Aircraft Performance And Engineering Approach 1st Edition Sadraey Solutions Manual

Contents Preface xv Author xix List of symbols xxi 1 Atmosphere 1 1.1 Introduction 1 1.2 General description of atmosphere 2 1.3 Major components 2 1.3.1 Oxygen and nitrogen 2 1.3.2 Carbon dioxide 3 1.3.3 Water vapor 4 1.3.4 Aerosols 4 1.3.5 Ozone 4 1.4 Atmospheric layers 4 1.4.1 Troposphere 5 1.4.2 Stratosphere 6 1.4.3 Mesosphere 6 1.4.4 Thermosphere 6 1.4.5 Ionosphere 7 1.5 International standard atmosphere 7 1.6 Atmospheric parameters 10 1.6.1 Temperature 10 1.6.2 Pressure 12 1.6.2.1 First layer 13 1.6.2.2 Second layer 14 1.6.3 Air density 16 1.6.4 Viscosity 17 1.7 Humidity 18 1.8 Altitude and its measurement 20 1.8.1 Pressure altimeter 23 1.8.2 Radar altimeter 23 1.8.3 Global positioning system 24 1.9 Speed of sound 24 viii CONTENTS 1.10 Atmospheric phenomena 27 1.10.1 Wind 27 1.10.2 Gust and turbulence 28 1.10.3 Icing 29 Problems 29 References 30 2 Equations of motion 33 2.1 Introduction 33 2.2 Aerodynamic forces 35 2.3 General governing equations of motion 39 2.3.1 Coordinate system 40 2.3.2 Unaccelerated versus accelerated ight 40 2.3.3 Flight phases 41 2.3.4 Steady-state ight versus perturbed-state ight 42 2.4 Application of Newton’s second law to ight phases 43 2.4.1 Straight-line ight 44 2.4.2 Climbing ight 46 2.4.3 Takeoff 48 2.4.4 Turn 49 2.5 True and equivalent airspeeds 50 2.5.1 Airspeed measurement 50 2.5.2 Airspeed indicator 52 2.5.3 Airspeed indicator corrections 52 2.5.4 Airspeed and ground speed 53 2.5.5 The unit of airspeed 54 2.6 Stall speed 55 Problems 59 References 62 3 Drag force and drag coefcient 63 3.1 Introduction 63 3.2 Drag classication 64 3.3 Drag polar 67 3.4 Calculation of C D o 71 3.4.1 Fuselage 72 3.4.2 Wing, horizontal tail, and vertical tail 74 3.4.3 High-lift devices 76 3.4.3.1 Trailing edge high-lift devices 76 3.4.3.2 Leading edge high-lift devices 77 3.4.4 Landing gear 78 3.4.5 Strut 78 3.4.6 Nacelle 79 3.4.7 External fuel tank 79 3.4.8 Cooling drag 80 3.4.9 Trim drag 81 3.4.10 C D o of other parts and components 82 3.4.10.1 Interference 82 3.4.10.2 Antenna 82 3.4.10.3 Pitot tube 83 3.4.10.4 Surface roughness 83 CONTENTS ix 3.4.10.5 Leakage 83 3.4.10.6 Rivet and screw 83 3.4.10.7 Pylon 83 3.4.10.8 Fairing for the ap mechanism 84 3.4.10.9 Compressibility 84 3.4.10.10 Icing 88 3.4.10.11 Refueling boom, receptacle, hose, probe, and drogue 88 3.4.10.12 External store 90 3.4.10.13 External sensors 90 3.4.10.14 Miscellaneous items 90 3.4.11 Overall CDo 90 3.5 Wave drag 91 3.5.1 Wave drag for wing and tail 92 3.5.2 Aircraft wave drag 98 3.6 CDo for various congurations 99 3.6.1 Clean conguration 100 3.6.2 Takeoff Conguration 100 3.6.3 Landing conguration 100 3.6.4 The effect of speed and altitude on CDo 101 Problems 103 References 108 4 Engine performance 109 4.1 Introduction 109 4.2 Aircraft engine classication 110 4.3 Piston or reciprocating engine 111 4.3.1 Piston engine congurations 112 4.3.2 Piston engine performance 113 4.3.3 Supercharged piston engines 117 4.4 Turbine engine 119 4.4.1 Turbojet engine 119 4.4.2 Turbofan engine 121 4.4.3 Turboprop engine 123 4.4.4 Turboshaft engine 125 4.4.5 Ramjet engine 126 4.4.6 Rocket engine 128 4.5 Other propeller-driven engines 131 4.5.1 Solar-powered engine 131 4.5.2 Electric engine 131 4.5.3 Human-powered engine 132 4.6 Engine performance criteria 133 4.6.1 Engine efciency 133 4.6.2 Engine performance at various altitudes and speeds 137 4.6.3 Specic fuel consumption 138 4.7 Engine performance calculations 143 4.7.1 Flat rating 143 4.7.2 Variations of power and thrust with aircraft speed 145 4.7.2.1 Piston-prop engine and turboprop engine 145 4.7.2.2 Turbojet engine 146 4.7.2.3 Turbofan engine 146 4.7.3 Variations of power and thrust with altitude 147 4.7.3.1 Piston engine 147 