Wing-Strake Juncture

. c. 1

NASA Technical Paper 1803

.. I. . - .~ ,. . Experimental " and Analytical .Study. . . ..

of the Longitudin al. Aero-dynamic . ~ , .- Characteristics of Analyticallyand -, -

Configurations at.. -Subcritical Speeds

.. John E. Lamar and ,Neal .T..Frink .~ TECH LIBRARY WFB, NY

NASA TechnicalPaper 1803

Experimentaland Analytical Study of theLongitudinal Aerodynamic Characteristics of Analytically and Empirically Designed Strake- Wing Configurationsat Subcritical Speeds

John E. Lamar and Neal T. Frink Latzgley ResearchCenter Humpton, Virgillia

National Aeronautics and Space Administration

Scientific and Technical Information Branch

1981 SUMMARY

Sixteenanalytically and empirically designed strakes havebeen tested experimentally on a wing-body at three subcritical speeds in such a way as toisolate thestrake-forebody loads from the wing-afterbody loads.Analyti- calestimates for these longitudinal results havebeen made using thesuction analogy and the augmented vortex lift concepts. The comparisons show thatthe pitchdata, both total and components, arebracketed well by the high- andlow- angle-of-attack modelings of thevortex lift theories. The lift dataare generally better estimated by thehigh-angle-of-attack vortex lift theory and then only until maximum lift orstrake-vortex breakdown occurs over the wing. The compressibilityeffects noted in thedata for the strake-forebody lift are explainedtheoretically by a reduction in the wing upwash associated with increasing Machnumber which leadsto smaller potential and vortex lifts on the forward lifting surfaces.

Aerodynamic synergism was investigatedexperimentally; as expected, there wasan additional lift benefit for all configurations as a result of the interaction. Furthermore, there was a delay in pitch-upassociated with the synergism.

Machnumber has a small effect on the"additional lifting surfaceeffi- ciencyfactor" whereas changes in thestrake geometry have largereffects. Geometry changes such asincreasing area orslenderness ratio generally produce a more efficientstrake. However, it is possibleto obtain the larger values of this factor with approximatelyhalf the area of theoriginal, also the largest,gothic strake by using a suitableanalytical design for the gothic leading edge. These resultscorrelate well with strake-vortex-breakdown observations in the water tunnel.

Strake geometry is also important in determiningthe maximum lift that a configuration will develop, with gothic leading-edgeshaping being preferred forratios of strakearea to wing referencearea of less than 0.25 based on the strakesconsidered herein.

INTRODUCTION

Strake-wing aerodynamics are becomingof increasinginterest due tothe mutual benefitsderived from the combination.(See ref. 1.) For the wing, thesebenefits include: (1) minimal interferenceat or below thecruise1 angle of attack, (2) upper-surface boundary-layer control at moderate to high angle

lIn particular, at cruise it is possiblethat the small impact of the strake may only be attainable by the use ofcamber or dihedral so as to "unload" thestrake under this condition.Neither oneof these is addressed in this paper,as only planar strakes are considered. of attack due to the strake vortex, (3) load redistribution due to effective useof the upper surface, and (4) reduced area required for maneuver loads. For the strake, thesebenefits are: (1) strake vortexstrengthened by upwash from the mainwing and (2) the need foronly a small area - hence, wetted area andcomparatively lightweight structure - to generate its significant contribution to the total lift becausethe strake provideslarge amounts of vortex lift.

Inview of these strake benefits, it is appropriate to consider how best to maximizethem by propershaping of the strake. One way would be to use an empiricalapproach based on previousknowledge, a second would be cut-and-try, a third would be analytical, and a fourth would be a combination of thepreced- ingthree. At the time ofdevelopment of the lightweightfighters F-16 and YF-17, onlythe first two procedures were available.After these airplanes were developed,reports were written,references 2 and 3, whichsummarized the wind-tunnel test results of about 100 different strakes foreach airplane, along with an analysis to helpguide future strake-wing integrations. However, thesereports still do notgive the aerodynamicist an analytical method for shapingthe strake leadingedge. One possible approachwould be to isolate some critical parameter,such as leading-edgesuction, and then design the strake inthe presence of the wing while monitoring this parameter.

As a stepin this direction, a simplerapproach with the emphasis on delayingstrake-vortex breakdown has been developed and reported inreference 4. There the shape of the isolated strake is determineduniquely in a flow which is simpler but related to thethree-dimensional potential by specifyingprimarily the leading-edgesuction distribution. Reference 4 reports the firstdesign application of this method in which the resulting shape was area scaled untilthe three-dimensional suction distribution over boththe strake and the wing was considered to be acceptable. Thewind- tunnel test of the strake-wingcombination showed it to perform well. How- ever, to determineif this method could be used to develop better strakes, it was applied to the developmentof over 200 configurations. Only 24 were consideredsuitable, or interesting enough, forfurther evaluation. These, alongwith 19 empiricallydesigned strakes mountedon the same wing-body, were tested, in a cooperativeprogram with the authors, in the Northrop 16- by 24-Inch Diagnostic Water Tunnel. From the results reported inreferences 5 and 6, only 16 strake-wingconfigurations, 7 analyticallydesigned and 9 empiricallydesigned, were considered of sufficient interest to be tested on a similar wing-body in a wind tunnel.These tests, like those in water, were to be done at zerosideslip because of the large test matrixinvolved. It is recognizedthat the effects of sideslip and leading-and trailing-edge flaps are important with regard to vortex breakdownand theresulting amount of usefullift attainable; however,these effects are beyond the scope ofthe presentstudy. This report documents the wind-tunnel results and presentsthe analytical estimates forboth the complete configurations and thecomponents using the method described inreferences 1, 4, and 7.

Use of trade names or names ofmanufacturers in this report does not constitute an officialendorsement of such products or manufacturers,either expressed or implied, by the NationalAeronautics andSpace Administration. SYMBOLS AND ABBREVIATIONS

Dimensionalquantities are given in both SI Units and U.S. CustomaryUnits. Measurementsand calculations were made in U.S. CustomaryUnits.

AD analyticallydesigned b span (b, = 50.8 cm (20 in.))

C constantpressure specification in strake design

Drag CD coefficient,drag - qSref cD,O experimentalvalue of drag coefficient at CL = 0

Lift CL liftcoefficient, - Gref

CL,maxmaximum valueof CL,tot

Cm pitching-momentcoefficient about 56.99 percent body lengthstation, Pitch ingmomen t qgrefcref

kP lifting pressure coefficient

CS leading-edgesuction-force coefficient, Kv, sin2le

Leading-edgethrust CT leading-edgethrust-force coefficient, %$ref

C chord, cm (in. ) - - C characteristiclength used determinationin of KVISe, cm (in.)

Crefreference chord, 23.33 cm (9.185 in.)

Section suction force CS sectionsuction-force coefficient, LC dFS differentialleading-edge suction force (see sketch D) dZ differentialleading-edge length

ED empiricallydesigned

3 f additional lifting surface efficiency factor,

a (Normal force/q,Sref) po tentia l lift factor,potential lift (KP in table IV) KP a(sin a cos a)

KV vortex lift factor (KV in table IV)

Kv, le leading-edgevortex lift factor,

1 a(IS.F-I le,left + Is-F-I Ie,right)~ " (KV LE in table IV) qmSre f a sin2 a

Kv ,se side-edgevortex lift factor,

(KV SE in table IV)

KV,Z augmented vortex lift factor, (Kv, le/2) c (see appendix A)

1 distancealong leading edgefrom apex, cm (in. )

M free-stream Machnumber

P polynomial pressure specification in strakedesign qco free-stream dynamic pressure, N/m2 (lb/ft2)

Ra ratio of exposed strakearea to wing referencearea, Ss/Sref

Rb exposed semispan ratio, [(b/2)s/(b/2)w]exp

RS strakeslenderness ratio, (Length/Semispan)e,p r radius of curvature, cm (in.)

S area

Sref reference wing area, 0.1032 m2 (1.1109 ft2)

S.F. potential-flowsuction force

CSC S - a2(b/2)

U free-streamvelocity, m/sec (ft/sec)

4 ~ .. . ._......

sum ofinduced downwash and Ua at a = 1 rad, m/sec (ft/sec)

averagevalue of wnet, m/sec (f t/sec)

local coordinatesdefining strake planform, cm (in.) (see 'table 111)

locationof centroid of particular loading, cm (in.)

locationof reference point from nose of model, 54.832 cm (21.587 in.) (X SUB REF in table IV) - = xref - xc,i, cm (in.) (i standsfor subscripts p, le, se, and se)

angle of attack, deg (ALPHA intable IV)

equivalentcirculation associated with leading-edge suction, m2/sec (ft2/sec)

averagevalue of r (11, m2/sec (ft2/sec)

fractionof exposed strake semispan

leading-edgesweep angle, deg

densityof fluid, kg/m3 (slugs/ft3)

three-dimensional

Subscripts :

BD-TE strake vortex breakdown at wing trailing edge in water tunnel

e XP exposed

inb'd inboard

le leadingedge max maximum

outb' d outboard

P potential

r root

S strake

se sideedge - se augmented sideedge

5 swb strake-wing-bodyconfiguration

tot total configuration

vz e vortexeffect due to leadingedge

vsevortex effect due to side edge - vsevortex effect due to augmented term

W wing

wb bodywing

MODEL DESCRIPTION AND TESTCONDITIONS

The model was composed of a basicwing-fuselage onto which were mounted anyof 16 pairsof strakes; theresulting configuration was testedin the LangleyHigh-speed 7- by 1 0-FootTunnel. Individual descriptions of the various modelcomponents follow.

Basic Wing-Body

The basic wing-body usedin this test is shown infigure 1. Themodel featuresforebody and afterbody components separated by a metric breakfor multiple componentaerodynamic testing. Total loads were measured by the main balance located inthe aft fuselage while strake-forebody loads were measured by theforebody balance attached to, butahead of, the metric break. Because a few strakes were verylong, wings had to be mountedon the aft fuselage in an aftposition for those runs. (See tables I and I1 forappropriate wing position and parametricdescriptions of the strakes.) The aft wing position was 4.39 cm (1.73 in.) rearward ofthe more commonly usedforward wing position which is shown in figure 1 .

Thewing hasan untwisted, 44O swepttrapezoidal planform with reference aspect ratio, taper ratio, and area of 2.5, 0.2, and 0.1032 m2 (1.1109 ft2), respectively. Its airfoil sections are symmetrical,uncambered, and biconvex andvary linearly in maximum thicknessfrom 6 percentof chord at the wing- fuselagejuncture to 4 percent at thetip. The precedingfeatures are based on thereference wingwhich includes area betweenthe leading and trailing edgesprojected to the model centerline. The moment referencepoint is defined as the longitudinal position of the quarter-chord point of the wing at thewing-fuselage juncture when the wing is mounted inthe forward position and corresponds to 56.99 percentof the body length.

Body and strake wipers were installed to preventflow through the metric breakbetween the two partsof the fuselage and the strake andwing. These wipersconsisted of thin-gage steel tack welded to the lower surfaceof the

6 strake andMylar2 glued around the forebody so as to transmit essentially no loadfrom one component to theother. (See ref. 7. ) Figure 2 shows a photographof a typical modelwith wipers on.

No. 120 carborundum grit was applied to theforebody in a ring 2.54 cm (1 in.)aft of the nose. This same sizegrit was also applied 2.54 cm (1 in.) aftof the leading edges of the strake andwing on boththe top andbottom surf aces.

Strakes

Figure 3 shows the strake planformsinitially tested in the water tunnel (ref.5), along with the prescribed suction distributions used to generatetheir shapes andwhether constant pressure specification C or polynomialpressure specification P was employed.The 16 strakes selectedfor the present wind- tunnel tests are delineated by shadingin figure 3. Intable 111, theplanform perimetersof the 16 strakes are defined. The groupsidentified refer to either thebasic shapes that resulted from the analytical studies - reflexive and gothic - or those strakes which were variationsof the AD 24 strake and were thereforedesignated "empirically designed."

All strakes were constructedof 0.318 cm (0.125in.) flat plate steel with theedges nominally beveled to a sharpedge. The strakes were attached to the forebodyahead of the metric breakthrough the use of small body slots and minimalexternal brackets. (It shouldbe mentioned that thestrake-body was testedalone with nowing to aidin the assessment of lift and pitching-moment synergisticeffects.) Figure 4 shows a photographof some ofthe strakes.

Analytically Designed Strakes

There are seven strakes inthe analytically designed group, andthey are designated by an AD prefix. One (AD 24) is theoriginal strake, tm others (AD 22 and AD 23) are different area scalingsof the AD 24 strake, and the remainder are composed ofthree gothic strakes (AD 14, AD 17, and AD 19) and one reflexivestrake (AD 9). Note thatthe reflexive stake AD 9 (fig.3(a)) has the same prescribed s-rl distribution as does the gothic strake AD 19 (fig. 3 (b)) ; theprimary difference in their design is due to thediffering pressure specification. For additional details ofthese analytically designed strakes, see table I andreference 5.

EmpiricallyDesigned Strakes

The nine strakes inthe empically designed group are designated by an ED prefix and are categorized by eitherbeing scaled (ED 12 and ED 13) or cut (ED 2, ED 4, ED 5, ED 6, ED 9, ED 10, and ED 11). The scaled strakes havetheir chords scaled to either 70 or 30 percent of the AD 24 strake. The cut series

'Mylar: Registeredtrademark of E. I. duPont de Nemours & Co., Inc.

7 are trimmed versionsof the AD 24 strake having area removed alongthe apex, trailing-edge, or inboard-edge regions. However the strake is altered, it alwaysabuts the fuselage and wing simultaneously. See table I1 andreference 5 for additional details.

TestConditions and Corrections

The tests were conductedin the Langley High-speed 7- by 10-FootTunnel at Mach numbers of 0.2, 0.5, and0.7 and atmospheric conditions. These Mach numberscorrespond to Reynoldsnumbers, based on cref, of 1 .08 x lo6, 2.39 x lo6, and2.87 x lo6, respectively. Themodel was mountedon thehigh- angle-of-attacksting support system shown in figure 5 and was tested only at zerosideslip. The angleof attack variedfrom approximately -2O to approximately 530.

Blockageand jet-boundary corrections have been applied to thedata, and theangle of attack usedherein has been corrected for stingdeflection. All dragmeasurements have been corrected to a conditionof free-stream static pres- surein the balance chambers and on the forebody base. For the main balance, thiscorrection was applied to the chamber onlysince the model base was feathered.

RESULTS AND DISCUSSION

Resultsfrom the wind-tunnel tests at thethree test Mach numbers are pre- sentedherein with an analysis of thevarious geometrical effects; the test results are comparedwith theoretical estimates, where appropriate. The theoretical methodused is detailed to show how thedifferent aerodynamic components are treatedin each angle-of-attack range. Aerodynamic synergism is discussed for both lift and pitching moment, alongwith the effectsof Mach number and strake geometryon the "additional lifting surface efficiency factor." The latter is a measureof how efficientthe strake-wing-body synergism is in relation to simplyincreasing the wing area by anamount equal to thatof the strake.

Basic Data Presentation

The basiclongitudinal data are presentedin figures 6 to 8.In these figuresthe effects of Machnumber on theaerodynamic loads are givenfor the completeconfiguration (fig. 6) and forthe wing-afterbcdy and strake-forebody components (figs. 7 and8, respectively).

Effect of MachNumber on Total Longitudinal Characteristics

Figures6(a) to 6(p)present the total-model longitudinalaerodynamic characteristics at Mach numbers of 0.2, 0.5, and0.7. For each of these three Mach numbers, the difference in maximum angle of attack was due to the model

8 reachingthe support system or balance limits, or encountering severe buffeting at differentvalues in the pitch run. Increasing Mach number hasthe expected effect of increasing CL,tot, although by a small amount, at the lower values of a, as well as providing a slightincrease in the longitudinal stability below CL,max. Forshorthand notation, all strake-wingconfigurations will henceforth be denoted by the strake designation. Some of thestrake-wing configurations, AD 9, AD 14, AD 17, AD 22, AD 23, AD 24, ED 9, and ED 11, exhibit a slightincrease in the value of CL,~~~withincreasing Mach number. A discussion of CL,max is presentedin more detail inthe section "Synergistic Effects." All butthe smallest configurations (Ra - 0.1) , AD 22, ED 4, ED 6, and ED 13, developpitch-up at thehigher values of C~,t~tand M = 0.2 becausethe strakes generate a significant portion of the total lift once the strake-vortex breakdownhas progressed ahead of the wing-strake juncture. For the test Mach number range,the drag-coefficient results show nostrong effect of compressibilityon CD,~;thus, there is little differencein CD with changing Mach numberup to near CL,~~~.The data themselvesvary as CD,~+ CL tan a.

