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Kirk, P. I. Aerodynaalcs (2) Wings and Airfoil* (6)

Kings - Lift (99169)| Lift - effect (5W9U)l 'ings, Swept-beck - Lift

(99306 J4) I Tfinga - Staling charaotariatlea (99179) of Mach number on naxlnm lift

aartfk

Royal Aircraft Eatabliahaent, Farnboroogh,

OtJtoit. Big. Raatr. Restr. Jen'ltf 27 table, graph*

Mach umber of fait on •axiom lift io detemlnod for unswept and swept-back wings. Swept1 back wings show the sane early tip stalling tendencies at high speeds as they do at low speeds. For unswept wings the C^ maXi of sections with far back positions of aaxlam thickness is higher than that of conventional sections, because of the further back posi- tion of upper surface srock ware. At high Mach nuabers thin airfoils haws higher Cj, than thicker ones.

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RESTRICTED NOTE \ AERO 1^67

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ROYAL AIRCRAFT ESTABLISHMENT Farnborough. Hants.

EFFECTS OF MACH NUMBER ON MAXIMUM LIFT

b.

F. N. KIRK, M.P.C.. I.D.N.

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Note I*. Aero.186?

January, 1947

ROYAL AIRCRAFT ESIAjLlJ:S3a?T. FARigQROUGH

Effects of Mach Number on maximum lift'

*y

F.N. Kirk, li.P.C, I.D.I!.

iSlMMARY

"

1. Unswept Wings

The data on the effect of Mach number on C^ m-xx are scanty and their ad-hoc nature permits only two conclusions.

(a) At a given Mach number, the C^ mfvx Of sections with far back position of the maximum thickness is higher than that of conventional sections, owing co the further back position of the upper surface shock wave.

(b) At high Maoh numbers t':.in aerofoils have higher C^ max than thicker ones.

Systematic research is needed and as the effect of Reynolds number on CT max appears to be email at high Maoh number the systematic

tests oould be made say in the N.P.L. high speed tunnel. The most important parauuters on which evidence of their effects is required are thickness-chord ratio, position of maximum thickness and camber.

No simple means of improving G^ max at high Maoh numbers can be suggested. Distributed suction over a portion of the upper surface may improve C^ aax as long as the suction is applied just behind the

shock wave. The testing of such a device would be of value although its practical applications are limited to the range of Mach numbers where the shook wave is in the region where suction is applied.

Griffith aerofoils seem likely to have relatively high CL max at high Mach numbers and an investigation of the high speed character- istics of a Griffith aerofoil would be well worthwhile.

2* Svft-ptb.-i.ck wings

No experimental evidenoe on the C^ ^nx of sweptbaok wings at high M is available. 3weptback wings at high speeds however, show the same early tip stalling tendencies as they do at low speeds. Low speed wind tunnel tests with suction are to be made shortly and should give some indication of the praeticabilit/ of this scheme at high M. The effect of sweepbaok is to increase the sectional CL max over the inner portion of the wing and a suitable remedy for the tip stalling may be sufficient to give high CL max «• hi^h M for sweptback wings.

1.

•MM MM —

rech. Koto No. Aero. 186?

LIST OF

1. Introduction - -

2. Unswopt Wings 2.1 Experimental evidence 2.2 riscujjion

2*21 Lov st.eed stalling properties ot' unswept 'wings 2*22 Efi'cots of compressibility on 0^ ^j^ on unswept wings

2.3 Possible methods of improvin* CL max 2.4 Conclusions

3. Swepfback wings • . 3.1 Exp -rim-.ntal evidence 3.2 Discussion

3«21 Low speed- stalling properties of sweptback wings 3»22 HLgh speed stalling on swepfback wings

3. 3 Conclus ioi)3

References Circulation

LIST OF APPENDICES

Aerofoil Kotation .

J 3 k k k l

i i

7 a a

i

LIST OF T.V»LES

Wins sections of American aircr-ift on which measurements of

°L ' .: IX have been made

LIST o/ i,:.i:.j^vjiOx.;

Effeot of It on Cj. ;liax - Y.'elkin and Spitfire

Variation of Cj, Eiax vdth Jiach number - A).«-rioan flight data Effect of Maoh number on CL ^^ of H.A.0.A. 0012-63 aerofoil

Effect of ;jioh nunber on C, of oth.r aerofoils , U lu'lX

Potential flow pressure distribution at !iigh incidence on a conventional .'lerofoil

Typical variation of CT ^^ with ICaoh nuaiter

Presaure distribution at max lift on a conventional and a lo.v drag aerofoil

Pressure distribution on upper and lower surfaces of M.A.C.A. 0012 section at several Mach numbers f

Spun.viae local .lift curves on a 3J° 3wuepback wing Si indM distribution of local CL'S for the sweptback wing of Fig. 8

Some variations of CV ^^ with .;• -o-pback at low speeds

Pitching moment:i against C^ for ..inss of various sweepbacks at U = 0.8

Pitching moments aga&Mt CL for \ings of various aweepbaolt: at M < 0.2

Fir,. 1 2

•

3 4

5a 5b

6 V.

-i • 8

9 10

11

12

i>

MM

Tech. Note No. Aero.lBo'?

