DLR(GermanAerospaceCenter),37073Göttingen,Germany
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Articlehistory:
Received25January2019
Receivedinrevisedform7March2019 Accepted7March2019
Availableonline1April2019
Keywords:
Flyingwing Gustloads Closedloop
Structuraloptimization
This work presents results of dynamic “one-minus-cosine” gust load simulations for a flying wing configuration.Thein-housetoolboxLoadsKernelisusedfortheloadsanalysisofthefreeflyingaircraft. Flight mechanical characteristics are captured by application of a non-linear equation of motion in thetimedomain. Theunderlyingaerodynamic methodsare theVortexLatticeandtheDoublet Lattice Method with a rational functionapproximation (RFA)for unsteady simulations in the time domain. ThestructuralmodelwascreatedusingDLR’sparametricModGen/Nastrandesignprocess.Thestructure is optimized for minimum structuralweight with typicaldesign load cases includingmaneuver, gust and landing loads.Inthisarticle,the focuslies ongustencounters andthe flight characteristicsofa flying wingconfiguration. It differs fromclassical configurations (wing-fuselage-empennage)due toa pronounced nose-uppitchingmotionwhenthe aircraftentersthegustfield.Finally,aflightcontroller is designedto increase the pitching stability. This is essential for the flight of a naturallyunstable configuration. It isshownthat the loadsduringagust encounter increasesignificantly.The influence onthe structural weight is smallas the layoutis veryrobust and the requiredmaterialthickness is belowtheminimumthicknessinmostareas.
©2019TheAuthor.PublishedbyElsevierMassonSAS.ThisisanopenaccessarticleundertheCCBY license(http://creativecommons.org/licenses/by/4.0/).
1. Introduction
ThemultidisciplinaryconfigurationMULDICONisaflyingwing configuration with wings of low aspect ratio. The geometry is usedfora widerangeofactivitiessuch asnumerical aerodynam-icsor wind tunnel investigations. Real-sizeddesign concepts are developed by Liersch et al. [1,2] and Krüger et al. [3] Aeroelas-ticmodelsaredevelopedbyVoßandKlimmek[4] andBramsiepe etal.[5]. Thesemodels have been used by Schäfer et al.[6] for body freedom flutter analyses and by Voß and Klimmek [7] for maneuverloadsanalysisusingcomputationalfluiddynamics(CFD) correctedpotentialmethods.Inaddition,theMULDICONis investi-gatedinternationallywithintheNATOSTOAVT-251workinggroup aspresentedby Cummingsetal.[8] and Schweigeratal.[9]. An overviewon further,geometrically similarconfigurations isfound inpreviouswork[7,4,5].
The pitching stability of an aircraft is determined by the lo-cation in longitudinal direction of the center of gravity (C G) in combinationwith the center of pressure (C P). A C G in front of C P results in a stableaircraft. This is the case for mostaircraft andmandatoryforallcivilaircraft.Typically,thereisamovement
E-mailaddress:[email protected].
ofC G duetopassengers,payloadorfueltanklevelswhiletheshift ofC P issmall.Tomaintainacertainlongitudinalstability,the hor-izontal tailis used.The same holds forflying wings, exceptthat they are very sensitive to any movement of C P and C G. There isnostabilizingtailandthecontrol surfacesaretypicallylocated alongthetrailingedgeandhaveshortleverarms.Therefore,flying wingsareexpectedtobeverysensitivetoanexternaldisturbance, such asgust encounter.This leads tothe followingobjectives for thiswork:
•
Extendthesimulationcapabilitiesofgustencountertoinclude rigidbodymotionandpenetrationeffectsalreadyinthe pre-liminarydesign.•
Assess theimpactofagustencounterontheMULDICONwith respecttoflightmechanicsandloads.•
Re-evaluateandquantify theresulting loadsinterms of sec-tionloadsandstructuralweightforagust encounterwithan activeflightcontrollertoincreasepitchingstability.Theworkisan extensionof[10] andisstructuredasfollows:The set-upofthestiffnessandmassmodelsispresentedinsection 2. Insection 3,thetheoretical backgroundofthetimesimulation is describedshortly.Insection4,theMULDICONisexposedtoa se-riesofgustencountersandthecorrespondingloadsareevaluated. https://doi.org/10.1016/j.ast.2019.03.049
Fig. 1.From 2-Dimensional model information to FE model. The layout andset-up ofa simple flight controllerfor the
pitch-ingmotionis presentedinsection 5.1.Sections5.2and5.3show theinfluenceofthecontrollerintermsofsectionloads,firstofthe naturalstable,thanoftheunstableconfiguration.Astructural op-timizationfollows in5.4.Finally,a conclusionandan outlook on futureworkisgiveninsection6.
