Cook Flight Dynamics Principles

A Linear Systems Approach to Aircraft Stability and Control
3. Auflage 2012
ISBN: 978-0-08-098276-2
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 608 Seiten

The study of flight dynamics requires a thorough understanding of the theory of the stability and control of aircraft, an appreciation of flight control systems and a grounding in the theory of automatic control. Flight Dynamics Principles is a student focused text and provides easy access to all three topics in an integrated modern systems context. Written for those coming to the subject for the first time, the book provides a secure foundation from which to move on to more advanced topics such as, non-linear flight dynamics, flight simulation, handling qualities and advanced flight control. - Additional examples to illustrate the application of computational procedures using tools such as MATLAB®, MathCad® and Program CC® - Improved compatibility with, and more expansive coverage of the North American notational style - Expanded coverage of lateral-directional static stability, manoeuvrability, command augmentation and flight in turbulence - An additional coursework study on flight control design for an unmanned air vehicle (UAV)

After graduating Michael Cook joined Elliott Flight Automation as a Systems Engineer and contributed flight control systems design to several major projects. Later he joined the College of Aeronautics to research and teach flight dynamics, experimental flight mechanics and flight control. Previously leader of the Dynamics, Simulation and Control Research Group he is now retired and continues to provide part time support. In 2003 the Group was recognised as the Preferred Academic Capability Partner for Flight Dynamics by BAE SYSTEMS and in 2007 he received a Chairman's Bronze award for his contribution to a joint UAV research programme.

Autoren/Hrsg.

Cook, Michael V.

Inhaltsverzeichnis

1;Front Cover;1
2;Flight Dynamics Principles;4
3;Copyright Page;5
4;Contents;6
5;Preface;16
6;Preface to the second edition;18
7;Preface to the first edition;20
8;Acknowledgements;22
9;Nomenclature;24
9.1;Subscripts;31
9.2;Examples of other symbols and notation;32
10;1 Introduction;34
10.1;1.1 Overview;34
10.2;1.2 Flying and handling qualities;36
10.3;1.3 General considerations;37
10.3.1;1.3.1 Basic control-response relationships;38
10.3.2;1.3.2 Mathematical models;38
10.3.3;1.3.3 Stability and control;39
10.3.4;1.3.4 Stability and control augmentation;39
10.4;1.4 Aircraft equations of motion;39
10.5;1.5 Aerodynamics;40
10.5.1;1.5.1 Small perturbations;40
10.6;1.6 Computers;41
10.6.1;1.6.1 Analytical computers;41
10.6.2;1.6.2 Flight control computers;41
10.6.3;1.6.3 Computer software tools;42
10.6.3.1;Matlab;42
10.6.3.2;Simulink;42
10.6.3.3;Matlab and Simulink, Student Version Release 14;42
10.6.3.4;Program CC, Version 5;42
10.6.3.5;Mathcad;43
10.6.3.6;20-sim;43
10.7;1.7 Summary;43
10.8;References;43
10.9;Sources;44
11;2 Systems of Axes and Notation;46
11.1;2.1 Earth axes;46
11.2;2.2 Aircraft body–fixed axes;47
11.2.1;2.2.1 Generalised body axes;47
11.2.2;2.2.2 Aerodynamic, wind, or stability axes;48
11.2.3;2.2.3 Perturbation variables;48
11.2.4;2.2.4 Angular relationships in symmetric flight;49
11.2.5;2.2.5 Choice of axes;51
11.3;2.3 Euler angles and aircraft attitude;52
11.4;2.4 Axes transformations;52
11.4.1;2.4.1 Linear quantities transformation;53
11.4.2;2.4.2 Angular velocities transformation;55
11.5;2.5 Aircraft reference geometry;58
11.5.1;2.5.1 Wing area;58
11.5.2;2.5.2 Mean aerodynamic chord;59
11.5.3;2.5.3 Standard mean chord;59
11.5.4;2.5.4 Aspect ratio;59
11.5.5;2.5.5 Location of centre of gravity;60
11.5.6;2.5.6 Tail moment arm and tail volume ratio;60
11.5.7;2.5.7 Fin moment arm and fin volume ratio;60
11.6;2.6 Controls notation;61
11.6.1;2.6.1 Aerodynamic controls;61
11.6.2;2.6.2 Engine control;61
11.7;2.7 Aerodynamic reference centres;62
11.8;References;64
11.9;Problems;64
