Delft University of Technology

A Physics-based Approach to Assess Critical Load Cases for Landing Gears withinAircraft Conceptual Design

Wu, Peijun

DOI10.4233/uuid:193f6664-0f19-488f-af6a-21b17ba75be0Publication date2019Document VersionFinal published versionCitation (APA)Wu, P. (2019). A Physics-based Approach to Assess Critical Load Cases for Landing Gears within AircraftConceptual Design. https://doi.org/10.4233/uuid:193f6664-0f19-488f-af6a-21b17ba75be0

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APhysics‐basedApproachtoAssessCriticalLoadCasesforLandingGearswithinAircraftConceptualDesign

Intentionallyblankpage

APhysics‐basedApproachtoAssessCriticalLoadCasesforLandingGearswithinAircraftConceptualDesign

Dissertation

forthepurposeofobtainingthedegreeofdoctoratDelftUniversityofTechnology

bytheauthorityoftheRectorMagnificusProf.dr.ir.T.H.J.J.vanderHagen,chairoftheBoardforDoctorates

tobedefendedpubliclyonThursday25April2019at12:30o’clock

by

PeijunWU

MasterofEngineeringinMechanicalEngineeringandAutomation,NorthwesternPolytechnicalUniversity,China

borninAnhui,China.

Thisdissertationhasbeenapprovedbythepromotors.

Compositionofthedoctoralcommittee:

RectorMagnificus, chairperson

Prof.dr.ir.L.L.M.Veldhuis DelftUniversityofTechnology,promotor

Prof.dr.ir.M.Voskuijl NetherlandsDefenceAcademy,copromotor

Independentmembers:

Ir.P.Vergouwen GKNFokker

Prof.dr.J.Rohacs Budapest University of Technology andEconomics

Prof.Dr.Ing.D.Moormann RWTHAachenUniversity

Dr.ir.I.J.M.Besselink EindhovenUniversityofTechnology

Prof.dr.R.Curran DelftUniversityofTechnology

Reservemember:

Prof.dr.ir.G.Eitelberg DelftUniversityofTechnology

Keywords: Flight Dynamics and Loads; Landing Gear; Load Cases; Multidisciplinary Design,Analysis,andOptimization

Front&Back:PictureprovidedbyMarkVoskuijl

Copyright©2019byP.WU

ISBN978‐94‐6384‐039‐2

An electronic version of this dissertation is available athttp://repository.tudelft.nl/.

I

Summary

TheEuropeanUnionandtheUnitedStatesareproposing tobring inmorestrict flightvehicleemissioncriteria intheirreportsof thehigh‐levelgroupsonaviationresearch,i.e. EU Flightpath 2050 and US Destination 2025.More fuel‐efficient aircraftmust bedevelopedtoachievethistarget.Moreover,theincreasinglycompetitiveaviationmarketalsoexpectsmorefuel‐efficientaircrafttobedesigned.Anefficientandreliableaircraftdesign with a decreasedweight could significantly contribute to the improvement ofaircraft economical and environmental performance. Various research studies havehighlighted thepotential for significantweight savingson the landing gear system. Ingeneral,thelandinggearaccountsforaround5%ofaircraftMaximumLandingWeight.Intheaircraftconceptualdesignstage,therearetwomethodstoachieveweightsavingsonthelandinggearsystem:

1. Investigationofconventionaldesigns2. Introductionofinnovativedesigns

In theuseof these twomethods,akeystep is toverify thedesignof the landinggearw.r.t certain critical load cases. A landing gear critical load case is defined as a set ofcombinations of aircraft flight attitudes and motions, control surfaces and enginethrottlesettings,andenvironmentalconditionsthatcouldleadtodamageandfailureofthe landing gear structure. These critical load cases reflect the possible extremeconditions that might occur in operation. These critical load cases are traditionallyobtainedbyutilizingthemethodsbasedonstatisticaldatawhileignoringspecificflightdynamicsandlandinggearcharacteristics.Thesemethodscouldleadtothreeproblems.

Firstly, for conventional landing gears, this leads to suboptimal designs because theobtainedcriticalloadcasesarenotnecessarilyaccurate.InaccordancetothereportsofEASA, FAA, and aircraft manufacturers, these approaches could result in a 15%differencebetweentheultimatevaluesofallowedcritical landinggearloadcasesusedintheconceptualdesignphaseandthoseobtainedduringthefinalexperimentalphase.

Secondly,statisticaldatacannotbeappliedreliablytoinnovativelandinggeardesigns.For example, the combination of the extreme aircraft flight attitudes and motions,control surfaces and engine throttle settings, and environmental conditions duringtouchdown, for innovative landing gear system design is commonly not available inexistingstatisticaldata.

Thirdly,whenthelandinggeardesigndepartmentlacksthedesignmethodsthatcanbeintegratedintotheoverallaircraftdesignprocessforcollaborativedesign,thedesignofthe landinggearwillbetypicallyperformedin isolation fromdesigndepartmentsthatareinchargeofotheraircraftcomponents, likewings,fuselage,etc.Hence,thelandinggeardesigndepartmentwillpassivelyconformtodesignrequirements,likecriticalload

II

cases and, allocation requirements.While the influence of landing gear design on theoverall aircraft system is ignored. Due to the snowball effect, the aircraft weightwillincrease by 7% of maximum takeoff weight over the optimal design. Therefore, theoptimaldesignfortheoverallaircraftsystemwillnotbeachieved.

In order to solve these problems, a physics‐based approach to predict landing gearcriticalloadcasestofacilitatelandinggeardesignwithintheconceptualdesignphaseisdevelopedinthisthesis.Aflightdynamicsandloadsmodelbasedonmultibody(rigid)dynamicssimulationisusedtoestimatelandinggearloadcasesbyperformingaircrafttakeoff and landing simulations. This model mainly consists of the automatic flightcontrol module, aerodynamics module, undercarriage module. An automatic flightcontrolsystemisdevelopedtoenable thesesimulations.Theclassicalcontrolstrategybasedonclosed‐loopcontrolsystemisusedintheautomaticflightcontrolsystem.Theaerodynamics model is established based on the look‐up table deployed with theaerodynamics coefficients calculated by the DATCOM and Tornado. DATACOM is anaccuratetoolbasedonasemi‐empiricalmethod.Tornadoisbasedonthevortexlatticemethod which is used as an extension to the DATCOM. Because the rudder controlderivativesarenotestimatedbytheDATCOM.Inordertoobtaintheequilibriumstatusof aircraft at specific flight conditions which is necessary for the initialization ofsimulations, the Jacobian Matrix Method is used to obtain the aircraft trimmedconditions.Theapproachisappliedtothreedifferenttestcases.

1. Conventionallandinggearssystem2. Catapultconceptforcivilaircraft3. Take‐offandlandingusingagroundbasedsystem(GABRIEL)

GABRIEL is an EU‐funded projectwhich aims to completely remove the conventionallanding gear system and replace it by a ground based system. The shock absorbersystemsareincludedinthesethreeundercarriagesystemswhicharemodeledbasedonthe classic spring and damper system. Besides the shock absorber, the side and dragstrutsarealsoincludedinthesethreetestcaseswhicharesimplifiedintoIbeammodels.Thetyremodelusedintheconventionallandinggearsandcatapultconceptforthecivilaircraft isbasedon theDelftTyremodel.This isasemi‐empiricalmodelbasedon theclassic Magic Formula. The catapult system and ground based system are modeledrespectivelyforthecatapultconceptforthecivilaircraftandGABRIEL.Boththeclassicopen‐loop and closed‐loop control system are used in the catapult thrust controlsystems located on the groundbased system.TheAirbusA320 is used as a referenceaircraft in this thesis, because most civil flight transportation is accomplished bymedium‐haul narrow body aircraftworldwide. For example, 80%of aircraft takes offandlandsatSchipholairport,locatedinAmsterdamintheNetherlands,arethesekindsof aircraft. The Airbus A320 is one of the most representative medium‐haul aircraftworldwide.

The takeoff and landing simulations areperformedunder the extreme flight attitudesand environmental conditions described in the open literature. Consequently, thecritical load cases canbe identified from them.Furthermore,Monte‐Carlo simulationsareincludedinthisapproachasanalternativetohavingarealisticrepresentationofthecombinationofextremeweatherconditionsandpilotbehavior.Hence, thedifficultyof

III

obtainingthecombinationoftheextremeflightattitudesandenvironmentalconditionswhenaircrafttouchesdown,especiallyforinnovativelandinggeardesign,canbesolved.Simultaneously, the flightdynamics and loadsmodelhas thepotential to improve thelevelof integrationof the landinggeardesign in theoverallaircraftconceptualdesignprocess.

Thisphysics‐basedapproach isverifiedandvalidatedrelativeto thereferencedata inthisthesis.TheaircraftperformanceisverifiedbycomparingthesimulationresultswithESDU reports. The aircraft stability and control derivatives are verifiedby comparingtheresultsfromtheDATCOMandTornado.Thelandinggearweightestimationmethodis validated with empirical data. The difference between them is less than 4%. Thelandinggearloadsareverifiedbycomparingwiththereferencedata.Theapproachofaircraft touchdown attitudes estimation (based on the Monte‐Carlo evaluation) isvalidatedwiththestatisticaldata.Comparedwiththestatisticaldata,theaccuracyofthetouchdownattitudes estimatedby the simulation can reachup to 96%.Basedon thisapproach,forthe3testcases,thereare16,4,and19loadcasesrespectivelyidentifiedas critical from 304, 4, and 139 load cases mentioned in the references. Besides thebenefitofprovidingareliabledesignreferenceforlandinggeardesign.Itisalsovaluableinimprovingtheefficiencyofthelandinggeardesignprocess.Becausealoweramountofloadcasesisrequiredtobeinvestigatedinthefollowingdesignsteps.Thisisvaluableinimprovingthedesignefficiency.Forexample,intheconventionallandinggeardesign,engineerscanfocusontheidentifiedcriticalloadcasesthatonlyaccountforlessthan5%ofthetotalloadcasesmentionedinthereference.

In order to prove the performance and benefits of this physics‐based approach forlandinggeardesign,ademonstrationoffindingtheeffectoflandinggearlayoutonthelandinggear loadcases in theaircraft conventional landingphase ispresented in thisthesis. Additionally, the preliminary design of GABRIEL technology is verified by thisphysics‐basedapproach.ThebenefitsofGABRIELtechnologyarealsoshowncomparedtoconventionallandinggearconcept,e.g.thesavinginaircraftweightcanreach1.5tons.Thisweightsavingcanleadtothereductionoffuelcosts79tonsperyearforanAirbusA320(basedon2700hoursflighttimeperyear).

In the future, the aircraft structural flexibility could be accounted for to improve theestimation accuracy of landing gear critical load cases. In principle, the structuralflexibilityofaircraftcouldaffectthemagnitudeofcriticalloadcasesbyabout3%.Atthesametime,moreelegantcriteriaforthesafetyanalysisandverificationoflandinggearsdesign can also be obtained. Several promising approaches can be used as solution.Multibody(flexible)dynamicssimulationandthefiniteelementmethodcanbeincludedfor the simulation and structural analysis of landing gear components. Hence, thedetailed geometric design of landing gears can be introduced into the aircraft earlydesign stage which is valuable for improving the overall aircraft design efficiency.Furthermore, thepossibility of integrating themethod into the overall aircraft designprocesscanalsobeinvestigated.Forexample,iftheassistedtakeoffandlandingsystemcanbeimplementedinanAirbusA320,theoptimal‐designbasedontheoverallaircraftdesigncansavetheaircraftweightaround7%ofmaximumtakeoffweight.

IV

Samenvatting

De Europese Unie en de Verenigde Staten hebben in de rapporten van hunonderzoeksgroepen met betrekking tot de luchtvaart, i.e. EU Flightpath 2050 en USDestination2025,voorgesteldomstrengereeisenoptestellenvooremissiecriteria.Omdit doel te bereiken, moeten er brandstofefficiëntere vliegtuigen worden ontwikkeld.Bovendien verwacht de steeds competitievere luchtvaartmarkt ook dat zuinigerevliegtuigen zullenworden ontworpen. Een efficiënt en betrouwbaar vliegtuigontwerpmet eenverlaagdgewicht zou aanzienlijkkunnenbijdragen totde verbetering vandeeconomischeenduurzameprestatiesvanvliegtuigen.Diversestudieshebbengewezenop het potentieel voor aanzienlijke gewichtsbesparingen op het landingsgestel. In hetalgemeen is het landingsgestel goed voor ongeveer 5% van het maximalelandingsgewichtvanvliegtuigen.Indeconceptueleontwerpfasevanhetvliegtuigzijnertweemethodenomgewichttebesparenophetlandingsgestel:

1. Onderzoekvanconventioneleontwerpen2. Introductievaninnovatieveontwerpen

Bijhetgebruikvandezetweemethoden,iseenbelangrijkestapomhetontwerpvanhetlandingsgesteltecontrolerenvoorbepaaldekritischebelastingen.Dekritiekebelastingvaneenlandingsgestelwordtgedefinieerdalseenreekscombinatiesvanvliegtuigstandenbewegingen, instellingenvankleppenengashendel,endeomgevingsvariabelendiekunnen leiden tot beschadiging en uitval van het landingsgestel. Deze kritischebelastingen weerspiegelen de mogelijke extreme omstandigheden die tijdens hetgebruik kunnen optreden. Deze kritische belastingen worden traditioneel verkregendoor gebruik te maken van de methoden op basis van statistische gegevens, terwijlbepaaldevliegdynamiekenkenmerkenvanhetlandingsgestelwordengenegeerd.Dezemethodenkunnentotdrieproblemenleiden.

Ten eerste leidt dit voor conventionele landingsgestellen tot suboptimale ontwerpenomdat de verkregen kritische belastingen niet noodzakelijk nauwkeurig zijn. Inovereenstemming met de rapporten van EASA, FAA en vliegtuigfabrikanten, zoudendezebenaderingenkunnen resulteren ineenverschilvan15%tussendeuiteindelijkewaarden van toegestanekritische ladingbelastingen van landingsgestellendiewordengebruikt in de conceptuele ontwerpfase en die verkregen worden tijdens de laatsteexperimentelefase.

Tentweedekunnenstatistischegegevensnietopbetrouwbarewijzewordentoegepastop innovatieve landingsgestelontwerpen. Zo is bijvoorbeeld de combinatie vanvliegtuigstand en bewegingen, instellingen van kleppen en gashendel, en deomgevingsvariabelentijdenshetlandenvooreeninnovatieflandingsgestelontwerpnietbeschikbaarinbestaandestatistischegegevens.

V

Ten derde, wanneer de ontwerpafdeling van het landingsgestel de ontwerpmethodenmistdiekunnenwordengeïntegreerd inhetalgemeneontwerpprocesvanvliegtuigenvoorgezamenlijkontwerp,zalhetontwerpvanhetlandingsgestelafzonderlijkwordenuitgevoerd van ontwerpafdelingen die de leiding hebben over andere vliegtuigencomponenten, zoals vleugels, romp, etc. Vandaar dat de ontwerpafdeling van hetlandingsgestel enkel op een passieve wijze zal voldoen aan ontwerpvereisten, zoalskritischebelastingenenvereisten.Daarnaastwordtdeinvloedvanhetontwerpvanhetlandingsgestel op het algehele vliegtuigsysteem genegeerd. Vanwege hetsneeuwbaleffectophetontwerp,zalhetgewichtvanhetvliegtuigtoenemenmet7%vanhet maximale startgewicht ten opzichte van het optimale ontwerp. Daarom zal hetoptimaleontwerpvoorhetalgehelevliegtuigsysteemnietwordenbereikt.

Om deze problemen op te lossen, is een op fysica gebaseerde aanpak om kritiekebelastingen van landingsgestellen te voorspellen ontwikkeld in dit proefschrift, zodathet ontwerp van landingsgestellen binnen de conceptuele ontwerpfase wordtvereenvoudigd.

Eenvliegdynamica‐modeleneenbelastings‐modelopbasisvaneen“multibody”(rigide)dynamica‐simulatie wordt gebruikt om een schatting te maken van de belasting oplandingsgestellen door start‐ en landingsimulaties uit te voeren. Dit model bestaatvoornamelijk uit de automatische vluchtregelmodule, aerodynamica module enlandingsgestel module. Voor deze simulaties is een automatisch vluchtregelsysteemontwikkeld. De klassieke controlestrategie op basis van een gesloten regelsysteemwordt gebruikt in het automatische vluchtregelsysteem. Het aerodynamica‐model isgebaseerd op een opzoektabel die wordt gevuld met aerodynamische coëfficiëntenberekenddoordeDATCOMenTornado.DATCOMiseennauwkeurigetoolopbasisvaneen semi‐empirischemethode. Tornado is gebaseerd op de vortex‐latticemethode enwordt gebruikt als een uitbreiding op DATCOM, omdat de afgeleiden van dedwarsbesturing niet worden geschat door DATCOM. Om de evenwichtstoestand vanvliegtuigenbij specifieke vluchtomstandigheden te bepalenwordtde JacobianMatrix‐methodegebruiktomhetvliegtuigtetrimmen.Ditisnoodzakelijkvoordeinitiatievandesimulaties.Deaanpakwordttoegepastopdrieverschillendetestgevallen:

1. Conventioneellandingsgestel‐systeem2. Katapultconceptvoorcivielevliegtuigen3. Opstijgen en landen met behulp van een op de grond geplaatst systeem

(GABRIEL)

GABRIEL is een door de EU gefinancierd project dat als doel heeft het conventionelelandingsgestel volledig te vervangen door een op de grond geplaatst systeem. Deschokdempersystemenzijninbegrepenindrielandingssystemendiezijngemodelleerdopbasisvanhetklassiekeveer‐endempersysteem.Naastdeschokdemperzijnookdezij‐ensleepsteunenopgenomenindezedrietestgevallen,welkezijnvereenvoudigdinI‐profiel modellen. Het bandenmodel dat wordt gebruikt in de conventionelelandingsgestellenenhetkatapultconceptvoorhetcivielevliegtuig isgebaseerdophetDelft Tyre‐model. Dit is een semi‐empirischmodel gebaseerd op de klassieke “MagicFormula”.HetkatapultsysteemenhetopdegrondgeplaatstesysteemzijngemodelleerdvoorhetkatapultconceptvoorburgerluchtvaartenGABRIEL.Zoweldeklassiekeopen

VI

en gesloten‐systeemworden gebruikt in de katapult‐besturingssystemen in het op degrondgeplaatstesysteem.DeAirbusA320wordtgebruiktalsreferentievliegtuig inditproefschrift, omdat het grootste deel van de burgerluchtvaart uitgevoerd wordt metzogeheten“narrow‐body”vliegtuigenovermiddellangeafstandenoverdegehelewereld.Tachtig procent van de opstijgende en landende vluchten op de luchthaven vanAmsterdam,Schiphol,inNederland,zijnvandittypevliegtuigen.DeAirbusA320iseenvandemeestrepresentatieve“mediumhaul”vliegtuigenwereldwijd.

De start‐ en landingsimulaties worden uitgevoerd onder de extreme stand enomgevingscondities beschreven in open literatuur. Derhalve kunnen de kritischebelastingen hieruit worden afgeleid. Bovendien zijn Monte‐Carlo‐simulaties in dezebenadering opgenomen als een alternatief, om een realistische weergave van decombinatie van extreme weersomstandigheden en pilootgedrag te krijgen. Op dezewijze kan de moeilijkheid om de combinatie van de extreme vliegstanden enomgevingscondities voor innovatieve landingsgestelontwerpen worden opgelost.Tegelijkertijd heeft het vluchtdynamica en belastings‐model het potentieel om hetintegratieniveau van het ontwerp van het landingsgestel te verbeteren in hetconceptueelontwerpvanhettotalevliegtuig.

Deze op fysica gebaseerde benadering wordt in dit proefschrift geverifieerd engevalideerd ten opzichte van de referentiegegevens. De prestaties van het vliegtuigwordengeverifieerddoordesimulatieresultatentevergelijkenmetESDU‐rapporten.Destabiliteitvanvliegtuigenendeafgeleidenvandedwarsbesturingwordengeverifieerddoor de resultaten van DATCOM en Tornado te vergelijken. Degewichtsschattingsmethodevoorhet landingsgestelwordtgevalideerdmetempirischegegevens. Het gevonden verschil bedraagt minder dan 4%. De belasting van hetlandingsgestel wordt geverifieerd door deze te vergelijken met referentie data. Debenaderingvanvliegtuiglandingstand(gebaseerdopdeMonteCarlosimulaties)wordtgevalideerdmetstatistischegegevens. Invergelijkingmetdestatistischegegevenskandenauwkeurigheidvanlandingstanddoordesimulatieoplopentot96%.Opbasisvandeze aanpak, zijn voor de 3 testgevallen respectievelijk 16, 4 en 19 belastingengeïdentificeerdalskritischtenopzichtevan304,4en139belastinggevallenvermeldinde referenties. Naast het voordeel van een betrouwbaar referentieontwerp voor hetlandingsgestel, is het ook waardevol voor het verbeteren van de efficiëntie van hetlandingsgestelontwerpproces, omdat een lager aantal belastingen in de volgendeontwerpfasesmoetworden onderzocht. Dit is waardevol voor het verbeteren van deontwerpefficiëntie.Inhetconventionelelandingsgestelontwerp,kunneningenieurszichconcentrerenopdegeïdentificeerdekritischebelastingendiezichbeperkentotminderdan5%vandetotalebelastingenvermeldindereferentie.

Om de prestaties en voordelen van deze op fysica gebaseerde benadering voorlandingsgestellentebewijzen,wordtinditproefschrifteendemonstratievanheteffectvandelay‐outvanlandingsgestellenopdebelastingenindeconventionelelandingsfasegepresenteerd. Bovendien, wordt het voorlopige ontwerp van GABRIEL‐technologiegeverifieerddoordezeopfysicagebaseerdebenadering.DevoordelenvandeGABRIEL‐technologie wordt ook aangetoond in vergelijking met het conventionelelandingsgestelconcept,zokandebesparinginvliegtuiggewichtanderhalvetonbereiken.

VII

Dezegewichtsbesparingkanleidentoteenbrandstofreductievan79tonper jaarvooreenAirbusA320(gebaseerdop2700vliegurenperjaar).

In de toekomst zou de structurele flexibiliteit van het vliegtuig beschouwd kunnenworden om de schatting en nauwkeurigheid van kritieke belastingen vanlandingsgestellen te verbeteren. In principe zou de structurele flexibiliteit de omvangvan kritische belastingenmet ongeveer 3% kunnen beïnvloeden. Evenzo kunnen ookelegantere criteria voor de veiligheidsanalyse en verificatie van het ontwerp wordenverkregen. Verschillende veelbelovend benaderingen kunnen als oplossing wordengebruikt.Multibody(flexibele)dynamicasimulatieseneeneindigeelementen‐methodekanwordenopgenomenvoordesimulatieenstructureleanalysevandecomponenten.Vandaar dat het gedetailleerde geometrische ontwerp van het landingsgestel kanwordengeïntroduceerdindevroegeontwerpfase,watwaardevolisvoorhetverbeterenvandealgeheleontwerpefficiëntievanhetvliegtuig.Verderkandemogelijkheidomdemethode te integreren in het algehele vliegtuigontwerpproces worden onderzocht.Wanneerbijvoorbeeldhetstart‐enlandingssysteemwordtgeïmplementeerddatvandegrondafondersteundwordt,kanhetoptimaleontwerpvooreenAirbusA320ongeveer7%vanhetmaximalestartgewichtbesparen.

VIII

IX

Contents

Summary....................................................................................................................................................................I 

Samenvatting........................................................................................................................................................IV 

Nomenclature.........................................................................................................................................................1 

LatinSymbols....................................................................................................................................................1 

Greeksymbols...................................................................................................................................................3 

Subscripts............................................................................................................................................................4 

Abbreviations....................................................................................................................................................4 

1  Introduction..................................................................................................................................................7 

1.1.  Background..........................................................................................................................................7 

1.2.  Classicallandinggeardesignmethods...................................................................................8 

1.3.  Advancedlandinggeardesignmethods.............................................................................10 

1.4.  Flightdynamicsandloadssimulation..................................................................................13 

1.4.1.Theneedforflightdynamicsandloadssimulation....................................................13 

1.4.2.Existingsolutionforphysics‐basedlandinggearmodeling....................................14 

1.4.3.Existingsolutionsforflightdynamicsmodeling..........................................................16 

1.4.4.Existingsolutionforaerodynamicsanalysis..................................................................17 

1.4.5.Existingsolutionforpilotandatmospheremodeling................................................19 

1.5.  Researchobjectives......................................................................................................................20 

1.6.  Thesisoutline..................................................................................................................................21 

2  Referenceaircraftandlandinggearconcepts............................................................................23 

2.1.  Referenceaircraft(A320)andConventionallandinggearsystems......................23 

2.2.  Unconventionallandinggearconcepts...............................................................................26 

2.2.1.Greentaxiingsystems...............................................................................................................26 

2.2.2.Catapultassistedtakeoff..........................................................................................................28 

2.2.3.Takeoffandlandingusingagroundbasedsystem......................................................29 

2.3.  Summary............................................................................................................................................34 

3  Physics‐basedApproachforAnalysisofLandingGearCriticalLoadCases.................37 

3.1.  Introduction.....................................................................................................................................37 

3.2.  Identificationofcriticalloadcases........................................................................................38 

X

3.2.1.Introduction...................................................................................................................................38 

3.2.2.Anapproachbasedonstatisticaldata...............................................................................39 

3.2.3.Aphysics‐basedapproachusingMonte‐Carloevaluation.......................................40 

3.2.4.Criticalloadcasesidentificationcriteria..........................................................................41 

3.3.  Landinggearweightanalysis...................................................................................................43 

3.3.1.Landinggearweightestimation...........................................................................................43 

3.3.2.Constraintsforlandinggeardesign....................................................................................44 

3.4.  Summary............................................................................................................................................44 

4  Flightdynamicsandloadsmodel.....................................................................................................47 

4.1.  Introduction.....................................................................................................................................47 

4.2.  Equationsofmotion.....................................................................................................................49 

4.2.1.Aircraftmassandinertia.........................................................................................................49 

4.2.2.Conventionallandinggearmodel........................................................................................50 

4.2.3.Catapultconceptforcivilaircraft........................................................................................56 

4.2.4.GABRIELconceptlandinggearsystemmodel...............................................................59 

4.3.  ExternalForces...............................................................................................................................65 

4.3.1.Propulsionsystem......................................................................................................................65 

4.3.2.Aerodynamicsanalysis.............................................................................................................66 

4.4.  Operationalconditions................................................................................................................68 

4.4.1.Atmosphericmodel....................................................................................................................68 

4.4.2.Flightcontrolsystem.................................................................................................................69 

4.4.3.Basicaircraftautomaticflightcontrolstrategy............................................................70 

4.5.  Numericalsimulations................................................................................................................73 

4.6.  Verificationandvalidation........................................................................................................76 

4.6.1.Introduction...................................................................................................................................76 

4.6.2.Aircraftperformanceverification........................................................................................76 

4.6.3.Aircraftstabilityandcontrolderivatives.........................................................................78 

4.6.4.Landinggearweightestimationmethodsverification..............................................79 

4.6.5.Landinggearmodelingapproachverification...............................................................80 

4.7.  Summary............................................................................................................................................81 

5  Identificationofcriticalloadcases..................................................................................................83 

5.1.  Introduction.....................................................................................................................................83 

5.2.  Simulationexamplesoftakeoffandlanding.....................................................................83 

XI

5.2.1.Simulationexampleofconventionaltakeoff..................................................................83 

5.2.2.Simulationexampleofconventionallanding.................................................................87 

5.2.3.Simulationexampleofcatapultconceptforcivilaircraft.........................................91 

5.2.4.SimulationexampleofGABRIELtakeoff..........................................................................94 

5.2.5.SimulationexampleofGABRIELlanding.........................................................................97 

5.3.  Overviewofanalysiscases........................................................................................................99 

5.3.1. Identification of the critical takeoff load case for the conventional landinggearsconcept.............................................................................................................................................99 

5.3.2. Identification of the critical landing load case for the conventional landinggearsconcept...........................................................................................................................................101 

5.3.3.Identificationofthecriticalloadcaseforthecatapultconcept...........................105 

5.3.4.IdentificationofthecriticaltakeoffloadcasefortheGABRIEL..........................106 

5.3.5.IdentificationofthecriticallandingloadcasesfortheGABRIEL.......................108 

5.3.6.EstimationoflandingattitudesbasedonMonte‐Carlosimulation...................110 

5.3.7.Approachofaircrafttouchdownattitudesestimation(basedonMonte‐Carloevaluation)validation..........................................................................................................................114 

5.4.  Resultsanddiscussion..............................................................................................................115 

5.4.1.Conventionallandinggearsconcept................................................................................115 

5.4.2.Catapultconceptforcivilaircraft......................................................................................117 

5.4.3.GABRIELconcept.......................................................................................................................118 

5.5.  Summary..........................................................................................................................................118 

6  ConclusionsandRecommendations.............................................................................................121 

6.1.  Researchconclusion...................................................................................................................121 

6.2.  Recommendationforfutureresearch................................................................................123 

AppendixA.Aircraftlandinggearlayouts...........................................................................................125 

AppendixB.Shockabsorber.......................................................................................................................131 

AppendixC.Retractionmechanism........................................................................................................135 

AppendixD.Wheelsandtyres...................................................................................................................137 

AppendixE.Applicationofphysics‐basedapproachinlandinggeardesign......................139 

Reference.............................................................................................................................................................143 

Acknowledgments...........................................................................................................................................157 

PublicationsandConferenceContributions.......................................................................................159 

1

Nomenclature

LatinSymbols

A area [m2]

aA pneumaticarea [m2]

oA areaoftheopeningholeintheorificeplate [m2]

pA areaofthemeteringpinintheplaneoftheorifice [m2]

AR wingaspectratio [‐]

b wingspan [m]

Tb tailplanespan [m]

Sb spoilerspan [m]

c wingchordatroot [m]

dC dischargecoefficient [‐]

DC dragcoefficient [‐]

plC rollmoment coefficient change in response to change in

aircraftrollrate(inthestabilityaxes)[1/rad]

qlC rollmoment coefficient change in response to change in

aircraftpitchrate(inthestabilityaxes)[1/rad]

rlC rollmoment coefficient change in response to change in

aircraftyawrate(inthestabilityaxes)[1/rad]

alC rollmoment coefficient change in response to change in

aircraftailerondeflection(inthestabilityaxes)[1/rad]

mC pitchmomentcoefficient [‐]

qmC pitchmomentcoefficientchangeinresponsetochangein

aircraftpitchrate(inthestabilityaxes)[1/rad]

emC

pitchmomentcoefficientchangeinresponsetochangeinaircraftelevatordeflection(inthestabilityaxes)

[1/rad]

rnC yawmomentcoefficientchange inresponse tochange in

aircraftyawrate(inthestabilityaxes)[1/rad]

pnC yawmomentcoefficientchange inresponse tochange in

aircraftrollrate(inthestabilityaxes)[1/rad]

yC side force coefficient change in response to change in

aircraftsideslipangle(inthestabilityaxes)[1/rad]

2

SLC liftcoefficientvariationcausedbyspoilerdeflection [1/rad]

d diameter [m]

iD induceddrag [N]

D dragforce [N]

se statictyreandshockdeflection [m]

F force [N]

g gravitationalacceleration [m/s2]

H altitudewithrespecttoworldaxessystem(geopotential) [m]

H resultantangularmomentum [kg·m2/s]

I massmomentofinertia [kg·m2]

J Jacobianmatrix [‐]

K gain [‐]

l length [m]

L overallaircraftlength [m]

L lift [N]

uL , vL , wL turbulencescalelengths [m]

M moment [N·m]

M resultantmoment [N·m]

n exponent for air compressionprocess in shock absorberstrut

[‐]

p rollratewithrespecttoaircraftbodyaxessystem [deg/s]

p pressure [N/m3]

0ap airpressureintheupperchamberoftheshockstrut [pa]

q pitchratewithrespecttoaircraftbodyaxessystem [deg/s]

r yawratewithrespecttoaircraftbodyaxessystem [deg/s]

p , q , r angularaccelerationinbodyaxessystem [deg/s2]

R non‐dimensionalradiusofgyration [‐]

R resultantexternalforce [N]

S surfacearea [m2]

S stroke [m]

AS aileronsarea [m2]

FS flapsarea [m2]

HS horizontaltailsurfacesarea [m2]

3

LSS leading‐edgeslatsarea [m2]

refS wingarea [m2]

SS spoilersarea [m2]

VS verticaltailsurfacesarea [m2]

WS wingarea [m2]

t time [s]

T thrust [N]

0v airvolumeforfullyextendedstrut [m3]

V airspeed [m/s]

gV vehiclegroundspeed [m/s]

u , v ,w velocityvectorinbodyaxessystem [m/s]

u , v ,w accelerationinbodyaxessystem [m/s2]

W weight [N]

W width [m]

ax rollcontrolstickposition [‐]

bx pitchcontrolstickposition [‐]

cx enginethrustthrottleposition [‐]

px yawcontrolstickposition [‐]

Greeksymbols

angleofattack [deg]

angleofsideslip [deg]

, , Eulerian angles defining the orientation of the air‐pathaxes

[deg]

dihedral [deg]

SEnose statictoextendpressureratio(noselandinggear) [‐]

CSnose compressedtostaticpressureratio(noselandinggear) [‐]

SEmain statictoextendpressureratio(mainlandinggear) [‐]

CSmain compressedtostaticpressureratio(mainlandinggear) [‐]

OPnose orifice hole radius to piston radius ratio (nose landinggear)

[‐]

OPmain orifice hole radius to piston radius ratio (main landing [‐]

4

gear)

angleneededforminimumwheelbase [deg]

controlsurfacedeflectionangle [deg]

angleneededforturnoverangle [deg]

, , Eulerian angles defining the orientation of the airplanebodyaxes

[deg]

u , v , w turbulenceintensities [m/s]

materialorairdensity [kg/m3]

Subscripts

A aileron

app approach

AC aircraft

cg thecenterofgravity

crosswind crosswindvelocity

E elevator

GS groundspoiler

HL highliftdevice

IGE ingroundeffect

LOF liftoff

m mainlandinggear

n noselandinggear

OGE outofgroundeffect

R rudder

RS rollspoiler

s spoiler

TD touchdown

trim trimmedaircraft

w theworldcoordinatesystem

Abbreviations

ABS Anti‐lockBrakeSystem

AEO AllEnginesOperative

AoA AngleofAttack

APU AuxiliaryPowerUnit

CAE ComputerAidedEngineering

CFD ComputationalFluidDynamics

5

CG CenterofGravity

DATCOM DataCompendium

DoF DegreeofFreedom

EASA EuropeanAviationSafetyAgency

EGTS ElectricGreenTaxiingSystem

EMALS Electro‐MagneticAircraftLaunchSystem

FAA FederalAviationAdministration

FCEE Flightattitudesandmotions,ControlsurfacesandEnginethrottlesettings,Environmentalconditions

FEM FiniteElementMethod

GABRIEL IntegratedGroundandon‐Board system for Support of theAircraft SafeTake‐offandLanding

GroLaS Ground‐basedLandingGearSystem

GSP Gas‐turbineSimulationProgram

IGE InGroundEffect

KBE KnowledgeBasedEngineering

MLW MaximumLandingWeight

MTOW MaximumTake‐offweight

MDO Multi‐disciplinaryDesignOptimization

MDS MultibodyDynamicsSimulation

OEF OneEngineFailure

OGE OutofGroundEffect

PHALANX Performance,HandlingQualitiesandLoadsAnalysisToolbox

PMC PolymerMatrixComposite

TIMPAN TechnologiestoIMProveAirframeNoise

UAV UnmannedAerialVehicle

6

7

1 Introduction1.1. Background

Operatingwithin the triad ofhigh efficiency, low cost, and environmental friendlinesshas become the ambitious objective for the global aviation industry. In the report offlightpath 2050, the European Union has set the target of decreasing NOX and CO2emissionsby90%and75%respectivelyandreducingtheperceivednoisefromaircraftby 65% relative to the capabilities of new aircraft in 2000 [1, 2].Many solutions areproposed and investigated to realize these goals, such as optimizingwing’s structureandairfoilgeometricalshapetoreducetheaircraftweightand improve fuelefficiency[3], developing innovative materials with low density and high strength for aircraftapplications[4,5],investigatingfuel‐efficientaircraftengines[6‐9].Thisthesispresentsthedevelopmentofananalysismethodwhichcanbeusedtoestimatethelandinggearcritical load casesused in theconceptualdesignprocess.This approach is valuable intheapplicationofreducingtheweightofanaircraft landinggearsystembyimprovingitsstructuraldesign.Inthisthesis,thetermoflandinggearcriticalloadcaseisdefinedasthecombinationsofaircraftFlightattitudesandmotions,ControlsurfacesandEnginethrottle settings, andEnvironmental conditions (FCEE) that could lead todamageandfailure of the landing gear structure. These critical load cases reflect the possibleextreme conditions thatmayoccur in operational practice. Currently, the critical loadcasesindicatedinthecertificationspecificationswhichhavebeenreleasedbytheEASAandFAAaremainlydeterminedw.r.tmanydataresources,e.g.experimental,empirical,and statistical data[10, 11]. For example, in accordance to the report released by theRoyalNetherlandsMeteorological Institute,more than0.3%of the time during1971‐1995at the Schiphol airporthad an averagewind speedhigher than15m/s [12]. Inaccordancetothetrafficreviewfrom2011to2018releasedbytheSchiphol,theannualaircraftmovementsincreasefrom420000to500000[13].