2. Weight optimized structural and mass models
Theaeroelastic modelsoftheMULDICON were builtand opti-mizedforstructuralweightinapreviousworkbyBramsiepe,Voß andKlimmek[4,5,11]. Thestructuralandmassmodels areset-up usingaparametric designprocess. Startingwithgeneral informa-tionoftheaircraftlayout,aparametric geometrymodelis gener-atedusingthein-housesoftwareModGen[12].FortheMULDICON, the profiles and the planform is already given. From that infor-mation,threedimensionalsegmentsareconstructed,onebetween eachoftheprofiles,asshowninFig.1aandFig.1b.Thepositions ofsparsandribsaredefined,resultinginFig.1c.Thatgeometrical layoutismeshedusingfiniteelements, resultinginFig.1d.Inthe caseoftheMULDICON,mainlyshellelementsareused.Beam ele-mentsareaddedasstiffeningelementsforthesparsandribs.For theupperandlower skin,stringers withhatprofiles support the shellelements.Fig.2showstheinnerlayoutwithsufficientspace fortheengine (red),thepayload bay(yellow)aswellasthenose andmainlandinggearbays(green).
The material of the shell elements is carbon fiber reinforced plastic(CFRP).Severallayersofunidirectional(UD)fibersare com-binedto alaminate. Thebehaviorofthe laminatecan betracked backtothepropertiesoftheindividuallayers.Thecalculation prin-ciples are based on the classical laminate theory (CLT). A very usefulsummaryofthestateoftheartandpracticaladviceonthe developmentandanalysisofCFRPcomponentsispublishedbythe Verein Deutscher Ingenieure in guideline VDI 2014, Part 3 [13], availableinGermanandEnglish.
TheenginemassisderivedfromarelateddesigntaskbyBecker etal.[14] andNauroz[15] withintheMephistoproject.Massesfor the landing gears are estimated using an in-housesoftware. The fueltanks aremodeled geometricallyusingModGen andfilledto arequiredlevel.Withthisprocedure,themass,inertiaandcenter ofgravityforeachsectionbetweentworibsandsparsisanalyzed
Fig. 2.Inner,structurallayoutandFEmodelingwithspacesforengine(red),payload (yellow)andlandinggears(green).(Forinterpretationofthecolorsinthefigure(s), thereaderisreferredtothewebversionofthisarticle.)
numerically.Foradditionalsystems,massesareestimated.The cor-responding mass discretization is shownin Fig. 3.Nine different mass configurations ranging from 5.9t (no fuel, no payload) to 13.1t(fullfuel,fullpayload)areusedtoreflectdifferentphasesof flightduringthemission.Thedynamicanalysisofthestiffnessand massmodelshouldresultinalmostonlyglobalmodesfora spec-ifiedfrequencyrange.Localmodesaretobeavoided.Becausethe configurationisratherstiff,onlythefirst10-19modeswillbe con-sideredinthisstudy.Theselectednumberofmodesisdetermined foreverymassconfigurationsindividually,astheeigenfrequencies changesignificantlywiththemassconfiguration.
In anext step,thestructuralmodelissubjectto an optimiza-tionusingMSC.NastranSOL200. Thedesignobjectiveisminimum structuralweight.Thedesignvariableistheskinthicknessofevery designfield,withonedesignfieldbeingtheareabetweentworibs and spars,while the topology ofthe structural layout, seeFig. 1 and2,remainsunchanged.Duringtheoptimizationprocessofthe structural model, a total of 306 maneuver load cases aswell as 336 gust load cases are taken into account. In addition, a new, simplifiedlanding impactsimulation[5] is introducedtoconsider 12 landingloadcases.Such a fairlyhighnumberofloadcases is necessarytocoverasufficientnumberofflightconditionsaswell astotakeintoaccountthatdifferentpartsoftheaircraftaresized bydifferentdesignloadcases.
Fig. 3.Two exemplary mass configurations of the MULDICON.
Fig. 4.Resulting material thickness distribution after optimization in [mm].