Introduction

Recent project work on some high speed high altitude designs has shown that one of the mo?t important parameters deciding the size of an aircraft for a given manoeuvrability*" is the Cj, ,5^ that can be at .ained at th high speeds considered. A knowledge of the maximum lift and the stalling incidence is also necessary when considering the effects of up gu3ts. For ooae win... sections C^ g,^ has teen found to be seriously affected by compressibility; the available data have there- fore teen analyst! in ardor to assidt in the selection of wing sections with suitable characteristics.

The wings of some of the high speed designs now envisaged are sweptback and, front a stalling point of view, this is a complicating feature. This note is the-refore divided into two main sections dealing with unswept and sweptback wings separately.

2 Unawupt wings

2.1 Experimental evidence

Some flight measurements of the variation of 0* „_ with inach number are given in Figs.1 and 2 and all show large effects.

Fig*3 contains all the known v/ind tunn I data on the N.A.C.A.0012-6.* section. Most of the experimental points are from three dimensional tests (Refs* 1, 2, 3 and 4) on aerofoils of aspect ratio 6 with taper ratio between 1.0 and 0*5. C^ max first drops rapidly from 1.5 at M = 0.2 to about 0.8 at to • 0.45. This is followed by a further but more gentle drop to a value of 0.6? at ii = 0.8, where Cj, max increases again. The lift carpet of this aerofoil (Ref. l) shows a peculiarity occurring fairly frequently in other similar high speed tests. The lift curves in the region 0.7< U *• 0.8 exhibit subsidiary maxima some- what lo./er than the true maxima. The reason for this is not clear as the corresponding pressure distributionu are not available but it is thought to be caused by the relative displacement of the shock waves on both surfaces. Several aircraft in X'light have been unable to reach their actual C^ max either through loss of control power or through severe bui'feting. Subsidiary maxima in the lift curves similar to those found on the N.A.C.A.0012-63 lift curves may be a possible cause of buffeting in flight and a practical limitation on C^ max*

Experimental points on the N.A.C.A.0012-6* section from inde^ iident sources are lacking above M = 0.V but a3 no large differences in C^ nMi

would be expected hetween the two dimensional case and the tests with an aspect ratio of 6 the data from Ref. 5 and 6 have also been plotted in fig. 3. These late indicate that the effect of Reynolds number is small above M = 0.45; below this value of M the aoxxea curve of Fig.3 3hows the probable variation of C^ max with to at constant Reynolds number.

Figures 1, 2, 3 and 4 contain all the known experimental data on the effect of Mach number on C^ Iflajc. The ad hoc nature of the tests makes it impossible to draw any general conclusions as to the effeot of the various parameters. There is however a marked difference

* Manoeuvrability is here U3ed in its old sense i.e. that of ability to do manoeuvres. A measure of this is the maximum normal accelera- tion and therefore CL max that can be attained in level flight.

3.

Tl

Tech. Note No. As.ro. 186?

botmjon the shap- oi' the C^ vs Waoh number curves for conventional and la. drag aerofoils as illustrated in Fig.2. At least up to M = 0»? low ding aerofoil a have higher CL m^ than conventional aerofoils of similar tbickness-c.iora ratio* Also thin aerofoils show a smaller loss of CL max at high liach nur.J-i.rs than do thicker ones*

* laee-u^ion

2.21 LjJ j i. stalling i:rorerti<.fi of ungwt.pt winga

A qualitative inaiijht into the stalling characteristics of a wing can be obtain' d by considering the growth of the boundary layer at hi{.;li incidences (Hef.7). A typical potential flow pressure distribution at high incidence;; is shown in Pi,:. 5a. The distance between A and B on the aerofoil surface is v=ry snail and it also shows a favourable pressure gradient so that along this part of the aerofoil the boundary layer will normally be laminar. Lownstream of the point of maximum Velocity the pressure gradient is unfavourable and depending on the Reynolds number >ind magnitude of the adverse pressure gradient, one of two thinga may occur, namely:

(a) Tb- boundary layer will separate from the surface at B while remaining laminar. This is what usually occurs at low Reynolds number and results in a gentle stall because the flow does not permanently leave the surface b:tt re-adheres as a turbulent layer further along. The maximum lift is poor and the lift incidence curve is flat topped.

(b) Transition -.'.'111 occur and because of its greater stability the turbulent layer vri.ll remain on the surface beyond B. Eventually the turbulent layer will begir to separate at the trailing edge and depending on the shape of the- pressure* distribution the separation will spread forward either gradually or abruptly giving a gentle or a sharp stall. In either case C,-^ j^^ will be considerably higher than if laminar separa- tion ooourred.

