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September , 1935 AIRCRAFT ENGINEERIN G 233 Th e Third Volume of "Aerodynamic Theory" and Two Germa n Books on Allied Subjects Aerodynami c Theory. Edited by W. F. of the Variable Density Tunnel and the High approximate method of Tohlhausen are de Durand . Vol. III. (Julius Springer, Berlin. Speed Tunnel a t the Langley Memorial Labora scribed, also the l/7th power law and the tory, U.S.A., together with some of the experi logarithmic law for the turbulent boundary 20 marks.) mental results obtained from them. layer. The first two volumes of this series on Aero dynamic Theory (reviewed in AIRCRAFT EN I t is perhaps of interest to add that three References to original papers are given in , Vol. VI, Sept. 1934, p. 249, and more volumes of this series (IV-VI) are to be footnotes, but, in most cases, the theory and Vol. VII, April 1935, p. 99 respectively) its applications are fully developed in the text. published. A. F. deal largely with fundamental mathematical H. M. L. theorems and methods applicable to a perfect Aerodynamik . Fuchs-Hopf-Seewald. II Turbulenz . Physikalische Statistik und fluid. The greater part of Vol. III is devoted Band . Theorie der Luftkrafte. By R. Hydrodynamik . By Dr. Hans Gebelein. to the Mechanics of a Real Fluid. Fuchs. (Julius Springer, Berlin. 30 RM.) (Julius Springer, Berlin. 12.50 RM.) The volume opens with a short contribution This second volume of the revised and Th e statistical investigation of the hydro- by Professor Witoszynski (Warsaw) and Fro- enlarged edition of "Aerodynamik " by Fuchs dynamical problem of fully developed turbu fessor Thompson (Michigan) on the Theory of and Hopf corresponds with the first part of the lence described in this book was begun at Single Burbling. This theory makes use of a earlier edition. A review of the revised first Göttingen under the direction of Professor discontinuous form of potential, and by this volume has already been published in AIRCRAFT Prandt l and is published by the author, not artifice Professor Witoszynski and his col ENGINEERING , Vol. VII, May 1935, p. 12G. as a complete explanation of turbulence laborators arc able to predict for profile forms, This second volume is concerned with the phenomena, but as a record of an attempt to derivable from a circle by the standard methods, theoretical investigation of aerofoil theory. apply new methods to an unsolved problem values of lift and moment which are in closer The first chapter summarises the mathe and in the hope that it may be of value to agreement with practice than those deduced matical methods used in the later chapters, future research. The investigation is of con b y the older and better known methods. such as Fourier series, the equations of Gauss siderable interest, but the development of the Predictions of form drag arc also made. and Stokes, and conformal representation. The method is often difficult to follow and not Nex t follows a valuable contribution by notation of vector analysis is used throughout always convincing. It does not appear to go th e book. Professor Prandtl on The Mechanics of Viscous an y farther towards solving the immediate Fluids. At the outset, fundamental theorems The classical equations of hydrodynamics, practical problem of turbulent flow in pipes associated with the flow of a viscous fluid claim including th e theory of vortices, are discussed in and in the boundary layer of a surface than attention . The Theory of Slow Motions, and th e second chapter, where it is shown that, in th e methods already evolved by Prandtl and th e known exact solutions of the Stokes-Navier potential flow, no forces act on a body com von Kármán, especially von Kármán's appli equations of viscous flow are also given. The pletely immersed in fluid in three-dimensional cation of the principle of mechanical similarity. treatmen t then leads to an exposition of space. The analysis of two-dimensional flow The ultimate value of the work will depend theories of boundary-layer flow and of the in the third chapter shows how a force normal on the use which may be made of it in future spreading and growth of turbulence in a free t o the wind direction may act on. a cylinder or research. stream. Relations of the velocity distribution aerofoil of infinite span due to a circulation A summary of the theory of probability and in turbulent streams flowing along smooth and round it. An analysis is also given of the field its application to statistical physics, as devel rough walls with the shearing stresses at the of flow due to a vortex sheet. In the fourth oped by von Mises and Kolmogoroff, is given surface, derived by Professor Prandtl and by chapter the two-dimensional theory is applied in the earlier chapters and is followed by the Professor von Kármán, naturally receive to the calculation of the lift and moment on an