The optimization is an iterative procedure. After three outer loops of loads calculation followed by an optimization, conver-genceisachieved.Theresultingmodelhasastructuralnetweight of1511kgandamaterialthicknessdistributionasshowninFig.4. Althoughthedimensioningcriterionisselectedconservatively,the materialthicknessisinmostareastheminimumthicknessof2.5 mmandonlysomeregionsalongtheleadingedgeandatthewing tiparereinforced.Thiscanbeexplainedbythegeometricalshape, whichisratherthickinthecenterregiontoaccommodatethe en-gineandtoprovidespaceforpayload,fuelandotheraircraft sys-tems.Atthesametime,thewingisveryshortandthusproduces comparatively low bending moments. Removing some structural members could result in an even lighter design. However, most sparsandribsarerequiredfortheattachmentofaircraftsystems orserveasfuelbays.Ribsarealsorequiredtomaintaintheshape oftheairfoil.Althoughpayloadandlandinggearbaysareplanned, theouterskinisclosedinthestructuralmodel.Additionalcutouts forpayload andlanding geardoors might weaken the structure, leadingtoadifferentresult.Investigationsonthistopicare ongo-ingandnotsubjectofthisarticle.
Fig. 5.Aerodynamic panel mesh of the MULDICON.
3. Theoretical methods
The classical aerodynamic approach with the steady Vortex Lattice Method (VLM) and the unsteady Doublet Lattice Method (DLM)is chosen. The formulationofthe VLM followsclosely the derivationgivenbyKatzandPlotkin[16] usinghorseshoevortices. The DLMisformulated asgivenby AlbanoandRodden[17].The VLMandtheDLMarebasedonamatrixofaerodynamicinfluence coefficients(AIC),whichdependsontheMachnumberMa,the re-ducedfrequency k
=
π·UF·cre f∞ andthe geometryof theaircraft. In general, thediscretizationofsuch ahighlysweptgeometryneeds to be a compromise between the long wing root and the short wingtip.Jumpsinthediscretizationaretobeavoided.The result-ingmeshisshowninFig.5andhas1248panels.Itincludesfour control surfacesalong the trailingedge, whichare highlighted in thetop viewinFig.5.Ingeneral, bothVLMandDLMarelimited tothesubsonicregime,butmaybecorrectedtoincludetransonic effectssuchascompressionshocks.Forsimplicity,inthiswork,the AICmatricesarenotcorrected,assuchacorrectionwouldmainly effectthe initialhorizontalflightcondition.Theassumptionisthat a gust encounter is dominated by unsteady aerodynamics, struc-turaldynamics,rigidbodymotionandtheinteractionwithaflight controller.
Inthiswork,unsteadyaerodynamicforcesinthetime domain are obtainedby a rational function approximation (RFA) as sug-gestedby Roger [18]. The time domainispreferred overthe fre-quencydomainasitallowsnon-linearitiesforexampleintherigid bodymotionandintheclosed-loopsystem.
Other authors, for example Karpel et al. [19] and Teufel and Kruse [20], perform a coupling of linear calculations in the fre-quencydomainwithselectednon-linearpartsinthetimedomain, aimingfora higherefficiencyintermsofcalculation time.In ad-dition, the approximation of the unsteady aerodynamic forces is avoidedbutamorecomplexmathematicalprocedureisintroduced includingseveraltransformationsfromfrequencyintotimedomain andviceversa. Theequation ofmotionislinearin thefrequency domain andproblemsmight arise fornaturally unstable configu-rations.Therefore,thetimedomainapproachismoregeneraland thepreferredsolutioninthiswork.
ThegustvelocityU isdefinedbythecertificationspecifications CS25.341[21] independenceofthedistancespenetratedintothe gustandthedesigngustvelocity Uds.The so-calledgustgradient H determines thelength (paralleltotheaircraft’s flightpath) for thegusttoreachitspeakvelocity.
U
=
Uds 2 1−
cosπ
s H f or 0≤
s≤
2H (1)Fig. 6.Temporal evolution of aerodynamic gust forces (red) and unsteady forces (cyan). Thegustencounterisalwaysconsideredontopofthe
horizon-tal level flight. Therefore, the quasi-steadytrimmed state of the horizontallevelflightiscalculatedfirstandtakenasinitial condi-tionforthetimedomainsimulationofthegustencounter.