The- effects of thickness chord ratio, oaofeer and leading edge radius of curvature can also be understood by examining their respective effects on the pressure distribution. This has been done partially by Young in Hef.ii, and the main conclusions are:

(a) Camber increases CL ^.^

(b) An iiicroase in thioknese above 9S* also increases C^ m£UC»

(c) Bringing the position of the maximum camber forward is detrimental.

(d) dmall lea.iing edge radius of curvature ( < O.OO^c) usually gives a relatively law but gentle type of stall provided that camber is small and the v/in^ thickness is not too large.

(e) Leading edge ri-dius of curvature above 0.01c'usually ^iv-u higher maximum lift but the character of the- stall is likely to be sudden.

2.22 Effects of compr<Js..ibility on C^ maX of> unswept wings

At velocities below the appearance of shock waves the main effect of compressibility ij to increase the potential flow pressures in in- compressible flow by 1 and therefore to increase suction peaks and

Ttcv.. Note ;;o. Aero.186?

pressure gradients in that rati*. As there is no evidence to su£ that the boundary layer is more static in compressible than in in- compressible flow the boundary layer will, if the transition point remains unaltered, separate under the same adverse pressure gradient and therefore at the- same lift coefficient. No appreciable effect on CL max would therefore be exacted except a slight reduction in the

dtv stalling incidence due to the increase in —• .

d •

At higher values of M a region of supersonic velocities occurs on the up£ ;:r surface bounded at fcha roar by a shock wave. Ackeret (riuf.9) has shown that the shape of this shock wave is determined by conditions in the boundary layer ahead of it; a forked shock -save foiming with laminar layers and a straight chock wave forming with turbulent layers. He also shows that if the boundary layer is laminar ahead of the shock wave transition occurs between the oblique and the rear members of the shock vave so that- the boundary layer behind a shock wave is always turbulent. We can therefore expert the effect of Reynolds number to be greatly reduced after the appearance of shock waves and this is supported by the experimental evidence on the K.A.G.A. 0012 section (Fig. 3). The evidence on the o'elkin and on the Spitfire of Fig.l is not conclusive. On the ".Yelkin the lift curves exhibit a kink at low niach numbers and subsidiary m-xima at high k so that the wind tunnel curves of Fi>>l may correspond to subsidiary maxima similar to those found on the K.A.C.A.0C12 section. In the case of the Spitfire the true 0^ ^ax was not attained b-eoause of severe buffeting.

Ackeret (Ref.9) also shows that the turbulent layer behind the shock wave is considerably tliickencd and therefore will tend to separate more easily. This rosult3 in a drop in CL mroc as has been found in all cases (Fig.l, 2, 3 and k)»

As M is further increased, the suction peaks are increased and the shock wwe on the urper surface is displaced towards the trailing edge. A number of pressure plotting measurements in the R.A.K. and H.P.L. high speed tunnels (Ref.10) have shown that except for small local peaVs there is a limiting value of the pressure ahead of the shock wave corresponding to about 0.3 of the total head of the un- disturbed strewn; on tjxainple of thi3 is given in ?ig.?. The pressure distribution? of Fig.6 indicate that, except for the peaks, the :aaxiiiium

local M are of the order of 1.4 which corresponds to a _£. of 0.31* HO

An exception to this occura at M = 0.68 on the N.A.C.A.23015 aerofoil and a posrdble explanation may be that the pressure distribution was taken" just beyond the stall instead of at the stall. As the absolute pressure on the aerofoil is limited, the upper surfaoe lift coefficient at a given :«ach number deeends mainly-on the position of the shock wave. Thii, is illustrated in Figs. 5b and 6 where the CV m^r and the pressure distributions of a conventional and a low drag aerofoil are compared. The early rearward shift of the shock wave accounts for the higher CL max °*' ^& low toag aerofoil. A further comparison Of C^ j^^ on conventional and lew drag aerofoils is given in Fig. 2.

Eventually the 3hock wave- on the upper Burfacc reaches the trailing edge and if, as fig*6 indicates, the lift contribution of the lower

surface- is small, a constant -£- Ho

°L max of the oniL'r of °»9 at K = 0.9»

of O..1! on the upper surfaoe gives a

Tech. Note No. Aero.186?

2.3 Possible methods of improving _'L j^^

There appear to be two main effects of compressibility on Cj, max*

(a) The first is purely a viscous effect occurring at relatively low Wfich numbers due to the thickening of the boundary layer by the shock wave with consequent early separation. The only possible remedy i"orthi3 is to apply suction at and immediately behind the shock wave. In practice this would only be possible for a small range of positions of the shock wave and therefore for a suiall range of Mach numbers. The best suction Mthod in this case would probably be distributed suction over a portion of the upper surface through a porous material (Ref.ll-12). Although of limited practical applica- tion the testing of this device would be of use and as most of the experimental evidence available is on the i".A.C.A. 0012-63 section the suction could conveniently be tested on this aerofoil.

