MINISTRY OF AVIATION

AERONAUTICAL RESEARCH COUNCIL

CURRENT FAPERS

Low-Speed Wi nd=Tunnel Tests on a Series of Cambered

Ogee Wings

LONDON: HER MAJESTY’S STATIONERY OFFICE

I964

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UvD,C. No* 533.6.055 : 533m6eO?l : 533.693.4

CwP. No.775 Noveniber 'I963

LOW-SPEED WIND-TUNXEL TESTS ON A SERIES OF CA:- OGEE WINGS

P. B. Earnshaw

A series of nine csnibered ogee mcdels, each having the same planform end area distribution, has been tested at low speeds. The camber variants have been designed by means of slender-wing theory and include variations both of lift coefficient for attached flow and of pitching moment at a given lift. For all wings, the flow developent was regular regardless of load distribution except at low incidences, where the flow was very sensitive to%defe.cts in the leading edges. Trailing-edge effects dominated the load distribution achieved in the attachment condition; when an appreciable part of the load was carried over the forward part of the wing, correspondence between theory and experiment was reasonable. Increase of lift coefficient for attached flow had favourable effects with regard to both (L/D)- and the rate of forward movement of aero-

dynamic centre with increasing lift.

I INTRODUCTION

2 DETAILS OF MODELS AND TESTS

3 DISCUSSION 03' RESULTS 3.1 Force measurements 3.2 Surface flow patterns

4 CONCWSIONS

SYIvE3OLS

REFERENCES

TABLE 1 - Details of models

ILLUSTM!TIONS - Figs. 'l-12

.DETAC&X%l3 ABSTRACT CARDS

ILLUSTMTIONS

Details of model planform

Cross-sectional area distribution Chordwise vwiation of cross-load

Chordwise variation of leading edge droop angle Variaticn of lift with incidence Variation of induced drag factor K with lift

Variation of induced drag factor KS with lift Variation of L/D with lift Variation of pitching moment with lift

Variation of position of aerodynamic centre Surface flow patterns for model 6 at design incidence with and

without transition wires Surface flow patterns for mcdel 4 at 2.5’ and at IO0 abcve design

incidence

2!%!z 3

3

5

5 6

6

7

8

12(a) & (b)

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I IN!TROD?JCTION

Lcngitudinal camber desiped intc the wing can produce a trimmed ccnditicn at cruise on a supersonic transPcrt aircraft for smaller drag penalty than by use of elevators'. . But, whilst it is known that the slender-wing thecry is capable of Producing camber shapes having attached flow at the design bcidence, experimental results for a wide range of such designs are desirable in order to

c investigate any limitations which could preclude regular vortex development off- design or indeed any limitations to the thecry itself. Such limitations might exist, for exaqAe, with respect to maximum permitted droop angle or rate of change of droop angle along the leading edge, or to the thickness effects of a practical area distribution which might become restrictive in the forward part of the wing. Equally, of course, it is necessary to determine the extent lx

which such factors influence the actual lead distributions compared with those predicted by the theory.

The basis for the Present work was the planform and thickness distribution resulting from a feasibility study comPleted in 1960. Owing t6 the comparative ease of manufacture of small wooden models for the R.A.E. & ft x 3 ft lcw-speed wind tunnel, an extensive series cf caMbered designs has been tested there during mid 1960 in order to ccver as wide a range cf parameters.as possible. The choice cf designs may be broadly divided into twc groups - forward.and rearward variations. At supersonic speeds, scme load distributions at the front cf the aircraft may be helpful in reducing wave drag due to lift while still attaining

5 a given pitching mcment; but, due to the excessive thickness and rate of change of span, might lead tc uneven flow develoPment at lcw speed and high incidence. The rear part cf the wing is affectedmainly by change of design lift coefficient which can be expected to influence the maximum lift/drag ratio as well as the maximum practical lift ccefficient which can be used for landing. At low speeds the trailing-edge effects, not considered in slender-wing theory, will also play a large part in this area of the wing. The series of measurements of lift, drag and pitching moment together with surface flow patterns reported in this Note helP to clarify some of these points.

