# Aerodynamics (Lanchester)/Preface

Preface.
The problems that arise in connection with the study of Aerial Flight are so numerous and of so diverse a character that, except for their relation to the title subject, they would scarcely find place in one volume. In the present work an attempt is made, it is believed for the first time, to treat the classification of the phenomena associated with the study of Flight on a comprehensive and scientific basis.
The origin of the present work may be said to date from some experiments carried out in the year 1894. These experiments, which were primarily directed as a test of certain theoretical views which the author then advanced, resulted in the production of flying models of remarkable stability, whose equilibrium was not destroyed by an ordinary gale of wind.
As originally formulated the theory was incomplete and in many ways imperfect, but it has been developed from time to time during the last twelve years to an extent that to-day renders the approximately correct proportioning of an aerodrome a matter of straightforward calculation.
The author has found the question of publication one of some difficulty. At first it was intended to arrange and publish the investigations simply in order of date, theoretical work being accompanied so far as possible by appropriate experimental ​demonstration. It soon became evident that there were considerable lacunae, and these were filled by subsequent investigations, the scope of the work being greatly extended. Finally it was decided to make the publication a complete treatise on Aerial Flight, the main classification being as follows:—
Vol. I. Aerodynamics, relating to the theory of aerodynamic support and the resistance of bodies in motion in a fluid.
Vol. II. Aerodonetics or Aerodromics, dealing with the forms of natural flight path, with the questions of equilibrium and stability in flight, and with the phenomenon of "soaring."
So far as has been found possible the work has been modelled on non-mathematical lines. The commonly distinctive feature of a modern mathematical treatise, in any branch of physics, is that the investigation of any problem is initially conducted on the widest and most comprehensive basis, equations being first obtained in their most general form, the simpler and more obvious cases being allowed to follow naturally, the greater including the less. The reader who is only moderately equipped with mathematical knowledge is thus frequently at a loss to comprehend the initial stages of the argument, and so has no great chance of fully appreciating the conclusions.
It is impossible, in connection with the present subject, to avoid the frequent use of mathematical reasoning, and occasionally the non-mathematical reader may find himself out of his depth. The author has endeavoured to minimise any difficulty on this score by dealing initially with the simpler cases and afterwards working up to the more general solutions; and further by the careful statement of all propositions apart from mathematical expression, and by the re-statement of conclusions in non-mathematical language. Wherever appropriate, numerical examples are given in order to more completely elucidate the methods employed and the results attained.
​Whenever the author has consciously derived assistance from the work of previous investigators, due acknowledgment has been made; the present work is, however, in the main, a connected series of personal investigations. Should the author inadvertently have put forward as new, results that have been previously published or methods that have been previously employed, he can at least claim in mitigation of the offence that very many of the present investigations were actually done more than ten years ago; the work has only been withheld to the present date in order that publication might take the form of a complete and connected account of the mechanical principles of flight such as could be the better understood by, and be of the greater service to, the Scientific and Engineering World.
In offering to the public the first instalment of the present work, the author desires to record his conviction that the time is near when the study of Aerial Flight will take its place as one of the foremost of the applied sciences, one of which the underlying principles furnish some of the most beautiful and fascinating problems in the whole domain of practical dynamics.
In order that real and consistent progress should be made in Aerodynamics and Aerodonetics, apart from their application in the engineering problem of mechanical flight, it is desirable, if not essential, that provision should be made for the special and systematic study of these subjects in one or more of our great Universities, provision in the form of an adequate endowment with proper scope for its employment under an effective and enlightened administration.
The importance of this matter entitles it to rank almost as a National obligation; for the country in which facilities are given for the proper theoretical and experimental study of flight will inevitably find itself in the best position to take the lead in its application and practical development. That this must be ​considered a vital question from a National point of view is beyond dispute; under the conditions of the near future the command of the air must become at least as essential to the safety of the Empire as will be our continued supremacy on the high seas.
The present volume deals exclusively with the Aerodynamics of Flight; the arrangement of this section is as follows:—
Chapters I.. II, and III, are devoted to the preliminary exposition of the underlying principles of fluid dynamics, examined from different points of view. Chapter I, is of an introductory character, and includes a discussion as to the nature of fluid resistance, the theory of the Newtonian medium, and a preliminary examination of the questions of discontinuous motion and streamline form. Chapter II, is devoted to the consideration of viscosity and skin-friction, the argument being largely founded on dimensional theory; and Chapter III, consists in the main of an account of the Fulerian hydrodynamic theory, in which the mathematical demonstrations are in general taken for granted; this chapter also includes some further discussion of the phenomenon of discontinuous flow and a review of the controversy relating to same.
