Table Of ContentModeling ofComplex Systems
Modeling of
Complex Systems
Application to Aeronautical Dynamics
Emmanuel Grunn
Anh Tuan Pham
Series Editor
Hisham Abou Kandil
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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.
