A theoretical and experimental study of the boundary layer flow on a 45º swept back wing

1^7» t T t

NDE Kanaalstraat 10 - DELFT

Kluyverweg 1 - 2ü29 HS DELR - g pf g_ 1957

THE COLLEGE OF AERONAUTICS

CRANFIELD

A THEORETICAL AND EXPERIMENTAL STUDY

OF THE BOUNDARY LAYER FLOW ON A 45°

SWEPT BACK WING

by

Kanaalstraat 10 - DELFT

- 6 1-1:^1957

CoA R e p o r t No.109 *«»* October 1956. T H E C O L L E G E O F A E R O N A U T I C S C R A N F I E L D

A T h e o r e t i c a l and E x p e r i m e n t a l S t u d y of t h e Boundary Layer Plow on a 45 Sv/ept Back ¥ i n g

b y

F . M» Burrovrs, D.C.Ae,

Smi'IARY

I n t h i s p a p e r an account i s p r e s e n t e d of a t h e o r e t i c a l and e x p e r i -m e n t a l s t u d y -made i n r e l a t i o n t o t h e boundary l a y e r flow on a 4 5 °

s\ifept back w i n g . P a r t i c u l a r a t t e n t i o n i s g i v e n t o t h e o n s e t of boundary l a y e r i n s t a b i l i t y and i t s a s s o c i a t i o n vri.th c r i t i c a l v a l u e s of secondary flow Reynolds mimbers as d e f i n e d b y 0\7en and R a n d a l l

( R e f . 1 7 ) .

S e v e r a l a s p e c t s of t h e problem a r e c o n s i d e r e d , each i n some d e t a i l , and some i n t e r e s t i n g r e s u l t s b o t h t h e o r e t i c a l and e x p e r i m e n t a l a r e p r e s e n t e d ,

To s a t i s f y t h e need f o r t e s t s a t Reynolds n-jmbers compatiblo vri.th f u l l s c a l e , t h e e x p e r i m e n t s wore performed, i n f l i g h t , on a l a r g e u n t a p e r e d , untvri.sted, 45° swept back ho.lf m n g mounted a s a d o r s a l f i n upon t h e mid upper f u s e l a g e of an Avro L a n c a s t e r ( r , A , 4 7 4 ) , t h e Reynolds number range t h u s a c h i e v e d b e i n g 0 . 3 8 x 10 - 1.92 x

10^ p e r f o o t .

Curves a r c p r e s e n t e d g i v i n g d e t a i l s of t h e measured d i s t r i b u t i o n s of s t a t i c p r e s s u r e , chordvri.se l o a d i n g s , and t h e boundary I r y e r f lav/, t h e l a t t e r i n extginsive d e t a i l , f o r v/ing g e o m e t r i c i n c i d e n c e s i n t h e range 0 - 10 , upper and loT//er s u r f a c e s , and f o r t e s t Reynolds numbersin t h e r a n g e d e f i n e d a b o v e .

No l a m i n a r flow V7as foujid t o e x i s t on c i t h e r t h e u p p e r o r lov/er s u r f a c e of t h e wing f o r Reynolds nuTiiDers a t , and i n e x c e s s of 1,55 x 10^ p e r f o o t t h u s showing t h e need f o r scr-ie form of boundary l a y e r c o n t r o l t o s u p p r e s s t h e e f f e c t s of sweep i n s t a b i l i t y .

Page

Preface 1 lAst of Symbols 3

1, IT Purpose of tliis work 5 1.2, Range and Extent of the Investigations • 5

1.3, Limitations of Present Work 6 1.4, Outline of the General Problem 7

1.5, Pinal Introductory Note 9 2, THEORETIO/iL CONSIDERiiTIONS 10 2.1, Choice of Wing ücction 10 2.2, The Co-ordinate Systems Used '11

2.3, Theoretical Distributions of Velocity and Pressure

for the Swept Back 'iï'ing 11 2.4, The Potential Plov/ Strenmline over the Infinite

Sheared ¥ing 13 2.5, The Boundary Layer in relation to the External

Stream Lino 14 2.6, The Calculation of the Three Dimensional Boundary

Layer in Steac3y Plov/ l6 2.6.1, General notes 16 2.6.2, The boiindary layer at the leading edge of the

svrept back xring 18

2.6.3, The boundary layer flow for a 'wedge' profile 19 2.7,Secondaa'y Plov/ Velocity and Associated Reynolds

Numbers 20

2,8.Secondary Flow'. General Notes 21

3 , EXPERIIvIENTAL CONSIDER^JIONS 23

3 . 1 . Suitable Test"Methods 23

3 . 2 , Choice of Experimental Plan, Techniques and

Procedure 24

4 , EX^RDffiJTAL EQÜIB.33OT 25

4.1, "The AircrtS't ' 25 4.2, The Pressure Plotting Mast 25 4.3» The 1/ing and Installation 26 4.4, Instrumentation^ The Manometer ojid Recording

Apparatus 27 4.5 • Directional Yawmeter 28

4.,6. The Boundary Layer Combs and Transition Indicators 28

5. DSTiJLS OF EXIERIi;L::NTS PEEFOroiED 29 5,1. Choice of Test jJLtitudes rjid Arrspeods 29

5*2, Measurement of S.P.E.C. and Calibration of the

Fuselage IPlow Field 30

5,3» Incidence Zero-Datum Setting of the Half Y/ing 30 5.4, Measurements of the Static Pressure Distribution

over the Ss/ept Back Half ïïing 3'' 5.5, Flow Visualisation on usin[5 the Tuft Technique 31

5.6, Exiplorations of the Boundary Layer 31 6, PRESENTATION OF EXFERIlvJEIff/Ji RESULTS 33 7. DISCUSSION OF THE EXEERD^lENTiiL RESULTS 33 7,1, Behaviour of the Aircraft and Equipment

undci-ExpcriiAcntal Conditions 33 7*2, Accuracy of Results 33 7,3» Distributions of Static Pressure 34

7.4. The Plow over the Ti/ingI Tuft Observations 35

7.5. Boiindary Layer Measi;ircments 36

7«5«I» Velocity profiles 36 7,5.2. Boundary layer transition 37

7«5»3« Displacement thickness, momentum thickness, and

shape poroTiieter variation 38 7.6. The Critical Reynolds Number for the Secondary Plow 38

8, COIOLUSIONS 39 List of References 41 Appendix I 45 Appendix II 46 Appendix III 50 Appendix IV 53 Tables I to III Figures

PREFACE

The experimental programme of vrark discussed in this report vra.s made possible by a Ministry of Supply Contract ( M . O . S , 6/Aircraft/ 9807/CB/6a).

The experiments were performed during the early summer of 1956,

following the design construction £md installation of the required model and equipment into the aircraft used as test vehicle

(Lancaster P.A, 4-74,) this work being almost entirely carried out at the College of Aeronautics.

To some extent the programme has been one of a previously untried nature, but the quality of the experimentail results obtained v/ould appear to suggest that the partioiüar methods of test adopted might Tje more fully exploited in the future in order to facilitate

aero-dynamic Investigations and explorations at Reynolds numbers compat-ible vri.th full scale.

The author is hov/ever avrare of the existence of some minor short-comings in the details of the techniques employed for the boundary-layer explorations, but suggests that these are by no means as

serious as might at first be supposed. Refinements to these techniques, if considei-ed necessary, might follow as logical developments.

The experimental programme was completed in a comparatively short length of time, this being made possible by the enthusiasm and close support of a number of persons, all of \7hom the author would grate-fully thank. Space considerations do not permit the presentation of a complete list of separately detailed references to all thos.e

directly and indirectly involved, and in making mention of but a few names the author implies references to all associates.