(b) The second effect is a limitation of the value of the pressure ahead of the chock wave which occurs at fairly high Mach numbers.

°L max is then mostly a function of the position of the shock wave

and the further back it is the higher CJJ n^ will be. The position of the maximum velocity ut high CL should therefore be as far back as possible. iieans of obtaining a :'ar back position of the maximum velocity arei (a) to use a section hiving a far back position of the •Tvucimum thickness. (b) to use a thin cambered section. Adoption of (a) normally leads to large trailing edge angles with consequent undesirable pitching moment characteristics at high speeds (Ref.l) so that the furthest back position of the maximum thickness which can be U3ed is probably only M);o of the chord from the leading edge.

A possible way of obtaining a far back position of the maximum thickness without large trailing edge angles is to have a discontinuity in the pressure distribution near the trailing edge as is done on the Griffith aerofoil. The high speed characteristics of Griffith aero- foil.:, are not known and should be investigated. The use of camber introduces undesirable tail loads at high speeds and some sort of compromise would have to be made on the oasis of systematic tests.

2.4 Conclusions

1. The experimental evidence available is scanty and its ad hoc nature makes it impossible to deduce the effect of the various para- meters influencing tht aerofoil shape. The only conclusions possible by examination of the data are:-

(a) At a giv<_n iiiach nui;iter. the C^ m^ of sections with far back position of the ..laxiuuia thickness is higher than that of conventional sections owing to the further back position of the upper surface shock wave.

(b) At high Mach numbers thin aerofoils have higher C-^ max than thicker ones.

2* Systematic research on the influence of profile shape is needed and as the effect of Reynolds number appears • small at high l^ach number the systematic tests could conveniently be made in the N.P.L. high speed tunnel. The most important paraiueters on which evidence is required are thickness-chord ratio, position of iu«»jcimum thickness and camber.

. r i . . .

3* Llstributed suction over the forward part of the v.ing upper Burfaco may improve CL max over a stall range of iiach numbers by removing the thickened boundary layer inmediately behind the shock wave. Although o; limited practical application the testing of this device would be of us- and as moat of the available experimental evidence is On the K.A.CA.0012-63 section the test? could conveniently be made on this aerofoil.

4* In viav/ of tht. far back, position of the maximum velocity at high CL obtained on Griffith aerofoils the high speed characteristics of these sections should be investigated.

3 Swept*:nek wings

3.1 Experimental evidence

No measurements of C^ max on swepthack wings at high liach number are known. Two cases are !cn0.vn haawv*wn liftS near the CL m£UC mm measured: in Ref. 21 a CL of C.6 v/aa measured at M = 0.84 on a H4i tlick symmetrical wing section ( maximum t/c at 0.4c) with 45° of sweepbaok and in Ref. 22 ft CL Of O.64 v.-as reached at M = 0.84 on a 12« symmetrical wing section (maximum t/o at 0.3c) with 45° of sweepbaok. In both oases the actual CL max was rv3^ reached but both lift curves shewed some curvature.

3.2 Discus.-ion

3.21 Low speed stalling properties of sweptbaok wings

All the remarks made in para, 2.21 concerning the variation of the type of stall with Reynolds number apply also to the swept wing.

Theoretical calculations and tunnel measurements (Ref.23-24) have sliOwn that, at a fixed incidence, sweepbaok results in a net loss of total lift with the greatest loss taking place at the centre of the span. At moderately large angles of sweepback this results in a span- vd.su distribution oi" local Cj/s showing a maximum usually in the wing tip region. Furthermore McKinnon Wood (Ref.25) and Griffith (Ref.26) have shown that sweepback has two main effects on the boundary layer, namely:

(a) A decrease in the effective pressure gradient due to the inclination of the flow to the isobars.

(b) A side travel of the boundary layer caused by the pressure gradient normal to the flow. On the inner part of the wing this side travel is outwards, near the tip the side travel is inwards thus causing a local thickening of the boundary layer.

The first effect is favourable- from the point of view of the boundary lrtyer stability} the seoend ia unfavourable. The worst possible oaae therefore occurs when the isobars are normal to the main stream because then the adverse effect only is present and the boundary layer is thickened by inward flow from both sides. Such a condition usually occurs in the wing tip region. This, together with the increased local "L at the tips, is thought to account for the premature stalling of 3wepteack v/ings.

Fig.8 gives the results of a pressure plotting investigation on a sweptback -.dng in the R.A.E. 24 ft. tunnel at a Reynolds number of 1»55 * 10" (Ref. 24). The wing plan fon.i ani sections ar~ shown in

Teoh. Note No. Aero. 186?

the same figure. These results are not fully corrected and Pig.R should only be taken qualitatively. Below the tip stalling incidence the spanwise distribution of local lift coefficient shows a nwximum at about 0*7 of this semi-span from the centre line. After the tip •tall the load is redistributed and the maximum occurs, at 0*4- of the semi-span from the- centre line - (Fig.9). CL max f°r the tip sections is low and the lift curve is flat toppel whilst the local 0^ max at the centre sections is higher than would be measured in a two- dimensional test. This is in agreement with the earlier remarks on the effect of sweepback on the boundary layer because at the centre sections only the stabilising effect due to the reduction in the effective pressure gradient is present. The C^ ^ of a sweptback wing is there- fore a complicated function of the- characteristics of the root and tip sections modified by the plan form and Keynoldu number. A typical variation of the spanwise lift distribution with incidence on a sweptback wing is illustrated in Fig.9* Some curves of C^ max against angle of sweepback(Ref. 21, 27, 28 and 29) are shown in Fig.10.