2 DETAILS 03? MODELS AND TESTS

Nine models have been tested, each having the same ogee planform with P = 0.45 and the same area distribution which corresponds very closely with that chosen for models -l5, 16, 17, I8 uf the 8 ft x 8 ft supersonic tunnel programme2.

The camber surfaces for these wings have been computed using the downwash distribution given by

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shcwn by Weber' to inc1u.k the conditicn for attachment. Adding to this distribu- tion the condition that the trailing edge is strai&t, the camber surface is designed-for any given centre-line Slope. The -atcambere~~ model of the present series corresponds with model 15 of the 8 ft x 8 ft superscnic tunnel programme, while models 1, 2 of the present series ccrresgcnd with mcdels 15, 16 of that programme except in that the latter have been designed to have the section at 95>: length unccambered, rather than the trailing edge itself. Local load distributions and leading-edge drocp distributicns are shown in Figs.j(a), 3(b), &b) and- 4bh

Models 1, 3, l+, 8 cmqxise a set cf Cies1gn3 each hli~hlg .zero lead over tne forward 207d of the wing* The design CT increa3vc3 in eqq.l increment3 from +J 0 to 0.07'5 while the ccrre3pmding ACm, which is defined as the pitching moment of the cambered wing minus the pitching moment of the plane wing of the same planform at the design CL; decreases in equal increments from 0.0335 to OeOOjO. Model 2, which is tlte only design loving a finite load ct the trailing ;dge, has been designed for a CL Of 0.02> and, by kl.~LoUing d~aoop allgleS Of up t0 JI , Carrie3 more load fom&rd in or&r tc reduce wave drag due to lift at sqersonic speeds. Model 5 Alas the same lead and tkrefcrc droop-a~qle distribution at the front cf the wing ?~ut the rear part of tl,~ x&ng is such as tc give zero desiLm CL. It Was hope2 t112t rz0d.e~ 5 m?dd 31~ i.3 intcrprct~aticn of my peculiarities which might arise in Model 2,, X0&A 7 rcsu.lts from a cmbinaticm of the mYC.iiates cf models 1 and 5 in such a mmler as * tc produce a UA.IX.U~ drcq angie of 60'. Xcdel 6 has the same lcao distribution as mc::el 5 c*fer the rear part of the wing but the droop a@e is m&e finite CA; I516 ayx, t&-m prm2mi.n~ a. fixite rate of' growth of lead Lt the apt:: and carrying ra.t,kr klcre load forWard.

Tlxse models were tested in the 4. ft x 3 ft lcw+drbiLenc~ -&nd tunnel, using a standard hire rig, ever <an incidence range cf -I+C i,c? 2&O where the design incidence for each model is regarded as zero. A knd s>etid of 2K) ft/sec was used thrctd&xit except at the highest inc idences where intense vibration of the mcdels necessitate2 a drcp to 100 ft/sec. Measurements were made of lift, drag and pitching mcment. Surface flo:-l patterns were produced using a mixture cf lamp black and paraffin, the models being sting mounted for this purpcse and a wind speed of IGO ft/sec being used. Lath m&cl has been tested both smooth and with transition wires on the u2~er surface. Tix latter took the f@l-m @f a semi-circular wire (26 S.Yl.G,) on the uqper su~facc cf the nose, approximate~Ly IO& centre-line chord behind the znc~:, tcgc.Ll:er \yitll a -:qire (32 S.V.G.), approximately lO$ local s&.-s pcan inboard of each leading edge. These transition wires were designed to eliminate the separations ccc~urring inboard of the shoulder lines over Ue re3-r part of the vrilq at incicdences close to AUhat for attached flew at the leading &ge. These sc.ixrations were sc serious that all the result3 plotted <are thcs:: produced with transition wires attached to the model.

