Theoretical Aerodynamics
1. Edition May 2013
560 Pages, Hardcover
Wiley & Sons Ltd
Short Description
This book provides a user-friendly treatment of theoretical aerodynamics for both newcomers to the field and engineers who want to understand things quickly. All topics are explained in simple terms, gradually progressing from the basics to a higher level. The theory of aerofoil, its design features, and performance aspects are introduced systematically, as are fluid mechanics, the theory and application of Joukowski transformation, the vortex dynamics, and wing theory. The examples are designed to fix the theory studied in an effective manner, while the physics behind the process is clearly explained throughout.
Theoretical Aerodynamics is a user-friendly text for a full course on theoretical aerodynamics. The author systematically introduces aerofoil theory, its design features and performance aspects, beginning with the basics required, and then gradually proceeding to higher level. The mathematics involved is presented so that it can be followed comfortably, even by those who are not strong in mathematics. The examples are designed to fix the theory studied in an effective manner. Throughout the book, the physics behind the processes are clearly explained. Each chapter begins with an introduction and ends with a summary and exercises.
This book is intended for graduate and advanced undergraduate students of Aerospace Engineering, as well as researchers and Designers working in the area of aerofoil and blade design.
* Provides a complete overview of the technical terms, vortex theory, lifting line theory, and numerical methods
* Presented in an easy-to-read style making full use of figures and illustrations to enhance understanding, and moves well simpler to more advanced topics
* Includes a complete section on fluid mechanics and thermodynamics, essential background topics to the theory of aerodynamics
* Blends the mathematical and physical concepts of design and performance aspects of lifting surfaces, and introduces the reader to the thin aerofoil theory, panel method, and finite aerofoil theory
* Includes a Solutions Manual for end-of-chapter exercises, and Lecture slides on the book's Companion Website
Preface xvii
1 Basics 1
1.1 Introduction 1
1.2 Lift and Drag 1
1.3 Monoplane Aircraft 4
1.4 Biplane 5
1.5 Triplane 6
1.6 Aspect Ratio 9
1.7 Camber 10
1.8 Incidence 11
1.9 Aerodynamic Force 12
1.10 Scale Effect 15
1.11 Force and Moment Coefficients 17
1.12 The Boundary Layer 18
1.13 Summary 20
Exercise Problems 21
Reference 22
2 Essence of Fluid Mechanics 23
2.1 Introduction 23
2.2 Properties of Fluids 23
2.3 Thermodynamic Properties 28
2.4 Surface Tension 30
2.5 Analysis of Fluid Flow 31
2.6 Basic and Subsidiary Laws 34
2.7 Kinematics of Fluid Flow 35
2.8 Streamlines 41
2.9 Potential Flow 42
2.10 Combination of Simple Flows 49
2.11 Flow Past a Circular Cylinder without Circulation 57
2.12 Viscous Flows 63
2.13 Compressible Flows 78
2.14 Summary 87
Exercise Problems 97
References 102
3 Conformal Transformation 103
3.1 Introduction 103
3.2 Basic Principles 103
3.3 Complex Numbers 107
3.4 Summary 112
Exercise Problems 113
4 Transformation of Flow Pattern 115
4.1 Introduction 115
4.2 Methods for Performing Transformation 115
4.3 Examples of Simple Transformation 119
4.4 Kutta.Joukowski Transformation 122
4.5 Transformation of Circle to Straight Line 123
4.6 Transformation of Circle to Ellipse 124
4.7 Transformation of Circle to Symmetrical Aerofoil 125
4.8 Transformation of a Circle to a Cambered Aerofoil 129
4.9 Transformation of Circle to Circular Arc 134
4.10 Joukowski Hypothesis 137
4.11 Lift of Joukowski Aerofoil Section 141
4.12 The Velocity and Pressure Distributions on the Joukowski Aerofoil 144
4.13 The Exact Joukowski Transformation Process and Its Numerical Solution 146