3.22 High speed stalling on 3.veptbaok wings

The general remarks of para. 2.22 on the steepening of the pressure gradients by compressibility apply also in this case. Because of symmetry the relieving effects of sweepback are least at the centre Motion and, as lias been observed in some German tests, a shook wave starts at the oentre section and spreads outwards.

Figs.ll and 12 show pitching moment measurements made in the R.A.E. high speed tunnel on a symmetrical 14$ thick wing section (max. t/o at 0.3c) aspect ratio of 5.8 and taper ratio of 0.57 at various angles of sweepback (Ref. 21). The wing was tested .with a fuselage. The low speed pitching moment curves at 33° and 45° sweepback indicate a tip stall in the neighbourhood of Cjv = 0.60 and 0*50 respectively. At il = 0.82 the tip stall occurs at CL a 0.45 (Old 0*5 respectively, indicating that part at least of the problem of the loss of stability at high M is the low speed problem of early tip stalling.

The fact that the final stall on a sweptback wing is preoeded by a tip stall is of special importance in the case of tailless designs* Recent high speed tunnel tests on the DH.108 (Ref.30) indicate that although CL max is probably in excess of 0.6 at M = 0.84 the mnrliram Or that can be trimmed is only of the order of 0.45 owing to the loss or elevon power due to tip stalling.

3*3 Conclusions

Although no measurements of Of, y. on sweptback wings at high Maoh number are known, the final stall of the wing is preoeded by the stalling of the tip sections which limits the trimmed C^ ^g^ Of the wing particularly on tailless designs. This is the same problem already experienced at low speeds and a suitable solution should first be found there. Suction at the critical points for the boundary layer separation appears to be the most promising remedy and various arrangements of slots are to be tested at low speeds (Ref. 3l). These tests should give an indication of the quantities of air required and of the practicability of the scheme. Owing to the favourable effect Of sweepback ov<-r th<- inner purt of the wing the local C^ ^^ at high If is likely to be high at the inboard sections so that attention need only be paid to the tip sections. Still higher values of C^ max oould possibly be obtained by using suction in the critical region in con- Junction with any of the previously mentioned methods to improve C^ BWI of unswept wings.

8.

teoh. Mote So. Aero.1867

ji

t

Author

B. Mother W.A. Mair

T.C. Muse

E.N. Jacobs R.M. Pinkerton H. Greenberg

J. Stack H.A. Fedziuk H.E. Cleary

W.F. Hilton C.F. Cowdrey G.A.M. Hyde

G. RLchter

7 ' &J. Richards

8 A.D. Young

9 J. Ackeret P. Feldmann N. Rott

10 J.S. Thompson

11 J.H. Preston

12 J.H. Preston

13 X.J* Richards .. Q.H. Burge

14 W.A, Hair

Title, etc.

German wind tunnel results. R.A.S. Tech. Note Ho. Aero. 1684. August, 1945.

Some effects of Reynolds and llach Numbers on the lift of a N.A.C.A. 0012 Rectangular fling in the N.A.C.A. 19 ft. pressure tunnel. A. R. 0.7054* Sept. 1943*

Tests of related forward camber airfoils in the N.A.C.A. Variable-density wUxi tunnel. N.A.C.A. Report .No.610. 1937*

Preliminary investigation of the effeot of compressibility on the maximum lift coefficient. A.R.C.6963. Aug., 1943*

Tests, on the N.A.C.A. 0012-63 Aerofoil in the hi.^h speed tunnel. A.R.C. 4715* Sept, 1940.

Messungen <vn Profil N.A.C.A. 0012-63 im D.V.L. - Hoohgeschwindigkeits-Windkanal. Report No. 127 Iilienthal-Gesellschaft fur Luft-'ahrtforschung. Sept., 1940.

Note on the stalling properties of wings* A.R.C. 937?. Jan., 1945.

A Review of recent stalling researches. R.A.E.. Report No. Aero. 1718. Feb. ,1942.

Untersuohungen - r. Verdic htung ss teas en und Grensschiehtcn in schnell bewegten Gasen ttitteroingen Aus Dc.a Institut Fur Aerodyriamik Nr.10. Zurich 1946*

Methods or presenting pressure plotting results at nigh speeds. R.A.E. Tech. Note No. Aero.1614. karch,1945

The boundary layer flow over a Permeable Surface through which suction is applied A.R.C. 9364. Feb.,1946.

