Index A Accelerating climb, 353, 355 Acceleration sensitivity, 958 963 Ackert s theory, 775 Adams-Bashfourth-Moulton, 1021, 1026 1027, 1033 1034, 1038 Adams-Moulton, 748 Additional section lift, 85 87, 108 Adiabatic, 19, 131 Advance angle, 173 174, 176, 186, 219 Advance ratio, 183 192, 197, 199, 214, 225 226, 478 479, 508, 513 Adverse yaw, 81, 337, 570 571, 691 Aerodynamic, 1 angle, 498 499, 525, 597 angle of attack, 63, 74, 78, 80, 175, 185, 189, 219 balance, 635, 637 coefficients, 3, 183, 224, 262, 497, 508, 684, 721, 723, 748, 773 774 controls, 605 coordinates, 1 2, 518, 717 coupling, 924, 928, 934 935, 986 derivatives, 500, 504, 565, 768 788, 846, 914, 917, 924 drag, 260 261, 338 efficiency, 262, 264, 266, 389, 426 force, 1 4, 14, 18, 28 30, 46, 49, 94, 99 107, 143, 259, 403 force vector, 102 hinge moment, 633 hysteresis, 942 moment, 1 4, 103 105, 107, 259, 403, 437, 455, 474, 497, 499, 548 nondimensional derivatives, 792 794 pitch angle, 169 170, 173, 175, 181 182, 185 186, 218 219 pitch length, 170, 183, 185 pressure, 403, 455 properties, 26 torsional spring, 752 twist, 51 55, 57 58, 63, 72, 553 554 yaw departure, 940 Aerodynamic center, 5 7, 30, 45, 120 130, 145, 381 395, 400, 403, 413, 420, 422, 424 425, 427, 430, 436, 438, 448, 453 472, 555, 560 561, 608, 624, 625, 635, 645, 647, 688 (see also Neutral point) definition, 458 459 general relations for, 464 471 ideal, theoretical, 30 of drag, 460 of lift, 460 semispan, 88 93 traditional approximation, 462 463 two-surface small-angle approximation, 471 472 vertical offset, 436 472 wings with constant sweep and dihedral, 463 Aerodynamics, 1, 3, 20, 28, 49, 135, 139 compressible, 131 inviscid, 16, 28 inviscid compressible, 131 134 overview, 1 Aeroelastic bending, wing, 679 Aeroelasticity, 624, 877 Aft CG limit, 615 620, 660, 967 968 Aft tail, 384 385, 389 390, 394 395, 436 437, 624, 627, 631, 634 636, 661 666 estimating downwash angle on, 411 421 Afterburner, 164, 241 242 Aileron, 9, 72 82, 377, 549, 567 568, 596 597, 666, 691 angle, 73, 567 568 deflection, 73 76, 78, 80 82, 567 570, 596 597, 680 681 Frise, 691 response, 921 reversal, 679 reversal speed, 681 saturation, 582, 584, 585, 589, 591 593 sizing, 574, 595, 921 Air density, 132 133, 230, 265, 268, 272 273, 277, 279, 282, 284, 287 289, 293 294, 298 299, 304, 311, 316, 327, 331 332, 345 346 Aircraft, 1, 10 11, 14 18, 48, 53, 94, 107 131, 138, 153 168, 245, 253 control response, 953, 976 986 controls, 605 design, 259, 263 264, 272, 565 dynamics, 727 engine, 154 155, 157, 190, 200, 236 237 equations of motion, 715, 719 fixed wing, 74, 681 flight simulation, 989 1060 handling qualities, 953 986 maneuverability, 605 performance, 16, 259 805 plane of symmetry, 95, 497 COPYRIGHTED MATERIAL 1113
1114 Index position, 1044 propulsion, 153 168, 191, 253 stability, 223, 380 381, 436, 447 stability and control, 225, 259 state, 957 tailless, 453, 517, 565 weight, 279, 292, 322, 356 Airflow, 1, 47, 131 Airfoil, 4, 26 28, 144, 318 cambered, 143 coordinates, 33 34 modern, 318 section, 3, 5, 26, 28, 32, 34, 38 50, 95 96, 100, 134, 138, 168, 384, 388, 427, 448 section geometry, 16 section moment data, 30 section theory, 50 supercritical, 139 supersonic, 138, 143, 145 symmetric, 26, 30, 143, 145, 318, 384, 388 393, 395 theory, 39 thickness, 28, 30, 38, 45 thin, 28, 134, 143, 145 Airplane high-wing, 558 560 low-wing, 558 spin, 693 695, 703, 706 spin-resistant, 705, 706 stall, 693 Airscrew, 170 (see also Propeller) Airspeed, 14, 16, 81, 158 161, 164, 171 179, 190 191, 197, 200, 216 219, 231 232, 259 368, 377 379, 387, 392 393, 397, 439, 557, 719 best climb, 281 best glide, 310 316 design, 318, 393 forward, 173 176, 187, 190, 207, 216 freestream, 205 indicated, 327, 331 landing, 351 352, 411 liftoff, 344 345, 411 maximum, 274 277 maximum endurance, 291 293, 299, 301 maximum range, 296 302, 305 minimum, 259, 317 minimum-control, 582 596 minimum drag, 264, 267, 296, 299 301 minimum power, 273, 307 minimum sink, 307 308 minimum thrust, 273 optimum, 265 subsonic, 155, 165, 168 supersonic, 144, 164, 253 true, 327 VNE, 325 326 All-flying tail, 385, 682, 687 All-movable trim adjustment, 688 689 Altitude, 10 12, 17, 190, 264 265, 272 273, 281 282, 289, 292, 294, 297 298, 305 307, 311, 327, 358, 377, 989, 1044 1049, 1052 1055, 1057 density, 306 geometric, 10, 17 geopotential, 10 11 obstacle clearance, 353 361, 364 Ambient pressure, 153, 203, 233 234, 246, 483 temperature, 237, 245 Amphibian, 456 Amplification factor, 817 818 (see also Dynamic gain) Angle advance, 173 174, 176, 186, 219 aerodynamic, 498 499, 525, 597 aerodynamic pitch, 169 170, 173, 175, 181 182, 185 186, 218 219 aileron, 73, 567 568 azimuth, 736, 990 (see also Heading) bank, 260, 321 324, 336, 497 499, 548 549, 736, 901, 990 climb, 260, 278, 282 286, 309, 321 324, 332 334, 357 360, 386, 392, 437 crab, 295 dihedral, 95, 550, 554, 565 566 downwash, 173 174, 176, 218 219, 387, 390 391, 394 395, 411, 413, 415, 417 420, 479 480, 484, 509, 571 Euler, 735 743, 753 754, 759, 927, 989 990 elevation, 437, 696, 736, 990 ground track, 295 heading, 295, 736 (see also Azimuth angle) induced, 173, 175, 181, 183, 218 Mach, 140, 142 143 orientation, 499 phase, 818 pitch, 169 170, 176, 180, 182, 185 186, 219 roll, 78 sideslip, 225, 497 503, 508 511, 516 519, 526, 548 549, 551, 557, 719, 721, 901 sidewash, 502 503, 509, 519 sweep, 95 96, 417 418 thrust, 171, 262, 265 270, 274, 278 279, 296, 320, 338 upwash, 422, 424 425, 428, 479 wind direction, 295 wind-track, 295, 308
