Brought to you by: WWW. t- DYN CS " J< D AUTQMATIC ,:- e_ >. "' 1 '\ ~ ~",~" Jan Roskam ~, ~~ Part I ---- ~ Airplane. Flight Dynamics and Automatic Flight , Controls Jan Roskam Ackers Distinguished Professor of Aerospace Engineering The University of Kansas, Lawrence Part I 2001 DARco,.poraflon Pn ell Design.
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No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by ,~"any means, electronic or mechanical, photocopying, recording, or otherwise, 'without written permission of the publisher, DARcorporation. TABLE OF CONTENTS PART I SYMBOLS AND ACRONYMS vii INTRODUCTION 1 1. EQUATIONS OF MOTION AND AXIS SYSTEMS 3 1.1 COORDINATE SYSTEMS AND EXTERNAL FORCES 3 1.2 DERIVATION OF THE EQUATIONS OF MOTION 3 1.3 EFFECT OF SPINNING ROTORS 13 1.4 ORIENTATION OF THE AIRPLANE RELATIVE TO THE EAKI'H FIXED COORDINATE SYSTEM X'Y'Z' 14 1.5 THE AIRPLANE FLIGHT PATH RELATIVE TO THE EARTH 15 1.6 THE COMPONENTS OF THE GRAVITATIONAL FORCE 20 1.7 REVIEW OF THE EQUATIONS OF MOTION 21 1.8 STEADY STATE EQUATIONS OF MOTION 24 1.1 CASE 1: Equations of motion for steady state =tilinearflight 25 1.2 CASE 2: Equations of motion for steady state turning flight 26 1.3 CASE 3: Equations of motion for steady symmetrical pull-up 26 1.9 PERTURBED STATE EQUATIONS OF MOTION 27 1.10 SUMMARY FOR CHAPTER 1 32 1.11 PROBLEMS FOR CHAPTER 1 33 1.12 REFERENCES FOR CHAPTER 1 34 2. REVIEW OF AERODYNAMIC FUNDAMENTALS 35 2.1 DEFlNfTION OF AIRFOIL PARAMETERS 35 2.2 AIRFOIL AERODYNAMIC CHARACTERISTICS 35 2.1 Airfoil aerodynamic center 38 2.2 Airfoil lift curve slope 41 2.4 COEFFICIENTS AND REFERENCE GEOMETRIES 44 2.5 AERODYNAMIC CHARACTElUSTICS OF PLANFORMS AND FUSELAGE 45 2.1 Uft~urve slope 45 2.3 Zero-lift angle ofattack 49 2.4 Moment coefficient about the aerodynamic center 50 2.5 Down-wash, up-wash and dynamic pressure ratio 51 2.6 Effect of the fuselage on wing aerodynamic center 56 Contents -i- Thble of Contents 2.7 MODERN AIRFOILS COMPARED TO NACA AIRFOn.8 SUMMARY FOR CHAPTER 2 62 2.9 PROBLEMS FOR CHAPTER 2 63 2.10 REFERENCES FOR CHAPTER 2 64 3.
AERODYNAMIC AND THRUST FORCES AND MOMENTS 6S 3.1 STEADY STATE FORCES AND MOMENTS 67 3.1 Longitudinal aerodynamic forces and moments 71 3.4 Airplane aerodynamic pitching moment 80 3.5 Longitudinal thrust forces and moments 90 3.6 Assembling the steady state longitudinal forces and moments 93 3.7 Lateral-directional aerodynamic forces and moments 94 3.8 Airplane aerodynamic rolling moment 9S 3.9 Airplane aerodynamic side force 109 3.10 Airplane aerodynamic yawing moment 114 3.11 Lateral-directional thrust forces and moments 122 3.12 Assembling the steady state lateral-directional forces and moments 123 3.2 PERTURBED STATE FORCES AND MOMENTS 125 3.1 Perturbed state, longitudinal aerodynamic forces and moments 131 3.2 Aerodynamic force and moment derivatives with respect to forward speed 132 3.3 Aerodynamic force and moment derivatives with respect tu angle of attack· 137 3.4 Aerodynamic force and moment derivatives with respect to angle of attack rate 140 3.5 Aerodynamic force and moment derivatives with respect tu pitch rate 143 3.6 Aerodynamic force and moment derivatives with respect tu longitudinal control surface and flap deflections 145 3.7 Assembling the perturbed, longitudinal aerodynamic forces and moments 147 3.8 Perturbed srate, lateral-directional aerodynamic forces and moments 148 3.9 Aerodynamic force and moment derivatives with respect tu sideslip 148 3.10 Aerodynamic force and moment derivatives with respect tu sideslip rate 148 3.11 Aerodynamic force and moment derivatives with respect to roll rate 149 3.12 Aerodynamic force and moment derivatives with respect to yaw rate IS7 3.13 Aerodynamic force and moment derivatives with respect to lateral-directional control surface deflections 160 3.14 Assembling the perturbed, lateral-directional aerodynamic forces and moments 162 3.15 Perturbed state longitodinal and lateral-directional thrust forces and moments 162 3.16 