equation 5-24 below: 𝐹 𝑚𝑎𝑥 = 𝑇 max_slew 2𝑟 𝑚𝑖𝑛 Equation 5-24 where 𝑇 max_slew is the maximum required slew torque, and the 2𝑟 𝑚𝑖𝑛 represents the shortest distance between the two thrusters. Next, the required RCS minimum impulse bit about each body axis, under the minimum disturbance torque vector (in body frame), is determined. This is obtained using the following minimum impulse bit (Ns) equation: 𝐼 𝑏𝑖𝑡 = √ 16𝐼 𝑎𝑥𝑖𝑠 𝜃 𝐷𝐵 𝑇 𝑒𝑥𝑡 𝑁 𝑟 𝑚𝑖𝑛 Equation 5-25 where 𝐼 𝑎𝑥𝑖𝑠 = the moment of inertia about a given body axis, 𝜃 𝐷𝐵 is the attitude control deadband during limit cycling, 𝑇 𝑒𝑥𝑡 is the magnitude of the external disturbance torque acting on the spacecraft, 𝑁 is the number of thrusters firing per axis (2), and 𝑟 𝑚𝑖𝑛 is the minimum RCS thruster moment arm. The overall minimum impulse bit requirement is then selected as the maximum 𝐼 𝑏𝑖𝑡 over all axes. 5.3.3.4.4.2.2 Selecting the RCS Thruster Given the RCS thrust and minimum impulse bit requirements, the RCS thruster is then selected from the thruster/engine database. Since the thruster/engine database includes a 197 variety of chemical thrusters and engines (mono-prop, bi-prop, solid rocket motors) and electric propulsion thrusters, the database is limited to only the mono-prop thrusters (example subset shown in Table 5-27 below). Since each thruster in the database can potentially have a minimum and maximum operational thrust, the average thrust is computed and used. The set of mono- prop thrusters that provide an average thrust greater than or equal to the required RCS thrust is then obtained. Table 5-27. RCS Thruster Database Subset (5 -100 N thrust) Manufacturer Model Fuel Max Isp (sec) Max Thrust (N) Thruster Mass (kg) Aerojet MR-111C Hydrazine 229 5.3 0.13 Northrop Grumman MRE-4.0 Hydrazine 217 9.8 0.5 Aerojet MR-50T Hydrazine 225 19.5 0.41 Astrium 20N Thruster Hydrazine 230 24.6 0.395 Aerojet MRM-106B Hydrazine 232 27 0.2 Northrop Grumman MRE-5.0 Hydrazine 232 28 1.5 Aerojet MR-106E 28V Hydrazine 235 30.7 0.635 Aerojet MR-106E 70V Hydrazine 235 30.7 0.23 Aerojet MRM-106E Hydrazine 235 30.7 4.1 Aerojet MR-50S Hydrazine 229 32 0.41 Aerojet MR-106L Hydrazine 235 34 0.59 Northrop Grumman MRE-15 Hydrazine 228 66 1.1 Aerojet MR-107P Hydrazine 226 98 0.65 Next, the thrusters in this set that have a minimum impulse bit less than or equal to the required minimum impulse bit are found. If no thrusters have a minimum impulse bit that meets this requirement, the one with the lowest minimum impulse bit is selected. Otherwise, the thruster with the smallest mass is identified and then selected as the desired RCS thruster. The power required to operate the associated thruster valve is also found directly from the database 198 given the assumed thruster valve current (a user-provided input) and the thruster valve voltage. Once the RCS thruster is selected, the average thruster force, average torque per thruster couple, and average specific impulse are found. Note that the selected RCS thrusters are one size for attitude control throughout the mission. Another possible architecture could be to have different-sized RCS thrusters, one set for fine attitude control and another set for Descent & Landing, for example. 5.3.3.4.4.2.3 Sizing RCS Propellant Mass Given the performance specifications of the RCS thruster, the total RCS propellant mass required to execute slews and provide attitude control (for pointing and Descent & Landing activities) is determined. The RCS propellant mass for pointing control for all ADCS control events is determined assuming 1-sided limit cycling. That is, a given RCS thruster pulses for a minimum pulse duration to provide a torque that counters the external disturbance torque acting on the spacecraft. First the disturbance torque vector (in body frame) is obtained for each ADCS control event at the final attitude. The time the spacecraft spends in this attitude until the next control event is found. If the event is a Delta-V burn, the burn duration is used. In either case, this time is used as the pointing control duration. Given the pointing control duration, the RCS propellant mass required for the thrusters to perform 1-sided limit cycling is calculated. This is done by first finding the RCS propellant mass expended during one firing of the thruster couple per the following equation. Δ𝑀 𝑝 _min_pulse = 𝑁 𝐼 𝑏𝑖𝑡 𝐼 𝑠𝑝 𝑔 0 Equation 5-26 where 𝑔 0 is the gravitational acceleration (in m/s 2 ) at the Earth’s surface. 199 Next the pulse cycle period (time between two pulses) about each axis is computed as follows: 𝑡 𝑝𝑢𝑙𝑠𝑒 = 2𝑁 𝑟 𝑚𝑖𝑛 𝐼 𝑏𝑖𝑡 𝑇 𝑒𝑥𝑡 Equation 5-27 The total number of pulses per axis over the elapsed period can be determined by dividing the pointing duration by the pulse cycle period per axis. Then the total RCS propellant mass per axis for limit cycling can be found by multiplying the RCS propellant mass for one pulse by the total number of pulses per axis. Then the total RCS propellant mass for limit cycling can be found by summing the values for all 3 axes. Next, the total RCS propellant mass to execute the slews for each ADCS control event is calculated. This is done by determining the thruster on-time during each slew about each axis. The thruster duty cycle about each axis is determined by dividing the required RCS slew torque by the available RCS torque per thruster couple as follows: 𝑓 𝑑𝑢𝑡𝑦 _𝑐𝑦𝑐𝑙𝑒 = 𝑇 𝑠𝑙𝑒𝑤 /𝑇 𝑡 ℎ𝑟𝑢𝑠𝑡𝑒𝑟 _𝑎𝑣𝑔 Equation 5-28 To check if the thrusters may inadvertently have been undersized for the required slew torque, a check is done on whether the duty cycle is greater than 100%. The thruster on-time per axis is then computed as: 𝑡 𝑜𝑛 = 2𝑁 𝑓 𝑑𝑢𝑡𝑦 _𝑐𝑦𝑐𝑙𝑒 Δ𝑡 𝑎 𝑐 𝑐𝑒𝑙 Equation 5-29 where Δ𝑡 𝑎𝑐𝑐𝑒𝑙 is the time to provide angular acceleration during the slew, and the factor of 2 accounts for both acceleration and deceleration. The on-time per axis is summed to get the total 200 RCS thruster on-time per slew. Then the list of on-times is summed to obtain the total RCS on- time for all slews. The RCS propellant mass for all slews can be found by multiplying the thruster mass flow rate, 𝑚 ̇ = 𝐹 𝐼 𝑠𝑝 𝑔 0 , by the total on-time. Δ𝑀 𝑝 _𝑠𝑙𝑒𝑤𝑠 = 𝑚 ̇ 𝑡 𝑜𝑛 Equation 5-30 Lastly, the RCS propellant mass required to provide attitude control or slewing during Descent & Landing is determined (see Section 5.3.8 for details on the Descent & Landing simulation). The Descent & Landing phase is characterized by the following sub-phases:  Braking Burn 1: engines thrusting in anti-velocity direction  Pitch-up: spacecraft slewing to align thrust axis in anti-gravity direction (no thrusting)  Braking Burn 2: thrust is vertical  Approach: thrust is vertical  Terminal Descent For braking burn 1, the total disturbance torque vector (in body frame) contribution from all firing engines is first obtained. This is done by taking the cross product of the thrust moment arm vector with the thrust per engine, and then summing the torque vector for all engines. The RCS propellant mass for attitude control during Braking Burn 1, Braking Burn 2, Approach, and Terminal Descent are then found using the 1-sided limit cycling function described earlier. The RCS propellant mass for the pitch-up maneuver is found by computing the RCS thruster on-time per the procedure described earlier, given the pitch-up maneuver duration and assuming bang-bang control for a slew about the X-axis. 201 5.3.3.4.4.2.4 Sizing RCS Tanks Now that the RCS thruster is selected and the total RCS propellant mass estimated, the next task is to size the entire Reaction Control Subsystem, including tanks. First, the mono- propellant fuel parameters are obtained from the selected RCS thruster (which originated in the Thruster/Engine database). The fuel and pressurant chemical properties (molar mass, density, etc.) are then obtained from the Propellant/Pressurant database. Additional RCS propellant above that required is then determined. The additional propellant is calculated according to the following definitions.  Reserve propellant: the required propellant mass plus margin or contingency  Usable propellant: the required propellant mass + reserve propellant mass  Residual propellant: propellant remaining in the lines and valves as a fraction of the usable propellant mass  Load uncertainty propellant: Additional propellant due to uncertainty in loading the propellant tanks on the ground prior to launch; a fraction of the usable propellant mass  Unusable propellant: the residual propellant mass + load uncertainty  Total loaded propellant: the combined usable + unusable propellant mass  Total extra propellant: the loaded propellant mass – required propellant mass Given the total RCS propellant load, the RCS tanks can then be sized. A generic propellant tank sizing function is called to estimate the RCS tankage mass. In the case of a mono-propellant RCS, two pressurization options are available: regulated vs. blowdown (see Figure 5-22 below). 202 Figure 5-22. RCS Pressurization Systems In the case of a regulated mono-prop the fuel and pressurant tank assemblies are sized. For this research, 2 fuel/pressurant tank assemblies each offset from the spacecraft centerline are assumed. Each assembly is also assumed to contain half of the total RCS propellant and pressurant for mass balancing purposes. First the fuel tank of each assembly is sized using a generic tank sizing function, followed by the pressurant tank. The generic tank sizing function first computes the volume needed for only the required RCS propellant mass, and then the volume needed for the usable RCS propellant mass. To get the required tank volume, the volume of gas ullage in the tank is estimated as the ullage fraction times the usable propellant volume. Then the tank volume is simply the required propellant volume + the gas ullage volume. V tank_req = 𝑉 𝑓𝑢𝑒𝑙 _𝑟𝑒𝑞 + 𝑉 𝑔𝑎𝑠 _𝑢𝑙𝑙𝑎𝑔𝑒 Equation 5-31 High Pressure Gas Propellant Tank Fill Valve Regulator Relief Valve Regulated Gas Propellant Fill Valve Fill Valve Blowdown 203 Since the pressure regulator in between the tank and thruster causes a pressure drop, and since the thruster has a range of operating feed pressures, the maximum tank pressure can be found as the maximum thruster feed pressure plus the negative of the regulator pressure drop. P tank_max = 𝑃 𝑡 ℎ𝑟 _𝑓𝑒𝑒𝑑 _𝑚𝑎𝑥 + Δ𝑃 𝑟𝑒𝑔 Equation 5-32 In the case of a blowdown mono-prop RCS, the required tank volume is computed by finding the blowdown ratio (ratio of initial tank pressure to final tank pressure) and using that, along with the usable propellant volume, to estimate the initial gas volume per Equation 5-33 below (see pg. 713 of (30)). B = P 0i 𝑃 0𝑓 V gf = 𝑉 𝑢𝑠𝑎𝑏𝑙𝑒 1− 1/𝐵 V gi = 𝑉 𝑔𝑓 𝐵 Equation 5-33 The required tank volume can then be found using Equation 5-31 above. Given the required tank volume, the tank inner radius can be found assuming a spherical tank: R inner_tank = ( 3 4 𝑉 𝑡𝑎𝑛𝑘 _𝑟𝑒𝑞 𝜋 ) 1 3 Equation 5-34 The volume required for the propellant control device can then be computed along with its outer radius. Next, the inner tank case radius can be found as the required inner tank radius plus the propellant control device material thickness. In the case of a metal tank, no tank liner is 204 assumed. In that case, the required inner tank case radius is just the previously computed inner tank radius. For a composite tank, on the other hand, the tank will have a metallic liner on the inside. The radius and volume of this thin metallic tank liner is then computed. So the composite tank inner tank case radius is then just the outer radius of the tank liner. The tank case thickness, whether metallic or composite, can then be found using the allowable stress formula for a spherical tank (30). σ = P max R inner_tank 2t Equation 5-35 where P is the maximum expected operating pressure and t is the tank case thickness. This equation can be solved for the tank case thickness, given the maximum tank pressure, a user- provided factor of safety, and assuming the allowable stress is equivalent to the tank material ultimate tensile strength 𝐹 𝑡𝑢 . t = f sf P max R inner_tank 2𝐹 𝑡𝑢 Equation 5-36 The tank outer radius is then the inner tank case radius plus the tank case thickness. The total tank thickness is then the tank case thickness plus the tank liner thickness, if present. The volume of the tank case spherical shell can then be found as follows: 𝑉 𝑡𝑎𝑛𝑘 _𝑐𝑎𝑠𝑒 = 4 3 𝜋 ( 𝑅 𝑜𝑢𝑡𝑒𝑟 _𝑡𝑎𝑛𝑘 _𝑐𝑎𝑠𝑒 3 − 𝑅 𝑖𝑛𝑛𝑒𝑟 _𝑡𝑎𝑛𝑘 _𝑐𝑎𝑠𝑒 3 ) Equation 5-37 The last step in sizing the tanks is to compute the mass of the tank. This is done by computing the mass of the propellant control device, the tank liner (if present), and the tank case, using the volume of each component times the density of that component. 205 Next the RCS dry mass is computed given the fuel mass, pressurant mass, tankage mass, thruster mass, etc. Finally, the total RCS power is estimated as the sum of the thruster valve power, the thruster valve heater power, and, in the case of a mono-prop system, the catalyst bed heater power. 5.3.3.4.5 Control System Selection Once the actuators (reaction wheels and thrusters) are selected and sized, the minimum mass control system (reaction wheels + RCS or RCS only) is identified and selected as the desired control system. Lastly, the heat generated by all selected sensors and actuators is estimated. 5.3.4 Propulsion Design Module The Propulsion subsystem design module is designed to estimate the propellant requirements to provide for all the Delta-V orbital maneuvers required in the trajectory and to size the propellant tanks for the total propellant load (including the Descent & Landing propellant). Note that the Descent & Landing propellant mass requirement itself is not estimated in this module, since that is sized separately in the Descent & Landing design module (see Section 5.3.8). The architecture of the Propulsion design module is depicted in Figure 5-23 below. 206 Figure 5-23. Propulsion Design Module Top-Level Architecture To make this design tool somewhat generic, it is assumed that more than one propulsion system may be present on the spacecraft. For example, a spacecraft may have a bi- propellant propulsion system to provide for the majority of Delta-V burns, but may use a solid rocket motor (SRM) for an orbit insertion burn. If the spacecraft is equipped with a propulsion subsystem (for example, a typical rover is not), then each propulsion system is sized separately. The total mass of all propulsion subsystems is then computed. This tool accepts the following MATLAB inputs: trajectory parameters (data structure), payload parameters (data structure), propulsion system identification number, and individual subsystem parameters (a separate data structure for each subsystem). The tool returns the Propulsion data structure with updated parameters and design results. First, the tool gets the required number of descent engines for Descent & Landing and sets it as the total available thrusters onboard the propulsion subsystem. Next, the tool obtains various propulsion inputs:  the user-input thruster model (originating in the Thruster/Engine database) Inputs Outputs Get propulsion system inputs Get total Delta-V for orbital maneuvers Get subsystem masses Size chemical propulsion system Size electric propulsion system Position engines Prop Type 207  the supported propellants (fuel, oxidizer, and pressurant)  the thruster feed pressure (min and max)  propellant mass factors (for fuel/oxidizer ullage, reserve margin, residual propellant fraction, load uncertainty fraction)  total required Delta-V (in km/s) for all orbital maneuvers in the trajectory  thruster performance specifications  miscellaneous component masses (electric propulsion power units, electric propulsion low/high pressure feed assemblies, thruster gimbals, thruster valves, thruster mass itself, etc.)  Propellant and pressurant chemical properties (molar mass, density, temperature, mixture ratio)  Maximum tank pressures (for fuel, oxidizer, and pressurant tanks)  Tank material properties (material, ultimate tensile strength, tank factor of safety, tank case density, tank liner density, tank liner thickness)  Propellant control device density and thickness  Total launch mass for each subsystem  Descent & Landing total propellant mass  The mass of any other separate propulsion systems (RCS thrusters are assumed part of ADCS) Given all the above inputs, the proper propulsion sizing module can be run. Note that the Propulsion design module assumes the main engine model has been specified at the user-input level and not as an internal trade within the tool itself. An example engine database is shown below in Table 5-28. 208 Table 5-28. Propulsion Engine Database Subset Manufacturer Model Fuel Oxidizer Max Isp (sec) Max Thrust (N) Engine Mass (kg) Aerojet R-1E MMH NTO 280 111 2 Aerojet R-4D MMH NTO 315.5 490 3.4 Aerojet HiPAT Liquid Apogee Motor MMH NTO 323 445 5.44 Aerojet HiPAT Dual Mode Liquid Apogee Thruster Hydrazine NTO 329 445 5.4 Aerojet R-42 MMH NTO 303 890 4.53 Aerojet R-42DM Hydrazine NTO 327 890 7.3 Aerojet AMBR Dual Mode Hydrazine NTO 333 623 5.4 Northrop Grumman TR-308 Liquid Apogee Engine Hydrazine NTO 322 470.64 4.76 Northrop Grumman TR-312 Liquid Apogee Engine MMH NTO 325 501.72 6.03 Northrop Grumman TR-312- 100YN Liquid Apogee Engine MMH NTO 330 555 6.03 For the purposes of this research, since the reference mission is to the lunar surface, the Propulsion design module was originally designed for either chemical or electric propulsion, given that the trajectory could employ either of these techniques. The other more exotic propulsion techniques were not investigated in this research. The emphasis of this research was placed on sizing the chemical propulsion, although the capability does exist in the tool to size an 209 electric propulsion system for use in a low-thrust trajectory (but this capability has not been fully tested with an integrated trajectory). Once the chemical propulsion system is sized (propellant mass estimation + tank sizing), the engines are positioned on the spacecraft. The number of engines required is determined by the Descent & Landing module, described in Section 5.3.8. Up to 6 engines can be placed at the base of the spacecraft. For a spacecraft without any solid rocket motors, an engine can be placed along the spacecraft centerline. Otherwise, if a solid rocket motor is present and positioned along the centerline, no engines can be placed on the centerline. For the purposes of this research, the MATLAB code currently only has engine positioning for the “without solid rocket motor” case. Potential future work could involve adding an engine positioning case for the SRM-equipped condition. The engine positioning for this has already been mapped out but not programmed in the Propulsion subsystem design module code. For the non-SRM case, if one engine is sufficient to provide for the Descent & Landing, it is place at the base of the Lander spacecraft along the centerline. Two required engines are positioned so that they are equidistance from the centerline along the X-axis. Three required engines are positioned in a triangular pattern. Four required engines are positioned in a square pattern. Five required engines are positioned such that one engine is along the centerline and the remaining 4 are arranged in a square pattern around the central engine. Six required engines are positioned in a rectangular pattern with three engines forming each row of the arrangement parallel to the X-axis. 210 5.3.4.1 Chemical Propulsion Sizing Module 5.3.4.1.1 Estimating Required Propellant Mass Three types of chemical propulsion systems can be sized in the chemical propulsion sizing module: mono-prop, bi-prop, and solid. Sizing the chemical propulsion system, regardless of the type, at this stage requires an iterative approach. This approach involves estimating the inert mass (assuming zero initial required propellant on the first iteration), required propellant mass to impart the required Delta-V, the loaded propellant mass, sizing the propellant and pressurant tanks, and then repeating this process by iteration, computing a new inert mass (now using the just-estimated propellant mass) until the total estimated spacecraft mass converges. The detailed calculations to do this are described next and the overall algorithm is depicted in Figure 5-24 below. 211 Figure 5-24. Chemical propulsion module sizing algorithm First, the inert masses are computed. The inert masses are all the masses that cannot be used in actually propelling or slowing down the spacecraft. That is, the inert mass consists of the masses of all the subsystems plus the unusable propellant mass. The reader may wonder how the unusable propellant mass can be estimated without knowing the required propellant mass. Since this is an iterative approach, the required propellant mass is assumed to be zero on the very first iteration of this method. Once the inert mass has been computed, an estimate of the total spacecraft mass can be made as the sum of the inert mass plus the usable propellant mass (i.e. the wet mass). 𝑚 𝑡𝑜𝑡 _𝑒𝑠𝑡 = 𝑚 𝑖𝑛𝑒𝑟𝑡 + Δ𝑀 𝑝 _𝑢𝑠𝑎𝑏𝑙𝑒 Equation 5-38 Given this, an estimate of the total Delta-V that can be imparted by the propulsion system can be made using the standard field-free rocket equation. Inputs Output s Initialize following masses to zero:  tank masses  propellant masses  inert mass  total est. mass  total req. mass Compute inert mass Compute total estimated mass Compute total estimated Delta-V Compute total required mass Compute total required propellant mass Compute loaded propellant mass or adjusted SRM propellant mass Size fuel, oxidizer, and pressurant tanks Compute diff. between current and previous iteration for total est. mass While loop 212 Δ𝑉 𝑒𝑠𝑡 = 𝐼 𝑠𝑝 𝑔 0 ln ( 𝑚 𝑡𝑜𝑡 _𝑒𝑠𝑡 𝑚 𝑖𝑛𝑒𝑟𝑡 ) Equation 5-39 In the above formulation, it is assumed that all the “usable” propellant is actually used, leaving only the inert mass (final mass). The same standard rocket equation can be used to compute the actual required total spacecraft mass to deliver the required Delta-V. m tot_req = 𝑚 𝑖𝑛𝑒𝑟𝑡 𝑒 Δ𝑉 𝑟𝑒𝑞 /𝐼 𝑠 𝑝 𝑔 0 Equation 5-40 Given this required total spacecraft mass, the required propellant mass for the orbital Delta-V maneuvers can be obtained as: ΔM p_req_DV = 𝑚 𝑡𝑜𝑡 _𝑟𝑒𝑞 − 𝑚 𝑖𝑛𝑒𝑟𝑡 Equation 5-41 Then the total propellant mass required for both Delta-V burns and Descent & Landing can be computed as: ΔM p_req_tot = ΔM p_req_DV + ΔM p_req_EDL Equation 5-42 Next, in the case of a bi-prop system, the usable and loaded propellant mass can be computed as follows: ΔM p_reserve = ΔM p_req_tot 𝑓 𝑚𝑎𝑟𝑔𝑖𝑛 ΔM p_usable = ΔM p_req_tot + ΔM p_reserve Equation 5-43 As the above equation shows, the usable propellant mass is just the total required propellant mass plus the reserve mass. 213 ΔM p_resid = ΔM p_usable 𝑓 𝑟𝑒𝑠𝑖𝑑 ΔM p_load_unc = ΔM p_usable 𝑓 𝑙𝑜𝑎𝑑 _𝑢𝑛𝑐 ΔM p_unusable = ΔM p_resid + ΔM p_load_unc Equation 5-44 Then the total loaded prop mass is just the sum of the usable and unusable propellant mass. ΔM p_loaded = ΔM p_usable + ΔM p_unusable Equation 5-45 The fuel and oxidizer mass can be found using the mixture ratio 𝑀𝑅 as: ΔM p_fuel = ΔM p_loaded 𝑀𝑅 + 1 ΔM p_ox = ΔM p_loaded − ΔM p_fuel Equation 5-46 If a solid rocket motor is being designed, propellant mass may need to be added or removed from the SRM’s standard design (i.e. the SRM is a commercial unit). The adjusted mass can be found as: Δ𝑀 𝑝 _𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 = ΔM p_req_DV − Δ𝑀 𝑝 _𝑒𝑥𝑝𝑒𝑙𝑙𝑒𝑑 Equation 5-47 where Δ𝑀 𝑝 _𝑒𝑥𝑝𝑒𝑙𝑙𝑒𝑑 represents the SRM propellant consumed, and is equivalent to the total SRM mass minus the burn out mass (as provided by the manufacturer). If propellant has to be added, the SRM case length will need to be extended. This can be obtained by taking the additional propellant mass and dividing it by the linear density of the SRM (kg/cm). 214 5.3.4.1.2 Sizing Propellant Tanks Once either the liquid or solid propellant mass is estimated, the associated tankage for the liquid system can be sized. The tank sizing for a mono-prop RCS was described in Section 5.3.3.4.4.2.4 and can be referred to for the actual tank sizing equations since the same functions are called again for the bi-prop fuel and oxidizer tanks. In the case of the bi-prop pressurant tank, an optimization method to find the proper tank pressure. To do this, the regulated pressure at the thruster feed is needed. Since there will be pressurant gas in the oxidizer and fuel tanks (as ullage), the total pressurant ullage volume can be found. The mass of this pressurant ullage gas can be found using the perfect gas law as follows: n mol_ullage = 𝑃 𝑟 𝑉 𝑢𝑙𝑙𝑎𝑔𝑒 𝑅𝑇 Equation 5-48 Then the total ullage mass can be found by multiplying the moles by the molar mass (kg/mol) of the pressurant gas. The pressurant ullage mass in the fuel and oxidizer tanks can each be estimated in a similar manner. The volume of the fuel and oxidizer usable propellant can then be estimated from their respective masses and densities. Next the regulated pressurant tank pressure is found by searching for the initial tank pressure (starting at a minimum pressure up to a pre-defined limit) that minimizes the pressurant tank mass. First, the pressurant volume stored in the pressurant tank is estimated. 𝑉 𝑝𝑟𝑒𝑠𝑠 _𝑠𝑡𝑜𝑟𝑒 = 𝑃 𝑟 𝑉 𝑢 𝑃 0𝑖 − 𝑃 0𝑓 Equation 5-49 215 Where 𝑃 𝑟 is the regulated fuel and oxidizer tank pressure, 𝑉 𝑢 is the total usable propellant volume (fuel + oxidizer), 𝑃 0𝑖 is the current guess of the initial pressurant tank pressure, and 𝑃 0𝑓 is the final pressurant tank pressure (equivalent to the minimum thruster feed pressure minus the pressure regulator drop). The moles of pressurant gas stored in the tanks can be found using the perfect gas law: n mol_press_store = 𝑃 𝑝𝑟𝑒𝑠𝑠 _𝑡𝑎𝑛𝑘 _𝑚𝑎𝑥 𝑉 𝑝𝑟𝑒𝑠𝑠 _𝑠𝑡𝑜𝑟𝑒 𝑅𝑇 Equation 5-50 The mass of the pressurant gas stored in the tanks can be found by multiplying the moles by the molar mass of the pressurant. The total mass of pressurant gas can then be found as follows: 𝑚 𝑝𝑟𝑒𝑠𝑠 = 𝑚 𝑝𝑟𝑒𝑠𝑠 _𝑢𝑙𝑙𝑎𝑔𝑒 + 𝑚 𝑝𝑟𝑒𝑠𝑠 _𝑠𝑡𝑜𝑟𝑒 Equation 5-51 Given the stored pressurant mass in the tanks, the generic tank sizing function can be called. The process of computing the stored pressurant mass and sizing the pressurant tank (mass, radius, thickness, volume) is repeated for every incremented initial tank pressure. The tank corresponding to the minimum pressurant tank mass is then selected as the desired pressurant tank. 5.3.4.2 Electric Propulsion Sizing Module An electric propulsion sizing module was also developed as part of this research for use in a low-thrust trajectory. However, the researcher was not able to design a low-thrust trajectory within the dissertation research timeline and so was not able to fully test deploy this capability. The original intent was for a Propulsion Stage module, separate from a Lander, to be equipped with a solar electric propulsion (SEP) module to provide low-thrust. This is an area for 216 possible future work. As such, the details of the electric propulsion sizing module are not described here. 5.3.5 Thermal Design Module The overall goal of the thermal design module is to estimate the mass of the thermal subsystem for each spacecraft, size the spacecraft radiator, and estimate the radiator heater power. The overall method to accomplish this is depicted in Figure 5-25 below. The details of the figure are described in the following sections. Figure 5-25. Thermal Design Module Top-Level Architecture 5.3.5.1 Thermal Mass Estimation The primary function of the Thermal design module is to estimate the total thermal subsystem mass and to estimate the thermal subsystem power for each spacecraft element in the mission. The total thermal subsystem mass can be estimated using a simple formula based on a fraction of the total spacecraft element dry mass, as shown below in Equation 5-52. Inputs Outputs Get dry mass w/o thermal Compute thermal subsystem mass Compute min/max S/C equilibrium temperature for each mission event Size S/C radiator for hot allowable S/C temperature Size heater power to keep S/C radiator at lower cold allowable S/C temperature 217 𝑚 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 = 𝑓 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 𝑚 𝑑𝑟𝑦 _𝑠𝑐 _𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 Equation 5-52 The thermal mass fraction is a user-input, specified in the MASD Excel tool, and is typically 2-5% of the spacecraft dry mass (36). In this research a value of 4% was used. The spacecraft dry mass without the thermal contribution is first computed by summing the dry masses of all other subsystems on the spacecraft element. Since the total spacecraft element’s dry mass includes thermal, the predicted dry mass must be computed according to the formula in Equation 5-53. 𝑚 𝑑𝑟𝑦 _𝑠𝑐 _𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 = 𝑚 𝑑𝑟𝑦 _𝑠𝑐 _𝑛𝑜 _𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 1− 𝑓 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 Equation 5-53 This predicted dry mass can then be multiplied by the thermal mass fraction to obtain the thermal subsystem mass estimate. 5.3.5.2 Spacecraft Equilibrium Temperature The next set of steps in the thermal design process is to compute the spacecraft heat dissipation for all events in the mission as part of an effort to size the spacecraft radiator and determine the radiator heater power. The procedure that was followed to size the spacecraft radiator and determine radiator heater power is outlined in Table 11-45 on pg. 443 of (30). The procedure as adapted in this research is described next. First, the surface area of the spacecraft element is estimated by adding the surface areas of the warm electronics box (WEB) and any appendages (such as surface area from wheels for the Rover, but not including the surface areas of the solar arrays or RPS radiators, if present). In the event the contributions to the total spacecraft surface area have been yet been 218 determine (i.e. if the Structures design module has not yet been run), a total spacecraft surface area of 1 m 2 is assumed. Next the diameter of a sphere with surface area equal to the spacecraft surface area is found. This sphere diameter is in turn used to find the cross-sectional area of the spacecraft. Given this, a procedure, as outlined in (30), is followed to determine the minimum and maximum spacecraft heat flux in each mission event. To do this, the maximum and minimum heat dissipation for each event are obtained from the Power MATLAB data structure, as estimated by the Power design module (see Section 5.3.7 for details). The maximum heat flux for each event assumes no battery discharge, whereas the minimum heat flux represents the heat flux during eclipses and includes battery discharge heat. Given the minimum and maximum spacecraft internal heat dissipation (in Watts) for a particular event, the spacecraft element’s maximum and minimum equilibrium temperatures are estimated. Since the spacecraft’s equilibrium temperature also depends on heat fluxes from all environmental sources, particularly the Sun. So the spacecraft’s heliocentric distance is obtained from the trajectory at the time of each mission event. The geocentric distance is also important, to calculate the heat flux from the Earth. The Earth’s angular size as viewed from the spacecraft’s position in its trajectory is determined using simple geometry, as given in the following equation. 𝜃 𝐸𝑎𝑟𝑡 ℎ = 𝑠𝑖𝑛 −1 ( 𝑅 𝐸𝑎𝑟𝑡 ℎ 𝑅 𝑠𝑐 _𝑔𝑒𝑜𝑐𝑒𝑛𝑡𝑟𝑖𝑐 ) Equation 5-54 where 𝑅 𝐸𝑎𝑟𝑡 ℎ is the Earth’s equatorial radius, and 𝑅 𝑠𝑐 _𝑔𝑒𝑜𝑐𝑒𝑛𝑡𝑟𝑖𝑐 is the distance from the Earth’s center to the spacecraft. 219 The distance from the spacecraft to the Moon is obtained to determine the heat flux from the Moon. The Moon’s angular size is then determined using the following equation. 𝜃 𝑀𝑜𝑜𝑛 = 𝑠𝑖𝑛 −1 ( 𝑅 𝑀𝑜𝑜𝑛 𝑅 𝑠 𝑐 _𝑠𝑒𝑙𝑒𝑛𝑜𝑐𝑒𝑛𝑡𝑟𝑖𝑐 ) Equation 5-55 where 𝑅 𝑀𝑜𝑜𝑛 is the Moon’s equatorial radius, and 𝑅 𝑠𝑐 _𝑠𝑒𝑙𝑒𝑛𝑜𝑐𝑒𝑛𝑡𝑟𝑖𝑐 is the distance from the Moon’s center to the spacecraft. Next, the view factors to the Earth and the Moon are determined according to the following equation. This equation represents the view factor of an infinitesimal sphere (the spacecraft) viewing a finite sphere. The view factor is a parameter that accounts for the geometry and orientation of a surface in relation to radiative heat exchange. 𝐹 = ( 1− 𝑐𝑜𝑠𝜌 ) 2 Equation 5-56 where ρ is the angular radius of the Earth in radians. The solar flux (W/m 2 ) at the spacecraft’s position can be estimated from: 𝐽 𝑠𝑜𝑙𝑎𝑟 = 𝑃 𝑠𝑢𝑛 4𝜋 𝑅 2 Equation 5-57 where 𝑃 𝑠𝑢𝑛 is the Sun’s total power output (3.856 x 10 26 W) and R is the spacecraft’s distance from the Sun (35). Given the spacecraft cross-section and surface areas, the relevant view factor, the solar flux at the spacecraft’s position, and the spacecraft emissivity 𝜖 and absorptivity 𝛼 , the heat absorbed by the spacecraft from various sources can be computed. These sources are solar, celestial body infrared heat and albedo (from the Earth or Moon), in addition to the spacecraft’s own internal heat dissipation. 