Curreydescribesthelandinggearofanaircraftas“theessentialintermediarybetweentheaeroplaneandcatastrophe”[14].Anaircraft’sstructurehastobeabletocopewithvarious load cases determinedby external conditions such as crosswinds, turbulence,terrain, and pilot actions [10, 15, 16]. Currently, the landing gear system typicallyaccountsforaround5%ofacommercialaircraftMaximumLandingWeight(MLW)[11].Areductionintheweightofthelandinggearwillhaveasignificanteffectontheoverallweight of an aircraft and thuson its performance [14].The reduction of landing gearweightcanbeachievedbytwoapproaches:

1. Investigationofconventionaldesigns

8

2. Introductionofinnovativedesigns

Inthefirstapproach,thelayoutandstructuraldesignofconventionallandinggearcanbe investigated to obtain the optimal designwhich hasminimal structural weight. Inaccordancetotheresearchshown inreferences [17‐19], thisapproachcanreduce theexistingconventional landinggearweightbyaround30%.BasedonthecalculationbyLufthansa Group [20], one‐kilogram mass reduction on all aircraft of Lufthansa’sGermanAirlinescansave30tonsoffueleachyear.

Inthesecondapproach,innovativetakeoffandlandingtechnologycanbedevelopedandrelatedlandinggearsystemsshouldbedesigned.Forexample,accordingtotheresearchillustratedinreference[21,22],iftheconventionallandinggearsystemcanberemovedfromA320aircraftandreplacedwithgroundbased landingsystem,duetoasnowballeffect, then the potential maximum takeoff weight saving and fuel weight saving canreachupto12%and13%respectively.

Feasibleandefficientdesigntoolsareessentialfordesigningsafeandefficientlandinggearsystems.At thismoment, the landinggeardesignapproachescanbedivided intotwocategories:

1. Classicallandinggeardesignmethods2. Advancedlandinggeardesignmethods

Adetaileddiscussionofthesemethodsisgiveninthefollowingsections.

1.2. Classicallandinggeardesignmethods

The classical landinggeardesignmethodsmainly refer tomethods,whichare for thedesignofconventionallandinggearandwhichusedesignprocessesandprinciplesthatarenotyetfullyintegratedintotheoveralldesignprocessofotheraircraftcomponents.They arebasedon analysis, experiments, and statistics.Due to the reliability of thesemethods, they are stillwidely used bymostmajor aerospace industries, for example,Fokker,AIRBUS,andBoeing[14,23,24].ThegeneralworkflowoftheclassicallandinggeardesignmethodsisshowninFigure1‐1.Firstly,thelandinggeardesigndepartmentor component subcontractor is given a set of design requirements from the otheraircraftdesigndepartments.Thiswillalsobebasedonbasiclandinggeardesignrules.Next,thelandinggeardesignermakesadesignthatfitstheserequirements.Afterward,thelandinggeardesignwillbevalidatedbyflightandgroundtests.

Inthefirststep,thelandinggeardesignrequirementsconsistofe.g.requirementonthelayoutandpositioning,loadcasestobeconsidered,etc.[10,25].Inprinciple,duringthedetermination process of these design requirements, the landing gear characteristicsshould be taken into consideration [14, 26]. Because they affect the ground reactionloadsonaircraft,seeFigure1‐2.Therefore,theycouldaffectthedesignofotheraircraftcomponents, like the wings, and fuselage [14, 26]. When the landing gear designdepartment lacks the design methods that can be integrated into the overall aircraftdesign process for collaborative design, the determination process of these designrequirements will ignore the landing gear system characteristics, like the shockabsorber characteristics, landing gear layouts. Currently, due to the complex

9

relationship between landing gears and the overall aircraft design and the lack ofeffectiveanalyticaltools,theconcurrentdesignforthemisstillachallengeforacademiaand industry. The aircraft design process is artificially decomposed into a series ofsubsystems,andlandinggeardesignisoneofthem.Theinteractionbetweenthelandinggearandotheraircraftdesigndepartmentsaresimplified.Whiletheinfluenceoflandinggear design on the overall aircraft system is ignored. Due to the snowball effect, theaircraft weight will increase by 7% of maximum takeoff weight (MTOW) over theoptimaldesign.Therefore,theoptimaldesignfortheoverallaircraftsystemwillnotbeachieved.[21,22].

Figure1‐1Classicallandinggeardesignprocedure[27,28]

Figure1‐2Landinggearimpactloadsfortail‐downandasymmetricallandings

Inthesecondstep,threesub‐stepsareinvolved.Firstly,basedonempiricalmethods,thelandinggearsystemdesignersproposeoneorseveralpromisingdesignsolutionsforalaterconceptevaluation step.Thecompatibilitybetweenand feasibilityof the landinggearsystemsandtheairframestructureshouldbereviewed.

Secondly, the landing gear design solutions are validated by performing numericalsimulations.Then,severalsetsofcriticalloadcasesareassessedfortheselandinggeardesign solutions [10, 25]. Currently, these critical load cases are obtained based onstatisticaldatawhereasinrealitytheywilldependontheinherentflightdynamicsandintended operational usage of each individual aircraft design. As shown in reference[29],theflightdynamicsandloadsshouldbeaccountedforintheestimationofcriticallandinggearloadcases.Otherwise,itmayleadtoaninaccuratedeterminationofcritical

10

loadcases.Currently,numericalsimulationmethodshavebeenusedindetailedlandinggeardesign[30‐34].However, theirapplication in landinggeardesign integratedwithaircraft flightdynamicsand loads isstill rare [10,25].Due to the lackofadesignandmodeling method that can integrate them, the concurrent simulation of them is notpossible. Therefore, these load cases based on statistical data are not necessarilyaccurate for the landing gear design under consideration. The use of statistical datacouldresultina15%differencebetweentheultimatevaluesofallowedcriticallandinggearloadcasesusedintheconceptualdesignphaseandthoseobtainedduringthefinalexperimentalphase[10,34,35].Furthermore,theclassicallandinggeardesignmethodsare not applicable to novel aircraft designs and innovative landing gears. Becausestatisticaldataofcriticalloadcasesforinnovativelandinggeardesignisnotavailable.

Thirdly,accordingtothecertificationspecificationofEuropeanAviationSafetyAgency(EASA)CS‐25[34],thelandinggeardesignisvalidatedbyperformingthegroundtestsbefore the real flight test, e.g. “drop test”. The “drop test” is the adopted validationmethodtodeterminethesafetyoflandinggearsystemdesign.This“droptest”isusedtoimitatethelandinggearloadcaseunderaspecificlandingconditione.g.maximumsinkrate.However,thisdroptestignoresmanyfactorsthatmightaffecttheresults,suchasan aircraft’s longitudinal and lateral aerodynamic loads, environmental conditions,aircraftflightattitudesandmotions(rollangle,rollrate,etc.).Thefatigueloadingofthelandinggearandaircraftshouldbecarefullyanalyzedinlandinggeardesignprocess[5,36,37].Thefatiguetestsoflandinggearandaircraftcommonlytakeseveralyears.Thefatigue lift of the landing gear and aircraft structure should meet the certificationspecification.

Inthefinalstep,thelandinggearsystemwillbeimplementedintheaircrafttoperformtheflightandgroundtestforthevalidationandverification.

The development of a new aircraft from conceptual design to commercial operationtakestime,intheorderof10years[3].Theinteractionofanaircraft’slandinggearwiththerestofthestructureiscomplexandmustbeconsideredinanearlydesignphase.Apoor landing gear design tool can lead to the need for inefficient backward designmodificationofotheraircraftsubsystemswhichiscostlyandtime‐consuming.Hencetowork efficiently with the other design departments is important for landing geardesigners[25,38,39].

Insummary,theclassicallandinggeardesignmethodshavetwolimitations.Firstofall,sincethedesignisconductedseparatelyfromtheaircraftdesign,theoveralldesign,e.g.airframeand landinggear,will be sub‐optimal [10,25]. Secondly, the identificationofcritical landing gear load cases is based on statistical data without comprehensiveaccounting the effect of flight dynamics and landing gear characteristics. Hence it isinaccurateorevennotrepresentativefornovelaircraftdesigns.

1.3. Advancedlandinggeardesignmethods

The advanced landing gear design methods refer to those methods that involveadvanced design and analysis methods, like Multidisciplinary Design, Analysis, andOptimization (MDAO), Knowledge Based Engineering (KBE), Computer AidedEngineering(CAE).However,theindustryhasnotyetfullyadoptedtheuseofadvanced

11

designmethods and still relies heavily on classicalmethods. Currently, the advancedlandinggeardesignmethodsarenotideallyintegratedtogetherwiththeoverallaircraftdesign process. The advanced design and modeling methods still have space to beimprovedtoenhancetheirapplicabilityintheco‐simulationandco‐analysisoflandinggear together with other aircraft subsystems design [38‐40]. The most importantresearchstudiesaresummarizedbelow.

SiemensdevelopstheLMSImagineLab[41]whichenablestheengineerstoassessthecompletemulti‐domain performance of the landing gear system (see Figure1‐3). Thelanding, extension, and retraction, braking and steering systems are included in thissystem. It is capable of simulating the landing gears subsystems (electrical, hydraulic,mechanicalandcontrol)togetherwithMultibodyDynamicsSimulation(MDS)andFiniteElement Method (FEM). The landing gear weight is estimated based on the class 2.5weight estimation method that accounts each of its components geometry [3]. Thissystem is used by several companies for landing gears design, e.g. Messier‐Bugatti‐Dowty [42]. This is essentially a multidisciplinary analysis tool. However, theidentification of accurate critical load cases is not included in this tool. The designrequirements, including the critical load cases, are provided by other aircraft designdepartmentsbasedonstatisticaldata.

Figure1‐3DiagramoflandinggeardesignprocessusingSiemensLMSImagineLab[41]

MDAO,KBE,andCAEhavebeenapplied to the landinggeardesignprocess.However,onlyalimitedamountofthisaroundofresearchhasbeencarriedoutanddemonstrated,e.g.byHeerens[39]andChaietal.[25,38].Chaietal.usestatisticaldataandclassicalstatics analysis methods to obtain the critical landing gear load cases. Chai et al.investigate the effects of landing gear characteristics, i.e. layout, configuration, onlanding gear weight. The objective is to obtain an optimal design with minimalstructuralweight.

12

Figure1‐4TheworkflowofHeerens’landinggeardesigntool[30]

Heerens’ [39] landing gears designmethodology is an automated landing gear designandanalysistool(seeFigure1‐4).ThelandinggearanalysistoolisestablishedbasedonKBE.Itcanbeusedintheautomaticdesignofthelandinggearandavarietyoflandinggear designs can be investigated, e.g. designs with different landing gear layout. Theiterationwillbestoppedwhenthelandinggeardesignresultisconverged.InHeerens’researchstudies,thecriticallandinggearloadcasesforthetop‐levelrequirementsarealsoidentifiedbasedonstatics.

Nevertheless,theapplicationofthemethodsintroducedbyChaietal.andHeerensinthedesign of innovative landing gear system has its limitation. Because possible landingattitudes and control inputs at touchdownarenot estimated.Theseparameters couldaffecttheidentificationofcriticallandinggearloadcases.

AnMDAOmethodforlandinggeardesignisdevelopedbyAltairHyperWorks[43]andappliedtoa testcase inwhichatorsionlinkdesignisoptimized.Themethodisbasedprimarily on a combination ofMDSandFEM. Theprocess is illustrated inFigure1‐5.Loadsarefirstsimulatedusingmultibodydynamics.Next,topologyoptimizationbasedonFEManalysis isconducted.Theobjectivesof thisCAEdrivendesignprocessare todetermine the damping coefficient of the landing gear, to find a torsion link with aminimal weight that meets the requirements, and to re‐design the lugs in order toreducecriticalstresses.Again,thisapproachislimitedwithregardstotheidentificationof thecritical loadcases. It is stillbasedonstatisticaldata.Furthermore,although theflightcontrolanddynamicscanbesimulatedbyusing tools like theMotionSolver forAerospace [44], the function ofmultidisciplinary design based on the flight dynamicsmodelandtheothersubsystems,e.g.weightsubsystem,strengthvalidationsubsystem,criticalloadcasesidentificationsubsystem,isnotincludedinthistool.

Insummary,thefollowingconclusionsmaybedrawnatthisstage.Firstly,theexistingadvancedlandinggeardesignmethodscannotfundamentallysolveoneoftheessentialproblems in classical landing gear designmethods, i.e. difficulty in predicting criticalload cases. Secondly, although flight dynamics and loads simulations are included insomestudies,itsintegrationinamultidisciplinarysimulationandanalysisframeworkisstillmissing.

13

Figure1‐5TheoptimizationworkflowofalandinggeartorsionlinkusingAltairHyperWorks[43]

1.4. Flightdynamicsandloadssimulation

1.4.1.Theneedforflightdynamicsandloadssimulation

Inviewofthedrawbacksofexistinglandinggeardesigntools,anoverallaircraftdesigntool/process based on the MDAO framework which comprehensively involves flightdynamics and landing gear characteristics should be developed. By utilizing this tool,engineerswho used to independently study the design of aircraft subsystems can beintegrated together. Hence, the overall aircraft design and optimization can beperformed(seeFigure1‐6).Thisalsoallowsforaphysics‐baseddesignofnovellandinggearsystemsforwhichstatisticaldataisnotyetavailable.Inordertorealizethistarget,a flight dynamics and loads simulation model should be developed. For readingconvenience, the term of flight dynamics and loadsmodel in this thesis includes theflightandlandinggeardynamicsmodels.

The flightdynamicsand loadsmodelshouldbeabletoaccuratelypredict landing loadcases under the presence of crosswind and atmospheric turbulence. Thus, bothlongitudinalandlateral‐directionaldynamicsmustbeincludedaswellasthedynamicsofthelandinggears.Torepresentthedynamicsofthelandinggears,aMDSisrequiredfor which stiffness and damping parameters are needed. In addition, a tyremodel isrequired. The simulation of the longitudinal and lateral‐directional dynamics of theairframereliesheavilyontheaerodynamicforcesandtherepresentationofatmosphericturbulence and crosswind. An accurate aerodynamic database should, therefore, bepresent which includes all relevant coefficients (stability and control derivatives at arangeofoperatingconditions).Themodellingrequirementsandpotentialsolutionswillbeextensivelydiscussedinthefollowingsections.

14

Figure 1‐6 The diagram of the flight dynamics and loads simulation model based onmultidisciplinaryanalysisframework[3,45]

1.4.2.Existingsolutionforphysics‐basedlandinggearmodeling

The landing gear system should bemodeled and implemented as a part of the flightdynamicsloadsmodel.Whendesigninglandinggearsforaircraft,thestressdistributionineachcomponentofthelandinggearmustbeanalyzedandthedynamicloadshavetobe taken intoaccount.Todo this efficiently it is necessary touse simulationmethodswhich can accuratelymodel thedynamics of the flight and landing gear systembeingstudied. The dynamic interactions and contacts between environment, aircraft, andground(runway)mustbesimulated.Thedynamicalbehaviorofthecomponentsintheaircraft landing gear system and the behavior of the control system, and all of thesefactorsneed tobe included into thesimulation inan integratedmanner rather thanaseparatecalculation.

A large number of numericalmodeling theories and simulation approaches exist thatcan be used to solve the problems [29, 46‐51] (see Figure 1‐7). In the methodsillustratedinthereferences[41‐44],FEMandMDSarethemostimportantapproachesused for landing gear systemdesign. The formermethod is noted for its high fidelitywhichmakesitsuitableforthestructuralanalysisofcomplexgeometries[30‐32,52,53].And it is commonly used to analyze the stress, thermal distribution of structuralcomponents.ThecommonlyusedFEMtoolsareANSYS,NASTRAN,etc.UsingMDS,thefocus is on the interaction and contact relationships between the components in themultibody dynamics system, like the dynamic interaction analysis, estimation ofcomponents motion, kinematics analysis etc. Commonly used MDS tools are, e.g.Matlab/Simmechanics,ADAMS,andSIMPACK.

15

The use of FEM supports a detailed structural investigation of a complex structurewithoutexpensivepracticalexperimentsbeingrequiredinthepreliminarydesignphase.However, FEMalsohas limitationswhich should bementioned. The FEM is primarilyuseful for static structures analysis rather than motion analysis, and it requires anextensive,expensivecomputingcapacitytoarriveatreliableresults.Restrictedbythislimitation, thismethodhascommonlybeenemployed toanalyze isolated landinggearperformancewithout interactionwiththeairframebeingtakenintoconsiderationandthesimulationsarelimitedtostaticsimulations[30‐32,52,53].

An analysis of the dynamic interactions between connected components in a landinggearssystemisakeypointinthelandinggearsdesignprocess,andtodothisMDShasrecentlybeenimplementedinlandinggearsystemdesignresearchtosolvethisproblem[54]. Generally, this method treats landing gear system components as multi (rigid)bodies connected with specialized defined kinematic pairs and interactions forcomputing saving purpose. The MDS method can also be used in the dynamicssimulation of the flexible structure. However, the multi (flexible) body dynamicssimulation needs the detailed parameters of structure and material property of thecomponents.This information iscommonlyunknownat theaircraftconceptualdesignstage.Furthermore,ashasbeenproveninreferences[49,55],thedifferenceinresultsbetween therigidand flexiblesimulationmodel isaround3%which isacceptable fortheaircraftconceptualdesignstage.

Figure1‐7Thecomparisonofphysics‐basedlandinggearmodelingmethods[56]

Insummary, in this thesis, regarding the landinggearmodel that isdeveloped for theconceptualdesignstage,themulti(rigid)bodydynamicssimulationmethodisused.Thereasonsaresummarizedasfollows:Firstly,theprimarytargetoflandinggeardesignatthe aircraft conceptual design stage is to provide a preliminary design rather than adetailed design. MDS approach is suitable for analyzing the interaction of thecomponents in landing gears, like those of a landing gear system and airframe undercertainflightconditions.WhilethemaintaskoftheFEMistoinvestigatethegeometrical

16

andstructuraldesignoflandinggearcomponentsinthedetaileddesignstage.TheMDSmethodissuitableforthelandinggeardesignataircraftconceptualdesignphase.Thesetwomethods,FEMandMDSarecomplementary, and thecombinationof themcanbeusedforflexibleMDS.Secondly,becausethedetailedstructuralandmaterialpropertiesofthe landinggearsystemarecommonlyunavailable intheaircraftconceptualdesignstage.Thesedataarenecessary toFEMandmulti (flexible)bodydynamicssimulationmethod. Hence, they are not suitable for the aircraft early design stage. Thirdly,comparedwiththemulti(flexible)bodydynamicssimulationmethod,themulti(rigid)bodydynamicssimulationmethodcanalsoobtainnecessarilyaccurateloadcaseswhicharesufficientfortheaircraftconceptualdesignstage.

1.4.3.Existingsolutionsforflightdynamicsmodeling

Therearemanymethodsavailableforthesimulationofflightdynamics,likelinearrigidbodysimulation,nonlinearrigidbodysimulation,multi‐rigid‐bodydynamics,andmulti‐flexible body dynamics simulation. The flight dynamics modeling method should becompatible with the fidelity and efficiency requirements of the aircraft conceptualdesignstage.Intheaircraftconceptualdesignstage,thesimulationaccuracyisacrucialfactorthatdeterminestheselectionofmodelingmethods.Theenginedynamics,aircraftcontrolandstabilityshouldbeincludedintheflightdynamicssimulation.Inthisstage,thedetaileddesignofeachaircraftsubsystemisnotnecessaryandevennotpossibleyet.Because in the aircraft early design stage, the key purpose is to obtain a preliminarydesignoftheoverallaircraftfromthetoplevelandmostofthedetailedaircraftdesignparameters are not know yet. Besides, the calculation time is also a crucial factoraffecting thedeterminationofmodelingmethods. Inprinciple, theaircraftstructure isflexible,e.g.airframe,wings, whichcouldaffecttheflightdynamicsloads.However, inaccordance to the references [49,55], similar to the selectionofmodelingmethod forlandinggearsystem,therigidmultibodydynamicssimulationmethodisacceptableforflightdynamicsmodelingattheaircraftconceptualdesignstageasthedifferenceintheresultsofloadcasesbetweentherigidandflexiblesimulationmodelisaround3%.Theaircraftcanbesimplified intoarigidbodydynamicssimulationmodel.Andasbothofthe longitudinal and lateral‐directional dynamics must be included in the flightdynamicssimulation,a6DegreeofFreedom(DoF)oftheflightdynamicsmodelshouldbedeveloped.

Yann [57] has created a 3 DoF mathematical aircraft simulation model whichencompasses vertical, longitudinal and pitch motion. This approach shows thepossibilityofusingcomputeraidedsimulationforaircraftflightdynamicsinvestigations.Basedonmultibodydynamicstheory,Voskuijl[58]hascreatedanMDSrigid‐bodyFlightMechanic Toolbox in Matlab which can be used for the dynamic flight simulation. Itintegratesthenecessarysubsystemsinmodernaircraft,e.g.propulsionsystem,controlsystem.Thistoolisbasedona6DoFMDSmodelanditsworkflowissimilartoYann’stool.ComparedwithYann’smethodwhichonlyaccountsthe loadsandmotions in thelongitudinal direction, Voskuijl’s tool accounts the loads and motions in longitudinal,lateral,andverticaldirections.

Usingahighfidelitysimulationmodel,P.Ohme[59]proposesa6DoFtoolforaircrafttakeoff and landing simulation. This tool, denoted MAPET II, can acquire flight

17

performancedatabasedonthedataprovidedbywindtunneltestsandCFDcalculations.P. C. Chen [60] proposes a nonlinear dynamic flight simulation method which canaccount for the aeroelastic coupling effect between structural dynamic and unsteadyaerodynamic effects. However, these methods are computationally expensive andrequire detailed geometrical data which are commonly not available in aircraftconceptualdesignstage.Inordertorealizethesimultaneoussimulationfortheoverallaircraft system, Antonio Filippone [45] presents a multidisciplinary simulationframework for the coupling of subsystems in modern aircraft, like aerodynamics,propulsion (see Figure 1‐8). Regarding this framework, the flight dynamics and loadsmodelsystemconsistsof foursub‐modules, i.e. input,discipline,discipline integration,anddataprocessing.This frameworkcanbeusedasareferencetoestablishthe flightdynamics model based on MDAO. In this thesis, a flight dynamics model will bedevelopedforaircraftconceptualdesignstage.Thesubsystems inmodernaircraft,e.g.airframe, engines, control systems, should be able to be integrated into it. Hence, theflightdynamicsmodelismodeledasa6DoFMDSmodelextendedfromVoskuijl’stool[58].Afterward,itwillbeintegratedwiththelandinggeardynamicsmodel.

Figure1‐8Multidisciplinary implementation of flight dynamics and loads simulation model [45]

1.4.4.Existingsolutionforaerodynamicsanalysis

Thefidelityoftheaerodynamicsanalysismethodisacrucialfactoraffecttheselectionofthemethod as it determines the flight dynamics load cases. The aircraft stability andcontrol derivatives should be obtained based on the aircraft 2D or 3D model in theaerodynamicsanalysisstep.Intheaircraftconceptualdesignstage,itshouldbeselectedfromhighormediumfidelitymethod(seeFigure1‐9)[61‐64].Thepreliminarydesignofaircraftobtainedintheearlydesignstageisbasedontheiterationofdifferentdesigns.Hence the chosen aerodynamics analysis methods should avoid requiring highexperimentalcostand longcalculationtime.Besides,as thedetailedaircraftgeometrydataisnotalwaysavailableintheaircraftearlydesignstage.Thechosenmethodshouldbe able to generate reliable stability and control derivatives based on the simplifiedaircraft geometry model. High fidelity methods, e.g. wind tunnel test and CFD, canprovidereliableandaccuratedata(seeFigure1‐9).A.DaRonchetal.[65]M.Ghoreyshietal. [66]demonstrate theresearchofusingaerodynamics lookuptablesbymeansofCFD in investigatingaircrafthandlingqualities,manoeuvres,and loadcases.However,

18

the implementation of high fidelity aerodynamics data is a challenge as accurateexperimentaldataandCFDmodels arenot alwaysavailable in theaircraft conceptualdesignstage.Besides,thehighexperimentalcostandlongcalculationtimealsolimittheapplicationofthehigh‐fidelitymethodsintheaircraftconceptualdesignstage.

DataCompendium(DATCOM) is anempiricalmethodwhichgivesaccurate results forconventionalaircraftconfigurations.ItwasdevelopedbytheUSAF[67].M.Baarspul[63]andMaria Pester [61] utilize DATCOM to acquire aerodynamic coefficients of CessnaCitation500andA320atlowairspeedconditionrespectively.Theresultsarevalidatedwith experimental data. Besides, the results prove that the application ofDATCOM inestimatingaerodynamiccoefficientsissuitableforuseintheaircraftconceptualdesignphase.However,theDATCOMisnotabletoestimatetheruddercontrolderivatives.

Figure1‐9Thecomparisonofexistingaerodynamicsanalysismethods[61‐64]

Ramón López Pereira [64] and Enrique Mata Bueso [68] illustrate the application ofTornadofortheestimationoftheaerodynamiccoefficientatlowairspeedconditionforA320.TheTornadoisatoolbasedonthevortexlatticemethod(seeFigure1‐10)[67,69,70]. The comparison of results obtained from Tornado and DATCOM shows thatTornadogivesreliableresults[61,64,67,69‐71].However,thedefinitionandmodelingofahighliftdeviceandafuselageinTornadoarenotpossible.

In this thesis, theDATCOM[63,67,70] is chosenas theaerodynamicsdatageneratorsfor flight dynamics and loads model. However, since it can not estimate the ruddercontrolderivatives,theTornado[64,69]isusedtogeneratethesedataasasupplement.Thereasonsforthischoiceare:

1. Thedetailedhighfidelityaerodynamicscoefficientsdataarenotavailableintheopenliterature.

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2. TheperformanceandaccuracyofTornadoandDATCOMhavebeenvalidatedintheliteraturewhichissufficientlyaccurateforaircraftconceptualdesignstage.

3. TheaircraftcharacteristicsrequiredbyTornadoandDATCOMforaerodynamicscoefficientsestimationareavailableintheopenliterature.

Figure1‐10TheworkflowforTornadotocalculateaerodynamicscoefficients[72]

1.4.5.Existingsolutionforpilotandatmospheremodeling

Pilotbehaviorisacrucialfactorthataffectsthelandinggearloadcasesasitdeterminesthe flight attitudes in aircraft takeoff and touchdown. In order to realize the flightdynamics simulations in this thesis, the automatic flight control systemwhich can beused to realizedaircraft takeoff and landingshouldbe included in the flightdynamicsand loads simulation model. Since the critical load cases of landing gears will besimulatedinthisthesis,thepilotmodelshouldbeabletohandlethetakeoffandlandingin the critical flight attitudes and environmental conditions, like the aborted takeoff,takeoff with one inoperative engine, one gear landing, crosswind, and turbulence.Furthermore, thenecessaryparametersused in thepilotmodel shouldbeavailable intheopenliteratureasitisusedintheaircraftearlydesignstage.Mudassiretal.reviewthepilotmodelsused inaircraft flightdynamicssimulation [73].Like theQuasi‐linearmodel [74, 75], optimal control model based on Kalman filter models [76, 77], andnonlinearmodel[78‐80].Thesemodelsaredesignedforanalyzingflighttrajectoriesandhandlingqualities.Hence,thesemodelsarenotdesignedspecificallyforaircrafttakeoffandlandingsimulationsintheaircraftconceptualdesignstage.Becauseitisachallengeto obtain the necessarily accurate and sufficient parameters to establish these pilot

20

models at the aircraft early design stage. This thesis uses the classic open‐loop andclosed‐loopcontrolmodelstorealizethetakeoffandlandingsimulations[81,82].Thesemodelsaresimpleandreliabletorealizetheaircrafttakeoffandlandinginthecriticalloadcasesasmentionedabove.Moreover,thenecessarygainfactorsusedinthecontrolloops of thesemodels can be obtained by tuning in accordance to the predeterminedflighttrajectory.Nevertheless,itisvaluabletointroducetheelaboratecontrolmodelsintheflightdynamicssimulationifthenecessarymodelingparametersareavailable.Morekindsoflandinggearloadcasecanbesimulatedandinvestigated.

Theatmosphericmodelisalsoacrucialfactoraffectstheaccuracyoflandinggearloadcasesestimationbasedonflightdynamicssimulation.Turbulenceandcrosswindmodelsshouldbeincludedtosimulatetheaircrafttakeoffandlandingincriticalconditions.Inaccordance to literature, turbulence is a stochastic process [83‐85]. The velocitycomponentsofturbulenceshouldbeestimatedw.r.ttheenvironmentalconditions,e.g.altitude, wind velocity. Wang [86] summarizes the primary turbulence modelingmethodsillustratedintheopenliterature,e.g.vonKarmanWindTurbulenceModel[83,84],DrydenWindTurbulenceModel[85].TheturbulencebothinthevonKarmanandDryden models are defined in terms of power spectral densities for the velocitycomponents. The effect of altitude andwind velocity can be taken into consideration.Therefore,thevelocitycomponentsoftheturbulencecanbe incorporatedintoaircraftequations of motion together with the crosswind. The von Karman model ischaracterized by irrational power spectral densities while the Dryden model ischaracterizedbyrationalpowerspectraldensities. ThevonKarmanWindTurbulenceModelisvalidatedbytheFAAandUSDepartmentofDefenseandchosenastheprimaryturbulencemodel[85].Hence,thispaperusesthevonKarmanWindTurbulenceModelintheatmosphericmodel.

1.5. Researchobjectives

The relationship between existing methods and the newly introduced method aremutually complementary. The existing methods occupy the dominant position in thelanding gear design process. They can provide reliable designs for traditional aircraftstructure which have been proved by decades of safety flight history. However, theimproving of environmental requirements and increasing competition in the aviationmarket encourage aircraft design to be safer, greener, andmore comfortable. Besidesthe continuous improvement of traditional aircraft design, some innovative aircraftdesignsarealsobeing investigated.Therefore, thestudyofamethodtoassesscriticalload cases for landing gearswithin aircraft conceptual design is necessary. Currently,the effects of flight dynamics on the critical loads estimation for landing gears aremissingintheexistingdesignmethods.Thisthesisproposesapotentialsolutionwhichwouldbevaluable in integratingthe flightdynamics intocritical loadcasesestimationforlandinggears.Duringthetakeoffandlandingprocess,theflightdynamicsloadsaretransferredtothelandinggearsthroughtheconnectionpositionsbetweenthemandtheairframe.Hencetheflightdynamicsloadscanaffectthelandinggearloads.Theexistingdesign approaches mainly rely on not necessarily accurate critical load cases. Thesecriticalloadcasesaregenerallyobtainedfromstatisticaldata.Thedifficultyofobtainingaccuratecriticalloadcasesforlandinggeardesignpreventsthefurtherimprovementoflanding gear design performance. Especially in the design of innovative concepts of

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landing gear systems when there is no statistical data available. This thesis aims toprovide a promising solution to this problem. Hence, the research objectives of thisthesiscanbesummarizedasfollows:

Developaphysics‐baseddesignapproachwhichcanbeusedtoestimatethecriticalload casesof conventionaland innovative landinggears in the conceptualdesignstage.

Inordertoachievethisresearchobjective,thisthesiscarriesoutthefollowingresearchwork.

A flight dynamics and loads model is developed by utilizing a multidisciplinaryframework.Thismodelisestablishedbasedonmulti(rigid)bodydynamicssimulationmethod.Thenthecriticallandinggearloadcasescanbeestimatedbyperformingtakeoffand landing simulations. Before performing the takeoff and landing simulations, theflight dynamics and loadsmodel shouldbe initializedwith specific conditions, i.e. theextremeFCEE.Theseconditionssignificantlydeterminethe landinggearcritical loads.Then the critical load cases can be identified. This thesis provides two solutions toobtainthedataoftheextremeFCEE.

In the case of the extreme FCEE is available in the open literature, then they can besummarized and used to perform takeoff and landing simulations. This is commonlyappliedtotheestimationofcriticalloadcasesfortheconventionallandinggears.IncasetherelevantdataoftheextremeFCEEisnotavailable,theapproachcanestimatethembased on the flight dynamics simulations. Monte‐Carlo simulation is included in thisapproach as a solution to having a realistic representation ofweather conditions andpilotbehaviors.ThenavarietyoftakeoffandlandingsimulationscanbeperformedandtheextremeFCEEcanbeobtained.This isespeciallyvaluable indealingwithadesignprojectforinnovativeconceptlandinggear.

1.6. Thesisoutline

Three landing gear concepts which serve as test‐cases in this research study arepresentedinChapter2.Thereferenceaircraft,whichisbasedonanAirbusA320,isalsodescribed in Chapter 2. The overall process in which load cases are predicted usingphysics‐based simulations is presented in Chapter 3. This is followed by a detaileddescriptionoftheflightdynamicsandloadsmodelinChapter4.Theflightdynamicsandloadsmodel is used in combinationwithMonte‐Carlo simulations to predict the loadcasesforthethree landinggeartest‐cases.ResultsarepresentedinChapter5.Finally,conclusions and recommendations are presented in Chapter 6. Appendix Edemonstrateshowthisapproachcan lead tobetter landinggeardesignsbasedon thecasestudy.

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2 Referenceaircraftandlandinggearconcepts

2.1. Reference aircraft (A320) and Conventional landing gearsystems

Theapproachdevelopedinthisthesisisvaluablefortheimprovementofconventionallanding gear design. For example, newmaterials canbeused to reduce the structuralweightofalandinggearsystem,e.g.thePolymerMatrixComposite(PMC)[19].Byusingthismaterial, the landing gearweight reduction can reach up to 30% comparedwithexistingmetallic structures [19]. Hence, the landing gear load cases are also changeddue to the fact thatoverallaircraftweight ischanged.Thecritical loadcases for theselandinggearsstructuresmadeofnewmaterialsshouldbeestimated.

AccordingtoWijnterpetal.[48],80%ofallflightsfromandtoSchipholairport,oneofthebusiestairportsinEurope,areconductedbyaircraftwithaweightlessthanorequalto 90 tons. The Airbus A320 is the most representative aircraft of this type. It istherefore chosen as the reference aircraft (see Figure2‐1andTable 2‐1). AshasbeendiscussedinChapter1,thecharacteristicsofthisreferenceaircraft,e.g.geometry,mass,etc.,areessentialwhenestablishingtheaircraftMDSmodelinthisresearch.References[35,69,87]providemoredetailedcharacteristicsoftheA320anditslandinggears.

Astheconventionallandinggearisthemostworldwidelyusedlandinggearstructure,itisdemonstratedasatestcasetoshowtheworkflowofthelandinggeardesignapproachdevelopedinthisthesis.Itconsistsofthenoseandmainlandinggears,asillustratedinFigure 2‐1. The nose landing gear keeps an aircraft balanced in the longitudinaldirectionwhile themain loadsaresustainedbythemain landinggear.Thenumberoflandinggears,tyresandthestructureofbogiescanbeadjustedaccordingtotheweightof the aircraft, as visualized in Figure 2‐2 for different tyre layouts of landing gears.AppendixApresentstherelevantdesignrequirements.

