# Category BASIC AERODYNAMICS

## Aerodynamic Force System

 Figure 1.13 illustrates several features of the force system on a moving body that is the focus of considerable attention throughout this book. The aerodynamic forces represent the integrated effect of a continuous distribution of pressure and shear forces acting on all of the exposed surfaces of the vehicle. The shape of the vehicle plays a crucial role in determining both the magnitude of the forces and their line

of action. In particular, notice that the net aerodynamic forces act at a point defined in the figure as the center of pressure. Clearly, to predict the vehicle-flight character­istics, it is necessary to know the precise location of this point relative to, say, the center of mass through which the vehicle weight acts. In level equilibrium flight, a component of the lift force is called on to balance the weight, W, of the airplane, expressed in vector form as W = mg, where m is the mass of the vehicle and g is the gravitational acceleration vector. Recalling the fundamental concepts of statics, it is clear that the balance of moments about the mass center also must be considered. Again, the latter considerations form the subject of stability and control; we con­centrate here on the generation of the forces and moments and their relationship to properties of the airflow and vehicle shape.

## The Fundamental Problem of Aerodynamics

The basic problem addressed in this book is the accurate determination of the aero­dynamic force system acting on a body moving through the air. Figure 1.13 shows a typical force system on an airplane in flight; only the resultant forces are shown. An important task is to relate these resultant effects to the distributions of pressure and frictional forces that create them. We focus only on the part of the force system related to the interaction of the airflow with the vehicle—that is, on the creation of lift (L) and drag (D), the aerodynamic forces normal and parallel to the vehicle velo­city vector, as defined in the figure. However, much aerodynamic influence also is implied in the creation of thrust, as depicted by the vector T in Fig. 1.13. Interaction of the vehicle flow field with propellers, engine exhaust stream, cooling air inlets and outlets, and airbreathing propulsion system ducting must be accounted for. These important related aspects of applied aerodynamics are used at several points in the book to emphasize their strong dependence on knowledge of the vehicle flow field.

## Basic Aerodynamics

This was the last first in aviation, we had always said, a milestone, and that made it unique. Would we do it again? No one can do it again. And that is the best thing about it.

Jeana Yeager and Dick Rutan “Voyager” 1987

1.1 Introduction

Aerodynamics is the study of the flow of air around and within a moving object. Its main objective is understanding the creation of forces by the interaction of the gas motion with the surfaces of an object. Aerodynamics is closely related to hydrody­namics and gasdynamics, which represent the motion of liquid and compressible-gas flows, respectively.

Aerodynamics is the essence of flight and has been the focus of intensive research for about a century. Although this might seem to be a rather long period of development, it is really quite short considering the time span usually required for the formulation and full solution of basic scientific problems. In this relatively short time, mankind has advanced from the first gliding and primitive-powered airplane flights to interplanetary spaceflight.

Perhaps the most important motivation for this rapid development is the challenge to the human spirit represented by manned flight. However, practical needs also have strongly affected these endeavors, and we often find periods of rapid growth in aerodynamic knowledge associated with the solution of compel­ling problems in transportation, military applications, industry, and even sporting competitions. Figure 1.1 illustrates this growth in terms of the maximum speed attained by manned aircraft. Speed is a key measure of performance in almost every aspect of flight. It is of obvious vital importance in commercial flight as well as in military operations.

Even a casual study of the history of aviation yields considerable insight into the pressures that have motivated periods of almost explosive growth in the technology of flight. Much of the increase in speed during the 1940s and several subsequent decades was motivated strongly by military considerations. However, notice that two radical departures (shown as dashed lines in Fig. 1.1) from the curve for conven­tional airplanes occur in the 1920s and in the two decades between 1940 and 1960.

 Figure 1.1. Evolution of aircraft speeds showing nearly exponential growth. Jet propelled aircraft speeds level off in the 1980’s as turbojet performance Mach number limits are exceeded.

The phenomenal growth in speed from the 100 miles per hour (mph) range to over 400 mph that occurred during the period 1920-1932 was spurred by international competition in the guise of the Schneider Trophy Seaplane Races. Rapid progress not only in high-speed aerodynamics but also in aeropropul – sion took place during that period. Similar growth occurred during the 1950s in supersonic flight. More recently, the international competitive spaceflight activities brought about rapid growth in propulsion, electronics, and materials, if not much in aerodynamics. There are signs that a new international competition is underway in the area of hypersonic aerodynamics and related technologies as policy decisions are made regarding the need for low-cost single-stage-to-orbit (SSTO) space vehicles.