Index 1115 Angle of attack, 3 5, 14 16, 28 32, 37 42, 45, 52 58, 75, 99 100, 107, 143, 185, 189, 200, 216, 219, 225, 246, 262 263, 266, 334 335, 338, 340, 344 346, 379 386, 390 403, 413, 423, 437 440, 443 444, 448 449, 453 455, 474, 476, 478, 484, 499 501, 523, 548, 611, 719 aerodynamic, 63, 74, 78, 80, 175, 185, 189, 219 blade, 189 190, 218 differential in, 551 effective, 50, 391, 411 equilibrium, 392, 730, 804 fuselage, 393, 396, 429 geometric, 51, 73 74 high, 15, 940 942, 987 induced, 50 51, 78, 96 local aerodynamic, 63, 74 local section, 50, 101, 106, 176, 183 low, 14 optimum, 349 propeller, 171 172, 201, 216 220, 222, 225, 480, 508 510, 513 515 small, 134 trim, 450 zero, 143, 391, 395 396, 404, 406, 428, 448, 450, 480, 484 zero-lift, 30 31, 40 42, 51, 59, 170, 184 185, 390, 424 Angular momentum equation, 206 207, 212 Anhedral, 95, 550 Area, 3 4 characteristic, 473 frontal, 3, 473 planform, 3, 53, 96 wing, 259, 265, 318, 345 Area rule, 139 Aspect ratio, 49, 53 54, 57, 62, 66 67, 70, 76, 83, 96, 102, 105 106, 262, 269, 272, 275, 318, 389, 391, 412 413, 415, 420, 426 428, 448 449, 505, 527, 552, 870 apparent, 505 effective, 505, 527 528 high, 102, 265 low, 106 true, 527 528 Atmosphere, 10 14 desert, 11 polar, 11 standard, 11, 14 Atmospheric pressure, 14 Atmospheric temperature, 14 Attitude, 380, 387, 423 descriptors, 1004 equilibrium, 379 381 liftoff, 337 quaternion representation, 1007, 1010 Autopilot, 969, 985 986 Axis of propeller rotation, 171, 173, 176, 216 Azimuth angle, 736, 990 (see also Heading) constraint, 1014 B B-17 Flying Fortress, 157, 159 B-29 Superfortress, 157 Bairstow approximation, 858 Balanced field length, 353 355, 363 365 Bank angle, 260, 321 324, 336, 497 499, 548 549, 736, 901, 990 load-limited, 323 324 maximum, 322 324 regulatory limit, 589 stall-limited, 322 324 Basic section lift, 85 87, 108 Beech Bonanza, 690 Bell Airacomet, 161 162 Bernoulli s equation, 203, 208 Betz condition, 179, 199, 217 Bifilar pendulum, 884 Biot-Savart law, 25, 412, 417, 518 Blade angle of attack, 189 190, 218 drag, 190, 200 interference, 159 section, 173, 175, 189, 218 wake, 199 Blade-tip vortex, 177 179, 215 helical, 215 Body, 3 (see also Fuselage) axis, 1 bluff, 3, 15 -fixed stability and control coordinates, 7 8 streamlined, 14, 15 Body force, 668 Boeing 707, 163 Boeing 747, 165 Boundary conditions, 38 Boundary layer, 14 17, 19, 42, 134, 138, 146, 199 concept, 14 equations, 14 flow, 14, 38 separation, 15 16, 29, 42, 138 solution, 39 theory, 14, 38 viscous, 14, 16 wake, 16 Bow shock, 143
1116 Index Brake power, 159, 171, 182, 184, 189 197, 205, 212 213, 293 British Fairey Delta, 597 British Spitfire, 158 159, 385, 487 488, 514, 599 Bypass ratio, 164, 245, 248 253 C C-130 Hercules, 166, 558 560 Camber, 26 28, 39, 84, 143 145 line, 26 28, 30 31, 37 42, 143, 145 maximum, 27, 30, 32 negative, 384 positive, 384, 390 Camber line geometry, 40 42 Camber line ordinate, 40 Cambered wing, pitch stability of, 381 384 Canard, 421 437, 449 453, 608 lift coefficient, 424, 426, 432 lift slope, 424 movable, 666 volume ratio, 425 426, 429 Cartesian aerodynamic coordinates, 1 2, 518, 717 Ceiling absolute, 282 service, 282 Center of aerodynamic force, 468 Center of drag, 460, 468 Center of gravity, 381 383, 386 395, 399 407, 422 425, 435 436, 439, 444 445, 448, 453 473, 500 501, 504 506, 560 limits, 407, 615 623, 646 661, 967 968 low, 664 vertical position, 663 Center of lift, 460, 468 Center of pressure, 5, 29 30, 145 fuselage, 473 474 Center of thrust, 386, 395, 422, 436 Center of vorticity, 415 417 Centripetal acceleration, 606, 616, 668, 698 Centroidal chord, 88 93 CFD, 39, 96, 105 107, 474, 482 Characteristic length, 99, 103 Characteristic polynomial, 974 Chord, 2, 27, 41 centroidal, 88 93 flap, 41 geometric mean, 83 length, 2 3, 27, 30, 51, 54 55, 59, 63, 77, 103, 175 176, 183 186, 200, 220 line, 1 5, 26 27, 46, 98, 143, 261 mean aerodynamic, 84, 89, 460 root, 55 tip, 55 Chord length ratio, 183 184, 186 Circulation, 21, 24, 48, 51, 78, 94, 98, 177, 180 181 distribution, 52, 55, 75 local section, 51, 177 vector, 555 Climb, 277 287 accelerating, 353, 355 Climb angle, 260, 278, 282 286, 309, 321 324, 332 334, 357 360, 386, 392, 437 load-limited, 333 334 stall-limited, 333 steady, 358 Clustering, 32, 104 cosine, 32 33, 104 105 Cobra maneuver, 334, 987 Coefficient, 3 4 axial force, 3 drag, 3 4, 15 16, 30, 52 55, 58, 62, 107, 138, 145 induced drag, 52 55, 58 59 lift, 3, 15 16, 30, 38, 41 42, 52 63, 66, 80, 106, 135, 146, 175, 182 183, 200, 262 267, 271 272, 277, 283 284, 310, 317, 320, 322, 334, 336 340, 344, 346, 357 360, 382 383, 387 391, 396, 398, 401, 411 412, 415, 424, 449 451, 455, 608 moment, 3, 5, 29, 36, 42, 135, 145 146, 382, 387, 392, 449, 609 normal force, 3, 5 pressure, 135 137, 142 143 yawing moment, 78 81 Cofactor, 973, 975 Combustion chamber, 228, 233 235, 237, 241, 247 Complex amplitude, 984 Compressibility, 131, 159, 196 Compressible flow theory, 230 Compressible subsonic flow, 134 139 Compressor, 228, 233, 237 238, 246 inlet, 234 235 outlet, 234 Computational fluid dynamics (CFD), 39, 96, 105 107, 474, 482 Conservation of mass, 203, 208 Constant-speed pull-up maneuver, 606 607 Constraint azimuth angle, 1014 design, 318 elevation angle, 1014 pitch, 1014 roll, 1013 rotational, 1013
Index 1117 yaw, 1014 Continuity equation, 16 18, 210 Contrails, 177 178 Control, 9, 48, 682 alternative, 666 anticipation parameter, 960, 962, 963, 967 automatic, 985 column, 632 derivatives, 597 inputs, 968 irreversible, 633 lateral, 666 loader, 633 longitudinal, 605, 669 orthogonality, 1026 1028 pitch, 9, 72, 385, 426, 472, 605, 632, 637, 638 641, 644, 655 658, 682 687 (see also All-flying tail; Elevator; Stabilator; V-tail) reversible mechanical, 633 roll, 9, 72 73, 567, 570, 691 692, 969 (see also Ailerons; Spoilers) stick, 632 surface deflection, 72, 74, 424 434, 670, 672, 675 weight-shift, 407 411 wheel, 632 yaw, 9, 504, 570, 692, 693, 704, 941, 969 (see also Rudder; V-tail) yoke, 632 Control derivative, 504, 512, 570, 597, 627, 681 Control force, 632 derivative, 639 gradient, 632, 637, 640, 643, 654, 660 in ground effect, 655 658, 661 per g, 637, 640, 643, 660 pitch, 605, 639, 656 658 Control point, 32 35, 99 105 Control problem generalized linear, 970, 977, 981 special linear, 970, 972, 978 Control response, 953, 968 986 Control reversal aileron, 679 elevator, 632 Control surface, 9, 72 asymmetric, 72 deflection, 72, 74, 424 434, 670, 672, 675 distribution function, 74, 80 effectiveness, 425 geometry, 76 hinge moment, 633 other configurations, 682 693 sign convention, 9, 73, 437, 513, 567, 597 598, 635, 676, 683, 918 spanwise asymmetric, 72 Control system, 633 autopilot, 969, 985 986 digital, 953 fly-by-wire, 633, 646, 692, 953 gain coefficient, 692 Control theory automatic, 986 classical, 985 modern, 985 optimal, 986 Control volume, 153 154, 228 229 Cooper-Harper rating scale, 954 955 Coordinated maneuver, 666, 668 turn, 322 324, 328 331, 337, 926, 927, 936 937 Coordinates, 1, 21, 523, 715 716 aerodynamic, 1 2, 518, 717 airfoil, 33 34 atmosphere-fixed, 717, 719, 726 body-fixed, 697 698, 717 718, 725, 735, 739, 741, 769, 770, 798, 926, 989, 993, 995 Cartesian, 717, 1044 Earth-fixed, 717 718, 735, 739, 741, 926, 989, 993, 995 fixed, 718 flat-earth, 967, 1044 geographic, 1044 1063 inertial, 717, 727, 732, 734, 735, 758, 989 990, 992, 995, 1002 nodal, 33 noninertial, 989 991, 995, 1002 panel, 33 polar, 21 right-hand, 499 surface, lower, 27 28 surface, upper, 27 28 transformation, 135 Corbett-Wright gain coefficient, 1022 1026, 1029 orthogonality control, 1021 1026, 1029, 1038 Coriolis acceleration, 732 Coriolis forces, 930 Cosine clustering, 32 33, 104 105 Crab angle, 295 Critical engine failure speed, 354 355, 364 365 Curl, 16, 18, 20 Curved vortex sheet, 32