The piloting of the aircraft was performed in the main by Mr. B.;^. Russell and to a lesser extent by Wing Commander C.G.B. McClure, A.P.C. The exacting skill exhibited by both pilots (assisted by G. Longland, Plight Engineer) in consistently and accurately reproducing tne

required experimental flight conditions, at all times left nothing to be desired, v/hilst the ready availability of the aircraft and its equipment.- is to be attributed to Mr, H.W. Gover, Chief Aircraft Engineer, Mr. Yf, Abbott, Chief aircraft Inspector, and their staff. The experiments were supervised by MrJd,C,Yifilson, A.P.C., Senior Lecturer in the Department of Flight, on whose experience in the field of flight testing the author v/as alloT/cd at all times freely to draw, whilst the laborious task, of reduction of the experimental results to the required form was to a large extent performed by Mr. J. Walton, who also flew -vd-th the author as an observer.

The design of the experimental -vdng and its installation was performed by Mr. A, MacDonald, working under the direction of Mr, A.P. Newell, Deputy Head of the Department of Aircraft Design. These designs received pre-fligjit approval from the Resident Technical Officer of

Messrs, A.V.Roe Ltd,, Manchester.

Helpful discussions m t h members of the staff of the Department of Aerodynamics are also gratefully acknoVidedged, as is the assistance

of Mr. SoW.Ingham in performing numerical computations.

By close cooperation between all concerned it has been possible to perform the ex^periments as reported and it is hoped that these will form the basis for future but more elaborate -crork of this kind at the College of Aeronautics, Granfield.

VLIE.

JV/IIUNDE Kanaalstraat 10 — DELFT

3

-LIST OP SIJfflOLS USED

Only the principal symbols used are listed, other symbols being

defined as and v/here they occur in the text.

x,y,z, orthogonal cartesian coordinate system (see para,

2,2 and fig. 14)

X,,

y . J

z , orthogonal cartesian coordinate system

Xg , y^, z , orthogonal curvilinear coordinate system

u,v,w, velocity components in the boundary layer referred

to x,y,z

VI,» V J w , v e l o c i t y components i n the boundary l a y e r r e f e r r e d

•to x^, y^ , s^

t^ , Vg , Wg, velocity components in the boundary layer referred

to x^, y^, z^

<l(x,y) p o t e n t i a l flovT v e l o c i t y a t the -wing siirface i n the

plane x,y

^ (x,y, ) potential flovr velocity at the wing surface in the

^ plane x^y^

UjVjYif, etc, velocity components just outside the boundary layer

along x,y,s, etc, (suffio'es denote a:x:eö of

reference)

q^ total local velocity along s-treamline just outside

the boundary layer

strenmline coordinate system (see fig, 16)

5,

^z Ue 9 = ^1

u^

u^

~)

(xj

cos A

velocity of the xindisturbed stream

A angle of sweepback (or shear)

Wo = UQ sin A velocity component parallel to vrijig leading edge

p local static pressure

Tj^

free stream static pressxire

static prossu370 coefficient

(L denotes lower surface of wing, U denotes upper

surface of -vving

R Reynolds number (particular cases are separately

denoted)

X Secondary flow Reynolds number

%-AC

P

P - P ,

ipUo'

= C -C PL

%

streamline curva-turc in the plane X2Z2 (y^ = O) angle between the streamline and the axis Xg air density

kinematic viscosity

T/ing chord measured parallel to the undisturbed stream

v/ing chord möasured normal to v/ing leading edge geometric incidence of v/ing

boundary layer thickness (absolute physical value)

jdy boundary layer displacement thickness

^ jdy Boundajry layer momentum thickness

1. INTRODUCTION

1,1 Purpose of this v/ork

The reason for and purpose of this work v/as to further the study of the sivcpt Vidng boundary layer, begun by W.E. Gray (rcf 28) with particular reference to the onset of bovindary layer instability, and subsequent transition, and its association iTith "critical" values of the Reynolds number ascribed to the secondary flow as defined by Ov/on sjid Randall

(ref. 17)

Since the scale effect is of prime importance in such a study, the idea of constructing the equipment and conducting an experiment at something approaching full scale Rejoiolds numbers was exploited, resulting in the testing of a large model sv/ept back half v/ing mounted as a dorsal fin upon the mid upper fusc2.agc of an A-vro Lancaster lik .VII, the aircraft being suitably adapted and modified to accommodate the necessary equipment.

By a suitable choice of both experimental equipment and techniques, it has been possible to make an extensive yet rapid exploratory survey of the boundary layer in this way for a number of conditions of Reynolds numbers and incidences, and a number of interesting results so obtained are to be discussed.

1.2. Range and Extent of the Investigations

The experiments v/ere performed on an untapered, untwisted, 45 Swept back half v/ing of general dimensions as given in figs. 3 & 4. It v/ill be noted from fig.4. that the -v/ing v/as of unconventional section, and the reasons for this choice of section are discussed in para. 2.1.

The range of the tests was to include measxirement of the static pressure distribution over the model from the position of maximum thickness to the dealing edge for a Reynolds number range of from 0.88 x 10 per foot to 1*92 X 10" per foot, and for a geometric incidence range of from

a = 0 to a = 10°, both upper and lov/er surfaces being considered.

Boimdary layer velocity profiles v/ere measijred at three spanv/ise stations, together v/ith the distributions of total head at, and near tojche v/ing surface at four spanv/ise stations, at suitably spaced intervals along the chord extending from near to the leading edge to the position of maximum thickness, and for selected values of Reynolds nijmber and geometric incidence in the ranges 0.88 to 1.92x 10° per foot and a = 0° - 10° respectively for both upper and lov/er surfaces.

Theoretical consideration is given to the boundary layer flov; neajr to the leading edge of the infinite sheared v/ing at zero incidence, the steady boundary layer flow being calculated using the method of Prandtl (rcf. 19.) and Sears (ref. 20) for the spanv/ise flow and the Blasius series for the chordv/ise (normal -to the leading edge) flow, the calculations being

performed on the basis of both the theoretically and experimentally derived velocity distribution for the section. Consideration is also given to

the secondary flov/ occurring in the boundary, layer of a v/edge shaped • profile using the methods of Hartree (ref.31) and Cooke (ref,32).

The experimental i-esults quoted give details of the general nature of the boiondary layer flov/ found to exist on the v/ing, and svmmarising

quite generally, show to the further support of already existing evidence (refs. 6, 26, 29) that v/ithout the application of some form of boundary layer control the possibility of maintaining regions of laminar flov/ of any appreciable magnitude on either the upper or lov/er siirface of a swept back vri.ng at f-ull scale Rejmolds numbers, is remote.

1.3. Limitations of Present Work

The investigation of the flov/ in the boundary layer on a swept back wing by the methods of test v/ith v/hich we are to be concerned, leads to a number

of problems v^ich wo-uld not arise in the case of similar experiments conducted in a v/ind t\annel. The main difficulties arise from the fact that the boundary layer is essentially throe diaensional in character and strictly speaking

does not permit the use of techniques established for tv/o dimensional flows for its meas\irement. For a detailed and precise exploration a traversing mechanism v/ith at least four degrees of freedom is required, and this need together v/ith the problem of pilot fatigue v/hich is very closely related to the satisfactory \ise of s-uch gear in flight (see para. 3.2.) leads to the adoption of more simple methods for measurement.

Now the n-umber and degree of the sirnplifications made to the experimental techniques v/ill depend upon the general nat-ure of the flov/ to be investigated and upon the information so required. Hence if v/e can distinguish tv/o

types of flow, the one in v/hich three dimensional effects are known to be of first order importance and v/hich definitely requires a three dimensional technique for its measxirement, end the other in v/hich tliree dimensional

effects are of lesser significance and v/hich can be measured to a good

firLt approximation using simplified techniques, then if v/e concern ourselves v/ith the latter v/e sure in a position to make a number of useful measurements by methods v/hich can be easily simply and rapidly applied in flight experiments. For the work to be discussed it was observed from v/ool t-uft observations that

for certain regions on the wing a fairly -wide range of wing incidence ~ speed configurations existed in v/hich three dimensional effects co\ild be considered as being small, such an observation being made -understanding the limits to v/hich the flow directions as indicated by v/ool tufts could be interpreted

(ref.9). Consequently it v/as assumed that techniques for measurement of the bo\ancliary layer, strictly correct for the tv/o dimensional case only, could be applied in the above regions on the vrang and vAiich could be expected to yield results accurate to a very good first order approximation, (see para. 3.2. for further details).

