[1st Edition] 9781483224879

Table of contents :
Content:
Front MatterPage iii
Copyright pagePage iv
PrefacePages vii-viii
Some Aerodynamic Principles for the Design of Swept WingsPages 1-85J.A. BAGLEY
Ducted Propellers—a Critical Review of the State of the Art*Pages 85-135A.H. SACKS, J.A. BURNELL
Experimental Facilities for Hypersonic ResearchPages 137-178R.N. COX
Meteorological and Aeronautical Aspects of Atmospheric TurbulencePages 179-232HANS A. PANOFSKY, HARRY PRESS
Author IndexPages 233-236
Subject IndexPages 237-240
Contents of Previous VolumesPage 241

Citation preview

Progress in AERONAUTICAL SCIENCES Volume 3 Edited by

ANTONIO FERRI Professor of Aerodynamics, Polytechnic Institute of Brooklyn, U.S.A.

D. KÜCHEMANN Royal Aircraft Establishment, Farnborough, England

L. H. G. STERNE Training Center for Experimental Aerodynamics, Belgium

PERGAMON PRESS OXFORD

· LONDON

· NEW YORK

1962

·

PARIS

PERGAMON PRESS LTD. Headington Hill Hall, Oxford. 4 and 5 Fitzroy Square, London W.l PERGAMON PRESS INC. 122 East 55th Street, New York 22, N.T. PERGAMON PRESS S.A.R.L. 24 Rue des Écoles, Paris Ve PERGAMON PRESS G.m.b.H., Kaiserstrasse 75, Frankfurt am Main

Copyright © 1962 PERGAMON PRESS LTD.

Library of Congress Card Number 60-15351

Set in Monotype Modern No. 7 ll/12pt. and Printed in Great Britain by J . W. Arrowsmith Ltd., Bristol.

PREFACE T H E third volume in this series contains four articles dealing with various topics mainly in the field of aerodynamics. I t is certain t h a t the last word has yet to be written on any one of these topics and certainly some of the information offered here, though not ephemeral, will merit amplification in a few years' time. As is only to be expected in a series of this kind, the individual articles are not interconnected but report on fields where advances happen to have been made. As such, they give perhaps some indication of the vigorous activity and continuing growth of the aeronautical sciences. Certainly there would appear to be no dearth of material for an annual volume in this series. In fact, this third volume appears only a few months after the second volume: what was originally intended to form one volume was split into two for the greater convenience of the reader. The first paper is a review of the aerodynamics of swept-winged air­ craft and as such is a contribution to the solution of the problem of present-day aerodynamic design which, as noted in Volume I, has emerged as a consequence of developments which have gone beyond the classical concepts of aircraft design. This paper is a first review of part of the research work, which was a co-operative effort on a large scale by British aircraft firms and research establishments, aimed at the development of supersonic airliners. Not all the individual refer­ ence papers concerned in the study have yet been published and it is hoped to report on other aspects of this research work in later volumes in this series. The second paper of this volume is concerned with ducted propellers which in recent years have attracted considerable interest owing to their potential application to a variety of aircraft types, notably the important category of those able to take off vertically or requiring a short take-off run. The paper gives an exhaustive survey of the widely dispersed literature in a way which does not ignore practical appli­ cations. The third paper, on hypersonic facilities, provides the reader with a balanced review of the, to some, bewildering multiplicity of means for experimenting with hypersonic flows. Even though development still proceeds at a rapid pace, the overall outlines and the usefulness of particular facilities for particular purposes begin to become more firmly established and a survey is, therefore, both opportune and wel­ come. vii

vin

PREFACE

The last paper gives an account of gust research—that fascinating field of work where meteorology, fluid dynamics and aircraft dynamics meet. The subject will be seen to be of great interest and prolific in its many aspects, one of which is, of course, the comfort and safety of ourselves as airline passengers.

SOME AERODYNAMIC PRINCIPLES FOR THE DESIGN OF SWEPT WINGS J.

A.

BAGLEY

Aerodynamics Department, Royal Aircraft Establishment, Farnborough

Contents L I S T OF SYMBOLS

2

1. INTRODUCTION

5

2. T H E CLASSICAL AIRCRAFT AND THE EXTENSION TO SWEPT WINGS

10

3. T H E SHEARED WING OF INFINITE SPAN

14

4. SWEPT WINGS OF FINITE ASPECT RATIO

22

5. T H E DESIGN OF SWEPT WINGS

5.1. 5.2.

30

Aerodynamic features of the flow over swept wings Design principles

6. CALCULATION METHODS AVAILABLE FOR DESIGN PURPOSES

6.1.