Tunnel constraint corrections, a.?plied to tjie fcrce measurements, allow for the slenderness of the models by the tcc!mique described by Zerndt'k, who uses slender-body theory e-ferywhere exce;d; in the drag ccrrection, Unfcrt- unately there is an appaent conflict between the value for the drag correcticn cbtained by the application of slender-body theory tc the conditicns at the

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trailing edge and that obtained by Berndt using &nk's stagger theorem which equates the -interference drag from a lifting surface to that due to a lifting line and which therefore predicts the same drag ccrrection irrespeotive of slenderness. As it has not yet been found possible to resolve the conflict, the slender-body correction has been used for all components simply on the grounds of consistency. In this instance, the difference between the drag corrections amounts,at maximum C- ,,, to only 0.5% of total drag.

3 DISCUSSION OF RESULTS,

3*1 Force measurements

Figs.5(a), (b) show that as expected the lift curves are all essentially parallel, each being displaced by the CL achieved at design incidence. This

achieved CL does not correspond well with CLD (i.e. the design CL) but the

differences can be explained at least qualitatively in terms cf the subsonic trailing-edge effects* &Wked on each curve is the incidence at which a line joining the trailing edge to a point 70% chord from the apex, makes an angle of 15O with the horizontal. This gives some indication of the restriction which undercarriage length vrculd place on landing attitude. These points demonstrate that on this basis, designing for a higher CLD results in a loss of CL for landing. However, each of these wings is convex towards the ground on the rear part cf the wing. It does net follow tlnerefore that this effect holds true in other cases.

O-wing to the fairly high incidence range &ovcred and consequently the need for heavy rigging wires, the accuracy of drag measurements at low incidence leaves muoh to be desired. However, the curves cf' variaticn of induced drag factor, K, with lift (Pig.6) show a clear trend at low CL, namely that an increase in C I,,, produces a reduction in K. The curves of induced drag factor,

K s, based on the minimum drag for the symmetrical wing do not disturb this trend (Fig.7) except in the case of model 8 where the minimum drag has risen to such >a level as to produce a minimum of KS in the neighbourhood of CL L 0.15. This effect is reflected also in the value of (L/D)-; see Figs.8(a), (b) and Table I. This indicates that (L/D)lW increases with increasing CLD at least

until c h = 0.075 but the trend suggests that further increases, if any, will be

small. At higher values of CL, two general trends of the induced drag factors

ten be distinguished: (a) an increase in C LD produces a decrease in K; 04 more extreme camber distributions produce increases in K. Thus the symmetrical model has a lower value of K than the highly cambered model 2 but greater than model 3 although both have the same C w

Pitching moments are plotted in Fig.9. As non-linear lift is not appreciable for CL 's up to abcut 0.05, it, seems not unreasonable to compare the

achieved ACm with the theoretical value at zero lift rather than at design

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incidencee Cumpariscn cf tYhe values SllC<al in Table 1 demenstratcs t3at where a large part of the camber leading is carried over the forward part of the wing, a greater proportion of the theoretical AC,n is ac?kved. A,@ll -this orfeE suppcrt 2 for the sucgesticn tha$ trailing-edge e?fects dominate any chmges in the theoretical lozimg &de to camber. Xodel 2 is perhaps a special case with regard to this ugument, as the theoretical finite load at the trailing edge could not be reccvzred in subsonic flow, thus r -2sulting in much closer agreement cf theoretical AC m with experiment Wan in cth3r cases.

A?1 the pitchkg-mcizent CUiTCE3 show wavizless in the ncighbcurhcud of Cx9 and at higher CL's, most cf the curves display "flats". Unfortunately there are insufficient experimentGal pcints to determine these accurately but, as XCst of the curves shcw thGse fe‘atures, it Secilltj certain that they do exist at least at this Reynolds n-tinber. ikxm~er in crkr to produce the curves showing variation of aeroclynaz&c centre with lift (Pig.?O(a), (b))smootkd pitching- moment curves have been us& Hero zgzin the effects cf increasing C-

b and of

introducing more ext mm ca.&zr distributions appear tc produce conflicting trends, name1.v that khe addition of cam&r increases the 1'or~:a.rd movcmcnt of the aerodynarkc centre while increase cf G

+D reduces it.