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12.45m

34.10m

7.59m

0.93m0.50m

8.95m

12.64m5.07m

4.14m

5.87m

37.57m

5.75m

11.91m

8.30m

11.12mV2500

11.19mCFM56

3.95m

4.87m

Figure2‐1AirbusA320geometry[35]

Table2‐1Characteristicsofthereferenceaircraft[69,87]

Description Symbol ValueWingaspectratio AR 9.5Wingarea SW 122.4m2Aileronsarea SA 2.7m2Flapsarea SF 21m2

Leading‐edgeslatsarea SLS 12.6m2Spoilersarea SS 8.6m2Verticaltailsurfacesarea SV 21.5m2Horizontaltailsurfacesarea SH 31m2

MLW WML 646800NMTOW WMTO 720300N

SINGLECESSNA

PIPERS-3AC-2A

TWIN(DUAL)

B 727B 737

DUALTWIN(TWIN TWIN)DH TRIDENTC-5A NOSE

TANDEMC-130

TWIN TANDEM(DUAL TANDEM)

B 707B 747

L-1011DC-8

TWIN TRICYCLE(TWIN DELTA TANDEM)

C-5A

TRIPLESR-71

TRI-TWIN TANDEM

DUAL TWIN TANDEMB-58

Figure2‐2Standardlayoutscenariosforconventionalmainlandinggear[14]

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AconventionallandinggearsystemisshowninFigure2‐3.ThelandinggearsshowninFigure2‐3arethenoseandmainlandinggearswhichconsistofashockabsorber,dragstrut, side strut, truck beam, and tyres. A conceptual drawing and an extensivediscussionof these components areprovided inChapter3 and4. Commercial aircraftmake use of retractable landing gears to reduce aerodynamic drag during the climb,cruiseanddescent flightphases.Thesidestrutanddragstrutenhancethestrengthofthestructureinlateralandlongitudinaldirectionsduringtouchdownandothergroundrunoperations,suchastaxiing.Themain impactabsorbinganddissipationappliancesare the vertical shock absorber and the tyres. The Anti‐skid Brake System (ABS) islocatedinthewheeltoshortenthegrounddecelerationphaseduringlandingorwhenperformingarejected takeoff in thecaseofa takeoffemergency.Ashimmydamper isalsoanappliancethatiscommonlyusedinthelandinggearsofthemoderncivilaircrafttoalleviatetheshimmyandbrakeinducedvibration.ThereaderisreferredtoAppendixD for more information about this appliance. The nose landing gear has a steeringsystemtoenabledirectionalcontroloftheaircraftduringtaxiingoperations.Adetailedview of the conventional landing gear, i.e. layout, shock absorber and tyre systems,retractionmechanism,ispresentedinAppendixAtoAppendixD.

500mm

Compressed

Extended

2265mm

2869mm

470mm

3453mm 80°RetractionAngle

927.10mm

2338mmCompressed

Extended

1957mm

430mm

Figure2‐3AirbusA320noseandmainlandinggears[35]

ThemassandCGpositionofaircraftcouldaffectthelandinggearcriticalloadcases.Inprinciple, the heavier the aircraft, the higher the critical loads on the landing gears.Togetherwithaircraftmass, theCGpositioncouldalsoaffect thecritical loadcasesoflandinggearsbecausetheyhaveinfluencesonmanycrucialfactorswhichdeterminethelandinggearcriticalloadcases,e.g.aircrafttouchdownattitudes,de‐rotationoperation,the loads distribution between the nose and main landing gears, etc. Besides, theconditionoftherunwayisalsoafactorcouldaffectthecriticallandinggearloadcases[11,14,36].Thetyrescouldgenerateirregularloadsonthestructuresoflandinggearsbasedontheconditionsoftherunway,e.g.unevenrunway,contaminatedrunway,etc.Inthelifeofanaircraft,thegroundoperationscouldalsoaffectthecriticalloadcasesonthelandinggears,e.g.towingmanoeuvresbetweentherunwayandgates.Forexample,the hook bar could destroy the nose landing gear if it applies too high loads on theconnectionposition.

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The design of landing gear should be safe in all critical load cases, e.g. landing in acrosswind. In general, there are two kinds of conventional landing procedure in thepresence of crosswind: the sideslip procedure and the crabbed approach landingprocedure,seeFigure2‐4.Forthesideslipapproachlandingprocedure,theaileronsareusedtomaintainafixedrollangle.Theliftgeneratedbythewingisusedtocounteractthelateralaerodynamicforceresultingfromthepresenceofcrosswind.Thepilotrollsthe aircraft to a wings level attitude by controlling the ailerons shortly beforetouchdown.

Inthecrabbedapproachlandingprocedure,thelateralcomponentofthethrustvectorisusedtooffsetthelateralaerodynamicforceresultingfromthepresenceofcrosswind.Atthe last moment before the aircraft touches down on the runway, the pilot uses therudder to align the nose of the aircraft with the runway centerline. For readingconvenience,thedetailedcritical loadcasesforlandinggeardesignwillbeextensivelydiscussedinChapter5.

Figure2‐4AircraftSideslipApproachversusCrabbedApproach[88]

2.2. Unconventionallandinggearconcepts

Several unconventional landing gear concepts have been introduced lately [89‐95].Some of these concepts are paper studies whereas other concepts are being used inoperationalpractice.Themethodintroducedinthisthesistoestimatecriticalloadcasesforlandinggearsisvaluableforthedevelopmentoftheseunconventionallandinggearconcepts.Theseconceptswillbediscussedinthefollowingsections.

2.2.1.Greentaxiingsystems

Taxiingisanimportantphaseofaircraftdailyoperation.Theaircraftneedstotaxifromtheterminalgatetotherunwayfortakeoffortaxitoaterminalgateafterlandingontherunway. Taxiing operations account for the largest part of emissions in a standardlanding/takeoffcyclecostingfuelaround60kgforanAirbusA320,and120‐140kgforanAirbusA340[96].

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Generally,theaircraftreliesonataxiingtruckoritsownenginestorealizethetaxiingoperation. There are several other solutions for green taxi operations by utilizingunconventionallandinggearconcepts(seeFigure2‐5)[89‐95].

TheElectricGreenTaxiingSystem(EGTS) TheTaxibot TheWheelTug

TheEGTSisaninnovativesystemproposedbySafranandHoneywellanditislocatedinthetwomainlandinggears.TheaircraftAuxiliaryPowerUnit(APU)providesthepowerrequiredtodrivethemotorlocatedinthemainlandinggear.TheEGTSwillreduceupto67% of fuel consumption currently used on taxiing [97]. However, The EGTS willincrease 400 kg of weight on landing gear [98]. Consequently, despite the weightincreasecausedbytheimplementationofEGTS,thefuelsavingcanreachupto4%perflightcycle(A320makinga950kmflight)[97,99].

The Taxibot is a semi‐robotic pilot‐controlled towing tractor system [89]. A driver islocated in the tractor, but the responsibilities of the driver are limited to pushbacks,emergencyandtractorreturnoperation[89].TheuseofTaxibotcanleadtoupto2700tonsoffuelsavingonlong‐haulflightsperyearatLufthansa’sFrankfurthub[100].

TheWheelTugisamotorsystemwhichprovidesahightorqueandcanbeimplementedinthenoselandinggear.Duringthetaxiingphase,theaircraftenginecanbeshutdowntosavefuelconsumption.TheWheelTugispoweredbyanaircraftonboardAPU.Afterimplementingthesetechnologies,thefuelconsumptionreductionforthetaxiingphasecan reachup to66%per flight cycle [101]. Installing theWheelTugwill increase theweight of 140kgon the landing gears [98].Nevertheless, despite theweight increasecausedby addingWheelTug, theworthof fuel consumption saving can reach around200USDperflightcycleastestedontheGermania737‐700aircraft[96,99,101].

The costs for the implementation of these technologies are unavailable in the openliterature.ComparedwiththeTaxibot,theEGTSandWheelTughaveadrawbackastheywilladdextraweighttotheexistinglandinggearstructure.

Figure2‐5Assistedtaxiingsystemsforcivilaircraft[92,102,103]

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2.2.2.Catapultassistedtakeoff

ThemostcommonlyusedcatapultassistedtakeoffisthesteamaircraftcatapultsystemimplementedonaircraftcarriersaspresentedinFigure2‐6[14,104].Itconsistsofthecatapult shuttle which is attached to the catapult piston. The piston is powered bycompressedsteamflowtoprovidelongitudinalthrust.Thecatapultshuttlehooksontothenose gearof amilitary aircraft andprovides extra thrust for aircraft before liftofffrom the carrier’s deck. Benefiting from this technology, aircraft can take off from anaircraftcarrierwhichhasa limitedlengthdeck.Theapproachdevelopedinthis thesiscanestimatethecriticalloadcasesoflandinggearsduringthecatapultphase.

Inrecentyears,theElectro‐MagneticLaunchSystem(EMALS)showninFigure2‐6hasbeen tested by the US NAVY [105]. This system is designed to substitute a steamcatapultsystemonanaircraftcarrier.Thekeydifferencebetweenthetwosystemsisthepower source that is used: the steam catapult uses compressed steam whileelectromagneticpower is used in thenewer technology.EMALShasmanyadvantagescomparedtothesteamcatapultsystem.ThesearesummarizedinTable2‐2.

Figure2‐6ThestructureofthesteamcatapultsystemandEMALS[106‐109]

Table2‐2PerformancecomparisonofsteamcatapultsystemandEMALS[105,110]

Parameters SteamCatapult EMALSEnergyTransferEfficiency 5% 89%MaxPeak‐to‐MeanAcceleration 1.25 1.05Volume(m3) 1133 425Weight(tons) 486 225MaxLaunchEnergy(MJ) 95 122

Compared with the conventional steam catapult system, the benefits of usingelectromagneticpowertopowerthecatapultare[105,110]:

highenergytransferefficiency morepreciselycontrolledoutputthrust lessspacetoinstallonanaircraftcarrier greatermaximumpoweroutput

Besidesthemilitaryapplication,theEMALScanbeusedpotentiallyasacatapultsystemforcivilapplications[111,112].Thisconcept issimilartothesystemshowninFigure2‐6.The landinggearsystemused in thiscivilaircraftcatapult technology ismodified

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basedonaconventionallandinggearsystem.Theredesignoftheconventionallandinggear system for this technology can be seen as an illustration of the transition fromconventionallandinggearsystemtoamoreinnovativelandinggearsystem.Inordertoshowtheusabilityofthecriticallandinggearloadcasesestimationmethoddevelopedinthis research, the landing gear design progress for civil aircraft catapult system isillustratedasatestcaseinthisthesis.

Thedesign of a catapult system for civil aircraft and aquantitative assessment of thepotential benefits is investigated by Vos et al. [112, 113]. Vos et al. investigate theconceptthatthecatapultsystemisattachedtothecivilaircraftairframethroughabar.AccordingtotheresearchofVosetal.[112,113],thefuelconsumptionduringtake‐offcan be reduced up to 20% as the aircraft can obtain extra thrust from the catapultsystem.Besides,theaircraftcanliftofffromtherunwayandclimbwithhigherairspeed.Therefore, thenoiseat theAmsterdamAirportSchipholcanbereducedby20%[112,113].Andthetake‐offtimecanbereducedupto50%astheaircraftcanachievehigheraccelerationduringthegroundrunphase. Itwill thushaveapositiveeffectonairportcongestion.

2.2.3.Takeoffandlandingusingagroundbasedsystem

Althoughalandinggearsystemplaysakeyroleintheaircrafttakeoffandlandingphase,over 95% of the flight time they are retracted into the airframe yet they account forapproximately5%ofMLW[14].Researchisthereforeperformedwhetheritispossibleto remove the landing gear from the aircraft and to replace it with a ground basedlandingsystem.

The European Union has funded a research project called: Integrated ground andonboardsystemforsupportoftheaircraftsafetake‐offandlanding(GABRIEL).TUDelftparticipatesinthisEU‐FP7fundedprojectwhichaimstoimprovethefuelconsumptionandemissionperformanceofmedium‐haulaircraftbyreducingitsweight.Itproposesapotential solution to remove conventional landing gear system from the airframeandinvestigate the possibility of assisting civil aircraft take‐off and landing using groundbasedsystem[114].Langenetal.[21,22]demonstratetheanalysisandbenefitsofthistechnology.Duetothesnowballeffect,theaircraftweightcanbereducedbyaround7%of maximum takeoff weight (MTOW). Therefore, the optimal design for the overallaircraft system can be achieved [21, 22]. This project focuses on the study of such asystem formedium‐haulaircraft.TheGABRIELconcept is chosenas a test case foraninnovative landing gear system to demonstrate the design feasibility of the designapproachdevelopedinthisthesis.

TheGABRIELsystemconsistsof a groundbasedsystemanda connectionmechanismbetween it and the aircraft (see Figure 2‐7). The ground based system consists of amobile platformon a ground‐based vehicle poweredbymaglev force. The connectionmechanismcalledharpoonsystemconsistsoftheonboardpart,aharpoonstick,andthegroundbasedpart,aharpoondisk.

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Figure2‐7Topviewsofthemobileplatformlocatedinthegroundbasesledge[115‐117]

Currently, the maximum crosswind specified in the certification specification of theEASAandFAAforcivilaircraftis15m/s[34,118].However,theautomaticflightcontrolsystem implemented on theAirbus A320 is only certified to perform safe landings incrosswind up to 10 m/s [119]. Hence, the landing in crosswind higher than 10 m/sshould be accomplished with manual flight operation. The de‐crab operation incrosswindlandingconditionshashighrequirementsforthepilot’sexperienceandskills.ThemobileplatformcanbealignedtotheaircraftyawangleasindicatedinFigure2‐7.Thismobile platform is valuable in assisting aircraft takeoff and landing in crosswindconditions.Thepilotsdon’tneedtoperformthede‐craboperationincrosswindlandingconditionasthemobileplatformcancaptureaircraftwithitsidenticalyawangle.Hence,the landing accuracy can be improved. The shock absorbers are moved from theconventionalairframeandallocatedonthemobileplatform(seeFigure2‐8).Eachshockabsorberisattachedtoonedragstrutandtwosidestruts.Thesestructuresaresimilartothoseusedintheconventionallandinggearconcept.

Thedetailedconnectionmechanismfortheaircraftandtheground‐basedsystemisstillinthedevelopmentphase[114,120‐122].Theharpoonsystemischosenasapossiblesolution for the connection mechanism between the aircraft and the ground‐basedsystem [123]. The harpoon system is a technology for aircraft landing on mobileplatforms,likeaircraftcarriershipdecklandingoperations,duetoitsreliabilityandlowcost[115].

The harpoon system used in GABRIEL consists of the harpoon stick and the harpoondisk[123].AsillustratedinFigure2‐7,theharpoonsticksareallocatedatthepositionsof the current landing gears.Theharpoongriddisk is attached to the shock absorberallocateduponthemobileplatform(seeFigure2‐8).Theharpoonstickcanlocktotheharpoon grid disk with the hook allocated at the end of its bottom. The reader isreferred to references [115, 122] for an extensive discussion about the harpoontechnology.

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Figure2‐8ThesketchofthemobileplatformandtheconnectionmechanismintheGABRIELconcept

ThetakeoffandlandingprocessofthesystemispresentedinFigure2‐9andFigure2‐10respectively. For takeoff phase, shown in Figure 2‐9, the aircraft is attached to thegroundbasevehicleatthestartpositionoftherunway.Afterauthorization,theaircraftstartstheaccelerationprocessassistedbythegroundbasedpowerandthenpitchesupitsnoseafter reachingrotationspeed.Afterward, thecontrolsystemsonboardwill letthe aircraft detach from the ground‐based vehicle once the aircraft lift equals to itsweight.Thenthefuselageliftsofffromground‐basedsystemtoanairbornephasewhichisfollowedbyanalogousconventionalclimboperation.ByutilizingtheGABRIELsystem,therequiredinstalledpowerofaircraftenginescanbedecreased.Becausetheaircraftweightisreducedbyremovingthelandinggearsystemandtheaircraftcanobtainextrathrustfromthegroundbasedsystem.

Figure2‐9TakeoffprocedureoftheGABRIELconcept[124]

The landing operation for GABRIEL is illustrated in Figure 2‐10. The ground‐basedvehicleawaitstheaircraftpassthroughcertainaltitudeintheapproachphaseandthenstartsthesynchronizationprocess.Thesynchronizationcontrolsystemimplementedontheground‐basedvehiclecanrealizebothitspositionandvelocitytobesynchronizedtothe aircraft. Themoment just before aircraft touchdown, the ground‐based vehicle isjust below it and then captures it. Next, the aircraft is clamped upon the vehicle anddeceleratedbyground‐basedpower.

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Figure2‐10LandingprocedureoftheGABRIELconcept[124]

Variouschallengesareidentified,whichneedtobeaddressedbyfutureresearch:

thecertification implementationcosts landingaccuracy emergencylanding

The first priority is the certification should be studied and issued by aviationadministration,i.e.EASA,FAA.Ontheonehand,theimplementationofGABRIELsystemneedstomodifytheairframe.Ontheotherhand,thetakeoffandlandingprocessesaredifferent fromconventionalones.Hence, thefeasibilityandreliabilityof implementingGABRIELinconventionalaircraftshouldbecertified.

Thecostsofmodifyingaircraft,airports,andrunwaystohandletheGABRIELsystemarethe main disadvantage of this technology and should be investigated. Theimplementationandannualmaintenancecostcanreachupto160millionand2millioneuros[125].Thiscost includesa2400meterlongrunway(45meterswide)plusa2x7.5meterwideshoulder,3rapidexitsandtaxiwayswithshoulders[125].

With respect to safety, landing accuracy for aircraft touch down under extremeenvironmental conditions, like extreme crosswinds, using a mobile sledge is still achallenge [126]. A more elaborate control system, i.e. the synchronization control inlongitudinal and lateraldirections, shouldbedeveloped for aircraft andgroundbasedsystemtoensurethelandingsafety.

(A) (B)

Figure2‐11EmergencyconditionsolutionsforlandingoperationadoptedbytheGABRIEL[127]

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Foremergencyconditions,theGABRIELprojectreportsprovidetwopotentialsolutionsin case the aircraft have to land at the airport without GABRIEL system [127]. Theparachute(left)andskid(right)conceptsarepreliminarydesignforGABRIELproposalrequirements(seeFigure2‐11).

Themainbenefitsofthissystemarethefollowing:

lighteraircraftstructureweight feweremissions lowerflightcost

Although the conventional landinggear systemaccounts for5%ofaircraftMLW[14],theinnovativedesignofremovingconventionallandinggearcanleadtothereductionofaircraftweightmorethan5%ofaircraftMLW[21,22].Becausethelandinggeardesignprocess can be integrated into the aircraft overall design process based on theMultidisciplinaryDesignandOptimization(MDO)[21,22].J.Sobieszczanski‐Sobieskietal. summarized the recent developments of multidisciplinary aerospace designoptimization[128‐130].Forexample,intheaircraftconceptualdesignphase,theweightsavingcausedbyremovinglandinggearscanleadtolessfuelconsumption.Therefore,thewingsandairframestructurecanbeoptimizedastheloadsgeneratedbyfuelweightisreduced.Hence,theweightofthewingsandairframecanbereduced.Inthisiterationprocess, the reduction in fuselage and airframe weight can further reduce fuelconsumption.Inaccordancewiththesnowballeffect,duetotheremovalofconventionallanding gear in GABRIEL, the aircraft can benefit up to 12% of previous MaximumTakeoffMass (MTOM) for A320‐200 implementedwith Cart‐Sledge Concept [21, 22].Andtheaviationindustryandpassengersshouldbenefitfromreducedfuelconsumptionby up to 13% savings on today’s usage [21, 22]. According to the research of Graaff[125], thecostreductioncanbeacquiredbyimplementingGABRIELsystemcanreachabout€1579per flight (forA320andeach flight is5000km),despite the investmentcostsinthemaglevsystem.

BesidestheGABRIELconcept,therearealsoothersimilarconcepts.TillMarquardtetal.and Airbus [131, 132] have developed assisted takeoff and landing concepts for civilaircraftcalledGround‐basedLandingGearSystem(GroLaS)andEco‐Climb,asshowninFigure 2‐12 respectively. These two concepts are similar to GABRIEL. The aircraft islaunched fromand capturedby a ground‐basedvehicle system in takeoff and landingrespectively.Thisallowsthecompleteremovalofthelandinggearfromtheairframe.

Figure2‐12GroLaStechnology(Left)[132]andAirbusEco‐Climbconcept(Right)[131]

34

TheGroLaS focuseson the studyw.r.t long‐haul cargo aircraftwhich isdifferent fromthemediumhaul civil aircraft investigated in theGABRIEL. In theGroLaS technology,the ground‐based cart is mounted on rails which are installed on both sides of therunway. This cart can both synchronize its longitudinal and lateral position to theaircraftbeforetouchdown.ComparedwithGABRIEL,ithasthebenefitofimprovingthelandingaccuracy.Duringthetakeoffphaseofaflight,thisrailcanprovideextrathrusttoassisttheaircrafttoreachlift‐offairspeed.Itcanalsobeusedtoprovideabrakingforceforrejectedtakeofforlandingdecelerationoperations.Reversethrustfromtheaircraftengines isnotrequiredandbrakingdistancescanbeshortened.Furthermore,brakingenergycanbecollectedandtransferred intoelectricalpower.Theenergyrecuperateddailycanreachupto13MWhinFrankfurtAirportwhichequalsto1600families’dailyenergy consumption [103]. The ground‐based system of Eco‐Climb has the structurewhich is similar to that used in the GroLaS technology. However, there is no rail onwhichtheground‐basedvehiclecanbemountedandthevehicleispoweredbyitsownonboardengines.Therearewheelslocatedunderthevehiclesanditcanmovefreelyontherunway.Nevertheless,thesetechnologiesdiscussedinthissectionarestillatalowtechnologyreadinesslevel.Currently,thereferencedataforthemisnotavailableintheopenliterature.

2.3. Summary

SeverallandinggearconceptsandtheircharacteristicsarediscussedinthischapterandadvantagesanddisadvantagesaresummarizedinTable2‐3.Althoughtheconventionallandinggearsystemhasmanydisadvantages,itstillwillbewidelyusedformanyyearsdue to its reliability.However, compared to conventional landing gear, the innovativelandinggearshavesomesignificantadvantages,suchasreducingfuelconsumptionandemission by up to 13%. So the aviation industry shows great interest in developinginnovative landing gears. Therefore, it is necessary to develop a reliable landing geardesignapproachwhichcansolvetheprobleminthecurrentlandinggeardesignprocess,e.g.difficultyofaccuratelypredictingthecriticalloadcases,isnecessaryandvaluable.

Threelandinggearsystemsarechosenastestcasesinthisthesis:

1. Conventionallandinggearsystem2. Catapultconceptforcivilaircraft3. Take‐offandlandingusingagroundbasedsystem(GABRIEL)

35

Table2‐3Summaryoflandinggearconceptsadvantagesanddisadvantages

Takeoffandlandingsystem

Advantages Disadvantages

Conventionallandinggearsystem

Technologyismature

Widelyusedaroundtheworld

Suitableforvariousconditionsoftherunway

Systemandstructurearesimple

Extraweightforaircraft

Highnoiseemissionsintheareaaroundtheairport

Electrictaxingsystem

Savethefuelfortaxiingphase

Reducetheemissionsatairport

Extraweightforaircraft

Highnoiseemissionsintheareaaroundtheairport

EMALS

Decreasetherunwaylengthrequirementfortakeoff

Savethefuelrequiredfortakeoff

Improvetheenergyefficiencyandtheoutputforceperformance(comparewiththesteamcatapultsystem)

Decreasethesystemweightandsize(comparewiththesteamcatapultsystem)

Notwidelyusedaroundtheworldyet

Applicationislimitedwithinmilitaryaircrafttakeoff

Extracostforrunwayandappendixappliancesmodification

Extracostforpilotandsystemoperatortraining

GABRIEL

Reducetheaircraftweightbyremovingthelandinggearsfromthefuselage

Decreasetheemissionsandnoisepollutioninairportsurrounds

Shorterrunwayrequirementcomparedwithconventionalconceptsystem

Easycrosswindtakeoffandlandingoperationforpilots

Reducenoiseemissionsintheareaaroundtheairport

Extraappliancesdevelopmentandimplementation

Developmentofcontrolsystemforcrosswindtakeoffandlanding

Extracostforpilotandoperatortraining

Runwaymodificationformaglevrailandsledgeimplementation

GroLaS

SamebenefitsofGABRIEL

Moveableplatforminthelateraldirectionforaneasiercrosswindlanding

SamedisadvantagesofGABRIEL

Extradevelopmentandimplementationrequiredforlateralmobilityplatform

Extratrainingforpilotandoperatorforlateralmobilityplatform

36

37

3 Physics‐basedApproachforAnalysisofLandingGear

CriticalLoadCases

3.1. Introduction

Thisthesispresentsananalyticalapproachtoestimatethecriticalloadcasesoflandinggears. It can be included in the physics‐based approach for the overall landing geardesignprocess in the future.Anoverviewof thisapproach ispresented inFigure3‐1.Themainstepsintheworkflowareasfollows:

1. Initializationofaircraftandlandinggearsystem2. Identificationofcriticalloadcases

In the first step, the reference aircraft in this thesis will be used to perform theaerodynamicsanalysis.Andthentheresultsofstabilityandcontrolderivativeswillbeusedtogetherwiththegeometry,mass,andinertiaofaircraftandlandinggearsystemto perform the flight dynamics and loads analysis by simulating aircraft takeoff andlanding.Thisstepis tightlyrelatedtothemodelingprocessof the flightdynamicsandloadssimulation.ThiswillbediscussedinmoredetailinChapter4.

Inthesecondstep,alistofcombinationsofFCEE(Flightattitudesandmotions,Controlsurface deflections andEngine throttle settings, Environmental conditions) is created.Thecriticalloadcaseswillbeidentifiedfromallpossiblecombinations.Forthetakeoffsimulation, a list of combination of FCEE can be obtained from references. For thelandingsimulation,theFCEEatthemomentoftouchdowndeterminesthelandinggearloadcases.TwoapproachescanbeusedtoobtainthispossiblecombinationofFCEE.Inthe firstapproach,thesedataareobtainedfromregulationsandstatisticaldata. Inthesecondapproach,thesedataareidentifiedbyusingMonte‐Carloevaluation.Thesetwomethods will be discussed in more detail in the following sections. Then thecombinationsofFCEEcanbeusedtoperformflightdynamicsandloadsanalysis.Thus,thecriticallandinggearloadcasecanbeidentifiedandusedforthefollowingdesignandoptimizationphase.

Thesemainstepsintheworkflowareextensivelydiscussedinthefollowingsections.

38

Figure3‐1Overviewoftheworkflowforthenovelapproachdesignedanddiscussedinthethesis

3.2. Identificationofcriticalloadcases

3.2.1.Introduction

Aflightdynamicsandloadssimulationbasedonmultibodydynamicsisusedtosimulatethelandinggearloadcases.AshasbeendiscussedinChapter1,thishastheadvantageover the existing landing gear design approaches that this leads to themore accurateandrealisticestimationofloadcases.

In this thesis, the takeoff and landing simulations are performed under differentcombinations of extreme FCEE [10, 14, 34, 35]. Afterward, based on the simulationresults, the combinations which may lead to critical landing gear load cases aresummarized.Thisprocessiscalledtheidentificationofcriticalloadcasesprocess.

TheprocesstoidentifycriticalloadcasesisillustratedinFigure3‐2.Thisprocesscanbedividedintotwosteps:

1. Calculationofloadcases2. Identificationofcriticalloadcases

Inthe firststep, theaircraftandlandinggearscharacteristicsareprovidedtoperformthe Multibody Dynamics Simulation (MDS) under all the load cases (combinations ofFCEE)illustratedintheopenliterature(and/orloadcasesestimationbasedonMonte‐Carloevaluation).Thenalltheloadcasesarecollectedandsortedintothelandinggearloadcasesdatabase.Thisdatabaseisthenprovidedtothesecondstep.

39

In this second step, all the FCEE combinationswhich can lead to critical loads in thelanding gearswill be identified. This thesis provides twokinds of criteria andwill beextensively discussed in the following sections. Once done critical load cases can beidentifiedfromtheseFCEEcombinations.

Figure3‐2Criticalloadcasesidentificationworkflow

Intheresearchreportedhere,twowaysareprovidedtodeterminetheaircraftFCEEfortakeoffandattouchdowninlandingsimulation:

1. anapproachbasedonliteraturereferencedata2. aphysicsapproachbasedonMonte‐Carloevaluation

3.2.2.Anapproachbasedonstatisticaldata

In the first solution, the extreme takeoff and touchdown conditions are provided ascandidatesfortheidentificationofcriticallandinggearloadcases.Thesecandidatesarecollected from the open literature, i.e. certification specification, references includestatisticaldata[10,14,34,35].

Fourtakeoffscenariosareconsideredinthisresearch:

1. accelerationandclimbwithallenginesoperative(AEO)2. accelerationandstopwithallenginesoperative3. accelerationandclimbwithoneenginefailure(OEF)4. accelerationandstopwithoneenginefailure

TheFCEEsummarizedinreferences[10,34]foraircraftlandinggeardesignaremostlyconcernedwithlandingoperations.Generally,thefollowingelementsareimportantandcriticalforasafelandinggeardesign:

40

crosswind aircraftattitude sinkrate turbulence aircraftangularrate

The environmental conditions used for identification of critical load cases are inaccordance with the certification specifications for the above scenarios. A detailedintroduction to these aspects is provided in the following chapter. Since the FCEE fordifferent landing gear concepts are different, the detailed critical load casesidentification process for the three test cases will be respectively presented anddiscussedinChapter5.

3.2.3.Aphysics‐basedapproachusingMonte‐Carloevaluation

The statistical dataof extremeFCEE for aircraft touchdownareonly available for theconventionallandinggear.Inthisthesis,thephysics‐basedapproachusingMonte‐Carloevaluation is proposed which can be used to estimate the extreme FCEE at aircrafttouchdownforinnovativelandinggearsdesign.

The Monte‐Carlo theory is a computational algorithm based on repeated randomsampling to obtain statistical numerical results. It has been demonstrated to give anexcellentperformance inseveral fieldsofengineering, likewindenergyyieldanalysis,fluiddynamicscalculation,andreliabilityengineering [133].ThegeneralmethodusedforaMonteCarlosimulationis[133]:

1. defineadomainofpossibleinputs2. generateinputsrandomlyfromaprobabilitydistributionoverthedomain3. performadeterministiccomputationontheinputs4. aggregatetheresults

Figure 3‐3 illustrates theworkflow of themethod used in this thesis to estimate thepossibleTouchdownAttitudesandControlinputs(TAC).Duringthelandingphase,thepresence of crosswind and turbulence is the primary cause that leads to the aircrafttouchdownwithdifferentattitudesandcontrolsettings[10,34]. In thisphysics‐basedapproachusingMonte‐Carlo evaluation, aircraft landing simulations are performed toobtain the samples w.r.t turbulence conditions. In these landing simulations, theaircraft’sinitialstateistrimmed.Theflarephaseisincludedintheselandingsimulations.The turbulence is a stochastic processwhich can bemodeled in accordancewith theMonte‐Carlotheory[126].

Ineachiterationstep,thetouchdownattitudesandcontrolinputsarecollectedbasedona flight dynamics simulation. As discussed in the Chapter2, the effect of turbulence isaccountedforandmodeledbythevonKarmanmodel[83,84].Theiterativeprocedurewill stop until a predetermined maximum amount of iterations is reached. In thisresearch,100 iterationsareconducted.Thus,100uniquesetsofstochastic turbulenceare simulated as part of 100 landing simulations. The modeling process of theturbulencewillbeextensivelydiscussed inChapter4.Afterward, theextremeFCEEataircrafttouchdowncanbeobtained.

41

Threecasesareinvestigatedinthisthesis.

GABRIELlanding Conventionallandingwithasideslipapproach Conventionallandingwithacrabbedapproach

A simulation example of a single aircraft landing using the GABRIEL system will beillustratedindetailinChapter5toenablethereaderstogetfamiliarwithitsspecifics.The two conventional landing approaches are included for verification and validationpurposes.

Figure3‐3Workflowofthemethodforestimatingflightattitudesandcontrolinputs

3.2.4.Criticalloadcasesidentificationcriteria

The critical load cases can be identified w.r.t. certain criteria. The selection of thesecriteriadependsonthedesignand/orverificationgoalsoflandinggears.Forexample,inorder toverify thedesignof the landinggear structural strengthcanmeet thecriticalloadcasesrequirement,Chaiet.al[25,39]demonstratesthemethodwhichverifiesthelandinggearsafetybycalculatingtheVonMisesstressandbucklingcriteriaof landing

42

gearparts.Thesecriteriadeterminethecriticalloadcasesbasedonthecombinationofforcesandmomentsonthe landinggearparts. It isnotnecessarilyaccurate in findingoutthecriticalforceontheshockabsorberoflandinggearwhenitisfullycompressedand extended. These data, especially the peak force in the extension and retractiondirectionsoftheshockabsorber,arethecrucialparametersinthedesignoflandinggearshockabsorber.Reference[134‐136]highlightstheapplicationofusingthepeakforcesoftheshockabsorberasthecriticalloadcasesduringthelandinggeardesign.Besides,since the shimmy vibration is also a critical load case for landing gear design, theshimmy damper is used in the landing gears, see Appendix D. Normally, the shimmydamperisconnectedtotheshockabsorber[14,137].Hence,thepeakforceinthelateralandhorizontaldirectionsoftheshockabsorbercanalsobeestimatedasthecriticalloadcasesfortheshimmydamperdesign[138].

Thisresearchprovidestwokindsofcriteriaasfollows:

w.r.tVonMisesstressandbucklingofthelandinggearparts w.r.tpeakforcesintheshockabsorberoflandinggear

ThefirstsolutionisbasedontheVonMisesstressandbucklingcriteriafortubecylinderandIbeamstructureswhicharecommonlyusedinidentifyingcriticallandinggearloadcases [25, 38]. As has been discussed in Chapter 1, the landing gear model will bedeveloped based on the multibody (rigid) dynamics simulation method. Hence, thelandinggearparts requireasimplification in themodelingprocesscompared tousingtheFEM.Inaccordancewiththegeometrycharacteristicsofthelandinggearparts,theparts are simplified into two kinds of structure: the tube cylinder and the I beamstructures[25].AsshowninFigure3‐4,thesidestrutanddragstrutcanbemodeledas

I beam,and the truckbeam, shockabsorberpistonand cylinderaremodeledas tubecylinders. The critical load cases can be identified w.r.t the criteria based on thecombinationofforceandmomentinthelandinggear.

In thesecriteriabasedonVonMisesstressandbuckling, theVonMisesstressofeachlandinggearcomponentwithtubestructurewillbecalculated.Andthebucklingcriteria

ofeachlandinggearcomponentwith I beamstructurewillalsobecalculated.Thentheload cases which could lead to peak Von Mises stress and buckling criteria will beidentified.Therefore,theeffectofbothbendingmomentandforceinthecomponentsofthelandinggearsystemwillbeaccounted.Thereaderisreferredtoreference[25,38]fordetailedintroductionaboutthecalculationofvonMisesforceandbulkingcriteria.

Inthesecondsolution,thecriticalloadcasescanalsobeidentifiedinanotherwaybasedonthepeakforceintheXYZdirectionsontheshockabsorber.Thismethodisvaluableforthedesignoftheoleo‐pneumaticstructureintheshockabsorber.Itcanidentifythepeak force appeared in the oleo‐pneumatic structure [14]. In accordance to thereference[14,25],thepeakforcesinshockabsorberaretheprimaryfactorsthataffectthelandinggearsafetyandperformance.ThedefinitionofthelandinggearcoordinatesystemcanbefoundinChapter2.Thefirststepistodeterminethepeakforceineachdirectionoftheshockabsorber.ThenthecombinationofFCEEatwhichthepeakforcesoccurneedstobeidentified.Inprinciple,thereare3x3x2=18peakforcesthatneedtobefound,(thefirstnumber3indicatesthereare3landinggears:noselandinggear,leftand

43

right main landing gears, the second number 3 indicates that the forces in the XYZdirections are included, the third number 2 means the positive/negative peak forcevalue).Thepositive/negativepeakforcesaredenotedwith“maximum”and“minimum”forceinrelativefiguresinthefollowingcontent.Thisgives18typesoffinalcriticalloadcases.TherecanbefewercriticalloadcasesifmorethanonepeakforceappearsduringonecombinationofFCEE.

rt

b

h

0r

Figure3‐4Sketchoflandinggearstructureforcriticalloadcasesidentification[25]

3.3. Landinggearweightanalysis

3.3.1.Landinggearweightestimation

Theclass2.5analyticalweightestimationmethodisusedtocalculatethelandinggearsystemgrossweight[14,25,139].Thismethodcalculatestheweightofeachkeypartofthe landing gear system in accordance to its geometry and material properties.ComparedtotheclassIandIIweightestimationmethodswhichrelyonstatisticaldata,thismethodgiveshigheraccuracyweightestimationforlandinggearsystem[140].Thelandinggearsystem,asshowninFigure3‐4,consistsofthenoseandmainlandinggear.Andeachlandinggearassemblyhasasidestrut,dragstrut,shockabsorber,truckbeam,and tyres. The geometrical data of the landing gear system can be obtained from thereferences [87, 141]. According to the reference [14, 25], although the state of artlanding gears usedifferentmaterials, e.g. composites, steel, titanium, themostwidelyusedmaterials used for the landing gears in the civil aircraft are steel and aluminumalloy.

Following the references [14, 38], 13 landing gear design and layout variables aredeterminedwhichhavea significant influenceon thedesignandweightof anaircraftlanding gear structure. They are listed below in Table 3‐1. The landing gear design,layoutandtheassociatedvariablesarepresentedinmoredetailintheAppendixA.TheparametersoftheshockabsorberwillbeextensivelydiscussedindetailinChapter4.