220 The heat absorbed from the Sun can be found from: 𝐽 𝑠𝑜𝑙𝑎𝑟 _𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 = 𝐴 𝑐𝑟𝑜𝑠𝑠 _𝑠𝑝 ℎ𝑒𝑟𝑒 𝐽 𝑠𝑜𝑙𝑎𝑟 𝛼 Equation 5-58 The heat absorbed from Earth infrared radiation can be found from: 𝐽 𝐸𝑎𝑟𝑡 ℎ_𝐼𝑅 = 𝐴 𝑠𝑢𝑟𝑓 _𝑠𝑐 𝐹 𝐸𝑎𝑟𝑡 ℎ 𝑞 𝑚𝑎𝑥 _𝐸𝑎𝑟𝑡 ℎ 𝜖 Equation 5-59 where 𝑞 𝑚𝑎𝑥 _𝐸𝑎𝑟𝑡 ℎ is the maximum Earth infrared heat flux, known to be 258 W/m 2 (30). The heat absorbed from Earth albedo radiation can be found from: 𝐽 𝐸𝑎𝑟𝑡 ℎ_𝑎𝑙𝑏𝑒𝑑𝑜 = 𝐴 𝑠𝑢𝑟𝑓 _𝑠𝑐 𝐹 𝐸𝑎𝑟𝑡 ℎ 𝐽 𝑠 𝑜𝑙𝑎𝑟 𝑎 𝐸𝑎𝑟𝑡 ℎ 𝛼 𝐾 𝑎𝐸𝑎𝑟𝑡 ℎ Equation 5-60 where 𝑎 𝐸𝑎𝑟𝑡 ℎ = 0.34 is Earth’s albedo, and 𝐾 𝑎𝐸𝑎𝑟𝑡 ℎ is an albedo correction factor that accounts for the reflection of collimated incoming solar energy off a spherical Earth. The Earth’s albedo correction factor is estimated as (30): 𝐾 𝑎𝐸𝑎𝑟𝑡 ℎ = 0.644+ 0.521𝜌 𝐸𝑎𝑟𝑡 ℎ − 0.203𝜌 𝐸𝑎𝑟𝑡 ℎ Equation 5-61 The heat absorbed from lunar infrared radiation and albedo can be determined in a similar manner, using 𝑞 𝑚𝑎𝑥 _𝑀𝑜𝑜𝑛 = 1311 W/m 2 (using the Moon’s maximum equatorial temperature and the Stefan-Boltzmann equation), 𝑎 𝑀𝑜𝑜𝑛 = 0.07, and 𝐾 𝑎𝑀 𝑜𝑜𝑛 = 1 (for lack of an available equation). The total maximum heat flux on the spacecraft can then be estimated by summing the fluxes from the Sun, Earth infrared radiation, Earth albedo radiation, the Moon’s infrared radiation, the Moon’s albedo radiation, and the spacecraft’s maximum internal heat dissipation. Given this, the spacecraft’s maximum equilibrium temperature (in Kelvin) can be found from the Stefan-Boltzmann equation as: 221 𝑇 𝑚𝑎𝑥 = ( 𝐽 𝑚𝑎𝑥 𝐴 𝑠𝑢𝑟𝑓 _𝑠𝑐 𝜎𝜖 ) 1 4 Equation 5-62 The total minimum heat load on the spacecraft can be found by summing the heat from the Earth IR, Moon IR, and spacecraft minimum internal heat dissipation (no input from the Sun or albedo since an eclipse condition is assumed). In a similar manner, the minimum equilibrium temperature can be found using this minimum total heat load. 5.3.5.3 Spacecraft Radiator Sizing Next the spacecraft radiator can be sized. First the allowable spacecraft internal temperature limits (high and low) are obtained from the user-specified inputs. Margin of about 5° C is added to both limits. The minimum overall spacecraft internal heat dissipation over all mission events is then found, followed by the maximum overall heat dissipation over all mission events. Given the upper allowable spacecraft temperature (with margin), the radiator heat flux (W/m 2 ) can be computed per the following equation. 𝐽 𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 = 𝜎𝜖 𝑇 𝑠𝑐 _𝑢𝑝𝑝𝑒𝑟 4 Equation 5-63 Then the required spacecraft radiator area can then be found given the maximum spacecraft internal heat generation (assumes no solar flux). 𝐴 𝑠𝑐 _𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 = 𝑄 𝑠𝑐 _𝑚𝑎𝑥 𝐽 𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 Equation 5-64 Then the heater power required to keep the radiator at the minimum allowable spacecraft temperature (including margin) is computed. First the radiator temperature under the worst-case cold condition is found: 222 𝑇 𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 _𝑐𝑜𝑙𝑑 = ( 𝑄 𝑠𝑐 _𝑚𝑖𝑛 𝐴 𝑠𝑐 _𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 𝜎𝜖 ) 1 4 Equation 5-65 Then the required heater power can be found as: 𝑄 𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 _𝑙𝑜𝑤 _𝑡𝑒𝑚𝑝 = 𝐴 𝑠𝑐 _𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 𝜎𝜖 𝑇 𝑠𝑐 _𝑙𝑜𝑤𝑒𝑟 4 Equation 5-66 This heater power is then set as the required thermal subsystem power. 5.3.6 Structures Design Module The purpose of the Structures design module is to estimate the structural mass of each spacecraft element: in the case of this research, a rover and a lander. The procedure to estimate the structural mass in each case is different given the unique nature of each spacecraft type and is described in the following sections. 5.3.6.1 Rover Structure Design The overall architecture of the rover structural design module is depicted below. Figure 5-26. Rover Structures Design Module Top-Level Architecture Inputs Outputs Estimate rover WEB area and mass (assume 0 on first iteration) Estimate rover mobility system mass (using historical data) Estimate rover total mass (mobility + remaining) Compute rover wheel diameter and width (using historical data) Compute rover overall length, width, height (using historical data) Compute rover wheel actuator power (using wheel theory) 223 The first step in sizing the Rover is to estimate the area of each side of the warm electronics box (WEB) that houses all the critical electronics, and the WEB mass. This is done taking into account the overall dimensions of the rover (determined later on) and subtracting the appropriate dimension of the rover wheels (width or diameter). For the very first call of the Structures module for the Rover, the WEB mass and panel area cannot be estimated, as these require the rover overall dimensions. So these parameters are assumed to be zero for the very first system iteration of the Rover. In any case, the next step is to compute the mass of all other Rover subsystems, not including the mobility system. That is, the mass of all instrument payloads is added to the masses of all other rover subsystems to obtain the “remaining” mass. Once this “remaining” mass is computed, it can be used to estimate the mass of the Rover mobility system. The mass of the mobility system has a simple linear relationship to the Rover “remaining” mass. 𝑚 𝑟𝑜𝑣𝑒𝑟 _𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦 = 𝛼 𝑚𝑜𝑏 𝑚 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 Equation 5-67 where 𝛼 𝑚𝑜𝑏 is the rover mobility sizing coefficient and can be found from the rover mobility coefficient (fit from historical data) as: 𝛼 𝑚𝑜𝑏 = 𝑓 𝑚𝑜𝑏 1− 𝑓 𝑚𝑜𝑏 Equation 5-68 This linear relationship was determined by obtaining publicly available mass data for flown Mars or lunar rovers and plotting the total mass against the “remaining” mass. This data is shown below in the following set of tables. Data was obtained for all successful NASA Mars rovers and the two Soviet Lunokhod rovers. 224 Table 5-29 shows historical mass and power data. Table 5-30 shows dimensional data (wheel diameter and width, and overall rover width, length, and height). Table 5-29. Historical Rover mass and power data Table 5-30. Historical Rover dimensional data Using this data, relationships between various aspects of the rover design can be found. A plot of the historical mobility system mass vs. rover remaining mass is shown in Figure 5-27. Mission Launch Date Destination Rover Planned Surface Mission Duration (days) Total Rover Mass (kg) Science Payload Mass (kg) Mobility System Mass (kg) Total Mass - Mobility System Mass (kg) Power supply max output (W) Power Source # Wheels Mars Pathfinder 4-Dec-96 Mars Sojourner 7 10.5 0.74 2.13 8.37 16.5 Solar array (GaAs/Ge) 6 Mars Exploration Rovers *June 10, 2003 (MER-A, Spirit) *July 7, 2003 (MER-B, Opportunity) Mars MER-A/B 92.4 174.5 9 35.40 139.10 140 Solar array (Ultra-triple junction) 6 Mars Science Laboratory 26-Nov-11 Mars Curiosity 730 899 75 182.38 716.62 110 Radiosiotope (Pu-238) 6 Luna 17 10-Nov-70 Moon Lunokhod-1 81 756 n/a 105.00 651.00 180 Solar array (Si) 8 Luna 21 8-Jan-73 Moon Lunokhod-2 81 840 n/a 116.67 723.33 1000 Solar array (GaAs) 8 Mission Rover Wheel Diameter (m) Wheel width (m) Width (m) Length (m) Height (m) Max Speed (cm/s) # Science Instruments Mars Pathfinder Sojourner 0.137 0.06 0.48 0.65 0.3 1 1 Mars Exploration Rovers MER-A/B 0.262 0.16 2.3 1.6 1.5 5 7 Mars Science Laboratory Curiosity 0.5 0.4 2.8 3 2.1 2.5 10 Luna 17 Lunokhod-1 0.51 0.2 1.6 1.7 1.35 22.2 4 Luna 21 Lunokhod-2 0.51 0.2 1.6 1.7 1.35 55.6 6 225 Figure 5-27. Historical rover mobility system mass vs. remaining rover mass A plot of rover wheel diameter vs. total mass is shown in Figure 5-28 below. Figure 5-28. Historical rover wheel diameter vs. total rover mass A plot of rover wheel width vs. total mass is shown in Figure 5-28 below. 226 Figure 5-29. Historical rover wheel width vs. total rover mass A similar procedure as that used for the mobility system can be followed to determine the dimensions of the rover wheels (diameter and width), and the overall rover width, height, and length. That is, the dimensional data was plotted against the total rover mass for all flight rovers to obtain curves. In the case of the wheel diameter and width, and the rover overall width, length, and height, the curves were fit to power laws. The rover wheel diameter can be found from: 𝐷 𝑤 ℎ𝑒𝑒𝑙 = 𝛼 𝑤 ℎ𝑒𝑒𝑙 _𝑑𝑖𝑎𝑚 𝑚 𝑡𝑜𝑡 _𝑟𝑜𝑣𝑒𝑟 𝛽 𝑤 ℎ𝑒𝑒𝑙 _𝑑𝑖𝑎𝑚 Equation 5-69 The rover wheel width can be found from: 𝑊 𝑤 ℎ𝑒𝑒𝑙 = 𝛼 𝑤 ℎ𝑒𝑒𝑙 _𝑤𝑖𝑑𝑡 ℎ 𝑚 𝑡𝑜𝑡 _𝑟𝑜𝑣𝑒𝑟 𝛽 𝑤 ℎ𝑒𝑒𝑙 _𝑤𝑖𝑑𝑡 ℎ Equation 5-70 The rover overall width, length, and height can be found using similar equations as above. Plots of historical rover width, length, and height vs. rover total mass are shown next. 227 Figure 5-30. Historical rover width vs. total rover mass Figure 5-31. Historical rover length vs. total rover mass 228 Figure 5-32. Historical rover height vs. total rover mass Next, the wheel actuator motor power can be estimated from historical rover data according to the following set of equations (53): 𝐹 𝑅 = 𝑚 𝑡𝑜𝑡 _𝑟𝑜𝑣𝑒𝑟 𝑔 𝑚𝑜𝑜𝑛 ( 𝑓 0 𝑐𝑜𝑠 𝜃 𝑚𝑎𝑥 _𝑠𝑙𝑜𝑝𝑒 + 𝑠𝑖𝑛 𝜃 𝑚𝑎𝑥 _𝑠𝑙𝑜𝑝𝑒 ) Equation 5-71 where 𝐹 𝑅 is the rover rolling resistance force against a maximum slope (provided by the user and set at 20 degrees in this research). 𝑃 𝑟 = 𝑉 𝑚𝑎𝑥 𝐹 𝑅 Equation 5-72 where 𝑃 𝑟 is the required wheel power to move at velocity 𝑉 𝑚𝑎𝑥 (provided by the user and set at 3 cm/s in this research). 𝑃 𝑤 ℎ𝑒𝑒𝑙 _𝑎𝑐𝑡𝑢𝑎𝑡𝑜𝑟 = 𝑃 𝑟 /𝜂 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 Equation 5-73 where 𝜂 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 is a power transmission efficiency (provided by the user and set at 0.9 in this research). 229 5.3.6.2 Lander Structure Design The purpose of the Lander structural design module is to estimate the total mass of all Lander structure given expected structural loads on the spacecraft. The overall architecture for the Lander Structural design is depicted in Figure 5-33 below. Figure 5-33. Lander Structures Design Module Top-level Architecture The first step is to obtain all the material properties from the Structures MATLAB data structure: primarily the ultimate tensile strength, the compressive yield strength, Young’s Elastic Modulus, the material density, separate safety factors for buckling and yielding, and a desired margin of safety. Next, the total mass from all other Lander subsystems is computed (without Structure, of course), given the subsystem masses estimated by the other subsystem sizing modules. The total lander mass without structures is used later on in sizing the landing legs. Then the dimensions of the Lander payload (i.e. the Rover) are obtained. Inputs Outputs Get material properties Get Lander subsystem masses Get payload mass Get Lander leg parameters Get max thrust acceleration Size RCS tanks support structure Size Propulsion tanks support structure Size Lander deck plate and beams Size Lander thrust structure columns Size Lander engine mounting structure Size Lander legs Sum lander total structural mass 230 Next, the landing leg parameters are obtained. These parameters are: the # of landing legs (4 for this research), Propulsion main engine length, height of a hazardous rock (a user input), the lander leg strut horizontal spacing, and the landing leg slant angles (elevation with respect to horizontal/ground and azimuth/clock angle). In this research, the landing leg elevation angle is assumed to be 70 degrees, whereas the azimuth angle is 45 degrees. Next, the maximum thrust acceleration is determined by taking the total available thrust (for the number of engines solved for in the Descent & Landing sizing module) and dividing by the final landed mass. On the very first system iteration, the final landed mass is taken to be the mass of all other lander subsystems plus the payload, including the rover and any other instrumentation). Otherwise, the final landed mass is obtained from the Descent & Landing solution and nominally includes the rover and its payload plus the lander mass minus the spent propellant mass (consumed in prior orbital Delta-V maneuvers and during de-orbit, descent, and landing). Note that since reserve and unusable propellant are added to the total propellant estimate in the Propulsion design module, this additional propellant will remain on the landed vehicle. 5.3.6.2.1 Sizing RCS tank Support Structure If a reaction control subsystem (RCS) using thrusters was selected by the ADCS design module, the RCS tank support structure is sized. A common MATAB function was developed to size support structure for any tanks, whether RCS or Propulsion. In the case of RCS tanks, the function obtains the number of fuel tanks, number of pressurant tanks, fuel tank mass, pressurant tank mass, as well as fuel mass and pressurant mass. Since the RCS is assumed to be mono-propellant based, the code distinguishes between the regulated and blowdown cases. For 231 this research, a blowdown system is assumed (provided as a user-input), so support structure for each set of RCS blowdown tanks is sized. The RCS tank support structure is modeled as two sets of a pair of cantilevered beams, one pair supporting the top of the tanks and the other supporting the bottom of the tanks, as depicted in Figure 5-34. Figure 5-34. Modeled RCS tank support structure The full tank load is set as the wet tank mass (tank structure + fuel) times the Earth’s gravitational acceleration times the maximum load factor (a user-input and set at 4 in this research). The per beam tank load V, acting transverse to the beams, is split in half and applied to the upper and lower beams. The beam lengths are set to the tank radius plus a small separation distance to the thrust structure. Since the load on each beam acts transverse to the beam, the members are under pure bending. Thus, beam theory can be used to find the required cross-section diameter and thickness to support the bending moment. Tank Top support beams Side View Bottom support beams Top View Pair of beams 232 The margin of safety is the ultimate criteria for structural safety against failure. The margin of safety (%) is defined as: 𝑀𝑆 = 100∗ ( 𝜎 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝜎 𝑑𝑒𝑠𝑖𝑔𝑛 − 1) Equation 5-74 where the allowable load or stress is the material strength against failure (yielding or ultimate failure), and the design load or stress is the limit load or stress times a factor of safety. Beam theory states that the bending stress of a beam under pure bending is: 𝜎 𝑥𝑥 = 𝑀 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝑐 𝐼 Equation 5-75 where 𝑐 is the cross-section distance from the extreme fiber to the neutral axis, and 𝐼 is the cross-section area moment of inertia (with units m 4 ). To save mass, the beams are assumed to have a ring cross-section. The ring cross- section inner diameter can be found from the beam theory stress equation using the appropriate area moment of inertia: 𝑑 𝑖𝑛𝑛𝑒𝑟 = (𝐷 𝑜𝑢𝑡𝑒𝑟 4 − 32𝑀 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝐷 𝑜𝑢𝑡𝑒𝑟 𝜋 𝜎 𝑥𝑥 ) 1/4 Equation 5-76 where 𝐷 𝑜𝑢𝑡𝑒𝑟 can be found by adding a small amount Δ𝑑 (say 1 mm) to the circular cross- section diameter form. 𝐷 𝑜𝑢𝑡𝑒𝑟 = 𝐷 𝑐𝑖𝑟𝑐 + Δ𝑑 𝐷 𝑐𝑖𝑟𝑐 = ( 32𝑀 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝜋 𝜎 𝑥𝑥 ) 1/3 Equation 5-77 In the above equations, the design bending moment is found according to the following equation: 𝑀 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 = 𝐿 𝑏𝑒𝑎𝑚 𝑉 𝑓 𝑆 Equation 5-78 where the bending safety factor 𝑓 𝑆 (a user-input) is assumed to be 2 in this research. 233 The bending stress 𝜎 𝑥𝑥 is the material allowable strength. If the ultimate tensile strength is less than the compressive yield strength, the bending stress is taken as the ultimate strength. Otherwise, the bending stress is taken as the yield strength. To compute the margin of safety, the allowable stress 𝜎 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 is set as the material bending stress. The design stress 𝜎 𝑑𝑒𝑠𝑖𝑔𝑛 is taken as the actual bending stress, computed using Equation 5-75, using the actual bending moment without the factor of safety applied. Given the cross-section dimensions and the beam length, the beam volume can be found. This volume can be multiplied by the material density to get the mass of a single beam. This mass is doubled for the pair of beams at the top and at the bottom of the given RCS tank. 5.3.6.2.2 Sizing Propulsion Tank Support Structure Next, the Propulsion system tank support structure can be sized. The Propulsion system tanks are supported in the same way as the RCS tanks, and so the MASS tool employs the same tank support structure sizing function as that used for the RCS tanks. This tank support structure sizing function is capable of sizing both mono-propellant and bi-propellant systems. Since the Propulsion system focused on in this research is bi-propellant, the tank structures for the fuel tank, oxidizer tank, and pressurant tank are sized. 5.3.6.2.3 Sizing Lander Deck Structure The lander deck must support the weight of the payload (i.e. rover) sitting on top. The maximum lander deck load is then taken as the payload mass times Earth’s gravitational acceleration times the maximum load factor (assumed to be 4 in this research). This load is increased by multiplying by the yield factor of safety (a user input, assumed to be 2). 234 The lander top deck is assumed to consist of 4 beams and a cross-beam, as shown in Figure 5-35. Figure 5-35. Lander top deck support beams The lengths of beams 1 and 3 are taken to be the length of the overlying payload. The lengths of beams 2 and 4 are taken to the width of the overlying payload. The beams are modeled as having uniform linear load (N/m) acting across the entire beam. The load force on each beam is taken as the maximum payload weight (including load factor) divided by 4. Beam theory, assuming fixed-fixed end conditions, is again used to get the maximum bending moment acting on the beams (54). The maximum bending moment is: 𝑀 𝑐 = 𝑤 𝐿 2 24 Equation 5-79 where 𝑤 is the uniform linear load and 𝐿 is the beam length. The beam cross-sectional width h can be found, assuming a solid rectangular beam for simplicity. Top View 4 1 2 3 235 ℎ= ( 6𝑀 𝑐 𝜎 𝑥𝑥 ) 1/3 Equation 5-80 where 𝜎 𝑥𝑥 is the maximum bending stress, taken to be either the material ultimate strength of the yield strength, whichever is smaller. Given the beam cross-sectional width h and the beam length, the beam cross-sectional area and beam volume can be computed. Then the beam mass can be found from the volume and material density. A plate is assumed to sit on top of the beams, to provide a cover, as well as the sides. The area, volume, and mass of the plates is then found, assuming a user-input plate thickness (the plates here are not sized for any structural load). 5.3.6.2.4 Sizing Lander Thrust Structure The main lander structure consists of 4 columns (a user-input) supporting the mass of the payload, top deck beams and top plate. The total load acting on the main structure is then this total mass times Earth’s gravitational acceleration times the maximum load factor. To reduce mass, the columns are assumed to have a ring cross-section. The length of the columns is determined by comparing the largest Propulsion tank diameter with a minimum thrust structure height and selecting the greater of the two. The thrust structure columns are then sized against buckling under compression. The theory of elastic buckling of a column is used. According to this theory, for columns of any end fixity condition, the buckling stress, or column critical stress, is: 𝐹 𝑐𝑟 = 𝑐 𝜋 2 𝐸 ( 𝐿 𝜌 ⁄ ) 2 Equation 5-81 where 𝑐 is the end-fixity coefficient, E is Young’s Modulus, L is the column length, and 𝜌 = √𝐼 /𝐴 is the radius of gyration of the column cross-section. 236 Using a ring cross section, the inner radius can be solved for as: 𝑑 𝑖𝑛𝑛𝑒𝑟 = (𝐷 𝑜𝑢𝑡𝑒𝑟 4 − 64𝑓 𝑠 _𝑏𝑢𝑐𝑘𝑙𝑖𝑛𝑔 𝑃 𝐿 2 𝑐 𝜋 3 𝐸 ) 1/4 Equation 5-82 where 𝑃 is the axial load on the member, 𝐿 is the column length, and 𝑓 𝑠 _𝑏𝑢𝑐𝑘𝑙𝑖𝑛𝑔 is the buckling factor of safety (a user-input and assumed to be 2 in this research). The outer ring diameter can be found from: 𝐷 𝑜𝑢𝑡𝑒𝑟 = 𝐷 𝑐𝑖𝑟𝑐 + Δ𝑑 𝐷 𝑐𝑖𝑟𝑐 = ( 64𝑓 𝑠 _𝑏𝑢𝑐𝑘𝑙𝑖𝑛𝑔 𝑃 𝐿 2 𝑐 𝜋 3 𝐸 ) 1/4 Equation 5-83 where a small value of 1 mm is added to the 𝐷 𝑐𝑖𝑟𝑐 to avoid computing a 𝑑 𝑖𝑛𝑛𝑒𝑟 of zero. Given the dimensions of the ring cross-section, the cross-sectional area, area moment of inertia, and radius of gyration can be found. For the case of a vertical column, there is only an axial load. Thus, the axial member stress can be found as: 𝑓 𝑐 = 𝑃 /𝐴 𝑐𝑠 Equation 5-84 Next, a check against yielding before buckling is done. The yield margin is safety is found as: 𝑀 𝑆 𝑦𝑖𝑒𝑙𝑑 = 100∗ ( 𝐹 𝑐𝑦 𝑓 𝑐 − 1) Equation 5-85 where 𝐹 𝑐𝑦 is the material compressive yield strength. If the computed yield margin of safety is less than the desired value (a user-input and assumed to be 200% in this research), the cross- sectional area is re-sized using Newton’s method to achieve the desired margin against yielding. In any case, the volume of the column is found, and with the material density the column mass can be found. Then the total thrust structure mass can be found for all 4 columns. 237 5.3.6.2.5 Sizing Lander Engine Mounting Structure The Propulsion main engines must themselves be mounted to the lander, and this mounting structure must be sized to support the load of the engines. Figure 5-36 below depicts the engine mounting structure, consisting of 4 vertical columns and an engine plate. Figure 5-36. Engine mounting structure (shown in gray) The load factor applied to the loads in this structure sizing routine is the maximum of the maximum load factor acceleration (user-provided max load factor times g 0) and the maximum thrust acceleration. The maximum thrust acceleration is the total thrust from all engines divided by the final landed mass. First the engine mount plate is sized according to plate theory. The length and width of the plate are determined by the dimensions required to support the number of engines on the lander (as determined by the Descent & Landing design module). The plate load is then found as the total load from all the engines (with the maximum load acceleration applied), times a yield Engine mounting struts Engine mounting plate 238 factor of safety, divided by the engine plate area. The material stress is taken as the ultimate tensile stress. Then a basic plate theory equation is used to size the plate thickness (55). 𝑡 𝑝𝑙𝑎𝑡𝑒 = √ 1 𝜎 ( 𝑐 2 𝑝 ∗ 𝑚𝑖𝑛 ( 𝐿 𝑥 ,𝐿 𝑦 ) ) Equation 5-86 where 𝑐 2 is an end-fixity coefficient, p is the plate stress from the load (assumed to be uniform across the plate), and 𝐿 𝑥 and 𝐿 𝑦 are the plate dimensions. Given the plate thickness, the volume can be found, and hence, with the material density, the mass. The vertical engine mounting struts are then sized using the same method (elastic buckling of a column) as used for the lander thrust structure columns (see Section 5.3.6.2.4). 5.3.6.2.6 Sizing Lander Legs Each landing leg is treated as an angled column with 2 support struts. with respect to the ground (at a user-input elevation angle of 70 degrees) and clocked with respect to the lander X-axis (at a user-input 45 degrees). Initially, 3 landing leg design configurations were under consideration: 1. Vertical columns 2. Angled columns 3. Single angled column with 2 support struts (3-member leg) Ultimately, the 3-member leg configuration was selected for use in this research, as depicted in Figure 5-37. 239 Figure 5-37. 3-member landing leg structure For the purposes of this research, the loads on the landing legs were assumed to be equal. That, since there are 4 legs, the load on each leg was taken as the total load divided by 4. This assumes the center of mass of the vehicle is along the body centerline. A more in-depth analysis would consider the off-center center of mass and use a method such as the Integrated Force Method (56) to solve Navier’s Table Problem to identify the loads operating on each of the 4 legs, and then use the worst-case load to size all legs. The total load is based on the total mass supported by the legs times the maximum load factor. The total mass supported by the legs was taken as the sum of the rover payload, the lander top deck beam and plates, the lander thrust structure, the RCS tank support structure, the Propulsion tank support structure, the engine mounting structure (plate + struts), and the total lander mass without structure. The landing leg height must consider the length of the engine nozzles, the length of the engine mounting struts, and the height of rocks considered hazardous for this mission. The rock hazard height was assumed to be 0.35 m based on research from NASA’s ALHAT project Primary leg AB Support struts AC (AD connected on adjacent edge of deck) b 240 (Autonomous Landing and Hazard Avoidance Technology) (50). Thus, the leg height can be obtained by adding the length of the nozzles, the length of the engine mounting struts, and the rock hazard height. Given this, and the elevation angle of the angled leg, the lander leg length can be found. This leg length can then be used in sizing the leg as a beam-column. The lengths of the 2 leg support struts AC and AD can be determined by the geometry of the primary landing leg structure AB and the spacing b between the primary leg and the support strut at the base of the lander (see Figure 5-37). The elevation and azimuth of struts AC and AD can also be found by simple geometry. Next the ground reaction load forces acting on the legs can be found using the method of joints. The member force on each leg member is then the negative of the ground reaction force. The primary leg AB can be sized as under compression (positive axial force) to prevent buckling using a similar procedure as outlined in Section 5.3.6.2.4. The support struts AC and AD will both be in tension (negative axial force), so a different procedure is used to size those members against rupture. The support struts are assumed here to use solid circular cross- section. The support struts can be sized by equating the member load (multiplied by a factor of safety) with the rupture load (the member cross-sectional area times the material ultimate tensile strength), and solving for diameter: 𝐷 𝑐𝑖𝑟𝑐 = √ 4𝑓 𝑠 𝑇 𝜋 𝐹 𝑡𝑢 Equation 5-87 where 𝑇 is the member tensile force (absolute value). Given the dimensions of the support struts and the material density, their masses can be computed. 241 Once the total mass of each leg is determined, the total mass of all legs on the lander can be estimated. Finally, the mass of all lander structural components are added together, along with the total mass of all other lander subsystems, to get the total lander structure mass. 5.3.7 Power Design Module The purpose of the Power design module is to estimate the power load and heat load in each mission event, identify the peak power load out of all events, and then to size the power subsystem for a given spacecraft element based on the power source technology specified in the inputs. In this research, each spacecraft element is assumed to have its own independent power system. The overall architecture of the Power design module is depicted in Figure 5-38 below. Figure 5-38. Power Design Module Top-level Architecture Inputs Get required power per component from other subsystems Estimate power load per mission event using component on/off flags Get overall peak sunlight power, eclipse power, and average power Size S/C power subsystem given power system type Size solar array and batteries Size radioisotope power system (RPS) and batteries Size fuel cell system and batteries Outputs 242 The first step is to obtain the required component power from the other subsystems, in addition to the peak payload power from the science instruments and any other instrumentation packages included on the spacecraft. Note that the heat output per component is set equal to the power dissipation of that component. For Telecom, the power required for transponders, transceivers, and RF amplifiers are obtained from the Telecom MATLAB data structure. For CDS, the overall power requirement is obtained. For ADCS, the required power for each sensor (IMU, star tracker, sun sensors) and actuators (reaction wheels, RCS thrusters) are obtained. For Propulsion, the required power to operate the engines and associated valves and electronics (if applicable) is obtained. For Thermal, the overall thermal power requirement is obtained. For Structures, no power requirement is currently assumed. Next the total power load per mission event is estimated. This is accomplished by setting on/off flags for each power component based on which mission events (or mode) they typically operate in. For example, the science payload on the rover operates during Science mode on the lunar surface, Telecom components operate during communication events, ADCS sensors are typically operating all the time, and Propulsion components operate during Delta-V events. Given the on/off flags per event, the total power requirement and heat load in sunlight and eclipse in each event are obtained by adding the contribution from all components, which are multiplied by the on/off flags (a 1 or a 0). Next the peak power in sunlight and eclipse over all mission events are obtained. These are used to determine an average power requirement and a peak power delta requirement (the difference between peak sunlight power and the average power). The maximum duration in 243 sunlight and eclipse, based on the trajectory geometry, are then obtained. This is used to obtain the fraction of time in sunlight over the trajectory. The minimum altitude to the Earth is then used to determine the solar visibility factor, a parameter used in estimating the Earth’s albedo radiation incident on the spacecraft for solar array sizing. Finally, given the peak power requirements, the power system is designed as determined by the power system type. The following power system types were considered in this research:  Solar array + batteries  Radioisotope + batteries  Fuel cell + batteries In the configurations generated for this research, the lander is specified has using solar arrays, whereas the rover can use any of the above 3 options. The sizing procedures for the 3 options are described in the following sections. 5.3.7.1 Battery Sizing If a battery is specified for the spacecraft, the first step is to obtain the required inputs for the battery technology the user selected: battery depth of discharge, discharge efficiency, cell discharge voltage, and specific energy (W-hr/kg) from the battery database, as well as the battery path efficiency. An example battery database is shown in Table 5-31 below. Table 5-31. Secondary Battery Database Chemistry Depth of Discharge (%) Transmission Efficiency (%) Cell Discharge Voltage (V) Specific Energy (W-hr/kg) Nickel Cadmium 40 94 1.25 40 Nickel Hydrogen (NiH 2) 60 94 1.25 45 244 Chemistry Depth of Discharge (%) Transmission Efficiency (%) Cell Discharge Voltage (V) Specific Energy (W-hr/kg) Nickel Metal Hydride (NiMH) 40 94 1.25 50 Li-ion 25 94 3.5 90 Lithium-polymer 25 94 3.5 100 Silver Zinc 25 94 1.5 130 Next, the proper power load is obtained. Assuming the battery is a secondary (rechargeable) battery, the peak eclipse power load is selected if eclipses are present along the trajectory (as determined by the JPL SPICE toolkit); otherwise the peak burst power is used. Next the battery energy capacity (W-hr) is sized according to the following equation (36): 𝐸 = 𝑃 𝑙𝑜𝑎𝑑 𝑡 𝑑𝑖𝑠𝑐 ℎ𝑎𝑟𝑔𝑒 𝑓 𝐷𝑂𝐷 𝜂 𝑑𝑖𝑠𝑐 ℎ𝑎𝑟𝑔𝑒 _𝑒𝑓𝑓 Equation 5-88 where 𝑡 𝑑𝑖𝑠𝑐 ℎ𝑎𝑟𝑔𝑒 is the discharge duration in hours, 𝑓 𝐷𝑂𝐷 is the depth of discharge (the fraction of total battery capacity removed during a discharge period), and 𝜂 𝑑𝑖𝑠𝑐 ℎ𝑎𝑟𝑔𝑒 _𝑒𝑓𝑓 is the discharge efficiency. The battery charge capacity (A-hr) is determined by the following equation: 𝐶 = 𝐸 /𝑉 𝑏𝑢𝑠 Equation 5-89 where 𝑉 𝑏𝑢𝑠 is the spacecraft bus voltage. A spacecraft’s power system bus voltage (usually DC) can be selected from the following standardized voltage levels: 28 V, 50 V, 70 V, 100 V, 120 V, and 160 V (42). Early spacecraft with small power loads used 28 V. The system bus voltage is typically selected based on the need to supply the required power at a reasonable current level (otherwise resistive loss in conductors reduces system efficiency). In the case of solar arrays, at voltages beyond 160 V undesirable interactions occur between exposed conductors and space plasma. The lunar surface, however, 245 which has no atmosphere, there is no space plasma; thus high-voltage power systems can safely operate there. On the other hand, out-gassing from adjacent equipment can create a local atmosphere that may be susceptible to high-voltage breakdown (42). The maximum expected current per discharge is found as: 𝐼 𝑚𝑎𝑥 = 𝐶 /𝑡 𝑑𝑖𝑠𝑐 ℎ𝑎𝑟𝑔𝑒 Equation 5-90 Using this as the battery string current (each battery string has the same current as one individual battery cell in that string), the total number of battery cells, number of parallel strings, and number of cells per string can be determined per the following set of equations. 𝐼 𝑙𝑜𝑎𝑑 = 𝑃 𝑙𝑜𝑎𝑑 /𝑉 𝑏𝑢𝑠 𝑁 𝑐𝑒𝑙𝑙𝑠 _𝑝𝑒𝑟 _𝑠𝑡𝑟𝑖𝑛𝑔 = 𝑐𝑒𝑖𝑙 ( 𝑉 𝑏𝑢𝑠 /𝑉 𝑐𝑒𝑙𝑙 ) 𝑁 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 𝑐𝑒𝑖𝑙 ( 𝐼 𝑙𝑜𝑎𝑑 /𝐼 𝑠𝑡𝑟𝑖𝑛𝑔 ) 𝑁 𝑐𝑒𝑙𝑙𝑠 = 𝑁 𝑐𝑒𝑙𝑙𝑠 _𝑝𝑒𝑟 _𝑠𝑡𝑟𝑖𝑛𝑔 𝑁 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 Equation 5-91 Finally, the battery mass can be estimated using the energy capacity 𝐸 and the specific energy (W-hr/kg) rating 𝜖 of the particular battery cell technology. 