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Turn Performance and Flight Dynamics of a Pterosaur and a Pterosaur-Inspired Variable-Placement Vertical Tail Aircraft

Permanent Link: http://ufdc.ufl.edu/UFE0024421/00001

Material Information

Title: Turn Performance and Flight Dynamics of a Pterosaur and a Pterosaur-Inspired Variable-Placement Vertical Tail Aircraft
Physical Description: 1 online resource (99 p.)
Language: english
Creator: Roberts, Brian
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: dynamics, flight, mav, performance, pterosaur, radius, tail, turn, uav, vertical
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Mission performance for small aircraft is often dependent on turn radius. Various biologically-inspired concepts have demonstrated that performance can be improved by morphing the wings in a manner similar to birds and bats; however, morphing of the vertical tail has received less attention because neither birds nor bats have an appreciable vertical tail. In contrast, pterosaurs have a large vertical crest on their heads that could have improved their flight performance to assist in tasks necessary for survival. This thesis investigates the flight dynamics of a pterosaur and analyzes the aerodynamic and weight effects of a pterosaur's head on performance. Additionally, aerodynamic interactions between the crest and a pterosaur's wing-sweep morphing capabilities are analyzed. The thesis uses these results to design an aircraft model that incorporates a morphing of the vertical tail based on the cranial crest of a pterosaur. The flight dynamics of the aircraft model demonstrate a reduction in turn radius of 13% when placing the tail over the nose in comparison to a traditional aft-placed vertical tail.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Brian Roberts.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Lind, Richard C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024421:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024421/00001

Material Information

Title: Turn Performance and Flight Dynamics of a Pterosaur and a Pterosaur-Inspired Variable-Placement Vertical Tail Aircraft
Physical Description: 1 online resource (99 p.)
Language: english
Creator: Roberts, Brian
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: dynamics, flight, mav, performance, pterosaur, radius, tail, turn, uav, vertical
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Mission performance for small aircraft is often dependent on turn radius. Various biologically-inspired concepts have demonstrated that performance can be improved by morphing the wings in a manner similar to birds and bats; however, morphing of the vertical tail has received less attention because neither birds nor bats have an appreciable vertical tail. In contrast, pterosaurs have a large vertical crest on their heads that could have improved their flight performance to assist in tasks necessary for survival. This thesis investigates the flight dynamics of a pterosaur and analyzes the aerodynamic and weight effects of a pterosaur's head on performance. Additionally, aerodynamic interactions between the crest and a pterosaur's wing-sweep morphing capabilities are analyzed. The thesis uses these results to design an aircraft model that incorporates a morphing of the vertical tail based on the cranial crest of a pterosaur. The flight dynamics of the aircraft model demonstrate a reduction in turn radius of 13% when placing the tail over the nose in comparison to a traditional aft-placed vertical tail.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Brian Roberts.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Lind, Richard C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024421:00001


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ThankstoDr.Lindforputtingmeonthisout-of-the-ordinaryandyetfullyengagingprojectandforhelpingmealongtheway.AveryappreciativethankstoDr.SankarChatterjeeforallofhispaleontologicalinsight.IwanttothankallofmylabmatesandclassmatesforanyadviceandideasIreceivedthroughcontactwiththem.IespeciallywanttothankDanielGrantforgettingmestartedonAVLandforallofhisassistancealongtheway. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 12 CHAPTER 1Introduction ...................................... 13 1.1Motivation .................................... 13 1.2ProblemStatement ............................... 16 1.3Contribution ................................... 17 2Background ...................................... 19 2.1AxisandMomentDenitions ......................... 19 2.2AircraftControlEectors ........................... 20 2.3AircraftEquationsofMotion ......................... 21 2.4StaticStability ................................. 23 2.5RotationDamping ............................... 24 2.6ControlEectiveness .............................. 25 2.7FlightPerformanceEquations ......................... 26 2.8AerodynamicsPrediction ............................ 28 2.9TurnPerformanceEvaluation ......................... 29 2.10EigenvectorAnalysis .............................. 30 3BiologicalInspiration ................................. 31 3.1History ...................................... 31 3.2PterosaurAnatomyasaModelforAircraftDesign ............. 31 3.3CranialCrest .................................. 34 3.4ChosenSpecies ................................. 35 4PterosaurFlightAnalysis .............................. 36 4.1PterosaurModel ................................ 36 4.1.1AerodynamicGeometry ......................... 37 4.1.2MassesandInertias ........................... 39 4.1.3WingControlEectors ......................... 40 4.1.4Morphing ................................ 40 4.1.5CranialMovement ............................ 44 4.1.6ModelSummary ............................. 44 4.2SteadyLevelFlightAnalysis .......................... 44 5

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............................. 44 4.2.2SymmetricSweepResults ........................ 46 4.2.2.1TrimmedFlightConditions ................. 46 4.2.2.2StaticStability ........................ 48 4.2.2.3RotationDamping ...................... 49 4.2.2.4ControlEectiveness ..................... 49 4.2.2.5RateofDivergence ...................... 51 4.2.3HeadFreeAsymmetricSweepResults ................. 54 4.2.3.1TrimmedFlightConditions ................. 54 4.2.3.2StaticStability ........................ 56 4.2.3.3ControlEectiveness ..................... 57 4.2.3.4RateofDivergence ...................... 58 4.2.4HeadFixedAsymmetricSweepResults ................ 61 4.2.4.1TrimmedFlightConditions ................. 61 4.2.4.2StaticStability ........................ 62 4.2.4.3ControlEectiveness ..................... 64 4.2.4.4RateofDivergence ...................... 64 4.3BankedTurningFlightAnalysis ........................ 67 4.3.1RunConditionsandAnalysisMethods ................ 67 4.3.2PerformanceEects ........................... 67 4.3.3TrimmedFlightConditions ....................... 70 5AicraftModelAnalysis ................................ 72 5.1AircraftModel ................................. 72 5.1.1AerodynamicGeometry ......................... 72 5.1.2MassesandInertias ........................... 73 5.1.3ControlEectors ............................ 74 5.1.4Adaptive-ConguringVerticalTail ................... 74 5.2SteadyLevelFlightAnalysis .......................... 76 5.2.1RunConditions ............................. 76 5.2.2TrimmedFlightConditions ....................... 76 5.2.3StaticStability ............................. 76 5.2.4RotationDamping ............................ 79 5.2.5ControlEectiveness .......................... 80 5.3BankedTurningFlight ............................. 83 5.3.1RunConditions ............................. 83 5.3.2PerformanceImprovements ....................... 83 5.3.3TrimmedFlightConditions ....................... 86 5.3.4StaticStability ............................. 88 5.3.5ControlEectiveness .......................... 91 6ResultsImplications ................................. 94 6.1BiologicalImplications ............................. 94 6.2AircraftImplications .............................. 95 6

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....................................... 97 BIOGRAPHICALSKETCH ................................ 99 7

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Table page 3-1PropertiesofFlightPlatforms ............................ 33 4-1MassesandInertiasofModeledPartsofTapejara 39 4-2JointRangeofMotion ................................ 42 4-3EigenvectorofNominalCongurationinSteadyLevelFlight ........... 53 5-1CharacteristicsoftheBaselineVehicle ....................... 73 5-2MassesandInertiasofModeledAircraftParts ................... 73 5-3TurnRadiusinmatExtremalValuesofPositionandAnglefortheVerticalTail 86 8

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Figure page 2-1DiagramofAnatomicalAxesandPlanes ...................... 19 3-1ImageofPterosaurActinobrils ........................... 33 3-2SkeletalReconstructionofanEarlyCretaceousPterosaur,Tapejarawellnhoferi 34 4-1ImageofMeasuredTapejaraSkeletalReconstruction ............... 36 4-2IsometricViewofTapejaraModelinNominalWingPosition ........... 38 4-3TopViewofTapejaraSkeletoninExtendedandFoldedWingPositions ..... 41 4-4TopViewofModelinVariousMorphedWingPositions .............. 42 4-5TopViewofTapejaraPterosaurWinginExtendedandFoldedWingPositions 43 4-6AngleofAttackandElevatorDeectioninSteadyLevelFlight .......... 46 4-7DragCoecientinSteadyLevelFlight ....................... 47 4-8DragandLift-to-DragRatioinSteadyLevelFlight ................ 47 4-9YawandRollStabilityinSteadyLevelFlight ................... 48 4-10LiftSlopeandPitchStabilityinSteadyLevelFlight ............... 49 4-11RollandYawDampinginSteadyLevelFlight ................... 50 4-12YawEectivenessofAileronsandRudderinSteadyLevelFlight ......... 50 4-13RollEectivenessofAileronsandRudderinSteadyLevelFlight ......... 51 4-14EectivenessofElevatorinSteadyLevelFlight .................. 52 4-15LargestTimeConstantinSteadyLevelFlight ................... 53 4-16AngleofAttackandElevatorDeectioninSteadyLevelFlightwithHeadFreeAsymmetricMorphing ................................ 55 4-17RudderandAileronDeectioninSteadyLevelFlightwithHeadFreeAsymmetricMorphing ....................................... 55 4-18DragandDragCoecientinSteadyLevelFlightwithHeadFreeAsymmetricMorphing ....................................... 56 4-19YawandRollStabilityinSteadyLevelFlightwithHeadFreeAsymmetricMorphing 57 4-20LiftSlopeandPitchStabilityinSteadyLevelFlightwithHeadFreeAsymmetricMorphing ....................................... 57 9

