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For junior/senior and graduatelevel courses in Aerodynamics, Mechanical Engineering, and Aerospace Engineering. This text also serves as a useful reference for professionals in the aeronautics industry.
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Revised to reflect the technological advances and modern application in Aerodynamics, the Sixth Edition of Aerodynamics for Engineers merges fundamental fluid mechanics, experimental techniques, and computational fluid dynamics techniques to build a solid foundation for readers in aerodynamic applications from lowspeed through hypersonic flight. It presents a background discussion of each topic followed by a presentation of the theory, and then derives fundamental equations, applies them to simple computational techniques, and compares them to experimental data.
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**** The first edition 1979 is cited in BCL3. A textbook for a course in aerodynamics for advanced undergraduates or grad students. Presumes basic physics, thermodynamics, and math. Annotation c. Book News, Inc., Portland, OR booknews.comBooknews
This textbook is for use in an intermediate to advanced aerodynamics course. Topics include fluid properties and mechanics, incompressible flow fields and boundary layers, compressible subsonic and transonic flows, hypersonic flows, and supersonic flows over wings and airplane configurations. Updates the 1989 second edition. Annotation c. by Book News, Inc., Portland, Or.Product Details
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This text is designed for use by undergraduate students in intermediate and advanced classes in aerodynamics and by graduate students in mechanical engineering and aerospace engineering. Basic fluid mechanic principles are presented in the first four chapters. Fluid properties and a model for the standard atmosphere are discussed in Chapter 1, "Fluid Properties." The equations governing fluid motion are presented in Chapter 2, "Fundamentals of Fluid Mechanics." Differential and integral forms of the continuity equation (based on the conservation of mass), the linear momentum equation (based on Newton's law of motion), and the energy equation (based on the first law of thermodynamics) are presented. Modeling inviscid, incompressible flows is the subject of Chapter 3, "Dynamics of an Incompressible, Inviscid Flow Field." Modeling viscous boundary layers, with emphasis on incompressible flows, is the subject of Chapter 4, "Viscous Boundary Layers." Thus, Chapters 1 through 4 present material that covers the principles upon which the aerodynamic applications are based. For the reader who already has had a course (or courses) in fluid mechanics, these four chapters provide a comprehensive review of fluid mechanics and an introduction to the nomenclature and style of the present text.
At this point, the reader is ready to begin material focused on aerodynamic applications. Parameters that characterize the geometry of aerodynamic configurations and parameters that characterize aerodynamic performance are presented in Chapter 5, "Characteristic Parameters for Airfoil and Wing Aerodynamics." Techniques for modeling the aerodynamic performance of twodimensional airfoils and, offinitespan wings at low speeds (where variations in density are negligible) are presented in Chapters 6 and 7, respectively. Chapter 6 is titled "Incompressible Flows around Wings of Infinite Span," and Chapter 7 is titled "Incompressible Flow about Wings of Finite Span."
The next five chapters deal with compressible flow fields. To provide the reader with the necessary background for highspeed aerodynamics, the basic fluid mechanic principles for compressible flows are discussed in Chapter 8, "Dynamics of a Compressible Flow Field." Thus, from a pedagogical point of view, the material presented in Chapter 8 complements the material presented in Chapters 1 through 4. Techniques for modeling highspeed flows (where density variations cannot be neglected) are presented in Chapters 9 through 12. Aerodynamic performance for compressible, subsonic flows through transonic speeds is the subject of Chapter 9, "Compressible Subsonic Flows and Transonic Flows." Supersonic aerodynamics for twodimensional airfoils is the subject of Chapter 10, "TwoDimensional Supersonic Flows about Thin Airfoils" and for finitespan wings in Chapter 11, "Supersonic Flows over Wings and Airplane Configurations." Hypersonic flows are the subject of Chapter 12.