44

Table3‐1Keylandinggeardesignandlayoutvariables

3.3.2.Constraintsforlandinggeardesign

Theconstraintsforlandinggeardesigncanbedividedintotwoaspects:

structuralsafetyrequirements landinggearlayoutrequirements

The strength standards for checking safety are based on the approach introduced inreference [25]. It is commonly used in landing gear conceptual design stage. In thisapproach, the von Mises yield criteria and column buckling are used to verify the

structural safety of a thin‐walled tube cylinder and an I truss bar respectively. Inaccordancetocertificationspecification[34],asafetyfactorof1.5forthepeakloadingcaseisusedinthisthesis.Inthisthesis,asafetyfactorof1.5ischosenfordemonstrationpurpose.Thisisaclassicalvalueacceptedbytheexistinglandinggeardesignmethods[11, 14]. In the investigation of the innovative landing gear system, engineers cananalyzetheeffectofsafetyfactorbyutilizingdifferentvalue.

The reader is referred to Appendix A for a discussion of landing gear layoutrequirements.Asmostmoderncivilaircraftareequippedwithretractablelandinggearstoreduce thedrag, thevolumeconstraintshouldbeaccounted for in the landinggeardesign.Thevolumeconstraintreferstotheconstraintofstoragespaceavailableintheairframetosorttheretractedlandinggear.Thisvolumeconstraintistightlyassociatedwith the airframedesignwhich isnot included in this thesis. So this constraint isnotaccounted for in this thesis. The reader is referred to references [14, 142] for theextensivediscussionofthistopic.

3.4. Summary

Theworkflowoftheapproachdemonstratedinthisthesisispresented.Theprincipleoflandinggearcriticalloadcasesidentificationbasedontakeoffandlandingsimulationisextensively discussed in this chapter. Compared with the classical approaches, theproposed approachnot only can be used to predict the combinations of FCEE for thedesignoftheconventionallandinggear,butalsoforthedesignoftheinnovativelandinggear. Two methods are used to obtain the combinations of FCEE for initialization of

Symbol Description NosegearpositionintheXdirection MaingearpositionintheX direction MaingearpositionintheY direction Shockabsorbertotalstroke(noselandinggear) Statictoextendpressureratio(noselandinggear) Compressedtostaticpressureratio(noselandinggear) Pistondiameter(noselandinggear) Orificeholeradiustopistonradiusratio(noselandinggear) Shockabsorbertotalstroke(mainlandinggear) Statictoextendpressureratio(mainlandinggear) Compressedtostaticpressureratio(mainlandinggear) Pistondiameter(mainlandinggear) Orificeholeradiustopistonradiusratio(mainlandinggear)

45

takeoff and landing simulation.One is basedon statistical datawhile the otherone isbased on Monte‐Carlo evaluation. The landing gear weight is estimated based on ananalytical weight estimation method which is a class 2.5 approach. Besides, anothercrucial benefit of theproposedapproach is that it accounts the flight dynamics in theidentification of critical load cases for landing gear. This is valuable in improving theaccuracy of critical load cases estimation. The criteria for identifying the critical loadcases of landing gear could be different w.r.t variety of design goals. Two kinds ofcriteriafordeterminingthecriticalloadcasesofthelandinggeararedemonstrated.Oneis based on the Von Mises stress and buckling criteria for tube cylinder and I beamstructureswhicharecommonlyusedinidentifyingcriticallandinggearloadcases.Thiskindofcriteria issuitable forverifyingthestructuralsafetyof landinggearparts.Theotherkindof criteria isbasedon thepeak forces in theshockabsorberof the landinggear. This kind of criteria is necessary for designing the spring and dampingcharacteristicsofshockabsorberinthelandinggear.

46

47

4 Flightdynamicsandloadsmodel

4.1. Introduction

The flight dynamics and loads model is a key element in this landing gear designapproach as all the dynamic simulations for takeoff and landing operations areperformed by this model. This flight dynamics and loads model is developed byextendingthePerformance,HandlingQualitiesandLoadsAnalysisToolbox(PHALANX)which is a flight dynamics and loads model developed by the Delft University ofTechnology [88,124,143,144].TheperformanceofPHALANXhasbeen illustrated in[58,143,144].

PHALANX is a flight dynamics simulation model which is established in theSimMechanicsenvironment.Itisbasedonthemultibodydynamicswiththepossibilityof implementing flexibilitywings, etc. The scripts/functions required to performMDSarewritten in theMatlabscript file. The trimmedstatusesof anaircraft ateach flightattitude initialization are obtained by trimming scripts/functions that performoperations on the model as a whole. SimMechanics is a multibody simulationenvironmentfor3DmechanicalsystemswhichhastightintegrationwiththerestoftheMatlab environment [145]. The multibody system can be modeled by using blocksrepresenting bodies, joints, constraints, force elements and sensors provided in theSimMechanics.Then theSimMechanics formulatesandsolves theequationsofmotionforthecompletemechanicalsystem.

Figure4‐1illustratestheflowchartoftheextendedversionofPHALANX.ComparedwiththeoriginalversionofPHALANX,theextendedversionhasbeenmodifiedasfollows.Inthe flightcontrolmodule, the takeoffand landingcontrolscenariosaredevelopedandimplementedinthepilotmodule.Intheaerodynamicmodule,theaerodynamicdatasetbasedonthecombinationofasemi‐empiricalmethodcalledDATCOMandvortexlatticemethodcalledTornadoisincludedintheextendedversionoftheaerodynamicmodule.This aerodynamic data set represents the stability and control characteristics of theAirbus A320. In the atmosphericmodule, the crosswind and turbulencemodules aredevelopedasanextension.Theundercarriageandrunwaymoduleare included in theextendedversionof thePHALANX.Finally, theMDSmodels for the three testcasesoflanding gear systems are developed in this undercarriage module. Accordingly, the

48

runwaymoduleisincludedinthePHALANX.ThedetaileddescriptionofeachmoduleinthePHALANXwillbeextensivelydiscussedinthefollowingsections.

Asshown inFigure4‐1, theairframemodule is locatedat thecenterof thePHALANXsimulation model. In PHALANX, the aircraft attitudes and flight‐related data, like theairspeed, position, and attitude, are provided to the pilot module to determine therequired power plant setting and control surfaces deflection for the propulsion andaerodynamic module respectively. Once the engines thrust and control surfacesdeflectionshavebeendetermined, thethrustandaerodynamic loadsthatare imposedontheairframecanbeestimated.Inadditiontoreceivingthecontrolsurfacedeflection,the aerodynamic module also receives flight attitudes delivered from the airframemodulewhichitusestocalculatetheaerodynamicforces.Theflightdynamicsandloadsmodelwillbeextensivelydiscussedinthefollowingsections.

Figure4‐1Workflowoftheflightdynamicsandloadsmodelusedinthisthesis

49

4.2. Equationsofmotion

4.2.1.Aircraftmassandinertia

TheequationsofmotionformthecoreofthePHALANXsimulationmodel.Theairframe,including the wings, engines, tail wings, etc., aremodeled as a rigid bodymodel, seeEquation (4.1).Theundercarriagesystemsaremodeledseparatelyw.r.t the three testcases. The weights given in references [11, 35, 87] are used for aircraft weightestimations.Tocalculateaircraftinertiatheclassicmethodproposedinreference[137]canbeusedasillustratedinEquation(4.2).

2 2

( )

( )

( )

( ) ( )

( ) ( )

( ) ( )

x

y

z

x xx zz yy xz

y yy xx zz xz

z zz yy xx xz

duF M wq vr

dtdv

F M ur wpdtdw

F M vp uqdt

dp drM I I I qr I pq

dt dtdq

M I I I pr I p rdtdr dp

M I I I pq I qrdt dt

(4.1)

Where , and are the components of external force on the aircraft in body axis

system, u, v,w and p, q, r are the components of aircraft velocity and angular ratedefinedinaircraftfixedreferenceframe, , , and , , arethemomentsofinertiaandproductsofinertiaforrelativeaxesandplanes

2 2

1

2 2

1

2 2

1

1

1

1

(y y ) (z z )

( ) ( )

( ) ( )

( )( )

( )( )

( )( )

n

xx i i cg i cgi

n

yy i i cg i cgi

n

zz i i cg i cgi

n

xy i i cg i cgi

n

yz i i cg i cgi

n

zx i i cg i cgi

I m

I m z z x x

I m x x y y

I m x x y y

I m y y z z

I m z z x x

(4.2)

50

Where , , and are the position of aircraft CG in longitudinal, lateral, and

vertical directions; is the mass of the aircraft components, , , and are itspositioninlongitudinal,lateral,andverticaldirections;

4.2.2.Conventionallandinggearmodel

4.2.2.1.Introduction

The representation of the assembly of the landing gears of the A320 in this researchstudyisbasedontheworkbyChaiandMason[25,39].Asimplifiedmultibodydynamicsmodel for a reference aircraft equippedwith the conventional landing gear system ispresentedinFigure4‐2.Themultibodydynamicssystemconsistsoftheairframebodyand landing gear multibody system. The landing gear multibody system includes thebodiesoftheshockabsorber,thesideanddragstrut,thetruckbeamandthetyre.

Figure4‐2Simplifiedsketchofthemultibodydynamicsmodelfortheaircraftimplementedwiththeconventionallandinggear[124]

Theequationsofmotionfortheaircraftmultibodydynamicsmodelcanbeestablishedand are illustrated in Equation (4.3). The types of joints between the landing gearcomponents shown in Figure 4‐2 are presented in this equation. The truck beamandshockabsorberaremodeledastubecylinders.Thesideanddragstrutsaremodeledas

I ‐beam. The detailed layouts and the geometry of each component can be found inChapter2andreferences[25,39].Thematerialusedinthisdesignis300Msteelwhichhasbeenwidelyusedinthelandinggearsofcivilaircraftformanyyears[14].

51

, , , , , , 1,2,3

( )

NLG MLG AF

TT T T T T T Ti T i TB i Pis i Cyl i SS i DS AFi

T TB TB Pis Pis Cyl Cyl SS Cyl DS AF SS

NLG MLG Aero Eng

diag

TqMq+Φ μ = B

Φ q,t = 0

M M M M

q q q q q q q q

Φ(q,t) = Φ Φ Φ Φ Φ Φ

B B B B B

(4.3)

WhereMisthemassmatrix,itconsistsofthemassmatrixofthenoseandmainlandinggearassembly,andairframe(includingthefuselage,wings,engines)whicharedenotedbythesubscriptofNLG,MLG,AF.

, isthesetofconstraintequations,itconsistsoftheconstraintequationsbetweenthepairsoftyreandtruckbeam,truckbeamandcylinder,pistonandcylinder,cylinderandsidestrut,cylinderanddragstrut,airframeandsidestrutwhicharedenotedbyT‐TB,TB‐Pis,Pis‐Cyl,Cyl‐SS,Cyl‐DS,AF‐SSrespectively.AsshowninTable4‐1,theconstraintsfunctionsillustratedinEquation(4.29)canbedividedinto3typesofgenerallyacceptedformulation.Thereaderisreferredtoreference[146]fortheintroductionandderivationfortheseconstraintsequations.

Table4‐1Thetypeofconstraintsusedintheaircraftmultibodydynamicsmodeling

ConstraintsConstraintstype

Explanation

T TBΦ , TB PisΦ Revolutejointrepresentsajointwithonerotationaldegreeoffreedom

Cyl SSΦ , Cyl DSΦ ,

AF SSΦ

Sphericaljoint

representsajointwiththreerotationaldegreesoffreedom

Pis CylΦ Prismaticjoint

representsa joint withonetranslationaldegreeoffreedom

is the Lagrange Multiplier, is the Jacobian Matrix of the constraint equations

, ,qisthegeneralizedcoordinatesmatrixforthebodiesinthemultibodysystem,the subscript of i=1,2,3 denotes to the nose, left, and right main landing gears,, , , , , ,B isthegeneralizedforcesmatrixwhichconsistsofthegeneralized

forces matrix for the nose and main landing gear assembly, aerodynamic loads, andengine thrust which are denoted by NLG, MLG, Aero, Eng respectively,

, , , , , , , , .

4.2.2.2.Shockabsorber

The conventional landing gear has an oleo‐pneumatic shock absorber. A schematicrepresentationofanoleo‐pneumaticshockabsorberisshowninFigure4‐3.Theshockabsorberisfilledwithairandliquid.Whentheshockabsorberiscompressed,thefluidwill flow through a small orifice and the airwill be compressed.The air compressionresults in a spring force and the fluid motion results in a damping force. When the

52

volumeoftheair isdecreasedduetotherelativemotionoftheoutercylinderandtheinner piston, pressure increases following Boyle's law [147]. There is ametering pinpresentintheorificebywhichthedampingcharacteristicscanbeadjusted.

ThespringforcecanbeestimatedusingEquation(4.4),andtheestimationapproachfordampingforceisillustratedinEquation(4.5).TheseequationsarebasedonthephysicalprinciplesofBoyle’slawandprovideaccurateresults[148].Springforce:

0

0

0

n

a a aa

vF p A

v A s

(4.4)

Where is the air pressure in the upper chamber of the shock strut; is the

pneumaticarea; istheairvolumeforfullyextendedstrut;sisthestrokedistance;nistheexponentforaircompressionprocessinshockabsorberstrut.Dampingforce:

32

22

hh

d n

AsF s

s C A

(4.5)

Where ; istheareaoftheopeningholeintheorificeplate; isthearea

of the metering pin in the plane of the orifice; is the hydraulic area; is thedischarge coefficient. In principle, this discharge coefficient varies from 0.6 to 1.0dependsonthefluidpropertiesandorificeshape[148].Inthelandinggearconceptualdesign stage, it is commonly set to 0.8 [39]. s is the stroke distance; is the liquiddensityfilledinthecavity.

Figure4‐3Shockabsorberstructurediagram[148]

Thesimulationworkflowoftheshockabsorbersystemisasfollows,seealsoFigure4‐4:

53

In step 1, the shock absorber geometry and characteristics data are provided to theEquation (4.4) andEquation (4.5) to calculate the spring anddamping forcew.r.t theinitializedstrokedistanceandrelativevelocityoftheshockabsorber.

In step 2, all of the related loads at thismoment, i.e. the loads transmitted from theairframe and tyres (provided by other sub‐module in PHALANX), and the spring anddamping forceobtained instep1, canbeapplied to the relatedelements in the shockabsorber. Consequently, the relative displacement and velocity of the piston andcylindercanbeupdatedbasedonthisloadcase.

In step3, then theobtainedupdate relativedisplacementandvelocity canbeused toupdatethespringanddampingforceinthenextintegrationstepforthenextmomentoft t .While of course, the loads from the airframe and tyre can also be updated byusingothersub‐moduleinPHALANX.

Instep4,returntostep1untilthedynamicssimulationtimeisreached.

?totalt tt t t

Figure4‐4Simulationworkflowoftheshockabsorbermodel

4.2.2.3.Tyres

Thetyremodelisattachedtothetruckbeamwithasinglerotationaldegreeoffreedom.The Delft‐Tyremodel [149‐151] is used tomodel the tyre dynamics. Thismodel hasbeen widely used by many tyre manufactures for tyre dynamics simulation, e.g.Goodyear,Michelin [149, 152, 153]. Many research studies [149, 151, 153‐156] havedemonstratedthattheDelft‐Tyremodelcandescribetyrecharacteristicsanddynamicssimulation verywell. For example, as shown in Figure 4‐5, the research presented in[153] validates the tyre performance and loads by comparing results obtained fromsimulationandthetypicalvehiclecleattest.Moreinformationaboutthetypicalvehiclecleat test can be found in the reference [153]. The research proves that simulation

54

results of tyre loads andmotions based on the Delft‐Tyremodel can fit experimentaldata well. This Delft‐Tyre model is based on the semi‐empirical method [154, 155].Hence, it has the drawback as its applications in the simulation of innovative tyrestructuresareconstrained. In this thesis, the inputs for theaircraft typeofDelft‐Tyremodel, e.g. the tyre geometry, stiffness coefficients, are obtained from the references[149]andtheTNO[152].

Figure 4‐6 provides a schematic view of the Delft‐Tyremodelwhich consists of rigidring/Tyrebelt,rimandroadsurface.Accordingtoreference[153],thedeformationsofthetyrebeltareverysmallsoitcanbeneglectedattheaircraftearlyconceptualdesignstage.Therefore,thetyrebeltismodeledasarigidringwhichhas6DoFrelatedtotherim.The rigid ring is elastically suspendedwith respect to the rimbyusing 3 sets ofstiffness and damping systemwhich represent the loads from the sidewall. The treadband stiffness & damping system is introduced between the ring and road as asupplement to improve the accuracy of overall tyre stiffness and dampingcharacteristics.

[N]zF

[N]xF

[rad/s]

Figure 4‐5 The validation result of tyre loads and motions for Delft‐Tyre in vehicle dynamicsexperiment[153]

The runway model used in this research is a part of the Delft‐Tyre model which isprovided by TNO [150, 151, 153, 156]. The determination of the contact behaviorbetweentyreandgroundisbasedonthespringanddampingmethod.Thecontactforce,slipratio,etc.canbeestimatedfromthemodelestablishedusingthismethod.

The tyre related loads in the Delft‐Tyre model [149‐151] are estimated based onPacejka’s“Magic”Formula[154,155].Thisisasemi‐empiricalequation.Equation(4.6)is the general expression of “Magic” Formula. The outputs of the equation are tyrerelatedloads,liketyreforcesandmomentsbyvaryingthecoefficientsw.r.t.specifictyreloads type, construction, and operating conditions. These coefficients are determinedbasedonexperimentaldata.ForfurtherdetailsoftheTNODelft‐Tyre,readerscanrefertoreferences[154,155].

55

Figure4‐6SchematicviewoftheTNODelft‐Tyremodel[152]

( ) sin [ arctan{ - ( - arctan ( ) )}] y x D C B x E B x B x (4.6)

WhereB,C,D,Earethefittingconstantsvectorswhicharedeterminedbyempiricaldata,xistheinputvectorwhichisdeterminedbyoutputstype,andyisthevectorofthetyreforces,moments,etc.

A typical cornering stiffness for an aircraft tyre calculated using this equation ispresentedinFigure4‐7.

Cor

neri

ng s

tiff

ness

Figure4‐7Thetypicalcomparisonbetweentheempiricalmethod(SmileyandHorne)andMagicFormulafortyrecorneringstiffness[36]

4.2.2.4.Anti‐skidBrakeSystem(ABS)

Inordertoimprovethedecelerationperformanceduringthegroundrun,theAnti‐skidBrake System (ABS) is always implemented in the two main landing gears of civil

56

aircraft [35,157].The reader is referred toAppendixD for adetaileddescriptionandexplanationofABS.Figure4‐8demonstratestheABScontrolstrategyusedinthisthesis.Thisisaclassiccontrolstrategythataimstocontroltheaircrafttyreslipratio[158‐161].ThissimpleABS is implemented forademonstrationpurposeto illustratethebrakingoperationofaircraft.Certainly,therearemoredecentandrobustABSmodelshavebeenstudied for aircraft landing gear system, e.g. ABS based on PID controller, Fuzzycontroller,etc.[158].TheforcethatthepilotappliesonthebrakingpedalcanbeusedastheinputoftheABSmodel.Thenthecontrolforcecalculatedbythecontrolmodule,e.g.PID controller, can be applied on the hydraulic pressure appliance to activate thebrakingdisk.Inthisthesis,thebrakingloadissimulatedasabrakingtorqueappliedonthe landing gears. In accordance to statistical data, the aircraft can obtain optimaldecelerationperformance,i.e.shortestdecelerationdistance,whenthedesiredslipratioissetto0.18[159‐161].TheerrorbetweenthetyreslipratioprovidedbytheTNO‐DelftTyreandthedesiredvalueiscalculated.Afterward,thebrakingtorquecanbeadjustedinaccordancetothiserrorofslipratio.

measuredS

SK

Figure4‐8ThediagramofABScontrolstrategy[158‐161]

4.2.3.Catapultconceptforcivilaircraft

Thenosegearcatapultconceptis largelythesameastheconventional landinggear interms of themodeling and simulation aspects. The only difference is amodel for theshuttleandaconstraintbetween thenosegearand theshuttle.Asimplified sketchofcatapultconceptforcivilaircraftisdemonstratedinFigure4‐9.

Figure4‐9Simplifiedsketchofmultibodydynamicsmodelforcivilaircraftusingcatapultconcept

ThesimulationmodelofcatapultconceptforcivilaircraftisshowninFigure4‐10.Theshuttleisimplementeduponthegroundfixedmaglevrail.Theshuttleonlyhasfreedom

57

inlongitudinaldirectionw.r.ttothemaglevrail.Theshuttleprovideslongitudinalthrustandconstraintforcesinthelateralandverticaldirectionforthenoselandinggear.

Theshuttlesystemconsistsof3components:

1. Thecontroller2. Thethrustmotormodel3. Theshuttlehookandpositioningdevice

Figure4‐10Thesimulationmodelstructureofcatapultconceptforcivilaircraft

The controller provides two types of control signals. Firstly, it controls the throttleposition of the shuttle thrustmotor.As illustrated in Figure 4‐11, this thrust positioncontrolsignal isdeterminedbyfeedbackofthehorizontalaccelerationsignal fromtheairframemodel. The thrust level control evaluates the feedback of aircraft horizontalacceleration. Then it adjusts the control signal of the thrust throttle position to theactuatortorealizeaconstanthorizontalacceleration.

Secondly, itprovidesthedetachingsignal fortheshuttlesystem.Theshuttlehookandpositioningdevicewilldetachfromtheaircraftnoselandinggeariftheairspeedoftheaircraftishigherthanthepredeterminedairspeedfordetachment.

Ku

u

Figure4‐11Thediagramofthecontrolstrategyforshuttlethrust

Thedynamiccharacteristicsofathrustmotor,e.g.responsefeatures,maximumthrust,could affect the nose landing gear loads [105, 110, 162]. Generally, the thrustmotormodel can be established based on a first or second order systemwith a time delay[162‐165].However,ontheonehand, in the landinggearconceptualdesignstage, thedetaileddynamicscharacteristicsofthrustmotoriscommonlyunavailable.Ontheotherhand,themaximumoutputthrustistheprimaryonethatdeterminesthecriticalloads

58

in thenose landinggear fromthe thrustmotoraspect [105]. Itdeterminesmore than95%ofcritical loadscases forallaircraft launches[105]. Inthis thesis,an idealthrustmotormodelwhichaccountsthemaximumoutputthrustisusedandtheshuttlethrustgeneratedfromitisshowninEquation(4.7)[105,110].

,

0,

,detach

Shu x u Shu detach

u Shu max

whenV V

F K P whenV V

K P F

(4.7)

Where , isthethrustforceinthehorizontaldirectionthatisprovidedbytheshuttle,Vistheaircraftairspeed, isthedetachairspeed, isthegainfactor, istheshuttlethrustthrottleposition, isthemaximumoutputthrust

ThejointsprovidedinSimmechanics,e.g.prismatic,cannotrealizethestatustransitionfromconnection todetachmentbetweenthecatapultshuttleandnose landinggear inthe takeoffsimulation.Hence, in themodelingprocessofshuttlehookandpositioningdevice, the lateral and vertical constraint forces are modeled as spring and dampingsystems which enable the nose landing gear located on the runway centerline andenable thenose landinggear tocontact therunwaysurfaceduringthecatapultphase.Thestiffnesscanbeobtainedfromreferences[166‐168].Thismodelingmethodhasthedrawback that it might cause numerical problems for simulation, e.g. cannot achieveconvergencewhensolvingtheequationsofmotionformultibodydynamicssimulation.Itcanbesolvedbyadjustingthetimestepsizeforsimulation.Therelativedisplacementandvelocityofthenose landinggearandrunwaycenterline inthe lateralandverticaldirections are measured as input for the lateral and vertical spring and dampingsystemsrespectively.Theothermodelcomponentsusedforanosecatapultareidenticaltothoseoftheconventionalconceptintroducedintheprevioussub‐section.

TheequationsofmotionforcatapultconceptforthecivilaircraftmodelareillustratedinEquation(4.8).

, , , , , , 1,2,3

Shu NLG MLG AF

TT T T T T T T TShu i T i TB i Pis i Cyl i SS i DS AFi

T Shu T TB Pis Cyl Cyl SS Cyl DS AF SS

Shu NLG MLG Aero Eng

diag

M M M M M

q q q q q q q q q

Φ(q,t) = Φ Φ Φ Φ Φ Φ

B B B B B B

(4.8)

Where the definitions of the symbols shown in Equation (4.8) are identical to thoseshownintheequationsofmultibodydynamicsmodelfortheconventionallandinggear;

is themassmatrixof theshuttle; is theconstraint functionbetween tyreand shuttlewhich is a revolute joint, the reader is referred to reference [146] for theintroductionandderivationofit; isthegeneralizedforcesmatrixoftheshuttle

Thegeneralstructureofthelandinggearsystemissimilartothatusedinaconventionallandinggearsystem.However,sincetheshuttleappliesthrustonthenoselandinggear,itsstructureshouldbereinforced.References[112,113]investigatethecatapultsystem

59

forcivilaircraft.Thestructuralmodificationforreinforcingisused[25],seeFigure4‐12.In order tomeet the safety requirements in CS‐25 [34], the structuralweight of noselandinggearcomponentsinanA320aircraftcanincreaseupto70%[112,113].

NCTC

C

rn

r

NCr

Cr0r

Ct

Cb

Ch

; ;NC NC NCI I I

C C Cb ht

t b hn n n

t b h

NCt

NCb

NCh

I

:

:

C conventional landing gear

NC nose gear in catapult concept

Figure4‐12ThesketchofIbeamandtubecylindergeometrymodificationforstrengthening

4.2.4.GABRIELconceptlandinggearsystemmodel

4.2.4.1.Introduction

The schematic of GABRIEL simulationmodel is shown in Figure 4‐13. ThemultibodydynamicssystemfortheGABRIELconceptincludesthebodiesrepresentingtheaircraft,the ground based cart (a mobile platform and a ground‐based sledge), and theconnectionmechanismbetweentheaircraftandtheground‐basedsystem.

The connectionmechanism includes the nose andmain connectionmechanisms. Themultibodysystemrepresentingthenoseconnectionmechanismincludesthe followingrigidbodiesandcontactpairs:

Bodyofharpoonstickwhichisattachedtotheairframe Bodyofthe innerpistonoftheshockabsorberwhichisattachedwithharpoon

diskonitstop Bodyoftheoutercylinderoftheshockabsorber Bodyofsideanddragstruts Contactpairbetweenharpoonstickanddisk Contactpairbetweentheoutercylinderandinnerpiston

Twopairsofmultibodysystemsforthemainconnectionmechanismsaresymmetricallyallocated on the ground based system. Each one has the same components as thoseinvolvedinthemultibodysystemofnoseconnectionmechanism.Themultibodysystemmodelingprocesswillbeextensivelydiscussedinthefollowingsections.

60

Main connection mechanism

Sledge

Nose connection mechanism

Maglev railMobile platform (yaw

and pitch motions)

Side strut

Drag strut

Front view Left side view

Harpoon disk (ground based)

FxFy FzFz

Harpoon stick (on board)

Outer cylinderFront view Left side view

FxFy FzFz

Inner piston

Figure4‐13ThesketchofthemultibodydynamicsmodelfortheGABRIELconcept[169]

4.2.4.2.GABRIELmultibodysystemmodeling

The sketch of the GABRIEL multibody dynamics model is shown in Figure 4‐14according to the GABRIEL workflow and mechanism introduced in Chapter 2. Thisschematicdiagramcanbedividedintothefollowingparts:

Maglevrail Ground‐basedcart(includethemobilesledgeandplatform) Aircraft

Themaglevrail ismodeledasa“body”andfixedtothegroundaspartof therunway.The ground‐basedmobile cart is suspended upon it. The ground‐basedmobile cart isattachedtothemaglevrailwiththe“prismaticjoint”.Therefore,itcanmovefreelyinthelongitudinaldirectionw.r.t.themaglevrail.Amobileplatformimplementedwithshockabsorbersisallocateduponit.Thisplatformisconnectedtothesledgewith“universaljoints”whichrepresenttworevoluteprimitives.Consequently,themobileplatformhaspitchandyawdegreesoffreedomw.r.tthesledge.

Theharpoonstickismodeledasarigidbodywithmassandinertiarepresentativeforacylindrical beam.The connectionmechanismof the ground‐based system is shown inFigure 4‐15, the harpoon disk is simplified into a circular disk attached to the shockabsorber.Thepistonandcylinderaremodeledastubesconnectedwithaprismaticjointwithasingletranslationaldegreeoffreedomintheverticaldirection.Thebottomofthecylinder is connected to the pitching platform on the ground‐based sledge. The dragstrutismodeledasanI‐beamandplacedontheleadingsideoftheshockabsorber.The

61

two side struts are located symmetrically to the right and left sides of the shock

absorberas I beams.Theupsideofthesideanddragstrutsareconnectedtotheshockabsorber cylinder and the bottom of them are all connected to the pitching platform.Similar to a conventional landing gear assembly, all of the joint relationships areestablished as the spherical joint. All the required geometrical data can be found inChapter2.

Figure4‐14ThestructureofthesimulationmodelfortheGABRIELconcept

Figure 4‐15 Sketch of the GABRIEL ground‐based connection mechanism based on harpoontechnology

Inthisresearch,the300Msteelwhichisawidelyadoptedmaterialforlandinggearisused in GABRIEL concept [39, 170]. For the side and drag struts, 6061 high strengthaluminum is used [14]. The aircraft module is very similar to that used for the

62

conventionallandinggearmodel.Nevertheless,theconventionallandinggearsystemissubstituted with GABRIEL onboard connection mechanism, i.e. harpoon stick. Theinteractionbetweenaircraftandground‐basedmobilecartconsistsoftwoparts:

motioncontrolandsynchronization contactrelationships

Thesewillbeextensivelydiscussed in the followingsections.TheequationsofmotionforGABRIELmodelareshowninEquation(4.9).

, , , , 1,2,3

Sle NCM MCM Pla AF

TT T T T T T TSle Pla i Pis i Cyl i SS i DS AFi

MR Sle Sle Pla Cyl Pis Cyl SS Cyl DS Pla SS Pla DS

Sle NCM MCM Aero Eng

diag

M M M M M M

q q q q q q q q

Φ(q,t) = Φ Φ Φ Φ Φ Φ Φ

B B B B B B

(4.9)

Where the definitions of the symbols shown in Equation (4.9) are identical to thoseshowninEquation(4.3)and(4.8);thesubscriptionofSle,Pla,NCM,MCM,MRdenotetosledge,platform,noseconnectionmechanism,mainconnectionmechanism,andmaglevrailrespectively

4.2.4.3.GABRIELcontrolsystemstrategy

The control system located in the ground‐based systemworks cooperativelywith thecontrolsystemlocatedintheaircraft,thisrelationshipisillustratedinFigure4‐16.Theground‐basedcontrolsystemconsistsofamobileplatformcontrolsystemandasledgecontrolsystem.The formeronecontrols theplatforminpitchandyawwhile the lateronecontrolsthemotionsoftheground‐basedsledgeinthelongitudinaldirection[123,171,172].

Figure4‐16Theschematicofcontrolsystemfortheonboardandground‐basedsysteminGABRIELconcept[123,171,172]

Thepitch andyawmotion control strategy is illustrated inFigure4‐17. In the takeoffprocedure, the ground‐based platform can pitch jointlywith the airframe. And in thepresenceofacrosswind,theplatformcanalsoyawjointlywiththeairframetoenabletheaircrafttooffsetthelateralaerodynamicloads[82,124].

63

Forthelanding,thepitchandyawangleofthegroundbasedsystemaresynchronizedwith the aircraft attitudes, i.e. and . Then, during the deceleration

phase, themobileplatformcanbemovedback to thedefaultposition, i.e. 0and 0,toprepareitforthefollowingtaxioperation.

Figure4‐17Sledgepitchandyawcontrol[82,124]

Control of the longitudinal motion of the sledge includes three modes: accelerationphase,motionsynchronizationinlanding,anddeceleration(oraccelerationfortakeoff).Firstly,once theaircraftpasses thepredetermined threshold, e.g. specific altitude, theopen control system is used to control the sledge to follow a prescribed accelerationscheme, see Figure 4‐18. This controller can enable the sledge to reach the positionclosedtotheaircrafttouchdownposition.Theexactshapeoftheprescribedaccelerationscheme depends on the aircraft horizontal velocity, glide slope, and flare maneuver[171].Secondly,thesynchronizationcontrolmoduledevelopedforlandingoperationisillustrated in Figure 4‐19. Before aircraft touchdown, this control system tries tominimizethepositionandvelocitydifferencebetweentheaircraftandthegroundbasedvehicle. The groundposition and velocity of the aircraft are used as feedback signals.Aftera successful synchronization and touchdown, the control systemswitches to thethird mode: deceleration. The deceleration control strategy, which is a closed loopcontrolsystem, ispresented inFigure4‐20.Thedesiredhorizontalaccelerationof thesledge is the reference signal for the control system and the feedback signal is themeasured sledge acceleration in the horizontal direction. The control signal istransferred to thrust after passing the actuator module. The acceleration control ofground‐basedsledgeinthetakeoffphasehasthesimilarcontrolstrategy.

Figure4‐18Accelerationphaseofhorizontalpositioncontrol forairbornephaseof landing in theGABRIELconcept[171]

64

Figure4‐19Theflowchartofaircraft‐sledgesynchronizationcontrolstrategy[82,124]

u

u

Figure4‐20TheflowchartofGABRIELsledgethrustcontrolstrategy[82,124]

4.2.4.4.Aircraftandground‐basedsystemcontactmodel

Accurate modeling of the contact and interaction relationships between the aircraftonboard and ground‐based systems is a challenge. There are two distinct modes:connected and detached. The connected situation is applicable when the aircraft iscatapultedduringtakeoffandcapturedduringthelandingphase.Thedetachedsituationoccurswhentheaircraftisairborne.

AsshowninFigure4‐13,theairframeconnectswithground‐basedsledgesystemusinga paired contacting force which only exists during the connected situation for theonboardandground‐basedsystem.Apossiblesolutionwhichhasbeenwidelyusedtomodel rigid contact relationships is tomodel a 3D spring and damping system [166].TheprinciplesofthisspringanddampingcontactmodelareillustratedinFigure4‐21.Thereare3pairsofspringanddampingforcesintheXYZdirections.Thestiffnesscanbe obtained from references [166‐168]. These paired forces are determined by therelativemotionbetweentheonboardandground‐basedsystemsineachdirection.

Figure4‐21SchematicoftheGABRIELonboardandground‐basedsystemcontactmodel

65

In the landing simulation for GABRIEL concept, the aircraft touches down on theground‐basedmobilecartattheendoftheflarephase.Thelogicusedinthemultibodydynamics model that needed to detect the contact between the onboard system (theharpoonstick)andground‐basedsystem(theharpoondisk)isasfollows:Thecontactineach connectionposition is simplified into a stick andplane contact relationship. Thestickrepresentstheonboardharpoonstick.Theplaneisacircularplanerepresentstheharpoon disk. The contact detecting logicmeasures the relative position between thestickbottomandplanesurface.Ifthestickpenetratestheplanearea,thenthemodel’slogicdeterminesthecontactandconnectsthem,seeEquation(4.10).

,

,

when

when

s d

0 S 0F

S K -V K S 0 (4.10)

WhereFistheclampingforcebetweenonboardandgroundbasedconnectionsystems;SandVare the relativedistanceandvelocitybetween them; and are thespringanddampingcoefficients

4.3. ExternalForces

4.3.1.Propulsionsystem

Inprinciple, enginedynamics can influence the touchdownattitudeof an aircraft andthereby the load cases of a landing gear system. Currently, many elaborate enginemodels have been developed. For example, the Commercial Modular AeropropulsionSystemSimulation(CMAPSS)packageisdevelopedattheNASAGlennResearchCenterbyusingMatlabandClanguage[7].Thisisaturbofanenginesimulationtoolbasedonthe engine thermodynamic principle [7]. It provides the user with a graphical userinterfacetotesttheenginedynamicsperformancew.r.tdifferentcontrolalgorithms.TheNumericalPropulsionSystemSimulation(NPSS)isdescribedinreference[173].Thisisa simulationmodel for comprehensiveevaluationofnewengineconcepts in theearlydesign phase. The Gas turbine simulation program (GSP) is implemented in thePHALANX by means of co‐simulation [174]. GSP is a method based on the aero‐thermodynamics equations which take into account the physical processes of aero‐engines[174].Inprinciple,theoutputoftheenginethrustofthesemodelsdependsonmanyfactors,i.e.throttlesetting,atmospherictemperature,andairdensity[175].Inthisthesis, the takeoff and landing simulations are performed w.r.t the atmosphericconditionsofatypicalairportlocatedatsealevelaltitudewithatemperatureof20°CasillustratedintheInternationalStandardAtmosphere(ISA)[119].