Chapter IV, consists in most part of an investigation on peripteral motion, dating from the year 1894-5 and offered to the Physical Society of London in the year 1897, but rejected. ​The hydrodynamic interpretation included in the present work has been added subsequently, and the latter portion of the original paper has been revised and rewritten on the more secure basis thus afforded.
Chapters V, and VI, constitute a resume of that which is known concerning the aeroplane treated both from a theoretical and experimental standpoint.
Chapters VII, and VIII, present, for the first time, a series of investigations made by the author (dating from 1894, 1898, and 1902, but not previously published) of the principles governing the economics of flight, and their application in the correct proportioning of the supporting member; these investigations are based on the peripteral theory of Chapter IV, aided by a hypothesis, being in the main an adaptation of Newtonian method.
Chapter IX, includes, with a discussion on the elementary theory of propulsion, an original investigation on the theory of the screw propeller founded on the peripteral theory of Chapters IV.. VII., and VIII. This theory leads to results that are in remarkable accord with experience, and enables a useful series of rules to be laid down as a guide to design; applied to the marine propeller, the theory gives a form quite in harmony with modern practice. The chapter concludes with a dissertation on the subject of the expenditure of power in flight.
Chapter X., with which the present volume concludes, is of the character of an appendix, being an account of the more important of the experimental researches in aerodynamics published to date, and to which references have been made in the body of the work. This chapter also includes an account of some hitherto ​unpublished experiments by the author, and some criticism of the conclusions formulated by earlier investigators.
A few terminological innovations have been made at one time and another, as necessity has arisen. New words, or words bearing a special or restricted meaning, are given in the glossary following Chapter X., in addition to the usual footnote references.
Numerical work has been done by the aid of an ordinary 25 c.m. slide rule, with a liability to error of about 1/5th of 1 per cent., an amount which is quite unimportant.
The author desires to express his thanks to Mr. P. L. Gray in connection with the preparation of the present volume for the Press, in particular for his most welcome assistance in the examination and correction of the proof sheets.
BIRMINGHAM, October, 1907.
* ↑ A word derived from the Greek, άερο-δρὀμος (lit. "traversing the air" or "an air-runner"), proposed by the late Prof. Langley to denote a gliding appliance or flying machine; hence also aerodromics, the science specifically involved in the problems connected with free flight. The word aerodrome has been grossly misapplied by Continental writers to denote a balloon shed. The author considers that from its derivation the word aerodromics may be given a more comprehensive meaning than that originally proposed, perhaps even to include both the aerodynamics and aerodonetics of flight. The question is merely one of terminology. (Compare Glossary, p. 393.)
* ↑ Derived from the Greek, άεροδὀνηγος (lit. "tossed in mid-air," "soaring").
* ↑ A passage occurs in the preface to Poynting and Thomson's "Sound" that may be quoted as being to the point:— "Even for the reader who is mathematically trained, there is some advantage in the study of elementary methods compensating for their cumbrous form. They bring before us more evidently the points at which the various assumptions are made, and they render more prominent the conditions under which the theory holds good."
* ↑ The reader is referred to "Hydrodynamics" (Horace Lamb, Cambridge University Press) for the complete mathematical treatment: a work to which the author desires to acknowledge his indebtedness.
* ↑ A term proposed and employed by the author to denote the type of fluid motion generated in the vicinity of a bird's wing, or the supporting member of an aerodrome essential to its supporting function (lit. "round about the wing," Gr. περι and πτερόν). The term has an architectural signification which can by no possibility clash with its present usage.
* ↑ The rejection of this paper was probably due to an unfortunate selection of the readers to whom it was submitted. The names of the Society's readers are not disclosed, but from the wording of the reports (which the author is not at liberty to quote), it would seem that the recognised application of the Newtonian method (as in the theory of propulsion) was a thing unknown to them.
* ↑ The essentially Newtonian character of all methods based on the principle of the direct communication of momentum, in hydrodynamics, is not so widely recognised as it ought to be. Thus the Rankine-Froude theory of propulsion is a simple and legitimate application of the Newtonian theory (see Chap. IX.). Newton was careful to specify the nature of the medium essential to the rigid application of his method (prop, xxxiv., Book II., Enunciation); subsequent writers have unfortunately not been so careful, and error has resulted.