Effect of MachNumber on Component Longitudinal Characteristics

Figures7(a) to 7(p)and 8(a) to 8(p) show theeffects of Mach number on thewing-afterbody and the strake-forebody longitudinal aerodynamic characteristics, respectively.There, CD and Cm are plottedagainst C~,t~tso that the contributions to the total model, shown in figure 6, canbe isolated andpresented in a similar format.In the discussion of figure 6 it was noted that CL forthe total configurationincreased with M at a fixedangle of attack. From figure 7 thewing-afterbody is seen to behave in the same manner as the total configuration;whereas, from figure 8 the strake-forebody shows a reductionin lift with increasing Mach number. It is somewhat surprising that thestrake-forebody lift coefficient should fall off with increasing Mach number sincethese 16 strake components are low-aspect-ratio liftingsurfaces andhence should exhibit very little sensitivity to changesin Mach number. Evidentlythe cause for the reductionin CL is the decrease in wingupwash associated withthe increasing subsonic Mach number, as reported in reference 1. This is discussedin more detail later. However, it is notsurpris- ingthat the increase in CL,max, whichoccurs for some strake-wing-bodycon- figurations at M = 0.5, showsup onthe wing-afterbody graphs since the wing is a moderate-aspect-ratio lifting surface and therefore Mach number sensitive. Due to model and/orbalance limitations, CL,max was notreached at M = 0.7. Lastly,the pitch-up reported previously for certainconfigurations results fromthe pitch-down tendency of thewing-afterbody at highervalues of or CL,tot beingexceeded by thepitch-up tendency of the strake-forebody. This hasbeen alluded to already.Configurations of this type withvortex breakdown on the lee side wouldneed to employ a low tail for stability andcontrol.

1 The analyticalestimation of the Mach effect onthe longitudinal aerodynamic characteristics is takenup later for both a complete configurationand its components.

9 Theoretical Results

Thissection contains a description of the manner in whichthe strake- forebcdyand the wing-afterbody were theoretically modeledusing the suction analogy. Also, comparisons are made betweenanalytical estimates and data results forboth total andcomponent aerodynamic loads.

Modeling Method

The suctionanalogy has been used successfully to estimate thevortex- flowcontributions to lift, drag, and pitching moment associated withthe potential-flowedge force (i.e., unaugmented terms) fordelta andrectangular wings. However, forconfigurations in whichforward-shed vorticity passes over theaft part of the configuration, another contribution to vortex lift can arise (ref. 8). It is designated "augmented vortexlift" in reference 9, and its basic derivation is repeatedin appendix A ofthe present paper for com- pleteness.These two separatetypes ofvortex lift (ref. 7) are illustrated insketch A for a strake-wingconfiguration.

VORTEX LATTICE - SUCTION ANALOGY \ FORCES,EDGE Ys\

REPRESENTED BY

Sketch A.- Basic theoreticalapproach.

References 4 and 7 pointout that, depending on the range of a, there are two different flow-field models which are appropriate for a strake-wing

10 configuration. These two models (ref. 7), shown insketch B, are determined fromoil-flow and water-vapor photographs in the Langley wind tunnel and from dyestudies in the Northrop water tunnel.Sketch B shows that at low angles

LOW a HIGH a

FLOW 1

Sketch B.- Theoretical vortex lift model for strake wing. of attack the strake andwing leading-edge vortices were individually dis- tinguishableover the wing.However, at highangles of attack the wing surface flowpattern evidenced one region of spanwisevortex flow. Althoughthe high- angle-of-attack flow patterns might be interpreted as strake- andwing-vortex coalescence,additional observations revealed the presence of the unburst wing leading-edgevortex core in addition to the strake core at thehigh values of CY. Theseobservations suggest that the wing vortex had not coalesced withthe strake vortex but merely hadbeen displaced away from the wingupper surface by the strake vortex,thus allowing the strake vortex to dominatethe surface flowpatterns. Accordingly, the vortex lift effects due to the wingleading- edgeand side-edge vortices may be decreased at highangles of attack because oftheir vertical displacement.

Putting all thepreceding concepts together leads to thegeneralized forms of theequations for CL, CD, and Cm associatedwith the following suction analogy.These equations contain the direct and augmented vortex lift terms and are explicitly

11 cD = cDI0 + cL tan c1 = cDI0+ K~ sin2 a cos a + (K~,~~+ K~,~~ + K~,;) sin3 a

- where theparticular - x-terms equal xref - xc,i with i standingfor p,le, se, or se. It is realizedthat each of the terms in equations (1) may be €or a single planformor be representative of combinational terms of the same type forthe strake-wing configuration. The values of Kv,le and KVISe areeasily obtainable €oreach planform by appropriate use of computer codes, - such asthe vortex-lattice method described in reference 10. However, the KVIse terms requireattention as totheir computation(appendix A), origin, and angle- of-attack range of validity.

From sketch C it canbe seen that at low angles of attack where thevortex is small,the negative augmentation factorassociated with the swept-back

LOLY ANGLE OF ATTACKHIGHANGLE OF ATTACK

I VORTEX LI FT GAINED HERE BYYJING DUE TO AUGMENTATION VORTEX LIFT HERE MAY BE DECREASED DUETO VERT1 CAL Dl SPLACEMENT VORTEX LIFTGAINED HERE BY WING

Sketch C.- Theoreticalvortex lift parameters€or strake wing. trailing edge of thestrake (ref. 9) will be negligible and is therefore taken to be zero in the computation. Augmented effects will occur on the wing due toboth the wing and strake vortices andmay be expressed as

12 (Kv,2e)w - (Kv, le)s + (Kv,se)s - (KV,Z)W = Coutb'd,w + Cinb'd,w 1W 1s

M where ZW is the-length of the exposed wing leadingedge, C0uf-b Id, is the tip chord,and Cinb'd,w is the wing chord at thestrake-wing juncture. (See sketch C.) At highangles of attack, vortex lift will be lost by the strake due to thetrailing-edge notch as would occur foran isolated strake. However, this vortex lift will not be lost to theconfiguration; it will berecovered by the wing as partof the augmented-vortex-lift effect due to the strake vortex. To approximatethe length which the strake vortexpersists over the wing, the chord at thewing-fuselage juncture was chosen. The augmented effects at high angles of attack may beexpressed as

and

Because vortex lift associatedwith the wing leading-edgeand side-edge vortices may bedecreased due to theaforementioned vertical displacement effects, it may be assumed that

as a limiting case for highangle of attack.

The precedingthen is the methodused to make the theoretical estimates of CL,CD, and C, forthe strake-forebody, the wing-afterbody, - and the total configuration.For reference, the values of Kp, Kv, and x are summarized forboth high-angle-of-attack andlow-angle-of-attack solutions in table IV for all configurations at M = 0.2, in table V forthe AD 19 configuration at M = 0.2, 0.5, and 0.7, and in table VI forthe basic wing-body (bothforward and aft wing positions) at M = 0.2, 0.5, and 0.7.

13 ComparisonWith Data at M = 0.2

Completeconfiguration.- Figures 9(a) to 9(p)present high-angle-of-attack andlow-angle-of-attack vortex lift estimates, alongwith data forthe longitudinal aerodynamiccharacteristics of completeconfigurations at M = 0.2. A comparisonfor CD shows that up to CL,max or vortex breakdown, thehigh angle-of-attackvortex lift theory(including CD,o) yieldsthe better agreement withthe CL and CD data.Within this range of c1, the CL datain some cases exceedsthe high-angle-of-attack theory. This indicates that the wing may becontributing some vortex lift to the total, and,therefore, all ofthe assumptionsfor the high-angle-of-attack theory are notrealized. Above this range of o! neithertheory appropriately models the flow. It is also seenthat the two theoriesgenerally bracket the Cm data,again up to CL,max or vortex breakdown. The abilityof the theories to do this is encouragingin that they are able to estimate collectivelythe general nonlinear Cm versus CL,tot characteristicsfor this class ofconfiguration. It can be notedthat the low- angle-of-attackvortex lift theory may, ingeneral, estimate betterthe C, resultsthan those obtained with the high-angle-of-attack theory (fig. 9 (m) , forexample). This occurs becausethe law-angle-of-attack theory produces a loadcenter farther aft at a particularvalue of C~,t~teven though thisvalue is largerthan the data at the same angleof attack.

The potential-flowcurve is added to the CL,tot versus c1 plotsfor reference. It is interesting to notethat for the configurations with the smaller valuesof Ra, inparticular AD 22, ED 4, and ED 13, the CL,tot data at thehigher angles of attack tend to followthe CL,~curve even though the flawthere is nothing like potential.

Components .- Thewing-af terbody and strake-forebody longitudinal aerodynamic data and thehigh-angle-of-attack and low-angle-of-attack estimates at M = 0.2 are givenin figures 10 (a) to 10 (p) . Just as forthe complete configuration,the individual data components are generally we11 estimated by the high-angle-of-attacktheory or a collectivecombination of theories up to CL,max or large-scalevortex breakdown. What is particularlyuseful is that theindividual Cm components are tightlybracketed by thehigh-angle-of-attack andlow-angle-of-attack vortex lifttheories. The CL data forthe strake- forebody are, ingeneral, reasonably well estimated by the two closelyspaced theories until the strake vortexbegins to break down on the strake at the highervalues of c1. The spacingbetween the two theories is largerfor the wing-afterbody,with the data tending to be generallyon or abovethe estimates from thehigh-angle-of-attack theory. This continues until the strake vortex begins to break down aheadof the wing trailingedge. From thesefigures it is seenthat, in general, those configurations whichhave thehigher values of Rb, i.e., AD 24, ED 4, ED 5, ED 6, ED 12,and ED 13,have their aerodynamic components better estimated by thehigh-angle-of-attack theory than do the others. A reasoncould be thatthe larger strake span is better modeled by thistheory since it may provideproportionately more area for a givenlength, which in turn enables the strake vortex to act more completelyon the strake and noton the fuselage. (See ref. 7.) Lastly,note that at thehigher angles of attack thewing-afterbody lift variations follow the potential curves even thoughthe flow is closer to a Helmhotz type.

14 Effect of MachNumber on the AD 19 Configuration

Figures 11 (a) and11 (b) present for the AD 19strake-wing-body a comparison of the effect of increasing Mach number onthe total andcomponent lift andpitching-moment characteristicsfor the high-angle-of-attack vortex lift theoryand data as taken from figures 6 (a), 7 (a), and 8 (a). Onlyone configuration was chosenwith which to performthis study since, for the limited Mach range, no large differences in compressibility effects were expected to existfor these models. A comparisonof the theory with data (fig. ll(a)) indicates at low angleof attack thatboth have the same trends for CL and Cm, though a differentmagnitude of change with increasing Mach number.For 01 > 16O, the CL estimates havean opposite trend with increasing Mach number thando data because the vortex lift contributions are decreas- ingfaster than the potential lift terms increase.(See table V and the Kp and Kv usagein equation (1 a) .) These two trends are delineatedin the com- ponentcharacteristics shown infigure 11 (b) . Therethe falloff in strake- forebody CL is seen to belarger than the increase in wing-afterbody CL with Mach number overthe upper range of Cy. The comparisondoes confirm that the wingupwash is decreasing its effect on the strake as postulatedpreviously becausethe changes that take placein the wing interference are automatically accountedfor by the theoryusing the Prandtl-Glauert rule for compressibility, i.e., theequivalent wing inincompressible flow being stretched longitudinally.

Effect of MachNumber on Basic Wing-Body Configuration

Figures12 (a) and 12(b) show the effect of Mach number onthe longitudinal datafor the basic wing-body configurationwith the wing in the fore and aft positions,respectively. Because ofearly vortex breakdownon the wing-body, thedata will notlikely demonstrate vortex lift and,therefore, may be approxi- mated by potentialtheory though the flow is notpotential. Even thisapproxi- mation is seennot to beespecially good for a > 17O. Thesedata certainly point up theneed for a flowcontrol device, such as a strake, which is able to organizethe wing flowfield from o! = 8O up to c1 = 30°. Figure12 also shows thatthe compressibility effects are ofthe same magnitudefor the wing ineither position, as wouldbe expected. These wing-body data and theoretical estimates are usedin the subsequent section "Strake Efficiency."

Synergistic Effects

The favorableinterference often produced by placementof two (or more) lifting surfaces in close proximity so thatthe aerodynamic results measured exceedthe sum ofthe individual components tested separately is oft-times referred to as a synergisticeffect. Plots of lift synergism are oftenused (see, forexample, ref. 1 ) sincethey provide a convenient way ofdisplaying oneof the principal benefits of strake-wing aerodynamics. Figures 13 (a) to 13(p)present the lift synergism for the configurations reported herein. Lift synergism is determinedusing the lift-coefficient results obtained from three sources. (These threesources are indicated,for example, by thethree curves of fig.13(a).) The first is the total liftcoefficient of the wingand body (short-dashcurve). The second is thelift coefficient for the wing-afterbody

15 obtainedin the presence of the forebody and then added to thestrake-forebody lift coefficient measured inthe presence of theafterbody (long-dash curve). The third is the total lift coefficient for thestrake-wing-body configuration (solid curve) . A comparisonof the first andsecond sources yields the direct area effectof adding the strake, whilecomparing the secondand third sources providesthe effect of aerodynamic synergism. (See fig. 13 (a) .)

Sincelift-synergism plots haveproven to bevaluable, figures 14 (a) to 14(p) havebeen prepared inorder to determinethe useful information that may be discerned from pitching-momentsynergism. (Their construction is similar to the lift synergism.) Both kindsof synergism plots were generated by data interpolation, and they are discussedin this section.

Lift

From figures 13 (a) to 13 (p) it is clear for all the strakes tested in combinationwith a wing-body thatfavorable interference was experiencedfor a > 13O. The extentof the maximum synergisticeffect, defined as thedif- ferencebetween the upper two curvesdivided by the middle curve times 100 percent,varied between configurations from a highof 53 percentfor the ED 5 strake to a low of 21 percentfor the AD 22 strake. The averagevalue for these maximum effects is around 42 percent:and for a fixed strake shape, AD 22 through AD 24, theeffect increases with increasing Ra. The maximum synergism effectgenerally occurs quite close to thevalue of a associated with CL,max forthe complete configuration.This value of ct is less thanthat for CL,~~~ ofthe components added togetherand, hence, points up anotheruseful feature ofthe aerodynamic synergism, i.e., a larger CL,max and thatoccurring at a lower a.

After CL,max hasbeen reached for the upper and middle curvesof figures 13 (a) to 13 (p) , thelift coefficient CL tends to fall off more rapidly forthe synergistic combination (upper curve) than when the component lift coefficients are addedtogether (middle curve).This falloff trend €or the middlecurve is most likelyassociated with its wing-afterbodycomponent in that this componentnever has available to it thebenefit of the strake forward-shed vorticity. Hence, when thestrake-vortex effect is curtailed at thehigher anglesof attack on thesynergistic combination, the reduction in wing-afterbody lift coefficient is much more severe.

Pitching Moment

By studyingthe pitching-moment synergistic plots, the data fromfig- ures 14 (a) to 14 (p) show that, apart from the expected lift-coeff icient range extension,there are two generalconclusions regarding longitudinal stability which result. They are discussedin order of theiroccurrence with increasing synergistic CL. First, from low to moderate CL, thestability is unchanged or slightlyreduced by synergism;second, from moderate CL to CL,max, synergism causes a delayin pitch-up onset. The precedingconclusions are a result ofthe interference effects keeping the total load centroidin about the

16 same locationduring most ofthe CL rangeand then permitting the load center to move forward as CL,max is approached.This forward movement is associated withthe wingupwash onthe strake vortexcausing the strake to generate a largerfraction of the total lift at thehigher angles of attack as thesynergistic sum decreases.(See figs. 10 (a) and 13(a) as examples.)The CL,max occurs when the strake vortexbreaks down inthe vicinity of the strake-wing juncture (ref. 11). (Seeappendix B foradditional discussion.) Thereafter, depending on the strake shape,the vortex breakdown point moves forwardon the strake at a rate which may keep CL near CL,max andthereby accentuate the positive moment generationtendency of the configuration.

Strake Efficiency

Oneway to assess strake efficiencywith regard to maneuver capability is to compare the increase in lift obtained with the strake inplace with what wouldhave been expected by enlargingthe wing area by anequal amount. In equationform, this can be quantified by theparameter f

(cL, tot)swb ( sref (cL, tot) swb

Total CL includingaerodynamic synergism - Scaled CL withincreased area which is giventhe name "additionallifting surface efficiencyfactor" in reference 7 where it was firstpresented. The conditionof f > 1 will exist when theincremented increase in CL associatedwith adding the area inthe formof a strake exceedsthe direct effect of thatproduced by increasingthe basic wing area. The satisfaction of thiscondition means that, from a liftproduction standpoint,adding strake area is more efficientthan just increasing wing area. Furthermore, with respect to weight, the low-aspect-ratioshape of the strake leads to a lighterweight structure (with lower gustresponse) than for the simplyenlarged wing. Although this additional wing area would lead to an increasein span and therefore cruise lift-drag ratio, it cannotbe done without an inherentweight penalty.