1118 Index Cycle analysis, 233 D Damped natural frequency, 736, 814 817, 839, 888, 890 Dutch roll, 891, 912 lateral mode, 888 phugoid/long period, 843, 854, 856, 864 short-period, 842, 848 Damped sinusoid, 814, 815, 825, 976 Damping Dutch roll, 891, 895, 909, 911 912, 916 919, 939, 943 944 drag, 869 870 phase, 863, 869 870 phugoid/long period, 854, 857, 863, 869 871, 939, 964 pitch, 610, 845, 869 870, 979 rate, 814 817, 839, 855, 888, 896, 899 901, 911 912 ratio, 815 818, 839, 888, 891, 960, 964, 966 requirements, 960 968 roll, 78, 895, 909, 914, 939, 965 short-period, 845, 848, 939, 963 964, 979 spiral mode, 901, 917, 939, 965 yaw, 918, 981 Decay rate, 816 (see also Damping) Deflection, 41 aileron, 73 82, 567 570, 596 597, 680 681 control surface, 72, 74, 424 434, 672, 675 efficiency, 43 44, 81 elevator, 389 400, 405 408, 438 444, 448, 606, 611 flap, 39 46, 99 100 rudder, 503 504, 510 515, 570 596, 676 Degrees of freedom, 497 lateral, 497, 596 longitudinal, 497, 596 DeHavilland Dash 8, 166 Derivatives (see also Gradient) aerodynamic, 500, 504, 565, 768 788, 846, 914, 917, 924 control, 597 force and moment, 768 788 nondimensional, 792 794 Design, 45, 260, 565, 597 aircraft, 259, 263 264, 272, 565 airspeed, 318, 393 constraint, 318 final, 259 260 parameters, 259 260, 263 preliminary, 45, 107, 259 260, 388 391, 411, 418, 473, 505 506, 515, 527 528 requirements, 259 tail, 524 525 Differential equations, 135 elliptic, 135 hyperbolic, 135, 139 partial, 135, 139 Differential operator, 733 Dihedral, 52 55, 94 98, 104 105, 413, 415, 517, 519, 558 angle, 95, 550, 554, 565 566 factor, 554, 565 tail, 529 547 Dihedral effect, 548, 550, 565 566 fuselage, 565 566 vertical stabilizer, 566 Dimensionless, 3 4, 75 77, 99 104, 107 Direction cosine, 992 formulation, 992 993, 1000, 1038 matrix, 992 transformation, 1004 Direction of flight, 261 (see also Heading) Distance acceleration, 337 338, 344 345, 349, 351, 361 braking, 351 352 FAR takeoff, 353 355, 358, 361 364 free-roll, 351 352 ground roll, 337, 353 liftoff, 337 rotation, 337 338, 344, 347, 351 Disturbance (see also Perturbation) lateral, 730, 885, 904 longitudinal, 730, 885 pitch, 451 452 roll, 904 to steady equilibrium flight, 730 yaw, 500, 904 Divergence directional, 904 drag, 138, 776 pitch, 939 940 spiral, 893 894, 897, 901, 904, 965 Divergent mode, 834 835, 858, 876, 942 Doublet, 21 Doubling time, 834, 893 894, 965 Douglas X-3 Stiletto, 524 Downwash, 48, 50, 94 96, 104, 172 177, 179, 340, 390 391, 411, 413, 415, 417 420, 449, 478, 484, 523, 564 angle, 173 174, 176, 218 219, 387, 390 391, 394 395, 411, 413, 415, 417 420, 479 480, 484, 509, 571 distribution, 390 gradient, 397, 420, 480, 484, 505, 509, 571 induced, 177, 416
Index 1119 uniform, 63 velocity, 391, 411 413 Drag, 2 3, 168, 171 174, 189, 216, 219 220, 228, 259 260, 267, 278, 296, 337, 339 340, 347, 379 380 additive, 229 232 aerodynamic, 260 261, 338 blade, 190, 200 coefficient, 3 4, 15 16, 30, 52 55, 58, 62, 107, 138, 145 curve, 138 damping, 869 870 divergence, 138, 776 effects of, 436 472 force, 2, 171, 174, 219, 228, 261 262, 277, 357, 381, 403, 455 induced, 50, 52 66, 171, 173, 176, 220, 262, 264, 272, 278, 339 340, 357, 380, 389, 425, 517 level flight, 278, 317 local section, 175 176 minimum, 298 299, 318 319 nacelle, 229, 232 nonlinear, 447 parasitic, 107, 171, 176, 200, 220, 262, 264 265, 272, 339 pre-entry, 229 section, 30, 145, 220 trim, 409 411 viscous, 146 wave, 145 146 zero-lift, 272, 318 Drag coefficient, 3, 176, 182 184, 200, 220, 265, 267, 336, 338, 345 347, 352, 357 360, 448 450 constant, 346 parasitic, 262, 265, 318 319 zero-lift, 319, 340, 346 Drift error, 1023, 1026 1028, 1038 Ducted fan, 165, 245 Dutch roll, 886, 893, 895, 906 919, 943 945, 966, 981, 983 amplitude, 892, 895, 907 approximation, 906 919 coupling ratio, 911, 912, 914, 917 damped natural frequency, 891, 912 damping, 891, 895, 909, 911 912, 916 919, 939, 943 944 eigenvalues, 906, 909 916, 983 eigenvectors, 891, 892, 906, 907, 913 frequency, 892, 909, 911, 916, 966 handling qualities, 966 mode, 886, 891, 892, 895, 912, 944 oscillation, 891, 895, 944 945 period, 893, 939 phase, 892 phase-divergence ratio, 911, 912, 914, 917 stability ratio, 911, 912, 914, 916 undamped natural frequency, 892, 916 Dynamic angular rates, 670 Dynamic frequency response, 984 Dynamic gain, 984 (see also Amplification factor) Dynamic handling quality predictions, 958 968 Dynamic margin, 615 620, 660, 853, 961 Dynamic pitch rate, 616, 670, 678, 679, 960 Dynamic pressure, 383, 387 388, 423 ratio, 504 Dynamic roll rate, 670 Dynamic yaw rate, 670 Dynamics, fundamentals of, 813 836 (see also Eigenproblem) E Earth, 1044 1063 ellipsoidal model, 1044 1051 equatorial plane, 1045 1046 equatorial radius, 1045 1046, 1051 polar axis, 1045 1046, 1052 polar radius, 1045 1046, 1051 spherical approximation, 1051 1057 Effective headwind, 297 Efficiency, 155, 158 159, 164 168, 191, 193, 197, 199, 245, 249 253 aerodynamic, 262, 264, 266, 389, 426 deflection, 43 44, 81 fuel, 168 hinge, 43 44, 81 ideal, 205 maximum, 159, 187, 190 191 propeller, 155, 158 159, 190 191, 200, 293 tail, 388 thermal, 236 250 thermodynamic, 168 Eigenaxis, 993 Eigenproblem, 813 836, 885 generalized, 819, 822, 826 827, 838, 887 special, 826 827, 838, 887 Eigenvalue, 814, 819 820, 823, 825 830, 834 835, 837 839, 886 888 complex, 814, 816 817, 823, 836 Dutch roll, 906, 909 916, 983 dimensionless, 839, 848, 855 856, 864, 867, 900 phugoid/long period, 843, 855, 856, 858, 861 864, 867 868 pure pitching motion, 873 pure yawing motion, 923