4.7.3.2 Turbojet engine 149 x CONTENTS 4.7.3.3 Turbofan engine 150 4.7.3.4 Turboprop engine 151 4.7.4 Variations of specic fuel consumption with altitude 152 4.7.4.1 Piston engine 152 4.7.4.2 Turbojet engine, turbofan engine, and turboprop engine 152 4.7.5 Variations of specic fuel consumption with speed 153 4.7.5.1 Piston engine 153 4.7.5.2 Turbojet engine 154 4.7.5.3 Turbofan engine 155 4.7.5.4 Turboprop engine 155 4.7.6 Power of electric engines 155 4.8 Propeller performance 156 4.8.1 Introduction 156 4.8.2 Denitions 157 4.8.3 Propeller classications 160 4.8.3.1 Fixed-pitch propeller 160 4.8.3.2 Ground adjustable propeller 161 4.8.3.3 Variable-pitch propeller 161 4.8.3.4 Constant-speed propeller 161 4.8.3.5 Special pitch modes 162 4.8.3.6 Contra-rotating propellers 163 4.8.4 Calculations 163 4.8.4.1 Propeller tip speed 163 4.8.4.2 Propeller twist angle 164 4.8.4.3 Modied momentum theory 166 4.8.4.4 Practical use of propeller charts 169 Problems 172 References 175 5 Straight-level ight: jet aircraft 177 5.1 Introduction 177 5.2 Fundamental equations 178 5.2.1 Steady-state trim equations 178 5.2.2 Drag, thrust, and velocity relationship 180 5.2.3 Velocity–angle-of-attack relationship 182 5.2.4 Maximum lift-to-drag ratio ((L/D)max) 183 5.3 Specic speeds in straight-line level ight 188 5.3.1 Maximum speed (Vmax) 189 5.3.2 Minimum drag speed 193 5.3.3 Maximum lift-to-drag ratio speed 197 5.4 Range 198 5.4.1 Denition 199 5.4.2 Calculation of range 200 5.4.2.1 Flight program 1: constant-altitude, constant-lift-coefcient ight 204 5.4.2.2 Flight program 2: constant-airspeed, constant-lift-coefcient ight 206 5.4.2.3 Flight program 3: constant-altitude, constant-airspeed ight 207 5.4.3 Speed for maximum range (VmaxR) 209 5.4.3.1 Constant-speed cruising ight 209 5.4.3.2 Non-constant-speed cruising ight 211 5.4.4 Calculation of maximum range 211 5.4.4.1 Constant-altitude, constant-lift-coefcient ight 211 5.4.4.2 Constant-airspeed, constant-lift-coefcient ight 212 5.4.4.3 Constant-altitude, constant-airspeed ight 212 CONTENTS xi 5.4.5 Practical considerations 214 5.4.5.1 Optimum fuel weight 214 5.4.5.2 Wind effect 215 5.4.6 Comparison and conclusion 219 5.5 Endurance 219 5.5.1 Denition of endurance 220 5.5.2 Endurance calculation 220 5.5.2.1 Flight program 1: constant-altitude, constant-lift-coefcient ight 221 5.5.2.2 Flight program 2: constant-airspeed, constant-lift-coefcient ight 222 5.5.2.3 Flight program 3: constant-altitude, constant-airspeed ight 222 5.5.3 Maximum endurance velocity 224 5.5.4 Maximum endurance 225 5.5.4.1 Constant-altitude, constant-lift coefcient 225 5.5.4.2 Constant-airspeed, constant-lift coefcient 226 5.5.4.3 Constant-altitude, constant-airspeed ight 226 5.5.5 Practical considerations 228 5.5.5.1 Altitude for maximum endurance 228 5.5.5.2 Comparison between tmaxR and Emax 228 5.5.5.3 Comparison between VmaxE and VmaxR 229 5.5.5.4 Effect of wind on endurance 229 5.6 Ceiling 230 5.6.1 Denition 230 5.6.2 Calculation 232 5.7 Cruise performance 236 5.7.1 Cruise speed 236 5.7.1.1 Based on engine chart 237 5.7.1.2 Based on range mission 238 5.7.2 Cruise altitude 239 Problems 246 References 251 6 Straight-level ight: propeller-driven aircraft 253 6.1 Introduction 253 6.2 Basic fundamentals 253 6.3 Specic speeds 256 6.3.1 Minimum power speed 256 6.3.2 Minimum drag speed ( ) VminD 263 6.3.3 Maximum lift-to-drag ratio speed 263 6.3.4 Maximum speed 265 6.4 Range 268 6.4.1 Introduction 268 6.4.2 Regular range calculation 268 6.4.2.1 Constant-lift-coefcient cruising ight 270 6.4.2.2 Non-constant-lift-coefcient cruising ight 271 6.4.3 Maximum range calculation 274 6.4.3.1 Constant-lift-coefcient cruising ight 274 6.4.3.2 Non-constant-lift-coefcient cruising ight 275 6.4.4 Maximum range speed 276 6.4.5 Comparison and conclusion 279 6.5 