Note On the quantities of air required on suction aerofoils of various types and on the ducting. N.P.L. Note (not numbered) April, 1946.

An aerofoil Designed to give laminar flow over the whole of the surface, with boundary layer suction. A.R.C.6789. June, 1943*

Effect of Mach number on maximum lift ooeffloicnts (comments on A 4 *i.K»B» Reports 808/14- a•1 692m/37)» R.A.K. Tech. Note No.Aero. 14S5. An*. ,1944.

9.

Tech. Mote Ho. Aero*l867

LOT O REFERENCES (Contd.)

15

16

17

IS

«

20

J.S. Thompson

2>

24

36

27

J.R. Spreiter- P.J. Staffen

W.F. Hilton

W.A. Malr Hutton Gentle

L.J* Briggs R.L. Dryden

J.Y.G. Evans CM. Britland

O.F. Bethwaite V. Fort R. HlllB

(fitter

V.M. ralkmr

D.J. Kettle

A* MOBLBPPP Wood

A.A. Griffith

R.F. Anderson

Title, etc

High speed wind tunnel measurements of pressure distribution of an aerofoil of M.;..C.«.23021 section. R.A.E. Report Ko. Aero.1985* Nov.,1944.

Effect of llach and Reynolds numbers on —adauB lift coefficient. N.A.C.A. Technical Note NO. 1044.

March, 1946.

An experimental analysis of the lift of 18 aerof o5.1s- at high speeds. A.R.C.6062. Aug., 1942.

High Speed Wind tunnel tests on the Meteor I. R.A.E. Report No. Aero. 1633* July, 1943.

Aerodynamic characteristics of circular- arc airfoils at high speeds. K.A.C.A. Report li>b* 1930.

Measurements of lift and pitching momcntB at high speedo on an EC.1540 aerofoil with 20$ flap. B.A.E. Report No. Aero. 2042. April, 1945*

Preliminary note on results of High Speed Tunnel tests of 3weptbaok .wings. R.A.E. Tech. Note No. Aero.1775 (revised)

Nov.,1946.

Hnohgeschwindigkeitsmessungen an einem Pfeilflugel. Deutscho Lui'tfahrtforschung. Forschungsbei-icnt Hr.1813.

The effect of sweepback on the aerodynaalo loading of a V wing. A.R.C.7786. June, 1944.

24 ft. Wind tunnel tests on the G.A. T wing tailless glider. Part II. Jressure distribution measure- ments. R.A.E. Report No. Aero. 2147. July, 1946.

Notes on Sweptback wings for high speeds. A.R.C8806 Sept. 1945.

The stalling of Swept Wings. A. R. C. 9357. Dec, 1945.

Determination of the oharaoteristios of tapered wings. N.A.C.A. Report No. 572. 1936.

10.

*

29

30

Author

HlUMD

Fuffert

J.X.G.

feeh. Note No. Awo.1867

g HsTBBHCB (Oontd. )

Title, etc.

Drvlkomponentenaessungen an Pfeilflugeln •it Spreizklappe.Deutsche Luftfahrtforsohung Porschungsbericht Nr.l626

5 Komponente Windtamlmeasungen an gepfeilten Flugeln und an einen R'eilflugel Gesaratmodell No.F.B.1726,

High Speed Tunnel teats on a model sweptbaok wing jet aircraft. B/18A5 (OH 108) (Restricted) R.A.E. Report No*Avi-o.21$9. ^ov., 19V>.

Pro grannie of tunnel tests on sweptbaok wings. R.A.E. Tech. Note No. Aero.1824. Aug.1%6.

i

I

AttWhed*

Appendix Table X Drg. Nos. 19840. S - 19851.S

Distribution t

C.S.(A) iMQ<l), P.D.S.R.U) A.D.A.R.D.(Res)

Mr* Hartshorn Action oopy T/A

A.D.S.ri. (Records) p a D.A.R.D. r P.D.T.D. F/J R.T.P./T.I«B. 200 H D.D.A.R.D. (Serv. ) 8 A.D.R.D.L.1 2 w A.D.R.D.L.2 2 T S.D.D.A.R.D. Supersonic D.C.A.R.D. (Civ.) A.D.R.D. A.C.1 D.D.R.D. (Bsrf.) D.D.R.D. (Airworthi

2 ness)

A.D.R.D.S. A.D.R.D.N. ; • . " • : , '"- *

A & A.K.E. A.R.C. 65 '.'<"

: :

* ; ^ ' ' '• •

(Perf. Sub.-Conn.) SAO " "

1 "":•:. '

Director " '•; 1 :' : >•

D.D.R.A.E. ""' ,. ' ' > •• ii!;: .

Library 1 . ! ' :

3.X. E. ." ^ ' : Oontrolled Weapons

11.

,'*4f;,/-r^'! Ssotw Nbte MO. Aoro.186?

