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Dynamic Characteristics of Morphing Micro Air Vehicles


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D YN AMIC CHARA CTERISTICS OF MORPHING MICR O AIR VEHICLES By MUJ AHID ABDULRAHIM A THESIS PRESENTED T O THE GRADU A TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQ UIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORID A 2004

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In the name of Allah, the Gracious, the Merciful. My thesis in its entirety (apart from one sentence in the be ginning of Chapter 4) is dedicated to my lo ving f amily who ha v e put up with my outrageous silliness in pursuit of academic achie v ements. T o my f ather who rst led me do wn the path of inno v ation by helping me b uild my o wn to ys. T o my mother who from the v ery be ginning has been my advisor counselor and best friend. T o my brother who is my co-pilot in the clouded airspace of life. And to my sister who is my ultimate role model for writing style and literary wit. The single outstanding sentence in Chapter 4 is dedicated to my rubber chick en, who pro vides irrele v ant comic amusement lik e no other inanimate domestic animal can. Looks real, feels real, stretchable. Hells yeah.

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A CKNO WLEDGMENTS The w ork presented in this thesis w as hea vily supported by a lar ge group of highly supporti v e people. The b ulk of the mentoring, advice, suggestions, and orders came from my research advisors, Dr Richard Lind and Dr Peter Ifju. Dr Lind has helped me de v elop an understanding of ight test objecti v es, modeling strate gies, and, more importantly the ef fect of our w ork on the future of aerospace. Dr Ifju has been the ultimate source for creati v e inspiration in aircraft design and f abrication technique. Martin W aszak of N ASA Langle y Research Center has supported the UF micro air v ehicle research ef fort for man y years. In addition to pro viding the funding for all the research presented here, he has hosted me at LaRC for tw o summers on MA V design and ight testing internships. Mark Motter also from LaRC, has pro vided considerable e xpertise in related projects. His inuence carries o v er to the current research. Se v eral students ha v e also been kind enough to support the research with time, kno wledge and hardw are. Jason W Grzywna and Jason Ple w ha v e pro vided much of the electronics hardw are support for the MA Vs. Jos Cocquyt, Baron Johnson, K enneth Boothe, Sha wn Mytrik, and Dan Claxton ha v e helped e xtensi v ely in solving design problems and supporting ight tests. Finally Alfred, my rubber chick en, helped pull me through the lo w times when e v en singing ”Al w ays Look On the Bright Side of Life” could not cheer me up. iii

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T ABLE OF CONTENTS page A CKNO WLEDGMENTS . . . . . . . . . . . . . . . . iii LIST OF T ABLES . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . vii ABSTRA CT . . . . . . . . . . . . . . . . . . . x 1 INTR ODUCTION . . . . . . . . . . . . . . . . 1 2 BIOLOGICAL INSPIRA TION . . . . . . . . . . . . . 4 3 MORPHING ON SMALL FLIGHT VEHICLES . . . . . . . . 8 4 ASYMMETRIC WING SHAPING FOR R OLL CONTR OL . . . . . 13 4.1 Aircraft Design . . . . . . . . . . . . . . . 13 4.2 Morphing Mechanism . . . . . . . . . . . . . 14 4.3 Flight Performance . . . . . . . . . . . . . . 17 4.4 Nonlinear Modeling of Lateral and Longitudinal Dynamics . . . 19 5 SYMMETRIC WING TWISTING FOR R OLL CONTR OL . . . . . 22 5.1 Aircraft Design . . . . . . . . . . . . . . . 22 5.2 Morphing Mechanism . . . . . . . . . . . . . 23 5.3 Flight Performance . . . . . . . . . . . . . . 24 5.4 Linear Modeling of Lateral Dynamics . . . . . . . . . 25 5.5 Spin Characteristics of W ing T wist Morphing . . . . . . . 27 6 MUL TI-POINT WING SHAPING . . . . . . . . . . . . 33 6.1 Aircraft Design . . . . . . . . . . . . . . . 33 6.2 Morphing Mechanism . . . . . . . . . . . . . 33 6.3 Flight Performance . . . . . . . . . . . . . . 35 7 V ARIABLE GULL-WING ANGLE MORPHING . . . . . . . 37 7.1 Aircraft Design . . . . . . . . . . . . . . . 37 7.2 Morphing Mechanism . . . . . . . . . . . . . 38 7.3 Flight Performance . . . . . . . . . . . . . . 41 7.3.1 Gliding Performance . . . . . . . . . . . 42 7.3.2 Climb Performance . . . . . . . . . . . . 43 i v

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7.3.3 Stall Characteristics . . . . . . . . . . . . 44 7.4 Lateral-Directional Dynamics . . . . . . . . . . . 45 7.4.1 Roll Con v er gence . . . . . . . . . . . . 45 7.4.2 Dutch Roll Mode . . . . . . . . . . . . 50 7.5 Longitudinal Dynamics . . . . . . . . . . . . . 56 8 FOLDING WING AND T AIL MORPHING . . . . . . . . . 59 8.1 Aircraft Design . . . . . . . . . . . . . . . 59 8.2 Morphing Mechanism . . . . . . . . . . . . . 59 8.3 Flight T rials . . . . . . . . . . . . . . . . 61 9 SUMMAR Y . . . . . . . . . . . . . . . . . . 63 9.1 Recommendations . . . . . . . . . . . . . . 63 9.2 Conclusions . . . . . . . . . . . . . . . . 64 REFERENCES . . . . . . . . . . . . . . . . . . 65 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . 68 v

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LIST OF T ABLES T able page 4–1 Properties of the 10 in and 12 in wing shaping MA Vs . . . . . . 14 5–1 Properties of the 24 in wing twisting MA V . . . . . . . . . 23 7–1 W ing geometry change o v er v ariable gull-wing morphing range . . . 38 7–2 Dutch roll modes for 0 o gull-wing . . . . . . . . . . . 54 7–3 Dutch roll modes for 15 o gull-wing . . . . . . . . . . . 55 7–4 Dutch roll mode eigen v ectors for 0 o gull-wing . . . . . . . . 55 7–5 Dutch roll mode eigen v ectors for 15 o gull-wing . . . . . . . 56 7–6 Longitudinal modes for 0 o gull-wing . . . . . . . . . . 57 7–7 Longitudinal modes for 15 o gull-wing . . . . . . . . . . 57 8–1 Properties of the folding wing-tail aircraft in tw o congurations . . . 60 vi

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LIST OF FIGURES Figure page 1–1 V ariable gull-wing morphing aircraft . . . . . . . . . . 2 2–1 A bird alters its gull-wing angle to af fect gliding angle . . . . . 5 2–2 A seagull uses dif ferential wing e xtension (left) and dif ferential wing sweep (right) . . . . . . . . . . . . . . . . 6 2–3 A seagull e xtends its wings for cruising ight (left) and descends at a steep angle using gull-wing morphing (right) . . . . . . . 7 3–1 Micro data acquisition system . . . . . . . . . . . . 10 3–2 Roll, pitch and ya w rate sensor board . . . . . . . . . . 11 4–1 W ing shaping morphing MA Vs 10 in wingspan high-wing aircraft (left) and 12 in span mid-wing aircraft (right) . . . . . . . . . 14 4–2 T op, front, and side vie ws of computer -aided design dra wings for 12 in MA V . . . . . . . . . . . . . . . . . . 15 4–3 K e vlar cables . . . . . . . . . . . . . . . . 15 4–4 Front vie w sho wing undeected wing (left) and morphed wing (right) . 16 4–5 Measured and predicted responses for roll rate (left), pitch rate (middle) and ya w rate (right) . . . . . . . . . . . . . . 21 5–1 W ing-twisting MA V . . . . . . . . . . . . . . . 22 5–2 Underside vie w of wing sho wing torque rod . . . . . . . . 23 5–3 Rear vie w of the 24 in MA V with undeected (left) and morphed (right) W ing . . . . . . . . . . . . . . . . . . 24 5–4 Doublet command to rudder (left), roll rate response (middle), and ya w rate response (right) . . . . . . . . . . . . . . 26 5–5 Doublet command to wing twist morphing (left), roll rate response (middle), and ya w rate response (right) . . . . . . . . . . 27 5–6 Pilot commands (left) and responses (right) during con v entional spin . 28 5–7 Pilot commands (left) and responses (right) during spin . . . . . 30 vii

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5–8 Pilot commands (left) and responses (right) during c yclic spin . . . 31 6–1 T op, side, and front vie ws of the 24 in span multiple-position wing shaping v ehicle . . . . . . . . . . . . . . . . 34 6–2 W ing shaping MA V sho wing neutral position (top left), wingtip morphing (top right), and full wing morphing (bottom) . . . . . . 35 6–3 Spar torque-tube morphing actuators. The 4 front serv os rotate concentric spar sections, aft 2 control rudder and ele v ator . . . . . . 35 7–1 T op and side vie w of v ariable gull-wing aircraft . . . . . . . 38 7–2 V ehicle under going neutral (top), positi v e (center), and ne gati v e (bottom) gull-wing morphing . . . . . . . . . . . . . . 39 7–3 V ariable gull-wing spar structure and control linkage, linear actuator visible inside fuselage at left . . . . . . . . . . . . 40 7–4 Underside vie w of left wing sho wing wing twist ef fector . . . . . 41 7–5 W ing-twist command and response from ight data . . . . . . 47 7–6 Pole migration with gull-wing morphing angle . . . . . . . 48 7–7 B-matrix v alue for rst-order roll mode systems . . . . . . . 49 7–8 W ing-twist command (top) at 0 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) . . . . . . . . . . . 50 7–9 W ing-twist command (top) at 15 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) . . . . . . . . . . . 50 7–10 W ing-twist command (top) at 30 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) . . . . . . . . . . . 51 7–11 W ing-twist command (top) at -20 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) . . . . . . . . . . . 51 7–12 Rudder control pulse at 0 o gull-wing angle with measured data (:) and simulated response (-) . . . . . . . . . . . . . 52 7–13 Rudder control pulse at 15 o gull-wing angle with measured data (:) and simulated response (-) . . . . . . . . . . . . . 52 7–14 Open-loop Dutch roll mode pole migration for tw o morphing positions . 55 7–15 Frequenc y response diagram for 0 o gull-wing (:) and 15 o gull-wing (-) . 56 7–16 Ele v ator pulse command (left), measured (:) and simulated( -) pitch rate responses (right) . . . . . . . . . . . . . . . 58 viii

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7–17 15 o gull-wing ele v ator pulse command (left), measured (:) and simulated( -) pitch rate responses (right) . . . . . . . . . . 58 8–1 T op vie w of unswept (left) and swept (right) congurations . . . . 59 8–2 Side vie w of unswept (top) and swept (bottom) congurations . . . 60 8–3 En visioned dynamic pitch up maneuv er for forw ard to re v erse ight transition . . . . . . . . . . . . . . . . . . 62 ix

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Abstract of Thesis Presented to the Graduate School of the Uni v ersity of Florida in P artial Fulllment of the Requirements for the De gree of Master of Science D YN AMIC CHARA CTERISTICS OF MORPHING MICR O AIR VEHICLES By Mujahid Abdulrahim December 2004 Chair: Richard Lind Major Department: Mechanical and Aerospace Engineering The research presented in this thesis is an approach to the study of ight dynamics of morphing v ehicles. Case studies of se v eral strate gies are addressed in order to determine some of the basic ight characteristics of dynamically and quasi-statically morphing aircraft. These strate gies include a e xible membrane wing that uses tensioned cables to shape the wing for roll control. The wing shaping for this v ehicle impro v es roll tracking and decreases coupling compared to a rudder e v en though the morphing is asymmetric. Acti v e morphing is also implemented by using torque-rods and torque-tubes to anti-symmetrically twist a e xible wing surf ace. This form of morphing pro vided aileron-lik e control without a hingeline. Quasi-static morphing is used to change the gull-wing angle of an aircraft in ight. This biologically-inspired shape change alters the performance characteristics and dynamics of the v ehicle and allo ws it to y in se v eral distinct ight modes. The v ehicles are equipped with sensors and data logging de vices and ight tested using a v ariety of maneuv ers and techniques. Data from these maneuv ers are used to estimate longitudinal and lateral-directional models for the aircraft morphing systems. Stability and controllability of the v ehicles x

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are e xamined in the conte xt of the high-agility and aerodynamic performance changes caused by the morphing. xi

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CHAPTER 1 INTR ODUCTION As en visioned morphing designs become increasingly comple x, the need for accurate ight dynamic analysis becomes e v en more important [ 38 ]. The comple x shapes achie v able by the ne w generation of actuators and structures can create dif culties in representing the v ehicle using e xisting methods. F or instance, an aircraft that morphs asymmetrically can under go aerodynamic and inertial changes that violate assumptions used to simplify the commonly used equations of motion. Existing modeling approaches typically do not account for time-v arying v ehicle geometry or lar ge changes in the aircraft conguration. The modeling predicament underscores one of the current realities of morphing research; namely the majority of morphing is being conducted in optimal aerodynamic shapes and static aeroelastic ef fects. The eld of morphing v ehicle ight dynamics is still highly underde v eloped. P art of this v oid is understandable since fe w if an y morphing aircraft e xist today to perform ight test e xperiments. Ho we v er the lack of w ork also points to potential future problems in morphing research. Flight dynamics must be de v eloped in parallel to other morphing ef forts in order to assess and control prototype v ehicles. The w ork presented in this thesis represents an initial foray into such an ef fort. The ight dynamics of simple morphing v ehicles, such as the aircraft sho wn in Figure 1–1 are discussed. Design of the morphing ef fectors is based on observ ations of biological systems. Dynamic ef fectors such as wing twisting and wing curling are tested on se v eral v ehicles. Such ef fectors are replacements to ailerons, which cannot be mounted to a e xible membrane wing. Such forms of morphing are similar to the roll control ef fectors used on the N ASA F/A-18 AA W [ 27 ]. Other ef fectors are operated 1

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2 quasi-statically such as a gull-wing morphing and a folding wing-tail system. These systems also include dynamic morphing ef fectors, b ut are intended to address the lar ger problem of changing ight modes. V ehicle design and morphing actuators are considered only enough to de v elop testbeds for ight dynamics e xperiments. No claim is made as to the optimality of the v ehicle shapes or morphing methods. It is suf cient to consider that the morphing causes a change in the ight performance, which is then the basis for studying an y accompan ying change in stability and control characteristics. Figure 1–1: V ariable gull-wing morphing aircraft The enabling f actor for this w ork is rapid prototyping of aircraft designs at the Uni v ersity of Florida Center for Micro Air V ehicles. De v eloping an e xperimental unmanned air v ehicle from concept to initial ight test occurs within one or tw o weeks [ 18 ]. F abrication tools such as CNC milling and composite lay-up f acilities allo w the entire airframe to be manuf actured in-house [ 17 ]. Small instrumentation and a vionics are commercially a v ailable, reducing de v elopment time and cost signicantly Using these resources, ine xpensi v e testbeds can be produced quickly to test ne w concepts in aircraft design and ight control. The material presented in this thesis is from ight tests of se v eral morphing micro air v ehicles. A v ariety of modeling approaches are used to identify the ight dynamics of the v ehicles. The initial modeling approach tak en is based on simple transfer

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3 function approaches. Initial models are de v eloped under the assumption of linearity in order to understand the broad ef fect of the v ariable geometry on the aircraft dynamics. Nonlinear modeling is considered for v ehicles with comple x, asymmetric morphing.

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CHAPTER 2 BIOLOGICAL INSPIRA TION Early a viators of the 20th century were lar gely inspired in their designs by natural ight systems such as birds, insects, and seeds. This inspiration is e vident in the design shapes the y chose, which featured wing and tail planforms that were highly similar to birds. Ev en the early airplane attempts were constructed using a rigid sk eleton frame co v ered in a cloth skin, to resemble the wings of birds and bats. W ith the e v entual success of the Wright Brothers and the modernization of the airplane, designs became more f aceted and less-birdlik e than their predecessors. Contemporary aircraft no w ha v e little apparent similarities to birds. The di v er gence of aircraft designs from early biological inspiration is lik ely a result of the v astly dif ferent ight re gimes encountered in natural and engineered systems. In particular lar ge, high-speed aircraft share v ery little in common with a typical bird, which is neither lar ge nor high speed by comparison. The stif f, x ed geometry of airplanes are opposite to the physiology of birds, which incorporate man y e xible and v ariable-shape members. Modern aircraft design is then based entirely on deri v ed aeronautical sciences and v ery little on direct biological-inspiration. The continued miniaturization of electronics has fueled a mo v ement opposite to that of the lar ge, supersonic jets. A ne w generation of small air v ehicles is under de v elopment using micro sensors and instruments. These v ehicles are getting smaller and lighter such that the y are no w in a class highly similar to the birds and bats which moti v ated the early aeronautical ef forts. Furthermore, with an emer gent need for multi-role, shape-changing v ehicles, biological-inspiration is coming to the forefront of design philosophy 4

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5 Morphing is under consideration as a means to adapt a ight v ehicle to changing mission requirements or ight conditions. This type of adaptability has al w ays been present with biological systems. Birds are forced to alter their wing shapes dramatically in order to accomplish cruise glides, steep descents, and aggressi v e maneuv ering as sho wn in Figure 2–1 Con v ersely con v entional aircraft are generally of x ed conguration and are optimized for a v ery specic ight condition. Outside of this condition, aircraft usually suf fer from poor ef cienc y and poor aerodynamic performance. By changing the v ehicle shape in ight, an aircraft can re-optimize itself for a v ariety of tasks, as birds do constantly Thus, morphing through biologicalinspiration for small v ehicles is both e xtremely rele v ant and highly desirable. Figure 2–1: A bird alters its gull-wing angle to af fect gliding angle Biological-inspiration in aircraft ight systems presents considerable challenges to the aircraft designer Natural and engineered systems dif fer greatly in structural composition, performance requirements, and a v ailable components. F or instance, birds rely on strong muscles, hollo w sk eletons, e xible joints, and feathers to achie v e the necessary motions and shapes for ight. Aircraft use motors, propellers, hinge lines, and mostly rigid structures to sustain ight. The dif ferences between the tw o systems means that direct emulation is not practical or e v en desirable. Thus, it is not the goal of this research to mimic bird kinematics. Rather the objecti v e is to use select

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6 biologically-inspired systems to impro v e the range of achie v able ying conditions for con v entional aircraft. Birds use a v ariety of morphing techniques in their wings and tail to accomplish dynamic maneuv ering and stabilization. Dif ferential wing twist, wing e xtension, and wing sweep are used for primary lateral-direction control. Dif ferential wing e xtension is observ ed on seagulls during steep bank turns, as sho wn in Figure 2–2 Dif ferential wing sweep is also sho wn, here used for roll and ya w control. Collecti v e v ariations of these morphing motions are used in conjunction to the tail for longitudinal control. These strate gies present an initial starting point for implementing morphing on a small v ehicle. Figure 2–2: A seagull uses dif ferential wing e xtension (left) and dif ferential wing sweep (right) In addition to morphing for maneuv ering, birds also implement a quasi-static morphing of gull-wing angle during glide and steep descent phases. Figure 2–3 sho ws a bird at tw o dif ferent gull-wing positions for dif ferent phases of ight. The gull-wing action depends on a set of parallel bones connecting the shoulder and elbo w joints of a bird wing. A rotation of the shoulder joint in the v ertical plane results in an e xtension or contraction of the entire wing. The sk eletal mechanism pro vides a geometric ratio between the e xtension of the inner and outer bones. Such a mechanism allo ws the bird

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7 Figure 2–3: A seagull e xtends its wings for cruising ight (left) and descends at a steep angle using gull-wing morphing (right) to morph into a v ariety of positions using a single mo v ement. Each of the positions is lar gely stable and af fords a unique capability within the ight en v elope. The purpose of this v ariable gull-wing action in birds is lik ely for a v ariety of reasons, including static aerodynamic [ 9 ], physiology and for apping control. Ho we v er it is studied here solely to in v estigate the quasi-static aerodynamic benet and the corresponding ef fect on the v ehicle dynamic response. This type of morphing is considered on a small v ehicle, e xploring the potential benets to the cruise, steep descent, and approach phases of ight.

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CHAPTER 3 MORPHING ON SMALL FLIGHT VEHICLES Implementing basic forms of morphing on micro air v ehicles in v olv es identifying morphing strate gies that can be readily adapted to the v ehicles. Identied forms of morphing in birds are adapted to aircraft using e xisting actuators or simple mechanisms. In this manner the focus has been placed on ight testing the morphing concepts as opposed to de v eloping optimal morphing shapes or actuators. This approach pro vides an essential look at the ight dynamics and controllability issues without depending on actuator and material technology Despite the simplicity of the approach to morphing, the v ehicles ha v e demonstrated impro v ed performance and control characteristics compared to aircraft with con v entional control ef fectors. F or instance, morphing can be used to pro vide roll control on an aircraft with e xible wings without the use of hinges. This method retains the benecial characteristics of the e xible wing [ 22 ] [ 37 ], without compromising control [ 14 ]. The w ork presented in this thesis summarizes the de v elopment and ight testing of se v eral morphing aircraft. Each aircraft type is essentially designed around a particular type of morphing. Although the essence of each design is based on se v eral generations of non-morphing v ehicles, each is adapted in structure, shape, and material to host the morphing mechanism. F or se v eral of the initial attempts at morphing, this adaptation is quite minimal and is limited to drilling holes in the airframe and attaching the actuator arm or cable to the wing. Ho we v er as the morphing shapes became increasingly comple x, the v ehicle shape and structure are then designed specically for the purpose of morphing. 8

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9 The aircraft design shapes are quite dif ferent from one another T w o primary scales are considered for morphing actuators, micro air v ehicles of approximately 12 in span and lar ger v ehicles with 24 in wingspans. Most of the v ehicles dif fer in fuselage shape, empennage planform, actuators, and weight. Thus, each v ehicle e xhibits absolute performance metrics quite dif ferent than the others. The dif fering geometry and dif fering performance metrics mak e direct comparison between the v ehicles impractical. As stated earlier the goal of the research is not to determine optimal morphing methods, b ut rather to in v estigate the ef fect of an y shape change on the v ehicle dynamics. This does not require comparisons between the v ehicles and morphing strate gies, as each case study is addressed as a separate e xperiment. The cumulati v e result of the indi vidual studies helps formulate a basic kno wledge base of morphing v ehicle ight dynamics. The e xperimental procedure is mostly similar for all the test v ehicles. The basic process includes design, f abrication, instrumentation, ight testing, data reco v ery and modeling stages. Apart from the instrumentation, these stages are co v ered in detail for each aircraft case study Details of the instrumentation procedures are co v ered here, as the same sensors and data acquisition de vices are used for all the ight tests. A partial suite of ight test instruments are used on-board the aircraft to gather ight data. Inertial measurements include roll rate, pitch rate, ya w rate, and 3-axis linear accelerations. The remaining inertial aircraft states, Euler angles and position are not included due to a lack of small instrumentation. Estimates of the Euler angles are computed o v er small time periods by inte grating angular rate data. Position measurements, as w ould be pro vided by a GPS sensor are not important for the type of ight testing conducted. Pressure sensors for airspeed and altitude measurement are included for some ight tests, although the data is not used in the analysis. The primary decienc y in the instrumentation is the lack of angle of attack and angle of sideslip data. Potentiometer -based v anes were considered for use, b ut the rotational

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10 friction pre v ented the sensors from pro viding an y useful information. Finally the control deections are measured for all the hinged and morphing ef fectors. The primary element of the instrumentation system is a micro data acquisition system (microD AS) de v eloped by N ASA Langle y Research Center The microD AS has 30 analog v oltage input channels measured with a 12-bit resolution. Sampling frequenc y is adjustable from 50 Hz to 500 Hz allo wing continuous data measurements from 20 minutes to 2 minutes respecti v ely Later v ersions of the board increased the storage capacity considerably Data presented in this thesis is collected at 50 or 100 Hz The board weight including the wiring harness is approximately 12 gr ams although this v aries depending upon the length of wire used to connect the sensors. Figure 3–1 sho ws the micro data acquisition system with the wiring harness connected. Leads from the harness are connected to sensor outputs and communication ports. Three linear accelerometers are inte gral to the board, allo wing 3-axis measurement within +/50 G Figure 3–1: Micro data acquisition system Data from the ne west v ersion of the microD AS is stored in a 128MB ash memory chip. As long as the unit retains po wer the measurement can be turned on or of f from the remote transmitter This permits the data to co v er only the ight test maneuv ers and e xclude non-research phases of ight, such as launch, climb, trim, and

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11 landing. Flight data is reco v ered to a laptop via a USB communications cable. An entire data set is do wnloaded in 6 minutes using the softw are pro vided with the de vice. Roll, pitch, and ya w rates are measured using muRata ENC-03J piezoelectric angular rate gyros. Each gyro sensor measures a single axis of rotation, requiring three orthogonally-oriented gyros for full rate measurement. A tw o-piece copper -plated circuit board f abricated at UF' s ECE department is used to align the gyros and pro vide signal outputs, as sho wn in Figure 3–2 The total weight of the board and the three gyros is 6 gr ams making it suitable suitable for the smaller MA Vs. The signal output from the gyros are stable enough such that no hardw are ltering is required to achie v e high signal to noise ratios and stable mean v alues. The rate measurement range for each gyro is specied by the manuf acturer as +/-300 os although calibration tests suggest that linear output e xists o v er +/-1000 os Figure 3–2: Roll, pitch and ya w rate sensor board Control surf ace deections are measured at the rotary actuator F or con v entionally hinged surf aces, a nominally rigid linkage connects the actuator output arm to the control surf ace. F or morphing ef fectors, the actuator is connected to some hardpoint on the wing surf ace. In either case, the actuator position is directly representati v e of the command input and the surf ace deection. F or simplicity in quantifying the morphing

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12 command, the actuator position is used to dene the magnitude of the control input, although the actual geometry may be too comple x to specify using a single parameter The rotary serv o actuators used in the v ehicles are commercial of f-the-shelf de vices. The position of the serv os is commanded using control sticks and knobs on a remote transmitter A pilot input on the sticks generates a pulse-width modulated signal to the serv os, where the width of the pulse is proportional to the commanded position. The internal circuitry in the serv o controls the rotation of the output arm to the commanded position by using a motor -gear system and a rotary potentiometer The v oltage feedback from the potentiometer is used to create an error signal to dri v e the position control system. This v oltage feedback is also a con v enient measure of actuator position. The center pin of each feedback potentiometer is connected to an analog input channel of the microD AS, resulting in a time-synchronized measure of control deection with the inertial data.