At this point, chapters have been dedicated to the development of basic models for calculating the aerodynamic performance parameters for each of the possible speed ranges. The assumptions and, therefore, the restrictions incorporated into the development of the theory are carefully noted. The applications of the theory are illustrated by working one or more problems. Solutions are obtained using numerical techniques in order to apply the theory for those flows where closedform solutions are impractical or impossible. In each of the chapters, the computed aerodynamic parameters are compared with experimental data from the open literature to illustrate both the validity of the theoretical analysis and its limitations (or, equivalently, the range of conditions for which the theory is applicable). One objective is to use the experimental data to determine the limits of applicability for the proposed models.
Extensive discussions of the effects of viscosity, compressibility, shock/boundarylayer interactions, turbulence modeling, and other practical aspects of contemporary aerodynamic design are also presented. Problems at the end of each chapter are designed to complement the material presented within the chapter and to develop the student's understanding of the relative importance of various phenomena. The text emphasizes practical problems and the techniques through which solutions to these problems can be obtained. Because both the International System of Units (Systeme International d'Unites, abbreviated SI) and English units are commonly used in the aerospace industry, both are used in this text. Conversion factors between SI units and English units are presented on the inside covers.
Advanced material relating to design features of aircraft over more than a century and to the tools used to define the aerodynamic parameters are presented in Chapters 13 and 14. Chapter 13 is titled "Aerodynamic Design Considerations," and Chapter 14 is titled "Tools for Defining the Aerodynamic Environment." Chapter 14 presents an explanation of the complementary role of experiment and of computation in defining the aerodynamic environment. Furthermore, the advantages, limitations, and roles of computational techniques of varying degrees of rigor are discussed. The material presented in Chapters 13 and 14 not only should provide interesting reading for the student but, should be useful to professionals long after they have completed their formal academic training.
COMMENTS ON THE FIRST THREE EDITIONS
The author would like to thank Michael L. Smith for his significant contributions to Aerodynamics for Engineers. Michael Smith's contributions helped establish the quality of the text from the outset and the foundation upon which the subsequent editions have been based. For these contributions, he was recognized as coauthor of the first three editions.
The author is indebted to his many friends and colleagues for their help in preparing the first three editions of this text. I thank them for their suggestions, their support, and for copies of photographs, illustrations, and reference documents. The author is indebted to L. C. Squire of Cambridge University; V G. Szebehely of the University of Texas at Austin; R A. Wierum of the Rice University; T. J. Mueller of the University of Notre Dame; R. G. Bradley and C. Smith of General Dynamics; G. E. Erickson of Northrop; L. E. Ericsson of Lockheed Missiles and Space; L. Lemmerman and A. S. W Thomas of Lockheed Georgia; J. Periaux of Avions Marcel Dassault; H. W Carlson, M. L. Spearman, and P R Coven of the Langley Research Center; D. Kanipe of the Johnson Space Center; R. C. Maydew, S. McAlees, and W. H. Rutledge of the Sandia National Labs; M. J. Nipper of the Lockheed Martin Tactical Aircraft Systems; H. J. Hillaker (formerly) of General Dynamics; R. Chase of the ANSER Corporation; and Lt. Col. S. A. Brandt, Lt. Col. W. B. McClure, and Maj. M. C. Towne of the U.S. Air Force Academy. R R. DeJarnette of North Carolina State University, and J. E Marchman III, of Virginia Polytechnic Institute and State University provided valuable comments as reviewers of the third edition.
Not only has T. C. Valdez served as the graphics artist for the first three editions of this text, but he has regularly located interesting articles on aircraft design that have been incorporated into the various editions.
THE FOUTH EDITION
Rapid advances in software and hardware have resulted in the everincreasing use of computational fluid dynamics (CFD) in the design of aerospace vehicles. The increased reliance on computational methods has led to three changes unique to the fourth edition.
Major D. C. Blake, Capt. J. R. Forsythe, and M. C. Towne were valuable contributors to the changes that have been made to the fourth edition. They served as sounding boards before the text was written, as editors to the modified text, and as suppliers of graphic art. Since it was the desire of the author to reflect the current role of computations (limitations, strengths, and usage) and to present some challenging applications, the author appreciates the many contributions of Maj. Blake, Capt. Forsythe, and Dr. Towne, who are active experts in the use and in the development of CFD in aerodynamic design.