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............................. 58 4-22ControlEectivenessonLateral-DirectionalStatesinSteadyLevelFlightwithHeadFreeAsymmetricMorphing .......................... 59 4-23LargestTimeConstantinSteadyLevelFlightwithHeadFreeAsymmetricMorphing 60 4-24AngleofSideslipandAileronDeectioninSteadyLevelFlightwithHeadFixedAsymmetricMorphing ................................ 61 4-25AngleofAttackandElevatorDeectioninSteadyLevelFlightwithHeadFixedAsymmetricMorphing ................................ 62 4-26DragCoecientandDraginSteadyLevelFlightwithHeadFixedAsymmetricMorphing ....................................... 63 4-27StaticStabilityinSteadyLevelFlightwithHeadFixedAsymmetricMorphing 63 4-28ControlEectivenessonLongitudinalStatesinSteadyLevelFlightwithHeadFixedAsymmetricMorphing ............................. 64 4-29ControlEectivenessonLateral-DirectionalStatesinSteadyLevelFlightwithHeadFixedAsymmetricMorphing ......................... 65 4-30LargestTimeConstantinSteadyLevelFlightwithHeadFixedAsymmetricMorphing ....................................... 66 4-31TurnRadiusImprovementsinBankedFlightwithAsymmetricMorphing .... 68 4-32VelocityandTurnRateinBankedFlightwithAsymmetricMorphing ...... 68 4-33AileronDeectionandAngleofSideslipinBankedFlightwithAsymmetricMorphing 70 4-34AngleofAttack,ElevatorDeection,andDragCoecientinBankedFlightwithAsymmetricMorphing ................................ 71 5-1BaselineVehicleinFlightConguration ...................... 72 5-2AerodynamicModel ................................. 74 5-3CongurationswithVerticalTailattheNose ................... 75 5-4SteadyLevelAngleofAttackandElevatorDeection ............... 77 5-5SteadyLevelDrag .................................. 77 5-6SteadyLevelPitchStability ............................. 78 5-7SteadyLevelRollStability .............................. 79 5-8SteadyLevelYawStability .............................. 80 10

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........................ 80 5-10ElevatorPitchMomentEectiveness ........................ 81 5-11ControlSurfaceRollMomentEectiveness ..................... 81 5-12ControlSurfaceRollMomentEectiveness ..................... 82 5-13TurningRadiusChangeswithrespecttoVerticalTailLongitudinalandVerticalPlacement ....................................... 84 5-14TurningRadiusChangeswithrespecttoVerticalTailDeectionandVerticalPlacement ....................................... 84 5-15TurningRadiusChangeswithrespecttoVerticalTailDeectionandLongitudinalPlacement ....................................... 85 5-16VelocityandTurnRateina45oBankedTurn ................... 86 5-17PowerNormalizedTurningRadiusImprovements ................. 87 5-18AngleofAttackandElevatorDeectionina45oBankedTurn .......... 87 5-19AileronDeectionandSideslipAngleina45oBankedTurn ........... 88 5-20PitchMomentCoecientwithrespecttoAngleofAttackina45oBankedTurn 89 5-21RollMomentCoecientwithrespecttoSideslipAngleina45oBankedTurn .. 90 5-22YawMomentCoecientwithrespecttoSideslipAngleina45oBankedTurn 91 5-23ElevatorControlEectivenessina45oBankedTurn ............... 92 5-24RudderControlEectivenessina45oBankedTurn ................ 92 5-25AileronControlEectivenessina45oBankedTurn ................ 93 11

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Missionperformanceforsmallaircraftisoftendependentonturnradius.Variousbiologically-inspiredconceptshavedemonstratedthatperformancecanbeimprovedbymorphingthewingsinamannersimilartobirdsandbats;however,morphingoftheverticaltailhasreceivedlessattentionbecauseneitherbirdsnorbatshaveanappreciableverticaltail.Incontrast,pterosaurshavealargeverticalcrestontheirheadsthatcouldhaveimprovedtheirightperformancetoassistintasksnecessaryforsurvival.Thisthesisinvestigatestheightdynamicsofapterosaurandanalyzestheaerodynamicandweighteectsofapterosaur'sheadonperformance.Additionally,aerodynamicinteractionsbetweenthecrestandapterosaur'swing-sweepmorphingcapabilitiesareanalyzed.Thethesisusestheseresultstodesignanaircraftmodelthatincorporatesamorphingoftheverticaltailbasedonthecranialcrestofapterosaur.Theightdynamicsoftheaircraftmodeldemonstrateareductioninturnradiusof13%whenplacingthetailoverthenoseincomparisontoatraditionalaft-placedverticaltail. 12

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PhaseI:Thevehicleiesfromalaunchsiteintoanurbanareausinghigh-altitudecruiseight.Thevehiclethendescendsrapidlybelowthebuildingrooines.Ittraversesaregionthroughimmersiveobstaclesbyagilemaneuveringuntilatargetsiteisidentied. PhaseII:Itiesaroundtheregiontoprovideaerialclose-proximitysensing.Thevehiclecirclestheareamonitoringtheregionofinterestandprocessingtheterraintondagoodplacetolandtoinvestigatethetargetmoreclosely.Onboardcomputersplanthevehicle'spathfromitslandingsitetothetargettooptimizeobstacleavoidanceandsensorcoverage PhaseIII:Thevehiclelands.Itthenwalksfromitslandingsitetothetargettogathermoreinformation.Thevehiclemayneedtostayhiddentocompleteitsmission,oritmayhavetoavoidlargeobstacles.Thephysicalorientationisshiftedtomaximizeinformationgatheringandmaintainsensorcoveragewhileremainingonthispath. PhaseIV:Thevehicletakesousingahigh-liftdesign.Itsuccessfullynavigatesitswayoutoftheurbanterrainandreturnstobase. Anumberofchallengesareelucidatedinthismissionscenario.Theindividualsegmentshaveuniquefeaturesthatmustbeconsidered;however,thecombinationofallsegmentsintothetotalmissiondrasticallyincreasestheaspectsforwhichthedesignmustaccount. 13

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Someoftheserequirementshavealreadybeensatised,whileothersarestilllacking. 14

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Roboticshasadvancedtothepointthatbuildingvehiclesthatarecapableofbothyingandwalkingisapossibility,butthetransitionswillprovetobethemostdicultpart.Thetaskofyingandthenwalkingcanbeaccomplishedinaverylimitedsenseusingcurrenttechnology;however,thereturntoighthasnotyetmatured. EortstomakeMAV'smoremissioncapablehavemadesomegains.Robustdesignmethodsandmaterialscontinuetondnewwaystomakesophisticatedsystemsmorereliableintheeld.Computerscienceisstilltryingtomakeuserinterfacesmoreintuitivetomakeyingvehiclesaccessibletoawiderrangeofusers.Multi-touchscreentechnologyrepresentsalargestepforwardinmakingtheupperlevelcontrolofvehiclesinstinctive.However,eventhoughMAV'shavebeenownforyearsasdemonstrationtools,theyhavenotyetbeenprovenmissioncapable. Mostimportanttothisthesisisthelackofvehiclecapabilityforurbannavigation.Morethananyotherreason,MAV'shavefailedtorealizetheirpotentialbecausetheyhavenotattainedthecombinationofhigh-performancemaneuverabilitycombinedwitharobustnesswithrespecttodisturbances. Thedesigncommunityisrapidlyadoptingbiologically-inspiredconceptsasavaluableparadigmtoenhancemissioncapability.Thegeneralconceptnotesthatbiologicalsystemsareoftenabletoperformmaneuversthatcannotbeduplicatedbyengineeredsystemsbasedontraditionaldesigns;consequently,theaspectsassociatedwiththatcapabilityforbiologicalsystemscouldbeincorporatedintotheengineeredsystemstoattainsimilarcapabilities.Thechemicalprocesses,suchasenergyandreproduction,arebeingstudiedbutremainchallenging;however,theissuesofshapechangingandmassdistributionthroughmorphingareoftenrealizableusingo-the-shelftechnology. 15

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1 ).Thatprojectstudiedvariousaspectsofmorphingdesignbutfocusedprimarlyonmaterialstechnology.Avehiclewasneverrealizedthroughthisproject;however,somelessonsaboutmorphingwerefundamentaltothelatersuccessoftheActiveAeroelasticWing( 2 ).AmorphingprogramwasalsoinitiatedbyDARPAwithstrongemphasisonbiologically-inspireddesign( 3 ).Thatprogramalsoplacedprimaryfocusonmaterialsandassociatedstructuraltechnologies;however,ithasapairofcontractorsbuildingvehiclesinhopesofaightdemonstration. TheUniversityofFloridaisacknowledgedforitsadvancementintobiologically-inspireddesignthroughanextensiveightprogramofmorphingmicroairvehicles( 4 { 7 ).Theirdesignsincludearticulatedwingsthatmimictheshouldersandelbowsofbirdstovaryboththedihedralandsweep.Ineachcase,thedesignswerelimitedtoconceptsinspiredbybirdsandrestrictedtostructuralmodicationstothewings. Additionally,manystudiesintomorphingaircrafthavefocusedonthesteady-statebenetsofalteringacongurationforissuessuchasfuelconsumption( 8 ),rangeandendurance( 9 ),costandlogistics( 10 ),actuatorenergy( 11 ),maneuverability( 12 ),andairfoilrequirements( 13 ).Additionally,aeroelasticeectshavebeenoftenstudiedrelativetomaximumrollrate( 14 );( 15 );( 16 )andactuatorloads( 17 ). 18 ).Thisdesignallowstheverticaltailtobeabletomoveforward,likethepterosaur,oraft,likeatraditionalaircraft,alongthefuselagetoaecttheturnperformance.Theightdynamicsareanalyzedtonotethatmovingtheverticaltailoverthenosereducestheturnradiusby13%. 16