Endurance 281 6.5.1 Regular endurance 281 6.5.1.1 Flight program 1: constant-altitude, constant-lift-coefcient ight 283 xii CONTENTS 6.5.1.2 Flight program 2: constant-airspeed, constant-lift-coefcient ight 283 6.5.1.3 Flight program 3: constant-altitude, constant-airspeed ight 283 6.5.2 Maximum endurance speed for prop-driven aircraft 284 6.5.2.1 Flight program 1: constant-altitude, constant-lift-coefcient ight 284 6.5.2.2 Flight program 2: constant-airspeed, constant-lift-coefcient ight 284 6.5.2.3 Flight program 3: constant-altitude, constant-airspeed ight 285 6.5.3 Maximum endurance 285 6.5.3.1 Flight program 1: constant-altitude, constant-lift-coefcient ight 285 6.5.3.2 Flight program 2: constant-airspeed, constant-lift-coefcient ight 286 6.5.3.3 Flight program 3: constant-altitude, constant-airspeed ight 287 6.5.4 Comparison and conclusion 289 6.6 Ceiling 290 6.6.1 Denition 290 6.6.2 Absolute ceiling for aircraft with piston-prop engine 291 6.6.3 Absolute ceiling for aircraft with turboprop engine 293 6.7 Cruise performance 295 6.7.1 Cruise speed 295 6.7.1.1 Based on engine chart 296 6.7.1.2 Based on range mission 297 6.7.2 Cruise altitude 297 6.8 Summary and comparison 298 Problems 299 References 302 7 Climb and descent 305 7.1 Introduction 305 7.2 Basic fundamentals 306 7.3 Governing equations of climb 310 7.4 Fastest climb 317 7.4.1 Jet aircraft 318 7.4.1.1 Calculation of speed for maximum rate of climb 318 7.4.1.2 Calculation of climb angle for maximum rate of climb 320 7.4.2 Propeller-driven aircraft 324 7.4.2.1 Airspeed for maximum rate of climb 324 7.4.2.2 Climb angle for maximum rate of climb 325 7.5 Steepest climb 328 7.5.1 Jet aircraft 331 7.5.2 Propeller-driven aircraft 335 7.5.2.1 Calculation of aircraft speed for maximum climb angle 335 7.5.2.2 Calculation of maximum climb angle 337 7.6 Interim summary 339 7.7 Graphical analysis 339 7.8 Most-economical climb 341 7.9 Time to climb and fuel to climb 342 7.10 Descent 345 7.11 Gliding ight 350 7.11.1 Gliding ight with maximum ground distance 352 7.11.2 Gliding ight with maximum ight time 353 Problems 357 References 362 CONTENTS xiii 8 Takeoff and landing 363 8.1 Introduction 363 8.2 Takeoff principles 364 8.3 Takeoff performance analysis 370 8.3.1 Ground segment 371 8.3.2 Rotation segment 378 8.3.3 Airborne segment 379 8.4 Landing 386 8.4.1 Landing segments 386 8.4.2 Landing calculations 388 8.4.2.1 Approach section 388 8.4.2.2 Transition 390 8.4.2.3 Ground roll 391 8.5 Effect of wind and slope on takeoff and landing 396 8.5.1 Effect of headwind on takeoff 397 8.5.2 Effect of slope on takeoff 398 Problems 401 References 405 9 Turn performance and ight maneuvers 407 9.1 Introduction 407 9.2 Fundamentals of turning ight 409 9.2.1 Governing equations 409 9.2.2 Load factor and bank angle 412 9.2.3 Turn radius 415 9.2.4 Turn rate 417 9.3 Level turn performance: jet aircraft 421 9.3.1 Maximum producible load factor 422 9.3.2 Corner velocity 423 9.3.3 Maximum of the maximum load factor 425 9.3.4 Airspeed that corresponds to the maximum of the maximum load factor 426 9.4 Level turn performance: prop-driven aircraft 434 9.4.1 Maximum producible load factor 434 9.4.2 Airspeed that corresponds to the maximum of the maximum load factor 435 9.4.3 Maximum of the maximum load factor 436 9.4.4 Corner velocity 436 9.5 Maneuverability: jet aircraft 442 9.5.1 Fastest turn: jet aircraft 442 9.5.2 Tightest turn: jet aircraft 448 9.6 Maneuverability: prop-driven aircraft 455 9.6.1 Fastest turn: prop-driven aircraft 455 9.6.2 Tightest turn: prop-driven aircraft 459 9.7 Vertical maneuvers 464 9.7.1 Pull-up and pull-out 465 9.7.2 Pull-down 468 9.8 Zero-gravity ight 469 9.8.1 Orbital ight 470 9.8.2 Free fall cruise 470 9.9 V-n diagram 474 9.9.1 Flight envelope 474 xiv CONTENTS 9.9.2 Load factor 475 9.9.3 