This text evolved from a set of notes that have been continually revised for over 30 years of teaching courses in Aircraft Performance, Aerodynamics, and Aircraft Design. The primary motivations for transforming these notes into textbook form were the unjustifiably high prices that book publishing companies set for engineering textbooks and the need for a single text that covered just enough basic aerodynamics and aircraft performance to satisfy the needs of a “stand-alone” course in airplane performance with a design emphasis.

There are many excellent textbooks that cover the subject of Aircraft Performance as well as related aerodynamic theory. These include the texts listed below:
• Anderson, John D., Jr., Aircraft Performance and Design, McGraw Hill, New York, 1999 and later editions.
• Houghton, E. L. and Carruthers, N. B., Aerodynamics for Engineering Students, Arnold, London, 1982 and later editions
• Eshelby, Martin E. Aircraft Performance, Theory and Practice, Arnold, London, 2000
• Mair, W. Austyn and Birdsall, David L. Aircraft Performance, Cambridge Aerospace Series 5, Cambridge University Press, 1992

I especially recommend the text of my long-time friend, John Anderson, who has inspired my increasing interest in aviation history with the historical inserts found in all of his excellent books and through his outstanding talks on the history of both aviation and aerodynamics. I only wish that the publishers of these texts could make them available to students at a reasonable price.

The major publishing houses like to tell us that the high prices they charge for engineering and technical texts are the result of publication of relatively small numbers of books (when compared to main line literature). The truth is that one can go to any professional printing company in the country and get 1000 copies of a professionally bound, 200 page, soft cover book printed at a cost of less than $10 per copy. I know this because I have done so with another book that I authored and published on my own. I also know that textbook industry often encourages authors to make un-needed revisions of their books every five or so years for the sole purpose of making used copies of their past editions “obsolete”, and that it is a common practice to increase the price of a textbook approximately $5 every year,  even if costs have not risen a penny.

Hence, as mentioned in the first paragraph above, one motivation behind creating this text is to allow my students to obtain a publication that will serve their needs at a savings of $100 or more. The other motive is to give them only the material that they really need for their course and allow them to find the coverage needed in other courses in the texts required for those courses. Too many authors today, often encouraged by their publishers, seem to want to create textbooks that cover multiple subjects. The result is that students end up having to buy three or four different texts, all covering the same wide range of subjects such as subsonic aerodynamics, supersonic aerodynamics, aircraft performance, and boundary layer theory in one volume, when the professors teaching those four separate courses all prefer books by different authors.

This text is designed for a course in Aircraft Performance that is taught before the students have had any course in fluid mechanics, fluid dynamics, or aerodynamics. The text is meant to provide the essential information from these types of courses that is needed for teaching basic subsonic aircraft performance, and it is assumed that the students will learn the full story of aerodynamics in other, later courses. The text assumes that the students will have had a university level Physics sequence in which they will have been introduced to the most fundamental concepts of statics, dynamics, fluid mechanics, and basic conservation laws that are needed to understand the coverage that follows. Separate courses in engineering statics and dynamics are helpful but not necessary. It is also assumed that students will have completed first year university level calculus sequence plus a course in multi-variable calculus. Any student who takes a course using this text after completing courses in aerodynamics or fluid dynamics should find the chapters of this book covering those subjects an interesting review of the material, perhaps with a different emphasis than previously seen.

