## Aerodynamics of Wings and Bodies

The manuscript of this book has gradually evolved from lecture notes for a two-term course presented by the authors to graduate students in the M. I.T. Department of Aeronautics and Astronautics. We shared with some colleagues a concern lest the essential content of classical aerodynamic theory—still useful background for the practice of our profession and the foundation for currently vital research problems—be squeezed out of the aeronautical curriculum by competition from such lively topics as hypersonic fluid mechanics, heat transfer, nonequilibrium phenomena, and magnetogasdynamics. We sought efficiency, a challenge to the enthusiasm of modern students with their orientation toward scientific rigor, and the comprehensiveness that can accompany an advanced point of view. Our initial fear that certain mathematical complexities might submerge physical understanding, or obscure the utility of most of these techniques for engineering applications, now seems unwarranted. The course has been well-received for three years, and it has made a noticeable impact on graduate research in our department.

We are able to offer a textbook that has successfully met its preliminary tests. We have tried to keep it short. Problems and extended numerical demonstrations are omitted in the interest of brevity. We believe that the instructor who essays the pattern of presentation suggested here may find it stimulating to devise his own examples. It is also our hope that working engineers, with a need for the results of modern aerodynamic research and a willingness to accept new analytical tools, will derive something of value.

There is no shortage of books on aerodynamic theory, so let us point to two threads which make this one certainly distinct and possibly an improvement. The first is the realization that the method of matched asymptotic expansions, developed primarily by Kaplun and Lagerstrom, provides a unifying framework for introducing the boundary-value problems of external flow over thin wings and bodies. Not always an unavoidable necessity nor the clearest introduction to a new idea, this method nevertheless rewards the student’s patience with a power and open-ended versatility that are startling. For instance, as apparently first realized by Friedrichs, it furnishes a systematic, rigorous explanation of lifting-line theory—the only approach of its kind which we know. In principle, every approximate development carried out along this avenue implies the possibility of improvements to include the higher-order effects of thickness, angle of attack, or any other small parameter characterizing the problem.

Our second innovation is to embrace the important role of the high-speed computer in aerodynamics. Analytical closed-form solutions for simple flow models are certainly invaluable for gaining an understanding of the physical and mathematical structure of a problem. However, rarely are these directly applicable to practical aerodynamic configurations. For such, one usually has to resort to some approximate or numerical scheme. Theoretical predictions are becoming increasingly important as a practical tool supplementing wind-tunnel measurements, in particular for the purpose of aerodynamic optimization taking advantage of the gains to be realized, for example, by employing unusual plan –

form shapes or camber distributions, from imaginative use of wing-body interference, adoption of complicated multiplane lifting surfaces, etc. We have, accordingly, tried to give adequate prominence to techniques for loading prediction which go far beyond the more elegant solutions at the price of voluminous routine numerical computation.

The plan of presentation begins with a short review of fundamentals, followed by a larger chapter on in viscid, constant-density flow, which recognizes the special character of that single division of our subject where the exact field differential equation is linear. Chapter 3 introduces the matched asymptotic expansions, as applied to one situation where physical understanding is attained with a minimum of subtlety. Chapter 4 warns the reader about the limitations and penalties for neglecting viscosity, and also illustrates the Kaplun-Lagerstrom method in its most powerful application. Thin airfoils in two dimensions and slender bodies are then analyzed. Three-dimensional lifting surfaces are treated in extenso, proceeding from low to high flight speeds and from single, planar configurations to general interfering systems. Chapter 12 attacks the especially difficult topic of steady transonic flow, and the book ends with a brief review on unsteady motion of wings. Only the surface is scratched, however, in these last two discussions.

Although we closely collaborated on all parts of the book, the responsibility for the initial preparation fell on Marten Landahl for Chapters 3, 4, 5, 6, 8, 9, 10, and 12, and on Holt Ashley for Chapters 1, 2, 7, 11, and 13. The first three groups of students in departmental courses 16.071 and 16.072 furnished invaluable feedback as to the quality of the writing and accuracy of the development, but any flaws which remain are attributable solely to us.

We recognize the generous assistance of numerous friends and colleagues in bringing this project to fruition. Professor Milton VanDyke of Stanford University and Arnold Kuethe of the University of Michigan most helpfully went over the penultimate draft. There were numerous discussions with others in our department, among them Professors Shatswell Ober, Erik Mollo-Christensen, Judson Baron, Saul Abarbanel, and Garabed Zartarian. Drs. Richard Kaplan and Sheila Widnall assisted with preliminary manuscript preparation and classroom examples. Invaluable help was given in the final stages by Dr. Jerzy Kacprzynski with the proofreading and various suggestions for improvements. The art staff of Addison-Wesley Publishing Company drew an excellent set of final figures. Typing and reproduction of the manuscript were skillfully handled by Mrs. Theodate Cline, Mrs. Katherine Cassidy, Mrs. Linda Furcht, Miss Robin Leadbetter, and Miss Ruth Aldrich; we are particularly appreciative of Miss Aldrich’s devoted efforts toward completing the final version under trying circumstances. Finally, we wish to acknowledge the support of the Ford Foundation. The preparation of the notes on which this book is based was supported in part by a grant made to the Massachusetts Institute of Technology by the Ford Foundation for the purpose of aiding in the improvement of engineering education.

Cambridge, Massachusetts May 1965