The author would also like to thank M. Gen. E. R. Bracken for supplying information and photographs regarding the design and operation of military aircraft. G. E. Peters of the Boeing Company and M. C. Towne of Lockheed Martin Aeronautics served as points of contact with their companies in providing material new to the fourth edition.
The author would like to thank John Evans Burkhalter of Auburn University, Richard S. Figliola of Clemson University, Marilyn Smith of the Georgia Institute of Technology, and Leland A. Carlson of Texas A & M University, who, as reviewers of a draft manuscript, provided comments that have been incorporated either into the text or into the corresponding CD.
The author would also like to thank the American Institute of Aeronautics and Astronautics (AIAA), the Advisory Group for Aerospace Research and Development, North Atlantic Treaty Organization (AGARD/NATO),' the Boeing Company, and the Lockheed Martin Tactical Aircraft System for allowing the author to reproduce significant amounts of archival material. This material not only constitutes a critical part of the fourth edition, but it also serves as an excellent foundation upon which the reader can explore new topics.
JOHN J. BERTIN
United States Air Force Academy
Table of Contents
PREFACE TO THE SIXTH EDITION xv
CHAPTER 1 WHY STUDY AERODYNAMICS? 1
1.1 Aerodynamics and the EnergyManeuverability Technique 2
1.1.1 Specific Excess Power 6
1.1.2 Using Specific Excess Power to Change the Energy Height 7
1.1.3 John R. Boyd Meet Harry Hillaker 8
1.1.4 The Importance of Aerodynamics to Aircraft Performance 8
1.2 Solving for the Aerothermodynamic Parameters 8
1.2.1 Concept of a Fluid 8
1.2.2 Fluid as a Continuum 8
1.2.3 Fluid Properties 10
1.2.4 Pressure Variation in a Static Fluid Medium 17
1.2.5 The Standard Atmosphere 22
1.3 Description of an Airplane 26
1.4 Summary 27
Problems 28
References 32
CHAPTER 2 FUNDAMENTALS OF FLUID MECHANICS 33
2.1 Introduction to Fluid Dynamics 34
2.2 Conservation of Mass 36
2.3 Conservation of Linear Momentum 40
2.4 Applications to ConstantProperty Flows 46
2.4.1 Poiseuille Flow 46
2.4.2 Couette Flow 50
2.4.3 Integral Equation Application 52
2.5 Reynolds Number and Mach Number as Similarity Parameters 55
2.6 Concept of the Boundary Layer 63
2.7 Conservation of Energy 65
2.8 First Law of Thermodynamics 66
2.9 Derivation of the Energy Equation 68
2.9.1 Integral Form of the Energy Equation 71
2.9.2 Energy of the System 71
2.9.3 Flow Work 72
2.9.4 Viscous Work 73
2.9.5 Shaft Work 73
2.9.6 Application of the Integral Form of the Energy Equation 74
2.10 Summary 76
Problems 76
References 87
CHAPTER 3 DYNAMICS OF AN INCOMPRESSIBLE, INVISCID FLOW FIELD 88
3.1 Inviscid Flows 89
3.2 Bernoulli’s Equation 90
3.3 Use of Bernoulli’s Equation to Determine Airspeed 93
3.4 The Pressure Coefficient 96
3.5 Circulation 99
3.6 Irrotational Flow 102
3.7 Kelvin’s Theorem 103
3.7.1 Implication of Kelvin’s Theorem 104
3.8 Incompressible, Irrotational Flow and the Velocity Potential 104
3.8.1 Irrotational Condition 105
3.8.2 Boundary Conditions 105
3.9 Stream Function in a TwoDimensional, Incompressible Flow 107
3.10 Relation between Streamlines and Equipotential Lines 109
3.11 Superposition of Flows 112
3.12 Elementary Flows 113
3.12.1 Uniform Flow 113
3.12.2 Source or Sink 114