1120 Index real, 814, 823 rigid-body displacement mode, 834, 844, 892 roll mode, 893, 896 897 short period, 842, 847 849, 983 spiral mode, 897, 898 900 Eigenvector, 819 820, 823, 824, 825, 826, 830, 835, 836, 838, 839, 844, 877, 887, 892, 924, 925, 934 complex components, 836 complex pair, 824 components, 825 Dutch roll, 891, 892, 906, 907, 913 lateral, 892 longitudinal, 844 phugoid/long period, 846, 855, 857 858, 864, 866 roll mode, 890, 897 short period, 845, 847, 849 spiral mode, 890, 898 901 Elastic deflection angle, 626 Electronic yaw damper, 918 Elevation angle, 437, 696, 736, 990 constraint, 1014 Elevator, 9, 377, 385, 390, 605, 635, 666 angle per g, 611, 660 angle to turn, 677 679 control reversal, 632 deflection, 389 400, 405 408, 438 444, 448, 606, 611 effectiveness, 627 631 hinge moment, 635 power, 621 623 response, 976 979 sizing, 646 661 Ellipsoidal-Earth model, 1044 1051 Empennage, 384 385, 690 Endurance, 287 295 maximum, 291 294, 299 300, 303 304, 317 specific, 292 294 Energy equation, 205, 212 potential, 272, 357, 845 846 rotational kinetic, 845 846 translational kinetic, 846 Engine, 157 168, 171, 173, 190, 195 198, 216, 228 233, 245, 247 251, 253, 260, 277, 282, 293, 484 air-cooled piston, 155, 159 air-cooled radial, 157 aircraft, 154 155, 157, 190, 200, 236 237 bypass, 164 failure, 353 355, 361, 363, 365, 582 596 failure reaction speed, 362 failure recognition speed, 362, 364 365 gas turbine, 160, 168, 228 horizontally opposed, 159 ideal, 233 internal combustion, 155 156, 158, 288 jet, 155, 160, 164, 270, 282, 482, 484 486 liquid-cooled piston, 155 piston, 158, 168, 190, 195, 197, 340 Rolls-Royce Griffon, 158, 161 radial, 156 157 reciprocating, 282 reciprocating jet, 160 reciprocating piston, 159 rotary-radial, 155 156 static-radial, 157 supercharger, 159 turbofan, 155, 164 166, 168, 245 249, 252 253, 306, 340, 482 483, 486 turbojet, 155, 160 166, 228 238, 241 242, 245, 248 249, 252, 268, 270, 274 275, 282, 286, 303, 340, 358, 361, 482 483, 486 turboprop, 166 168 turboshaft, 168 Engine-out flight configuration, 596 Engine-propeller combination, 155, 159 161, 164, 173, 196, 198, 245, 270, 282, 482, 486 Enthalpy, 154, 205, 235 freestream, 205 Equations of motion, 716, 735, 1032 6-DOF, rigid body, 753 aircraft, 715, 719 general linearized, 928 lateral, 886, 943 linearized, 754 767, 943, 970, 977, 986 longitudinal, 886, 977 nondimensional linearized, 788 798, 931 nonlinear, 969, 986 rigid-body, 715 716, 753, 834, 943, 989 Equator, 1044, 1049, 1050, 1052, 1053, 1057, 1060, 1062 Equilibrium, 377 381, 386, 451 angle of attack, 392, 730, 804 neutrally stable, 379 stable, 377 379, 452 static, 377 383, 386 387, 390 unstable, 377 381, 664 Error drift, 1023, 1026 1028, 1038 orthogonality, 1021 1023, 1026 1029, 1038 quaternion, 1010 round-off, 1028 1029 simulation, 1025, 1029, 1034 1036
Index 1121 truncation, 1029, 1033, 1034 Euler angle, 735 743, 753 754, 759, 927, 989 991, 997, 1000, 1003 1008, 1013, 1016 1018 definitions, 735 737, 990 991 formulation, 735 753, 989 993, 996, 1003, 1013, 1037 1038 integration of, 743 rotation, 993 994 singularities, 743 time derivatives of, 741 transformation, 743, 1003, 1013, 1038 Euler axis, 993 995, 1009 formulation, 993 996 rotation, 993 996, 999 vector, 1009 1010 Euler instability, 1022 Euler integration, 1030, 1036 Euler-Rodrigues quaternion, 996, 1000, 1004, 1008 1012, 1037 quaternion conjugate, 1002 quaternion formulation, 996 1005, 1009 1010, 1017 1020, 1037 1038 symmetric parameters, 996 997, 999 1002, 1009 Euler s formula, 993, 997 Euler s theorem, 997 Exhaust jet, 482 484, 525 entrainment, 525 Exhaust nozzle, 233 235 Exit nozzle, 228, 235 Exit plane, 229 Exponential method, 1030 1031 (see also Local linearization method) External stores, 472 474, 505 506 F F-14 Tomcat, 524, 580, 582, 585 591 F/A-18 Hornet, 595, 687 FAR takeoff, 353 355, 358, 361 364 Failure state, 958 Fan nozzle, 246 248 Fang and Zimmerman algorithm, 1025 Feathering the prop, 189 Feedback control system, 918 919 Finite thickness, 38 Finite wing, 25, 46 49, 54, 58, 94, 97, 99, 172, 390, 555 theory, 46 94 First law of thermodynamics, 153 154, 234 235, 241, 246 Fixed-wing aircraft, 74, 681 Flap, 39 46 chord fraction, 42 chord length, 40 deflection, 39 46, 99 100 sealed, 43 44 trailing-edge, 39 46, 51, 72 Flap effectiveness, 39, 42 43, 45, 567 568 ideal section, 41 42 local section, 75 Flaperons, 666 Flat-Earth approximation, 717, 1037 coordinate system, 989, 1044 quaternion formulation, 1035 1042 Flat vortex panels, 32 Flex-wing aircraft, 681 Flight accelerating, 605 envelope, 325 326, 957 equilibrium, 730, 744, 756 759, 763, 792 free, 379 380, 383, 392 gliding, 306, 309, 312, 317 level, 269, 278 279, 295 296, 317, 322, 386, 389 mechanics, 1, 253, 259 260, 715 powerless, 307 308 simulation, 259, 989, 996, 1029, 1032 simulator, 1002 steady, 17 18 steady level, 260 263, 267 271, 274 275, 279 283, 287 290, 293, 295, 298, 306, 317, 358, 377 testing, 253 trimmed, 377, 379 380, 384, 392, 425, 444, 452 453 turning, 321 322, 670, 672 Flight envelope, 957 operational, 957, 968 permissible, 957 service, 957 Flight phase categories, 955 956 Floatplane, 514 515 Flow, 14 adiabatic, 19, 131 axisymmetric, 209 boundary layer, 14, 38 compressible, 20, 131, 134 135, 139 compressible subsonic, 134 139 core, 246, 248 doublet, 2-D, 21 entrained, 482, 525 fan, 246 field, 18, 47, 136, 411, 557 fluid, 16, 143 freestream, 17, 20, 171, 216
1122 Index incompressible, 18, 20, 26, 46, 132, 134 136, 193 194, 200 203, 212 induced, 215 inviscid, 14, 15 19, 94, 131, 135 inviscid irrotational, 17 irrotational, 20, 131, 133, 139 isentropic, 19, 131, 230, 246 247 leakage, 42 lifting, 2-D, 24 over multiple lifting services, 94 107 potential, 20 25, 29 30, 32, 37 38, 49, 131, 136, 199 separation, 232, 940 (see also Stall) source, 2-D, 21 stagnation, 2-D, 21 streamtube, 203, 214 subsonic, 30, 134, 139, 143, 145 supersonic, 134 139, 143 three-dimensional, 716 turbine, 233 two-dimensional, 716 uniform, 18, 20 22, 28, 32, 34, 99, 131, 133, 206 209, 212, 229, 502 viscous, 232 vortex, 2-D, 21 Fluid, 19 compressible, 19 density, 177 flow, 16, 143 inviscid, 232 statics, 10 Flying qualities (see Handling qualities) Flying wing, 383 384 Force, 2, 259, 384 aerodynamic, 1 4, 14, 18, 28 30, 46, 49, 94, 99 107, 143, 403 axial, 2 4 braking, 355 buoyant, 18, 228 center of aerodynamic, 468 derivatives, 768 788 drag, 2, 171, 174, 219, 228, 261 262, 277, 357, 381, 403, 455 friction, 351 gradient, 508 lift, 261, 322 323, 381, 455 normal, 2, 172, 216, 223 227, 476 478, 480, 482 483 off-axis, 216 pressure, 14 18, 38, 138, 455, 474 resultant aerodynamic, 18 rolling friction, 340 section, 2 shear, 403, 455 side, 2, 216, 223, 225, 319, 322, 377, 381, 387, 497, 499, 501, 506 508, 513, 526, 548, 560 thrust, 171, 216, 270, 352, 357 358 vector, 270 viscous, 38, 138 viscous shear, 14 Forced response, 813, 817 Forcing frequency, 818 Ford Tri-motor, 156 157 Forebody blowing, 