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| موضوع: كتاب Aerodynamics - a Complete Course in Elementary Aerodynamics With Experiments and Examples الثلاثاء 22 يونيو 2021, 10:31 pm | |
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أخوانى فى الله أحضرت لكم كتاب Aerodynamics - a Complete Course in Elementary Aerodynamics With Experiments and Examples By N. A. V. Piercy D.sc., M.inst.c.e., M.i.mech.e., F.r.ae.s. Reader in Aeronautics in the University Of London Head of the Department Ofaeronautics, Queen Mary College Member Of the Association of Consulting Engineers Second Edition Art. Preface Notation
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Contents Chapter I Page V xiii AIR AT REST, THE ATMOSPHERE AND STATIC LIFT 14. Properties of Air ; Density ; Pressure 57. Hydrostatic Equation. Incompressibility Assumption. Measurement of Small Pressures . 8-9. Buoyancy of Gas-filled Envelope. Balloons and Airships . 10. Centre of Pressure 1115. Relation between Pressure, Density, and Temperature of a Gas. Isothermal Atmosphere. Troposphere. The International Standard Atmosphere. Application to Altimeters . 16-17. Gas-bag Lift in General. Vertical Stability 18. Atmospheric Stability and Potential Temperature 19-20. Bulk Elasticity. Velocity of Sound CHAPTER II AIR FLOW AND AERODYNAMIC FORCE 21. Streamlines and Types of Flow . 22. Absence of Slip at a Material Boundary 23-25. Viscosity : Qualitative Theory ; Maxwell's Definition ; Experimental Laws 26-28. Relation between Component Stresses in Non-uniform Flow ; Static Pressure. Forces on an Element 29-33. Bernoulli's Equation : Variation of Density and Pressure ; Adiabatic Flow ; Temperature Variation ; the Incompressible Flow Assumption ; Pitot Tube ; Basis of Velocity Measurement 34-41. Equation of Continuity. Experimental Streamlines. Stream Function. Circulation and Vorticity. Gradient of Pitot Head across Streamlines. Irrotational Flow . 42-43. The Boundary Layer Experimentally Considered 44-46. Constituents of Aerodynamic Force. Integration of Normal Pressure and Skin Friction 47-49c. Rayleigh's Formula. Reynolds Number. Simple Dynamically Similar Motions. Aerodynamic Scale. Mach Number. Froude Number. Corresponding Speeds CHAPTER III WIND-TUNNEL EXPERIMENT 50-53. Nature of Wind-tunnel Work. Atmospheric Tunnels 54. Coefficients of Lift, Drag, and Moment vii 46 11 13 18 20 21 23 26 26 32 35 44 52 54 58 68 75Vlll CONTENTS ART. 66-69. 69A. 60. 61-63. 64-66. Suspension of Models. Double Balance Method. Aerodynamic Balance. Some Tunnel Corrections Pitot Traverse Method Aerofoil Characteristics . Application of Complete Model Data ; Examples. Arrangement of Single Model Experiment. Compressed-air Tunnel Practical Aspect of Aerodynamic Scale. Scale Effects. Gauge of Turbulence . PAGE 77 86 89 92 97 CHAPTER III A EXPERIMENT AT HIGH SPEEDS 66. Variable-density Tunnel 103 66A. Induced-flow Subsonic Tunnel. Wall Adjustment. Blockage 106 66B-66C. Supersonic Tunnel. Illustrative Results 109 66D. Pitot Tube at Supersonic Speeds. Plane Shock Wave . 114 CHAPTER IV AIRCRAFT IN STEADY FLIGHT 67-69. Examples of Heavier-than-air Craft. Aeroplanes v. Airships. Aeroplane Speed for Minimum Drag . 70-72. Airship in Straight Horizontal Flight and Climb 73-76. Aeroplane in Level Flight. Size of Wings; Landing Conditions ; Flaps 77-79. Power Curves ; Top Speed ; Rate of Climb 80. Climbing, Correction for Speed . 81-83. Effects of Altitude, Loading, and Partial Engine Failure . 84-85. Gliding; Effects of Wind; Motor-less Gliders 86-89. Downwash. Elevator Angle; Examples; C.G. Location. 90. Nose Dive 91-96. Circling and Helical Flight. Rolling and Autorotation. Handley Page Slot. Dihedral Angle 118 126 129 137 140 143 146 149 155 156 CHAPTER V FUNDAMENTALS OF THE IRROTATIONAL FLOW 96-100. 101-106. 106-109. 110-114. 115. 116-117. 