Cover image for Aircraft flight dynamics and control
Title:
Aircraft flight dynamics and control
Personal Author:
Series:
Aerospace series
Publication Information:
Chichester, West Sussex : Wiley, 2013
Physical Description:
xix, 286 pages : ill. ; 26 cm.
ISBN:
9781118646816

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30000010325296 TL570 D867 2013 Open Access Book Book
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Summary

Summary

Aircraft Flight Dynamics and Control addresses airplane flight dynamics and control in a largely classical manner, but with references to modern treatment throughout. Classical feedback control methods are illustrated with relevant examples, and current trends in control are presented by introductions to dynamic inversion and control allocation.

This book covers the physical and mathematical fundamentals of aircraft flight dynamics as well as more advanced theory enabling a better insight into nonlinear dynamics. This leads to a useful introduction to automatic flight control and stability augmentation systems with discussion of the theory behind their design, and the limitations of the systems. The author provides a rigorous development of theory and derivations and illustrates the equations of motion in both scalar and matrix notation.

Key features:

Classical development and modern treatment of flight dynamics and control Detailed and rigorous exposition and examples, with illustrations Presentation of important trends in modern flight control systems Accessible introduction to control allocation based on the author's seminal work in the field Development of sensitivity analysis to determine the influential states in an airplane's response modes End of chapter problems with solutions available on an accompanying website

Written by an author with experience as an engineering test pilot as well as a university professor, Aircraft Flight Dynamics and Control provides the reader with a systematic development of the insights and tools necessary for further work in related fields of flight dynamics and control. It is an ideal course textbook and is also a valuable reference for many of the necessary basic formulations of the math and science underlying flight dynamics and control.


Author Notes

Wayne Durham, Virginia Polytechnic Institute and State University, USA

Wayne Durham is an Associate Professor Emeritus in the College of Engineering at Virginia Polytechnic Institute and State University. His area of research focuses on aircraft flight dynamics and control and he teaches a course (AOE 5214) on this subject at Virginia Tech University. He previously worked as a flight instructor at various Navy Schools in the US.