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CHAPTER 4 ASYMMETRIC WING SHAPING FOR R OLL CONTR OL 4.1 Aircraft Design Small v ehicles ha ving wingspans of less than 12 in are being de v eloped for military and ci vilian reconnaissance missions. Fle xible wings are typically used in conjunction with con v entional ele v ator and rudder control surf aces. The lateral-directional control ef fecti v eness of the rudder is suitable for open-loop control, b ut suf fers from signicant coupling and saturation issues that preclude its use for ne ight path tracking. W ing curling is an attracti v e type of morphing for this class of MA V The attraction lies in both its simplicity of implementation and its ef fecti v eness for morphing. In this case, a MA V will simply be retrotted to accommodate a basic type of wing curling. The objecti v e of this study is to in v estigate the ef fect of wing shape on basic maneuv ering. Specically the roll performance and associated coupling with pitch and ya w will be studied for wings which curl into asymmetric congurations. The ef fects of reduced area and increased camber along with their corresponding changes in lift and drag on each wing, are of particular interest. T w o MA Vs, sho wn in Figure 4–1 are the platforms used to in v estigate wing curling. The only control surf ace on the 12 in wingspan MA V is an ele v ator for longitudinal control; therefore, morphing will be used as the only ef fector to control the lateral-directional dynamics. The 10 in includes a rudder control surf ace in order to compare with the ef fecti v eness of the morphing for lateral-directional control. The fuselage of each aircraft houses a 3-axis gyro and 3-axis accelerometer along with a data logger to record ight responses. The airfoil used on the wings is similar to a competition airfoil de v eloped by Dr Mark Drela. The airfoil w as modied using XFOIL to impro v e lift magnitude at lo w 13

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14 Figure 4–1: W ing shaping morphing MA Vs 10 in wingspan high-wing aircraft (left) and 12 in span mid-wing aircraft (right) angles of attack. The modications included increasing the camber to 8% and mo ving the maximum camber position forw ard along the chord to the 29% position. The wings are f abricated with no appreciable thickness using thin carbon-ber and late x membrane. The shape of the airfoil on the physical wing is in line with the XFOIL modeling, which assumes a thin, undercambered airfoil. A 3-vie w schematic of the 12 in aircraft geometry is sho wn in Figure 4–2 Aircraft properties for the 10 in and 12 in v ehicles are sho wn in T able 4–1 T able 4–1: Properties of the 10 in and 12 in wing shaping MA Vs Property 10 in high-wing MA V 12 in mid-wing MA V W ing Span 10 in 12 in W ing Area 31 in 2 44 in 2 W ing Loading 13.93 ozf t 2 14.19 ozf t 2 Aspect Ratio 3.27 3.27 Po werplant coreless motor 2.5 in prop geared motor 3.5 in prop T otal W eight 3.00 oz 4.33 oz 4.2 Morphing Mechanism W ing curling is accomplished using rotary actuators connected to the wing structure by tensioned K e vlar cables as sho wn in Figure 4–3 As the actuator adjusts the tension on the cable, the wing deforms into a twisted form that is appropriate for ight control. Namely the resulting shape increases the angle of incidence of the morphed wing and increases the lifting force produced. When one wing side is morphed, a lift dif ferential is created which causes the aircraft to incur a roll rate.

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15 Figure 4–2: T op, front, and side vie ws of computer -aided design dra wings for 12 in MA V Figure 4–3: K e vlar cables

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16 The morphing achie v ed by this strate gy is directly dependent upon the attachment points of the threads. The threads attach to serv os by passing through the fuselage near the leading edge of the wings. The corresponding attachment to the wings is actually at separate hardpoints. One attachment point is near the mid-chord point at the wing-tip outboard. Another attachment point is the trailing edge near the tw o-thirds span location. The morphing that results by actuating the serv o is sho wn in Figure 4–4 The serv o rotates and causes the threads to pull against the attachments on the wing. The morphing resulting from this strate gy is clearly be yond simple w arping. In this case, the pulling of the threads to w ard the leading-edge attachment at the fuselage causes the wing to both twist and bend. The ef fect is similar in nature to a curling of the wings. The basic parameters that are readily observ ed to change are the twist, camber chord, and span. Figure 4–4: Front vie w sho wing undeected wing (left) and morphed wing (right) The e xtent and shape of the morphing can be adjusted by v arying the amount of tension in the K e vlar lines or adjusting the location of the attachment hardpoint on the wing. The shape is also dependent on the direction of the tensile force from the K e vlar which is determined by the position of the actuator arm with respect to the wing hardpoint. A lar ge v ertical separation between these tw o points, as on this MA V

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17 causes the tensile force to be applied in a more spanwise direction so the wing e xhibits the predominantly curled motion in Figure 4–4 The e xtent and shape of the morphing can be adjusted by v arying the amount of tension in the K e vlar lines or adjusting the location of the attachment hardpoint on the wing. The shape is also dependent on the direction of the tensile force from the K e vlar which is determined by the position of the actuator arm with respect to the wing hardpoint. A lar ge v ertical separation between these tw o points, as on this MA V causes the tensile force to be applied in a more spanwise direction so the wing e xhibits the predominantly curled motion in Figure 4–4 4.3 Flight Performance A series of ight tests are performed to e v aluate wing curling for roll performance. The v ehicle actually contains separate serv os that allo w symmetric curling; ho we v er the current discussion only considers asymmetric morphing. As such, the ight test considers maneuv ers in response to a single wing being curled while the other wing remains undeected. The wing curling causes a signicant roll moment. The direction of roll is determined by an increase in lift on the curled wing. Essentially the curling causes a greater angle of incidence and angle of attack on the morphed wing. This ef fect causes a lift increase on the left wing, and consequently a positi v e roll moment, when the left wing is curled. Of course, some amount of coupling to pitch and ya w results from the asymmetric conguration [ 14 ]. An immediate benet from the morphing is realized when comparing this MA V to similar types that do not ha v e morphing. This shape of v ehicle, with a range of wing span, has been pre viously o wn using only ele v ator and rudder for control. The v ehicle is noticeably easier to pilot using ele v ator and morphing. The wing morphing generates roll moments that f acilitate ight path tracking be yond the rudder o v er the majority of the ight en v elope.

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18 The wing-curling morphing e xhibits good control response near the neutral, trim position. Small inputs are necessary in performing turns and in making slight adjustments to the ight path. The morphing pro vides an adequate le v el of control under these circumstances The aircraft responds predictably to v arious magnitudes of control input, although the physical deformation of the wing surf ace is not necessarily linear In particular the morphing is suitable for both commanding turns and for correcting for attitude perturbations from wind gusts or other disturbances. Roll controllability remains satisf actory throughout the airspeed range encountered during cruise, high-speed di v es, and landing or approach phases. Although turns and rolls are easily accomplished with the wing curling, aggressi v e maneuv ers are considerably more dif cult. The aircraft is quite sensiti v e to departure when morphing is commanded while the aircraft is at high loading conditions, such as in a steep turn or during a lar ge pitch angle change. The wing deection incurred during wing curling generates lar ge incidence angles near the deformed re gion of the wing. The incidence angles generate the requisite change in aerodynamic forces and moments to control the aircraft during le v el or cruise ight conditions. Also, if the aircraft is already at a lar ge angle of attack, such as during an aggressi v e maneuv er lar ge morphing commands can e xceed the critical angle of attack and force a stall on the deformed wing. Such a situation generates a rolling moment opposite to the commanded direction. F or instance, during high angle of attack ight, deforming the left wing slightly increases the angle of attack and lift on the left wing and causes a roll rate to the right. Ho we v er lar ge morphing commands cause a stall o v er portions of the left wing, reducing the lift compared to the right wing, and causing a stall-spin departure to the left. Departures caused by stall due to morphing are generally terminal on this type of aircraft, as the morphing can be controlled only in a single direction for each wing. Once a spin has de v eloped, the morphing pro vides

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19 insuf cient control po wer to generate the required anti-spin forces and reco v er to le v el ight. Finally roll handling qualities tend to be quite sensiti v e to the location of the hardpoint on the wing and to the tension in the cable. Slight asymmetries in the right and left side cable tensions often contrib ute to dif culties in control and non-zero trim condition. Unintentional v ariations in the control linkage tension cause control responses to change slightly o v er a series of ights. Additionally deterioration of the late x membrane noticeably reduces the wing surf ace tension. The natural rubber used in the late x material decays when e xposed to the sun. The reduced tension of the decayed late x pre v ents the deformation from propagating smoothly throughout the wing structure. In turn, the twist deformation caused by the b uckling remains localized around the hardpoint and reduces control ef fecti v eness. 4.4 Nonlinear Modeling of Lateral and Longitudinal Dynamics Flight data from the v ehicle is analyzed to estimate models of the ight dynamics. Se v eral techniques were attempted to estimate these models, including system identication [ 24 ] and parameter estimation [ 19 ], b ut with limited success. This v ehicle is particularly dif cult to model because the morphing causes time-v arying asymmetries which violate man y assumptions used by standard routines. Furthermore, the estimation is dif cult because of limited ight data. The MA V is equipped with gyros and accelerometers b ut the ight data from the accelerometers is actually too noisy to be useful for modeling. Thus, se v eral critical measurements, such as angle of attack and angle of sideslip, are not a v ailable. Some dynamics are not easily observ able, especially in the presence of noise, using only the a v ailable sensors. A nonlinear auto-re gressi v e model is used to represent the ight dynamics. The general form of this model is sho wn in Equation 4.1 This model relates the gyro measures of roll rate, pk, pitch rate, qk, and ya w rate, rk, to the morphing

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20 command, d mk, and ele v ator command, d ek, at the sampling instance of k The matrices, A iR 33 and B iR 32 represent the dynamics. pk1qk1rk1 n n n n rA 1 pkqkrk n n n n A 2 pk1qk1rk1 n n n n A 3 pk pk qk qk rk rk n n n n A 4 pk1 pk1 qk1 qk1 rk1 rk1 n n n n A 5 pkqkqkrkrkpk n n n n A 6 pk1qk1qk1rk1rk1pk1 n n n n B 1 d mkd mk1 n B 2 d mk d mk d mk1 d mk1 n B 3 d ekd ek1 n (4.1) The model in Equation 4.1 contains quadratic terms of the rates and commands. Such quadratic terms are included to account for unkno wn relationships between the wing shape and the aerodynamics. In this case, the terms utilize an absolute v alue to allo w the contrib utions from the quadratics to change in sign. The model in Equation 4.1 also contains coupling terms. These terms multiply the gyro measurements by each other The standard equations of motion for a rigid-body aircraft include coupling terms which scale by the moments of inertia [ 26 ]. This MA V is ob viously asymmetric during the morphing so the coupling is essential. Finally Equation 4.1 computes the update to the gyro measurements as a function of the measurements from tw o pre vious sampling times. These terms are included to account for the time-v arying nature of the dynamics which arise by altering the wing

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21 shape. The dynamics are assumed to be suf ciently described by tw o sampling times although a rigorous study of the sampling times w as not conducted. The v alues of the matrices, A i and B i in Equation 4.1 are determined by a leastsquares t to the ight data. The resulting model is used to simulate the responses to the morphing and ele v ator commands. Such responses are sho wn in Figure 4–5 0 1 2 3 4 5 6 -15 -10 -5 0 5 10 15 Time (s)Roll Rate (deg/s) datasim 0 1 2 3 4 5 6 10 5 0 5 Time (s)Pitch Rate (deg/s) datasim 0 1 2 3 4 5 6 8 6 4 2 0 2 4 6 8 Time (s)Yaw Rate (deg/s) datasim Figure 4–5: Measured and predicted responses for roll rate (left), pitch rate (middle) and ya w rate (right) The responses in Figure 4–5 demonstrate the model captures the basic trend of the dynamics b ut is not completely accurate. The predicted responses are not perfect matches to the measured responses b ut yet the y clearly sho w similarities. Thus, the model indicates the time-v arying asymmetries associated with the morphing causes nonlinearities and coupling in the ight dynamics of this MA V

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CHAPTER 5 SYMMETRIC WING TWISTING FOR R OLL CONTR OL 5.1 Aircraft Design W ing twisting is another type of morphing that is particularly interesting, and suitable, for a MA V The concept of wing twisting is an ob vious choice based on its use as a control ef fector for the Wright Flyer It is also being adopted for the Acti v e Aeroelastic W ing [ 27 ]. W ing twisting will be in v estigated for a MA V in a similar f ashion as those pre vious aircraft; namely wing twisting will be used to generate roll moments. A mechanism for wing twisting is implemented on the MA V sho wn in Figure 5–1 This aircraft has an ele v ator and rudder as control surf aces. Also, the fuselage is lar ge enough to house the sensor package comprised of gyros and accelerometers along with the data logger Figure 5–1: W ing-twisting MA V The wing has se v eral features adv antageous to twisting. The leading-edge strip is a relati v ely thin piece of uni-directional carbon ber Also, the wing surf ace is a n ylon lm which is not o v erly e xtensible. These properties result in a wing which smoothly 22

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23 and continuously deforms across the entire surf ace due to a small perturbation at a single point. Se v eral basic properties of the v ehicle are gi v en in T able 5–1 T able 5–1: Properties of the 24 in wing twisting MA V Property W ing T wisting MA V W ing Span 24 in W ing Area 100 in 2 W ing Loading 20.32 ozf t 2 Aspect Ratio 5.76 Po werplant Brushless motor 4.75 in prop T otal W eight 14.11 oz 5.2 Morphing Mechanism Morphing is accomplished using an steel torque-rod af x ed to a batten at approximately the 66% span position. Actuating this rod with a serv o forces the wing to under go a twisting deformation. Although the actuating point is localized to a single wing batten, the wing surf ace distrib utes the deformation o v er the entire wing. The magnitude of the twist deformation is lar gest at the actuation point and is tapered to w ard the wing tip and wing root. Figure 5–2: Underside vie w of wing sho wing torque rod The use of torque-rods admits a bi-directional wing twisting that resists the ef fects of loading. The bi-directionality of twist results from actuating the wing to twist in either trailing-edge up and trailing-edge do wn directions. The resistance to loading

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24 results from the stif fness of the aluminum rod, along with stif fness of the leading-edge strip, to maintain shape unless e xcessi v e loads are encountered. Thus, the control of the wing shape is lar gely a function of the actuator position with only small ef fects from response to airloads. Figure 5–3 compares the 24 in MA V wing in undeected and morphed congurations. Figure 5–3: Rear vie w of the 24 in MA V with undeected (left) and morphed (right) W ing 5.3 Flight Performance The wing twisting aircraft e xhibits highly desirable control characteristics in ight [ 14 ]. Roll control is e xtremely responsi v e across a wide range of airspeeds. At slo w speeds, such as near le v el ight stall, the wing twisting remains ef fecti v e at commanding a turn and reco v ering from turb ulent disturbances. At higher speeds, the roll response is also ef fecti v e, although the magnitude of the roll rate increases. Modeling of the control characteristics suggests that the roll response is lar gely linear o v er the airspeed range. The morphing is ef fecti v e at pro viding small, high-rate control inputs needed to maintain a specic attitude or ight path. In such cases, the v ehicle responds quickly to the initial command and reco v ers to unaccelerated ight as the command is returned to neutral. The wing twisting also pro vides positi v e control characteristics at lar ge amplitude deections. Maximum roll command, which twists the wings anti-symmetrically

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25 10 o generates a roll rate in e xcess of 1000 os within 02 seconds. Neutralizing the morphing stops the roll in approximately the same time. During continuous rolls, the v ehicle incurs relati v ely little ya w coupling. Y a w rate di v er gence from wing twisting is approximately an order of magnitude lo wer than the corresponding roll rate. At high roll rates, for instance, se v eral complete rolls can be completed without an appreciable change in heading or pitch attitude. Basic ying tasks such as turns and bank angle correction are f acilitated with mor phing as compared to rudder -only control. The need for correcti v e control input during the maneuv er is decreased because of the decreased coupling. T urns commanded solely through morphing are impro v ed, where minimal rudder corrections are needed to maintain coordination throughout the turn. The turn performance is especially impro v ed in windy and gusty conditions, where the need to independently control bank angle and heading angle is increased. 5.4 Linear Modeling of Lateral Dynamics Flight testing of the acti v e wing-shaping 24 in MA V is performed in the open area of a radio controlled (R/C) model eld during which wind conditions range from calm to 7 knots throughout the ights. Once the ight control and instrumentation systems are po wered and initialized, the MA V is hand-launched into the wind. This launch is an ef fecti v e method to quickly and reliably allo w the MA V to reach ying speed and be gin a climb to altitude. This airplane is controlled by a pilot on the ground who maneuv ers the airplane visually by operating an R/C transmitter The data acquisition system be gins recording as soon as the motor is po wered. This aircraft design allo ws either rudder or wing shaping to be used as the primary lateral control for standard maneuv ering. The airplane is controlled in this manner through turns, climbs, and le v el ight until a suitable altitude is reached. At altitude, the airplane is trimmed for straight and le v el ight. This trim establishes a

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26 neutral reference point for all the control surf aces and f acilitates performing ight test maneuv ers. Open-loop data is tak en to indicate the ight characteristics of the MA V Specifically the rates and accelerations are measured in response to doublets commanded separately to the serv os. Se v eral sets of doublets are commanded ranging in magnitude and duration to obtain a rich set of ight data. The dynamics of the MA V in response to rudder commands is in v estigated to indicate the performance of the traditional conguration for this MA V A representati v e doublet command and the resulting aircraft responses are sho wn in Figure 5–4 0 1 2 3 4 5 6 15 10 5 0 5 10 15 Time(sec)Rudder Command 0 1 2 3 4 5 200 150 100 50 0 50 100 150 Time(sec)Roll Rate (deg/sec) 0 1 2 3 4 5 200 150 100 50 0 50 100 150 Time(sec)Yaw Rate (deg/sec) Figure 5–4: Doublet command to rudder (left), roll rate response (middle), and ya w rate response (right) The roll rate and ya w rate measured in response to this command are sho wn in Figure 5–4 The roll rate is suf ciently lar ge and indicates the rudder is able to pro vide lateral-directional authority; ho we v er the ya w rate is clearly lar ger than desired. Actually the ya w rate is similar in magnitude to the roll rate so the lateral-directional dynamics are v ery tightly coupled. The ef fect of the rudder in e xciting the dutch roll dynamics is clearly e videnced in the magnitude and phase relationship of the response measurements. Doublets, such as the pulse sequence sho wn in Figure 5–5 are also commanded to the morphing serv o. The roll rate and ya w rate in Figure 5–5 are measured in response to the doublet. These measurements indicate the roll rate is considerably higher than the ya w rate.

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27 0 0.5 1 1.5 2 8 6 4 2 0 2 4 6 8 Time(sec)Morphing Command 0 0.5 1 1.5 2 200 150 100 50 0 50 100 150 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 200 150 100 50 0 50 100 150 Time(sec)Yaw Rate (deg/sec) Figure 5–5: Doublet command to wing twist morphing (left), roll rate response (middle), and ya w rate response (right) Thus, the morphing is clearly an attracti v e approach for roll control because of the nearly-pure roll motion measured in response to morphing commands. The data from open-loop ights is then used to approximate a linear time-domain model using an ARX approximation [ 24 ]. This model is generated by computing optimal coef cients to match properties observ ed in the data. The assumption of linearity is reasonable since the maneuv ers are small doublets around a trim condition. Also, the twisting command is anti-symmetric about the centerline of the aircraft. The resulting model, ha ving poles at -4.95 and -0.1194, is used to simulate responses of the aircraft. The simulated v alues of roll and ya w rates are sho wn in Figure 5–5 as dashed lines. The simulated responses sho w good correlation with the actual data. The model is thus considered a reasonable representation of the aircraft. The e xistence of such a model is important for future design of autopilot controllers b ut it is also v aluable for interpreting the morphing. Essentially the ability to identify a linear model with poles relating to the roll con v er gence and spiral con v er gence modes indicate the aircraft with morphing acts lik e an aircraft with ailerons. 5.5 Spin Characteristics of W ing T wist Morphing Figure 5–6 sho ws the command and rotation rates during a con v entional spin. This maneuv er is initiated from le v el ight by commanding positi v e ele v ator to increase the pitch rate and angle of attack. Right rudder command is then applied to

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28 generate a ya wing moment as the aircraft approaches stall. In this case, the ya w causes an asymmetric stall and starts the spin rotation. The aircraft response is relati v ely constant throughout the maneuv er although the roll rate tends to b uild up as the ight path changes from le v el to v ertical. The autorotation continues as long as the positi v e ele v ator and rudder commands are held. Once the commands are neutralized, the rotation slo ws and comes to a stop with little or no opposite rudder input. Positi v e ele v ator is used to reco v er the aircraft to le v el ight at 363 seconds. Although this type of spin has been e xperienced se v eral times, the entry procedures tend to be dif cult to reproduce. Specically applying rudder command at a lo w angle of attack (too early) pre v ents a stall from de v eloping and results in a high-speed spiral di v e. Both wind tunnel and CFD analysis ha v e sho wn that the thin-undercambered airfoils used on the v ehicle ha v e delayed stall response. This delay af fords such v ehicles increased resistance to stall-spin departure, at least for positi v e loadings. The ef fect of morphing on positi v e (upright) spins is to accelerate the onset of the spin and to assist in the reco v ery process. This ef fect is most pronounced during cross-coupled controls, where the rudder direction is opposite to that of the morphing. In such a case, the high angle of attack at the inside wing tip is further increased by the morphing actuation, leading to a subsequent stall-spin. Releasing the morphing command ef fecti v ely reduces the wing angle of attack and produces nearly immediate reco v ery from an upright, con v entional spin. 359 360 361 362 363 364 40 30 20 10 0 10 20 30 40 Command (deg)Time (s) elevatorruddermorphing 359 360 361 362 363 364 100 50 0 50 Response (deg/s)Time (s) roll ratepitch rateyaw rate Figure 5–6: Pilot commands (left) and responses (right) during con v entional spin

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29 Con v entional spins are also performed with ne gati v e (do wn) ele v ator actuation to produce a starkly dif ferent response. In particular the spin modes observ ed are of considerably higher ener gy The rotation rates of a ne gati v e spin compared with an upright spin tend to be between 2 to 6 times greater Based on rudimentary analysis, the stall characteristics of a thin under -cambered wing at ne gati v e angles of attack are f ar more se v ere than the characteristics at high angles of attack. In ight, the airplane is observ ed to ha v e a v ery immediate and violent response to lar ge ne gati v e ele v ator commands. Such an input is belie v ed to cause a ne gati v e stall quickly where an y asymmetry about the ya w axis then produces a lar ge rate of rotation. Figure 5–7 sho ws an identied ne gati v e spin mode initiated by a morphing command with ele v ator and rudder At 401 seconds, the aircraft responds to the constant control deection by b uilding up rotation rates on all three axis. The entry into the maneuv er is relati v ely gradual and only after one second of control inputs ha v e the pitch, roll, and ya w rates become signicant. This particular type of spin stabilizes independently of the initial pro-spin control deections. At 402 seconds, the controls are released, while the aircraft continues to spin. The application of positi v e ele v ator (for reco v ery) shortly afterw ards appears to maintain the spin for some time. It is only with correcti v e opposite rudder command that the aircraft arrests the rotation and reco v ers from the spin. It is dif cult to dra w solid conclusions from this spin sequence. Ho we v er the tw o distinct modes observ ed in Figure 5–7 are attrib uted to primary and secondary spin characteristics, where the latter is caused by a premature reco v ery attempt. Similar spins ha v e been observ ed from both left and right directions. Alternati v ely Figure 5–8 sho ws a considerably dif ferent spin beha vior for similar control combinations. Although initiated by commands similar to the pre vious spins, this type of spin e xhibits a c yclic or periodic motion. It is perhaps with the timing of the control inputs or entry ight conditions that a dif ference can be found. Whereas

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30 400 401 402 403 404 405 40 30 20 10 0 10 20 30 40 Command (deg)Time (s) elevatorruddermorphing 400 401 402 403 404 405 100 50 0 50 Response (deg/s)Time (s) roll ratepitch rateyaw rate Figure 5–7: Pilot commands (left) and responses (right) during spin in Figure 5–7 the ele v ator input lagged behind the rudder and morphing inputs, the spin depicted by Figure 5–8 sho ws the ele v ator leading slightly The precise ef fect this has on the spin is unkno wn. Ho we v er the resulting aircraft response is sho wn to be 6 times greater in magnitude than a con v entional spin. From le v el, trimmed ight, the aircraft is subjected to full left wing morphing, full left rudder and full ne gati v e ele v ator command. The initial reaction of the aircraft is to pitch do wn at a constant rate and incur a left roll and ya w from the wing morphing and rudder deections. Once the wing has reached the ne gati v e stall angle, presumably f acilitated by the deected wing, a rapid spin ensues, nearly doubling the roll and ya w rates and reducing pitch rate. This pattern is repeated four times throughout the spin while pilot commands are held constant. Each c ycle is proceeded by a period of lo w momentum, follo wed by a sharp change in pitch rate along with peaks in both the roll and ya w rates. Throughout the spin, the mean pitch rate is near zero. Each c ycle generates a lar ge ne gati v e pitch rate follo wed by a lar ge positi v e pitch rate. Mean roll and ya w rate responses are non-zero during the spin. The lateral rates remain ne gati v e, achie ving small ne gati v e v alues only as the pitch rate re v erses direction. While the dynamics of such a maneuv er are not v ery well understood, it appears that the morphing of the wing plays a lar ge roll in both inducing and reco v ering from the spin. F or instance, similar spin entries performed without morphing are characterized by considerably lo wer rotation rates and a continuation of the spin after command inputs are neutralized. Ho we v er the reco v ery of this c yclic spin mode occurs

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31 nearly immediately after the controls are neutralized. As seen at 176 in Figure 5–8 the aircraft is incurring maximum rotation rate when command is returned to neutral. The rotation rates continue to follo w the characteristic spik e pattern and nally con v er ge to zero. 171 172 173 174 175 176 177 40 30 20 10 0 10 20 30 40 Command (deg)Time (s) elevatorruddermorphing 171 172 173 174 175 176 177 100 50 0 50 Response (deg/s)Time (s) roll ratepitch rateyaw rate Figure 5–8: Pilot commands (left) and responses (right) during c yclic spin In ight, this immediate con v er gence has the ef fect of stopping the aircraft in mid-rotation. Unlik e the other spin modes observ ed, the c yclic spin mode has no apparent reco v ery apart from neutralizing the controls. The aircraft will continue to the end of a gi v en c ycle, cease rotation, and simply return to steady controlled ight. The nose-do wn reco v ery typical of other spin modes is contrasted with an immediate reco v ery to le v el ight. The usefulness of the c yclic spin mode depicted in Fig. 5–8 is perhaps questionable, although it may gi v e rise to a dif ferent mode of maneuv ering for morphing aircraft. F or instance, the abo v e maneuv er may be useful for a controlled v ertical displacement. On initiating the entry the airspeed quickly decays and starts the aircraft on a relati v ely slo w v ertical ight path. During this portion of the maneuv er the aircraft incurs a series of high rate of rotations, each separated by a period of lo w momentum. As e videnced by the reco v ery from the maneuv er this period can be used to reco v er the aircraft into stable ight. While pre vious spin modes required correcti v e rudder and signicant altitude losses for reco v ery this c yclic spin mode stopped once the controls were neutralized.