118-120. Boundary Condition. Velocity-potential. Physical Meaning of . Potential Flow. Laplace's Equation Source. Sink. Irrotational Circulation. Combined Source and Sink. Doublet . Flow over Faired Nose of Long Board. Oval Cylinder. Circular Cylinder without and with Circulation Potential Function. Examples. Formulae for Velocity Circulation round Elliptic Cylinder or Plate. Flow through Hyperbolic Channel . Rankine's Method. Elliptic Cylinder or Plate in Motion . Acceleration from Rest. Impulse and Kinetic Energy of the Flow Generated by a Normal Plate 163 167 172 180 184 186 190CONTENTS IX CHAPTER VI TWO-DIMENSIONAL AEROFOILS ART. 121-124. PAGE Conformal Transformation; Singular Points. Flow past Normal Plate by Transformation. Inclined Plate 194 125-127. Joukowski Symmetrical Sections ; Formulae for Shape. Velocity and Pressure. More General Transformation Formula. Karman-Trefftz Sections 203 128-129B. Piercy Symmetrical Sections. Approximate Formulae. Velocity over Profile. Comparison with Experiment and Example 212 130-133A. Circular Arc Aerofoil. Joukowski and Piercy Wing Sections 220 134-139. Joukowski's Hypothesis ; Calculation of Circulation ; Streamlines with and without Circulation. Investigation of Lift, Lift Curve Slope and Moment 227 140. Comparison with Experiment . 235 CHAPTER VIA THIN AEROFOILS AT ORDINARY SPEEDS 140A-140B. Method and Equations . 140c. Application to Circular Arc 140D-140F. General Case. Aerodynamic Centre. Example 237 240 241 CHAPTER VIB COMPRESSIBLE INVISCID FLOW 140G-140i. Assumptions. General Equation of Continuity , . 245 140J-140K. Euler's Dynamical Equations. Kelvin's (or Thomson's) Theorem 247 140L-140M. Irrotational Flow. Integration of Euler's Equations . 260 140N-140O. Steady Irrotational Flow in Two Dimensions. Electrical and Hydraulic Analogies 252 CHAPTER VIC THIN AEROFOILS AT HIGH SPEEDS 140P-140Q. Subsonic Speeds. Glauert's Theory. Comparison with Experiment. Shock Stall 259 140R-140T. Supersonic Speeds. Mach Angle. Ackeret's Theory. Comparison with Experiment .262 CHAPTER VII VORTICES AND THEIR RELATION TO DRAG AND LIFT 141-147. Definitions. Rankine's Vortex. General Theorems . 267 148-150. Induced Velocity for Short Straight Vortex and Vortex Pair. Analogies 272X CONTENTS ART. PAGE 151-155. Constraint of Walls. Method of Images ; Vortex and Vortex Pair within Circular Tunnel; Other Examples. Application of Conformal Transformation; Streamlines for Vortex between Parallel Walls . 276 155A-155B.Lift from Wall Pressures. Source and Doublet in Stream between Walls 283 156-162. Generation of Vortices ; Impulse ; Production and Disintegration of Vortex Sheets. Karman Trail ; Application to Circular Cylinder. Form Drag 287 163-168. Lanchester's Trailing Vortices. Starting Vortex. Residual Kinetic Energy ; Induced Drag ; Example of Uniform Lift. Variation of Circulation in Free Flight. Example from Experiment . 295 CHAPTER VIII WING THEORY 169-171. General Equations of Monoplane Theory 309 172-177. The 'Second Problem.' Distribution of Given Impulse for Minimum Kinetic Energy ; Elliptic Loading. Minimum Drag Reduction Formulae ; Examples .312 178-180. Solution of the Arbitrary Wing by Fourier Series. Elliptic Shape Compared with Others. Comparison with Experiment . 320 181-186. General Theorems Relating to Biplanes. Prandtl's Biplane Factor ; Examples. Equal Wing Biplane Comparison with Monoplane ; Examples . 327 187-188. Tunnel Corrections for Incidence and Induced Drag 335 189-192. Approximate Calculation of Downwash at Tail Plane ; Tunnel Constraint at Tail Plane ; Correction Formulae. Tail Planes of Biplanes 339 CHAPTER IX VISCOUS FLOW AND SKIN DRAG 193-199. Laminar Pipe Flow : Theory and Comparison with Experiment. Turbulent Flow in Pipes ; the Seventh-root Law. Flow in Annular Channel. Eccentric and Flat Cores in Pipes 346 200-204. General Equations for Steady Viscous Flow. Extension of Skin Friction Formula 357 205-207. Viscous Circulation. Stability of Curved Flow . 365 208-209. Oseen's and Prandtl's Approximate Equations . 369 210-2 1 7 . Flat Plates with Steady Flow : Solutions for Small and Large Scales ; Formation of Boundary Layer ; Method of Successive Approximation. Karman's Theorem ; Examples 370 2 18-2 ISA. Transition Reynolds Number. Detection of Transition . 384 219-221. Flat Plates with Turbulent Boundary Layers : Power Formulae. Transitional Friction. Experimental Results 387 221A-221B. Displacement and Momentum Thicknesses. Alternative Form of Kdrm&n's Equation .391CONTENTS XI ART. 222-223. 