Methods of designing the basic wing section 6.1.1. Incompressible flow 6.1.2. Compressible flow 6.2. Design methods for the finite wing, at subsonic speeds 6.2.1. Planform, camber and twist 6.2.2. Thickness 6.2.3. Compressible flow 6.2.4. Thickness and lift combined 6.3. Design methods for the wing-fuselage combinations at subsonic speeds 6.4. Design methods for the wing-fuselage combinations at supersonic speeds 6.4.1. Thickness problems 6.4.2. Lifting configurations

30 38 43

45 45 48 51 51 57 61 62 63 67 68 75

ACKNOWLEDGEMENTS

79

L I S T OF REFERENCES

80

1

SOME AERODYNAMIC PRINCIPLES FOR THE DESIGN OF SWEPT WINGS J. A. BAGLEY Aerodynamics Department, Royal Aircraft Establishment, Farnborough S u m m a r y — T h e design of swept wings has now reached the stage where a coherent set of aerodynamic principles has emerged. The pur­ pose of this paper is to summarize these principles, and to indicate methods of designing wings in accordance with them. I t is important to design wings so that the type of flow obtained in practice is the same as that assumed in the design theory, and so that it is a flow which is usable—i.e. which can be predicted and controlled. I t is shown that these requirements lead to the concept of a sub-critical flow which can be obtained on certain swept wings. These are restricted to a fairly narrow band of sweep angles, depending on the design Mach number, and the aspect ratio and thickness of the wings are correspond­ ingly limited. Practical design methods are discussed in order to illustrate the physical principles used in design, but a critical comparison of different calculation methods is not attempted.

List of Principal Symbols a Local speed of sound a(y) = CL(y)l*e(y) Sectional lift slope on swept wing a0 Speed of sound in free stream (except in Eq. 59A) A Aspect ratio of wing A a Aspect ratio of analogous wing A\, A2 Constants in Eqs. 61 and 62

B = {l-Jfo 2 [(l-Opi)cos2 Çt -Opi(l-|/i|)sin2 9t ]}* c(y) c CD ÖD(y) @DB(y) CD-F CD0 = ^Di(y) ODV CW GL CL(2/) CLCT Cm

Wing chord Geometric mean chord Overall drag coefficient Sectional drag coefficient Sectional drag coefficient due to boundary layer effects Drag coefficient due to skin friction (complete wing) Do/qS Sectional drag coefficient due to thickness Vortex drag coefficient (complete wing, or sectional) Wave drag coefficient due to lift Overall lift coefficient Sectional lift coefficient Cruising lift coefficient Value of CL for (L/D)m Overall pitching moment of wing 2

Aerodynamic Principles for the Design of Swept Wings Cp Cp* Cpi

3

Pressure coefficient Critical pressure coefficient, denned by Eq. (17) Pressure coefficient at zero lift in incompressible flow (Eq. 47) (7PT Pressure coefficient at trailing edge CVu(%) Pressure coefficient on upper surface of wing Cpi(x) Pressure coefficient due to wing thickness Op2(#) Pressure coefficient due to wing lift D Total drag of wing or wing-fuselage combination DL Drag due to lift of wing or combination Do = D —DL. Drag independent of the lift distribution DT Wave drag due to volume of configuration Dw Wave drag due to lift of configuration 1 + sin φ /(φ) = l o g r— 1 — sin φ Q(B) See Eq. (83) Η(θ) See Eq. (84) K = π^4((7z)v+Crz)w)/CrL2. Drag due to lift factor K\(y) Spanwise interpolation factor used in Eqs. (68) and (76) Ky = TTACDYJGL2' Vortex drag factor Kw = TT.4Z 2 CW/2J3 2 $ 2 CL 2 . Wave drag due to lift factor I Overall length of configuration, except in Eqs. (83) and (84) l(x), l(x, y) Local load coefficient, — Δ(7Ρ L Overall lift on wing or combination L(x) Lift on section of combination intercepted by plane x = constant L(x, Θ) Lift on section of combination intercepted by oblique Mach plane (see Eq. (84)) (L/D)m Maximum lift-drag ratio (L/D)cr Cruising lift^-drag ratio M = V/a Local Mach number Mo = Vo/ao Free-stream Mach number Merit Critical Mach number, i.e. value of Mo when M = 1 first on body Mes Sheaved wing critical Mach number, i.e. value of M0 when Eq. (15) is first satisfied n Chordwise loading parameter, defined by Eqs. (57), (57A) n a = n(y&, vz, Vf, νη Velocity increments in x-, y-, z-, ξ- and ^-directions vx9 vy> A z Velocity increments in incompressible flow on analogous wing vXq, vzq Velocity increments due to source distributions νχγ, νζγ Velocity increments due to vortex distributions V Local flow velocity Vo Free-stream velocity; flight velocity of aeroplane Vx* Vyt Vzy Vf, Vv Components of V parallel to #-, y-, z-, f-, and η-directions Vxof Vzo Components of Vo parallel to x- and z-directions TTp, Wi Final and initial weights of aeroplane x Streamwise co-ordinate xn End of pressure "plateau" on rooftop aerofoil section y Spanwise co-ordinate y& ~ ßy Spanwise co-ordinate on analogous wing z Vertical co-ordinate z(x) Aerofoil surface Zs{x), zs(x, y) Wing camber line or surface zt{x)y zt{x, y) Aerofoil or wing thickness distribution. a Wing incidence o.(y) Sectional incidence 2y

^6V^*\j^*

60 hh

Y 40r

*R 4

1

I

*\

V

*

y

Cp

/

| N^r-U.S.

x i **-^

30l·l· Cp

s

*

Il·

Uli

^L.S.

