Theoretical Aerodynamics	1
	Contents	9
	About the Author	17
	Preface	19
	1 Basics	21
	1.1 Introduction	21
	1.2 Lift and Drag	21
	1.3 Monoplane Aircraft	24
	1.3.1 Types of Monoplane	25
	1.4 Biplane	25
	1.4.1 Advantages and Disadvantages	26
	1.5 Triplane	26
	1.5.1 Chord of a Profile	27
	1.5.2 Chord of an Aerofoil	28
	1.6 Aspect Ratio	29
	1.7 Camber	30
	1.8 Incidence	31
	1.9 Aerodynamic Force	32
	1.10 Scale Effect	35
	1.11 Force and Moment Coefficients	37
	1.12 The Boundary Layer	38
	1.13 Summary	40
	Exercise Problems	41
	Reference	42
	2 Essence of Fluid Mechanics	43
	2.1 Introduction	43
	2.2 Properties of Fluids	43
	2.2.1 Pressure	43
	2.2.2 Temperature	44
	2.2.3 Density	44
	2.2.4 Viscosity	45
	2.2.5 Absolute Coefficient of Viscosity	45
	2.2.6 Kinematic Viscosity Coefficient	47
	2.2.7 Thermal Conductivity of Air	47
	2.2.8 Compressibility	48
	2.3 Thermodynamic Properties	48
	2.3.1 Specific Heat	48
	2.3.2 The Ratio of Specific Heats	49
	2.4 Surface Tension	50
	2.5 Analysis of Fluid Flow	51
	2.5.1 Local and Material Rates of Change	52
	2.5.2 Graphical Description of Fluid Motion	53
	2.6 Basic and Subsidiary Laws	54
	2.6.1 System and Control Volume	54
	2.6.2 Integral and Differential Analysis	55
	2.6.3 State Equation	55
	2.7 Kinematics of Fluid Flow	55
	2.7.1 Boundary Layer Thickness	57
	2.7.2 Displacement Thickness	58
	2.7.3 Transition Point	59
	2.7.4 Separation Point	59
	2.7.5 Rotational and Irrotational Motion	60
	2.8 Streamlines	61
	2.8.1 Relationship between Stream Function and Velocity Potential	61
	2.9 Potential Flow	62
	2.9.1 Two-dimensional Source and Sink	63
	2.9.2 Simple Vortex	65
	2.9.3 Source-Sink Pair	66
	2.9.4 Doublet	66
	2.10 Combination of Simple Flows	69
	2.10.1 Flow Past a Half-Body	69
	2.11 Flow Past a Circular Cylinder without Circulation	77
	2.11.1 Flow Past a Circular Cylinder with Circulation	79
	2.12 Viscous Flows	83
	2.12.1 Drag of Bodies	85
	2.12.2 Turbulence	90
	2.12.3 Flow through Pipes	95
	2.13 Compressible Flows	98
	2.13.1 Perfect Gas	99
	2.13.2 Velocity of Sound	100
	2.13.3 Mach Number	100
	2.13.4 Flow with Area Change	100
	2.13.5 Normal Shock Relations	102
	2.13.6 Oblique Shock Relations	103
	2.13.7 Flow with Friction	104
	2.13.8 Flow with Simple T0-Change	106
	2.14 Summary	107
	Exercise Problems	117
	References	122
	3 Conformal Transformation	123
	3.1 Introduction	123
	3.2 Basic Principles	123
	3.2.1 Length Ratios between the Corresponding Elements in the Physical and Transformed Planes	126
	3.2.2 Velocity Ratios between the Corresponding Elements in the Physical and Transformed Planes	126
	3.2.3 Singularities	127
	3.3 Complex Numbers	127
	3.3.1 Differentiation of a Complex Function	130
	3.4 Summary	132
	Exercise Problems	133
	4 Transformation of Flow Pattern	135
	4.1 Introduction	135
	4.2 Methods for Performing Transformation	135
	4.2.1 By Analytical Means	136
	4.3 Examples of Simple Transformation	139
	4.4 Kutta-Joukowski Transformation	142