I have tried to present much of the material in this text from the point of view of a pilot since it is essential that the aircraft performance engineer be able to relate to pilots and their needs and vocabulary. While being an aerospace engineer or even a performance specialist has little to do with actually flying an airplane, it could easily be argued that one’s real world experience at the controls of an airplane gives a valuable perspective in teaching either aerodynamics or aircraft performance. I owe my own “hands-on” flying experience to two people, my father who began flying in his early teens and continued to pilot his own plane almost until he died at age 80, and to a former undergraduate and Masters student, David Manor, who challenged me to finally get my pilot’s license and provided free flight instruction. I will never live up to my father’s wish that I share his intense love of being in an airplane whenever possible or to Dr. Manor’s desire that all of this flight students become aerobatic pilots; however, even the relatively mundane experience of flying in a straight line from point A to point B has its satisfying moments if one is willing to put up with the hassles imposed by the FAA and the weather and the outrageous expenses of flight that seem to result primarily from government regulation and the unlimited greed of American lawyers. A few years ago I fell victim to those high costs and frustrations of flying and airplane ownership and sold my airplane. Nonetheless, the experience of being a pilot will always flavor the way I teach any aerospace engineering course.

On the subject of the emphases of this text, the reader will find that, unlike many technical books this one spends less time and space than normal on rigorous derivations of theory and more time emphasizing the practical uses and limitations of the resulting theories. I have also tried to stress a need for assessing the practicality of one’s answers and for the rigorous tracking of units through problem solutions. It has been my experience that the average student today, like the general population, has very little “feel” for physical reality and even less appreciation for reality expressed in unfamiliar unit systems. Unfortunately, the stress on the use of the SI unit system in every course taken from kindergarten through college has greatly exacerbated this lack of appreciation for physical reality.

Other than some understanding of the physical size of a liter (or is it litre?) that comes from buying everything from Coke to beer in liter containers, the typical American student has absolutely no feel for the physical size any SI unit. The exception might be some appreciation for the physical length of a meter (or is it a metre?) among people who have been involved in some form of track or swimming or those who were taught that a meter is a few inches longer than a yard. Despite the fact that American students have been inundated by SI units in school since their fifth birthday, few would have any idea of their own weight in Newtons (or mass in kilograms) or their height in meters. It is no wonder that when the student in Aircraft Performance calculates that the speed of flight of a Cessna 152 is 750 meters per second, he or she goes merrily on his or her way without questioning the physical reality of that answer.

And it is not just the SI system that is the problem. Since most students have been taught most courses using SI units instead of the more familiar everyday “English” units (the British call these “American” units), they also often lack any ability to think about technical problems and the physical reality of their solutions in terms of “English” unit answers. Would 1000 feet per second be an acceptable speed for that Cessna 152? Throw in a few pressures in Pascals or pounds per square foot and mix in a few densities in kilograms per cubic meter or slugs per cubic foot and today’s student has absolutely no idea if the magnitude of any number is right or wrong. It is even rare today to find an American student who has any idea how many feet are in a mile.

Contrary to the beliefs of those who strongly advocate conversion of American society to SI units, this is definitely not an American problem. I have worked with students from all over the world and have yet to find one who can give his own body weight in Newtons or has any sense of how many Pascals might represent a higher than standard air pressure. And has anyone anywhere seen an advertisement for a car that bragged about how many Watts the piston engine could produce?

It would also be nice if the aircraft performance engineer could relate to the airplane pilot who is used to measuring altitudes in feet, speeds in knots, and air pressures in either millibars or inches of mercury, regardless of his or her country of origin. In order to deal with all of these problems, a strong emphasis will be placed on the need to always carry the proper units with every number (except, of course, those that are unitless) completely through any problem and to make absolutely sure that the final units associated with any answer are the proper ones. In a problem where the student is asked to calculate the top speed of an aircraft, if the answer comes out with units of meters squared per second, it should be obvious that an error has been made somewhere. The same strong emphasis will be placed on assessing the physical reality of the magnitudes of all answers. Can a Cessna 152, a single engine piston powered aircraft, fly at a speed of 600 ft/sec or 300 meters per second or 100 knots? (one of these is reasonable).

In addition to the use of mixed units (with a preference for “English”) I have provided graph paper with the homework problems at the end of the text and I insist that my own students plot the results of their work on this paper by hand rather than using computer plotting routines.