Figure 15 shows the manner in which f is presented andcompares repre- sentativedata (AD 19) withtheory. The theory uses thehigh-angle-of-attack vortexlift theory for the strake-wing configuration (fig. 9(d)) and potential theoryfor the wing-body (fig. 12 (a)) sinceeach best approximates its respec- tivedata. Figure 15 shows that above c1 = 14O thetheoretical andexperi- mentalvalues of f exceedunity because of the synergistic vortex lift being generatedon the configuration. This figure also shows thatfor 17O <, 12 40° theexperimental results producevalues of f greaterthan predicted by the theory.This increase is due to the loss of lifteffectiveness on the wing associatedwith its own leading-edgevortex breakdown and large-scale stall. Ifthe usual leading-edge flow control devices were applied to thewing, thedifference between the two f curves would beexpected to diminish

17 considerably.This experimental increase in f canbe traced to figure12(a) where, inparticular for M = 0.2, (C~,tot)wb departsfrom the potential theory at a = 17O. As a furthernote, it canbe seen by comparingfigure 15 withfigure 9 (d) thatthe maximum or peak valueof f occurs at the same angle of attack as the maximum (C~,t~t)swb,as would be anticipated. Thesecond peak in f versus a, which occurs at a = 44O, resultsfrm the sudden post-stall loss of measurable lift on the wing-body, (CL,tot)wb, at M = 0.2. (See figs.12(a) and 12(b).)

Mach number effects on f foreach strake-wing combination are discussed next,followed by a comparisonof f forvarious combinations at M = 0.2 which highlightthe various geometrical effects over the range of a tested. For the complete configuration, CL,max is discussed more fully at the end of this section.

Effect of Mach Number

Though therange of a is not as extensivefor M = 0.5 and M = 0.7 as at M = 0.2 infigures 16 (a) to 16 (p) , there is enoughrange to establish two generalconsequences of increasing Mach number on the plots of f versus a: (1) f increasesnear the largest test valueof a and (2) f decreasesnear c1 = 6O. Thus, at thehigher angles of attack, theeffect of compressibility is to producelarger lifts on thestrake-wing-body, and, conversely, at lower anglesof attack the effect is largeron the wing-body.

An explanation may be that at lower anglesof attack withthe wing-body being more Mach number dependentthan the more slenderstrake-wing-body, and withvortex flow not yet dominating the aerodynamic characteristics, the denom- inatorof f, given in equation (6),

increasinglyexceeds its numerator

(cL, tot) swb therebyproducing these smaller valueswith increasing Mach number.However, at thehigher angles of attack thevortex flows dominate, with their effects beinglarger on the strake-wing-body (the mre slenderconfiguration) than on the wing-body.The (CL,tot)swb dataindicate that near a = 16O theeffect of Mach number is small, due in part to theconfiguration slenderness but also due to theunchanging type of flowfield since, for the latter, thevortex systems do notgenerally break down overthe wing until a largerangle of attack is reached.Although true of thestrake-wing-body, this is not true forthe wing-body inthat (CL, tot)wb fallsoff with increasing Mach number at c1 = 160 becausethe leading-edge vortex has already undergone breakdown at a lower value of a. The post breakdown (CL, tot) wb characteristicsindicate a reversing

18 influenceof increasing M and a to theextent that at a = 16O an inverse Mach number effect is seen. (Seefigs. 12 (a) and12 (b) .)

Effect of Strake Geometry

Thissection examines the effect of strake geometry on f versus 01 by concentratingon the various geometrical features that can be totally or par- tiallyisolated. Among them are (1) area effectfor a fixedleading-edge shape, (2) area and slendernesscombination associated with simple chordwisescaling, (3)fixed area butwith differing shapes, (4) shapeeffect for a fixed semispan,and (5) others which includethe empirically designed series andthe indirecteffect of pressure specification, i.e., special strake shapes.For additionalinsight into theseeffects, corresponding strake-vortex breakdown angledata from the Northrop water tunnel is also discussed.

, Area effect.-Figure 17 shows theeffect of area scalingfor a fixed strake shape,and therefore slenderness Rs = 7.00, by usingthe AD 22, AD 23, and AD 24 strake series. Threeeffects of increasing area are notedfrom this figure: (1) increasingfmax with Ra, (2) increasing a required to reach f = 1 withincreasing Ra, and(3) the a at which thefirst f "hump" occurs increaseswith Ra. The first effect is simplyassociated with the larger strake developingthe higher values of (CL,tot)swb. The secondeffect is associatedwith the increasing downwash being imposedon the wingby the strakes oflarger area, hencesemispan, thereby requiring the configuration to reach a highervalue of 01 before f becomes largerthan unity. The third effect is due to thelarger values of (CL,tot) swb occurring at largervalues of a, withboth being proportional to the Ra increase.Additional pertinent informationhas already been given in the section on lift synergism and the generaldiscussion of strake efficiency. Both pertain to thethird effect, hence it will not be discussedfurther for any of the other geometrical variations.

The ~BD-TE results fromthe water tunnel(ref. 6) followthe same trend with Ra asdoes fmax.

Chordwisesca1inq.- Figure 18 shows the AD 24, ED 12,and ED 13config- urations, all withthe same valueof Rb = 0.297 but eachhaving a different fractionof the AD 24 chordvariation. There are two major geometricalvaria- tionshere: increasing area and slenderness ratio. Togetherthey yield (1)increasing fmax and (2) increasing a required to reach f = 1.The impactof these geometrical features has been noted previously, particularly forthe first item. The second item is caused by thelarger area producing an additionally imposed downwash onthe wing.

These CLBD-~results also followthe same trendwith Ra as doesfmax (ref. 6).

Fixed area.- Figures19(a) to 19(d) show thevariation of f with a for a set of strakes havingvalues of Ra = 0.119, Ra - 0.169, Ra - 0.185, and Ra - 0.263, respectively. For theempirically designed strakes, theeffect of slenderness is slight on the first f "hump" at Ra - 0.119,but not so at 19 Ra = 0.263. The ED 9 strake(fig. 19(d)) is seento have a largervalue of fma,. This is apparentlyassociated with the more stablevortex system arising from themre slender strake and its smoother leading-edgeshape variation (ref. 5).

The analyticallydesigned strakes in figure 19 (b) , Ra FJ 0.169, have the same value of Rs and Rb and differ only slightly in their shape. The one with a slightlyhigher value of Ra (less than 4 percentlarger), lower initial sweep, and higher ~BD-TE (from ref. 6) has a highervalue of fmax.

Figure 19(c) showstwo analyticallydesigned strakes andone empirically

designedstrake for Ra TJ 0.185. These resultsalso show that,although there is less than 3 percentdifference in Ra between thethree strakes, the ED 5 (which has thelarger value of Ra) has thelargest value of fmax. The ED 5 hasthe largest value of Rb and produces f = 1 at thesmallest value of a. This is different fromwhat was noted forthe area effect, which means thatnot only is areaimportant but also its distribution - associated with theleading- edge shape - in producing relativelylarge values of (CL,tot)swb at lower angles of attack.

Fixedsemispan.- Figure 20 shows resultsfor four analytically designed strakes with Rb fixed at 0.212. The AD 14, AD 17, and AD 19 have values of fmax which, though approximatelythe same, vary in order of increasing Rae (Note thatthese three strakes have mre than 18 percentdifferences in Ra.) Reference 6 also shows thevalues of ~BD-TE to have that same order; and although all are of approximatelythe same value,there is a difference in maximum magnitudeof about 2O. The AD 23 strake has a somewhat smallervalue of fmax than do theother three, although its value of Ra is notthat different from thevalue for the AD 14. They all have aboutthe same value of a at which f = 1.

In figure 21 the AD 14, AD 17, and AD 19 configurations have curves of f versus a compared with those of the AD 24. The comparison shows fma, of all four to be similar, though thevalue of fmax forthe AD 24 is slightly higher. What is particularlyinteresting is thatthe AD 74, AD 17, and AD 19 strakes have areas which range from 53 to 63 percent of the AD 24 strake and still produce these high values offmax. This means thatthese smaller area strakes have efficienciesequivalent to the larger AD 24, up tofmax andmay, therefore, be classifiedas "better" strakes. Two otherfeatures of figure 21, apart from theincreased angle of attackrequired to reach f = 1 forthe AD 24 (larger Rb), arethat (1) fmax occurs at a slightlyhigher angle of attack forthe AD 24 and that (2) thecurve of f versus a beyond fmax is signif- icantlyhigher for the AD 24 thanfor the other configurations. Both features areassociated with thevalue of Ra forthe AD 24 strakebeing larger; the firstfeature is attributedto the larger lift deficiency, in terms of f, which must be initially overcome, and the second featureresults from the (CL,tot)swb retaining a highervalue beyondfmax, which is associated with thelarger area that the flow from thestrake vortex can act upon.

Other parameters.-Figures 22(a) to 22 (c) show thevariations of f and CY forthe apex, trailing-edge, and inboard-edge cut series,respectively. Taking the cut series as a group, the ED 5 strake and ED 9 strakeare as effec-

20 tive up to fmax asthe AD 24 strake,while having areas of 58 percent and 80 percentless, respectively. Therefore, it can be seen thatselected empirical alterations ofan analytically designed strake are possible which have only a small impact on thevalue of fmax. The preferred methodsof empirical- strake-shapealtering appear to be those ofremoving small amountsof area along theinboard or trailing edges. Reference 5 also shows these methods leadingto improvements in strake-vortexstability, i.e., larger values of ~BD-TE.

Figure 23 has been prepared to examine indirectly the effect of pressure specification on f versus Cr. The comparison is indirect because thedifferent pressurespecifications, constant and polynomial,taken in conjunction with the same suctionprescription yield two differentstrake shapes.Figure 23 shows thevalue of fmaxto be largerfor the gothic strake (AD 19) - designed using theconstant type - thanfor the reflexive strake (AD 9). The AD 19 strake does howeverhave largervalues of Ra and Rb thanthe AD 9, due in partto the AD 9 strake beingvery long (i.e., more slender)for the same value of Rb. Hence, on thesurf ace one couldconclude thatthe effect of Rawas the major causefor thedifference. However, it canbe seen from figure 21 thatthere areanalytically designed strakes, of the same or smallerarea and largervalues of Rb thanfor the AD 9, whichhave values offmax comparable tothose of the AD 19. The strakes in figure 21 areall gothic and were generated with the constantpressure specification. Thus thearea distribution/leading-edge shape areimportant. Also, since reference 5 determined thatthe polynomial pressure specificationleads to strakes which tend toreflex toward the tip and have, as a group,a lower values of it can be concluded that theconstant pres- surespecification yields preferable strake shapes and characteristics of f versus c1.

Generation of CL,max

Themaximum lift coefficientsthat the configurations generate are examined with theaid of figure 24. It is seen thatfor all analytically designed strakes using theconstant pressure specification and for all thosedesigned empirically andemployed herein,the variations ofCL,max with Ra followthe same curve. Though this curvehas a markedly differentgradient on eitherside of Ra - 0.20, thevalues of the curve areall well above thosefor the reference curve (CL,max)wb(l + Ra) . This is another wayof seeingthat addition of area in the formof a strake - some ranges of strake Ra arebetter than others - is a more efficient producer of CL,max than just enlargingthe wing while keeping thereference area constant. The reasonfor the rapid reduction in CL,max with Ra forthe gothic strakes having Ra > 0.2 is unclear.Further efforts in strakedesign may enable CL,max to be increased in sucha way as to lie alongthe extrapolated curve.

Similardata for three empirically designed ogee (reflexive)strakes tested on the samewing-body were obtained from reference 12 andhave been plotted in figure 24. A faired curve of thesedata passes very closeto the data point for theanalytically designed reflexivestrake (AD 9) and has a differentvariation thanthe other data curve for Ra greaterthan approximately 0.20. In particular , forvalues of Ra below 0.25 thegothic or more gothic-likestrakes gen-

21 d erate a largervalue of CL,max than do theempirically designed ogee strakes fromreference 12 or theanalytically designed reflexive strake reportedherein.

Better Strakes

A criterion is sought by which the strakes may be more rigorouslydelin- eatedinto categories so thatthe "better" ones may beexposed. From thestudy of f versus cy (figs. 17 to 23)and CL,max versus Ra (fig. 24) better performing strakes havebeen discussed; however, a concisestatement as to what qualifies a strake to be a better onehas not yet been established. This will now be attempted.

Since f is a functionof Ra, (CL,tot)swbr and(CL,tot)wb and since (CL, tot)swb is also a functionof R,, a, and M, it is clear that Ra is a primevariable. Therefore, one should seek, at anappropriate angle of attack, notonly the maximum value of (C~,t~t)swb and f but a way to maximize the variationof the aerodynamic synergistic effect with area change Ra, i.e., beformulated as

1 a (cL, tot)swb aRa -3

where

(cL, tot swb

L- (CL,tot)wb(l + Ra)

One couldsolve directly for the value of Ra at whichaf/aRa is maximized by examininga2f/aRa2 = 0. However, thedetermination of af/aRa at a fixed cy is difficult enough to accomplishfrom the data; hence the second partial derivative is even more subject to question. Thus,those strakes that maximizeaf/aRa belong to a familywhich should produce better strakes; hence, thismaximization may beused as one possible criterion.

Table VI1 presentsthe af/aRa results forthe gothic-like strakes at the valueof ci requiredfor (C~,~~~)swb. (Note that strakes havingessentially the same value of 0: are used inthe determination of a (CL,tot)swb/aRa from figure 24 foruse in eq. (7) .) From thetable it canbe seen that those strakes which generally show up asthe better ones all havevalues of af/aRa > 3.0,and furthermore these values are thelargest obtained. By maxi- mizingaf/aRa it is clearthat the intention is to determinethose strakes for which a givenchange in Ra producesthe most benefitin f for a fixed valueof a. Thisdoes not say whether CL,max or fmax is among thehighest or not,only that for a value of ci increasing Ra, forthose strake shapes whichhave high values of af/aRa,should produce a rapidincrease in f.

22 The preceding,therefore, provides another criterion for better strake shape determination,the criterion being that strakes from anysource which have a value of af/aRa > 3.0 should be consideredgood shape candidates.

As a point of interest, if a strake could be designed so as to yield (CL,~~~)~~~= 2.0 at Ra = 0.245 (theend point ofthe extrapolated lower part of thecurve as given by

a (cL, tot swb PJ 5.0 aRa at a for (CL,max) swb

forgothic-like configurations in fig. 24) , it wouldproduce f (at CL,~~~)- 2.0 with af/aRa = 3.0 at c1 = 28O. Hence, thisconfiguration wouldhave all the good featurespreviously identified, i.e., largevalues of CL,~~~,fmax (also, f at CLlmax), and af/aRa, andtherefore be theoretically able to generateeven largervalues of f and CLlmax if its shape were scaled up. (It should be notedthat even without area scalingthis value of f at CL,~~~is larger than any obtained to date.)

CONCLUSIONS

An experimentaland analytical study has beenpresented for 16 analytically and empiricallydesigned strake-wing-body configurations at Mach numbersof 0.2, 0.5, and 0.7. From thebasic data, both total andcomponent, synergism studies, comparisonswith theoretical estimates, andthe strake lifteffectiveness study, thefollowing conclusions have been made:

1. Pitch-upappears fundamental for many of theconfigurations and would therefore require a low tail for stability and control.

2. High-angle-of-attackvortex lift theory reasonably estimates the lift andthe lift dependentdrag up to strake-vortex breakdown.

3. High-angle-of-attackand low-angle-of-attack vortex lift theories bracketboth the total andcomponent pitching-moment data up to maximum lift of strake-vortexbreakdown.

4. Overallcompressibility effects are slight onthe total components,due primarily to a falloff in lift andupwash on thestrake-forebody compensated by an increase in lift onthe wing-afterbody associated with the increasing subcritical Mach number.

5. Synergistic lift effect is usuallyaccompanied by a delayin pitch-up.

23 6. It is possible to generateessentially the same levelof f, the additional lifting surface efficiency factor, withgothic strakes having areas from about one-half to two-thirds the size of the original gothic analytically designed strake (AD 24).

7. Basedon the strakes studiedherein, those having af/a(Strakearea/Reference wing area) > 3.0 belong to a familyof strakes that are betterperformers.

LangleyResearch Center NationalAeronautics and SpaceAdministration Hampton, VA 23665 February 24, 1981

24 APPENDIX A

AUGMENTED VORTEX LIFT

The conceptof an augmented vortex lift term arises fromthe well- established fact that for many deltawings the leading-edge vortex generated on the wing persists for a considerabledistance downstream and, therefore, can act on othersurfaces such as the aft part of more generalizedplanforms or aircrafthorizontal tails. Upon examiningexperimental results forthe more generalizedplanforms, one concludes that the augmentation effect just introduced is notaccounted for by thesuction analogy although for simple deltas it is. The primaryproblem appears to bethe interaction, or lack of it, when bothleading-edge and side-edge vortex flows are involved.This situation as well as when thetrailing edgeof a simpledelta is notched positively or negativelyappear not to be modeled by thesuction analogy. Sketch D shows examplesof two systemsemployed that account for vortex lift

\ PLANAR POTENTIAL

KUTTA - JOUKOWSKIRELATIONSHIP dF, =-p wnet (2) r (Z) dZ

LEADS TO

Sketch D.- Conceptof augmented vortex lift. on delta and cropped-deltawings; the first system is a theoreticalone developedfrom a planarpotential theory and utilizingthe suction analogy alongthe leading edge and sideedge, and the second system is anextension thataccounts for the action of the leading-edge shed vortex in the vicinity ofthe side edge of cropped-deltawings. The followingimportant points are made from sketch D: (1) The leading-edgesuction distribution has a peak value somewhere alongthe leading edge away from the extremitiesand goes to zero at the tip because no-edge forces are present beyond the point of maximum

25 APPENDIX A

span,and (2) for thecropped-delta wing, the aft part ofthe wing cangen- erate additional(augmented) vortex lift (above that associated with the direct side-edge effect) becauseof the presence of the leading-edge vortex (as discussed inref. 8).