Such an assumption does hov/ever constitute a limitation which must be imposed upon the interpretation and validity of the experimental results quoted and the reader should quite clearly \inderstand that taken all in all these results give only a general pict-ure of the bound^üry layer on the swept back wing.

It is possible that there v/ere cases in v/hich the effects of transverse flow assumed greater significance than has here been assigned, but until

such time as a great deal of effort has been expended in making more detailed and accurate measurements, then experimental results such as those quoted v/ill be of value v/ith regard to the assessment of the sv/ept -v/ing boundary layer.

As far as the theoretical work is concerned so little is lonov/n of the beha-viour of the swept -vving boundary layer that for its calculation v/e

may only apply existing theories -«ri-th some researvation. By means of the

Independence Principle ho\-/ever (ref.4.), calculations of the steady boundary layer flov/ over sufficiently short distances of the vdjng s-urface can be made using existing methods (e.g. ref, 20), and since the effects of secondary flow in which v/e are in-terested occur in the neighbourhood of the leading edge v/e may accordingly take steps leading to results of interest. Such a procedure does lead to approximations, and hence, v/c must endeavoior to make

sxire that these are both reasonably accurate and -valid.

Thus with regard to the interpretation of both the theoretical and experimental ros-ults quoted the reader should quite clearly understand the limitations and assumptions vrfiich it has been found necessary to impose and make in this treatment of the problem. They will accordingly be detailed as and when they occur in the text,

1.4-. Outline of the General Problem.

Although it is some time now since the sv/ept back \ving i7as introduced in aircraft design, there is little knov/n as yet relating to the characteristics of the strictly three dimensional boundary layer associated v/ith this type of v/ing. We can generalise by saying that although the coinpressibility drag rise accompanying the attainment of the critical Mach n-umber can be success-fully delayed by using a wing of swept planf orm, other phenomena are knov/n to occur v/hich -Q-ffect the boundary layer flov/ over the v/ing to such an extent that the skin friction and hence profile drag become increased to the detriment of the lav/ speed characteristics. By lov/ speed character-istics we do of course make reference to speeds belov/ that range in v/hich compressibility effects must be taken into account, speeds v/hich might readily be associated v/ith the problems of, f or example, the long range

cruise of ci-vil transport aircraft. If from the results of both experiment and theory a sound understanding and a-ppreciation of the nature and mechanics of the flow in the boundary layer on the swept back -wing at low speed may be obtained then it beccmes possible to give consideration to further associated problems such as the possibility of using devices incorporating distributed

or discreetly applied boimdary layer s\jction, for its improvement.

It v/as the observations of W.E. Gray (ref. 28) that first brought to light the presence of swept vnng boundary layer phenomena of a special nat-ure and his investigations at full scale Re3molds number suggested that for most flight conditions the possibility of maintaining any appreciable areas

than somewhat remote. Gray's observations (ref.33) of the striations occurring in the laminar bo-undary la.yer above certain values of Reynolds number (subsequently to become termed critical Reynolds numbers) v/ere to provide in subsequent years oji experimentally determined basis for more

elaborate studies of the flov/ problems of the three dimensional boundarj'-layer v/ith special reference to its stability. The trend in this direction was towards a theoretical investigation of the effect of small perturbations

of the type u(x, y, z) e-"^'. , (where \ is in general complex and dependent on time) upon the eque.-tions of motion for steady flow in the three dimensional boundary layer. These investigations perfonned by Owen and Rondall and by Stuart (refs. 16, 17.) have quite clearly shov/n that under certain conditions of the flow just outside the boundary layer we can expect the development of systems of vortices, (of a type similar to that considered by Gortler..in a study of the bound-ory layer flow over a concave surface), v/ithin the boxjndary layer itself, v/hich, for certain external flov/ conditions tend to res\ilt in a drastic change over from laminar to t-urbulent flov/ occiarring. The vortex formation to be expected differs from the usual Gcrtler formation in that the rotation of the flov/ about each vortex axis is in the same sense (ref. 17) as coiirpa.red with the opposite rotation of adjacent vortices v/hich occur in the flow over concave surfaces.

The alignment of the axes of the vortices is such that they are very nearly parallel to the stream lines at the outer edge of the boundary layer .and trail downstream as shovm in fig. 16a. It is due to the presence of such a

system of vortices that striations may be observed in the surface pattern on a swept -wing when making liquid film studies of the boundery layer flov/, the spacing of the striations coirresponding to the spacing of the vortices or more particularly to one disturbance wavelength (ref. 17.).

The theoretical studies of Stuart ajid Owen and Randall shov/ed that v/hilst for steady boundary layer flov/ in three dimensions the independence principle may be applied, in the case of the dist-urbed flov/ there is no longer an

independence of the main and spanv/ise flov/s and the study of the disturbances resolves itself into an eigen value problem for the compounded motion.

Following the initiation of these preliminary ideas on the cause and effect of sv/ei3t v/ing boundary layer instability a n-umber of experiments have been performed to provide further data (refs. 6, 29). These experiments have in general prcvided information of great value but perhaps the most noticeable feature o-f all was the surprising result, obtained from both theoretical and experimental consideration, (e.g. ref, 29) that an increase of incidence or Rejmolds n-umber, the latter to beyond values Rcrit. ^^ accompanied by bo-undary layer instability of considerable intensi-ty giving rise to rapid

forward movements of the transition fronts on the lower surfe.se of a swept back v/ing. Similar results in flight experiments v/ere also observed by Allen and Burrov/s (ref, 26.),

With regard to the flov/ conditions on the lov/er surface, the forv/ard movement of the transition fronts occiorring with increase of incidence is

on v/hich favourable pressiire gradients existed, and it is here that the true significance of the possible consequences of a three dimensional

boundary layer flov/ is illustrated. That such a i^henomcnon can occxir

in the presence of favourable pressure gradients also gives some idea of the magnitude of the destabilising influence.

The root of the problem may be found in the flo"// conditions over the nose of the wing as it is in this region that for both upj^er rjid lower surfaces the curvature of the streai-n linos j-ust outside the boundary layer is large, If v/e resolve the steady boimd^'xy layer flow jnto conTponents rlong and normal to this streamline, v/e find that whilst the component distribution of velocity along the streamline is well ordered, the component distribution normal to the streamline contains a point of inflexion (see fig,l6.) the velocity of this sooondaxy flov/ reaching a maximTJm at some fraction (i.e. a/5 < -) ) of the boundary layer thickness from the -wing surface. Owen and Randzill have put forvra.rd sound physical arguments for the existence of this type of flov/ v/hich have been strongly substantiated by ca.lculation,

Thus given the existence of such flov/ conditions v/e are further led to suppose (e.g. ref, 34) that since this secondory flov/ profile contains a point of inflexion then for values of secondary flov/ Reynolds Number x above the critical it is inherently unstable to the effect of sni*oll disturbances, such a supposition follov/ing on nat-urally from a study of the flov/ in laminar v/akes,

Ue can therefore argue to shov/ that since the secondary/ flov/ profile depends

upon the local streamline curvatxire, (just outside the bciindary layer.) ^'^^ the magnitude of the local velocity, it in turn depends upon the distribution of velocity along the span and along the chord (normal to the leading edge) v/hich aga.in and in themselves depend upon the nose radius of ci;irvature and upon the angle of s^veep,

Since due to the magnitude of the secondary flow Reynolds number required for instability to occur, the general effect on the sv/ept ^ving boundary layer is one of full scale then it is only by systematic tests at something

approaching or even at full scale (e.g. Gray's experiments) that v/e can hope to obtain further experimental information to maie for a better understanding of the behaviour of the sv/ept v/ing boiuidary layer, and it was thus to this end that the experiment to bo discussed was directed.