987 Forebody strakes, 941, 987 Forebody suction, 987 Forward airspeed, 173 176, 187, 190, 207, 216 Forward CG limit, 407, 621 623, 653 654, 658, 660, 661 Fourier, 52 coefficients, 52 62, 67 81 integral, 77 series, 52 55 Free response, 813 814, 817, 834 Freestream, 2 3, 18, 29 30, 50, 98 99, 133 134, 139 141, 143, 154, 171, 205, 216, 230 234, 386, 476, 482 airspeed, 205 conditions, 132 density, 3 dynamic pressure, 387 388 enthalpy, 205 flow, 17, 20, 171, 216 Mach number, 136, 138, 139 143, 237, 775 pressure, 154, 205, 208, 228 static pressure, 202, 207, 210, 231 temperature, 230 velocity, 2, 17, 21, 35, 48, 51, 133 136, 139, 153 154, 182, 203 204, 207, 222, 236, 386, 391, 411, 413, 422, 436, 485, 555 Frequency Dutch roll, 892, 909, 911, 916, 966 phugoid/long period, 856, 858, 863, 868 869, 877, 964 response, 817, 983, 984 response curves, 985 short period, 846, 848, 959 964 Frise ailerons, 691 Fuel consumption, 287, 289 290, 295, 304 minimum, 289 291 power-specific, 287, 317 rate, 289 292, 303 304 specific, 159, 287 290, 298 299, 303 304 thrust-specific, 304, 306 total rate, 289, 292, 303 Fuel injection, 159 Full-stall landing, 652, 655
Index 1123 Fuselage angle of attack, 393, 396, 429 bending, 627 628, 630 center of pressure, 473 474 contribution of, 472 476 dihedral effect, 565 566 effect, 505 reference line, 261, 386, 391, 393, 395, 401, 422, 424, 436 439, 448, 479 480, 484 Fuselage-wing interaction, 558 G Gain, 984 Corbett-Wright, coefficient, 1022 1026, 1029 coefficient, 1021, 1025, 1029 dynamic, 984 static, 984 Gas turbine, 160, 168, 228 Gauss elimination, 827 Geocentric angle, 1052, 1055 Geocentric coordinates, 1052 Geocentric latitude, 1046 Geodesic, 1049 1057, 1060, 1061 Geodetic bearing, 1050 Geodetic latitude, 1046, 1051 Geographic coordinates, 1044 1063 Geometric mean chord, 83 Geometric shape, 26 Geometric twist, 51 52, 55, 95, 105, 553 554 Geometric washout, 169 Gimbal lock singularity, 743, 989 993, 996, 1007 1009, 1038 Glide ratio, 308 315 maximum, 311 317 zero-wind, 310 311, 317 Gliding flight, 306 Gloster Meteor, 161 162 Gloster/Whittle E28/39, 161 162 Goldstein s hypothesis, 180, 199 Goldstein s kappa factor, 180 Goldstein s vortex theory, 179 180, 185, 187, 196, 200 202, 214, 217 Gossamer Albatross, 272 Gossamer Condor, 272 Gradient, 17 19 control force, 632, 637, 640, 643, 654 downwash, 397, 420, 480, 484, 505, 509, 571 moment, 508 normal force, 478 479 pressure, 15, 19 sidewash, 503 505, 509, 511, 518 525 temperature, 11, 19 upwash, 425, 428 velocity, 19 Great circle, 1056, 1060 1063 navigation, 1060 1063 Gross weight, 259 262, 267, 290 292, 299 301, 312, 314, 318 319, 322, 326 327, 345 maximum, 323 326 Ground control speed, 346 Ground effect, 339 340, 357 359, 646 658 Ground roll, 337 341, 344, 346, 349 350, 352, 358 landing, 351 352 takeoff, 353 Ground speed, 295 296, 309, 338, 354, 719 Ground track, 295 Gyroscopic coupling, 805 807, 924 925, 928, 934, 986, 1037 Gyroscopic effects, 155, 806 H Half-chord, 53, 145 Handling qualities, 377, 381, 633, 953 968, 983, 986 aircraft, 953 987 Dutch roll, 966 lateral phugoid, 965 phugoid/long period, 964 prediction, 958 968 roll mode, 964 short period, 958 963 spiral mode, 965 Heading, 295, 736 (see also Azimuth angle) Headwind, 295 298, 310 316, 338 effective, 297 Heavily damped motion, 74, 845, 886 Heaviside expansion theorem, 975 Heinkel He-162, 596 Heinkel He-178, 160 Heinkel He-280, 160 Helical blade-tip vortex, 215 path, 177 179 surface, 179 vortex, 177, 179, 180 Helix, 170, 215 High-lift device, 318, 338, 340, 351, 427, 435, 564 High thrust vector, 472 Hinge-efficiency, 43 44, 81 Horizontal tail, 384, 386, 389, 391, 395, 411, 413, 420, 444 447, 482, 501 505 dihedral, 529 547 Horizontal tail volume ratio, 394 395, 504
1124 Index Horseshoe vortex, 96 99, 101 104, 105 Householder method, 839 I Ideal gas, 10, 14, 131, 230, 233 constant, 10, 12, 19, 230, 239 law, 141 Incompressible, 18, 205 flow, 18, 20, 26, 46, 132, 134 136, 193 194, 200 203, 212 inviscid flow, 18, 203 velocity potential, 18 Induced angle, 173, 175, 181, 183, 218 downwash, 177, 416 Induced drag, 50, 52 66, 171, 173, 176, 220, 262, 264, 272, 278, 339 340, 357, 380, 389, 425, 517 minimum, 62 Inertia tensor, 717, 725, 735 Inertia, moment of, 617, 725 728, 752, 794, 806, 871, 873, 874, 876 Inertial coordinates, 717, 727, 732, 734, 735, 758, 989 990, 992, 995, 1002 Inertial coupling, 805 807, 924 925, 928, 934, 939 940, 986, 1037 Inertial cross coupling, 732 Inertial reference frame, 726 Infinite series, 29, 31 Inlet, 233 duct, 228 plane, 229 pressure, 232 velocity, 164 Inverse rotation, 1002 Inverse transformation, 721 722, 975 equations, 722 Inviscid, 14 19 adiabatic flow, 19, 131 aerodynamic force, 28 aerodynamic moment, 28 aerodynamics, 16, 28 CFD solution, 105 107 compressible aerodynamics, 131 134 flow analysis, 15 fluid, 232 forces, 106 lift coefficient, 36 37 moments, 106 panel codes, 107 theory, 146, 199 Irreversible controls, 633 Irrotational, 18, 20, 131, 139 Isentropic, 19, 131, 142, 233 J Jacobian, 101 Jet engine, 155, 160, 164, 270, 282, 482, 484 486 contribution of, 482 486 Jet propulsion, 160 161 Jet transport, 785, 794, 804 K Kalman filtering, 1000 Kinematic equations, 1021 formulation, 992 transformation equations, 742, 753, 989, 991, 996, 999, 1018 Kinetic energy, 153, 236, 242, 247 248, 357 Kutta, 46 condition, 28, 34 lift, 49 Kutta-Joukowski law, 24, 29, 48 49 L Landing, 337 353 Landing configuration, 659 Landing gear, 338, 340, 342 tail-dragger, 338, 345, 513 514 tricycle, 338, 345 346 Landing performance, 337 Laplace equation, 18, 132, 134 136 transform, 970 971, 974, 975, 983, 985 Lapse rate, 11 Lateral control and maneuverability, 666 Lateral disturbance, 730, 885, 904 Lateral dynamics, linearized, 885 945 Lateral equations, 886 linearized, 763, 836 Lateral mode, 958 damped natural frequency, 888 damping rate, 888 undamped natural frequency, 888 Lateral motion, 669 670, 836, 885 887 Lateral phugoid, 895, 966 handling qualities, 965 Lateral static stability, 497 597 Lateral trim, 497 597 generalized small-angle requirements, 574 577 steady-heading sideslip, 577 582 Latitude, 989, 1003, 1008, 1044, 1046 1052, 1054, 1055, 1057, 1062 Leading edge, 1 2, 4 5, 26 27, 33, 53, 95, 143 blunt, 143 moment coefficient, 30