In order toestimate theaugmented vortex lift, it is firstnecessary to quantify'the circulation of the shed vortex along the wing leadingedge. This can be done as indicated by the lower sketchin sketch D. The Kutta-Joukowski law has beenemployed to relate the differential suction force alongthe leading edge to an unknown circulation r (2) by dF, = -PWnet( 2)(2) dl.Using a coordinatetransformation, it can also be related to the leading-edgesuction distributionalong the span as

-r (z)wnet, le Sketch E showsan idealizeddistribution of the product ; note dU2 -%et, le that it is basicallylinear, along with a fairlyreasonable (upwash) U

-'net, le U

0 0 .5b/ 2 b/ 2 Y

"" AFT PART

2r net, se I U I 8 C 0 .5b/ 2 b/ 2 I 0 .5ct t Y Ax

Sketch E.- Variables used inaugmented-vortex-lif t determination for cropped delta wings, delta partidealized. (Note: b = Wing span, ct = Tipchord, Ax = Distancealong side edge,and y = Distancealong semispan.)

26 I

APPENDIX A

distribution for a cropped-deltawing, also basicallylinear. As a consequencs, r- (2) canbe estimated as shown. Because the actual circulationdoes not go to

zero(hence the vortex persists downstream) , the distribution of circulation, essentiallyconstant, cannot be used. Instead, an average value is employed. r(2) With an averagevalue used for -- , it is consistent to utilize anaverage 'Wnet, le ci ZU valuefor as well. This result canbe expressed in terms theof U leading-edgevortex lift factor by

Hence,

Ehployingthis result in the Kutta-Joukowski law, this time alongthe side edge,permits the estimation of the augmented vortexlift. The details yield

- Augmented vortex lift alongoneedge - - r(z) - - -pwnet,se - C a2 a2

'%et ,se where the distribution and its average are againreasonably depicted U - at thebottom right of sketch E, and c is a characteristic streamwise length. By inspection of sketch E,

Wnet,se Wnet, = le U U

27 APPENDIX A

The term in bracketsresults fromthe use of averagevalues and amounts to assuming thatthe leading-edge vortex lift factor is developed at a constant rate alongthe leading-edge length (b/2) sec A. Forcropped-delta wings the value of 2 is taken to be thelength of the tip chord.

From thepreceding discussion, the contributions of the augmented term to vortex-flowaerodynamics are determined to be

c~,vSe= %,se-)sin cxlsin cx cos cx

and - XE cmIvg= ~,,~(sincxlsin cx - Cref

- where xg is takenfrom the reference point to thecentroid of the augmented vortexlift. This location is generallytaken to occur at thecentroid of the affectedarea.

28 APPENDIX B

STRAKE-VORTEX BREAKDOWN IN AIR AND WATER

From previous sections in this paper, a qualitative correlation has been pointedout to exist betweenthe fmax variation,determined from wind-tunnel data, and theangle for strake-vortex breakdown at thetrailing edge, observed inthe water tunnel (ref. 5). Basedon thatcorrelation, it is interesting to consider how well thequantitative values of QBD-TE in air wouldagree with thoseobserved in water. For delta wingsthe agreement was determinedin reference 3 to begood; however, not as much is known aboutthe agreement for configurations like that of the strake-wing-body.During the wind-tunnel test reported in this paper , theatmospheric water vaporand tunnel temperature were such as to causethe strake vortex, and sometimes the wing vortex, to be visible for the AD 24 configuration.Because of thevortex visibility a videotape was made forthe range of c1 from 16O to >35O at M = 0.3. From the tape, still photographshave been prepared and arepresented in figure 25. Since the AD 24 was also a configurationtested in the water tunnel,photographs from that test (ref. 5) are availableover a similar rangeof c1 and are also presentedin figure 25 forcomparison. (The anglesof attack for thewater-tunnel data are corrected forwall effectsusing the wind-tunnellift-coefficient data.)

From these two sets offlow-field data it can be seenthat there are at least three items whichdeserve comment. The first is thatthe strake vortex is better able to persist in the wing pressurefield while in air thanin water. This is most likelyassociated with the Reynolds number (1.76 x lo4 in water and1.51 x lo6 in air) and its effect on the upper-surfacepressure field associated withthe different characteristics of the boundarylayers. The second item is thevery rapid progression in air with small increasein cy over the wing for the strake-vor tex breakdown position once the trailing edge hasbeen reached.

The different rates ofvortex breakdown progressionfor configurations tested in the water andwind tunnelcan also beseen for the delta wings of Wentz (ref. 13) tested inair and thewater-tunnel results published by Headley (ref.3) . They are compared infigure 26 and eventhough the values of CXBD-TE agree,the higher swept deltas are seen to exhibit a much more rapid forward progressionof vortex breakdown positionin air thanin water. The third item is that cx forstrake-vortex breakdown at the strake-wingjunction is about 32O inboth air and water. Thissignifies that once the wing pressurefield is traversed,the strake-vortex breakdown progression commences from the same posi- tionat about the same a.

Basedon the second item, oneshould expect some differencesin the force data inthe Cr rangefrom approximately 22O to approximately 32O. Wind-tunnel data at the same Mach number (0.3) as thatfor the strake-vortex photographs are available and are presentedin figure 27. Force data for the water-tunnel model is notavailable for comparison;however , it is interesting to examine thewind-tunnel data for CL versus cy inlight of both sets of strake-vortex photographs. From these data it canbe seen that CL,max occursin the cy rangefrom 30° to 35O. It is inthis range that the strake vortexbegins to

29 f APPENDIX B

break down in air aheadof the wing trailingedge. This breakdown occurs at a values some loo to 13O largerin air thanin water, and so onemight specu- late thatwater-tunnel force tests would show CL,max occurring at a lower valueof a.

Figure9(g) presented the CL versus a data forthe AD 24 strake- wing-body configuration at M = 0.2 incomparison with theory and, thereby, demonstratesthat the falloff in lift-curve slope is a part ofan expected theoreticaltrend for ci > 20°. Thisfact, coupled with the wind-tunnel strake- vortex-breakdownphotographs for the model, should encourage the reader to employ cautionin inferring from water-tunnel photographs quantitative information about theforce data, as suggestedin reference 11 forfighter-type configurations.

The use ofwater-tunnel photographs has been shown inreference 5 to be usefulin sorting out thequantitative effects of different configurations. Thisappendix points out thatfurther study is needed inorder to more fully appreciate and accountfor the impact of Reynolds number on strake-vortex breakdown.

30 REFERENCES

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2. Smith, C. W.; Ralston, J. N.; and Mann, H. W.: Aerodynamics Characteristics ofForebody and Nose Strakes Based on F-16Wind Tunnel Test Experience. Volume I: Summary andAnalysis. NASA CR-3053, 1979.

3. Headley, Jack W.: Analysisof Wind Tunnel Data Pertaining to HighAngle of Attack Aerodynamics. Volume I - Technical Discussion andAnalysis of Results. AFFDL-TR-78-94, U.S. Air Force,July 1978. (Available from DTIC as AD A069 646.)

4. Lamar, John E.: Analysis andDesign of Strake-Wing Configurations. J. Aircr., vol.17, no. 1, Jan. 1980, pp. 20-27.

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6. Frink, Neal T. ; and Lamar, John E. : An Analysisof Strake Vortex Breakdown Characteristicsin Relation to DesignFeatures. J. Aircr., vol.18, no. 4, Apr. 1981, pp. 253-258.

7. Luckring, James M.: Aerodynamicsof Strake-Wing Interactions. J. Aircr., vol.16, no. 11, Nov. 1979, pp. 756-762.

8. Lamar, John E.: Predictionof Vortex Flow Characteristicsof Wings at Subsonic and SupersonicSpeeds. J. Aircr., vol.13, no. 7,July 1976, pp. 490-494.

9. Lamar, John E. : Some RecentApplications of theSuction Analogy to Vortex- Lift Estimates. AerodynamicAnalyses Requiring Advanced Computers, Part 11, NASA SP-347, 1975, pp. 985-1011.

10. Lamar, John E.; and Gloss, Blair B.: SubsonicAerodynamic Characteristics of Interacting Lifting Surfaces WithSeparated Flow Around SharpEdges Predicted by a Vortex-Lattice Method. NASA TN D.7921,1975.

11. Erickson,Gary E.: Water TunnelFlaw Visualization: Insight Into Complex Three-DimensionalFlowfields. J. Aircr., vol.17, no.9, Sept. 1980, pp. 656-662.

12. Luckring, James M.: SubsonicLongitudinal and Lateral AerodynamicCharac- teristics for a SystematicSeries of Strake-WingConfigurations. NASA TM-78642, 1979.

13.Wentz, William H., Jr.; and Kohlman, David L.: Wind TunnelInvestigations of Vortex Breakdown onSlender Sharp-EdgedWings. NASA CR-98737, 1968.

31 TABLE I .- PERTINENT GEOMETRIC PROPERTIES OF ANALYTICALLY

DESIGNED STRAKES

[From ref. 51

T "- S trake A(V = 0), Wing designation de9 RS Rb Ra position

" AD1 76.76 4.92 0.212 0.100 Forward AD2 83.55 6.51 .212 .loo AD3 77.14 5.33 .212 .110 AD4 83.75 7.04 .212 .112 AD5 72.06 3.94 .212 .079 AD6 71.29 3.55 .212 .070 AD7 69.01 4.99 .212 .126 AD8 80.70 5.76 .212 .108 v AD 9a 75.10 10.65 .197 .183 Aft AD 10 79.41 5.91 .212 .112 Forward AD 11 73.29 3.56 .212 .066 AD 12 73.43 3.01 .212 .038 AD 13 77.19 8.69 .212 .199 AD 14a 46.18 6.99 .212 .172 AD 15 63.65 5.92 .212 .140 AD 16 65.52 5.29 .212 .123 AD 17a 70.78 7.77 .212 .185 AD 18 74.54 4.98 .212 .103 AD 19a 56.80 8.50 .212 .205 AD 20 66.14 5.07 .212 .127 AD 21 69.97 4.65 .212 .092 AD 22a 60.65 7.00 .144 .077 AD 23a 60.65 7.00 .212 .166 Y AD 24a 60.65 - 7.00 .297 .325 Aft aStrakes reported on i.n this paper.

32 TABLE 11.- PERTINENT GEOMGTRIC PROPERTIESOF EMPIRICALLY

DESIGNED STRAKES

[From ref. 51

___ ~ . ." Strake A(n = 018 Chord Wing designation deg RS Rb Ra modification pas it ion - AD 24a 60.65 7.00 0.297 0.325 Aft

60.00 6.10 0.297 0.305 Removal of apex Forward 60.00 5.19 .297 .266 region 60.00 3.98 .297 .195 60.00 2.77 .297 .114

60.65 5.83 0.262 0.188 Removal of 60.65 5.22 .226 .124 trailing-edge 60.65 4.53 .181 .065 reg ion 60.65 3.65 .119 .021 - 73.32 7.79 0.253 0.259 Removal of A€ t 77.57 8.62 .208 .192 inboard- Forward 80.12 9.59 .163 .131 edge reg ion

ED 12a 56.89 5.18 0.297 0.227 Chordwise ED 13a 50.42 2.78 .297 .098 scaling - ~- ED 14 50.42 2.78 0.297 0.078 Chordwiseextension ED 15 50.42 2.78 .297 .076 (snag)on ED 13 strake

" ED 16 50.42 5.63 0.297 0.325 Addition of side- ED 17 50.42 4.64 .297 .246 edge/trailing- ED 18 50.42 3.63 .297 .166 edge area to ED 13 strake . . .. aStra kes reported on in this paper. bAnalyticallydesigned strake fromwhich empirical variations are made.

33 . ._. , , ..

TABLE I11 .- STRAKE PLANFORM PERIMGTER POINTS

X X II YI c Y cm in. cm in. cm in.

0.000 0.000 0.000 0.000 0.000 0.000 0.201 0.079 0.325 0.128 0.229 0.090 0.401 0.158 0.818 0.322 0.457 0.180 0.599 0.236 1.433 0.564 0.686 0.270 0.800 0.315 2.154 0.848 0.914 0.360 1.001 0.394 2.974 1.171 1.143 0.450 9.268 3.649 1.201 0.473 3.086 1.530 1.374 0.541 13.724 5 .bo3 1.600 0.630 5.982 2.355 1.831 0.721 18.626 7.333 2.002 0.788 8.440 3.323 2.289 0.901 23.891 9.406 2.400 0.945 11.298 4.448 2.746 1.081 29.385 11.569 2.802 1.103 14.623 5.757 3.203 1.261 34.557 13.605 3.200 1.260 18.590 7.319 3.660 1.441 39.119 15.401 3.602 1.418 23.589 9.287 4.120 1.622 42.606 16.774 4.001 1.575 31.991 12.595 4 * 577 1.802

t X Y X Y cm in. cm in cm in. cm in.

0.000 0.000 0.000 0.000 0.000 0. ooc 0.000 0.000 0.693 0 273 0.229 0.090 0.455 0.179 0.229 0.090 1.473 0.580 0.457 0.180 1.115 0.439 0.457 0.180 2.334 0.919 0.686 0.270 1 935 0.762 0.686 0.270 3.274 1.289 0.914 0.360 2.893 1.139 0 314 0.360 4.290 1.689 1.143 0.450 3.980 1.567 1.143 0.450 5.385 2.120 1.374 0.541 5.189 2.043 1.374 0.541 7.813 3.076 1.831 0.721 7.968 3.137 1.831 0.721 .o .577 4.164 2.289 0.901 11.247 4.428 2.289 0.901 .3.721 5.402 2.746 1.081 15.085 5.939 2.746 1.081 -7.328 6.822 3.203 1.261 19.558 7.700 3.203 1.261 11.560 8.488 3.660 1.441 24.491 9.642 3.660 1.441 16.817 10.558 4.120 1.622 30.170 11.878 4.120 1.622 ;5.550 13.996 4.577 1.802 38.892 15.312 4.577 1.802

34 TABLE 111.- Continued

X AD 22 45 +X AD 23 TI .~ X Y X Y

cm in. cm in. cm in. cm in.

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.318 0.125 0.155 0.061 0.465 0.183 0.229 0.ogo 0.721 0.284 0.312 0.123 1.062 0.418 0.457 0.180 1.201 0.473 0.467 0.184 0.694 0.686 1.763 0.270 1.748 0.688 0.622 0.245 2.565 1.010 0.914 0.360 0.928 0.780 2.357 0.307 1.362 1.143 3.459 0.450 3.028 1.192 0.935 0.368 4.445 1.750 1.374 0.541 4.552 1.792 1.247 0.491 6.683 2.631 1.831 0.721 6.327 2.491 1.557 0.613 3.658 2.289 9.291 0.901 8.387 3.302 1.869 0.736 12.319 4.850 2.746 1.081 10.777 4.243 2.182 0.859 15.827 6.231 3.203 1.261 13.477 5.306 2.492 0.981 19.792 7.792 3.660 1.441 16.693 6.572 2.804 1.104 9.651 4.120 24.514 1.622 21.836 8.597 3.117 1.227 32.070 12.626 4.577 1.802

” t A Y cm in. cm in.

0.000 0.000 0.000 0.000 0.653 0.257 0.320 0.126 1.486 0.585 0.643 0.253 2.471 0.973 0.379 0.963 3.597 1.416 1.283 0.505 4.849 1.909 1.603 0.631 6.231 2.453 0.758 1.925 9.365 3.687 2.565 1.010 13.023 5 0127 3.208 1.263 17.262 6.796 3.848 1.515 22.179 8.732 4.491 1.768 27.739 LO. 921 5.131 2.020 34.356 ~3.526 5.773 2.273 44.943 ~7.694 6.414 2.525

35 TABLE I11 .-’Continued

X Y

I cm I in. cm in. - 0.000 0.000 4.034 1.588 4.041 1.591 4.491 1.768 5.131 2.020 5.773 2.273 6.030 2.374 6.414 -2.525

36 TABLE 111.- Continued

ED 5

X Y ”- 1 cm in. cm in.