Normally, the elaborate characteristics of aircraft engine are not known yet at theaircraftconceptualdesignstage.Accordingtotheresearchillustratedin[11,175],inthetakeoff and landing phases, the throttle setting is the primary factor that affects theengine thrustoutput.Especially intheaircraftconceptualdesignstage,accounting thecalculationaccuracyandtime,theenginemodelcanbesimplified[11,175].Soanidealengine simulation model based on a linear thrust vs. throttle setting schedule iscommonlyusedinlandinggearconceptualdesignstage[14,25,176].Amoreelaborateenginemodelcanbeimplementedinfuturework.

66

The ideal engine model is a simplified propulsion model and the input and outputrelationships are shown in Equation (4.11). The thrust is acquired by multiplyingthrottlesettingwithacertaingainvalue.Because the timeused toaccomplish takeoffand landing operation in each flight are only several minutes and the weight of fuelconsumedduring thisperiod isnot significantwhencomparedwith theweightof thewholeaircraft.Therefore, theweightvariationcausedby fuel consumption is ignored.Thespoolupanddowntimearetakenintoconsiderationw.r.treferences[112,177].

thro ttle

max

T K P

T T

(4.11)

Where T is the output thrust of the engine,K is the gain ratio, is the enginethrottleposition, isthemaximumthrust

4.3.2.Aerodynamicsanalysis

Thestabilityandcontrolderivativesandthelift‐dragpolararecomputedwithDATCOM[63, 67, 70]. The dataset is extended with specific data obtained with Tornado torepresenttheruddercontrolderivatives[64,69].Referenceaircraftfeatures,likeaspectratio, chord length, airfoil geometry, control surface layout, and flight conditions, likealtitudeandairspeed,mustbeprovided toTornadoorDATCOM.A listof thedetailedinput for aerodynamicestimation canbe found inChapter2 and references [35, 178‐180].

Within the PHALANX simulation model, the aerodynamic model is modeled w.r.t.Equation(4.12)[181].Thenthedesiredaerodynamicdataissortedinthelook‐uptablesandusedbytheaerodynamicmoduleintegratedintoPHALANX.

1

2( )C ( ) ( ) ( ) ( ) ( )

C ( ) ( ) ( ) ( ) ( ) ( )

C ( ) ( ) ( ) ( ) ( ) ( )

q GSE HL

q E HL GS

q E HL GS

x

DD D D D D

zL L L L L L

m m m m m m Ey

HL

GS

F cqS VCC C C C

qcFC C C C C

VqSC C C C CM

qSc

C ( , ) C ( , ) C ( ) C ( ) ( ) ( )( )

C ( , ) C ( , ) C ( ) C ( ) ( ) ( ) ( )

( )C ( , ) C ( , ) C ( ) C ( ) ( )

p r A RSR

p r A R RS

p r RA

y

y y y y y yy

xl l l l y l l

nn n n n yz

F

qS C CCM

C C CqSb

CCM

qSb

2

2

( ) 2RS

n

A

R

RS

b

Vpb

Vrb

C V

(4.12)

67

Where istheaerodynamicforceofaircraft, istheaerodynamicmomentofaircraft,theirsubscriptof , , denotestothedirections inthestabilityaxessystem, is thedynamic pressure, is the wing platform area, is the wing span, ̅is the meangeometricchord, , , isthevectorofaircraftrotationrate, istheaircraftairspeed,istheaerodynamicscoefficient,itssubscriptindicatesthemeaningofderivativewhich

canbefoundinthesectionofNomenclature.

Inaircrafttake‐offandlandingsimulations,itisimportanttotakethegroundeffectintoaccountasitaffectsthelandinggearloads.Inthepreliminaryaircraftdesignstage,theliftandinduceddragcoefficientsarethemainparametersaffectedbythegroundeffect,and the reader is referred to [182] foran in‐depthdiscussionof thesephenomena. Inprinciple,thedragcoefficientconsistsofthecomponentsofinduceddrag,parasitedrag,andprofiledragasshowninEquation(4.13).However,the induceddragcoefficient isnotcalculatedbytheDATCOM.Thus,theinduceddragcoefficientisobtainedbasedonEquation(4.14)[175].

In the research presented here, the ground effect estimation methods based onreferences[137,183,184]areused.Theliftandinduceddragcoefficientsarethemainparameters affected by ground effect and their variation can be estimated usingEquations(4.15)to(4.17).Afterward, thevalueofthedifferencebetweenthe induceddrag and lift coefficients with and without ground effect can be obtained andimplemented in thePHALANX.The accuracyof these equations for estimatinggroundeffecthasbeenvalidatedin[137,183,184].

D Di Dn DpC C C C (4.13)

2( )

( ) L OGEDi OGE

CC

Ae (4.14)

( ) ( )Di IGE Di OGEC C (4.15)

2

2

16

1 16

h b

h b

(4.16)

2 1.5

1.52

( ) ( ) 33

( ) ( ) 1 33

Di IGE L IGE h

Di OGE L OGE

C C h b

C C h b

(4.17)

Where istheinduceddragcoefficient, istheparasitedragcoefficient, istheprofiledragcoefficient,IGEandOGEareInGroundEffectandOutofGroundEffect,histheaircraftaltitude,andbisthewingspan, istheOswaldfactor.

TheA320hasbothrollandgroundspoilers.Therollspoilerwilldeflect togetherwiththe aileron to enhance roll authority and response [157, 185‐187]. The controlderivatives associated with roll spoiler deflection can be obtained by DATCOM. Thegroundspoilerisusedasa“liftdumper”duringlandingaftertouchdown.Thedeflectionof the ground spoiler during landing ground run phase causes the aircraft lift to

68

decreaseanddragtoincrease.Theextensionofliftdumpercanaffecttheloadcasesoflanding gears by changing the aircraft lift and drag. Normally, the lift dumper isprogressively extended after the aircraft touchdown and stability deflected to thedesired deflection angle. In this thesis, these effects are estimated by the approachdescribed in reference [188, 189], as shown in Equations (4.18) and (4.19). This is avalidatedmethod[188,189],basedonanempiricalapproach.

1.9sin( )GS

GSD GS

ref

SC

S (4.18)

GS C

GSL L

bC C

b (4.19)

Where isthedragcoefficientcausedbygroundspoilerdeflection, isthegroundspoilerdeflectionangle, istheareaofthegroundspoiler, isthewingarea, istheliftcoefficientcausedbygroundspoilerdeflection, istheliftcoefficient, isthegroundspoilerspan,andbisthewingspan

Therefore, based on the data from references [67, 88, 122, 124] and approachmentionedabove,theA320aerodynamicsdatacanbeacquired.

4.4. Operationalconditions

4.4.1.Atmosphericmodel

TheatmosphericmodelinPHALANXisbasedontheInternationalStandardAtmosphere(ISA)[190].Thismodelreceivestheflightaltitudeasinputandoutputstheairdensitybasedontheatmosphericdataillustratedinreference[190].Inaddition,crosswindandturbulencemodelsareadded to thisatmosphericmodel to enable takeoff and landingsimulationsunderrestrictingatmosphericconditions.

Theeffectofacrosswindistakenintoaccountinthisresearchbyadding tothe

aircraftgroundvelocityvector .Thecrosswindvectorandaircraftvelocityvector

are defined in the world coordinate system according to the crosswind criteriadeterminedinCS‐25[34].

AS w CW w AC w V V V (4.20)

Wherethe isthevectorofaircraftairspeedinworldcoordinatesystem, is

thevectorofcrosswindvelocityvectorinworldcoordinatethesystemand isthe

vectorofaircraftgroundvelocityintheworldcoordinatesystem.

The turbulence ismodeled based on the von Karmanwind turbulencemodel [83‐85,191]. The component spectra functions of turbulence are shown in Equation (4.21).Basedontheapproachintroducedinreference[83,84],theturbulencevelocitycanbegenerated. Afterward, the velocity imposed by turbulence is added to the velocity ofaircraft.

69

2

2 5/6

2 2

2 11/6

2 2

2 11/6

2 1

1 1.339

2 1 8 3 1.339

1 1.339

( )[ ( ) ]

( )( )

[ ( ) ]

( )2 1 8 3 1.339

1 1.339( )

[ ( ) ]

u uu

u

v v vv

v

w w ww

w

L

V L V

L L V

V L V

L L V

V L V

(4.21)

Wherethevariable representstheaircraftwingspan,thevariables , , representthe turbulence scale lengths and the variables , , represent the turbulenceintensities, istheairspeed, isthespatialfrequency

AsshowninEquation(4.21),theturbulencemodelinvolvestheeffectofflightconditionsand relative aircraft characteristics, e.g. crosswind speed, airspeed, flight altitude, andwingspan.Theirvaluesareacquiredbasedonreference[34,35,157,185]w.r.t.safetyregulations. This stochastic wind turbulencemodel accounts for the effect of aircraftaltitude,soittakesthegroundeffectintoaccount.Theperformanceandaccuracyofthismodel have been validated and confirmed bymany institutions, e.g. U.S. Military andNASA[85,192].

4.4.2.Flightcontrolsystem

TheflightcontrolsystemusedinPHALANXconsistsoffollowingcomponents[193]:

flightcontrolmodule pilotmodule

Theflightcontrolmoduleincludestheautomaticflightcontrolsystem,i.e.controllaws,andthemechanicalcontrolcomponentsintheflightcontrolsystem,i.e.controlsurfacedeflectionactuator.Thepilotmodulerefereestothecomponentswhichprovideinputtotheflightcontrolmodule,i.e.thepilotinputmodules.

Theequationsrepresentingtheflightcontrolsystemareasfollows:

trim linearization

max

δ t = K u t +u +u

δ t δ (4.22)

Where is the vector of control surface deflections and the throttle setting as afunctionoftime;K isthevectorofgearingratio; isthevectorofpilotinputsw.r.t.the time; is thevectorofpilot inputsobtained fromaircraft trimmedconditions;

is the vector of pilot inputs for linearization of the multibody dynamicsmodel; isthemaximumcontrolsurfacesdeflections

Theflightcontrolsystemconsistsoftwosections:

1. controlsurfacesdeflectioncontrol2. enginesthrottlecontrol.

70

Thefirstsectioncontrolsthedeflectionofeachcontrolsurface,likeailerons,elevators,rudder,etc.Whenanautomatic flightcontrolsystemisactive,therecanstillbeapilotpresentprovidinginputstotheautomaticflightcontrolsystem.Thegearingratiomodelconverts the control stick position into the deflection control signal for the aircraftcontrol surfaces. The control allocationmodel determineswhich control surfaces aredeflectedandtheactuatorsrealizethedeflections.Thetrimpilotinputisseparatedfrommaneuver pilot input. The trim pilot input routine is used to trim aircraft and themaneuver pilot input routine is used for aircraft takeoff and landing operation. Thelinearizationfunctionisimplementedtoenabletheaircraftmodeltobetransferredtoalinearmodelbynumericallyperturbingsimulation.

Theenginesthrottlecontrolsectionhasthreeinputs:pilotthrottlemaneuverinput,triminputandlinearizationinput,andtheirfunctionsonthrottlesettingaresimilartothosedescribedaboveforthecontrolsurfacesystem.

4.4.3.Basicaircraftautomaticflightcontrolstrategy

Duringtheaircraftlandingphase,thecontrolstrategiesdeterminetheaircraftattitudesattouchdown.Theaircraftattitudesandenvironmentconditionsattouchdownmomentdeterminethelandinggearloadcases.Therefore,theestimationoftheseparametersisnecessaryforlandinggearloadcasesestimation.Especiallyfortheaircraftimplementedwithinnovativelandinggearsystemwhichhaslimitedorevennoreferenceorempiricaldata in the open literature. Therefore, the flight control strategy developed in thisresearch involves the flight operation during the aircraft steady descent phase.Consequently, the Monte‐Carlo Simulation can be used to estimate the aircrafttouchdownattitudesasmentionedinChapter3.

As has been extensively discussed in Chapter 1, the classic control strategy based onclosed‐loop control system [81] is used to realize aircraft takeoff and landingsimulationsinthisthesis.Itrepresentsarealautomaticflightcontrolsystemusedintheaircraft. The gains used in this thesis are tuned in accordance to the desiredperformance,robustness,stability,etc.whicharedemonstratedintherelatedreferences.Thegainswillaffecttheloadcasesoflandinggears.Forexample,thegainsusedintheschematicsofthe flightcontrol lawfor landingaretunedinordertotrackthedesiredflare trajectorywhich is demonstrated in the reference [194]. The error between thesimulationresultsandthedesiredflighttrajectoryareusedasthereferenceduringthetuning. The tuning of gains used in the control law schematics for extreme landingconditions, e.g. in the presence of crosswind and turbulence, should account for therobustness.Itmeansthetunedgainscanlettheaircraftsafelytakeoffandlandagainstthe effects of crosswind and turbulence. Thedesired touchdownpositions, e.g. lateraland longitudinal position on the runway, and touchdown attitudes, e.g. roll angle andangular rate, mentioned in the open literature are used as the reference during thetuning.

Five kinds of control surfaces are used in an A320 and their control strategies arepresentedinthefollowingsections.

Ailerons Elevators

71

Rudder Spoilers(rollandgroundspoilers) Highliftdevices(leadingedgeslatandtrailingedgeslottedflap)

InFigure4‐22,theaileronandrollspoilercontrolstrategyconsistsof2loops.Thetwoloops include the roll rate andangle. The result ismultipliedby the gainmodule andprovidedtothesecondcontrolloopasthereferencesignal.The issetto0degintakeoff simulation. In the landing simulation, the is obtained from aircrafttrimmed under specific flight status. The trim algorithm will be presented in thefollowingsections.AscanbelearnedfromtheFigure4‐22,afterthe2ndcontrolloop,thecontrolsignal isprovidedtothestickgearingmodule.Thismodelconvertsthecontrolsignal into the stick position. Then control stick position data is transferred into theaileron and roll spoiler deflection angles. The tuning process based on takeoff andlanding simulations will be performed to determine the gains used in the controlsystemsshowninthissection[81,82].

Figure4‐22Theflowchartofaileronandrollspoilercontrolsystem[82,124]

Figure4‐23Theflowchartoftheelevatorcontrolsystemfortakeoffsimulation[82,124]

TheelevatorcontrolstrategiesfortakeoffandlandingareillustratedinFigure4‐23andFigure4‐24.Inthetakeoffsimulation,asshowninFigure4‐23,thedesiredpitchangleisprovidedasthereferencesignalandcombinedwiththemeasuredpitchattitudes.Next,thissignalismultipliedbyagainandprovidedtotheinnercontrolloopasareferencesignal. The inner control loop is based on the pitch rate measured from the aircraftequationofmotionmodule.Thecontrolsignal is thentransferred intotheelevatorbythestickpositionandcontrolsurfacedeflectionactuatormodules.

Inthelandingsimulation,asshowninFigure4‐24,theflightpathangleisprovidedasthe reference signal in the loops of the control strategy. In this research, the desired

72

flight path is a ‐3 degree glide slope followed by a flare. The following equationdescribestheflare[194].

0th h e (4.23)

Wherehisthealtitudeofaircraft; isthealtitudeatwhichtheflarestarts;tisthetime,measuredfromthestartoftheflareand isaparametertodescribethegeometryoftheflare

Figure4‐24Theflowchartofelevatorcontrolsystemforlandingsimulation[82,124]

The flightpathangleandpitchangleobtained fromaircraftunder trimmedstatusareincluded in the loop of this control strategy. The control strategy is similar to thosedevelopedforthetakeoffcontrolstrategy.

The rudder control strategy consists of 3 nested control loops (see Figure 4‐25). Thestructureofthiscontrolstrategyissimilartotheaileroncontrolsystem.However,thefeedbacksignalsfromtheaircraftequationsofmotionmoduleforthesecondandinnercontrolloopsaredifferentfromtheaileroncontrolstrategy.Inthiscontrolsystem,theyare yaw rateandanglemeasuredby theaircraftmotionmodule.The is set to0degree in takeoff simulation. Its value in landing simulation can be nonzero in casecrosswindispresented.

Figure4‐25Theflowchartofruddercontrolsystem[82,124]

The flowchart of a control system for sideslip is shown in Figure 4‐26. For aircraftsideslipoperation,theaircraftsideslipangleisusedasafeedbacksignalandcomparedwith the desired value. Then after passing the gainmodule, the control signal can betransferredintothestickpositionandrealizerudderdeflection.Thecontrolsystemfor

73

de‐craboperationhasasimilarflowchart.Forthede‐craboperation,theaircraftsideslipangle is substituted with yaw angle in the control loop shown in Figure 4‐26. Thedesiredsideslipangleissubstitutedwithzeroyawangleasthereferenceinput.

Figure4‐26Theflowchartofthecontrolsystemforsideslipandde‐craboperation[82]

ThehighliftdevicecontrolstrategyisshowninFigure4‐27.InFigure4‐27,thefeedbacksignalofthehighliftdevicedeflectionangleobtainedfromthehighliftdevicemoduleiscompared with the desired value. This desired value is determined by the pilotoperationmanual [178, 180, 195]. The reader is referred to Chapter 5 for a detailedintroductionaboutit.Thenthecontrolsignalreachesthehighliftdeviceactuatorafterpassingthegainmodule.

HLD

HLD

Figure4‐27Theflowchartofthecontrolsystemforthehighliftdevice

4.5. Numericalsimulations

Thesolveraffectstheefficiencyandaccuracyofnumericalsimulations[167,196‐198].Therearemanysolversavailable,e.g.solverbasedontheEulermethod,Rounge‐Kuttamethod.Theclassical4thorderRunge‐Kuttamethodisarepresentativeapproachwhichissuitableformulti(rigid)bodydynamicssimulation.ComparedwiththeEulermethod,ithashigheraccuracyforsimulationandthecalculationcostissuitablefortheaircraftconceptual design stage. This solver is integrated into the Simmechanics. For moreinformationabout this iterativemethod, the reader is referred to the references [167,196‐198].

Theinitializationoftheaircraftintakeoffandlandingsimulationsshouldberealisticasitaffectsthelandinggearcriticalloadcases.Hence,theequilibriumstatusisusedastheinitialization of aircraft takeoff and landing simulations [175, 185]. In this thesis, theequilibriumstatusoftakeoffcanbeobtainedbyrunningatimedomainsimulation.Thismeansthesumsofexternalforcesandmomentsactingontheaircraftarebothzero.Theprocess of obtaining the equilibrium status of aircraft, like the equilibrium status of

74

landinggearstroke,controlsurfacedeflectionangles,aircraftattitudes,iscalledaircrafttrim.Inthisthesis,theaircrafttrimconsistsoftwosteps:trimfortakeoffandtrimforlanding.

Fortheinitializationfortakeoffsimulation,theequilibriumstatusofaircraftandlandinggearscanalsobeobtainedbasedontheapproachillustratedinthereferences[199‐201].Whentheaircraftachievedequilibriumstatusontherunway,thesumsoftheforcesandmomentsappliedtotheaircraftarebothzeroasshownintheEquation(4.24).

LG LG LG A W EB LMLG B RMLG B NLG B Aero B B Eng

LMLG RMLG NLG Aero Eng

L F + L F + L F + L F + L G+ L F = 0

M + M + M + M + M = 0 (4.24)

Where is the transformationmatrixwhich transforms coordinates to coordinates,

thesubscriptofLG,A,B,E,Wdenotetothe landinggear,air‐path,engines,andworldaxis systemrespectively, theirdefinitioncanbe found inChapter3; is thevectorofforces , , obtained from ,the subscript of LMLG, RMLG, NLG, Aero, and Eng

denotetotheleft,right,andnoselandinggear,Aerodynamics,andenginesrespectively;denotes to the vector of moments , , obtained from , the meaning of the

subtitleof issametothoseusedin , isthevector 0,0, thatconsistsofaircraftweightG;

The transformation matrix between two axis systems can be formed based on theapproachillustratedinthereference[202].ThenequilibriumstatusoftheforceinthelongitudinaldirectionofthelandinggearshockabsorbercanbeshowninEquation(4.25)

,

, , , , , , , , ,, , , ,

i z i i

Ti x i y i z LG i T x i T y i T z

F s

F F F F F F

L

(4.25)

Where , , , , , denotestothevectorof force in theshockabsorber; the 1,2,3

denote to thenose, left,andrightmain landinggearsrespectively; , , , , , , , , is

thevectorofreactionforcebetweentyreandrunwayinthe landinggearwhichcanbe estimated based on the semi‐empirical approach described in the reference[199];

isthetransformationmatrixfromtyrecoordinatesystemtolandinggearcoordinatesystem; and are the spring coefficient and stroke of landing gear shock absorber,thespringcoefficientcanbeestimatedwiththeapproachshowninChapter4.9.

ThentheEquation(4.24)to(4.25)areassociatedandsolvedbyNewton’sapproach,theaircraft Euler angles , , and shock absorber stroke , 1,2,3can be obtained[199]. Therefore, the equilibrium status of aircraft and landing gear for takeoffinitializationcanbeobtained.

Fortheinitializationofthelandingsimulation,theJacobianMethodisusedtotrimthesimulationmodel [203]. It is suitable for3D flight trimbysolvingasystemofaircraftequationsofmotion.Forthedetailedintroductionofthemathematicalprincipleofthismethod, the reader is referred to references [203, 204]. The workflow of this trimalgorithmisshowninFigure4‐28anditsprocessisasfollows[193,205]:

75

1. determineinitialflightconditions2. setcontroltargetsa ,andinthiscase, a 0

p q r u v w a s (4.26)

3. settrimvariables c andassociatedperturbation c

a b c px x x x c s (4.27)

4. setinitialconditionsfor 0c andrunthePHALANXtoobtain 0a

5. varyone trimvariableata timeas ( ) ( )i ic c andrun thePHALANXtoobtain

ia

6. formtheJacobianmatrix:

0( )( )

i:,ii

a a

Jc

(4.28)

7. obtain 1J 8. settheupdateof

1 ( )n ew o ld o ld

c c J a a (4.29)

9. runthePHALANXtoobtain newa

10. checkwhether new a a ,ifnot,gobacktostep8,istheerrortolerance

Initial flight conditions and control vector

Estimate new control vector

Aircraft trimmedCalculate Jacobian

Calculate aircraft accelerations

?newa a No Yes

Figure4‐28Thediagramofaircrafttrimprocessforlandingsimulation[193]

Instep1, the initial flightconditions includethe following, i.e.altitude,airspeed, flightpathangle,turnrate,headingangle,theangleofsideslip.Instep2, , , isthevectorofaircraftangularacceleration, , , isthevectorofaircraftlinearacceleration, istheangularaccelerationofaircraftsideslipangle, is thestrokeaccelerationvectorof

76

thenose,left,andrightmainlandinggearshockabsorber.Instep3,the istheaileroncontrolsetting, istheelevatorcontrolsetting, istheenginethrottlecontrolsetting,istheruddercontrolsetting, istheaircraftrollangle, istheaircraftpitchangle,

istheaircraftazimuthangle, isthestrokevectorofnose, left,andrightmain landinggear shock absorber. A typical disadvantage of this method is that an inappropriateinitial guess would lead to a premature convergence [205]. It means the iterativeprocess stops before it reaches the correct solution. However, this can be solved byrestartingwithanewlyinitialguess[205].

4.6. Verificationandvalidation

4.6.1.Introduction

Theestimationapproachoflandinggearcriticalloadcasesreportedinthisresearchisbased on the multi (rigid) body dynamics simulation model, the verification andvalidationaredemonstrated todetermine theaccuracyandreliabilityof this researchmethodandthemodelscreated.

Detailed characteristics of the flight dynamics and loads of the Airbus A320 are notavailableintheopenliterature.Therefore,anoverallvalidationofthis flightdynamicsandloadsmodelcannotbeconducted.However,varioussub‐aspectsofthemodelsareverifiedandvalidatedinordertohaveconfidenceinthecompletesimulations.

Four sub‐aspects of the simulationmodels described in this chapter are verified andvalidated:

aircraftperformance stabilityandcontrolderivatives estimationoflandinggearloads estimationoflandinggearweight

4.6.2.Aircraftperformanceverification

GiventhatthereislittleaircraftflightperformancedataoftheAirbusA320availableintheopenliterature,theaircraftperformanceverificationisbasedonthegenericaircraftmodelpresentedintheESDUreport[177].

TheESDU report provides flightperformancedata and related figures for the aircrafttakeoffphase.Themethodisbasedon3DoFrigiddynamicsmodelforflightsimulation.Theequationoftranslationalmotionandrotationalmotionforarigidaircraftare:

2

2indVd s

R m mdt dt

(4.30)

Where is the resultant external force acting on the aircraft, including any reactiveforces, is the velocity relative to an inertial frame of reference, s is the distancetraveledand istheinstantaneousmass.

dHM

dt

(4.31)

77

Where is the resultant moment, including components arising from any reactiveforces, istheresultantangularmomentum.

Acomparisonoftheresultsobtainedfrommulti(rigid)bodydynamicssimulationandESDU report results is given in Figure 4‐29 to Figure 4‐31. The detailed parametersrelatedtomodelingcanbefoundinreference[177].AsshowninFigure4‐29(A)and(C),the results of the required takeoff time and field length obtained from the simulationandtheESDUreportareveryclose.Nevertheless,asillustratedinFigure4‐29(A),thevariationoftheangleofattackthroughoutthemaneuvershowsdiscrepanciesbetweentheESDUmodeland theMDS.Thiscanbeexplainedby the fact that thepitchmotioninitiatedbythepilotisaninputtothemodels.TheexactpitchinputintheESDUmodelisunknown.Therefore,ameanpitchuprateisusedintheMDS[34,177].Furthermore,theexactcontrollawoftheelevatordeflectionisnotpresentedintheESDUmodel.TheelevatorcontrolsystemintroducedinChapter4.4.3. isusedtoperformtheMDS.Thisdifferentpitchinputandelevatorcontrolstrategymayhaveledtothedifferenceintheangle of attack shown in Figure 4‐29. This angle of attack difference causes thedifferencesindragandliftvaluesshowninFigure4‐29.Additionally,thedifferentpitchinput and elevator control strategy will lead to the different aerodynamic loadsgenerated by the horizontal tail of the aircraft. This difference could also lead to thedifferentlandinggearloadsshowninsubfiguresFigure4‐30(B),(C),and(D).

0 20 40 60 800

500

1000

1500

V (m/s)

Dis

tanc

e (m

)

ESDU reportSimulation

0 10 20 300

50

100

150

200

Time (s)

Airc

raft

Dra

g (k

N)

ESDU reportSimulation

0 10 20 30-5

0

5

10

15

Time (s)

(

deg)

ESDU reportSimulation

0 10 20 300

500

1000

1500

2000

Time (s)

Airc

raft

Lift

(kN

)

ESDU reportSimulation

Figure4‐29VerificationResults:(A)Angleofattack(B)Lift(C)TakeoffdistanceVSvelocity(D)Drag

Anotherdifferencebetween theESDUreportand the simulation reportedhere is thattherunwaysurfaceisassumedtoberigidintheESDUreport.Thisisnotpossibletoberealized in the SimMechanics modeling environment. Because the specific contactsimulation submodule is unavailable in the SimMechanics now. For the researchreported here, the stiffness and damper ground contact modeling method given inreference[166]isused.Asaresultoftheflexiblerunwaymodelingapproach,therearesmallvariationsintheangleofattackduringthegroundrunphase,whichisthesourceof small discrepancies between the flight dynamics and loads model and the ESDUmethod.Duetothisdifference,asshowninFigure4‐31(B),thevelocityobtainedinthesimulationisslightlydifferentfromthoseobtainedfromtheESDUreport.Sincethedrag

78

of theengines isdirectlyproportional to thedynamicpressure,smalldiscrepancies inenginedragarealsopresentedinFigure4‐31(A).

0 10 20 300

500

1000

1500

Time (s)

MLG

For

ce (

kN)

ESDU reportSimulation

0 10 20 30200

300

400

500

600

700

Time (s)Gro

ss E

ngin

e T

hrus

t (k

N)

ESDU reportSimulation

0 10 20 300

50

100

150

Time (s)N

LG F

orce

(kN

)

ESDU reportSimulation

0 10 20 300

10

20

30

Time (s)

Rol

ling

Res

ista

nce

(kN

)

ESDU reportSimulation

Figure 4‐30 Verification Results: (A) Gross engines thrust (B) Gross rolling resistance (C)Mainlandinggearreactionforce(D)Noselandinggearreactionforce

0 10 20 300

50

100

150

Time (s)

Eng

ines

Dra

g (k

N)

ESDU reportSimulation

0 10 20 300

20

40

60

80

Time (s)

V (

m/s

)

ESDU reportSimulation

Figure4‐31VerificationResults:(A)Totalenginesdrag(B)Velocity

4.6.3.Aircraftstabilityandcontrolderivatives

The aircraft stability and control derivatives computed with DATCOM are comparedwithTornadoforverificationpurposes,seeTable4‐2.Fromthistable,itcanbeseenthatthe lift and drag coefficients obtained using DATCOM are higher than those obtainedusingTornado.Besides,thelateralstabilityderivativesofDATCOMarelargerthanthoseobtained with Tornado, like the static stability derivative and dynamic stability

derivative . This is expected since the volume effects of the fuselage cannot be

modeledwithinTornado[122].

79

Table4‐2Thecomparisonofaircraftstabilityandcontrolderivativesobtained fromTornadoandDATCOM

4.6.4.Landinggearweightestimationmethodsverification

TheflightdynamicsmodelbasedonMDSmethodisusedinthisresearchtoestimatethelanding gear load cases. In this MDS method, the mass of each body needs to beestimated before the dynamics simulation can be performed. The mass of thecomponents affect the interaction forces and motions of the bodies in the dynamicssimulationsystem.Therefore,thelandinggearweightneedstobeaccuratelyestimated.

The performance of the 2.5 classweight estimationmethods used in this research isillustrated in Table 4‐3 [25]. The data is based on the geometry of the landing gearpresentedinreferences[14,35].Unfortunately,dataontheactuallandinggearsweightfor A320 is not available. In accordance to statistical data, the 4.6% of aircraft grossweightischosenasthereferenceactuallandinggearweightforA320andillustratedinTable4‐3[14].ThelandinggearweightestimationresultsbasedonTorenbeek[11]andGD [140]methods for commercial transport airplanes are illustrated for comparison.Although the Torenbeek method reaches higher accuracy in this verification case, itrelies on the statistical and empirical data which commonly are not available forinnovativelandinggears.Hence,the2.5classweightestimationmethodisusedinthisresearch.ThereaderisreferredtoChapter1foradetailedexplanationofthe2.5classweight estimation method. The weight estimated using the 2.5 class method in thisthesishastwolimitations.Firstly,thedataontheactualgeometryofthesideanddragstrutsisnotavailable.Accordingtothereferencesmentionedabove,inthisresearch,the

strutistreatedasan I beamstructureforsimplification.Secondly,thereisnoavailabledetailedinternalstructuredatafortheA320shockabsorber.

AoA(deg) ‐5 0 5 10

LC Tornado ‐0.02 0.5 0.95 1.38DATCOM ‐0.03 0.5 1 1.40

DC Tornado 0.005 0.01 0.03 0.068DATCOM 0.02 0.03 0.058 0.102

mC Tornado 0.24 ‐0.1 ‐0.375 ‐0.575DATCOM 0.36 0.07 ‐0.2 ‐0.5

qmC (1/rad)

Tornado ‐39.2 ‐39.45 ‐39.9 ‐39.65DATCOM ‐41.5 ‐41.5 ‐41.5 ‐41.5

rnC (1/rad)

Tornado ‐0.26 ‐0.26 ‐0.25 ‐0.235DATCOM ‐0.41 ‐0.425 ‐0.435 ‐0.44

plC (1/rad)

Tornado ‐0.46 ‐0.46 ‐0.46 ‐0.46DATCOM ‐0.518 ‐0.488 ‐0.358 ‐0.153

yC (1/rad)Tornado ‐0.475 ‐0.458 ‐0.433 ‐0.4DATCOM ‐1.303 ‐1.303 ‐1.303 ‐1.303

alC (1/rad)

Tornado ‐0.1075 ‐0.107 ‐0.1055 ‐0.1028DATCOM ‐0.041 ‐0.041 ‐0.041 ‐0.041

emC (1/rad)

Tornado ‐2.68 ‐2.705 ‐2.71 ‐2.655DATCOM ‐2.205 ‐2.205 ‐2.205 ‐2.205

80

Table4‐3ThecomparisonofweightestimationresultsforA320landinggears

Referencevalue Methods Value Error

2967kg(basedonstatisticalestimation)

2.5classmethod(kg) 2750 0.93Torenbeekmethod(kg) 2878 0.97

GDmethod(kg) 2113 0.71

4.6.5.Landinggearmodelingapproachverification

Adroptestsimulationiscarriedouttoverifythecorrectnessofthelandinggearmodel.InaccordancetothediscussioninChapter2,therequirementssetoutinCS‐25forthedrop test is used in the verification. The verification is done under critical landingconditionswithamaximumlandingweight,andatouchdownsinkrateof10 ft/s.Theliftisassumedtobeequaltotheweight.Reference[39]illustratesadroptestsimulationfortheA320mainlandinggearundertheaboveconditions.Figure4‐32illustratesthecomparisonbetweenthedroptest resultsofasimulationandthereferencedata fromreference [39]. The detailed A320 shock absorber characteristic parameters are notgivenin[39].Therefore,theexactnonlinearspringanddampingfeaturesofthelandinggear shock absorber used in this reference are not known. Airbus provides a reliablereference [35]which illustrates thegeometrical data tomodel the landinggear shockabsorber. So data taken from reference [35] is used to obtain the shock absorbernonlinear spring and damping parameters for the A320 main landing gear. Thenonlinear spring and damping parameters are calculated by using the classic oleo‐pneumatic equations presented in chapter 4.2.2.2. As illustrated in Figure 4‐32, thiscouldexplainthediscrepanciesbetweentheliteraturedataandthesimulationresults.

Inordertofurtherexplaintheinfluenceofthesedifferences,Figure4‐32illustratesthesimulationresultsusingvarioussetsofcombinationforspringanddampingcoefficients.In principle, compared with the landing gear shock absorber spring coefficient, thelanding gear absorber damping coefficient is the primary factor that determines thepeakshockforceofthelandinggearshockabsorber.

0 0.5 1 1.5 2 2.5 3 3.5 4-6

-4

-2

0

x 105

Time (s)

Sho

ck F

orce

(N

)

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Literature DataSimulationSimulation(+50%Damping)Simulation(-50%Damping)Simulation(+50%Spring)Simulation(-50%Spring)

Figure4‐32Thevalidationresultsoflandinggearloadsusingdroptestsimulation

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AsshowninFigure4‐32(A),ahigherdampingcoefficientleadstoahigherpeakshockload.Thelandinggearshockabsorberdampingcoefficientdeterminestheamountoftheimpact energy that can be dissipated before the landing gear shock absorber reachespeak shock force. As shown in Figure 4‐32 (B), the shock absorber with a higherdamping coefficient has a shorter stroke when the peak shock force is reached.Therefore, less impactenergywillbedissipatedduring thisshorterstroke.Thespringcoefficient mainly influences the shock stroke of the landing gear shock absorber.Becausethespringcoefficientaffectstherequiredstrokewhichprovidesdesiredspringforce.Forexample,asshowninFigure4‐32(B),ifthespringcoefficientisincreasedby50%,thentherelativestrokeisdecreasedaccordingly.

4.7. Summary

The flight dynamics and loadsmodel is discussed in this chapter. This is amultibody(rigid) dynamics simulation model. It is established by extending the existing flightdynamics simulation tool of PHALANX which is developed at the Delft University ofTechnology.The flightdynamicsand loadsmodelconsistsof theairframe,propulsion,control, aerodynamics, atmosphere, and undercarriage modules. The stability andcontrol derivatives are obtained by using DATCOM, as well as Tornado for asupplementary of the control derivatives associated with the rudder. The turbulenceand ground effect are taken into account by using the von Karman model and theclassical equations respectively. The propulsion system ismodeled as an ideal enginesystem. The automatic flight control laws based on the closed loops feedback controlsystems are implemented to realize the takeoff and landing simulations. The controlsystemdevelopedforthegroundbasedvehicleintheGABRIELconsistsofacceleration,synchronization, and deceleration control laws. The acceleration control law isdeveloped based on the open‐loop control systemwhile the others are based on theclosed‐loopcontrolsystem.Themultibodydynamicsmodulesofundercarriage for thethree test cases are established respectively w.r.t their mechanical structures. Thenonlinearspringanddampingcoefficientsofshockabsorberarecalculatedbyusingtheclassical oleo‐pneumatic equations. The Delft‐Tyre model is used in the conventionaland nose landing gear catapult concept. The shuttle in themodel of the nose landinggearcatapultconceptispoweredbyanidealthrustmotormodel.Aspringanddampingsystem is used to develop the contactmodel between the onboard and groundbasedsystem for the GABRIEL. The equilibrium status of aircraft for the initialization ofsimulation can be obtained by using the trim algorithm based on the time domainsimulationandJacobianMethod.