Theequationofmotionissplitintwoparts.Anon-linearpart for the rigid body motion is derived from Waszak, Schmidt and Buttrill [22–24]. Structural flexibility is incorporatedusing a sec-ond,linearelasticequationonmotiononamodalbasis.
Formoredetails onthetheoretical backgroundandthe corre-spondingequations,pleaseconsultsections3,4and5in[10]. 4. Physical effects during a gust encounter, open loop
Ingeneral, theMULDICON hasavery distinct,physical behav-ior during an gust encounter, deviating from classical configura-tions.Oneeffectisthepenetrationintothegustfield,visualizedin Fig.6.Theaerodynamicforcevectorsduetothegustareshownin redcolorandthe unsteadyaerodynamic contributionsare shown in cyan color. Note that the magnitude of the vectors is scaled non-linearlyto highlight small forces.The qualitative meaning is enhancedwhilethequantitativemeaningislost.Theselectedgust isthe shortestaccordingtocertification specifications,hasa gra-dient (total length = 18 m) and has a positive orientation (gust frombelow/upgust).In Fig.6a,the gust hasjustreachedthe air-craftnose,resultinginthegustforces(red)topointupwards.The additional liftat the nose immediately induces velocities on the other areas ofthe aircraft, forexample on the rear fuselage and thewingtips.Thedelayintimeisnotcaptured.Duetothesudden change in downwash, unsteady aerodynamic forces (cyan) occur, counteractingtheimpactofthegustandthusintroducingthe lag-gingbehavior.InFig.6b,theaircraftisapproximatelyinthecenter ofthegustfield.Thegustshapeisclearlyvisiblewhenlookingat thegustforcevectors(red).InFig.6c,theaircrafthasjustleftthe gust field and there are no more aerodynamic gust forces (red). However,thegusthasstillanindirectaerodynamicimpactonthe aircraft as the unsteady aerodynamic forces (cyan) still exist. In contrastto themiddle picture,they point upwards. Their magni-tudewilldecreasequicklywithinthenexttimesteps.Notethatin thisimplementation,unsteadyeffectsarealsocalculatedfor flexi-bleandrigidbodymotion.Astheaircraftisstillinmotion,some unsteadyforceswillremain.
This physical behavior is also reflected in the section loads. Here,a quantitativeassessmentispossible.Fig. 7showsthe con-tributionsofdifferentforcestotheshearforce Fz atthewingroot.
Withthegreendashedlinethequasi-steadyandwithredtriangles the unsteady aerodynamics are plotted. As expected from Fig. 6, the unsteady aerodynamic forces first act in the same direction
Fig. 7.Composition of the right wing root shear forceFzin detail.
asthequasi-steadyaerodynamics(positivesign)andthenstart to counteract(negativesign)andhavea peakat0.7 swhenthe air-craftiscompletelyimmersedinthegustfield,comparewithFig.6. Therefore,theynotonlyreducethepeakofthequasi-steady aero-dynamicsbutalsocausethepeaktooccurmoreearlyintime.The sum of both lead to the aerodynamic forces plotted with green squares. The inertia force is plotted with cyan crosses. The sum of both leads to the total force, plotted with blue dots. Finally, theaerodynamicforceduetostructuralflexibilityareplottedwith blackstars.Onecanseethattheyonlyhaveaminorcontribution.
Another physically interesting effect is the rigid body motion of theaircraft inthe gust field. TheMULDICON is designedwith onlyasmallstabilitymarginof3
.