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32 Attitude and airspeed entry conditions into the spin trials ha v e been observ ed to ha v e some impact on the stabilized spin modes; ho we v er accurate measurements of the entry conditions were not possible. The lack of pressure sensors on the airframe precluded the gathering of such data. Excitation of a particular spin mode depended on the pilot ability to position the aircraft properly based on control feel and v ehicle observ ations. The spin entry maneuv ers were also attempted for other control combinations. Specically c yclic spins were attempted without wing twisting by using ne gati v e ele v ator and rudder deection. These trials resulted in a stabilized spin b ut with considerably lo wer rotation rates than the c yclic spin. Additionally this mode did not e xhibit the periodic beha vior achie v ed through wing twisting during a spin.

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CHAPTER 6 MUL TI-POINT WING SHAPING 6.1 Aircraft Design The multi-point wing-shaping aircraft emplo ys a simple strate gy to e x ercise increased control o v er the wing in twist. Actuation of the wing is accomplished through four concentric rotating spars that are attached to a e xible, e xtensible wing skin. The basic idea of this form of morphing is to ha v e some control of the lift distrib ution o v er the wingspan. Since each of the four rotating spars can be controlled independently the wing surf ace can be commanded to a v ariety of comple x shapes. In this manner the morphing can be useful for longitudinal control, longitudinal trim, minimum drag, maximum drag, or stall resilience in addition to commanding roll rate. From a design perspecti v e, the v ehicle geometry is similar to the 24 in wingtwisting aircraft, as seen in Figure 6–1 The wing planform and airfoil are identical in f act, although the wing structure and membrane dif fer some what to accommodate the morphing spars. The wings are mounted along the middle of the fuselage to f acilitate the mounting of the morphing actuators and mechanisms. The lo wer wing position and reduced dihedral also help eliminate e xcessi v e roll-ya w coupling. Figure 6–2 sho ws the wing under going morphing to the outboard (wingtip) spar tubes alone and to both wingtip and midboard spar tubes simultaneously Deformation is visually apparent by e xamining light reections of f of the leading edge and the shape of the trailing edge. 6.2 Morphing Mechanism Concentric tube spars act as both primary load-bearing members and as control linkages (torque-tubes). A lar ge diameter tube is x ed to the fuselage and acts as a bearing support for the rotating spars. The root section of the wing surf ace is 33

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34 Figure 6–1: T op, side, and front vie ws of the 24 in span multiple-position wing shaping v ehicle also attached to this tube, creating an immobile joint between the inboard wing and fuselage. T w o smaller tubes, one within the other are supported by the x ed tube. The smallest tube e xtends the full span, while the center tube e xtends to the 60% position. Each of the outboard and midboard spars is actuated in twist via serv os mounted in the fuselage, sho wn in Figure 6–3 Each serv o is then able to command the incidence angle of the corresponding wing section independently A e xible wing surf ace is attached to each of the three wing spar tubes. Attachment points near the spar joints are left unconstrained in pitch angle. This freedom allo ws the incidence to smoothly taper between the rigidly attached sections of the wing surf ace. This structure permits twist morphing of each controlled wing section

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35 Figure 6–2: W ing shaping MA V sho wing neutral position (top left), wingtip morphing (top right), and full wing morphing (bottom) Figure 6–3: Spar torque-tube morphing actuators. The 4 front serv os rotate concentric spar sections, aft 2 control rudder and ele v ator from10 o to10 o incidence angle. Each of the four wing sections are commanded independently allo wing for considerable dif ferential or collecti v e congurability 6.3 Flight Performance The aircraft has under gone basic performance and handling ight tests. Roll control is achie v ed by dif ferentially actuating the wingtip spars. The handling qualities and maximum roll rate are similar to the 24 in wing twisting aircraft. Actuating the

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36 entire wing dif ferentially (i.e. using both wingtip and midboard sections), achie v es roll rates and performance measures considerably higher The morphing is also being considered for use in conjunction with other control surf aces. Basic ight tests of combining collecti v e midboard wing deection with ele v ator command ha v e sho wn potential for impro v ement in pitch rate performance. Additionally this morphing may be suited for quasi-statically reconguring the wing twist to optimize spanwise lift distrib ution in ight. Such techniques are currently used by sailplane and commercial jet pilots to alter the lift properties of the wing for cruise, steep descent, and maximum performance ight phases.

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CHAPTER 7 V ARIABLE GULL-WING ANGLE MORPHING 7.1 Aircraft Design The aircraft discussed thus f ar ha v e been limited in concept to relati v ely simplistic twisting or bending of the aircraft structure. Ho we v er because of the nature of such mechanisms, control o v er the aircraft is limited to high-bandwidth stabilization, maneuv ering control, or retrimming. The morphing shapes achie v ed by such methods are not suitable for the gross aerodynamic reconguration that is typically associated with morphing. A ne w morphing aircraft design is proposed that uses a jointed spar structure to achie v e a biologically-inspired form of morphing in addition to the twist control used on pre vious aircraft. The design of the aircraft is identical to the multiple-position wing shaping aircraft in all components e xcept for the jointed spar and actuator The aircraft conguration, sho wn in Fig. 7–1 is traditional in the sense of a single lifting surf ace, horizontal and v ertical stabilizers, and tractor propeller Apart from the morphing mechanisms, the aircraft is equipped with ele v ator rudder and throttle control. The v ehicle airframe is lar gely composite carbon-ber and mylar plastic. The monocoque fuselage is made using carbon-ber cloth wrapped o v er a male mold [ 12 ]. Once cured and e xtracted, the structure is strong enough to withstand wing and tail loads without additional supporting structure. The aircraft is considered small enough to be considered in the class of micro air v ehicles, since the wingspan at full e xtension is 26 in The tail surf aces consist of a mesh of unidirectional carbon ber strips. The perimeter strips support the o v erall planform, while the interior strips b uild up the surf ace rigidity Hinges for the control surf aces are embedded within the carbon structure during the layup process. Additionally mylar plastic co v ering is used for 37

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38 Figure 7–1: T op and side vie w of v ariable gull-wing aircraft skin material on the tail feathers and portions of the wing. The resulting structure adds minimal weight to the v ehicle, yet is strong enough to withstand ight loads and the occasional crash. 7.2 Morphing Mechanism The wing planform shape pro vides suf cient area to k eep the fully-instrumented aircraft at a reasonable wing loading, yet is also high enough in aspect ratio to pro vide good aerodynamic performance. Morphing the wings changes the wing geometry in se v eral parameters. T able 7–1 lists the basic geometry changes incurred during gull-wing morphing. Figure 7–2 sho ws a frontal vie w of the v ehicle during three congurations resulting from gull-wing morphing. T able 7–1: W ing geometry change o v er v ariable gull-wing morphing range P arameter Min Max W ingspan 20 in 26 in Planform area 77.7 in 2 101.4 in 2 Inboard wing relati v e to fuselage -40 o 40 o Outboard wing relati v e to fuselage -40 o 40 o

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39 Figure 7–2: V ehicle under going neutral (top), positi v e (center), and ne gati v e (bottom) gull-wing morphing A hinged spar structure, based loosely on bird sk eletal physiology [ 33 ], pro vides the de gree of freedom needed for gull-wing morphing. Each spar side consists of tw o tub ular spars with one hinge at the fuselage joint and another between the tw o spars. The angle of the inboard spar is controlled by a v ertical linear actuator A telescoping shaft connects the spar with the output arm of the actuator The shaft allo ws the actuator to mo v e o v er the entire range without mechanically binding the spar The angle of the outboard spar is passi v ely controlled via a mechanical linkage parallel to the inboard spar This linkage connects the control arm on the outboard spar directly to the fuselage. During actuation, the linkage causes the inboard and outboard sections to deect in opposite directions. The ratio of these relati v e deections is adjusted by changing the moment arm on the fuselage control arm and/or the outboard spar control arm. An important feature of the system is its ability to withstand ight loads without acti v e control or ener gy consumption. Figure 7–3 sho ws the left side of the hinged spar in a positi v e gull-wing position. A e xible wingskin is attached to the jointed spar so that the spar comes under the point of maximum camber This position approximately corresponds with the

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40 Figure 7–3: V ariable gull-wing spar structure and control linkage, linear actuator visible inside fuselage at left point of minimum pitching moment, in addition to reducing the frontal area of the wing. The wing skin consists of chordwise carbon-ber battens and a single spanwise leading-edge member Each batten is free to deform within the limits of the wing skin e xtension and carbon-ber e xibility In ight, this compliance allo ws the airfoil sections to deform in response to b uf feting or steady airloads. As a result, the wing passi v ely deforms and reduces the ef fect of atmospheric perturbations such as gusts and wind shear on the v ehicle' s ightpath. Con v entional ele v ator and rudder control surf aces are used for pitch and ya w control. These surf aces are hinged to the x ed stabilizing surf aces with strips of T yv ek. Rotary actuators mounted in the fuselage control the surf ace deection. Control actuation limits are +/30 o of tra v el, with actuation rate limits of 400 os Roll control is pro vided by articulating wing tips on the outboard spar section. A rotary serv o mounted to the wingskin actuates against the spar causing the wing surf ace to rotate about the spar The surf ace is attached to the outboard spar so that rotation about the spar is unrestrained, e xcept by the actuator motion. Ho we v er since the wingskin is continuous along each side of the aircraft, the result is a twist deformation centered at the actuator and e xtending both inw ard to w ard the fuselage

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41 and outw ard to w ard the wingtips. Figure 7–4 sho ws a close-up vie w of the wing twist mechanism, outboard spar and actuator Figure 7–4: Underside vie w of left wing sho wing wing twist ef fector Control of the gull-wing is accomplished using a linear lead-scre w actuator dri v en by a rotary serv o. Rotating the lead-scre w causes the output arm to slide v ertically within the fuselage. At the lo west position, the inboard spars are deected 40 o upw ard. The lead-scre w pro vides control of the wing shape without ha ving to withstand the lifting loads directly; ho we v er the actuation rate of the morphing is quite slo w in comparison to the other surf aces. This slo w actuation is not problematic since the morphing is being in v estigated strictly as a quasi-static ef fector Command and response data are measured in-ight using an on-board micro data acquisition system. The de vice supports 30 channels of analog sensor input and samples between 50Hz to 500Hz. The data presented here is measured at 100Hz. Se v eral e xternal sensors are interf aced to the data logging, including 3-axis rate gyros, linear accelerometers and control surf ace position sensors for the ele v ator rudder wingtwist, and gull-wing angle. 7.3 Flight Performance The v ariable gull-wing morphing suf ciently changes the ight performance for the v ehicle to operate in se v eral distinct ight re gimes. Morphing the wings controls

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42 se v eral aerodynamic and dynamic parameters, including lift to drag ratio, sideslip coupling, and roll stability These f actors in turn af fect the handling qualities of the v ehicle to mak e certain ight tasks easier to perform in a particular morphing conguration. The change in ight performance is the primary incenti v e behind the morphing; ho we v er this paper is strictly concerned with the change in handling qualities and dynamic characteristics that accompan y the performance changes. A more detailed analysis of the performance benet enabled by gull-wing morphing w as pre viously published [ 1 ]. 7.3.1 Gliding Performance Po wer -of f gliding performance is tested to identify the ef fect of the morphing conguration. Glide performance is an important measure of lift to drag ratio. In turn, lift to drag ratio is representati v e of the aircraft' s capability in range, endurance, maneuv ering, airspeed range, and ef cienc y Thus, by testing the glide performance, inferences can be made about much of the remainder of the ight en v elope, which is often more dif cult to test. Glide tests are performed by cutting of f motor po wer and allo wing the v ehicle to stabilize in a constant airspeed di v e. The shallo west, sustainable di v e angle corresponds to the maximum lift to drag ratio for a specied conguration. The numerical v alue of the lift to drag ratio is e xactly equal to the glide ratio, which is the horizontal distance tra v eled di vided by the altitude lost during the di v e. The glide ratio can be determined using airspeed and altitude measurements from on-board the aircraft or by estimating distances from the ground. In the unmorphed conguration (0 o gull-wing angle), the v ehicle attains an approximate maximum glide ratio of 11. This v alue is typical for aircraft of this size and shape. As the wing is morphed in the positi v e direction, the glide ratio become

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43 progressi v ely lo wer At 15 o gull-wing angle, the glide ratio is noticeably reduced, causing the aircraft to descend at a much steeper angle. At 30 o the lift to drag ratio becomes v ery lo w Ground estimates for the glide ratio are between 1 and 2. The result is that the aircraft is capable of descending at a 45 o angle without gaining airspeed. Furthermore, the high gull-wing angle adds considerable lateral-stability allo wing the v ehicle to attain a steep, stabilized di v e without control departure tendencies. Such a conguration could be benecial in allo wing the v ehicle to descend safely without requiring much horizontal distance. Ne gati v e gull-wing morphing has a similar ef fect on glide ratio. At -20 o gull-wing angle, the glide ratio is approximately 3. The ef fect of the morphing on a stabilized di v e is similar to the positi v e morphing, e xcept that the benets of sideslip to roll stability is greatly reduced. In f act, control input required to maintain a constant airspeed and glide angle is higher than both neutral and positi v ely morphed cases. Actuating the gull-wing morphing during a glide test illustrates the impact on lift to drag performance. During a steep, stabilized di v e at -30 o morphing, the gull-wing angle w as slo wly increased to 0 o The resulting ight path, when vie wed from the side, resembled an e xponential decay As the morphing became less ne gati v e, the glide ratio became progressi v ely shallo wer Pitch control w as used during this maneuv er to nd a trim airspeed corresponding to the maximum glide performance. Thus, the gull-wing morphing is suf ciently ef fecti v e to control the glide angle of the aircraft and can be used to change the glide angle throughout the descent. 7.3.2 Climb Performance The ef fect of gull-wing angle on climb performance is similar in nature to the ef fect on glide angle. Maximum climb performance is attained at a neutral gull-wing angle. Morphing the aircraft either in the positi v e or ne gati v e direction reduces climb rate, although the ef fect is more pronounced for positi v e gull-wing angles.

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44 7.3.3 Stall Characteristics Stall ight testing is performed to determine the ef fect of the morphing on departure characteristics. In particular it is used to determine conditions where a stabilizing controller may be required to pre v ent loss of control. Additionally the stall characteristics are useful in assessing whether certain stall-spin modes may be useful as e v asi v e or high-performance ight maneuv ers. Flight testing a v ehicle for stall characteristics requires a pilot to y at high altitudes and be well v ersed in reco v ery techniques [ 32 ]. The stalls are entered by reducing the airspeed and using the ele v ator to pitch abo v e the critical angle of attack. Ele v ator pressure is applied slo wly to help eliminate an y dynamic ef fects that might inuence stall entry Stalls are allo wed to fully de v elop by holding positi v e ele v ator pressure throughout the test. Reco v ery from the stall or ensuing spin is performed when the aircraft has clearly demonstrated a particular mode or when altitude loss has become substantial. Stalls performed at neutral morphing are relati v ely benign and resulted in moder ate altitude loss during reco v ery The wing planform has a tendenc y to stall abruptly b ut then re gains control quickly Control is lost for only a brief period as the aircraft pitches do wn and reduces angle of attack. Stalls at positi v e gull-wing angles are more dif cult to enter and result in a smaller altitude loss during reco v ery At high angles of attack and lar ge positi v e ele v ator pressure, the v ehicle simply enters a di v e and b uf fets slightly When pro v ok ed to stall with aggressi v e ele v ator deection, the stall break is of lo wer intensity than the pre vious conguration. Reco v ery from a stall at high positi v e gull-wing angle is more immediate. P art of this impro v ed resilience comes from a signicantly decreased tendenc y to depart into a spin. The high angle of the wings has a stabilizing ef fect and seems to f a v or a symmetric stall when at high angles of attack.

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45 Ne gati v e morphing contrib utes to a much more aggressi v e stall mode than observ ed with the pre vious congurations. The stall reco v ery also requires a greater amount of altitude and control input. Stalls also ha v e a greater tendenc y of escalating into a spin. The spins are generally non-terminal, although one stall test resulted in an unreco v erable spin that resulted in some v ehicle damage. Although the testing performed is hardly e xhausti v e, the observ ed characteristics indicate that the positi v e gull-wing contrib utes to highly desirable stall and reco v ery characteristics. Ho we v er the testing did not re v eal an y spin modes that could be useful as ight maneuv ers. 7.4 Lateral-Directional Dynamics Morphing introduces considerable comple xity to ight dynamics because of v ariable geometry of the airframe. The v ariable gull-wing aircraft in particular morphs the wings in a manner that has considerable ef fect on man y of the stability and control deri v ati v es that control the lateral-directional modes. Modeling of the lateral-directional dynamics is restricted to Dutch roll and roll con v er gence. Spiral mode identication w as not possible, considering that the data sets in analysis were relati v ely short in duration. Proper identication of this mode w ould require long data sets with little or no pilot input. Such tests are dif cult to accomplish using small remotely piloted v ehicles. 7.4.1 Roll Con v er gence The roll mode is one of the most fundamental descriptions of the aircraft lateraldirectional motion. The mode essentially describes resistance to rolling, whether through a control surf ace deection or a perturbation. Aircraft handling qualities and lateral controller designs are highly dependent on the roll mode. The roll mode, or roll con v er gence, is lar gely a function of the C l p deri v ati v e, which describes the change in rolling moment as a function of roll rate. This deri v ati v e in turn is a function of the v ehicle geometry As the v ehicle shape changes, as in the

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46 case of a gull-wing morphing aircraft, the C l p parameter and the corresponding roll mode are e xpected to change. The change in roll mode with morphing deection then becomes a basic assessment of the change in handling qualities incurred due to morphing. W ing-twist pulses are used to perturb the v ehicle from a trimmed ight condition. The response of the v ehicle to these pulses is used to identify important stability and control characteristics, namely the roll mode and the wing twist ef fecti v eness. Pulse maneuv ers are performed at cruise airspeed from straight and le v el ight. The pulse is repeated for a v ariety of command magnitudes and morphing positions. The pulse maneuv ers are performed such that the aircraft' s perturbation from the entry trim condition is relati v ely small. Lar ger pulses may e xceed the range of aircraft responses that can be adequately represented by a linear model; ho we v er the small size of the v ehicle requires that the maneuv er be lar ge enough to be clearly e vident to the remote pilot. In practice, the control pulses are performed to 30 or 40 o bank angle in each direction. A typical wingtwist control pulse is sho wn in Figure 7–5 Commanded wingtwist deection is measured along with the roll and ya w rate response. The roll angle data sho wn is estimated from the roll rate. The estimate is assumed to be a reasonable representation o v er short time periods and small angles of attack. Although the estimate may be of f in absolute magnitude due to calibration or estimation errors, the trends clearly sho w the relati v e bank angle response. The top tw o plots in Figure 7–5 sho w a close correspondence between command input and roll response. Such response is typical of aircraft with high aileron control po wer The ya w rate incurred during the maneuv er is closely in phase with the estimated bank angle. The roll mode is modeled by computing a transfer function between the roll command and the roll rate response [ 24 ], [ 19 ]. Secondary ef fects of the command such

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47 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 -10 0 10 Command (deg) 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 -500 0 500 Roll Rate (deg/s) 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 -200 0 200 Roll angle (deg) 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 -500 0 500 Yaw Rate (deg/s) Time (sec) Figure 7–5: W ing-twist command and response from ight data as adv erse ya w and pitch coupling are ne glected due to relati v ely small disturbance magnitudes. Other ya w ef fects such as sideslip or bank angle induced ya w rate are also not considered in the model. A MA TLAB Auto-Re gressi v e with Exogenous Input (ARX) discrete-time model is used to represent the roll mode. The coef cients of the model are computed from least-squares t to the command and response data. The discrete-time model is used in simulation to determine the accurac y of the computed model. A nal transformation is made to represent the model as a continuous-time state-space formulation. The formulation of the model assumes rst-order rigid-body dynamics. Although structural modes may v ery well be present, the model structure and ltering techniques assume that an y response abo v e 7 Hz is strictly noise and is therefore not considered in the model. The models are represented in the state-space nomenclature sho wn in Equations 7.1 and 7.2 x rAxb u (7.1) and yrcxd u (7.2)

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48 Where x is the state v ector and y is the output. u is the control input and A,b,c,d are the state-space matrices. Of particular importance are A and b which are considered the system plant and control ef fecti v eness matrices. Pole locations for the roll mode at se v eral gull-wing positions are sho wn in Figure 7–6 The plot sho ws the poles migrating to a less ne gati v e v alue as the wing is morphed in the positi v e or ne gati v e direction from neutral. This migration accounts for the decreased sensiti vity to command input as the wing is morphed. -20 -10 0 10 20 30 -45 -40 -35 -30 -25 -20 -15 -10 Gull-wing angle (deg)Open-Loop Pole (Real Axis) Figure 7–6: Pole migration with gull-wing morphing angle The physical signicance of the change in poles is the ef fect on the lateraldirectional handling qualities throughout the morphing range. The most ne gati v e v alue, occurring at 0 o morphing position, indicates that the v ehicle quickly attains a steady-state roll v alue when subjected to a control input or disturbance. Increasing the gull-wing morphing in the positi v e direction increases the response time of the v ehicle to similar inputs. At the most positi v e morphing position of 30 o the v ehicle is considerably less responsi v e than at the neutral morphing position. Morphing the gull-wings in the ne gati v e direction produces a similar ef fect on the roll mode. The migration of the open-loop poles from neutral to -20 o is similar to a 15 o positi v e morphing from neutral.

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49 The controllability of the simulated systems also under goes a change with gullwing morphing position. Figure 7–7 sho ws the change in the b-matrix v alues o v er the tested range of morphing. The qualitati v e shape of the plot appears as a mirror image of the pole locations. In particular the neutral gull-wing position here is a maxima while the b-matrix v alue f alls as the wing is deected in either direction. The plotted v alues represent the control ef fecti v eness of the twisting wingtips in producing a roll acceleration. The higher the b-matrix v alue, the higher the control po wer of the wingtips. 20 10 0 10 20 30 500 600 700 800 900 1000 1100 1200 1300 1400 Gullwing angle (deg)Bmatrix value Figure 7–7: B-matrix v alue for rst-order roll mode systems Physically this is lik ely a result of a combined ef fect of the increased gull-wing angle, decreased wingspan, and angled control surf aces. The latter change occurs because of the normal direction of the wingtips de viates from perpendicular to the span as the wing is morphed. Thus, some component of the added lift from the wingtip twisting occurs in the spanwise direction and has no ef fect on the roll moment. The change in the roll moment produced by the wingtips v aries approximately with the cosine of the deection angle of the outboard wing section. Figures 7–8 through 7–11 sho w results of the simulation models compared to ight data. Measured and simulated roll rates are generally in close agreement for all the models.