Finally, the flight dynamics and loadsmodel is verified and validated in four aspects:aircraftperformance,stabilityandcontrolderivatives,estimationoflandinggearloadsandweights.Theaircraftperformanceisverifiedbycomparingthetakeoffperformanceresults of simulation and the ESDU report. The stability and control derivatives areverified based on the DATCOM and Tornado. The correctness of landing gear loadsestimation is verified based on the reference data of A320 landing gear drop testobtainedfromtheopenliterature.Thecorrectnessofthelandinggearweightestimationmodule is verified by comparing the results obtained from the simulation, statisticaldata, Torenbeek, and GD methods. In the verification and validation of the flightdynamics and loads model, there are visible differences between simulation and

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referencedataresults,butthesedifferencesareallexplainable.Therefore,summarizedfromtheseexplanations,despitethedifference,itcanbeconcludedthatthecorrectnessandvalidityofthemethodsandmodelsareproven.

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5 Identificationofcriticalloadcases

5.1. Introduction

Inthischapter,thecriticalloadcasesforthreetypesoflandinggearswillbeidentifiedandanalyzedbasedonsimulations.Thetypesoflandinggearstructuresinvestigatedare:

aconventionallandinggearsystem anosegearcatapulttechnologylandinggearsystem theGABRIELlandinggearsystem

Ingeneral, therearetwomaintypesof loadcases:takeoff loadcasesandlandingloadcases.Eachcategorycanbefurtherdecomposedw.r.t.specificfactorswhichmightaffectthelandinggearloadcases.Inthissection,thetop‐leveloverviewofthesimulationplanforthiscriticalloadcaseidentificationisillustratedinTable5‐1.BoththeconventionalandGABRIELtechnologiesaresimulatedfortakeoffandlandingsimulation.Inthecaseofcatapultconceptforcivilaircraft,thetakeoffsimulationisaccountedfor.Inordertoavoid repetition, the detailed explanation for choosing this simulation plan and thefurtherdecompositionof the load cases canbe found in the following sectionsof thischapter.

Table5‐1Simulationplanofcriticalloadcaseidentificationforthethreelandinggearconcepts

5.2. Simulationexamplesoftakeoffandlanding

5.2.1.Simulationexampleofconventionaltakeoff

Anexampleofthetakeoffsimulationwithconventionallandinggearsystemisshowninthissection.ThecharacteristicsoftheconventionallandinggearsystemareprovidedinAppendixA.Thespringanddampingcoefficientscanbeobtainedbasedontheapproach

TypeoflandinggearLoadcasesTakeoff Landing

Conventionallandinggearsystem √ √Nosegearcatapulttechnology √ GABRIELconcept √ √

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illustratedinChapter4.ThegeometricaldataforothercomponentsinlandinggearscanbefoundinChapter2andChapter4respectively.

The most widely used material in landing gear design is 300M steel. Therefore, it ischosenasthematerialforthelandinggearandthedetailedpropertiesofthismaterialcanbefoundinreference[170].Besidesthe300Msteel,thereareotherkindsoflandinggearmaterialsusedinindustrialapplications,suchastitaniumandcompositematerials.However, as thematerials selection isnot the research focusof thisdissertation, onlythemostwidelyusedmaterial300Msteelischosenforthelandinggear.TheaircraftisinitializedusingthedataprovidedinTable5‐2.ThisisatypicalinitializationforaircrafttakeoffunderacriticalconditioninaccordancewithCS‐25andreferencedata[34,180].

Table5‐2Initialconditionsofthetakeoffsimulationusingconventionallandinggear[34,180]

Theresultsofaconventionallandinggearsimulationforanaccelerate‐climbtakeoffincrosswindconditionsareshowninFigure5‐1toFigure5‐5.AsindicatedinFigure5‐1,thenosegearrotatesupat25stoincreasethepitchangleandthenliftoffoccursaround27s.Theaircraftyawangleisaround‐2degreeinpresenceofthecrosswindload.Themaximumlateraldriftingdistancecausedbylateralcrosswindconditionsisaround2m.Therequiredtakeoffdistanceis1100m.

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Figure5‐1AircraftEuleranglesanditsc.g.positioninthetakeoffwithconventionallandinggear

As illustrated in Figure 5‐2, the true airspeed constantly increases after takeoff start.Theaircrafthasgroundvelocityw.r.t.therunwayinthelateraldirection.Thisiscaused

Parameter ValueCrosswind(m/s) 12.8Maximumsingleenginethrust(kN) 118Leadingedgeslat(deg) 20Trailingedgeslottedflap(deg) 19.5Elevatordeflection(deg) 0Ailerondeflection(deg) 0Rudderdeflection(deg) 0

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by lateral aerodynamic loads generated by the crosswind in the takeoff process. InFigure5‐2,theaircraftverticalvelocityalsoincreasesw.r.t.theincreaseofpitchangleasshowninFigure5‐1.Becausetheincreaseofpitchanglecanleadtotheincreaseofliftwhichenablestheaircraftliftofffromtherunway.Thisliftoffmotionisreflectedintheincreaseofaircraftverticalpositionafter27s(seeFigure5‐1).

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Figure5‐2Aircrafttrueairspeedanditsc.g.groundvelocityinthetakeoffwithconventionallandinggear

Figure 5‐3 illustrates the aircraft angle of attack and sideslip angle in aircraft takeoffsimulation. The angle of attack is increased as a result of the increase of the pitchattitude.Sincethecrosswindispresent,thesideslipangleis90degreeatthestartofthesimulation. As the forward speed increase, the sideslip angle reduces. In this takeoffsimulationexample,yawanglevariationissmallcomparedtothevariationinairspeed.Thus, thesideslipangleshowninFigure5‐3issmootherthantheyawangleshowninFigure5‐1.

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Figure5‐3Aircraftangleofattackandsideslipangleinthetakeoffwithconventionallandinggear

Figure 5‐4 indicates the control inputs and angular rate of aircraft in the takeoffsimulation. The aileron and rudder are used to maintain the aircraft lateral andlongitudinal attitudes. The aileron and rudder control implemented in this takeoffsimulationmodeliseffectiveastherollandyawangularrateareclosetozeroasshowninFigure5‐4.Theelevatorisusedtorealizethepitchingoperationat26s.Thedeflected

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elevatorprovidesextrapitchupmomentontheaircraftandletstheaircraftnoserotateup.ThisaircraftpitchnoseupmotionisindicatedintheincreaseofpitchangularrateasshowninFigure5‐4.

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Figure5‐4Aircraftcontrolinputsandangularrateforthetakeoffwithconventionallanding

The takeoff simulationconditionsand the landinggears loadsaregiven inFigure5‐5.Duringthetimefrom0s~1s,thebrakeslocatedonmainlandinggearsclampthewheelstoavoidaircraftdriftinginthepresenceofcrosswind.Consequently,theXforcesinthetwomainlandinggeargearsareasymmetrical.ThestepvariationofXforceappearsat2s is causedby the tyremotion transfers fromstatic friction torollingresistance.Thereader is referred to reference [149, 152, 206] for an extensive discussion about thisphenomenon.

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Nose landing gear load case

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Right main landing gear load case

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Left main landing gear load case

Figure5‐5Theresultsoflandinggearloadsinconventionaltakeoffsimulation

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The force in the Z direction (vertical direction) of the landing gears is alleviatedgradually in thegroundrunaccelerationphase.This isduetothe increaseofairspeedcanleadtotheincreaseofthelift.ThedecreaseoftheZforcealsoleadstoadecreaseofforceintheXdirection.Becausethefrictionforceisdirectlyproportionaltothenormalforceactingonthewheel.

5.2.2.Simulationexampleofconventionallanding

Asimulationexampleofalandingwithaconventionallandinggearsystemisillustratedin this section. An asymmetric landing is modeled at the moment of touchdown, thebankangleis5degreeandtherollrateis14deg/s,seeFigure5‐6.Theotherparametersfor landing simulation are provided in Table 5‐3. These values are typically criticalaccordingtothecertificationspecificationandstatisticaldata[10,35].

Figure5‐6Flightattitudeofasymmetricalaircraftlanding

Table5‐3Initialconditionsofthelandingsimulationforaircraftequippedwithconventionallandinggear[34,35,117]

Approachairspeed(m/s) 70 Ailerondeflection(deg) 0Altitude(m) 0 Rudderdeflection(deg) 0Sinkrate(m/s) 3.7 Pitchangle(deg) 8Crosswind(m/s) 5.4 Pitchrate(deg/s) 0Maximumsingleenginethrust(kN) 118 Rollangle(deg) 5Leadingedgeslat(deg) 27 Rollrate(deg/s) 14Trailingedgeslottedflap(deg) 35 Yawangle(deg) 0Spoilerdeflection(deg) 35 Yawrate(deg/s) 0Elevatordeflection(deg) 0

The results of this landing simulation are shown from Figure 5‐7 to Figure 5‐11. Asillustrated in Figure 5‐7, the peak forces of the nose landing gear in the X, Y, and Zdirection appear when it touches down. As this is a simulation for the asymmetrictouchdown cases, the touchdownmoment illustrated in Figure 5‐7 for left and rightmain landing gears aredifferent.ThepeakX force is causedby thenose landing geartouchdown spin‐up phenomenon. The peak Y force is caused by the asymmetricalaircraft lateralmotionwhen thenose landinggear touchesdown.ThepeakZ force iscausedbythehighsinkratewhennoselandinggeartouchesdown.

Thepeakforcesintheleftandrightmainlandinggeararesimilartothoseforthenoselandinggear.However,thepeakforcesintheZdirectionofthemaingearsaredifferent:peakforceintheZdirectionoftheleftmainlandinggearislowerthanthatintheright

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mainlandinggear.Thisisduetothreereasons:theexistenceofacrosswind,thepositiverollangle(5deg),andthepositiverollrate(14deg/s).

At the standstill status, the loads in the left and right main landing gears areasymmetrical,seeFigure5‐7.Thisisbecauseinthissimulationcase,duetothepresenceof a crosswind, the aircraft ground speed is zero while the airspeed is not zero. Thecrosswindcouldgenerateasymmetricalaerodynamicloadsontheaircraft.Besides,thecrosswindcouldalsogenerateapitchmomenton theaircraft.Hence the loadson thenoselandinggearcanreacharound200kN.

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Figure5‐7Aircraftlandinggearsloadsofconventionallanding

The flight attitudes, positions and control inputs of this landing simulation areillustrated inFigure5‐8 toFigure5‐11.As canbe seen inFigure5‐8, the roll angle isinitialized as 5 degrees and increases to 7 degree after the right main landing geartouches down. This is caused by the initial value of the roll rate (14 deg/s). The rollmotioncausestheaircrafttorolltoitsrightsidewhichcausesafurtherincreaseinrollangle.Afterward,therollanglestartstodecreasetozero.Theimpactloadsontherightmainlandinggearandaircraftsinkmotionlettheaircraftrolltoitsleftside.Thepitchangle of aircraft decreases due to thede‐rotation operation in the landingphase. Theyaw angle is not zero because the crosswind condition is 5 m/s. The decelerationdistanceforthislandingsimulationis500m.TheenginereversethrustandABSareusedtoslowdowntheaircraft.Themaximumlateraldriftingdistanceis2.5m.

As shown in Figure 5‐9, the aircraft touches down with an airspeed of 70 m/s. Theaircraftfirsttouchesdownontherunwaywithmainlandinggearandthenrotatesuntilthenose landinggear touchdownthe runway.This rotationphase isaccomplishedataround 1.5s and then the aircraft starts to decelerate. Themaximum aircraft groundvelocity in the lateral direction is around 1m/s. This lateralmotion is caused by thecrosswindwhichgenerateslateralaerodynamicloads.Thenegativeverticalvelocity(Zdirection)showninFigure5‐9istherateofdescent.

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Figure 5‐10 illustrates the aircraft angle of attack and sideslip angle of this landingsimulation. The angle of attack decreases from11 deg to ‐1 deg in the first 12s. Thiscurve is representative for the rotation phase which is in accordance with the pitchattitudevariation,seeFigure5‐8.Thenegativeangleofattackat1.5siscausedbyapitchdown motion of the nose of the aircraft. This motion is caused by the decelerationduringthegroundrunphase.Attheendofthedeceleration,theairspeedisverylowandthereforetheAoAincreasesat12s.

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Figure5‐8AircraftEulerangleanditsc.g.positionofthelandingwithconventionallandinggear

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Figure5‐9Aircrafttrueairspeedanditsc.g.groundspeedofthelandingwithconventionallandinggear

90

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Figure5‐10Aircraftangleofattackandsideslipangleofthelandingwithconventionallandinggear

AsshowninFigure5‐10,thesideslipangleisinitializedas‐4degduetothepresenceofcrosswind. The sideslip angle is slightly increased to around 0 deg before 5s in thisfigure.Thisvariationofsideslipangleiscausedbythechangeoftheaircraftyawangle.The aircraft is controlled to maintain a certain yaw angle to resist the lateralaerodynamicloadsgeneratedbycrosswind.Themagnitudeofsideslipangledecreasesafter5sinthecurve.Thisisaresultofareductioninthelongitudinalvelocitywhilstthecrosswindremainsconstant.Therefore, thedirectionofaircraft trueairspeedchangesandleadstotheincreaseinmagnitude.

Because this landing simulation is a “one gear touchdown landing” scenario, theasymmetricaltouchdownattitudeoftheaircraftcanleadtoan“oscillation”motionbothinverticalandlateraldirection.This“oscillation”motioncanbeobservedinFigure5‐8andFigure5‐11.

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Figure5‐11Aircraftcontrolsurfacesdeflectionandangularrateof the landingwithconventionallandinggear

As shown in Figure 5‐11, the aircraft uses the rudder and aileron simultaneously toresist this “oscillation”motion and the effect of the crosswind. The aileron is used tomaintain the aircraft with a level attitude in the crosswind condition. The aileronactivelystartsat2.5sandresiststhewavyrollmotionofaircraft.Therudderisusedto

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controltheaircraftheadingangletoenabletheaircrafttotracktherunwaycenterline.Theelevatorisusedmainlyintherotationphase.

5.2.3.Simulationexampleofcatapultconceptforcivilaircraft

Anexampleofatakeoffsimulationforthecivilaircraftcatapultconceptisdescribedinthissection.ThecharacteristicsofthelandinggearsystemareillustratedinAppendixA.

TheaircraftisinitializedinthesimulationusingthedatapresentedinTable5‐4.Thisisaninitializationfornosegearcatapulttakeoffunderextremeconditioninaccordancetoreferencedata[34,113,180].

Table5‐4Initialflightconditionforthetakeoffsimulationofthecatapultconceptforcivilaircraft[34,113,180]

The results of a takeoff simulation for civil aircraft catapult concept can be seen inFigure5‐12toFigure5‐15.

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Figure5‐12AircraftEulerangleand its c.g.position in the takeoff simulationof the civilaircraftcatapultconcept

Figure 5‐12 shows the aircraft attitudes and c.g. position. The aircraft roll and pitchattitudesarearound0degduringthegroundrunphase.However,duetothepresenceof a crosswind, the aircraft yaw angle increases from 0 to ‐3 deg. An increase indynamics pressure during the acceleration results in increased lateral aerodynamicloads.Theaircrafttyreshavesomelateral flexibility.Therefore, theaircrafthas lateralmotionsinthegroundrunphase.ThevariationofthelateralpositionisshowninFigure

Rotationspeed(m/s) 67 Trailingedgeslottedflap(deg) 19.5Crosswind(m/s) 12.8 Elevatordeflection(deg) 0Maximumsingleenginethrust(kN) 118 Ailerondeflection(deg) 0Desiredacceleration(m/s2) 5 Rudderdeflection(deg) 0Desireddecelerationrate(m/s2) 3 Maximumcatapultthrust(kN) 227Leadingedgeslat(deg) 20

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5‐12. During the ground phase, the aircraft X position is increasing and the takeoffdistanceforthisspecificsimulationexampleis720m.Atapproximately15second,theaircraftliftsoff.

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Figure5‐13Aircraftairspeedanditsc.g.groundvelocityinthetakeoffsimulationofthecivilaircraftcatapultconcept

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Figure5‐14Aircraftangleofattackandsideslipangle inthetakeoffsimulationofthecivilaircraftcatapultconcept

Theairspeedandaircraftc.g.groundvelocitiesareshowninFigure5‐13.Theairspeedhasaninitialvalueof12.8m/sduetothepresenceofcrosswind.Themaximumaircraftc.g.groundvelocityinYdirectionforthegroundrunphaseisaround0m/s.Afterthe15s,boththeaircraftvelocitiesinYandZdirectionstarttoincrease.Thisisbecausetheaircraftstartstopitchandthenliftofffromtherunway.

Figure 5‐14 shows the aircraft angle of attack and sideslip angle in the takeoffsimulation. The accelerationof the aircraft causes the angle of attack to increase to 1degreeataround1.5s.At15stherotationphasecanbeobserved.Duetothepresenceofacrosswind,thesideslipangleisinitializedas90degreeforthissimulation.Accordingtotheincreaseofaircraftlongitudinalvelocity,thesideslipangleisdecreasedtoaround3degreeattheendoftakeoff.

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The aileron, elevator, and rudder are used during the takeoff to control the aircraftattitudes.ThedeflectionsofthesecontrolsurfacesareshowninFigure5‐15.Theaileronandrudderaredeflected toresist the lateralaerodynamic loadscausedbycrosswind.The elevator is deflected to realize the aircraft rotation after the rotation speed isreached.

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Figure5‐15Aircraft control surfacesdeflectionandangular rates in the takeoffsimulationof thecivilaircraftcatapultconcept

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X forceY forceZ force

Figure 5‐16 Landing gear loads and catapult force in the takeoff simulation of the civil aircraftcatapultconcept

As shown in Figure 5‐16, in the nose landing gear, the peak load in the X direction(longitudinaldirection)appearsduring theaccelerationphasewhen it is connected tothe catapult shuttle. The longitudinal load in nose landing gear is consistentwith thecatapultforceshowninFigure5‐16.Beforethecatapulttakeoffstarts,theaircraftmodel

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is in equilibrium. The lateralmotion of nose landing gear is constrained to resist theengine thrust and crosswind.Afterward, this constraint is removed.This is consistentwiththestepvariationofthelateralforceactingonthenoselandinggearthatappearsat1s.ThelandinggearloadsintheZdirection(verticaldirection)aredecreasedduringthegroundaccelerationphase.Thisiscausedbytheincreaseoflift.

For themain landinggear, thepeak loads in theXdirection appearwhen the aircraftstartstoaccelerate.TheinitialXforceinrightmainlandinggearishigherthanthatinthe left one. Before the catapult takeoff starts, brake forces are applied on the mainlandinggears toresist theengine thrust.However,due to theyawmomentcausedbythecrosswind,thebrakeforceintherightandleftmainlandinggearsareasymmetrical.Thelateralloadsincreaseasairspeedincreasesduetothecrosswindloads.Theverticalload level in rightmain landinggear ishigher than the left one.This is causedby thecrosswindwhichappliesrollingmomentinthelateraldirection.

5.2.4.SimulationexampleofGABRIELtakeoff

An example of GABRIEL takeoff simulation is illustrated in this section. Thecharacteristics of the landing gear system for GABRIEL are illustrated in Appendix A.TheinitialconditionfortheGABRIELtakeoffsimulationissummarizedinTable5‐5[34,117,180].

Table5‐5InitialflightconditionfortheGABRIELtakeoffsimulation[34,117,180]

Rotationspeed(m/s) 67 Trailingedgeslottedflap(deg) 19.5Crosswind(m/s) 12.8 Elevatordeflection(deg) 0Maximumsingleenginethrust(kN)

118 Ailerondeflection(deg) 0

Desiredacceleration(m/s2) 4 Rudderdeflection(deg) 0

Desireddecelerationrate(m/s2) ‐3Maximumground‐basedsystemthrust(kN)

400

Leadingedgeslat(deg) 20

The results of theGABRIEL takeoff simulation are presented in Figure 5‐17 to Figure5‐21.AsshowninFigure5‐17,theaircraftisinitializedwiththestandstillstatusatthestarting point of the runway. Then the aircraft starts to accelerate its longitudinalvelocity powered by its engines and the ground based sledge. The aircraft Y positionstarts to increase from0m at the time of 16.5s. There are two reasons lead to this Ypositionincrease.

Firstly,becausethistakeoffsimulationaccountsforcrosswind, theaircraftwillyawtothe direction of oncoming airflow when it reaches the rotation speed. As shown inFigure 5‐18, this yaw operation enables the aircraft to lift off from the ground‐basedsystem with zero sideslip angle. This is done to resist the lateral aerodynamic loadscausedbythecrosswind.Secondly,althoughtheaircraftismaintainingcertainsideslipangletoresistthecrosswind,itstillhasunavoidablelateraldrifting.Thislateraldriftingcould be decreased if some more elaborate aircraft motion control systems can bedeveloped.

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Figure5‐19andFigure5‐20 illustrate theairspeed, aircraft c.g. groundspeed, controlsurfacesdeflections,androtationratewhichareaccordingtotheaircraftpositionandEuleranglesvariationshownabove.Ingeneral,theyaresimilartothesimulationresultsof the conventional takeoff. In order to avoid repetition, the reader is referred to therelative section for explanation.However, in the conventional takeoff, the aircraft c.g.longitudinalvelocityincreasesfrom0m/sto80m/swithin30s.IntheGABRIELtakeoff,theaircraftaccomplishesthisaccelerationphasewithin20swhich is10sshorter thanconventionaltakeoff.Thisisbecause,besidesthethrustoftheengines,theaircraftcanobtain thrust from the ground based system. Hence the aircraft can achieve higheraccelerationcomparedwithconventionaltakeoff.

0 5 10 15 20 25-10

0

10

20

Eul

er [

deg]

Time [s]

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Pos

ition

[m

]

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ositi

on [

m]

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4

5

6

7

8

Time [s]

Z P

ositi

on [

m]

Figure5‐17AircraftEulerangleanditsc.g.positioninthetakeoffsimulationfortheGABRIELconcept

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15

20

Time [s]

[

deg]

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-80

-60

-40

-20

0

Time [s]

[d

eg]

Figure5‐18Aircraft angleof attack and sideslip angle in the takeoff simulation for theGABRIELconcept

Theloadsattheconnectionpositionbetweentheaircraftandground‐basedsledgeareshowninFigure5‐21.Duringtheaccelerationphase,theforcesintheXandYdirectionsof the nose and main connection positions increase due to the increase of drag andlateral crosswind loads.The loads in theZdirectionof thenose andmain connectionpositionsdecreaseduetothe increaseof lift. Theaircraftstarts topitchupataround17s and lifts off from the ground‐based system at the 20s. The thrust applied to the

96

groundbasedsledge is illustrated inFigure5‐21.Ashasbeenpresented inChapter3,both the aircraft and ground based system have engine spool up and down time.Therefore, the thrust of the ground‐based system is increasingbefore5s to offset theshortageofaircraftenginethrust.Andthenitismaintainedat350kNtoobtaindesiredaircraft acceleration of 4 m/s2 until aircraft liftoff. Afterward, the sledge starts todecreasethrustandpreparestoreturntothedefaultlocation.

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e ai

rspe

ed [

m/s

]

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elo

cty

[m/s

]

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1.5

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eloc

ty [

m/s

]

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0

2

4

6

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Z V

eloc

ty [

m/s

]

Figure5‐19Airspeedandgroundvelocityofaircraftc.g.inthetakeoffsimulationfortheGABRIELconcept

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2

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4

5

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Aile

ron

Def

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[deg

]

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vato

r D

efle

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n [d

eg]

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der

Def

lect

ion

[deg

]

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p, q

, r

[deg

/s]

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pqr

Figure5‐20AircraftcontrolsurfacesdeflectionsandangularratesinthetakeoffsimulationfortheGABRIELconcept

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0 5 10 15 20 25-400

-200

0

200

400

For

ce [

kN]

Time [s]

Right main connection position load case

X forceY forceZ force

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400

For

ce [

kN]

Time [s]

Sledge ThrustTotal Engines Thrust

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400

For

ce [kN

]

Time [s]

Nose connection position load case

X forceY forceZ force

0 5 10 15 20 25-400

-200

0

200

400

For

ce [kN

]

Time [s]

Left main connection position load case

X forceY forceZ force

Figure 5‐21 Aircraft landing gear connection positions loads and catapult thrust in the takeoffsimulationfortheGABRIELconcept

5.2.5.SimulationexampleofGABRIELlanding

An example of a landing simulation with the GABRIEL system is illustrated in thissection.TheinitialconditionforthissimulationcanbefoundinTable5‐6.ThealgorithmrequiredtoobtainthetrimmedflightparameterscanbefoundinChapter4.

Table5‐6InitialflightconditionforthesimulationofGABRIELlanding[34,35,117]

Approachairspeed(m/s) 70 Ailerondeflection(deg) 0Sinkrate(m/s) 3.7 Rudderdeflection(deg) 0MaximumCrosswind(m/s) 15.4 Pitchangle(deg) 6Maximumsingleenginethrust(kN) 118 Pitchrate(deg/s) 0Desireddecelerationrate(m/s2) ‐3 Rollangle(deg) 0Leadingedgeslat(deg) 27 Rollrate(deg/s) 0Trailingedgeslottedflap(deg) 35 Yawangle(deg) ‐12Spoiler(deg) 35 Yawrate(deg/s) 0Elevatordeflection(deg) ‐9 Maximumsledgethrust(kN) 400

TheresultsofthisGABRIELlandingsimulationare illustrated inFigure5‐22toFigure5‐25.AsshowninFigure5‐22,theaircraftisinitializedwithapitchattitudeof6degree.The roll and yaw angles are initialized to 0 degree and ‐12 degree respectively. Theaircraft c.g. position is initialized to 0.9 m from the runway centerline in the lateraldirection.Thisiscausedbythenon‐zeroaircraftyawangleofinitialflightcondition.Theaircraftisinitialized4.5mabovethegroundbasedplatform.

After clamping the nose andmain connection position, the platformwill return to itsdefault position, i.e. parallel to the runway centerline in the longitudinal direction.AsshowninFigure5‐22,theaircraftYandZpositionsaredecreasinginaccordancetothereturnmotionoftheground‐basedplatform.ThemaximumXpositionis800mwhichisthe required distance for GABRIEL landing. The aircraft angle of attack and sideslipangleareshowninFigure5‐23whicharesimilartoaconventionallanding.

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-10

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5

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uler

Ang

le [

deg

]

Time [s]

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500

1000

Time [s]

X P

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[m]

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0.2

0.4

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1

Time [s]

Y P

ositi

on [

m]

0 5 10 15 20 253.6

3.8

4

4.2

4.4

4.6

Time [s]Z

Pos

ition

[m

]

Figure5‐22AircraftEulerangleanditsc.g.positioninthelandingsimulationfortheGABRIELconcept

0 5 10 15 20 25-5

0

5

10

Time [s]

[

deg]

0 5 10 15 20 25-100

-50

0

50

Time [s]

[d

eg]

Figure5‐23Aircraftangleofattackand sideslipangle in the landing simulation for theGABRIELconcept

AsshowninFigure5‐24,theairspeeddecreasesfrom70m/sto15.4m/s.Thevariationof aircraft Y velocity between 0s to 2s demonstrates the de‐crab operation of aircraftand ground‐based sledge introduced in the above section. The aircraft Z velocitychangesfrom‐3.7m/sto0m/safterittouchesdownonthegroundbasedsledge.

Loadsoftheconnectionpositionbetweenaircraftandground‐basedsledgeareshowninFigure5‐25.Inthenoseandmainconnectionpositions,thepeakforcesintheXandYdirections appear when the ground‐based system starts the de‐rotation operation toreturntheground‐basedplatformtoazeroyawangle.ThepeakforceintheZdirection(verticaldirection)occursatthetouchdownmoment.Theground‐basedsystemusesathrustofaround‐150kNtorealizeadecelerationof‐3m/s2.

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0 5 10 15 20 25 300

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80

Time [s]

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e A

irspe

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m/s

]

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Time [s]

X V

eloc

ity [

m/s

]

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eloc

ity [

m/s

]

0 5 10 15 20 25-4

-2

0

2

Time [s]

Z V

eloc

ity [

m/s

]

Figure5‐24AircraftairspeedandgroundvelocityinthelandingsimulationfortheGABRIELconcept

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For

ce [

kN]

Time [s]

Right main connection position load case

X forceY forceZ force

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ce [

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X forceY forceZ force

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ce [

kN]

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GABRIEL sledge thrust

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500

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For

ce [

kN]

Time [s]

Left main connection position load case

X forceY forceZ force

0 1 2 3

-500

0

500

Figure 5‐25 Aircraft landing gear connection positions loads and sledge thrust in the landingsimulationfortheGABRIELconcept

5.3. Overviewofanalysiscases

5.3.1.Identificationof thecritical takeoff loadcase for the conventional landinggearsconcept

Thesimulationmodelisinitializedatstandstillatthestartoftherunwaywith12.8m/scrosswind. This is the maximum allowed crosswind value determined in CS‐25. Arotationspeedof67m/sischosenbasedontheinformationprovidedinreference[112].In general, this value should be obtained through optimization. However, this fallsoutsidethescopeoftheresearchreported.TheotherinitializationparametersusedforthetakeoffsimulationareillustratedinTable5‐2basedon[111,180].

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During the takeoff phase, the decision speed is the critical speed for the pilot beforewhich the takeoff can be safely aborted in the case of an emergency [11, 175]. If oneenginefailsoranotherproblemoccursbeforeanaircraftreachesthisvelocity,thepilotscan decide to turn off engine thrust and activate the brake system to decelerate theaircraft toastandstillbefore theendof the runway.Whenaproblemoccursafter thedecisionspeed,thepilotcontinuesthetakeoff[34].

AsshowninFigure5‐26,fourkindsoftakeoffscenariosaresimulated:

AccelerationandclimbwithAllEngineOperative(AEO) AccelerationandstopwithAEO AccelerationandclimbwithOneEngineFailure(OEF) AccelerationandstopwithOEF

Thedecisionspeed for takeoff simulation is53m/s in thecrosswindconditionof12.8m/s. The critical load cases for the takeoff simulations are summarized in Table 5‐7.This table isestablishedbasedon thecritical load cases identification criteriaofpeakforcesinlandinggears,seeChapter3.Itillustratesthepeakforcesineachdirectionofthe landing gears. The format of thepeak load case shown in this table is the vector:[PeakFx(takeoffscenario),PeakFy(takeoffscenario),PeakFz(takeoffscenario)].PeakFx,PeakFyand,PeakFzarethepeakforces intheXYZdirectionsof the landinggear.The “takeoff scenario” followedby eachpeak force in the vector indicates the takeoffscenario inwhich thepeak force is obtained. The “takeoff scenario” is denoted as thenumbershowninTable5‐7.

35 40 45 50 55 60 65500

1000

1500

2000

2500

3000

Engine Failed Speed (m/s)

Dis

tanc

e R

equi

red

(m)

acc-climb(AEO)acc-stop(AEO)acc-climb(OEF)acc-stop(OEF)

Figure5‐26Takeoffbalancedfieldlengthcalculationfortakeoffusingconventionallandinggear

The peak loads in the different directions of each landing gear may not occursimultaneously.Thecritical loadsinlongitudinal(Xdirection)andlateral(Ydirection)directionmainlyappearintheacc‐stoptakeoffscenarios.Thecriticallongitudinalloadin nose landing gear is caused by the brake operationduring the acc‐stopprocedure.Thecriticallateralloadsarecausedbythecrosswind.Becauseacc‐stoptakeoffscenariohasalongergroundrunphasecomparedtotheacc‐climbtakeoffscenarios.Therefore,

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thecrosswind leads to larger lateralmotionsand loads.Themaximumstress in theXdirectionofthemainlandinggearoccursatthebeginningofthesimulationwheretheairplane is subjected to a crosswind load and the landing gear brakes are actuated toavoiddrift.

Themaximum vertical (Z direction) loads occur during the acc‐stop takeoff scenario.This is because the acc‐stop uses the aircraft brake system to decelerate during theground run which generates a pitch moment about the center of gravity. This pitchmotion leads tomaximum loads in the Z direction of the landing gear. Theminimumvertical (Zdirection) loadsoccur inac‐climb(AEO)scenarios.Theminimumloadsarenegativevalueswhichmeanthelandinggearshavelefttherunwayduetoliftoff.

Asthepeakloadsonlyappearintheacc‐climb(AEO),acc‐stop(AEO)andacc‐stop(OEF)takeoffscenarios,thesethreescenariosareidentifiedastobethecriticalloadcasesfortheconventionaltakeoffprocedure.

Table5‐7Criticalloadcasesidentificationforconventionaltakeoff

5.3.2.Identificationof thecritical landing loadcase for theconventional landinggearsconcept

The aircraft landing simulations are performed in this section to identify the criticallandingloadcases.Thereferencedatabasedonstatisticalandempiricaldataaretakenfrom[10,34,179,180,195,207‐210]andusedastheinitializationoflandingsimulation,seeTable5‐8andTable5‐9.Asymmetricalmainlandinggearlandingandlevellandingconditions are accounted for by initializing the aircraftwith a non‐zero and zero rollanglesrespectively.Simulationsofaircraftlandingwithoutcrosswindarealsoincludedbecauseitcouldleadtocriticallandinggearloadsinlongitudinalandlateraldirections.

Thekeyfactorsthataffectlandinggearloadsaresinkrate,crosswind,rollangle,androllrate[208,209].TheirextremevaluesillustratedinTable5‐8willbeusedtoperformthesimulations basedon full factorial experiment design, i.e. all the combinationswill besimulated.

Part Peakloadcases(kN) NotesNoselandinggear

(maximum)[24(2),37(4),275(2)]

1. AccelerationandClimb(AEO)

2. AccelerationandStop(AEO)

3. AccelerationandClimb(OEF)

4. AccelerationandStop(OEF)

Leftmainlandinggear(maximum)

[80(1),97(2),301(2)]

Rightmainlandinggear(maximum)

[60(1),127(2),338(4)]

Noselandinggear(minimum)

[‐57(4),‐32(4),‐4(1)]

Leftmainlandinggear(minimum)

[‐195(4),‐84(2),‐6(1)]

Rightmainlandinggear(minimum)

[‐236(4),‐81(2),‐6(1)]

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Table5‐8ExtremeFCEEforcriticalloadcasesidentificationofconventionallandinggear[10,34,210]

Values forother flightattitudesparametersarebasedonreferences [10,34,179,180,195,207‐209]andaregiven inTable5‐9.Thehigh liftdevicesareset inanapproachdeflectionconfiguration:slats27degandflaps35deg[157].Thereversethrustappliedafter a touchdown is set to 80% of maximum engine thrust [211]. The spoiler isdeflectedbyamaximumangle(35deg)aftertouchdown[185].Thecriticalconditionssummarized above are sufficient to generate a conservative landing gear designaccordingtoreferences[141,157].

Table5‐9Aircraftattitudesandcontrolsurfacessettingsinitializationforcriticalloadcasesidentificationofconventionallandinggear[10,34,179,180,195,207‐209]

The landing accuracy requirements for civil transport aircraft are summarized inreference[212].AsshowninFigure5‐27,theaircraftlandinggearsneedtotouchdownon the blue area. In this landing simulation cases, the reference aircraft is the A320whichhasatrackof7.6m.Therefore,thismeansithasalaterallandingpositionmarginofupto35m[171].

Figure5‐27Touchdownpositionrequirements foraircraft landingwithconventional landinggear[212]

Basedonthisdesignofexperiments,thereare300combinationsofcrosswind,sinkrate,rollrateandrollanglethataresimulated.ThemainfindingsaresummarizedinFigure5‐28toFigure5‐31.ThelandinggearloadsrelatedtoaircraftsinkrateareprovidedinFigure5‐28.Thisfigureisbasedonacrosswindof15.4m/s,therollangleof0degandrollrateof0deg/s.InFigure5‐28,thepeakforcesinthenoseandmainlandinggearsarepresented.ThedefinitionoftheforcesintheX,Y,andZdirectionhasbeenshowninChapter 3. In the load cases shown in this figure, the aircraft touches downwith the

Parameters ExtremeValueSinkrate(m/s) 3.7Crosswind(m/s) 15.4Rollangle(deg) ±5Rollrate(deg/s) ±14

Pitchattitude 8deg Airspeed 70m/s Rudder 0degPitchrate 0deg/s Aileron 0deg Slats 27degYawangle 0deg Elevator 0deg Flaps 35degYawrate 0deg

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main landing gears first and thus absorb most of the landing impact. Therefore, theverticalloadsinmainlandinggearsincreaseproportionallytotheincreaseinsinkrate.Thenoselandinggearloadisalmostindependentofthesinkrate.