Thrust force and moment derivatives with respect to forward speed 163 3.17 Thrust force and moment derivatives with respect to angle of attack 168 3.18 Thrust force and moment derivatives with respect to angle of sideslip 172 Contents - ii- Thble of Contents 3.19 Assembling the perturbed state longitudinal and lateral-<Iirectional thrust forces and moments 174 3.17 REVIEW OF IMPORTANT SIGN CONVENTIONS 3;3 OVERVIEW OF USUAL SIGNS FOR AERODYNAMIC COEFFICIENTS AND DERIVATIVES 175 3.4 SUMMARY FOR CHAPTER 3 175 3.5 PROBLEMS FOR CHAPTER 3 180 3.6 REFERENCES FOR CHAPTER 3 182 4. STABILITY AND CONTROL DURING STEADY STATE FLIGHT .1 INTRODUCTION TO STATIC STABILITY AND ITS CRITERIA 184 4.1 Static stability criteria for velocity perturbations 186 4.2 Static stability criteria for angle of attack and sideslip perturbations 191 4.3 Static stability criteria for angular velocity perturbations 193 4.4 Discussion of pitching moment due to forward speed and rolling moment due to sideslip stability· 195 4.2 STABILITY AND CONTROL CHARACTERISTICS FOR STEADY STATE, STRAIGHT LINE FLIGHT 197 4.1 Longitudinal stability and control characteristics for steady state, straight line flight 198 4.2 The airplane trim diagram 205 4.3 Stable and unstable pitch breaks 212 4.4 Use of windtunnel data in determining dE/da 214 4.5 Effect of thrust on the trim diagram 214 4.6 lateral-directional stability and control characteristics for steady state, straight line flight 216 4.3 STABILITY AND CONTROL CHARACTERISTICS FOR STEADY STATE, MANEUVERING FLIGHT 224 4.1 Stability and control characteristics for steady state, turning flight 224 4.2 Stability and control characteristics for steady state, symmetrical pull-up (push-over) flight 231 4.4 TRIM COMPARISONS FOR CONVENTIONAL, CANARD AND THREE- SURFACE CONFIGURATIONS 234 4.1 Trim of a conventional configuration 234 4.2 Trim of a canard configuration 235 4.3 Trim of a three-surface configuration 236 4.5 EFFECTS OF THE FLIGHT CONTROL SYSTEM ON STABILITY AND CONTROL IN STEADY STATE FLIGHT 238 4.1 Variation of stick-force and stick-force-speed gradient 240 4.2 Effect of control surface reversibility on static longitudinal stability 251 4.3 Another look at the stick-forco-versu .4 Calculation of stick-force-per-' g' 254 4.5 Effect of control surface tabs, down-spring and bob-weight 257 Contents -iii- Thble of Contents 4.1 Effect of trim tabs 257 4.2 Effect of balance or geared tabs 259 4.3 Effect of a blow-down tab 261 4.4 effect ofa down-5pring 264 4.5 Effect of a bob-weight 266 4.6 Stick force equation in the presence of a trim tab, dowD-5pring and bob-weight 266 4.6 LATERAL-DIRECTIONAL COCKPIT CONTROL FORCES 267 4.1 Rudder pedal controlforces 267 4.2 Pedal-free directional stability, pedal forces in sideslip and rudder lock 268 4.3 Aileron wheel (stick) control forces 270 4.1 Steady state roll rate 272 4.2 Steady state, straight line flight 274 4.7 A MATRIX APPROACH TO THE GENERALLONGlTUDINAL TRIM PROBLEM 275 4.8 A MATRIX APPROACH TO THE GENERAL LATERAL-DIRECTIONAL TRIM PROBLEM 283 4.9 THE TAKEOFF ROTATION PROBLEM 288 4.10 INTRODUCTION TO IRREVERSmLE FUGHT CONTROL SYSTEMS 293 4.11 SUMMARY FOR CHAPTER 4 296 4.12 PROBLEMS FOR CHAPTER 4 299 4. STABnJTY AND CONTROL DURING PERTURBED STATE FLIGHT 303 5.1 DYNAMIC STABlllTY AND RESPONSE BEHAVIOR OF A SPRING- MASs.,PAMPER SYSUlM AND ITS STABlllTY CRITERIA 309 5.2 WNGlTUDINAL, DYNAMIC STABlllTY AND RESPONSE 318 5.1 Longitudinal equations and transfer functions 318 5.2 Longitudinal characteristic: equation roots and their connection to dynamic stability 325 5.3 Connection between dynamic and static longitudinal stability 328 5.4 Examples of longitudinal transfer functions 329 5.5 The short period approximation 333 5.6 The phugoid approximation 338 5.7 Response to an elevator step input 340 5.8 Standard format for the longitudinal transfer functions 341 5.9 The longitudinal mode shapes 341 5.3 LATERAL-DIRECTIONAL, DYNAMIC STABILllY AND RESPONSE 346 ·5.1 Lateral-directional equations and transfer functions 346 5.2 Lateral-directional characteristic equation roots and their connection to dynamic stability 355 5.3 Connection between dynamic and static Iateral-directional stability 356 5.4 Examples of lateral-directional transfer functions 356 5.5 The dutch roll approximation. 