1.5. Final Introductory note.

The v/ork presented is essentially divided into tv/o sections: one devoted to a theoretical discussion of the jproblem, the other to experimental

considerations etc. In general, only res-ults are quoted in the text, the details of their deri-vation being relegated to appendices to v/hich attention is drawti as and where neccss.ary.

2. Thccreticrl Considerations. 2.1, Choice of Wing Section.

The three dimensional bound-xry layer instability phenomena in v/hich v/e are interested requires a study of the flow over a-nd near to the leading edge of the -vving at something in the region of full scale Reynolds numbers for an understanding of its essential details. Consequently if we suppose that v/e c m simulate the flow conditions in this region by using a. represen-tative or effective v/ing section having a foreshortened trailing edge v/ithout so incurring arty imdesirable effects in the generol flov/ over the v/ing, then ideally we need only concern ourselves v/ith the flow over the forward x'ortion of such a representritive v/ing (i.e. from the position of maxim-urn thickness to the leading edge) in making our study of the bound-ory layer. Moreover, v/hen considered in the absence of sv/eep instability, the boundary layer flov/

characteristics depend upon the Reynolds n-umber referred to the distance from the starnation point (tv/o dimensional case) or line (three dimensional case) to the plane considered, and so in attempting to reduce the effects of scale

to a minimum, v/e endeavour to construct owe test model with the largest possible

dimensions consistent v/ith the experimental facilities available.

The aerofoü section chosen for this experimentrl work is shown in fig.4» -^rid was intended to form a compromise between the above two factors. It v/as mr-.de up of tv/o semi ellip)ses, one of v/hich constituted a faired or foreshortened trailing edge, the other corresponding to the leading edge portion of a 1C^ thickness to chord ratio aerofoil of some 130" chord (measured in the free stream direction). This 1C^ thickness to chord ratio, 130" chord aerofoil v/e shall subsequently refer to as the "effective" section since it was tov/prds

this section that the representation, by double ellipse and partiol chord, wr.s directed. The wing section used v/e shall refer to as the "actucl" section. By the use of a foreshortened or faired trailing edge the maximum test

Reynolds Number, based on the len;^h betv/eon the leading edge and the position of maximum thickness (which for wings of conventional section corresponds to the distance to maximum suction at zero incidence) mr.y be obtained for a v/ing of rela.tively small area and v/hich v/hen at incidence and thus pro-vLding lift would pi-ovide accepitable conditions •'.vith regard to the aircraft fu3ela.ge design lon.d liri-iitations ,and also from the point of viev/ of aircraft liandling in flight.

It might be argued tlia-t in using what really cmo-unts to a "bluff" trailing edge some difficulties migjit be encountered due to wake instability, but as v/e shall see later, experimental evidence has shown (para.7.4) that for this particular v/ing no trace of such a flov/ condition could lue detected. It is evident both from the present series of tests rnd from irirevious v/ork of a more qualitative natxare (ref. 26.) on a sweptback vrin.g of similar

section, that this supposed representation of an effective section constitutes an erroneous argument as far as the simulation of flow conditions is concerned. This v/e shall show later by recourse to both theory .and experiment.

At the same time hovrever, it does not morn that the Oirperiment.'\l results obtained are invalidr'.ted. It siriiply means that the results quoted may be compared, with reservation as dictated by circuiistance, to those for wings on which similrjr distributions of pressure mr.y be found to exist in the regions considered.

2.2. The Co-ordinate Systems Used.

For both the theoretical and experimental v/ork it is convenient to use three orthogonal co-ordinate systems of reference, these being as shov/n in fig,14. The system x, y, z, has its origin at a point olong the chord line corresi^onding -to -fche position of mcocimum thickness of the vdng and the axis x is along the direction of the imdisturbed stream. The axis z is normal to x ond lies in the plane of symmetry of the wing section, and y is orthogonal v/ith x rJid z,

The second system of vjx.es, x,, y^ , z, , has the axis x^ rlong the direction

of the v/ing chord norm?l to "the leading edge and its origin coincident with

that for X, y, z ; z and y are orthogonrl v/ith x as before.

To describe the bound'-ry layer flov/ we shall require an orthogonal rurvilinerr

system of races Xg, y^, z^; the axis Xg having its origin on the star.Tiation line

at the leading edge of the wing and following the contour of the -^ving surl'acc

in a pilane normal to the leading edge. The axis z^ v/ill be talcen parallel to

the leading edge and lies in the plane of the -i^-ing surface whilst y^ is

orthogonrl with x and z

Components of velocity etc. referred to in one or other of the above systems of rjxes will unless otherwise defined bear the sanie suffix as the axes to v/hich they may be referred,

The physical -visualisation of these systems of axes in relation to the v/ing

is simplified by reference to tym planes (plane x y and plane A ) these being

as shov/n in fig. 14.

2.3. Theoretical Distributions of Velocity and Pressure for the Sv/ept Back Wing.

To facilitate the study of the boundary layer flov/ pjid to m?.ke comparison

betv/eon the res\£Lts of theory and experiment we require to knov/ the distributions of velocity and static pressure over the sv/ept back h'-lf v/ing. If this

requirement is restricted to the zero incidence .and hence zero circulation

(symmetric?! section) case then it is possible to moJce the necessary calculations to a s-ufficiently high degree of acGur.?vCy by considering the v/ing to be of

infinite sp>an ajid. representing the section thickness by a system of sources

distributed along the chord line. In this ivr.y the perturbation potential takes the

form:-T.E.

~'= -^; j er' ( ? ) l n ( z - g ) d ? ( 2 . 3 . 1 )

L.E.

- i n v/hich the tot.al soiirce strength é\long an elementary length dx i s

given by a' (x) dx. For the v,dng of i n f i n i t e sprn sheared by an

angle A ajid having the "actual" section of f i g , 15, i t

C.?JI

be shov/n

(see appendix I I . ) the.t the v e l o c i t y d i s t r i b u t i o n i s given by an equation

of t h e

form:-^J ~ 44-) + sin'A (2.3.2)

0 ^vu

^ 0 vdiere 2 n """ (2,3.3) and the pressure coefficient by:

- in v/hich expressions the co-ordinates are as defined in para. 2.2 and shov/n in figs. 14 ond 15.

A n adequ?.te e^cccunt relo.ting to the derivation of the above expressions is given in a.ppendix II. v/here both the tv/o dimensional and the infinite

sheared causes are discussed. The "effective" section (fig,15) referred to in para,2,1. is else considered in appendix II

The pressure distribution calculated from (2.3.4.) is shov/n in fig.l7. v/here it is compared with tho.t calculated for the "effective" section the marked differences in the tv/o distributions being very evidentc

We may at once deduce that pro-vided good agreement is to be obtained be-tween the calculated (e.g. 2.3.4.) and measured distributions of static pressure for the actual v/ing section then v/e shoiild no longer concern o\arselves with the idea of m effective section as discussed in para. 2.1. As we shall see, this is subsequently/ confirmed.

2,4 The Potential Flov/ Streamline Over the Infinite Sheared Wing. For the sheared wing at incidence the components of the free stream

velocity U parallel to and normal to the leading edge are respectively (ref. 5 ) :

-U cosasinA 0

and U cos^acos^A+sin^a (2,4.1)

where the true wing incidence is given by:

/9 = tan (tan a sec A ) . (2.4.2) For sufficiently small values of incidence a, (2.4.1) and (2,4,2)

reduce to U sinA = W , 0 0 U cosA 0 /5 ^asecA, (2,4.3) Nov/ -the effect of the wing thickness distribution is to cause the

flow velocity along the wing surface in a direction normal to the leading edge to vary v/ith chordv/ise position, v/hilst the spanwise component remains constant since the v/ing s-urface in this case is

a stream surface. Hence, using the orthogonal cur-vllinear oo-ordinate

system Xg y^ Z2(fig,14.) as a frame of reference, for any streamline

in potential flow v/e have

dz W a t 2

- since the streamline l i e s v/holly i n t h e plane x z ( i . e . t h e v/ing

2 2

sixrface). Thus any streamline i s given by

z =f 'o dx + c ( 2 . 4 , 5 ) •I 2 2

- v/here c i s an a r b i t r a r y constant of i n t e g r a t i o n depending on t h e spanv/ise p o s i t i o n of the s t r e a m l i n e .

