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TURN PERFORMANCE and FLIGHT DYNAMICS of a PTEROSAUR and a PTEROSAUR-INSPIRED VARIABLE-PLACEMENT VERTICAL TAIL AIRCRAFT by Brian C

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TURN PERFORMANCE and FLIGHT DYNAMICS of a PTEROSAUR and a PTEROSAUR-INSPIRED VARIABLE-PLACEMENT VERTICAL TAIL AIRCRAFT by Brian C TURN PERFORMANCE AND FLIGHT DYNAMICS OF A PTEROSAUR AND A PTEROSAUR-INSPIRED VARIABLE-PLACEMENT VERTICAL TAIL AIRCRAFT By BRIAN C. ROBERTS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009 1 °c 2009 Brian C. Roberts 2 I dedicate this thesis to all of my teachers, from grade school to grad school 3 ACKNOWLEDGMENTS Thanks to Dr. Lind for putting me on this out-of-the-ordinary and yet fully engaging project and for helping me along the way. A very appreciative thanks to Dr. Sankar Chatterjee for all of his paleontological insight. I want to thank all of my labmates and classmates for any advice and ideas I received through contact with them. I especially want to thank Daniel Grant for getting me started on AVL and for all of his assistance along the way. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................. 4 LIST OF TABLES ..................................... 8 LIST OF FIGURES .................................... 9 ABSTRACT ........................................ 12 CHAPTER 1 Introduction ...................................... 13 1.1 Motivation .................................... 13 1.2 Problem Statement ............................... 16 1.3 Contribution ................................... 17 2 Background ...................................... 19 2.1 Axis and Moment De¯nitions ......................... 19 2.2 Aircraft Control E®ectors ........................... 20 2.3 Aircraft Equations of Motion ......................... 21 2.4 Static Stability ................................. 23 2.5 Rotation Damping ............................... 24 2.6 Control E®ectiveness .............................. 25 2.7 Flight Performance Equations ......................... 26 2.8 Aerodynamics Prediction ............................ 28 2.9 Turn Performance Evaluation ......................... 29 2.10 Eigenvector Analysis .............................. 30 3 Biological Inspiration ................................. 31 3.1 History ...................................... 31 3.2 Pterosaur Anatomy as a Model for Aircraft Design ............. 31 3.3 Cranial Crest .................................. 34 3.4 Chosen Species ................................. 35 4 Pterosaur Flight Analysis .............................. 36 4.1 Pterosaur Model ................................ 36 4.1.1 Aerodynamic Geometry ......................... 37 4.1.2 Masses and Inertias ........................... 39 4.1.3 Wing Control E®ectors ......................... 40 4.1.4 Morphing ................................ 40 4.1.5 Cranial Movement ............................ 44 4.1.6 Model Summary ............................. 44 4.2 Steady Level Flight Analysis .......................... 44 5 4.2.1 Run Conditions ............................. 44 4.2.2 Symmetric Sweep Results ........................ 46 4.2.2.1 Trimmed Flight Conditions ................. 46 4.2.2.2 Static Stability ........................ 48 4.2.2.3 Rotation Damping ...................... 49 4.2.2.4 Control E®ectiveness ..................... 49 4.2.2.5 Rate of Divergence ...................... 51 4.2.3 Head Free Asymmetric Sweep Results ................. 54 4.2.3.1 Trimmed Flight Conditions ................. 54 4.2.3.2 Static Stability ........................ 56 4.2.3.3 Control E®ectiveness ..................... 57 4.2.3.4 Rate of Divergence ...................... 58 4.2.4 Head Fixed Asymmetric Sweep Results ................ 61 4.2.4.1 Trimmed Flight Conditions ................. 61 4.2.4.2 Static Stability ........................ 62 4.2.4.3 Control E®ectiveness ..................... 64 4.2.4.4 Rate of Divergence ...................... 64 4.3 Banked Turning Flight Analysis ........................ 67 4.3.1 Run Conditions and Analysis Methods ................ 67 4.3.2 Performance E®ects ........................... 67 4.3.3 Trimmed Flight Conditions ....................... 70 5 Aicraft Model Analysis ................................ 72 5.1 Aircraft Model ................................. 72 5.1.1 Aerodynamic Geometry ......................... 72 5.1.2 Masses and Inertias ........................... 73 5.1.3 Control E®ectors ............................ 74 5.1.4 Adaptive-Con¯guring Vertical Tail ................... 74 5.2 Steady Level Flight Analysis .......................... 76 5.2.1 Run Conditions ............................. 76 5.2.2 Trimmed Flight Conditions ....................... 76 5.2.3 Static Stability ............................. 76 5.2.4 Rotation Damping ............................ 79 5.2.5 Control E®ectiveness .......................... 