12;3 Static Equilibrium and Trim;66
12.1;3.1 Trim equilibrium;66
12.1.1;3.1.1 Preliminary considerations;66
12.1.2;3.1.2 Conditions for stability;67
12.1.3;3.1.3 Degree of longitudinal stability;70
12.1.4;3.1.4 Variation in stability;71
12.1.4.1;Power effects;71
12.1.4.2;Other effects;73
12.2;3.2 The pitching moment equation;75
12.2.1;3.2.1 Simple development of the pitching moment equation;75
12.2.2;3.2.2 Elevator angle to trim;77
12.2.3;3.2.3 Condition for longitudinal static stability;78
12.3;3.3 Longitudinal static stability;78
12.3.1;3.3.1 Controls-fixed stability;78
12.3.2;3.3.2 Controls-free stability;82
12.3.3;3.3.3 Summary of longitudinal static stability;87
12.4;3.4 Lateral-directional static stability;88
12.4.1;3.4.1 Lateral static stability;89
12.4.2;3.4.2 Directional static stability;94
12.5;3.5 Calculation of aircraft trim condition;96
12.5.1;3.5.1 Defining the trim condition;97
12.5.2;3.5.2 Elevator angle to trim;98
12.5.3;3.5.3 Controls-fixed static stability;99
12.5.4;3.5.4 “AeroTrim”: A Mathcad trim program;100
12.6;References;103
12.7;Source;103
12.8;Problems;103
13;4 The Equations of Motion;106
13.1;4.1 The equations of motion for a rigid symmetric aircraft;106
13.1.1;4.1.1 The components of inertial acceleration;106
13.1.2;4.1.2 The generalised force equations;110
13.1.3;4.1.3 The generalised moment equations;111
13.1.4;4.1.4 Perturbation forces and moments;113
13.2;4.2 The linearised equations of motion;113
13.2.1;4.2.1 Gravitational terms;114
13.2.2;4.2.2 Aerodynamic terms;115
13.2.3;4.2.3 Aerodynamic control terms;117
13.2.4;4.2.4 Power terms;117
13.2.5;4.2.5 The equations of motion for small perturbations;118
13.3;4.3 The decoupled equations of motion;120
13.3.1;4.3.1 The longitudinal equations of motion;120
13.3.2;4.3.2 The lateral-directional equations of motion;122
13.4;4.4 Alternative forms of the equations of motion;123
13.4.1;4.4.1 The dimensionless equations of motion;123
13.4.2;4.4.2 The equations of motion in state space form;126
13.4.3;4.4.3 The equations of motion in American normalised form;132
13.5;References;139
13.6;Problems;139
14;5 The Solution of the Equations of Motion;142
14.1;5.1 Methods of solution;142
14.2;5.2 Cramer’s rule;143
14.3;5.3 Aircraft response transfer functions;145
14.3.1;5.3.1 The longitudinal response transfer functions;146
14.3.2;5.3.2 The lateral-directional response transfer functions;148
14.4;5.4 Response to controls;150
14.5;5.5 Acceleration response transfer functions;154
14.6;5.6 The state-space method;156
14.6.1;5.6.1 The transfer function matrix;156
14.6.2;5.6.2 The longitudinal transfer function matrix;158
14.6.3;5.6.3 The lateral-directional transfer function matrix;158
14.6.4;5.6.4 Response in terms of state description;161
14.6.4.1;Eigenvalues and eigenvectors;162
14.6.4.2;The modal equations;163
14.6.4.3;Unforced response;164
14.6.4.4;Impulse response;165
14.6.4.5;Step response;165
14.6.4.6;Response shapes;166
14.7;5.7 State-space model augmentation;169
14.7.1;5.7.1 Height response transfer function;170
14.7.2;5.7.2 Incidence and sideslip response transfer functions;171
14.7.3;5.7.3 Flight path angle response transfer function;172
14.7.4;5.7.4 Addition of engine dynamics;172
14.8;References;175
14.9;Problems;176
15;6 Longitudinal Dynamics;180
15.1;6.1 Response to controls;180
15.1.1;6.1.1 The characteristic equation;185
15.2;6.2 The dynamic stability modes;186
15.2.1;6.2.1 The short-period pitching oscillation;186
15.2.2;6.2.2 The phugoid;187
15.3;6.3 Reduced-order models;188
15.3.1;6.3.1 The short-period mode approximation;189
15.3.2;6.3.2 The phugoid mode approximation;192
15.3.2.1;The Lanchester model;192
15.3.2.2;A reduced-order model;193
15.4;6.4 Frequency response;199
15.4.1;6.4.1 The Bode diagram;201
15.4.2;6.4.2 Interpretation of the Bode diagram;203
15.5;6.5 Flying and handling qualities;208
15.6;6.6 Mode excitation;208
15.7;References;212
15.8;Problems;212
16;7 Lateral-Directional Dynamics;216
16.1;7.1 Response to controls;216