Index 1125 sharp, 143 Length, 2 3 characteristic, 99, 103 l Hospital s rule, 67 Lift, 2 3, 138, 175 176, 216, 219, 259 260, 267, 277 278, 337 additional section, 85 87 basic section, 85 87 force, 261, 322 323, 381, 455 maximum, 108 119 vector, 50, 78, 173, 176 177, 220, 319 Lift coefficient, 3, 15 16, 30, 38, 41 42, 52 63, 66, 80, 106, 135, 146, 175, 182 183, 200, 262 267, 271 272, 277, 283 284, 310, 317, 320, 322, 334, 336 340, 344, 346, 357 360, 382 383, 387 391, 396, 398, 401, 411 412, 415, 424, 449 451, 455, 608 canard, 424, 426, 432 design, 62, 81 differential, 337 inviscid, 36 37 maximum, 16, 39, 108 119, 318, 327, 330 331, 342, 346, 351, 384, 408 optimum, 347, 350 section, 3, 30 31, 36 39, 46, 99 100, 106, 144, 175 tail, 388 thin airfoil, 41 wing, 388 Lift slope, 37, 39 42, 53 56, 59, 62, 77, 145, 383, 390, 394, 402, 405, 424, 644 canard, 424 in situ section, 551 554 section, 30, 42, 51, 55, 220 Lift-to-drag ratio, 262 267, 310, 314 Lifting-line, 96 97 equation, 52, 94, 96, 527 528, 553, 555 numerical method, 96, 105 107, 391, 525 527, 552, 561, 570, 648, 690 solution, 98 theory, 48 94, 96, 105, 106, 391, 412, 414, 417, 505, 518 519, 552, 555, 569, 779, 782 783 Liftoff, 342, 346, 351, 353, 355 360 attitude, 337 speed, 342 346, 353, 361 364 Linear control problem generalized, 970, 977, 981 special, 970, 972 Linear time-invariant systems, 970 Linearized equations coupled, 836 847, 885 lateral, 763, 836 longitudinal, 763, 836 of motion, 754 767, 943, 970, 977, 986 Linearized lateral dynamics, 885 945 Linearized longitudinal dynamics, 813 876 Load factor, 322 324, 327, 331, 333, 335, 357, 605 606, 646, 672, 958 allowable, 326 327 load-limited, 325, 327, 329, 336 maximum, 324, 326 stall-limited, 325, 327, 329, 336 Load-limit, 330 331 negative, 323, 325 positive, 323, 325 327, 330 331 Local linearization method, 1030 1036 (see also Exponential method) Lockheed C-5 Galaxy, 165 Lockheed P-38 Lightning, 524, 571 596, 602, 631 632 Lockheed P-80, 163 Long-period, 846, 854 (see also Phugoid) amplitude, 843 844 approximation, 854 871 damped natural frequency, 843, 854, 856, 864 damping, 854, 857, 863, 869 871, 939, 964 damping rate, 855 856, 864, 939 eigenvalues, 843, 855, 856, 858, 861 864, 867 868 eigenvectors, 846, 855, 857 858, 864, 866 frequency, 856, 858, 863, 868 869, 877, 964 handling qualities, 964 lateral oscillation, 966 mode, 837, 842 843, 846, 858, 871, 877 motion, 846, 859, 862, 868 oscillations, 843, 877, 979 period, 843, 939 phase, 843 844 phase-divergence ratio, 863 pitch-damping-ratio, 863 stability ratio, 863, 868 871 undamped natural frequency, 843, 856, 863, 868 Longitude, 989, 1003, 1008, 1044, 1047 1049, 1053 1055, 1057, 1062 Longitudinal control, 605, 669 Longitudinal disturbance, 730, 885 Longitudinal dynamics, 837 linearized, 813 876, 885 stick-fixed, 876 Longitudinal equations, 886 linearized, 763, 836 Longitudinal-lateral coupling, 596 597, 924 939, 986, 1037 nonlinear effects, 986 987
1126 Index Longitudinal mode, 839, 877, 958 Longitudinal motion, 497, 596, 836 847 Longitudinal static stability, 377 486 Longitudinal trim, 377 486 M Mach angle, 140, 142 143 Mach lines, 143 144 Mach number, 18 19, 132 139, 166, 168, 196, 200, 235, 240, 242, 247, 262 critical, 134, 136 139 design, 232 design cruise, 231 exit, 241 flight, 131, 134 135, 230 232, 237 245, 249, 252 253 freestream, 136, 138, 140, 142 143, 237, 775 hypersonic, 134 inlet, 230 232 local, 136, 200 low, 36 subsonic, 134 135 supersonic, 134, 140, 142 tip, 196 transonic, 134 zero, 135 Maneuver, 325 326 cobra, 334, 987 coordinated, 666, 668 margin, 612, 613, 960 961, 968 point, 612 621, 643 646, 660, 853, 854, 960 post-stall, 334, 661 pull-up, 605 607, 610, 633, 637, 644, 969, 979 Maneuverability, 605, 666, 682 aircraft, 605 analysis, 605 Maneuvering speed, 326 327, 330 331 Mass flow rate, 153, 154, 159, 164 165, 193, 204, 228 230, 245, 483, 727 Mass moment of inertia tensor, 725, 874 Mass transfer, 726 Maximum lift coefficient, 108 119 Maximum range, 259, 297 302, 304 306, 317 Mean aerodynamic chord, 84, 89, 460 Mean chord length, 3, 383, 387, 394, 402 Mean-sea-level ellipsoid, 1044 1052 Meridian, 1044 1046, 1050 1054, 1057 prime, 1044, 1050, 1062 Messerschmitt Me-262, 161 Minimum-control airspeed, 582 596 absolute, 588 592 aileron limited, 584, 586, 588 590 ground-, 595 596 rudder limited, 584, 586, 588 590 Minimum power required, 280, 289 Minimum runway length, 353 (see also FAR takeoff) Mirror image model, 648 649 Mission task elements, 955 Mode convergent, 835, 858, 942, 984 critically damped, 816, 823 Dutch roll, 886, 891, 892, 895, 912, 944 damped, 835 divergent, 834 835, 858, 876, 942 long-period, 837, 842 843, 846, 858, 871, 877 longitudinal, 839, 877, 958 nonoscillatory, 835 oscillatory, 835, 943 overdamped, 816, 823 phugoid, 836, 842 843, 846, 858, 877, 895, 964 rigid-body, 831, 834, 835, 844, 892 roll, 886, 890 896, 909, 943, 965 short-period, 837, 842, 844 847, 877, 895, 958 spiral, 886, 890, 893 895, 897 905, 943, 965 time constant, 965 undamped, 835 underdamped, 816, 823 Moment, 1 4, 259, 384 about leading edge, 4 aerodynamic, 1 4, 103 105, 107, 259, 403, 437, 455, 474, 497, 499, 548 bending, 90 93 coefficient, 3, 5, 29, 36, 42, 135, 145 146, 382, 387, 392, 449, 609 derivatives, 768 788 gradient, 508 nondimensional derivatives, 792 794 pitching, 2, 120 130, 138, 145, 216, 223, 225, 377, 381 387, 390 397, 400, 403, 420, 422, 445, 449 450, 474, 476 477, 482, 484, 497 propeller-induced, 171 propeller yawing, 508, 510, 515, 572 quarter-chord, 30, 32, 41 42, 45, 103 restoring, 500 501 rolling, 2, 72 74, 76 77, 80 82, 171, 176, 216, 377, 381, 387, 497 499, 526, 549 550, 556 564, 567 596, 885 section, 2 semispan components, 88 93 slope, 45, 392, 404, 475, 481