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50 243.5 244 244.5 245 245.5 246 10 5 0 5 10 Wingtwist (deg) 243.5 244 244.5 245 245.5 246 400 200 0 200 400 Roll Rate (deg/s)Time (sec) Figure 7–8: W ing-twist command (top) at 0 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) 271.5 272 272.5 273 273.5 10 5 0 5 10 Wingtwist (deg) 271.5 272 272.5 273 273.5 400 200 0 200 400 Roll Rate (deg/s)Time (sec) Figure 7–9: W ing-twist command (top) at 15 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) 7.4.2 Dutch Roll Mode The Dutch roll mode is an dynamic in v olving coupling between roll, sideslip, and ya w [ 28 ]. Poor Dutch roll properties can cause dif culties in stabilization and control, causing poor ight path tracking [ 26 ]. Unlik e the roll mode, the Dutch roll mode in v olv es signicant coupling between the lateral-direction states and often with the longitudinal states. The characteristics of the mode are highly dependent on wing geometry The wing shape directly af fects f actors such as roll and ya w damping, sideslip cross-coupling, and inertial properties,

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51 332 332.5 333 333.5 334 334.5 335 10 5 0 5 10 Wingtwist (deg) 332 332.5 333 333.5 334 334.5 335 600 400 200 0 200 400 Roll Rate (deg/s)Time (sec) Figure 7–10: W ing-twist command (top) at 30 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) 422 422.5 423 423.5 424 10 5 0 5 10 Wingtwist (deg) 422 422.5 423 423.5 424 400 200 0 200 400 Roll Rate (deg/s)Time (sec) Figure 7–11: W ing-twist command (top) at -20 o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) all of which in turn af fect the Dutch roll characteristics. In terms of v ehicle geometry the mode is lar gely dependent on dihedral angle, wingspan, v ertical area distrib ution, and v ertical center of gra vity Rudder control pulse maneuv ers are used to e xcite the Dutch roll mode of the v ehicle at tw o dif ferent gull-wing positions. The pulses are a series of consecuti v e step inputs in opposite directions. Each pulse perturbs the v ehicle from trimmed ight in sideslip, roll, and ya w The resulting v ehicle response is then lar gely an indication of the Dutch roll mode. Control pulses are performed at 0 o and 15 o gull-wing angles.

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52 Command and response data from rudder control pulses at 0 o and 15 o gull-wing angle are sho wn in Figures 7–12 and 7–13 respecti v ely The most apparent dif ference between the tw o pulses is the tw o-fold increase in the roll response magnitude for the 15 o gull-wing case. Roll coupling with rudder and/or sideslip has increased dramatically with positi v e gull-wing deection. The response at this morphing position is dominated by roll. Reco v ery oscillations in both roll and ya w are smaller and damp out f aster than the neutral morphing case. 0 50 100 150 200 250 20 15 10 5 0 5 10 15 20 25 Rudder (deg) 0 50 100 150 200 250 200 150 100 50 0 50 100 150 200 250 300 Roll rate (deg/s) 0 50 100 150 200 250 300 200 100 0 100 200 300 Yaw rate (deg/s) Figure 7–12: Rudder control pulse at 0 o gull-wing angle with measured data (:) and simulated response (-) 0 50 100 150 200 250 300 30 20 10 0 10 20 30 Rudder (deg) 0 50 100 150 200 250 300 600 400 200 0 200 400 600 Roll rate (deg/s) 0 50 100 150 200 250 300 400 300 200 100 0 100 200 300 400 Yaw rate (deg/s) Figure 7–13: Rudder control pulse at 15 o gull-wing angle with measured data (:) and simulated response (-) The model formulation required that the system account for both the roll rate and ya w rate response to rudder deection. W ith one input and tw o outputs, a dif ferent system identication method w as needed than w as used pre viously Using the ARX approach to modeling the Dutch roll dynamics resulted in a relati v ely poor t compared with the roll mode modeling.

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53 A 4th-order state-space model is used to identify the lateral dynamics from the rudder control pulse data. Attempting to model strictly the Dutch roll mode as a second-order system resulted in poor t in both roll rate and ya w rate. Increasing the order of the system to 4 considerably impro v ed the t for both states. The resulting model has tw o pairs of comple x conjugate poles, although classical Dutch roll modes for con v entional aircraft ha v e only a single pair The identied Dutch roll dynamics for tw o morphing models are sho wn in the equations belo w The dynamics are gi v en in state-space format. The state-space matrices are sho wn for the 0 o gull-wing system in Equation 7.3 7.6 the rst set of equations and for the 15 o system in Equation 7.7 7.10 Ar 000728007607 006432 0001042 01299004688 001308 005232006621 0004354002822 005985 00239600845100712005431n n n n n n n x 1 x 2 x 3 x 4n n n n n n n (7.3) br 0001507000044780001323 00003071000149700002368 00003202000413700071360001106001099 0003608n n n n n n n x 1 x 2 x 3 x 4n n n n n n n (7.4) cr 34994886 3619966869 17652261 2435n y 1 y 2n (7.5) dr 0 09822 0 0 02639 182 n y 1 y 2 n (7.6)

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54 Ar 000963007148 005012 000286401124004497 001106003917007133006225003205 01023001097 001318008323002391 n n n n n n n x 1 x 2 x 3 x 4 n n n n n n n (7.7) br 00015240000431100009517 00002664 00006908 8541 e00500001861 00014690006974000110100068930001574n n n n n n n x 1 x 2 x 3 x 4n n n n n n n (7.8) cr 465 1348 5786196590122231836 1216n y 1 y 2n (7.9) dr 0 1556 0 009075 1335n y 1 y 2n (7.10) The pole migration sho wn in Figure 7–14 depicts a considerable change in the aircraft characteristics during morphing actuation. The tw o comple x pairs shift to w ard the right-hand plane during positi v e gull-wing angle changes. This pole migration has the ef fect of decreasing both the a v erage natural frequenc y and the damping of the modes. The particular modal properties are listed in T able 7–2 and T able 7–3 The tw o modes listed are not necessarily Dutch roll modes; rather the y represent the more general rudder pulse response dynamics. F or this reason, the dynamics are represented by tw o comple x conjugate poles as opposed to the single pair associated with most con v entional aircraft. T able 7–2: Dutch roll modes for 0 o gull-wing Natural frequenc y Damping Mode1 0.6276 Hz 0.3993 Mode2 0.7584 Hz 0.2359

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55 0.042 0.04 0.038 0.036 0.034 0.032 0.03 0.028 0.026 0.024 0.022 0.1 0.05 0 0.05 0.1 0.15 Real axisImaginary axis 0 degree15 degree Figure 7–14: Open-loop Dutch roll mode pole migration for tw o morphing positions T able 7–3: Dutch roll modes for 15 o gull-wing Natural frequenc y Damping Mode1 0.5220 Hz 0.2847 Mode2 0.7879 Hz 0.2522 The eigen v ectors associated with each morphing system are sho wn in T ables 7–4 and 7–5 for gull-wing cases 0 o and 15 o respecti v ely The 15 o case sho ws that the morphing causes increased coupling between the states, in addition to introducing considerable phase changes. Such changes are apparent by e xamining the rudder control pulse data from Figures 7–12 and 7–13 where the coupling of the rudder input to roll rate and ya w rate changes with morphing. T able 7–4: Dutch roll mode eigen v ectors for 0 o gull-wing State Magnitude Phase (de g) Mode1 x1 0.4769 74.4588 o x2 0.7309 0 o x3 0.0753 101.3212 o x4 0.4824 96.7250 o Mode2 x1 0.0323 71.4868 o x2 0.4240 78.8885 o x3 0.4948 83.0143 o x4 0.7575 180.000 o

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56 T able 7–5: Dutch roll mode eigen v ectors for 15 o gull-wing State Magnitude Phase (de g) Mode1 x1 0.4525 67.8550 o x2 0.3209 146.2772 o x3 0.7064 180.000 o x4 0.4396 -96.0538 o Mode2 x1 0.3758 -84.8100 o x2 0.5526 50.4414 o x3 0.4516 -83.7154 o x4 0.5912 0.00000 o Figure 7–15 sho ws bode plots for the tw o morphing systems. The top tw o plots depict the magnitude and phase response from rudder input to roll rate while the bottom tw o plots sho w the responses from rudder input to ya w rate. The most notable change between the tw o occurs in the magnitude of the roll rate response. F or the 15 o case, the peak response has a lar ger amplitude and occurs at a lo wer frequenc y than the neutral case. This result is in agreement with the eigen v alues, which sho w a lo wer natural frequenc y for the 15 o morphing position. Bode Diagram Frequency (rad/sec)Magnitude (dB) ; Phase (deg) 50 0 50 To: y1 From: u1 50 0 50 To: y2 0 180 360 To: y1 10 3 10 2 10 1 10 0 10 1 180 0 180 To: y2 Figure 7–15: Frequenc y response diagram for 0 o gull-wing (:) and 15 o gull-wing (-) 7.5 Longitudinal Dynamics Longitudinal system identication is performed on ele v ator pulse data to determine the short period pitch mode and the Phugoid mode. T w o morphing conditions are

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57 considered for this analysis, 0 o gull-wing and 15 o gull-wing. A transfer function is computed between the ele v ator deection and pitch rate response data using an output-error model. T ables 7–6 and 7–7 sho ws the results of the modeling in terms of the frequenc y and damping of the longitudinal modes. F or each of the longitudinal dynamic models, the system identication process also predicted a ne gati v e real pole near zero. T able 7–6: Longitudinal modes for 0 o gull-wing Natural frequenc y Damping Phugoid Mode 0.2945 Hz 0.5422 Short Period Mode 19.75 Hz 0.0303 T able 7–7: Longitudinal modes for 15 o gull-wing Natural frequenc y Damping Phugoid Mode 0.6131 Hz 0.3912 Short Period Mode 19.95 Hz 0.1445 The system poles sho w a distinct change in the longitudinal dynamics during morphing. Specically the short period damping ratio has increased dramatically The natural frequenc y of the mode is predicted to remain constant o v er the 15 0 change in gull-wing angle. F or the Phugoid Mode, the simulation predicted an increase in the natural frequenc y with a corresponding decrease in the damping. These results, especially in the short period mode, are in agreement with pilot feedback. Pitch control during high gull-wing morphing is highly damped and responds sluggishly to ele v ator deection. Ho we v er the limited data set precludes rigorous e v aluation of the predicted models. Additionally the noise in the data during the ele v ator pulse sequence ight test seemed higher in magnitude than noise in other data sets. The noise le v el creates dif culties in dif ferentiating physical dynamics with sensor noise or vibration. Figure 7–16 sho ws simulated pitch rate response to an ele v ator pulse sequence plotted against measured pitch rate. The pulse is performed with a gull-wing angle

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58 of 0 o The simulated response is in good agreement with the general trends of the measured response, although has a poor t of the high frequenc y content. As a result, the predicted models are useful only as basic descriptions of the actual dynamics. Figure 7–17 sho ws the measured and simulated responses for a 15 o gull-wing conguration. Again, the simulation model e xhibits discrepancies with the measured data at high frequenc y oscillations. The data from the ele v ator pulse sequences is plotted against simulation time steps, with each step equal to 1/100th of a second. 1100 1150 1200 1250 1300 1350 1400 1450 1500 400 300 200 100 0 100 200 300 400 Time (steps)Pitch Rate (deg/s) 1100 1150 1200 1250 1300 1350 1400 1450 1500 100 80 60 40 20 0 20 40 60 80 100 Time (steps)Pitch Rate (deg/s) Figure 7–16: Ele v ator pulse command (left), measured (:) and simulated( -) pitch rate responses (right) 950 1000 1050 1100 1150 1200 1250 1300 400 300 200 100 0 100 200 300 400 Time (steps)Elevator Command (deg) 950 1000 1050 1100 1150 1200 1250 1300 100 80 60 40 20 0 20 40 60 80 100 Time (steps)Pitch Rate (deg/s) Figure 7–17: 15 o gull-wing ele v ator pulse command (left), measured (:) and simulated( -) pitch rate responses (right)

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CHAPTER 8 FOLDING WING AND T AIL MORPHING 8.1 Aircraft Design A quasi-static morphing has also been implemented on a tandem-wing micro air v ehicle, Figure 8–1 to allo w the aircraft to achie v e tw o distinct mission requirements in a single ight. The aircraft is designed to achie v e stable, controllable forw ard ight for climb, cruise, and loiter phases, then transition to re v erse ight for a slo w v ertical descent. A single control actuator is used to sweep both front and aft wings forw ard, in addition to collapsing and e xtending v ertical stabilizer surf aces. T able 8–1 summarizes the important properties of the aircraft. Figure 8–1: T op vie w of unswept (left) and swept (right) congurations 8.2 Morphing Mechanism The aircraft incorporates a dual-wing sweep angle morphing to change the location of the aircraft center The wings are designed to sweep f ar enough forw ard such that the neutral point becomes forw ard of the center of gra vity In this conguration (Figure 8–2 ), forw ard ight is destabilized and re v erse ight is stabilized. In order to impro v e re v erse ight stability the wing sweep incorporates a collapsing v ertical stabilizer on the aft wing and an e xpanding stabilizer on the forw ard wing. 59

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60 T able 8–1: Properties of the folding wing-tail aircraft in tw o congurations Property F olding W ing-T ail (Airigami) W ing Span 12 in W ing Area (unswept) 60 in 2 W ing Area (swept) 65 in 2 V ertical Stab Area (unswept) 7.61 in 2 V ertical Stab Area (swept) 3.44 in 2 W ing Loading (unswept) 11.02 ozf t 2 Po werplant DC motor 4 in prop T otal W eight 4.59 oz Each stabilizer is initially b uilt into the wing structure and allo wed to fold along n ylon hinges. Figure 8–2: Side vie w of unswept (top) and swept (bottom) congurations Re v erse ight is achie v ed only in descents with a near v ertical ightpath. As such, the thrust from the propeller serv es as both a drag producer and as a stabilizing de vice. The primary purpose of the wings and v ertical stabilizer during this descent prole is to pre v ent the v ehicle from di v er ging from the v ertical attitude. In this orientation, the thrust serv es to directly counteract the weight of the aircraft and slo w the sink rate. The current po werplant uses a DC electric motor with a 4:1 gear reduction to turn a 4 in plastic prop. The thrust to weight ratio of the aircraft is slightly less than one, allo wing for a substantial reduction in the sink rate at full throttle. Alternati v e motor

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61 options may be used to increase thrust to weight ratio to greater than one. In such a case, the thrust could be used to achie v e a zero sink rate and ho v er the aircraft during the descent phase. Although the aircraft is designed primarily for v ertical re v erse ights, other descent modes such as a controlled at spin or high-alpha, oscillatory f alling leaf mode may be possible with the sweep morphing. 8.3 Flight T rials Basic ight trials ha v e been conducted with the folding wing-tail v ehicle to determine the feasibility of the design for enhanced v ehicle agility Although the objecti v es of fully-stabilized re v erse ight descents were not met, the v ehicle concept sho ws promise with additional de v elopment. The v ehicle e xhibits good handling and control characteristics in the tandemwing forw ard ight mode. The hinged ele v ons on the aft wing are used collecti v ely to command pitch rate and dif ferentially to command roll rate. Pitch and roll rate responses to ele v on deection is suf cient to control the v ehicle in climbs, turns, di v es, and le v el ight. The v ehicle is considerably easier to control using the hinged control surf aces on the aft wing than using the wing twisting on the fore wing. The e xact reason for this disparity in control is unclear as dif ferent combinations of ef fector -wing placement were not conducted. Figure 8–3 sho ws the dynamic pitch up maneuv er is used to transition the v ehicle from con v entional forw ard ight to re v erse ight. This maneuv er in v olv es achie ving cruise airspeed in le v el ight, then increasing the pitch angle and ight path to near 90 o v ertical. The folding wing-tail morphing is then actuated to shift the aerodynamic center and center of lateral area forw ard. Flight trials of this maneuv er ha v e resulted in only short periods of re v erse ight before the v ehicle di v er ges into a at spin. Stabilizing the aircraft in re v erse ight requires additional thrust in addition to increased sweep angle.

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62 Figure 8–3: En visioned dynamic pitch up maneuv er for forw ard to re v erse ight transition

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CHAPTER 9 SUMMAR Y 9.1 Recommendations Flight tests of the morphing v ehicles sho ws that shape change actuators ha v e a considerable ef fect on the v ehicle ight dynamics. This is certainly not an une xpected result, gi v en that v ehicle dynamics are directly dependent upon geometry and conguration. The tests sho wed that both dynamic and quasi-static morphing strate gies can ha v e a highly desirable impact on both the ight performance and the control ef fecti v eness. Ho we v er the quantication of these changes is some what arbitrary considering that no comparisons were made to established handling quality or performance metrics. An important part of the future research will be to conte xtualize the benets of the morphing for a v ehicle in a realistic mission scenario. Doing so will ultimately determine the benet of morphing and will also help identify the practical ef fects of the changes to the v ehicle dynamics. The models identied from the ight data are quite limited in usefulness. The simple models sho w interesting ef fects of the morphing, b ut still do not address the more important problem of maneuv ers and actuations be yond simple perturbations. F or a more generalized morphing actuation, the ef fects of inertial and aerodynamic asymmetries will introduce considerable coupling and nonlinearity that can only be modeled using a much more comple x approach. The de v elopment of such an approach is currently underw ay Higher delity modeling approaches become increasingly important for stabilization and control. A better understanding of the actual dynamics will help de v elop appropriate control theory for morphing v ehicles. Whether con v entional linearized controllers are appropriate for morphing or not will be seen. Perhaps a better approach 63

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64 is to design the controller with implicit kno wledge of the morphing ef fect. These issues are being addressed from a theoretical and computational standpoint. Once satisf actory results are obtained from this ef fort, the focus will transition to implementing these controllers on ight v ehicles and e xperimentally v alidating controller designs. 9.2 Conclusions Simple strate gies for morphing on small v ehicles ha v e been demonstrated in ight. These strate gies, although not optimal, ha v e impro v ed the performance of the v ehicles in man y cases and increased the size of the ight en v elope through shape changes. The morphing has been used to demonstrate high-agility and aggressi v e maneuv ering. Small sensors were used to record the v ehicle responses during a v ariety of ight test conditions. Models of the v ehicle generated from the ight data indicate that linear symmetric assumptions are reasonably accurate in representing the dynamics for small morphing commands. V ehicle dynamics observ ed during lar ge morphing commands, ho we v er were highly non-linear The quasi-static morphing demonstrated on the v ariable gull-wing aircraft sufciently changed the ight performance to allo w the v ehicle to operate in se v eral dif ferent modes. Such performance changes are critically important to the realization of morphing in commercial and military ight systems. The v ehicle w as also used to demonstrate the e xtent of the change in dynamics and handling qualities that occurs as a result of the geometric change. The change in dynamics illustrates the need for ight controllers that adapt or change with morphing condition. Such controllers are currently under de v elopment using the results of the ight testing, in addition to wind tunnel and theoretical modeling approaches.

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REFERENCES [1] M. Abdulrahim “Flight Performance Characteristics of a Biologically-Inspired Morphing Aircraft” Presentation at 54th AIAA Re gional Student Conference, Memphis, TN, April 2004. [2] M. Amprikidis and J.E. Cooper “De v elopment of Smart Spars for Acti v e Aeroelastic Structures, ” AIAA-2003-1799, 2003. [3] J. Blondeau, J. Richeson and D.J. Pines, “Design, De v elopment and T esting of a Morphing Aspect Ratio W ing using an Inatable T elescopic Spar ” AIAA-20031718. [4] J. Bo wman, B. Sanders and T W eisshar “Ev aluating the Impact of Morphing T echnologies on Aircraft Performance, ” AIAA-2002-1631, 2002. [5] M.J. Brenner Aer oservoelastic Modeling and V alidation of a Thrust-V ectoring F/A-18 Air cr aft N ASA-TP-3647, September 1996. [6] D. Cadogan, T Smith, R. Lee and S. Scarborough, “Inatable and Rigidizable W ing Components for Unmanned Aerial V ehicles, ” AIAA-2003-1801, 2003. [7] B.D. Caldwell, “FCS Design for Structural Coupling Stability ” The Aer onautical J ournal December 1996, pp. 507-519. [8] C.E.S. Cesnik and E.L. Bro wn, “ Acti v e W arping Control of a Joined-W ing Airplane Conguration, ” AIAA-2003-1716, 2003. [9] J.B. Da vidson, P Chw alo wski, and B.S. Lazos, “Flight Dynamic Simulation Assessment of a Morphable Hyper -Elliptic Cambered Span W inged Conguration, ” AIAA-2003-5301, August 2003. [10] M. Drela and H. Y oungren XFOIL 6.94 User Guide MIT Aero & Astro, Aerocraft, Inc. http://raphael.mit.edu/xfoil/, Dec 2001 [11] B. Etkin Dynamics of Flight Stability and Contr ol 2nd Edition John W ile y & Sons, Ne w Y ork, 1982. [12] S.M. Ettinger M.C. Nechyba, P .G. Ifju, and M.R. W aszak, “V ision-Guided Flight Stability and Control for Micro Air V ehicles, ” Pr oceedings of the IEEE International Confer ence on Intellig ent Robots and Systems October 2002, pp. 2134-2140, IEEE, Lausanne, Switzerland. 65

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66 [13] G.A. Fleming, S.M. Bartram, M.R. W aszak, and L.N. Jenkins, “Projection Moire Interferometry Measurements of Micro Air V ehicle W ings, ” Pr oceedings of the SPIE International Symposium on Optical Science and T ec hnolo gy P aper 448-16, August 2001. [14] H. Garcia, M. Abdulrahim, and R. Lind, “Roll Control for a Micro Air V ehicle using Acti v e W ing Morphing, ” AIAA-2003-5347, August 2003. [15] J.M. Grasme yer and M.T K eennon, “De v elopment of the Black W ido w Micro Air V ehicle, ” AIAA-2001-0127, 2001. [16] I.M. Gre gory “Dynamic In v ersion to Control Lar ge Fle xible T ransport Aircraft, ” AIAA-98-4323, 1998. [17] P .G. Ifju, S. Ettinger D.A. Jenkins and L. Martinez, “Composite Materials for Micro Air V ehicles” Presentation at Society for Adv ancement of Materials and Process Engineering Annual Conference, Long Beach, CA, May 2001. [18] P .G. Ifju, D.A. Jenkins, S.M. Ettinger Y Lian, W Shyy and M.R. W aszak, “Fle xible-W ing Based Micro Air V ehicles, ” AIAA-2002-0705, January 2002. [19] K.W Ilif f, “ Aircraft P arameter Estimation, ” N ASA-TM-88281, 1987. [20] C.O. Johnston, D.A. Neal, L.D. W iggins, H.H. Robertsha w W .H. Mason and D.J. Inman, “ A Model to Compare the Flight Control Ener gy Requirements of Morphing and Con v entionally Actuated W ings, ” AIAA-2003-1716, 2003. [21] S.M. Joshi and A.G. K elkar “Inner Loop Control of Supersonic Aircraft in the Presence of Aeroelastic Modes, ” IEEE T r ansactions on Contr ol Systems T ec hnolo gy V ol. 6, No. 6, No v ember 1998, pp. 730-739. [22] Y Lian and W Shyy “Three-Dimensional Fluid-Structure Interactions of a Membrane W ing for Micro Air V ehicle Applications, ” AIAA-2003-1726, April 2003. [23] E. Li vne, “Inte grated Aeroserv oelastic Optimization: Status and Direction, ” J ournal of Air cr aft V ol. 36, No. 1, January-February 1999, pp. 122-145. [24] L. Ljung, System Identication Prentice Hall, Engle w ood Clif fs, NJ, 1987. [25] P de Marmier and N. W erele y “Morphing W ings of a Small Scale U A V Using Inatable Actuators for Sweep Control, ” AIAA-2003-1802. [26] R.C. Nelson Flight Stability and A utomatic Contr ol McGra w Hill, Boston, MA, 1998. [27] E.W Pendleton, D. Bessette, P .B. Field, G.D. Miller and K.E. Grif n, “ Acti v e Aeroelastic W ing Flight Research Program: T echnical Program and Model Analytical De v elopment, ” J ournal of Air cr aft V ol. 37, No. 4, 2000, pp. 554-561.