224-230. PAGE Note on Laminar Skin Friction of Cylindrical Profiles. Breakaway. Effect of Wake. Frictions of Bodies and Flat Plates Compared 393 Turbulence and Roughness. Reynolds Equations of Mean Motion. Eddy Viscosity. Mixing Length. Similarity Theory. Skin Drag. Application to Aircraft Surfaces. Review of Passage from Model to Full Scale . 399 CHAPTER IX A REDUCTION OF PROFILE DRAG 230A-230B. Normal Profile Drag. Dependence of Friction on Transition Point 230c-230F. Laminar Flow Wings. Early Example. Maintenance of Negative Pressure Gradient. Position of Maximum Thickness. Incidence Effect ; Favourable Range. Velocity Diagrams. Examples of Shape Adjustment. Camber and Pitching Moment . 230G-230H. Boundary Layer Control. Cascade Wing 230i. Prediction of Lift with Laminar Boundary Layer . 230j~230K. High Speeds, back Minimum Maximum Velocity Ratio. Sweep- 409 412 419 421 423 CHAPTER X AIRSCREWS AND THE AUTOGYRO 231-232. The Ideal Propeller ; Ideal Efficiency of Propulsion 425 233-238. Airscrews. Definitions. Blade Element Theory. Vortex Theory ; Interference Factors ; Coefficients ; Method of Calculation ; Example 427 239. Variable Pitch. Static Thrust 438 240-241. Tip Losses and Solidity. Compressibility Stall 440 242. Preliminary Design : Empirical Formulae for Diameter and Inflow ; Shape ; Stresses 443 243-245. Helicopter and Autogyro. Approximate Theory of Autogyro Rotor. Typical Experimental Results , 446 CHAPTER XI PERFORMANCE AND EFFICIENCY 246-260. Preliminary Discussion. Equivalent Monoplane Aspect Ratio. Induced, Profile and Parasite Drags; Examples 451 251. Struts and Streamline Wires 457 252-263. Jones Efficiency ; Streamline Aeroplane. Subdivision of Parasite Drag 469 254-258. Airscrew Interference ; Example .461 259-260A. Prediction of Speed and Climb ; Bairstow's and the LesleyReid Methods. Method for Isolated Question 466 261-262. Take-off and Landing Run. Range and Endurance. , 473Xll CONTENTS ART. PAGE 262A-262F. Aerodynamic Efficiency ; Charts. Airscrew Effects ; Application to Prediction ; Wing-loading and High-altitude Flying ; Laminar Flow Effect 477 263. Autogyro and Helicopter 487 263A. Correction of Flight Observations . 489 CHAPTER XII SAFETY IN FLIGHT 264-265. General Problem. Wind Axes. Damping Factor 493 266-269. Introduction to Longitudinal Stability : Aerodynamic Dihedral ; Short Oscillation ; Examples ; Simplified Phugoid Oscillation ; Example 496 270-273. Classical Equations for Longitudinal Stability. Glauert's Non-dimensional System. Recast Equations. Approximate Factorisation . 503 274-278. Engine-off Stability : Force and Moment Derivatives. Example. Phugoid Oscillation Reconsidered 508 279-280. Effects of Stalling on Tail Efficiency and Damping 513 281-284. Level Flight ; High Speeds ; Free Elevators ; Climbing . 514 285. Graphical Analysis .516 286. Introduction to Lateral Stability 618 287-289. Asymmetric Equations ; Solution with Wind Axes ; Approximate Factorisation 519 290-292. Discussion in Terms of Derivatives. Example. Evaluation of Lateral Derivatives 521 293-295. Design and Stalling of Controls. Control in Relation to Stability. Large Disturbances. Flat Spin . 523 296. Load Factors in Flight ; Accelerometer Records 526 AUTHOR INDEX 629 SUBJECT INDEX 531NOTATION (Some of the symbols are also used occasionally in connections other than those stated below.) A . Aerodynamic force ; aspect ratio ; transverse moment of inertia. A.R.C.R. & M. Aeronautical Research Committee's Reports and Memoranda. A.S.I . Air speed indicator. a . Axial inflow factor of airscrews ; leverage of Aerodynamic force about C.G. of craft ; slope of lift curve of wings ; velocity of sound in air. a 9 . Slope of lift curve of tail plane. a . Angle of incidence. a, . Tail-setting angle. B . Gas constant ; longitudinal moment of inertia ; number of blades of an airscrew. B lt B* Stability coefficients. b . Rotational interference factor of airscrews. fi . Transverse dihedral ; twice the mean camber of a wing. C . Directional moment of inertia ; sectional area of tunnel. C.A.T . Compressed air tunnel. C lf C2 Stability coefficients. C L, CD, etc Non-dimensional coefficients of lift, drag, etc., on basis of stagnation pressure. C.G . Centre of gravity. C.P . Centre of pressure. c . Chord of wing or aerofoil ; molecular velocity. y . Ratio of specific heats ; tan'1 (drag/lift). D . Diameter ; drag. D lt D2 Stability coefficients. A, 8 Thickness of boundary layer; displacement thickness. E . Elasticity ; kinetic energy. E lt Et Stability coefficients.MV NOTATION e . Base of the Napierian logarithms. e . Angle of downwash. F . Skin friction (in Chapter II) ; Froude Number. ~ Frequency. . Vorticity. g . Acceleration due to gravity. H . Horse power ; the boundary layer ratio 8/0. h . Aerodynamic gap ; height or altitude. 