This, like my insistence on carrying units through solutions with all numbers, is something that I firmly believe encourages students to actually take the time to think about their work. There is far too much tendency for students to want to merely plug numbers into equations and let the computer do the math and the plotting and then to assume that it is impossible for the computer to do anything wrong. The provided graphs already have their axes defined and enumerated, thus providing the student with some idea of the range of values that should come out of his or her calculations.

In this third edition of this work I have completely rewritten the first three chapters of the text and added a ninth chapter dealing with the subject of “constraint analysis”. In the first three chapters I have attempted to better organize the presentation of the basic aerodynamic and fluid dynamic concepts that will be needed for the later development of aircraft performance relationships. I have eliminated some of the more rigorous derivations of fluid dynamic theory and tried instead to present those resulting equations and concepts, such as Bernoulli’s equation and mass and momentum conservation, in their most useable forms and to emphasize the assumptions related to these forms and the limitations that they place on the use of those concepts and equations. I have always felt that the main value in actually taking students through the complete derivation of the equations they will eventually use is in showing where the important assumptions come from and why they were made. However, it has been my experience that most students simply tune out during such derivations or, if they think they will have to feed back the derivations on a test, they resort to mindless memorization of the steps involved and totally lose sight of the important aspects of the derivations, that is, the impact of the often purely mathematically based assumptions on the subsequent utility of the final equations.

I have totally replaced the third chapter of the previous editions, a chapter that was originally written for another purpose and which was written in a different style and form from the rest of the text. Many of the concepts presented in that chapter were simply not relevant for a first course in aircraft performance. The important parts of that material have been merged into the first two chapters of this edition in such a way as to follow a better progression than before and to relate better to the subsequent direction of the text.

The third chapter now contains some optional (for an introductory aircraft performance course) coverage of two-dimensional (airfoil) and three-dimensional (wing) theory basics. These should help satisfy the curiosity of those students who would like some very basic tools that will enable them to perform their own elementary assessments of the way geometry factors such as airfoil camber and wing aspect ratio might affect both aerodynamic and aircraft performance.

Chapter nine covers new material that I first introduced in my sophomore level aircraft performance course in the Spring of 2003. The chapter covers the concept of “constraint analysis”, a widely used method of making a simultaneous assessment of several performance parameters such that an aircraft can be designed to meet these objectives in an optimum manner even though the outcomes might not be optimum when considered individually. In other words, even though earlier chapters have discussed how to get the best range or best endurance in cruise or the minimum takeoff distance or the maximum rate of turn, there was no real discussion of how to put these together in a single aircraft design. The best thrust or wing area for optimum range may be far different from those for best rate of turn or climb. Constraint analysis is a method of assessing aircraft performance in its various modes in terms of two ratios, the thrust-to-weight ratio and the wing loading (weight to planform area ratio).

While some introductory level aerospace engineering texts discuss a form of constraint analysis, they usually do so in a very limited context or are aimed at one particular type of aircraft (fighters, for example). Chapter 9 attempts to present this method in a general way that can be applied to any type of aircraft. Many textbooks on aircraft design also look at constraint analysis methods but they usually do so in an overly terse manner which assumes that the student can read between the lines to figure out the basis for the various plots presented. The coverage in chapter nine is based on the material I present in my own senior level aircraft design course and that presented in the design text that I co-authored with Lloyd Jenkinson (Aircraft Design Projects for Engineering Students, AIAA, 2002).

James F. Marchman, III
Summer 2004

About the Author

Dr. James F. Marchman, III is Professor Emeritus of Aerospace and Ocean Engineering and a former Associate Dean of Engineering at Virginia Tech where he taught and conducted research in aerodynamics, aircraft performance, aircraft design and other areas over a 40 year career.  His textbook, Aircraft Design Projects For Engineering Students, coauthored by Professor Lloyd R. Jenkinson of Loughborough University in the United Kingdom, published by Butterworth-Heinemann in 2003 has been used by students around the world.