	4.5 Transformation of Circle to Straight Line	143
	4.6 Transformation of Circle to Ellipse	144
	4.7 Transformation of Circle to Symmetrical Aerofoil	145
	4.7.1 Thickness to Chord Ratio of Symmetrical Aerofoil	147
	4.7.2 Shape of the Trailing Edge	149
	4.8 Transformation of a Circle to a Cambered Aerofoil	149
	4.8.1 Thickness-to-Chord Ratio of the Cambered Aerofoil	152
	4.8.2 Camber	154
	4.9 Transformation of Circle to Circular Arc	154
	4.9.1 Camber of Circular Arc	157
	4.10 Joukowski Hypothesis	157
	4.10.1 The Kutta Condition Applied to Aerofoils	159
	4.10.2 The Kutta Condition in Aerodynamics	160
	4.11 Lift of Joukowski Aerofoil Section	161
	4.12 The Velocity and Pressure Distributions on the Joukowski Aerofoil	164
	4.13 The Exact Joukowski Transformation Process and Its Numerical Solution	166
	4.14 The Velocity and Pressure Distribution	167
	4.15 Aerofoil Characteristics	175
	4.15.1 Parameters Governing the Aerodynamic Forces	177
	4.16 Aerofoil Geometry	177
	4.16.1 Aerofoil Nomenclature	177
	4.16.2 NASA Aerofoils	181
	4.16.3 Leading-Edge Radius and Chord Line	181
	4.16.4 Mean Camber Line	181
	4.16.5 Thickness Distribution	182
	4.16.6 Trailing-Edge Angle	182
	4.17 Wing Geometrical Parameters	182
	4.18 Aerodynamic Force and Moment Coefficients	186
	4.18.1 Moment Coefficient	189
	4.19 Summary	191
	Exercise Problems	200
	Reference	201
	5 Vortex Theory	203
	5.1 Introduction	203
	5.2 Vorticity Equation in Rectangular Coordinates	204
	5.2.1 Vorticity Equation in Polar Coordinates	206
	5.3 Circulation	208
	5.4 Line (point) Vortex	212
	5.5 Laws of Vortex Motion	214
	5.6 Helmholtz’s Theorems	215
	5.7 Vortex Theorems	216
	5.7.1 Stoke’s Theorem	220
	5.8 Calculation of uR, the Velocity due to Rotational Flow	224
	5.9 Biot-Savart Law	227
	5.9.1 A Linear Vortex of Finite Length	230
	5.9.2 Semi-Infinite Vortex	231
	5.9.3 Infinite Vortex	231
	5.9.4 Helmholtz’s Second Vortex Theorem	236
	5.9.5 Helmholtz’s Third Vortex Theorem	240
	5.9.6 Helmholtz’s Fourth Vortex Theorem	240
	5.10 Vortex Motion	240
	5.11 Forced Vortex	243
	5.12 Free Vortex	244
	5.12.1 Free Spiral Vortex	246
	5.13 Compound Vortex	249
	5.14 Physical Meaning of Circulation	250
	5.15 Rectilinear Vortices	255
	5.15.1 Circular Vortex	256
	5.16 Velocity Distribution	257
	5.17 Size of a Circular Vortex	259
	5.18 Point Rectilinear Vortex	259
	5.19 Vortex Pair	260
	5.20 Image of a Vortex in a Plane	261
	5.21 Vortex between Parallel Plates	262
	5.22 Force on a Vortex	264
	5.23 Mutual action of Two Vortices	264
	5.24 Energy due to a Pair of Vortices	264
	5.25 Line Vortex	267
	5.26 Summary	268
	Exercise Problems	274
	References	276
	6 Thin Aerofoil Theory	277
	6.1 Introduction	277
	6.2 General Thin Aerofoil Theory	278
	6.3 Solution of the General Equation	281
	6.3.1 Thin Symmetrical Flat Plate Aerofoil	282
	6.3.2 The Aerodynamic Coefficients for a Flat Plate	285
	6.4 The Circular Arc Aerofoil	289