I f we now define t h e non dimensional -velocity Q a s Q A U (x )

U cosA ( 2 . 4 . 6 )

then ( 2 . 4 . 4 . ) t r k e s the f o m ;

-dz t r n A

2

dx "" Q

2 2

together with d^z - tan A dQ (2.4.7.)

2 "2

dx^ Q^ dx

2 2 8

SO tha.t for the curvature of the streoxiline v/e obtcin

-i ^ - Q^ton A ^Q

2

' (QI . t a n ^ A ? / ^ ^ ^ ^'•^•"•^

It can be seen from (2.4.8) that, since the velocity gradient 2

dx

₂

is relatively large for regions close to the stagnation line at

the leading edge, the strermline c\nrva-ture will rlso be Irrge in that

region (rcf.17.). That thiis is true for the sv/ept back v/ing under

consideration may be seen from en inspection of figs. 20 and 23b., the

Curve shov/n in fig.20 being derived by noting that if ^ is the rngle

be-tween

ony

streamline and the ajcis x , then from (2.4.4.)

2

-1

(p = tan Vg

^'^^

(2.4.9)

The significance of this streemline curvature in relation to the boundary

layer flov/ is one of major ix-rportance for it gives rise to the secondcry

flow with which v/e have learned (refs. I6 rnd 17) to associate the phenomena

of sv/eep instability.

2.5. The Boundory Lo.yer in Relation to the External Strcoxi lane.

The strecdaline just outside the boundary layer v/e choose to regard as

0.

da-tum

to v/hich the flov/ in the boundcry layer may be referred. It is, to a very

close approximation, curved according to the relationship (2.4.B.) and it is

convenient to sot up a right cngled planar co-ordiiiatc system ^ , ,

^^ ,

vvith

its origin at

axiy

arbitrarily chosen position on the streamline as shov/n in

Pig.l6. If the total local velocity along the strccxiline is q then together

* Note here that v/e may v/ith sufficient accuracy associate the potential flow

streamline

xrith

the streamline in viscous flov/ just external to the bound^iry

v d t h t h e a n g l e <f> c a l c u l a t e d from ( 2 . 4 . 9 ) > v/e may v^rite cos 0 \ w^ 1 — = 1 ^ s v/ u - 2- • A 2 — s m 'P + — q. q. v/ u = 2 J 2 — cos 9 % %

±ni> (2.5.1)

in v/hich Ug. and v/y are the components of the steady boundary loyer flow resolved clong and normal to the st-^eomline respectively, and Ug and w ere the components of the steady boundary layer flow referred

respectively to the ojces x , z , end v/hich may be calculated from equa.tion (A.3.7.)

Nav Stuprt (Ref. 23) and Ov/en and Randell (Ref. 17) hove independently shown that the boundary layer velocity distribution char-acterised by u„ yields a profile of the usual form, v/hilst that given by v/y (secondrjry flow) contains

a point of inflexion, the t\/o profile forms being illustrated in Fig.l6. Isi

associa.tion of the form of the -v/ profile v/ith that developed in a Icminar v/ake together with its inherent inflexional instability formed the basis for

theoreticrl studies og a three dimensional boundary layer flow of this kind by the above authors (Refs. 23 and I7). It appears that v/e can conveniently relate the onset of the inflexional instobility of the secondoory flow to the

extemel flow conditions by an expression of the form

-X c r i t . N UQO

r

= — > R =

-R I ? , ^ i t ( 2 . 5 . 2 ) i n which x i s t h e Reynolds Number r e f e r r e d t o t h e secondory flov/ raid

v/hich t a k e s t h e form

-^\

_{^ , m a j c}

5

_{( 2 . 5 . 5 )}

t h e modulus b e i n g t a k e n s i n c e Wv- i s i n g e n e r a l n e g a t i v e v/ith r e s p e c t t o t h e c o - o r d i n a t e s ? , ^ , of P i g . 1 6 .

With the onset of this t3rpe of instability, a system of vortices is formed, in the outer region of the boundary layer, v/hich trail approximately dov/nstream from the disturbance origin and the effect of their growth is to lead to an ultimate breakdov/n of the flow into turbulence. The axes have discreet spacing corresponding approx-imately to one disturbance v/ave length (ref, 17) and are so aligned as to be very nearly parallel to the external stream lines.

Experimental observations of the initial formation of striations in the laminar boundary layer using the liquid film ~ china clay tech-nique, (e,g, ref, 6) and the association of these striations with the vortex formations referred to above have led to the possibility of fixing a value for N in equation (2.5,3) (see ref, 34). On the supposition that the initial appearance of the striations coincides approximately v/ith the initial formation of the vortices, it has been suggested that N lies somewhere in the region of 100 - 150 v/hich is of the same order of magnitude as that fo-und in the case of a laminar wake, Thus from a knowledge of the distribution of x over the surface of the v/ing -under consideration, it would appear possible to estimate the Reynolds number R ., referred to the external flow abo-ve which laminar flaw may be expected to break dov/n,

The restriction imposed at present on the use of such an empirically derived relationship is the lack of e-vidence a-vailable with regard

to its generality. Furthermore, the evidence obtained from the present experiments does not permit an attenipt to give confirmation to the above chosen value for N since the techniques required to illustrate the

presence of the striations were not and could not readily be employed. Fran a knowledge of the extent of laminar flow observed, together with

the external flov/ Reynolds number, we are, hov/ever, in a position to infer both an upper and lov/er bound to the value of N as v/e shall see later, (para 7.6)

2.6. The Calculation of the Three Dimensional Boundary Layer in Steady Flov/

2.6.1 General Notes

The difficulties to be encountered in attenipting a calculation of three dimensional boundary layers cannot readily be suimounted because, since so little is accixrately knov/n of their beha-viour, any approximations made must ine-vitably be associated v/ith some degree of uncertainty. As far as the yav/ed cylinder and the sheared v/ing of infinite spcn is concerned, it has been suggested (ref.4) that since the equations of motion for the bo-undary layer flov/ show no interdependence between the chordwise and spanv/ise component expressions, then v/e may calculate the

boundary layer gi-ving separate consideration to each component flov/.

As to haw the actual calcul.ations are perfonned is a question of

choice in relation to the degree of acc-uracy required together v/ith the methods a-vaila.ble, but it is nevertheless usual to encounter * severe restrictions in applying more exact methods to the problem. Prandtl, Sears and Cooke (refs. 19, 20 and 32) have given

consid-eration to the equations for three dimensional laminar boundary layer flow and the calciilations due to Sears (v/hich were later extended by Gortler, Ref. 10) have facilitated the application of a solution by method of series. This latter method received a thorough treatment by Hov/arth (ref. 7) for the two dimensional case and the extension to three dimensional flow is for convenience summarised in Appendix III. In practice we find that to apply this method to the oalciilation of the three dimensional swept v/ing boundary layer, the problem reduces to one of expressing the velocity normal to the leading edge as a pov/er series in the arc length from the stagnation line, the form being

m

Ug (xg) = y \ n 1 ^2^'** n = 0>^2,....m n 0

- the upper bound in the s-ummation occ-urring by -virtue of the at present restricted range of tabulated functions f(r/) and g(n) (see /ppendix III) necessary for the calculation of the required flow components,

Although a n-umber of flaw configurations exist v/hich can be acciorate-ly described by putting 0 < m < 4, the type of velocity distribution U2(x-) in vifoich v/e arc interested (i.e. swept v/ing, lev/ incidence

case) does not in genercl lend itself to expression in the above series f orm with m limited, (for the sake of argument, to 4, say,) if v/e are to proceed for any appreciable distance from the stag-nation line, and the difficulties (both analytical and numerical)

* The supposition that the principle of independence is true can only be asserted for the steady flov/ case as is shov/n by Stuart (ref.l6) v/ho has studied the equations of motion for disturbed flov/.

become more serious as the thickness to chord ratio is decreased. Hov/ever, if we restrict ourselves to a consideration of relatively

short distances from the stagnation line, then the calci.ilations not

only become possible but can in fact be made quite simple. In • passing we may note that the extension of the Von Karman-Pohlhausen

approximate tv/o dimensional solution to the three dimensional case has been performed by Wild (ref. 35) and Rett and Crabtree (Ref.36) have shown that the calculation of the laminar boundary layer to an adequate degree of acciiracy may be accordingly simplified. We shall not however concern ourselves v/ith a discussion of these methods here.