16.1.1;7.1.1 The characteristic equation;224
16.2;7.2 The dynamic stability modes;225
16.2.1;7.2.1 The roll subsidence mode;225
16.2.2;7.2.2 The spiral mode;227
16.2.3;7.2.3 The dutch roll mode;228
16.3;7.3 Reduced order models;230
16.3.1;7.3.1 The roll mode approximation;231
16.3.2;7.3.2 The spiral mode approximation;232
16.3.3;7.3.3 The dutch roll mode approximation;233
16.4;7.4 Frequency response;237
16.5;7.5 Flying and handling qualities;243
16.6;7.6 Mode excitation;244
16.7;References;248
16.8;Problems;248
17;8 Manoeuvrability;252
17.1;8.1 Introduction;252
17.1.1;8.1.1 Manoeuvring flight;252
17.1.2;8.1.2 Stability;253
17.1.3;8.1.3 Aircraft handling;253
17.1.4;8.1.4 The steady symmetric manoeuvre;254
17.2;8.2 The steady pull-up manoeuvre;254
17.3;8.3 The pitching moment equation;256
17.4;8.4 Longitudinal manoeuvre stability;258
17.4.1;8.4.1 Controls-fixed stability;258
17.4.2;8.4.2 Normal acceleration response to elevator;260
17.4.3;8.4.3 Controls-free stability;261
17.4.4;8.4.4 Elevator deflection and stick force;265
17.5;8.5 Aircraft dynamics and manoeuvrability;266
17.6;8.6 Aircraft with stability augmentation;267
17.6.1;8.6.1 Stick force;268
17.6.2;8.6.2 Stick force per g;268
17.7;References;274
18;9 Stability;276
18.1;9.1 Introduction;276
18.1.1;9.1.1 A definition of stability;276
18.1.2;9.1.2 Non-linear systems;276
18.1.3;9.1.3 Static and dynamic stability;277
18.1.4;9.1.4 Control;277
18.2;9.2 The characteristic equation;278
18.3;9.3 The Routh-Hurwitz stability criterion;279
18.3.1;9.3.1 Special cases;281
18.4;9.4 The stability quartic;283
18.4.1;9.4.1 Interpretation of conditional instability;284
18.4.2;9.4.2 Interpretation of the coefficient E;285
18.5;9.5 Graphical interpretation of stability;286
18.5.1;9.5.1 Root mapping on the s-plane;286
18.6;References;290
18.7;Problems;290
19;10 Flying and Handling Qualities;292
19.1;10.1 Introduction;292
19.1.1;10.1.1 Stability;292
19.2;10.2 Short term dynamic models;293
19.2.1;10.2.1 Controlled motion and motion cues;293
19.2.2;10.2.2 The longitudinal reduced order model;294
19.2.3;10.2.3 The “thumb print” criterion;299
19.2.4;10.2.4 Incidence lag;300
19.3;10.3 Flying qualities requirements;300
19.4;10.4 Aircraft role;303
19.4.1;10.4.1 Aircraft classification;303
19.4.2;10.4.2 Flight phase;304
19.4.3;10.4.3 Levels of flying qualities;304
19.4.4;10.4.4 Flight envelopes;304
19.4.4.1;Permissible flight envelope;304
19.4.4.2;Service flight envelope;305
19.4.4.3;Operational flight envelope;305
19.5;10.5 Pilot opinion rating;307
19.6;10.6 Longitudinal flying qualities requirements;309
19.6.1;10.6.1 Longitudinal static stability;309
19.6.2;10.6.2 Longitudinal dynamic stability;310
19.6.2.1;Short-period pitching oscillation;310
19.6.2.2;Phugoid;311
19.6.3;10.6.3 Longitudinal manoeuvrability;312
19.7;10.7 Control anticipation parameter;312
19.8;10.8 Lateral-directional flying qualities requirements;314
19.8.1;10.8.1 Steady lateral-directional control;314
19.8.2;10.8.2 Lateral-directional dynamic stability;315
19.8.2.1;Roll subsidence mode;315
19.8.2.2;Spiral mode;315
19.8.2.3;Dutch roll mode;316
19.8.3;10.8.3 Lateral-directional manoeuvrability and response;317
19.9;10.9 Flying qualities requirements on the s-plane;317
19.9.1;10.9.1 Longitudinal modes;318
19.9.2;10.9.2 Lateral-directional modes;319
19.10;References;323
19.11;Problems;323
20;11 Command and Stability Augmentation;326
20.1;11.1 Introduction;326
20.1.1;11.1.1 The control law;328
20.1.2;11.1.2 Safety;328
20.1.3;11.1.3 Stability augmentation system architecture;329
20.1.4;11.1.4 Scope;332
20.2;11.2 Augmentation system design;332
20.3;11.3 Closed-loop system analysis;335
20.4;11.4 The root locus plot;339
20.5;11.5 Longitudinal stability augmentation;345
20.6;11.6 Lateral-directional stability augmentation;352
20.7;11.7 The pole placement method;363
20.8;11.8 Command augmentation;368
20.8.1;11.8.1 Command path filter design;369
20.8.2;11.8.2 The frequency response of a phase compensation filter;371