3.12.3 Doublet 116
3.12.4 Potential Vortex 117
3.12.5 The Vortex Theorems of Helmholtz 120
3.12.6 Summary of Stream Functions and of Potential Functions 123
3.13 Adding Elementary Flows to Describe Flow Around a Cylinder 126
3.13.1 Velocity Field 126
3.13.2 Pressure Distribution on the Cylinder 128
3.13.3 Lift and Drag 130
3.14 Lift and Drag Coefficients as Dimensionless FlowField Parameters 134
3.15 Flow Around a Cylinder with Circulation 139
3.15.1 Velocity Field 139
3.15.2 Lift and Drag 140
3.15.3 Applications of Potential Flow to Aerodynamics 142
3.16 Source Density Distribution on the Body Surface 144
3.17 Incompressible, Axisymmetric Flow 149
3.17.1 Flow Around a Sphere 150
3.18 Summary 152
Problems 152
References 165
CHAPTER 4 VISCOUS BOUNDARY LAYERS 166
4.1 Equations Governing the Boundary Layer for a Steady, TwoDimensional, Incompressible Flow 167
4.2 Boundary Conditions 170
4.3 Incompressible, Laminar Boundary Layer 171
4.3.1 Numerical Solutions for the FalknerSkan Problem 174
4.4 BoundaryLayer Transition 189
4.5 Incompressible, Turbulent Boundary Layer 193
4.5.1 Derivation of the Momentum Equation for Turbulent Boundary Layer 195
4.5.2 Approaches to Turbulence Modeling 197
4.5.3 Turbulent Boundary Layer for a Flat Plate 199
4.6 Eddy Viscosity and Mixing Length Concepts 202
4.7 Integral Equations for a FlatPlate Boundary Layer 204
4.7.1 Application of the Integral Equations of Motion to a Turbulent, FlatPlate Boundary Layer 208
4.7.2 Integral Solutions for a Turbulent Boundary Layer with a Pressure Gradient 213
4.8 Thermal Boundary Layer for ConstantProperty Flows 215
4.8.1 Reynolds Analogy 216
4.8.2 Thermal Boundary Layer for Pr _ 1 218
4.9 Summary 221
Problems 221
References 225
CHAPTER 5 CHARACTERISTIC PARAMETERS FOR AIRFOIL AND WING AERODYNAMICS 226
5.1 Characterization of Aerodynamic Forces and Moments 227
5.1.1 General Comments 227
5.1.2 Parameters That Govern Aerodynamic Forces 230
5.2 Airfoil Geometry Parameters 231
5.2.1 AirfoilSection Nomenclature 232
5.2.2 LeadingEdge Radius and Chord Line 233
5.2.3 Mean Camber Line 234
5.2.4 Maximum Thickness and Thickness Distribution 234
5.2.5 TrailingEdge Angle 235
5.3 WingGeometry Parameters 236
5.4 Aerodynamic Force and Moment Coefficients 244
5.4.1 Lift Coefficient 244
5.4.2 Moment Coefficient 250
5.4.3 Drag Coefficient 252
5.4.4 BoundaryLayer Transition 256
5.4.5 Effect of Surface Roughness on the Aerodynamic Forces 259
5.4.6 Method for Predicting Aircraft Parasite Drag 263
5.5 Wings of Finite Span 273
5.5.1 Lift 274
5.5.2 Drag 279
5.5.3 Lift/Drag Ratio 283
Problems 288
References 292
CHAPTER 6 INCOMPRESSIBLE FLOWS AROUND AIRFOILS OF INFINITE SPAN 294
6.1 General Comments 295
6.2 Circulation and the Generation of Lift 296
6.2.1 Starting Vortex 296
6.3 General ThinAirfoil Theory 298
6.4 Thin, FlatPlate Airfoil (Symmetric Airfoil) 301
6.5 Thin, Cambered Airfoil 306
6.5.1 Vorticity Distribution 306
6.5.2 Aerodynamic Coefficients for a Cambered Airfoil 308
6.6 LaminarFlow Airfoils 317
6.7 HighLift Airfoil Sections 321
6.8 Multielement Airfoil Sections for Generating High Lift 327
6.9 HighLift Military Airfoils 334
Problems 337
References 339
CHAPTER 7 INCOMPRESSIBLE FLOW ABOUT WINGS OF FINITE SPAN 341
7.1 General Comments 342
7.2 Vortex System 345
7.3 LiftingLine Theory for Unswept Wings 346