80 5.3 Banked Turning Flight ............................. 83 5.3.1 Run Conditions ............................. 83 5.3.2 Performance Improvements ....................... 83 5.3.3 Trimmed Flight Conditions ....................... 86 5.3.4 Static Stability ............................. 88 5.3.5 Control E®ectiveness .......................... 91 6 Results Implications ................................. 94 6.1 Biological Implications ............................. 94 6.2 Aircraft Implications .............................. 95 6 REFERENCES ....................................... 97 BIOGRAPHICAL SKETCH ................................ 99 7 LIST OF TABLES Table page 3-1 Properties of Flight Platforms ............................ 33 4-1 Masses and Inertias of Modeled Parts of Tapejara ................. 39 4-2 Joint Range of Motion ................................ 42 4-3 Eigenvector of Nominal Con¯guration in Steady Level Flight ........... 53 5-1 Characteristics of the Baseline Vehicle ....................... 73 5-2 Masses and Inertias of Modeled Aircraft Parts ................... 73 5-3 Turn Radius in m at Extremal Values of Position and Angle for the Vertical Tail 86 8 LIST OF FIGURES Figure page 2-1 Diagram of Anatomical Axes and Planes ...................... 19 3-1 Image of Pterosaur Actino¯brils ........................... 33 3-2 Skeletal Reconstruction of an Early Cretaceous Pterosaur, Tapejara wellnhoferi . 34 4-1 Image of Measured Tapejara Skeletal Reconstruction ............... 36 4-2 Isometric View of Tapejara Model in Nominal Wing Position ........... 38 4-3 Top View of Tapejara Skeleton in Extended and Folded Wing Positions ..... 41 4-4 Top View of Model in Various Morphed Wing Positions .............. 42 4-5 Top View of Tapejara Pterosaur Wing in Extended and Folded Wing Positions . 43 4-6 Angle of Attack and Elevator Deflection in Steady Level Flight .......... 46 4-7 Drag Coe±cient in Steady Level Flight ....................... 47 4-8 Drag and Lift-to-Drag Ratio in Steady Level Flight ................ 47 4-9 Yaw and Roll Stability in Steady Level Flight ................... 48 4-10 Lift Slope and Pitch Stability in Steady Level Flight ............... 49 4-11 Roll and Yaw Damping in Steady Level Flight ................... 50 4-12 Yaw E®ectiveness of Ailerons and Rudder in Steady Level Flight ......... 50 4-13 Roll E®ectiveness of Ailerons and Rudder in Steady Level Flight ......... 51 4-14 E®ectiveness of Elevator in Steady Level Flight .................. 52 4-15 Largest Time Constant in Steady Level Flight ................... 53 4-16 Angle of Attack and Elevator Deflection in Steady Level Flight with Head Free Asymmetric Morphing ................................ 55 4-17 Rudder and Aileron Deflection in Steady Level Flight with Head Free Asymmetric Morphing ....................................... 55 4-18 Drag and Drag Coe±cient in Steady Level Flight with Head Free Asymmetric Morphing ....................................... 56 4-19 Yaw and Roll Stability in Steady Level Flight with Head Free Asymmetric Morphing 57 4-20 Lift Slope and Pitch Stability in Steady Level Flight with Head Free Asymmetric Morphing ....................................... 57 9 4-21 Control E®ectiveness on Longitudinal States in Steady Level Flight with Head Free Asymmetric Morphing ............................. 58 4-22 Control E®ectiveness on Lateral-Directional States in Steady Level Flight with Head Free Asymmetric Morphing .......................... 59 4-23 Largest Time Constant in Steady Level Flight with Head Free Asymmetric Morphing 60 4-24 Angle of Sideslip and Aileron Deflection in Steady Level Flight with Head Fixed Asymmetric Morphing ................................ 61 4-25 Angle of Attack and Elevator Deflection in Steady Level Flight with Head Fixed Asymmetric Morphing ................................ 62 4-26 Drag Coe±cient and Drag in Steady Level Flight with Head Fixed Asymmetric Morphing ....................................... 63 4-27 Static Stability in Steady Level Flight with Head Fixed Asymmetric Morphing . 63 4-28 Control E®ectiveness on Longitudinal States in Steady Level Flight with Head Fixed Asymmetric Morphing ............................. 64 4-29 Control E®ectiveness on Lateral-Directional States in Steady Level Flight with Head Fixed Asymmetric Morphing ......................... 65 4-30 Largest Time Constant in Steady Level Flight with Head Fixed Asymmetric Morphing ....................................... 66 4-31 Turn Radius Improvements in Banked Flight with Asymmetric Morphing .... 68 4-32 Velocity and Turn Rate in Banked Flight with Asymmetric Morphing ...... 68 4-33 Aileron Deflection and Angle of Sideslip in Banked Flight with Asymmetric Morphing 70 4-34 Angle of Attack, Elevator Deflection, and Drag Coe±cient in Banked Flight with Asymmetric Morphing ................................ 71 5-1 Baseline Vehicle in Flight Con¯guration
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