0%M AC.Therefore,thecenterof pressureisclosetothecenterofgravity.Inagustencounter,this normallyresultsinacomparativelylargeheavemotionandonlya small pitchingmotion becausethepitching moment aboutC G is small.However,duetothelackofan empennage,theMULDICON isverysensitive tothepitchingmotion.Inaddition,alargeshare oftheaerodynamicsurface isinfrontofC G.Theflight character-isticsarestudiedmorecloselybyexaminingthepitchangleand thepitchrateq.Fig.8showstheresultsforaselectednumberof positive gust encounters (gust from below/upgust) of one exem-plary massconfigurationandgust gradientsrangingfrom H
=
9m to 107m.In all cases,theaircraftexperiencesa positive,nose up pitching motion. This is contrary to the behavior observed with classical configurations which typically dive into the gust (nose down)andpresumablyincreasestheaircraftloads.A quantification of the loads due to the pitching motion is achievedbycomparingafree-freegust encounterwithagust en-counterwithsuppressedpitchingmotion.Theresultsfortheshear
5. Physical effects during a gust encounter, closed loop 5.1.Activepitchcontrol
TheflightcontrollerfortheMULDICONconsideredinthiswork isrestricted to the control of the pitching motion only. The aim isto maintain a commanded pitchrate qcom even when the air-craft is subject to external disturbances such a gust encounter. Theproposed flightcontrolleris showninFig. 10andconsistsof twocascadedfeedbackloops.Thecommandedpitchrateqcom may stemfromthepilot’sstick command ora flightpath control sys-temshowningraycolor.Forsimplicity,thecommandedpitchrate qcomisassumedtobegiven.Thepitchcontrollerconsistsofa pro-portionalandanintegralcontrolelementwithcoefficientsKp and
Ki.Ifa moreaggressivebehavior isdesired, adifferentiating
ele-mentwithcoefficient Kd maybe added.The output ofthe pitch
controlleristhe commandedcontrol surface deflection
η
com.TheFig. 8.Pitch angleand pitch ratepfor selected gust encounters.
actuatormodelinthesimulation.Theactuatorhasaproportional coefficient Kpandbecomesnon-linearbyenforcingamaximal
ac-tuatorrate
η
˙
= ±
40◦/
storeflecttheabilitiesofatypicalhydraulic actuationsystem.Thetwocontrolloopsofthepitchcontrollerand the actuator are closed by the feedback of the actual pitch rate qcurrentandtheactualcontrolsurfacedeflectionη
current ofthe air-craft. Notethat a loadreduction is notthe driving factorforthe selection ofthecontrol coefficients.The valuesofthecoefficients KpandKiaredeterminedinasimple,iterativeproceduretomini-mizetheIntegralofAbsoluteErrorCriterion AIAE,whichdescribes thedifference betweencommandedsignalqcom andsystem reac-tionq.
5.2. Naturallystableconfigurations
TheMULDICONisexposedtoaseriesofgustencountersagain, this time with the flight control system switched on. The flight control system presented in the previous section has been im-plemented in the flight loads environment. The dashed lines in Fig. 11 show the pitch angle
and the pitch rate q of the un-controlledaircraft.Again,encountersofapositivegust(gustfrom below/upgust)ofoneexemplarymassconfigurationsandgust gra-dients ranging from H
=
9m to 107m are shown. The blue lines show the resultsof theclosed loop system. Comparingthe open andclosed loop system, themaximumpitch angleis reducedby approximately 60% and the minimum pitch angle is reduced by approximately30% with respectto theinitialvalue. Fortheopen loop system, the minimum andmaximumvalues are reachedby the longer gusts while in the closed loop system, the minimum andmaximum values are causedby the short gusts. In addition, theshortgustsshowamorepronouncedovershoot,whichisalso reflectedinthepitchrateq.Summingup,itisobservedthe con-troller ofthe closed loopsystem performs excellently withsome troubles withtheshorter gusts.This behavioris asexpectedandFig. 11.Pitch angleand pitch rateqfor the closed loop system.
Fig. 12.Commanded control surface deflectionηand control surface rateη˙.
Fig. 13.Load factorNzfor the closed loop system.
causedby physicallimitationssuch asthe controlsurface rate
η
˙
. Fig. 12 shows the control surface deflectionη
and the control surface rateη
˙
. Although only small deflections are required,the controlsurfaceismovedathighrates,hittingthelimitof±
40◦s−1 inseveralcases.Theperformance forshortgustscanonlybe im-proved withhigherrates,asdiscussed before,orby addingprior knowledgeofthegust.Forclassicalwing-fuselage-empennage con-figurations,suchinformationcouldbeobtainedbyasensoratthe aircraft nose. For flying wings such as the MULDICON, a future alternative could be LIDAR techniques, measuring the flow field several meters in front of the aircraft, see for example Wang et al.[25].Toobtaina first glanceon theeffecton loads,theload factor Nz showninFig. 13canbe consulted. Becausethepositive, nose
fromthe timesimulation,andout of336gust simulations,every gustsimulationproducesseveraldots.Forreference,thegustloads oftheopenloopsimulationareshownaswell.Itcanbeseenthat while the controller reduced the loadfactor Nz, thisis not
gen-erallythecaseforthesectionloads.Theenvelopesofshearforce Fz andbendingmoment Mx haveasimilarshapewiththeclosed
loopsystemleadingtoaslightlylowershearforcesFz andslightly
higher bendingmoments Mx.The envelopes ofbending moment
Mx and torsion moment My of the closed loop system appear
larger. In Fig. 15 the control surface attachment loads in terms of shearforce Fz andtorsion moment My areshown forthe
in-nerandoutercontrolsurface.Obviously,theactuatoroftheclosed loopsystemcausesmuchhigherloadscomparedtotheopenloop system,whichisasexpected.