	6.4.1 Lift, Pitching Moment, and the Center of Pressure Location for Circular Arc Aerofoil	291
	6.5 The General Thin Aerofoil Section	295
	6.6 Lift, Pitching Moment and Center of Pressure Coefficients for a Thin Aerofoil	298
	6.7 Flapped Aerofoil	303
	6.7.1 Hinge Moment Coefficient	306
	6.7.2 Jet Flap	308
	6.7.3 Effect of Operating a Flap	308
	6.8 Summary	309
	Exercise Problems	314
	References	315
	7 Panel Method	317
	7.1 Introduction	317
	7.2 Source Panel Method	317
	7.2.1 Coefficient of Pressure	320
	7.3 The Vortex Panel Method	322
	7.3.1 Application of Vortex Panel Method	322
	7.4 Pressure Distribution around a Circular Cylinder by Source Panel Method	325
	7.5 Using Panel Methods	329
	7.5.1 Limitations of Panel Method	329
	7.5.2 Advanced Panel Methods	329
	7.6 Summary	349
	Exercise Problems	350
	Reference	350
	8 Finite Aerofoil Theory	351
	8.1 Introduction	351
	8.2 Relationship between Spanwise Loading and Trailing Vorticity	351
	8.3 Downwash	352
	8.4 Characteristics of a Simple Symmetrical Loading – Elliptic Distribution	355
	8.4.1 Lift for an Elliptic Distribution	356
	8.4.2 Downwash for an Elliptic Distribution	356
	8.4.3 Drag Dv due to Downwash for Elliptical Distribution	358
	8.5 Aerofoil Characteristic with a More General Distribution	359
	8.5.1 The Downwash for Modified Elliptic Loading	361
	8.6 The Vortex Drag for Modified Loading	363
	8.6.1 Condition for Vortex Drag Minimum	365
	8.7 Lancaster – Prandtl Lifting Line Theory	367
	8.7.1 The Lift	369
	8.7.2 Induced Drag	370
	8.8 Effect of Downwash on Incidence	373
	8.9 The Integral Equation for the Circulation	375
	8.10 Elliptic Loading	376
	8.10.1 Lift and Drag for Elliptical Loading	377
	8.10.2 Lift Curve Slope for Elliptical Loading	379
	8.10.3 Change of Aspect Ratio with Incidence	379
	8.10.4 Problem II	380
	8.10.5 The Lift for Elliptic Loading	383
	8.10.6 The Downwash Velocity for Elliptic Loading	386
	8.10.7 The Induced Drag for Elliptic Loading	386
	8.10.8 Induced Drag Minimum	389
	8.10.9 Lift and Drag Calculation by Impulse Method	390
	8.10.10 The Rectangular Aerofoil	391
	8.10.11 Cylindrical Rectangular Aerofoil	392
	8.11 Aerodynamic Characteristics of Asymmetric Loading	392
	8.11.1 Lift on the Aerofoil	392
	8.11.2 Downwash	392
	8.11.3 Vortex Drag	393
	8.11.4 Rolling Moment	394
	8.11.5 Yawing Moment	396
	8.12 Lifting Surface Theory	398
	8.12.1 Velocity Induced by a Lifting Line Element	398
	8.12.2 Munk’s Theorem of Stagger	401
	8.12.3 The Induced Lift	402
	8.12.4 Blenk’s Method	403
	8.12.5 Rectangular Aerofoil	404
	8.12.6 Calculation of the Downwash Velocity	405
	8.13 Aerofoils of Small Aspect Ratio	407
	8.13.1 The Integral Equation	408
	8.13.2 Zero Aspect Ratio	410
	8.13.3 The Acceleration Potential	410
	8.14 Lifting Surface	411
	8.15 Summary	414
	Exercise Problems	421
	9 Compressible Flows	425
	9.1 Introduction	425
	9.2 Thermodynamics of Compressible Flows	425
	9.3 Isentropic Flow	429
	9.4 Discharge from a Reservoir	431