0.000 0.000 0.000 0.000 0.653 0.257 0.320 0.126 1.486 0.585 0.643 0.253 2.471 0.973 0.963 0.379 3.597 1.416 1.283 0.505 1.909 1.603 4.849 0.631 6.231 2.453 1.925 0.758 9.365 3.6872.565 1.010 13.023 5.127 3.208 1.263 17.262 6.796 3.848 1.515 22.179 8.7324.491 1.768 25.425 10.010 4.874 1.919 28.953 11.399 5.260 2.071 13.048 5.667 33.142 2.231

ED 6 1 +..x”----i t X Y i cm in.

0.000 0.000 0.000 0.000 0.653 0.257 0.320 0.126 1.486 0.585 0.643 0.253 2.471 0.973 0.963 0.379 3.597 1.416 1.287 0.505 4.849 1.909 1.603 0.631 6.231 2.453 1.925 0.758 9.365 3.687 2.565 1.010 13.023 5 127 3.208 1.263 17.262 6.796 3.848 1.515 22.179 8.732 4.491 1.768 25.425 10.010 1.919 4.874

37 TABLE 111.- Continued

ED 10 t>

X Y X Y 7 cm in. cm in. cm in. 0.000 0.ooc 0.000 0.000 0.000 0.000 0.321 0.126 1.505 0.592 0.321 0.126 0.641 0 253 3.136 1.235 0.641 0.253 0.962 0.379 6.793 2.674 1.283 0.505 1.603 0.631 11.033 4.344 1.924 0.758 2.245 0.884 15.951 6.280 2.565 1.010 2.886 1.136 21.509 8.468 3.207 1.263 3.527 1.389 28.126 11.073 3.848 1.515 4.169 1A41 38.714 15.242 4.489 1.768 4.810 1.894 5.451 2.146

0.000 0.126 0.379 0.631 0.884 1.136

38 TABLE 111.- Concluded

cm in. cm in.

0.000 0.000 0.000 0.000 0.549 0.216 0.320 0.126 1.224 0.482 0.643 0.253 2.007 0.790 0.963 0.379 2.885 1.136 1.283 0.505 3.856 1.518 1.603 0.631 4.912 1.934 1.925 0.758 7.290 2.870 2.565 1.010 10.033 3.950 3.208 1.263 13.183 5.190 3.848 1-515 16.805 6.616 4.491 1.768 20.876 8.219 5.131 2.020 25.687 -0.113 5.773 2.273 33.271 -3.099 6.414 2.525

ED 13 +=-x X Y 1 cm in. cm in.

0.000 0.000 0.000 0.000 0.411 0.162 0.320 0.126 0.879 0.346 0.643 0.253 1.392 0.548 0.963 0.379 1.946 0.766 1.283 0.505 2.540 1.000 1.603 0.631 3.170 1.248 1.925 0.758 4.544 1.789 2.565 1.010 6.076 2.392 3.208 1.263 7.780 3.063 3.848 1.515 9.690 3.815 4.491 1.768 11.791 4.642 5.131 2.020 14.209 5.594 5.773 2.273 17.818 7- 015 6.414 2.525

39 TABLE 1V.- TBEOREX'ICAL LOADING FACTORSAND 'IBEIR CENTROIDS FOR HIGH-

ANGLE-OF-ATTACK AND LOW-ANGLE-OF-ATTACK SOLUTIONS AT M = 0.2

CUhFIGURATION NO. AD 9

AEi?ODYNAEIC PAPAMETFQS

INPUT KPJ KV, AND CENTRQIDS F3P RESPECTlV2 COMPONENTS

CkNTtR OF PRESSURE (CM. 1 (IN.) STRAKE KP- 041229 27058463 1O.86009 KV LE= 1.57299 18077365 7.30120

* AUGMEqTED KV AP4D RESPEClIVE CENTROID

CENTER IF PRESSUQE (CWO 1 fTN.1 LciW ALPHA STRAKE """""""" "-"" """_ W I 1.1 G YV us- e94005-13.34557 -5.25416 KV UT= 6098 1 -20095045 -5.24R22 HIGH ALPHA STRAKE K V= -ai4224 027883070927 WING KV WR= 1.09716 -1Z008363 -4.75734

Lr?W ALPHA HIGH 4LPHA

1.43075 1.09716 20 52791

* WS - WING-STRAKE JUNCTUPF, 'riT 4ING TIP9 WR - WING ROOT AT BODY

Nul€: CENTK!IIDS PSSITIVE AHEAO OF X SUB REF

40 TABLE 1V.- Continued

CONFiGUWATI3N NO. AD 14

AERDDYYAMICPA2AMETEPS

* AUGMErJTED KV AND RESPECTIVE CCNTUOXD

CENTER 3F ORESSIJRF (CY. 1 (IN.) LCIK ALPHA ST9AKE """""""" """- """_ WING KV WS- a91167 -9.42461 -3.71047 KV WT= .53377 -16.78056 -6.60652 HIGH ALPHA STPAKE KV- -016172 4.50743 1.77459 WING KV WR- 1.09051 -8.04471 -3.167?1

TOTAL KV TEHIIS FdR RESpiiCTIVE COMPONENTS

LOW ALPHA HIGH ALPqA

STRAKE 1.18831 1.02659 w It4G 30786G3 1.09051 TCITAL 4.97500 2. 1.1703

* WS - WING-STRAKE JUNCTURE, iJT - WING TI09 WR - WING RDOT AT B'3DY

NU1.E: CEhTRUlDS POSITIVE AYEAD nF X SUR RF?

41 TABLE 1V.- Continued

CONFIGURATIO~h00 AD 17

bERODYNAPiIC PAPAflSTE9S

IrJPUT KPI KV, AND CENTROTOS FOR RESPECTIVE COMPONFNTS

CfNTiR OF PSETSURE (CMe 1 (IN.) STRAKE KP= 05175427.47658 11 001440 KV LE= 1.3'444323.469730024005

* AUGMENTEO KV ANU RESPECTAVE CCNTRDID

CENTER I3F DRESSURF (CY.) (IN. 1 LOW ALPH4 STRAKE """""""" """_ -""" WING KV WS- 096713-9.42461 -3. 71047 KV ;JT= 05342Ei -16078056 -6060652 HIGH ALPHA STRAKE r< V= 4.50743-017153 107746R WING KV WR= 1.15659-8004471 -3.16721

TQTAL YV TERIYS FOR RESPECTIVE rr)WDONENTS

LfIW ALPHA HIGH 4LPYA

STRAKE 1.39443 1. 22390 WING 3.84450 1. 15659 TOTAL 5023893 2. 37950

* WS - WING-STKAKE JUhCTURF, wT - WING TIP, IdR - UING R!7!IT AT BnDY

NOTE: CENTRCIIUS PIlSIlIV€ AYEAD @f X SUB REF

42 TABLE 1V.- Continued

CnNFIGURATION NO. AD 19

INPIIT KPp KV, AND CENTRnIDS FOR RCSPECTIVE COMPONFNTS

NING KP- 2.47571 -6.96455 -70741QS KV LE= 1.86943 -5054314 -3.18234 KV SE- 47676 -36090992 -6.65745 * AUGIIEIJTEr) KV AND RESPECTIVE CENTROID

CENTFR OF PREISSUPE (CY. 1 (IN.) LOW ALPHA STRAKE """""""" """_ """_ WlrJG KV JS- -9042461096798-3.71047 KV UT- 053509 -10079056 -6060652 HIGY ALWk STQAKt K V= -e17164 4 50743 1 a 77438 WI NG KV WR- 1.15749-a.o4471 -3016721

TOTAL KV TERMS FOP RESPECTIVE COMPONENTS

LIIW ALPHA HlGH ALPYA

STRAKE 105250Y 1035343 w IN6 3.84917 1015749 TOTAL 5.37426 2.51092

* rJS - WING-STRAKE JUNCTURE, WT - WING TIP, VR - WING R30T AT 8ODY NOTE: CENTR-]IDS POSITIVE AHEAD OF X SUR REF 43 TABLE Iv.- Continued

CONFIGURATION hO. AD 22

INPLIT KP, KVP AhD CENTRClIDS FOR RESPECTIVE CUMPONFNTS

* AUGMENTED KV AYD RkSPtCTIVE CENTROID

CfNTE9 If: PRESSUBE (CY. 1 (TN. 1 LGW ALPHA iTRAKk """""""" """_ "-"" WING KV US= 1.G1560 -8.79326 -3.46191 KV WT= 0307E9 -10.78 Q56 -5.6065? HIGH ALPYA SI FAKE I< V= -.11543 5.44753 2. I4470 W I WI NG KV vlR- 1.143il -7.P6352 -3.09599

TOTAL KV TECiMS FUS RESPECTlVE Cr3V00NENTS

LO9 ALPHA HIGH 4LPHA

* WS - WING-STRAKE JUNCTURE, YT - 4ING TIP, WR - WING ROOT AT BODY

FilJTE: CtNTkUIOS POSlTIVE AHEAD OF X SU9 REF

44 TABLE 1V.- Continued

CONFIGURATI'2iI NU. AD 73

AEROOYNAYIC PAHAMETERS

INPUT KP, KV, AliD CStuTR9TDS FOR RESPECTiVE COMPONEMTS

CENTER OF PRESS!JPE (CE. 1 fTN.1 STRAYE K P= .51110 25.71595 10.12439 KV LE= 1.23796 19.06619 7.50637 WIflJG KP= 2.45116 -Po19130 -3.22492 KV Ltz 1oY64C1 -6.80517 -2.67920 KV st- 0 47797 -180 16710 -7 ~15240 * AUGYENTED KV A~DREljPtCr1vf CENTRCTD

CENTER 1F PRESSL!QE (CMO 1 (IN.) LOW ALPHA SSkAKE """""""" ""-" """_ W1 NG KV 4:- 094t.00 "9.42461 -3.71047 KV JT- 053371 -1b.78056 -6b60h52 HIGH ALPHA STRAKE KV= -* 16~9 4.50743 1.77458 WING KV rlP= 1013479 -8.04471 -3.16721

LOW ALPHA HIGH ALPYA

STRAKE 1. 2 3796 1.06967 WING 3aE2520 1.13470 TOTAL 5mC6316 2*?0446

* WS - WING-STRAKE JUNCTURE, UT - WING TID, WR - HING PdO'F AT BODY hOTE:CENTROiOS PJSITIVE AHZAD CIF X SUB REF

45 TABLE 1V.- Continued

CUNFIGURATLOH t\iO. A@ 24

AER30YhAMIC PARAYtTEDS

TOTAL KV TERYS FOR RESPECTIVE CCJMa~JNFMTS

46 CrJNFIGURATION N&. k0 ?

INPUT KPP KV, 4IJG CENTROTDS FOR kESPECT1V.E CUHPONFNTS

* AUGqEYTfD KV AND RZSPECTIVE CENTR3ID

TOTAL YV TEiiMS FUq RESPECTIVECOMOONENTS

LOW ALPHA HlGH 4LPYA

* WS - WING-STRAKE JUIICTURE, WT dINGTIP, WR - UING KCJOT AT amy FIOTEt CENTROIDS POSITIVE AHEAD OF X SUQ REF

47 TABLE,IV.- Continued

CUNFIGURATIOd NG. ED 4

AEKODYNAflIC PARAflETfRS

INPUT KY, KV, AhD CENTROIDS FORRESPECTLVE COFlPONFNfS

CENTER OF PRESSURE (CM.1 (IN.) ST2AKE K P- 063951 19.136a2 f.53418 K V LE= KV a81712 13.03442 5.13166

WING KP- 2.36253 -7.16318 -2.62015 KV Lk= 2.07982 -5013568 -2r031Q2 KV SEI 048295 -16090952 -6.65729 * AUGMEIJTED YV AlvD RESPEC JIVE CENTRrJLD

CZNTFP 'IF PRE'SStJRE (CMO 1 (IN.) LOWALPHA STRAKE -"""-b"""- """_ """_ WING KV WS= 1005164 -10.2189% -4.02320 KV UT= 06073a -16.78056 -6060657 HIGH ALPHA STRAKE KV= -029370 3.32467 1.30892 WING KV WRm 1a365Ul -8.25705 -3.25081

T3TALKV TERMS FCIR RESPECTIVECrlMDONENTS

LOU ALPH4 HIGH 4LPqA

STRAKE .81712 53342 W TqG 4.26179 1.36501 TUTAL 5.09891 i.99843

* WS - WING-STRAKEJUNCTURE, AT - WING TIDY WR - WlNG RlJOT AT BODY - TABLE 1V.- Continued

CUt4FIGUPATlON NO. tD 5

AEPODYhAYIC OARAMtTEQS

INPUT KP0 KV, 4k(i CENTROID% FOR RESPECTIVE COMPONFrJTS

C€NTER OF PRESSURE (CM.1 (IN.) STRAKE KP- 61122 25.27465 9.95065 KV Ltz 108148E. 17.79000 7.00000

* AUGMENTED KV AWO PESPECTIVF CENTQqID

CkNTEo 3F DRESSURE (CM. 1 IN. 1 LOU ALPHA STRAKE """""""" "-"" """_ WING KV WS- 1027772 -9,89605 -3.89608 KV 'AT- 065476 -1607R055 -6.50657 HIGHALPYA STRAKE KV= -029434 3.80~ 1.49P2D WING KV NK= 106C264 -80172Qa -3021763

TOTAL KV TERMS FOR RESPECTIVE COMPONENTS

LOW ALPHA HIGH ALPqh

* WS - WING-STKAKE JUt.(CTURE, WT - dING T13r WR - WING POOT AT BODY

NOTE: CENTPOIOS POSITIVE AHEAD OF X SUR REF

49 TABLE 1V.- Continued

CONFIGURATInN NO. ED h

AERODYNAMIC PARAMfTEpS

XiJPUf KP, KV, AND CENTROIDS FOR RESPECTIVE COMPONENTS

CtPifER OF PRESSURE (CP. 1 (JN. 1 STRAKE K Pa b51109 23eQ0473 3.41131 KV LE- 1.28527 15.71219 h.l@590

* AUGMENTED KV AND RESPECTIVE CENTROID

CEqTER 3F DRESSUQE (CM. 1 (IN.) LOW ALPYA STRAKE """""""" -""" """_ NING KV US- 1.21764-9.55342 -3.76119 YV WT= ,65443 -16.75055 -6.60652 HIGH ALgYA STRAKE K v* -e23299 4.31562 1.69906 WIHG KV ilJR= 1.47493 -8.08034 -3mlPI24

TOTAL KV TERYS FOR PtiSPECTIVE CIMPONENTS

LBW ALPHA HIGY ALPL4A

STPAK E 1.28527 1.05229 WING 4.53711 1.47499 TOTAL 5.66238 2. E2727

* ws - AING-STRA~E JUNCTUR~, WT - WING ~17~ WR - WING ROOT AT BODY NOTE: CENTRCllDS PCISITIVE AHEAD flF X SUP REF 50 TABLE 1V.- Continued

CUNFIGURATIUN NO. ED 9

AERODYNAPICPAkAMETERS

IlYPUTKP, KV, AhD CENTROIDS FOR R.ESPECTIVE COMPONENTS

CENTER OF DRESSIJRE (CMe ('CN.) STRAKE KP= 058661 26.20599 10.31732 KV LE= 2.17464 Ice57205 7.70553

WING KP= 2.42399 -11.11763 -4.37702 kV LEI 1.76518 -10.23904 -4.03112 KV SE- 049116 -21eli42(1 -9.31665 * AI!GMENTED KV AND RESPECTIVE CCKTROID

CENTER OF PRESSURE (CY. 1 (IN. 1 Lnh. ALPHA STRAKE """""""" "-"" """_ WING KV WS- 1.21596-13.97295 -5.50116 KV WT- 053266-2009504~ -8.24022 YIGH ALPHA STRAKE KV= -e26690 -0 2? 599 -008897 WING KV irQ= 1.51077 -12.23265 -4.91601

TOTAL KV TERrlS FOR RESPECTIVE C'IMPONEYTS

LOW ALPHA HIGH ALPYA

STRAKE 2.17464 1.90774 W TNG 4.00496 1.51077 TOTAL 6. 17960 3.418 52

* WS .- WIt4G-STRAKE JUNCTURE, i4f - WING TIP, WR - WING ROOT AT i3ijDY

NOTE:CEiJTROIOS ?3SITIVE +,HEAD OF X SUR QEF

51 TABLE 1V.- Continued

CnNFICU4ATION ih.13. ED 10

AE~OOYI~AMICPAKAMETEQS

CENTES .IF DRE5SURF (CM. 1 (XY .I LUUALPYA STRAK E """""""" """w -""" WING YV AS= 1.14091 -9.38705 -3.69569 YV AT= r513F1.F -1O.7'3C56 -6.6O652 41 GH AL PdA

STRAKE KV= 1.79660-04.56336 19777 WING KV WR- 1.35936 -de03424 -3.16309

LO4 ALPqA HlGY AL P'4A

* MS - WINS-SlRAKt JUNCTURE, iJT - ~1NcTIDj WR - MING RQOT AT BODY

52 TABLE 1V.- Continued

CONFIGURATION ND. ED 11

AEROUYNAKICPARAMETEPS

INPUT KP, KVJ ANDCENTROIDS F@R RESPECTIVE COMPONFNTS

C€NIER OF PRESSURE (CKo 1 (fN. 1 STRAKE KP= 040680 28.47213 11.20950 KV LE= 1.44936 21.37585 9.41569

WING KP- 2.57467 -6.64505 -2.61616 KV LE- 2.00681 -4.90713 -1.93194 KV St= e47403 -16091361 -6.65890 * AUGMENTEUKV AND RESPECTIVE CENTRqID