7.3.1 Trailing Vortices and Downwash 348
7.3.2 Case of Elliptic Spanwise Circulation Distribution 351
7.3.3 Technique for General Spanwise Circulation Distribution 357
7.3.4 Lift on the Wing 362
7.3.5 VortexInduced Drag 362
7.3.6 Some Final Comments on LiftingLine Theory 373
7.4 Panel Methods 375
7.4.1 Boundary Conditions 376
7.4.2 Solution Methods 377
7.5 Vortex Lattice Method 379
7.5.1 Velocity Induced by a General Horseshoe Vortex 382
7.5.2 Application of the Boundary Conditions 386
7.5.3 Relations for a Planar Wing 387
7.6 Factors Affecting Drag DuetoLift at Subsonic Speeds 401
7.7 Delta Wings 404
7.8 LeadingEdge Extensions 414
7.9 Asymmetric Loads on the Fuselage at High Angles of Attack 418
7.9.1 Asymmetric Vortex Shedding 419
7.9.2 Wakelike Flows 422
7.10 Flow Fields for Aircraft at High Angles of Attack 422
7.11 Unmanned Air Vehicle Wings 424
7.12 Summary 426
Problems 426
References 428
CHAPTER 8 DYNAMICS OF A COMPRESSIBLE FLOW FIELD 431
8.1 Thermodynamic Concepts 432
8.1.1 Specific Heats 432
8.1.2 Additional Important Relations 435
8.1.3 Second Law of Thermodynamics and Reversibility 435
8.1.4 Speed of Sound 438
8.2 Adiabatic Flow in a VariableArea Streamtube 441
8.3 Isentropic Flow in a VariableArea Streamtube 445
8.4 Convergingdiverging Nozzles 451
8.5 Characteristic Equations and PrandtlMeyer Flows 454
8.6 Shock Waves 462
8.7 Viscous Boundary Layer 473
8.7.1 Effects of Compressibility 476
8.8 ShockWave/BoundaryLayer Interactions 480
8.9 Shock/Shock Interactions 482
8.10 The Role of Experiments for Generating Information Defining the Flow Field 486
8.10.1 GroundBased Tests 486
8.10.2 Flight Tests 490
8.11 Comments About The Scaling/Correction Process(es) for Relatively Clean Cruise Configurations 494
8.12 Summary 495
Problems 495
References 502
CHAPTER 9 COMPRESSIBLE, SUBSONIC FLOWS AND TRANSONIC FLOWS 505
9.1 Compressible, Subsonic Flow 506
9.1.1 Linearized Theory for Compressible Subsonic Flow About a Thin Wing at Relatively Small Angles of Attack 507
9.1.2 The Göthert Transformation 509
9.1.3 Additional Compressibility Corrections 512
9.1.4 The Motivation for Determining the Critical Mach Number 513
9.1.5 Critical Mach Number 513
9.1.6 Drag Divergence Mach Number 516
9.2 Transonic Flow Past Unswept Airfoils 517
9.3 Wave Drag Reduction by Design 526
9.3.1 Airfoil Contour Wave Drag Approaches 526
9.3.2 Supercritical Airfoil Sections 526
9.4 Swept Wings at Transonic Speeds 527
9.4.1 Wing—Body Interactions and the “Area Rule” 529
9.4.2 SecondOrder AreaRule Considerations 538
9.4.3 Forward Swept Wing 540
9.5 Transonic Aircraft 543
9.6 Summary 548
Problems 548
References 548
CHAPTER 10 TWODIMENSIONAL, SUPERSONIC FLOWS AROUND THIN AIRFOILS 551
10.1 Linear Theory 553
10.1.1 Lift 555
10.1.2 Drag 556
10.1.3 Pitch Moment 558
10.2 SecondOrder Theory (Busemann’s Theory) 561
10.3 ShockExpansion Technique 566
10.4 Summary 572
Problems 572
References 575
CHAPTER 11 SUPERSONIC FLOWS OVER WINGS AND AIRPLANE CONFIGURATIONS 577
11.1 General Remarks About Lift and Drag 579
11.2 General Remarks About Supersonic Wings 581
11.3 Governing Equation and Boundary Conditions 583
11.4 Consequences of Linearity 584
11.5 Solution Methods 585
11.6 ConicalFlow Method 585
11.6.1 Rectangular Wings 586
11.6.2 Swept Wings 591
11.6.3 Delta and Arrow Wings 595
