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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. About the author: 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. New to this edition: 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). 0i_Front-matter......Page 1 Flight Dynamics Principles......Page 2 Copyright ......Page 3 Preface to the first edition......Page 4 Preface......Page 6 Preface to the second edition......Page 8 Acknowledgements......Page 10 Nomenclature......Page 12 Subscripts......Page 19 Examples of other symbols and notation......Page 20 1.1 Overview......Page 21 1.2 Flying and handling qualities......Page 23 1.3 General considerations......Page 24 1.3.2 Mathematical models......Page 25 1.4 Aircraft equations of motion......Page 26 1.5.1 Small perturbations......Page 27 1.6.2 Flight control computers......Page 28 Program CC, Version 5......Page 29 References......Page 30 Sources......Page 31 2.1 Earth axes......Page 32 2.2.1 Generalised body axes......Page 33 2.2.3 Perturbation variables......Page 34 2.2.4 Angular relationships in symmetric flight......Page 35 2.2.5 Choice of axes......Page 37 2.4 Axes transformations......Page 38 2.4.1 Linear quantities transformation......Page 39 2.4.2 Angular velocities transformation......Page 41 2.5.1 Wing area......Page 44 2.5.4 Aspect ratio......Page 45 2.5.7 Fin moment arm and fin volume ratio......Page 46 2.6.2 Engine control......Page 47 2.7 Aerodynamic reference centres......Page 48 References......Page 50 3.1.1 Preliminary considerations......Page 52 3.1.2 Conditions for stability......Page 53 3.1.3 Degree of longitudinal stability......Page 56 Power effects......Page 57 Other effects......Page 59 3.2.1 Simple development of the pitching moment equation......Page 61 3.2.2 Elevator angle to trim......Page 63 3.3.1 Controls-fixed stability......Page 64 3.3.2 Controls-free stability......Page 68 3.3.3 Summary of longitudinal static stability......Page 73 3.4 Lateral-directional static stability......Page 74 3.4.1 Lateral static stability......Page 75 3.4.2 Directional static stability......Page 80 3.5 Calculation of aircraft trim condition......Page 82 3.5.1 Defining the trim condition......Page 83 3.5.2 Elevator angle to trim......Page 84 3.5.3 Controls-fixed static stability......Page 85 3.5.4 “AeroTrim”: A Mathcad trim program......Page 86 Source......Page 89 4.1.1 The components of inertial acceleration......Page 91 4.1.2 The generalised force equations......Page 95 4.1.3 The generalised moment equations......Page 96 4.2 The linearised equations of motion......Page 98 4.2.1 Gravitational terms......Page 99 4.2.2 Aerodynamic terms......Page 100 4.2.4 Power terms......Page 102 4.2.5 The equations of motion for small perturbations......Page 103 4.3.1 The longitudinal equations of motion......Page 105 4.3.2 The lateral-directional equations of motion......Page 107 4.4.1 The dimensionless equations of motion......Page 108 4.4.2 The equations of motion in state space form......Page 111 4.4.3 The equations of motion in American normalised form......Page 117 References......Page 124 5.1 Methods of solution......Page 127 5.2 Cramer’s rule......Page 128 5.3 Aircraft response transfer functions......Page 130 5.3.1 The longitudinal response transfer functions......Page 131 5.3.2 The lateral-directional response transfer functions......Page 133 5.4 Response to controls......Page 135 5.5 Acceleration response transfer functions......Page 139 5.6.1 The transfer function matrix......Page 141 5.6.3 The lateral-directional transfer function matrix......Page 143 5.6.4 Response in terms of state description......Page 146 Eigenvalues and eigenvectors......Page 147 The modal equations......Page 148 Unforced response......Page 149 Step response......Page 150 Response shapes......Page 151 5.7 State-space model augmentation......Page 154 5.7.1 Height response transfer function......Page 155 5.7.2 Incidence and sideslip response transfer functions......Page 156 5.7.4 Addition of engine dynamics......Page 157 References......Page 160 6.1 Response to controls......Page 164 6.1.1 The characteristic equation......Page 169 6.2.1 The short-period pitching oscillation......Page 170 6.2.2 The phugoid......Page 171 6.3 Reduced-order models......Page 172 6.3.1 The short-period mode approximation......Page 173 The Lanchester model......Page 176 A reduced-order model......Page 177 6.4 Frequency response......Page 183 6.4.1 The Bode diagram......Page 185 6.4.2 Interpretation of the Bode diagram......Page 187 6.6 Mode excitation......Page 192 References......Page 196 7.1 Response to controls......Page 199 7.1.1 The characteristic equation......Page 207 7.2.1 The roll subsidence