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Theverticaltail'sdeectionangleisanobviousplacetostarttoexaminetheroleofthiscontrolsurface.Theverticaltailisdeectedatarangeofangles,andtheresultingchangesintrimmedightconditionsandlineardynamicsareexamined. Verticaltailplacementisalsovariedtotrytondnewwaystomanipulatethecontrolsurfacetocreatethedesiredperformanceimprovements.Placementalongboththelongitudinal(fronttoback)andvertical(toptobottom)axesisinvestigated. Wingsweepmorphingisalsoincludedtoprovideanotherdimensionalitytotheresearchmatrix.Bothadditiveandreductivetrendsarenotedbetweenverticaltaildeectionandmorphingconguration. 17

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19 ).Positiverollmovestherightwingdownandtheleftwingup. 19 ).Positiveyawrotatesthenoseofthevehicletotheright. 19 ).Positivepitchrotatesthenoseofthevehicleup. Figure2-1. DiagramofAnatomicalAxesandPlanes Thesedenitionsdescribeabody-xedcoordinatesystem.Thedirectionofairowpastavehiclerarelycoincideswithoneofthebodyaxes,andthus,belongsinitsown 19

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19 ). Tworotationsarerequiredtoalignthebody'slongitudinalaxiswiththewindaxis.Therstrotationiscalledtheangleofsideslip,,andalignstheaircraft'slongitudinalaxiswiththewindaxisinthecoronalplane.Positivepointsthenosetotheleftoftheoncomingairow.Thesecondrotationisreferredtoastheangleofattack,,andalignsthelongitudinalaxiswiththewindaxisinthesagittalplane.Apositivepointsthenoseabovetheairow( 19 ). u=sin1v V(2{2) 20 ). 20 ). 20

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20 ). 20 ). 19 ). Instead,theaircraftwillbeassumedtofollowlinearizedequationsofmotionaboutasteady-statetrimcondition( 19 ). 21

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Theforcesandmomentsareassumedtobalanceatthetrimcondition,allowingtheequationstobemanipulatedtoreveallinearequationsfortheincrementalchangesinthoseforcesandmoments( 19 ). 22

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2{5 Therstcoecientindicatesiftheaircraftislongitudinallystable.Thiscoecient,Cm,isthederivativeofthepitchmomentwithrespecttochangesintheaircraft'sangleofattack.AnegativevalueforCmisstablebecauseapositiveangleofattackisnose-upandapositivepitchmomentisalsonose-up.So,anegativeCmproducesanose-downpitchingmomentwhenthenoseisdeectedupward,restoringtheaircrafttoitstrimcondition( 21 ). 23

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qSwc(2{6) Thesecondstaticstabilitycoecientyieldsthedirectionalstabilityoftheaircraft.Cnisthederivativeoftheyawmomentwithrespecttoangleofsideslip.ApositiveCnisstablebecauseapositiveangleofsideslippointsthenosetotheleft,requiringapositiveyawmoment(nose-right)torestoreitstrimcondition( 21 ). qSvb(2{7) Finally,therollstabilitycoecient,Cl,isthederivativeoftherollmomentwithrespecttotheangleofsideslip.Thisderivativemustbenegativetobestabilizing.Ifapositivesideslipanglecausestheplanetorollitsrightwingdown,thenapositivesideslipanglewillbeinduced,creatinginstability.Instead,geometryoftheaircraftneedstorolltheplane'sleftwingdown.Thiseectisproducedpartiallybytheverticaltail.Averticaltailabovethecenterofgravitywouldproduceanegativerollinthepresenceofpositivesideslip.Thewinggeometrycanalsocontributetothestabilizingeectbycreatingahigherlocalangleofattackontherightwing,hence,greaterliftonthatwing.Theliftdierentialproducesanegativerollingmoment,pointingtheleftwingdown.Astheplanerolls,thesideslipisreduced( 21 );( 19 ). qSwb(2{8) Therstistheproductionofpitchmomentbyanincrementalpitchrate,Cmq,andislargelyignoredbythisthesis.Thisderivativeisaectedpredominantlybythehorizontal 24

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21 ). Thesecondistheproductionofrollmomentbyanincrementalrollrate,Clp.Thisderivativeisaectedbythesizeandspanofwings,horizontaltail,andverticaltail.Anyincreaseinthesizeorspanofthesesurfacesincreasestherolldampingderivative( 21 ). Finally,Cnristheincreaseinyawmomentfromanincreaseinyawrate.Theverticaltail'ssizeandseparationfromthecenterofmassalongthelongitudinalaxisarethemostimportantvariablestoCnr.Anincreaseineitherofthosevariableswouldincreasetheyawdampingderivative( 21 ). ThecontroleectivenesscoecientsrelevanttothisthesisaregiveninEquations 2{12 2{18 ( 21 ). 25

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20 ). 26

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Inlevelturningight,theaircraftisbankedsothattheliftvectorprovidestheforcerequiredtoturn.Theforcesmustchangetomaintainforcebalanceintheverticaldirection( 20 ). Theresultantforceontheaircraftbecomesafunctionoftheweightofthevehicleanditsloadfactor( 20 ). W=1 cos(2{22) AccordingtoNewton'ssecondlaw,theradialaccelerationofanobjectisafunctionofitsvelocityandtheradiusofcurvatureofitspath( 20 ). So,theresultantforcemustcreatethisacceleration.Equatingtheresultantforcetotheinertialforcecreatedbythecentripetalacceleration( 20 ). 27

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gV21 Thisequationcanbesolvedforeitherturningradius,R,orangularvelocity,!,yieldingtheequationsbelow( 20 ). Notethatonlytwovariablesimpacttheturningperformanceoftheaircraft,thevelocityatwhichthevehicleistravelinganditsloadfactor.RecallfromEquation 2{22 thatloadfactorisjustafunctionofthebankangle.Thus,itisconcludedthattoimproveturnperformance,ie.reduceturnradiusandincreaseturnrate,thenitsvelocityshouldbereducedandbankangleshouldbeincreased. Avortexlatticemethodofaerodynamicspredictionrstdividestheliftingsurfacesandbodiesintosmallsurfaces.Then,bymodelingthepathofvorticesoofthemodel,thecodecalculatestheowvelocityorthogonalandparalleltoeachincrementalsurfacearea.Theowvelocitiesarethenconvertedintonormalandshearforcesonthatsectionofthebody.Finally,theforcesarecompiledtondthetotalforcesandmomentsontheentiremodel. 28

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Thephysicallimitationofthepowerplantsupplyingthrustforthevehicleischosentobethatmetric.Bytestingcasesatvaryingvelocities,theresearchuncoveredtheintersectionbetweentherequiredplantoutputinthetestcasematrixandthevehicle'slimits.However,therearetwomethodstoconstraintheoutputoftheplant:constantavailablethrustorconstantavailablepower.Thrustmustbeequaltodragattrimmedightconditions;so,thelimitsplacedonthevehicleareequivalenttoconstantrequiredthrust(equivalenttoconstantdrag)andconstantrequiredpower(equaltoaconstantproductofdragandvelocity)( 20 ). Aconstantavailablethrustmodelisastandardassumptionforjetaircraft,whereasaconstantavailablepowermodelistypicallyappliedtopropeller-poweredaircraftandbiologicalorganisms.Simplyput,ajetenginecanproducethesamethrustforceatallvelocities,whileapropellerengineoranimalcanproducegreaterforcesatlowerspeedsthanathigherspeeds( 20 ). 29

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2{27 ( 22 ). Ifthematrix,A,representsthelinearizeddynamicsofasystemaboutanequilibriumpoint,thenitseigenvaluesandeigenvectorstellagreatdealaboutthesystem'smodes.Eacheigenvalue-eigenvectorpairrepresentsthedynamicsofonemode. Theeigenvalue(alsocalledthemode'stimeconstant)tellswhetherthemodeisoscillatoryornot,andhowquicklythesystemwillconvergebacktosteady-stateconditionsordivergeawayfromsteady-stateconditions.Anegativeeigenvalueisstableandwillreturnthesystemtoitsequilibrium,whileapositiveeigenvaluewilldrivethesystemaway.Imaginaryeigenvaluesindicateoscillatorymotion. Therelativemagnitudesofthecomponentsoftheeigenvectortellhowmucheachstateisaectedbythemodeandwhetherthestatesareinoroutofphase.Largereigenvectorcomponentsindicateagreatereectonthatstate. 30

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18 ). Pterosaurssucceededinagreatvarietyofsizerangesandmodesofight.Pterosaursthrivedfor160millionyearsuntilthesuddenbiologicalcatastrophethatdrovemuchoftheglobe'sspeciestoextinction.Duringtheirtime,pterosaursevolvedintoagreatrangeofdiverseorganisms.Wingspansrangedfrom0.4mto10.4m.Similarly,bodymasses 31

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18 ). TheenvironmentthatpterosaursinhabitedforcedthemtoovercomemanyofthechallengesthatengineersfacewhentryingtodesignaMAVcapableofurbansurveillance.Manysmalltomediumsizedpterosaurslivedintheforests,sotheymusthavebeencapableofsophisticatedobstacleavoidance.Mediumtolargesizedpterosaursstayedpredominantlynearthecoast,livinglikecommondaypelicansandusingthehighwindstogainsucientlift:so,thesepterosaursmusthavebeenabletomaintainstabilityinwindyconditions( 18 ). PterosauranatomyisuniquelyunlikethatofbatsandbirdsandremarkablysimilartothestructurecommonlyusedinmodernMAV's.Pterosaursusedaleadingedgespartosupportamembranethatservesastheliftingsurface.Thismembranewasalsostienedbyadenselyspacedsetofberscalledactinobrils.ThesebersactedmuchlikethecarbonberusedtosupporttheliftingmembraneonMAV's,transportingthestressestotheleadingedgespar,preventingextremeairfoilshapechange,andreducingthelikelihoodofcatastrophicdamagetothewingmembrane( 18 ). AfurthercomparisonbetweenbiologicalandmechanicalightsystemsisshownbelowtodemonstratetheaptitudeformodelingasmallMAVdesignonpterosaurs. 32