7] .A co-ordinate ; efficiency ; elevator angle. 6 . Airscrew blade angle ; angle of climb ; angular co-ordinate ; temperature on the Centigrade scale ; momentum thickness. / . Impulse ; second moment of area. i . V-l ; as suffix to D : denoting induced drag ; incidence of autogyro disc. / . The advance of an airscrew per revolution in terms of its diameter. K . Circulation. k . Radius of gyration ; roughness. ^A ^B *c Inertia coefficients. *L *D etc - Non-dimensional coefficients of lift, drag, etc., on basis of twice the stagnation pressure. k 99 kx British drag and lift coefficients of autogyro rotor. L . Lift ; rolling moment. / . Length ; leverage of tail lift about C.G. of craft. X . Damping factor ; mean free path of molecule ; mean lift per unit span. M Pitching moment ; Mach number. m . Mass ; with suffix : non-dimensional moment derivative ; Mach angle, ji . Coefficient of viscosity ; * relative density of aeroplane ' ; a co-ordinate. N . Yawing moment. N.A.C.A National Advisory Committee for Aeronautics, U.S.A. N.P.L . National Physical Laboratory, Teddington. n . Distance along a normal to a surface ; revolutions per sec. v . Kinematic coefficient of viscosity ; a co-ordinate. 5 .A co-ordinate. P . Pitch of an airscrew ; pressure gradient ; total pressure.NOTATION XV p . Angular velocity of roll ; pressure or stress. p . Density of air in slugs per cu. ft. Q . Torque. q . Angular velocity of pitch ; resultant fluid velocity. R . Radius ; Reynolds number. R lt Rt Routh's discriminant. R.A.E . Royal Aircraft Establishment, Farnborough. r . Angular velocity of yaw ; lift/drag ratio ; radius. r a . Over-all lift /drag ratio. 5 . Area, particularly of wings. s . Distance along contour or streamline ; semi-span, a . Density of air relative to sea-level standard ; Prandtl's biplane factor ; sectional area of vortex ; solidity of an airscrew. r . Thickness ; thrust. t . Period of time in sec. ; the complex co-ordinate 5 + j. Unit of time in non-dimensional stability equations. T . Absolute temperature ; skin friction in Chapter IX ; tail angle of aerofoil section ; tail volume ratio.
. Aerodynamic stagger ; angle of bank ; angle of helical path of airscrew element ; velocity 'n>n ; yaw. f undisturbed velocity in the direct Oz. jcity of a body. lircraft. / components in the directions Ox, o. Deity ; mean loading of wing in at ; potential function $ + i^. it ibrce. )f stability charts. 'dinates ; with suffixes : non-dimenderivatives.NOTATION z The complex co-ordinate x + iy. & - Angular velocity of an airscrew. o> . Angular velocity. t& - . Impulsive pressure. V2 . 9'/ 9*1 + V4 AUTHOR INDEX The numbers refer to pages. Abbot, 406 Ackeret, J., 264 Aihara, T., 253 Bailey, A., 106 Bairstow, L., 119, 369, 470, 493 Baker, G. S., 390 Beavan, J. A., 106 Bell, A. H., 102 Bernoulli, D., 35, 252 Betz, A., 88, 224, 323 Bioletti, C., 450 Blasius, H., 352, 373, 390, 394 Boss, N. K., 334 Boussinesq, J., 196, 401 Bradfield, Miss F. B., 89 Bryan, G. H., 119, 493 Bryant, L. W., 498, 528 Burgers, J. M., 341, 386 Busemann, A., 266 Cave, Miss B. M., 369 Cierva, J. de la, 446 Clark, K. W., 89 Cope, W, F., 6 Cowley, W. L., 504 D Diehl, W. S., 454 Douglas, G. P., 442, 443 Dryden, H. L., 412 Drzewieki, S., 430 Eiffel, G., 68 Euler, L., 247 Fage, A., 211. 