20.8.3;11.8.3 Introduction of a command path filter to the system state model;372
20.9;References;381
20.10;Problems;381
21;12 Aerodynamic Modelling;386
21.1;12.1 Introduction;386
21.2;12.2 Quasi-static derivatives;387
21.3;12.3 Derivative estimation;389
21.3.1;12.3.1 Calculation;390
21.3.2;12.3.2 Wind tunnel measurement;390
21.3.3;12.3.3 Flight test measurement;391
21.4;12.4 The effects of compressibility;393
21.4.1;12.4.1 Some useful definitions;393
21.4.2;12.4.2 Aerodynamic models;394
21.4.3;12.4.3 Subsonic lift, drag, and pitching moment;395
21.4.4;12.4.4 Supersonic lift, drag, and pitching moment;396
21.4.5;12.4.5 Summary;397
21.5;12.5 Limitations of aerodynamic modelling;401
21.6;References;401
22;13 Aerodynamic Stability and Control Derivatives;404
22.1;13.1 Introduction;404
22.2;13.2 Longitudinal aerodynamic stability derivatives;404
22.2.1;13.2.1 Preliminary considerations;404
22.2.2;13.2.2 Aerodynamic force and moment components;406
22.2.3;13.2.3 Force derivatives due to velocity perturbations;406
22.2.3.1;Xu =.X/.U Axial force due to axial velocity;406
22.2.3.2;Zu =.Z/.U Normal force due to axial velocity;407
22.2.3.3;Xw =.X/.W Axial force due to normal velocity;408
22.2.3.4;Zw =.Z/.W Normal force due to normal velocity;408
22.2.4;13.2.4 Moment derivatives due to velocity perturbations;409
22.2.4.1;Mu =.M/.U Pitching moment due to axial velocity;409
22.2.4.2;Mw =.M/.W Pitching moment due to normal velocity;410
22.2.5;13.2.5 Derivatives due to a pitch velocity perturbation;410
22.2.5.1;Xq =.X/.q Axial force due to pitch rate;411
22.2.5.2;Zq =.Z/.q Normal force due to pitch rate;412
22.2.5.3;Mq =.M/.q Pitching moment due to pitch rate;412
22.2.6;13.2.6 Derivatives due to acceleration perturbations;413
22.2.6.1;Xw =.X/.w Axial force due to rate of change of normal velocity;415
22.2.6.2;Zw=.Z/.w Normal force due to rate of change of normal velocity;416
22.2.6.3;Mw =.M/.w Pitching moment due to rate of change of normal velocity;416
22.3;13.3 Lateral-directional aerodynamic stability derivatives;417
22.3.1;13.3.1 Preliminary considerations;417
22.3.2;13.3.2 Derivatives due to sideslip;417
22.3.2.1;Yv =.Y/.V Sideforce due to sideslip;418
22.3.2.2;Lv =.L/.V Rolling moment due to sideslip;419
22.3.2.3;Nv =.N/.V Yawing moment due to sideslip;426
22.3.3;13.3.3 Derivatives due to rate of roll;427
22.3.3.1;Yp =.Y/.p Sideforce due to roll rate;427
22.3.3.2;Lp =.L/.p Rolling moment due to roll rate;428
22.3.3.3;Np =.N/.p Yawing moment due to roll rate;430
22.3.4;13.3.4 Derivatives due to rate of yaw;431
22.3.4.1;Yr =.Y/.r Sideforce due to yaw rate;432
22.3.4.2;Lr =.L/.r Rolling moment due to yaw rate;433
22.3.4.3;Nr =.N/.r Yawing moment due to yaw rate;436
22.4;13.4 Aerodynamic control derivatives;437
22.4.1;13.4.1 Derivatives due to elevator;438
22.4.1.1;X. =.X/.. Axial force due to elevator;438
22.4.1.2;Z. =.Z/.. Normal force due to elevator;439
22.4.1.3;M. =.M/.. Pitching moment due to elevator;439
22.4.2;13.4.2 Derivatives due to aileron;439
22.4.2.1;Y. =.Y/.. Sideforce due to aileron;440
22.4.2.2;L. =.L/.. Rolling moment due to aileron;441
22.4.2.3;N. =.N/.. Yawing moment due to aileron;441
22.4.3;13.4.3 Derivatives due to rudder;442
22.4.3.1;Y. =.Y/.. Sideforce due to rudder;442
22.4.3.2;L. =.L/.. Rolling moment due to rudder;443
22.4.3.3;N. =.N/.. Yawing moment due to rudder;443
22.5;13.5 North American derivative coefficient notation;443
22.5.1;13.5.1 The longitudinal aerodynamic derivative coefficients;445
22.5.2;13.5.2 The lateral-directional aerodynamic derivative coefficients;449
22.5.3;13.5.3 Comments;451
22.6;References;468
22.7;Problems;468
23;14 Flight in a Non-steady Atmosphere;474
23.1;14.1 The influence of atmospheric disturbances on flying qualities;474
23.2;14.2 Methods of evaluation;475
23.3;14.3 Atmospheric disturbances;476
23.3.1;14.3.1 Steady wind;476
23.3.2;14.3.2 Wind shear;477
23.3.3;14.3.3 Discrete gusts;477
23.3.4;14.3.4 Continuous turbulence;477
23.4;14.4 Extension of the linear aircraft equations of motion;479