CENTER Tlp PRESSURE (CY.) (IW. 1 LOW ALPHA STRAKE """""""" """_ ""-" W ING KV WING WSs 1.10913 -8.97117 -30531Qh KV YT= 54106 -16.78056 -6.60652 HIGH ALPHA STRAKE K V= -014511 5.1R262 2.04040 WING KV WR= 1.26942 -7.91582 -3.11646

TilTAL KV TEQMS FOR RESPECTIVECOM?iWENTS

LOU ALPHA HIGH ALPHAALPHAHIGHLOU

STRAKE 1. 44936 1.30425 WING 4. 13104 1.26943 TOTAL 5.58040 2.57367

* WS - WING-STRAKE JUNCTURE, WT - WIhG TIP, WR - WING RLlOT AT BODY

NOTE: CENTROIDS POSITIVE AHEAD OF X SUR REF

I 53 TABLE IV.- Continued

AEROOYNAMlC PARAaCTERS

INPlJT KPP KVP AND CENTPCITDS FOR XEWEC rlvE CGMPOMNTS

CENTtR OF PPCSSIJRE (2M.I (TN.1 STKAKE K P= 7c071 24062352 9069430 KV LE= 1.85714 17.32354 6.82029

Lr3Y 4LPYA YlGY ALP'i4

S TKAK E led5714 1051Q82 WING 4. 53976 1.62298 TLYTP L 6.39690 3.14280

NOTE: CENTRJXDS PdSiTIVE nHEAI? flF Y SUR REG

54 TABLE 1V.- Concluded

CUNFIGURATiIJN NO. Er) 13

AEKODYbiAMIC PARAMtTERS

INPUT KP, KV, AhD CENTROIDS FOR PESPECTIVf CCJMPONFNTS

CFNTCR OF PRESStJRE (CW.1 (Tt4.f STRAKE KP= 19.2069760003 7.56200 KV 1.E- 1.29273 10.49254 4 a13092

WING KP= 2.39 454 -7.08858 -2 .7907F KJ LE- 2.04864-5.1'3236 -2.04030 kV SF- 047730 -1boY14fj2 -6.65926 * AUGYtNTED KV AND RESPECTIVE CCNTQOTD

CENTER YF PRESSURE (CM. 1 (IN.) LOW ALPHA STRAKE """""""" """_ """- WING KV 4.5~ 1.55413 -11)[email protected] KV YT= 06573P -16079056 -6.60652 HIGh AL PYA STRAKE K V- -0419263.32467 1. 30802 WJNG KV Y8- 2.01723 -8.75705 -3.25081

T3'FAL YV 1'EKYS FdR QESPEClIV€ COMPONEYTS

LIIW ALPHA HIGH AL PqA

STRAKE 1.29273 097347 WING 4.73744 2.01723 TO TAL 6.03017 2.P9070

* US - WIMG-ST24KE JUNCTURE, WT - WING TID, WR - WING RUOT AT RODY

NOTE: CENTROIDS P3SITIVE 4HEAD OF X SUB REF

55 TABLEV.- TEIEORETICAL IDADING FACTORS AND TBEIR.CENTROIDS FORHIGH-ANGLE-

AERODYNAMICPARAMETERS

INPUT KPp KV, ANDCENTROIDS FOR RESPECTIVECOMPONENTS

CENTER OF PRESSURE (CY.) (IN.) STRAKE KP- 051920 29.0982111045599 KV LE- 1.5250924.7155073051 9.

WING KP- 2.47571 06.96455-2.74195 KV LE- 1.86943-5.54314 -2.18234 KV SE- 47676016090992 -4.65745 * AUGMENTED KV ANDRESPECTIVE CENTROID

CENTER OF PRESSURE tcn. 1 (XN. 1 LOW ALPHA STRAKE ”””””””- “0”” ““”I WING KV US= -9.42461096788-3.71047 KV WT- 053509 -16.78056-6060652 HIGHALPHA S TRA KE KV=STRAKE -017166 4.1.77458 50743 W ING KVWING WR- 1.15749-e.04471-3.16721

TOTALKV TERMS FOR RESPECTIVECOMPONENTS

LOW ALPHAALPHAHIGH

STRAKE 1.52509 1.33343 UING 3.84917 1.13749 TOTAL 5.37426 2.51092

* US WING-STRAKEJUNCTURE9 UT - WING TIPS WR - WING ROOT AT BODY NOTESCENTROIDS POSITIVE AHEAD-OF X SUB REF

56 TABLE v.- Continued

CONFIGURATION NO. AD19r H-0.5

AERODYNAMICPARAMETERS

INPUT KP, KV9AND CENTROIDS FOR RESPECTIVE:COHPONENTS

CENTER OF PRESSURE ccn., (IN.) STRAKE KP- 29.2024311.49702051203 KV LE- KV 1.2843624.710529.72655

WING KP- 2.60191 -6.94693 -2.73501 KV LEI 1.91991 -5.70278 -2.24519 KV SEI 052424 016.90406 96.65514 * AUGflENTEDKV AND RESPECTIVE CENTROID

CENTER OF PRESSURE (CM. 1 ( IN. 1 LOUALPHA STRAKE """""""" """- """- WING KV us= e81510-9.42461-3.71047 KV WT= e54954-16.78056 -6.60652 HIGH ALPHA STRAKE KV-1.77458 4.507439.14456 WING KV WR= -6.04411e97478-3.16721

TOTAL KV TERMS FOR RESPECTIVECOMPONENTS

LOW ALPHA HIGH ALPHA

STRAKE 1.28436 1.13980 WING 3.80880 097478 TOTAL 5.09316 2. 11458

* WS - WING-STRAKEJUNCTURE, WT - WINGTIP, WP - WINGROOT AT BODY

NOTE8CENTROIDS POSITIVE AHEAD OF X SUB REF

57 TABLE V.- Concluded

CONFIGURATION NO. ADlFB Nm0.7

AERODYNAMICPARAMETERS

INPUT KPIKV, AND CENTROIDS fORRESPECTIVE COMPONENTS

CENTER OF PRESSURE (cn. 1 (IN.) STRAKE KP= 0 4998029.42991 11058658 KV LE- 100081324.900269.80325

WING KP- 2.78608 -6093080 -2.72666 KV LED 1098825 95094225 -2.33947 KV SE- 59649 -160e9273 4.65066 * AUGMENTEDKV AND RESPECTIVE CENTROID

CENTER OF PRESSURE (CH. 1 (IN.) LOU ALPHA STRAKE -0""""""- ""-" ""-0- W ING KV WING US- -9042461063980-3.71047 KV UT- KV 056910-16.76056 -6.60652 HIGH ALPHA S TRA KE KV=STRAKE le774584.50743-011347 W ING KV WING WR= -8004471076514-3.16721

TOTALKV TERMS FOR RESPECTIVECOMPONENTS

LOW ALPHAHIGH ALPHA

STRAKE 1000813 089466 WING 3.79364 076514 TOTAL 4.80177 le65979

* US 0 WING-STRAKEJUNCTURE9 UT - WING TIP9 WR - WINGROOT AT BODY NOTE8CENTROIDS POSITIVE AHEAD OF X SUB REF

58 TABLE VI.- THEORETICAL WADING FACTORS FOR BASIC WINGBODY CONFIGURATION8

CONFIGURATION NO. WB (FORWARD10 MmO.2

AERODYNAMICPARAMETERS

INPUTKP0 KV, AND CENTROIDS FOP RESPECTIVECOMPONENTS

CENTER OF PRESSURE ( CMo 1 t IN. 1 FUKE BODY KP= 40.6088115.98772014528 KV LE- 07952525.5387610.05463

WING KP- 2082136 -5086677 -2.30975 KV LE= 2.08937 -4050195 -1.77242 KV SE- 47270 -16089933 -6065328

CONFIGURATION NO0 WB (AFT), M-0.2

AERODYNAFIC PARAMETERS

INPUT KPO KV9 AND C5NTROIDS FOR RESPECTIVECOMPONENTS

CENTER OF PRESSURE ( CMo 1 (IN. 1 FORE RUDY KP= 44.1549017.38382.1242a KV LE= 0 7165526.26426 10.34026

WING KP= 2.68387-12.27110 -4oe3114 KV LE- 1.88166-10026772 -4.04241 KV SEI 46007-21012594 -0.31730

NOTE: . CENTROIDS POS-ITIVE.AHEAD OF X SUB REF

59 TABLE VI.- Continued

CONFIGURATION NO0 WE (FORWARD), H-0.5

AERODYNAMIC PARAMETERS

INPUTKP, KVY AND CENTROIDS FORRESPECTIVE COMPONENTS

CEWTER OF FRESSURE (CMo 1 (IN.) FOREBODY KP- 02395916023606a14084 41 KV LE- 0770812506970e 10.11696

WING KP- 2.95294 -5.97690 -2.31374 KV LE- 2013494 -4074203 -1086694 KV SE- 0 52153 016.89377 06.65109

CONFIGURATION NO. WB (AFT)#fl10.5

AERODYNAMICPARAMETERS

INPUT KP, KVI AND CENTROIDS FOR RESPECTIVECOMPONENTS

CENTER OF PRESSURE (CMO 1 (IN. FOREBODY KP- 0 1223744.55653 17.54194 KV LF- 0 7060126033711 10.36894

WING KP- 2.82370 -12027750 -4.83366 KV LE- 1.92481 010046036 -4a11825 KV SE- 048500 -21012427 -8031664

NOTE:CENTROIDS POSITIVE AHEAD OF x SUB REF

60 TABLE VI.- Concluded

CONFIGURATION NO. WB (FORWARD19 M-007

AERODYNAHICPARAMETERS

INPUT KP, KVs ANDCENTROIDS FOR RESPECTIVECOHPONENTS

CENTER OF PRESSURE (CHO, (IN.) FORE BODY Kf-. 4202567901344316063653 KV LE- KV 07394725093050 10020886 WING KP- 3.14255 ~5090174 -2032352 KVLE- 2.19310 -3010675 -2001053 KV SE- 59623 -16.86247 -6064664

CONFIGURATION NO. WB (AFT), M-007

AERODYNAMICPARAMETERS

INPUTKPs KVI ANDCENTROIDS FOR RESPECTIVECOHPONENTS

,CENTER OFPRESSURE ( CMo 1 (IN. 1 FJRE BODY KP- 0 1198745010319 17075716 KV LE- KV @ 6927326.43553 10.40769 WING KP- 3.02807 -12.28616 -4.83707 KV LE= 1.97715 -10077852 -4.24351 KV SE- 0 55497 -21011832 -8031430

NOTESCENTROIDS POSITIVE AHEAD OF X SUB REF - 61

TABLE VII.- af/aRa RESULTS AT M = 0.2

~- -. .. - .. . . Ia (cL, tot) swb I af Stra ke I (CL, tot)wb I f - Ra Rb a* designation deg at a* at a* aRa

"" ~ ~ ." . .. - --. .- - .._ .:= -. . 1. ~~ ~ ~~ - ___. .. ..

AD9 0.183 0.197 26.8 0.87 Not ava i lable 1.50 "" AD 14 .172 .212 27.3 .86 -5.0 1.62 3.58 AD 17 .185 .212 28.4 .88 m5.0 1.63 3.42 AD 19 .205 .212 29.3 .90 m5.0 1.64 3.25 AD 22 .077 .144 36.0 .97 -3.5 1.19 2.25 AD 23 .166 .212 34.2 .96 m4.0 1.44 2.34 AD 24 ,325 .297 31.9 .92 a3.O 1.63 1.23 ED2 .266 .297 36.9 .96 m3.5 1.55 1.66 ED4 .114 .297 30.3 .91 m3.5 1.34 2.25 ED 5 .188 .262 28.3 .88 m5.0 1.65 3.39 ED6 .124 .226 33.2 .95 m3.0 1.32 1.64 ED9 .259 .253 30.6 .91 -3.5 1.63 1.76 ED 10 .192 .208 28.4 .88 -5.0 1.59 3.43 ED 11 .131 .163 38.4 .95 -3.5 1.31 2.10 ED 12 .227 .297 33.4 .95 1.13.0 1.53 1.33 ED 13 .098 .297 34.2 .96 -4.0 1.26 2.65 "_ Note :

Figure 2.- Three-quarter rear view of typical configuration. 60

25 IAD 3

AD 4 I AD 101 Orll P4 P4 1-1 P

AD 121 dcI L I C - CONSTANTAC cc P S S= P - 3-D OR POLYNOMIAL AC P a2(b/2)

(a)Analytical, reflexive group.

Figure 3 .- Analytically and empirically designed strakes. (Shadingindicates those strakestested in wind tunnel.) t 1 \ AD 207

7tE!0 I AD 15 1 I AD 211

IC II L1n( I 1 AD 16- AD 22 IC C

IL C - CONSTANT AC P

(b) Analytical, gothic group.

Figure 3.- Continued. AD 24 "- I 1 1 I ED 1 to ED 4-----LEAD-ING ED4 1 IED12 1 I ...... :.:.:.:.* I HdCZZX7I...... I t I. I. I I ED 5 to ED 8----TRAILING EDGq w0...... I t I >ED& [ED 16 to ID18 TRAILING AREA I (ED 9 to ED 11 ----INBOARDEDGE I

L"""

Figure 3.- Concluded. 679-656 Figure 4.- Typical strakes. 4 0

L-79-657 Figure 5.- Three-quarterfront view of model mountedon high-angle-of-attack sting support in LangleyHigh-speed 7- by 10-Foot Tunnel. 2.4

1.6

CD .a

a. deg

.- -.4 0 .4 1.6.a 1.2 2.0 n

(a) AD 9.

Figure 6.- Effect of Machnumber on basic longitudinal characteristics for complete configuration.

71 2.4

1.6

a. deg

-.4 0 .4 .a 1.2 1.6 2.0 c LL tot (b) AD 14.

Figure 6.- Continued.

72 .a

cnl 0

-. 4

-. 8 2.4

1.6

0 56

32 a. deg

0 -.4 0 .4 .8 1.2 1.6 2.0

n LL tot

Figure 6.- Continued.

73 2. a

1.6

a. deg

-.a 0 .4 .a 1.2 1.6 2.0

CL tot

(d) AD 19.

Figure 6.- Continued.

74 2.4

1.6

a. deg

-.4 0 .4 .a 1.2 1.6 9-tot

(e) AD 22.

Figure 6.- Continued.

75 .4

-. 4

-. a

2.4

1.6

0 56

-.4

CL tot

(f) .AD 23. Figure 6 .- Continued.

76 2.4

1.6

.. -.4 0 .4 .a 1.2 1.62.4 2.0 cL tot

Figure 6.- Continued.

77 .8

-. 4

-. 8

2.4

0 56

-A.- -.4 0 .4 .8 1.2 1.6 2.0 CL tot

(h) ED 2.

Figure 6.- Continued.

78 .4

-. 4

-. 8

2.4

1.6

0 56

32 a. deg

0 -A.. -.4 0 .4 .a 1.2 1.6 CL tot

(i) ED 4.

Figure 6.- Continued.

79 2.4

1.6

.- -.4 0 .4 .8 1.2 1.6 2.0 LL tot

Cj) ED 5.

Figure 6.- Continued.

80 .4

cm 0

-.4

-. 8

2.4

1.6

0 56

32 a. deg

0 -A.- -.4 0 .4 .8 1.2 1.6 CL tot

(k) ED 6.

Figure 6.- Continued.

81 2.4

1.6

cD .a

.- -.4 0 .4 .a 1.2 1.6 2.0 CL tot

(1) ED 9.

Figure 6.- Continued.

82 .4

-. 4

-. 8

2.4

1.6

0 56

32 a. deg

-.4 0 .4 .a 1.2 1.6 2.0 CL tot

(m) ED 10.

Figure 6.- Continued.

83 2.4

1.6

a. deg

.. -.4 .4 .8 1.2 1.6 CL tot

(n) ED 11.

Figure 6 .- Continued.

84 .a

-.4

-. 8

2.4

1.6

0 56

32 a. deg

-A.- -.4 0 2.0.4 1.6.a 1.2 LL tot

(0)ED 12.

Figure 6 .- Continued.

85 2.4

1.6

CD .a

a. deg

-.4 0 .4 .a 1.2 1.6 cL tot

Figure 6.- Concluded.

86 .4

-.4

-.8

1.2

.8 cD .4

1.6

1.2

.8 cL .4

-. 4 -8 0 a 16 24 32 4 56 a. deg

(a) AD 9.

Figure 7.- Effect of Mach number on basic longitudinal characteristics for wing-afterbody.

87 .. -8 0 8 16 24 32 56 a. deg

(b) AD 14.

Figure 7.- Continued.

