Aerodynamics for Engineers SIXTH EDITION John J. Bertin

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Contents

PREFACE 9
CHAPTER 1 WHY STUDY AERODYNAMICS? 11
1.1 Aerodynamics and the Energy-Maneuverability
Technique 12
1.2 Solving for the Aerothermodynamic
Parameters 18
1.3 Description of an Airplane 36
1.4 Summary 37
Problems 38
References 42
CHAPTER 2 FUNDAMENTALS OF FLUID MECHANICS 43
2.1 Introduction to Fluid Dynamics 44
2.2 Conservation of Mass 46
2.3 Conservation of Linear Momentum 50
2.4 Applications to Constant-Property Flows 56
2.5 Reynolds Number and Mach Number as
Similarity Parameters 65
2.6 Concept of the Boundary Layer 73
2.7 Conservation of Energy 75
2.8 First Law of Thermodynamics 76
2.9 Derivation of the Energy Equation 78
2.10 Summary 86
Problems 86
References 97
CHAPTER 3 DYNAMICS OF AN INCOMPRESSIBLE,
INVISCID FLOW FIELD 98
3.1 Inviscid Flows 99
3.2 Bernoulli’s Equation 100
3.3 Use of Bernoulli’s Equation to Determine
Airspeed 103
3.4 The Pressure Coefficient 106
3.5 Circulation 109
3.6 Irrotational Flow 112
3.7 Kelvin’s Theorem 113
3.8 Incompressible, Irrotational Flow and the
Velocity Potential 114
3.9 Stream Function in a Two-Dimensional,
Incompressible Flow 117
3.10 Relation between Streamlines and Equipotential
Lines 119
3.11 Superposition of Flows 122
3.12 Elementary Flows 123
3.13 Adding Elementary Flows to Describe Flow
Around a Cylinder 136
3.14 Lift and Drag Coefficients as Dimensionless
Flow-Field Parameters 144
3.15 Flow Around a Cylinder with Circulation 149
3.16 Source Density Distribution on the Body
Surface 154
3.17 Incompressible, Axisymmetric Flow 159
3.18 Summary 162
Problems 162
References 175
CHAPTER 4 VISCOUS BOUNDARY LAYERS 176
4.1 Equations Governing the Boundary Layer
Flow 177
4.2 Boundary Conditions 180
4.3 Incompressible, Laminar Boundary Layer 181
4.4 Boundary-Layer Transition 199
4.5 Incompressible, Turbulent Boundary Layer 203
4.6 Eddy Viscosity and Mixing Length
Concepts 212
4.7 Integral Equations for a Flat-Plate Boundary
Layer 214
4.8 Thermal Boundary Layer for Constant-Property
Flows 225
4.9 Summary 231
Problems 231
References 235
CHAPTER 5 CHARACTERISTIC PARAMETERS FOR AIRFOIL
AND WING AERODYNAMICS 236
5.1 Characterization of Aerodynamic Forces and
Moments 237
5.2 Airfoil Geometry Parameters 241
5.3 Wing-Geometry Parameters 246
5.4 Aerodynamic Force and Moment
Coefficients 254
5.5 Wings of Finite Span 283
Problems 298
References 302
CHAPTER 6 INCOMPRESSIBLE FLOWS AROUND AIRFOILS
OF INFINITE SPAN 304
6.2 Circulation and the Generation of Lift 306
6.3 General Thin-Airfoil Theory 308
6.4 Thin, Flat-Plate Airfoil (Symmetric Airfoil) 311
6.5 Thin, Cambered Airfoil 316
6.6 Laminar-Flow Airfoils 327
6.7 High-Lift Airfoil Sections 331
6.8 Multielement Airfoil Sections for Generating
High Lift 337
6.9 High-Lift Military Airfoils 344
6.10 Summary 347
Problems 347
References 349
CHAPTER 7 INCOMPRESSIBLE FLOW ABOUT WINGS
OF FINITE SPAN 351
7.2 Vortex System 355
7.3 Lifting-Line Theory for Unswept Wings 356
7.4 Panel Methods 385
7.5 Vortex Lattice Method 389
7.6 Factors Affecting Drag Due-to-Lift at Subsonic
Speeds 411
7.7 Delta Wings 414
7.9 Asymmetric Loads on the Fuselage at High
Angles of Attack 428
7.10 Flow Fields for Aircraft at High Angles of Attack 432
7.11 Unmanned Air Vehicle Wings 434