298, 353, 384, 394, 397, 409, 410, 423 Fairey, Sir R., 476 Fairthorne, R. A., 89 Falkner, V. M., 211, 390, 393, 394, 397 Farren, W. S., 82 Froude, W. and R. E., 65, 425 Garrard, W. C., 238, 415 Garner, H. M., 524 Gates, S. B., 516 Gebers, 390 Glauert, H., 174, 211, 234, 242, 259, 320, 339, 341, 354, 379, 440, 446, 493 Glauert, Mrs. H., 221, 234 Goett, 88 Goldstein, S., 108, 237, 415, 441 Gouge, A., 456, 473 Gray, W. E., 386 H Hagen, G., 350 Handley Page, Sir F., 161 Hansen, M., 385 Hartshorn, A. S., 341, 442 Helmholtz, H. v., 270, 289 Hiemenz, K , 394 Hocker, C., 405 Hooker, S. G., 263, 266 Hooper, M. S., 354 Houghton, R., 6 Howarth, L., 393, 421 Hugoniot, 116 Hyde, G. A., 106 Imai, I., 253 Jeans, Sir J. H., 362 Jeffreys, H., 528 Jennings, W. G., 422 Jones, Sir B. M., 87, 397, 459, 493 Jones, E. T., 422 Jones, R., 102. 397, 410 Jouguet, E., 264 Joukowski, N., 203, 228 K Kaplan, C., 253 Karden, H., 300 Karman, Th. v., 210, 253, 291, 341, 387, 390, 402 Kelvin, Lord, 192, 248, 270 Keinpf, G., 390 Kerber, L. V., 461 629530 Keune, 224 Klemin, A., 528 Kutta, W., 221 Lachmann, G. V., 498 Lamb, Sir H., 237, 286, 287 Lanchester, F. W., 68, 118, 430, 493, 501 Lang, Miss, 369 Langley, 68 Lavender, T., 397, 623 Lees, C. H., 352, 357 Lesley, E. P., 470 Levy, H., 604 Lindsey, W. F., 262 Lilienthal, O., 68 Liptrot, R. N., 473 Littell, R. E., 262 Lock, C. N. H., 106, 430, 446 M Maas, Van der, 452 Maccoll, J. W., 269 Marshall, Miss D., 385 Maxwell, J. C., 29, 32 Mines, R., 44 Mises, R. v., 234 Munk, M., 328, 498 N Nagamiya, T., 474 Nazir, P. P., 162, 514 Nikuradse, 392 AUTHOR INDEX O Oseen, C. W., 370 Otten, G., 452 Ower, E., 523 Pannell, J. R., 351 Perring, W. G. A., 442 Phillips, H., 118 Piercy, N. A. V., 44, 53, 151, 212, 219, 290, 301, 354, 362, 371, 373, 393, 395, 415 Piper, R. W., 212 Pohlhausen, K., 394 Poiseuille, J. L. M., 350 Prandtl, L., 88, 266, 289, 300, 330, 334, 370, 387, 392, 395, 401, 405, 420, 440 Prescott, J., 362 Preston, J. H., 212, 219, 373, 393 R Rankine, W. J. M., 116, 188, 267, 426 Rayleigh, Lord, 32, 58, 117, 188, 253, 367 Reid, E. G., 470 Relf, E. F., 102, 118, 276, 397, 405, 413, 623 Reynolds, O., 60, 350, 399 Riaboushinsky, D., 254 Richardson, E. G., 290, 369, 379, 395 Rolinson, D., 149 Routh, E. J., 280, 505 Rubach, 291 Saph, 351 Schlichting, H., 405 Schoder, 351 Sharman, C. F., 254 Simmons, L. F. G., 298 Squire, 395, 410 Stack, J., 262 Stanton, Sir T., 261, 351, 404 Stokes, Sir G., 370 Takenouti, Y., 474 Taylor, Sir G., 108, 254, 259, 266, 368, 402, 422 Tchapliguine, A., 263 Terazawa, K., 336 Thomson, Sir W., see Kelvin Theodorsen, T., 237 Tietjens, O. G., 232, 350 Tomotika, S., 474 Townend, H. C. H., 353, 452 Trefftz, E., 210 Tsien, H., 263 Tyler, R. A., 393 W Walker, W. S., 211, 397 Weick, R. E., 422 Wheatley, J. B., 460 White, C. M., 355 Whitehead, L. G., 212, 219, 393, 415, 423, 424 Wieselsberger, C., 390 Williams, D. H., 397, 410, 528 Winny, H. R, 354, 371, 386 Wood, S. A., 106 Wood, 422 Wright Brothers, 119 Wright, D., 135 Wright, K. V., 524 Young, A. D., 89, 395, 396 Zijnen, 386SUBJECT INDEX The numbers refer to pages. Acceleration from rest, of flow, 191 of aerofoil, 296 Accelerometer, 527 Ackeret's theory, 264 Actuator, 425 Acyclic flow, 171 Adiabatic flow, 37 Aerodynamic centre, 92, 243, 497 climb of airship, 129 efficiency, 477 force, 54, 75 coefficient, 76 scale, 61, 67, 97 smoothness, 404 Aerofoil characteristics, preliminary, 89 shaping, 207, 210, 215, 219, 225, 414, 417, 423 testing, 80, 106, 335, 413 theory, 194, 237, 259, 309, 412, 424 velocity curves, 416 Aerofoils, Joukowski, 203, 221 Karman-Trefftz, 210, 219, 224 laminar flow, 412 Piercy, 212, 219, 225, 413 rectangular and tapered, 323 Ailerons, 119, 158, 161, 418, 624 Air brakes, 136 Air, properties of, 1 Aircraft, types of, 9, 118, 446 Airscrew factors, 434 interference, 461 slipstream effects, 465, 471, 481, 486 Airscrews, approximations for, 443 blade element theory, 429 compressibility losses, 442 practical formulae, 435, 444 , Speed, 471 static thrust, 439 tip losses, 440 variable pitch, 139, 438 vortex theory, 432 Airships, 9, 18, 122, 126, 478 Airspeed indicator, 43 Altimeter, 17, 490 Altitude effects, 17, 22, 67, 143, 466, 476, 484 Arbitrary wing, 320 Aspect ratio, 89, 302, 316, 319, 333, 337, 486 Atmosphere, standard, 16 isothermal, 13 Atmospheric tunnel, 71 Autogyro, 446, 487 Autorotation, 160 Balance, aerodynamic, 82 Balloons, 8, 18 Bank, angle of, 167 Bernoulli's equation, 35, 40, 50, 163, 186, 