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67 [28] W .F Phillips Mec hanics of Flight John W ile y & Sons, Hobok en, NJ, 2004. [29] B. Sanders, F .E. Eastep and E. F orster “ Aerodynamic and Aeroelastic Characteristics of W ings with Conformal Control Surf aces for Morphing Aircraft, ” J ournal of Air cr aft V ol. 40, No. 1, January-February 2003, pp. 94-99. [30] L.V Schmidt Intr oduction to Air cr aft Flight Dynamics American Institute of Aeronautics and Astronautics, Inc., Reston, V A, 1998. [31] M.J. Solter L.G. Horta, and A.D. P anetta, “ A Study of a Prototype Actuator Concept for Membrane Boundary Control, ” AIAA-2003-1736, April 2003. [32] R.W Stone, and B.E. Hultz, Summary of Spin and Reco very Char acteristics of 12 Models of Flying-W ing and Uncon ventional-T ype Airplanes N A CA-RM-L50L29, March 1951. [33] H. T ennek es The Simple Science of Flight: F r om Insects to J umbo J ets The MIT Press, Cambridge, MA, 1997. [34] S. T ung, and S. W itherspoon, “EAP Actuators for Controlling Space Inatable Structures, ” AIAA-2003-1741, April 2003. [35] D. V iieru, Y Lian, W Shyy and P Ifju, “In v estigation of T ip V orte x on Aerodynamic Performance of a Micro Air V ehicle, ” AIAA-2003-3597, 2003. [36] M.R. W aszak, J.B. Da vidson, and P .G. Ifju, “Simulation and Flight Control of an Aeroelastic Fix ed W ing Micro Air V ehicle, ” AIAA-2002-4875, August 2002. [37] M.R. W aszak, L.N. Jenkins, and P .G. Ifju, “Stability and Control Properties of an Aeroelastic Fix ed W ing Micro Air V ehicle, ” AIAA-2001-4005, August 2001. [38] R.W Wlezien, G.C. Horner A.R. McGo w an, S.L. P adula, M.A. Scott, R.J. Silcox, and J.O. Simpson, “The Aircraft Morphing Program, ” AIAA-98-1927, April 1998.

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BIOGRAPHICAL SKETCH Lik e most people, Mujahid Abdulrahim w as born. His childhood teemed with the man y adv entures typically associated with adolescent life, including placing metal objects into electrical sock ets and making inappropriate f aces at the monk e ys in the zoo. Luckily he soon outgre w such shenanigans and be gan focusing on his career Professional hopes of being an in v entor repairshop o wner electrical engineer and aerial photographer soon ga v e w ay to his one true passion – aeronautical engineering. Mujahid rmly decided his life' s path by consulting a poster in his 8th grade algebra class. This poster listed man y professions and the types of math required on the job The only profession that had checkmarks from basic algebra all the w ay up to string theory w as aeronautical engineering – and so a dream w as born. Mujahid has been acti v e in v arious academic and competiti v e pursuits o v er his 6-year career at the Uni v ersity of Florida. These include the International Micro Air V ehicle Competition, AIAA Re gional/National Student Conferences, research paper competitions, mountain bik e racing, SCCA autocross racing, IMA C R/C scale aerobatics, R/C Funy competitions, R/C on-road racing, and of course lab che wing gum Olympics. Mujahid' s primary research interest is in morphing aircraft design and ight v ehicle dynamics. He has pursued a v ariety of no v el approaches to morphing and ight control throughout his master' s research. The w ork follo ws his e xtracurricular interest in racing and maximum performance v ehicle control. Mujahid' s life started in the Calgary W omen' s Hospital in room A32 on the third oor His tra v els ha v e tak en him quite f ar a w ay from that hospital bed, all the w ay to 68

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69 remote villages in Syria to visit his relati v es and sho w them ho w to perform donuts on a motorbik e. Life has been good.


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Permanent Link: http://ufdc.ufl.edu/UFE0008500/00001

Material Information

Title: Dynamic Characteristics of Morphing Micro Air Vehicles
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0008500:00001

Permanent Link: http://ufdc.ufl.edu/UFE0008500/00001

Material Information

Title: Dynamic Characteristics of Morphing Micro Air Vehicles
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0008500:00001


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Full Text











DYNAMIC CHARACTERISTICS OF MORPHING MICRO AIR VEHICLES


By

MUJAHID ABDULRAHIM

















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


2004





























In the name of Allah, the Gracious, the Merciful.


My thesis in its entirety (apart from one sentence in the beginning of Chapter 4) is

dedicated to my loving family, who have put up with my outrageous silliness in pursuit

of academic achievements. To my father, who first led me down the path of innovation

by helping me build my own toys. To my mother, who from the very beginning has

been my advisor, counselor, and best friend. To my brother, who is my co-pilot in the

clouded airspace of life. And to my sister, who is my ultimate role model for writing

style and literary wit. The single outstanding sentence in Chapter 4 is dedicated to

my rubber chicken, who provides irrelevant comic amusement like no other inanimate

domestic animal can.


Looks real, feels real, stretchable. Hells yeah.















ACKNOWLEDGMENTS

The work presented in this thesis was heavily supported by a large group of highly

supportive people. The bulk of the mentoring, advice, suggestions, and orders came

from my research advisors, Dr. Richard Lind and Dr. Peter Ifju. Dr. Lind has helped

me develop an understanding of flight test objectives, modeling strategies, and, more

importantly, the effect of our work on the future of aerospace. Dr. Ifju has been the

ultimate source for creative inspiration in aircraft design and fabrication technique.

Martin Waszak of NASA Langley Research Center has supported the UF micro air

vehicle research effort for many years. In addition to providing the funding for all the

research presented here, he has hosted me at LaRC for two summers on MAV design

and flight testing internships. Mark Motter, also from LaRC, has provided considerable

expertise in related projects. His influence carries over to the current research.

Several students have also been kind enough to support the research with time,

knowledge and hardware. Jason W. Grzywna and Jason Plew have provided much of

the electronics hardware support for the MAVs. Jos Cocquyt, Baron Johnson, Kenneth

Boothe, Shawn Mytrik, and Dan Claxton have helped extensively in solving design

problems and supporting flight tests. Finally, Alfred, my rubber chicken, helped pull

me through the low times when even singing "Always Look On the Bright Side of

Life" could not cheer me up.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................................ iii

LIST OF TABLES ........................... ..... vi

LIST OF FIGURES ................................... vii

ABSTRACT ................................. ..... x

1 INTRODUCTION ................................ 1

2 BIOLOGICAL INSPIRATION .......................... 4

3 MORPHING ON SMALL FLIGHT VEHICLES ............... 8

4 ASYMMETRIC WING SHAPING FOR ROLL CONTROL .......... 13

4.1 Aircraft Design .... .. ... .... ... ... .... ... ... 13
4.2 Morphing Mechanism ........................... 14
4.3 Flight Performance ........................... 17
4.4 Nonlinear Modeling of Lateral and Longitudinal Dynamics ..... 19

5 SYMMETRIC WING TWISTING FOR ROLL CONTROL .......... 22

5.1 Aircraft Design .............................. 22
5.2 Morphing Mechanism ........................... 23
5.3 Flight Performance ............................ 24
5.4 Linear Modeling of Lateral Dynamics ................. 25
5.5 Spin Characteristics of Wing Twist Morphing ............. 27

6 MULTI-POINT WING SHAPING ....................... 33

6.1 Aircraft Design .... .. ... .... ... ... .... ... ... 33
6.2 Morphing Mechanism ........................... 33
6.3 Flight Performance ............................ 35

7 VARIABLE GULL-WING ANGLE MORPHING .............. 37

7.1 Aircraft Design .............................. 37
7.2 Morphing Mechanism ........................... 38
7.3 Flight Performance ............................ 41
7.3.1 Gliding Performance ....................... 42
7.3.2 Climb Performance ........................ 43









7.3.3 Stall Characteristics . . . . . . 44
7.4 Lateral-Directional Dynamics . . . . . 45
7.4.1 Roll Convergence . . . . . . 45
7.4.2 Dutch Roll Mode . . . . . . 50
7.5 Longitudinal Dynamics . . . . . . 56

8 FOLDING WING AND TAIL MORPHING .... . . 59

8.1 Aircraft Design . . . . . . . 59
8.2 Morphing Mechanism . . . . . . 59
8.3 Flight Trials . . . . . . . . 61

9 SUM M ARY . . . . ....... ..... . 63

9.1 Recommendations . . . . . . . 63
9.2 Conclusions . . . . . . . . 64

REFERENCES . . . . . . . . . 65

BIOGRAPHICAL SKETCH .............................. 68















LIST OF TABLES
Table page

4-1 Properties of the 10 in and 12 in wing shaping MAVs . . . 14

5-1 Properties of the 24 in wing twisting MAV .. . . 23

7-1 Wing geometry change over variable gull-wing morphing range . 38

7-2 Dutch roll modes for 0 gull-wing . . . . . 54

7-3 Dutch roll modes for 15 gull-wing . . . . . 55

7-4 Dutch roll mode eigenvectors for 0 gull-wing .. . . .. 55

7-5 Dutch roll mode eigenvectors for 15 gull-wing . . . 56

7-6 Longitudinal modes for 0 gull-wing ...... . . 57

7-7 Longitudinal modes for 15 gull-wing ..... . . 57

8-1 Properties of the folding wing-tail aircraft in two configurations . 60















LIST OF FIGURES
Figure page

1-1 Variable gull-wing morphing aircraft . . . . . 2

2-1 A bird alters its gull-wing angle to affect gliding angle . . 5

2-2 A seagull uses differential wing extension (left) and differential wing
sweep (right) . . . . . . . .... 6

2-3 A seagull extends its wings for cruising flight (left) and descends at a
steep angle using gull-wing morphing (right) . . . 7

3-1 Micro data acquisition system . . . . . . 10

3-2 Roll, pitch and yaw rate sensor board ...... . . 11

4-1 Wing shaping morphing MAVs 10 in wingspan high-wing aircraft (left)
and 12 in span mid-wing aircraft (right) .. . . 14

4-2 Top, front, and side views of computer-aided design drawings for 12 in
M AV . . . . . . ... . 15

4-3 Kevlar cables . . . . . . . . 15

4-4 Front view showing undeflected wing (left) and morphed wing (right) 16

4-5 Measured and predicted responses for roll rate (left), pitch rate (middle)
and yaw rate (right) . . . . . . . 21

5-1 Wing-twisting MAV . . . . . . . 22

5-2 Underside view of wing showing torque rod . . ... 23

5-3 Rear view of the 24 in MAV with undeflected (left) and morphed (right)
W ing . . . . . . .... . 24

5-4 Doublet command to rudder (left), roll rate response (middle), and yaw
rate response (right) . . . . . . . 26

5-5 Doublet command to wing twist morphing (left), roll rate response (mid-
dle), and yaw rate response (right) ...... . . 27

5-6 Pilot commands (left) and responses (right) during conventional spin 28

5-7 Pilot commands (left) and responses (right) during spin . . ... 30









5-8 Pilot commands (left) and responses (right) during cyclic spin . ... 31

6-1 Top, side, and front views of the 24 in span multiple-position wing shap-
ing vehicle . . . . . . . . 34

6-2 Wing shaping MAV showing neutral position (top left), wingtip morph-
ing (top right), and full wing morphing (bottom) . . . 35

6-3 Spar torque-tube morphing actuators. The 4 front servos rotate concen-
tric spar sections, aft 2 control rudder and elevator . . . 35

7-1 Top and side view of variable gull-wing aircraft . . ... 38

7-2 Vehicle undergoing neutral (top), positive (center), and negative (bottom)
gull-wing morphing . . . . . . . 39

7-3 Variable gull-wing spar structure and control linkage, linear actuator vis-
ible inside fuselage at left . . . . . . 40

7-4 Underside view of left wing showing wing twist effector . . 41

7-5 Wing-twist command and response from flight data . . . 47

7-6 Pole migration with gull-wing morphing angle . . . 48

7-7 B-matrix value for first-order roll mode systems . . . 49

7-8 Wing-twist command (top) at 0 gull-wing, measured roll rate (:) and
simulated roll rate (-) (bottom) . . . . . 50

7-9 Wing-twist command (top) at 15 gull-wing, measured roll rate (:) and
simulated roll rate (-) (bottom) . . . . . 50

7-10 Wing-twist command (top) at 30 gull-wing, measured roll rate (:) and
simulated roll rate (-) (bottom) . . . . . 51

7-11 Wing-twist command (top) at -20 gull-wing, measured roll rate (:) and
simulated roll rate (-) (bottom) . . . . . 51

7-12 Rudder control pulse at 0 gull-wing angle with measured data (:) and
simulated response (-) . . . . . . 52

7-13 Rudder control pulse at 15 gull-wing angle with measured data (:) and
simulated response (-) . . . . . . 52

7-14 Open-loop Dutch roll mode pole migration for two morphing positions 55

7-15 Frequency response diagram for 0 gull-wing (:) and 15 gull-wing (-) 56

7-16 Elevator pulse command (left), measured (:) and simulated( -) pitch rate
responses (right) . . . . . . . 58









7-17 15 gull-wing elevator pulse command (left), measured (:) and simu-
lated( -) pitch rate responses (right) ..... . . . 58

8-1 Top view of unswept (left) and swept (right) configurations . .... 59

8-2 Side view of unswept (top) and swept (bottom) configurations . ... 60

8-3 Envisioned dynamic pitch up maneuver for forward to reverse flight tran-
sition . . . . . . .. . 62















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

DYNAMIC CHARACTERISTICS OF MORPHING MICRO AIR VEHICLES

By

Mujahid Abdulrahim

December 2004

Chair: Richard Lind
Major Department: Mechanical and Aerospace Engineering

The research presented in this thesis is an approach to the study of flight dynamics

of morphing vehicles. Case studies of several strategies are addressed in order to

determine some of the basic flight characteristics of dynamically and quasi-statically

morphing aircraft. These strategies include a flexible membrane wing that uses

tensioned cables to shape the wing for roll control. The wing shaping for this vehicle

improves roll tracking and decreases coupling compared to a rudder, even though the

morphing is asymmetric. Active morphing is also implemented by using torque-rods

and torque-tubes to anti-symmetrically twist a flexible wing surface. This form of

morphing provided aileron-like control without a hingeline. Quasi-static morphing is

used to change the gull-wing angle of an aircraft in flight. This biologically-inspired

shape change alters the performance characteristics and dynamics of the vehicle and

allows it to fly in several distinct flight modes. The vehicles are equipped with sensors

and data l',gging devices and flight tested using a variety of maneuvers and techniques.

Data from these maneuvers are used to estimate longitudinal and lateral-directional

models for the aircraft morphing systems. Stability and controllability of the vehicles









are examined in the context of the high-agility and aerodynamic performance changes

caused by the morphing.















CHAPTER 1
INTRODUCTION

As envisioned morphing designs become increasingly complex, the need for accu-

rate flight dynamic analysis becomes even more important [38]. The complex shapes

achievable by the new generation of actuators and structures can create difficulties in

representing the vehicle using existing methods. For instance, an aircraft that morphs

asymmetrically can undergo aerodynamic and inertial changes that violate assump-

tions used to simplify the commonly used equations of motion. Existing modeling

approaches typically do not account for time-varying vehicle geometry or large changes

in the aircraft configuration.

The modeling predicament underscores one of the current realities of morphing

research; namely, the majority of morphing is being conducted in optimal aerodynamic

shapes and static aeroelastic effects. The field of morphing vehicle flight dynamics

is still highly underdeveloped. Part of this void is understandable since few, if any,

morphing aircraft exist today to perform flight test experiments. However, the lack of

work also points to potential future problems in morphing research. Flight dynamics

must be developed in parallel to other morphing efforts in order to assess and control

prototype vehicles.

The work presented in this thesis represents an initial foray into such an effort.

The flight dynamics of simple morphing vehicles, such as the aircraft shown in Figure

1-1, are discussed. Design of the morphing effectors is based on observations of

biological systems. Dynamic effectors such as wing twisting and wing curling are

tested on several vehicles. Such effectors are replacements to ailerons, which cannot be

mounted to a flexible membrane wing. Such forms of morphing are similar to the roll

control effectors used on the NASA F/A-18 AAW [27]. Other effectors are operated









quasi-statically, such as a gull-wing morphing and a folding wing-tail system. These

systems also include dynamic morphing effectors, but are intended to address the larger

problem of changing flight modes.

Vehicle design and morphing actuators are considered only enough to develop

testbeds for flight dynamics experiments. No claim is made as to the optimality of

the vehicle shapes or morphing methods. It is sufficient to consider that the morphing

causes a change in the flight performance, which is then the basis for studying any

accompanying change in stability and control characteristics.













Figure 1-1: Variable gull-wing morphing aircraft


The enabling factor for this work is rapid prototyping of aircraft designs at the

University of Florida Center for Micro Air Vehicles. Developing an experimental

unmanned air vehicle from concept to initial flight test occurs within one or two

weeks [18]. Fabrication tools such as CNC milling and composite lay-up facilities

allow the entire airframe to be manufactured in-house [17]. Small instrumentation and

avionics are commercially available, reducing development time and cost significantly.

Using these resources, inexpensive testbeds can be produced quickly to test new

concepts in aircraft design and flight control.

The material presented in this thesis is from flight tests of several morphing micro

air vehicles. A variety of modeling approaches are used to identify the flight dynamics

of the vehicles. The initial modeling approach taken is based on simple transfer







3

function approaches. Initial models are developed under the assumption of linearity in

order to understand the broad effect of the variable geometry on the aircraft dynamics.

Nonlinear modeling is considered for vehicles with complex, asymmetric morphing.















CHAPTER 2
BIOLOGICAL INSPIRATION

Early aviators of the 20th century were largely inspired in their designs by natural

flight systems such as birds, insects, and seeds. This inspiration is evident in the design

shapes they chose, which featured wing and tail planforms that were highly similar to

birds. Even the early airplane attempts were constructed using a rigid skeleton frame

covered in a cloth skin, to resemble the wings of birds and bats. With the eventual

success of the Wright Brothers and the modernization of the airplane, designs became

more faceted and less-birdlike than their predecessors. Contemporary aircraft now have

little apparent similarities to birds.

The divergence of aircraft designs from early biological inspiration is likely a

result of the vastly different flight regimes encountered in natural and engineered

systems. In particular, large, high-speed aircraft share very little in common with a

typical bird, which is neither large nor high speed by comparison. The stiff, fixed

geometry of airplanes are opposite to the physiology of birds, which incorporate many

flexible and variable-shape members. Modem aircraft design is then based entirely on

derived aeronautical sciences and very little on direct biological-inspiration.

The continued miniaturization of electronics has fueled a movement opposite

to that of the large, supersonic jets. A new generation of small air vehicles is under

development using micro sensors and instruments. These vehicles are getting smaller

and lighter, such that they are now in a class highly similar to the birds and bats which

motivated the early aeronautical efforts. Furthermore, with an emergent need for

multi-role, shape-changing vehicles, biological-inspiration is coming to the forefront of

design philosophy.









Morphing is under consideration as a means to adapt a flight vehicle to changing

mission requirements or flight conditions. This type of adaptability has always

been present with biological systems. Birds are forced to alter their wing shapes

dramatically in order to accomplish cruise glides, steep descents, and aggressive

maneuvering as shown in Figure 2-1. Conversely, conventional aircraft are generally

of fixed configuration and are optimized for a very specific flight condition. Outside

of this condition, aircraft usually suffer from poor efficiency and poor aerodynamic

performance. By changing the vehicle shape in flight, an aircraft can re-optimize

itself for a variety of tasks, as birds do constantly. Thus, morphing through biological-

inspiration for small vehicles is both extremely relevant and highly desirable.















Figure 2-1: A bird alters its gull-wing angle to affect gliding angle


Biological-inspiration in aircraft flight systems presents considerable challenges

to the aircraft designer. Natural and engineered systems differ greatly in structural

composition, performance requirements, and available components. For instance,

birds rely on strong muscles, hollow skeletons, flexible joints, and feathers to achieve

the necessary motions and shapes for flight. Aircraft use motors, propellers, hinge

lines, and mostly rigid structures to sustain flight. The differences between the two

systems means that direct emulation is not practical or even desirable. Thus, it is not

the goal of this research to mimic bird kinematics. Rather, the objective is to use select








biologically-inspired systems to improve the range of achievable flying conditions for
conventional aircraft.
Birds use a variety of morphing techniques in their wings and tail to accomplish
dynamic maneuvering and stabilization. Differential wing twist, wing extension, and
wing sweep are used for primary lateral-direction control. Differential wing extension
is observed on seagulls during steep bank turns, as shown in Figure 2-2. Differential
wing sweep is also shown, here used for roll and yaw control. Collective variations
of these morphing motions are used in conjunction to the tail for longitudinal control.
These strategies present an initial starting point for implementing morphing on a small
vehicle.







A^



Figure 2-2: A seagull uses differential wing extension (left) and differential wing
sweep (right)

In addition to morphing for maneuvering, birds also implement a quasi-static
morphing of gull-wing angle during glide and steep descent phases. Figure 2-3 shows
a bird at two different gull-wing positions for different phases of flight. The gull-wing
action depends on a set of parallel bones connecting the shoulder and elbow joints of a
bird wing. A rotation of the shoulder joint in the vertical plane results in an extension
or contraction of the entire wing. The skeletal mechanism provides a geometric ratio
between the extension of the inner and outer bones. Such a mechanism allows the bird






















Figure 2-3: A seagull extends its wings for cruising flight (left) and descends at a
steep angle using gull-wing morphing (right)


to morph into a variety of positions using a single movement. Each of the positions is

largely stable and affords a unique capability within the flight envelope.

The purpose of this variable gull-wing action in birds is likely for a variety

of reasons, including static aerodynamic [9], physiology, and for flapping control.

However, it is studied here solely to investigate the quasi-static aerodynamic benefit

and the corresponding effect on the vehicle dynamic response. This type of morphing

is considered on a small vehicle, exploring the potential benefits to the cruise, steep

descent, and approach phases of flight.















CHAPTER 3
MORPHING ON SMALL FLIGHT VEHICLES

Implementing basic forms of morphing on micro air vehicles involves iden-

tifying morphing strategies that can be readily adapted to the vehicles. Identified

forms of morphing in birds are adapted to aircraft using existing actuators or simple

mechanisms. In this manner, the focus has been placed on flight testing the morph-

ing concepts as opposed to developing optimal morphing shapes or actuators. This

approach provides an essential look at the flight dynamics and controllability issues

without depending on actuator and material technology.

Despite the simplicity of the approach to morphing, the vehicles have demon-

strated improved performance and control characteristics compared to aircraft with

conventional control effectors. For instance, morphing can be used to provide roll

control on an aircraft with flexible wings without the use of hinges. This method re-

tains the beneficial characteristics of the flexible wing [22] [37], without compromising

control [14].

The work presented in this thesis summarizes the development and flight testing of

several morphing aircraft. Each aircraft type is essentially designed around a particular

type of morphing. Although the essence of each design is based on several generations

of non-morphing vehicles, each is adapted in structure, shape, and material to host the

morphing mechanism. For several of the initial attempts at morphing, this adaptation is

quite minimal and is limited to drilling holes in the airframe and attaching the actuator

arm or cable to the wing. However, as the morphing shapes became increasingly

complex, the vehicle shape and structure are then designed specifically for the purpose

of morphing.









The aircraft design shapes are quite different from one another. Two primary

scales are considered for morphing actuators, micro air vehicles of approximately

12 in span and larger vehicles with 24 in wingspans. Most of the vehicles differ

in fuselage shape, empennage planform, actuators, and weight. Thus, each vehicle

exhibits absolute performance metrics quite different than the others. The differing

geometry and differing performance metrics make direct comparison between the

vehicles impractical. As stated earlier, the goal of the research is not to determine

optimal morphing methods, but rather to investigate the effect of any shape change

on the vehicle dynamics. This does not require comparisons between the vehicles and

morphing strategies, as each case study is addressed as a separate experiment. The

cumulative result of the individual studies helps formulate a basic knowledge base of

morphing vehicle flight dynamics.

The experimental procedure is mostly similar for all the test vehicles. The basic

process includes design, fabrication, instrumentation, flight testing, data recovery, and

modeling stages. Apart from the instrumentation, these stages are covered in detail for

each aircraft case study. Details of the instrumentation procedures are covered here, as

the same sensors and data acquisition devices are used for all the flight tests.

A partial suite of flight test instruments are used on-board the aircraft to gather

flight data. Inertial measurements include roll rate, pitch rate, yaw rate, and 3-axis

linear accelerations. The remaining inertial aircraft states, Euler angles and position

are not included due to a lack of small instrumentation. Estimates of the Euler angles

are computed over small time periods by integrating angular rate data. Position

measurements, as would be provided by a GPS sensor, are not important for the type

of flight testing conducted. Pressure sensors for airspeed and altitude measurement

are included for some flight tests, although the data is not used in the analysis. The

primary deficiency in the instrumentation is the lack of angle of attack and angle of

sideslip data. Potentiometer-based vanes were considered for use, but the rotational









friction prevented the sensors from providing any useful information. Finally, the

control deflections are measured for all the hinged and morphing effectors.

The primary element of the instrumentation system is a micro data acquisition

system (microDAS) developed by NASA Langley Research Center. The microDAS

has 30 analog voltage input channels measured with a 12-bit resolution. Sampling

frequency is adjustable from 50 Hz to 500 Hz, allowing continuous data measurements

from 20 minutes to 2 minutes respectively. Later versions of the board increased

the storage capacity considerably. Data presented in this thesis is collected at 50 or

100 Hz. The board weight including the wiring harness is approximately 12 grams,

although this varies depending upon the length of wire used to connect the sensors.

Figure 3-1 shows the micro data acquisition system with the wiring harness connected.

Leads from the harness are connected to sensor outputs and communication ports.

Three linear accelerometers are integral to the board, allowing 3-axis measurement

within +/- 50G.















Figure 3-1: Micro data acquisition system


Data from the newest version of the microDAS is stored in a 128MB flash

memory chip. As long as the unit retains power, the measurement can be turned on

or off from the remote transmitter. This permits the data to cover only the flight test

maneuvers and exclude non-research phases of flight, such as launch, climb, trim, and









landing. Flight data is recovered to a laptop via a USB communications cable. An

entire data set is downloaded in 6 minutes using the software provided with the device.