APPENDIX

Aerofoil Notation

N.A.C.A. notation for Conventional Sections

1* Ref. N.A.C.A. Technical Report No.^0.

x, y, z — a,b.

x Maximum camber (5) y Position of maximum camber (1/10 tha) z Haxiaum thickness (#) (2 Fi<:s.) a Leading edge radius index fc Rssition of maximum thickness (tylO ths)

•jLsaai

Values of a, 0 Sharp leading edge 3 V*- normal

6 Normal £ = i.i Vo^tax

9 3 times nonnal.

At 21,09 — 3k 2* camber at W# chord, 9# thick,

at kOjt chord. V4 normal leading edge radius.

2. Ref. N.A.C.A. Technical Report No. 537.

x, y, z.

x —xiaurn camber (£) y position of maximum camber x 2 (jj) (2 Figs.) £ maximum thickness (jg) (2 Figs.)

I 23012 2£ camber at 15fr chord, 12# thick. Those seotions all have their maximum thiokness at JiOji ohoxd.

B. N.A.O.A. Notation for Low Drag Sections

Ref. A.R.C.5427, R.A.E. Technical Note No.Aero. 1019

x,y - - z - - a,fc.

z denotes family to which suction belongs y position of pressure minimum (1/10 ths) z amplitude of optimum w range, measured from design Qi, ( A0 ths) a design CL (V^O ths) b maximum thickness ($>) (2 Figs.)

ei 66 - 216 6 family, peak suction at 60)J chord.

lift range (optimum) = 0.2 Design C. 0.2 - l6jt thick In the original notation z was omitted.

1*

teen. Nbte Mb. Asro.1867

0. British natation tor ham Iran Seotions

J* x.r. / a, b

x BMdBUB thickness ($5) (2 Figs*) y position of max* thickness " a —ad— camber (1/1000 ths) • b position of maximum camh«r "

£i 1240/0640 12$ thick at 40$ chord, 0.6$ camber at 40$ ohord. These numbers may be preceded by combinations of the letters B» C, Q, H. E = elliptic referring to nose shape as far as

position of maximum thickness

0 * cubic ) Q • quartic ) referring, to tail shape H B hyperbolic)

8* Bef. R.A.E. Technical Note No.1306

Tor sections .designed according to the approximate aerofoil theory with velocity distribution of the "roof-top" type* The section is defined as!

2Uj,} a, b, o; 210^1 a1 b1 oll Cj,

2L means that the velocity distribution designed for consists of 2 straight lines

aV excess of velocity at the nose

bV0 maximum velocity at the point X, • •

oVQ excess velocity at the trailing edge

2L means that the distribution of the pressure difference between upper and lover surface divided by ipV0 consists of 2 straight lines*

»1 pressure difference ftt the leading ^

b mwTlmum pressure difference at ppjjt Xi1

*PV02

o1 wessure difference at th0 trailing edge

4PV02

OV value of the low speed lift ooeffioient at ehioh the specified loading is obtained*

13.

toon. Hot. No. A*ro.l867

Wag Motions of American aircraft an whioh the Measurements of Cj, n^ given in Fig.2 have boon

Aircraft Boot Section Up Seotion

CONVENTIONAL SECTIONS

H.A.C.A.U12 N. A. C. A. 23009

N. A. C. A. 2 3009

P-38F (Lightning) F6P-3 (Hellcat)

B-39N (Airacobra)

N.A.C.A»230l6 N.A.C.A. 23015.6

(modified) N.A.C.A*0015

LOW DRAG SECTIONS

N.A.C.A. North American

Compromise 16$ thick

N.A.C.A. North American

Compromise llff thick

F-51B (Mustang)

P-63A (King Cobra) N.A.C.A.66, 2X-116 a a 0.6

N.A.C.A.66, 2X-216 a = 0.6

XB-80A (Snooting Star )

N.A.C.A.65 - 213 N.A.C.A.65 - 213

tt.

••49_]?g40._S. TN.AE9C

FIG. I. cO

1) t n u H _l 2. I Z •

|_ X i

Ul _ III

X 19

/ /

/ y X / X

2k // / /

/ <3 0 O. / _i o 0 X u. k. rt n

111 »- 111

z J- IL

(0 3E

z z

X e« i r » ^

5 <

r M

6 hi

a.

to

u

5 1

£ ^ <n o A

*fc P o s j rs ui "^ 5

5 in ul

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i

t- x 111 ^*r

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FIG. 2

5 j

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I- z ttl o u. IL u O u

r X

1

0-2 0-S 0-4- 0-5 0-6 0-7 OB 0-9

FIG.2 VARIATION OE CL MAX. WITH MACH NUMBER

AMERICAN FLIGHT TESTS (REF. 16)

(WING SECTIONS IN TASUE I) (NOTATION APPENMX l)

»«.-iae«.a__ TN AE90 I6«7

FIG.3

,«LJ5S45.-A-. '.N. kZRO iB6_

FIG. 4.

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FIG5AC5B.