7.12 Summary 436
Problems 436
References 438
6 Contents
CHAPTER 8 DYNAMICS OF A COMPRESSIBLE FLOW FIELD 441
8.1 Thermodynamic Concepts 442
8.2 Adiabatic Flow in a Variable-Area
Streamtube 451
8.3 Isentropic Flow in a Variable-Area Streamtube 455
8.4 Converging-diverging Nozzles 461
8.5 Characteristic Equations and Prandtl-Meyer
Flows 464
8.6 Shock Waves 472
8.7 Viscous Boundary Layer 483
8.8 Shock-Wave/Boundary-Layer Interactions 490
8.9 Shock/Shock Interactions 492
8.10 The Role of Experiments for Generating
Information Defining the Flow Field 496
Process(es) for Relatively Clean Cruise
Configurations 504
8.12 Summary 505
Problems 505
References 512
CHAPTER 9 COMPRESSIBLE, SUBSONIC FLOWS
AND TRANSONIC FLOWS 515
9.1 Compressible, Subsonic Flow 516
9.2 Transonic Flow Past Unswept Airfoils 527
9.3 Wave Drag Reduction by Design 536
9.4 Swept Wings at Transonic Speeds 537
9.5 Transonic Aircraft 553
9.6 Summary 558
Problems 558
References 558
CHAPTER 10 TWO-DIMENSIONAL, SUPERSONIC FLOWS
AROUND THIN AIRFOILS 561
10.1 Linear Theory 563
10.2 Second-Order Theory (Busemann’s Theory) 571
10.3 Shock-Expansion Technique 576
10.4 Summary 582
Problems 582
References 585
Contents 7
CHAPTER 11 SUPERSONIC FLOWS OVER WINGS
AND AIRPLANE CONFIGURATIONS 587
11.1 General Remarks About Lift and Drag 589
Wings 591
11.3 Governing Equation and Boundary
Conditions 593
11.4 Consequences of Linearity 594
11.5 Solution Methods 595
11.6 Conical-Flow Method 595
11.7 Singularity-Distribution Method 608
11.8 Design Considerations for Supersonic
Aircraft 635
and of the HSCT 637
11.10 Slender Body Theory 644
11.11 Base Drag 646
11.12 Aerodynamic Interaction 649
11.13 Aerodynamic Analysis for Complete
Configurations in a Supersonic Free
Stream 652
11.14 Summary 653
Problems 654
References 656
CHAPTER 12 HYPERSONIC FLOWS 659
12.1 The Five Distinguishing Characteristics 662
12.2 Newtonian Flow Model 667
12.3 Stagnation Region Flow-Field
Properties 670
12.4 Modified Newtonian Flow 675
12.5 High L/D Hypersonic Configurations—
Waveriders 692
12.6 Aerodynamic Heating 701
12.7 A Hypersonic Cruiser for the Twenty-First
Century? 707
12.8 Importance of Interrelating CFD, Ground-Test
Data, and Flight-Test Data 710
12.9 Boundary-Layer-Transition Methodology 712
12.10 Summary 716
Problems 716
References 718
8 Contents
CHAPTER 13 AERODYNAMIC DESIGN CONSIDERATIONS 721
13.1 High-Lift Configurations 722
13.2 Circulation Control Wing 735
13.3 Design Considerations for Tactical Military
Aircraft 737
13.4 Drag Reduction 741
13.5 Development of an Airframe Modification to
Improve the Mission Effectiveness of an Existing
Airplane 752
13.6 Considerations for Wing/Canard, Wing/Tail, and
Tailless Configurations 768
13.7 Comments on the F-15 Design 773
13.8 The Design of the F-22 774
13.9 The Design of the F-35 777
13.10 Summary 780
Problems 780
References 782
CHAPTER 14 TOOLS FOR DEFINING THE AERODYNAMIC
ENVIRONMENT 785
14.1 Computational Tools 787
14.2 Establishing the Credibility of CFD
Simulations 793
14.3 Ground-Based Test Programs 795
14.4 Flight-Test Programs 798
14.5 Integration of Experimental and Computational
Tools: The Aerodynamic Design Philosophy 799
14.6 Summary 800
References 800
APPENDIX A THE EQUATIONS OF MOTION WRITTEN
IN CONSERVATION FORM 802
APPENDIX B A COLLECTION OF OFTEN USED TABLES 808
INDEX 821