11//

Assumed pressure //// distribution ////

0

!

0-2

1

0-4

1

0-6

I

0-8

1

1-0

1

1-2

_J

1-4

I

1-6

I 1-8

1 2-0

M0 (b) Rooftop

distributions;

xR=0-3

F I G . 3. Variation of critical GL with sweep and assumed pressure distribu­ tion.

21

22

J.

A.

BAGLEY

boundary layer remains attached. I t is much harder to find sections on which sub-critical flows are possible corresponding to XB, = 0-5 or 0-7, and the compromise with the low-speed properties may also be much more difficult. I t may even be worth while to develop schemes for boun­ dary layer control in order to utilize sections with large adverse pressure gradients. Figure 3(b) provides a summary of results for a range of wing sweeps and Mach numbers. Again, roof-top pressure distributions with XR = 0-3 and RAE 101 thickness distributions with thickness-chord ratios of 10% normal to the leading-edge, have been assumed. These curves define the minimum sweep angle (for the assumed distributions) at which it should be possible to obtain sub-critical flow at a given design Mach number and lift coefficient. They show that wings designed to sustain this type of flow fall into a fairly narrow band : swept wings are needed above about Mo = 0-7, and there is a smooth transition through MQ = 1 into supersonic flight speeds. These considerations appear to be fundamental to the design of swept-wing aircraft—at least to that large class where a major design problem is to cruise at as high a speed as possible with high efficiency. This implies a need for an orderly, controlled flow with low drag, which can be met if the sub-critical Kutta-Joukowsky flow can be maintained. I t does not always seem to have been properly appreciated in the past t h a t this requirement could be immediately used to define the necessary wing sweep and thickness-chord ratio within fairly narrow limits. A preliminary outline of these requirements, and an indication of some ways of meeting them by exploiting various features of the aero­ foil pressure distribution, were given by Bagley 11 . A much more detailed review has been given by Pearcey 12 , who has placed the whole subject on a sounder basis by producing experimental evidence to show that the development of supercritical flow can in fact be related to the uppersurface pressure distribution only, in the way assumed here. Thus the theoretical ''exchange rates" discussed above do have a real meaning in practice.

4. Swept Wings of Finite Aspect Ratio In Section 3, the aerodynamic properties of the sheared wing of infinite span were discussed. I n practice, the aerodynamic character­ istics of a configuration comprising a swept wing of finite aspect ratio attached to a central fuselage are of greater interest. The details are briefly considered in Section 5, but first the analysis of Section 2 is con­ tinued, to demonstrate that only swept wings lying in a fairly narrow

Aerodynamic Principles for the Design of Swept Wings

23

band of aspect ratios and sweeps need be considered for many practical applications. Many of the features of the classical aeroplanes are retained in this genus of aircraft—namely the separate components for lifting, propul­ sion and for carrying the payload. In special circumstances, especially for single-engined aeroplanes, the turbojet propulsion units may be integrated with the fuselage or wings, but in what follows no considera­ tion is given to the special problems of these layouts. The swept wing is assumed to support a type of flow essentially simi­ lar to that on the infinite sheared wing, with separation fixed along the trailing edges only and viscous effects confined to a thin surface bound­ ary layer. Under these circumstances, vorticity is shed in an essentially plane sheet, and the basic division of drag, into a term independent of lift and a term associated with the lift distribution, which applied to the classical aircraft can be retained. The only fundamental difference occurs at flight speeds where Mo > 1, because the wave drag terms associated with volume and lift then have to be taken into account. If the design principles described here are followed, and a swept wingfuselage combination is designed so t h a t the flow over the wings is of the sub-critical type already discussed for the infinite sheared wing, then it is reasonable to expect t h a t the shock system generated is one giving a low wave drag. I t is not (at present) possible to associate this with any mathematical derivation of a ''minimum" value for certain specified conditions, but experience suggests t h a t the zero-lift wave drag of a well-designed wing-fuselage combination can be at least as small as t h a t of a well-designed body of revolution of equal length and volume. For the crude performance estimate required here, this drag is assumed to be a constant increment to Ο# 0 for Mach numbers above about 1-1, with some arbitrary variation below this speed down to zero at about Mo = 0-9. The actual value of the drag increment is related to the fuselage length and volume. Similarly, the wave drag due to lift on a wing-fuselage combination can be of the same order as R. T. Jones' lower bound,* which is obtained by not-so-slender wing theory 1 3 for an elliptical streamwise distribution of the lift over a length l. This lower bound can be written as

or

/>w = — .(M