3m2 Surface flo+4 patterns

Surface flow patterns produced by a su,spension of lamp black in kerosine show in I~ig.ll(a) the extezive laknar separations occurring at the shoulder lines at the design incidence* These separations are Frcscr1-t to a greater or lesser degree on a.11 the cambered mo7els0 IIcwever, the use of transition V&es as shown in FigelI completely <.liminate~ tnis problem> and results in an increase in CD

rni.rI' fcr example fXXU~ OaO07Z to O.OOd? on model 4*

At low incidence when the loading-edge voi-tcx is weak, thG flovJ develops in an irregular manner at the le,?&nyJ edge xsult~ ing i i l what are apparently streamwise vortices, as shewn in i'ig.l2(a) fcr Z.5c abcve design incidence. All of the fairly well defined traces on this end on other models could be seen to criginate at barely perceptible defects in the leading edges. On increasing the incidence these traces disappeared, so that at 5° only those due to relatively sericus defects remained, while at ?O@ the flow pattern was developing quite smoottiy (SW Fig.'l2(b)) and did net chanp,e in character up to the maximum incidence of 25'. 'The sensitivity of the flc37 at low incidences to small irregularities in shape at the 1eGling edge must be attributed to the ccmbina- ticn of planform and thickness diotributicn of tilis series of mod&s0 Camber, within the range tested, had no evident effect on tl:e regularity of flov< development,

In the neiglibourhccd of the apex, tile flop; remained attached at the leading edges but, in this region, difficulties cf mcdel manufacture ensure that the leading edge is by no means shzr-p so khz;t this f'czture might well be expected*

4 - CONZLUSICXS

Cn all of the wings tgst e2 the floiz d.CVClCpiflGiIt bCC3iiE regular abcve some incidence between 5o and q0 . At lower incidenccs, tIiC flew was very sensitive

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to the smoothness of the leading edge where very smsll defects in a model could give rise to noticeable disturbances downstream. This sensitivity d5d nut appear to be influenced by the caxiber distribution.

The difference between the load distribution achieved and that predicted by slender-wing theory seemed to be dominated by trailing-edge effects, and agreement with design value s was gcod only when an appreciable part of the load was carried over the fonvard part of-the wing. The introduction of camber in order to produce a given pitching moment resulted also in an increase of in&tic& clrag and consequently a reduction in (L/D)mU. An increase indesign lift coefficient CLD was more favourable in increasing (L/D)ma as well as reducing the increased rate of forward movement of aerodynamic centre produced by the addition of camber. A less favourable characteristic was the reductiun in attainable CL for landing.

A

c 0

Z C

qpD

Cm

CID min

c%p

%D

K

KS

SYMEBLS

aspect ratio

centre-line chord

aerodynamic mean chord

downwash at centre section cf car6ber surface

coefficients of lift and drag

pitching moment coefficient taken about C.66 co and referred to g

minimum drag coefficient

minirn~~~ drag coefficient of symmetrical wing

design lift ccefficient

CJJ - FD& Z

+A 9 induced drag factor

'D - 'Ds Z ym

+A ' induced drag factor based on symnetrical wing drag

cross loti

local seami-span

semi-span at trailing edge

CiCUSS- sectional area distribution

total volume

Cartesian coordinates; origin at the wing apex; x along the free stream direction, y spanwise, s positive upwards; all lengths made dimensioniess with the root chord loading edge droop angle in cross-plane

Z -7-r sx , non-dimensional spanxise ordinate

non-dimensional spanwise position of "shoulder"

Author Title, etc

Richardson, J.R. Supersonic trim drag of delta wings. mldley Page Ltd. XP/Aero/JOO. Aug. 1957.