251, 426, etc. Biplane, 123 definitions, 327 factor, 330, 454 of least drag, 331 Biplanes, tail planes of, 345 theorems relating to, 328 Blade angle, 428 Blockage, 108 Boundary, 26, 163, 187, 237, 261, 265, 364 layer, 52, 219; see flat plate control, 419 theory, 370 et seq. Breakaway, 178, 190, 219, 290, 393, 396, 409, 412, 419, 422 Buoyancy, 8, 18 Camber, 221, 224, 226, 237, 418, 423, 443 Cascade wing, 421 Cavitation, 170, 269 Ceiling, 19, 144, 469, 483 Centre of pressure coefficient, 80 of aerofoil, 90, 236, 237, 243, 418 of aeroplane, 154 of bulkhead, 11 stationary, 234, 244 travel, 91 Chattock gauge, 6 Circling flight, 156 Circular arc skeleton, 220, 226, 240 cylinder, 176, 195, 263, 292, 394, 397 Circulation and lift, 179, 230, 259 definition of, 49 generation of, 296 irrotational, 169, 228, 260, 366 persistence of, 248 631532 SUBJECT INDEX Circulation and lift contd prediction of, 228, 421 round wing, 228, 239, 260, 300, 310, 314, 323, 422 viscous, 365, 367 Climb, 129, 139, 438, 469, 472, 479, 488 correction for atmosphere, 491 slipstream, 472, 481 speed, 140 wind, 148 diagram, 492 Complex variable, 180 velocity, 181 Compressed-air tunnel, 96, 105 Compressible flow, 37, 103, 245, 259, 423 analogies, 254 Compressibility effects, 41, 108, 113, 253, 261, 266, 442 stall, see shock stall Condensation, 257 Conformal transformation, 194 applied to aerofoils, 203, 210, 212, 221, 225 normal and inclined plate, 198 parallel walls, 280 Constraint, tunnel, 108, 113, 276, 304, 335 Continuity, equation of, 44, 166, 245 Controls, 119, 129, 133, 152, 158, 161, 623 Convergent flow, 85, 169, 413 nozzle, 72 Critical angle, 89, 135, 161 Mach number, 113, 262, 423 Reynolds number, 100, 350, 355 Curved flow, 367 Cyclic flow, 171 Cylinder in motion, 186 D Damping factor, 495, 500, 503, 606, 612, 514 Density, definition, 1 of air, 2 of hydrogen and helium, 8 of water, 6 variation of in air flow, 37, 103, 116, 247, 253, 259 with altitude, 17, 67, 490 Derivatives, 505, 608, 614, 521 Descending flight, 146, 155, 158 Dihedral, longitudinal, 496 lateral, 162, 518 Displacement thickness, 391 Divergence, 496, 500 Divergent duct, 71, 185 Doublet, 172, 182, 285 Downwash, 149, 304, 339, 497, 609, 513 Drag, absence of in potential flow, 190 coefficients, 75 components of, 66, 364 form, 294, 410, 414, 418, 452, 455, 469 Drag, glider, 461, 471 induced, 123, 299, 311, 315, 328, 336, 453, 459 minimum, 126, 312, 331, 458, 478 of aerofoil, 90, etc. aircraft parts, 466, 459, 464 airship, 123, 127, 398 autogyro, 449, 488 circular cylinder, 62 core in pipe, 366 flap, 134 flat plate, 99, 370, 385, 387, 398 normal plate, 136, 190 pipe, 350, 352, 403 rough plate, 406 sphere, 99, 409 streamline wire, 457 strut, 99, 398, 467 profile, 113, 409, 442, 445, 452 skin, 403 total parasitic, 123, 147, 486 Dynamical equations, Euler's, 247 Dynamic head, 41, 115 Dynamically similar motions, 60, 66, 75, 92, 96 E Eccentric core in pipe, 356 Eddy viscosity, 400 Efficiency, Aerodynamic, 477 Jones, 459 of airscrew, 429, 437, 466 propulsion, 427, 477 Elasticity of air, 21 Electrical analogies, 264, 276 Elevator angle, 152 lag, 525 Elevators, 119 free, 516 Elliptic cylinder, 185, 188, 394, 422, 424 loading, 314, 322 wing, 315 Endurance, 476 Engine failure, 145 performance, 466, 471, 476, 485 Equal wing biplane, 332 Equipotentials, 164 Equivalence theorem, Munk's, 328 Equivalent monoplane aspect ratio, 463 Experiment, methods of, 61, 68, 304, 378, 386, 407, 509, 526 at high speeds, 103 Experimental mean pitch, 429 Fairing, 68 Fin, 119, 146, 454, 518 Fineness ratio, 176, 211, 467 Flaps, 133 Flat core in pipe, 356 ' Flat plate ' glider drag, 452 Flat plate boundary layer, 372, 388, 392 friction, 373, 383, 386, 388SUBJECT INDEX 633 Flow over faired nose, 172 in tunnel, 285 near stagnation point, 183 types of, 23 Form drag, see drag Fourier series, use of, 243, 321 Frequency, 61, 292 Friction velocity, 402 Froude's law, 66 theory of propulsion, 425 Fuel consumption, 475 Gap, 327 Gas laws, 13, 15 Geometric pitch, 428 Glauert's dimensionless system, 505 lift theorem, 259 Glider drag, see drag stability, 508 Gliders, 148 Gliding, 146 H Handley Page slot, 161 Helical flight, 158 