	9.5 Compressible Flow Equations	433
	9.6 Crocco’s Theorem	434
	9.6.1 Basic Solutions of Laplace’s Equation	438
	9.7 The General Potential Equation for Three-Dimensional Flow	438
	9.8 Linearization of the Potential Equation	440
	9.8.1 Small Perturbation Theory	440
	9.9 Potential Equation for Bodies of Revolution	443
	9.9.1 Solution of Nonlinear Potential Equation	445
	9.10 Boundary Conditions	445
	9.10.1 Bodies of Revolution	447
	9.11 Pressure Coefficient	448
	9.11.1 Bodies of Revolution	449
	9.12 Similarity Rule	449
	9.13 Two-Dimensional Flow: Prandtl-Glauert Rule for Subsonic Flow	449
	9.13.1 The Prandtl-Glauert Transformations	449
	9.13.2 The Direct Problem-Version I	451
	9.13.3 The Indirect Problem (Case of Equal Potentials): P-G Transformation – Version II	454
	9.13.4 The Streamline Analogy (Version III): Gothert’s Rule	455
	9.14 Prandtl-Glauert Rule for Supersonic Flow: Versions I and II	456
	9.14.1 Subsonic Flow	456
	9.14.2 Supersonic Flow	456
	9.15 The von Karman Rule for Transonic Flow	459
	9.15.1 Use of Karman Rule	460
	9.16 Hypersonic Similarity	462
	9.17 Three-Dimensional Flow: The Gothert Rule	464
	9.17.1 The General Similarity Rule	464
	9.17.2 Gothert Rule	466
	9.17.3 Application to Wings of Finite Span	467
	9.17.4 Application to Bodies of Revolution and Fuselage	468
	9.17.5 The Prandtl-Glauert Rule	470
	9.17.6 The von Karman Rule for Transonic Flow	474
	9.18 Moving Disturbance	475
	9.18.1 Small Disturbance	476
	9.18.2 Finite Disturbance	477
	9.19 Normal Shock Waves	477
	9.19.1 Equations of Motion for a Normal Shock Wave	477
	9.19.2 The Normal Shock Relations for a Perfect Gas	478
	9.20 Change of Total Pressure across a Shock	482
	9.21 Oblique Shock and Expansion Waves	483
	9.21.1 Oblique Shock Relations	484
	9.21.2 Relation between ? and ?	486
	9.21.3 Supersonic Flow over a Wedge	489
	9.21.4 Weak Oblique Shocks	491
	9.21.5 Supersonic Compression	493
	9.21.6 Supersonic Expansion by Turning	495
	9.21.7 The Prandtl-Meyer Function	497
	9.21.8 Shock-Expansion Theory	497
	9.22 Thin Aerofoil Theory	499
	9.22.1 Application of Thin Aerofoil Theory	500
	9.23 Two-Dimensional Compressible Flows	505
	9.24 General Linear Solution for Supersonic Flow	506
	9.24.1 Existence of Characteristics in a Physical Problem	508
	9.24.2 Equation for the Streamlines from Kinematic Flow Condition	509
	9.25 Flow over a Wave-Shaped Wall	511
	9.25.1 Incompressible Flow	511
	9.25.2 Compressible Subsonic Flow	512
	9.25.3 Supersonic Flow	513
	9.25.4 Pressure Coefficient	514
	9.26 Summary	515
	Exercise Problems	529
	References	532
	10 Simple Flights	533
	10.1 Introduction	533
	10.2 Linear Flight	533
	10.3 Stalling	534
	10.4 Gliding	536
	10.5 Straight Horizontal Flight	538
	10.6 Sudden Increase of Incidence	540
	10.7 Straight Side-Slip	541
	10.8 Banked Turn	542
	10.9 Phugoid Motion	543
	10.10 The Phugoid Oscillation	545
	10.11 Summary	549
	Exercise Problems	551
	Further Readings	553
	Index	555