𝑚 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 = 𝐸 /𝜖 Equation 5-92 One final note about the batteries is that they do not operate well at very low temperatures. For example, Li-ion battery performance is extremely poor below -40 C, due to higher viscosity (and possible freezing) of the electrolyte. For a battery required on the rover operating in a permanently-shadowed region at the lunar South Pole, the thermal design would be an area for future work. 246 5.3.7.2 Solar Array Sizing The first step in sizing the solar arrays is to get the solar cell inputs: peak power load in sun and eclipse, average power load, delta peak power load, the duration in sunlight along the trajectory, the duration in eclipse, the duration for the delta peak power load, the total duration of the trajectory, the solar visibility factor, the shadowing factor (% of time in sunlight), battery path efficiency (if batteries are also present), solar array path efficiency, bus voltage, as well as solar cell specific parameters (obtained from the solar cell database). The solar cell database is shown below in Table 5-32 for reference. Table 5-32. Solar Cell Database Solar Cell Type Manufacturer BOL Cell Efficiency (%) Si High Efficiency unknown 17 GaAs/Ge Spectrolab 19 GaInP2/GaAs on Ge Dual Junction Spectrolab 21.8 GaInP2/GaAs/Ge Triple Junction Spectrolab 25.1 GaInP2/GaAs/Ge Triple Junction Spectrolab 29.3 Next, the incident solar radiation flux (W/m 2 ) on the spacecraft, and the albedo reflection and the thermal radiation fluxes from the Earth are computed. The solar radiation flux at a distance R from the Sun can be obtained from the following equation. 𝐽 𝑠𝑜𝑙𝑎𝑟 = 𝑃 𝑠𝑢𝑛 4𝜋 𝑅 2 Equation 5-93 The body albedo flux can be obtained from: 𝐽 𝑎𝑙𝑏𝑒𝑑𝑜 = 𝑎 𝐹 𝑠𝑜𝑙𝑎𝑟 𝐽 𝑠𝑜𝑙𝑎𝑟 Equation 5-94 where 𝑎 is the Earth’s albedo, and 𝐹 𝑠𝑜𝑙𝑎𝑟 is the solar visibility factor mentioned earlier. The Earth’s thermal radiation flux can be obtained from: 247 𝐽 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 = 234( 𝑅 𝑒𝑓𝑓 𝑅 ) 2 Equation 5-95 where 𝑅 𝑒𝑓𝑓 is the Earth effective radiating radius, and 𝑅 is the distance of the spacecraft from the center of the Earth. The solar flux received by the solar array can then be found as: 𝑄 𝑠𝑜𝑙𝑎𝑟 = 𝐽 𝑠𝑜𝑙 𝑎 𝑟 𝛼 Equation 5-96 where 𝛼 is the solar array absorptance. The Earth thermal flux received by the solar array can then be found as: 𝑄 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 = 𝐽 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 𝜖 sin ( 𝜃 𝐸𝑎𝑟𝑡 ℎ ) 2 Equation 5-97 where 𝜃 𝐸𝑎𝑟𝑡 ℎ is the Earth’s angular radius as viewed from the spacecraft. The Earth albedo flux received by the solar array can be found as: 𝑄 𝑎𝑙𝑏𝑒𝑑𝑜 = 𝐽 𝑎𝑙𝑏𝑒𝑑𝑜 𝛼 𝐾 𝑎 sin( 𝜃 𝐸𝑎𝑟𝑡 ℎ ) 2 Equation 5-98 where 𝐾 𝑎 is the albedo correction factor described in Equation 5-61. The solar power generated can then be computed as: 𝑄 𝑠𝑜𝑙𝑎𝑟 _𝑝𝑜𝑤𝑒𝑟 _𝑔𝑒𝑛 = 𝐽 𝑠𝑜𝑙𝑎𝑟 𝜂 𝑐𝑒𝑙𝑙 Equation 5-99 where 𝜂 𝑐𝑒𝑙𝑙 is the solar cell efficiency. The solar array operating temperature can then be computed using the Stefan- Boltzmann equation: 𝑇 𝑜𝑝 _𝑠𝑜𝑙𝑎𝑟 _𝑎𝑟𝑟𝑎𝑦 = ( 𝑄 𝑡𝑜𝑡 𝜎𝜖 ) 1/4 Equation 5-100 In the above equation, 𝑄 𝑡𝑜𝑡 = 𝑄 𝑠𝑜𝑙𝑎𝑟 + 𝑄 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 + 𝑄 𝑎𝑙𝑏𝑒𝑑𝑜 + 𝑄 𝑠𝑜𝑙𝑎𝑟 _𝑝𝑜𝑤𝑒𝑟 _𝑔𝑒𝑛 . Solar arrays are subject to various sources of degradation. Solar array design can be affected by charged particles trapped in a planet’s magnetic field. In the case of a lunar rover mission, the solar array would have to operate partly within Earth’s Van Allen radiation belt for 248 some duration and partly outside (near the Moon). As the Moon has a negligible magnetic field, however, solar charged particles reach the surface and can degrade any solar arrays operating there (for the lunar rover). In addition, a higher micrometeoroid impact rate than in low Earth orbit can result in increased damage to solar arrays. Given the solar cell inputs, solar cell operating temperature, and the solar array degradation rates (radiation degradation, miscellaneous degradation, and thermal degradation), the solar array can be sized. The solar array degradation factors can be obtained as follows: 𝑓 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 _𝑙𝑜𝑠𝑠 = 1− 𝑟 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 ( 𝑇 𝑜𝑝 _𝑠𝑜𝑙𝑎𝑟 _𝑎𝑟𝑟𝑎𝑦 − 𝑇 𝑟𝑒𝑓 ) Equation 5-101 where 𝑟 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 is the solar array thermal degradation rate (%/yr expressed as a fraction). The inherent degradation can be found from: 𝑓 𝑖𝑛 ℎ𝑒𝑟𝑒𝑛𝑡 _𝑙𝑜𝑠𝑠 = 𝑓 𝑎𝑠𝑠𝑒𝑚𝑏𝑙𝑦 𝑓 𝑑𝑖𝑜𝑑𝑒 _𝑙𝑜𝑠𝑠 𝑓 𝑝𝑎𝑐𝑘𝑖𝑛𝑔 𝑓 𝑡 ℎ𝑒𝑟𝑚𝑎𝑙 _𝑙𝑜𝑠𝑠 𝑓 𝑠 ℎ𝑎𝑑𝑜𝑤𝑖𝑛𝑔 Equation 5-102 where the assembly loss, diode loss, and packing factor are solar cell properties, and 𝑓 𝑠 ℎ𝑎𝑑𝑜𝑤𝑖𝑛𝑔 is the fraction of the trajectory time spent in eclipse. The radiation degradation, miscellaneous degradation, and mission life degradation can be found from the following set of equations: 𝑓 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 = ( 1− 𝑟 𝑟𝑎𝑑 ) 𝑡 𝑚𝑖𝑠𝑠𝑖𝑜𝑛 Equation 5-103 where 𝑟 𝑟𝑎𝑑 is the radiation degradation rate and 𝑡 𝑚𝑖𝑠𝑠𝑖𝑜𝑛 is the trajectory duration in years. 𝑓 𝑚𝑖𝑠𝑐 = ( 1 − 𝑟 𝑚𝑖𝑠𝑐 ) 𝑡 𝑚𝑖𝑠𝑠𝑖𝑜𝑛 Equation 5-104 where 𝑟 𝑚𝑖𝑠𝑐 is the miscellaneous degradation rate. 𝑓 𝑙𝑖𝑓𝑒 _𝑑𝑒𝑔𝑟𝑎𝑑 = 𝑓 𝑟𝑎𝑑𝑖 𝑎 𝑡𝑖𝑜𝑛 𝑓 𝑚𝑖𝑠𝑐 Equation 5-105 The solar cell power density can then be found using the solar intensity flux times the solar cell efficiency. 249 𝑃 𝑐𝑒𝑙𝑙 _𝑖𝑑𝑒𝑎𝑙 = 𝐽 𝑠𝑜𝑙𝑎𝑟 𝜂 𝑐𝑒𝑙𝑙 Equation 5-106 Given this, the cell beginning-of-life power density can be found as: 𝑃 𝑐𝑒𝑙𝑙 _𝐵𝑂𝐿 = 𝑃 𝑐𝑒𝑙𝑙 _𝑖𝑑𝑒𝑎𝑙 𝑓 𝑖𝑛 ℎ𝑒𝑟𝑒𝑛𝑡 cos ( 𝛼 𝑖𝑛𝑐 ) Equation 5-107 where 𝛼 𝑖𝑛𝑐 is the solar energy incidence angle. The solar cell power density at the end of the trajectory can then be obtained from: 𝑃 𝑐𝑒𝑙𝑙 _𝑙𝑖𝑓𝑒 = 𝑃 𝑐𝑒𝑙𝑙 _𝐵𝑂𝐿 𝑓 𝑙𝑖𝑓𝑒 _𝑑𝑒𝑔𝑟𝑎𝑑 Equation 5-108 Next, the power load to use for sizing the array is selected. If eclipses are present during cruise along the trajectory, and a battery is included in the power system, the power load is: 𝑃 𝑙𝑜𝑎𝑑 = ( 𝑃 𝑝𝑒𝑎𝑘 _𝑠𝑢𝑛 𝑡 𝑠𝑢𝑛𝑙𝑖𝑔 ℎ𝑡 𝜂 𝑠𝑜𝑙𝑎𝑟 _𝑝𝑎𝑡 ℎ_𝑒𝑓𝑓 + 𝑃 𝑝𝑒𝑎𝑘 _𝑒𝑐𝑙𝑖𝑝𝑠𝑒 𝑡 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 𝜂 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 _𝑝𝑎𝑡 ℎ_𝑒𝑓𝑓 ) 1 𝑡 𝑠𝑢𝑛𝑙𝑖𝑔 ℎ𝑡 Equation 5-109 Here, the solar array must provide power during sunlight and charge the batteries for eclipses. If there are no eclipses and a battery is still present, the power load is the average power plus the delta peak power divided by the battery path efficiency: 𝑃 𝑙𝑜𝑎𝑑 = 𝑃 𝑎𝑣𝑔 + Δ𝑃 𝑝𝑒𝑎𝑘 𝜂 𝑠𝑜𝑙𝑎𝑟 _𝑝𝑎𝑡 ℎ_𝑒𝑓𝑓 Equation 5-110 The solar array path efficiency depends on the power control method. There are two main power control techniques for solar array generated power (36):  Peak power tracking (PPT): This is a non-dissipative method that draws the exact power required to support the power load (up to a maximum of the peak array power). This uses 4-7% of the total spacecraft power.  Direct energy transfer (DET): This method dissipates excess power not required to support the power loads. This dissipation can be done at the arrays or through external shunt resistors. Such a system is very efficient and low-mass. The solar array path efficiencies for the above methods are summarized below: 250 Table 5-33. Power Path Efficiencies by Power Control Method Power Control Method Solar Array Load Power Path Efficiency Battery Load Path Efficiency Peak Power Tracking 0.6 0.8 Direct Energy Transfer 0.65 0.85 The solar array area can then be found from the power load (W) and the solar cell power density (W/m 2 ): 𝐴 𝑠𝑜𝑙𝑎𝑟 _𝑎𝑟𝑟𝑎𝑦 = 𝑃 𝑙𝑜𝑎𝑑 /𝑃 𝑐𝑒𝑙𝑙 _𝑙𝑖𝑓𝑒 Equation 5-111 The solar array number of cells, number of strings, and number of parallel strings can be found in a similar manner as done for the batteries. Finally, the solar array mass can be found using the solar array power load and the solar cell specific power 𝑝 (W/kg). 𝑚 𝑠𝑜𝑙𝑎𝑟 _𝑎𝑟𝑟𝑎𝑦 = 𝑃 𝑙𝑜𝑎𝑑 𝑝 Equation 5-112 The solar cell specific power is a function of the solar array structural packaging and deployment method, as summarized in the following table. Table 5-34. Solar array specific power options Solar array structure type Specific Power (W/kg) Flexible Fold-up Blankets 22.2 Rigid panel 26.6 Flexible Roll-up Blankets 47.4 In this research, the flexible fold-up blanket method is assumed for both the rover and the lander. 251 5.3.7.3 RPS sizing The first step in sizing the radioisotope power system is to obtain the peak power loads (in sunlight, eclipse, the average power, the delta peak power) and the durations in sunlight and eclipse along the trajectory. If the system is equipped with a battery, the battery path efficiency is obtained from the inputs. Next, the properties of the specific RPS system (such as the MMRTG and Advanced Stirling Reactor Generators) are obtained. These properties are parameters such as the power delivered per RPS module, the hot and cold sink temperatures, the system efficiency, the radiator emissivity, the GPHS (general purpose heat source) heat generation, the radiator sink temperature, and the number of radiator fins. An example table containing radioisotope power systems is given below in Table 5-35. Table 5-35. Radioisotope Power System Database RPS Type BOL Net Electrical Power (W) Hot-end Temperature (deg C) Cold-end Temperature (deg C) # GPHS modules System Efficiency (%) Total Mass (kg) MMRTG 125 538 210 8 6.3 44.2 SRG110 116 650 80 2 23.2 32.5 ASRG-650 143 650 90 2 28 20.2 ASRG-850 160 850 90 2 32 19 Given this information, the RPS can be sized. This involves first getting the actual power load. If there is a battery and it operates during eclipses only, the power load can be found as: 𝑃 𝑙𝑜𝑎𝑑 = (𝑃 𝑝𝑒𝑎𝑘 _𝑠𝑢𝑛 𝑡 𝑠𝑢𝑛𝑙𝑖𝑔 ℎ𝑡 + 𝑃 𝑝𝑒𝑎𝑘 _𝑒𝑐𝑙𝑖𝑝𝑠𝑒 𝑡 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 + Δ𝑃 𝑝𝑒𝑎𝑘 𝑡 Δ𝑃 𝜂 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 _𝑝𝑎𝑡 ℎ_𝑒𝑓𝑓 ) 1 𝑡 𝑡𝑜𝑡𝑎𝑙 Equation 5-113 where 𝑡 𝑡𝑜𝑡𝑎𝑙 is the duration in both sunlight and eclipse. Otherwise, the power load is just the peak power load (the greater of the sunlight or eclipse power loads). 252 The RPS heat input can be found from the delivered power per RPS module and the system efficiency 𝜂 𝑟𝑝𝑠 . 𝑄 ℎ𝑒𝑎𝑡 = 𝑃 𝑟𝑝𝑠 _𝑚𝑜𝑑𝑢𝑙𝑒 𝜂 𝑟𝑝𝑠 Equation 5-114 The RPS waste heat is then just: 𝑄 𝑤𝑎𝑠𝑡𝑒 = 𝑄 ℎ𝑒𝑎𝑡 − 𝑃 𝑟𝑝𝑠 _𝑚𝑜𝑑𝑢𝑙𝑒 Equation 5-115 The RPS radiator area can be found from the Stefan-Boltzmann equation: 𝐴 𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 = 𝑄 𝑤𝑎𝑠𝑡𝑒 𝜎𝜖 ( 𝑇 𝑐𝑜𝑙𝑑 _𝑠𝑖𝑛𝑘 − 𝑇 𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 _𝑠𝑖𝑛𝑘 ) Equation 5-116 where 𝜖 is the radiator emissivity. The number of GPHS modules required can be found from dividing the total RPS heat generated by the heat output per GPHS module. 𝑁 𝑔𝑝 ℎ𝑠 = 𝑐𝑒𝑖𝑙 ( 𝑄 ℎ𝑒𝑎𝑡 𝑄 𝑔𝑝 ℎ𝑠 ) Equation 5-117 The number of RPS modules required depends on the total power load that the RPS is required to support divided by the power capability per RPS module. 𝑁 𝑟𝑝𝑠 = 𝑐𝑒𝑖𝑙 ( 𝑃 𝑙𝑜𝑎𝑑 𝑃 𝑟𝑝𝑠 _𝑚 𝑜𝑑𝑢𝑙𝑒 ) Equation 5-118 The actual delivered power is then the number RPS modules times the delivered power per RPS module. And the total waste heat can be found from the number of RPS modules times the per module waste heat. 5.3.7.4 Fuel cell sizing The first step in sizing the fuel cells is to obtain the peak power loads and durations in sunlight and eclipse. If a battery is present, the battery path efficiency is obtained. Next, the fuel 253 cell properties are obtained for the specific fuel cell type in use (either H 2/O 2 or H 2/H 2O 2). These properties include parameters such as the sizing method (minimizing mass is used in this research vs. minimizing power density), the fuel cell operating temperature, the limiting current, the exchange current, and fuel crossover current, the internal resistance, the fuel cell area, the design factor (kg/m 2 ), the chemical parameters, the reaction parameters, and the tank parameters. Further discussion of these parameters is provided in Appendix B2: Power, under the Fuel Cells heading. Given these inputs, the fuel cell system sizing procedure can be followed. The first step is to obtain the reaction parameters: the number of moles of reactants (fuel and oxidizer) and product (water) in the fuel cell reaction. Next, the fuel cell reaction enthalpy and entropy for the reactants and products are obtained, followed by the reactant and product tank temperatures and pressures. The coefficients of specific heat at constant pressure (c p) for the reactants are obtained from the chemical parameter inputs. Next the number of electrons for reactants and products is obtained, followed by the molar mass (g/mol) of the reactants and product. Given all this information, the reaction enthalpy and entropy can be calculated at the system operating temperature. Then the Gibbs free energy at the operating temperature can be found. Finally, the equilibrium cell potential at the operating temperature and pressure can be computed per the Nernst equation (see Equation 10-24 in the Appendix). Next, the actual power load is obtained. If the system is equipped with a battery, the power load can be found as: 254 𝑃 𝑙𝑜𝑎𝑑 = (𝑃 𝑝𝑒𝑎𝑘 _𝑠𝑢𝑛 𝑡 𝑠𝑢𝑛𝑙𝑖𝑔 ℎ𝑡 + 𝑃 𝑝𝑒𝑎𝑘 _𝑒𝑐𝑙𝑖𝑝𝑠𝑒 𝑡 𝑒𝑐𝑙𝑖𝑝𝑠𝑒 + Δ𝑃 𝑝𝑒𝑎𝑘 𝑡 Δ𝑃 𝜂 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 _𝑝𝑎𝑡 ℎ_𝑒𝑓𝑓 ) 1 𝑡 𝑡𝑜𝑡𝑎𝑙 Equation 5-119 Otherwise, the power load is just the maximum of the sunlight or eclipse power loads. Once the power load and reaction calculations are complete, the optimal fuel cell system can be sized. The mass minimization method is used in this research. In effect, the sizing goal is to find the operating voltage and current per cell that result in the minimum overall total fuel cell system mass. To obtain the minimum mass fuel cell system, the fuel cell design space is searched by computing the fuel cell operating voltage for a range of current densities (A/cm 2 ) (from zero up to the limiting current density) using the fuel cell polarization curve (57). Once the cell operating voltage over the range of current densities is obtained, the minimum overall fuel cell system mass and associated parameters can be found. The calculations to accomplish this are described next. Essentially, the cell operating voltage is the equilibrium cell potential minus the voltage activation loss, concentration loss, and ohmic (resistive) loss. The equations to calculate these losses are described in Appendix B2: Power. Next, the per cell operating current is computed as the current density 𝑖 times the cell area. 𝐼 𝑐𝑒𝑙𝑙 _𝑜𝑝 = 𝑖 𝐴 𝑐𝑒𝑙𝑙 Equation 5-120 This is followed by computing the number of fuel cells required to deliver the total power required at the current fuel cell power. 255 The mass flow rate of reactants and products are obtained using Faraday’s law of an electrochemical reaction. The molar flow rate N ̇ i (mol/sec) is found for fuel, oxidizer, and product from Faraday’s law as: N ̇ i = 𝐼 𝑐𝑒𝑙𝑙 _𝑜𝑝 𝑛 𝑒 𝐹 Equation 5-121 where 𝐼 𝑐𝑒𝑙𝑙 _𝑜𝑝 is the cell operating current, n e is the number of electrons for each reactant or the product, and F is Faraday’s constant (96485.3 Coulombs/mol). From this, the mass flow rate (g/sec) of the fuel, oxidizer, and product can be computed using the fuel, oxidizer, or product molar mass 𝔐 i (g/mol). m ̇ i = N ̇ i 𝔐 i Equation 5-122 Then the amount of fuel and oxidizer mass required can be found by multiplying the mass flow rate times the lifetime (i.e. the required operating duration). In this research, the required operating lifetime is take as the combined duration in sunlight and eclipse. m i = m ̇ i Δt Equation 5-123 Note that the sum of the mass flow rates of fuel and oxidizer must equal the mass flow rate of the product. This requires correctly identifying the number of electrons involved in species consumption or production. The total mass of fuel or oxidizer required for the entire fuel stack can then be expressed as: m i,tot = N cells m i Equation 5-124 where N cells is the total number of cells required to deliver the total system voltage and current, and the subscript i denotes the species (fuel or oxidizer). 256 Next, the power density 𝑃 𝑎 (W/cm 2 ) of the fuel cell can then be found from the cell operating voltage and the current density 𝑖 (A/cm 2 ): 𝑃 𝑎 = 𝐸 𝑐𝑒𝑙𝑙 _𝑜𝑝 𝑖 Equation 5-125 Then the specific mass (kg/W) can be calculated from: 𝑚 𝑠 = 𝑓 𝑑𝑒𝑠𝑖𝑔𝑛 𝑃 𝑎 Equation 5-126 where 𝑓 𝑑𝑒𝑠𝑖𝑔𝑛 is the fuel cell design factor (kg/m 2 ) obtained from the inputs. Then the specific power (W/kg) can be found as the inverse of the specific mass: 𝑝 = 1/𝑚 𝑠 Equation 5-127 The per cell power can then be found as: 𝑃 𝑐𝑒𝑙𝑙 = 𝐼 𝑐𝑒𝑙𝑙 _𝑜𝑝 𝐸 𝑐𝑒𝑙𝑙 _𝑜𝑝 Equation 5-128 The per fuel cell mass can be obtained by multiplying the specific mass 𝑚 𝑠 times the per cell power: 𝑚 𝑐𝑒𝑙𝑙 = 𝑃 𝑐𝑒𝑙𝑙 𝑚 𝑠 Equation 5-129 The fuel cell stack mass can be computed by multiplying the number of required fuel cells by the per cell mass. 𝑚 𝑠𝑡𝑎𝑐𝑘 = 𝑁 𝑐𝑒𝑙𝑙𝑠 𝑚 𝑐𝑒𝑙𝑙 Equation 5-130 The total fuel cell system mass is defined to be the sum of the mass of the stack of fuel cells needed to deliver the required power plus the total required reactant mass for the life of the mission. 𝑚 𝑡𝑜𝑡 _𝑓𝑢𝑒𝑙 _𝑐 𝑒 𝑙𝑙 _𝑠𝑦𝑠 = 𝑚 𝑓𝑢𝑒𝑙 _𝑐𝑒𝑙𝑙 _𝑠𝑡𝑎𝑐𝑘 + 𝑚 𝑡𝑜𝑡 ,𝑓𝑢𝑒𝑙 + 𝑚 𝑡𝑜𝑡 ,𝑜𝑥𝑖𝑑𝑖𝑧𝑒𝑟 Equation 5-131 257 Both the fuel cell stack mass and the total amount of fuel and oxidizer all depend on the total number of fuel cells. The total number of fuel cells itself depends on the number of cells in series (defined as a string of cells) to deliver the required total system bus voltage and the total number of parallel strings to deliver the required total system current. Recall the following expressions for computing the total number of “cells” required for any power system: 𝑁 𝑐𝑒𝑙𝑙𝑠 _𝑝𝑒𝑟 _𝑠𝑡𝑟𝑖𝑛𝑔 = 𝑉 𝑡𝑜𝑡 /𝑉 𝑐𝑒𝑙𝑙 Equation 5-132 where 𝑉 𝑐𝑒𝑙𝑙 for a fuel cell is computed from the fuel cell polarization curve. 𝑁 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 _𝑠𝑡𝑟𝑖𝑛𝑔𝑠 = 𝐼 𝑡 𝑜𝑡 /𝐼 𝑐𝑒𝑙𝑙 Equation 5-133 where 𝐼 𝑡𝑜𝑡 is found from the total system power required divided by the total system voltage. Thus, the total number of cells is: 𝑁 𝑐𝑒𝑙𝑙𝑠 = 𝑁 𝑐𝑒𝑙𝑙𝑠 _𝑝 𝑒𝑟 _𝑠𝑡𝑟𝑖𝑛𝑔 𝑁 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 _𝑠𝑡𝑟𝑖𝑛𝑔𝑠 Equation 5-134 Once the fuel cell system is sized, the overall efficiency can be calculated by taking the cell operating voltage and dividing by the thermo-neutral potential. This potential is the maximum potential if all the reaction enthalpy Δ𝐻 could be converted to electricity. It can be calculated from the following equation. 𝐸 𝑡 ℎ𝑒𝑟𝑚𝑜𝑛𝑒𝑢𝑡𝑟𝑎𝑙 = − Δ𝐻 𝑛 𝑒 _𝑓𝑢𝑒𝑙 𝐹 Equation 5-135 Given this, the fuel cell efficiency can be found as: 𝜂 𝑓𝑢𝑒𝑙 _𝑐𝑒𝑙𝑙 = 𝐸 𝑐𝑒𝑙𝑙 _𝑜𝑝 𝐸 𝑡 ℎ𝑒𝑟𝑚𝑜𝑛𝑒𝑢𝑡𝑟𝑎𝑙 Equation 5-136 Lastly, the total fuel cell stack heat generation can be found as: 𝑄 ℎ𝑒𝑎𝑡 = ( 𝐸 𝑡 ℎ𝑒𝑟𝑚𝑜𝑛𝑒𝑢𝑡𝑟𝑎𝑙 − 𝐸 𝑐𝑒𝑙𝑙 _𝑜𝑝 ) 𝐼 𝑐𝑒𝑙𝑙 _𝑜𝑝 𝑁 𝑐𝑒𝑙𝑙𝑠 Equation 5-137 258 5.3.8 Lunar Descent & Landing Design Module 5.3.8.1 Overview The purpose of the Descent & Landing design module is to estimate the mass of the propellant required to execute de-orbit, descent, and landing to the lunar surface. The phases of de-orbit, descent, and landing being modeled in this research are depicted in the following figure. Figure 5-39. Descent & Landing phases These phases are described in the following bullets:  Braking Burn 1 (BB1): This phase has the lander vehicle (and its attached rover payload) starting in a circular low lunar orbit with altitude h 0. The vehicle prepares for the de- orbit burn by orienting itself such that the thrust direction is opposite the orbit velocity direction. The vehicle then initiates the burn, keeping the thrust direction in the anti- velocity direction until a desired transverse velocity is reached, at which point the burn 259 terminates. This transverse velocity is the transverse velocity required during the Approach phase, which occurs later on.  Pitch-up & Free Fall: During the pitch-up phase, the vehicle re-orients itself from the last attitude during BB1 so that the thrust axis is aligned with the local vertical direction. While the vehicle is pitching up, it is also free-falling under lunar gravity, as no thrust is being applied. The free fall period can extend beyond the duration needed for the pitch- up.  Braking Burn 2 (BB2): This phase begins with the vehicle re-starting the main engines (now that the thrust axis is aligned with the local vertical, i.e. in the anti-gravity direction) to further slow the vehicle down. The burn is terminated when the horizontal and vertical position and velocity match that required at the start of the Approach phase.  Approach: This phase is needed to provide suitable approach geometry to perform onboard detection of ground hazards (large craters, rocks, and slopes). The slant range to the original landing site is nominally kept at 1 km to provide sufficient range for the LIDAR (light detection and ranging) terrain mapping sensor. This slant range requirement was derived by NASA’s ALHAT (Autonomous Landing and Hazard Avoidance Technology) project, which tested an onboard hazard detection system (actual software and hardware) on the Johnson Space Center-built Morpheus lander testbed (50). A constant 30-degree approach angle also provides suitable geometry for the LIDAR sensor operations. To maintain this approach angle during the Approach phase, the vehicle thrust is assumed vertical and is throttled to match the vehicle weight. 260  Terminal Descent: Once the vehicle reaches 150m slant range from the original landing site, a horizontal divert is performed (to simulate hazard avoidance), followed by touchdown to the new landing site. The Descent & Landing design module is essentially an iterative approach based on converging the total estimated propellant mass with the solved propellant mass such that all descent and landing requirements are met. The algorithm to achieve this is described next. 5.3.8.2 Design Algorithm The Descent & Landing design module consists of a main function that collects all the required inputs, and then a sub-function call that actually executes the D&L design algorithm. The first step in the Descent & Landing design module main function is to obtain the set of trajectory requirements. These include the lower and upper bounds on the de-orbit altitude h 0, the Approach phase constant velocity magnitude, the Approach slant angle, the Approach slant range, the slant range at Terminal descent start, the divert distance, the maximum number of engines allowed during descent and landing, and the number of integration steps for the BB1 integrator (affects computation given the number of steps). Next, the main engine parameters are obtained from the Propulsion inputs. These include the single engine thrust, the engine I sp, the single engine mass, the Propulsion system dry mass without engines, the reserve propellant mass estimate, and the unusable propellant mass estimate. Other important parameters include the average thrust of the RCS thrusters, and the total vehicle moment of inertia matrix at the start of descent and landing (as estimated by the Structures design module). 261 Then, the masses of all the modeled subsystems of the lander are obtained, followed by the mass of any onboard lander science and other instrument payloads. In this research, the lander is assumed to carry only a hazard detection instrument package (the mass and power are user-inputs). The subsystem and instrument masses are added together to estimate the lander dry mass without any main engines. The main engines are not included at this stage because the number of engines required for descent and landing is determined by the Descent & Landing algorithm. Then, the rover mass is obtained. Next, the starting value for the lower bound on h 0 is set, depending on whether the system iteration is the very first. If the MASS tool is in the first system iteration, the user- provided lower bound on h 0 is used—assumed to be 15 km in this research. Otherwise, if the tool has progressed beyond the first system iteration, the code checks whether the lander dry mass (without engines) has grown since the previous system iteration. If so, it sets the lower bound on h 0 to be the last solution of h 0 found in the previous call to the Descent & Landing algorithm. If not, it re-sets the lower bound on h 0 to the initial user-provided value. Once the above steps are complete, the tool is ready to call the sub-function that actually performs the Descent & Landing design. This function requires an initial guess of the combined BB1 and BB2 propellant mass (hard-coded at 100 kg). An overall depiction of the Descent & Landing sizing algorithm sub-function is shown in Figure 5-40. 262 Figure 5-40. Descent & Landing Algorithm The D&L algorithm first begins with computing the gravitational acceleration (m/s 2 ) at the Moon’s surface within several decimal places, according to the following equation: 𝑔 𝑚 = 𝜇 𝑚𝑜𝑜𝑛 𝑅 𝑚𝑜𝑜𝑛 2 Equation 5-138 where 𝜇 𝑚𝑜𝑜𝑛 = 4902.8 𝑘 𝑚 3 /𝑠 2 is the Moon’s gravitational parameter and 𝑅 𝑚𝑜𝑜𝑛 = 1738.4 𝑘𝑚 is the Moon’s equatorial radius. This gives a gravitational acceleration of ~1.622 m/s 2 . Then the algorithm computes the initial conditions for the Approach phase (based on the user-inputs): the horizontal velocity, vertical velocity, initial downrange (horizontal) distance S 0 from the original landing site, and initial altitude. The final conditions at the end of the Approach phase are also set. The D&L algorithm starts off with an outer while loop to perform the D&L propellant mass iteration. The maximum number of propellant mass iterations allowed is hard-coded at 15, Inputs Outputs Compute Term. Descent prop mass and initial conditions Compute Approach prop mass and initial conditions Compute BB1 prop mass and final conditions Iterate # engines & altitude until BB1 solution found or search space exhausted Compute FF & BB2 so altitude & vertical velocity boundary conditions match & Approach phase initial conditions reached Compute new estimate of BB1 + BB2 propellant mass using Newton or secant method Stop mass iteration if converged, exceed 15 iterations, or BB1 solution invalid Prop mass iter 263 based on the convergence behavior observed in initial testing of the integrated MASS tool. The mass convergence tolerance is hard-coded at 0.001 kg. Within the outer loop, the first step is to set the estimate of the combined BB1 and BB2 propellant mass. If the propellant mass iteration is the first in a given system iteration’s call to the Descent & Landing module, the BB1 + BB2 propellant mass estimate is set to the initial guess of 100 kg, and the minimum value of the required de-orbit altitude h 0 is set to the initial value passed into the D&L algorithm. Otherwise, the BB1 + BB2 propellant mass estimate is set to the last estimate from the previous propellant mass iteration plus a delta mass estimated by either Newton’s iterative method or the secant method (discussed in Section 5.3.8.2.7); and the minimum required de-orbit altitude h 0 is set to the solution from the previous propellant mass iteration. In this manner, once the propellant mass iteration is underway and as the total D&L propellant mass estimate grows, mass iterations are reduced by taking advantage of the previous mass iteration’s solution to h 0. The algorithm next checks whether the BB1 + BB2 propellant mass estimate is negative, indicating an inability to converge using either Newton’s method or the secant method. If it is negative, a design feasibility flag is set to FALSE and the mass iteration outer loop is terminated. Otherwise, the design feasibility flag is set to TRUE and the mass iteration is allowed to continue. Next the algorithm proceeds to an inner for-loop to step through a range of de-orbit altitudes h 0. The altitude range starts from the minimum required de-orbit altitude to the maximum allowed de-orbit altitude (100 km in this research), at a user-defined step size. The maximum de-orbit altitude is equal the circular low lunar orbit altitude that the vehicle inserts into after the lunar orbit insertion (LOI) burn and is fixed by the GMAT trajectory. 264 Then the algorithm moves onto a second inner for-loop to step through the number of engines, starting from the maximum of 6 down to 1. Within this second inner for-loop, the propellant mass is estimated for Terminal Descent, Approach, and BB1, in that order. The number of engines and initial de-orbit altitude are iterated on until the altitude search space is exhausted or a valid BB1 solution is found. After completing or exiting the altitude loop, the optimal free fall time (after BB1) is found that permits BB2 start conditions required to achieve the initial state at Approach phase start. A new estimate of the combined BB1 + BB2 propellant mass is calculated using either Newton’s method (the default), or the secant method (under certain conditions). The propellant mass iteration process continues until either the mass has converged with a valid BB1 solution, an invalid BB1 solution is found, or the maximum number of mass iterations has been reached. The following sections describe the calculations to estimate propellant masses and obtain initial or final conditions for Terminal Descent, Approach, BB1, Free Fall (no propellant required), and BB2. 5.3.8.2.1 Terminal Descent The first major calculations within the engine iteration inner for-loop are for Terminal Descent. The burn duration, propellant mass, initial vehicle mass, and touchdown velocities are calculated for this phase based on the optimal control method identified in (58). To do this, first the total engine mass for the current number of engines is found, along with the total thrust. Next, the horizontal and vertical velocity at the start of Terminal Descent are set to the final conditions from the Approach phase. The final landed mass at the end of Terminal Descent is computed by summing the dry mass of the lander (without engines but including the reserve 265 and unusable propellant mass from the Propulsion design), the engine total mass, and the rover mass. The Terminal Descent design function first finds the descent duration (within a hard- coded range of 1 to 120 seconds) that minimizes the touchdown velocities v xf_term and v yf_term, using the MATLAB fminbnd() function. The cost function to minimize is given in the following equation: 𝐽 = 1 2 ( 𝑣 𝑥𝑓 2 + 𝑣 𝑦𝑓 2 ) Equation 5-139 The touchdown velocities for a given Terminal Descent duration are obtained from the following equations: 𝑣 𝑥𝑓 = 𝑥 1𝑇 = 1 2 ( 1 1+ 𝑟 4 )( 3𝐷 𝑇 − 𝑥 10 ) Equation 5-140 where 𝑥 10 = the initial Terminal Descent horizontal velocity, 𝐷 = the divert distance, 𝑇 = the descent duration, and 𝑟 = 𝑇 /𝑊 , where 𝑊 is a weighting factor, assumed to be 1 sec for this research. 𝑣 𝑦𝑓 = 𝑥 1𝑇 = −3 2𝑇 ( 1 1+ 𝑟 4 )(ℎ 0 + 𝑇 𝑥 20 3 + 𝑔 𝑇 2 6 ) Equation 5-141 where ℎ 0 is the initial terminal descent altitude, 𝑥 20 is the initial vertical velocity, and 𝑔 is the Moon’s surface gravitational acceleration. Next, optimal control theory is used to calculate the required Terminal Descent propellant mass. The optimal thrust acceleration time profile can be found as: 𝑎 𝑥 ( 𝑡 )= 𝑢 1 ( 𝑡 )= 𝐿 4 𝑡 − 𝐿 1 𝑎 𝑦 ( 𝑡 )= 𝑢 2 ( 𝑡 )= 𝐿 2 𝑡 − 𝐿 3 Equation 5-142 266 where the control constants are found according to the following equations: 𝐿 1 = ( 𝑥 10 /𝑊 1 + 𝑟 4 ) − 𝑇 Δ [𝐷 ( 1+ 𝑟 2 )− 𝑥 10 𝑇 ] 𝐿 2 = 1 Δ [𝑇 ( 1+ 𝑟 2 )𝑥 20 + ( 1+ 𝑟 ) ℎ 0 − 𝑔 2 𝑇 2 ] 𝐿 3 = 𝑇 Δ [𝑇 ( 1+ 𝑟 3 )𝑥 20 + ( 1+ 𝑟 2 )ℎ 0 − 𝑔 2 𝑇 2 ( 1+ 𝑟 6 ) ] 𝐿 4 = 1 Δ [𝑥 10 𝑇 ( 1+ 𝑟 2 )− 𝐷 ( 1+ 𝑟 ) ] where Δ = − T 3 3 ( 1+ 𝑟 4 ) . Equation 5-143 The optimal thrust acceleration equations can be integrated to give the Delta-V imparted during Terminal Descent for the optimal descent duration (which minimizes the touchdown velocities). Δ𝑉 𝑥 = 1 2 𝐿 4 𝑡 𝑓 2 − 𝐿 1 𝑡 𝑓 Δ𝑉 𝑦 = 1 2 𝐿 2 𝑡 𝑓 2 − 𝐿 3 𝑡 𝑓 Equation 5-144 The total Delta-V can then be found as Δ𝑉 𝑡𝑒𝑟𝑚 = √Δ𝑉 𝑥 2 + Δ𝑉 𝑦 2 . From this total Delta-V, the rocket equation can be used to compute the required Terminal Descent propellant mass. Δ𝑚 𝑝 _𝑡𝑒𝑟𝑚 = 𝑚 𝑓 _𝑙𝑎𝑛 𝑑𝑒𝑑 (𝑒 Δ𝑉 𝑡𝑒𝑟𝑚 𝐼 𝑠𝑝 𝑔 0 − 1) Equation 5-145 This propellant mass is added to the final landed mass to determine the initial Terminal Descent mass. 267 Since the optimal thrust acceleration profile requires throttling the main engines, the maximum optimal control thrust required must be compared to the available thrust from all engines. To obtain the thrust history, the Terminal Descent equations of motion must be integrated over the descent duration. The equations of motion are outlined below: ṙ x = 𝑣 𝑥 ṙ y = 𝑣 𝑦 v ̇ x = 𝑎 𝑥 v ̇ x = 𝑎 𝑦 − 𝑔 𝑚 m ̇ = − T 𝐼 𝑠𝑝 𝑔 0 Equation 5-146 where T = 𝑚𝑎 is the instantaneous thrust, 𝑎 = √𝑎 𝑥 2 + 𝑎 𝑦 2 , and the instantaneous acceleration components can be found from the optimal acceleration profile shown in Equation 5-142. 5.3.8.2.2 Approach Phase Next, the Approach phase burn duration, initial mass, and propellant mass are computed. Since the Approach phase occurs relatively close to the ground, a local horizontal, local vertical frame is assumed. The Approach phase initial position and velocity components can be determined from the required slant range (1 km) and slant angle (30 degrees) using simple geometry as given in the following equations: 𝑟 𝑥 0_𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ = r 0 cos𝜃 𝑠𝑙𝑎𝑛𝑡 𝑟 𝑦 0_𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ = r 0 sin𝜃 𝑠𝑙𝑎𝑛𝑡 𝑣 𝑥 0_𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ = v 0 cos𝜃 𝑠𝑙𝑎𝑛𝑡 𝑣 𝑦 0_𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ = −v 0 sin𝜃 𝑠𝑙𝑎𝑛𝑡 Equation 5-147 268 For a desired Approach phase velocity magnitude of 10 m/s (a user-provided value), 𝑣 𝑥 0_𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ = 8.66 𝑚 /𝑠 and 𝑣 𝑦 0_𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ = −5 𝑚 /𝑠 . The Approach phase is characterized by constant velocity throughout (zero acceleration). The Approach burn duration can then be derived as: t f_approach = 𝑟 𝑦𝑓 − 𝑟 𝑦 0 𝑣 𝑦 0 Equation 5-148 During the Approach phase, the total thrust is assumed to be equal to the instantaneous vehicle lunar weight, T = 𝑚 𝑔 𝑚 , to provide zero acceleration. This results in a mass flow rate that is a non-linear function of time. The mass flow rate can be integrated and then combined with the final Approach phase mass to derive the initial Approach phase mass, as given in the following equation. 