11.7 SingularityDistribution Method 598
11.7.1 Find the Pressure Distribution Given the Configuration 600
11.7.2 Numerical Method for Calculating the Pressure Distribution Given the Configuration 608
11.7.3 Numerical Method for the Determination of Camber Distribution 622
11.8 Design Considerations for Supersonic Aircraft 625
11.9 Some Comments about the Design of the SST and of the HSCT 627
11.9.1 The Supersonic Transport (SST), the Concorde 627
11.9.2 The HighSpeed Civil Transport (HSCT) 629
11.9.3 Reducing the Sonic Boom 630
11.9.4 Classifying HighSpeed Aircraft Designs 631
11.10 Slender Body Theory 634
11.11 Base Drag 636
11.12 Aerodynamic Interaction 639
11.13 Aerodynamic Analysis for Complete Configurations in a Supersonic Free Stream 642
11.14 Summary 643
Problems 644
References 646
CHAPTER 12 HYPERSONIC FLOWS 649
12.1 The Five Distinguishing Characteristics 652
12.1.1 Thin Shock Layers 652
12.1.2 Entropy Layers 653
12.1.3 ViscousInviscid Interactions 653
12.1.4 High Temperature Effects 654
12.1.5 LowDensity Flows 655
12.2 Newtonian Flow Model 657
12.3 Stagnation Region FlowField Properties 660
12.4 Modified Newtonian Flow 665
12.5 High L/D Hypersonic Configurations–Waveriders 682
12.6 Aerodynamic Heating 691
12.6.1 Similarity Solutions for Heat Transfer 694
12.7 A Hypersonic Cruiser for the TwentyFirst Century? 697
12.8 Importance of Interrelating CFD, GroundTest Data, and FlightTest Data 700
12.9 BoundaryLayerTransition Methodology 702
12.10 Summary 706
Problems 706
References 708
CHAPTER 13 AERODYNAMIC DESIGN CONSIDERATIONS 711
13.1 HighLift Configurations 712
13.1.1 Increasing the Area 712
13.1.2 Increasing the Lift Coefficient 713
13.1.3 Flap Systems 716
13.1.4 Multielement Airfoils 719
13.1.5 PowerAugmented Lift 723
13.2 Circulation Control Wing 725
13.3 Design Considerations for Tactical Military Aircraft 727
13.4 Drag Reduction 731
13.4.1 VariableTwist, VariableCamber Wings 731
13.4.2 LaminarFlow Control 734
13.4.3 Wingtip Devices 737
13.4.4 Wing Planform 740
13.5 Development of an Airframe Modification to Improve the Mission Effectiveness of an Existing Airplane 742
13.5.1 The EA6B 742
13.5.2 The Evolution of the F16 745
13.5.3 External Carriage of Stores 752
13.5.4 Additional Comments 758
13.6 Considerations for Wing/Canard, Wing/Tail, and Tailless Configurations 758
13.7 Comments on the F15 Design 763
13.8 The Design of the F22 764
13.9 The Design of the F35 767
13.10 Summary 770
Problems 770
References 772
CHAPTER 14 TOOLS FOR DEFINING THE AERODYNAMIC ENVIRONMENT 775
14.1 Computational Tools 777
14.1.1 Semiempirical Methods 777
14.1.2 Surface Panel Methods for Inviscid Flows 778
14.1.3 Euler Codes for Inviscid Flow Fields 779
14.1.4 TwoLayer Flow Models 779
14.1.5 Computational Techniques That Treat the Entire Flow Field in a Unified Fashion 780
14.1.6 Integrating the Diverse Computational Tools 781
14.2 Establishing the Credibility of CFD Simulations 783
14.3 GroundBased Test Programs 785
14.4 FlightTest Programs 788
14.5 Integration of Experimental and Computational Tools: The Aerodynamic Design Philosophy 789
14.6 Summary 790
References 790
APPENDIX A THE EQUATIONS OF MOTION WRITTEN IN CONSERVATION FORM 793
APPENDIX B A COLLECTION OF OFTEN USED TABLES 799
ANSWERS TO SELECTED PROBLEMS 806
INDEX
Preface