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ImageofPterosaurActinobrils platform wingsurfacemuscleactuationappingmotionverticaltailwingextendersstructuralelements insect rigidlowhighnonochord-spanbird featherhighhighnofeathersspanbat membranehighhighnojointschord-spanpterosaur membranelowlowyesjointsspanMAV membranelowlowyesjointsspan Table3-1. PropertiesofFlightPlatforms Pterosaursareofparticularinterestduetotheabilitytobothwalkonthegroundandsailoverwaterinadditiontoight.Suchmulti-modallocomotionenablesanincalculablerangeofmissions.Anaircraftbasedonpterosaurconceptsmaybeabletoytoarooftopthenwalkunderanoverhangtomountasensorinadarkcorner.Additionally,theirquadrupedalgaitismuchsimplertomanufactureandcontrolthanthebipedalgaitthatbirdsandbatscommonlyemploy. So,pterosaurshaveaproventrackrecordofaerodynamicsuccessandduetotheiranatomyandmethodsoflocomotion,serveasasensiblemodelaroundwhichtobaseamulti-locomotivesensorysystemcapableofnavigatingdenseobstacleeldsandecientlysensingtheirenvironment. 33

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Figure3-2. SkeletalReconstructionofanEarlyCretaceousPterosaur,Tapejarawellnhoferi 34

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7 );( 5 ).Tapejarahadawingspanof1.35metersandhadseveraljointsalongitswingthatpermittedrotationinthecoronalplane( 18 ).TheresultofjointrotationsalongTapejara'swingisaleadingedgewingsweepchangeatdiscretelocationsalongthespanwiseaxis,whichisexactlytheeectproducedbypreviousresearchbyGrant( 7 ).Thissimilarityallowedtheresearcherstoexaminetheinteractionbetweentheforwardplacedverticaltailandwingsweepmorphing. Thisparticularspeciesalsohadanunusuallylargecrest,makingtheaerodynamiceectsduetothepresenceofthatsurfacemoredominantandeasiertoidentify.Additionally,anearlycompleteandthree-dimensionalskeletonofTapejarawasfoundintheSantanaFormationinBrazilwithasofttissuecrestonthehead.Thisuniquediscoveryincreasestheknowledgebaseofthebiologicalsystemsothatthedynamicsandpotentialmovementscanbemodeledwithgreaterdelity. 35

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Figure4-1. ImageofMeasuredTapejaraSkeletalReconstruction 36

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18 ).Theheadisalsomodeledusingthegeometryofaskeletalcastby16setsofcoordinates,spacedevenlyalongtheverticaldirection.ThesepartsofTapejaraaremodeledasinnitelythinliftingsurfaces,whichisjustiablebecauseofthenatureofthemembranestructureofthepterosaur'swing. TheotherpartsofTapejaraaremodeledascylindricalbodies.So,theneckisdenedasaconstantdiametercylinderextendingfromthefrontofthetorsointothemiddleoftheheadtoincludetheeectsofthethicknessoftheheadthatexceedsnegligiblelimits.Thelegsaremodeledastwoseparateconstantthicknesscylindersextendingfromthehipjointonthebackofthetorso.Thehipjointislocatedusingskeletalreconstructions.Thetorsoismodeledasacylindricalbodywithbothadiameterandcenterlinethatarevariablesothatthemodelcancaptureboththelengthwisechangesinthicknessofthetorsoanditsrelativelyatdorsalsurface. Theresultinggeometricmodelisshownbelow. 37

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IsometricViewofTapejaraModelinNominalWingPosition 38

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BodyPart Mass(g)Ixx(gcm2)Iyy(gcm2)Izz(gcm2)Ixy(gcm2)Ixz(gcm2)Iyz(gcm2) Torso 200160024672467000Head 1201854243192247300172020Neck 2040260260000LeftInboardWing 2013475181861-19500RightInboardWing 201347518186119500LeftOutboardWing 102268629289611600RightOutboardWing 1022686292896-11600LeftLeg 101.251.25334000RightLeg 101.251.25334000 Table4-1. MassesandInertiasofModeledPartsofTapejara 39

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4-3 ,areanalyzedtoestimatetherangeofmovementduringterrestrialandaeriallocomotion. Theshoulderjointhadaverticalrangeofmotionof85o,usedforappingthewing,andcanbefoldedbackwardsfromafullyextendedlongitudinalpositiontowithin25oofitsanteroposterioraxis.Themodelassumesthisjointtobexedinitsfullyextendedhorizontalpositionbecausethemodelintendstoanalyzeglidingratherthanpowered 40

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TopViewofTapejaraSkeletoninExtendedandFoldedWingPositions ight,andbecausefoldingthewingtowardsthebodyattheshoulderjointcollapsestheentirewingtothebodytoassistinwalking. Theelbowjoint'snominalpositionputtheradiusandulnaofTapejara'swingata145oangletothehumerusandcouldsweepforwardtomakea90oangletothehumerus.Themodelallowstheelbowjoint30oofitsfull55orangeofmotion.Therangeofmotionisconstrainedbecausetheextremejointanglesdrasticallyreducethewingarea,makingightatsuchcongurationsunlikely. Thewristjointhadthesmallestrangeofmotionofanyofthejoints,allowingonly30oofsweepbackwardfromitsnominalposition.Thewristjointwasheldxedinthemodelbecauseithassuchasmallrangeofmotionandisclosetotheknucklejoint,whichproducesanearlyidenticaleectonalargerscale. Theknucklejointwasheldata165oangleinTapejara'snominalpositionandcouldfoldbackwardtoformanangleassmallas35o.Themodelallowsarangeofmotionofonly65obecauseoncetheknucklejointisfoldedthatclosetothebody,theoutboardwingareabecomesnegligible,sofurtherrotationatthatjointwouldhavelittleeect. Theresearchismadetractablebyxingtheshoulderandwristjointsattheirextendedpositions,andbyallowingtheknuckleandelbowjointsalimitedrangeofmotion,themodelstillallowsbothsweepintheforeandaftdirectionstocapture 41

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4-2 ,andsomeimagesofasamplingofmorphedmodelsareshowninFigure 4-4 Joint SweepDirectionTrueRangeofMotionTestedRangeofMotion Shoulder Backward55oxedElbow Forward55o30oWrist Backward30oxedKnuckle Backward130o65o JointRangeofMotion Figure4-4. TopViewofModelinVariousMorphedWingPositions Figure 4-5 showshowmorphingattheknucklejointiscomplicatedbythefactthatdeectioncausesthewingtobegintofoldintoitself,thusreducingthesurfaceareaoftheoutboardsectionofthewing.So,someoftheactinobrilsaremodeledastheyrotatewiththewing,providingcoordinatesfortherotatedleadingandtrailingedgecoordinates.Theanglesbetweentheactinobrilsareassumedtodecreaseproportionatelytotheangleofknucklerotationuntiltheycompletelyfoldtogetheratanangle10opasttheposterioraxis.Justicationfortheselimitscomesfromdiagramsoffoldedpterosaurwings( 18 ). 42

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TopViewofTapejaraPterosaurWinginExtendedandFoldedWingPositions 43

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18 ). 4.2.1RunConditions 44

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Duringthesymmetricsweepruns,theelbowandknucklejointanglesaremorphedthroughthemodel'srangeofmotionwiththeleftandrightwingsremainingidentical.Asaresult,themostdominanttrendsarechangesinthelongitudinalightconditions,withsomeaccompanyingeectsseeninthelateralandlongitudinaldynamics. Asymmetricsweepsareconductedbyexingtheleftelbowandtherightknucklethroughthesamepositionsusedinthesymmetriccongurations.Thesecombinationsofmorphingareconductedtoattempttocapturethemostextremeyawingandrollingeects,thusshowingtheconditionsthroughwhichTapejaracouldmaintainsteady,levelight. Alltestrunsaredoneatavelocityof10m/s.ThisvelocityischosenbecauseitisnearthecruisingspeedofTapejaraof8m/s( 18 ).However,AVLencountersdicultiesndingtrimconditionsforthemodelatvelocitiesbelow9m/s.Consistentwiththesteady,leveltrimmedightdenition,thebankangleandallrotationalratesandmomentsareforcedtozero.Thewingcontrolsurfacesareallowedtorotatetobalancepitchingandrollingmoments,whiletheangleofattackisconstrainedtoprovidesucientliftforthemodeltomaintainlevelight. Insomecases,theheadcontroldeectionangleisallowedtovarytomaintainaconstantsideslipangleofzero.Intheseteststheheadisessentiallyactingasaruddertobalancemomentwhilemaintainingadesiredaircraftbodycondition,soitisreferredtoasrudderangleintheplots.Inothercasestheheadcontroldeectionangleisforcedtozero,sothattheheadwillnotbepermittedbyAVLtorotatetobalancetheyawingmoment.Thesecasesarereferredtoashead-xedanalysis.Itisnecessarytoexaminethisconditionbecauseholdingtheheadxedisanimportantbiologicalconguration.Tapejaraneededtohavethefreedomtopointitsvisioninthedirectionofprey,apossiblenestingsite,oranyotherregionofinterest.Thisneedcreatedwhatisessentiallyasensorpointing 45