88 .b

-.4

-.8

1.2

.8 cD .4

1.6

1.2

.8 cL .4

-A.- -8 0 8 16 24 32 48 0. deg

Figure 7.- Continued.

89 -a 0 8 16 24 32 40 48 56 a. deg

(a) AD 19.

Figure 7.- Continued.

90 .4

-.4

-. 8

1.2

.a cD .4

1.2

.a cL .4

-. 4 -8 0 8 16 24 32 40 48 56 (I. deg

(e) AD 22.

Figure 7.- Continued.

91 .4

-. 4

-. 8

1.2

cD .4

0 .. cL tot 1.6

1.2

cL .4

-.4 -8 0 a 16 24 32 48 56 a. deg

(f) AD 23.

Figure 7.- Continued.

I .4

cm 0

-.4

-. 8

1.2

.8 cD .4

0 -.4 0 .4 .8 1.2 2.41.6 2.0 CL tot 1.6

1.2

-.4 8 0 8 16 24 32 48 56 a. deg

(9) AD 24. Figure 7 .- Continued.

93 1.2

-.4 -8 0 8 16 24 32 48 a, deg

Figure 7.- Continued.

94 I

-.4

-. a

1.2

LLtot

1.2

-A.- -a 0 a 16 24 32 48 56 a. deg

(i) ED 4.

Figure 7 .- Continued.

95 .4

-.4

-. a

1.2

0- cL tot

1.6

1.2

-. 4 -a 0 8 16 24 32 40 56 a. deg

Figure 7.- Continued.

96 .4

-.4

-.8

1.2

.8 cD .4

cL tot

1.2

.8 cL .4

-.4 -8 0 8 16 24 32 % a. deg

(k) ED 6.

Figure 7.- Continued.

97 .4

-.4

-. 8

1.2

cD .4

1.6

1.2

.8 5 .4

-. 4 -8 0 8 16 24 4832 40 a. deg

Figure 7 .- Continued.

98 cL tot 1.6

1.2

-A.- -a 0 a 16 24 32 48 56 a. deg

(m) ED 10.

Figure 7.- Continued.

99 cL tot 1.6

1.2

.. -8 0 8 16 24 32 40 48

a. deg

(n) ED 11.

Figure 7.- Continued.

100 .4

cm 0

-. 4

-. 8

1.2

.8 % .4

cL tot

1.2

.8 cL .4

-8 0 8 16 24 32 40 48 (I. deq

(0)ED 12. Figure 7 .- Continued.

101 cL tot

1.2

cL .4

-8 0 a 16 24 32 40 48 56 a. deg

Figure 7.- Concluded.

102 -a 0 8 16 24 32 56 a. deq

(a) AD 9.

Figure 8.- Effect of Mach number on basic longitudinal characteristics for strake-forebody.

103 0 .4 1.6 .8 1.2 2.0 tot

cL .A

-.A -8 0 8 16 24 32 40 48 56 a. deg

(b) AD 14.

Figure 8.- Continued.

104 .8 cL .4

-_4 -8 0 a 16 24 32 a. deg

105 -8 0 40 a 32 16 24 4a 56 a. deg

(a) AD 19.

Figure 8 .- Continued.

106 .a

-.4

-. a

1.2

cD .4

0 cL

-. A -a 0 8 16 24 32 40 48 56 a. deg

(e) AD 22.

Figure 8.- Continued.

107

I .E

-. 4

-. 8

1.2

cD .4

0 -.4 0 .4- 1.6 1.2 2.0 tot

cL .4

-_4 -8 0 a 16 24 32 40 48 56 a. deg

(f) AD 23.

Figure 8.- Continued.

108 -8 0 a 16 24 32 48 56 a. deg

(9) AD 24.

Figure 8.- Continued.

109 LLtot

1.2

-.4 -8 0 8 16 24 32 40 48 a. deg

(h) ED 2.

Figure 8.- Continued.

110 .4

cm 0

-.4

-. 8

1.2

cO .4

.8 cL .4

-.4 -8 0 a 16 24 32 40 48 56 a. deg

(i) ED 4.

Figure 8.- Continued.

111 1.2

-. 4

-.a

1.2

.a cO A

cL tot

.- -a 0 a 16 24 32 40 48 56 a. deg

Figure 8.- Continued. .a cL .4

-A.- -a 0 0 16 24 32 40 48 56 a. deg

(k) ED 6.

Figure 8 .- Continued.

113 1.2

-.A

-.a

1.2

-a 0 a 16 24 32 40 a. deg

(1) ED 9.

Figure 8 .- Continued.

114 .a cL .4

-_4 -8 0 8 16 24 32 40 48 56 a. deg

(m) ED 10.

Figure 8.- Continued.

115 (n) ED 11. Figure 8 .- Continued.

116 1.2

-.4

-. 8

1.2

.- -8 0 8 16 24 32 40 48 a. deg

(0) ED 12. Figure 8 .- Continued.

117 L L tot

-8 0 24 8 16 32 40 48 56 a. deg

Figure 8.- Concluded.

118 2.4

1.6

cD .a

a. deg

-.4 0 .4 .a 1.2 1.6 21 0 tot

(a) AD 9.

Figure 9.- Complete-configuration longitudinal aerodynamic characteristics at M = 0.2; data and theoretical estimates.

119 2.4

1.6

a. deg

.. -.4 0 .4 .a 1.2 1.6 2.0 5-tot

(b) AD 14. Figure 9 .- Continued.

120 2.4

1.6

cD .a

a. deg

.. -.4 0 .4 .a 1.2 1.6 2.0 CL tot

Figure 9.- Continued.

121 .4

-.4

-. 8

2. A

1.6

0 56

-. 4 .4 0 .4 .a 1.2 1. 6 2.0 tot

.(a) AD 19. Figure 9 .- Continued.

122 .4

crn J

-.4

-. 8

2.4

1.6

0 56

32 a. deg

0 -A.- -.4 0 .4 .81.6 1.2 CL tot

(e) AD 22.

Figure 9.- Continued.

123 2.4

1.6

cD .a

-.4 0 .4 1.6.a 1.2 2.0 cL tot

(f) AD 23-

Figure 9.- Continued.

124 a

cm 0

-. 4

-. 8

2.4

1.6

0 56

a. deg

.* -.4 0 .4 .a 1.2 1.6 2.0 2.4 cL tot

Figure 9.- Continued.

125

E 2.4

1.6

a. deg

._. -.4 0 .4 .a 1.2 1.6 2.0 tot

Figure 9.- Continued.

126 .4

-.4

-. a

2.4

1.6

0 56

32 a. deg

-A._1 -.4 0 .4 .a 1.2 1.6 CL tot

(i) ED 4.

Figure 9.- Continued.

127 2.4

1.6

a. deg

-.4 0 .4 .a 1.2 1.6 2.0 CL tot

Figure 9.- Continued.

128 2.4

1.6

a. deg

.. -.4 0 .4 .a 1.2 1.6 LL tot

(k) ED 6.

Figure 9.- Continued.

129 ...... ". . ..

2.4

1.6

CD .a

a. deg

.- -.4 0 .A .a 1.2 1.6 2.0 CL tot

(1) ED 9.

Figure 9.- Continued.

130 2.4

1.6

cD .a

a. deg

.. -.4 0 .4 .a 1.2 1.6 2.0 CL tot

(m) ED 10.

Figure 9.- Continued.

131

n 2.4

1.6

a. deg

-. 4 0 .4 .8 1.2 1.6

cL tot

(n) ED 11.

Figure 9 .- Continued.

132 2.4

1.6 cD .a

-.4 0 .4 .a 1.2 1.6 2.0 CL tot

(0) ED 12.

Figure 9.- Continued.

133 2.4

1.6

CD .a

a. deg

-.4 0 .4 1.6.8 1.2 cL tot

(PI ED 13.

Figure 9.- Concluded.

134 .a

-.4

-.8 -.4 0 .4 .8 1.2 1.6 CL tot 1.2 0 Wing-Afterbody 0 Strake-Forebody "" PotentlalTheory "_ Low a Vortex Lift Theory High a Vortex Lift Theory

-.4 0 .4 .a 1.2 1.6 CL tot 1.6

1.2

cL .4

-A -8 0 8 16 24 32 48 56 a. deg

(a) AD 9.

Figure 10.- Component longitudinal aerodynamic character istics at M = 0.2; data and theoretical estimates.

135 .- -.4 0 .4 .a 1.2 1.6 2.0 tot 1.2 0 Wing-Afterbody 0 Strake-Forebody "" Potentlal Theory .8 "_ Low a Vortex Lift Theory High a Vortex Lift Theory cD .4

0 -.4 0 .4 .8 1.2 1.6 2.0 CL tot

.. -8 0 8 16 24 32 48 56 a. deg

(b) AD 14.

Figure 10.- Continued.

136 ." -.4 0 .4 .81.6 1.2 2.0 CL tot 1.2 0 Wing-Afferbody 0 Strake-Forebody

Low a Vortex Lift Theory .8 cD .4

0 -.4 0 .A .a 1.2 1.6 2.0 CL tot 1.6

1.2

.a cL .4

-A.- -8 0 8 16 24 32 40 48 a. deg

Figure 10.- Continued.

137 1.2

-.4

." -.4 0 .4 .a 1.2 1.6 2.0 CL tot 1.2 0 Wing-Afterbody 0 Strake-Forebody "" Potential Theory .a "- Low a Vortex Lifl Theory High a Vortex Lifl Theory cD .4

0 -.4 0 .4 .a 1.2 1.6 2.0 tot

-8 0 8 32 16 24 40 48 56 a. deg

(d) AD 19.

Figure 10.- Continued.

138 .8

-.4

-x... -.4 0 .4 .8 1.2 1.6 cL tot 1.2 0 Wing-Afterbody D Strake-Forebody "" Potential Theory .8 "_ Low a Vortex Lift Theory High a Vortex Lift Theory cD .4

0 -.4 0 .4 1.6.a 1.2 CL tot

.. -8 0 8 16 24 32 56 40 48 a. deg

(e) AD 22.

Figure 10.- Continued.

139 .a

-.4

-. 8 -.4 0 2.0.4 1.6.a 1.2 CL tot 1.2 0 Wing-Afterbody 0 Strake-Forebody "" PotentialTheory "_ Low a Vortex Lift Theory High a Vortex Lifl Theory

-.4 0 .4 .a 1.2 1.6 2.0

1.2

-. 4 -8 0 8 16 24 32 48 56 a. deg

(f) AD 23.

Figure 10.- Continued.

140 1.2

.4 cm 0

-. 4

-... a -.4 2.40 .42.0 1.6.a 1.2 cL tot 1.2 0 Wing-Afterbody 0 Strake-Forebody

0 -.4 2.40 2.0.4 1.6.8 1.2 cL tot 1.6

1.2

-.4

Figure 10.- Continued.

141 1.2

-.4

-.8 -.4 0 .4 .8 1.2 1.6 2.0 CL tot 1.2

0 -.4 0 .4 .8 1.2 1.6 2.0 CL tot

.. -8 0 8 16 24 32 a. deg

(h) ED 2.

Figure 10.- Continued.

142 ." -.4 0 .4 .8 1.2 1.6 cL tot 1.2 0 Wing-Afterbody 0 Strake-Forebody "" PotentialTheory .8 "- Low a Vortex Lift Theory High a Vortex Lift Theory cD .4

0 -.4 0 .4 .81.6 1.2 CL tot

1.2

.8 cL .4

-A.. -8 0 8 16 24 32 40 48 56 a. deg

(i) ED 4.

Figure 10.- Continued.

143 1.2

-.4

-.a .4 0 2.0 .4 1.6.a 1.2 r

Figure 10.- Continued.

144 .a

-. 4

-..- 8 -.4 0 .4 .a 1.2 1.6 CL tot 1.2 0 Wing-Aflerbody 0 Strake-Forebody

"" PotentialTheory .a "_ Low a Vortex Lifl Theory High a Vortex Lift Theory cD .4

0 -.4 0 .4 .a 1.2 1.6

1.2

.a cL .4

-.4 8 240 8 16 32 56 a. deg

(k) ED 6.

Figure 10.- Continued.

145 -.4 0 2.0.4 1.6.8 1.2 CL tot 1.2

cD .4

0 -.4 0 .4 1.6.8 1.2 2.0 CL tot

-8 0 8 16 24 32 40 48 a. deg

(1) ED 9.

Figure 10.- Continued.

146 1.2

-.4

-. a -.4 0 .4 .a1.6 1.2 2.0

1.2 0 Wing-Afterbody 0 Strake-Forebody "" Potential Theory Low Vortex Llft Theory .8 "_ u High a Vortex Lift Theory cO .4

0 0 .4 1.6.a 1.2 2.0 tot 1.6

1.2

-A -8 0 8 16 24 32 48 56 a. deg

(m) ED 10.

Figure 10.- Continued.

147 f .8

-. 4

-R.- -.4 0 .4 .8 1.2 1.6

0 Wing-Afferbody 0 Strake-Forebody "" PotentialTheory "_ Low a Vortex Lift Theory High a Vortex Lift Theory

.. -8 0 8 16 24 32 40 48

a. deg

(n) ED 11.

Figure 10.- Continued.

148 1.2

-.4

-Q." -.4 0 .4 2.0 .a1.6 1.2 cL tot 1.2 0 Wing-Afterbody 0 Strake-Forebody .a

0 -.4 0 .4 2.0 .a1.6 1.2 cL tot

.. -a32 0 24 a 16 48 a. deg

(0)ED 12.

Figure 10.- Continued.

149 IIIIII IIIIIIIIIIIII I

-.4 0 .4 1.6.a 1.2 L L, tot 1.2 0 Wing-Afterbody 0 Strake-Forebody ”” Potential Theory .a ”- Low a Vortex Lift 1‘heory High a Vortex Lift Theory cD

0 -.4 0 .4 .8 1.2 1.6 cL. tot

1.2

-.4 8 0 8 16 24 32 48 56 u. deg

(PI 13.

Figure 10.- Concluded.

150 -.4 0 .8 .4 1.2 1.6 2.0 L. tot

.. 0 8 16 24 4832 40 56 a. deg

(a) Complete configuration.

Figure 11.- Effect of Mach number on lift and pitching-moment characteristics for AD 19 configuration; data and theoretical estimates.

151 1.2

-. 4

-. 8 -. 4 0 .42.0 .81.6 1.2 1.6

1.2

-. 4 -

(b) Components.

Figure 11 .- Concluded.

152 2.4

1.6

a. deg

.. -.4 0 .4 .a 1.2 1.6

CL tot

(a) Forward wingposition.

Figure 12.- Effect of Mach number on longitudinal aerodynamic characteristics for basic wing-body configuration: data and theoretical estimates.

153 2.4

1.6

CL tot

(b) Aft wing position.

Figure 12.- Concluded.

154 1.6

1.4 Synergism Effect 1.2

1.0 CL,tot .8

9.2

-.4 0 , 9 I. 8 16 24 32 40 48 56 a, degrees

(a) AD 9.

Figure 13.- Aerodynamic synergism effect on configurationlift at M = 0.2.

155 1.8

1.6

1.4

1.2

1.0 CL,tot .8

-.2

-e4 -i 8 24 32 48 56

(b) AD 14.

Figure 13.- Continued.

156 1.8

1.6 1.4 1.2

1.0 I /' " CL,tot .8

-.2

9.4 I I 1 I I I 1 I I 0 8 16 24 32 40 48 56 CY,degrees

Figure 13.- Continued.

157 If 1.8

1.6 1.4

I r- - I 1.2

1.0 CL,tot .8

-.2 -.4 4 8 16 24 32 40 48 56 a,degrees

(d) AD 19.

Figure 13.- Continued.

158 1.4 1.2

.2 / 0

-.2

-.4 1 1 1 1 1 1 1 I 8 16 24 32 40 48 56 CY,degrees

(e) AD 22.

Figure 13.- Continued.

159

I -1

1.8 1.6 1.4

1.2

1.0 C L,tot .8

.4 'A I

"" ' "-," IL "=-" / L-x + .2

-.2

-.4 1 1 1-1 I T 8 16 24 32 40 48 56 a,degrees

(f) AD 23.

Figure 13 .- Continued.

160 2.2

2.0

1.8

1.6

1.2

1.o CL,tOt .8

.4 "" """ + &-:"A .2

-.2 0.4 0 8 16 24 32 40 48 56 a,degrees

(9) 24.

Figure 13.- Continued.

161 2.0

1.8

1.6

1.4

1.2

1.0 CL,tot .8

-.4 1 1 1 1 1 I-1.-.I."~ _I -8 0 8 16 24 32 40 48 56 a,degrees

(h) ED 2.

Figure 13.- Continued.

162 r

1.4

1.2

1.0 CL,tot .8

-.2

-.4 I 1 I I I I I 0 8 16 24 32 40 48 56 a,degrees

(i)ED 4.

Figure 13.- Continued.

163 1.8

1.6

1.4

1.2

1.0 CL,tot .8

0 / -.2 -.4 -8 0 8 16 24 32 40 48 56 a, degrees

Cj) ED 5.

Figure 13.- Continued.