Roll, pitch, and yaw rates are measured using muRata ENC-03J piezoelectric

angular rate gyros. Each gyro sensor measures a single axis of rotation, requiring three

orthogonally-oriented gyros for full rate measurement. A two-piece copper-plated

circuit board fabricated at UF's ECE department is used to align the gyros and provide

signal outputs, as shown in Figure 3-2. The total weight of the board and the three

gyros is 6 grams, making it suitable suitable for the smaller MAVs. The signal output

from the gyros are stable enough such that no hardware filtering is required to achieve

high signal to noise ratios and stable mean values. The rate measurement range for

each gyro is specified by the manufacturer as +/-300/s, although calibration tests

suggest that linear output exists over +/-10000/s.
















Figure 3-2: Roll, pitch and yaw rate sensor board


Control surface deflections are measured at the rotary actuator. For conventionally

hinged surfaces, a nominally rigid linkage connects the actuator output arm to the

control surface. For morphing effectors, the actuator is connected to some hardpoint on

the wing surface. In either case, the actuator position is directly representative of the

command input and the surface deflection. For simplicity in quantifying the morphing









command, the actuator position is used to define the magnitude of the control input,

although the actual geometry may be too complex to specify using a single parameter.

The rotary servo actuators used in the vehicles are commercial off-the-shelf

devices. The position of the servos is commanded using control sticks and knobs on

a remote transmitter. A pilot input on the sticks generates a pulse-width modulated

signal to the servos, where the width of the pulse is proportional to the commanded

position. The internal circuitry in the servo controls the rotation of the output arm to

the commanded position by using a motor-gear system and a rotary potentiometer. The

voltage feedback from the potentiometer is used to create an error signal to drive the

position control system. This voltage feedback is also a convenient measure of actuator

position. The center pin of each feedback potentiometer is connected to an analog

input channel of the microDAS, resulting in a time-synchronized measure of control

deflection with the inertial data.















CHAPTER 4
ASYMMETRIC WING SHAPING FOR ROLL CONTROL

4.1 Aircraft Design

Small vehicles having wingspans of less than 12in are being developed for military

and civilian reconnaissance missions. Flexible wings are typically used in conjunction

with conventional elevator and rudder control surfaces. The lateral-directional control

effectiveness of the rudder is suitable for open-loop control, but suffers from significant

coupling and saturation issues that preclude its use for fine flight path tracking. Wing

curling is an attractive type of morphing for this class of MAV. The attraction lies in

both its simplicity of implementation and its effectiveness for morphing. In this case, a

MAV will simply be retrofitted to accommodate a basic type of wing curling.

The objective of this study is to investigate the effect of wing shape on basic

maneuvering. Specifically, the roll performance and associated coupling with pitch and

yaw will be studied for wings which curl into asymmetric configurations. The effects

of reduced area and increased camber, along with their corresponding changes in lift

and drag on each wing, are of particular interest.

Two MAVs, shown in Figure 4-1, are the platforms used to investigate wing

curling. The only control surface on the 12 in wingspan MAV is an elevator for

longitudinal control; therefore, morphing will be used as the only effector to control

the lateral-directional dynamics. The 10 in includes a rudder control surface in order

to compare with the effectiveness of the morphing for lateral-directional control. The

fuselage of each aircraft houses a 3-axis gyro and 3-axis accelerometer along with a

data logger to record flight responses.

The airfoil used on the wings is similar to a competition airfoil developed by Dr.

Mark Drela. The airfoil was modified using XFOIL to improve lift magnitude at low



















Figure 4-1: Wing shaping morphing MAVs 10 in wingspan high-wing aircraft (left)
and 12 in span mid-wing aircraft (right)

angles of attack. The modifications included increasing the camber to 8% and moving

the maximum camber position forward along the chord to the 29% position. The

wings are fabricated with no appreciable thickness using thin carbon-fiber and latex

membrane. The shape of the airfoil on the physical wing is in line with the XFOIL

modeling, which assumes a thin, undercambered airfoil. A 3-view schematic of the 12

in aircraft geometry is shown in Figure 4-2. Aircraft properties for the 10in and 12in

vehicles are shown in Table 4-1.
Table 4-1: Properties of the 10 in and 12 in wing shaping MAVs

Property 10 in high-wing MAV 12 in mid-wing MAV
Wing Span 10 in 12 in
Wing Area 31 in2 44 in2
Wing Loading 13.93 oz/ft2 14.19 oz/ft2
Aspect Ratio 3.27 3.27
Powerplant coreless motor 2.5in prop geared motor 3.5in prop
Total Weight 3.00 oz 4.33 oz


4.2 Morphing Mechanism

Wing curling is accomplished using rotary actuators connected to the wing

structure by tensioned Kevlar cables as shown in Figure 4-3. As the actuator adjusts

the tension on the cable, the wing deforms into a twisted form that is appropriate

for flight control. Namely, the resulting shape increases the angle of incidence of

the morphed wing and increases the lifting force produced. When one wing side is

morphed, a lift differential is created which causes the aircraft to incur a roll rate.








































Figure 4-2: Top, front, and side views of computer-aided design drawings for 12 in
MAV


Figure 4-3: Kevlar cables









The morphing achieved by this strategy is directly dependent upon the attachment

points of the threads. The threads attach to servos by passing through the fuselage

near the leading edge of the wings. The corresponding attachment to the wings is

actually at separate hardpoints. One attachment point is near the mid-chord point at the

wing-tip outboard. Another attachment point is the trailing edge near the two-thirds

span location.

The morphing that results by actuating the servo is shown in Figure 4-4. The

servo rotates and causes the threads to pull against the attachments on the wing. The

morphing resulting from this strategy is clearly beyond simple warping. In this case,

the pulling of the threads toward the leading-edge attachment at the fuselage causes the

wing to both twist and bend. The effect is similar in nature to a curling of the wings.

The basic parameters that are readily observed to change are the twist, camber, chord,

and span.


Figure 4-4: Front view showing undeflected wing (left) and morphed wing (right)


The extent and shape of the morphing can be adjusted by varying the amount of

tension in the Kevlar lines or adjusting the location of the attachment hardpoint on

the wing. The shape is also dependent on the direction of the tensile force from the

Kevlar, which is determined by the position of the actuator arm with respect to the

wing hardpoint. A large vertical separation between these two points, as on this MAV,









causes the tensile force to be applied in a more spanwise direction so the wing exhibits

the predominantly curled motion in Figure 4-4.

The extent and shape of the morphing can be adjusted by varying the amount of

tension in the Kevlar lines or adjusting the location of the attachment hardpoint on

the wing. The shape is also dependent on the direction of the tensile force from the

Kevlar, which is determined by the position of the actuator arm with respect to the

wing hardpoint. A large vertical separation between these two points, as on this MAV,

causes the tensile force to be applied in a more spanwise direction so the wing exhibits

the predominantly curled motion in Figure 4-4.

4.3 Flight Performance

A series of flight tests are performed to evaluate wing curling for roll performance.

The vehicle actually contains separate servos that allow symmetric curling; however,

the current discussion only considers asymmetric morphing. As such, the flight test

considers maneuvers in response to a single wing being curled while the other wing

remains undeflected.

The wing curling causes a significant roll moment. The direction of roll is

determined by an increase in lift on the curled wing. Essentially, the curling causes a

greater angle of incidence and angle of attack on the morphed wing. This effect causes

a lift increase on the left wing, and consequently a positive roll moment, when the left

wing is curled. Of course, some amount of coupling to pitch and yaw results from the

asymmetric configuration [14].

An immediate benefit from the morphing is realized when comparing this MAV to

similar types that do not have morphing. This shape of vehicle, with a range of wing

span, has been previously flown using only elevator and rudder for control. The vehicle

is noticeably easier to pilot using elevator and morphing. The wing morphing generates

roll moments that facilitate flight path tracking beyond the rudder over the majority of

the flight envelope.









The wing-curling morphing exhibits good control response near the neutral,

trim position. Small inputs are necessary in performing turns and in making slight

adjustments to the flight path. The morphing provides an adequate level of control

under these circumstances The aircraft responds predictably to various magnitudes of

control input, although the physical deformation of the wing surface is not necessarily

linear. In particular, the morphing is suitable for both commanding turns and for

correcting for attitude perturbations from wind gusts or other disturbances. Roll

controllability remains satisfactory throughout the airspeed range encountered during

cruise, high-speed dives, and landing or approach phases.

Although turns and rolls are easily accomplished with the wing curling, aggressive

maneuvers are considerably more difficult. The aircraft is quite sensitive to departure

when morphing is commanded while the aircraft is at high loading conditions, such

as in a steep turn or during a large pitch angle change. The wing deflection incurred

during wing curling generates large incidence angles near the deformed region of the

wing. The incidence angles generate the requisite change in aerodynamic forces and

moments to control the aircraft during level or cruise flight conditions.

Also, if the aircraft is already at a large angle of attack, such as during an

aggressive maneuver, large morphing commands can exceed the critical angle of attack

and force a stall on the deformed wing. Such a situation generates a rolling moment

opposite to the commanded direction. For instance, during high angle of attack flight,

deforming the left wing slightly increases the angle of attack and lift on the left wing

and causes a roll rate to the right. However, large morphing commands cause a stall

over portions of the left wing, reducing the lift compared to the right wing, and causing

a stall-spin departure to the left. Departures caused by stall due to morphing are

generally terminal on this type of aircraft, as the morphing can be controlled only in

a single direction for each wing. Once a spin has developed, the morphing provides









insufficient control power to generate the required anti-spin forces and recover to level

flight.

Finally, roll handling qualities tend to be quite sensitive to the location of the

hardpoint on the wing and to the tension in the cable. Slight asymmetries in the right

and left side cable tensions often contribute to difficulties in control and non-zero trim

condition.

Unintentional variations in the control linkage tension cause control responses

to change slightly over a series of flights. Additionally, deterioration of the latex

membrane noticeably reduces the wing surface tension. The natural rubber used

in the latex material decays when exposed to the sun. The reduced tension of the

decayed latex prevents the deformation from propagating smoothly throughout the

wing structure. In turn, the twist deformation caused by the buckling remains localized

around the hardpoint and reduces control effectiveness.

4.4 Nonlinear Modeling of Lateral and Longitudinal Dynamics

Flight data from the vehicle is analyzed to estimate models of the flight dynamics.

Several techniques were attempted to estimate these models, including system identi-

fication [24] and parameter estimation [19], but with limited success. This vehicle is

particularly difficult to model because the morphing causes time-varying asymmetries

which violate many assumptions used by standard routines.

Furthermore, the estimation is difficult because of limited flight data. The MAV

is equipped with gyros and accelerometers but the flight data from the accelerometers

is actually too noisy to be useful for modeling. Thus, several critical measurements,

such as angle of attack and angle of sideslip, are not available. Some dynamics are not

easily observable, especially in the presence of noise, using only the available sensors.

A nonlinear auto-regressive model is used to represent the flight dynamics. The

general form of this model is shown in Equation 4.1. This model relates the gyro

measures of roll rate, p(k), pitch rate, q(k), and yaw rate, r(k), to the morphing








command, 8m (k), and elevator command, 8e(k), at the sampling instance of k. The
matrices, Ai c R3x3 and Bi C R3x2, represent the dynamics.


p(k + 1)
q(k + 1)
r(k + 1)

p(k) p(k-1) ||p(k)||p(k) ||p(k-1)||p(k-1)
= Al q(k) +A2 q(k-1) +A3 ||q(k)||q(k) +A4 ||q(k-1)||q(k-1)

r(k) r(k- 1) |r(k)||r(k) r(k- 1)||r(k- 1)

p(k)q(k) p(k- 1)q(k- 1)
+A5 q(k)r(k) +A6 q(k- 1)r(k- 1)

Sr(k)p(k) r(k- 1)p(k- 1)

[ m(k) 1 |5, ||(k) llm(k) 1e(k)
+B +B2 + B3 (k) (4.1)
,m (k 1) ||Sm(k- 1)||5m(k- 1) 5 8(k- 1)

The model in Equation 4.1 contains quadratic terms of the rates and commands.
Such quadratic terms are included to account for unknown relationships between the
wing shape and the aerodynamics. In this case, the terms utilize an absolute value to
allow the contributions from the quadratics to change in sign.
The model in Equation 4.1 also contains coupling terms. These terms multiply the
gyro measurements by each other. The standard equations of motion for a rigid-body
aircraft include coupling terms which scale by the moments of inertia [26]. This MAV
is obviously asymmetric during the morphing so the coupling is essential.
Finally, Equation 4.1 computes the update to the gyro measurements as a function
of the measurements from two previous sampling times. These terms are included to
account for the time-varying nature of the dynamics which arise by altering the wing










shape. The dynamics are assumed to be sufficiently described by two sampling times

although a rigorous study of the sampling times was not conducted.

The values of the matrices, Ai and Bi, in Equation 4.1 are determined by a least-

squares fit to the flight data. The resulting model is used to simulate the responses to

the morphing and elevator commands. Such responses are shown in Figure 4-5.








0 1 2 3 4 6 10 1 2 3 4 5 80 1 2 3 4 5 6
Time (s) Time (s) Time (s)

Figure 4-5: Measured and predicted responses for roll rate (left), pitch rate (middle)
and yaw rate (right)


The responses in Figure 4-5 demonstrate the model captures the basic trend of

the dynamics but is not completely accurate. The predicted responses are not perfect

matches to the measured responses but yet they clearly show similarities. Thus, the

model indicates the time-varying asymmetries associated with the morphing causes

nonlinearities and coupling in the flight dynamics of this MAV.















CHAPTER 5
SYMMETRIC WING TWISTING FOR ROLL CONTROL

5.1 Aircraft Design

Wing twisting is another type of morphing that is particularly interesting, and

suitable, for a MAV. The concept of wing twisting is an obvious choice based on its

use as a control effector for the Wright Flyer. It is also being adopted for the Active

Aeroelastic Wing [27]. Wing twisting will be investigated for a MAV in a similar

fashion as those previous aircraft; namely, wing twisting will be used to generate roll

moments.

A mechanism for wing twisting is implemented on the MAV shown in Figure 5-1.

This aircraft has an elevator and rudder as control surfaces. Also, the fuselage is large

enough to house the sensor package comprised of gyros and accelerometers along with

the data logger.













Figure 5-1: Wing-twisting MAV


The wing has several features advantageous to twisting. The leading-edge strip is

a relatively thin piece of uni-directional carbon fiber. Also, the wing surface is a nylon

film which is not overly extensible. These properties result in a wing which smoothly









and continuously deforms across the entire surface due to a small perturbation at a

single point. Several basic properties of the vehicle are given in Table 5-1.

Table 5-1: Properties of the 24 in wing twisting MAV

Property Wing Twisting MAV
Wing Span 24 in
Wing Area 100 in2
Wing Loading 20.32 oz/ft2
Aspect Ratio 5.76
Powerplant Brushless motor 4.75 in prop
Total Weight 14.11 oz


5.2 Morphing Mechanism

Morphing is accomplished using an steel torque-rod affixed to a batten at ap-

proximately the 66% span position. Actuating this rod with a servo forces the wing to

undergo a twisting deformation. Although the actuating point is localized to a single

wing batten, the wing surface distributes the deformation over the entire wing. The

magnitude of the twist deformation is largest at the actuation point and is tapered

toward the wing tip and wing root.














Figure 5-2: Underside view of wing showing torque rod


The use of torque-rods admits a bi-directional wing twisting that resists the effects

of loading. The bi-directionality of twist results from actuating the wing to twist in

either trailing-edge up and trailing-edge down directions. The resistance to loading









results from the stiffness of the aluminum rod, along with stiffness of the leading-edge

strip, to maintain shape unless excessive loads are encountered. Thus, the control of

the wing shape is largely a function of the actuator position with only small effects

from response to airloads. Figure 5-3 compares the 24 in MAV wing in undeflected

and morphed configurations.













Figure 5-3: Rear view of the 24 in MAV with undeflected (left) and morphed (right)
Wing


5.3 Flight Performance

The wing twisting aircraft exhibits highly desirable control characteristics in

flight [14]. Roll control is extremely responsive across a wide range of airspeeds.

At slow speeds, such as near level flight stall, the wing twisting remains effective at

commanding a turn and recovering from turbulent disturbances. At higher speeds,

the roll response is also effective, although the magnitude of the roll rate increases.

Modeling of the control characteristics suggests that the roll response is largely linear

over the airspeed range.

The morphing is effective at providing small, high-rate control inputs needed to

maintain a specific attitude or flight path. In such cases, the vehicle responds quickly

to the initial command and recovers to unaccelerated flight as the command is returned

to neutral.

The wing twisting also provides positive control characteristics at large amplitude

deflections. Maximum roll command, which twists the wings anti-symmetrically









100, generates a roll rate in excess of 10000/s within 0.2 seconds. Neutralizing the

morphing stops the roll in approximately the same time.

During continuous rolls, the vehicle incurs relatively little yaw coupling. Yaw rate

divergence from wing twisting is approximately an order of magnitude lower than the

corresponding roll rate. At high roll rates, for instance, several complete rolls can be

completed without an appreciable change in heading or pitch attitude.

Basic flying tasks such as turns and bank angle correction are facilitated with mor-

phing as compared to rudder-only control. The need for corrective control input during

the maneuver is decreased because of the decreased coupling. Turns commanded solely

through morphing are improved, where minimal rudder corrections are needed to main-

tain coordination throughout the turn. The turn performance is especially improved in

windy and gusty conditions, where the need to independently control bank angle and

heading angle is increased.

5.4 Linear Modeling of Lateral Dynamics

Flight testing of the active wing-shaping 24 in MAV is performed in the open area

of a radio controlled (R/C) model field during which wind conditions range from calm

to 7 knots throughout the flights. Once the flight control and instrumentation systems

are powered and initialized, the MAV is hand-launched into the wind. This launch is

an effective method to quickly and reliably allow the MAV to reach flying speed and

begin a climb to altitude.

This airplane is controlled by a pilot on the ground who maneuvers the airplane

visually by operating an R/C transmitter. The data acquisition system begins recording

as soon as the motor is powered.

This aircraft design allows either rudder or wing shaping to be used as the

primary lateral control for standard maneuvering. The airplane is controlled in this

manner through turns, climbs, and level flight until a suitable altitude is reached. At

altitude, the airplane is trimmed for straight and level flight. This trim establishes a










neutral reference point for all the control surfaces and facilitates performing flight test

maneuvers.

Open-loop data is taken to indicate the flight characteristics of the MAV. Specif-

ically, the rates and accelerations are measured in response to doublets commanded

separately to the servos. Several sets of doublets are commanded ranging in magnitude

and duration to obtain a rich set of flight data.

The dynamics of the MAV in response to rudder commands is investigated to

indicate the performance of the traditional configuration for this MAV. A representative

doublet command and the resulting aircraft responses are shown in Figure 5-4.

15 150 150
10 100 100
50 150
1 00

S-100o -100
-2 10 \ [ -150 -150
0 1 2 3 4 5 6 0 1 2 3 4 200 1 2 3 4 5
Time(sec) Time(sec) Time(sec)

Figure 5-4: Doublet command to rudder (left), roll rate response (middle), and yaw
rate response (right)


The roll rate and yaw rate measured in response to this command are shown in

Figure 5-4. The roll rate is sufficiently large and indicates the rudder is able to provide

lateral-directional authority; however, the yaw rate is clearly larger than desired.

Actually, the yaw rate is similar in magnitude to the roll rate so the lateral-directional

dynamics are very tightly coupled. The effect of the rudder in exciting the dutch roll

dynamics is clearly evidenced in the magnitude and phase relationship of the response

measurements.

Doublets, such as the pulse sequence shown in Figure 5-5, are also commanded to

the morphing servo.

The roll rate and yaw rate in Figure 5-5 are measured in response to the doublet.

These measurements indicate the roll rate is considerably higher than the yaw rate.










150 150


60 02
y \ / \ 100 100
\ 1 50 150

2 20-
-4 \-1

S 0 1 12 0 05 1 1.5 0.5 1 1.5 2
Time(sec) Time(sec) Time(sec)

Figure 5-5: Doublet command to wing twist morphing (left), roll rate response (mid-
dle), and yaw rate response (right)


Thus, the morphing is clearly an attractive approach for roll control because of the

nearly-pure roll motion measured in response to morphing commands.

The data from open-loop flights is then used to approximate a linear time-domain

model using an ARX approximation [24]. This model is generated by computing

optimal coefficients to match properties observed in the data. The assumption of

linearity is reasonable since the maneuvers are small doublets around a trim condition.

Also, the twisting command is anti-symmetric about the centerline of the aircraft.

The resulting model, having poles at -4.95 and -0.1194, is used to simulate

responses of the aircraft. The simulated values of roll and yaw rates are shown in

Figure 5-5 as dashed lines.

The simulated responses show good correlation with the actual data. The model

is thus considered a reasonable representation of the aircraft. The existence of such a

model is important for future design of autopilot controllers but it is also valuable for

interpreting the morphing. Essentially, the ability to identify a linear model with poles

relating to the roll convergence and spiral convergence modes indicate the aircraft with

morphing acts like an aircraft with ailerons.

5.5 Spin Characteristics of Wing Twist Morphing

Figure 5-6 shows the command and rotation rates during a conventional spin.

This maneuver is initiated from level flight by commanding positive elevator to

increase the pitch rate and angle of attack. Right rudder command is then applied to










generate a yawing moment as the aircraft approaches stall. In this case, the yaw causes

an asymmetric stall and starts the spin rotation. The aircraft response is relatively

constant throughout the maneuver, although the roll rate tends to build up as the flight

path changes from level to vertical. The autorotation continues as long as the positive

elevator and rudder commands are held. Once the commands are neutralized, the

rotation slows and comes to a stop with little or no opposite rudder input. Positive

elevator is used to recover the aircraft to level flight at 363 seconds.

Although this type of spin has been experienced several times, the entry pro-

cedures tend to be difficult to reproduce. Specifically, applying rudder command

at a low angle of attack (too early) prevents a stall from developing and results in

a high-speed spiral dive. Both wind tunnel and CFD analysis have shown that the

thin-undercambered airfoils used on the vehicle have delayed stall response. This delay

affords such vehicles increased resistance to stall-spin departure, at least for positive

loadings.

The effect of morphing on positive (upright) spins is to accelerate the onset of

the spin and to assist in the recovery process. This effect is most pronounced during

cross-coupled controls, where the rudder direction is opposite to that of the morphing.

In such a case, the high angle of attack at the inside wing tip is further increased by

the morphing actuation, leading to a subsequent stall-spin. Releasing the morphing

command effectively reduces the wing angle of attack and produces nearly immediate

recovery from an upright, conventional spin.

40
30
20 50

20
S10 -50

elevator roll rate
-30 --- rudder -100 --- pitch rate
morphing -- yaw rate
459 360 361 362 363 364 359 360 361 362 363 364
Time (s) Time (s)
Figure 5-6: Pilot commands (left) and responses (right) during conventional spin









Conventional spins are also performed with negative (down) elevator actuation

to produce a starkly different response. In particular, the spin modes observed are of

considerably higher energy. The rotation rates of a negative spin compared with an

upright spin tend to be between 2 to 6 times greater. Based on rudimentary analysis,

the stall characteristics of a thin under-cambered wing at negative angles of attack are

far more severe than the characteristics at high angles of attack. In flight, the airplane

is observed to have a very immediate and violent response to large negative elevator

commands. Such an input is believed to cause a negative stall quickly, where any

asymmetry about the yaw axis then produces a large rate of rotation.

Figure 5-7 shows an identified negative spin mode initiated by a morphing

command with elevator and rudder. At 401 seconds, the aircraft responds to the

constant control deflection by building up rotation rates on all three axis. The entry

into the maneuver is relatively gradual and only after one second of control inputs have

the pitch, roll, and yaw rates become significant.

This particular type of spin stabilizes independently of the initial pro-spin control

deflections. At 402 seconds, the controls are released, while the aircraft continues to

spin. The application of positive elevator (for recovery) shortly afterwards appears to

maintain the spin for some time. It is only with corrective opposite rudder command

that the aircraft arrests the rotation and recovers from the spin.

It is difficult to draw solid conclusions from this spin sequence. However, the two

distinct modes observed in Figure 5-7 are attributed to primary and secondary spin

characteristics, where the latter is caused by a premature recovery attempt. Similar

spins have been observed from both left and right directions.

Alternatively, Figure 5-8 shows a considerably different spin behavior for similar

control combinations. Although initiated by commands similar to the previous spins,

this type of spin exhibits a cyclic or periodic motion. It is perhaps with the timing of

the control inputs or entry flight conditions that a difference can be found. Whereas










40
elevator
30 rudder
morphing 50

20 -- --- -


-20

-30 -100 --- pitch rate
yaw rate
S 4 4)5 400 401 402 403 404 405
Time (s) Time (s)
Figure 5-7: Pilot commands (left) and responses (right) during spin


in Figure 5-7 the elevator input lagged behind the rudder and morphing inputs, the

spin depicted by Figure 5-8 shows the elevator leading slightly. The precise effect this

has on the spin is unknown. However, the resulting aircraft response is shown to be 6

times greater in magnitude than a conventional spin.