At this point, the reader is ready to begin material focused on aerodynamic applications. Parameters that characterize the geometry of aerodynamic configurations and parameters that characterize aerodynamic performance are presented in Chapter 5, "Characteristic Parameters for Airfoil and Wing Aerodynamics." Techniques for modeling the aerodynamic performance of twodimensional airfoils and, offinitespan wings at low speeds (where variations in density are negligible) are presented in Chapters 6 and 7, respectively. Chapter 6 is titled "Incompressible Flows around Wings of Infinite Span," and Chapter 7 is titled "Incompressible Flow about Wings of Finite Span."
The next five chapters deal with compressible flow fields. To provide the reader with the necessary background for highspeed aerodynamics, the basic fluid mechanic principles for compressible flows are discussed in Chapter 8, "Dynamics of a Compressible Flow Field." Thus, from a pedagogical point of view, the material presented in Chapter 8 complements the material presented in Chapters 1 through 4. Techniques for modeling highspeed flows (where density variations cannot be neglected) are presented in Chapters 9 through 12. Aerodynamic performance for compressible, subsonic flows through transonic speeds is the subject of Chapter 9, "Compressible Subsonic Flows and Transonic Flows." Supersonic aerodynamics for twodimensional airfoils is the subject of Chapter 10, "TwoDimensional Supersonic Flows about Thin Airfoils" and for finitespan wings in Chapter 11, "Supersonic Flows over Wings and Airplane Configurations." Hypersonic flows are the subject of Chapter 12.
At this point, chapters have been dedicated to the development of basic models for calculating the aerodynamic performance parameters for each of the possible speed ranges. The assumptions and, therefore, the restrictions incorporated into the development of the theory are carefully noted. The applications of the theory are illustrated by working one or more problems. Solutions are obtained using numerical techniques in order to apply the theory for those flows where closedform solutions are impractical or impossible. In each of the chapters, the computed aerodynamic parameters are compared with experimental data from the open literature to illustrate both the validity of the theoretical analysis and its limitations (or, equivalently, the range of conditions for which the theory is applicable). One objective is to use the experimental data to determine the limits of applicability for the proposed models.
Extensive discussions of the effects of viscosity, compressibility, shock/boundarylayer interactions, turbulence modeling, and other practical aspects of contemporary aerodynamic design are also presented. Problems at the end of each chapter are designed to complement the material presented within the chapter and to develop the student's understanding of the relative importance of various phenomena. The text emphasizes practical problems and the techniques through which solutions to these problems can be obtained. Because both the International System of Units (Systeme International d'Unites, abbreviated SI) and English units are commonly used in the aerospace industry, both are used in this text. Conversion factors between SI units and English units are presented on the inside covers.