7 64 1.6

1.4

1.2

1.0 CL,tot .8

.4 L-;7""_ " + &-=" A .2

-.2

-.4 1-~A 32 40 48 56 a,degrees

(k) ED 6.

Figure 13.- Continued.

165 2.0 - L8 -

1.6 -

1.4 -

" 4 1.2 - \

1.0 -

.8 -

.6 -

.4 - ""

*2 - .""""

1.2 -

-.4 + I I 1-"I -8 0 8 16 24 32 40 48 56 a, degrees

(1) ED 9.

Figure 13.- Continued.

166 1.8

1.6

1.4

1.2

1.0 CL,tot .8

0 1

-.2

9.4 0 -8 1 8 16 24 32 56 a,degrees

(m) ED 10.

Figure 13.- Continued.

167 1.4

1.2

1.0 CL,tot '. .8

.4 ""

.2 """"_

-2

0.4 I I 1 1 I 1 -8 0 8 16 24 32 40 48 CX,degrees

(n) ED 11.

Figure 13.- Continued.

168 2.0

1.8

1.6

1.4

1.2

1.o

-.2 -.4 -8 0 8 16 24 32 40 48 56 a, degrees

(0)ED 12.

Figure 13.- Continued.

169 1.4

1.2

1.0 CL,tot .8

-.4 I 4 0 8 16 24 32 40 48 56 a, degrees

(PI 13-

Figure 13.- Concluded.

170 *1

-* 1

-.2

-.3

-a4

-.5

-.6 0.7

-.8 1 1 1 1 1 1

(a) AD 9.

Figure 14.- Aerodynamic synergistic effecton configuration pitching moment at M = 0.2.

171 .8

.1 \

-.1 Cm 0.2 -.s

-.4

-.5

""_"._ -.7

-.8 I I I I I I I J -.4 -.2 0 .2 .4 .6 ,8 1.0 1.2 1.4 1.6 1.8

(b) AD 14.

Figure 14.- Continued.

172 ::1 .1 #' /' I

-.4

-.5 "" "_ -Os I -- =+ L"-"A

Figure 14.- Continued.

173 T \ \ \ I I

-.4 -*2 I

(a) AD 19.

Figure 1'4.- Continued.

174 .I

-.1 Cm -.2

-.3

-.4

-.5 "" "+ L-="A -.6

-.7 -.8 -.4 -.2 0.2. 4. 6. 8 1.0 1.2 1.4

%tot

(e) AD 22.

Figure 14.- Continued.

175

If .3

1 .1 \ \ 3 0 -.1 Cm -*2

-*3

-.4

0.5

-.6

-3

-.a 1 1 1 1 1 1 1 1 -. .2 .4 .6 .8 1.0 1.2 1.4 1.6

(f) AD 23.

Figure 14.- Continued.

176 .5

.4 .s

.2 .1

0 -.1 -\ crn '*. -.2 ". -3 . "" ""-r + &-:"A -.4

-.5

-.6

-.7 -.8

Figure 14.- Continued.

177 .5

-.l Cm -.2

-.3

-.4 d -.5 "" "-"-L + L-:--A -.6

-.7

-.8 I I I I I I I ..! . I 1 -.4 -9 0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0

(h) ED 2.

Figure 14.- Continued.

178 .1

0 -.1 Cm -.2

-.3

-.4

-.5

-.7

-.8 1 -.2 0 .2 .4 .6 .8 1.0 1.2

(i) ED 4.

Figure 14.- Continued.

179 Ill I II Ill I I

-.l Cm -.2

-.3

-.4

-.5 9" + L"-" "" ""_ /I -.6

-.7

-.8 1 - .2 .4 .6 .8 1.0 1.2 1.4 1.8 1.6

Cj) ED 5.

Figure 14.- Continued.

180 I

0.1 Cm -.2

-04

0.5

-.6

cL,tot

(k) ED 6.

Figure 14.- Continued.

181 I Ill Ill II I1 I I

.1 . \ ** F

-.2 -

-3 -

-.4 -

-5 -

-.6 -

-.7 -

-.a . I I I 1 I I I I I IJ -.4 -2 3 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 c,,m

(1) ED 9.

Figure 14.- Continued.

182 .4

"1 Cm "2

-3

-.5

-.6 "7

-.a I_. I ~ L I I I I I I I - -.2 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8

(m) ED 10.

Figure 14.- Continued.

183 .1

-.1 Cm -.2

-.3

-.4

-3 A -.6

-.7

-.8 I I I I I I I -.4 -.2 0.2. 4. 6. 8 1.0 1.2 1.4

(n) ED 11.

Figure 14.- Continued.

184 .4 .s

-.1 Cm -.2

-.3

-.4

-.5

-.6

-.7 -.8 I I I I I I I I I 1 -. -.2 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 CL,tOt

(0) ED 12.

Figure 14.- Continued.

185 .1

1.1 Cm -.2

-.3

-.4

-.5

-.6

-.7

1.8 1 I I I I I I -AP -.2 0.2. 4. 6 .8 1.0 1.2 1.4 CL,tot

(PI ED 13.

Figure 14.- Concluded.

186 1.75 / / 160 / /' / / 1.25 / /

f 1.00

f= ('L, tot'swb .75 ('L, tot' wb

DATA "" H IGH a VORTEXLIFT THEORY, (CL, tot)swb ; .25 ANDPOTENTIAL THEORY, (CL,tot)wb

0 1 I 1 0 8 16 24 52 40 48 56 a, degrees

Figure 15.- Theoretical and experimentalvariation of f with o! for AD 19 at M = 0.2.

187 .75 Mach No. .2 “.5 ”” .7

0 I c 8 16 2Lf 32 YO 48 56 a, degrees

(a) AD 9.

Figure 16.- Effectof Mach number on additional lifting surface efficiencyfactor f.

188 1.75

1.25

f 1.00

.75 Mach No. .2 - -. 5 -" -. 7

0 I I I I 1 I 8 16 2Y 32 110 Y8 56 a, degrees

(b) AD 14.

Figure 16 .- Continued.

189 L75

125

f 1.00

.75

Mach No. .2 - -.5 ””.7 .25

0 I I I Id I 8 16 2Ll 32 LfO 118 56 a, degrees

Figure 16 .- Continued.

190 Mach No. .2 ".5 "".7

1 I I I I I I 8 16 2Lf 32 YO Y8 56 a, degrees

(d) AD 19. Figure 16 .- Continued.

191 1.50

1.25

f 1.00

.75 Mach No. .50 .2 - - .5 "".7

.25

0 I I 8 16 2!l 32 LlO 98 56 a, degrees

(e) AD 22.

Figure 16.- Continued.

192 L75

1.50

1.25

f 1.00

.75

Mach No. .50 .2 ".5 "" .7 .25

0 1 I 8 16 2Y 32 YO Y8 56 a, degrees

(f) AD 23.

Figure 16.- Continued.

193 1.75

1.50

1.25

f 1.00

.75 Mach No. ,60 .2 ".5 "" .7 .25

0 ( 8 16 21f 32 LfO 1f8 56 CY, degrees

Figure 16.- Continued.

1 94 1.75

125 f 1.00

.75 Mach No. .2 - -.5 ”“-7

0 8 16 2Y 32 Y8 56 CY, degrees

(h) ED 2.

Figure 16.- Continued.

195 .. "...... -

f Loo

Mach M) No. .2 - -.5 "".7

0 I I I 1 1 I I 8 16 2g 32 Lfo Lf8 26 a, degrees

Figure 16.- Continued.

196 1.75

1.50

1.25 f 1.00

.75

Mach No. .50 .2 ".5 "" .7 .25

0 1 1 21f 32 Lfo Y8 56 a, degrees

Figure 16.- Continued.

197 f 1.00

Mach No. .2 ".5 - "- .7 25

0 I

(k) ED 6.

Figure 16.- Continued.

198 I

1.75

1.50

1.25

f 1.00

Mach No. .2 - - .5 "".7 .25

0 -" - I 16 2Ll 32 YO 48 56 a, degrees

(1) ED 9.

Figure 16.- Continued.

199 L76

.76

Mach No. .2 - - .5 "- -.7

I I 1 1 1 1 1 8 16 21f 32 Lfo 98 56

(m) ED 10.

Figure 16.- Continued.

200 1) I

1.50’

1.25

f 1.00

.75

Mach No. .50 .2 “.5 ”“-7

.25

0 I I 0 8 16 24 32 40 48 56 CY, degrees

(n) ED 11.

Figure 16.- Continued.

201 L75

Mach No. .2 - -.5 "" .7

.25

0 J 1 ( 16 261 32 LfO 618 56 a, degrees

(0) ED 12.

Figure 16.- Continued.

202 1.50

1.25

f 1.00

.75

Mach .ti0 A No. .2 ".5 "".7 .25

0 I I 8 16 2Y 32 YO Y8 56 a, degrees (PI 13. Figure 16. - Concluded .

203 .75 -

- AD 24 0.325 0.297 .50 "" AD 23 0.166 0.212 """" AD 22 0.077 0.144

.25 -

0 I 0 8 16 2Lf 32 LfO Lf8 56 CX, degrees

Figure '17.- Effect of Ra on f for a fixedgothic-strake shape at M = 0.2 and R, = 7.00.

204 r

L75 -

150 -

1.26 -

f 1.00

AD 24 0.325 7.00 "" ED 12 0.227 5.18 *751.50 ------ED 13 0.098 2.78

1 " 1 ~ ~"I - 1 1 1 8 16 2Lf 32 LfO Lf8 56 a, degrees

Figure 18.- Effect of chordwise scaling on f for AD 24 strake at M = 0.2 and Rb = 0.297.

205 1.50

1.25

f 1.00 e

.75

ED 6 0.124 0.226 5.22

"" .50 ED 4 0.114 0.297 2.77

.25

0 ~~ ." 1"~L 8 16 32 LfO 1f8 56 a, degrees

(a) Ra - 0.119. Figure 19.- Effect of strake shape, Rs, and at fixed Ra and M = 0.2.

206 1.75

1.50

1.25

f 1.00

.75 R -S AD 23 0.166 0.212 7.00 .50 "" AD 14 0.172 0.212 6.99

.25

0 - -1-~ LL I 8 16 2Lf 32 LfO Lf8 56 01, degrees

(b) R, - 0.169. Figure 19.- Continued.

207 1.75

1.50

125

f 1.00

.75

ED 5 0.188 0.262 5.83 .50 "" AD 17 0.185 0.212 7.77 """" AD 9 0.183 0.197 10.65

0 I I I I I 8 16 2Y 32 YO Y8 56 a, degrees

Figure 19.- Continued.

208 1.75

1.50

1.25

f 1.00 /

.75

ED 2 0.266 0.297 5.19 .50 “” ED 9 0.259 0.253 7.79

.25

0 ( a, degrees (d) R, - 0.263. Figure 19.- Concluded.

209 1.26::r

,75 - -RS AD 19 0.205 8.50 "" AD 17 0.185 7.77 ------507 - AD 14 0.172 6. 99 "" AD 23 0.166 7.00

25 -

0, I I 0 8 16 2Lf 32 LfO Lf8 56 a, degrees

Figure 20.- Effect of strake shape on f at Rb = 0.21 2 and M = 0.2.

21 0 1.75

150

L25

,// L 1, f 1.00

.75 -Rb -R*

AD 24 0.325 0.297 7.00 "" AD 19 0.205 0.212 8.50 """" AD 14 0.172 0.212 6.99 "" AD 17 0.185 0.212 7.77 35

0 J I I I I 1 I 8 16 2Li 32 40 5i6 01, degrees

Figure 21 .- Effect of Ra, Rb, and Rs on f forthe "better" gothic strakes at M = 0.2.

21 1 1.75

1.60

125

f 1.00

.75 R R -a -S

AD 24 0.325 7.00 .w "" ED 2 0.266 5.19 """" ED 4 0.114 2.77

.25

0 I 1 ( 8 16 29 32 Llo '48 56 a, degrees

(a) Apex cut.

Figure 22.- Effect of removing area from AD 24 stake on f at M = 0.2.

21 2 1.75

1.25

f 1.00

.75 - R -5

AD 24 0.325 0.297 7.00 - "" ED 5 0.188 0.262 5.83 .50 ------ED 6 0.124 0.226 5.22

.25 -

0 I I 1 1 I 0 8 16 2Li 32 LlO Li8 56 a, degrees

(b) Trailing-edge cut.

Figure 22.- Continued.

21 3 1.75

L25

f 1.00

.75 R R a -S AD 24 0.325 0.297 7.00 .50 ---- ED9 0.259 7.79 0.253 """" ED 10 0.1928.62 0.208 - - - - ED11 0.1319.59 0.163

.25

0 a 16 24 32 40 48 56 a, degrees

Figure 22.- Concluded.

21 4 1.75

1.50

1.S

f 1.00

ACSPECIFICATION .75 Rb "RS AD 19 0.205 0.212 8.50 CONSTANT "- AD 9 0.183 0.197 10.65 P OLY NOM I AL .50 -

.25

0 1 ( 8 16 2Lf 32 LfO Lf8 56 a,degrees

Figure 23.- Effect of strake-design pressure specification (fora fixed prescribed suction distribution) on f at M = 0.2.

21 5 0 ANALYTICALLY DES IGNED - rapo;;n "2 CONSTANTPRESSURE ./ * /" 0 ANALYTICALLY DESIGNED - POLYNOMIAL PRESSURE 0 EMP IR ICALLY DES IGNED %/ I + EMP I R ICALLY DES IGNED OGEE STRAKES FROM REF. 12 ) (1+Ra) ('L, ('L, max wb

I I I 1 I II I I 1 .04 .08 .12 .16 .20 .24 .28 .32 .36 .32 .28 .24 .20 .16 .12 .080 .04

Figure 24.- Effect of strake shape on swb at M = 0. AIR M = 0.3

a = 16" a = 18.3' a .= 20.4"

WATER

a 16.3' a 21.7"

(a) 16O I a 5 21.7O.

Figure.25.- Strake vortex as observed in air and water onAd 24 configuration. a = 23" a = 25.4O a = 27.8O

WATER

a 27.2"

(b) 23O I a 6 27.8O.

Figure 25.- Continued. a 32.5'

WATER

a = 32.8"

Figure 25.- Continued. AIR M =O1.3

u < 35.4" hrv

WATER

(d) a <, 35.4O.

Figure 25.- Continued. AIR M = 0,,3

u 35.4"

WATER

a = 37.6" (e) a h 35.4').

Figure 25.- Concluded. iHEF. 13) 60 (REF. 3)

20 65' 55O

,I.. I I 1 I 1 0 .2 .4 .6 .8 1.0

Figure 26.- Vortex breakdown progression on delta wings in air and water. 2.2 AIR

2.0

1.8

1.6

1.4 cL 1.2

1.o

Figure 27.- Effect of strakevortex on lift data. AD 24; M = 0.3. 1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No. NASA TP-1803 4. Title and Subtitle 5. Report Date EXPERIMENTAL AND ANALYTICAL STUDY OFTHE LONGITUDINAL June 1981 AERODYNAMIC CHARACTERISTICS OF ANALYTICALLY AND 6. PerformingOrganization Code AT 505-31-43-03 EMPIRICALLY DESIGNED STRAKE-WING CONFIGURATIONS

”” SUBCRITICAL SPEEDS 8. PerformingOrganization Report No. 7. Author(s) L-14041 John E. Lamar and Neal T. Frink , 10. Work UnitNo, 9. PerformingOrganization Name and Address NASA Langley Research Center 11. Contractor Grant No. Hampton, VA 23665

13. Type ofReport and Period Covered 12. Sponsoring Agency Name and Address Technical Paper National Aeronauticsand Space Administration Washington, DC 20546 14. Sponsoring Agency Code

I 15. SupplementaryNotes

16. Abstract Sixteen analytically and empirically designed strakes have been tested experimentally on a wing-body at three subcritical speeds in such asa wayto isolate the strake-forebody loads from the wing-afterbody loads. Analytical estimates for these longitudinal results have been made using the suction analogy and the augmented vortex lift concepts. The synergistic data are reasonably well estimated or bracketed by the high- and low-angle-of-attack vortexlift theories over the Mach number range and up to maximum or lift strake-vortex breakdown over the wing. Also, the strake geometry is very importantin the maximum lift value generated and the lift efficiency of a given additional area. Increasing size and slenderness ratios are important in generating lift efficiently, but similar efficiency can also be achieved by designing a strake with approximately half the area of the largest gothic strake tested. These results correlate well with strake- vortex-breakdown observations in the water tunnel.

- 7. Key Words (Suggested by Author(s)) 18. DistributionStatement Strake efficiencyStrakeStrake-wing Unclassified - Unlimited Theoreticalestimates Analytical and Longitudinalaerodynamic empirical charact eristics designscharacteristics Subcritical speeds Vortex-flow aerodynamics 9. Security Classif. (of this report) I 20. Security Classif. (of this page) Unclassified 223 Unclassified 1 A1 0 For sale by the National Technical Information Service, Springfield. Vlrgrnla 22161

NASA-Langley, 1981