From level, trimmed flight, the aircraft is subjected to full left wing morphing, full

left rudder, and full negative elevator command. The initial reaction of the aircraft is

to pitch down at a constant rate and incur a left roll and yaw from the wing morphing

and rudder deflections. Once the wing has reached the negative stall angle, presumably

facilitated by the deflected wing, a rapid spin ensues, nearly doubling the roll and yaw

rates and reducing pitch rate. This pattern is repeated four times throughout the spin

while pilot commands are held constant. Each cycle is proceeded by a period of low

momentum, followed by a sharp change in pitch rate along with peaks in both the

roll and yaw rates. Throughout the spin, the mean pitch rate is near zero. Each cycle

generates a large negative pitch rate followed by a large positive pitch rate. Mean roll

and yaw rate responses are non-zero during the spin. The lateral rates remain negative,

achieving small negative values only as the pitch rate reverses direction.

While the dynamics of such a maneuver are not very well understood, it appears

that the morphing of the wing plays a large roll in both inducing and recovering

from the spin. For instance, similar spin entries performed without morphing are

characterized by considerably lower rotation rates and a continuation of the spin after

command inputs are neutralized. However, the recovery of this cyclic spin mode occurs











nearly immediately after the controls are neutralized. As seen at 176 in Figure 5-8, the

aircraft is incurring maximum rotation rate when command is returned to neutral. The

rotation rates continue to follow the characteristic spike pattern and finally converge to

zero.

40
elevator roll rate
30 rudder -- pitch rate
morphing 50 yaw rate
20
10

-10 -50
-20
-30 -100
-4 71 172 173 174 175 176 177 171 172 173 174 175 176 177
Time (s) Time (s)
Figure 5-8: Pilot commands (left) and responses (right) during cyclic spin



In flight, this immediate convergence has the effect of stopping the aircraft in

mid-rotation. Unlike the other spin modes observed, the cyclic spin mode has no

apparent recovery apart from neutralizing the controls. The aircraft will continue to

the end of a given cycle, cease rotation, and simply return to steady, controlled flight.

The nose-down recovery typical of other spin modes is contrasted with an immediate

recovery to level flight.

The usefulness of the cyclic spin mode depicted in Fig. 5-8 is perhaps ques-

tionable, although it may give rise to a different mode of maneuvering for morphing

aircraft. For instance, the above maneuver may be useful for a controlled vertical dis-

placement. On initiating the entry, the airspeed quickly decays and starts the aircraft on

a relatively slow vertical flight path. During this portion of the maneuver, the aircraft

incurs a series of high rate of rotations, each separated by a period of low momentum.

As evidenced by the recovery from the maneuver, this period can be used to recover

the aircraft into stable flight. While previous spin modes required corrective rudder and

significant altitude losses for recovery, this cyclic spin mode stopped once the controls

were neutralized.









Attitude and airspeed entry conditions into the spin trials have been observed to

have some impact on the stabilized spin modes; however, accurate measurements of

the entry conditions were not possible. The lack of pressure sensors on the airframe

precluded the gathering of such data. Excitation of a particular spin mode depended

on the pilot ability to position the aircraft properly based on control feel and vehicle

observations.

The spin entry maneuvers were also attempted for other control combinations.

Specifically, cyclic spins were attempted without wing twisting by using negative

elevator and rudder deflection. These trials resulted in a stabilized spin but with

considerably lower rotation rates than the cyclic spin. Additionally, this mode did not

exhibit the periodic behavior achieved through wing twisting during a spin.















CHAPTER 6
MULTI-POINT WING SHAPING

6.1 Aircraft Design

The multi-point wing-shaping aircraft employs a simple strategy to exercise

increased control over the wing in twist. Actuation of the wing is accomplished

through four concentric rotating spars that are attached to a flexible, extensible wing

skin. The basic idea of this form of morphing is to have some control of the lift

distribution over the wingspan. Since each of the four rotating spars can be controlled

independently, the wing surface can be commanded to a variety of complex shapes.

In this manner, the morphing can be useful for longitudinal control, longitudinal trim,

minimum drag, maximum drag, or stall resilience in addition to commanding roll rate.

From a design perspective, the vehicle geometry is similar to the 24 in wing-

twisting aircraft, as seen in Figure 6-1. The wing planform and airfoil are identical in

fact, although the wing structure and membrane differ somewhat to accommodate the

morphing spars. The wings are mounted along the middle of the fuselage to facilitate

the mounting of the morphing actuators and mechanisms. The lower wing position and

reduced dihedral also help eliminate excessive roll-yaw coupling.

Figure 6-2 shows the wing undergoing morphing to the outboard (wingtip) spar

tubes alone and to both wingtip and midboard spar tubes simultaneously. Deformation

is visually apparent by examining light reflections off of the leading edge and the shape

of the trailing edge.

6.2 Morphing Mechanism

Concentric tube spars act as both primary load-bearing members and as control

linkages (torque-tubes). A large diameter tube is fixed to the fuselage and acts as

a bearing support for the rotating spars. The root section of the wing surface is














/ I,


S,.__


Figure 6-1: Top, side, and front views of the 24 in span multiple-position wing shap-
ing vehicle

also attached to this tube, creating an immobile joint between the inboard wing and
fuselage. Two smaller tubes, one within the other, are supported by the fixed tube. The
smallest tube extends the full span, while the center tube extends to the 60% position.
Each of the outboard and midboard spars is actuated in twist via servos mounted in
the fuselage, shown in Figure 6-3. Each servo is then able to command the incidence
angle of the corresponding wing section independently.
A flexible wing surface is attached to each of the three wing spar tubes. Attach-
ment points near the spar joints are left unconstrained in pitch angle. This freedom
allows the incidence to smoothly taper between the rigidly attached sections of the
wing surface. This structure permits twist morphing of each controlled wing section


a K
MEMERI.-T-


444%t'%






























Figure 6-2: Wing shaping MAV showing neutral position (top left), wingtip morphing
(top right), and full wing morphing (bottom)














Figure 6-3: Spar torque-tube morphing actuators. The 4 front servos rotate concentric
spar sections, aft 2 control rudder and elevator


from -10 to +10 incidence angle. Each of the four wing sections are commanded

independently, allowing for considerable differential or collective configurability.

6.3 Flight Performance

The aircraft has undergone basic performance and handling flight tests. Roll

control is achieved by differentially actuating the wingtip spars. The handling qualities

and maximum roll rate are similar to the 24 in wing twisting aircraft. Actuating the







36

entire wing differentially (i.e. using both wingtip and midboard sections), achieves roll

rates and performance measures considerably higher.

The morphing is also being considered for use in conjunction with other control

surfaces. Basic flight tests of combining collective midboard wing deflection with

elevator command have shown potential for improvement in pitch rate performance.

Additionally, this morphing may be suited for quasi-statically reconfiguring the wing

twist to optimize spanwise lift distribution in flight. Such techniques are currently used

by sailplane and commercial jet pilots to alter the lift properties of the wing for cruise,

steep descent, and maximum performance flight phases.















CHAPTER 7
VARIABLE GULL-WING ANGLE MORPHING

7.1 Aircraft Design

The aircraft discussed thus far have been limited in concept to relatively simplistic

twisting or bending of the aircraft structure. However, because of the nature of such

mechanisms, control over the aircraft is limited to high-bandwidth stabilization,

maneuvering control, or retrimming. The morphing shapes achieved by such methods

are not suitable for the gross aerodynamic reconfiguration that is typically associated

with morphing. A new morphing aircraft design is proposed that uses a jointed spar

structure to achieve a biologically-inspired form of morphing in addition to the twist

control used on previous aircraft.

The design of the aircraft is identical to the multiple-position wing shaping aircraft

in all components except for the jointed spar and actuator. The aircraft configuration,

shown in Fig. 7-1, is traditional in the sense of a single lifting surface, horizontal and

vertical stabilizers, and tractor propeller. Apart from the morphing mechanisms, the

aircraft is equipped with elevator, rudder, and throttle control. The vehicle airframe is

largely composite carbon-fiber and mylar plastic. The monocoque fuselage is made

using carbon-fiber cloth wrapped over a male mold [12]. Once cured and extracted,

the structure is strong enough to withstand wing and tail loads without additional

supporting structure. The aircraft is considered small enough to be considered in the

class of micro air vehicles, since the wingspan at full extension is 26 in.

The tail surfaces consist of a mesh of unidirectional carbon fiber strips. The

perimeter strips support the overall planform, while the interior strips build up the

surface rigidity. Hinges for the control surfaces are embedded within the carbon

structure during the layup process. Additionally, mylar plastic covering is used for













"i l lI1 ''


Figure 7-1: Top and side view of variable gull-wing aircraft

skin material on the tail feathers and portions of the wing. The resulting structure adds

minimal weight to the vehicle, yet is strong enough to withstand flight loads and the

occasional crash.

7.2 Morphing Mechanism

The wing planform shape provides sufficient area to keep the fully-instrumented

aircraft at a reasonable wing loading. yet is also high enough in aspect ratio to provide

good aerodynamic performance. Morphing the wings changes the wing geometry

in several parameters. Table 7-1 lists the basic geometry changes incurred during

gull-wing morphing. Figure 7-2 shows a frontal view of the vehicle during three

configurations resulting from gull-wing morphing.

Table 7-1: Wing geometry change over variable gull-wing morphing range

Parameter Min Max
Wingspan 20 in 26 in
Planform area 77.7 in2 101.4 in2
Inboard wing relative to fuselage -400 400
Outboard wing relative to fuselage -400 400


QUM


























Figure 7-2: Vehicle undergoing neutral (top), positive (center), and negative (bottom)
gull-wing morphing


A hinged spar structure, based loosely on bird skeletal physiology [33], provides

the degree of freedom needed for gull-wing morphing. Each spar side consists of two

tubular spars with one hinge at the fuselage joint and another between the two spars.

The angle of the inboard spar is controlled by a vertical linear actuator. A telescoping

shaft connects the spar with the output arm of the actuator. The shaft allows the

actuator to move over the entire range without mechanically binding the spar. The

angle of the outboard spar is passively controlled via a mechanical linkage parallel to

the inboard spar. This linkage connects the control arm on the outboard spar directly

to the fuselage. During actuation, the linkage causes the inboard and outboard sections

to deflect in opposite directions. The ratio of these relative deflections is adjusted by

changing the moment arm on the fuselage control arm and/or the outboard spar control

arm. An important feature of the system is its ability to withstand flight loads without

active control or energy consumption. Figure 7-3 shows the left side of the hinged spar

in a positive gull-wing position.

A flexible wingskin is attached to the jointed spar so that the spar comes under

the point of maximum camber. This position approximately corresponds with the






















Figure 7-3: Variable gull-wing spar structure and control linkage, linear actuator visi-
ble inside fuselage at left


point of minimum pitching moment, in addition to reducing the frontal area of the

wing. The wing skin consists of chordwise carbon-fiber battens and a single spanwise

leading-edge member. Each batten is free to deform within the limits of the wing

skin extension and carbon-fiber flexibility. In flight, this compliance allows the airfoil

sections to deform in response to buffeting or steady airloads. As a result, the wing

passively deforms and reduces the effect of atmospheric perturbations such as gusts and

wind shear on the vehicle's flightpath.

Conventional elevator and rudder control surfaces are used for pitch and yaw

control. These surfaces are hinged to the fixed stabilizing surfaces with strips of

Tyvek. Rotary actuators mounted in the fuselage control the surface deflection. Control

actuation limits are +/- 30 of travel, with actuation rate limits of 4000/s.

Roll control is provided by articulating wing tips on the outboard spar section.

A rotary servo mounted to the wingskin actuates against the spar, causing the wing

surface to rotate about the spar. The surface is attached to the outboard spar so that

rotation about the spar is unrestrained, except by the actuator motion. However,

since the wingskin is continuous along each side of the aircraft, the result is a twist

deformation centered at the actuator and extending both inward toward the fuselage









and outward toward the wingtips. Figure 7-4 shows a close-up view of the wing twist

mechanism, outboard spar, and actuator.















Figure 7-4: Underside view of left wing showing wing twist effector


Control of the gull-wing is accomplished using a linear lead-screw actuator driven

by a rotary servo. Rotating the lead-screw causes the output arm to slide vertically

within the fuselage. At the lowest position, the inboard spars are deflected 40 upward.

The lead-screw provides control of the wing shape without having to withstand the

lifting loads directly; however, the actuation rate of the morphing is quite slow in

comparison to the other surfaces. This slow actuation is not problematic since the

morphing is being investigated strictly as a quasi-static effector.

Command and response data are measured in-flight using an on-board micro

data acquisition system. The device supports 30 channels of analog sensor input and

samples between 50Hz to 500Hz. The data presented here is measured at 100Hz.

Several external sensors are interfaced to the data lwing. including 3-axis rate gyros,

linear accelerometers and control surface position sensors for the elevator, rudder,

wingtwist, and gull-wing angle.

7.3 Flight Performance

The variable gull-wing morphing sufficiently changes the flight performance for

the vehicle to operate in several distinct flight regimes. Morphing the wings controls









several aerodynamic and dynamic parameters, including lift to drag ratio, sideslip

coupling, and roll stability. These factors in turn affect the handling qualities of

the vehicle to make certain flight tasks easier to perform in a particular morphing

configuration.

The change in flight performance is the primary incentive behind the morphing;

however, this paper is strictly concerned with the change in handling qualities and

dynamic characteristics that accompany the performance changes. A more detailed

analysis of the performance benefit enabled by gull-wing morphing was previously

published [1].

7.3.1 Gliding Performance

Power-off gliding performance is tested to identify the effect of the morphing

configuration. Glide performance is an important measure of lift to drag ratio. In

turn, lift to drag ratio is representative of the aircraft's capability in range, endurance,

maneuvering, airspeed range, and efficiency. Thus, by testing the glide performance,

inferences can be made about much of the remainder of the flight envelope, which is

often more difficult to test.

Glide tests are performed by cutting off motor power and allowing the vehicle to

stabilize in a constant airspeed dive. The shallowest, sustainable dive angle corresponds

to the maximum lift to drag ratio for a specified configuration. The numerical value of

the lift to drag ratio is exactly equal to the glide ratio, which is the horizontal distance

traveled divided by the altitude lost during the dive. The glide ratio can be determined

using airspeed and altitude measurements from on-board the aircraft or by estimating

distances from the ground.

In the unmorphed configuration (0 gull-wing angle), the vehicle attains an

approximate maximum glide ratio of 11. This value is typical for aircraft of this size

and shape. As the wing is morphed in the positive direction, the glide ratio become









progressively lower. At 15 gull-wing angle, the glide ratio is noticeably reduced,

causing the aircraft to descend at a much steeper angle.

At 30, the lift to drag ratio becomes very low. Ground estimates for the glide

ratio are between 1 and 2. The result is that the aircraft is capable of descending at

a 450 angle without gaining airspeed. Furthermore, the high gull-wing angle adds

considerable lateral-stability, allowing the vehicle to attain a steep, stabilized dive

without control departure tendencies. Such a configuration could be beneficial in

allowing the vehicle to descend safely without requiring much horizontal distance.

Negative gull-wing morphing has a similar effect on glide ratio. At -20 gull-wing

angle, the glide ratio is approximately 3. The effect of the morphing on a stabilized

dive is similar to the positive morphing, except that the benefits of sideslip to roll

stability is greatly reduced. In fact, control input required to maintain a constant

airspeed and glide angle is higher than both neutral and positively morphed cases.

Actuating the gull-wing morphing during a glide test illustrates the impact on lift

to drag performance. During a steep, stabilized dive at -30 morphing, the gull-wing

angle was slowly increased to 0. The resulting flight path, when viewed from the side,

resembled an exponential decay. As the morphing became less negative, the glide ratio

became progressively shallower. Pitch control was used during this maneuver to find a

trim airspeed corresponding to the maximum glide performance. Thus, the gull-wing

morphing is sufficiently effective to control the glide angle of the aircraft and can be

used to change the glide angle throughout the descent.

7.3.2 Climb Performance

The effect of gull-wing angle on climb performance is similar in nature to the

effect on glide angle. Maximum climb performance is attained at a neutral gull-wing

angle. Morphing the aircraft either in the positive or negative direction reduces climb

rate, although the effect is more pronounced for positive gull-wing angles.









7.3.3 Stall Characteristics

Stall flight testing is performed to determine the effect of the morphing on

departure characteristics. In particular, it is used to determine conditions where a

stabilizing controller may be required to prevent loss of control. Additionally, the stall

characteristics are useful in assessing whether certain stall-spin modes may be useful as

evasive or high-performance flight maneuvers.

Flight testing a vehicle for stall characteristics requires a pilot to fly at high

altitudes and be well versed in recovery techniques [32]. The stalls are entered by

reducing the airspeed and using the elevator to pitch above the critical angle of attack.

Elevator pressure is applied slowly to help eliminate any dynamic effects that might

influence stall entry. Stalls are allowed to fully develop by holding positive elevator

pressure throughout the test. Recovery from the stall or ensuing spin is performed

when the aircraft has clearly demonstrated a particular mode or when altitude loss has

become substantial.

Stalls performed at neutral morphing are relatively benign and resulted in moder-

ate altitude loss during recovery. The wing planform has a tendency to stall abruptly,

but then regains control quickly. Control is lost for only a brief period as the aircraft

pitches down and reduces angle of attack.

Stalls at positive gull-wing angles are more difficult to enter and result in a smaller

altitude loss during recovery. At high angles of attack and large positive elevator

pressure, the vehicle simply enters a dive and buffets slightly. When provoked to

stall with aggressive elevator deflection, the stall break is of lower intensity than the

previous configuration. Recovery from a stall at high positive gull-wing angle is more

immediate. Part of this improved resilience comes from a significantly decreased

tendency to depart into a spin. The high angle of the wings has a stabilizing effect and

seems to favor a symmetric stall when at high angles of attack.









Negative morphing contributes to a much more aggressive stall mode than

observed with the previous configurations. The stall recovery also requires a greater

amount of altitude and control input. Stalls also have a greater tendency of escalating

into a spin. The spins are generally non-terminal, although one stall test resulted in an

unrecoverable spin that resulted in some vehicle damage.

Although the testing performed is hardly exhaustive, the observed characteristics

indicate that the positive gull-wing contributes to highly desirable stall and recovery

characteristics. However, the testing did not reveal any spin modes that could be useful

as flight maneuvers.

7.4 Lateral-Directional Dynamics

Morphing introduces considerable complexity to flight dynamics because of

variable geometry of the airframe. The variable gull-wing aircraft in particular morphs

the wings in a manner that has considerable effect on many of the stability and control

derivatives that control the lateral-directional modes.

Modeling of the lateral-directional dynamics is restricted to Dutch roll and roll

convergence. Spiral mode identification was not possible, considering that the data sets

in analysis were relatively short in duration. Proper identification of this mode would

require long data sets with little or no pilot input. Such tests are difficult to accomplish

using small remotely piloted vehicles.

7.4.1 Roll Convergence

The roll mode is one of the most fundamental descriptions of the aircraft lateral-

directional motion. The mode essentially describes resistance to rolling, whether

through a control surface deflection or a perturbation. Aircraft handling qualities and

lateral controller designs are highly dependent on the roll mode.

The roll mode, or roll convergence, is largely a function of the C1p derivative,

which describes the change in rolling moment as a function of roll rate. This derivative

in turn is a function of the vehicle geometry. As the vehicle shape changes, as in the









case of a gull-wing morphing aircraft, the C1p parameter and the corresponding roll

mode are expected to change. The change in roll mode with morphing deflection

then becomes a basic assessment of the change in handling qualities incurred due to

morphing.

Wing-twist pulses are used to perturb the vehicle from a trimmed flight condition.

The response of the vehicle to these pulses is used to identify important stability and

control characteristics, namely the roll mode and the wing twist effectiveness. Pulse

maneuvers are performed at cruise airspeed from straight and level flight. The pulse is

repeated for a variety of command magnitudes and morphing positions.

The pulse maneuvers are performed such that the aircraft's perturbation from the

entry trim condition is relatively small. Larger pulses may exceed the range of aircraft

responses that can be adequately represented by a linear model; however, the small size

of the vehicle requires that the maneuver be large enough to be clearly evident to the

remote pilot. In practice, the control pulses are performed to 30 or 40 bank angle in

each direction.

A typical wingtwist control pulse is shown in Figure 7-5. Commanded wingtwist

deflection is measured along with the roll and yaw rate response. The roll angle data

shown is estimated from the roll rate. The estimate is assumed to be a reasonable

representation over short time periods and small angles of attack. Although the

estimate may be off in absolute magnitude due to calibration or estimation errors, the

trends clearly show the relative bank angle response.

The top two plots in Figure 7-5 show a close correspondence between command

input and roll response. Such response is typical of aircraft with high aileron control

power. The yaw rate incurred during the maneuver is closely in phase with the

estimated bank angle.

The roll mode is modeled by computing a transfer function between the roll

command and the roll rate response [24], [19]. Secondary effects of the command such












E 0
r0 1U -------------------------------------------------------__


10
241 6 241 8 242 2422 2424 2426 2428 243 2432 2434
500

o
-500
241 6 241 8 242 242 2 242 4 242 6 242 8 243 243 2 243 4
200

Cc 0
-200
241 6 241 8 242 242 2 242 4 242 6 242 8 243 243 2 243 4



241 6 241 8 242 242 2 242 4 242 6 242 8 243 243 2 243 4
Time (se-)


Figure 7-5: Wing-twist command and response from flight data


as adverse yaw and pitch coupling are neglected due to relatively small disturbance

magnitudes. Other yaw effects such as sideslip or bank angle induced yaw rate are also

not considered in the model.

A MATLAB Auto-Regressive with Exogenous Input (ARX) discrete-time model

is used to represent the roll mode. The coefficients of the model are computed from

least-squares fit to the command and response data. The discrete-time model is used in

simulation to determine the accuracy of the computed model. A final transformation

is made to represent the model as a continuous-time state-space formulation. The

formulation of the model assumes first-order rigid-body dynamics. Although structural

modes may very well be present, the model structure and filtering techniques assume

that any response above 7 Hz is strictly noise and is therefore not considered in the

model.

The models are represented in the state-space nomenclature shown in Equations

7.1 and 7.2.




x Ax+bu (7.1)


and


y = cx+du


(7.2)











Where x is the state vector and y is the output. u is the control input and A,b,c,d

are the state-space matrices. Of particular importance are A and b, which are consid-

ered the system plant and control effectiveness matrices.

Pole locations for the roll mode at several gull-wing positions are shown in

Figure 7-6. The plot shows the poles migrating to a less negative value as the wing is

morphed in the positive or negative direction from neutral. This migration accounts for

the decreased sensitivity to command input as the wing is morphed.

-10

-15 X

-20-

-25-
0j
o -30

0 -35

-40 -

-45
-20 -10 0 10 20 30
Gull-wing angle (deg)

Figure 7-6: Pole migration with gull-wing morphing angle



The physical significance of the change in poles is the effect on the lateral-

directional handling qualities throughout the morphing range. The most negative

value, occurring at 0 morphing position, indicates that the vehicle quickly attains a

steady-state roll value when subjected to a control input or disturbance. Increasing

the gull-wing morphing in the positive direction increases the response time of the

vehicle to similar inputs. At the most positive morphing position of 30, the vehicle

is considerably less responsive than at the neutral morphing position. Morphing the

gull-wings in the negative direction produces a similar effect on the roll mode. The

migration of the open-loop poles from neutral to -20 is similar to a 15 positive

morphing from neutral.











The controllability of the simulated systems also undergoes a change with gull-

wing morphing position. Figure 7-7 shows the change in the b-matrix values over

the tested range of morphing. The qualitative shape of the plot appears as a mirror

image of the pole locations. In particular, the neutral gull-wing position here is a

maxima while the b-matrix value falls as the wing is deflected in either direction. The

plotted values represent the control effectiveness of the twisting wingtips in producing

a roll acceleration. The higher the b-matrix value, the higher the control power of the

wingtips.

1400
1300 X
1200
1100 X
1000-
900-
800
700-
600-
500
-20 -10 0 10 20 30
Gull-wing angle (deg)

Figure 7-7: B-matrix value for first-order roll mode systems



Physically, this is likely a result of a combined effect of the increased gull-wing

angle, decreased wingspan, and angled control surfaces. The latter change occurs

because of the normal direction of the wingtips deviates from perpendicular to the span

as the wing is morphed. Thus, some component of the added lift from the wingtip

twisting occurs in the spanwise direction and has no effect on the roll moment. The

change in the roll moment produced by the wingtips varies approximately with the

cosine of the deflection angle of the outboard wing section.

Figures 7-8 through 7-11 show results of the simulation models compared to

flight data. Measured and simulated roll rates are generally in close agreement for all

the models.


















105 244 244
243 5 244 244 5 245 245 5 246


-I 200


-200
-400
243 5 244


Figure 7-8: Wing-twist command (top)
simulated roll rate (-) (bottom)


271 5


244 5 245 245 5 246
Time (sec)


at 0 gull-wing, measured roll rate (:) and


272 272 5


273 273 5


200 -
0-


-400"
271 5 272 272 5 273 273 5
Time (sec)


Figure 7-9: Wing-twist command (top) at 15 gull-wing, measured roll rate (:) and
simulated roll rate (-) (bottom)



7.4.2 Dutch Roll Mode

The Dutch roll mode is an dynamic involving coupling between roll, sideslip, and

yaw [28]. Poor Dutch roll properties can cause difficulties in stabilization and control,

causing poor flight path tracking [26].