𝑚 0_𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ = m f_approach 1− ln( 1+ 𝑐 𝑡 𝑓 _𝑎𝑝𝑝𝑟𝑜𝑎𝑐 ℎ 𝑔 𝑚 ) Equation 5-149 where 𝑐 = 1/𝑔 0 𝐼 𝑠𝑝 , and the final Approach phase mass is set equal to the initial Terminal Descent phase mass. The Approach phase propellant mass can then be calculated as the difference between the initial and final Approach phase masses. 5.3.8.2.3 Braking Burn 1 The algorithm then jumps to the design of Braking Burn 1 (e.g. the de-orbit burn) and the free fall phase that occurs afterward (assuming there is no Braking Burn 2). This procedure requires first obtaining an estimate of the total Descent & Landing (D&L) propellant by adding the current solved Terminal Descent and Approach phase propellant masses to the current estimate of the combined BB1 + BB2 propellant mass (as obtained by Newton’s method or the secant method). Then, the BB1 burn time, final conditions (position, velocity, and mass), and 269 required propellant mass can be estimated given the initial position and velocity, the current estimate of the total D&L propellant mass, and the current assumed number of engines. These design results are obtained by integrating the BB1 equations of motion until either the desired transverse velocity 𝑢 𝑓 _𝑑𝑒𝑠 is achieved or the final BB1 altitude is negative (in which case the vehicle has crashed into the lunar surface). The desired transverse velocity is equal to the horizontal velocity at the start of the Approach phase (calculated to be 8.66 m/s as described in Section 5.3.8.2.2). Before presenting the BB1 equations of motion, the orbital reference frame in which they were derived must be briefly described. Figure 5-41 depicts the geometry of the Braking Burn 1 de-orbit and descent problem. In this figure, the vehicle starts at a radius 𝑟 from the lunar center (at an altitude ℎ 0 ) in lunar orbit. The vehicle is traveling at a velocity v in the counter-clockwise direction. The components of v are 𝑢 (in the transverse direction) and 𝑣 (in the radial direction). The vehicle applies thrust 𝑇 in the anti-velocity direction, at thrust angle 𝜓 with respect to the radial direction. Note the thrust vector has a negative thrust angle, as defined in the figure. The angle 𝜃 represents a position angle with respect to an arbitrary y-axis. 270 Figure 5-41. Geometry of the Lunar Braking Burn 1 De-orbit and Descent Problem (59) Given this geometry, the BB1 equations of motion, adapted from Appendix B of (59), can be derived: 𝑟 ̇ = 𝑣 θ ̇ = − 𝑢 𝑟 𝑢 ̇ = 𝑇 𝑚 sin𝜓 − 𝑢𝑣 𝑟 𝑣 = 𝑇 𝑚 cos𝜓 − 𝜇 𝑟 2 + 𝑢 2 𝑟 m ̇ = − T 𝐼 𝑠𝑝 𝑔 0 Equation 5-150 To maintain the thrust in the anti-velocity direction throughout BB1, the thrust angle can be derived from the velocity components as follows: sin𝜓 = − 𝑢 √𝑢 2 + 𝑣 2 Equation 5-151 v r u v T Ψ < 0 x y θ 271 cos𝜓 = − 𝑣 √𝑢 2 + 𝑣 2 The BB1 equations of motion are integrated until either of two conditions is met: the desired transverse velocity is met or the final altitude is negative. In any case, the code checks whether the consumed BB1 propellant mass exceeds the total available propellant mass (and sets a flag to indicate this). 5.3.8.2.4 Maximum Pitch-up/Free Fall Once BB1 final conditions are obtained (for the currently assumed initial de-orbit altitude h 0 and the available number of engines), the maximum duration of the Pitch-up maneuver attitude slew is calculated. The Pitch-up maneuver re-orients the vehicle to a vertical, anti-gravity direction. The slew angle 𝜃 𝑚𝑎𝑥 is assumed to be 90 degrees to estimate a maximum duration for Pitch-up, which is equivalent to the maximum duration for free fall (no thrusting applied). The maximum slew duration is found from the following equations: Δ𝑡 𝑝𝑖𝑡𝑐 ℎ𝑢𝑝 _𝑚𝑎𝑥 = 2Δ𝑡 𝑎𝑐𝑐𝑒𝑙 Δ𝑡 𝑎𝑐𝑐𝑒𝑙 = √ 2𝐼 𝜃 𝑚𝑎𝑥 𝑇 𝑟𝑐𝑠 Equation 5-152 where 𝐼 is the maximum vehicle transverse moment of inertia and 𝑇 𝑟𝑐𝑠 is the average thrust of the RCS thrusters. Next the altitude change during the maximum duration pitch-up maneuver is calculated as follows: Δr y = v y0_free_fall Δ𝑡 𝑝𝑖𝑡𝑐 ℎ𝑢𝑝 _𝑚𝑎𝑥 − 1 2 𝑔 𝑚 Δ𝑡 𝑝𝑖 𝑡 𝑐 ℎ𝑢𝑝 _𝑚𝑎𝑥 2 Equation 5-153 This altitude change is added to the Approach phase initial altitude to determine a minimum allowable final altitude for BB1 (assuming no BB2). 272 ℎ min_BB1 = ℎ 0_𝑎𝑝𝑝𝑟 𝑜 𝑎𝑐 ℎ + Δ𝑟 𝑦 Equation 5-154 5.3.8.2.5 Identifying BB1 Solution Recall that all the calculations described to this point occur within two for-loops, the first being the de-orbit altitude loop and the second being a nested loop for the number of engines. After the BB1 and maximum pitch-up maneuvers have been designed, the code next checks whether the final BB1 altitude is greater than the minimum allowed final BB1 altitude. If it is, the BB1 solution is marked as valid and the code attempts to re-do all the previous calculations by going to the next lower the number of engines to check if a viable solution still exists. Otherwise, the current BB1 solution is marked as invalid. If the BB1 solution is invalid on the first iteration of the engines loop (using the maximum number of engines), the code proceeds to the next altitude h 0 in the range of allowable altitudes and performs all the calculations again. Otherwise, for invalid BB1 solutions identified in iterations of the engines loop after the first, the code reverts to the valid solution from the previous engines iteration and stops checking for solutions using fewer engines. Once outside of the engines loop, the code checks if the current assumed de-orbit altitude h0 is equal to the maximum allowed de-orbit altitude. If it is, and the BB1 solution is still invalid, the code prints out a warning message that the h0 design space has been searched without finding a valid BB1 solution. The D&L design is then marked as infeasible, because all subsequent calculations will be based on an invalid BB1 solution. In any case, if a valid BB1 solution is found during the altitude search, the code breaks out of the altitude loop, and the required initial de-orbit altitude h 0 and required number of engines are set. 273 5.3.8.2.6 Free Fall/Braking Burn 2 Altitude & Velocity Matching Now that valid final conditions for BB1 have been found, the required duration for free fall (FF) can be found such that the altitude and velocity at the FF/BB2 boundary match (if BB2 is required). To do this, the free fall duration must be bounded. The minimum duration for free fall is equal to the required pitch-up duration. The required pitch-up duration itself can be found using the final thrust angle ψ 𝑓 at the end of BB1. The maximum free fall duration (to reach the Approach phase starting altitude) can then be solved for using the quadratic solution, given the initial FF vertical velocity, the initial FF vertical position, and the final FF vertical position (equal to the Approach phase initial altitude), as follows: 𝑡 𝑓 _𝐹𝐹 _𝑚𝑎𝑥 = −𝑣 𝑦 0_𝐹𝐹 ± √𝑣 𝑦 0 2 + 2𝑔 𝑚 ( 𝑟 𝑦 0_𝐹𝐹 − 𝑟 𝑦𝑓 _𝐹𝐹 ) −𝑔 𝑚 Equation 5-155 The maximum solution of the two from the above equation is then used as the maximum FF duration. Next, the algorithm proceeds to find the required free fall duration at which the FF/BB2 boundary altitude and velocity match. This is done by using the MATLAB fminbnd() function to find the free fall duration that minimizes the FF/BB2 boundary condition cost function, shown below: 𝐽 = 1 2 [( 𝑟 𝑦 0_𝐵𝐵 2 − 𝑟 𝑦𝑓 _𝐹𝐹 ) 2 + ( 𝑣 𝑦 0_𝐵𝐵 2 − 𝑣 𝑦𝑓 _𝐹𝐹 ) 2 ] Equation 5-156 To do this, the free fall final conditions for a given free fall duration can be found analytically: 𝑟 𝑥 𝑓 _𝐹𝐹 = 𝑟 𝑥 0_𝐹𝐹 + 𝑣 𝑥 0_𝐹𝐹 𝑡 𝐹𝐹 Equation 5-157 274 𝑟 𝑦𝑓 _𝐹𝐹 = 𝑟 𝑦 0_𝐹𝐹 + 𝑣 𝑦 0_𝐹𝐹 𝑡 𝐹𝐹 − 1 2 𝑔 𝑚 𝑡 𝐹𝐹 2 𝑣 𝑥𝑓 _𝐹𝐹 = 𝑣 𝑥 0_𝐹𝐹 𝑣 𝑦𝑓 _𝐹𝐹 = 𝑣 𝑦 0_𝐹𝐹 − 𝑔 𝑚 𝑡 𝐹𝐹 The BB2 initial conditions can be found by reverse integrating the BB2 equations of motion until the initial BB2 altitude (equal to the FF final altitude) is achieved. The BB2 equations of motion are outlined below. ṙ x = 𝑣 𝑥 ṙ y = 𝑣 𝑦 v ̇ x = 𝑎 𝑥 = 0 v ̇ x = 𝑎 𝑦 − 𝑔 𝑚 m ̇ = − T 𝐼 𝑠𝑝 𝑔 0 Equation 5-158 where the full available thrust during BB2 is applied only in the vertical direction, so that 𝑎 𝑦 = 𝑇 /𝑚 . This vertical thrust acceleration reduces the vertical velocity under lunar gravity. The reverse integration starts by setting the final BB2 conditions equal to the Approach phase initial conditions. The reverse integration then proceeds from a hard-coded maximum integration duration of 1000 seconds until the altitude equals the desired BB2 altitude. The BB2 propellant consumed is then estimated using the engine mass flow rate and solved BB2 burn duration. Given the optimal free fall duration, the free fall final conditions are re-computed (as fminbnd() does not return results other than the optimized variable value and the minimized cost function). The BB2 initial conditions are also re-computed. The final FF altitude and vertical 275 velocity are then compared to the initial BB2 altitude and vertical velocity to ensure they actually match. 5.3.8.2.7 Propellant Mass Iteration At this point, the propellant mass has been calculated for BB1, BB2, Approach, and Terminal Descent. The total solved propellant mass is determined by adding the calculated propellant masses from all D&L phases. The difference between the solved and estimated total D&L propellant mass is then found: δM p_err = Δ𝑀 𝑝 _𝑡𝑜𝑡 _𝑠𝑜𝑙𝑣𝑒𝑑 − Δ𝑀 𝑝 _𝑡𝑜𝑡 _𝑒𝑠𝑡 Equation 5-159 To reduce this difference to zero requires using a root-finding method to compute a new estimate for the combined BB1 + BB2 propellant mass. Using this new estimate, another iteration of the outer mass iteration loop can be executed, in which all the preceding calculations for all D&L phases are re-done. This process is repeated until one of the following conditions occurs: 1) the total propellant mass has converged, the maximum number of allowed mass iterations has been reached, or a valid BB1 solution was not found during the mass iteration (in which case the mass iteration is terminated). Two root-finding methods are available to the re-estimate the BB1 + BB2 propellant mass: the Newton-Raphson method, and the secant method. Newton’s method involves calculating a new estimate of the variable to be solved for using the following equation: 𝑥 𝑛 +1 = 𝑥 𝑛 − 𝑓 ( 𝑥 𝑛 ) 𝑓 ′( 𝑥 𝑛 ) Equation 5-160 where 𝑓 ( 𝑥 ) is the function whose root is sought. For the problem presented here, 𝑓 ( 𝑥 )= 𝛿 𝑀 𝑝 _𝑒𝑟𝑟 , where 𝑥 = Δ𝑀 𝑝 _𝐵𝐵 1_𝐵𝐵 2 . The 𝑓 ′( 𝑥 ) term is just the slope of the 𝛿 𝑀 𝑝 _𝑒𝑟𝑟 , which can be calculated as: 276 𝑓 ′ ( 𝑥 )= Δ𝑦 Δ𝑥 = 𝛿 𝑀 𝑝 _𝑒𝑟 𝑟 𝑛 − 𝛿 𝑀 𝑝 _𝑒𝑟 𝑟 𝑛 −1 Δ𝑀 𝑝 _𝐵𝐵 1_𝐵𝐵 2 𝑛 − Δ𝑀 𝑝 _𝐵𝐵 1_𝐵𝐵 2 𝑛 −1 Equation 5-161 Newton’s method is the default method used at the start of the propellant mass iteration process. The secant method assumes the function is approximately linear in an interval [x 0, x 1] around the root (i.e. a line connecting the limits of the interval crosses zero). 𝑥 𝑛 +1 = 𝑥 𝑛 − 𝑥 𝑛 − 𝑥 𝑛 −1 𝑓 ( 𝑥 𝑛 )− 𝑓 ( 𝑥 𝑛 −1 ) 𝑓 ( 𝑥 𝑛 ) Equation 5-162 where, again, 𝑓 ( 𝑥 )= 𝛿 𝑀 𝑝 _𝑒𝑟𝑟 and 𝑥 = Δ𝑀 𝑝 _𝐵𝐵 1_𝐵𝐵 2 . The root-finding method in the D&L algorithm switches to the secant method only under the following conditions: 1) a zero-crossing has occurred in δM p_err ; 2) the current total propellant mass estimate is < 0; 3) the difference 𝛿𝑚 = 𝛿 𝑀 𝑝 _𝑒𝑟 𝑟 𝑛 − 𝛿 𝑀 𝑝 _𝑒𝑟 𝑟 𝑛 −1 is > 0 after the first propellant mass iteration; or 4) a flag to explicitly use the secant method is set to TRUE. 5.4 GENERATING DESIGN DATA Once a set of system configuration .m files have been generated (as described in Section 5.1.3), the next task would ideally be to run them all through the Mission and Spacecraft Sizing (MASS) MATLAB tool. An issue is that each configuration can take up to 7.5 minutes to converge, as identified in initial MASS tool testing. This estimate is derived by taking an average system- iteration run time of 30 sec (to design all spacecraft subsystems and to run the Descent & Landing design module once) and a maximum allowed number of 15 system-level iterations. That results in (30 sec/iteration)*(15 iterations) = 450 minutes/config = 7.5 min/config. Given 7920 configurations, that would require 41.25 days of continuous run time on a single MATLAB 277 license, one configuration at a time. This amount of run time was not available and in general seems too large. An option to reduce the total continuous run time would be to run the list of system configurations in batches on multiple instances of MATLAB. To run all configurations in about a day would require running on approximately 40 MATLAB instances. While multiple instances of MATLAB (at least of the Student license used in this research) can be started, there is a limit in computing memory available for each instance. Another alternative would be to investigate use of MATLAB’s Parallel Processing capability to split the configuration runs among different processors; however, that toolbox was not purchased during this research. Thus, to generate design results for a reasonable amount of system configurations in a reasonable run time, a decision was made to reduce the 7920 configurations into a handful of interesting cases. The process to arrive at this reduced set is described next. 5.4.1 Selecting Configurations to Run In the 7 subsystems available to a given spacecraft, a set of 6 trade parameters were identified. These are: 1. ADCS RCS pressurant gas: Helium or Nitrogen 2. ADCS RCS tank material type: Metal or Composite 3. Propulsion bi-propellant engine: 9 available engines > 200 N thrust from the Thruster/Engine database 4. Propulsion pressurant gas: Helium or Nitrogen 5. Propulsion tank material type: Metal or Composite 6. Spacecraft power source type: Solar array + battery, RPS + battery, fuel cell + battery 278 To whittle the thousands of system configurations down into a reasonable set, a Unix script was written to search the system configuration .m files for a reduced set of trade values per trade item listed above. The script starts off filtering all system configuration .m files by rover power source. The script repeats the filtering process 3 times, one for each Rover power source type (solar, RPS, and fuel cell). For the first cycle, of the available list of 5 solar cell types, only the minimum cell efficiency and maximum cell efficiency candidates were considered (Silicon high efficiency at 17 % and GpInP2/GaAs/Ge triple junction XTJ cells from Spectrolab at 29.3 %). For the second cycle, the available RPS types are constrained to MMRTG (delivering 125W of electrical power in total per 44.2 kg module at a system efficiency of 6.3 %) and ASRG- 850 (delivering 160W of electrical power in total per 19 kg module at a system efficiency of 32%). Note that the ASRG (Advanced Stirling Radioisotope Generator) technology is currently not being pursued by NASA 7 , and so represents a futuristic option. For the third cycle, the available fuel cell options were kept at the 2 available in the fuel cell database (hydrogen/oxygen or H 2/O 2, and hydrogen/hydrogen peroxide or H 2/H 2O 2). Whichever Rover power system option was being filtered, the Unix script next searched for the set of system configuration files with Lander RCS pressurant set to Helium (the reasoning being that Helium gas has a smaller average bulk density at standard temperature and pressure than Nitrogen). Next, of the set of system configuration files that met the Rover power and Lander RCS pressurant filters, the subset of configurations with engine mass flow rate at the minimum and maximum of the 9 available bi-propellant engines (> 200 N thrust), and a middle 7 NASA Glenn Research Center had been planning to develop an ASRG for flight by 2016, but discontinued the program in 2013 (72). 279 mass flow rate were down-selected. The set of 9 available bi-propellant engines are listed below (60) (61): Table 5-36. Available Bi-propellant Engines for Lander Propulsion System Model Manufacturer Max Isp (sec) Max Thrust (N) Mdot (kg/s) Flight Status R-4D Aerojet 315.5 490 0.158 Flight proven HiPAT Liquid Apogee Motor Aerojet 323 445 0.140 Flight proven HiPAT Dual Mode Liquid Apogee Thruster Aerojet 329 445 0.138 Qualified R-42 Aerojet 303 890 0.299 n/a R-42DM Aerojet 327 890 0.277 Ready for formal qualification, TRL 6 2008 AMBR Dual Mode Aerojet 333 623 0.191 Ready for formal qualification, TRL 6 2008 TR-308 Liquid Apogee Engine Northrop Grumman 322 470.64 0.149 Flight proven TR-312 Liquid Apogee Engine Northrop Grumman 325 501.72 0.157 Flight Prototype TR-312-100YN Liquid Apogee Engine Northrop Grumman 330 555 0.171 Flight Prototype According to this table, the minimum mass flow rate engine (0.138 kg/s) is the Aerojet HiPAT Dual Mode Liquid Apogee Thruster (flight qualified), the maximum mass flow rate engine (0.299 kg/s) is the Aerojet R-42 (no information available on qualification status), and the middle value mass flow rate engine (0.171 kg/s) is the Northrop Grumman TR-312-100YN Liquid Apogee Engine (flight prototype). 280 Lastly, the Unix script further filtered the list of matching system configuration .m files by searching for those with Lander solar cell efficiencies the same as those searched for the Rover (Si high efficiency at 17%, and XTJ at 29.3 %). The number of system configurations found for each of the 3 Rover power source search cycles and associated filters is summarized in below. Table 5-37. Filtering System Configurations into Runnable Set Filter Criteria # Results Found  Rover solar cell efficiency = 17% or 29.3%  Lander RCS pressurant = Helium  Lander RCS tank material type = Metal or Composite  Lander engine mass flow rate = min, max, middle value  Lander solar array cell efficiency = 17% or 29.3 % 48  Rover RPS type = MMRTG or ASRG  Lander RCS pressurant = Helium  Lander RCS tank material type = Metal or Composite  Lander engine mass flow rate = min, max, middle value  Lander solar array cell efficiency = 17% or 29.3 % 96  Rover fuel cell type = H2/O2 or H2/H2O2  Lander RCS pressurant = Helium  Lander RCS tank material type = Metal or Composite  Lander engine mass flow rate = min, max, middle value  Lander solar array cell efficiency = 17% or 29.3 % 96 Total 240 Overall, applying these search filters reduced the number of system configurations down to 240, by keeping only Lander RCS pressurant as Helium, keeping both Lander RCS tank material types as metal and composite, eliminating the majority of Propulsion engines and 281 avoiding Rover solar cell options with middle cell efficiencies and avoiding Rover RPS options aside from the MMRTG and best performing ASRG. Overall, the end result of this system configuration filtering was a list of configuration IDs for all matching configurations. To estimate the run time for these 240 system configurations, it was decided to look at the run time performance for the first 20 configurations in the MASS tool. After doing an initial test run it was found that some of the designs terminated early due to infeasibility 8 . For 20 configuration design runs, the total run time on a single instance of MATLAB was 1 hour and 13 minutes = 73 min. So that results in 3.65 min/configuration. So, for 240 configurations, that turns out to be (240 configurations)*(3.65 min/config) = 876 min = 14.6 hours of run time. To aid in debugging any potential MATLAB error as a result of the automated running of so many system configurations, to allow monitoring of the design runs (to avoid walking away and returning hours later only to find that the runs have terminated early due to error in one of the system configurations), it was decided to split the 240 configurations into subsets of 32 configurations each for the first 160 configurations and 40 each for the remaining 80 configurations. Thus, the configuration IDs for the 240 system configurations were also split into subset files that could be passed directly to the MASS tool. 5.4.2 Design Runs To reduce the total run time down from 14.6 to something achievable during a typical work day (say 7 hours), it was decided to start two instances of the MATLAB student license and run them in parallel. This was a very good idea, as the total run time for all 240 configurations 8 Infeasibility here is defined as some reason in which the design does not meet some requirement as determined by MASS. 282 turned out to be 6 hours and 50 minutes. It is conceivable that the total run time could be reduced through using more MATLAB instances or investigating the use of the MATLAB Parallel Processing toolbox. In addition, the run time of each system iteration could be improved by finding faster algorithms for obtaining the subsystem designs, to reduce the system iteration run time below 30 sec per iteration. The design run process was free of any errors due to missing parameters in the MATLAB system configuration .m files, MATLAB syntax errors, or divergence cases (resulting in infinite loops, if not properly checked). Several data files are generated per system configuration (placed within a “sys_configN” subfolder in the “Results” folder). These files per system configuration are:  The summary of Delta-Vs that are present within the trajectory SPK file and simulation data file  A saved MATLAB .fig file of the MASS GUI showing plots of the total Rover mass, total Lander mass, Rover subsystem masses, Lander subsystem masses, and Iteration run time (in seconds) all per system-level iteration.  A saved MATLAB .mat file containing the workspace variables used during the system configuration design run  A mission system configuration design log text file, containing printed results of each subsystem design module and the Descent & Landing sizing module for each system- level iteration.  A system configuration iteration text file containing the subsystem mass breakdown and total masses for Rover and Lander in each system-level iteration (to aid in reviewing convergence) 283 Given that all these take up disk space, another initial concern in running thousands of system configurations using the MASS tool was total disk usage. For all 240 configurations, the total disk usage came up to 819 MB (or an average of 3.48 MB per configuration). The file with the largest file size is the mission design log, since it prints out results for each system-level iteration until convergence or infeasibility is detected. The largest file size for the mission design log wound up being 7.8 MB. This file size could be reduced by finding more efficient subsystem and Descent & Landing sizing algorithms that require fewer printed lines. The next section describes the results obtained after running all filtered system configurations. 6 ANALYSIS OF RESULTS 6.1 CONFIGURATION DESIGN FEASIBILITY To process the design data (available as saved MATLAB .mat files containing workspace variables for each system configuration), an analysis MATLAB script was written. The first step in the analysis process was to distinguish design results between those that successfully ran until system mass convergence (feasible designs), or those that did not run successfully and terminated early due to some numerical or other condition (infeasible designs). If an infeasible design condition was reached, the MASS tool was written to print out the word “infeasible” in an output message to the mission design log file. So, a Unix egrep search was done on all mission design log files for files that contained the word “infeasible” or not. In addition, a “feasible” flag was set to TRUE in the MASS tool if the final iteration of a configuration was feasible, and to FALSE otherwise. 284 The MASS tool was coded to capture 3 types of design infeasibility: 1. Telecom module: Telecom link design (either DTE links or relay links) did not have links with > 3 dB link margin for all communication events being modeled. 2. Descent & Landing module: the propellant mass estimate for braking burns 1 and 2 during the propellant mass convergence search was negative, thereby invalidating the design. That is, if the design run were allowed to continue, the integration of the braking burn 1 equations of motion would operate on negative mass and would produce unrealistic results (causing acceleration instead of deceleration during the intended descent). 3. Descent & Landing module: the braking burn 1 design algorithm ran out of search space for the initial de-orbit altitude h 0 (reaching the maximum allowed). That is, the algorithm could not find a starting altitude within bounds by which braking burn 1 could be achieved with a final condition above the lunar surface (positive altitude). The design feasibility results for the system configurations run are summarized in the following table. Table 6-1. System Configuration Design Feasibility Results Case Count % of total Feasible designs 100 41.7 Infeasible designs 140 58.3 Infeasible designs as a result of negative BB1 + BB2 propellant mass estimate 0 0 (of all designs) 0 (of all infeasible designs) Infeasible designs as a result of exhausting BB1 h0 search space 140 58.3 (of all designs) 100 (of all infeasible designs) Out of 240 system configurations run, ~41.6% or 100 were feasible designs. Of the 140 infeasible designs, 0 were infeasible as a result of estimating negative BB1 + BB2 propellant 285 mass, while the remaining 140 were all due to the BB1 search algorithm exhausting the h 0 search space. Section 6.2.3 discusses the design infeasibility results in more detail, while Section 6.2 describes the design feasibility results. 6.2 FEASIBLE DESIGN CONFIGURATIONS 6.2.1 Design Results The characteristics of the 100 feasible designs are described in this section. The total launch mass vs. combination run order (i.e. system configuration ID order) is shown in Figure 6-1. This figure simply depicts the logical order in which the system configuration combinations were generated (as described in Section 5.1.3.4). According to this figure, the total converged launch mass varied between 880.2 kg and 3262.8 kg. Figure 6-1. Feasible design total launch mass vs. combination run order To understand the breakdown of these feasible designs, plots of total launch mass vs. final landed mass can studied. The first of these plots, shown in Figure 6-2, reveals two distinct 286 families: at total launch masses < 2000 kg, all the feasible designs involve the use of the medium mass flow rate TR-312-100YN Liquid Apogee Engine (68 in total); at total launch masses above 2450 kg, all the feasible designs involve use of the R-42 high mass flow rate (32 in total). There are no feasible designs involving use of the low mass flow rate HiPAT Dual Mode Liquid Apogee thruster. The highest total launch mass feasible design in the TR-312-100YN family is 1799 kg, while the lowest total launch mass feasible design in the R-42 family is 2459 kg, a difference of 660 kg. For the R-42 feasible designs, there also appear to be several sub-families based on other configuration characteristics. In addition, the plot shows a fairly linear relationship between the total launch mass and the final landed mass for each engine family. Figure 6-2. Feasible design total launch mass vs. final landed mass (by engine family) The plot in Figure 6-3 below shows the same plot with the lander’s Propulsion tank material marked. It can be seen that there are 72 cases using composite tanks, whereas there are 28 cases using metal tanks. The composite tank cases span all the way from the low total 287 launch mass end to the high total launch mass end, whereas the metal tanks exist strictly between 500 and 700 kg final landed mass. Figure 6-3. Feasible design total launch mass vs. final landed mass (by Prop tank material type) The plot in Figure 6-4 below shows that all rover power sources are represented in the feasible designs. There are 24 solar-powered rover feasible designs, 28 RPS-powered rover feasible designs, and 48 fuel-cell powered rover feasible designs. The minimum and maximum total launch mass designs for all three rover power source cases is summarized in Table 6-2 below. The minimum total launch mass design is a fuel cell-powered rover, and the maximum total launch mass design is an RPS-powered rover. The minimum total launch mass solar- powered rover design is 904.8 kg, and the maximum total launch mass solar-powered rover design is 2879.1 kg. The minimum total launch mass RPS-powered rover design is 1125.1 kg, and the maximum total launch mass RPS-powered rover design is 3262.8 kg (which happens to be the maximum overall total launch mass design). The minimum total launch mass fuel cell- 288 powered rover design is 880.2 kg (which happens to be the minimum overall total launch mass design), and the maximum total launch mass fuel cell-powered rover design is 2863.6 kg. Table 6-2. Feasible design total launch masses (min and max) for each Rover power configuration Rover Power Configuration # Feasible Designs Minimum Total Launch Mass (kg) Maximum Total Launch Mass (kg) Solar 24 904.8 2879.1 RPS 28 1125.1 3262.8* Fuel cell 48 880.2** 2863.6 * Maximum total launch mass overall; **Minimum total launch mass overall Figure 6-4. Feasible design total launch mass vs. final landed mass (by Rover power source) A plot of the total loaded propellant mass vs. total launch mass (by engine family) is shown in Figure 6-5 below. This plot clearly shows two distinct curves by engine family: one group with total loaded propellant less than ~1200 kg (for the medium mass flow rate engine TR-312-100YN), and a second group between ~1700 and 2400 kg (for the maximum mass flow rate engine R-42). Thus, the total loaded propellant mass is in general higher using the R-42 and lower using the TR-312-100YN. The minimum total loaded propellant mass in the whole plot is 562.6 kg, and the maximum total loaded propellant mass is 2341.9 kg. The delta in total loaded 289 propellant mass, between the highest propellant mass TR-312-100YN case and the lowest propellant mass case is ~500 kg. Figure 6-5. Feasible design total loaded propellant mass vs. total launch mass (by engine family) Another interesting plot is the propellant mass fraction vs. total launch mass, as shown in Figure 6-6 below. The propellant mass fraction in this plot is defined as the total loaded propellant mass (for both orbital Delta-V maneuvers and Descent & Landing) divided by the total launch mass. The plot shows that for the medium mass flow rate TR-312-100YN engine, the propellant mass fraction ranges from 0.64 to 0.67, whereas for the maximum mass flow rate R- 42 engine, the propellant mass fraction ranges from 0.687 to 0.718. Notice that in the R-42 family, there appear to be 2 sub-families based on other configuration characteristics. 290 Figure 6-6. Feasible design propellant mass fraction vs. total launch mass (by engine family) The above plots of total loaded propellant mass and mass fraction vs. total launch mass do not show the effect of engine mass flow rate according to the mass of the primary payload, the rover. In the feasible designs, there are 5 distinct total rover masses, as summarized in Table 6-3. Case 1 is the lowest mass rover at 74.3 kg, configured for fuel cell power (H 2/O 2). Case 2 is the next largest mass rover at 77.8 kg, configured for fuel cell power also, but using (H 2/H 2O 2) reactants. Case 3 is next at 78.1 kg, configured for Si solar array power. The next largest mass is Case 3 at 112.6 kg, configured for RPS-power using the ASRG-850. The greatest mass rover is Case 4 at 183 kg, configured for RPS-power using MMRTG technology. Table 6-3. Feasible design Rover total mass summary Case Rover total mass (kg) # Feasible Designs Rover Power Configuration 1 74.3 24 Fuel cell-powered rovers (H 2/O 2) 2 77.8 24 Fuel cell-powered (H 2/H 2O 2) 3 78.1 24 Solar-powered rover (Si High efficiency) 4 112.6 20 RPS-powered rover (ASRG-850) 5 183.019 8 RPS-powered rover (MMRTG) 291 The effect of different Propulsion main engines on total loaded propellant mass as a function of Rover mass can be seen in Figure 6-7. For the 5 sets of Rover masses, use of the medium mass flow rate TR-312-100YN engine requires less propellant than use of the higher mass flow rate R-42. Thus, for delivery of the same Rover payload, it would seem more efficient to use the medium mass flow rate engine TR-312-100YN. However, using reduced mass flow rate appears to work only up to a point, as there are no feasible design, low mass flow rate HiPAT Dual Mode Liquid Apogee Engines. Figure 6-7. Feasible design total propellant mass vs. total Rover mass Figure 6-8 shows a plot of the final solved de-orbit altitude h 0 at the start of braking burn 1 during Descent & Landing vs. final landed mass. It can be seen that there are 2 curve families: one using the TR-312-100YN engine with required h 0 from 15 to ~67 km, and the other using the R-42 engine requiring h 0 from 42 km to 85 km. Thus, in addition to requiring less propellant, the TR-312-100YN engine can achieve Descent & Landing from lower de-orbit altitudes h 0. The overlap between 40 km and 70 km, however, indicates that the higher mass 292 flow rate R-42 engine can be used to deliver higher final landed mass from the same de-orbit altitude than can the lower mass flow rate TR-312-100YN engine. Also note that there appear to be two families of required h 0 for the R-42 cases, depending on other configuration characteristics. Figure 6-8. Feasible design solved h0 required vs. final landed mass (by engine family) The number of engines required for all feasible designs was found to be the maximum of 6 engines, as shown in Figure 6-9. This indicates that the maximum available thrust in each engine case was required in each feasible design. So, per the Descent & Landing algorithm described in Section 5.3.8.2, attempting to reduce the number of engines in these designs would have resulted in invalid BB1 designs. 