mode......Page 208 7.2.2 The spiral mode......Page 210 7.2.3 The dutch roll mode......Page 211 7.3 Reduced order models......Page 213 7.3.1 The roll mode approximation......Page 214 7.3.2 The spiral mode approximation......Page 215 7.3.3 The dutch roll mode approximation......Page 216 7.4 Frequency response......Page 220 7.5 Flying and handling qualities......Page 226 7.6 Mode excitation......Page 227 References......Page 231 8.1.1 Manoeuvring flight......Page 235 8.1.3 Aircraft handling......Page 236 8.2 The steady pull-up manoeuvre......Page 237 8.3 The pitching moment equation......Page 239 8.4.1 Controls-fixed stability......Page 241 8.4.2 Normal acceleration response to elevator......Page 243 8.4.3 Controls-free stability......Page 244 8.4.4 Elevator deflection and stick force......Page 248 8.5 Aircraft dynamics and manoeuvrability......Page 249 8.6 Aircraft with stability augmentation......Page 250 8.6.2 Stick force per g......Page 251 References......Page 257 9.1.2 Non-linear systems......Page 258 9.1.4 Control......Page 259 9.2 The characteristic equation......Page 260 9.3 The Routh-Hurwitz stability criterion......Page 261 9.3.1 Special cases......Page 263 9.4 The stability quartic......Page 265 9.4.1 Interpretation of conditional instability......Page 266 9.4.2 Interpretation of the coefficient E......Page 267 9.5.1 Root mapping on the s-plane......Page 268 References......Page 272 10.1.1 Stability......Page 274 10.2.1 Controlled motion and motion cues......Page 275 10.2.2 The longitudinal reduced order model......Page 276 10.2.3 The “thumb print” criterion......Page 281 10.3 Flying qualities requirements......Page 282 10.4.1 Aircraft classification......Page 285 Permissible flight envelope......Page 286 Operational flight envelope......Page 287 10.5 Pilot opinion rating......Page 289 10.6.1 Longitudinal static stability......Page 291 Short-period pitching oscillation......Page 292 Phugoid......Page 293 10.7 Control anticipation parameter......Page 294 10.8.1 Steady lateral-directional control......Page 296 Spiral mode......Page 297 Dutch roll mode......Page 298 10.9 Flying qualities requirements on the &ce:italic;s&/ce:italic;-plane......Page 299 10.9.1 Longitudinal modes......Page 300 10.9.2 Lateral-directional modes......Page 301 References......Page 305 11.1 Introduction......Page 307 11.1.2 Safety......Page 309 11.1.3 Stability augmentation system architecture......Page 310 11.2 Augmentation system design......Page 313 11.3 Closed-loop system analysis......Page 316 11.4 The root locus plot......Page 320 11.5 Longitudinal stability augmentation......Page 326 11.6 Lateral-directional stability augmentation......Page 333 11.7 The pole placement method......Page 344 11.8 Command augmentation......Page 349 11.8.1 Command path filter design......Page 350 11.8.2 The frequency response of a phase compensation filter......Page 352 11.8.3 Introduction of a command path filter to the system state model......Page 353 References......Page 362 12.1 Introduction......Page 366 12.2 Quasi-static derivatives......Page 367 12.3 Derivative estimation......Page 369 12.3.2 Wind tunnel measurement......Page 370 12.3.3 Flight test measurement......Page 371 12.4.1 Some useful definitions......Page 373 12.4.2 Aerodynamic models......Page 374 12.4.3 Subsonic lift, drag, and pitching moment......Page 375 12.4.4 Supersonic lift, drag, and pitching moment......Page 376 12.4.5 Summary......Page 377 References......Page 381 13.2.1 Preliminary considerations......Page 383 Xu ∘=∂X∂U Axial force due to axial velocity......Page 385 Zu ∘=∂Z∂U Normal force due to axial velocity......Page 386 Zw ∘=∂Z∂W Normal force due to normal velocity......Page 387 Mu ∘=∂M∂U Pitching moment due to axial velocity......Page 388 13.2.5 Derivatives due to a pitch velocity perturbation......Page 389 Xq ∘=∂X∂q Axial force due to pitch rate......Page 390 Mq ∘=∂M∂q Pitching moment due to pitch rate......Page 391 13.2.6 Derivatives due to acceleration perturbations......Page 392 Xw≐̸ ∘=∂X∂w≐̸ Axial force due to rate of change of normal velocity......Page 394 Mw≐̸ ∘=∂M∂w≐̸ Pitching moment due to rate of change of normal velocity......Page 395 13.3.2 Derivatives due to sideslip......Page 396 Yv ∘=∂Y∂V Sideforce due to sideslip......Page 397 Lv ∘=∂L∂V Rolling moment due to sideslip......Page 398 Nv ∘=∂N∂V Yawing moment due to sideslip......Page 405 Yp ∘=∂Y∂p Sideforce due to roll rate......Page 406 Lp ∘=∂L∂p Rolling moment due to roll rate......Page 407 Np ∘=∂N∂p Yawing moment due to roll rate......Page 409 13.3.4 Derivatives due to rate of yaw......Page 410 Yr ∘=∂Y∂r Sideforce due to yaw rate......Page 411 Lr ∘=∂L∂r Rolling moment due to yaw rate......Page 412 Nr ∘=∂N∂r Yawing moment