23.4.1;14.4.1 Disturbed body incidence and sideslip;480
23.4.2;14.4.2 The longitudinal equations of motion;481
23.4.3;14.4.3 The lateral-directional equations of motion;483
23.4.4;14.4.4 The equations of motion for aircraft with stability augmentation;484
23.5;14.5 Turbulence modelling;489
23.5.1;14.5.1 The von Kármán model;490
23.5.2;14.5.2 The Dryden model;490
23.5.3;14.5.3 Comparison of the von Kármán and Dryden models;492
23.5.4;14.5.4 Turbulence scale length;492
23.5.5;14.5.5 Turbulence intensity;494
23.6;14.6 Discrete gusts;495
23.6.1;14.6.1 The “1-cosine” gust;495
23.6.2;14.6.2 Determination of maximum gust velocity and horizontal length;497
23.7;14.7 Aircraft response to gusts and turbulence;498
23.7.1;14.7.1 Variance, power spectral density, and white noise;498
23.7.2;14.7.2 Spatial and temporal equivalence;500
23.7.3;14.7.3 Synthetic turbulence;501
23.7.4;14.7.4 Aircraft response to gusts;503
23.7.5;14.7.5 Aircraft response to turbulence;505
23.8;References;517
24;15 Coursework Studies;520
24.1;15.1 Introduction;520
24.1.1;15.1.1 Working the assignments;520
24.1.2;15.1.2 Reporting;520
24.2;15.2 Assignment 1: Stability augmentation of the North American X-15 hypersonic research aeroplane;521
24.2.1;15.2.1 The aircraft model;521
24.2.2;15.2.2 The solution tasks;521
24.3;15.3 Assignment 2: The stability and control characteristics of a civil transport aeroplane with relaxed longitudinal stati...;522
24.3.1;15.3.1 The aircraft model;522
24.3.2;15.3.2 The governing trim equations;524
24.3.3;15.3.3 Basic aircraft stability and control analysis;524
24.3.4;15.3.4 Relaxing the stability of the aircraft;525
24.3.5;15.3.5 Relaxed stability aircraft stability and control analysis;525
24.3.6;15.3.6 Evaluation of results;525
24.3.7;15.3.7 Postscript;525
24.4;15.4 Assignment 3: Lateral-directional handling qualities design for the Lockheed F-104 Starfighter aircraft;525
24.4.1;15.4.1 The aircraft model;526
24.4.2;15.4.2 Lateral-directional autostabiliser structure;527
24.4.3;15.4.3 Basic aircraft stability and control analysis;527
24.4.4;15.4.4 Augmenting the stability of the aircraft;528
24.4.5;15.4.5 Inclusion of the washout filter in the model;530
24.4.6;15.4.6 Designing the aileron-rudder interlink gain;530
24.5;15.5 Assignment 4: Analysis of the effects of Mach number on the longitudinal stability and control characteristics of the ...;531
24.5.1;15.5.1 The aircraft model;531
24.5.2;15.5.2 The assignment tasks;531
24.5.2.1;Assembling the derivatives;531
24.5.2.2;Solving the equations of motion;531
24.5.2.3;Assessing the dynamic stability characteristics;531
24.5.2.4;Stability augmentation;532
24.5.2.5;Assessing the effects of Mach number;532
24.6;15.6 Assignment 5: The design of a longitudinal primary flight control system for an advanced-technology UAV;534
24.6.1;15.6.1 The aircraft model;534
24.6.2;15.6.2 The design requirements;536
24.6.3;15.6.3 The assignment tasks;537
24.6.3.1;Solving the equations of motion;537
24.6.3.2;Designing the speed control loop;537
24.6.3.3;Assessing the performance of the speed controller;537
24.6.3.4;Re-arranging the system state model with speed loop closed;537
24.6.3.5;Designing the pitch rate control loop;538
24.6.3.6;Designing the pitch attitude control loop;538
24.6.3.7;Assessing the performance of the pitch attitude controller;538
24.7;References;538
25;Appendix 1: AeroTrim: A Symmetric Trim Calculator for Subsonic Flight Conditions;540
25.1;1. Aircraft Flight Condition;540
25.2;2. Air Density Calculation;540
25.3;3. Set up Velocity Range for Computations;540
25.4;4. Aircraft Geometry—Constant;541
25.5;5. Wing-Body Aerodynamics;541
25.6;6. Tailplane Aerodynamics;542
25.7;7. Wing and Tailplane Calculations;542
25.8;8. Downwash at Tail;542
25.9;9. Induced Drag Factor;542
25.10;10. Basic Performance Parameters;543
25.11;11. Trim Calculation;543
25.12;12. Trim Variables Calculation;544
25.13;13. Conversions of Angles to Degrees;544
25.14;14. Total Trim Forces Acting on Aircraft;544