Helicopter, 120, 446, 487 High speeds, see Mach, pitot, subsonic, supersonic, etc. Hot wire anemometry, 43, 379 Hydraulic analogy, 254 mean depth, 355 Hydrostatic equation, 5 Hyperbola, inversion of, 212, 225 Hyperbolic channel, 186 Images, method of, 276, 338, 342 Impulse, 191, 287, 293, 298, 312 Impulsive pressure, 165 Incidence, 89, 229, 311, 316, 325 effect on laminar flow, 415 Indicated air speed, 44 Induced drag, see drag method, 147 flow tunnel, 107 velocity, 270 Integration of Euler's equations, 250 Interference, 77, 108, 132, 152, 327 et seq., 399, 451, 452, 455, 457 et seq. Isothermal flow, 37 Jet constraint, 338 propulsion, 142, 452, 484 Joukowski transformation formula, 203 aerofoils, 204, 221 approximate formulae for, 206 Joukowski's hypothesis, 227, 236, 297 K Karman's boundary layer theorem, 380 modified form of, 392 similarity theory, 402 Karman trail, 292 Karman-Trefftz aerofoils, 210, 224 approximate formulae for, 211 Kelvin's theorem, 248 Kinematic coefficient of viscosity, 59, 67 Kinetic energy of irrotational flow, 192 minimum, 193, 312 of slipstream, 427 of trailing vortices, 299 Laminar flow, 23, 29, 49, 347, 354, 359, 373, 392 wings, 412 sub-layer, 353 Landing conditions, 132 run, 473 Laplace's equation, 166 Lapse rate, 17 Lateral oscillation, 519, 521 stability, 518 Lift, aerodynamic, of airship, 128 and circulation, 179, 230, 259, 296, 311 coefficients, 75 favourable range of, 415 curve slope, 233, 236, 261, 266, 317 evaluation from aerofoil pressures, 66, 109, 364 from trailing vortices, 301 from wall pressures, 109, 283 -drag balance, 79 ratio, 57, 75, 90, 92, 101, 266, 477, 488 elliptic, 314 generation of, 296 -grading, 323 effect on rolling moment, 523 of aerofoils, 90, 93, 102, 131, 133, 232, 236, 311, 315, 321 at subsonic speeds, 114, 259, 442 at supersonic speeds, 114, 264 of autogyro, 449, 488 of spinning cylinder, 180 of elliptic cylinder, 422 static, 8, 10, 18 uniform, 300, 324 Load, disposable, 122, 145 factor, 526 Longitudinal stability, 494, 496 graphical analysis, 516 M Mach number, 64, 103, 423 angle, 262 Maxwell's law, 31 Maximum velocity ratio, 220, 417, 423 thickness location, 206, 210, 215, 219, 414, 418534 SUBJECT INDEX Mean camber, 224 motion, equations of, 399 Minimum flying speed, 131, 488 Mixing length, Prandtl's, 401 Moment, pitching, 92, 119, 152, 233, 239, 418, 495 coefficients of, 75 rolling, 158, 162, 495, 522 yawing, 146, 168, 495, 623 Momentum thickness, 391 Monoplane theory, equations of, 311 N Non-dimensional coefficients, 76, 505 Normal plate, 136, 189, 193, 198, 313 profile drag, 409 Nose dive, 155 O Open jet tunnel, 74, 97 constraint, 338 Operational methods, 528 Orthogonal biplane, 327 Oscillation, see phugoid, short, etc. Oseen's approximation, 369 for flat plate, 370 Oval cylinder, 1 75 Parachute, 57 Parallel flow, see laminar Path lines, 24, 189, 274, 282, 287 Parasite drag, 77, 137, 456, 460 Performance, prediction of, 451, 466, 471, 482 reduction of, to standard conditions, 148, 489 Phugoid oscillation, 501, 507, 512, 525 Piercy aerofoils, 207, 212, 219, 225, 410, 413 approximate formulae for, 215, 227 Pipe flow, steady, 349, 354 turbulent, 351, 355 Pitch, of aircraft, 119, 495 of airscrew, 428 variable, 139, 438 Pitot boundary, 53 head, 41 and vorticity, 51 at supersonic speed, 114 -static tube, 43 tube, 41 fractional, 379 Potential flow, 166, 250 function, 180 temperature, 21 Power curves, 137, 143, 157, 468 dive, 146 factor of tunnel, 71, 103 formulae, 387 loading, 127, 459, 480, 482 Prandtl's approximation, 370, 385 Pressure diagrams, aerofoil, 65, 91, 219 airship, 127 circular cylinder, 178 strut, 219 static, 2, 17, 34 variation in flow, 39, 115 Profile drag, see drag Propeller, ideal, 425 Pusher airscrew, 462, 464 Q Qualitative compressibility effect, 253 theory of viscosity, 27 R Range, 475 Rankine-Hugoniot law, 116 Rankine's method, 187 vortex, 267 Rarefied air tunnel, 104 Rayleigh's formula, 68 Rectangular aerofoil, 323 Reduction formulae, 317 Relative density, of air, 17, 44 of aeroplane, 496, 506 Reynolds number, 60, 97, 104, etc. ' effective,' 408 transition, 384, 386, 389 Rolling subsidence, 518, 621 Rotating cylinder, 365 Roughness, 403, 