Maneuver diagram 477 9.9.4 Gust V-n diagram 478 9.9.5 Flight envelope: combined V-n diagram 481 Problems 486 References 490 10 Aircraft performance analysis using numerical methods and MATLAB® 491 10.1 Introduction 491 10.2 Takeoff rotation analysis using numerical methods 492 10.2.1 Mission analysis 492 10.2.2 Governing equations 492 10.3 Free fall simulation 495 10.3.1 Flight analysis 495 10.3.2 Governing equations 495 10.4 Takeoff airborne section analysis using numerical methods 500 10.4.1 Mission description 500 10.4.2 Governing equations 500 10.5 Climb analysis using numerical methods: construct the hodograph 504 10.5.1 Review of fundamentals 504 10.6 Fastest climb analysis using numerical methods 506 10.6.1 Fastest climb analysis 506 10.7 Time to climb analysis using numerical methods 509 10.7.1 Review of fundamentals 509 10.8 Parabolic path for a zero-gravity ight 510 10.8.1 Mission analysis and governing equations 510 Problems 513 References 515 Appendix A: Standard atmosphere, SI units 517 Appendix B: Standard atmosphere, English units 519 Appendix C: Performance characteristics of several aircraft 521 Appendix D: Flight records 527 Appendix E: A typical project for students 537 Index 539 xv Preface Flight is the process in which a vehicle moves through the air without any direct mechanical support from the ground. In physics, the science of the action of forces on material bodies is referred to as mechanics. Mechanics is basically divided into two branches: (1) dynamics and (2) statics. The branch of mechanics that deals with the motion of objects in relation to force, mass, momentum, and energy is referred to as dynamics. Flight mechanics (or ight dynamics) is the study of the motion of ying objects (e.g., aircraft, missile) through air. It covers two main areas: 1. Flight performance 2. Flight stability and control As aircraft do not usually have a static motion (except for VTOL aircraft), we mostly deal with ight dynamics. On the other hand, there are two types of aircraft motions: (1) steady-state motion and (2) perturbed-state motion. It is customary that steady-state motion be studied in a course called ight dynamics I and that perturbed-state motion be studied in ight dynamics II. In some institutions, ight mechanics is referred to as ight dynamics I, and ight stability and control is referred to as ight dynamics II. The rst topic (ight dynamics I) includes subjects such as maximum speed, absolute ceiling, rate of climb, range, endurance, turn performance, and takeoff run. The second topic (ight dynamics II) is mainly to examine such subjects as aircraft trim, control, stability, maneuverability, and ying qualities. The subject of aircraft performance mainly deals with the forces applied to the aircraft, but the subject of ight dynamics concentrates on various moments (either aerodynamic or non-aerodynamic) that determine the trajectory. Time span in aircraft performance is mostly in the range of hours, but time span in ight dynamics is primarily in the range of seconds. The objective of this book is to introduce ight performance analysis techniques of xed-wing air vehicles, particularly heavier-than-air craft. This subject will be interesting for aeronautical/mechanical engineers, aircraft designers, pilots, aircraft manufacturing companies, airlines, air forces, and primarily students of the eld of aeronautical/ aerospace engineering. This group of people often face the following questions: 1. How fast can this airplane y in a cruising ight? 2. How high can this airplane y? 3. How far can this airplane y? 4. How long must be the runway for takeoff? 5. How long can this airplane be airborne? 6. How fast can this airplane climb to a certain altitude? 7. How fast can this airplane turn? 8. How tight can this airplane turn?