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4.2.2.1TrimmedFlightConditions Figure4-6. AngleofAttackandElevatorDeectioninSteadyLevelFlight However,increasingtheknucklejointanglealsodecreasesthewingareasothatanyincreasesindragcoecientareosetandtheresultingdragdecreases.So,sweepingthe 46

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DragCoecientinSteadyLevelFlight wingforwardattheelbowandbackattheknucklewouldhaveallowedTapejaratoywiththeleasttotaldrag. Figure4-8. DragandLift-to-DragRatioinSteadyLevelFlight ThisresultshowsthatTapejaralikelyusedwingmorphingtoalteritstrimightconditiontobemoreecient.Sowhenhighvelocityightisnecessary,Tapejaracouldmorphitswingsintoacongurationthatwouldproducelessdrag. 47

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Figure4-9. YawandRollStabilityinSteadyLevelFlight Thewingsarefarlesseectiveatproducingliftwhenthewingsaresweptbackwardattheknucklejoint,butimprovetheireectivenesswhentheysweepforwardattheelbowjoint.Thistrendisconsistentwithperformanceimprovementsseeninforward-sweptwingaircraft( 20 ).Thelongitudinalstaticstabilitycoecientincreaseswithelbowsweepforwardandincreaseswithsweepbackwardattheknucklejoint.So,theeectshowsconsistentlythatasthewingareaispushedfurtheraftthedistancebetweenthecenterofliftandthecenterofmassincreases,makingtheaircraftmorepitchstable. 48

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LiftSlopeandPitchStabilityinSteadyLevelFlight 49

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RollandYawDampinginSteadyLevelFlight andknucklejointsareexed,theyawmomentsbecomedominatedbytheactionsofthehead.Cnbecomesincreasinglynegativewithmorphingatbothjoints,showingthatthedestabilizingeectoftheheadinfrontofthecenterofmassisbecomingevenmoredominant. ThecontrolcoecientCnaildecreaseswithincreasingexionateachjoint,whileCnruddincreases,showingthatmorphingdecreasestheeectthatthewingshaveonyawingTapejaraandincreasestheeectthattheheadhasonyaw. Figure4-12. YawEectivenessofAileronsandRudderinSteadyLevelFlight Thistrendindicatesthatasthewingismorphed(eitherforwardattheelbowjointorbackwardattheknucklejoint)theheadbecomesamoredominantcontrolsurface, 50

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Astheknucklejointisexed,thesameeectsareseenwithrespecttorollmoments.Anincreaseinknuckleexionreducesthewingareafurthestfromtheanteroposterioraxis,thusreducingthewing'scontroloverroll.Clincreases,Claildecreases,andClruddincreasesastheknucklesweepsback.However,astheelbowjointisexed,thewing'seectonrollisincreased. Figure4-13. RollEectivenessofAileronsandRudderinSteadyLevelFlight 51

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EectivenessofElevatorinSteadyLevelFlight fromasteadylevelightpathwithoutcontrolactuation.Asthewingissweptforwardattheelbow,thelargesttimeconstantisincreasing.ThistrendindicatesthatsweepforwardattheelbowjointincreasestherateatwhichTapejaradivergesfromitstrimightcondition.Increasingsweepbackwardsattheknucklereducesthelargesttimeconstant,reducingtherateatwhichTapejaradivergesfromitstrimightcondition.Onlythecongurationswiththeknuckleexionatitslargestandelbowexionatitssmallestachievestability. AcloserexaminationoftheeigenvectorsofthesysteminTable 4-3 showsthatthelargesttimeconstantrelatestoayaw-dominatedmode.Recallthatmorphingattheknucklejointgreatlyincreasestheyawdampingcoecient,Cnr,asshowninFigure 5-15 .So,itisnotunexpectedthatknuckleexionwouldimproveTapejara'sstability. Thus,Tapejaracouldalteritsstabilityinightbymorphingitswings,givingTapejaratheperformancebenetsthataccompanyinstability,yetcapableofsoaringwithlesscontrolactuationinamorestableconguration. 52

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LargestTimeConstantinSteadyLevelFlight TimeConstant6.117 u-component0w-component0q-component0-component0v-component-0.6964p-component-0.2189r-component-0.7453-component0.0358x-component0.2091e-06y-component0.04836z-component0.4510e-07-component0.1218 Table4-3. EigenvectorofNominalCongurationinSteadyLevelFlight 53

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Asymmetricsweepdiersfromsymmetricsweepinthatitcreatesyawandrollmoments,forcingrudderandailerondeectiontoincreasetocompensate.Areductioninrightwingarearesultsinadecreaseinliftontherightwing,whichcreatesarollmomentthatrequiresailerondeection.Thereductioninrightwingareaalsocausesthedragontherightwingtodecrease;furthermore,theliftdierentialproducesanevengreaterdragdierentialduetotheinduceddrageects.Thelargedragdierentialyieldsayawmomentthatrequiresarudderdeectiontocompensate.Thus,therudderandaileronfollownearlyidenticaltrendsforthiscase. 54

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AngleofAttackandElevatorDeectioninSteadyLevelFlightwithHeadFreeAsymmetricMorphing Figure4-17. RudderandAileronDeectioninSteadyLevelFlightwithHeadFreeAsymmetricMorphing Thecontroldeectionsoftherudderandaileronscreateanevenlargerdragthanthatlostbytherightwing.Infact,therudderisbyfarthemostdominantfactorintheamountofdragcreatedascanseenbythefactthatdragincreasesalmostexactlywithincreasesinthemagnitudeofrudderdeection.Flexionattheelbowhasminimalimpactontheliftordragcreatedbytheleftwing;so,ithasminimalimpactontheheaddeection,ailerondeection,orthedragcreated.Elbowexionseemstoreducethesetrimconditionsbyaverysmallmargin. 55

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DragandDragCoecientinSteadyLevelFlightwithHeadFreeAsymmetricMorphing ThecorrelationbetweenrudderdeectionanddragshowsthattheaerodynamiceectoftheheadisextremelypowerfulandmustbeunderstoodbettertofullyexplaintheightphenomenaofTapejara.Evenasthewingareaoftherightwingisbeingreduced(whichtypicallywouldleadtoadecreaseindrag),thenecessaryrudderdeectionforcompensationiscreatingdragincreasesof30%. 4-19 andFigure 4-9 .However,intheasymmetricsweeprunsonlyonewingsweepsbackward,sotheneteectisreduced. Thelongitudinaldynamicsbehavesimilarlytothesymmetricwingsweeps,withCLdecreasingwithknuckleexionbecausethewing'saspectratioisdecreasing.Cmdecreaseswithelbowexionbecausethepitchingmomentarmbetweenthecenterofliftandthecenterofgravityisdecreasing.Theonlynoticeabledierenceisseeninthecritical 56

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YawandRollStabilityinSteadyLevelFlightwithHeadFreeAsymmetricMorphing pointalongthecurveofCmwithrespecttoknuckleangle.Thedatareachesalowpointataknuckleangleof10oforasymmetricwingsweeps,whereasitslowoccursat50oforsymmetricwingsweeps. Figure4-20. LiftSlopeandPitchStabilityinSteadyLevelFlightwithHeadFreeAsymmetricMorphing 57

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Figure4-21. ControlEectivenessonLongitudinalStatesinSteadyLevelFlightwithHeadFreeAsymmetricMorphing 58

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ControlEectivenessonLateral-DirectionalStatesinSteadyLevelFlightwithHeadFreeAsymmetricMorphing 59

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LargestTimeConstantinSteadyLevelFlightwithHeadFreeAsymmetricMorphing 60

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Figure4-24. AngleofSideslipandAileronDeectioninSteadyLevelFlightwithHeadFixedAsymmetricMorphing ThisresultdemonstratesthatTapejarahadtheabilitytoalteritstrimsideslipangleinightbyusingwingmorphingratherthanturningitshead,thusallowingitsheadtobefreetotrackobjectsofinterest. TheelevatorandangleofattackplotslooknearlyidenticaltothoseinFigure 4-16 fortheheadfreeruns.Forcingtheheadintoanonzeroangle,therebyproducinganonzero 61

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Figure4-25. AngleofAttackandElevatorDeectioninSteadyLevelFlightwithHeadFixedAsymmetricMorphing Dragremainslargelyconstantoverthevariousasymmetrictestedcongurationsduetocompetingeectsbetweensideslipangleandangleofattack.Withtheheadheldataxedangletothebody,thesideslipangledetermineshowmuchthatcontrolsurfaceisdeectedintotheoncomingairow.Theangleofattackdictateshowmuchthewingsurfaceisdeectedintotheairow.Thus,thesetwoanglesareverylargecontributorstothedragonthevehicle.Fortheseruncases,whenangleofattackisatitslowestpoint,sideslipangleisatitshighestvalueandvice-versa.Thiscombinationproducesarelativelyconstantdragoverarangeofasymmetricsweepcongurations. 4-24 isnearlyidenticaltotherudderdeectionseeninFigure 4-17 ,exceptthatitisosetby10o.ItisapparentthatthesideslipangleisrotatingTapejarasuchthattheheadisatanearlyidenticaldirectionwithrespecttotheoncomingairowasoccursinthecaseswhentheheadisallowedtorotatefreely.Thus,theonlydierencebetweentheightconditionsproducedbyhead-freeandhead-xedruncasesisa10odierencebetweentheorientationofthebodyandthehead.Adierencethissmallisnotenoughtodisturbthemodelawayfromitspreviouslyhelddynamics.For 62

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DragCoecientandDraginSteadyLevelFlightwithHeadFixedAsymmetricMorphing thisreason,theasymmetricmorphingstaticstabilityderivativesarenearlyidenticalforthehead-xedcaseasforthehead-free. Figure4-27. StaticStabilityinSteadyLevelFlightwithHeadFixedAsymmetricMorphing 63