Taylor, C.R. *Measurements at Mach numbers up to 2.8 of the longitu- dinal characteristics of one plane and three caxibered slender cgee w-inps. ARC R & IV! 3328. Deeember 1961.

3 Weber, J. Design of VTarpod slender VV%~S with the attachment line alcng the leading edge. xtc 20054. ZepteEber 1957.

4 Eerndt, S.E. Wind tunnel interference due to lift fcr delta Wings of small aspect ratio. Kungl. Tckniska %gskolcn K7.H - Aero TN IT. September, lY50.

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-P- Printed in hkglana for Her hajestyls Stationery Office by the RoyaZ Aircraft Establ$shment, Tarnbwouqh. k.I’.!JO.K.U.

I I ‘ti CHORD = 27 INS ‘k CHORD = 27 INS ; ; SEMI -SPAN = 5.633 INS. SEMI -SPAN = 5.633 INS.

1 1 I I I 1

i I I

f ; I

EQUATION OF LEADING EDGE S(IC)= s$c (l~2-2*4X~~.2x~t3~-3x4)

EQUATION OF SHOULDER LINE t&)=0*5, JC 5 0.5

= 0.5 + (% -0.5); x 3 0*5

FIG. I. DETAILS OF MODEL PLANFORM

co . 0

cu . 0 .

0*4 0.6 3-L 0*0

FIG. 4.(b) CHORDWISE VARIATION OF LEADING - EDGE DROOP ANGLE

+ MODEL a X MODEL @ @ MODEL @ 4f MODEL @ I V’ WMMElRlCAL MODEL

NLlM0ERS IN CIRCLES INOICATE INCIDENCE AT WHICH TRAIL IriG -

EDGE TOUCHES GROUNO FOR TYWCAL UNOERCARRIAGE

5.0 IO-0 15.0 z!o*o 25.0

I I DEGREES INCIDENCE 1 I

FGS(a) VAFUATrON OF LIFT WITH INCIDENCE

- O-9

0-a

O--?

=‘ o-5

Q*4

O-3

- O-2

A --I-

g A

5.0 IO*0 15-o 20-o DEGREES INCIOENCE

FIG. 5. (b) VAFUATION OF LlFT WITH INCIDENCE \

C

+ r4ODfL a

x r400EL Q

A MODEL @ @ MODEL @ El MODEL @ 4ji MODEL @ @ M00EL @ A MODEL @ V WM. MODEL

0.4 0.6 CL

C

FIG. 6. VARIATION OF INDUCED DRAG FACTOR K WI

0.8

+MODEL @I

~MODEL, @ A MODEL @ ~3 MODEL @ - CI MODEL (3 *MODEL 63 0 MODEL @I

4 MODEL @ - v SYMMETRICAL MODEL -

b 0 0.2 04 0.6 ’ c 08 I

L

FlG.7. VARIATION Of INDUCED DRAG FACmR KS WITH LIFT.

3-c

FIG. 8(a) VARIATION OF ‘ID VVW-I LU.

x MOOEL C3 a MODEL 0 AC MODEL 63 I Q MODEL (3 v SYMMETRICAL MODEL

2 0.4 0.6 CL

00

FIG. B.(b) VARIATION OF ‘/D WITH LIFT.

+ MODEL @ El MODEL @ X MODEL @ 46 MODEL @ A MODEL @ 0 MODEL @ 0 MODEL @ A MODEL @

V 5YM. MODEL

/

A

A

FlG.9. VARIATION OF PITCHING MOMENT WITH LIFT

WING, @ WING @ ------

WING@ --- SYMM WING 3

n’ -0.2 0.2 O-4 O-6 CL 043 J-Q

FIGlO@) VARIATION OF POSITION OF AERODYNAMIC CENTRE

WING @ WING @ ------

SYMM. WING

I I

O-2 o-4 O-6 CL O-8

FIG IO(b) VARIATION OF POSITION OF AERODY NAM IC CENTRE

,

A.R.C. C.P. No.775 533.6.055: 533.6.071: 533.693.4

LNMPEED WIND- TE3’S ON A SEXIES OF CAMBm CXXE WINGS. Earnshai?, P. B. Novertber 1963.