1 2 3 4-500

0

500

1000Peak nose landing gear loads

Sink Rate (m/s)

For

ce (

kN)

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0

500

1000Peak left main landing gear loads

Sink Rate (m/s)

For

ce (

kN)

1 2 3 4-500

0

500

1000Peak right main landing gear loads

Sink Rate (m/s)

For

ce (

kN)

Figure 5‐28 Effect of sink rate on the peak landing gear loads based on the simulation of aconventionallanding

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ce (

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Peak nose landing gear loads

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Peak right main landing gear loads

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For

ce (

kN)

Peak left main landing gear loads

Figure 5‐29 Effect of crosswind on the peak landing gear loads based on the simulation of aconventionallanding

TheFigure5‐29 illustrates theaircraft landing loadcasesunder theeffectofdifferentcrosswind conditions. Crosswind conditions mainly affect the lateral loads. As thecrosswindvalueincreasesfrom0to15.4m/s(maximumallowedcrosswind),thepeaklateralforceinthelandinggearalsoincreases.

Themaximumlateralforceonthelandinggearislimitedbythemaximumfrictionforcebetweenlandinggearandrunway.Anotherfactorthatalleviatesthelateralloadisthe

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damping characteristics of the tyre. The rubber tyre can absorb and dissipate impactloadsbydeformation.

-5 0 5-500

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500

1000

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For

ce (

kN)

Peak nose landing gear loads

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500

1000

Roll Angle(deg)

For

ce (

kN)

Peak right main landing gear loads

-5 0 5-500

0

500

1000

Roll Angle(deg)

For

ce (

kN)

Peak left main landing gear loads

Figure 5‐30 Effect of roll angle on the peak landing gear loads based on the simulation of aconventionallanding

-15 -10 -5 0 5 10 15-500

0

500

1000

Roll Rate(deg/s)

For

ce (

kN)

Peak nose landing gear loads

-15 -10 -5 0 5 10 15-500

0

500

1000

Roll Rate(deg/s)

For

ce (

kN)

Peak left main landing gear loads

-15 -10 -5 0 5 10 15-500

0

500

1000

Roll Rate(deg/s)

For

ce (

kN)

Peak right main landing gear loads

Figure 5‐31 Effect of roll rate on the peak landing gear loads based on the simulation of aconventionallanding

Basedonthisdesignofexperiments,thereare300combinationsofcrosswind,sinkrate,rollrateandrollanglethataresimulated.ThemainfindingsaresummarizedinFigure5‐28toFigure5‐31.ThelandinggearloadsrelatedtoaircraftsinkrateareprovidedinFigure5‐28.Thisfigureisbasedonacrosswindof15.4m/s,therollangleof0degandrollrateof0deg/s.InFigure5‐28,thepeakforcesinthenoseandmainlandinggearsarepresented.ThedefinitionoftheforcesintheX,Y,andZdirectionhasbeenshowninChapter 3. In the load cases shown in this figure, the aircraft touches downwith themain landing gears first and thus absorb most of the landing impact. Therefore, the

105

verticalloadsinmainlandinggearsincreaseproportionallytotheincreaseinsinkrate.Thenoselandinggearloadisalmostindependentofthesinkrate.

TheloadcasesoflandinggearsshownintheFigure5‐31revealthattherollratehasapronouncedeffectonthecriticalloads.Ifanaircrafthasapositiverollrate,theaircraftis rolling toward to its right side when it touches down. This roll kinetic energy isabsorbedpartlybythe landinggear that touchesdown first.Asshown inFigure5‐31,the right sidemain landing gear load increases as the aircraft roll rate increases.Thesummarywillbepresentedanddiscussedintheendofthischapter.

5.3.3.Identificationofthecriticalloadcaseforthecatapultconcept

The landing phase for the catapult concept is the same as that of a landing with aconventionallandinggear.Therefore,onlythetakeoffprocedureissimulated.TheinitialconditionsforthetakeoffcanbefoundinTable5‐4andaresimilartothoseusedfortheconventionaltakeoff.Thecatapultshuttledetachesfromtheaircraftwhenitreachesthedetachment speed of 65m/s [113]. The catapult shuttle assists the aircraft to beacceleratedataconstantrate(5m/s2)duringthegroundaccelerationprocedure.Thedecisionvelocityisdeterminedtobe25m/sandthebalancedfieldlengthis900m(seeFigure 5‐32). Compared with the conventional takeoff decision speed (53 m/s), thisdecision speed is much lower. This is caused by a much higher acceleration andshortenedaccelerationclimbdistance,bothwithall enginesoperativeandoneengineinoperative. The derived decision speed is used to determine the critical takeoff loadcases.Resultsof these simulationsareshown inTable5‐10, and they indicate that allfourtakeoffscenariosmustbetakenintoconsiderationandusedascriticalloadcases.

20 25 30 35 40400

600

800

1000

1200

1400

1600

1800

Engine Failed Speed (m/s)

Dis

tanc

e R

equi

red

(m)

acc-climb(AEO)acc-stop(AEO)acc-climb(OEF)acc-stop(OEF)

Figure5‐32Takeoffbalancedfieldlengthcalculationforcivilaircraftcatapultconcept

InTable5‐10,themaximumforceintheXdirectionofthenoselandinggearis240kN.Thispeakloadoccurswhentheacc‐climbwithoneengineinoperativeisperformed.Inthistakeoffscenario, theaircraftreachestherotationspeedandthenliftsoff fromtherunway.Therefore,themaximumaerodynamicdragofaircraftinthisscenarioishigherthanthoseintheacc‐stop(AEO)andacc‐stop(OEF).Furthermore,thereisoneengine

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failure in this scenario. Therefore, the required catapult force for it to maintain thedesiredaccelerationishigherthanthatrequiredbythescenarioofallenginesoperativeacc‐climb,i.e.acc‐climb(AEO).ThemaximumandminimumforcesintheXdirectionformain landinggearshappeninthescenariosofacc‐stop(AEO)andacc‐stop(OEF).Thebraking loadsappliedonthemain landinggears leadtopeak longitudinal loads inthemainlandinggears.

Table5‐10Criticaltakeoffloadcaseidentificationforthecatapultconceptforcivilaircraft

Themaximumandminimum lateral forcesactingon thenoseandmain landinggearsmainlyoccurintheacc‐climb(AEO)andacc‐stop(OEF)scenarios.Thisiscausedbytwofactors.Firstly, comparedwith theacc‐stopscenario, thecrosswind loads inacc‐climbaregreater as it reachesahigher airspeed. Secondly, theone engine failure scenarioswillleadtoanasymmetricalthrustcondition.ThemaximumloadsintheZdirectionoflanding gears are mainly caused by the acc‐stop scenarios. Because during thesescenarios,theaircraftneedstobedeceleratedduringthegroundrunphase.ThebrakingloadsappliedonthemainlandinggearscouldcausethepitchmotionofaircraftwhichcanleadtothepeakloadsintheZdirectionoflandinggears.TheminimumforcesinZdirectionappearinthescenariosofacc‐climb(AEO)andacc‐climb(OEF).Thenegativevalueofthisforceappearswhenaircraftliftsofffromtherunway.

5.3.4.IdentificationofthecriticaltakeoffloadcasefortheGABRIEL

TheGABRIELtakeoff issignificantlydifferentfromaconventionaltakeoff.Ashasbeenpresented in Chapter 2, aircraft is catapulted by the GABRIEL system with a higheracceleration.ThebalancedfieldlengthforGABRIELconceptisillustratedinFigure5‐33.Adecisionspeedof41m/sisdeterminedfortheinnovativeGABRIELtakeofftechnology.This is caused by the higher acceleration and shortened acceleration climb distance,both with all engines operative and one engine inoperative. Besides the differentdecisionspeed,thecriticaltakeoff loadcases for theGABRIELwouldalsobedifferent.Hence,thetakeoffphaseisincludedintheGABRIELcriticalloadcaseidentification.

TheinitialconditionsarethesameasthoseinTableA‐4andTable5‐5.ThecriticalloadsfortakeoffscenariosaresummarizedinTable5‐11.Therearenocriticalloadsintheall‐enginesoperativeacceleration‐stopscenario.

Positions Peakloadcases(kN) NotesNoselandinggear

(maximum) [240(3),106(4),264(4)]1. Accelerationand

Climb(AEO)2. Accelerationand

Stop(AEO)3. Accelerationand

Climb(OEF)4. Acceleration and

Stop(OEF)

Leftmainlandinggear(maximum)

[72(2),46(4),303(4)]

Rightmainlandinggear(maximum)

[220(4),43(4),347(4)]

Noselandinggear(minimum)

[‐18(4),‐26(1),‐17(3)]

Leftmainlandinggear(minimum)

[‐228(4),‐23(4),‐7(1)]

Rightmainlandinggear(minimum)

[‐270(4),‐18(4),‐7(1)]

107

In thenose andmain connections, themaximum longitudinal forces occur in the acc‐climb(OEF)scenario.Thisiscausedbythecatapultoperation.Theminimumforcesinthelongitudinaldirectionofthenoseandmainconnectionpositionsappearintheacc‐stop(OEF)scenario.Thisiscausedbythebrakeoperation.

25 30 35 40 45 50 55200

400

600

800

1000

1200

1400

Engine Failed Speed (m/s)

Dis

tanc

e R

equi

red

(m)

acc-climb(AEO)acc-stop(AEO)acc-climb(OEF)acc-stop(OEF)

Figure5‐33TakeoffbalancedfieldlengthcalculationforGABRIEL

Inthenoseandmainconnections,themaximumandminimumlateralforcesappearintheacc‐stop(OEF)scenario.Thisiscausedbytheasymmetricalenginethrustduringthebrakingphaseincombinationwiththepresenceofcrosswind.Themaximumforces inverticaldirectionappearintheacc‐stop(OEF)scenario.Itappearsinthebrakingphaseas the deceleration maneuver can lead to the aircraft pitching motion. This pitchingmotioncancausethemaximumforces inthenoseandmainconnectionpositions.Theminimumforcesintheverticaldirectionsofthenoseandmainpositionsappearintheacc‐climb(AEO)scenario.Thenegativevaluesofvertical forceshappenas theaircraftliftsofffromthegroundbasedsystem.

Table5‐11CriticaltakeoffloadcaseidentificationforGABRIEL

Positions Peakloadcases(kN) NotesNoseconnectionposition

(maximum) [50(3),48(4),173(4)]1. Accelerationand

Climb(AEO)2. Accelerationand

Stop(AEO)3. Accelerationand

Climb(OEF)4. Acceleration and

Stop(OEF)

Leftmainconnectionposition(maximum)

[63(3),64(4),279(4)]

Rightmainconnectionposition(maximum)

[108(3),62(4),296(4)]

Noseconnectionposition(minimum)

[‐81(4),‐18(4),‐4(1)]

Leftmainconnectionposition(minimum)

[‐95(4),‐7(4),‐2(1)]

Rightmainconnectionposition(minimum)

[‐94(4),‐7(4),‐2(1)]

108

Summarizing,basedontheconditionsdiscussedabove,theacc‐climb(AEO),acc‐climb(OEF) and acc‐stop (OEF) are chosen as the critical load cases for a GABRIEL takeoffoperation.

5.3.5.IdentificationofthecriticallandingloadcasesfortheGABRIEL

The critical landing load cases identification is performed in this section for theGABRIEL.TheaircraftmodelisinitializedwiththeconditionsandattitudesillustratedinTable 5‐12. This referencedata canbeused as a reference for theprovisionof safetystandardsintheearlystagesofGABRIELresearch.

Table5‐12GABRIELlandingsimulationinitializationandcondition[10,34]

AsillustratedinTable5‐13,threelandingscenariosaresimulatedinthisresearch:levellanding,rightandleftonesidemaingearlanding.Theaircraftsimulationisinitializedata roll angle and rate between ‐5~5 degree and ‐14~14 degree/s to representdisturbancesduetoturbulenceandcorrectiveactionbythepilot.Theflareoperationisnot included in this part of the GABRIEL concept simulation which means thatsimulationsstartatthelastsecondbeforeaircrafttouchdown.

Table5‐13GABRIELlandingsimulationscenarios[10,34]

Accordingtoreferences[114,123,127,213],sinkrate,horizontalrelativevelocity,andcrosswind are the key parameters that determine the critical landing load cases. The

Approachairspeed(m/s)

70 Elevatordeflection(deg) Trimmed

Sinkrate(m/s) 3.7 Ailerondeflection(deg) TrimmedMaximumcrosswind

(m/s)15.4 Rudderdeflection(deg) Trimmed

MaximumPerenginethrust(kN)

118 Rollangle(deg) 0

Desireddecelerationrate(m/s2)

3 Rollrate(deg/s) 0

Leadingedgeslat(deg) 27 Pitchrate(deg/s) 0

Trailingedgeslottedflap(deg)

35 Yawrate(deg/s) 0

Spoiler(deg) 35Maximumlongitudinalrelativevelocity

betweenaircraftandgroundbasedcart(m/s)±1

GABRIELlandingsimulationscenarios

Rollangle(deg)

Rollrate(deg/s)

Crosswind(m/s)

Description

Levelattitudelanding

0

0 Nocrosswindlanding

‐14~14 0~15.4Zerobankanglelandingin

crosswindlandingcondition

Onesidemaingearlanding(left)

‐5 ‐14~14 0~15.4 Asymmetricallanding

Onesidemaingearlanding(right) 5 ‐14~14 0~15.4 Asymmetricallanding

109

effectsofthethreefactorsontheGABRIELlandingloadsarediscussedwith3examples(seeFigure5‐34toFigure5‐36).AnexampleoftheGABRIELlandingloadsrelatedtothesink rate is illustrated in Figure 5‐34. The sink rate at touchdownmainly affects thelandingloadinZ‐directionasillustratedinFigure5‐34.ThepeakimpactforcesintheZdirectiongeneratedduringlandingincreasewiththegrowthofsinkrate.Thisisbecausethe higher sink rate leads to higher aircraft vertical kinematic energy needed to bedissipated.

1 1.5 2 2.5 3 3.5 4-500

0

500

Peak nose nose connection position loads

Sink Rate (m/s)

For

ce (

kN)

1 1.5 2 2.5 3 3.5 4-500

0

500

1000

Peak left main connection position loads

Sink Rate (m/s)

For

ce (

kN)

1 1.5 2 2.5 3 3.5 4-500

0

500

1000

Peak right main connection position loads

Sink Rate (m/s)

For

ce (

kN)

Figure5‐34EffectofsinkrateontheconnectionpositionloadsinGABRIELlanding

-1 -0.5 0 0.5 1-500

0

500

Relative Velocity (m/s)

For

ce (

kN)

Peak nose connection position loads

-1 -0.5 0 0.5 1-500

0

500

1000

Peak left main connection position loads

Relative Velocity (m/s)

For

ce (

kN)

-1 -0.5 0 0.5 1-500

0

500

1000

Peak right main connection position loads

Relative Velocity (m/s)

For

ce (

kN)

Figure5‐35EffectofhorizontalrelativevelocityonconnectionpositionloadsinGABRIELlanding

An example of the relationship between the landing impact forces and the horizontalvelocitydifferencebetweensledgeandaircraftisshowninFigure5‐35.Apositivevalueofthehorizontalrelativevelocitymeansthattheground‐basedsledgemovesfasterthan

110

theaircraft.Fromthisfigure,itcanbeconcludedthattherelativevelocitymainlyaffectsthe longitudinal loads. This figure can be used to determine a maximum allowablerelative velocity difference for a given structural design or vice versa to design astructureforapre‐specifiedmaximumallowablerelativevelocitydifference.

0 5 10 15-500

0

500

Crosswind (m/s)

For

ce (

kN)

Peak nose connection position loads

0 5 10 15-500

0

500

1000

Peak left main connection position loads

Crosswind (m/s)

For

ce (

kN)

0 5 10 15-500

0

500

1000

Peak right main connection position loads

Crosswind (m/s)

For

ce (

kN)

Figure5‐36EffectofcrosswindonconnectionpositionloadsinGABRIELlanding

AnexampleoftheeffectofcrosswindontheloadsintheconnectionsbetweenaircraftandgroundbasedcartispresentedinFigure5‐36.Itisconcludedthatcrosswindmainlyaffectsanaircraft’slandingimpactinthelateraldirectionbecausetheforcesintheXandZ directions are almost constantwhen the crosswind value varies. The force in the Ydirection increases from0toaround250kNascrosswindvelocity increases from0to15.4m/s.Theincreaseofcrosswindleadstotheincreaseoflateralaerodynamicloadsonaircraft.

5.3.6.EstimationoflandingattitudesbasedonMonte‐Carlosimulation

Ashasbeen introduced inChapter3, thereare twoapproacheswhichwill beused todeterminethetouchdownattitudeofaircraftimplementedwithinnovativelandinggearsystem. The first one based on statistical data has been illustrated with simulationexamplesofconventionallandinggearandGABRIELintheprevioussections.Theotherestimation approach, which is based onMonte‐Carlo simulation, will be presented inthissection.Theaircraftlandingsimulationsinturbulenceconditionsareperformedtoobtainthepossibletouchdownattitudes.ThevonKarmanturbulencemodeldescribedin[85]isused.ThereaderisreferredtoChapter3foradetailedintroductionaboutthisturbulencemodel.

A simulation of an aircraft landing in turbulence and crosswind condition will bepresented and compared to a landing simulation without turbulence. Simulationparameters are shown in Table 5‐14. The aircraft simulation is initialized withoutturbulenceinatrimmedconditionat70maltitude,adescentangleof3degand5m/s

111

crosswind.Turbulenceisappliedafterthesimulationmodelistrimmed.Thesimulationendswhentheaircrafttouchesdownontherunway[175].

Table5‐14Parametersforlandingsimulationinturbulenceconditions[34,35,117]

Comparisons between the results of the simulation with and without turbulence areshown in Figure 5‐37 to Figure 5‐40. As shown in Figure 5‐37, the aircraft landingtrajectory obtainedunder turbulence conditions is similar to thatwithout turbulence.Although there is turbulence in this simulation, the aircraft can still land with anaccuracy of ±3meters in the lateral direction.As shown in Figure5‐37, the curves ofEuler angles With Turbulence (WT) are more oscillating than those obtained fromlanding simulation WithOut Turbulence (WOT). The turbulence affects the aircraftattitudes and motions even though the (auto) pilot corrects for it. The aircraft pitchattitudesandangleofattackstarttoincreaseafter15swhenitstartstheflareoperation.The yaw angle is maintained around ‐5 deg during the landing phase. The de‐craboperationisnotincludedinthissimulationbecauseit isnotrequiredfortheGABRIELlanding process. Consequentially, the sideslip angle is maintained around 0 deg asshowninFigure5‐38.

0 10 20 30-10

-5

0

5

10

Eul

er A

ngle

s[de

g]

Time [s]

WT WT WT WOT WOT WOT

0 10 20 300

500

1000

1500

2000

Time [s]

X P

ositi

on [

m]

0 10 20 30-3

-2

-1

0

1

Time [s]

Y P

ositi

on [

m]

0 10 20 300

20

40

60

80

Time [s]

Z P

ositi

on [

m]

Figure5‐37AircraftEulerangleanditsc.g.positionforflightsimulationwithandwithoutturbulence

The aircraft airspeed and ground velocity are shown in Figure 5‐39. The aircraftairspeeddecreasesfrom70m/sto65m/sduringtheflarephase.Duringtheflarephase,

Approachairspeed(m/s) 70 Ailerondeflection(deg) 0Altitude(m) 70 Rudderdeflection(deg) 0Sinkrate(m/s) 3.7 Pitchangle(deg) 6Maximumcrosswind(m/s) 15.4 Pitchrate(deg/s) 0Maximumsingleenginethrust(kN) 118 Rollangle(deg) 0Leadingedgeslat(deg) 27 Rollrate(deg/s) 0Trailingedgeslottedflap(deg) 35 Yawangle(deg) ‐4Spoiler(deg) 35 Yawrate(deg/s) 0Elevatordeflection(deg) ‐9

112

see Figure 5‐39, the aircraft sink rate decreases from 3.7m/s to around 0.5m/s. Theaircraftdragisalsoincreasedasaresultoftheflaremaneuver.

AsshowninFigure5‐40,theaircraft’sailerons,elevators,rudderandthrottleareusedtotrackthedesiredflighttrajectorywhichistakenfromthereference[88].Thecurvesobtainedfromthesimulationwithturbulencearemoreoscillatingthanthosefromthesimulation without turbulence. The turbulence causes disturbance to the aircraftattitudesandmotions.Therefore,thedeflectionsofcontrolsurfacesaremoreoscillatingtocorrectfortheturbulence.Inthesimulationscenariowithoutturbulence,theaileron,elevator,rudderandthrottlearekeptconstantastheaircraftneedstotrackaconstantdescendingtrajectory.After15s,theaircraftelevatorstartstodeflecttoinitiatetheflaremaneuver.Inthepresenceofacrosswind,theaircraftenginethrustismaintainedatalow levelandcontrolledtomaintaintheaircraftattitudes in the longitudinaldirection[214],seeFigure5‐40.

0 10 20 306

8

10

12

Time [s]

[

deg]

0 10 20 30-2

-1

0

1

2

Time [s]

[d

eg]

Figure5‐38Comparisonofaircraftangleofattackandsideslipangle for landingsimulationswithandwithoutturbulence

0 10 20 3065

70

75

Time [s]

Tru

e A

irspe

ed [m

/s]

0 10 20 3064

66

68

70

72

Time [s]

X V

eloc

ity [

m/s

]

0 10 20 30-0.4

-0.2

0

0.2

0.4

Time [s]

Y V

eloc

ity [m

/s]

0 10 20 30-4

-2

0

2

Time [s]

Z V

eloc

ity [m

/s]

Figure5‐39Comparisonofairspeedandgroundvelocityofaircraftc.g.forlandingsimulationswithandwithoutturbulence

As an example, 100 landing simulations in turbulence and crosswind conditions areperformed.Theresultsofthese100simulationsaresummarizedinFigure5‐41.Therollangleandratearemaintainedbetween±2degreesand±4degree/srespectively.Ideally,the roll angle and rate are approximately 0 degree. However, due to the presence of

113

turbulence,theaircrafthastheoscillatingrollmotionsintheselandingsimulations.Thepitch angle and pitch rate aremaintained between 6~12 degrees and ‐2~4 degree/srespectively. In order to decrease the aircraft sink rate before touchdown, the pitchangle and rate are not zero during the flare phase. The yaw angle and rate aremaintainedbetween‐8~0degreeand±4degree/srespectively.

0 10 20 300

1

2

3

4

5

Time [s]Sin

gle

Eng

ine

Thr

ust

[kN

]

0 10 20 30-5

0

5

10

Time [s]

Aile

ron

Def

lect

ion

[deg

]

0 10 20 30-14

-12

-10

-8

-6

Time [s]

Ele

vato

r D

efle

ctio

n [d

eg]

0 10 20 30-2

0

2

4

Time [s]

Rud

der

Def

lect

ion

[deg

]

Figure5‐40Comparisonofcontrolsurfacesdeflectionsandenginethrustforflightsimulationswithandwithoutturbulence

-4 -2 0 2 4-2

0

2

4

Roll Rate [deg/s]

Pitc

h R

ate

[deg

/s]

2 4 6 8 10 12-8

-6

-4

-2

0

Pitch Angle [deg]

Yaw

Ang

le [

deg]

-2 0 2 4-4

-2

0

2

4

Pitch Rate [deg/s]

Yaw

Rat

e [d

eg/s

]

-2 -1 0 1 20

5

10

15

Roll Angle [deg]

Pitc

h A

ngle

[de

g]

Figure5‐41EvaluationofaircrafttouchdownattitudesbasedonMonte‐Carlosimulationina10ktscrosswind

The control inputs at the moment of touch down are presented in Figure 5‐42. Theailerondeflectionanglevariesfrom‐25degreesto‐10degreesinordertocompensatefortherollingmotioncausedbythecrosswindandturbulence.Theelevatordeflectionangle isshowntobebetween±10degrees.Theelevator isusedtocontroltheaircraftpitch attitude, and is maintained between ±15 degrees. The thrust throttles aremaintainedbetween0~6kNatthetouchdownmomentforaGABRIELconceptlanding.

114

The corresponding flight trajectories are presented in Figure 5‐43. Only 10 flighttrajectoriesareshownforclarity.Theaircraftflighttrajectoriesshowfluctuationsbothverticallyandlaterally.However,theflightcanstillcompletewithanacceptablelateralpositionmarginof±3.

-15 -10 -5 0 5 10-25

-20

-15

-10

-5

Elevator Deflection [deg]

Aile

ron

Def

lect

ion [

deg]

-4 -2 0 2 40

2

4

6

8

Rudder Deflection [deg]

Sin

gle

Eng

ine

Thr

ust

[kN

]

Figure5‐42EvaluationofaircrafttouchdowncontrolsurfaceandthrottlesettingbasedonMonte‐Carlosimulationina10ktscrosswind

0 500 1000 1500 20000

20

40

60

80

Horizontal Position [m]

Alti

tude

[m

]

0 500 1000 1500 2000

-20

-10

0

10

20

Horizontal Position [m]

Late

ral P

ositi

on [

m]

Figure 5‐43 Evaluation of aircraft flight trajectory based on Monte‐Carlo simulation in a 10ktscrosswind

5.3.7.Approachofaircrafttouchdownattitudesestimation(basedonMonte‐Carloevaluation)validation

Two types of conventional landingprocedures are included, i.e. the sideslip approachprocedure and the crabbed landing procedure, to validate the performance of theapproach based on Monte‐Carlo evaluation in estimating the aircraft touchdownattitudes. For both landing control strategies, landing simulations will be performedwith100kindsofturbulence.Theenvironmentalconditionscanbefoundinreferences[10,34].

A comparison of aircraft touchdown attitudes obtained from reference data andpredicted data based on simulation results is shown in Table 5‐15. The simulationresultsbasedontheMonteCarloevaluationareanalyzedwithstatisticalmethods.The95%confidencelevelcriterionismetandiscalculatedforeachflightattitudeobtainedbysimulation.Specific referencedata for the landingattitudesof theAirbusA320arenotavailableintheopenliterature.Thereferencedatacollectedfromreference[10,35,157,185]arebasedon thestatisticalandempiricaldata for twin‐enginecivilaircraft.Theseaircraftcanbecategorizedasthesametypeofthereferenceaircraftshowninthisthesis. As shown in Table 5‐15, the flight attitudes obtained from reference data andsimulationsarecomparableinmagnitude.Thesimulationsperformedinthisthesisonlyaccount for the sideslip and the crabbed approach landing procedures under specificcrosswind and turbulence conditions. Therefore, a more extensive simulation which

115

covers more kinds of condition can be performed to improve the accuracy of thismethod.Nevertheless,basedonthecomparisonshowninTable5‐15,thefeasibilityandreliabilityofthisapproachinestimatingaircrafttouchdownattitudescanbevalidated.

Table5‐15Comparisonofaircrafttouchdownattitudesbetweenreferencedataandsimulationresults[10,35,157,185]

5.4. Resultsanddiscussion

5.4.1.Conventionallandinggearsconcept

The purpose of this section is to summarize the critical load cases identified forconventional landing gears. This research carries out 304 takeoff and landingsimulations and summarizes them in this section. For the conventional landing geartakeoffsimulations,asthepeakloadsonlyappearintheacc‐climb(AEO),acc‐stop(AEO)and acc‐stop(OEF) takeoff scenarios, these three scenarios are identified as to be thecriticalloadcases.

Fortheconventionallandinggearlandingsimulations,asstatedinChapter3,therearetwocriteriathatcanbeusedtodeterminethecriticalloadcases.Theyare:

1. Criteriabasedonpeakforcesoflandinggears2. CriteriabasedonVonMisesstressandbucklinganalysis

Inthefirstone,thecriticalloadcasesareselectedwhichcanleadtopeakforcesonthelandinggearstrut.Summarizingtheresultsfromthe300kindsoflandingsimulation,aspresented inTable5‐16, thereare13combinationsof load casesare identifiedas thecriticalone.

Thehighsinkrate(3.7m/s)givestothecriticalloadcasesintheverticaldirectionwhilethe high crosswind (15.4 m/s) causes the peak loads in the lateral directions. Theaircraftsimulatedinazerocrosswindconditionhadthemaximumgroundspeed.Thisisbecausetheinitialvalueoftheapproachairspeedoftheaircraftisconstant.Sothelowerthecrosswind,thehighertheaircraftgroundspeed.Thehighergroundspeedcanleadto the increase of longitudinal load in landing gears. These conditions can lead to thecriticalloadingcaseinthelongitudinaldirectionofthenoseandmainlandinggears.Therollrate(14degree/s)andangle(5degree)canalsoleadthecritical loadcasesintheverticaldirection.Thisisbecausetherollmotionofaircraftattouchdownmomentcanleadtohigherimpactloadsbetweenthelandinggearsandrunway.

Parameters ReferencedataSimulationresult

(>95%confidencelevel)Sinkrate(m/s) [0,3] [0,2.3]

Pitchangle(degree) [0,8] [0,8.5]

Rollangle(degree) [0,4.5] [0,5.1]

Rollrate(degree/s) [0,6] [0,4.7]

Yawangle(degree) [0,5] [0,5.2]

116

Table5‐16Summarizedcriticalloadcasesforconventionallanding(criteriabasedonpeakforcesinlandinggears)

Thesecondcriteriaconsistof identifyingthecritical loadcases foreachcomponent inthe landinggearsystemseparately.Becausethepartsof the landinggearsystemhavedifferentstructure.Inthissolution,eachelementisdeterminedbasedontheirstructureasmentionedinChapter3.Thecriticalloadcasesforsideanddragbracesareidentifiedusingbucklingcriteria.ThevonMisesstress ischosenasthe identificationcriteria forthecriticalloadcaseoftheshockabsorberwhichisatubestructure.

Asshown inTable5‐17,9 typesof critical loadcasescanbe identified in this step. Inordertoavoidrepetition,theintroductionofthecomponentsoflandinggearillustratedintheTable5‐17canbefoundinChapter3.

InTable5‐17,all thecritical loadcaseswere identifiedundermaximumsinkrateandcrosswind conditions. Therefore, in this case, the sink rate and crosswind are theprimary factors affect the load cases in landing gear components. The sink ratedetermines the vertical load case while a crosswind influences the lateral loads. Thehigher vertical loads lead to the increase of vonMisses stress in the shock absorber.Besides,theincreaseofverticalloadsinshockabsorberalsoleadstotheincreaseofitslongitudinal loads.Becausethetyrefrictionforceswiththerunwayarealsoincreased.Therefore,thehighersinkratealsoleadstotheincreaseofloadsinthedragbracewhichisattached to the front sideof the shockabsorber.The lateral loadsgeneratedby thecrosswind lead to the increaseof the force in the sidebrace.Beside thecrosswind,asshown in Table 5‐17, the roll rate and angle also affect the lateral load cases in thelandinggears.Becausewhentheaircrafttouchesdownwithasymmetricalattitude, i.e.nonzero roll rate,andangle, thevertical landing impact loadswill transfer to the sidebraceswhichisattachedtothelateralsideoftheshockabsorber.

SinkRate(m/s) CrossWind(m/s) RollAngle(deg) RollRate(deg/s)2.4 10.3 ‐5 ‐141.2 15.4 5 141.2 10.3 5 141.2 0 0 143.7 0 ‐5 ‐143.7 5.1 5 143.7 15.4 5 141.2 0 ‐5 ‐143.7 15.4 5 ‐143.7 0 2.5 ‐143.7 10.3 ‐5 143.7 15.4 ‐5 143.7 5.1 5 7

117

5.4.2.Catapultconceptforcivilaircraft

Thereare4kindsoftakeoffscenariosshouldbetakenintoaccountforthecivilaircraftcatapult concept as the critical load cases. Most of the peak loads in the X, Y, and Zdirection appear in acc‐stop(OEF)) and acc‐climb(OEF) condition. The key factorsdeterminethelandinggearloadscanbesummarizedastheasymmetricalenginethrust,

Table5‐17Summarizedcriticalloadcasesforconventionallanding(criteriabasedonVonMisesstressandbucklinganalysis)

Component

Criticalloadcase

Forceandmom

entsValue:kN·morkN

sink

rate

(m/s)

crosswind

(m/s)

roll

angle

(deg)

roll

rate

(deg/s)

Mx

My

Mz

Fx

Fy

Fz

SideBrace

(Nose)

3.7

12.9

2.5

14

00

0‐0.1

210

351

DragBrace

(Nose)

3.7

12.9

50

00

0259

0.2

433

Shock

absorber

(Nose)

3.7

12.9

‐5

0‐113

025

‐92

‐25

300

SideBrace

(RightMain)

3.7

12.9

514

00

00.2

63

153

DragBrace

(RightMain)

3.7

12.9

0‐14

00

0403

0.3

‐959

Shock

absorber

(RightMain)

3.7

12.9

57

‐5

2187

‐10

‐223

282

SideBrace

(LeftM

ain)

3.7

12.9

‐5

14

00

0‐0.1

‐38

92

DragBrace

(LeftM

ain)

3.7

12.9

2.5

00

00

318

‐0.3

755

Shock

absorber(Left

Main)

3.7

12.9

‐2.5

0161

‐0.1

‐2

‐2

‐166

197

118

landing gear brake maneuver, and crosswind loads. In order to avoid repetition, thereaderisreferredtoChapter5.3fortheextensivediscussion.

5.4.3.GABRIELconcept

AccordingtotheGABRIELtakeoffsimulations,theacc‐climb(AEO),acc‐climb(OEF)andacc‐stop(OEF)areidentifiedasthecriticalloadcases.Inordertoavoidrepetition,thereaderisreferredtoChapter5.3forextensivediscussion.

Table5‐18SummarizedcriticalloadcasesforGABRIELlanding

ThecriticalloadcasesidentifiedfromGABRIELlandingsimulationsareshowninTable5‐18.Thereareabout16combinationsofloadcaseswhichneedtobeconsideredasthepeakloadoccurred.Themaximumsinkrate(3.7m/s)leadstothecriticalloadcasesinthe vertical direction of the nose and main connection positions. The maximumcrosswind(15.4m/s)affectstheaircrafttouchdownyawangleandlateralaerodynamicloads. These effects cause the critical load cases in the lateral direction of mainconnection positions. The asymmetrical roll attitude andmotion (5 deg and 14deg/s)causeonesidemainlandinggeartouchdown,andthecriticalverticalloadcasesofmainlandinggearsarederivedfromthesesituations.Thepeakhorizontalrelativevelocity(1m/sand‐1m/s)leadstothecriticalloadsinthelongitudinaldirectionofthenoseandmainconnectionpositions.

Summarizing,itisfoundthatsinkrateaffectedthepeakloadinaverticaldirection;thehorizontalrelativevelocitydifferencesmainlydeterminethecriticallongitudinalloads;thepressureofcrosswindsisthemainfactordetermininglateralloads.

5.5. Summary

Firstly, the takeoff and landing simulation examples of three types of landing gearsystem are presented. The flight parameters and landing gear loads variation areobtained and discussed. The performance of the approach based on Monte‐Carlo

Sinkrate(m/s)

Crosswind(m/s)

Rollangle(deg)

Rollrate(deg/s)

Horizontalrelativevelocity(m/s)

2.5 15.4 0 0 11.2 7.7 5 ‐14 ‐13.7 0 0 0 ‐11.2 15.4 ‐5 ‐14 ‐12.5 15.4 5 14 ‐13.7 15.4 ‐5 ‐14 11.2 0 5 14 ‐11.2 15.4 ‐5 ‐14 03.7 0 5 14 11.2 0 0 0 ‐11.2 7.7 ‐5 14 ‐13.7 15.4 0 0 01.2 15.4 ‐5 ‐14 13.7 7.7 ‐5 ‐14 11.2 0 0 0 11.2 15.4 5 14 ‐1

119

evaluation to estimate the aircraft touchdownattitudes is validatedby comparing thesimulationresultswiththereferencedata.

Secondly, various combinations of FCEE are used to perform takeoff and landingsimulationstoidentifythecriticallandinggearloadcases.Inthissection,theeffectsofthekeyfactorsonlandinggearloadsarediscussed.Intheconventionallandinggeartestcase,bothtakeoffandlandingsimulationsareaccountedintheidentificationofcriticalloadcases.Inthetakeoffsimulation,fourtakeoffscenariosareinvolved.Inthelandingsimulation, the effects of sink rate, crosswind, roll angle, roll rate in aircraft landinggearsloadsareinvestigated.Sinkrateandcrosswindcanaffecttheverticalandlateraldirectionloadsrespectively.Theloadsonmainlandinggearsarealsoaffectedbytherollangleandratewhenaircraft roll toaspecificsideof themain landinggear, i.e. leftorright. Using the roll angle initialization variation as a basis, the level and one mainlandinggeartouchdownscenariosareinvestigatedinthisresearch.

Only takeoff simulation is performed to investigate the critical load cases for landinggear in nose gear catapult scenario because its landing operation is identical to aconventionallanding.TheGABRIELconceptischosenasaninnovativetestcaseinthisthesis. Both takeoff and landing simulations are performed based on the multibodydynamics model for the GABRIEL concept. These simulations are based on variouscombinationsofsinkingrate,horizontalrelativevelocity,crosswind,rollangleandrate.Theeffectofthesefactorsonlandinggearloadsisdiscussedrespectively.