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Figure4-28. ControlEectivenessonLongitudinalStatesinSteadyLevelFlightwithHeadFixedAsymmetricMorphing 64

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ControlEectivenessonLateral-DirectionalStatesinSteadyLevelFlightwithHeadFixedAsymmetricMorphing 65

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LargestTimeConstantinSteadyLevelFlightwithHeadFixedAsymmetricMorphing 66

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4.3.1RunConditionsandAnalysisMethods Then,theoutputdataarenormalizedtoconstantdragequalto1Newton.ThismethodisjustiedbecausetheresearchisinvestigatingglidingightofTapejara,sothelifttodragratioisthemostimportantdatum.Iftheresearchfocusedonappingight,thentheoutputdatawouldhavetobenormalizedtoTapejara'savailablepower.Turnperformancedataisthenderivedfromthevelocitythatproducesadragforceon1Newton.Thevalueof1Newtonischosenbecauseitisfoundfromtestrunsthatthemodelisbuetedbyadragforceofroughly1Newtonwhenthevelocityis10m/s. Similartrendsareseenintheturnrate,withanincreaseinturnratewithknuckleexionandforelbowexionatlargeknuckleangle.Theseperformanceimprovementsarecreatedbythedecreaseinvelocityduringtheturn. Theincreaseinturnradiuswithrespecttoknuckleexionmakessense,becausemovingtherightwingareaclosertotheanteroposterioraxisproducesarollmomentthat 67

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TurnRadiusImprovementsinBankedFlightwithAsymmetricMorphing Figure4-32. VelocityandTurnRateinBankedFlightwithAsymmetricMorphing requiresgreaterwingtwisttoholdTapejara'sbankangle.Theleftwingislargerthantherightwing,sotheincreaseddeectionproducesmoredragontheleftwing,whichyawsTapejaratotheleft.TheyawmomentcombineswiththerolltotherighttoallowTapejaratomakeatighterturn. Aforwardsweepoftheleftwingwouldseemtobenetturnperformancefromtheimprovedlifttodragseenfrompreviousanalysis.Anincreaseinliftwouldrolltheplanerightandadecreaseindragwouldyawtheplaneright,aswell.Itappearsthatthiseectisoccurringwhentherightknuckleangleislarge,butthatsomeotherunexplainedeectsmaybeoccurringwhentherightwingisclosetoitsnominalposition. 68

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69

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4-33 andFigure 4-34 supportthejusticationforperformanceimprovement.SweepbackattheknucklejointoftherightwingproducesaliftdierentialthatrollsTapejaratotheright.Negativeailerondeectioncountersthismoment,creatingmoredragintheprocess.Theliftdierentialbetweenthewingsisaccompaniedbyadragdierentialthatcreatesayawleftmoment.ThismomentreducestheneedforpositivesidesliptorotateTapejara'screstoutoftheoncomingow;thus,thesideslipangledecreases. Figure4-33. AileronDeectionandAngleofSideslipinBankedFlightwithAsymmetricMorphing Particularlynotetheincreaseinangleofattackandrudderdeectionthatoccurswhentheknuckleisfullyexed.Thereductioninwingareacreatedbymorphingattheknucklejointrequiresanincreaseinliftcoecienttosustainlevelight.Thatincreaseinliftcoecientisaccomplishedbyincreasingtheangleofattack.Anincreaseinangleofattackcreatesadirectincreaseindragandapitchingmomentthatwillrequiremoreelevatordeection,creatingevenmoredrag.TheseescalationsindragvaluesslowTapejaradown,allowingittomakequickerturns. 70

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AngleofAttack,ElevatorDeection,andDragCoecientinBankedFlightwithAsymmetricMorphing 71

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23 ).TheplanformandassociatedcomputationalmodelareshowninFigure 5-1 Figure5-1. BaselineVehicleinFlightConguration Thevehiclehasthreedistinctbodies:fuselage,afttailboom,andforetailboom.Theoriginaldesigndoesnothaveatailboominfrontofthefuselage,butitisnecessarytoaddthistothedesigntoallowverticaltailplacementinfrontofthefuselage ThespecicparametersofthevehiclearegiveninTable 5-1 72

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Wingspan:31.6inWingArea:146.5in2ReferenceChord:4.7inCenterofGravity[-0.5,0.0,-1.25]inVerticalTailArea:13.0in2VerticalTailChordLength:2.9inVerticalTailSpan:4.5inHorizontalTailArea:29.4in2HorizontalTailChordLength:3.3inHorizontalTailSpan:11.5inFuselageLength:11.6inFuselageWidth:3.8in Table5-1. CharacteristicsoftheBaselineVehicle BodyPart Mass(g)Ixx(gcm2)Iyy(gcm2)Izz(gcm2)Ixy(gcm2)Ixz(gcm2)Iyz(gcm2) Fuselage 2959039030000Battery 1303982498130-5690Motor 50113112510130-3380LeftWing 45283364289742700RightWing 452833642897-42700VerticalTail 8014581458000HorizontalTail 8721530145803240AftTailBoom 15.01351219108403830ForeTailBoom 15.01351219108403830 Table5-2. MassesandInertiasofModeledAircraftParts 73

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Figure5-2. AerodynamicModel 5-3 74

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CongurationswithVerticalTailattheNose Thepurposeofaverticaltailisacriticalelementofanyaircraftdesign.Thetraditionalplacementofaverticaltailthatpointsupischosentoprovidestaticstabilityinbothrollandyawaxes.Ataillessvehiclelacksthatstabilizingcontributionsothewingsweepisincreasedtoprovideastabilizinginuenceinrollandyaw.Ineachcase,thedesignisfocusedonstability. Thisnovelvehiclewillactuallyfocusonagilityasitsmetricfordesign.Assuch,theverticaltailwillbeplacedtoenhancemissionperformanceratherthanstaticstability.Thistradeobetweenperformanceandstabilityiscertainlywellknowninthedesigncommunitysomorphingprovidesanabilitytoalterthattradeoduringight. 75

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5.2.1RunConditions Theelevatordeectionisconstrainedtobalancethepitchmoment,theaileronsaredeectedtobalancetherollmoment,andtherudderisusedtoholdtheyawmomenttozero.Theangleofattackisconstrainedtoprovidethenecessaryliftcoecientforsteadylevelightandtheangleofsideslipisheldtozero. 76

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SteadyLevelAngleofAttackandElevatorDeection Figure5-5. SteadyLevelDrag masslongitudinally.Itmakessensethatthepositionoftheverticaltail,apredominantlylateral-directionalightcontrolsurface,wouldhavelittleimpactonlongitudinalstability;thus,theaircraftremainspitch-stableforalltestedverticaltailpositionsinboththelongitudinalandverticaldirections. ThecoecientofrollmomentwithrespecttosideslipasshowninFigure 5-7 showsamoredominantrelationwithrespecttoverticalpositionoftheverticaltail,increasingasthetailmovesdown,andaslighttrendtowardsincreasingasthetailmovesforward. 77

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SteadyLevelPitchStability HoweverClalsoshowssomepeculiarnonlinearitiesintheregionneartheorigin,indicatingthatsomecouplingorinterferenceeectsoccurwhentheverticaltailisnearthefuselage.Awayfromtheorigin,Clbecomesincreasinglystableastheverticaltailmovesup,andtoalesserextent,astheverticaltailmovesforward.Thetrendwithrespecttotheverticalpositionoftheverticaltailfollowsintuitivelyfromtherecognitionthattheverticaltail'seectonrollmomentcomesfromthesizeoftheverticaltailanditsrollingmomentarmlength,essentiallythedistancefromtheaerodynamiccenteroftheverticaltailtotheaircraft'scenterofmassalongitsverticalaxis.However,theslightcorrelationwithrespecttolongitudinalpositiondoesnotseemtohaveadirectrelationandcouldbecreatedfromsomeaerodynamicbody/surfaceinteractions.Theendresultisthattheaircraftisonlyrollstablewhentheverticaltailisplacedfaraboveandbehindtheaircraft'scenterofmassandisincreasinglyunstablewhenmoveddownandforward. ThecoecientofyawingmomentwithrespecttosideslipangleasshowninFigure 5-8 isnearlyconstantastheverticaltailismovedupanddown.However,itincreaseslinearlyastheverticaltailpositionismovedfurtheraftalongthelongitudinalaxis.Itiseasytounderstandthatastheverticaltailmovesvertically,theyawingmoment 78

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SteadyLevelRollStability willnotbeimpacted,becausetheprimaryfactorsaectingtheyawingmomentcreatedbytheverticaltailarethetail'ssize,ie.theforceinducedattheverticaltailbyasideslip,andtheverticaltail'syawingmomentarm,whichisessentiallythedistancefromtheaerodynamiccenteroftheverticaltailtotheaircraft'scenterofmassalongthelongitudinalaxis;hence,thestrongcorrelationbetweenlongitudinalpositionandCn.Theaircraftisyaw-stableforverticaltailpositionssucientlybehindtheaircraft'scenterofmassandincreasinglyunstableastheverticaltailmovesfartherforward. 79

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SteadyLevelYawStability orfaraftofthecenterofmass,thenitexperiencesmuchgreatercrosswind,andthusprovidesamuchlargerrestoringmoment. Figure5-9. SteadyLevelRollandYawDamping 5-4 .Asanycontrolsurfacedeectiondecreases,iteectivenessincreases. 80