Table of Contents

Series Prefacep. xiii
Glossaryp. xv
1 Introductionp. 1
1.1 Backgroundp. 1
1.2 Overviewp. 2
1.3 Customs and Conventionsp. 6
Referencesp. 6
2 Coordinate Systemsp. 7
2.1 Backgroundp. 7
2.2 The Coordinate Systemsp. 7
2.2.1 The inertial reference frame, F Ip. 7
2.2.2 The earth-centered reference frame, F ECp. 8
2.2.3 The earth-fixed reference frame, F Ep. 8
2.2.4 The local-horizontal reference frame, F Hp. 8
2.2.5 Body-fixed reference frames, F Bp. 10
2.2.6 Wind-axis system, F Wp. 12
2.2.7 Atmospheric reference framep. 12
2.3 Vector Notationp. 13
2.4 Customs and Conventionsp. 14
2.4.1 Latitude and longitudep. 14
2.4.2 Body axesp. 14
2.4.3 'The' body-axis systemp. 14
2.4.4 Aerodynamic anglesp. 15
Problemsp. 16
Referencesp. 16
3 Coordinate System Transformationsp. 17
3.1 Problem Statementp. 17
3.2 Transformationsp. 18
3.2.1 Definitionsp. 18
3.2.2 Direction cosinesp. 18
3.2.3 Eider anglesp. 21
3.2.4 Euler parametersp. 25
3.3 Transformations of Systems of Equationsp. 26
3.4 Customs and Conventionsp. 27
3.4.1 Names of Euler anglesp. 27
3.4.2 Principal values of Euler anglesp. 27
Problemsp. 27
Referencep. 29
4 Rotating Coordinate Systemsp. 31
4.1 Generalp. 31
4.2 Direction Cosinesp. 34
4.3 Euler Anglesp. 34
4.4 Euler Parametersp. 36
4.5 Customs and Conventionsp. 38
4.5.1 Angular velocity componentsp. 38
Problemsp. 38
5 Inertial Accelerationsp. 43
5.1 Generalp. 43
5.2 Inertial Acceleration of a Pointp. 43
5.2.1 Arbitrary moving reference framep. 43
5.2.2 Earth-centered moving reference framep. 46
5.2.3 Earth-fixed moving reference framep. 46
5.3 Inertial Acceleration of a Massp. 47
5.3.1 Linear accelerationp. 48
5.3.2 Rotational accelerationp. 49
5.4 Statesp. 53
5.5 Customs and Conventionsp. 53
5.5.1 Linear velocity componentsp. 53
5.5.2 Angular velocity componentsp. 54
5.5.3 Forcesp. 54
5.5.4 Momentsp. 56
5.5.5 Groupingsp. 56
Problemsp. 57
6 Forces and Momentsp. 59
6.1 Generalp. 59
6.1.1 Assumptionsp. 59
6.1.2 State variablesp. 60
6.1.3 State ratesp. 60
6.1.4 Flight controlsp. 60
6.1.5 Independent variablesp. 62
6.2 Non-Dimensionalizationp. 62
6.3 Non-Dimensional Coefficient Dependenciesp. 63
6.3.1 Generalp. 63
6.3.2 Altitude dependenciesp. 64
6.3.3 Velocity dependenciesp. 64
6.3.4 Angle-of-attack dependenciesp. 64
6.3.5 Sideslip dependenciesp. 66
6.3.6 Angular velocity dependenciesp. 68
6.3.7 Control dependenciesp. 69
6.3.8 Summary of dependenciesp. 70
6.4 The Linear Assumptionp. 71
6.5 Tabular Datap. 71
6.6 Customs and Conventionsp. 72
Problemsp. 73
7 Equations of Motionp. 75
7.1 Generalp. 75
7.2 Body-Axis Equationsp. 75
7.2.1 Body-axis force equationsp. 75
7.2.2 Body-axis moment equationsp. 76
7.2.3 Body-axis orientation equations (kinematic equations)p. 77
7.2.4 Body-axis navigation equationsp. 77
7.3 Wind-Axis Equationsp. 78
7.3.1 Wind-axis force equationsp. 78
7.3.2 Wind-axis orientation equations (kinematic equations)p. 80
7.3.3 Wind-axis navigation equationsp. 81
7.4 Steady-State Solutionsp. 81
7.4.1 Generalp. 81
7.4.2 Special casesp. 83
7.4.3 Vie trim problemp. 88
Problemsp. 89
Referencep. 91
8 Linearizationp. 93
8.1 Generalp. 93
8.2 Taylor Seriesp. 94
8.3 Nonlinear Ordinary Differential Equationsp. 95
8.4 Systems of Equationsp. 95
8.5 Examplesp. 97
8.5.1 Generalp. 97
8.5.2 A kinematic equationp. 99
8.5.3 A moment equationp. 100
8.5.4 A force equationp. 103
8.6 Customs and Conventionsp. 105
8.6.1 Omission of ¿p. 105
8.6.2 Dimensional derivativesp. 105
8.6.3 Added massp. 105
8.7 The Linear Equationsp. 106
8.7.1 Linear equationsp. 106
8.7.2 Matrix forms of the linear equationsp. 108
Problemsp. 111
Referencesp. 112
9 Solutions to the Linear Equationsp. 113
9.1 Scalar Equationsp. 113
9.2 Matrix Equationsp. 114
9.3 Initial Condition Responsep. 115
9.3.1 Modal analysisp. 115
9.4 Mode Sensitivity and Approximationsp. 120
9.4.1 Mode sensitivityp. 120
9.4.2 Approximationsp. 123
9.5 Forced Responsep. 124
9.5.1 Transfer functionsp. 124
9.5.2 Steady-state responsep. 125
Problemsp. 125
10 Aircraft Flight Dynamicsp. 127
10.1 Example: Longitudinal Dynamicsp. 127
10.1.1 System matricesp. 127
10.1.2 State transition matrix and eigenvaluesp. 127
10.1.3 Eigenvector analysisp. 129
10.1.4 Longitudinal mode sensitivity and approximationsp. 132
10.1.5 Forced responsep. 137
10.2 Example: Lateral-Directional Dynamicsp. 140
10.2.1 System matricesp. 140
10.2.2 Slate transition matrix and eigenvaluesp. 140
10.2.3 Eigenvector analysisp. 142
10.2.4 Lateral-directional mode sensitivity and approximationsp. 144
10.2.5 Forced responsep. 148
Problemsp. 149
Referencesp. 150
11 Flying Qualitiesp. 151
11.1 Generalp. 151
11.1.1 Methodp. 152
11.1.2 Specifications and standardsp. 155
11.2 MTL-F-8785C Requirementsp. 156
11.2.1 Generalp. 156
11.2.2 Longitudinal flying qualitiesp. 157
11.2.3 Lateral-directional flying quantitiesp. 158
Problemsp. 166
Referencesp. 166
12 Automatic Flight Controlp. 169
12.1 Simple Feedback Systemsp. 170
12.1.1 First-order systemsp. 170
12.1.2 Second-order systemsp. 172
12.1.3 A general representationp. 177
12.2 Example Feedback Control Applicationsp. 178
12.2.1 Roll modep. 178
12.2.2 Short-period modep. 184
12.2.3 Phitgoidp. 188
12.2.4 Coupled roll-spiral oscillationp. 198
Problemsp. 206
Referencesp. 207
13 Trends in Automatic Flight Controlp. 209
13.1 Overviewp. 209
13.2 Dynamic Inversionp. 210
13.2.1 The controlled equationsp. 212
13.2.2 The kinematic equationsp. 215
13.2.3 The complementary equationsp. 221
13.3 Control Allocationp. 224
13.3.1 Backgroundp. 224
13.3.2 Problem statementp. 225
13.3.3 Optimalityp. 231
13.3.4 Sub-optimal solutionsp. 232
13.3.5 Optimal solutionsp. 235
13.3.6 Near-optimal solutionsp. 241
Problemsp. 243
Referencesp. 244
A Example Aircraftp. 247
Referencep. 253
B Linearizationp. 255
B.1 Derivation of Frequently Used Derivativesp. 255
B.2 Non-dimensionalization of the Rolling Moment Equationp. 257
B.3 Body Axis 2-Force and Thrust Derivativesp. 258
B.4 Non-dimensionalization of the Z-Force Equationp. 260
C Derivation of Euler Parametersp. 263
D Fedeeva's Algorithmp. 269
Referencep. 272
E MATLAB® Commands Used in the Textp. 273
E.1 Using MATLAB®p. 273
E.2 Eigenvalues and Eigenvectorsp. 274
E.3 State-Space Representationp. 274
E.4 Transfer Function Representationp. 275
E.5 Root Locusp. 277
E.6 MATLAB® Functions (m-files)p. 277
E.6.1 Example aircraftp. 278
E.6.2 Mode sensitivity matrixp. 278
E.6.3 Cut-and-try root locus gainsp. 278
E.7 Miscellaneous Applications and Notesp. 280
E.7.1 Matricesp. 280
E.7.2 Commands used to create Figures 10.2 and 10.3p. 281
Indexp. 283