25.15;Summary Results of Trim Calculation;545
25.15.1;15. Definition of Flight Condition;545
25.15.2;16. Trim Conditions as a Function of Aircraft Velocity;545
25.15.3;17. Some Useful Trim Plots;546
26;Appendix 2: Definitions of Aerodynamic Stability and Control Derivatives;548
26.1;A2.1 Notes;548
27;Appendix 3: Aircraft Response Transfer Functions Referred to Aircraft Body Axes;556
27.1;A3.1 Longitudinal Response Transfer Functions in Terms of Dimensional Derivatives;556
27.2;A3.2 Lateral-Directional Response Transfer Functions in Terms of Dimensional Derivatives;558
27.3;A3.3 Longitudinal Response Transfer Functions in Terms of Concise Derivatives;559
27.4;A3.4 Lateral-Directional Response Transfer Functions in Terms of Concise Derivatives;560
28;Appendix 4: Units, Conversions, and Constants;562
29;Appendix 5: A Very Short Table of Laplace Transforms;564
30;Appendix 6: The Dynamics of a Linear Second Order System;566
31;Appendix 7: North American Aerodynamic Derivative Notation;570
32;Appendix 8: Approximate Expressions for the Dimensionless Aerodynamic Stability and Control Derivatives;572
33;Appendix 9: Transformation of Aerodynamic Stability Derivatives from a Body Axes Reference to a Wind Axes Reference;576
33.1;A9.1 Introduction;576
33.2;A9.2 Force and Moment Transformation;576
33.3;A9.3 Aerodynamic Stability Derivative Transformations;577
33.3.1;A9.3.1 Force-Velocity Derivatives;577
33.3.2;A9.3.2 Moment-Velocity Derivatives;578
33.3.3;A9.3.3 Force-Rotary Derivatives;578
33.3.4;A9.3.4 Moment-Rotary Derivatives;579
33.3.5;A9.3.5 Force-Acceleration Derivatives;580
33.3.6;A9.3.6 Moment-Acceleration Derivatives;581
33.3.7;A9.3.7 Aerodynamic Control Derivatives;581
33.4;A9.4 Summary;582
34;Appendix 10: Transformation of the Moments and Products of Inertia from a Body Axes Reference to a Wind Axes Reference;586
34.1;A10.1 Introduction;586
34.2;A10.2 Coordinate Transformation;586
34.2.1;A10.2.1 Body Axes to Wind Axes;586
34.2.2;A10.2.2 Wind Axes to Body Axes;587
34.3;A10.3 Transformation of the Moment of Inertia in Roll from a Body Axes Reference to a Wind Axes Reference;587
34.4;A10.4 Summary;588
35;Appendix 11: The Root Locus Plot;590
35.1;A11.1 Mathematical Background;590
35.2;A11.2. Rules for Constructing a Root Locus Plot;591
35.2.1;Rule 1;592
35.2.2;Rule 2;592
35.2.3;Rule 3;592
35.2.4;Rule 4;592
35.2.5;Rule 5;592
35.2.5.1;Method 1;593
35.2.5.2;Method 2;593
35.2.6;Rule 6;593
35.2.7;Rule 7;593
35.2.8;Rule 8;593
36;Index;596

Leseproben

Chapter 1
Introduction
1.1 Overview
This book is primarily concerned with the provision of good flying and handling qualities in conventional piloted aircraft, although the material is equally applicable to uninhabited air vehicles (UAV). Consequently, it is also very much concerned with the stability, control, and dynamic characteristics which are fundamental to the determination of those qualities. Since flying and handling qualities are of critical importance to safety and to the piloting task, it is essential that their origins are properly understood. Here, then, the intention is to set out the basic principles of the subject at an introductory level and to illustrate the application of those principles by means of worked examples. Following the first flights made by the Wright brothers in December 1903, the pace of aeronautical development quickened and the progress made in the following decade or so was dramatic. However, the stability and control problems that faced early aviators were sometimes considerable since the flying qualities of their aircraft were often less than satisfactory. Many investigators were studying the problems of stability and control at the time, although it is the published works of Bryan (1911) and Lanchester (1908) which are usually credited with laying the first really secure foundations for the subject. By conducting many experiments with flying models, Lanchester was able to observe and successfully describe mathematically some dynamic