Advanced material relating to design features of aircraft over more than a century and to the tools used to define the aerodynamic parameters are presented in Chapters 13 and 14. Chapter 13 is titled "Aerodynamic Design Considerations," and Chapter 14 is titled "Tools for Defining the Aerodynamic Environment." Chapter 14 presents an explanation of the complementary role of experiment and of computation in defining the aerodynamic environment. Furthermore, the advantages, limitations, and roles of computational techniques of varying degrees of rigor are discussed. The material presented in Chapters 13 and 14 not only should provide interesting reading for the student but, should be useful to professionals long after they have completed their formal academic training.
COMMENTS ON THE FIRST THREE EDITIONS
The author would like to thank Michael L. Smith for his significant contributions to Aerodynamics for Engineers. Michael Smith's contributions helped establish the quality of the text from the outset and the foundation upon which the subsequent editions have been based. For these contributions, he was recognized as coauthor of the first three editions.
The author is indebted to his many friends and colleagues for their help in preparing the first three editions of this text. I thank them for their suggestions, their support, and for copies of photographs, illustrations, and reference documents. The author is indebted to L. C. Squire of Cambridge University; V G. Szebehely of the University of Texas at Austin; R A. Wierum of the Rice University; T. J. Mueller of the University of Notre Dame; R. G. Bradley and C. Smith of General Dynamics; G. E. Erickson of Northrop; L. E. Ericsson of Lockheed Missiles and Space; L. Lemmerman and A. S. W Thomas of Lockheed Georgia; J. Periaux of Avions Marcel Dassault; H. W Carlson, M. L. Spearman, and P R Coven of the Langley Research Center; D. Kanipe of the Johnson Space Center; R. C. Maydew, S. McAlees, and W. H. Rutledge of the Sandia National Labs; M. J. Nipper of the Lockheed Martin Tactical Aircraft Systems; H. J. Hillaker (formerly) of General Dynamics; R. Chase of the ANSER Corporation; and Lt. Col. S. A. Brandt, Lt. Col. W. B. McClure, and Maj. M. C. Towne of the U.S. Air Force Academy. R R. DeJarnette of North Carolina State University, and J. E Marchman III, of Virginia Polytechnic Institute and State University provided valuable comments as reviewers of the third edition.
Not only has T. C. Valdez served as the graphics artist for the first three editions of this text, but he has regularly located interesting articles on aircraft design that have been incorporated into the various editions.
THE FOUTH EDITION
Rapid advances in software and hardware have resulted in the everincreasing use of computational fluid dynamics (CFD) in the design of aerospace vehicles. The increased reliance on computational methods has led to three changes unique to the fourth edition.
Major D. C. Blake, Capt. J. R. Forsythe, and M. C. Towne were valuable contributors to the changes that have been made to the fourth edition. They served as sounding boards before the text was written, as editors to the modified text, and as suppliers of graphic art. Since it was the desire of the author to reflect the current role of computations (limitations, strengths, and usage) and to present some challenging applications, the author appreciates the many contributions of Maj. Blake, Capt. Forsythe, and Dr. Towne, who are active experts in the use and in the development of CFD in aerodynamic design.
The author would also like to thank M. Gen. E. R. Bracken for supplying information and photographs regarding the design and operation of military aircraft. G. E. Peters of the Boeing Company and M. C. Towne of Lockheed Martin Aeronautics served as points of contact with their companies in providing material new to the fourth edition.
The author would like to thank John Evans Burkhalter of Auburn University, Richard S. Figliola of Clemson University, Marilyn Smith of the Georgia Institute of Technology, and Leland A. Carlson of Texas A & M University, who, as reviewers of a draft manuscript, provided comments that have been incorporated either into the text or into the corresponding CD.
The author would also like to thank the American Institute of Aeronautics and Astronautics (AIAA), the Advisory Group for Aerospace Research and Development, North Atlantic Treaty Organization (AGARD/NATO),' the Boeing Company, and the Lockheed Martin Tactical Aircraft System for allowing the author to reproduce significant amounts of archival material. This material not only constitutes a critical part of the fourth edition, but it also serves as an excellent foundation upon which the reader can explore new topics.
JOHN J. BERTIN
United States Air Force Academy