5.3. Naturallyunstableconfigurations
TheMULDICON hasbeendesignedwithapositivelongitudinal stability anda desired center of gravity approximatelyat C Gx
≈
−
3.
0[
%M AC]
withtheexactvaluedepending onthemass config-uration.Inthissection,thatdesignrestrictionwillbeliftedanda rearwardshiftofC Gx willbeallowed,resultinginanaturallyun-stableconfiguration.Theinfluenceongustloadsisexpectedtobe high asthe demand on the flight controller is even higher than intheprevioussection:nodisturbancesandgustsarepossiblefor naturallyunstableconfigurationswithoutcontrol.
A naturally unstable configuration might occur dueto several reasons. The fuel tanks could be drained unbalanced, either on purposeorduetoasystemfailure, resultinginashiftofC G.The payloadof2
×
1000 kg isassumedtobeinthecenterofthe pay-load bays. This is probably true fora payload of uniform shape and density. To create an unstable configuration, the payload is shifted fromits designpositionat x=
5.
9m slightlyrearwardsto x=
7.
0masindicatedinFig.16.Thepayloadisstilllocatedwithin theboundsofthepayloadbayandthelocationofC G ischanged from−
2.
9 to+
2.
4[
%M AC]
, where a positive value indicates an unstable configuration,because the C G ifaftof theaerodynamic center.In a first step, the rigid body motion is re-evaluated for the naturally unstableclosed loopconfigurationandcomparedto the naturally stable closed loop configuration. Note that the closure ofthenaturallyunstablesystemactuallyleadstoa stablesystem. Fig. 17showsthe pitchangle
andpitchrateq. Itcan be seen that the controller performs reasonably well for short gusts but worse for longer gusts. The maximum pitch angle
is approx-imately
+
1.
1◦ and comparable to the results for the open loop system, see thedashed line inFig. 11.The dynamic overshoot is muchlarger,leadingtoaminimumpitchangleofabout
−
0.
05◦. The long gustsare moredifficult tocontrol than theshortgusts. Thisis alsoreflectedinthe pitchratesq.Still,theproposed con-trolleroftheclosedloopsystemmanagestomaintainstabilityand leadstheaircraftsafelybackintoahorizontalflightcondition.Note thatthereisasmalloffsetbetweenthenaturallystableand unsta-bleconfigurationalreadyatt=
0.
0s.ThiscanbeexplainedbytheFig. 15.Envelope of control surface attachment loads.
Fig. 16.A rearward shift of payload creates a unstable configuration. Left: stable, Right: unstable. initialtrimcondition.Duetothemodifiedmassconfiguration,the
controlsurfacesareemployedtobalancetheaircraft,leading toa newpitchangle
.
FromFig.18itcanbeseenthatfortheshortgusts,the allow-ablecontrolsurface rate
η
˙
isagainthelimitingfactor.Thelonger gustsrequirelargercontrolsurface deflectionsη
comparedtothe naturallystableconfigurationbutarateη
˙
≤ ±
40◦ issufficient.The maximum load factors Nz are approximately
+
6.
6 and−
3.
6. With thehorizontal flight condition Nz=
1.
0 as reference,thisisan increase by 22% and58% respectively compared tothe naturallystableclosedloopconfiguration (seeFig.19).
InFig.20,theloadsenvelopes ofshearforce Fz,bending
mo-ment Mx andtorsionmoment My are shownforthe right wing
root.Theenvelopeofshearforce FzandthebendingmomentMx
issignificantly larger compared tothe naturally stable configura-tion but the increase is not as large as for the load factor Nz.