A series of nine cambered ogee models, each having the ssme planform and area distribution, has been tested at low speeds. The camber variants have befn designed by means of slender-wing theory and include variations both of lift coefficient for attached flow and of pitching moment at a giver lift. For all wings, the flow developsmnt was regular regard.@& of Joad distribution except at low incidences, where the flow was very sensitive to defects in the leading edges. Trailing-edge effects dominated the load distribution ezhieved in the attachment condition; when an appreciable

A&C. C.P. N0.m 533.6055: 533Ao7l: 533.693.4

A.R.C. C.P. No.775 533.6.055: 533.6.03: 533.693.4

LOW-SW WIlD-lVNNEl, TES’IS ON A SmIIZ3 OF CAH5ERED CZEE I&W-SP=D WIND-TIJNNEL TESTS ON A SERIFS OF CAhBERED OGEE KINGS. Eiamshaw, P. B. November 1%3. WINGS. Earnshaw, P. B. November 1%3.

A series of nine cambered ogee modeis, each having the same planform and area distribution, has been tested at low speeds. The camber variants

A series of nine cambered ogee models, each having the same planform and area distribution9 has been tested at low speeds. The camber variants

have been designed by means of slender-wing theory and include variations 30th of lift coefficient for attached flow and of pitching moment at a given

have been designed by means of slender-wing theory and include variations

lift. For all wings, the flow development was regular regardless of load both of lift coefficient for attached flow and of pitchifg moment at a given lift.

distribution excapt at low incidences, where the flow vms very sensitive to For all wings, the flow devel cpment was regular regardless of load

defects in the leading edges. Trailing-edge effects dominated the load distribution except at low incidences, where the flow was vary sensitive to defects in the leading edges. Trailing-edge effects dominated the load

distribution achieved in the attachment condition; when an appreciable distribution achieved in the attachment condition; when an appreciable

A.R.C. C.P. No.775 533.6.055: 533.6.071: 533.693.4

LOW-SPEED WIND-TDNNEL TFSTS ON A SERIES OF CAMBERED GEE WINGS. Earnshaw, P. B. Novetier 1%3.

A series of nine cambered ogee models, each having the same planform and area distribution, has been tested at low speeds. The camber variants have been designed by means of slenderwing theory and include variations both of lift coefficient for attached flow and of pitching xroment at a given lift. For all wings, the flow development was regular regardless of load distribution except at low incidences, where the flow was very sensitiva to defects in the leading edges. ‘Ixailing-edge effects dmuinated the load distribution achieved in the attac~t condition; when an appreciable

part of the load was carried over the forward part of the wing9 correspond- part of the load was carried over the forward part of the riing, correspond- ence between theory and experiment was reasonable0 Increase of lift ence between theory and experiment was reasonable* Increase of lift coefficient for attached flow had favodable effects with regard to both coefficient for attached flow had favourable effects with regard to both WWm and the rate of forward movement of aerodynamic centre with L/D)mx and the rate of fo& movement of aerodynamic centre wjtk increasing 1ifL increasing 1ifL

part, of the load was carried over the forward paH of the wing9 correspond- ence between theory and experiment was reasonable0 Increase of lirt coefficient for attached flow had favourable effects with regard to both WN- and the rate of forward movement of aerodynamic centre with increasing lif tO

part of the load was carried over the forwz:d wt. of the wing9 correspond- ence betwen theory and experlrert was reaso.u.bleO Increase of lift coefficient for attached flow Fad favourable effects with regard to both O&l - and Lhe rate of forward movement of aerodynamic cer tre with

increasing lift0

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