4.14 The Velocity and Pressure Distribution 147
4.15 Aerofoil Characteristics 155
4.16 Aerofoil Geometry 157
4.17 Wing Geometrical Parameters 162
4.18 Aerodynamic Force and Moment Coefficients 166
4.19 Summary 171
Exercise Problems 180
Reference 181
5 Vortex Theory 183
5.1 Introduction 183
5.2 Vorticity Equation in Rectangular Coordinates 184
5.3 Circulation 188
5.4 Line (point) Vortex 192
5.5 Laws of Vortex Motion 194
5.6 Helmholtz's Theorems 195
5.7 Vortex Theorems 196
5.8 Calculation of uR, the Velocity due to Rotational Flow 204
5.9 Biot-Savart Law 207
5.10 Vortex Motion 220
5.11 Forced Vortex 223
5.12 Free Vortex 224
5.13 Compound Vortex 229
5.14 Physical Meaning of Circulation 230
5.15 Rectilinear Vortices 235
5.16 Velocity Distribution 237
5.17 Size of a Circular Vortex 239
5.18 Point Rectilinear Vortex 239
5.19 Vortex Pair 240
5.20 Image of a Vortex in a Plane 241
5.21 Vortex between Parallel Plates 242
5.22 Force on a Vortex 244
5.23 Mutual action of Two Vortices 244
5.24 Energy due to a Pair of Vortices 244
5.25 Line Vortex 247
5.26 Summary 248
Exercise Problems 254
References 256
6 Thin Aerofoil Theory 257
6.1 Introduction 257
6.2 General Thin Aerofoil Theory 258
6.3 Solution of the General Equation 261
6.4 The Circular Arc Aerofoil 269
6.5 The General Thin Aerofoil Section 275
6.6 Lift, Pitching Moment and Center of Pressure Coefficients for a Thin Aerofoil 278
6.7 Flapped Aerofoil 283
6.8 Summary 289
Exercise Problems 294
References 295
7 Panel Method 297
7.1 Introduction 297
7.2 Source Panel Method 297
7.3 The Vortex Panel Method 302
7.4 Pressure Distribution around a Circular Cylinder by Source Panel Method 305
7.5 Using Panel Methods 309
7.6 Summary 329
Exercise Problems 330
Reference 330
8 Finite Aerofoil Theory 331
8.1 Introduction 331
8.2 Relationship between Spanwise Loading and Trailing Vorticity 331
8.3 Downwash 332
8.4 Characteristics of a Simple Symmetrical Loading - Elliptic Distribution 335
8.5 Aerofoil Characteristic with a More General Distribution 339
8.6 The Vortex Drag for Modified Loading 343
8.7 Lancaster - Prandtl Lifting Line Theory 347
8.8 Effect of Downwash on Incidence 353
8.9 The Integral Equation for the Circulation 355
8.10 Elliptic Loading 356
8.11 Aerodynamic Characteristics of Asymmetric Loading 372
8.12 Lifting Surface Theory 378
8.13 Aerofoils of Small Aspect Ratio 387
8.14 Lifting Surface 391
8.15 Summary 394
Exercise Problems 401
9 Compressible Flows 405
9.1 Introduction 405
9.2 Thermodynamics of Compressible Flows 405
9.3 Isentropic Flow 409
9.4 Discharge from a Reservoir 411
9.5 Compressible Flow Equations 413
9.6 Crocco's Theorem 414
9.7 The General Potential Equation for Three-Dimensional Flow 418
9.8 Linearization of the Potential Equation 420
9.9 Potential Equation for Bodies of Revolution 423
9.10 Boundary Conditions 425
9.11 Pressure Coefficient 428
9.12 Similarity Rule 429
9.13 Two-Dimensional Flow: Prandtl-Glauert Rule for Subsonic Flow 429
9.14 Prandtl-Glauert Rule for Supersonic Flow: Versions I and II 436
9.15 The von Karman Rule for Transonic Flow 439
9.16 Hypersonic Similarity 442
9.17 Three-Dimensional Flow: The Gothert Rule 444
9.18 Moving Disturbance 455
9.19 Normal Shock Waves 457
9.20 Change of Total Pressure across a Shock 462
9.21 Oblique Shock and Expansion Waves 463
9.22 Thin Aerofoil Theory 479
9.23 Two-Dimensional Compressible Flows 485
9.24 General Linear Solution for Supersonic Flow 486
9.25 Flow over a Wave-Shaped Wall 491
9.26 Summary 495
Exercise Problems 509
References 512
10 Simple Flights 513
10.1 Introduction 513
10.2 Linear Flight 513
10.3 Stalling 514
10.4 Gliding 516
10.5 Straight Horizontal Flight 518
10.6 Sudden Increase of Incidence 520
10.7 Straight Side-Slip 521
10.8 Banked Turn 522
10.9 Phugoid Motion 523
10.10 The Phugoid Oscillation 525
10.11 Summary 529
Exercise Problems 531
Further Readings 533
Index 535