293 Figure 6-9. Feasible design solved # D&L engines required vs. combination run order The total duration for Descent & Landing feasible designs is plotted vs. final landed mass in Figure 6-10 below. This plot shows that the total duration varies from ~439 seconds (7.3 minutes) to ~820 seconds (13.6 minutes) for configurations using the TR-312-100YN engine, and from ~660 seconds (11 minutes) to ~928 seconds (15.46 minutes) for configurations using the R- 42 engine. 294 Figure 6-10. Feasible design solved Descent & Landing total duration vs. final landed mass (by engine family) The timing breakdown of the Descent & Landing phase for the feasible designs is shown in Figure 6-11 below. From this figure, it can be seen that the BB1 duration dominates the contribution to the total D&L duration, and that there are two curve families (corresponding to the TR-312-100YN and R-42 engines). The durations for the Approach phase and Terminal Descent appear to be relatively constant for different final landed masses, as shown in the zoomed view of Figure 6-12. This plot has a couple interesting characteristics. First, the free fall duration remains mostly below 55 sec for final landed masses < 700 kg. This same trend is also present for final landed masses > 900 kg; however, there are 16 cases where the FF duration reaches above 75 sec. These same cases also show a jump in BB2 burn duration. The possible distinguishing factors for these cases could be the RCS tank material type (metal or composite), or the lander Propulsion system pressurant gas. Further investigation shows that these cases include both RCS tank material options, and both Helium and Nitrogen Propulsion system pressurants. Another interesting characteristic of 295 Figure 6-12 is that the BB2 duration goes from 6.3 seconds to ~39 seconds between 360 and 700 kg final landed mass, then appears to have two families in the 900 to 1100 kg range. Figure 6-11. Feasible design solved Descent & Landing sub-phase durations vs final landed mass Figure 6-12. Zoom of Feasible design solved Descent & Landing FF, BB2, Approach, and Terminal Descent durations vs. final landed mass 296 Figure 6-13 below shows the required propellant mass contributions for the D&L sub- phases BB1, BB2, Approach, and Terminal Descent. As expected, the BB1 propellant mass contribution dominates, and there appear to be two families of curves (against corresponding to the two engines feasible engines). Figure 6-13. Feasible design solved Descent & Landing required propellant mass breakdown vs final landed mass Figure 6-14 shows a zoom of the BB2, Approach, and Terminal Descent required propellant masses. This figure shows that the Approach and Terminal Descent phase propellant masses steadily increase with final landed mass. The Approach phase required propellant mass generally remain below 30 kg for final landed masses < 700 kg, and between 45 and 55 kg for final landed masses between 900 and 1100 kg. The Terminal Descent required propellant mass remains below 40 kg for final landed masses < 700 kg, and between 28 and 35 kg for final landed masses between 900 and 1100 kg. 297 Figure 6-14. Zoom of Feasible design solved Descent & Landing required propellant mass breakdown vs. final landed mass In terms of the run time performance of the feasible designs, it can be seen from Figure 6-15, a plot of total run time vs. total launch mass, that the total configuration run time varied from just over 3 minutes to ~7.25 minutes. Around 1800 kg total launch mass, there appear to be 6 cases with run time above 6.5 min. Of these cases, 4 use the TR-312-100YN engine and the others use the R-42. The 4 cases that use the TR engine are configured to use the ASRG-850 powered Rover and Lander Propulsion tanks made of Aluminum; the two cases that use the R- 42 are configured to use the fuel cell-powered (H 2/H 2O 2) rover and lander Propulsion tanks made of composite. 298 Figure 6-15. Feasible design total configuration run time vs. total launch mass The total # of iterations for each configuration to converge (up to the maximum limit of 15) follows the same trend as the total configuration run time, as shown in Figure 6-16. There were 2 cases that took the maximum # of iterations (15), and 24 cases that took the fewest # of iterations (7). Finding cases taking the maximum # of iterations in the middle of the total launch mass range indicates that a tool like MASS can be used to identify outliers in the design space. 299 Figure 6-16. Feasible design total # convergence iterations vs. total launch mass The average system iteration run time per configuration vs. total launch mass is shown in Figure 6-17. The minimum average system iteration run time was 25.9 seconds and the maximum was 31.8 seconds. This was in family with previous estimates of the average system iteration run time that were used to estimate the total time to run all desired system configurations. 300 Figure 6-17. Feasible design average iteration run time vs. total launch mass Lastly, the breakdown of the average system iteration run time per configuration can be analyzed to understand which subsystem design modules contribute the most time. Figure 6-18 shows the average run time per subsystem design module for the rover vs. combination order. This figure shows that the Telecom design module took the longest amount of run time, between 9.5 and 10.5 seconds, for all feasible designs run. This was followed by the Power design module, which in some cases took fractions of a second, and in others took between 2.8 and 3.1 seconds. All the other subsystem design modules took fractions of a second. Thus, for the rover, the driving subsystem design modules are Telecom, followed by Power. 301 Figure 6-18. Feasible design rover average subsystem run time vs. combination run order In terms of the lander subsystem designs, the average subsystem run time vs. combination order is shown in Figure 6-19. This figure shows that Telecom is again the driving subsystem design module in terms of run time, taking between 12 and 13 seconds. This is followed by the ADCS design module, which took about 0.6 sec on average. So, the Telecom design module’s algorithm is an area for future improvement, to reduce the run time per call. Recall that the Telecom design module uses several nested for-loops to identify the proper antenna size and RF power to achieve > 3 dB link margin for all communication events modeled. This approach takes a lot of computational resources and when multiplied hundreds or thousands of times, renders the total time to run all desired design configurations extensive. It is conceivable that another approach to identifying a feasible Telecom design could reduce that subsystem’s run time, and thus reduce the overall run time of a given system configuration. 302 Figure 6-19. Feasible design lander average subsystem run time vs. combination run order In addition to the subsystem design modules, there is also the Descent & Landing design module. The algorithm employed also takes some time to run (until either the propellant mass estimate converges or the search space is exhausted). This is shown in Figure 6-20 below. According to this figure, the average Descent & Landing run times takes between 2.4 seconds to 5.35 seconds. Note that this average run time per call is less than that of the Telecom design module but more than all the other subsystem modules in general (except for some cases where the rover Power design takes ~3 seconds). 303 Figure 6-20. Feasible design average Descent & Landing module run time vs. combination order To get further insight into the average Descent & Landing run time, Figure 6-21 shows a plot of this vs. final landed mass. It can be seen that there are two clear groups, which differ by the main engine model used. For final masses less than 700 kg, the average run time varied between 2.4 and 5 seconds. For final masses between 900 and ~1100 kg, the average run time varied between 3.7 and 5.4 seconds. Thus, it appears that, in general, higher final land mass requires more run time for the Descent & Landing design module to converge in its propellant mass estimate, but that the run time is also a function of the main engine in use. 304 Figure 6-21. Feasible design average Descent & Landing module run time vs. final landed mass (grouped by engine family) 6.2.2 Selected Designs Since the rover payload configurations are categorized by power source, 3 designs are of interest: the minimum total launch mass configurations for the solar-powered rover, RPS- powered rover, and fuel cell-powered rover. The total launch masses for these configurations were summarized in Table 6-2 in the previous section. These designs are selected because they represent 3 different rover missions. The solar-powered Rover, for example, can only operate at sunlit lunar South Pole locations (or at the boundary of a sunlit and permanently-shadowed region); the RPS and fuel-cell powered rovers, in contrast, can operate within the permanently- shadowed craters. A graphical comparison of the rover subsystem masses for the selected 3 rover configurations is shown below in Figure 6-22. This figure shows that the driving masses for the rover are from Structures and Power. The RPS-powered rover has the highest Structures and 305 Power subsystem masses, followed by the solar-powered rover, and then the fuel cell-powered rover. Figure 6-22. Feasible Rover Design Subsystem Mass Comparison A graphical comparison of the Lander subsystem mass breakdown for the 3 selected configurations is show in Figure 6-23. This figure shows that the Propulsion subsystem mass is the driving mass for the Lander, followed by Structures and then ADCS. Figure 6-23. Feasible Lander Design Subsystem Mass Comparison 306 The subsystem mass breakdown for these designs are summarized in Table 6-4 through Table 6-6. Table 6-4. Minimum mass solar-powered Rover mass breakdown (config ID = 342) Parameter Rover Lander Total mass (kg) 78.13 826.7 Telecom mass (kg) 2.13 5.0 CDS mass (kg) 10.5 10.5 ADCS mass (kg) 0.748 28.9 Propulsion mass (kg) n/a 636.9 Thermal mass (kg) 1.925 9.1 Structures mass (kg) 19.4 107.6 Power mass (kg) 8.646 8.6 Table 6-5. Minimum mass RPS-powered Rover mass breakdown (config ID = 6102) Parameter Rover Lander Total mass (kg) 112.5 1012.6 Telecom mass (kg) 2.1 5.0 CDS mass (kg) 10.5 10.5 ADCS mass (kg) 0.748 30.8 Propulsion mass (kg) n/a 792.6 Thermal mass (kg) 3.3 10.5 Structures mass (kg) 27.8 134.5 Power mass (kg) 38.1 8.6 Table 6-6. Minimum mass Fuel cell-powered Rover mass breakdown (config ID = 6822) Parameter Rover Lander Total mass (kg) 74.3 805.96 Telecom mass (kg) 2.1 5.0 CDS mass (kg) 10.5 10.5 ADCS mass (kg) 0.748 28.7 Propulsion mass (kg) n/a 619.6 Thermal mass (kg) 1.77 8.9 Structures mass (kg) 18.447 104.6 Power mass (kg) 10.671 8.6 307 Table 6-7. Rover subsystem characteristics of minimum total launch mass solar-powered Rover configuration 342 Rover Subsystem Description Telecom  Relay architecture  Cincinatti Electronics (L3) CTT-505 UHF transceiver o 45W DC transmitter power o 4.9W DC receiver power o 1.85 kg transceiver mass CDS  Software size (MB) = 818.8  Max telemetry rate (Mbps) = 35.6 ADCS  LN-200S IMU o Power (W) = 12 o Mass (kg) = 0.748 Thermal  Total power (W) = 40.3 Structures  Rover mobility system mass (kg) = 19.397  Wheel diameter (m) = 0.23  Wheel width (m) = 0.13  Wheel actuator power (W) = 1.6  Rover overall width (m) = 1.22  Rover overall length (m) = 1.26  Rover overall height (m) = 0.8 Power  Battery type = Li-ion o Energy capacity (W-hr) = 10.0 o Charge capacity (A-hr) = 0.1 o # battery cells = 29 o Total battery mass (kg) = 0.11 o Total battery power (W) = 177.3  Solar array cell type = Si High Efficiency o # solar cells = 9374 o Total solar array mass (kg) = 13.3 o Total solar array power (W) = 295.5 Table 6-8. Lander subsystem characteristics of minimum total launch mass solar-powered Rover configuration 342 Lander Subsystem Description Telecom  Relay architecture  X-band Small Deep Space Transponder o 15.8 W DC transmitter power o 12.5 W DC receiver power o 3.175 kg transceiver mass CDS  Software size (MB) = 1350  Max telemetry rate (Mbps) = 142 308 Lander Subsystem Description ADCS  LN-200S IMU o Power (W) = 12 o Mass (kg) = 0.748  Andrews Space Star Tracker o Total mass (kg) = 0.93 o Total power (W) = 4.4  SSBV Space and Ground Sun Sensors o # sensors = 6 o Total mass (kg) = 0.21 o Total power (W) = 4.36  RCS thrusters only design o Astrium 20N thrusters using Hydrazine  24.6 N max thrust  230 sec Isp  Thruster mass (kg) = 0.395 kg o RCS loaded propellant mass (kg) = 13.6 o # RCS tanks = 2 o Tank outer radius (m) = 0.13 o Single tank mass (kg) = 0.38 Propulsion  Propellant pressurant = Helium  Tank material type = Composite Carbon Fiber Torayca T1000G  Main engine = TR-312-100YN o Isp (sec) = 330 o Max thrust (N) = 555  Fuel tank outer radius (m) = 0.41  Oxidizer tank outer radius (m) = 0.377  Pressurant tank outer radius (m) = 0.185  Total loaded propellant mass (kg) = 579.4  Orbital DV propellant mass (kg) = 213.1  Descent & Landing propellant mass (kg) = 320.23  Reserve + unusable propellant mass (kg) = 46.3 Thermal  Total power (W) = 20.5 Structures  Lander deck width (m) = 1.259  Lander leg diameter (m) = 2.4  Lander leg height (m) = 1.78 Power  Battery type = Li-ion o Energy capacity (W-hr) = 3.76 o Charge capacity (A-hr) = 0.04 o # battery cells = 29 o Total battery mass (kg) = 0.04 o Total battery power (W) = 66.3  Solar array cell type = GaInP2/GaAs/Ge Triple Junction (XTJ) o # solar cells = 1849 309 Lander Subsystem Description o Total solar array mass (kg) = 8.6 o Total solar array power (W) = 191 o Solar array area (m 2 ) = 0.851 Table 6-9. Rover subsystem characteristics of minimum total launch mass RPS-powered Rover configuration 6102 Rover Subsystem Description Telecom  Relay architecture  Cincinatti Electronics (L3) CTT-505 UHF transceiver o 45W DC transmitter power o 4.9W DC receiver power o 1.85 kg transceiver mass CDS  Software size (MB) = 818.8  Max telemetry rate (Mbps) = 35.0 ADCS  LN-200S IMU o Power (W) = 12 o Mass (kg) = 0.748 Thermal  Total power (W) = 40.3 Structures  Rover mobility system mass (kg) = 27.8  Wheel diameter (m) = 0.256  Wheel width (m) = 0.151  Wheel actuator power (W) = 2.29  Rover overall width (m) = 1.41  Rover overall length (m) = 1.42  Rover overall height (m) = 0.95 Power  Battery type = Li-ion o Energy capacity (W-hr) = 10.0 o Charge capacity (A-hr) = 0.1 o # battery cells = 29 o Total battery mass (kg) = 0.11 o Total battery power (W) = 177.3  RPS type = ASRG-850 o # RPS modules = 2 o Total RPS mass (kg) = 38 o Total RPS power (W) = 320 310 Table 6-10. Lander subsystem characteristics of minimum total launch mass RPS-powered Rover configuration 6102 Lander Subsystem Description Telecom  Relay architecture  X-band Small Deep Space Transponder o 15.8 W DC transmitter power o 12.5 W DC receiver power o 3.175 kg transceiver mass CDS  Software size (MB) = 1350  Max telemetry rate (Mbps) = 142 ADCS  LN-200S IMU o 12W power o 0.748 kg mass  Andrews Space Star Tracker o Total mass (kg) = 0.93 o Total power (W) = 4.4  SSBV Space and Ground Sun Sensors o # sensors = 6 o Total mass (kg) = 0.21 o Total power (W) = 4.36  RCS thrusters only design o Astrium 20N thrusters using Hydrazine  24.6 N max thrust  230 sec Isp  Thruster mass (kg) = 0.395 kg o RCS loaded propellant mass (kg) = 15.4 o # RCS tanks = 2 o Tank outer radius (m) = 0.136 o Per tank mass (kg) = 0.41 Propulsion  Propellant pressurant = helium  Tank material type = Composite Carbon Fiber Torayca T1000G  Main engine = TR-312-100YN o Isp (sec) = 330 o Max thrust (N) = 555  Fuel tank outer radius (m) = 0.446  Oxidizer tank outer radius (m) = 0.407  Pressurant tank outer radius (m) = 0.2  Total loaded propellant mass (kg) = 730.83  Orbital DV propellant mass (kg) = 263.71  Descent & Landing propellant mass (kg) = 408.7  Reserve + unusable propellant mass (kg) = 58.4 Thermal  Total power (W) = 20.5 Structures  Lander deck width (m) = 1.42  Lander leg diameter (m) = 2.66 311 Lander Subsystem Description  Lander leg height (m) = 1.77 Power  Battery type = Li-ion o Energy capacity (W-hr) = 3.76 o Charge capacity (A-hr) = 0.04 o # battery cells = 29 o Total battery mass (kg) = 0.04 o Total battery power (W) = 66.3  Solar array cell type = GaInP2/GaAs/Ge Triple Junction (XTJ) o # solar cells = 1849 o Total solar array mass (kg) = 8.6 o Total solar array power (W) = 191 o Solar array area (m 2 ) = 0.851 Table 6-11. Rover subsystem characteristics of minimum total launch mass fuel cell-powered Rover configuration 6822 Rover Subsystem Description Telecom  Relay architecture  Cincinatti Electronics (L3) CTT-505 UHF transceiver o 45W DC transmitter power o 4.9W DC receiver power o 1.85 kg transceiver mass CDS  Software size (MB) = 818.8  Max telemetry rate (Mbps) = 35.0 ADCS  LN-200S IMU o Power (W) = 12 o Mass (kg) = 0.748 Thermal  Total power (W) = 40.3 Structures  Rover mobility system mass (kg) = 18.45  Wheel diameter (m) = 0.228  Wheel width (m) = 0.128  Wheel actuator power (W) = 1.53  Rover overall width (m) = 1.19  Rover overall length (m) = 1.24  Rover overall height (m) = 0.79 Power  Battery type = Li-ion o Energy capacity (W-hr) = 10.0 o Charge capacity (A-hr) = 0.1 o # battery cells = 29 o Total battery mass (kg) = 0.11 o Total battery power (W) = 177.3  Fuel cell type = H 2/O 2 o # fuel cells = 110 312 Rover Subsystem Description o Total fuel cell system mass (kg) = 10.6 o Total fuel cell system power (W) = 178.95 Table 6-12. Lander subsystem characteristics of minimum total launch mass fuel cell-powered Rover configuration 6822 Lander Subsystem Description Telecom  Relay architecture  X-band Small Deep Space Transponder o 15.8 W DC transmitter power o 12.5 W DC receiver power o 3.175 kg transceiver mass CDS  Software size (MB) = 1350  Max telemetry rate (Mbps) = 142 ADCS  LN-200S IMU o 12W power o 0.748 kg mass  Andrews Space Star Tracker o Total mass (kg) = 0.93 o Total power (W) = 4.4  SSBV Space and Ground Sun Sensors o # sensors = 6 o Total mass (kg) = 0.21 o Total power (W) = 4.36  RCS thrusters only design o Astrium 20N thrusters using Hydrazine  24.6 N max thrust  230 sec Isp  Thruster mass (kg) = 0.395 kg o RCS loaded propellant mass (kg) = 13.4 o # RCS tanks = 2 o Tank outer radius (m) = 0.13 o Single tank mass (kg) = 0.38 Propulsion  Propellant pressurant = Helium  Tank material type = Composite Carbon Fiber Torayca T1000G  Main engine = TR-312-100YN o Isp (sec) = 330 o Max thrust (N) = 555  Fuel tank outer radius (m) = 0.41  Oxidizer tank outer radius (m) = 0.37  Pressurant tank outer radius (m) = 0.18  Total loaded propellant mass (kg) = 562.58  Orbital DV propellant mass (kg) = 207.44 313 Lander Subsystem Description  Descent & Landing propellant mass (kg) = 310.24  Reserve + unusable propellant mass (kg) = 44.9 Thermal  Total power (W) = 20.5 Structures  Lander deck width (m) = 1.237  Lander leg diameter (m) = 2.4  Lander leg height (m) = 1.77 Power  Battery type = Li-ion o Energy capacity (W-hr) = 3.76 o Charge capacity (A-hr) = 0.04 o # battery cells = 29 o Total battery mass (kg) = 0.04 o Total battery power (W) = 66.3  Solar array cell type = GaInP2/GaAs/Ge Triple Junction (XTJ) o # solar cells = 1849 o Total solar array mass (kg) = 8.6 o Total solar array power (W) = 191 o Solar array area (m2) = 0.851 A side-by-side comparison of the rover and lander masses (wet, dry, and propellant, if applicable), power, dimensions, and other configuration parameters for these 3 configurations are provided below in Table 6-13. The mass difference between the lightest rover (fuel cell- powered rover at 74.3 kg) and the next heaviest rover (solar-powered rover at 78.1 kg) is 3.8 kg. All other configuration parameters being equal, it can be seen that the additional 3.8 kg in the rover power subsystem requires an 826.7 kg lander for the solar-powered rover vs. 805.96 kg for the fuel cell-powered rover, or an additional 20.74 kg. The mass difference between the solar-powered rover (at 78.1 kg) and the RPS-powered rover (at 112.6 kg) is 34.5 kg. This additional mass requires a lander that is 185.6 kg heavier in the RPS-powered rover configuration than in the solar-powered rover configuration. 314 Table 6-13. Comparison of Selected System Configurations Config 342 Config 6102 Config 6822 Total Launch Mass (kg) 904.8 1125.2 880.2 Parameter Rover Lander Rover Lander Rover Lander Power source Solar Solar RPS Solar Fuel Cell Solar Wet Mass (kg) 78.1 826.7 112.6 1012.57 74.3 805.96 Dry Mass (kg) 78.1 247.3 112.6 281.74 74.3 243.38 Loaded Propellant Mass (kg) n/a 579.4 n/a 730.83 n/a 562.58 Peak Power (W) 177.3 114.6 177.3 114.6 177.3 114.6 RCS tank material type n/a Composite n/a Composite n/a Composite Propulsion Main Engine n/a TR-312- 100YN n/a TR-312- 100YN n/a TR-312- 100YN Propellant Pressurant n/a Helium n/a Helium n/a Helium Propulsion tank material type n/a Composite n/a Composite n/a Composite Rover Length x Width x Height (m) 1.26 x 1.22 x 0.81 n/a 1.42 x 1.41 x 0.95 n/a 1.24 x 0.94 x 0.56 n/a Lander Leg Height (m) n/a 1.77 n/a 1.77 n/a 1.77 Lander Leg Diameter (m) n/a 2.43 n/a 2.66 n/a 2.4 Plots of the MASS tool rover/lander total mass, subsystem masses, and runtime history are provided next to illustrate how the above 3 designs converged (see Figure 6-24 through Figure 6-26). In Figure 6-24, depicting system configuration 342, it can be seen that the lander design converged in 7 system iterations, while the rover design converged after 3 iterations. The entire system design took 3.1 minutes to converge, with the average run time per iteration falling between 25.8 and 27.1 seconds. In Figure 6-25 it can be seen that system configuration 6102 converged after 9 iterations, taking 4.13 minutes. In Figure 6-26 it can be seen that system configuration 6822 converged after 7 iterations for a lander mass close to that of Figure 6-24. 315 Figure 6-24. MASS GUI for feasible system configuration 342 Figure 6-25. MASS GUI for feasible system configuration 6102 316 Figure 6-26. MASS GUI for feasible system configuration 6822 Note that the total mass estimates for the 3 configurations in Table 6-13 do not include any system-level margin for growth as the mission concept proceeds into design and development. Standard practice for NASA Pre-phase A concepts is to add 30% to the system- level mass (62). Thus, it is prudent to add this margin onto the total system launch masses for the 3 configurations, as shown in Table 6-14. According to this table, the total system mass with margin for the solar-powered rover configuration (ID = 342) is 1176.24 kg. For the RPS-powered rover configuration (ID = 6102), the total system launch mass with margin is 1462.76 kg. For the fuel cell-powered rover configuration (ID = 6822), the total system launch mass with margin is 1144.26 kg. The masses of the 3 lander configurations can be compared with the lander mass estimates from 3 proposed lunar polar missions: Luna-Glob, Chandrayaan-2 and a NASA International Lunar Network (ILN) concept study. The landers in these concepts are all solar- powered. The Chandrayaan-2 lander, with a wet mass of 1230 kg, is 156 kg heavier than the configuration 342 lander. 317 Table 6-14. Comparison of 3 Selected Configurations and Other Lunar Polar Mission Concepts Config 342 + 30% margin Config 6102 + 30% margin Config 6822 + 30% margin Russian Luna-Glob Lander (63) Chandrayaan- 2 Mission (64) NASA ILN Lunar Polar Rim Concept (65) Solar- powered rover RPS- powered rover Fuel cell- powered rover Solar & RTG powered lander Solar- powered rover Solar- powered lander Rover mass (kg) 101.53 146.38 96.59 n/a 20 n/a Lander wet mass (kg) 1074.71 1316.34 1047.75 1450 (incl. 19kg payload) 1230 1391 (incl. 19 kg payload) Total System mass (kg) 1176.24 1462.76 1144.26 1450 1250 1391 Finally, the Descent & Landing phase breakdown in terms of burn time (or free fall time), initial mass, final mass, propellant mass consumed, and position and velocity components are given in Table 6-15 through Table 6-17 for the 3 selected designs. In Table 6-15, the solar- powered rover system (configuration ID 342) started the de-orbit from a 16 km altitude low lunar orbit, with an initial mass of 691.9 kg and a final landed mass of 371.7 kg. The total propellant required is 320.3 kg for a total duration for all sub-phases of 452 seconds (or 7.53 minutes). In Table 6-16, the RPS-powered rover system (configuration ID 6102) started the de- orbit from a 26 km altitude low lunar orbit, with an initial mass of 861.6 kg and a final landed mass of 452.7 kg. The total propellant required is 408.9 kg for a total duration for all sub-phases of 550 seconds (or 9.1 minutes). In Table 6-17, the fuel cell-powered rover system (configuration ID 6822) started the de-orbit from a 15 km altitude low lunar orbit, with an initial mass of 672.9 kg and final landed mass of 362.5 kg. The total propellant required is 310.3 kg for a total 318 duration for all sub-phases of 439.8 seconds (or 7.3 minutes). In all 3 cases, the minimum touchdown velocity components were -0.109 m/s horizontal and -1.482 m/s vertical. Table 6-15. Descent & Landing design for system configuration 342 Phase Dur (sec) m 0 (kg) m f (kg) Δm p (kg) h 0 (m) v x0 (m/s) v y0 (m/s) BB1 277.1 691.9 406.8 285.1 16,000 1671.7 0.0 Free fall 27.3 406.8 406.8 0.0 1580.9 8.66 -9.48 BB2 7.34 406.8 399.3 7.56 717.36 8.66 -53.78 Approach 85.0 399.3 382.6 16.7 500.0 8.66 -5.0 Terminal 55.3 382.6 371.7 10.9 75.0 8.66 -5.0 Table 6-16. Descent & Landing design for system configuration 6102 Phase Dur (sec) m 0 (kg) m f (kg) Δm p (kg) h 0 (m) v x0 (m/s) v y0 (m/s) BB1 348.9 861.6 502.6 358.97 26,000 1666.95 0.0 Free fall 45.0 502.6 502.6 0.0 3469.3 8.66 -13.23 BB2 15.89 502.6 486.3 16.35 1229.5 8.66 -86.27 Approach 85.0 486.3 465.96 20.3 500.0 8.66 -5.0 Terminal 55.3 465.96 452.7 13.3 75.0 8.66 -5.0 Table 6-17. Descent & Landing design for system configuration 6822 Phase Dur (sec) m 0 (kg) m f (kg) Δm p (kg) h 0 (m) v x0 (m/s) v y0 (m/s) BB1 269.1 672.9 395.993 276.9 15,000 1672.175 0.0 Free fall 23.995 395.993 395.993 0.0 1376.1 8.66 -9.84 BB2 6.38 395.993 389.43 6.57 673.0 8.66 -48.76 Approach 85.0 389.4 373.2 16.3 500.0 8.66 -5.0 Terminal 55.3 373.2 362.5 10.6 75.0 8.66 -5.0 6.2.3 Launch Vehicle The capability of a launch vehicle to launch a lunar polar volatiles mission is briefly discussed in this section. A cursory extrapolation of the payload capability of the Atlas V launch vehicle (551 series), for example, shows that a ~5400 kg payload can be delivered to an apogee radius equal to that of the Moon’s orbit around Earth, per the Atlas V payload user’s guide (66). However, this is from a low Earth orbit with an inclination of 27 degrees from Cape Canaveral Air Force Station (CCAFS) in Florida and a transfer orbit perigee altitude of 185 km. Recall that the 319 trajectory used in this research assumed a transfer orbit perigee of 150 km and an orbit inclination of 20.95 degrees. Thus, a plane change of 6.05 degrees would be required at some point prior to the start of the lunar transfer burn (provided by the Centaur upper stage). The plane change Delta-V from a 150 km altitude circular low Earth orbit is 0.824 km/s, whereas from a 185 km altitude orbit it is 0.823 km/s, a difference of only 1 m/s. NASA has made publicly available a Launch Vehicle Performance website, provided by its Launch Services Program, from which the payload capability to transfer from a 185 km perigee altitude (at an orbit inclination of 20.95 degrees) to the lunar vicinity can be estimated (67). Using this tool, a plot of payload mass vs. transfer orbit apogee altitude can be generated, as shown in Figure 6-27 below. This plot shows the payload curve for two Atlas V variants: the 401 (4m payload fairing, 0 to 3 solid rocket boosters) and the 551 (5m payload fairing, 0 to 5 solid rocket boosters). Assuming the plot can be linearly extrapolated beyond the limit of 100,000 km perigee altitude, out to the lunar vicinity, the payload capability can be estimated. For the Atlas V 551, the extrapolated payload capability to the Moon is 2922.3 kg. Since the total launch mass for the heaviest lander/rover candidate design is 1462.8 kg, it seems feasible that the Atlas V 551 can loft this payload to the Moon. Further analysis is needed to determine the Atlas V payload launch capability to the Moon from a 150 km transfer orbit perigee instead of 185 km. This analysis can also be extended to the Delta IV and Falcon 9 launch vehicles. 320 Figure 6-27. Atlas V payload mass vs. Apogee altitude 6.3 INFEASIBLE DESIGN CONFIGURATIONS As mentioned in Section 6.1, there were 140 infeasible designs out of the 240 that were run. The reason for infeasibility is that the BB1 solution algorithm reached the user-defined search limit of 100 km for the initial de-orbit altitude h 0. The particular value of 100 km exists because the GMAT trajectory design ends with the spacecraft stack entering a 100 km circular low lunar orbit (LLO). To increase this Descent & Landing search limit to, say, 150 km would require designing a new GMAT trajectory to target an LLO of 150 km. The range of infeasible total launch masses ranges from ~1200 kg to just over 4000 kg, as the plot of total launch mass vs. configuration run order shows below in Figure 6-28. 321 Figure 6-28. Infeasible design total launch mass vs combination run order Since the reason for infeasibility in the above designs is that the Descent & Landing design module ran out of viable h 0 search space, an analysis of the D&L results was performed. Figure 6-29 shows a plot of infeasible de-orbit altitude h 0 vs. total launch mass. As expected, the de-orbit altitude h0 sits at 100 km in all cases, as that was the upper limit of the search space. In addition, it is interesting to note that the cases involve configurations that use all 3 available Propulsion primary engines: the TR-312-100YN, R-42, and HiPAT Dual Mode engines. The first two options were found in the feasible design results; however, the HiPAT engine was not. So, this means that all HiPAT engine configurations resulted in infeasible designs. The HiPAT engine has the lowest mass flow rate of all 3 engine options. Of the 140 infeasible designs, 80 used the HiPAT engine, 12 used the TR-312-100YN, and 48 used the R-42. 322 Figure 6-29. Infeasible designs solved h0 vs. total launch mass These infeasible cases also all stayed at 6 engines when the 100 km limit of h 0 was reached, per the following plot of the number of D&L engines required vs. combination run order. Figure 6-30. Infeasible design # engines vs. combination run order 323 The total configuration run time for all infeasible cases varied from ~1.1 minutes up to 6.84 minutes (4 cases above the 6-minute mark). This time represents the duration that the MASS tool ran in each configuration until a design infeasibility condition was reached. The near 7 minute cases represent configurations in which several system iterations were achieved before design infeasibility was reached. That is, the designs were considered feasible until the very last system iteration. Figure 6-31. Infeasible design total configuration run time vs. combination run order When the infeasible design total configuration run time is plotted again total launch mass, as shown in Figure 6-32, it can be seen that the total run time remains below 2.25 minutes for all configurations with total launch mass < 2000 kg, then there is a spike just after the 2000 kg mark past 6 minutes, followed by another grouping between 3000 and 4000 kg in which the run time varies between 2 and 5 minutes. According to Figure 6-33, the spike around 2000 kg total launch mass involved cases reaching up to 13 iterations (2 cases) before design infeasibility was reached. 324 Figure 6-32. Infeasible design total configuration run time vs. total launch mass Figure 6-33. Infeasible design total # convergence iterations (until infeasibility) vs. total launch mass The two cases reaching 13 iterations (configuration 5967 and 6111) are of interest. The MASS GUI for both these cases are displayed below in Figure 6-34 and Figure 6-35. In both of these cases, it appears that the iterations were on the way to converging if only there were 325 additional search space in h 0. Although these cases do not represent the highest total mass configurations, they do represent an interesting set of data points in studying the iteration behavior of infeasible designs. Figure 6-34. MASS GUI for infeasible system configuration 5967 Figure 6-35. MASS GUI for infeasible system configuration 6111 326 According to Figure 6-36, a plot of total launch mass vs. final landed mass, it can be seen that the handful of large run time cases near 2000 kg total launch mass appear to be configurations using the TR-312-100YN liquid apogee engine and the HiPAT engine. The infeasible designs near the high total launch mass end of the plot appear to use the R-42 high mass flow rate engine. Most of the infeasible designs on the low total launch mass end of the plot appear to use the HiPAT engine. Figure 6-36. Infeasible design total launch mass vs. final landed mass (by engine family) When the same data is plotted by groupings of the Propulsion tank material type, as shown in Figure 6-37 below, it can be seen that the majority of infeasible designs appear to use metal tanks (in this case Aluminum). Overall, 48 of the 148 infeasible cases (or 34.3%) involved use of composite Propulsion system tanks, and 92 (or 65.7%) involved use of metal tanks. 