:

FIG. 5 A. POTENTIAL FLOW PRESSURE DISTRIBUTION

AT HIGH INCIDENCE ON A CONVENTIONAL AEROFOIL

to

10

SYMMETRICAL NACA 0012

CONVENTIONAL NACA 23015 . LOW DRAG AEROFOIL,

S (NACA C6-22I5) _21

M

OZ 0-4 06 08 10

FIG.5B. TYPICAL VARIATION OF CL MAX WITH MACH NO

IS845.S TN.AE9C 6£^

FIG6.

NACA 2S0»» NACA 66-2-2lS

-4_

u

u 5 m u ar Q.

.Me«l'73 M> -63 .M*»l-40 CuMAX-|»OB

o<-IO«

O 20 40 60 BO 100 O SO 40 GO BO tOO m.~> , PERCENT CHORD FIG.6

PRESSURE DISTRIBUTION AT MAX.LIFT ON A CONVENTIONAL AND A LOW DRAG AEROFOIL

(FROM REF.IGJ

NS 19846. s

FIG.7

FIG.7 PRESSURE DISTRIBUTION ON UPPER & LOWER SURFACES

AT SEVERAL MACH NUMBERS

AEROFOIL MACA. O OO 12-0 55 50/0-5 * - 6 (REPHObUCEb FROM REF. I \

NO . J3R£bP. T.N. AERO 166"

FIG.8

© 0-93&S

FIG8. SPANWISE LOCAL LIFT CURVES ON A 36! SWEEPBACK WING. (REF. 24)

M° . ...iafl.4ft.--4 T.N. AERO.IB67

FIG.9

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FIG. IO. a

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FIG.II

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N«_.j5ft?I..S__ T.N. AERO 1S6-' FIG.I2.

ru

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AtABl Tme. Effeeta of Knch mobar on r-nHmn lift

FCSO-N. TITUi

OOKKNATWG AGENCY, Bojral Aircraft Botabllflhcant, Farnborough, Hanta TOANSiATtON. ,

C3aPraO»(0fclCS}

Klrk„ F. D.

AUTKOCMS)

QGCSSDCSCO DfVKOM. Aerodynenlco (2) KCTttW. Dings and Airfoilo (6) (BOSS OmOBtCBS, Dings - Lift (99169)| lift - Each

nuriber Of feet (5J*6?t»)} Wings, Saopt-bock - Lift (99306Jt)) Pings - Stalling characteristics (99179)

2076U .AGENCY KU^

Aero-1867

Q2VE38T

COUNTflr Ot.Brit.

lANGUAGf Reotr.

U.&CLASS. OAR (PACES Eoatr. Jan'1*7 I £7

mus. raAruaKJ tablo, grapho

Haeh nunber effect on r»\irirmr> lift is datomlncd for unsuopt end onopt-back Dingo. Suopt-back ulngo oboa tho oarx> early tip stalling tendencies at high spoeds as they do at lea speeds. For unsuopt ningo tha C^ p^g of occtiosa ulth for back poeitioao of coainm thiclmeao Is hlghor than that of conventional sections, because of the further back posi- tion of upper surface shock uavo. At high Had) manors thin alrfcdlfl havs hlghor Cj, naiT than thicker onee.

T-l KO, AQ MATEtSH COttttAKD WJHSHI fCIO, OMEO. USAAF JZ

STRDCTED 20C2ETK®: R-2-4-35

ODPCJO0(g)tC3C!)

Kirk. F. H.

AUTHORS)

IHVB-ON. Aerodynmleo _ S5CTOW, tangs and Airfoila (6) cnOSS tSFEBBJCES. Bingo - lift (99.169)j Lm - Koch

miabar effect (5lȣ9U)t Wings, Soopt-bock - Lift (99506A)i Pings - Stalling charactorlstloa (99179)

AMEQ. Tmfc Effects of Each mcbar on mstoo lift

FOSCN. Tina

03KSWATWG AGB«CY, Royal Aircraft EotabllDhcant, Poraborcmgh, Honto TBANHATIONi coumar Qt.Brlt.

tt. S.CLASS. I DATE IPAGSS Rostr. Jan'U7 I 27

LANGUAGE [ OGG'NJCIA Rastr. tablo, graphs

amnaGS . &xh mxobor offset on nywirmp 31ft ±o determined for unsuopt end ouopt-*ack ulngo.

&7opt-toack uingo ahan tho anm early tip stalling tondancioa at high opoede ae they do at leu opoede. For unsnopt Dingo tho Cj p^ of occtloao uith far back positions of noxirnn thickness Is highor than that of conventional sections, becauso of tho further beck pool-

££ motor «Sf O^f^gbl1 Tcfs^^^ "W®?^ "^ °L«»

T-2, KQ»An MATEita COMMAND l^Yi ECHNICAlUNDJK vimaHt flap, oxa, USAAE

SCP-i , AUTH: DOD DIR 5200.10, 29 June 00 . ""*