Thirdly,thecriticalloadcasesareidentifiedforthesethreelandinggearconcepts.Thisphysics‐based approach is proved to be feasible and valuable in identifying criticallandinggearloadcases,seeTable5‐19.

Table5‐19Criticalloadcasesidentificationcontribution

LandinggearconceptOriginalloadcases

mentionedinreferencesIdentifiedcritical

loadcases

Conventionallandinggearssystem 304 16Catapultconceptforcivilaircraft 4 4

GABRIELconcept 139 19

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6 ConclusionsandRecommendations

6.1. Researchconclusion

This thesis discusses the state of the art in landing gear design methods. Classicallanding gear design methods mainly rely on empirical and statistical data. As aconsequence,theyhavesomekeylimitations.Firstofall,theestimationofcriticalloadcases is based on statistical data and therefore it can be inaccurate or even notrepresentative for novel aircraft designs. More advanced landing gear designapproaches are employed both in industry and research institutions and academia.These include multi‐disciplinary design optimization techniques and more detailedsimulationmodels, such asFEM.The state of the art of advanced landing geardesignmethodshasonemajorlimitation.Thereisnoapproachavailabletopredictcriticalloadcases.Furthermore,althoughflightdynamicsanalysesareincludedinsomestudies,itsintegration in a multidisciplinary simulation and analysis framework is not yetthoroughly investigated. Finally, landing gear design, whether based on advancedmethodsorclassicalempiricalmethodsistypicallynottightlyintegratedintotheoverallaircraftdesignprocess.Therefore,theoveralldesign(airframeandlandinggear)willbesub‐optimal.Alandinggeardesignapproachwhichcanaddressthelimitationsofbothexistingclassicalandadvanceddesignapproachesshouldbedeveloped.

Currently, most of civil aircraft in operation are equipped with the highly reliableconventional landing gear system. The landing gear system generally accounts forapproximately5%oftheMLWofanaircraft.Ifthereisanopportunitytodesignamorelightweight landing gear, it will have a significant impact on aircraft performance.Therefore, more optimal landing gear systems should be developed to meet thechallengesofmorestrictflightvehicleemissioncriteriaandtheincreasingcompetitivecivil aviation market. An overview of innovative landing gear concepts, i.e. catapult‐assistedtake‐off,GABRIEL,arepresentedanddiscussedinthisthesis.Anovelphysics‐basedapproachtopredictthecriticallandinggearloadcasesattheaircraftconceptualandpreliminarydesignphases ispresented in this thesis.Theapproach isbasedonaphysics‐based flight dynamics and loadsmodel inwhich the equations ofmotion aremodelledusingmultibodydynamicssimulations.Themodelisusedtoestimatecriticalloadcasesbyperforminglargesetsofaircrafttake‐offandlandingsimulations.Monte‐Carlosimulationsareakeyfeatureofthisapproachasanalternativetohavingarealisticrepresentationofallweatherconditionsandpilotbehavior.

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Theflightdynamicsandloadsmodel isusedtosimulatethreetest‐cases.Firstofall,aconventionalmediumrangeaircraftwithaconventionallandinggear.Second,thesameaircraftassistedwithacatapult launchsystem.Third, thesameaircraftwithagroundbased take‐off and landing system, designated the GABRIEL concept. For all threesimulationmodels,theaerodynamiccharacteristicsoftheaircraftarerepresentedwithlargemultidimensional look‐up tables.Theaerodynamicdataset isbasedprimarilyontheDATCOMmethod.Ruddercontrolderivativesarecomputedbasedonavortexlatticemethod. The flight control system and ground vehicle control system strategies areextensivelydiscussedinthisthesis.Asimpleenginemodelisusedinthemodelsandtheatmosphericpropertiesaremodelledbasedon the internationalstandardatmosphereandthevonKarmanturbulencemode.Thekeydifferencebetweenthethreesimulationmodelsisthemultibodydynamicssimulationofthelandinggear/undercarriagesystem.

Thesimulationmodels areverifiedandvalidatedwith respect tovariousaspects.Theairfield performance such as take‐off distance, is validated by comparisonwith ESDUdata. Aircraft stability and control derivatives are verified by comparing DATCOMresults to a low fidelity vortex lattice method called Tornado. The estimation of thelanding gear weight is validated by comparing it to empirical data. The landing gearmodelling approach and dynamic loads simulations are verified by comparison withsimulationspublishedinopenliterature.Finally,touchdownattitudes,e.g.rollandpitchattitudeencountered inaconventional landingprocedureareestimatedandvalidatedwithstatisticaldata.

For each of the three representative test cases, the critical load cases are determinedwith the approach proposed in this thesis in order to demonstrate the performance.Based on this approach, there are 16, 4, and 19 load cases identified respectively ascriticalfrom304,4,and139loadcasesmentionedinreferences.

Theapplicationof thephysics‐basedapproach in landinggeardesign isdemonstratedfortwocases.Inthefirstcase,theconventionalmainlandinggearlayoutischanged.Thechangeinthemainlandinggearloadcasescausedbythismodificationisestimatedbyusingthephysics‐basedapproach.Thisisvaluableinhelpingtheengineerstoquantifythe potential reduction of the peak load cases in the landing gears and thereby thepotentialweight reductionasa resultof suchadesignchange. In thesecondcase, thefeasibility of the GABRIEL is demonstrated. By utilizing this approach, the feasibility,reliability,andbenefitsofdevelopingan innovative landinggearsystem, i.e.GABRIEL,areanalyzedanddiscussed.

Theapproachpresentedhere is designed such that it canbe implemented inawholeaircraftdesignprocess thus improving its integration level. In a future aircraft designprocess,eachdesignsubsystem,suchasthewing,fuselage,landinggear,etc.willneedtobe connected so that the interactionof thevarious systemscanbe accounted for at aconceptual design phase. The constraints, limitations, and interactions betweendifferent subsystems need to be treated fully, automatically and efficiently to obtainmodern environmentally cost‐effective aircraft designs, the approach presented hereprovidesafurtherstepforwardinginachievingthisgoal.

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Summarizingfromtheextensivediscussionofthecontributionsofthisresearchintheabovesections,theycanbeconcludedasfollows. 

1. Thisthesissummarizesanddiscussestheexistingclassicandadvancedlandinggear design approaches. The comparisons of thesemethods are analyzed anddemonstrated.Althoughexistingdesignmethodscanprovidereliabledesignre‐sults,itisstillvaluabletoinvestigatethepossibilityofdevelopinginnovativede‐signmethods.Hencetheaircraftcanbedesignedsaferandgreener.

2. Anapproachtosolvethedifficultyofestimatingcriticallandinggearloadcasesin the landing gear conceptual design stage is proposed. The flight dynamicsmodel is introduced in the critical load cases estimation process for landinggears.Theconventionallandinggearisdemonstratedasthetestcaseofutilizingthistechnologyintheexistinglandinggearconcept.

3. The feasibility and benefit of innovative landing gear concept are investigatedanddiscussed.TheGABRIELconceptisdemonstratedinthisthesis.Itcouldpo‐tentiallyreducetheaircraftweightupto7%byremovingtheconventionalland‐inggearsystemfromtheaircraft.

4. Thisthesisproposesthesolutiontoimprovetheintegrationlevelofthelandinggeardesignapproach.Apromisingplatformwhichcouldintegratemultipledis‐ciplinariestorealizeoptimallandinggeardesignisdiscussedinthisthesis.Notonlytheflightdynamicsbutalsootherfactorswhichcouldaffecttheaircraftde‐signcanbeaccountedtorealizetheoverallaircraftdesignoptimization.

6.2. Recommendationforfutureresearch

Althoughacontributionhasbeenmadetowardsautomatingand includingthe landinggear phase into the aircraft conceptual design phase, there are still many possiblefurtherareasofinterestthatneedfurtherinvestigation.

Duetocomputationlimitationsatthismoment,onlyalimitednumberofFCEEcouldbeinvestigatedfortheresearchreportedinthisthesis.UsingamoreextensivesetofFCEEcombination samples could improve the performance and ability of this approach fordetermining the critical load cases. The more parameters of FCEE introduced in theaircraft conceptual design phase the better and more accurate the results. A parallelcomputing method might be helpful in solving this problem. The approach can besupplemented and improved with a more accurate and efficient multidisciplinaryoptimization approach. And the characteristics of components expressed in the MDSmodel canbe further researchedby implementedhigh fidelity analysis approach, likeFEA.

Besides, further research w.r.t to the GABRIEL concept can be carried out, e.g.experimentalvalidation,newcontrolstrategies.Inthisresearch,thefocusisplacedonlandinggearsystemdesign.However,theapproachcanbeimplementedintheaircraftdesign progress as a sub‐system to improve the integration level of aircraft systemdesign engineering. Hence, MDO studies that quantify the benefits of integrating thedifferentdepartmentscanalsobecarriedoutinthefutureresearch.

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125

AppendixA. Aircraftlandinggearlayouts

The first step in the preliminary landing gear design phase is to determine theappropriatepositions for the landinggears.The information illustrated in this sectioncould be used in the landing gear design approach reported in this thesis as designrequirements and constraints. The positioning constraints for landing gears aredescribedinmanyreferences[11,14,39,142]andairworthinessregulations[34].Themainlandinggearscomparedtothenoselandinggearprovidemostoftheloadbearingcapabilityduringtouchdownandstaticloadingconditions.Inafinaldesignscheme,theload acts on thenose gear shouldbe controlled towithin8% to15%of the aircraft'sgross weight under static state [14]. This is because the center of gravity (CG) of anaircraft is close to the main landing gears in a longitudinal direction otherwise anairframecouldbedamagedbybendingmomentgeneratedfromtheaircraftCG.

Additionally, forsafety reason, theairframeshouldbekeptacertainheightabove theground to avoid a tail strike during takeoff and landing operations. Themain landinggearmust also beplaced a certain distance from the center of gravity as indicated inFigure A‐1 to give stability during ground turnover operations. To avoid instabilityduring ground turnover operations, the sideways turnover angleѰ, defined in FigureA‐2, has to be constrained according to the equationprovided inTableA‐1.ThenoselandinggeardistancetoaircraftCGandmainlandinggearlateralpositionrequirementsfor commercial aircraft can be found in Table A‐1 and Figure A‐3. In high crosswindconditions, anaircraft can rollover toonesidewhichcan lead toawingtipor enginehittingtheground.Designingtopreventthis,thewingandengineclearancesmissionofthelandinggeardesignphasecanbesatisfiedbyguaranteeingthedesigncriteriashowninFigureA‐4.ThecharacteristicsofthelandinggearsystemareprovidedinTableA‐2toTableA‐4.

126

TableA‐1Landinggearlayoutgeometricconstraints[11,14,39,142]

FigureA‐1Landinggearlayoutfortakeoffandlandingstability[11,14,39,142]

Takeoffstability

tan Symbolsare

illustratedinFigureA‐1

Landingstability

tan Symbolsare

illustratedinFigureA‐1

Sidewayturnoverand

groundstability

tansincg

n

h

l

( 63 )

where

tan2( )m n

t

l l

,

andothersymbolscanbefoundinFigureA‐2

lg min

0.54tan arcsin cg

m stability n mn

hy l l

l

SymbolsindicatedinFigureA‐3

min

0.54tan arcsin 2

sincg

n mm

hl t l

l

arctan

2ml

t

,

symbolsindicatedinFigureA‐3

Wingandengineclearance

2tan tan tan tangh

b t

( 5 )

SymbolsprovidedinFigureA‐4

127

FigureA‐2Thesketchofdimensionforturnoverlimitationcalculationusages[11,39]

FigureA‐3Airplane’stopviewforgroundstabilityestimation[11,39]

128

FigureA‐4Clearancecheckforlandinggearlayout[11,39]

TableA‐2Thecharacteristicsofconventionallandinggearsystem[35,148]

TableA‐3Thecharacteristicsoflandinggearsystemforcivilaircraftcatapultconcept[35,113,148]

Parameter ValueNoselandinggearpositionintheX direction 10mMainlandinggearpositionintheXdirection 2.58mMainlandinggearpositionintheYdirection 3.8mShockabsorbertotalstroke(noselandinggear) 0.43mStatictoextendpressureratio(noselandinggear) 1.5Compressedtostaticpressureratio(noselandinggear) 6pistondiameter(noselandinggear) 0.19mOrificeholeradiustopistonradiusratio(noselandinggear) 0.067Shockabsorbertotalstroke(mainlandinggear) 0.42mStatictoextendpressureratio(mainlandinggear) 1.5Compressedtostaticpressureratio(mainlandinggear) 6pistondiameter(mainlandinggear) 0.21mOrificeholeradiustopistonradiusratio(mainlandinggear) 0.067

Parameter ValueNoselandinggearpositionintheXdirection 10mMainlandinggearpositionintheXdirection 2.58mMainlandinggearpositionintheY direction 3.8mShockabsorbertotalstroke(noselandinggear) 0.43mStatictoextendpressureratio(noselandinggear) 1.5Compressedtostaticpressureratio(noselandinggear) 6pistondiameter(noselandinggear) 0.24mOrificeholeradiustopistonradiusratio(noselandinggear) 0.067Shockabsorbertotalstroke(mainlandinggear) 0.42mStatictoextendpressureratio(mainlandinggear) 1.5Compressedtostaticpressureratio(mainlandinggear) 6pistondiameter(mainlandinggear) 0.23mOrificeholeradiustopistonradiusratio(mainlandinggear) 0.067

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TableA‐4ThecharacteristicsoflandinggearsystemfortheGABRIEL[35,117,148]

Parameter ValueNoseconnectionpositionintheXdirection 10mMainconnectionpositionintheXdirection 2.58mMainconnectionpositionintheYdirection 3.8mShockabsorbertotalstroke(noselandinggear) 0.43mStatictoextendpressureratio(noselandinggear) 1.5Compressedtostaticpressureratio(noselandinggear) 6pistondiameter(noselandinggear) 0.29mOrificeholeradiustopistonradiusratio(noselandinggear) 0.067Shockabsorbertotalstroke(mainlandinggear) 0.42mStatictoextendpressureratio(mainlandinggear) 1.5Compressedtostaticpressureratio(mainlandinggear) 6pistondiameter(mainlandinggear) 0.31mOrificeholeradiustopistonradiusratio(mainlandinggear) 0.067

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131

AppendixB. Shockabsorber

One of the key components of the landing gear system is the shock absorber. Theselectionofanappropriatetypeofshockabsorberiscrucialforlandinggeardesign.Sothe selection principle and process for the shock absorber used in the landing geardesign approach developed in this research are illustrated in this section. Some lightaircraft,likeasmallunmannedaviationvehicle(UAV),arenotequippedwithdedicatedshockabsorbers.Commercialaircraft,however,areheavyandthereforeitisessentialtodissipatetheenergyresultingfromthelandingimpact.TherearemanydifferenttypesofshockabsorberandtheirmaincharacteristicsaredescribedinTableB‐1[14,142].

TableB‐1Shockabsorbertypes[14]

Springtype Shockabsorbertype PerformanceSolidspring Steelcoilspringsandringspring Steelcoilspringsandringspring,

areseventimesheavierthanOleo‐Pneumaticsystemwhiletheshockabsorbingefficiencyis60%,seeEquation(B.1)

Steelleafspring Simple,reliable,easymaintenance,mostlyusedinsomelightairplanesandgliders

Rubberspring Alwaysintheformofrubberdiskscanreach60%efficiency,thedesignerusesthistypewiththeideatosavestrategicmaterialsandcost.

Fluidspring Air Heavier,lessefficientandlessreliablecomparedwithoilshockabsorber

Oil 75%efficiencyreliablebasedonrobustdesign,however,thiskindoffluidspringiseasilyaffectedbytemperatureasthevolumeoftheoilchangesatlowtemperature

Oleo‐Pneumatic Upto80%efficientanditisthemostusageofnowday’saircraftdesign

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FigureB‐1(a)shockabsorberefficiency;(b)efficiency/weightofdifferentshockabsorbers[14]

The efficiency of a shock absorber is defined as the ratio between actual dissipateenergyandthetheoreticaldissipatingenergycalculatedbasedonpistonmovement,seeEquation(B.1).AndthedefinitionsoftheparameterscanbefoundinFigureB‐2.

2 22 1

1( )

2

piston

shock absorber

shock absorber

ActualDissipateEnergyEfficiency

TheoryDissipateEnergy

ActualDissipateEnergy m g h v v

TheoryDissipateEnergy F Stroke

EfficientyEfficiency

Weight Weight

(B.1)

Where is the aircraft weight,∆ is the aircraft altitude change, and are theaircraft vertical velocities before and after shock absorber dissipating energy, is theoleo‐pneumaticforce.

FigureB‐2Parametersusedinshockabsorberefficiencycalculations

Duetothesuperiorperformanceoftheoleo‐pneumaticshockabsorbercomparedtotheother solutions, as can be seen in Figure B‐1, this type of shock absorber is used innearlyallcommercialtransportaircraft.Theresearchreportedinthisthesisutilizesthiskindof shock absorber and itsmathematicmodel is establishedbasedon thephysics

133

principle of it. The detailed introduction to this mathematic model is illustrated inChapter4.Thissectionprovidesthegeneralintroductionforthephysicsprincipleofanoleo‐pneumaticshockabsorber.Aschematicrepresentationofanoleo‐pneumaticshockabsorberispresentedinFigureB‐3.Itconsistsofaninnerpistonandanoutercylinderwhich provides one translational degree of freedom. The airframe is supported andconnected to the top of the cylinder. The wheels and tyres are attached to the axlelocatedbelowthepiston.Theinsideofthepistonandcylinderarechambersfilledwithairandoiltogenerateaspringanddampingforce.Whenaforceactsonthepistonandcylindertheywillmoverelativetoeachotherandtheairinthechamberiscompressed.Duringthecompressionphase,oilflowsthroughtheorificeintheupperchamber.Intheextensionphase,theprocessisinverted,indoingso,theimpactenergyistransformedinto heat and kinetic energy in the air and oil. In modern civil aircraft landing gearsystems,ameteringpinisintroducedtoadjusttheareaoforificeopenedtotheoilflow.Thispincanimprovetheshockabsorberperformanceforheavyaircraftby increasingthedamping forcedue to increaseoil flowdrag.Thetypicalspringanddampingforcecharacteristicsofoleo‐pneumaticshockabsorbersareshowninFigureB‐3.

FigureB‐3Oleo‐pneumaticshockabsorber[14]andAtypicalcurvesetforoleospringanddamper[215]

134

135

AppendixC. Retractionmechanism

Theretractionmechanismisusedtoretractandextendthelandinggearduringtakeoffand landing.Aproperselectionof retractionmechanismis important for landinggeardesign. The retraction mechanism determines the way to model the landing gearstructure inthe landinggeardesign.ThemainkinematicsolutionsusedtoretractandextractlandinggearsareshowninFigureC‐1.Type(a)isawidelyusedsolutionduetoits simplicityandsomevariantshaveevolved from this concept. In someaircraft, likethe DHC‐4 Caribou, A‐300B, and DC‐10, there are also bracing struts implementedbetweentheshockabsorberandside/dragstrut,toimprovethestrengthofthelandinggears structure. Concepts (b) and (c) are useful in situationswhich require retractioninto a limited space. Scheme (e) provides the choice to implement the retractionactuators in the bracewhichdiffers from the allocation in type (a). The possibility torotatetheupsideoftheshockabsorbercylinder introducedinconcept(b)isshowninFigure (e). The structure shown in (f) is used for some Navy aircraft in the 1930’sbecauseofitsexcellentperformance,simplicity,andreliability,thislandinggearcanberaisedintothesideofafuselageorintoaflyingboathull[14].

FigureC‐1Exampleoflandinggearkinematicconcepts[14]

136

137

AppendixD. Wheelsandtyres

Thewheelsandtyresarecrucialcomponentsoflandinggearsystem.Asthepurposeofthis section is to provide a general introduction to the landing gear system and itscomponents, so thedetailedmodelingmethodsofwheelsandtyres forsimulationareillustratedinChapter4.Abrakingsystemisemployedinaircraftlandinggearsystemsto assist deceleration during the ground run. The brake system is generallyimplementedasbrakediskscheme,asshowninFigureD‐1,theexcellentperformanceofwhichhasbeenprovenforhighloadcases.Themostpopularmaterialforbrakediskstoday is a carbon/carbon composite material due to its low density, outstandingperformance in resistance to thermal shock and abrasion [216]. Analogous to landvehicles,topreventskiddingphenomenon,anABSisimplementedtoactuatebrakediskpressure.Duringthebrakingphase,iftheslipratioishigherthanthedesiredvalue,theABS can release the loads applied on the brake disks, and the brake pressurewill beincreasedinthecaseofaslipratiolowerthanpreferredlevel.

Thedefinitionoftheslipratiois:

100%Vehicle Wheel

Vehicle

V VS

V

(D.1)

Wherethe istheslipratio, indicatesvehiclespeedwhichisthespeedoftheCGof the vehicle, indicates the wheel speed which is the wheel rotation angularvelocitymultipliedwiththewheelradius

Typically,theforgedaluminumisusedforaircraftwheelschosenforitslightweight,lowcost and low manufacturing costs. Other materials have been proposed for use inlandinggears,likesteelwhichleadstoheavyweightduetoitshighdensity,andtitanium,which is rarely used because the make and manufacture cost for it is extremelyexpensive [39]. These materials are not commonly used for the reasons given andaluminumremainsthechoiceforaircraftlandinggears.

FigureD‐1Wheelincorporatedwithbrakesystem[217]

138

AschematicrepresentationofamodernaircraftlandinggeartyreisgiveninFigureD‐2.Inmostcases,airplanetyresmustbeabletoworkunderhigh‐pressureconditions,atahigh friction level, and under extreme temperatures. Therefore, aircraft tyres aredesigned for this specific purpose with a multilayer structure. The interlayers aredesignedtoimproveitsresistancetothethermalandpressureshockcausedbyspin‐upandahardtouchdown.

FigureD‐2Theschematicofaircrafttyrestructure[218]

Nosewheelshimmyisacommonproblemintheconventionaltricyclelayoutoflandinggeardesign[137].Besidesthenosewheelshimmy,themainlandinggearscanalsohaveshimmyphenomenon.However, the shimmyoccurson themain landing gear ismorerare [36].Besselink [36] extensivelydiscussed the landinggearshimmyphenomenon.Theviolentdynamicinstabilitycouldleadtotheunbalancingforcesonthetrailinglinkinthelandinggears,whichisacommonreasonthatcanleadtothefailureofthelandinggearstructure.Itcanhappeninmanycases,e.g.aircraftmovesovertheunevenrunway,orevenduetoworntiresorlandinggearparts[29,137].Theshimmyvibrationinthelanding gear is a violent oscillation affected bymany factors, e.g. speed, landing gearmass, inertia characteristics. Hence, many solutions are proposed to alleviate theshimmyof landing gears. The shimmy damper is commonly used in the nose landinggear to reduce the shimmy vibration. The shimmy damper is implemented in themovablepartof the landinggear,which isasmallcylinder‐pistonstructure filledwithhydraulic fluid [14, 137]. Besides, the active control system is also studied andimplementedinthelandinggearasasolutiontoalleviatetheshimmy.Theactivecontrolsystem provides torque and force on the landing gear parts to resist the shimmyvibration[138].

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AppendixE. Applicationofphysics‐basedapproachin

landinggeardesign

Thischapterdemonstratesthepossibilityofusingthephysics‐basedmethodtoimprovethelandinggeardesign.Twodemonstrationsareshowninthischapter.Thefirstoneisitsapplicationinestimatingconventionallandinggearloadcasesw.r.tdifferentlandinggear layout. The second one demonstrates its performance in saving aircraft landinggearweightbydesigningtheinnovatelandinggearstructure,i.e.theGABRIEL.

Thevarietyoflandinggearlayoutscanaffectthelandinggearloadcasesandthereforeaffect the final landing gear design.Byusing thephysics‐based approach, this sectionshowstheeffectoflandinggearlayoutontheloadcasesofthemainlandinggearsintheconventional landing phase. The relationship of the main landing gear track and itsverticalloadcaseintheaircraftlandingphaseisdemonstrated.Themainlandinggeartrackisthelateraldistancebetweentheleftandrightmainlandinggears.Intheoverallprocessoflandinggeardesign,therearestillmanyotherrequirementstoconsiderandjustifythepresentvalueofthetrack,e.g.thelayoutrequirement.Theexampleshowninthissectionisademonstrationoftheapproachforthelandinggeardesign.Theoptimaltrack value would decrease the peak loads in themain landing gears. Therefore, themainlandinggearcanbemadewithlessmaterialtosavetheweight.

The A320 is used as the reference aircraft in this demonstration [35]. The detailedlandinggearparameterscanbefoundintheAppendixA.Includingthereferenceaircraft,5 sets of landing gear layout are created by varying the track of the landing gears asfollows:

0.9*TrackofA320 0.95*TrackofA320 TrackofA320 1.05*TrackofA320 1.1*TrackofA320

The larger the wheelbase means the main gear position is put more outward in thelateral direction, vice versa. The aircraft attitudes and environmental conditions areinitializedasshowninTableE‐1.

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TableE‐1Initialconditionofthelandingsimulationforaircraftequippedwithconventionallandinggear[31,32,94]

Approachairspeed(m/s) 70 Ailerondeflection(deg) 0Altitude(m) 0.5 Rudderdeflection(deg) 0Sinkrate(m/s) 0.3 Pitchangle(deg) 8Crosswind(m/s) 0 Pitchrate(deg/s) 0Maximumsingleenginethrust(kN) 118 Rollangle(deg) 0Leadingedgeslat(deg) 27 Rollrate(deg/s) 14Trailingedgeslottedflap(deg) 35 Yawangle(deg) 0Spoilerdeflection(deg) 35 Yawrate(deg/s) 0Elevatordeflection(deg) 0 Ailerondeflection(deg) 0

Inthisexample,thepeakloadsintheverticaldirectionofthelandinggeararechosenasthecriteria.Formoreinformationaboutthecriteria,thereaderisreferredtoChapter3.Inprinciple,thechangeoftrackmayleadtoanothercombinationofparameters(pitch,roll,etc.)becomecritical in theoverall landinggeardesignprocess.Hence, thecriticalload cases should be estimated in accordance to the specific track value by using theMonte Carlo simulation. This section focuses on the demonstration of using theapproachtoestimatethepeakloadsw.r.tthechangeofspecificdesignparameters, i.e.track. Themain landing gear loads are shown inFigureE‐1 andFigureE‐2. Since theinitial roll rateof theaircraft is14deg/s, theaircraft rightmain landinggear touchesdownontherunwayfirst.Theincreasesinthetrackvaluecanaffectthepeakloadsonthe right main landing gear. On the one hand, increasing the track will increase thevelocityoftherightlandinggear.Hence,itwillleadtohigherimpactload.Ontheotherhand,increasingthetrackcausesanincreaseinthearmoftherightmainlandinggearrelated toaircraftCG, thereby reducing the impact load. In thisexample,although thetwo effects have an offsetting effect, the latter still plays a leading role as a whole.Therefore,theimpactloadoftherightlandinggearisreduced.

0 5 10 15

0

100

200

300

400

500

For

ce [

kN]

Time [s]

Right main landing gear load case

RF-10%RF-5%RFRF+5%RF+10%

FigureE‐1The relationshipof rightmain landinggear trackand its vertical load case inaircraftlandingphase

141

0 5 10 15

0

100

200

300

400

500

For

ce [

kN]

Time [s]

Left main landing gear load case

RF-10%RF-5%RFRF+5%RF+10%

FigureE‐2Therelationshipofleftmainlandinggeartrackanditsverticalloadcaseinaircraftlandingphase

Theleftmainlandinggeartouchdownlaterthantherightone.Thepeakloadsintheleftmainlandinggearhaveanon‐linearrelationshipwiththevariationofmainlandinggeartrackvalue.Therearetworeasonsforthis.Ontheonehand,theincreaseoftrackcouldincrease the armof the leftmain landing gear related to aircraft CG. In principle, theimpactloadsintheleftmainlandinggeararesmaller.However,ontheotherhand,theincreaseoftrackvaluewouldalsoincreasethearmoftheaircraftCGrelatedtotherightmainlandinggear. Hence,thisistheaspectofafactorthatwouldincreasetheimpactloadsintheleftmainlandinggear.

It should be noted, however, that this is a preliminary estimated value based on thesimulationmodel’sfidelityandtheassumptionsmadeinthisresearch.Someofthemarelistedasfollows:

The flexibility of the aircraft and landing gear structures are assumed to beneglected.

Thelandinggearsystemisassumedtoconsistof I beamandtubestructures. Theaerodynamiccoefficientsobtainedfromtheempiricalmethodareassumed

tobereliable.

ThisresearchchoosesarigidMDSinsteadofa flexibledynamicssimulationmodel.Asthis landing geardesign approach is developed for landinggear conceptual design, sothe relativelydetailed characteristic of landing gear systemmightbeunavailable.Thedynamics of the airframe should also be taken into account in future research toimprovetheaccuracyofcriticalloadcasessimulation.

Besides, this research simplifies the landing gear components, for example, the shock

absorberstrut issimplifiedas tubestrut, theside,anddragbracesaresimplifiedas Ibeam struts, and the presence of a bolt is ignored. In this research, the aerodynamiccoefficientsareobtainedfromDATCOMandTornadowhicharebasedonempiricaldata

142

and vortex lattice method, a more accurate aerodynamics coefficient could beimplementedinfutureresearch.

TheGABRIELconceptisapromisingtechnologytosignificantlysavetheaircraftweight.ApreliminarysetofdesignandlayoutfortheGABRIELconceptcanbefoundinChapter4andAppendixA.Afterbeingvalidatedwiththelayoutlimitationsinreference[14]andthe critical load cases assessed by the physics‐based approach, the comparison oflandinggearweightbetweenGABRIELtechnologyandconventionallandinggearsystemare presented in Table E‐2. If an aircraft design is implemented with a conventionallandinggearssystem,thenthispartoftheweightcouldbeasheavyas2750kg.However,when GABRIEL technology is implemented instead of a conventional landing gearconcept, theaircraftonboardlandinggearsystemweightcanbedecreased from2750kgto1256kg.Thiscangiveanestimatedfuelconsumptionsavingupto79tonsperyearperaircraftusingGABRIEL.Reference[22]illustratesaninvestigationintofuelsavingsforanA320“like”aircraftusingGABRIELtechnology.Afterincludingthesnowballeffect,thetakeoffweightreductioncanreachupto9.3%afteroptimizationofanairframeforGABRIEL technology. After taking the total fuel weight saving into consideration, thereductionoftakeoffweightmaybeasmuchas18.1%.

TableE‐2Thecomparisonoftheenvironmentalperformanceofconventional landinggearsystemandGABRIEL[99]

Landinggearconcept

Onboardsystemweight

Ground‐basedsystemweight

(connectionparts)

FuelconsumptionsavingperyearforA320(2700hoursflighttimeperyear)

Conventionallandinggears

2750kg 0 0

GABRIEL 1256kg 6550kg 79tons

Theapplicationofthephysics‐basedapproachinlandinggeardesignisdemonstratedinthischapter.Byusingthephysics‐basedapproach,theeffectoflandinggearlayoutonitsload cases in the landing phase is demonstrated. Besides, themain advantages of theGABRIEL technology concept are demonstrated and it is shown that a conventionallandinggearcanberemovedfromanairframe.Asreportedinthisthesis,aconventionallandinggearsystemweighs2750kgwhiletheonboardsystemforGABRIELweighsonly1256kg,sofittinganaircraftwithaGABRIELconceptsystemcansavearound1500kgof aircraft empty weight. This is the preliminary estimation without considering thesnowballeffect.Ifthesnowballeffectistakenintoconsideration,thetakeoffweightcanbe reduced by18.1%.Hence, thephysics‐based approach is valuable for landing geardesign.

143

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Acknowledgments

GettingaPhDdegree isa journeyofdiscovery.Firstof all, Iwould like toexpressmyappreciation to Prof. Leo Veldhuis my exploration leader for this PhD journey whosupervised the research presented in this PhDdissertation and ismypromotor. Prof.Veldhuis,thankyouforthetrustandfreedomyougavemetofollowmypath.AsafullprofessorintheDelftUniversityofTechnology,youarealwaysbusy,butyouarewillingto spend a lot of time discussing research direction and progress with me. I cannotimagineIwouldhaveaccomplishedthisPhDjourneywithoutyourpatienceandcarefulsupervision.Youinspiredmetopushmyboundariesandseektodomybestandguidedmyresearchprogresshelpingmetoconsolidateeachmilestone.

AnotherpersonwhocontributedalottomyPhDresearchandhelpedmefindmydailypathisProf.MarkVoskuijl.Iamverygratefulforhiscarefulsupervision.Youansweredlotsofquestionsandguidedmeonmywaywithvaluablefeedbackduringourregularmeetings.IreallyappreciatetheeffortandtimeyouspentmakingsureIdidnotlosemywayorbecomediscouragedinPhDcountry.IwouldliketoexpressmyappreciationtoProf.MichelvanTooren,whoismysupervisorforthefirsttwoyearsatTUDelft.Thankyou for your supervision during this period which helps me improve my skills andabilitiesinperformingscientificresearch.

Iwould liketothankProf.GeorgEitelbergwhostimulatedmetopresentmyresearchwork at the AIAA conference held in Zwolle. Your interest in my research is a realmotivation tome and it confirms tome thatmy research is useful for future aviationindustrydevelopment.Thetripyou ledtovisit theDutch‐GermanyWindTunnel leftagreatimpressiononme.

Prof.EgbertTorenbeekprovidedvaluable feedbackandsupportwhenIhadquestionswhilereadinghisbookonaircraftdesign.Thevividandclearexplanationsprovidedbyyouduringourdiscussiongavemeremarkablehelpinsolvingmypathfindingproblemsandresearchdifficulties.

I would thank Miranda Aldham‐Breary MSc. P.G.C.E. who helped me to improve myEnglish.BeingabletocommunicatewiththenativesinthelandofPhDresearchisvital.

AsamemberoftheFlightPerformanceandPropulsionresearchgroup,Iwanttothankforthesupportandhelpontheway fromRoelof,Arvind,Gianfranco, JorisandDurk. Istill remember the first day I arrived in the faculty, Roelof showed me around andintroduced me to my fellow members, the building and how the faculty functioned.Thank you for warm welcome which made my task of finding my way as a PhDresearchersomucheasier.Youallhelpedmeandimmersedmeinthepoolsofdifferentcultures and traditions, such as Indian, Italian and Dutch. This broadened myperspectiveontheworldoutsidePhDresearchandhasgivenmevaluabletoolstomaptherestofmylifeinthismulticulturalworld.

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Thesecretariesinourgroup:Lin,Bettie,NanaalsogavemequitealotofhelpduringmyresearchandlifeatTUDelft.Thankyouverymuchforyourcontributionandkindhelp.ManyissuesaresolvedbyyouandIwillneverforgetyourexcellentsupport.

I would like to thankmy officemates and friends Dipanjay, Jan,Maurice, Ali, Tomas,Yannian,Reinier,Xiaojia,Zaoxu,Fengnian,Li,Feijia,Peijian,Jia,Haiqiang,Qingxi,Tiemo,Irene, Emiliano, Zhang, Changlin, Zhiwei, Yang. Thank you all formakingmy life hereveryinterestingandIreallyenjoyedthetimetogetherwithyou.

Thisjourneyhascometoanend,Iwishallwhohelpedmeonthisexpeditiontheverybestontheirlifejourneys.WepartwaysnowbutIhopewewillmeetagain.

Lastbutnot least, Iwouldtothankstomyparents.YoureallysupportedmeandgavemecourageonthewaytopursuemyPhDdegree.Yourselflessloveandconsiderationencouragedme to believe and insist on thedecision to continuePhD research inTheNetherlands.

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PublicationsandConferenceContributions

Wu,P.,“Take‐offandlandingusinggroundbasedpower(MAGLEV)‐Preliminaryconceptinvestigation”,in:SymposiumonExperimentsandSimulationofAircraftinGroundProximity(AIAA&DNW),AmericanInstituteofAeronauticsandAs‐tronautics&German‐DutchWindTunnels,Zwolle,TheNetherlands,2013

Wu,P.,Voskuijl,M.,andJ.L.V.T.Michael,“Take‐offandlandingusinggroundbasedpower‐landingsimulationsusingmultibodydynamics”,in:52ndAero‐spaceSciencesMeeting(AIAA),AmericanInstituteofAeronauticsandAstro‐nautics.,TheNationalHarbor,USA,2014

Wu,P.,Voskuijl,M.,vanTooren,M.,andVeldhuis,L.,"Take‐OffandLandingUs‐ingGround‐BasedPower‐SimulationofCriticalLandingLoadCasesUsingMulti‐bodyDynamics."J.Aerosp.Eng.,2015

Wu, P., Voskuijl, M., and Veldhuis, L., “An approach to estimate aircrafttouchdownattitudesandcontrolinputs”Aerosp.Sci.andTech.,2017