Unlike the roll mode, the Dutch roll mode involves significant coupling between

the lateral-direction states and often with the longitudinal states. The characteristics

of the mode are highly dependent on wing geometry. The wing shape directly affects

factors such as roll and yaw damping, sideslip cross-coupling, and inertial properties,














-, 5



332 332 5 333 333 5 334 334 5 335

400




-6 _400- -------
332 332 5 333 333 5 334 334 5 335
Time (sec)


Figure 7-10: Wing-twist command (top) at 30 gull-wing, measured roll rate (:) and
simulated roll rate (-) (bottom)

10------------------------
10






422 4225 423 4235 424

400,,
200

-20

-400 "'""
422 422 5 423 4235 424
Time (sec)


Figure 7-11: Wing-twist command (top) at -20 gull-wing, measured roll rate (:) and
simulated roll rate (-) (bottom)


all of which in turn affect the Dutch roll characteristics. In terms of vehicle geometry,

the mode is largely dependent on dihedral angle, wingspan, vertical area distribution,

and vertical center of gravity.

Rudder control pulse maneuvers are used to excite the Dutch roll mode of the

vehicle at two different gull-wing positions. The pulses are a series of consecutive step

inputs in opposite directions. Each pulse perturbs the vehicle from trimmed flight in

sideslip, roll, and yaw. The resulting vehicle response is then largely an indication of

the Dutch roll mode. Control pulses are performed at 0 and 15 gull-wing angles.










Command and response data from rudder control pulses at 0 and 15 gull-wing

angle are shown in Figures 7-12 and 7-13, respectively. The most apparent difference

between the two pulses is the two-fold increase in the roll response magnitude for

the 15 gull-wing case. Roll coupling with rudder and/or sideslip has increased

dramatically with positive gull-wing deflection. The response at this morphing position

is dominated by roll. Recovery oscillations in both roll and yaw are smaller and damp

out faster than the neutral morphing case.

a0s--------------------------
12 210 200---








Figure 7-12: Rudder control pulse at O gull-wing angle with measured data (:) and
simulated response (-)
simulated response (-)


Figure 7-13: Rudder control pulse at 15 gull-wing angle with measured
simulated response (-)


data (:) and


The model formulation required that the system account for both the roll rate and

yaw rate response to rudder deflection. With one input and two outputs, a different

system identification method was needed than was used previously. Using the ARX ap-

proach to modeling the Dutch roll dynamics resulted in a relatively poor fit compared

with the roll mode modeling.









A 4th-order state-space model is used to identify the lateral dynamics from the

rudder control pulse data. Attempting to model strictly the Dutch roll mode as a

second-order system resulted in poor fit in both roll rate and yaw rate. Increasing the

order of the system to 4 considerably improved the fit for both states. The resulting

model has two pairs of complex conjugate poles, although classical Dutch roll modes

for conventional aircraft have only a single pair.

The identified Dutch roll dynamics for two morphing models are shown in the

equations below. The dynamics are given in state-space format.

The state-space matrices are shown for the 0 gull-wing system in Equation 7.3-

7.6 the first set of equations and for the 15 system in Equation 7.7-7.10.



-0.00728 -0.07607 0.06432 0.001042 xl

0.1299 -0.04688 0.01308 0.05232 x2
A = (7.3)
-0.06621 0.004354 -0.02822 0.05985 x3

0.02396 -0.08451 -0.0712 -0.05431 x4

-0.001507 -0.0004478 -0.001323 xl

0.0003071 -0.001497 -0.0002368 x2
b = (7.4)
0.0003202 -0.004137 -0.007136 x3

-0.001106 -0.01099 0.003608 x4

34.99 -488.6 3.619 -9.66 yl
c = (7.5)
-869 176.5 -22.61 2.435 y2

d = 0 0.9822 0 yl (7.6)
0 0.2639 (7.6)
0 0.2639 1.82 y2












-0.00963 -0.07148 0.05012 0.002864 xl

-0.1124 -0.04497 0.01106 -0.03917 x2
A = (7.7)
-0.07133 -0.06225 -0.03205 0.1023 x3

-0.01097 0.01318 -0.08323 -0.02391 x4

-0.001524 -0.0004311 -0.0009517 xl

0.0002664 0.0006908 8.541e-005 x2
b = (7.8)
-0.0001861 0.001469 -0.006974 x3

-0.001101 -0.006893 -0.001574 x4

-46.5 1348 5.786 -19.65 yl
c = (7.9)
-901 -222.3 -18.36 1.216 y2

0 1.556 0 yl (7.10)

0 -0.9075 1.335 y2

The pole migration shown in Figure 7-14 depicts a considerable change in the

aircraft characteristics during morphing actuation. The two complex pairs shift toward

the right-hand plane during positive gull-wing angle changes. This pole migration has

the effect of decreasing both the average natural frequency and the damping of the

modes. The particular modal properties are listed in Table 7-2 and Table 7-3. The

two modes listed are not necessarily Dutch roll modes; rather, they represent the more

general rudder pulse response dynamics. For this reason, the dynamics are represented

by two complex conjugate poles as opposed to the single pair associated with most

conventional aircraft.

Table 7-2: Dutch roll modes for 0 gull-wing

Natural frequency Damping
Model 0.6276 Hz 0.3993
Mode2 0.7584 Hz 0.2359










015





01

E
-005

-01

-0042 -004 -0038 -0036 -0034 -0032 -003 -0028 -0026 -0024 -0022
Real axis

Figure 7-14: Open-loop Dutch roll mode pole migration for two morphing positions

Table 7-3: Dutch roll modes for 15 gull-wing

Natural frequency Damping
Model 0.5220 Hz 0.2847
Mode2 0.7879 Hz 0.2522


The eigenvectors associated with each morphing system are shown in Tables 7-4

and 7-5 for gull-wing cases 0 and 15, respectively. The 15 case shows that the

morphing causes increased coupling between the states, in addition to introducing

considerable phase changes. Such changes are apparent by examining the rudder

control pulse data from Figures 7-12 and 7-13, where the coupling of the rudder input

to roll rate and yaw rate changes with morphing.

Table 7-4: Dutch roll mode eigenvectors for 0 gull-wing

State Magnitude Phase (deg)
Model
xl 0.4769 74.45880
x2 0.7309 0
x3 0.0753 101.32120
x4 0.4824 96.72500
Mode2
xl 0.0323 71.48680
x2 0.4240 78.88850
x3 0.4948 83.01430
x4 0.7575 180.0000









Table 7-5: Dutch roll mode eigenvectors for 15 gull-wing

State Magnitude Phase (deg)
Model
xl 0.4525 67.85500
x2 0.3209 146.27720
x3 0.7064 180.0000
x4 0.4396 -96.05380
Mode2
xl 0.3758 -84.81000
x2 0.5526 50.44140
x3 0.4516 -83.71540
x4 0.5912 0.000000


Figure 7-15 shows bode plots for the two morphing systems. The top two plots

depict the magnitude and phase response from rudder input to roll rate while the

bottom two plots show the responses from rudder input to yaw rate. The most notable

change between the two occurs in the magnitude of the roll rate response. For the 150

case, the peak response has a larger amplitude and occurs at a lower frequency than

the neutral case. This result is in agreement with the eigenvalues, which show a lower

natural frequency for the 150 morphing position.















Figure 7-15: Frequency response diagram for 00 gull-wing (:) and 150 gull-wing (-)


7.5 Longitudinal Dynamics

Longitudinal system identification is performed on elevator pulse data to determine

the short period pitch mode and the Phugoid mode. Two morphing conditions are









considered for this analysis, 0 gull-wing and 15 gull-wing. A transfer function

is computed between the elevator deflection and pitch rate response data using an

output-error model. Tables 7-6 and 7-7 shows the results of the modeling in terms

of the frequency and damping of the longitudinal modes. For each of the longitudinal

dynamic models, the system identification process also predicted a negative real pole

near zero.

Table 7-6: Longitudinal modes for 0 gull-wing

Natural frequency Damping
Phugoid Mode 0.2945 Hz 0.5422
Short Period Mode 19.75 Hz 0.0303


Table 7-7: Longitudinal modes for 15 gull-wing

Natural frequency Damping
Phugoid Mode 0.6131 Hz 0.3912
Short Period Mode 19.95 Hz 0.1445


The system poles show a distinct change in the longitudinal dynamics during

morphing. Specifically, the short period damping ratio has increased dramatically. The

natural frequency of the mode is predicted to remain constant over the 150 change

in gull-wing angle. For the Phugoid Mode, the simulation predicted an increase in

the natural frequency with a corresponding decrease in the damping. These results,

especially in the short period mode, are in agreement with pilot feedback. Pitch control

during high gull-wing morphing is highly damped and responds sluggishly to elevator

deflection. However, the limited data set precludes rigorous evaluation of the predicted

models. Additionally, the noise in the data during the elevator pulse sequence flight

test seemed higher in magnitude than noise in other data sets. The noise level creates

difficulties in differentiating physical dynamics with sensor noise or vibration.

Figure 7-16 shows simulated pitch rate response to an elevator pulse sequence

plotted against measured pitch rate. The pulse is performed with a gull-wing angle










of 0. The simulated response is in good agreement with the general trends of

the measured response, although has a poor fit of the high frequency content. As

a result, the predicted models are useful only as basic descriptions of the actual

dynamics. Figure 7-17 shows the measured and simulated responses for a 15

gull-wing configuration. Again, the simulation model exhibits discrepancies with

the measured data at high frequency oscillations. The data from the elevator pulse

sequences is plotted against simulation time steps, with each step equal to 1/100th of a

second.


-400 1 '- '-j -100--
1100 1150 1 00 1250 1300 1350 1400 1450 1500 1100 1150 1200 1250 1300 1350 1400 1450 1500
Time (steps) Time (steps)

Figure 7-16: Elevator pulse command (left), measured (:) and simulated( -) pitch rate
responses (right)


Time (steps) Time (steps)

Figure 7-17: 15 gull-wing elevator pulse command (left), measured (:) and simulated(
-) pitch rate responses (right)















CHAPTER 8
FOLDING WING AND TAIL MORPHING

8.1 Aircraft Design

A quasi-static morphing has also been implemented on a tandem-wing micro air

vehicle, Figure 8-1, to allow the aircraft to achieve two distinct mission requirements

in a single flight. The aircraft is designed to achieve stable, controllable forward flight

for climb, cruise, and loiter phases, then transition to reverse flight for a slow, vertical

descent. A single control actuator is used to sweep both front and aft wings forward, in

addition to collapsing and extending vertical stabilizer surfaces. Table 8-1 summarizes

the important properties of the aircraft.













Figure 8-1: Top view of unswept (left) and swept (right) configurations


8.2 Morphing Mechanism

The aircraft incorporates a dual-wing sweep angle morphing to change the location

of the aircraft center. The wings are designed to sweep far enough forward such

that the neutral point becomes forward of the center of gravity. In this configuration

(Figure 8-2), forward flight is destabilized and reverse flight is stabilized.

In order to improve reverse flight stability, the wing sweep incorporates a collaps-

ing vertical stabilizer on the aft wing and an expanding stabilizer on the forward wing.









Table 8-1: Properties of the folding wing-tail aircraft in two configurations

Property Folding Wing-Tail (Airigami)
Wing Span 12 in
Wing Area (unswept) 60 in2
Wing Area (swept) 65 in2
Vertical Stab Area (unswept) 7.61 in2
Vertical Stab Area (swept) 3.44 in2
Wing Loading (unswept) 11.02 oz/ft2
Powerplant DC motor 4 in prop
Total Weight 4.59 oz


Each stabilizer is initially built into the wing structure and allowed to fold along nylon

hinges.

















Figure 8-2: Side view of unswept (top) and swept (bottom) configurations


Reverse flight is achieved only in descents with a near vertical flightpath. As such,

the thrust from the propeller serves as both a drag producer and as a stabilizing device.

The primary purpose of the wings and vertical stabilizer during this descent profile is

to prevent the vehicle from diverging from the vertical attitude. In this orientation, the

thrust serves to directly counteract the weight of the aircraft and slow the sink rate.

The current powerplant uses a DC electric motor with a 4:1 gear reduction to turn a

4 in plastic prop. The thrust to weight ratio of the aircraft is slightly less than one,

allowing for a substantial reduction in the sink rate at full throttle. Alternative motor









options may be used to increase thrust to weight ratio to greater than one. In such a

case, the thrust could be used to achieve a zero sink rate and hover the aircraft during

the descent phase. Although the aircraft is designed primarily for vertical reverse

flights, other descent modes such as a controlled flat spin or high-alpha, oscillatory

falling leaf mode may be possible with the sweep morphing.

8.3 Flight Trials

Basic flight trials have been conducted with the folding wing-tail vehicle to

determine the feasibility of the design for enhanced vehicle agility. Although the

objectives of fully-stabilized reverse flight descents were not met, the vehicle concept

shows promise with additional development.

The vehicle exhibits good handling and control characteristics in the tandem-

wing forward flight mode. The hinged elevons on the aft wing are used collectively

to command pitch rate and differentially to command roll rate. Pitch and roll rate

responses to elevon deflection is sufficient to control the vehicle in climbs, turns, dives,

and level flight.

The vehicle is considerably easier to control using the hinged control surfaces on

the aft wing than using the wing twisting on the fore wing. The exact reason for this

disparity in control is unclear, as different combinations of effector-wing placement

were not conducted.

Figure 8-3 shows the dynamic pitch up maneuver is used to transition the

vehicle from conventional forward flight to reverse flight. This maneuver involves

achieving cruise airspeed in level flight, then increasing the pitch angle and flight

path to near 90 vertical. The folding wing-tail morphing is then actuated to shift the

aerodynamic center and center of lateral area forward. Flight trials of this maneuver

have resulted in only short periods of reverse flight before the vehicle diverges into a

flat spin. Stabilizing the aircraft in reverse flight requires additional thrust in addition

to increased sweep angle.











































Figure 8-3: Envisioned dynamic pitch up maneuver for forward to reverse flight transi-
tion















CHAPTER 9
SUMMARY

9.1 Recommendations

Flight tests of the morphing vehicles shows that shape change actuators have a

considerable effect on the vehicle flight dynamics. This is certainly not an unexpected

result, given that vehicle dynamics are directly dependent upon geometry and con-

figuration. The tests showed that both dynamic and quasi-static morphing strategies

can have a highly desirable impact on both the flight performance and the control

effectiveness. However, the quantification of these changes is somewhat arbitrary, con-

sidering that no comparisons were made to established handling quality or performance

metrics. An important part of the future research will be to contextualize the benefits

of the morphing for a vehicle in a realistic mission scenario. Doing so will ultimately

determine the benefit of morphing and will also help identify the practical effects of the

changes to the vehicle dynamics.

The models identified from the flight data are quite limited in usefulness. The

simple models show interesting effects of the morphing, but still do not address the

more important problem of maneuvers and actuations beyond simple perturbations.

For a more generalized morphing actuation, the effects of inertial and aerodynamic

asymmetries will introduce considerable coupling and nonlinearity that can only be

modeled using a much more complex approach. The development of such an approach

is currently underway.

Higher fidelity modeling approaches become increasingly important for stabi-

lization and control. A better understanding of the actual dynamics will help develop

appropriate control theory for morphing vehicles. Whether conventional linearized

controllers are appropriate for morphing or not will be seen. Perhaps a better approach









is to design the controller with implicit knowledge of the morphing effect. These issues

are being addressed from a theoretical and computational standpoint. Once satisfactory

results are obtained from this effort, the focus will transition to implementing these

controllers on flight vehicles and experimentally validating controller designs.

9.2 Conclusions

Simple strategies for morphing on small vehicles have been demonstrated in flight.

These strategies, although not optimal, have improved the performance of the vehicles

in many cases and increased the size of the flight envelope through shape changes.

The morphing has been used to demonstrate high-agility and aggressive maneuvering.

Small sensors were used to record the vehicle responses during a variety of flight test

conditions. Models of the vehicle generated from the flight data indicate that linear,

symmetric assumptions are reasonably accurate in representing the dynamics for small

morphing commands. Vehicle dynamics observed during large morphing commands,

however, were highly non-linear.

The quasi-static morphing demonstrated on the variable gull-wing aircraft suf-

ficiently changed the flight performance to allow the vehicle to operate in several

different modes. Such performance changes are critically important to the realization

of morphing in commercial and military flight systems. The vehicle was also used to

demonstrate the extent of the change in dynamics and handling qualities that occurs

as a result of the geometric change. The change in dynamics illustrates the need for

flight controllers that adapt or change with morphing condition. Such controllers are

currently under development using the results of the flight testing, in addition to wind

tunnel and theoretical modeling approaches.















REFERENCES


[1] M. Abdulrahim "Flight Performance Characteristics of a Biologically-Inspired
Morphing Aircraft" Presentation at 54th AIAA Regional Student Conference,
Memphis, TN, April 2004.

[2] M. Amprikidis and J.E. Cooper, "Development of Smart Spars for Active
Aeroelastic Structures," AIAA-2003-1799, 2003.

[3] J. Blondeau, J. Richeson and D.J. Pines, "Design, Development and Testing of a
Morphing Aspect Ratio Wing using an Inflatable Telescopic Spar," AIAA-2003-
1718.

[4] J. Bowman, B. Sanders and T. Weisshar, "Evaluating the Impact of Morphing
Technologies on Aircraft Performance," AIAA-2002-1631, 2002.

[5] M.J. Brenner, Aeroservoelastic Modeling and Validation of a Thrust-Vectoring
F/A-18 Aircraft, NASA-TP-3647, September 1996.

[6] D. Cadogan, T. Smith, R. Lee and S. Scarborough, "Inflatable and Rigidizable
Wing Components for Unmanned Aerial Vehicles," AIAA-2003-1801, 2003.

[7] B.D. Caldwell, "FCS Design for Structural Coupling Stability," The Aeronautical
Journal, December 1996, pp. 507-519.

[8] C.E.S. Cesnik and E.L. Brown, "Active Warping Control of a Joined-Wing
Airplane Configuration," AIAA-2003-1716, 2003.

[9] J.B. Davidson, P. Chwalowski, and B.S. Lazos, "Flight Dynamic Simulation As-
sessment of a Morphable Hyper-Elliptic Cambered Span Winged Configuration,"
AIAA-2003-5301, August 2003.

[10] M. Drela and H. Youngren XFOIL 6.94 User Guide MIT Aero & Astro, Aero-
craft, Inc. http://raphael.mit.edu/xfoil/, Dec 2001

[11] B. Etkin Dynamics of Flight Stability and Control 2nd Edition John Wiley &
Sons, New York, 1982.

[12] S.M. Ettinger, M.C. Nechyba, P.G. Ifju, and M.R. Waszak, "Vision-Guided
Flight Stability and Control for Micro Air Vehicles," Proceedings of the IEEE
International Conference on Intelligent Robots and Systems, October 2002,
pp. 2134-2140, IEEE, Lausanne, Switzerland.









[13] G.A. Fleming, S.M. Bartram, M.R. Waszak, and L.N. Jenkins, "Projection Moire
Interferometry Measurements of Micro Air Vehicle Wings," Proceedings of the
SPIE International Symposium on Optical Science and Technology, Paper 448-16,
August 2001.

[14] H. Garcia, M. Abdulrahim, and R. Lind, "Roll Control for a Micro Air Vehicle
using Active Wing Morphing," AIAA-2003-5347, August 2003.

[15] J.M. Grasmeyer and M.T. Keennon, "Development of the Black Widow Micro Air
Vehicle," AIAA-2001-0127, 2001.

[16] I.M. Gregory, "Dynamic Inversion to Control Large Flexible Transport Aircraft,"
AIAA-98-4323, 1998.

[17] P.G. Ifju, S. Ettinger, D.A. Jenkins and L. Martinez, "Composite Materials for
Micro Air Vehicles" Presentation at Society for Advancement of Materials and
Process Engineering Annual Conference, Long Beach, CA, May 2001.

[18] P.G. Ifju, D.A. Jenkins, S.M. Ettinger, Y. Lian, W. Shyy, and M.R. Waszak,
"Flexible-Wing Based Micro Air Vehicles," AIAA-2002-0705, January 2002.

[19] K.W. Iliff, "Aircraft Parameter Estimation," NASA-TM-88281, 1987.

[20] C.O. Johnston, D.A. Neal, L.D. Wiggins, H.H. Robertshaw, W.H. Mason and
D.J. Inman, "A Model to Compare the Flight Control Energy Requirements of
Morphing and Conventionally Actuated Wings," AIAA-2003-1716, 2003.

[21] S.M. Joshi and A.G. Kelkar, "Inner Loop Control of Supersonic Aircraft in
the Presence of Aeroelastic Modes," IEEE Transactions on Control Systems
Technology, Vol. 6, No. 6, November 1998, pp. 730-739.

[22] Y. Lian and W. Shyy, "Three-Dimensional Fluid-Structure Interactions of a
Membrane Wing for Micro Air Vehicle Applications," AIAA-2003-1726, April
2003.

[23] E. Livne, "Integrated Aeroservoelastic Optimization: Status and Direction,"
Journal of Aircraft, Vol. 36, No. 1, January-February 1999, pp. 122-145.

[24] L. Ljung, System Lh ,lifi,. aiin. Prentice Hall, Englewood Cliffs, NJ, 1987.

[25] P. de Marmier and N. Wereley, "Morphing Wings of a Small Scale UAV Using
Inflatable Actuators for Sweep Control," AIAA-2003-1802.

[26] R.C. Nelson Flight Stability and Automatic Control McGraw Hill, Boston, MA,
1998.

[27] E.W. Pendleton, D. Bessette, P.B. Field, G.D. Miller, and K.E. Griffin, "Active
Aeroelastic Wing Flight Research Program: Technical Program and Model
Analytical Development," Journal of Aircraft, Vol. 37, No. 4, 2000, pp. 554-561.









[28] W.F. Phillips Mechanics of Flight John Wiley & Sons, Hoboken, NJ, 2004.

[29] B. Sanders, F.E. Eastep and E. Forster, "Aerodynamic and Aeroelastic Characteris-
tics of Wings with Conformal Control Surfaces for Morphing Aircraft," Journal of
Aircraft, Vol. 40, No. 1, January-February 2003, pp. 94-99.

[30] L.V. Schmidt Introduction to Aircraft Flight Dynamics American Institute of
Aeronautics and Astronautics, Inc., Reston, VA, 1998.

[31] M.J. Solter, L.G. Horta, and A.D. Panetta, "A Study of a Prototype Actuator
Concept for Membrane Boundary Control," AIAA-2003-1736, April 2003.

[32] R.W. Stone, and B.E. Hultz, Summary of Spin and Recovery Characteristics of 12
Models of Flying-Wing and Unconventional-Type Airplanes, NACA-RM-L50L29,
March 1951.

[33] H. Tennekes The Simple Science of Flight: From Insects to Jumbo Jets The MIT
Press, Cambridge, MA, 1997.

[34] S. Tung, and S. Witherspoon, "EAP Actuators for Controlling Space Inflatable
Structures," AIAA-2003-1741, April 2003.

[35] D. Viieru, Y. Lian, W. Shyy and P. Ifju, "Investigation of Tip Vortex on Aerody-
namic Performance of a Micro Air Vehicle," AIAA-2003-3597, 2003.

[36] M.R. Waszak, J.B. Davidson, and P.G. Ifju, "Simulation and Flight Control of an
Aeroelastic Fixed Wing Micro Air Vehicle," AIAA-2002-4875, August 2002.

[37] M.R. Waszak, L.N. Jenkins, and P.G. Ifju, "Stability and Control Properties of an
Aeroelastic Fixed Wing Micro Air Vehicle," AIAA-2001-4005, August 2001.

[38] R.W. Wlezien, G.C. Homer, A.R. McGowan, S.L. Padula, M.A. Scott, R.J. Silcox,
and J.O. Simpson, "The Aircraft Morphing Program," AIAA-98-1927, April 1998.















BIOGRAPHICAL SKETCH

Like most people, Mujahid Abdulrahim was born. His childhood teemed with

the many adventures typically associated with adolescent life, including placing metal

objects into electrical sockets and making inappropriate faces at the monkeys in the

zoo. Luckily, he soon outgrew such shenanigans and began focusing on his career.

Professional hopes of being an inventor, repairshop owner, electrical engineer, and

aerial photographer soon gave way to his one true passion aeronautical engineering.

Mujahid firmly decided his life's path by consulting a poster in his 8th grade algebra

class. This poster listed many professions and the types of math required on the job.

The only profession that had checkmarks from basic algebra all the way up to string

theory was aeronautical engineering and so a dream was born.

Mujahid has been active in various academic and competitive pursuits over his

6-year career at the University of Florida. These include the International Micro

Air Vehicle Competition, AIAA Regional/National Student Conferences, research

paper competitions, mountain bike racing, SCCA autocross racing, IMAC R/C scale

aerobatics, R/C Funfly competitions, R/C on-road racing, and of course lab chewing

gum Olympics.

Mujahid's primary research interest is in morphing aircraft design and flight

vehicle dynamics. He has pursued a variety of novel approaches to morphing and flight

control throughout his master's research. The work follows his extracurricular interest

in racing and maximum performance vehicle control.

Mujahid's life started in the Calgary Women's Hospital in room A32 on the third

floor. His travels have taken him quite far away from that hospital bed, all the way to







69

remote villages in Syria to visit his relatives and show them how to perform donuts on

a motorbike.

Life has been good.