Index 1127 thrust, 437 twisting, 90 93 yawing, 2, 78 82, 172, 216, 224 225, 377, 381, 387, 497 501, 504 510, 513, 515, 548 550, 556 561, 567 570, 703, 885 Moment coefficient, 3, 5, 29, 36, 42, 135, 145 146, 382, 387, 392, 449, 609 bending, 90 93 leading edge, 30 pitching, 3, 5, 45, 120 130, 144 145, 224, 384, 390, 392, 394, 405 406, 424, 434 435, 445, 450 456, 473, 477, 479 quarter-chord, 30, 32, 41 rolling, 76 77, 82 section, 3, 103 semispan, 88 93 twisting, 90 93 yawing, 78 82, 224 225, 504, 548 Moment of inertia, 617, 725 728, 752, 794, 806, 871, 873, 874, 876, 1082 1085 Momentum, 94, 153, 204, 229 angular, 206 208, 211 axial, 228 downward, 94 equation, 16 18, 131, 141, 206 209, 211, 228 fluid, 173, 204 flux, 215, 228 229 theory, 204, 207, 212 216 Motion critically damped, 815 lateral, 596 longitudinal, 497, 596, 836, 838 overdamped, 814 815 phugoid, 846, 859, 862, 868 pure pitching, 871 873, 1015 underdamped, 814 815 Multiple lifting surfaces, 94 107 N Nacelle, 228 229, 391, 394, 411, 472 474, 505 506 contribution of, 472 476 drag, 229, 232 effect, 505 506 Natural frequency damped, 736, 814 817, 839, 888, 890 undamped, 815, 818, 836, 839, 868, 888, 891 Navier-Stokes equations, 14, 132 Navigation, 1046, 1058 1060 great circle, 1060 1063 rhumb line, 1051 1059 Neutral axis, 462 464, 467, 470 471 definition, 462 Neutral point, 401, 403 404, 407, 428, 475, 481, 647 (see also Aerodynamic center) Neutral roll stability, 904 905 Newtonian mechanics, 207, 715 Newton s corrector equation, 274 Newton s law of gravitation, 10 Newton s method, 101 102, 274 275, 316, 440 Newton s second law, 2, 94, 153, 228 229, 260, 338, 355, 362, 483, 605, 669, 725 727, 730, 732, 735, 741, 753, 757, 821, 876, 989, 1017 Nodes, 32 35, 97, 99, 102, 104 Nondimensional derivatives, 792 794 Nonlinear effects, 436 472, 939 943, 969, 986 Nonlinear inertial coupling, 939 940 Normal force coefficient, 3 5 gradient, 478 479 North American XB-70, 164 Notation, 1, 716, 728 730, 740, 790, 993 Nozzle, 246 core, 246 248 exhaust, 233 235 exit, 228, 235 fan, 246 248 Numerical lifting-line method, 96, 105 107, 391, 525 527, 552, 561, 570, 648, 690 Numerical panel method, 30, 105 106 O Operating conditions, 259 Optimum, 54, 62, 346, 349 airspeed, 265 angle of attack, 349 flight profile, 306 induced drag, 63 lift coefficient, 347, 350 thrust angle, 265 266 total washout, 62 washout, 62, 64 65, 80 82 washout distribution, 63 66, 80 washout distribution function, 69, 71 Orthogonality control, 1026 1028 error, 1021 1023, 1026 1029, 1038 Oscillations Dutch roll, 891, 895, 944 945 limit-cycle, 943 long-period lateral, 895, 966 phugoid/long period, 843, 877, 979 pilot induced, 943 rolling, 886 short period, 845, 877 sideslipping, 886
1128 Index sinusoidal, 984 yawing, 886 Oscillatory roll-spiral mode, 895, 966 Oswald efficiency, 262, 265, 272, 318 319 P P-38 Lightning, 524, 571 594, 601 602, 631 632, 713 P-3C Orion, 583 P-51 Mustang, 514 Panel codes, 36, 98, 136, 482 3-D, 96, 505 inviscid, 107 vortex, 137 Panel methods, 106, 474 numerical, 30, 105 106 vortex, 32, 36 39, 42 45, 391, 648 Panels, source, 2-D, 22 24 Panels, vortex, 2-D, 24 25 Payload-to-power ratio, 272 Performance, 16, 168, 171, 197, 203, 249 aircraft, 16, 259 260 characteristics, 304 landing, 337 takeoff, 337, 344, 346 turning, 336 Perturbation, 133 134, 141 (see also Disturbance) Phase angle, 818 Phase damping, 863, 869 870 phugoid, 871 Phugoid, 846, 854, 964, 979 (see also Longperiod) amplitude, 843 844 approximation, 854 871 damped natural frequency, 843, 854, 856, 864 damping, 854, 857, 863, 869 871, 939, 964 damping rate, 855 856, 864, 939 eigenvalues, 843, 855, 856, 858, 861 864, 867 868 eigenvectors, 846, 855, 857 858, 864, 866 frequency, 856, 858, 863, 868 869, 877, 964 handling qualities, 964 lateral, 895, 966 mode, 836, 842 843, 846, 858, 877, 895, 964 motion, 846, 859, 862, 868 oscillations, 843, 877, 979 period, 843, 939, 964 phase, 843 844 phase damping, 871 phase-divergence ratio, 863 pitch-damping-ratio, 863 stability ratio, 863, 868 871 undamped natural frequency, 843, 856, 863, 868 Pilot compensation, 954 opinion, 953 960, 968, 983 reaction time, 351, 352, 363, 894, 944 945, 965 response time, 944, 964 technique, 357 Piloting task classification, 956 definitions, 955 Pitch, 2, 72, 170, 180, 183, 185, 195, 377, 379 381, 390, 445, 548, 736 737 angle, 169 170, 176, 180, 182, 185 186, 219 constraint, 1014 control, 9, 72, 385, 426, 472, 605, 632, 637, 638 641, 644, 655 658, 682 687 (see also All-flying tail; Elevator; Stabilator; V-tail) control force, 605, 639, 656 658 damping, 610, 845, 869 870, 979 disturbance, 451 452 divergence, 939 940 length, 170 171, 183, 185, 200 stiffness, 383 Pitch-acceleration-sensitivity limit, 617 618 Pitch-damping derivative, 610, 780 Pitch rate, 607 608, 742 dynamic, 616, 670, 678, 679, 960 traditional dimensionless, 608, 610, 616 Pitch stability, 381 385, 394 395, 404, 421, 422, 424, 426, 505, 631 contribution of jet engines, 482 486 contribution of running propellers, 476 481 derivative, 383, 397, 401, 405, 424, 447 448, 451, 455, 473, 480, 485, 500 501, 506, 550, 611, 627, 645 effect of the fuselage, nacelles, and external stores, 472 475 nonlinear effects, 436 472 static, 421, 435, 500 501 wing-canard combination, 421 436 wing-tail combination, 384 400 Pitch-to-diameter ratio, 158, 183 199, 225 226, 478 Pitching, 2 moment, 2, 88 93, 120 130, 138, 145, 216, 223, 225, 377, 381 387, 390 397, 400, 403, 420, 422, 445, 449 450, 474, 476 477, 482, 484, 497 moment of inertia, 874 motion, pure, 871 873, 1015
Index 1129 Planar, 22 curve, 26 segment, 22 source sheet, 22 Planform, 3, 49, 52 55, 57 58, 60, 62, 66, 76, 96, 100, 103, 183 arbitrary, 59, 62, 66, 77, 199 elliptic, 49, 58, 62 63, 77, 184 rectangular, 66 67, 69 spanwise symmetric, 76 tapered, 70 wing, 60, 62, 72, 77, 80 Poisson s kinematic equations, 992 Position and orientation, 735 753 (see also Euler angle; Quaternion) Position factor, 420, 428 Position vector, 753 time rate of change, 741 Post-stall dynamic turn, 334 maneuver, 334, 661 stability, 661, 663 Potential energy, 312, 357, 845 846 field, 22 perturbation, 141 perturbation velocity, 133 134 scalar field, 20 scalar velocity, 132 uniform flow, 133 velocity, 18, 131 134 velocity field, 21 Potential flow, 20 25, 29 30, 32, 37 38, 49, 131, 136, 199 compressible, 132, 141 elementary, 20, 22 incompressible, 20, 135 136 linearized approximation, 134, 139 small angle, 140, 142 145 solution, 37 38, 96, 106, 647 supersonic, 140, 143, 145 theory, 38, 48, 145 Potential line, 140 Power, 153, 155, 159, 165 168, 171, 187 190, 193 197, 200, 206, 236, 245, 248 available, 274, 277, 279 284, 293, 295, 298, 303, 306, 321 322 brake, 159, 171, 182, 184, 189 197, 205, 212 213, 293 coefficient, 182, 184, 187 188, 192, 197, 201 202 distribution, 185 186 excess, 279 280, 321 322 failure, 306 full throttle, 273, 275, 279, 284 input, 154, 194 propulsive, 171, 189, 198, 205, 236, 273, 293 required, 270 277, 279 284, 288 290, 293, 295, 298, 303, 305, 307, 321 322 Power-specific fuel consumption, 287, 317, 370 Power-to-weight ratio, 155 160, 168, 274 275, 285 Prandtl-Glauert compressibility correction, 134 135, 774 776 Prandtl s tip loss factor, 181 Pressure, 15, 94, 143 aerodynamic, 403, 455 ambient, 153, 203, 233 234, 246, 483 