due to yaw rate......Page 415 13.4 Aerodynamic control derivatives......Page 416 Xη ∘=∂X∂η Axial force due to elevator......Page 417 13.4.2 Derivatives due to aileron......Page 418 Yξ ∘=∂Y∂ξ Sideforce due to aileron......Page 419 Nξ ∘=∂N∂ξ Yawing moment due to aileron......Page 420 Yζ ∘=∂Y∂ζ Sideforce due to rudder......Page 421 13.5 North American derivative coefficient notation......Page 422 13.5.1 The longitudinal aerodynamic derivative coefficients......Page 424 13.5.2 The lateral-directional aerodynamic derivative coefficients......Page 428 13.5.3 Comments......Page 430 References......Page 447 14.1 The influence of atmospheric disturbances on flying qualities......Page 452 14.2 Methods of evaluation......Page 453 14.3.1 Steady wind......Page 454 14.3.4 Continuous turbulence......Page 455 14.4 Extension of the linear aircraft equations of motion......Page 457 14.4.1 Disturbed body incidence and sideslip......Page 458 14.4.2 The longitudinal equations of motion......Page 459 14.4.3 The lateral-directional equations of motion......Page 461 14.4.4 The equations of motion for aircraft with stability augmentation......Page 462 14.5 Turbulence modelling......Page 467 14.5.2 The Dryden model......Page 468 14.5.4 Turbulence scale length......Page 470 14.5.5 Turbulence intensity......Page 472 14.6.1 The “1-cosine” gust......Page 473 14.6.2 Determination of maximum gust velocity and horizontal length......Page 475 14.7.1 Variance, power spectral density, and white noise......Page 476 14.7.2 Spatial and temporal equivalence......Page 478 14.7.3 Synthetic turbulence......Page 479 14.7.4 Aircraft response to gusts......Page 481 14.7.5 Aircraft response to turbulence......Page 483 References......Page 495 15.1.2 Reporting......Page 497 15.2.2 The solution tasks......Page 498 15.3.1 The aircraft model......Page 499 15.3.3 Basic aircraft stability and control analysis......Page 501 15.4 Assignment 3: Lateral-directional handling qualities design for the Lockheed F-104 Starfighter aircraft......Page 502 15.4.1 The aircraft model......Page 503 15.4.3 Basic aircraft stability and control analysis......Page 504 15.4.4 Augmenting the stability of the aircraft......Page 505 15.4.6 Designing the aileron-rudder interlink gain......Page 507 Assessing the dynamic stability characteristics......Page 508 Assessing the effects of Mach number......Page 509 15.6.1 The aircraft model......Page 511 15.6.2 The design requirements......Page 513 Re-arranging the system state model with speed loop closed......Page 514 References......Page 515 3. Set up Velocity Range for Computations......Page 516 5. Wing-Body Aerodynamics......Page 517 9. Induced Drag Factor......Page 518 11. Trim Calculation......Page 519 14. Total Trim Forces Acting on Aircraft......Page 520 16. Trim Conditions as a Function of Aircraft Velocity......Page 521 17. Some Useful Trim Plots......Page 522 A2.1 Notes......Page 524 A3.1 Longitudinal Response Transfer Functions in Terms of Dimensional Derivatives......Page 531 A3.2 Lateral-Directional Response Transfer Functions in Terms of Dimensional Derivatives......Page 533 A3.3 Longitudinal Response Transfer Functions in Terms of Concise Derivatives......Page 534 A3.4 Lateral-Directional Response Transfer Functions in Terms of Concise Derivatives......Page 535 Appendix 4: Units, Conversions, and Constants......Page 537 Appendix 5: A Very Short Table of Laplace Transforms......Page 538 Appendix 6: The Dynamics of a Linear Second Order System......Page 539 Appendix 7: North American Aerodynamic Derivative Notation......Page 543 Appendix 8: Approximate Expressions for the Dimensionless Aerodynamic Stability and Control Derivatives......Page 545 A9.2 Force and Moment Transformation......Page 548 A9.3.1 Force-Velocity Derivatives......Page 549 A9.3.3 Force-Rotary Derivatives......Page 550 A9.3.4 Moment-Rotary Derivatives......Page 551 A9.3.5 Force-Acceleration Derivatives......Page 552 A9.3.7 Aerodynamic Control Derivatives......Page 553 A9.4 Summary......Page 554 A10.2.1 Body Axes to Wind Axes......Page 558 A10.3 Transformation of the Moment of Inertia in Roll from a Body Axes Reference to a Wind Axes Reference......Page 559 A10.4 Summary......Page 560 A11.1 Mathematical Background......Page 561 A11.2. Rules for Constructing a Root Locus Plot......Page 562 Rule 5......Page 563 Rule 8......Page 564 Index......Page 566 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. About the author: 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. New to this edition: Additional examples to illustrate the application of computational procedures using tools such as MATLABa, MathCada and Program CCa. 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)