Surprisingly, the torsional moments My has the same minimum
andmaximumamplitude comparedtothe naturallystableclosed loopconfiguration.Duetothecombinationwiththebending mo-ment Mx,theenvelopeis stilllarger. Inthe previous section,the
increaseoftorsionalmomentMycouldbetracedbacktothe
con-trolsurface attachmentloads,addinghigher forcesandmoments
alongthe trailingedge comparedtotheopen loopsystem. Inthe case of the naturally unstable system, it can be concluded that thecontrolsurfaceattachmentloadshaveapproximatelythesame amplitudes as for the naturally stable system, leading to a sim-ilar torsionalmoments My along the wing. As discussed before,
the flight controller is limitedby the maximal allowable control surfacerate
η
˙
andthatlimitistouchedfortheshortergustswith H=
9mand15mforboththenaturallystableandunstable config-uration.Therefore,the controlsurfacesmove inasimilar manner andexperienceasimilarloading.5.4. Influenceintermsofstructuralweightandloading
Fromtheseobservations,thenextstepisareassessmentofthe structural optimizationfor minimumstructural weight, including gust loads of theclosed loop systems. The convergencebehavior isgood asshowninFig.21.Three outer loopsleadto converged results in all cases. The use of three loops also has a physical meaningwhichcan beinterpretedasfollows.Thefirstloop gives afirstestimate.Ifnecessary,thesecondloopadjuststheestimate slightlyandthethirdloopconfirmstheresults.FortheMULDICON, thefirstestimateisconfirmedtwice.Theconvergencecanbe con-sideredasverytrustableifnogeneraltrendisvisible.
Fig. 17.Pitch angleand pitch rateqfor the naturally unstable system.
Fig. 18.Commanded control surface deflectionηand control surface rateη˙.
Fig. 19.Load factorNzfor the naturally unstable system.
During later phases of the aircraft design, for example dur-ing thedetail design, the globalstructural stiffness might be re-duced byholes and cut-outsin theouter skin. Thesemight lead todifferentresults.Also,amoredetailedattachmentoflarge non-structuralsystemmasses,suchastheengine,mightinfluencethe structuralcharacteristics,modeshapesandfrequencies ofthe air-craftandchangeitsglobalstiffness.
The optimizationresultsareverysimilar andmainly the lead-ing edgeandthe frontsparare affected,ascanbe seenfromthe material thickness distributions plotted in Fig. 23. Apparently, a modification ofthese designfields hasthe largestimpact on the overalldesignobjectiveofminimumweight.Thiscanbeexplained by thenatureoftheflightcontroller tosteertheaircraftintothe gust. This increases the effective angle of attack, resulting in a higher lift, which acts on the aircraft justbehind the front spar (approximatelyatalocalchordlengthof25%).Tofurtherimprove thestructurallayoutintermsofgeometry,thefrontsparcouldbe shiftedrearwards,whichwouldincreaseitsheightandsecondarea moment.
Ingeneral,itcanbeconcluded thatsuchacompactflyingwing configuration of low aspect ratio is sized mainly by local loads.
Fig. 21.Convergence history of structural net mass.
This is contrary to the experience with high aspect ratio wing-fuselage-empennageconfigurations, wherethestructuralsizing is dominated for example by large bending moments at the wing root.
figurations.The MULDICONalsoshowsapronounced tendencyto pitchupwhenenteringagust field.Itcanbeshownthattheuse ofthePrattformulaforquasi-steadygustloadsisunsuitable.
Inanextstep,theMULDICONisexposedtoaseriesofgust en-counterswithflight control switchedon.The pitching stability is
be interesting, butvery computationally expensive, torepeat the calculationsusingCFDtoseeifthatassumptionholdstrue. Conflict of interest statement
Thereisnoconflictofinterest. References
[1]C.M. Liersch, K.C.Huber, Conceptual designand aerodynamicanalyses ofa genericUCAVconfiguration,in:32ndAIAAAppliedAerodynamicsConference, AmericanInstituteofAeronauticsandAstronautics,Atlanta,GA,2014. [2]C.M. Liersch, K.C. Huber,A.Schütte, D. Zimper, M.Siggel, Multidisciplinary
designandaerodynamicassessmentofanagileandhighlysweptaircraft con-figuration,CEASAeronaut.J.7(2016)677–694.
[3]W.R.Krüger,S.Cumnuantip,C.M.Liersch,Multidisciplinaryconceptualdesign ofaUCAVconfiguration,in:ProceedingsAVT-MP173,NorthAtlanticTreaty Or-ganization,Sofia,Bulgaria,2011.