For the present v/ork two methods of calculating the laminar boundeiry layer over the leading edge of the swcp)t v/ing v/ere tried which we shall now discuss.

2.6.2. The Boundary Layer at the leading edge of the Swept Back Yfing. Por an enquiry into the nature of the secondary flow occiorring near to the leading edge of the swept back v/ing at zero incidence used in the present experiments v/e refer first to the measiired and calculated c'istributions of velocity, betv/een which there is excellent agreement

(see Fig.19). Ideally v/e require to calculate the boundary layer over an extensive region of the wing, but the shape of the velocity

distribution (Fig.19) does not lend itself to expression as a series ->, of the required form (see A,3.5.) ha-ving small number of terms. We

oan however, represent the distribution over the leading edge very »-acQ-urately by an expression of the form

(see A.3.12) for o < x < 2.5 (where x^ is in dimensional form (inches) siiice v/e are considering a partic-ular case) and hence proceed to a calculation of the boundary layer by the method of series. The chosen procedure is given adequf.te discussion in A^jpcndix III.

Resolution of the calcTjlated chordwise and spanwise boundary layer velocity coniponents on to the co-ordinate system ? ., ^. of the

external streamline (Fig.l6) yields the primary and secondpjry distributions shown (Pig.2l) and in this case the secondary flow Rejmolds number is

given by: X • 1 R ^^^max

%

''s

Wc COS A 0 (2.6.1) in which q_ = ^s , and where 77- is the value of TJ chosen to

represent the boundary layer thickness. In this case it is

con-venient to take the -value of "n corresponding to i;ig- =0.99 thus

referring the second^iy flow Rejmolds number to a "physical profile width". It would no doubt prove more suitable to choose -values for n corresponding to the boundary layer displacement or momentum

thickness along the streamline since these quantities are more readily defined precisely. However, as stated above, the choice -v/as made for convenience, and the resulting distribution of x / i_

R^ is shown in fig.24.

2.6.3. The Boimdary Layer Flow for a "W-edge" Profile

Referring again to fig.19. it can be seen that to the exclusion of regions in the immediate -vicinity of the leading edge an approxi--mately similar velocity distribution to that existing over the

forward part of the v/ing is represented by an expression of the

form :

Q = A X 2 1 2

for which the boundary layer may be readily calculated follov/ing the methods of Hartree (ref,31.) and Cooke (ref,32), (see Appendix W for details). More particularly a velocity distribution of this kind describes the flow in the neighbourhood of the leading edge of a wedge shaped profile (for -vviiich in the plane A, the v/edge angle /? is given by /9 *" , and the nose radius is vanishingly small) and

"itvrr

hence does not strictly bear any relation to the present work as far as the experiments are concerned but is nevertheless an interesting example v/orthy of some consideration from a theoretical point of view. We -use it here together v/ith the res-ults of para, 2,6.2. to illustrate

(para. 2.7.) the effects of nose radius upon the secondary flov/ for regions very close to the leading edge.

The calciolations (performed as outlined in Appendix IV yield the velocity distributions shown in fig. 22., v/hilst the Reynolds numbers for the secondary flow (fig. 24) are given by:

X R 2 ~ 4 max 1

i "'s

^s Md. (2.6.2) 2.7. Secondary Flov/ Velocity and Associated Reynolds Nimibers.

The calculated distributions of the maximum values of the secondary flow velocities associated with the two types of external stream considered, exhibit very different properties in the neighbourhood of the leading edge, as was expected. The results clearly show the important influence of the absolute magnitude of the leading edge nose radius upon the majcimum velocity attained in the secondary flow and its corresponding influence upon the profile Reynold's Numbers, Illustration of this effect in relation to the velocity along the

external streamline is facilitated by reference to the ciox-vcs shov/n in fig.24,

From the calcuJations m.ade for the bc-undaiy layer flov/ ovex" the v/ing leading edge (according to the method of p;ira,2.6,2) it may be seen

{ X

that the secondary flov/ Reynolds Number reaches a peak value \.±.

-0,0485 ) at a short distance from the stagnation line, this

trend .agreeing qualitatively v/ith that given by the calculations of Owen and Randall (ref.17.).

The calculations do not lonfortunately give any definite indication of

the behaviour of —^ for regions further downstream, than those

R2

considered. To obtain such information using the more exact methods of boundary layer theory would involve a step by step integration starting from some chosen calciilated velocity profile,from thence proceeding the requisite distance dov/nstream. However, on the assumption that the peak shov/n (fig. 24) represents the maximum value attained by V - D 2 , then following Ov/en and Randall (ref. 17) the condition for instability to occur in the secondary flow may be v/ritten

as:-max N

~J.— = " i

^^ ^crit. (2,7.1)

-with ^Wix 0.0485 from the calcula,tions.

I

Thus by experiment oily determining the Reynolds number \I^„„^+ = U .. c \ at v/hich the first indication of secondary flow

0 crit. 0 V

instability is apparent, N can be fixed. 2.8. Sccond,-iry Flov/; General Notes

The calculation of the boundary layer by the method of para.2.6,2. yields sn accurate representation of the flov/ conditions occ-urring

over a short distance from the stagnation line. It has sho-ivn the principal effects of the secondary flov/ to be confined well v/ithin the region considered, thus rendering them readily calculable.

Furthermore, since the distribution of /„-§• is accurately knov/n v/ith regard to distance along the iving s-urface then the regions in 1^/hich some form of boundary layer control sho-uld be applied to suppress the secondary flow instability are correspondingly v/ell defined,

The calculations for the wedge profile suggest that, since for the case considered —i increases continuously v/ith increase in x

R^

then a detailed stuc3y of secondary flov/ instability together v/ith the subsequent vortex formation in its relation to the Reynolds number of the external stream, is jjossible.

3. EXPERUffiNTAL CONSIDERATIONS. 3.1. Suitable Test Methods

In para. 1.4. v/e have made reference to the fact that the study of the three dimensional boundary layer occurring on a swept b.ack v/ing is one in v/hich the effects of scale are of great significance and it was ]pointed out that the needs v/ere, therefore, for experiments enquiring into the nature of this flow to be conducted at something a.pproaching full scale Reynolds Numbers. To achieve this object we can proceed in one of tv/o ways; we can choose either to perform our tests using a. very large wind timnel or by moTjnting the test v/ing on to a suitable aircraft as test vehicle, in the manner described. The problem was reviewed by Britland (Ref. 15.) and the various problems associated v/ith either technique briefly outlined.

