## 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

for a Steady, Two-Dimensional, Incompressible

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

6.1 General Comments 305

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

7.1 General Comments 352

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

7.8 Leading-Edge Extensions 424

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

8.11 Comments About the Scaling/Correction

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

11.2 General Remarks About Supersonic

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

11.9 Some Comments About the Design of the SST

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

ANSWERS TO SELECTED PROBLEMS 816

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,

and readable manner; (3) to update the technical innovations and advancements

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

inclusion of all of this additional material helpful and informative.

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

• Answers to selected problems

Enjoy your study of aerodynamics!