327 Figure 6-37. Infeasible design total launch mass vs. final landed mass (by Prop tank material family) Plotting the same data by Rover power source shows that all 3 power sources are represented among the infeasible designs (fuel cell at the lower final landed mass end, and RPS at the upper final landed mass end). Figure 6-38. Infeasible design total launch mass vs. final landed mass (by Rover power source) 328 Finally, the MASS GUI for the highest total launch mass infeasible configuration (5782 at 4020.3 kg) is shown below. This GUI clearly shows that the total lander mass is diverging by the time the 5 th system iteration is in progress, at which point the design becomes infeasible. Figure 6-39. MASS GUI for infeasible system configuration 5782 7 CONCLUSIONS The goals of the research presented in this dissertation were two-fold: 1) to evaluate multiple candidate designs for a lunar polar volatiles rover mission, and 2) to develop a spacecraft design tool to generate these numerous candidate designs. These objectives were both met at the conclusion of this research. This section summarizes the overall design results, including the performance of the design tool itself, and draws several conclusions. In an effort to obtain multiple candidate designs for a lunar polar volatiles mission, a design tool named the Mission and Spacecraft Sizing (MASS) tool was developed. In this tool, subsystem design modules were built to estimate the mass and power required of each subsystem. A science payload of 30 kg and 100 W peak power was assumed. This payload was 329 assumed to be housed on the rover, and the rover housed on the lander. The lander was assumed to perform standard spacecraft functions as well as perform the Descent & Landing maneuvers to soft land on the Moon. The development of the MASS tool itself was an exercise in investigating an approach to the multi-disciplinary design problem, as applied to a lunar lander mission. This approach utilized a sequential design of the spacecraft subsystems, with iteration required at the system level to attain design convergence (or not). The tool was developed in MATLAB to design a full system (lander and rover) based on sets of system configuration inputs. These system configurations represent different combinations of choices for specific spacecraft design elements (i.e. subsystem technologies) or design parameters. The system configuration inputs were defined in an Excel-based Mission and Spacecraft Definition (MASD) tool, the final output being a set of numerous system configuration input .m files (for ingestion into the MATLAB- based MASS tool). Although 7920 system configuration inputs were generated, it was decided to run a smaller subset given that the total time required to run all configurations in MASS was extensive. This subset was identified by accepting configurations that used helium propellant for the RCS pressurant, filtering those that used one of 3 representative bi-propellant main engines (at low, medium, and high mass flow rate), and filtering those that used either low or high efficiency rover power systems. The process of defining numerous system configurations and running them through a design tool resulted in the successful generation of numerous designs. That is, the operation of the MASS tool demonstrated that a sequential-iterative approach can result in design convergence. Some of the designs were infeasible (because of invalid Descent & Landing phase 330 solutions), while the remaining designs were considered feasible due to their ability to converge in total system launch mass. The results of these design runs were analyzed to down-select from the set of feasible designs down to 3 candidate designs: a solar-powered rover mission, an RPS- powered rover mission, and a fuel cell-powered rover mission. A general summary of the findings of the MASS tool design runs of the lunar polar volatiles rover system configurations is provided next:  Feasible designs: o 240 system configurations were run in the MASS tool, which required almost 7 hours of run time. o Of the 240 configurations run in the MASS tool, 41.7% were feasible (100) and 58.3% were infeasible (140). o For the feasible designs, the total converged launch mass varied between 880.8 kg and 3262.8 kg. o There were no feasible designs that used the low mass flow rate engine, HiPAT Dual Mode Liquid Apogee thruster. Only the medium mass flow rate TR-312- 100YN engine and maximum mass flow rate R-42 engines had feasible system designs. o The low mass flow rate TR-312-100YN engine can achieve de-orbit for braking burn 1 at lower altitudes than the high mass flow rate R-42 engine can. o The two feasible design engines show two distinct families when total launch mass is plotted against final landed mass: a low mass family (corresponding to the low mass flow rate engine) and a high mass family (corresponding to the high mass flow rate engine). 331 o Both metal and composite Propulsion tanks were featured in the feasible designs. o Designs for all 3 Rover power source were represented in the set of feasible designs. o There are 5 distinct total Rover masses in the set of feasible designs, ranging from 74.3 kg (fuel cell powered) to 183 kg (RPS-powered). o All feasible designs required 6 engines. o The run time per configuration varied from ~3.1 minutes to 7.3 minutes, or 7 iterations to 15 iterations. o The average system iteration run time varied between ~26 and 32 seconds. o For the rover, the largest contributors to the average system iteration run time were Telecom and Power, whereas for the Lander the largest contributors were Telecom and ADCS. This was in general followed by the Descent & Landing design module, which took between 2.4 and 5.4 seconds, depending on final landed mass and the main engine in use.  Infeasible designs: o The infeasible designs were marked so as a result of exhausting the BB1 h 0 solution search space (in many cases after up to 13 iterations). Some of these designs would have been feasible had more search space been available, while the rest just did not converge in total system launch mass. o The range of infeasible non-converged total launch mass ranged from 1200 kg to just over 4000 kg. 332 o The infeasible designs included configurations that used each of the 3 available engine options. All low mass flow rate HiPAT engine configurations were infeasible. o The total run time per configuration (until design infeasibility was reached) varied between 1.1 minutes up to 6.84 minutes (between 1 and 13 system iterations). o About 65.7% of the infeasible designs used metal Propulsion system tanks on the lander, whereas 34.3% used composite tanks. o All 3 rover power source options were present in the infeasible designs Overall, this research has demonstrated that a space mission concept can be designed using an automated sequential-iterative approach—that is, this approach does result in feasible (converged) design cases. This mission & system design tool can be used to design a couple hundred configurations within a few hours, although potentially thousands of configurations can be designed with sufficient time and computing resources. Although thousands of configurations may be possible, it may not be necessary to run them all to get reasonable results, as the bounding cases in terms of technology characteristics can be used to filter out the intermediate configurations. If it is desired to run all possible system configurations, this suggests a need to reduce the total run time per configuration. The ability to successfully use such a tool is directly related to both the total run time per configuration and the fidelity of the subsystem design modules. First, the run time per system iteration itself depends on the complexity of the algorithms used in each subsystem design module (or other sizing module, such as Descent & Landing), as more complex modules can translate into longer run time per module. For example, the Telecom design module 333 included several for loops that cost significant run time per system iteration. The Descent & Landing module came in second place, in general, in terms of run time per system iteration. Efforts to reduce the run time of each module, such as Telecom and Descent & Landing, would be beneficial in that that more of the system configurations could be run in a given amount of time and given set of computing resources. Second, the fidelity of the sizing algorithms in each subsystem or landing module determines the level of confidence in the design results. More mature algorithms are expected to produce results with higher fidelity, whereas less mature algorithms will have more uncertainty in the results. However, the fidelity of the sizing algorithms is also tied to the run time, as more complex algorithms (especially those that use loops extensively) in general require more run time. Thus, there is a balance between algorithm complexity and run time that can and should be achieved. Lastly, the 3 candidate designs generated by the design tool show that 3 unique missions are possible: 1) a solar-powered rover that can explore a sunlit region at the lunar South Pole (possibly including brief excursions into a nearby permanently-shadowed region); 2) a radioisotope-powered rover (using an ASRG) that can exclusively explore a permanently- shadowed region; and 3) a fuel cell-powered rover that can explore a permanently-shadowed region. The fuel cell-powered rover, in particular, represents a new concept for a lunar polar volatiles mission, and for a space mission in general. 334 8 FUTURE WORK 8.1 DESIGN APPROACH The method developed in this research to select candidate lunar rover spacecraft system designs can be generalized to any particular class of space mission. The approach can be adopted for any landed mission. These missions could include, for example, other lunar surface missions with different propulsive technology to reach the Moon (e.g. low-thrust trajectories to reach low lunar orbit, or weak stability boundary methods), or lunar ascent missions (such as lunar sample return). A lunar ascent mission would require an additional Ascent & Orbit design module to design the ascent phase of the mission, along with a return-to-Earth trajectory designed by some trajectory software. Similarly, a Europa lander could also be designed using the method outlined in this research, where the mass of shielding needed to protect the lander’s electronics from Jupiter’s intense radiation field would need to be estimated. Mars missions with landers and rovers could also be designed using this method, but would have to include a method for designing the Entry, Descent, and Landing (EDL) subsystem (thermal protection system, aero-shell, parachutes, descent rockets, etc.) as well the EDL trajectory. The approach outlined in this research could also apply to non-landed missions as well, such as flyby missions and traditional orbital missions. In those cases, the spacecraft structure design module would need to be re-designed to support structural loads expected in a free- flying spacecraft. The orbital phase of such missions, in which science is typically conducted, would also require more detail in the subsystem design modules in terms of power modes for 335 science observations, attitude control for pointing science instruments at planet ground targets, and telecommunications links. Apart from adapting the sequential-iterative design approach used in this research for other deep space missions, the approach itself could be modified slightly. For example, a simpler method of estimating subsystem masses than used in this research could be explored. In this research, some of the subsystem design modules relied on component databases to estimate subsystem mass (Telecom, ADCS, Propulsion, Power), whereas others relied on simpler mass estimating relationships (CDS mass based on complexity, Thermal mass based on mass fraction), or more complex methods (Structures sizing based on structural loads). Instead of this mixture of mass estimating methods, all the subsystem design modules could use mass estimating relationships (MERs) based on driving parameter inputs to estimate subsystem mass. This could significantly reduce the run time per subsystem module, the total run time per system iteration, and thus the total run time until convergence per system configuration. The use of MERs was not explored in this research due to the lack of publicly available historical system and subsystem mass data (as much of this data is proprietary or considered export-sensitive). Alternatively, all subsystem design modules could be component-based—although this would require maintenance of the component databases to remove obsolete technology or add newly developed technology. The sequential/serial-iterative approach used in this research employed one particular subsystem design module ordering: Telecom, CDS, ADCS, Propulsion, Thermal, Structures, Power. However, given that there are 7 subsystems modeled, they can be ordered in 7! = 5040 ways (permutation without repetition). More investigation of various subsystem orderings could 336 be done to determine if there is a converged mass dependency on order, or whether some orderings produce the converged design in fewer system iterations. Another improvement to the current method would be to improve the run time per system iteration by reducing key subsystem run times. This would enable faster system configuration design run times and so more configurations could be run in a given time period. In this research, the Telecom and Descent & Landing design modules took the most run time. If a way to perform the design of both these modules (along with the other subsystem design modules) in, say, a total of 5 seconds per system iteration, then the 7920 configuration combinations initially identified could be run on a single MATLAB instance in less than 7 days (assuming 15 system iterations per converged design) instead of the expected 41 days. Another way to reduce the total run time per configuration would be to investigate the use of MATLAB’s Parallel Processing toolbox. This toolbox could potentially enable runs of thousands of system configuration. The Parallel Processing toolbox could be combined with calling multiple instances of MATLAB to reduce the total run time for thousands of configurations even further. The validity of the design results could also be assessed by comparing the design results of certain point designs to those obtained in other tools (using the same set of mission/spacecraft assumptions and requirements). This would help validate the correctness of the design results and also validate the sizing algorithms used in the tools. Finally, the overall sequential/serial subsystem design architecture could be compared against a parallel subsystem design architecture. This would require use of a different programming language than MATLAB that allows parallel execution of subsystem design 337 modules (such as C or C++). This comparison would help identify which method is faster in overall run time when attempting to perform thousands of designs. 8.2 LUNAR POLAR VOLATILES MISSION Aside from the specifics of the design approach taken in this research, additional research can be conducted into the lunar polar volatiles mission that was explored. For example, a more detailed characterization of the instrument payload could be performed, such as the science observation power profile on the lunar surface to improve the rover power subsystem design. This power profile implies that a more in-depth study of the surface mission, including comparing different mission durations and the impact on the rover power system design, could be performed. Also, the thermal subsystem design of the instruments could be investigated further to ensure they can all operate in the cold environment of the permanently-shadowed craters. Other trajectory approaches to reaching the Moon than a chemical propulsion-driven ballistic trajectory could also be explored. For example, use of an optimal low-thrust trajectory could be investigated as a way to reduce the overall system mass to deliver the heaviest rover configuration to the Moon. Another alternative could be the use of weak stability boundary theory to produce a ballistic trajectory that takes advantage of solar and lunar gravitational perturbations. This could reduce the Delta-V for a trajectory to the Moon by up to 222 m/s (68). Lastly, the use of a relay satellite in a suitable orbit about the Moon could be explored as another way for the lunar rover to communicate with the Earth. This telecommunications architecture would require the design of the relay satellite orbit, as via a separate trajectory design software package, or by incorporating orbital mechanics equations into the MASS tool to 338 identify the best relay satellite orbit for the lunar rover telecom equipment and relay link data rates. Another relay option could be a relay satellite sitting in a halo orbit at the Earth-Moon Lagrange Point 1 (L1). This type of relay satellite has been studied as pole-sitters, or satellites that are visible from the lunar poles (69). 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[Cited: October 4, 2016.] https://en.wikipedia.org/wiki/Orbit_of_the_Moon. 71. Roncoli, Ralph B. Lunar Constants and Models Document. Pasadena : JPL D-32296, 2005. 72. C. N. Guiar, F. L. Lansing. Antenna Pointing Systematic Error Model Derivations. Pasadena : Jet Propulsion Laboratory, 1986. 73. Wikipedia. Multi-Mission Radioisotope Thermoelectric Generator. Wikipedia. [Online] [Cited: September 30, 2012.] http://en.wikipedia.org/wiki/Multi- Mission_Radioisotope_Thermoelectric_Generator. 74. Space Radioisotope Power Systems: Multi-Mission Radioisotope Thermoelectric Generator. [Online] U.S Department of Energy (DoE), 2006. [Cited: October 1, 2012.] http://www.ne.doe.gov/pdffiles/MMRTG_Jan2008.pdf. 75. NASA Glenn Technology. www.nasa.gov. [Online] NASA Glenn. [Cited: October 16, 2012.] http://www.nasa.gov/centers/glenn/technology/fuel_cells.html. 344 76. H2O2-Based Fuel Cells for Space Power Systems. Luo, Nie, et al. 3, s.l. : Journal of Propulsion and Power, 2008, Vol. 24. 77. NASA. Stirling Converter Technology. Radioisotope Power Systems. [Online] NASA. [Cited: September 13, 2016.] https://solarsystem.nasa.gov/rps/asrg.cfm. 345 10 APPENDICES APPENDIX A: CHARACTERISTICS OF THE MOON Appendix A1: Lunar Orbital Characteristics In the design of a simple patched conic trajectory to the Moon, the Moon’s orbit is usually assumed circular with a radius of r m = 384,400 km. In the real world, however, the Moon’s orbit is somewhat eccentric. In fact, the Moon’s orbital elements vary over time as a result of perturbations from various sources (Sun, planets, etc.). The following is a description of the classical orbital elements of the Moon’s orbit about the Earth. Figure 10-1 illustrates the Moon’s orbital geometry.  Semi major axis: the mean semi-major axis of the Moon’s orbit about Earth is a m = 384,400 km, resulting in a mean sidereal period of 27.317 days, varying by as much as 7-hrs due to solar perturbations. The period of the Moon about the Earth with respect to the Sun, known as the synodic period, is almost 2 days longer at 29.531 days. As such, the synodic period is the time between full Moons as viewed from Earth or the time between lunar sunrises as viewed from the lunar surface.  Eccentricity: the mean eccentricity of the Moon’s orbit about Earth is e m = 0.0549, varying over a period of 31.8 days due to solar perturbations.  Inclination: the mean inclination of the Moon’s orbit about Earth with respect to the ecliptic plane is nearly constant at 5.13 degrees, varying between 4.99 degrees and 5.3 deg. However, given that the Earth’s equator is inclined 23.45 degrees with respect to the ecliptic, the Moon’s inclination with respect to the Earth’s equator will vary between a maximum of 5.13 346 + 23.45 = 28.58 degrees (when the ascending node aligns with the direction of vernal equinox) and a minimum of 23.45 – 5.13 = 18.32 degrees (when the descending node aligns with vernal equinox).  Longitude of the Ascending Node: This variation, oscillating between ±13 degrees relative to the vernal equinox, occurs with a period of 18.6 years.  Argument of Perigee: the lunar line of apsides, and thus argument of perigee, rotates a full 360 degrees within the mean orbit plane every 8.9 years. Figure 10-1. Moon Orbital and Equatorial Inclination (70) The Moon is gravitationally locked in its orbit about the Earth. This results in a synchronous rotation of the Moon. That is, the Moon rotates 360 degrees about its axis in nearly the same time it completes one full orbital revolution about the Earth (the sidereal orbital period). This means that the same side (the near side) always faces the Earth, while the opposite side (far side) is not visible from Earth. 347 At any given time, only 50% of the surface of the Moon is visible from Earth. However, a phenomenon known as lunar libration allows about 59% of the Moon’s surface to be seen from Earth. Libration is an apparent “rocking motion” that affects the amount of the lunar surface visible from the Earth over time. This apparent lunar libration has three components: 1) A libration in latitude due to the ~6.7 degrees inclination of the Moon’s equator with respect to its orbital plane. That is, at one point in time the lunar North Pole is tipped toward Earth, and two weeks later the lunar South Pole is tipped toward Earth. This geometry is shown in Figure 10-2. Figure 10-2. Lunar Libration in Latitude (71) 2) A libration in longitude due to the Moon’s orbital eccentricity, wherein 8.16 degrees around each limb of the Moon is visible as a result of the Moon’s uniform rotation about its axis while in its orbital motion it speeds up at perigee and slows down at apogee. That is, in the time the moon rotates a full 90 degrees, it has traveled less than 90 degrees around its orbit. This allows an observer on Earth to see a little bit of the “far side” of the moon, as depicted in Figure 10-3. 348 Figure 10-3. Lunar Libration in Longitude (71) 3) There is also a physical diurnal libration, in which an observer on Earth views the Moon from different angles as the Earth rotates. Over a period of 12 hours, the observer can see almost 2 degrees more of the moon at its limbs (71). This geometry is shown in Figure 10-4. Figure 10-4. Physical diurnal libration of Moon as a result of Earth’s rotation (71) Appendix A2: Lunar Surface Environment As previously mentioned, the Moon is in synchronous rotation about the Earth, i.e. the rotation period of the Moon about its axis is the same as its sidereal orbital period of 27.31 days, as a result gravitational tidal forces between the Earth and Moon. In contrast, the average length of the Moon’s solar day is the synodic period of 29.531 days. This means that most of the Moon is bathed in sunlight for approximately half the synodic period, or 14.77 days, a little over 2 weeks. Due to the tilt of 1.543 degrees of the Moon’s axis relative to the ecliptic plane, 349 however, there are regions at the poles that are either bathed in continuous sunlight or experience continuous shadow. For example, the rim of Shackleton crater at the lunar south pole experiences sunlight for 80% of the lunar day. The Moon has only 1.2% the mass of the Earth within a diameter only 27.25% that of the Earth. Using Newton’s law of gravity, the Moon therefore has surface gravitational acceleration of 1.62 m/s 2 at the lunar equator. This is approximately 1/6 th that of the Earth’s surface gravitational acceleration of 9.81 m/s 2 . The lunar gravity field, however, is not totally uniform, as a consequence of lunar mass concentrations, i.e. “mascons”, beneath the surface. These are due in part to the presence of dense basaltic lava flows within some of the giant impact basins. The non-uniform lunar gravity field can have significant influence on the orbit of any spacecraft orbiting the Moon. The Moon has an extremely thin atmosphere, technically known as a surface boundary exosphere. This thin atmosphere has a total estimated mass of gases of only 104 kg and a mean atmospheric pressure of 3x10 -15 bar (where 1 bar = 100,000 Pascals = 0.987 atm). As such, for most intents and purposes, the environment at the Moon’s surface can be considered a vacuum. The gases in the thin atmosphere come mostly from outgassing from rocks on the lunar surface and possibly from the lunar interior. These gases are quickly lost to space either due to energy imparted by solar heating or the magnetic field of the solar wind (for ionized particles). The following is a list of the gases detected in the thin lunar atmosphere either by Earth-based spectrometers or instruments on spacecraft: Hydrogen, Helium-4, Sodium, Potassium, Radon- 222, Polonium-210, Argon-40, Oxygen (O 2), Methane (CH 4), Nitrogen (N 2), Carbon monoxide (CO), Carbon dioxide (CO 2). The hydrogen and helium most likely originate from the solar wind, while argon is likely from the lunar interior (53). 350 As a consequence of the thin atmosphere and the long synodic day, the temperature of the lunar surface varies widely in both time (from day to night) and location. The average surface temperature during the day is ~107 degrees Celsius, reaching up to 280 degrees Celsius at noon on the equator. During the lunar night, the average temperature is -153 degrees Celsius and can reach as low as -233 degrees Celsius in the permanently-showed polar regions. Below the surface, the temperature is relatively constant. For example, at 1 m below the surface the temperature is a constant -35 degrees Celsius. During the lunar day, any objects on the lunar surface are heated more due to the ground emitting infrared radiation as a result of solar heating, than due to heating from the Sun itself (53). As for geothermal activity, there has been photographic evidence of small-scale volcanic activity. If confirmed, this may suggest warm magma near the surface that could provide a useful energy source for landed surface assets. The Moon currently lacks a global magnetic field since it does not have an internal dynamo at its core. Thus, the weak magnetic field that is present at the surface, from 3 nT to 0.33 µT, is local to the crust and may be an effect of giant impacts that occurred on the opposite side of the Moon. 9 There is also a weak external magnetic field at 5-10 nT that comes from the solar wind. There are three main types of terrain of the Moon: the relatively flat plains called lunar maria, lunar highlands, and cratered regions. The lunar near side is covered in area 31.2% by lunar mare, whereas the far side is bereft of lunar mare at only 2.6%. The lunar mare regions are thought to be ancient basaltic lava, containing the elements iron, titanium and magnesium. 9 The Earth’s magnetic field, in contrast, ranges from 30-60 µT at the surface, several hundred times stronger. 351 These ancient plains are believed to have formed by the impact of giant meteoroids that formed large impact basins. The large mountains found along the periphery of the impact basins are thought to be the impact rims. The lack of an atmosphere and active geology renders most of the lunar surface as well preserved. The largest impact crater on the Moon, which is also the largest in the solar system, is the South Pole Aitken basin on the lunar far side. It has a diameter of 2240 km and a depth of 13 km. The lunar surface is covered with a well-mixed layer of soil and rocks called regolith. The regolith soil consists of pulverized rock grains that resulted from ancient meteoroid impacts. Using the specimens acquired during the Apollo 11 mission, the grain size distribution is typically less than 20 µm up to 270 µm. In the lunar mare plains, the regolith layer thickness varies between 3-5m, whereas in the lunar highlands it is 10-20m. Below this regolith layer lies a layer of highly fractured bedrock. The regolith itself consists of the following elements: Sulfur, Iron, Magnesium, Manganese, Calcium, and Nickel. These elements are typically bound in oxides. Of good source of oxygen is the mineral ilmenite (FeTiO 3), typically found in the lunar mare plains. Other useful elements such as carbon, hydrogen, helium and nitrogen in the regolith were likely deposited by the solar wind. The dust grains themselves are electrically charged. This allows them to adhere to almost anything and can be a hazard for both robotic vehicles, equipment, and astronauts. For example, the Apollo astronauts reported that lunar dust was brought onboard the lunar excursion module (LEM) after extravehicular activities (EVAs). The dust consists mostly of silicon dioxide glass (SiO 2) created during ancient meteoroid impacts. Since the dust particles have jagged shapes, they easily interlock and can pose a health hazard for lunar astronauts if breathed in. In addition, the charged dust particles fly on parabolic arcs if disturbed and raised 352 from the ground. Disturbance sources can range from rocket engines during landing, rover wheels, meteoroid impacts, solar ultraviolet radiation, and astronaut boots. Thus, electrostatic devices on future robotic and crewed lunar missions may be needed to prevent the lunar dust from contaminating mechanisms and being breathed in by astronauts. In general, the lunar surface has good bearing capacity for heavy vehicles, habitats, and other structures. The cohesive bearing strength if 300 Pa on the surface and 3 kPa at 0.2m depth (53). This is good news for future lunar exploration, although this could make mining and other construction activities somewhat difficult. As previously mentioned, it is thought that after its formation the Moon received large amounts of water from comet impacts. The liquid and solid water at the lunar surface quickly evaporated. In addition, sunlight splits the water into hydrogen and oxygen, which easily escape due to the Moon’s weak gravity. It is believed, however, that trapped water ice exists at the lunar poles in permanently-shadowed craters (see Section 3.1.1 for details). Radiation on the lunar surface is another concern for lunar vehicles and astronauts. The thin atmosphere does not provide any protection against direct sunlight, the solar wind, or cosmic rays. The lack of a global magnetic field also allows radiation through. It turns out that lunar regolith, however, does provide good radiation protection. Solar wind can only penetrate about a micron, solar flares can penetrate up to 1 cm, and cosmic rays can penetrate up to a few meters. Thus, any future lunar habitats will likely need to employ lunar regolith for radiation protection. Lastly, although the Moon lacks plate tectonics, moonquakes have been detected. Only a few moonquakes up to 4 on the Richter scale have been measured. This seismic activity is attributed to gravitational tidal forces and secondary effects of impacts. Since the Moon itself 353 provides low damping, any seismic activity that does occur can be felt over long distances. Some have suggested this the good seismic propagation of waves allows for a form of communication between points on the Moon. However, seismic activity can also lead to collapsed crater walls and landslides (53). APPENDIX B: SUBSYSTEMS Appendix B1: Telecommunications The uplink communications data rate (direct-from-Earth) depends on the need to receive the ground-specified spacecraft commands, and a navigation ranging signal from Earth. The downlink communications data rate (for a direct-to-Earth link) depends on the need to transmit the following types of data: spacecraft health and safety (H&S) telemetry, science or user-data, and a re-transmitted ranging signal (offset from the received ranging signal by a pre- determined ratio). The downlink data rate can be computed from the telemetry sampling frequency 𝑓 𝑠 (samples/sec) times the number of bits per sample 𝑛 , to derive the required bits per second (bps). 𝑅 = 𝑓 𝑠 𝑛 Equation 10-1 The sampling frequency (for a digitized signal) must at a minimum meet the Nyquist criterion, which is a sampling rate twice that of the highest frequency component in the signal. Following this criterion allows for a theoretical reconstruction of the source analog signal. Other system considerations, however, limit the sampling frequency to be 2.2 times the maximum input frequency (30). 