Several of the key historical aircraft identified in Fig. 1.1 are illustrated in Figs. 1.2-1.12. Progressive improvements in aerodynamic configuration are apparent. In this textbook, we focus on the physical laws and related analytical and computa­tional methods used to arrive at the aerodynamic-problem solutions implied in the evolving vehicle shapes depicted in the aircraft illustrated in this chapter.

 Figure 1.2. Beginnings: The 1903 Wright Flyer (Smithsonian Institute).

 Figure 1.4. Outright winner of the Schneider Trophy: Supermarine S6B (1931).

 Figure 1.5. Supermarine Spitfire Mk II – an outcome of the Schneider Trophy racing seaplane research.
 Figure 1.6. Messerschmitt ME 262. The first operational jet-propelled aircraft, 1944.

 Figure 1.8. X-15: First hypersonic airplane.

 Figure 1.10. Boeing 787 Dreamliner transonic jet transport during first flight test.

 Figure 1.12. NASA X-43 hypersonic test vehicle using Scramjet propulsion.

Although it is not required to gain an understanding of the text material, the student is encouraged to supplement the text coverage with a parallel study of the history of aeronautics. Those interested in engaging in creative work as their careers in aeronautics develop will benefit greatly from this extra effort. References at the end of each chapter and frequent historical notes (usually provided as footnotes) serve as a guide for such an in-depth study. Much useful material is now available on the Internet and other large-scale computer networks.

In solving the problems of aerodynamics, those involved have been required to create basic technology along with the associated mathematical and experimental methodology. It is vital that the student understand the framework of this technology in detail and learn not only the application of the tools but also the deeper physical meaning they represent. This textbook is designed to promote this type of critical study of the subject. A carefully paced discussion of the traditional tools, such as mathematical analysis and experiment along with modern computational methods, is used to provide the student a broad understanding of both the physical meaning and the modern implementation of a wide variety of techniques and problem solu­tions. It is significant that the book outline follows closely the historical outline in terms of the need for each successive new idea and problem solution.

## the fundamentals of aerodynamic analysis

This textbook presents the fundamentals of aerodynamic analysis. Major emphasis is on inviscid flows whenever this simplification is appropriate, but viscous effects also are discussed in more detail than is usually found in a textbook at this level. There is continual attention to practical applications of the material. For example, the concluding chapter demonstrates how aerodynamic analysis can be used to predict and improve the performance of flight vehicles. The material is suitable for a semester course on aerodynamics or fluid mechanics at the junior/ senior undergraduate level and for first-year graduate students. It is assumed that the student has a sound background in calculus, vector analysis, mechanics, and basic thermodynamics and physics. Access to a digital computer is required and an understanding of computer program­ming is desirable but not necessary. Computational methods are introduced as required to solve complex problems that cannot be handled analytically.

The objective of this textbook is to present in a clear and orderly manner the basic concepts underlying aerodynamic-prediction methodology. The ultimate goal is for the student to be able to use confidently various solution methods in the analysis of practical problems of current and future interest. Today, it is important for the student to master the basics because technology is advancing at such a rate that a more directed or specific approach often is rapidly outdated. In this book, the basic concepts are linked closely to physical principles so that they may be under­stood and retained and the limits of applicability of the concepts can be appreciated. Numerous example problems stress solution methods and the order of magnitude of key parameters. A comprehensive set of problems for home study is included at the end of each chapter.

Physical insights are developed primarily by constructing analytical solutions to important aerodynamics problems. In doing this, we follow the example set by Theodore von Karman and we subscribe to Dr. Kuchemann’s concept of “ingenious abstractions and approximations.” However, after graduation, the student in the workplace will encounter many numerical-analysis techniques and solutions. Thus, the textbook introduces the fundamentals of modern numerical methods (as they are used in aerodynamics and fluid mechanics) as well. Physical understanding plays a valuable role in computational analysis because it provides an important check on the expected ranges of magnitude of numerical solutions that are generated by these techniques.

A feature of this textbook is a companion Web site (www. cambridge. org/flandro) that con­tains numerical-analysis codes of three types: (1) codes for performing routine algebraic calcu­lations for evaluating atmospheric properties or compressible flow properties, which are often found only in tables or charts; (2) menu-driven codes that allow the student to observe the effects of parametric variations on solutions that are developed in the text; and (3) numerical- analysis codes for complex flow problems. The latter codes arise when solving linear prob­lems using panel methods or nonlinear problems using finite-difference methods. Sample

applications of these codes are presented as needed to illustrate their use in addressing realistic aerodynamics problems.