development of the equations of statistical attention . Many researches connected with inclined flat plate, a circular arc, a Joukowski hydrodynamics, with the equations of the problems of turbulent flow which have been aerofoil in its original and generalised forms classical theory as a limiting case. According mad e in Germany under Professor Prandtl's and other types of aerofoils, including those with t o the author's conception, turbulent motion supervision are fully dealt with. The treatment constan t centre of pressure. The lift distribu is characterised by an ever-changing distri soon reveals that these researches fit into a tion along the chord of thin sections, including bution of vorticity throughout the fluid, definite scheme, and that both theory and th e effect of flaps and rudders, is analysed, and experiment have been made to yield valuable caused by contact with a rough surface. The tande m and biplane wings are also considered. instantaneous velocity a t any point is a function contributions. The fifth chapter deals with the aerofoil of of the instantaneous distribution of vorticity finite span and the effects of aspect ratio and of The third division of the volume is written and, with certain limiting assumptions, it th e distribution of circulation along the span by Professor Taylor and Dr. Maccoll, and deals is shown that the root-mean-square of the on the lift and induced drag. The relationship with the Mechanics of Compressible Fluids. deviations from the mean velocity is approxi between the plan form of the wing and the General effects of compressibility on fluid flow mately proportional to the fourth root of the distribution of circulation along the span is are first discussed, and it is shown tha t classical modulus of the mean value of the vorticity analysed in th e sixth chapter. The lift distribu mathematical methods are capable of giving a t the same point. In the application of the tion is derived for unwarped wings of various useful information on important practical theory certain assumptions are made as to forms and also the warping required to give an problems, such as Design of High Speed Wind th e mean direction of the axes of the vortices elliptic distribution. In an appendix, a new Tunnels, and Two-Dimensional Flow at High near the boundary. and useful scries of diagrams is given, from Speeds past Projectiles, Cylinders, and Aero which the lift distribution, effective angle of I n the final chapters the theory is compared foils. The practical significance of such incidence and induced drag on a tapered wing with the results of the experimental investi problems need no t be stressed, for compressibility ca n be found for various aspect ratios and effects arc now experienced within the range gations carried out by Nikuradse and others degrees of taper. The effects of flaps and of high-speed modern aeroplanes. Important a t Göttingen. While qualitatively consistent ailerons is also examined. The theory is applied developments in this field of research are to with the results, the theoretical expressions t o th e biplane in th e seventh chapter. The form be expected, and this division of the book is contain non-dimensional factors which vary drag due to the wake between two surfaces of destined to receive close attention. from point to point in the fluid and can be discontinuity is investigated by the Helmholz- determined solely by empirical methods for The last division deals with Experimental Kirchhoff method for a frictionless fluid in the each particular case. The experiments do not Methods (Wind Tunnels) and is divided into eighth chapter and the stability and resistance therefore give any proof of the validity of the two parts. Part I, by A. Toussaint (France), of the Kármán vortex sheet are discussed. An theory. H. M. L. gives a brief classification of experimental analysis is given of the growth of circulation methods used in Aerodynamic Research, and Th e Seal Aeroplane. Air Publication and lift on a wing as it accelerates. short descriptions of various types of Wind 1465 . (H.M.S.O. 3s. 6d.) Tunnel. Correction formula; associated with Th e effect of viscosity is dealt with in the Th e Vildebeest Aeroplane. Air Publica wind-tunnel methods of measurement are also ninth chapter, where the boundary layer tio n 1439. (H.M.S.O. 2s. 6d.) discussed. Finally, Part II, by Eastman equations are developed and the occurrence of Two more of the Air Ministry handbooks on Jacobs (U.S.A.), presents a short section on separation is explained. The Blasius equations service types of aeroplanes. Both are fully up Scale Effect, and includes general descriptions for the laminar flow on a flat plate and the to the usual high standard of this scries.
Aircraft Engineering and Aerospace Technology – Emerald Publishing
Published: Sep 1, 1935
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