363 Contents -iv- Thble of Contents 5.6 The spiral approximation 365 5.7 The roll approximation 367 5.8 Response to aileron and rudder step inputs 371 5.9 Standard format for the lateral-directional transfer functions 372 5.10 The lateral-directional mode shapes 372 5.4 CENTER-OF-GRAVITY AND DERIVATIVE ROOT-LOCI AND THE ROLE OF SENSITIVITY ANALYSES 378 5.1 Effect of center-of-gravity and mass distribution on longitodinal dynamic stability 378 5.2 Effect of stability derivatives on longitudinal dynamic stability 380 5.3 Effect of center-of-gravity and mass distribution on lat.4 Effect of stability derivatives on lateral-<lirectional dynamic stability 386 5.5 EQUIVALENT STABIlJTY DERIVATIVES, STABIlJTY AUGMENfATION AND DEPENDENCE ON CONTROL POWER 395 5.1 Equivalent pitch damping derivative 395 5.2 Equivalent yaw damping derivative 397 5.3 Equivalent longitodinal stability derivative 398 5.6 INERTIAL COUPLING DUE TO ROLL RAm AND PITCH RAm 400 5.1 Inertial coupling due to roll rate 400 5.2 Inertial coupling due to pitch rate 407 5.7 SUMMARY FOR CHAPmR 5 409 5.8 PROBLEMS FOR CHAPmR 5 409 5.9 REFERENCES FOR CHAPmR 5 412 6.
FLYING QUALITIES AND PILOT RATINGS, REGULATIONS AND APPLICATIONS 413 6.1 FLYING QUALITIES AND PILOT RATINGS 413 6.2 MILITARY AND C1VILIAN FLYING QUALITY REQUIREMENTS: INTRODUCTION AND DEFINITIONS 415 6.1 Definition of airplane classes 417 6.2 Definition of mission flight phases 417 6.3 Definition of flying quality levels and allowable failure probabilities 417 6.3 LONGITUDINAL FLYING QUALITY REQUIREMENTS 423 6.1 Longitudinal control forces 423 6.1 Control forces in maneuvering flight 423 6.2 Control forces in steady state flight 423 6.3 Control forces in takeoff and landing 426 6.4 Control forces in dives 426 6.3 Flight path stability 427 6.4 Short period frequency and damping 428 6.5 Control anticipation parameter 431 Contents -v- Thble of Contents 6.4 LATERAL-DIRECfIONAL FLYING QUALITY REQUIREMENTS 434 6.1 Lateral--<lirectional control forces 434 6.1 Roll control forces 434 6.2 Directional control forces with asymmetric loadings 435 6.3 Directional and roll control forces with one engine inoperative 435 6.2 Dutch roll frequency and damping 436 6.4 Coupled roU-spiral (=lateral phugoid) stability 437 6.5 Roll mode time constant 438 6.6 RoU control effectiveness 439 6.7 Yawing moments in steady sideslips 439 6.8 Side forces in steady sideslips 442 6.9 Rolling moments in steady sideslips 442 6.5 CHARACTERISTICS OF TIlE FLIGHT CONIROL SYSTEM 443 6.6 RELATION BETWEEN FLYING QUALITY REQUIREMENTS AND DESIGN 445 6.1 Design for roll control effectiveness 445 6.2 Design for inherent spiral·and dutch roll stability 446 6.3 Design for augmented static and dynamic stability in pitch 451 6.1 Effect of horizontal tail size on longitudinal stability and control derivatives 451 6.2 Stability augmentation by angle-of-attack and pitch-rate feedback 455 6.3 Effect of horizontal tail area on controllability in gust and on maneuvering 456 6.4 Effect of horizontal tail area on trim 457 6.7 SUMMARY FOR CHAPTER 6 459 6.8 PROBLEMS FOR CHAPTER 6 459 6.9 REFERENCES FOR CHAPTER 6 460 APPENDIX A: DESCRIPTION OF THE ADVANCED AIRCRAFT ANALYSIS (AAA) PROGRAM 461 AI GENERAL CAPABILITIES OF TIlE AM PROGRAM 461 A2 BRIEF DESCRIPTION OF AM PROGRAM MODULES 461 A3 STABILITY AND CONIROL CAPABILITIES OF TIlE AM PROGRAM 464 A4 REFERENCES FOR APPENDIX A 466 APPENDIX B: AIRPLANE DATA 479 APPENDIX C: SUMMARY OF LAPLACE TRANSFORM PROPERTIES 551 APPENDIX D ON THE EFFECT OF FREE, REVERSffiLE FLIGHT CONTROLS ON AIRPLANE DYNAMIC STABILITY 555 INDEX TO PART I 561 Contents -vi- SYMBOLSANDACRO~S Symbol Description Unites) Reglllar abw Moment arm of bobweight (see Figure 4.