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ElevatorPitchMomentEectiveness Theeectivenessofaileronstoaecttherollmomentoftheaircraftbarelychangesinanonlinearfashionastheverticaltailmoves.Theaileronsarethemosteectivewhentheverticaltailisfarthestforward,andleasteectivewhenthetailisfarthestaftandhighest.Therudderalsoproducesarollmoment,butcanproducerollmomentsofoppositedirection,dependingonwhethertheverticaltailisplacedaboveorbelowthecenterofmass.Thetrendisslightlynonlinear,buttheverticalplacementofthetailisthedominantfactor. Figure5-11. ControlSurfaceRollMomentEectiveness 81

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Figure5-12. ControlSurfaceRollMomentEectiveness 82

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5.3.1RunConditions Theelevatordeectionisconstrainedtobalancethepitchmomentandtheaileronsaredeectedtobalancetherollmoment.However,inturningight,themodelisalsoanalyzedatvaryingverticaltailincidenceangles.Thesevariationsareusedtondperformanceeectsfromrudderdeections.Consequently,theangleofsideslipisconstrainedtobalancetheyawmoment,resultinginnon-zerosideslipangles.Theangleofattackisstillconstrainedtoprovidethenecessaryliftcoecienttomaintainaltitude. Careistakentochangetheverticaltailincidenceangleratherthantherudderdeectiontoensurethatthecorrectdynamicsarecaptured.Ifinstead,arudderangleisspecied,theneventhoughtheaircraftcongurationmaybeidentical,theprogramwilltreatitasacontrolinputratherthanageometricchange;so,AVL'soutputdynamicswouldbeidenticaltothoseofanundeectedverticaltail. Turningradiusisconstantwithrespecttoverticalandlongitudinalplacementoftheverticaltailataconstantincidenceangle. 83

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TurningRadiusChangeswithrespecttoVerticalTailLongitudinalandVerticalPlacement Whenturnradiusisexaminedwithrespecttothedeectionandverticalplacementoftheverticaltailataconstantlongitudinalposition,adistincttrendisdiscerniblewithrespecttothedeectionoftheverticaltail,butnoneisseenwithrespecttotheverticalposition. Figure5-14. TurningRadiusChangeswithrespecttoVerticalTailDeectionandVerticalPlacement 84

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Figure5-15. TurningRadiusChangeswithrespecttoVerticalTailDeectionandLongitudinalPlacement ThevaluesofturnradiusareextractedfromFigure 5-15 atcongurationswiththelargestvaluesofpositionandanglefortheverticaltail.Thesevalues,asgiveninTable 5-3 ,clearlydemonstratethatplacingtheverticaltailoverthenosehasalowerradiusandthusgreateragilityascomparedtoplacingtheverticaltailinthetraditionallocationovertherear.Noteagainthatthecoordinatesystemusesapositivevaluetowardstherearandanegativevaluetowardsthenose. Thereductioninturnradiusiscausedbyadecreaseinthevelocitythatcreates2Newtonsofdrag.Thisdecreaseinvelocityalsoproducesanincreaseinturnrate. 85

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84.43m58.02m84.05mForwardPlacement(x=-14in) 50.40m57.65m50.31m TurnRadiusinmatExtremalValuesofPositionandAnglefortheVerticalTail Figure5-16. VelocityandTurnRateina45oBankedTurn Theseperformanceimprovementscouldbeexpectedforjetpoweredaircraftandforglidingight.However,muchofthecurrentMAVeetusepropellersandelectricmotorsforpropulsion.Toaddressthisissue,thedataanalysisisrepeatedwhilenormalizingtherequiredpowertomaintainlevelight.Figure 5-17 showsthatsimilarimprovementsoccurwhenthedataisnormalizedforconstantavailablepower. 86

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PowerNormalizedTurningRadiusImprovements Thedominanttrendseeninangleofattackistoincreaseastheverticaltaildeectionincreases.Thisincreaseinangleofattackproducesadecreaseintherequiredelevatordeectiontobalancethepitchingmoment. Figure5-18. AngleofAttackandElevatorDeectionina45oBankedTurn Ailerondeectionhasnorelationshipwiththelongitudinalplacementoftheverticaltail,butdecreaseslinearlyastheverticaltailisrotatedinthepositivedirection(trailing 87

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Simultaneously,themodelaltersitssideslipangletobalancetheyawmomentsproducedbytheverticaltail'sdeection.Asexpected,thesideslipangleroughlyfollowsthetaildeectioninmagnitudeandalternatesdirectionsdependingonwhethertheverticaltailislocatedforwardoraftofthemodel'scenterofmass. Figure5-19. AileronDeectionandSideslipAngleina45oBankedTurn ThedeectionofthecontrolsurfacesshowninFigure 5-18 andFigure 5-19 forthe45obankedturnsarereasonableandwellwithinthelimitsofexistingactuators. ThecoecientofpitchingmomentwithrespecttoangleofattackasshowninFigure 5-20 exhibitsaparabolictrendwithrespecttoverticaltaildeections,centered 88

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Figure5-20. PitchMomentCoecientwithrespecttoAngleofAttackina45oBankedTurn Thecoecientofrollingmomentwithrespecttoasideslipangle,seeninFigure 5-21 ,showsdistincttrendswithrespecttobothlongitudinalpositionanddeectionoftheverticaltail.Thisstabilityderivativeincreasesinaroughlylinearfashionastheverticaltailismovedforward,and,saveforadiscontinuityaroundsmallnegativedeectionangles,exhibitsaroughlyinverseparabolicshapewithrespecttoverticaltaildeectionangles.Theinverseparabolafromthelattertrendiscenteredaboutadeectionangleofzero;thus,producingthehigheststabilityderivativevalueforsmalltaildeectionsandthelowestvalueforlargetaildeections,whethertheyarepositiveornegative.Thetrendwithrespecttolongitudinalpositionoftheverticaltailisalsoseeninthesteadylevelightanalysis;andjustasbefore,isprobablyaneectproducedbycomplexaerodynamic 89

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Figure5-21. RollMomentCoecientwithrespecttoSideslipAngleina45oBankedTurn ThecoecientofyawingmomentwithrespecttosideslipangleasshowninFigure 5-22 isnearlyconstantwithrespecttodeectionsoftheverticaltail,butshowsalinearcorrelationwithrespecttoitslongitudinalposition.Asexplainedbefore,itmakesphysicalsensethatthisstabilityderivativewouldbehighlydependentonthelongitudinalpositionoftheverticaltail,becausethepositionimpactsthetail'smomentarmlength,andthus,themomentthatwouldbeinducedinthepresenceofanonzerosideslipangle.Similartotheevidencefromthesteadylevelightanalysis,theaircraftisyaw-stablefor 90

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Figure5-22. YawMomentCoecientwithrespecttoSideslipAngleina45oBankedTurn 5-19 .Theselargechangesinsideslipangledramaticallyaltertheowovertheelevator,therebyreducingitseect.Theeectismoredramaticwhenthetailislocatedaftofthecenterofmass,becausewhentheverticaltailisinfrontofthecenterofmass,itisalsoinfrontofthewing.Thewingexperiencestheverticaltailsidewashwhentheverticaltailisforwardofthewing;thus,reducingthelocalangleofsidesliponthewing. Therudder'seectofyawmomentislinearwithrespecttothelongitudinalpositionoftheverticaltail.Asexplainedbefore,thiscoecientishighlydependentonthelengthofthemomentarmbetweentheaerodynamiccenteroftheverticaltailandthecenterofmassoftheaircraft.Verticaltaildeectionhasnoimpactontheeectivenessoftherudderinyawmoment. 91

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ElevatorControlEectivenessina45oBankedTurn Figure5-24. RudderControlEectivenessina45oBankedTurn Theaileronslosecontroleectivenesswhentheverticaltailisdeectedatlargeangles.Theeectisevenmorepronouncedwhenthetailislocatedaftofthevehicle'scenterofmassthanwhenlocatedfartherforward.Asseenintheelevatorcontroleectiveness,thistrendistheresultofthelargechangesinsideslipangleseenin 92

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5-19 whentheverticaltailisdeected.Theselargechangesinsideslipangledramaticallyaltertheowovertheailerons,therebyreducingtheireect. Figure5-25. AileronControlEectivenessina45oBankedTurn 93

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Furthermore,pterosaurslikelyswepttheirwingsbackwardsymmetricallytoadoptacongurationthatproduceslessdrag,therebyallowinghigherspeeds,whileatthesametimeimprovingitsstability,makingiteasiertocompensatefordisturbancesintheaironthewindycoastlinesofprehistoricPangaea.Itisinterestingtonote,thatwhilethetimeconstantdecreaseswithbackwardwingsweep,theeectivenessoftherudderonyawmomentdoesnotdegrade. Pterosaursalsowouldhaveusedasymmetricwingmorphingtoenablethemtolookatatargetofinterest,whilestillmaintainingtheirdesiredightpath.Thepterosaurmodelshowstheabilitytobalanceyawmomentsusingacombinationofheaddeection,sideslipangle,andasymmetricwingsweep;thus,pterosaurhadgreaterfreedominchoosingitsdesiredlineofsight,ightdirection,andightdynamics. TheaerodynamiceectsofTapejara'scranialcrestcannotbeoverstated.Inthepresenceofasymmetricwingsweep,theheadisresponsiblefora30%increaseindrag,asshowninFigures 4-17 and 4-18 .ThecrestalsohasauniquerelationshipwiththewingsweepmorphingthatTapejaracouldmanipulate,asseenintheincreasesincontroleectivenessthroughoutallrunconditions,bothsteadylevelandturning.Tapejara'screstcouldevenbeusedinconjunctionwithwingsweepmorphingtoimproveturningradiusandturnrate. 94

