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Performance Quantification of Heliogyro Solar Sails Using Structural PERFORMANCE QUANTIFICATION OF HELIOGYRO SOLAR SAILS USING STRUCTURAL, ATTITUDE, AND ORBITAL DYNAMICS AND CONTROL ANALYSIS by DANIEL VERNON GUERRANT B.S., California Polytechnic State University at San Luis Obispo, 2005 M.S., California Polytechnic State University at San Luis Obispo, 2005 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Doctor of Philosophy Department of Aerospace Engineering Sciences 2015 This thesis entitled: Performance Quantification of Heliogyro Solar Sails Using Structural, Attitude, and Orbital Dynamics and Control Analysis written by Daniel Vernon Guerrant has been approved for the Department of Aerospace Engineering Sciences ________________________________________ Dr. Dale A. Lawrence ________________________________________ Dr. W. Keats Wilkie Date______________ The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. Guerrant, Daniel Vernon (Ph.D., Aerospace Engineering Sciences) Performance Quantification of Heliogyro Solar Sails Using Structural, Attitude, and Orbital Dynamics and Control Analysis Thesis directed by Professor Dale A. Lawrence Solar sails enable or enhance exploration of a variety of destinations both within and without the solar system. The heliogyro solar sail architecture divides the sail into blades spun about a central hub and centrifugally stiffened. The resulting structural mass savings can often double acceleration verses kite-type square sails of the same mass. Pitching the blades collectively and cyclically, similar to a helicopter, creates attitude control moments and vectors thrust. The principal hurdle preventing heliogyros’ implementation is the uncertainty in their dynamics. This thesis investigates attitude, orbital and structural control using a combination of analytical studies and simulations. Furthermore, it quantifies the heliogyro’s ability to create attitude control moments, change the thrust direction, and stably actuate blade pitch. This provides engineers a toolbox from which to estimate the heliogyro’s performance and perform trades during preliminary mission design. It is shown that heliogyros can create an attitude control moment in any direction from any orientation. While their large angular momentum limits attitude slewing to only a few degrees per hour, cyclic blade pitching can slew the thrust vector within a few minutes. This approach is only 13% less efficient than slewing a square sail during Earth escape, so it does not offset the overall acceleration benefits of heliogyros. Lastly, a root pitch motor should be able to settle torsional disturbances within a few rotations and achieve thrust performance comparable to that of flat blades. This work found no significant dynamic hurdles for heliogyros, and it provides key insight into their practical capabilities and limitations for future mission designers. iii DEDICATION To my wife, Tania, and my son, Carter. ACKNOWLEDGEMENTS I would like to thank: Dr. Dale Lawrence for all his guidance and insight and for never letting me get away with anything unsubstantiated or imprecisely worded as my advisor. Dr. W. Keats Wilkie for spearheading heliogyro research at NASA, acting as my NASA mentor, and hosting me for two internships at NASA Langley Research Center. Dr. Jay Warren at NASA Langley Research Center for guidance with structural dynamics and corroborative finite element simulation work in Abaqus. Andy Heaton (NASA Marshall Space Flight Center) and Dr. Laura Jones (NASA Jet Propulsion Laboratory) for guidance in spacecraft mission design and attitude control and for hosting me for internships. the NASA Office of the Chief Technologist for supporting this work with Space Technology Fellowship NNX11AM89H. v CONTENTS CHAPTER 1. INTRODUCTION ............................................................................................. 1 A. Motivation for Solar Sailing ............................................................................................ 1 B. Solar Sail Architectures and History ................................................................................ 2 C. Coordinate Reference Frames .......................................................................................... 4 D. Heliogyro Blade Pitch Profiles for Attitude and Thrust Control ..................................... 8 E. Typical Solar Sail Operations ........................................................................................ 10 F. Research Questions and Expected Contributions .......................................................... 12 1. How can one achieve a desired attitude and thrust with blade pitch profiles? ........... 12 2. How does the heliogyro compare to a flat sail for Earth escape? ............................... 14 3. How can one control the pitch of highly flexible blades, ensuring stability? ............ 15 G. Heliogyro Design Concept Performance Comparison to Other Sail Designs ............... 17 CHAPTER 2. ATTITUDE CONTROL VIA BLADE PITCHING ....................................... 22 A. Forward Mapping with the HGForce Algorithm ......................................................... 23 B. Attitude Control Tactics ................................................................................................. 28 1. Spin Control Tactic ..................................................................................................... 29 2. Precession Tactic ........................................................................................................ 36 3. Lateral Thrust Tactic .................................................................................................. 41 C. Tactic Comparison ......................................................................................................... 44 1. Lateral Thrust Capability ............................................................................................ 45 2. Estimated Slew Times ................................................................................................ 48 D. Chapter Summary and Recommendations ..................................................................... 51 CHAPTER 3. EARTH ESCAPE STRATEGIES ................................................................... 53 A. Canonical Planetary Escape Strategies .......................................................................... 53 vi 1. Sun-orthogonal trajectories (s⊥) ................................................................................. 54 2. Sun-coplanar trajectories (s||) ..................................................................................... 56 B. Analytical Performance Metrics .................................................................................... 58 C. Strategy Analysis and Comparison ................................................................................ 62 1. Sun-orthogonal trajectories (s⊥) ................................................................................. 63 2. Sun-coplanar trajectories (s||) ..................................................................................... 68 D. Chapter Summary and Recommendations ..................................................................... 71 CHAPTER 4. BLADE CONTROL ........................................................................................ 73 A. Finite Element Model .................................................................................................... 73 B. Linear Control and Stability Analysis............................................................................ 78 1. Linearization and conversion to state space ............................................................... 79 2. Steady-State Blade Shape and Impedance .................................................................. 81 3. Control Law Design and Optimization ....................................................................... 83 4. Frequency Response and Stability Analysis ............................................................... 86 C. Blade Tip Control by Local Reflectivity Modulation .................................................... 91 1. Incorporating RCDs into the Membrane Ladder FEM ............................................... 92 2. RCD Control System .................................................................................................. 94 3. RCD Parameter Optimization ..................................................................................... 96 4. Closed Loop Linear Stability Analysis ..................................................................... 101 D. Model validation with hanging blade experiments ...................................................... 106 1. Experimental Setup................................................................................................... 106 2. Experimental Results ................................................................................................ 110 E. Nonlinear blade control................................................................................................ 120 1. Steady-state solution by Fourier harmonic expansion .............................................. 122 2. Structural Dynamics Concerns and Mitigation with Single Harmonic Solution ...... 126 vii 3. Root Control Law Performance with Multi-harmonic Solution ..............................
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