[4]A.Voß,T.Klimmek,Designandsizingofaparametricstructuralmodelfor aUCAVconfigurationfor loadsandaeroelasticanalysis,CEASAeronaut. J.8 (2017)67–77.
[5]K.Bramsiepe,A.Voß,T.Klimmek,Designandsizingofanaeroelastic compos-itemodelforanUCAVconfigurationwithmaneuver,gustandlandingloads,in: Deutscher Luft- undRaumfahrtkongress,DeutscheGesellschaftfürLuft- und Raumfahrt,München,2017.
[6]D. Schäfer,C. Vidy,C.Mack, J.Arnold, Assessment of body-freedomflutter foranunmannedaerialvehicle,in:DeutscherLuft- undRaumfahrtkongress, DeutscheGesellschaftfürLuft- undRaumfahrt,Braunschweig,2016. [7]A.Voß,T.Klimmek,Maneuverloadscalculationwithenhanced
aerodynam-icsforaUCAVconfiguration,in:AIAAAVIATIONForum,AmericanInstituteof AeronauticsandAstronautics,Washington,D.C.,2016.
[8]R.M. Cummings,C.M. Liersch,A.Schütte, Multi-disciplinarydesignand per-formanceassessmentofeffective,agileNATOairvehicles,in:AIAAAVIATION Forum,AmericanInstituteofAeronauticsandAstronautics,Atlanta,Georgia, 2018.
Verbund- Berechnungen,RichtlinieVDI2014Blatt3,VereinDeutscher Inge-nieure,2006.
[14]R.-G.Becker,S.Reitenbach,C.Klein,T.Otten,M.Nauroz,M.Siggel,An inte-gratedmethodforpropulsionsystemconceptualdesign,in:ASMEGasTurbine TechnicalCongressandExposition,ASME,Montréal,Canada,2015.
[15]M.Nauroz,AntriebskonzepteineragilenhochgepfeiltenFlugzeugkonfiguration, in:Deutscher Luft- und Raumfahrtkongress,DeutscheGesellschaftfür Luft-undRaumfahrt,Rostock,2015.
[16]J.Katz,A.Plotkin,Low-SpeedAerodynamics:FromWingTheorytoPanel Meth-ods,McGraw-HillSeriesinAeronauticalandAerospaceEngineering, McGraw-Hill,NewYork,1991.
[17]E.Albano,W.P.Rodden,Adoubletlatticemethodforcalculatinglift distribu-tionsonoscillationsurfacesinsubsonicflows,in:AIAA6thAerospaceSciences Meeting,AmericanInstituteofAeronauticsandAstronautics,NewYork,1968. [18]K.L. Roger, Airplane math modeling methods for active control design, in:
AGARD-CP-228,NATOAdvisoryGroupforAerospaceandDevelopment,1977. [19]M.Karpel,A.Shousterman,C.Maderuelo,H.Climent,Dynamicaeroservoelastic
responsewithnonlinearstructuralelements,AIAAJ.53(2015)3233–3239. [20]P.Teufel,M.Kruse,Efficientmethodforcouplingdiscretegustloadsanalysis
inthefrequencydomainwithafullynon-linearflightcontrolsystem simula-tion,in:IFASD,InternationalForumforAeroelasticityandStructuralDynamics, Stockholm,Sweden,2007.
[21] European Aviation SafetyAgency (Ed.),CertificationSpecifications for Large AeroplanesCS-25,Amendment16,2015.
[22]C.Buttrill,T.Zeiler,P.Arbuckle,Nonlinearsimulationofaflexibleaircraftin maneuveringflight,in:FlightSimulationTechnologiesConference, Guidance, Navigation, and Control and Co-Located Conferences, American Institute of AeronauticsandAstronautics,1987.
[23]M.Waszak,C.Buttrill,D.Schmidt,ModelingandModelSimplificationof Aeroe-lasticVehicles:anOverview,TechnicalReportNASATechnicalMemorandum 107691,NASALangleyResearchCenter,1992.
[24]M.R.Waszak,D.K.Schmidt,Flightdynamicsofaeroelasticvehicles,J.Aircr.25 (1988)563–571.
[25]Y.Wang,A.DaRonch,M.GhandchiTehrani,Adaptivefeedforwardcontrolfor gust-inducedaeroelasticvibrations,Aerospace5(2018)86.