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Thecharacteristicsofaturnareobviouslycriticaltoagilemaneuvering.Inparticular,asmallerradiusofturnandcorrespondinglyhigherrateofturncandirectlycorrelatetooperatingamongstdenserobstacles.Thisturnradiusisactuallyproportionaltothesquareofthevelocityandtheinverseoftheg-factorloadingasshowninEquation 2{25 Theverticaltailhasasignicanteectonturning;consequently,varyingthelocationofthattailwillvarytheturncharacteristics.Thiseectisshownbycomputingtheaerodynamicsforavehicleduringa45oturn.Theresultingdataforturnradius,showninFigure 5-15 ,showstheinuenceofbothpositionandrotationoftheverticaltail.Inthiscase,averticaltailplacedforwardofthevehicle'scenterofmassisclearlyshowntolowertheturnradiusascomparedtothetraditionalcongurationofaverticaltailplacedfarbehindthecenterofmass.Thisdataindicatesthatavehiclewithavariable-placementverticaltailcouldmaneuverinlessairspaceandthusoperateinmoreconstrainedenvironmentsthanatraditionalconguration. Thevariationsinturnradiusresultfromassociatedvariationsinbothvelocityandturnrate.TheseparametersareshowninFigure 5-16 forarangeoflocationsandanglesoftheverticaltail.Asexpected,thecongurationswithaverticaltailovertheheadandinfrontofthecenterofgravityareabletoreducethevelocityandincreasetheturnrate. AfeatureofnoteinFigure 5-15 thatcorrelateswithFigure 5-16 isthesymmetrywithrespecttoangle.Essentially,theresultsindicatethatasimilarturnradiuscanbeachievedwhetherthetailisrotatedintotheturnoroutoftheturn.Sucharesultissomewhatunexpected;however,thesymmetryarisesbyconsideringtheangleofsideslip.Abankedturnisoftenperformedwithoutanyangleofsideslipbut,asshowninFigure 5-19 ,thisvehicletrimsusinganoticeableangleofsideslip.Theuseofsideslipactuallyinducesmore 95

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Thedynamiceectsonyawrotationsarecomputedforthesecongurations.TheplotsshowninFigures 5-8 and 5-9 demonstratethederivativeofthecoecientofyawmomentwithrespecttobothyawrateandangleofsideslip.Asexpected,theplotofCnrissymmetricaboutperturbationstopositionwhiletheplotofCnissymmetricaboutperturbationstoheadangle.ThevalueofCnrdependsonthelengthofthemomentarmandthus,isindependentofforeoraftpositioning.ThevalueofCnhasastabilizingrestoringmomentaslongasthetailisaftofthecenterofgravityandisalwaysdestabilizingforanyforwardpositioning. Alsonotethattheyaweectsproducedbylongitudinalvariationsinverticaltailplacementaecttheturningperformanceoftheaircraft,buttherolleectsproducedbyverticalvariationsinthetailplacementdonot.Thisresultindicatesthatthekeytoproducingmoreagileandmissioncapableaircraftliesnotinrollingtheaircraft,thewaythatlargecommercialjetsturn,butinproducinglargeyawmomentstospinthevehicleintoitsnewdirection. 96

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[1] Wlezien,R.W.,Horner,G.C.,McGowan,A.R.,Padula,S.L.,Scott,M.A.,Silcox,R.J.andSimpson,J.O.,\TheAircraftMorphingProgram,"AIAAStructures,StructuralDynamicsandMaterialsConference,AIAAPaper98-1927,April1998. [2] Pendleton,E.W.,Bessette,D.,Field,P.B.,Miller,G.D.andGrin,K.E.,\ActiveAeroelasticWingFlightResearchProgram:TechnicalProgramandModelAnalyticalDevelopment,"JournalofAircraft,Vol.37,No.4,July2000,pp.554-561. [3] Wall,R.,\DarpaEyesMaterialsforMorphingAircraft,"AviationWeekandSpaceTechnology,April8,2002. [4] Abdulrahim,M.,Garcia,H.,Dupuis,J.andLind,R.,\FlightCharacteristicsofWingShapingforaMicroAirVehiclewithMembraneWings,"InternationalForumonAeroelasticityandStructuralDynamics,IFASD-US-24,June2003. [5] Abdulrahim,M.,Garcia,H.,Ivey,G.F.andLind,R.,\FlightTestingaMicroAirVehicleusingMorphingforAeroservoelasticControl,"AIAAStructures,StructuralDynamicsandMaterialsConference,AIAA-2004-1674,April2004. [6] Garcia,H.,Abdulrahim,M.andLind,R.,\RollControlforaMicroAirVehicleusingActiveWingMorphing,"AIAAGuidance,NavigationandControlConference,AIAA-2003-5347,Aug.2003. [7] Grant,D.T.,Abdulrahim,M.andLind,R.,\FlightDynamicsofaMorphingAircraftutilizingIndependentMultiple-JointWingSweep,"AIAA-2006-6505,Aug.2006. [8] Bowman,J.,\AordabilityComparisonofCurrentandAdaptiveandMultifunctionalAirVehicleSystems,"AIAA-2003-1713,April2003. [9] Gano,S.E.andRenaud,J.E.,\OptimizedUnmannedAerialVehiclewithWingMorphingforExtendedRangeandEndurance,"AIAA-2002-5668,Sept.2002. [10] Bowman,J.,SandersB.andWeisshar,T.,\EvaluatingtheImpactofMorphingTechnologiesonAircraftPerformance,"AIAA-2002-1631,April2002. [11] Prock,B.C.,Weisshaar,T.A.andCrossley,W.A.,\MorphingAirfoilShapeChangeOptimizationwithMinimumActuatorEnergyasanObjective,"AIAA-2002-5401,Sept.2002. [12] Rusnell,M.T.,Gano,S.E.,Perez,V.M.,Renaud,J.E.andBatill,S.M.,\MorphingUAVParetoCurveShiftforEnhancedPerformance,"AIAA-2004-1882,April2004. [13] Secanell,M.,Suleman,A.andGamboa,P.,\DesignofaMorphingAirfoilforaLightUnmannedAerialVehicleusingHigh-FidelityAerodynamicShapeOptimization,"AIAA-2005-1891,April2005. 97

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Khot,N.S.,Eastep,F.E.andKolonay,R.M.,\MethodforEnhancementoftheRollingManeuverofaFlexibleWing,"JournalofAircraft,Vol.34,No.5,September-October1997,pp.673-678. [15] Gern,F.H.,Inman,D.J.andKapania,R.K.,\StructuralandAeroelasticModelingofGeneralPlanformWingswithMorphingAirfoils,"AIAAJournal,Vol.40,No.4,April2002,pp.628-637. [16] Bae,J.,Seigler,T.M.,Inman,D.J.andLee,I.,\AerodynamicandAeroelasticConsiderationsofaVariable-SpanMorphingWing,"JournalofAircraft,Vol.42,No.2,March-April2005,pp.528-534. [17] Love,M.H.,Zink,P.S.,Stroud,R.L.,Bye,D.R.andChase,C.,\ImpactofActuationConceptsonMorphingAircraftStructures,"AIAA-2004-1724,April2004. [18] Chatterjee,S.andTemplin,R.J.,\Posture,Locomotion,andPaleoecologyofPterosaurs,"GeologicalSocietyofAmericaSpecialPublication376,2004,pp.1-64. [19] B.EtkinandL.D.Reid,DynamicsofFlight:StabilityandControl,3rdedition,1996,JohnWileyandSons,Hoboken,NJ,pp.15-127. [20] J.D.Anderson,Jr.,IntroductiontoFlight,4thedition,2003,McGrawHill,Boston,MA,pp.299-662. [21] D.P.Raymer,AircraftDesign:AConceptualApproach,4thedition,2006,AIAA,Reston,VA,pp.467-560. [22] D.Lay,LinearAlgebraandItsApplications,3rdedition,2003,AddisonWesley,Boston,MA,pp.302-303. [23] Kehoe,J.J.,Causey,R.S.,Abdulrahim,M.andLind,R.,\WaypointNavigationforaMicroAirVehicleusingVision-BasedAttitudeEstimation,"TheAeronauticalJournal,Vol.110,No.1114,December2006,pp.821-829. 98

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BrianChristopherRobertswasborninBaltimore,Marylandin1985.HegrewupinRaleigh,NorthCarolina,wherehegraduatedvaledictorianoftheclassof2003fromJesseO.SandersonHighSchool.Hereturnedtothestateofhisbirthforcollege,whereheattendedtheUniversityofMarylandatCollegePark.Duringcollege,BrianspentonesemesterinValencia,SpainatthePolytechnicUniversityofValenciabeforereturningtoMarylandtoreceivehisBachelorofSciencedegreeinMayof2007.BriangraduatedwithAerospaceHonorsforhisresearchintoornithopterswithDr.JamesE.Hubbard,Jr.attheNationalInstituteofAerospaceinHampton,Virginia.HehasbeenagraduatestudentattheUniversityofFloridaundertheguidanceofDr.RickLindsinceJune,2007.Hehasresearchedpterosaurightdynamicsandtheirpotentialtoinspireminiatureaerialvehicle(MAV)design.DuringhistimeintheFlightControlLaboratory,BrianhashelpedtowriteproposalstoDefenseAdvancedResearchProjectsAgency(DARPA)andtheNationalScienceFoundation(NSF).HisproposaltoNSFtostudytheeectsofmorphingMAVdesignonurbanturbulencerejectionwasaccepted,andhewillspendthesummerof2009inMelbourne,Australiapursuingthatinitiative.AfterreceivinghisMasterofSciencedegreeinMayof2009,BriancontinuestopursuehisMAVresearchintereststoobtainhisdoctoraldegree. 99