As far as vraJid tunnel tests are concerned, in the case of a sv/ept wing of finite span v/e are very much more i-estricted than v/o\ild be the case v/ith the tv/o dimensional v/ing. Briefly, this is mainly due to the compounded effect of sidewash and v/ind tunnel constraint, the result being tliat a relatively large working section is required for the satisfactory testing of a model of relatively small sport. There is also the added effect of -wind tunnel t-urbulence v/hich is necessarily rela.ted to and has an effect upon the beha-viour of boimdfiry layer transition. On the other hand, if v/e moijnt our test wing in the manner to be described and in fn.ct make free flight tests, v/e have firstly the added ad-vantage of an easily obtained high -value of Reynolds number and secondly the further advantage of a

presumo.bly small degree of free air turbulence. Arguments v/ill inevitably arise that the effects of propeller noise on the stability of the boundary-layer might lead to prematvire movement of the transition fronts, but in reality little is known of the precise significance of such oji effect. Hov/ever, in some previous experiments test work performed in flight on the boi^ndary layer characteristics of a sv/ept back vnng (Ref,26,) it v/as foimd possible to achieve appreciable areas of laminar flow and we may conclude that the effects of propeller noise and the disturbance effects of the slip

stream tubes did not influence the beh-avioxor of bo-undary layer transition to any apparent extent. In tests on the 'King Cobra' vri-ng. Gray observed also that there appeared to be no apparent effects of any significance, arising from propeller noise and slip stream disturbance, in relation to the boundary layer flow,

Consideration of both the ad-vantages and disad-vantages inherent in either method of test led . to the choice of testing in free flight (using an Avro Lancaster MC VII as test veliicle), the experimental v/ing being mounted as a dorsal fin upon the mid upper fuselage. Tested in this way the -wing may be considered free from any constraint whatsoever on its induced side wash. Such a procedure however necessitated the deri-vation of a simplified test

technique for the measurement of the boundi-jry layer so that the experiments

could easily, simply and r.".pidly be OLCcomplished V/ith the minimum of flying time ojnd whilst, in -view of these simplifications, v/e are necessarily res-tricted to some degree in our interpretation of the experimcntol results so obtained, it has nevertheless boon found tho,t the chosen test method v/as most satisfactory in its application,

3»2, Choice of Experimental Plan. Techniques and Procedure

In the initial stages of the conception of this experimental work It v/as hoped that press-ure tronsducers could be used for the required aerodynamic measurements, but lack of experience -v/ith this type of equipment resulted in reverting to the usual liquid manometer methods for the recording of pressures. In -view of the relatively high test Reynolds Numbers to be encoijntcred and the liquids o.-vn.ilable as mano-metric fluids, together with the degree of acctiracy required in measure-ment, it v/as necessary to use a very lojrge vertical manom^^ter installed in the aircraft. Although at first this presented a problem of some difficulty it was evcnt\io.lly overcome ojid as described in Ref. 25 a. 50 tube manometer, some 7 ft.in height, v/as installed in the rear fuse-lage of the aircraft together v/ith camera observation -unit. This lat-ter is a necessity for experiments of this kind v/hen conducted in flight for altho-ugh the required experimental conditions can bo set vnth a high degree of accuracy and stability by the pilot, such conditions coji only be set and maintained for a relatively short space of time due to the combined effects of pilot fatigue ond natural disturbrjices to the steady flight of the aeroplane. Thus the requirement is for measuring apparatus in v/hich pressures can be displayed and recorded v.ith an absolute

minimum of time delay so as to eliminate as nearly as possible the inevitable discrepancies v/hich v/ould occur in measurements of this kind made over relatively long periods of time. Experience had pre-viously

shown that a maximum time delay of 10 seconds w,as all tho.t could be allowed betv/een the initial establishment of the required experimental conditions and the recording of the displayed pressures if the degree of accuracy aimed at v/as to be achieved. To this end, therefore, the design and construction of the experimental eqiaipment was directed from the outset, The measurement of the static pressure distribution over the sv/ept vnng model presented no difficulty at all, the pressures being measured in the usual v/ay and displayed on the manometer. Hov/ever, for the measiorements in the boundary layer, the ciioice of a suitable experimental technique v/as at first one of some difficulty because of the very nature of the

boundary layer flow to be expected on a v/ing of this kind. Nevertheless as v/as stated in Pojragraph 1.3. it v/as thought possible for the v/ing under consideration to greatly simplify the boundary layer measurements by apply^ ing techniques strictly correct for the tv/o dimensional case only, to

certain regions of the v/ing. The act-ual techniques chosen v/ere similar to

those used in the flight experiment of Stevens and Haslam, (Ref.1l) the

type of bo-undary lo.yer combs used in this case being as shov/n in Figs, 12 and 13, The method of ex^poriment v/as to study first the boundary layer at the maximum thickness of the v/ing by attaching a number of the boundary layer combs to the v/ing surface by means of Sellotape at various positions along the span, from thence proceeding in stages of chosen length tov/ards the leading edge of the -wing. In this v/ay it was possible to conduct the exjjeriment v/ith the best possible surface finish alv/ays existing in regions ahead of the plane of measurement. With the combs in position at any one chordwise station, on one sxirface of the v/ing a flight v/as made ojid the bound-ary layer measured for a n-umber of configurations of speed and wing incidence. The measurements were referred to both upper and lower surfaces of the wing;

this being possible because the v/ing was of symmetrical section and the installation in the aircrcft permitted its rotation in cither direction about the QS:±S of the main spcr cictension to an extent of - 10O, Thus since the iücastiremcnts v/cre made using one side of the ",;ing only, the effects of

£iL:y contour irregularities v/ould thus be cor:ffaon to the results obtoaned for

both upper :nd lo\/er surfaces, 'v/ith a view to pilot and cre'vv fatigue, a boundary layer explorrition of -'Gbls kind v/as found to consti-buto sufficient experimental -./ork for one flight, those occupying on the average about 1-g- hours flying from toke-off to landing toid roughly involving moasurements in seme 230 boundary layers. Provided the limitations imposed upon the results so obtained by the na-bure of the technique used are tindorstood, it can be seen that -chc method does nevertheless consti-tute 0, very rapidly detcrrained assessment of the boundary layer flov,',

By v/ay of comparison v/e refer to a ntomber of other s-//cpt -..ing boundtry layer tests -v/hJ-ch have boon conducted at the Colloge using a -bra-vorsing gear as described in Ref ,26, the measurement of all components of the boundary layer flow in curvilinear planes adjacent to the "i/ing surface being possible \/ith

this Qccr. It v/as found that,to explore the boundary layer at one chordvriso

station for one value of v/ing incidence .'.md test Reynolds Number, a flight of a.pproximo.tely 30 minutes duration was required (inclusive of tciko off and Iruiding).

4. EXPERIl/IEHTAL EQUIFuEI-lT. ••'• "~ . .• 4.1. The Aircraft

The aircraft used as vehicle for the series of tests under consideration was an iivro Lancaster x.K 7 P»A, 474. This aircraft -v/as subjected to a number

of struc-fcurol modifications in order that the '.ling could be mounted above the mid upper fuselage. The position chosen for the mounting of the v/ing on the mid upper fuselage v/as a ccmijranise betv/een fuselage structural design considerations and the results of preliminary cxploro.tory tests relating to the na"fcure of the flow field over the fuselage, '„'e shall not concern our-selves with a discussion of the various design features in this report;, the

reader's attention being drav/n to Rcf.23 for a detriled discussion of the

v/ork involved.

4.2. The Pressure Plotting Mast

Consideration of the nature of the flov/ field over tlic mid upper fuselage of the aircraft into v/hich the v/ing wn.s to be immersed has been the subject of discussion in Ref .24 in v/hich the equipment iuethods ïind techniques employed for calibrating t M s field v/cro treated. Since a full description of the

pi'csEurc plotting mast is therein contained,further consideration in this v/ork is unnecessary.