characteristics of aircraft. The beauty of Lanchester’s work was its practicality and theoretical simplicity, which facilitates easy application and interpretation. Bryan, on the other hand, was a mathematician who chose to apply his energies, with the assistance of a Mr. Harper, to the problems of aircraft stability and control. He developed the general equations of motion of a rigid body with six degrees of freedom to successfully describe aircraft motion. His treatment, with very few changes, is still in everyday use. What has changed is the way in which the material is now used, due largely to the advent of the digital computer as an analysis tool. Together, the stability and control of aircraft is a subject which has its origins in aerodynamics, and the classical theory of the subject is traditionally expressed in the language of the aerodynamicist. However, most advanced-technology aircraft may be described as an integrated system comprising airframe, propulsion, flight controls, and so on. It is therefore convenient and efficient to utilise powerful computational systems engineering tools to analyse and describe the system’s flight dynamics. Thus, the objective of the present work is to revisit the development of the classical theory and to express it in the language of the systems engineer where it is more appropriate to do so. The subject of flight dynamics is concerned with the relatively short-term motion of aircraft in response to controls or to external disturbances such as atmospheric turbulence. The motion of interest can vary from small excursions about trim to very-large-amplitude manoeuvring when normal aerodynamic behaviour may well become very non-linear. Since the treatment of the subject is introductory, a discussion of large-amplitude dynamics is beyond the scope of the present work. The dynamic behaviour of an aircraft is shaped significantly by its stability and control properties, which in turn have their roots in the aerodynamics of the airframe. Previously the achievement of aircraft with good stability characteristics usually ensured good flying qualities, all of which depended only on good aerodynamic design. Expanding flight envelopes and the increasing dependence on an automatic flight control system (AFCS) for stability augmentation means that good flying qualities are no longer a guaranteed product of good aerodynamic design and good stabilitycharacteristics. The reasons for this apparent inconsistency are now reasonably well understood and, put very simply, result from the addition of flight control system dynamics to those of the airframe. Flight control system dynamics are of course a necessary, but not always desirable, by-product of command and stability augmentation. Modern flight dynamics is concerned not only with the dynamics, stability, and control of the basic airframe but also with the sometimes complex interaction between the airframe and flight control system. Since the flight control system comprises motion sensors, a control computer, control actuators, and other essential items of control hardware, a study of the subject becomes a multidisciplinary activity. Therefore, it is essential that the modern flight dynamicist has not only a thorough understanding of the classical stability and control theory of aircraft but also a working knowledge of control theory and of the use of computers in flight-critical applications. Modern aircraft comprise the airframe together with the flight control equipment and may be treated as a whole system using the traditional tools of the aerodynamicist and the analytical tools of the control engineer. Thus in a modern approach to the analysis of stability and control, it is convenient to treat the airframe as a system component. This leads to the derivation of mathematical models which describe aircraft in terms of aerodynamic transfer functions. Described in this way, the stability, control, and dynamic characteristics of aircraft are