coefficient, 135 137, 142 143 difference, 94 distribution, 37 38 dynamic, 383, 387 388, 423 force, 14 18, 38, 138, 455, 474 freestream, 154, 205, 208, 228 gradient, 15, 19 local static, 18 stagnation, 19, 131, 230, 233 235, 241 uniform, 206, 209 Pressure ratio, 165, 234, 237 238, 248 compressor, 166, 237 245, 249, 252 253 fan, 248 253 stagnation, 246 Propeller, 153 216, 253 angle of attack, 171 172, 201, 216 220, 222, 225, 480, 508 510, 513 515 blade, 168 169, 173 174, 176 177, 181, 199 blade shape, 159 blade theory, 173 202, 214 blade-tip speed, 159 brake power, 171 constant-pitch, 171, 185, 340 constant-speed, 158 159, 190 191 contribution of, 476 482 counter-rotating, 503, 524 diameter, 159, 182 183, 194, 197 199 disk, 202 204, 207 211, 215, 219, 222, 224 downwash angle, 479 480 downwash gradient, 481 effect of, 506 efficiency, 155, 158 159, 190 191, 200, 293 fixed-pitch, 171, 184, 187, 189 190, 192, 197, 288, 478 forces and moments, off-axis, 216 228 geometry, 181, 201 202 induced velocity, 172 176 momentum theory, 202 216
1130 Index normal force, 477 478 performance, 171, 200 201 pitch, 191 192, 200 201, 293, 346 plane of rotation, 171 172, 216, 222 223 slipstream, 476, 502 503, 508, 513, 524, 564 565 theory, 199 thrust, 182, 184, 201, 222 variable-pitch, 158 159, 171, 189 191, 273, 293 yawing moment, 508, 510, 515, 572 Proper orthogonal transformation, 993 Propulsion, 153, 253 aircraft, 153 157, 159 160, 168, 191, 253 overview, 153 253 Propulsion system, 153, 155, 228 aircraft, 153, 155 ideal, 153 155, 159, 164 Propulsive efficiency, 154, 159, 164 165, 171, 184, 187 190, 197 198, 205 206, 213 214, 236 237, 245, 248 252, 485 486 Propulsive power, 171, 189, 198, 205, 236, 273, 293 available, 287, 304 Pull-up maneuver, 605 607, 610, 633, 637, 644, 969, 979 constant speed, 606 607 Pure pitching motion, 871 876, 1015 eigenvalues, 873 Pure rolling motion, 919 922, 1015 Pure yawing motion, 922 923, 1015 eigenvalues, 923 Q QR method, 839 Quarter-chord, 30, 45, 99, 105 line, 50, 53, 95 97, 104 moment coefficient, 30, 32, 41 moment slope, 41 42 wing, 390, 394, 399 400, 405 407, 417, 428 Quaternion, 997, 1000 1004, 1009 1011 algebra, 997, 1000 1001, 1025, 1038 attitude, 1010 bank angle constraint, 1013 closed-form solution, 1013 1020 command-attitude, 1010 components, 1011, 1030 conjugate, 1001 1002 Euler-Rodrigues, 996, 1000, 1004, 1008 1012, 1018, 1037 (see also Euler- Rodrigues symmetric parameters) error, 1010 formulation, 743, 989, 1003, 1013 1015, 1020 1021, 1030 1031, 1038 1040 magnitude, 1001 numerical integration of, 1019 1034 of finite rotation, 996 product, 1000 1004 relations with other attitude descriptors, 1004 1011 renormalization, 1022 1023, 1026, 1038, 1042 rotational constraints, applying, 1011 1013 transformation, 743, 1013, 1038 unit, 1009 1010 R Radius of curvature, 606 Radius of gyration, 617, 853, 876, 960, 961, 968, 1082 1085 Ramjet, 160, 379 Range, 295 maximum, 259, 297 302, 304 306, 317 specific, 295 305 Rate gyro, 918 Rate of climb, 259 260, 277 287, 306, 321 322 maximum, 280, 282, 284 286 steady, 277, 306 307 Reaction force, 153 Reaction time, 351, 352, 363, 894, 944 945, 965 Redundancy relations, 993 Relative air flow, 1 Relative airspeed, 177 Relative wind, 2 local, 50 Residual, 137 Resonance, 818, 877 Response frequency, 817, 983 984 maximum, 836 Response time, 944, 964 Response to control inputs, 968 986 Restoring moment, 500 501 Reversible mechanical controls, 633 Reynolds number, 14 16, 57 Rhumb line, 1051, 1058 1062 bearing, 1058 navigation, 1051 1059 Right-hand rule, 499 Rigid body, 260 displacement, 833 dynamics, 725 735, 836 equations, 6-DOF, 756 equations of motion, 715 716, 721, 753, 834, 943, 989 mode, 831, 834 835, 844, 892 Rigid-wing aircraft, 681
Index 1131 Roll, 2, 72 74, 78, 80, 377, 379 381, 736 737, 885 acceleration, 73 74, 965 amplitude, 892 angle, 78 approximation, 896 897 constraint, 1013 control, 9, 72 73, 567 574, 691 692, 969 (see also Ailerons; Spoilers) convergence, 893 coupling, 915 Dutch, 886, 893, 895, 906 919, 943 945, 966, 981, 983 damping, 78, 895, 909, 914, 939, 965 disturbance, 904 eigenvalue, 893, 896 897 eigenvector, 890, 897 handling qualities, 964 mode, 886, 890 896, 909, 943, 965 moment, 2, 72 74, 76 77, 80 82, 88 93, 171, 176, 216, 377, 381, 387, 549 550, 556 564, 567 596, 885 oscillations, 886 rate, 72 75, 77, 80 82, 742, 885, 896, 965 response, 74 rotation, 497 time constant, 965 trim requirements, 567 596 Roll-axis, 499, 570 Roll-damping, 78, 895, 909, 914, 939, 965 derivative, 778, 914, 917 rate, 920 921 ratio, 909, 914 Roll-spiral pair, 891, 895 Roll stability, 517, 548 566, 915 derivative, 549 551, 554, 557 566, 917 dihedral effect, 548 566 effect of rotating propellers, 563 565 effect of wing dihedral, 550 554 effect of wing sweep, 554 557 influence of the fuselage, nacelles, and external stores, 557 560 influence of the tail, 560 563 insufficient, 904 neutral, 904 905 ratio, 915 Roll-yaw coupling, 676, 904, 916 derivatives, 917 Rolling friction, 338 340, 344, 346, 351 Rolls-Royce Griffon, 158, 161 Rollup, 50 Rotary-radial configuration, 155 Rotation constant, 1015 1016, 1034 rate, 344 triad, 729 Rotational constraint, 1013 speed, 176, 342 Round-off error, 1028 1029 Rudder, 9, 377, 666 deflection, 503 504, 510 515, 570 596, 676 effectiveness, 504 response, 980 982 saturation, 582, 584, 585, 589, 591 593 sizing, 592 596 Runge-Kutta fourth-order, 747, 1021, 1023 1025, 1028 1029, 1035, 1038 second-order, 1029 1030, 1035 S Sailplane, 318 Scalar potential field, 20 Secant method, 137, 198 Section flap deflection-efficiency, 43 44 Section flap effectiveness, 39 46, 75 Section flap hinge-efficiency, 43 44 Section lift, 2, 52, 63, 75, 78, 106, 144, 175 additional, 85 87 basic, 85 87 Section lift coefficient, 3, 30 31, 36 39, 46, 99 100, 106, 144, 175 Segment, 22, 25 26, 97 98, 107 bound, 97, 99, 102, 104 differential, 22, 24, 29 trailing, 97 Semispan, 73 74 aerodynamic center, 88 93 moment components, 88 93 Shape of the Earth, 1044 1051 Shock, 138 bow, 143 waves, 138, 232 Short-period, 844, 845, 847, 979 amplitude, 843 844 approximation, 847 854, 857 approximation errors, 853 damped natural frequency, 842, 848 damping, 845, 848, 939, 963 964, 979 damping rate, 848, 852 damping ratio, 852, 960 eigenvalues, 842, 847 849, 983 eigenvectors, 845, 847, 849 frequency, 846, 848, 959 964 handling qualities, 958 963 mode, 837, 842, 844 847, 877, 895, 958 oscillation, 845, 877