406 Routh's discriminant, 505, 517 Rudder, 119, 157, 518, 523 Scale effect, 62, 93, 98, 101, 385, 398, 407, 410 ' Second problem, aerofoil theory,' 312 Sesqiii-plane, 327 Seventh-root law, 352, 387 Shock stall, 113, 262, 442 wave, 106, 112, 115, 262, 266, 423 Short oscillation, 498, 507, 512, 625 Singular points, 198, 216, 286 Sink, 168 Slip, absence of, 25, 350 of airscrew, 429 Slipstream, 425, 463, 465, 472, 480 Skin drag, 403 friction, 31, 55, 363 coefficient, 397 distribution on monoplane, 459 measurement of, 378 of aerofoils, 398, 410 of airships, 398 of cylinders, 393 of plates, see flat plate of pipes, see pipe reduction of, on wings, 411 transitional, 389SUBJECT INDEX 535 Smoothness, aerodynamic, 405, 406 Smooth-turbulent formulae, 404 Soaring, 149 Solidity, of airscrew, 427, 434 of rotor, 488 Sonic throat, 38, 106, 110 Sound, velocity of, 22 wave, 259, 263, 265 Source, 167, 285 and sink, 171 Span-grading, 323 -loading, 315 Specific consumption, 476 Spin, 74, 160, 526 Spinning divergence, 521 Spoilers, 137, 524 Stability, asymmetric, see lateral atmospheric, 20 coefficients, 504, 507, 511, 520 graphical analysis, 153, 497, 516 longitudinal, see longitudinal of fluid motion, 292, 355, 367, 418 Stagger, 327 Stagnation point, 41, 183, 227, 368, 395 pressure, 42, 115 Stalling, 89, 102, 131, 135, 160, 290, 301, 420, 422, 438, 440, 449, 488 of Controls, 75, 153, 161, 418, 524 Starting vortex, 296 Stilling length, 351 Stoke's approximation, 369 operator, 247 Stratosphere, 1, 14, 21, 22, 63, 67, 485 Stream function denned, 47 Streamline, 23 aeroplane, 459 wall, 107 wires, 457 Stresses, component, 32, 360, 400 Strip method, 159, 430, 522 Strut, 99, 210, 219, 442, 457 Subsidence, 496, 500 Subsonic flow, 63, 250, 259, 423 experiment in, 103, 113, 442 Successive approximation method, 373 Supersonic flow, 114, 115, 262 et scq. experiment in, 109, 113, 261, 166 Surface of discontinuity, 238, 288 Symmetric flight, 122, 494 T Tail angle, 210, 214 efficiency, 513 -first lay-out, 498, 513 plane, 119, 149, 339, 497, 500, 509 -setting angle, 152, 154, 497 Take-off, 134, 136, 149, 438, 473 Tank, electric, 254, 276 ship, 66 Tapered wing, 323, 326 Temperature variation in flow, 37 Thomson's theorem, see Kelvin Thrust and torque coefficients, 435, 440, 443, 467, 471 apparent, 462 Townend ring, 452 Trailing vortex pair, 297 et seq. Transformation formula?, 194, 198, 203, 210, 213, 216, 281 Transformed sections, 204, 207, 210, 219, 226, 230, 417, 419 Transition, 385, 398, 409 curve, 389, 398 delay of, 412, 413, 419 effect on friction, 389, 411 effect on form drag, 455 effect 011 profile drag, 413, 486 effect of incidence, 416 detection, 386 point, 386 Reynolds number, 386, 472, 481 tunnel and flight, 399, 407, 410 Troposphere, 1, 14 Tunnel, atmospheric, 71 compressed air, 96 constraint, 108, 276, 281, 335 full-scale or giant, 74, 98 high-speed, 103, 106 laminar flow, 413, 455 supersonic, 109 variable-density, 103 vertical spinning, 74 Turbulence factor, 407 gauge of, in tunnel, 101 Turbulent flow, 24, 99, 351, 387, 395, 309 et scq., 407, 409 et scq. U Uniform flow, 23, 181 lift, 300 Upgust, 319, 528 Upward wind, 148 Velocity amplitude, 368, 395 defect, 403 induced, 270, 272, 310, 329 in potential flow, 183, 208 -potential, 163 physical explanation of, 165 ratio diagram, 416 maximum, 220, 423 Venturi tube, 44, 186 Viscosity, coefficient of, 31 theory and laws of, 27-31 eddy, 400636 SUBJECT INDEX Viscous flow, equations of, 362 Vortex, between walls, 281 bound, 272, 283 laws of inviscid, 270 pair, 274, 278 energy of, 290 impulse of, 287 Rankine's, 268 sheet, 288 starting, 296 street, 291 theory of airscrews, 432 Vortices, generation of, 287 trailing, 298 et scq. wing-tip, 300 Vorticity, 49-51, 237, 245, 250, 267, 298, 349, 359, 364, 371, 402 W Wake blockage, 108 effect on pressures, 393 on tail plane, 513 exploration, 86, 109 Wall, flexible tunnel, 107 Wave, see shock, sound -making resistance, 65 Waves in water channel, 256 Wind axes, 495 effects on flight, 148 -tunnel corrections, 84, 169, 335, 344 Wing-loading, 122, 131, 136, 479, 484 Yaw, 119, 146, 156, 162, 454, 455, 495, 518,
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