Preface

A great deal has happened since the preface to the fifth edition of Aerodynamics for Engineers
was written early in 2008. During the spring and early summer of 2008, John Bertin and
I were busy checking chapter proofs for “The Book” (as he liked to call it). John was at home
in Houston and teaching at his beloved Rice University (you may have noticed that covers
of the various editions of Aerodynamics for Engineers were usually blue and light gray, the
colors of Rice University). I was a visiting researcher at the Institute of Aerodynamics and
Flow Technology at The German Aerospace Center (DLR) in Braunschweig. John had two
major struggles in his life at the time: he was working through the last stages of the illness that
would take his wife, Ruth, from him. He had also been diagnosed with pancreatic cancer, and
was dealing with doctors, treatments, and hospitals. We spoke on the phone often about the
various challenges he was facing, both with his wife’s and his own health. Through the support
of his family, as well as his desire to finish the fifth edition, he made it through the summer
of 2008 in reasonably good shape. Copies of the book were shipped to us in July 2008, and
he was very glad that we had finished the undertaking we had started so many years earlier.
Unfortunately, John’s pancreatic cancer took a turn for the worse in late summer
of 2008, and he passed away on October 11, 2008. A large number of former co-workers
from NASA and various universities, as well as his family and friends, attended his funeral
later that month, and we all knew that a very special person had passed from our ranks.
One of the things that John and I talked about during his last months of life was
his desire for Aerodynamics for Engineers to continue to grow and evolve, even if he
was not around to help with that task. I cannot help but think that he asked me to be
his co-author for the fifth edition for this purpose. So, in spite of the fact that John is no
longer with us, his spirit and excitement for learning will continue to live.
So, there were many goals for writing the sixth edition of Aerodynamics for Engineers
: (1) to continue the legacy of Professor Bertin; (2) to rewrite many of the sections
that provide readers with a motivation for studying aerodynamics in a more casual, enjoyable,
that have taken place in aerodynamics since the writing of the previous edition; and (4) to
add aerodynamics concept boxes throughout the book to enhance the interest of readers.
To help achieve these goals, I provided readers with new sections, listed under What’s
New to This Edition on the next page. In addition, there are numerous new figures containing
updated information, as well as numerous, additional up-to-date references throughout
the book. Finally, numerous new example problems have been added throughout the book
to enhance the learning of aerodynamics by the reader, and answers to selected problems
have been added to help students know when they have done the problems correctly.
Users of the fifth edition of the book will find that all material included in that edition
is still included in the sixth edition, with the new material added throughout the book to
bring a real-world flavor to the concepts being developed. I hope that readers will find the
Finally, no major revision of a book like Aerodynamics for Engineers can take place without
the help of many people. I am especially indebted to everyone who aided in collecting new
materials for the sixth edition. I want to especially thank Preston A. Henne and Robert van’t
Riet of McDonnell Douglas; Eli Reshotko of Case Western Reserve University; David W. Hall
of DHC Engineering; Stuart Rogers of NASA Ames Research Center; David McDaniel of the
University of Alabama, Birmingham; Hans Hornung of Caltech; Andreas Schütte, Thomas
Streit, and Martin Hepperle of DLR; Patrick Champigny of ONERA; Aaron Byerley of the
U.S. Air Force Academy; John McMasters of The Boeing Company; and William H. Mason
of Virginia Tech. In addition, I am very grateful for the excellent suggestions and comments
made by the reviewers of the sixth edition: Roger L. Simpson of Virginia Tech, Tej R. Gupta
of Embry-Riddle Aeronautical University, Serhat Hosder of Missouri University of Science
and Technology, and Lisa Grega of The College of New Jersey. The editorial and production
staff at Pearson has been outstanding in their support of this new edition: I greatly appreciate
their efforts. I am also extremely grateful to the many students at the U.S. Air Force Academy
who have pointed out errors that they found in the previous edition. I hope that everyone
who reads this book will find it useful and educational.
The publishers would like to thank Ramesh Kolluru of BMS College of Engineering,
Bangalore for reviewing the content of the International Edition.

WHAT’S NEW TO THIS EDITION?

• Aerodynamics concept boxes added throughout the book to bring real-world examples
and applications to light as new material is being learned
• Chapter objectives to give readers a better understanding of the goal of each chapter
and what concepts they should understand after reading through the chapter
• Significant re-writing of material and derivations from previous editions to improve
clarity and usefulness
• Extra example problems to improve understanding of how to apply concepts to
useful applications
• Significant new sections added on the topics of: importance of aerodynamics to
aircraft performance, a description of the airplane, the irrotational flow condition,
applications of potential flow theory to aerodynamics, expanded description of
airfoil geometry and nomenclature, high lift military airfoils, the effect of taper
ratio on wing efficiency, induced drag estimation, converging-diverging nozzles,
shock/shock interactions, subsonic compressible transformations, additional compressibility
corrections, critical Mach number, drag divergence Mach number,
base drag, and the distinguishing characteristics of hypersonic flow
• Updated figures and photographs to help readers see concepts from real examples
and on real aircraft