Modeling ofComplex Systems Modeling of Complex Systems Application to Aeronautical Dynamics Emmanuel Grunn Anh Tuan Pham Series Editor Hisham Abou Kandil Firstpublished2013inGreatBritainandtheUnitedStatesbyISTELtdandJohnWiley&Sons,Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced, storedortransmitted,inanyformorbyanymeans,withthepriorpermissioninwritingofthepublishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentionedaddress: ISTELtd JohnWiley&Sons,Inc. 27-37StGeorge’sRoad 111RiverStreet LondonSW194EU Hoboken,NJ07030 UK USA www.iste.co.uk www.wiley.com ©ISTELtd2013 TherightsofEmmanuelGrunnandAnhTuanPhamtobeidentifiedastheauthorofthisworkhavebeen assertedbytheminaccordancewiththeCopyright,DesignsandPatentsAct1988. LibraryofCongressControlNumber: 2013945048 BritishLibraryCataloguing-in-PublicationData ACIPrecordforthisbookisavailablefromtheBritishLibrary ISBN:978-1-84821-448-4 PrintedandboundinGreatBritainbyCPIGroup(UK)Ltd.,Croydon,SurreyCR04YY Table of Contents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Chapter1.0DAnalyticalModelingof theAirplaneMotions. . . . . . . . . 1 1.1.References:axissystemsonuse. . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1.Galileanreference:R . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 1.1.2.Airplanereference:R (body)alsocalled“linkedreference”. . . . 2 B 1.1.3.Resultantangularvelocity. . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.Equationsofmotionoftheairplane . . . . . . . . . . . . . . . . . . . . . 9 1.2.1.ExpressionofNewton’sprinciple . . . . . . . . . . . . . . . . . . . . 10 1.2.2.Expressionofthedynamicmomentum . . . . . . . . . . . . . . . . . 11 1.3.Descriptionofexternalforcesandtorques . . . . . . . . . . . . . . . . . 14 1.3.1.Aerodynamicforcesandtorques. . . . . . . . . . . . . . . . . . . . . 14 1.3.2.Signrules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4.Descriptionofaerodynamiccoefficients. . . . . . . . . . . . . . . . . . . 18 1.4.1.Dragcoefficient: C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 x 1.4.2.SideliftcoefficientC . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Y 1.4.3.Verticalliftduetoattackangle:C . . . . . . . . . . . . . . . . . . . 20 Zα 1.4.4.Liftduetopitchangularvelocity:C . . . . . . . . . . . . . . . . . . 21 Zq 1.4.5.Rollcoefficients(duetoβ,δ ,p). . . . . . . . . . . . . . . . . . . . . 22 l 1.4.6.Pitchcoefficients(duetoα,δ ,q,staticcurvature) . . . . . . . . . 25 m 1.4.7.Yawcoefficients(duetoβ,δ ,r). . . . . . . . . . . . . . . . . . . . . 27 n 1.5.Aerodynamicdataofasupersonicairlinerforvaluationofthesoftware 32 1.6.Horizontalflightasaninitialcondition . . . . . . . . . . . . . . . . . . . 33 1.7.Effectofgravitationalforces. . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.8.Calculationofthetrajectoryoftheairplaneinopenspace . . . . . . . . 39 1.9.ValidationbycomparisonwithONERAConcordedata . . . . . . . . . 47 1.10.Definitionsofaerodynamiccoefficientsandderivatives . . . . . . . . 51 1.10.1.Aerodynamiccoefficients . . . . . . . . . . . . . . . . . . . . . . . . 51 vi ModelingofComplexSystems 1.10.2.Totalliftcoefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 1.10.3.Dragcharacteristics:(dimensionless) . . . . . . . . . . . . . . . . . 55 1.10.4.Sideliftcoefficient:C (dimensionless). . . . . . . . . . . . . . . . 58 Y 1.10.5.Rollcoefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.10.6.Pitchcoefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 1.10.7.Yawcoefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Chapter2.DesignandOptimizationofanUnmannedAerial Vehicle(UAV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.1.Generaldesignofthedrone . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.2.Weightestimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.3.Sizeestimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.4.Massandinertiaevaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.4.1.Massevaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.4.2.Measurementoftherollinertia(A) . . . . . . . . . . . . . . . . . . . 77 2.4.3.Measurementofpitchinertia(B). . . . . . . . . . . . . . . . . . . . . 79 2.4.4.Measurementofyawinertia(C) . . . . . . . . . . . . . . . . . . . . . 80 2.5.Convergencetowardthetarget . . . . . . . . . . . . . . . . . . . . . . . . 82 Chapter3.OrganizationoftheAuto-Pilot. . . . . . . . . . . . . . . . . . . . . 91 3.1.Positionofthedroneinopenspace. . . . . . . . . . . . . . . . . . . . . . 93 3.2.TheDogLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.3.Flighttests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.4.Altitudecontrolsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.5.Altitudemeasurementonanactualdrone . . . . . . . . . . . . . . . . . . 102 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Introduction The development of an airplane project closely follows a design process which defines the characteristics required to achieve the performanceexpectationsandthedesiredflyingcriteria. The principal purpose of this book is to offer readers a design tool which enables them to solve the different problems that can occur during the planning phase of a private project. As such, this bookmay beusefulfordesignengineersaswellasforkeenairplaneamateurs. For the purpose of this book, we will assume that the preliminary design has been established and that an overall drawing, detailing the general shape of the airplane (i.e. surfaces, wingspan, aspect ratios, different levers, wing and stabilizer sections, as well as engine power requirements),hasbeencompleted. In the following chapters, we will focus our attention on the dynamicbehavioroftheplane. The study of flying qualities makes use of a special mathematical tool known as MATLAB/SIMULINK, outlined in Chapter 1, entitled “0DAnalyticalModeling”. Weshallnowlistthevariousphaseswhichoccurduringthedesign processofanairplane. viii ModelingofComplexSystems Chapter1 –Building a design tool under the form of a 0D mathematical model(dimensionless,timedependentonly); –describingthebehavioroftheplane; –helpingtooptimizetheflyingqualities. As validation of this model, a numerical result is given with data from an existing plane (Supersonic airliner CONCORDE, with data supplied by Office National de Recherche Aerospatiale (ONERA, FrenchAerospaceResearchOfficeandSud-Aviation). Chapter2 Dimensional process, leading to presumed principal characteristics oftheplane: –massdistribution,inertialmatrix; – air loads, wing and stabilizer areas, wingspan, pitch and yaw levers,alldataconditioningtheflyingqualitiesoftheplane; –selectionofwingandstabilizerairfoils; – outlining all necessary aerodynamic coefficients or derivatives, aswellasallcouplingterms; –applicationtoarealisticdroneproject. Chapter3 – Tuning the balancing equilibrium state of the plane to reach the previousobjectives; –flighttests.