354 In addition, the analog signal amplitude must be converted to a digital sample word, represented by a number of bits per sample 𝑛 . For example, an analog-to-digital conversion process splits the total expected range of the amplitude signal ΔA into M=2 n quantization levels. This results in a quantization step size of ΔV = ΔA/M. The maximum quantization error can then be found as ±0.5ΔV. Thus, the higher the number of bits per sample (the larger the number of quantization levels), the lower the quantization error (and more accurate the digital data). However, the number of bits per sample also depends on the type of mission data: e.g. gray- scale image data might need 8 bits per sample to properly distinguish shades of gray. The number of bits per sample also determines the data precision. To determine the spacecraft health and safety telemetry data rate, the number of signals N being monitored must be considered. These signals can consist of data such as voltages, temperatures, currents, status flags, and other derived sensor signals (spacecraft quaternions, rates, accelerations, position, velocity, etc.). Each of these signals may be sampled at a different rate, depending on how quickly the data is expected to change (and this sampling rate can be ground-commandable). Next the number of bits per sample for each signal must be considered. Finally, we simply add all the data rates for each signal to determine the total health and safety telemetry data rate. To determine the command uplink data rate, we must consider the capability of the ground station or relay satellite and the duration over which the command data must be sent to the spacecraft. The command uplink rate is usually pretty low for a typical spacecraft. To size the antenna system onboard the spacecraft, the link budget for the downlink path from the spacecraft to the ground station must be determined. To do this requires use of the well-known link equation: 355 𝐸 𝑏 𝑁 0 = 𝑃 𝑡 𝐿 𝑙 𝐺 𝑡 𝐿 𝑠 𝐿 𝑎 𝐺 𝑟 𝑘 𝑇 𝑠 𝑅 Equation 10-2 where P t is the spacecraft transmitter power, L l is the line loss from the transmitter to antenna, G t is the transmit antenna gain, L s is the propagation space loss, L a is the atmospheric attenuation transmission path loss, G r is the ground station receiver gain, k is Boltzmann’s constant, T s is the system noise temperature of the receiving antenna, and R is the data rate (for downlink in this case). The result E b/N 0 represents the ratio of received energy-per-bit to noise density. Typically, an E b/N 0 between 5 and 10 is sufficient to receive data with limited error. The product of the spacecraft transmitter power, transmitter to antenna line loss, and transmitter antenna gain is also known as the effective isotopic radiated power, or EIRP: 𝐸𝐼𝑅𝑃 = 𝑃 𝑡 𝐿 𝑙 𝐺 𝑡 Equation 10-3 The same EIRP from a transmitting antenna can be produced using either a low-gain high power antenna system, or a high-gain low power system. The transmitting antenna gain G t, can be calculated from the following equation. 𝐺 𝑡 = 4𝜋𝜂𝐴 𝜆 2 Equation 10-4 The above equation is for the peak gain. However, the transmitting antenna may be slightly pointed off from the desired direction such that strength of the beam reaching the receiving antenna is reduced. In other words, the antenna pointing error leads to reduced antenna gain. The following equation is an estimate of the gain reduction due to pointing error: 𝐿 𝜃 = −12( 𝑒 𝜃 ) 2 Equation 10-5 For DSN antenna pointing, a good rule of thumb is that the pointing error should be 10% of the 3-dB (half-power) antenna full beam-width (72). The propagation space loss can be calculated from the following equation: 356 𝐿 𝑠 = ( 𝜆 4𝜋𝑆 ) 2 Equation 10-6 where 𝑆 is the propagation distance. For the atmospheric transmission path loss L a, the worst-case atmospheric attenuation is accounted for assuming the signal passes through the most atmosphere. In reality, the DSN ground stations (in Goldstone, CA, Madrid, Spain, and Canberra, Australia) vary in altitude from just over 0.6 to 1.1 km. To simplify the atmospheric transmission path loss, the DSN ground stations can be assumed to be all at sea level. The system noise temperature T s is the sum of two noise sources: those originating outside the receiver antenna system and those originating within the receiver antenna system. Noise originating outside the receiver antenna system is known as the antenna noise temperature T ant. Such noise sources include galactic noise, noise from local weather, solar noise in the main beam or a sidelobe, Earth noise in a sidelobe, human-made noise, local buildings and objects, and blockage items in the way of the antenna such as booms and feeds. Noise originating within the receiver antenna system is caused by transmission lines and filters (characterized by L r), and the low-noise amplifier (characterized by the noise figure F). The system noise temperature can be found using the following equation: 𝑇 𝑠 = 𝑇 𝑎𝑛𝑡 + ( 𝑇 0 ( 1− 𝐿 𝑟 ) 𝐿 𝑟 )+ ( 𝑇 0 ( 𝐹 − 1) 𝐿 𝑟 ) Equation 10-7 The first term is the noise external to the receiving antenna, the second is the transmission line and filter loss, and the third is the low noise amplifier loss in the receiver. The parameter T 0 is a reference temperature, usually taken as the 290 K. The link equation itself can be expressed in terms of decibels by taking 10*log 10(E b/N 0). This expands the equation into the following (each term has units of decibels): 357 𝐸 𝑏 𝑁 0 = 𝐸𝐼𝑅𝑃 + 𝐿 𝑠 + 𝐿 𝑎 + 𝐺 𝑟 + 228.6− 10log 10 𝑇 𝑠 − 10log 10 𝑅 Equation 10-8 In addition to the link equation, one must consider how the signal is modulated and coded. In modulation, the signal containing data is processed onto a carrier wave. The wave characteristics that can be modified are amplitude, phase, frequency, and polarization. Demodulation is the reverse process, where the original signal is deduced from the received signal. There are many modulation techniques, depending on the application. For digital modulation, the three general types of modulation are amplitude shift keying (ASK), frequency shift keying (FSK), and phase shift keying (PSK). For spacecraft transmitters, two common modulation techniques are binary phase shift keying (BPSK) and Quadriphased Phase Shift Keying (QPSK). BPSK transmits a binary 0 by setting the carrier wave phase to 0 deg, and transmits a binary 1 by setting the phase to 180 deg. In QPSK, four phases are available (0 deg, 90 deg, 180 deg, and 270 deg). Each phase option transmits two bits. The DSN exclusively uses coherent digital modulation. Deep space spacecraft have commonly used binary phase shift keying (BPSK) modulation on the subcarrier for maximum power capture. Other bandwidth efficient methods have recently been employed, such as QPSK and offset QPSK. In demodulating a received signal, the energy per bit (E b) must be larger than the noise spectral density (N 0). Thus, the required E b/N 0 is specified at a desired bit error rate (BER). The BER is the probability that an erroneous bit will be received. A typical BER is 1e-5. Often, extra parity bits are added to the digital signal to allow the receiver to perform limited error correction, when bit errors caused by noise or interference are present. A famed error 358 correction technique is convolutional coding with Viterbi decoding. In this technique, two error correction bits are added for each data bit to be transmitted. Since the actual data content is ½ the transmission rate, the coding is termed rate-1/2 convolutional code. When the signal is received, the demodulated signal data is stored in memory as sequences using the Viterbi algorithm. The stored sequences are compared with other coded sequences until the most likely transmitted sequence is found. Viterbi decoding has the advantage of reducing the required E b/N 0, thereby reducing the required transmission power (30). Another coding technique is Reed-Solomon coding. In this scheme, the binary signal is coded using a 255-bit code with 32 parity bits (the actual data is encoded in 223 bits). The DSN can accommodate several error correction codes. Examples include (7, ½) convolutional code with frame-based Reed-Solomon (255, 223) coding with Viterbi decoding, (15, 1/6) convolutional code, and Turbo codes. As previously mentioned, the modulation scheme and error coding determines the required signal to noise ratio (E b/N 0) for a desired bit error rate (BER). For the current rover mission, a BER of 1e-6 can be achieved at a required E b/N 0 of 5 dB when using BPSK and QPSK plus R-1/2 Viterbi decoding. Note that the theoretical minimum E b/N 0 possible, known as the Shannon limit, is -1.6 dB. At any E b/N 0 below this limit, no error-free links can occur (at any data rate). This is related to the Shannon-Hartley theorem, which determines the maximum data rate that can be achieved over a transmission with bandwidth B, as shown in the following equation. 𝑅 𝑚𝑎𝑥 = 𝐵𝑙𝑜 𝑔 2 ( 1 + 𝐶 𝑁 ) Equation 10-9 where B is the transmission channel bandwidth and C/N is the carrier-to-noise power ratio. In practice, the Shannon limit cannot be reached because of increased complexity in the coding scheme. 359 Appendix B2: Power The following sections describe some important aspects of the various power sources studied in this research, as well as some of the fundamental operational principles. Solar Arrays One important consideration in solar array design is the effect of temperature. Consider low-temperature circuits for a solar array on a rover operating in permanently shadowed regions (PSRs) at the lunar South Pole (such a rover would could have brief forays into the PSRs and then return to sunlight areas to recharge the batteries). Such low-temperature circuits would eliminate the need for isotope heaters, which can result in overheating during launch. Temperatures within lunar PSRs do not exceed 100 K (-173 C), based on recent LRO Diviner data. It is known that some semiconductor devices have improved performance down to temperatures of ~83 K (-190 C), the temperature of liquid nitrogen. The reason is that at such low temperature, these devices have reduced leakage current and susceptibility to latch-up, as well as higher operating speed (42). Radioisotope Power Systems A radioactive power system (RPS) provides power using the heat of isotopic decay to generate electricity. An RPS has the potential to provide continuous power throughout a mission’s operational life. In cases where there is no peak power load, this can even be accomplished without the need for a battery system. A primary disadvantage, however, is that electronics near RPS systems require extensive radiation shielding (42). 360 The mass of a radioisotope decays exponentially according to the half-life, T 1/2. Since the decay heat is proportional to the isotopic mass, the thermal power will also decay exponentially, according to the following equation. 𝑃 ( 𝑡 )= 𝑃 0 𝑒 −0.7𝑡 𝑇 1/2 Equation 10-10 In an RPS system, either a thermoelectric converter (TEC) or dynamic alternator is used to generate electricity from the heat source. The amount of electrical power generated can be determined from the conversion efficiency. This efficiency is defined as the ratio of electrical power produced to thermal power from decay. RTGs have been used on several NASA missions, from Apollo, Viking, Voyager, Galileo, Cassini, and Pluto New Horizons. NASA has recently been investing in the development of advanced radio-isotope power systems with higher efficiency power conversion. Higher efficiency power conversion requires less radio-isotope fuel than the previous generation of RTG and improves the specific power 10 . The MMRTG program began in June 2003, when the U.S. Department of Energy (DoE) awarded Boeing the MMRTG contract (through its Rocketdyne Propulsion and Power Division) 11 . Boeing and its partner Teledyne Energy Systems developed the MMRTG design based on the SNAP 19 RTGs, which powered NASA’s Pioneer 10 and 11 spacecraft, as well as the Viking 1 and 2 Mars landers (73). 10 The current practical RPS specific power limit appears to be 10 W/kg. 11 Pratt & Whitney later acquired Rocketdyne Propulsion and Power. 361 The MMRTG can operate in the environment of space as well as the surface of a planetary body or moon. The MMRTG is powered by 8 plutonium-238 dioxide general purpose heat source (GPHS) modules, carrying a total of 4.8 kg of Pu-238 dioxide. The MMRTG employs solid state PbTe/TAGS 12 thermoelectric couples to convert the decay heat into electricity. At the beginning of life, the MMRTG can generate ~2 kW thermal power. The MMRTG can generate a minimum of 125 W electrical power at 28 V DC (direct current) at the beginning of life, which is reduced to 100 W after a design life of at least 14 years (74). The MMRTG has a mass of 43 kg and has a specific power of 2.9 W/kg. It is packaged in a cylindrical structure with radiator fins, having dimensions of 64 cm diameter (fin tip to fin tip), and a length of 66 cm. Fuel Cells A fuel cell provides power by converting the energy of a chemical reaction into electricity. The reactants consist of fuel (such as hydrogen gas) and oxidizer (such as oxygen gas), which are separated by an electrolyte. The fuel reacts at the anode and the oxidizer at the cathode. As long as fuel and oxidizer are supplied the fuel cell does not run out of energy. As a result, a typical fuel cell can generate several watts of power (and maintain constant voltage) for several days or even several weeks. In 1839, Sir William Grove discovered the fundamentals of fuel cell physics—that gaseous reactants can produce electricity. 13 Over a century passed before an English engineer by 12 Previous space-qualified RTG technology used SiGe thermoelectric couples; however, these are no longer produced (65). 13 Swiss scientist Christian F. Shoenbein is also sometimes credited with an independent discovery of this principle. 362 the name of Francis T. Bacon developed the first fuel cell (generating 6 kW) during the 1950s. The first practical fuel cells, however, were developed for the U.S. Space Program. For example, fuel cells were used in the Gemini manned space program of the early 1960s and also during the Apollo program, most famously on the manned lunar rovers. Later, fuel cells were adapted for use on the U.S. Space Shuttles (as alkaline fuel cells had water management problems). Fuel cells were also considered in place of batteries for the International Space Station. Fuel cells are typically categorized by the type of electrolyte that separates the anode from the cathode. Examples of types of fuel cells are described in the following table. Table 10-1. Fuel Cell Types (57) Fuel Cell Type Electrolyte Catalyst on Electrodes Example Application Alkaline Fuel Cells (AFC) 14 85% potassium hydroxide (KOH) at high temperature operation (250 C) 35-60% KOH for lower temperature operation (< 120 C) Nickel, Silver, Metal Oxides or Noble Metals Apollo and Space Shuttle missions (aqueous alkaline). This fuel cell type is easily poisoned by the presence of CO 2 in either fuel or oxidant Polymer Electrolyte Membrane or Proton Exchange Membrane Fuel Cells (PEMFC) Thin (<50 μm) solid proton conductive polymer membrane at 60-80 C operating temperature Platinum on porous carbon. Typical platinum loadings are 0.3 mg/cm 2 First used on the Gemini missions. Currently, considered the future of space fuel cells Phosphoric Acid Fuel Cells (PAFC) ~100% phosphoric acid contained in SiC matrix at 150-220 C operating temperature Platinum Commercial ground- based power generation Molten Carbonate Fuel Cells (MCFC) Combination of Alkali (Li, Na, K) carbonates in a LiAlO 2 matrix at 600-700 C operating temperature Noble metal catalysts typically not required Pre-commercial stage for ground power 14 A lightweight alkaline fuel cell technology has been recently developed by United Technologies Corporation for NASA 363 Fuel Cell Type Electrolyte Catalyst on Electrodes Example Application Solid Oxide Fuel Cells (SOFC) Solid, non-porous metal oxide (Y 2O 3 with ZrO 2) at 800-1000 C operating temperature Precious-metal catalyst not needed due to high temperature Pre-commercial stage for ground power Most of the fuel cells in the above table utilize hydrogen as the fuel and oxygen as the oxidizer and produce water as a byproduct. 15 Other hydrogen-rich fuels such as alcohols (methanol, ethanol) and hydrocarbons can be used. In the direct methanol fuel cell (DMFC), pure methanol mixed with steam is used as the fuel. Methanol is easier to store than hydrogen as it has a higher energy density. Oxidizers other than pure oxygen or oxygen in air are also being considered. Research is currently being conducted on regenerative fuel cell (RFC) technology. This technology takes advantage of the fact that a fuel cell reaction is reversible—e.g. in a hydrogen- oxygen fuel cell, the water byproduct can be turned back into reactants via electrolysis. In an RFC, however, separate units are required to generate electricity and electrolyze the water. Such a system could be very useful in a long-duration mission given input electricity from another power source operating at low electrical loads. RFCs were not considered for this research as they were considered beyond the scope of the project. RFCs could, however, be the subject of future research for lunar rover applications. Of all the fuel cell types described previously, PEM technology is considered the most useful for spacecraft. For instance, the NASA Glenn Research Center is currently studying 15 The SOFC utilizes oxygen in air and a variety of fuels, even carbon monoxide 364 PEMFC, RFC, and SOFC technology for launch vehicles, interplanetary spacecraft, planetary surface power, aircraft propulsion and other ground-based use (75). The PEMFC is currently regarded as better suited for spacecraft applications as it provides several benefits over other fuel cell types: improved safety and reliability, longer life, lower mass, more power, and potentially lower cost (42). Given these advantages, PEM fuel cells are considered a viable, state-of-the art technology for the lunar mission in this research. PEM fuel cells use a solid polymer membrane as the electrolyte. The electrodes are constructed of porous carbon containing a platinum catalyst. The hydrogen/oxygen PEM typically operates at low temperatures of ~80 C, which reduces warm-up time. A disadvantage is the expensive platinum catalyst, which is needed to separate hydrogen gas into protons and electrons. Another potential downside is the large tank volume needed to store enough compressed hydrogen gas, given hydrogen’s low energy density. To be able to properly size a fuel cell power system some fundamental theory is needed, although it is a bit involved. In a hydrogen-oxygen PEM fuel cell, electrochemical reactions take place simultaneously at the anode and the cathode. At the anode, incoming hydrogen gas is ionized: H 2 → 2H + + 2e − Equation 10-11 The two free electrons can then travel from the anode through the electrical circuit to the load and then to the cathode. Meanwhile, the hydrogen ions migrate from the anode to the cathode through the electrolyte that separates them. At the cathode, the incoming oxygen combines with the hydrogen ions (protons) and returning electrons to form water (either as a liquid or gas): 365 1 2 O 2 + 2H + + 2e − → H 2 O Equation 10-12 Thus the overall hydrogen-oxygen fuel cell reaction is: H 2 + 1 2 O 2 → H 2 O + heat Equation 10-13 The input (thermal) energy into a hydrogen-oxygen reaction is defined by the reaction enthalpy Δ𝐻 (kJ/mol). This reaction enthalpy is the difference between the heats of formation of products and reactants: ΔH = ∑n i h f,products,i k i=1 − ∑n j h f,reactants,j m j=1 Equation 10-14 where n i are the number of moles of each product and n j are the number of moles of each reactant, per the chemical equation. For the hydrogen-oxygen reaction, the reaction enthalpy is then: ΔH = h f,H 2 O − h f,H 2 − 1 2 h f,O 2 Equation 10-15 The heat of formation of water at 25 C and atmospheric pressure is -286.02 kJ/mol (for liquid water). The negative value means that the reaction is exothermic (generates heat). The heat of formation of elements is defined to be zero. Thus, the reaction enthalpy for a hydrogen- oxygen reaction is simply the heat of formation of water. This water can be in liquid form if the exact amount of reactants is consumed and the water is allowed to cool to standard conditions (25 C and atmospheric pressure). If there is excess oxygen, the water product will be in the form of vapor mixed with the residual oxygen, at a lower heat of formation. 366 Since every chemical reaction produces some entropy Δ𝑆 , not all of the reaction enthalpy in a fuel cell can be converted into electricity. The entropy is the difference between the entropies of formation of the products and the entropies of formation of the reactants. The reduction in reaction enthalpy as a result of entropy creation (an irreversible process) is known as the Gibbs free energy. In a fuel cell, the Gibbs free energy is the amount of reaction enthalpy that can be converted into electricity. Δ𝐺 0 = Δ𝐻 − 𝑇 Δ𝑆 Equation 10-16 The theoretical voltage produced by the fuel cell is dependent on the Gibbs free energy as follows: E 0 = − Δ𝐺 0 𝑛𝐹 Equation 10-17 where 𝑛 is the number of electrons per molecule of fuel (H 2 in this case), and 𝐹 is Faraday’s constant (96,485 Coulombs/mol). Note that the Gibbs free energy is a function of temperature, implying that increasing temperature lowers the theoretical cell potential. Also consider that enthalpy and entropy are also functions of temperature, as they depend on the specific heat at constant pressure (itself a function of temperature). The reaction enthalpy and entropy as functions of temperature can be found from the following equations, where the reference temperature is 298.15 K (25 C). h( T)= h( T ref )+ ∫ c p dT T T ref s( T)= s( T ref )+ ∫ c p T dT T T ref Equation 10-18 367 The specific heat at constant pressure (J/mol-K) of a gas is a function of temperature. An empirical relationship is: c p ( T)= a+ bT+ cT 2 Equation 10-19 Integrating Equation 10-18 yields the following expressions for the reaction enthalpy and entropy as a function of temperature. Δ𝐻 = Δ𝐻 𝑟𝑒𝑓 + Δ𝑎 ( 𝑇 − 𝑇 𝑟𝑒𝑓 )+ Δb ( T 2 − T ref 2 ) 2 + Δc ( T 3 − T ref 32 ) 3 Equation 10-20 Δ𝑆 = Δ𝑆 𝑟𝑒𝑓 + Δ𝑎 ln 𝑇 𝑇 𝑟𝑒𝑓 + Δb( 𝑇 − 𝑇 𝑟𝑒𝑓 )+ Δc ( T 2 − T ref 2 ) 2 Equation 10-21 where the coefficients Δ𝑎 , Δ𝑏 , and Δ𝑐 are the differences of the respective coefficients for products and reactants: Δa = ∑n i a product,i k i=1 − ∑n j a reactant,j m j=1 Δb = ∑n i b product,i k i=1 − ∑n j b reactant,j m j=1 Δc = ∑n i c product,i k i=1 − ∑n j c reactant,j m j=1 Equation 10-22 For the hydrogen/oxygen fuel cell, the differences in these coefficients are: Δa = a H 2 O − a H 2 − 1 2 a O 2 Δb = b H 2 O − b H 2 − 1 2 b O 2 Δc = c H 2 O − c H 2 − 1 2 c O 2 Equation 10-23 368 The reaction Gibbs free energy is also a function of pressure, according to the Nernst equation: ΔG = ΔG 0 + RTln( ∏ P product,i n i k i=1 ∏ P reactant,j n i m j=1 ) Equation 10-24 where ΔG 0 is the Gibbs free energy at operating temperature, R is the gas constant (8.314 J/mol- K), T is the operating temperature (K), and 𝑃 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 ,𝑖 and P reactant,j are the partial pressures of the products and reactions, respectively. Incorporating the above gives the equilibrium, or reversible, cell voltage: E equil = E 0 + RTln( ∏ P reactant,j n i m j=1 ∏ P product,i n i k i=1 ) Equation 10-25 For the hydrogen/oxygen fuel cell, this equation becomes: E equil = E 0 + RTln( P H 2 P O 2 1/2 P H 2 O ) Equation 10-26 The above theory has been described using hydrogen/oxygen fuel cells as the example. Other fuel/oxidizer pairs have been considered for space applications. For example, researchers at the University of Illinois have recently proposed a hydrogen/hydrogen peroxide (H 2O 2) fuel cell as a potential power source for space applications (76). In such a fuel cell, hydrogen gas is ionized (losing 2 electrons) and migrates through the electrolyte to the cathode (as is the case with hydrogen/oxygen fuel cell). The electrons travel through the electrical circuit to the load and then to the cathode. At the cathode, an aqueous solution of hydrogen peroxide (H 2O 2) combines with the returning electrons (undergoing a reduction reaction) and dissociates into hydroxyl ions (OH - ). 369 H 2 O 2 + 2e − → 2OH − Equation 10-27 The hydroxyl ions then combine with the hydrogen ions at the cathode to produce water. 2OH − + 2H + → 2H 2 O Equation 10-28 The overall reaction is thus: H 2 + H 2 O 2 → 2H 2 O Equation 10-29 For this research, both the hydrogen/oxygen PEMFC and hydrogen/hydrogen peroxide PEMFC are considered as the two PEM fuel cell technologies to be sized and traded. Last in the theory of fuel cells is the dependence of voltage on current. At zero current (when no load is applied), the fuel cell voltage will be the open circuit voltage. This voltage is less than the theoretical equilibrium voltage due to some inherent voltage losses. Once a load is applied and current is drawn, the cell voltage drops even further. The sources of voltage loss in a fuel cell are:  Activation polarization loss: the voltage difference, or over-potential, from equilibrium needed to activate the electrochemical reaction. These losses occur at both anode and cathode; however, the oxidizer reduction at the cathode requires higher over-potential than the fuel oxidation reaction.  Fuel cross-over loss and internal currents: although the electrolyte is not electrically conductive and is impermeable to reactant gases, a small amount of fuel may diffuse from the anode to cathode through the electrolyte, and some electrons may also find a pathway through the electrolyte.  Concentration polarization loss: Concentration gradients are established as a reactant is consumed by an electrode, which results in voltage loss. Since reactant concentration at 370 the catalyst surface of an electrode depends on current density, reactant concentration will increase with current density. The reactant surface concentration reaches zero when the consumption rate goes beyond the allowable diffusion rate. In theory, at this point no more current density can be produced.  Ohmic (resistive) polarization loss: the electrolyte has some internal resistance to ion flow, and fuel cell components also have some internal resistance to electron flow. The net current density from both cathode and anode reactions is related to the difference, or over-potential, between the cell potential and an equilibrium potential (as derived from the Nernst equation). At the cathode the over-potential is negative. As such, the activation polarization loss can be expressed as a function of current from the Butler-Volmer equation. ΔV act = E equil − E = RT αF ln( 𝑖 + 𝑖 𝑐𝑟𝑜𝑠𝑠𝑜𝑣𝑒𝑟 𝑖 0 ) Equation 10-30 where T is the oxidizer temperature (K), α is the cathode charge transfer coefficient, F is Faraday’s constant, 𝑖 is the fuel cell current density (A/cm 2 ), 𝑖 0 is the exchange current density, and 𝑖 𝑐𝑟𝑜𝑠𝑠𝑜𝑣𝑒𝑟 is the fuel cross-over current. The charge transfer coefficient α is the portion of electrical energy used to activate the electrochemical reaction. The exchange current density 𝑖 0 corresponds to the rate constant in a chemical reaction. It is the current density generated at equilibrium (when there is zero net current density) by both oxidation of fuel at the anode and reduction of the oxidizer at the cathode simultaneously within the fuel cell. It depends on reactant concentration, temperature, and electrode surface properties. In particular, the exchange current density i 0 depends on the metal catalyst in the electrode. For example, for platinum (Pt) catalyst, i 0 = 5e-4 A/cm 2 ; for nickel (Ni) catalyst i 0 = 6e-6 A/cm 2 ; for silver (Ag) catalyst = 4e-7 A/cm 2 . 371 An increase in fuel cell operating temperature reduces the theoretical equilibrium voltage (by reducing the Gibbs free energy). However, voltage losses are also a function of temperature. Increasing fuel cell temperature should result in higher activation polarization loss, assuming a constant exchange current density. In reality, however, the exchange current density itself increases with temperature, thereby reducing the activation polarization loss. The reduction in losses more than compensates for the reduction in equilibrium voltage so that higher voltages are realizable in practice. As a result, in an actual fuel cell, elevated temperature increases voltage performance. The concentration polarization voltage loss is a function of current density, limiting current density, and the number of electrons n transferred at the electrode surface: ΔV conc = RT nF ln( 𝑖 𝐿 𝑖 𝐿 − 𝑖 ) Equation 10-31 This equation suggests that as the cell current density approaches the limiting current density, there would be a large concentration polarization voltage loss and hence large drop in cell voltage. In practical fuel cells, however, this limiting current density is almost never reached, as the current density is typically not uniform over the entire porous electrode area. In other words, some electrode regions would reach the limiting current density whereas others would not. The limiting current density can be found by equating the reactant flux (mol/s) at an electrode from Faraday’s law to the reactant flux from the concentration gradient at steady state (Fick’s law of diffusion). Fick’s law is modified by assuming zero reactant concentration at the catalyst surface. Thus the limiting current density can be found from (57): 372 i L = nFDC B δ Equation 10-32 where 𝐷 is the diffusion coefficient (cm 2 /s) of the reacting species (say hydrogen gas), C B is the bulk concentration (mol/cm 3 ) of the reactant, and δ is the diffusion distance (cm). For a hydrogen/oxygen fuel cell, limiting current density is on the order of 1200 – 2000 mA/cm 2 . The above equation states that the limiting current density is equal to the rate of maximum reactant supply by diffusion. The fuel cell also experiences ohmic (resistive) voltage losses as a result of electrolyte resistance to ion flow, and resistance to electron flow in fuel cell electronics and electrical contacts. This voltage loss depends on the total cell internal resistance R i . The most significant are ionic and contact resistances, which yield an internal resistance typically between 0.1 and 0.2 Ωcm 2 . The ohmic voltage loss can be expressed by Ohm’s law as: ΔV ohmic = iR i Equation 10-33 The resultant cell potential is the equilibrium potential reduced by the various voltage losses. E cell = E equil − ΔV act − ΔV conc − ΔV ohmic Equation 10-34 The above equation describes the fuel cell voltage polarization curve as a function of current density (contained within the various voltage losses). When no power load is applied (zero current density), the fuel cell voltage is the open circuit voltage. This open circuit voltage is less than the equilibrium voltage due to internal currents and fuel-cross-over current. On the other end of the polarization curve, the short-circuit current density (when cell voltage reduces to zero) is represented by the limiting current density. 373 The maximum possible theoretical energy conversion efficiency of the fuel cell can be found as: η = Δ𝐺 Δ𝐻 = 𝐸 𝑐𝑒𝑙𝑙 𝐸 𝑡 ℎ𝑒𝑟𝑚𝑜𝑛𝑒𝑢𝑡𝑟𝑎𝑙 Equation 10-35 where the thermo-neutral potential—the maximum potential if all the reaction enthalpy could be converted to electricity—can be found from: 𝐸 𝑡 ℎ𝑒𝑟𝑚𝑜𝑛𝑒𝑢𝑡𝑟𝑎𝑙 = − Δ𝐻 𝑛𝐹 Equation 10-36 For a hydrogen/oxygen fuel cell, the maximum theoretical efficiency is 83 % at standard temperature and pressure (25 C and 1 atmosphere). This corresponds to a theoretical cell equilibrium potential of 1.23 V. Various voltage losses, however, as discussed in previous paragraphs, reduce this potential to less than 1 V. Since the energy conversion efficiency is a function of cell voltage, which in turn is a function of cell current density, the efficiency can run as high as 80% for low currents in some fuel cells. The efficiency also typically reduces to 40-60% as current draw increases (30). A representative fuel cell voltage polarization curve for a hydrogen/oxygen fuel cell is shown in the following figure. The operating temperature and pressure are 60 C and 1 atmosphere, respectively. In this example, note that the open circuit voltage is less than 1 V and corresponds to an efficiency of 64%. The per cell power density (W/cm 2 ) reaches a maximum at a high current density (1.46 A/cm 2 ) and thus at low voltage and low efficiency. 374 Figure 10-5. Example H2/O2 fuel cell voltage polarization curve Recall that the mass flow rate of reactants, and hence the total mass of reactants, is a linear function of the fuel cell current. In other words, less total reactant mass is required at low currents, whereas more total reactant mass is required at high currents. As previously mentioned, the total fuel cell stack mass depends on the total number of cells required. The total number of cells depends on the selected fuel cell operating current and voltage, such that it can also be expressed as inversely proportional to the fuel cell power density (operating current density times operating voltage). As shown in Figure 10-5, the fuel cell power density peaks at high current. As a result, the total number of fuel cells is minimized at high current. However, the total reactant mass is large at high current and is known to dominate the total fuel cell system mass. Therefore, although high power density may mean fewer fuel cells, it means greater total mass as a result of higher total reactant mass. As such, low total reactant mass and low fuel cell stack mass are typically at odds. Nevertheless, an optimal current density and voltage can be found to minimize 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Fuel cell voltage polarization curve, efficiency, power density i current density (A/cm2) Voltage (V) and Power density (W/cm2) Voltage Power density Efficiency 375 the total fuel cell system mass. This is depicted in Figure 10-6 for a representative hydrogen/oxygen fuel cell system. In this example, the total power requirement is 500 W and the fuel cell operating temperature is 60 C; the pressure of reactants and product are 1 atmosphere for both. At these conditions, the minimum total system mass is achieved at very low current (correspondingly high voltage) and hence low power density. The disadvantage is many fuel cells are needed to deliver the total required system voltage and current. Figure 10-6. Example H2/O2 fuel cell system mass vs. current density 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 4 Total fuel cell system mass vs. current density i current density (A/cm2) Total system mass (kg)