The authors express their gratitude to members of the aerodynamics faculties at Georgia Institute of Technology (GIT) and the University of Tennessee Space Institute (UTSI) for many helpful discussions during the writing of this textbook. In addition, Professors Jagoda (GIT) and Collins (UTSI) kindly used draft copies of certain chapters in their classes to provide valuable feedback. We are indebted to Professors Harper and Hubbartt of GIT for allowing the use of materials developed in their classroom notes. Finally, the first two authors thank their teachers and research advisors for insight into the inner workings of fluid mechanics and aerodynamics attained duri ng their graduate studies in aeronautics at the California Institute of Technology. Giants such as Clark Millikan, Hans Liepmann, Lester Lees, Frank Marble, and Anatol Roshko deserve special mention for their influence on our understanding of this subject.

The three authors of this book represent more than 90 years of teaching and practical experi­ence in aeronautics and associated disciplines. We wish you success in your study of aero­dynamics and hope that it is as fulfilling to you as it has been to us.

Gary A. Flandro Howard M. McMahon Robert L. Roach

## For Howard

Dr. Howard McMahon spent 26 years of his career as a professor and researcher at the Georgia Institute of Technology in Atlanta. Having been born just a few weeks after Charles Lindbergh’s flight across the Atlantic, he moved through the age of biplanes to the modern era of jets and rockets, working first as a researcher and followed by his years as a teaching professor. His retirement from education allowed him to focus his energy on the completion of this textbook in collaboration with Dr. Gary Flandro and former student Dr. Bob Roach. Though he did not live to see the benefits of this book for aerospace students, we, his wife and children, are happy and proud that his work will be recognized.

Dr. McMahon’s tenure at Georgia Tech occurred during a time of rapid change within the university. His work in the classroom and as a departmental colleague and leader helped to define the Aerospace Engineering department’s identity and solidify the school’s recognition for excellence and high standards. Dr. McMahon’s strengths were his attention to meticulous detail and understanding of people. He directed the under­graduate fluid dynamics laboratories and guided students through cooperative work – study programs, placing them in research and laboratory settings throughout the country.

Whether at the university or at home, Dr. McMahon’s office was an obvious destin­ation for anyone who needed advice on how to handle a difficult problem. He blended a knowledge and love of people with an ability to always make the complex seem simple. He shared his talents with much energy and passion during his tenure at the university, having taught more than 4000 aerospace engineers. We know that through the gift of this textbook many more people will learn from his wisdom and insights. As family members, we were fortunate to have that experience throughout our own lives.

With loving memory,

The McMahon Family June 2011

## BASIC AERODYNAMICS

In the rapidly advancing field of flight aerodynamics, it is important for students to completely master the fundamentals. This textbook, written by renowned experts, clearly presents the basic concepts underlying aerodynamic prediction methodology. These concepts are closely linked to physical principles so that they may be more readily retained and their limits of applicability fully appreciated. The ultimate goal is to provide the student with the necessary tools to confidently approach and solve practical flight-vehicle design problems of current and future interest. The text is designed for use in a course in aerodynamics at the advanced undergraduate or graduate level. A comprehensive set of exercise problems is included at the end of each chapter.

Gary A. Flandro is the Boling Chair (Emeritus) of Mechanical and Aerospace Engineering at the University of Tennessee Space Institute. He is also Vice President and Chief Engineer of Gloyer-Taylor Laboratories, LLC. He is a Fellow of the American Institute of Aeronautics and Astronautics. His research interests include acoustics, aerodynamics, rocket propulsion, flight mechanics and performance, hypersonic aerodynamics, propulsion, and vehicle design. Dr. Flandro received the National Aeronautics and Space Administration Exceptional Achievement Medal (1998) and the Federation Aeronautique Internationale Diamond Soaring Badge (1979) for his work.

Dr. Howard McMahon was a Professor Emeritus of Aerospace Engi­neering at the Georgia Institute of Technology. Following his graduate work at Santa Clara and doctoral research at the California Institute of Technology, he worked for CARDE (the Canadian Armament and Research Development Establishment) near Quebec City, with top rocketry researchers in Canada, including Gerald Bull. His desire to teach and expand his research work led him to the Georgia Institute of Technology, where he guided undergraduate and graduate students for 26 years. His particular area of focus was in aerodynamics, and he spent many years guiding research in the university wind tunnel with pro­jects involving rotary aviation, compressible flow, and fluid mechanics. Following his retirement from the university in 1990, he continued to col­laborate with both teaching and research faculty until his death in 2008.

Robert L. Roach currently teaches mathematics and science at the Kfar Hayarok School in Ramat Hasharon, Israel. He was formerly an Assistant Professor of Aerospace Engineering at the University of Tennessee Space Institute. He also taught aerodynamics, rocket pro­pulsion, and mathematics at the Georgia Institute of Technology and at the U. S. Air Force Institute of Technology. He is an Associate Fellow of the American Institute of Aeronautics and Astronautics. His research interests include numerical solutions of the canonical equations of engineering, propulsion, and many aspects of solar energy.