4,5. The Wing and Installation

The swept back half v/ing constructed for the tests under discussion v/as of general dimensions as shown in Figs.3 and 4. It -was of 45 sv/eep, -untapered and imtwisted and its streomwise section was intended to

effectively represent a 10^ thickness to chord ratio aerofoil of 130 inches chord (as discussed in paragraph 2.1.), the representation being attempted by geometrically constructing the v/ing section of tv/o semi ellipses each

of minor axis 13 inches and of major axes 104 inches and 68 inches for the forward and rear portions respectively. Although the leading edge itself was detachable so that different nose radii co-uld be fitted if so desired ,

only one -value of leading edge nose radius has been considered in the present series of tests, this value being 0.822 inches.

Consideration of the struct-ural design ojid surface finish requirements together v/ith the constructional problems involved led to the choice of a com];)osite wood metal structure for the v.dng. Basically it consists of a conventional metal spar, having birch ply bonded to each face of the ^-./ing, and leading

and trailing edge beams of spruce. The v/ooden ribs v/ere closely spaced (o-t

6inches centre line to centre line), and. the skin v/as 16 S.W.G. Light

Alloy Sheet bonded to birch ply. The skin v/as attached to the ribs using the norma.l glueing technique and dixring assembly an internal himiidity seal was effected by spraying the v/ooden members with phenoglaze G.300 as and v/here necessary. The leading and trailing edge members themselves were

of laminated mahogany construction, these also being coated v/ith phenoglaze, For o.ttachment of the wing to the aircraft,tv/o hea-vy steel joint plates

are used to carry the spar boom end loads into both the root end rib and the v/ing spar extension, the latter of v/hich is attached to internal members of the aircraft fuselage (see Ref,23) and is suitably hinged to permit rotation of the v/ing about the axis of the sioar extension so that the axis of symmetry of the v/ing section may be moved to any desired angular position relative to the plane of symmetry of the aircraft -within the range ± 1 0 ° (see Fig,6b), The ojigular position of the v/ing in relation to the plane of symmetry of the aircraft (i.e. v/ing geometric incidence) could be fixed as desired by means of tv/o simple spigot clamps as shov/n in Pig,6o, Betv/een the forz/ard spigot clomp and a suitably chosen fuselage member a hea-vy incidence actioating jack v/as attached, and the arrangement

of the whole assembly was such that the v/ing geometric incidence (i.e, angular position relative to aircraft plane of symmetry) could be

conveniently adjusted to any desired position in the rrJige - 10 , indexing being achieved by reference to the incidence sector plate and pointer as

shov/n in Fig, 6c.

To reduce the interference effects of the aircraft fuselage bovjndary layer upon the flov/ over the wing, a. v/ide boundary layer fence v/as fitted as

shown in Pig,6c, This fence v/as not lo.rge e n o u ^ hov/ever to consitute a reflection plate,

Por pressure distribution meo.surement chordv/ise rov/s of sto.tic pressure tappings were bixilt into the v/ing at tltree spanv/ise stations. There v/ere th-irteen tappings in each rov/ and their positions along both the span and chord of the wing are given in Table I and Pig. 3. The leads from the sta,tic press-mre tapi?ings v/ere of 5/32" diameter copper tubing and j^assed through the interior of the v/ing adjacent to the main spar and from thence into the interior of the aircraft fuselage and so on to the manometer. Pro-vision for a nimiber of additional static pressiire tappings positioned

around the nose of the wing v/as made hy means of neoprene tubing let into

the leading edge as shown in Fig. 6a.. In this v/ay a ntmber of closely spaced static pressure tappings covild be obtained by simply drilling into the neoprene tubes at chosen chordv/ise positions, each hole so formed being sealed with beesv/ax upon becoming rcdundon-t.

The wing surface v/as finished usinf Titanine lo.cquers (colour, black) cjid to meet the requirements for surface v/a-viness in relation to lojninar flow 0. number of measurements v/ore ntide during the preparation of the s-urfo.ce for the purpose of locating "high si^ots" etc., so to direct the co\arse of the "rubbing dovm" and filling processes. Initial measurements v/ere made to this end by means of a c\jrvature g.auge of the usual type, but difficulties encoutered with the interpretation of such measurements together vnth the times required to so inspect the sinrface led to the choice of an oblique lighting technique not unlike that devised by Gray

(Ref,27), In this case a fluorescent strip light was suitably mounted alongside the v/ing in the painting room and by observing an oblique

reflection of this light in the v/ing surface local high spots and surface v/a-viness could be simply and ro.pidly detected. Using this technique the

spraying, rubbing dawn and filling processes became one of continuity, and by much careful work the desired res-ults v/ere eventually achieved. For the convenience of surface position reference on the wing, a v/hite.

"grid" was sprayed onto the surface (see Pig. 10.) this being made possible by suitably masking the wing and proceeding in the usual v/ay. Only an

extremely thin coat of p:Lint was required to achieve this object and so •whilst in fact each line of the "grid" does constitute a discontinuity of surface contour, the magnitude of this discontiniiity was considered small enough to be neglected. As a final measure the wing surface v/as finished to very high gloss using wax polish,

The v/ing struct-ure and assembly weighs approximately 5OO lbs, and was constructed by and under the direction of Mr.Mortin in the v/orkshops of the Department of Plight ,at the College of Aerono.utics.

4,4, Instrumentation: The Manometer and Recording Apparatus

A fifty tube manometer, some 7 feet in height ond 30 inches wide, complete with camera observer unit, v/as installed in the rear fuselage of the

aircro^ft as indicated in Fig.2, A detailed description of the design, construction, and installation of this large instrument in the relatively confined interior of the olrcraft fuselage may be found in Ref. 25 and

we shall not therefore concern otxrselves v/ith the -varioxis design features of the unit here. Suffice it to say that sto,tic and dynamic pressures supplied from connections made in the usual v/ay to the chosen pressure sources, v/ere displayed as required on the instrument, the free stream dynamic head (-uncorrected for S.P.E.C.) being directly indicated on a separate 'U' tube imit incorporated in the manometer and connected to the aircraft pitot static system. Tv/o further tubes, one at each side of the manometer face v/ere connected to the aircroft s-tatic system for the purpose of pro-viding under test conditions a datum to v/hich all mco.s-tirements could be referred. By this meojis allov/once could be made for the effect of small ortgles of bank occurring during tests and the corresponding settling of the fluid to its gravitational level, Depending upon the range of pressures to bo measured tv/o different manometriuc fluids were used o..s required. These

v/ere:-Carbon Tetrachloride S.G. = 1.599

Distilled Water (using fluorescene for colouration) Observations of the manometer v/ere facilitated by means of an P. 24

cojnera in a form slightly modified for imjiroved film economy, illumination of the manometer being acconiplished in a most satisfactory manner by

means of a system of back lighting (see Ref.25 for full details) supplied from one of the 24 V. pov/er circioits a-vailable on the aircraft,

4«5» Directional Yav/meter

Since one of the basic requirements of the tests performed vra,s for steady, straight and level flight at predetermined angles of sideslip a -vane type yawmeter was fitted to the starboard wing tip of the aircraft as shov/n in Pig,2, This yawmeter was connected to a Desynn type indicator mounted on

the pilot's instrument panel, and following a suitable calibration pro-•vided an accurate means of consistently reproducing the required angles of sideslip (to approximately i ^ ) in ste.?.dy flight,

4.6. The Bovmdary Layer Combs and Transition Indicators

For an exploration of the boundary layer on the wing, two tjrpes of comb v/ere used, these being as shov/n in Pigs,12 and 13, the one for the piorpose

of determining the boundary layer velocity profile (Pig.13 and the other (Fig, 12) for the purpose of measuring the distribution of total head, at, near to, and along the -wing surface respectively. They were designed to give sa-tisfactory oiDero.tion for a fairly wide rojige of experimento.1

conditions and v/ere conveniently ond simply attached o.s and v/here required to the v/ing surface by rneojis of Sellotape, the brass strap ond moverble brass stirrup (see Fig, 13) of the boundary layer comb serving not only as a brace but also as a datum fixing for the tube assembly. A full description

of both types of comb together v/ith details of some simple wind tijnnel tests performed to assess their usefulness may be foiond in Ref.25.