readily interpreted with the aid of very powerful computational systems engineering tools. It follows that the mathematical model of the aircraft is immediately compatible with, and provides the foundation for integration with, flight control system studies. This is an ideal state of affairs since today it is commonplace to undertake stability and control investigations as a precursor to flight control system development. The modern flight dynamicist tends to be concerned with the wider issues of flying and handling qualities rather than with the traditional, and more limited, issues of stability and control. The former are, of course, largely determined by the latter. The present treatment of the material is shaped by answering the following questions which a newcomer to the subject might be tempted to ask: How are the stability and control characteristics of aircraft determined, and how do they influence flying qualities? The answer to this question involves the establishment of a suitable mathematical framework for the problem, the development of the equations of motion and their solution, investigation of response to controls, and the general interpretation of dynamic behaviour. What are acceptable flying qualities; how are the requirements defined, interpreted, and applied; and how do they limit flight characteristics? The answer to this question involves a review of contemporary flying qualities requirements and their evaluation and interpretation in the context of stability and control characteristics. When an aircraft has unacceptable flying qualities, how may its dynamic characteristics be improved? The answer to this question involves an introduction to the rudiments of feedback control as the means of augmenting the stability of the basic airframe. 1.2 Flying and handling qualities
The flying and handling qualities of an aircraft are those properties which describe the ease and effectiveness with which the aircraft responds to pilot commands in the execution of a flight task, or mission task element (MTE). In the first instance, therefore, flying and handling qualities are described qualitatively and are formulated in terms of pilot opinion; consequently, they tend to be rather subjective. The process involved in pilot perception of flying and handling qualities may be interpreted in the form of a signal flow diagram, as shown in Fig. 1.1. The solid lines represent physical, mechanical or electrical signal flow paths; the dashed lines represent sensory feedback information to the pilot. The author’s interpretation distinguishes between flying qualities and handling qualities as indicated. The pilot’s perception of flying qualities is considered to be a qualitative description of how well the aeroplane carries out the commanded task. On the other hand, the pilot’s perception of handling qualities is considered to be a qualitative description of the adequacy of the short-term dynamic response to controls in the execution of the flight task. The two qualities are therefore very much interdependent and in practice are probably inseparable. To summarise, then, flying qualities may be regarded as being task-related whereas the handling qualities may be regarded as being response-related. When the airframe characteristics are augmented by a flight control system, the way in which that system may influence the flying and handling qualities is clearly shown in Fig. 1.1. Figure 1.1 Flying and handling qualities of conventional aircraft. Most advanced modern aeroplanes employ fly-by-wire (FBW) primary flight controls, and these are usually integrated with the stability augmentation system. In this case, the interpretation of flying and handling qualities is modified to that shown in Fig. 1.2. Here the flight control system becomes an integral part of the primary signal flow path, and the influence of its dynamic characteristics on flying and handling qualities is of critical importance. The need for very careful...