Abstract (if available)

Abstract Recent lunar missions have provided evidence of the presence of hydrogen and other volatiles at both lunar poles. This evidence has led to several questions regarding the form of the hydrogen (potentially as water-ice), its distribution, and its origin. In addition, the presence of volatiles at the lunar poles provides a potential source of oxygen and water for future crewed lunar missions, as well as propellant for future lunar launches and orbiting lunar fuel depots. To answer the scientific questions and evaluate the potential for resource utilization, scientists have suggested that in-situ exploration of the lunar poles is a next logical step. Several space agencies, including NASA, the Russian Space Agency, and the Indian Space Research Organization (ISRO), are developing missions to explore a sunlit region at one of the lunar poles. Several lunar polar volatiles concept studies have also been conducted within the past several years by industry, academia, and government agencies. While informative, these studies and planned missions have only considered limited options in term of the design trade space for a lunar polar volatiles mission (e.g. sunlight-only operation in some cases, as well as use of specific heritage hardware and subsystem technology options). As such, a more thorough evaluation of the trade space for a lunar polar volatiles mission is needed. To achieve this, a MATLAB-based tool was developed to design multiple candidate lunar polar volatiles system concepts based on traded subsystem technologies. Such a tool also encounters the multidisciplinary design problem, in which the design of the whole system is determined by the design of the inter-dependent subsystems. Thus, this research aimed to accomplish two goals: to develop an automated design tool approach to generate multiple candidate designs of a space mission, and to use this tool to generate numerous designs of a lunar polar volatiles mission. Overall, this research has demonstrated that it is possible to develop an automated multidisciplinary design tool, using a sequential-iterative approach, that produces feasible (converged mass) designs. In addition, the design results show that feasible low-mass designs exist for 3 lunar polar volatiles mission concepts: a solar-powered rover, a radioisotope-powered rover, and a fuel cell-powered rover. These 3 concepts represent viable options to explore either a permanently-shadowed region or a sunlit region at the lunar South Pole for volatiles, a key step for both future robotic and human exploration of the Moon.

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Asset Metadata

Creator Luna, Michael Edward (author)

Core Title Systems engineering and mission design of a lunar South Pole rover mission: a novel approach to the multidisciplinary design problem within a spacecraft systems engineering paradigm

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Astronautical Engineering

Publication Date 11/18/2016

Defense Date 10/20/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag lunar polar volatiles,lunar rover,lunar South Pole,mission design,multidisciplinary design problem,OAI-PMH Harvest,systems engineering

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kunc, Joseph (committee chair), Gruntman, Mike (committee member), Meshkati, Najmedin (committee member), Sweetser, Theodore (committee member)

Creator Email bruinmike2000@yahoo.com,michael.luna@jpl.nasa.gov

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-323235

Unique identifier UC11213899

Identifier etd-LunaMichae-4939.pdf (filename),usctheses-c40-323235 (legacy record id)

Legacy Identifier etd-LunaMichae-4939.pdf

Dmrecord 323235

Document Type Dissertation

Format application/pdf (imt)

Rights Luna, Michael Edward

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA