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ValidatiOn o_ComputerCode for Analysis ofSubsonic Aerodyna_cPerformance of Wings WithFlaps "m Combination Witha Canard or Horizontal

Tail and an Applicationto Optimizatio_

Harry W. Carlson, ._

Christine M. Darden; _

and Michael J. Manri-_

(NASA-TP-2VAI) VALT_ATIuN _?F A C_!_O_cRCODF FOR ANALYSTS OF subSONIC AErOdYNAMIC

PFRFORMANCE OF WINGS WITH FLAPS IN

COM_INATInN WITH A CANARD OR HORIZONTAL TAIL

AND AN APPLICATIuN TO OPTIMIZATION (NASA)

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https://ntrs.nasa.gov/search.jsp?R=19900004871 2020-06-29T11:21:34+00:00Z

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NASATechnical

Paper2961

1990

National Aeronautics andSpace Administration

Office of Management

Scientific and TechnicalInformation Division

Validation of a ComputerCode for Analysis ofSubsonic AerodynamicPerformance of Wings WithFlaps in Combination Witha Canard or Horizontal

Tail and an Applicationto Optimization

Harry W. Carlson

PRC Kentron, Inc.

Aerospace Technologies Division

Hampton, Virginia

Christine M. Darden

and Michael J. Mann

Langley Research Center

Hampton, Virginia

Summary

Extensive correlations of computer-code resultswith experimental data are employed to illustratethe use of a linearized-theory, attached-flow methodfor the estimation and optimization of the longitu-dinal aerodynamic performance of wing-canard andwing-horizontal-tail configurations that may employsimple hinged-flap systems. Use of an attached-flowmethod is based on the premise that high levels ofaerodynamic efficiency require a flow that is as nearlyattached as circumstances permit. The results ofthis study indicate that linearized-theory, attached-flow, computer-code methods (modified to includeestimated attainable leading-edge thrust and an ap-proximate representation of vortex forces) provide arational basis for the estimation and optimization ofaerodynamic performance at subsonic speeds belowthe drag-rise Mach number, Generally, good predic-tion of aerodynamic performance, as measured bythe suction parameter, can be expected for near-optimum combinations of canard or horizontal-tailincidence and leading- and trailing-edge-flap deflec-tions at a given lift coefficient (conditions which tendto produce a predominantly attached flow).

Introduction

The linearized-theory analysis method of refer-ence 1 provides estimates of the performance of wingsat subsonic speeds; these estimates include the ef-fects of attainable leading-edge thrust and separatedleading-edge vortex flow. The method, which origi-nally was applicable to flat wings or wings with mod-erate twist and camber, was modified in reference 2

to cover wings with leading- and trailing-edge flaps.Extensive comparisons of theoretical and experimen-tal wind-tunnel data for a wide variety of wing-bodyconfigurations presented in references 3 and 4 provideevidence of the range of application of this method.Generally, good predictions of lift, drag, and pitchingmoment are achieved. Poor correlations are shown

only for undeflected flaps at high lift coefficients andfor highly deflected flaps at low lift coefficients; theseconditions tend to promote severe flow detachmentand poor performance.

This report describes an additional modificationof the method of reference 2 to permit the han-

- dling of two separate coplanar lifting surfaces, a wingwith flaps in combination with either a canard or ahorizontal tail. This code differs from other more

complete multisurface codes (e.g., refs. 5 to 7) inthat it is structured primarily to serve the needs

of preliminary-design engineers for a simple-to-usemethod for the rapid estimation of the longitudi-nal aerodynamic characteristics, including drag due

to lift, of conceptual-airplane lifting-surface arrange-ments. In this study, as in the previous wing-alonestudies, the use of what is basically an attached-flow

method is justified by the premise that high levelsof aerodynamic performance require a flow as nearlyattached as circumstances allow. Thus, if reason-ably accurate prediction of aerodynamic performancecan be achieved for flap deflections and auxiliarysurface incidence that result in high levels of aero-dynamic efficiency, poorer correlations can be toler-ated for less interesting off-design conditions. Thisreport provides extensive correlations of theory withexperimental results to illustrate the applicabilityand limitations of the computer-code-generated data.

Symbols

AR

b

CA

CD

/'CO

CD,O

eL

CL,_

Cm

Crn,cg

CN

c

CL

CT

Exp.

i,j

M

R

aspect ratio, b2/S

span, in.

axial- or chord-force coefficient

drag coefficient

drag coefficient due to lift,

Co - CD,o

drag coefficient at a = 0 ° for aconfiguration with no camber ortwist, no flap deflections, and nosecond-surface incidence

lift coefficient

lift-curve slope at a = 0°, per deg

pitching-moment coefficient aboutmoment reference center

pitching-moment coefficient aboutassumed center of gravity

normal-force coefficient

local chord, in.

mean aerodynamic chord, in.

leading-edge-flap chord, in.

trailing-edge-flap chord, in.

experiment

index of wing-element longitudinaland lateral positions, respectively,within numerical-solution gridsystem (see fig. 1)

Mach number

Reynolds number based on meanaerodynamic chord

leading-edge radius, in.

S

$8

t

x, y, z

(2

_c

_H

_L,n

_L,s

_T,n

6T, s

Ah,L

Ah,T

reference area, in 2

suction parameter,eL tan(CL/CL,a) -- AC D

CL tan(CL/CL,a - C2/(_rAR)

section thickness, in.

Cartesian coordinates, positive aft,starboard, and up, respectively, in.

angle of attack, deg

=

incidence of canard reference planewith respect to wing referenceplane, positive with leading edgeup, deg

incidence of horizontal-tail reference

plane with respect to wing reference

plane, positive with leading edgeup, deg

leading-edge-flap deflection anglemeasured normal to hinge line,positive with leading edge down(segmented flap deflection specifiedas inboard/outboard), deg

leading-edge-flap streamwise de-flection angle, positive with leadingedge down (segmented flap deflec-tion specified as inboard/outboard),deg

trailing-edge-flap deflection anglemeasured normal to hinge line,positive with trailing edge down(segmented flap deflection specifiedas inboard/outboard), deg

trailing-edge-flap streamwise de-flection angle, positive with trailingedge down (segmented flap deflec-tion specified as inboard/outboard),deg

location of maximum wing-sectionthickness as a fraction of chord

leading-edge-flap hinge-line sweepangle, deg

trailing-edge-flap hinge-line sweepangle, deg

Theoretical Considerations and Description

of Computer Code

The computer code used for the analysis of thewing-canard and wing-horizontal-tail configurations

2

treated in this report is the result of a recent modifi-cation to a code that has already undergone severalstages of development. The description of the codegiven here is concerned only with an outline of someessential features of the numerical method as previ-ously developed and with a discussion of the changesnecessary to accommodate a second lifting surface.For the most part, the reader is directed to specificreferences for details.

The original computer code described in ref-erence 1 was applicable to a twisted and cam-bered wing without leading- or trailing-edge flaps.This code offers a unique approach to the theoret-

ical analysis of wings at subsonic speeds. Amongthe features are linearized-theory solutions by pureiteration and the use of leading-edge singularity pa-rameters to identify separate velocity-distributioncomponents with and without singularities. Thelatter feature permits more accurate determinationof theoretical leading-edge thrust distribution forwings with twist and camber and provides for im-proved pressure-distribution integration techniques.An empirical determination of attainable leading-edge thrust and detached vortex flow forces is also

included in the estimation of overall wing perfor-mance. The influence function used, the boundaryconditions imposed, and the convergence test for ter-mination of the iteration (which have remained un-changed throughout all stages of code development)are discussed in detail in reference 1.

Extension of the original wing-alone code to per-mit handling of leading- and trailing-edge-flap sys-tems is described in reference 2. The revised code

provides for convenient input of flap-system geome-try. This code is arranged so that, with little ad-ditional expense, solutions can be found for various

combinations of leading- and trailing-edge-flap de-flections. Further development of the computer code(ref. 4) provides for an improved accounting of hinge-line singularities in the determination of wing forcesand moments.

The present modification of the computer codeto handle two separate lifting surfaces requires asubstantial increase in computation and storage, butinvolves no new theoretical concepts. The majorchanges are geometric and can be represented bylifting-surface arrangements depicted in figure 1. Asin the previous applications of the code, the winglifting surface is used to model both the actual wingand a surface representation of the fuselage. Forclarity, fewer elements than usual are shown.

An array of trapezoidal elements employed inan iterative solution of linearized theory for a wingalone is depicted in figure l(a). Only a very smallnumber of elements are shown for the purpose of

illustration; in practice,severalhundredelementswouldbeemployed.Theelementsaresuperimposedonarectangulargrid; the inboardandoutboardele-mentboundarieslie alongunit valuesofthespanwiseparameterBY,andthe midspanof elementleadingand trailing edgeslie on unit valuesof the chord-wiseparameterx/Ax. The scaling of the wing frommodel or airplane dimensions to program dimensionsis chosen to provide the desired number of elementsin the spanwise direction. The distance Ax controlsthe chordwise spacing of the elements; it is selectedby specification of an element aspect ratio that isconstant for all but the leading- and trailing-edge ele-ments. Each element is assigned a number (fig. l(a)),and a record is kept of the number assigned to the

leading- and trailing-edge elements in each chordwiserow. The indices i and j are used in determining theorder of solution; elements are selected first accordingto advancing values of the i index and then accordingto advancing values of the j index. The order of solu-tion thus marches front to rear and inboard and out-board. Because of the nonuniform chords of the code

leading-edge elements, errors in the numerical solu-tion are introduced. However, a strategy describedin reference 1 provided an effective correction.

Figure l(b) depicts the way in which the presentmodified code represents a typical wing-canard con-

figuration. The inboard and outboard boundaries ofthe second surface are made to lie along unit valuesof the spanwise parameter _y. The code routine thatprovides for this adjustment also changes the second-surface chords to preserve the surface area (but notthe aspect ratio). There may be some overlap ofthe canard and the wing in the region of the wing-fuselage juncture. This overlap and the change inaspect ratio introduce a small error in the numericalsolution. This error and other errors associated with

discretization are reduced as the number of spanwisesubdivisions is increased. Second-surface elementsare numbered in the same manner as those of the

wing, and a code index distinguishes between the twosurfaces. The order of solution still marches fromfront to rear and inboard to outboard and either a

wing or a second-surface element is taken as its turncomes up.

The computer code has no provision for verti-cal displacement of the two lifting surfaces. Forlarge vertical-separation distances, this could leadto appreciable errors, but for more moderateseparations, the planar representation should be ad-equate. Experimental-theoretical comparisons pre-sented in this paper help demonstrate the applicabil-ity and limitations of the method.

An additional description of the code as nowamended to provide for a second lifting surface, with

particular emphasis on code input and output data,is given in appendix A.

Analysis of Configuration Performance

The comparisons of theory and experiment usedin this paper to explore the applicability of alinearized-theory, attached-flow method to the anal-ysis of wing-canard and wing-horizontal-tail config-urations are restricted to force and pitching-momentdata. With the proper treatment, however, thesedata can provide much useful information for a studyof the behavior of the lifting systems. The usual lift-drag polars and the data obtained by plotting Cmagainst CL are supplemented with plots of axial- andnormal-force coefficients versus angle of attack thatallow a piece-by-piece study of the factors contribut-ing to aerodynamic performance. Because of the flator nearly flat wing surfaces (in the absence of flap de-flection) of most of the configurations in this study,it is possible to isolate to a large degree the sepa-rate contributions of leading- and trailing-edge flapsto the aerodynamic performance. (See ref. 3.)

Data from a variety of experimental programshave been used in this analysis. Wing leading-edgesweep angles vary from -20 ° to 71 °, Mach numbersfrom 0.09 to 0.9 are considered, and Reynolds num-bers (l:;ased on _) range from 1.35 to 4.19 x 106. Thetest conditions and sketches of the wing-body plan-forms are given in each of the correlation figures.

Notes on application of the code to the specificconfigurations and test conditions included in thisstudy are given in appendix B. Sample code inputdata for the configurations studied are given in ta-ble I. Code representation of the lifting-surface plan-form for selected configurations is shown in figure 2.To avoid instabilities in the numerical solution, it isnecessary to provide an adjustment so that all ele-ments have inboard and outboard boundaries corre-

sponding to unit values of the 3y parameter. Thisadjustment sometimes brings about a change in wingplanform that is most evident in figure 2(d). It alsogenerally requires a lateral relocation of the secondsurface. (See figs. 2(a) and 2(b).) The code routinethat provides the necessary relocation also providesan adjustment to preserve the surface area. Leading-and trailing-edge-flap surfaces are also adjusted tomeet the boundary condition and preserve the area.This last adjustment is most evident in figure 2(e).The net effect of these adjustments on the numericalsolution can be judged only by results. Comparisonsof code results with changes in modeling similar tothose shown indicate only a small change in com-puted aerodynamic characteristics. The comparisonsof theory with experimental data given in this reportalso indicate that the errors are not substantial.

In the basic aerodynamic data figures, data foran attached-flow computer-code solution that in-

cludes no leading-edge thrust forces and no sepa-rated leading-edge vortex forces are shown by theshort-dash lines. Solutions which include attainable

thrust and the effects of a separated vortex whosestrength is determined by the Polhamus leading-edgesuction analogy (ref. 8) are shown by the long-dash-short-dash line. For reference, drag upper and lower

nds are also shown. The theoretical lower bound

+ CL2/(_AR)/ is the drag for a wing with an}0

elliptical span-load distribution and a uniform down-J

wash. A theoretical upper bound shown on the

figures [CD,0 + CL tan(CL/CL,_)] is the drag for aflat wing with no leading-edge thrust and no vortex

forces. The zero-lift drag CD,O was obtained fromexperimental data for a flat configuration (an un-cambered wing-body configuration with undeflectedflaps at _ = 0 ° in combination with a second surfaceat zero incidence).

Unswept Wing Canard

As previously mentioned, the computer code

used in generating theoretical data for the corre-lations presented in this paper has no provisionfor vertical displacement of the two lifting surfaces.Experimental-theoretical comparisons presented inthis paper help to assess the effect of vertical sepa-ration and to demonstrate the applicability and lim-itations of the method. The first such comparison(fig. 3) shows data from reference 9 for a wing-canardconfiguration with three different vertical-separationdistances. Both the wing and the canard had rect-angular planforms and employed a relatively thickairfoil section (13 percent) with appreciable camber.The canard had an incidence angle of 2 ° relative tothe wing surface. Because data presented in the ref-erence are intended to represent a wing-canard ar-rangement only, a tare composed of forces measuredby the support apparatus with the wing and canardremoved was subtracted from all the data. The data

presented in reference 9 were not corrected for thewind-tunnel wall effect. The drag data presentedhere have been corrected to remove that effect byusing information from reference 9.

As shown in the three parts of figure 3, canardvertical position has an appreciable effect on the lift-drag relationship only for lift coefficients in excessof 1.4. For lift coefficients in the range of about0.4 to 1.2, excellent aerodynamic performance (drag

values close to the lower bound) is achieved. Thereis, in general, a very good theoretical prediction ofthis performance. At higher lift coefficients, there isevidence of flow separation which is influenced by the

canard location and which the theory is incapableof predicting. The theory gives a poor account ofthe moment characteristics. However, a part of thediscrepancy may be caused by a measured momentthat is influenced by support-apparatus interference.Reference 9 is not clear on this point.

An interesting characteristic of the code-predictedresults is the presence of some amount of attainablethrust at all angles of attack, as indicated by the com-plete separation of the theoretical axial-force curveswith and without thrust. This thrust comes aboutbecause of the camber of the two surfaces and the

2° incidence of the canard. Although the thrust ofone surface may be nearly zero at some angle of at-tack, the other surface at this same condition pro-duces thrust.

The theory indicates that the wing and canardcamber, in combination with the relatively thickairfoil section, provides a high level of attainablethrust, equal to full theoretical thrust up to an angleof attack of about 6° or a lift coefficient of about 1.1.

The experimental data indicate that full theoreticalthrust is nearly achieved over an even larger range.

60°-Swept Trapezoidal-Wing Fighter WithCanard

Additional data relative to the effect of canard

height on aerodynamic performance (fig. 4) for a 60 °-swept trapezoidal-wing fighter measured at M = 0.70and R -- 1.35 x 106 was obtained from reference 10.

In contrast with the previous configuration, theselifting surfaces were uncambered and were relativelythin with circular-arc sections; therefore, high levelsof performance are not expected.

Data in figure 4(a) for a midfuselage canard lo-cation indicate the presence of a small but signifi-cant amount of leading-edge thrust (the curvaturein the plot of CA versus _ near c_ = 0 °) as wellas a small separated leading-edge vortex force (thechange in curvature in the plot of CA versus (_ andthe increased slope of the ptot of CN versus (_ nearc_ = 6°). Predicted results that account for an as-sumed constant leading-edge radius of 0.002 in. forthe circular-arc wing sections provide a good esti-mate of both effects. Reasonably good predictionsof the lift-drag polar curve and the pitching momentare also noted. For the low canard position in fig-ure 4(b), there is little change in the experimentaldata (the theoretical data are, of course, identical),and the correlation remains good. For the high ca-nard position in figure 4(c), there is a greater dis-crepancy between theory and experiment, but theoverall correlation is still reasonable. Thus, data for ,this and the previous configuration indicate that the

4

theoreticalmethodcanbeapplicableto twolifting-surfacesystemswith moderatevertical-separationdistances.

44°-SweptTrapezoidal-Wing Fighter WithCanard

Reference 11 provides data shown in figure 5 for

a generic fighter configuration tested in the Lang-ley 7- by 10-Foot High-Speed Tunnel at M = 0.4and R = 1.9 x 106 . A matrix of canard and flap

deflections is covered by the measured data. Thematrix is not complete, but there are sufficient datafor specified leading- and trailing-edge-flap deflec-tions with specified canard incidence angles to pro-vide a test of code prediction capabilities for reason-ably efficient arrangements. In reference 4 it wasshown that, in the absence of moment restraints,near-maximum performance for the wing alone wasachieved with equal leading- and trailing-edge-flapdeflections measured normal to the flap hinge line.

Figure 5 presents data for such matched deflection

angles (_L,n and _T,n = 00, 12°, and 20°) withselected canard-incidence angles.

In this section, comparisons of these data with

theoretical results (figs. 5 to 8) provide a test of theability of the theory to predict performance-and iden-

tify optimized arrangements within this limited fam-ily. A subsequent section of this report (Examples ofConfiguration Optimization) illustrates an optimiza-tion process using theoretical data alone in whichleading-edge-flap deflection, trailing-edge-flap deflec-tion, and canard or horizontal-tail incidence may bevaried independently.

Figure 5(a) shows data for undeflected flaps anda canard at _C = 0°. There is evidence of an ap-preciable amount of leading-edge thrust and a smallvortex force. There is a good theoretical predictionof the measured results. As shown in figures 5(b) and

5(c), a negative incidence of the canard affects axialforce in much the same way that leading-edge flapdeflection does. The slope of the curve and the nega-tive CA values can offer performance improvements.The remaining parts of figure 5 treat deflected flapsin combination with canard incidence. Changes in

aerodynamic forces and moments due to flap deflec-tion follow much the same pattern as for the wing-alone situation in reference 4. In general, the theoryprovides a good estimate of the force-and-momentcharacteristics. Correlation is best for negative inci-dence angles which offer reduced drag. Correlation ispoorest for 5C = 10° for which the theory predicts anaxial force at high angles of attack much larger thanthat measured. Canard flow separation is probably

responsible for the less-than-anticipated performancepenalty.

Suction-parameter data for the flap-deflection andcanard incidence combinations of figure 5 are givenin figure 6. Experimental and theoretical suction pa-rameters are shown as a function of lift coefficient.

Generally, there is good agreement between theoryand experiment for deflection and incidence combi-nations which result in high suction-parameter lev-els. The primary purpose of these data is their usein the following figures to determine as accurately aspossible the maximum aerodynamic efficiency of theflap-canard system and the flap deflection and canardincidence combinations required. This informationis helpful in assessing the applicability of linearized-theory, attached-flow methods to the analysis offlap-canard systems operating at or near maximumefficiency.

Suction parameters evaluated from experimentaldata are shown as functions of the matched leading-

and trailing-edge-flap deflection angle for three ca-nard incidence angles and for four lift coefficients atthe top of figure 7. At the bottom of the figure, thesame data are shown as functions of the canard de-

flection angles. The data represented by the symbolswere obtained from fairings of the experimental dataof figure 6. The fairing of the data points in figure 7is intended to represent as accurately as possible thevariation of suction parameter with deflection anglesand canard incidence. An attempt was made to havethe curves bear a "family" resemblance to each otherand to display changes in a progressive manner.

The dashed curves in figure 7 represent an en-velope; the maximum suction parameter obtainablewith the optimum value of 5C is shown in the upperplots, and the maximum suction parameter obtain-able with the optimum value of _L,n and _T,n is shownin the bottom plots. The points to generate thesecurves were obtained by referring to both the topand bottom plots for a given lift coefficient. For ex-ample, the maximum value of suction parameter for agiven leading- and trailing-edge-flap deflection curvefrom the bottom plot is entered in the top plot at the

designated leading- and trailing-edge-flap deflectionangle. This procedure always gives a point equal toor greater than the points representing the faired ex-perimental data from figure 6. An additional checkon the generation of the envelope curves is that themaximum suction parameter of each of the pairs ofcurves must be identical--there can be only one peak.

The completed fairings provide data that describe themaximum suction parameter and the correspondingoptimum leading- and trailing-edge deflection anglesand canard incidence angles (the arrows) as a func-tion of the lift coefficient.

Envelope data from the dashed curves of fig-ure 7 and similar data for theoretical results (not

presented)areshownin figure8. Optimummatchedleading-andtrailing-edge-flapdeflectionangles,op-timum canardincidenceangle,and maximumsuc-tion parameterfor this limited familyareshownasa functionof lift coefficient.Thetheorywith attain-ablethrust andvortexforceestimatesgivesa goodpredictionof the maximumsuctionparameterandthe requireddeflectionandincidenceangles.In theabsenceof anymomentconsiderations,theoptimumcanardincidenceresultsin a surfacethat is nearlyalignedwith the freestreamand produceslittle orno lift. Apparently,thedownwash-upwashfieldpro-ducedby a lifting canardhasanunfavorableeffecton theleading-edge-flaploadingsresponsiblefor theflapperformancebenefits.In thesection"Examplesof ConfigurationOptimization,"the problemof se-lectingoptimumangleswhenleading-edge-flapde-flection,trailing-edge-flapdeflection,andcanardin-cidencemaybe variedindependentlyis addressed.Solutionssubjectto momentconstraints,aswellasfullyoptimlzedsolutions,areconsidered.

An examinationof figure8 in conjunctionwith areexaminationof figure5showsthat a goodcorrela-tionoftheoryandexperimentisobtainedforflapandcanardsettingsthat resultinnear-maximumperfor-manceforthe lift-coefficientrangeof interest.Poorerbut still acceptablecorrelationis displayedfor set-tingsfar fromtheoptimum.If canard-generatedliftis requiredto provideairplanetrim, thesedataindi-catethat thecodecanprovidea reasonableestimateof trim dragpenalties.

Figure9providesdatasimilarto thoseoffigure5,but foraMachnumberof 0.8.Dataforthecodepre-dictionwithoutattainablethrust andvortexforces,aswellas the theoreticalbounds,areomittedbe-causetheprimarypurposehereis to assesstheeffectof Machnumberontheexperimental-theoreticalcor-relation. It is not surprisingthat the correlationoftheoryandexperimentatthishigherMachnumberissomewhatpoorer.Forundeflectedflapsandacanardincidenceof zero,thereis abreakawayin axial forcefor theexperimentaldata(probablycausedbyshockdevelopment)aboveanangleof attackof about8° orabovea lift coefficientof about0.5. Whentheflapdeflectionsare increasedto 20° with a canardinci-denceof -10°, thereisevidenceof trailing-edge-flapflowseparation(failureto developthepredictedCNincrement) and shock effects, and the overall corre-lation is relatively poor.

44°-Swept Trapezoidal-Wing Fighter WithHorizontal Tail

The 44°-swept-wing fighter of reference 11 wasalso tested with a horizontal tail instead of the ca-

nard. Figure 10 presents data for matched leading-

and trailing-edge-flap deflection angles (_L,n :

_T,n _- 0°, 12°, and 20 °) with selected horizontal-tail incidence angles. In figure 10(a), for undeflectedsurfaces, there is evidence of a significant attainablethrust contribution to axial force, as was the casefor the canard configuration. However, there is lit-tle evidence of the predicted vortex-force contribu-tion to normal force. A similar failure of the pre-dicted vortex force to materialize for a 45°-sweptdelta wing was noted in reference 12. A reasonableprediction of drag is obtained only for lift coefficientsbelow about 0.5 for all the data with undeflected

flaps (figs. 10(a) to 10(c)). There is also a signifi-cant discrepancy between experimental and theoret-ical pitching-moment coefficient for the higher liftcoefficients. Similar discrepancies occurred for thisconfiguration with undeflected flaps and without acanard or a horizontal tail. (See ref. 4.) For the12° and 20 ° deflection of both flaps in the remainingparts of figure 10 (figs. 10(d) to 10(i)), there is gen-erally a better prediction of drag at the higher liftcoefficients. For _H : 0° and _H : 10°, which pro-duce relatively good performance, the correlation isreasonably good. The greatest discrepancy betweentheory and experiment is for _H = --10°, an inci-dence angle which produces poor performance. How-ever, the measured drag penalty is less than that pre-dicted. For these deflected-flap cases, there is alsoreasonable agreement between the level of theoreti-cal and experimental pitching moment for horizontal-tail deflections that produce good performance. Thederivative dCm/dCL, however, is not well predicted,because the vortex contribution is overestimated.

Suction-parameter data for all the combinationsof flap deflection and horizontal-tail incidence cov-ered in figure 10 are shown as functions of lift coeffi-cient in figure 11. Figure 12 shows suction parameteras a function of matched leading- and trailing-edge-flap deflection angle and horizontal-tail incidence an-gle for each of four selected lift coefficients. Thisfigure is similar to figure 7 for the previous canardconfiguration. A detailed description of the genera-tion of these plots and their use is given in the pre-ceding section.

Envelope data from figure 12 and similar datafrom theoretical results (not presented) are shown infigure 13. Optimum matched leading- and trailing-edge-flap deflection angles, optimum horizontal-tailincidence angles, and the maximum suctionparameter are plotted as functions of lift coeffi-cient. The theoretical data with attainable thrust

and vortex forces included provide a good estimateof the maximum suction parameter and the requireddeflection and incidence angles. In the section"Examples of Configuration Optimization," the

problemof selectingoptimumangleswhenleading-edge-flapdeflection,trailing-edge-flapdeflection,andhorizontal-tailincidencemay be varied indepen-dentlyis addressed.

An examinationof figure13in conjunctionwitha reexaminationof figure 10showsthat a reason-ablygoodcorrelationoftheoryandexperimentisob-tainedfor flapandhorizontal-tailsettingsthat resultin near-maximumperformancefor the lift-coefficientrangeof interest. Poorcorrelationis displayedforsettingsfar from theoptimum.Thesediscrepanciesfor thehorizontal-tailconfigurationaremuchlargerthanthosefor thecanardconfigurationandpresentaproblemif negativehorizontal-tailincidenceanglesarerequiredto trim the airplane. Onesavingfea-ture is that thecodeprovidesareasonableestimateof the pitching-momentchangedue to a changeinhorizontal-tailincidenceandprovidesa conservativeestimateof trim dragpenalties.

Figure14providesdata similar to thoseof fig-ure 10,but for a Machnumberof 0.8. Data forthe predictionwithoutattainablethrust andvortexforces,aswellasthetheoreticalbounds,areomitted,becausetheprimarypurposehereis to assesstheef-fectof Machnumberontheexperimental-theoreticalcorrelation.It isnotsurprisingthatthecorrelationoftheoryandexperimentat this higherMachnumberispoorer.Forundeflectedflapsanda horizontal-tailincidenceof zero,thereisa breakawayin axial forcefortheexperimentaldata(probablycausedbyshockdevelopment)abovean angleof attackof about6°or a lift coefficientof about0.4. With the flapde-flectionsincreasedto 20° with a horizontal-tailinci-denceof 10°, there is evidenceof trailing-edge-flapflowseparation(failureto achievethepredictedCNincrement) as well as shock effects, and the overallcorrelation is relatively poor.

60°-Swept Delta-Wing Fighter With Canard

Reference 11, which provided data for the pre-vious two configurations, also provides data for a60°-swept delta-wing fighter tested in the Lang-ley 7- by 10-Foot High-Speed Tunnel at M -- 0.4and R = 2.4 x 106 . Figure 15 presents data formatched leading- and trailing-edge-flap deflection an-

gles (SL,n = 5T,n = 0°, 10°, and 20 °) with selected ca-nard incidence angles. As in the case of the 44°-swepttrapezoidal-wing-canard configuration, the theorygenerally provides a reasonably good estimate of theforce-and-moment characteristics. Again, correlationis best for negative incidence angles because they of-fer reduced drag.

Suction-parameter data for all the flap-deflectioncanard incidence combinations in figure 15 are shownas functions of lift coefficient in figure 16. Figure 17

shows suction parameter as a function of matchedleading- and trailing-edge-flap deflection angles andcanard-incidence angles for each of four selected liftcoefficients. This figure is similar to figure 7 for theprevious canard configuration. A detailed descrip-tion of the generation of these plots and their use isgiven in the preceding section.

Envelope data from figure 17 and similar datafrom theoretical results (not presented) are shown infigure 18. Optimum matched leading- and trailing-edge deflection angles, optimum canard incidence an-gles, and the maximum suction parameter are plottedas functions of lift coefficient. The theoretical data

with attainable thrust and vortex forces included pro-vide a reasonably good estimate of the maximumsuction parameter and the required deflection and

incidence angles. As for the 44°-swept trapezoidal-wing-canard configuration, the optimum canard inci-dence in the absence of moment restraints results in

a surface that is nearly aligned with the free stream.

Figure 19 provides data similar to those of fig-ure 15, but for a Mach number of 0.8. There issome deterioration in the ability of the theory to pre-dict the aerodynamic characteristics at this higherMach number, but not as much as for the 44°-swepttrapezoidal-wing configuration. The higher sweepangle probably delays the onset of shock-inducedseparation.

60°-Swept Delta-Wing Fighter WithHorizontal Tail

Data for the 60°-swept delta-wing fighter witha horizontal tail (ref. 11) are shown in figure 20.The theory generally provides a better predictionof measured characteristics than it did for the 44 °-

swept horizontal-tail configuration. Again, however,there is some deterioration in the prediction abilityof the theory for conditions which produce pooraerodynamic efficiency.

Figures 21 to 23 are similar to figures 11 to 13 forthe 44°-swept trapezoidal-wing fighter with horizon-tal tail and again provide data for the determinationof optimum flap and horizontal-tail settings and themaximum suction parameter.

An examination of figure 23 in conjunction with areexamination of figure 20 shows that, as for the pre-vious configurations, a reasonably good correlationof theory and experiment is obtained for flap andhorizontal-tail settings that result in near-maximumperformance for the lift-coefficient range of interest.Poorer correlation is displayed for settings far fromthe optimum.

Figure 24 provides data similar to those of fig-ure 20, but for a Mach number of 0.8. There againis some deterioration in the ability of the theory to

7

predicttheaerodynamiccharacteristicsat thishigherMachnumber.

Forward-Swept-Wing Fighter With Canard

Figure 25 presents data for a fighter configurationwith a forward-swept wing, employing twist andcamber, and a canard surface. The data taken fromreference 13 were measured in the Langley 16-FootTransonic Tunnel at M = 0.6 and R -- 2.5 × 106.

Data for undeflected flaps and for a canard at 5C =

0° (fig. 25(a)) show good agreement between theoryand measured results for lift coefficients up to about

1.0. The wing apparently has a highly efficientcamber surface as evidenced by the close approach

of measured drag to the theoretical lower limit forCL ,._ 0.4 to CL .'_ 0.8. The canard incidenceangle of 10 ° in figure 25(b) causes a severe loss inaerodynamic efficiency, depicted by the departurefrom the minimum curve, which is predicted by the

theory. As shown in figure 25(c), a canard incidenceangle of -10 ° offers good performance, which equatesto suction parameters of 0.9 or greater, for CL ,_ 0.5to CL _ 0.8. Figures 25(d) to 25(f) form a seriesin which the leading-edge-flap deflection varies whilethe trailing-edge-flap deflection remains fixed at 10°and the canard remains fixed at 5C = 0 °. Thepitching moment is poorly predicted, especially atthe lower lift coefficients. The prediction of lift anddrag, however, is excellent in all three of the figuresfor CL = 0.4 to CL ----1.2.

Figure 26 demonstrates the ability of the theoryto predict the variation of drag with changes in ca-nard incidence for each of four selected lift coeffi-

cients. These data for undeflected flaps were ob-tained from figures 25(a), 25(b), and 25(c). As mightbe expected, the optimum canard incidence angle (5cfor a minimized drag coefficient) becomes more neg-ative with increasing lift coefficient. For CL = 0.8,the optimum canard incidence is close to -10 °. Asshown in figure 25(c), a lift coefficient of 0.8 requiresan angle of attack of about 9° . The result is that,as before, the canard at optimum incidence is nearly

aligned with the free stream and produces little orno lift. Optimum canard incidence angle is discussedfurther in the section "Examples of ConfigurationOptimization."

The ability of the theory to predict aerodynamicperformance at high Mach numbers is shown in fig-ure 27. These data apply only to undeflected flaps

and a canard at 5C = 0°. A comparison of fig-ure 27(a) with 25(a) shows that there is only a smalldeterioration in the code prediction at M = 0.8. At

M = 0.9, however, appreciable discrepancies appearat CL .._ 0.8, and the correlation becomes progres-sively poorer as CL increases. The code is obviously

8

not applicable to transonic speeds, which are abovethe drag-rise Mach number.

Arrow-Wing Supersonic Transport

The application of the computer code to a highlyswept arrow-wing supersonic transport with a hori-zontal tail may be examined with the aid of figure 28.Experimental results for this configuration were ob-tained from reference 14. The wing is twisted andcambered for supersonic cruise at a Mach number

of 2.2 (wing W2 of ref. 15) and is equipped withleading- and trailing-edge flaps. The leading-edgeflap is full span and is broken into six segments. Thetrailing-edge-flap system is composed of inboard andoutboard segments of single-slotted flaps (ref. 14).The tests were run in the Langley 30- by 60-FootTunnel at M = 0.09 and R = 4.19 × 106 (based

on C).

The deflectionsof the horizontaltailand the

flapsinreference14 were not sufficientto determineoptimum settings.However, sufficientconfigurationswere testedto determinethe accuracy of the code

and to examine some trends.

Figures28(a)to 28(f)show resultsforzeroflapdeflections.Figure 28(a) shows data with the tail

and nacellesremoved, and the other figuresshow

data forvarioustailincidenceangles. The theory

givesa good predictionof the forcedata for each

of the configurationsshown. The most accurate

predictionof the drag at the higherliftcoefficientsoccurswith the tailoffand with tailincidencesetto

0° or 5°. These configurationsalsoproduce the best

performance(lowestdrag)and the smallestpitching

moment fora typicallow-speedliftcoefficientof0.6.The axial-forcecalculationsshow the effectof the

attainableleading-edgethrust,and the normal-forcecalculationsshow the effectofthe vortexforce.The

mildnessof the wing twistand camber isshown by

the slightslopein the axialforcewithout attainable

leading-edgethrustand vortexforcethatresultsfrom

distributedthruston the wing camber surface.

Significantdiscrepanciesbetween theoryand ex-

perimentoccurinthepitchingmoment forsome con-

ditions.The theoryprovidesfora reasonablygood

estimate of the pitching moment with the tail off andwith it set to 0° or 5°. These are the configurationsthat produced the lowest drag. For the negative tailincidence angles, the moment is well predicted at low

positive lift coefficients.Figures 28(g) to 28(i) show results with the

leading- and trailing-edge flaps deflected and withthree tail deflections. Although the theory does notmodel the flow through the trailing-edge-flap slot, thetheory gives a reasonably good prediction of the lift

anddragcharacteristics.Themostaccuratepredic-tionof the dragat the higherlift coefficientscorre-spondsto conditionsfor whichthe measureddragcomesclosestto the lowerbound(CL= 0.4to 0.6).Thepredictionalsotendsto bebetter for dfH = 0 °.The prediction of the pitching moment is also bestwhere the drag comes closest to the minimum curve.

The normal-force results indicate that a signifi-cant vortex did not develop in the experiment. Theaxial-force results indicate that the experimentaldata have more leading-edge thrust at the higher an-gles of attack than is predicted by the theory. Theseeffects tend to counteract each other, so that the liftand drag prediction is good.

Results for the drag and pitching moment at sev-eral lift coefficients are summarized in figures 29 and30 as a function of tail incidence. These figures show,

for example, that at CL = 0.2, where lower dragoccurs with the flaps undeflected, the best correla-tion between theory and experiment for the pitchingmoment also occurs with the flaps undeflected. AtCL = 0.4 and 0.6, where flap deflection reduces drag,the best correlation for pitching moment occurs withthe flaps deflected.

Examples of Configuration Optimization

The experimental data used in the preceding sec-tion of this paper for configuration performance op-timization were limited. The search for optimum ar-rangements was restricted to a special case in whichleading- and trailing-edge-flap deflections measured

normal to the hinge line were equal (_L,n = _T,n).The theory, however, has no such restrictions andpermits an optimization process in which leading-edge-flap deflection, trailing-edge-flap deflection, andcanard or horizontal-tail incidence angle may be var-ied independently. Performance contour maps serveas the basis of a graphical optimization process. Theprocedures that may be employed are discussed fortwo examples, one with a canard and one with a hor-izontal tail.

44°-Swept Trapezoidal-Wing Fighter WithCanard

Figure 31 is a comparison of theoretical and ex-perimental performance contour maps for the limitedfamily of flap and canard deflections previously dis-cussed. This figure is simply another form of thedata presented in figure 5. The maps show con-tour lines of equal suction parameter (the solid lines)and contour lines of equal moment coefficient (thedashed lines) for a representative lift coefficient of

0.6. The theory shows a reasonable ability to repre-sent the experimental data in the peak performance

region. There is a fairly broad range of angles overwhich near-maximum performance may be achieved;thus, precise definition of the required angles is notnecessary.

The performance contour maps of figure 32 showhow independent variation of leading-edge-flap de-flection, trailing-edge-flap deflection, and canard in-cidence angle may be considered in an optimization

study. The data were generated by a series of com-puter entries as follows:

1. 5L,n ----10°; 5T,n

2. _L,n = 10°; _T,n

3. 5L,n = 20°; _T,n

4. 5L,n = 20°; 5T,n

=10°; 6C=0 °,10 ° , --10 °

=20°; 6C=0 °,10 °,-10 °

=10°; 6C=0 ° , 10° ,--10 °

= 20°; _C = 0°, 10°,-10°

These input data sets also provided results for com-binations of leading- and trailing-edge deflections inwhich one or both of the deflections is zero throughthe use of TXMLEFD and TXMTEFD factors de-

scribed in appendix A. Data for the three canardincidence angles were obtained in one computer en-try by use of the successive-run provision describedin appendix A. The matrix of nine points used in thegeneration of the contour maps provides a general,but not detailed, description of the variation of suc-tion parameter with changes in flap deflection angles.That matrix, however, permits a sufficiently accuraterepresentation for illustration purposes.

Figure 33 uses data obtained from figure 32 toshow the variation of suction parameter with leading-edge-flap deflection angle, subject to a restraint ofCm = 0°. The variations of the required trailing-edge-flap deflection angle and the canard incidenceangle are also shown. A peak suction parameter ofabout 0.82 is obtained for a trailing-edge-flap de-flection of about 3°, a canard incidence of about

-7 °, and a leading-edge-flap deflection of about 17°.These data and similar data for plots with other mo-ment restraints (not shown) were used in derivationof the curves shown in figure 34. In this figure, max-imum suction parameter is shown as a function ofthe imposed moment restraint. The required flap de-flection angles and the required canard incidence an-gle are also shown. There is a substantial variationin aerodynamic performance over the range of mo-ment coefficients shown. A peak suction parameterof about 0.91 is obtained for a moment coefficient of

about -0.09. The required leading-edge-flap deflec-tion is about 15° , the trailing-edge-flap deflection isabout 11°, and the canard incidence angle is about-9 ° . This peak performance is very close to that

9

achievedbythewing-aloneconfigurationanalyzedinreference4. Theflap deflectionanglesrequiredforoptimizationarealsoverycloseto thoserequiredforthe wing-alongconfiguration.SketchA depictstheoptimized-configurationmean-cambersurface. Atthe angleof attack (_7.5°) requiredto generatealift coefficientof 0.6,the optimumcanardincidenceangleresultsinasurfacenearlyalignedwith timfree-streamflowsoasto produceonlya smallamountoflift (in this case,slightlynegative).The optimumcanardsettingapparentlyaltersthe flowabout anoptimizedwing-aloneconfigurationto a very smalldegree.In thesecircumstances,thenearequivalenceof the drag-due-to-liftperformanceof the optimizedwing-canardconfigurationand the wing-alonecon-figurationisnot surprising.

SketchA

Thecurvesof figure34showthat preservationofmaximumperformanceovera rangeof momentco-efficientsrequireslargechangesin trailing-edge-flapdeflectionbut only smallchangesin the canardin-cidenceangle. An examinationof tabulatedcodetheoreticaldata(notpresentedhere)showsthat thechangein trailing-edge-flapdeflectionfrom 13° to-3 ° isresponsiblefor about85percentofthechangein momentcoefficientfrom -0.12 to 0.08.Therearenoexperimentaldatato validatethetheoreticalpre-dictionof the variationof lifting efficiency$8 withpitching moment for these theoretically optimized ar-rangements. Sketch B gives some indication of thedegree of correlation that might be expected. Thiscorrelation is for the previous limited set of experi-

mental data (_L,n = _T,n) for this same configurationpresented in figure 31. Because the optimized ar-rangements, wherein leading- and trailing-edge flapsare free to vary independently, should be more effi-cient, the correlation should be somewhat better thanthat shown in sketch B.

The small contribution of the canard to the forces

generated by an optimized configuration may beexplained by the following arguments. A canard

1.0

S S

.5

0-.12 -.08-.04

" Exp.

ii. I I I I I I

0 .04 .08

Cm

Sketch B

inclined at a positive angle with respect to the freestream so as to produce a lifting force also producesa downwash along the wing leading edge behind thecanard. This downwash reduces the thrust force

created by the deflected leading-edge flap, and someof the flap benefits are lost. Upwash acting on thewing leading edge outboard of the canard tips is notstrong enough to counteract the unfavorable effect.

A canard inclined at a negative angle with re-spect to the free stream could, in the presence of astrong upwash field, produce a favorable thrust force,

as does a leading-edge flap; but the wing-generatedupwash field ahead of the wing in the vicinity of thecanard is too weak to produce a significant bene-fit. Perhaps a more efficient arrangement for a liftingcanard configuration would employ segmented wingleading-edge flaps with different deflections inboardand outboard of the canard. The wing-design pro-gram described in reference 4 provides a capabilityfor the design of flap surfaces in the presence of in-terference flow fields and can be used to explore thesepossibilities.

44°-Swept Trapezoidal-Wing Fighter WithHorizontal Tail

Figure 35 is a comparison of theoretical and ex-perimental performance contour maps for the previ-ously treated limited family of flap deflections for thehorizontal-tail configuration. The lift coefficient forconfiguration optimization is again selected as 0.6.As for the canard configuration, the theory shows areasonable ability to represent the experimental datain the peak performance region.

Figure 36 presents contour maps for thehorizontal-tail configuration that allow independentvariation of leading-edge-flap deflection, trailing-edge-flap deflection, and horizontal-tail incidence.These maps were generated in a manner similar tothat for the previously described maps in figure 32.

Figure 37 uses data derived from figure 36 toshow the variation of maximum suction parameterwith leading-edge-flap deflection angle subject to a

10

restraintof Cm = 0°. The required trailing-edge-

flap deflection angle and the horizontal-tail incidenceangle are also shown. A peak suction parameter ofabout 0.82 is obtained for a trailing-edge-flap deflec-tion of about 5°, a horizontal-tail deflection angleof about -2 °, and a leading-edge-flap deflection ofabout 16° . These data and similar data for plotswith other moment restraints (not shown) were usedin the derivation of the curves shown in figure 38. Inthis figure, which is similar to figure 34 for the canardconfiguration, maximum suction parameter is shownas a function of the imposed moment restraint. Apeak suction parameter of about 0.91 is obtained fora moment coefficient of about -0.09. The required

leading-edge-flap deflection is about 15° , the trailing-edge-flap deflection is about 10°, and the horizontal-tail incidence angle is about 4°. This performancelevel is very close to that achieved for the canardconfiguration (fig. 34) and for the wing-alone config-uration (ref. 4). The required flap deflection anglesare also similar. Sketch C shows the mean-camber

surface of the optimized arrangement. The trailing-edge-flap deflection provides a benefit by reducingthe angle of attack for a given lift coefficient. Thehorizontal-tail deflection serves the same purpose.

Sketch C

The curves of figure 38 show that preservationof maximum performance over a range of momentcoefficients requires large changes in the horizontal-tail incidence angle and moderate changes in thetrailing-edge-flap deflection. Theoretical estimatesshow that the change in horizontal-tail incidence an-gle from 6° to -8 ° is responsible for 95 percent ofthe change in moment coefficient from -0.12 to 0.08.Sketch D gives some indication of the ability of thetheory to predict the variation of lifting efficiencySs with pitching moment for these theoretically op-timized arrangements. The correlation of sketch Dis for the previous limited set of experimental data

(_L,n = _T,n) for the same configuration presentedin figure 35. Because the optimized arrangements,wherein both leading- and trailing-edge flaps are free

to vary independently, should be more efficient, thecorrelation for that case should be better than thatshown in sketch D.

Ss 1.o.5f The___°rY Exp"

0 I I I I i I-.12-.08-.04 0 .04 .08

Cm

Sketch D

Comparison of Canard and Horizontal-TailConfigurations

In the absence of moment constraints, the canard

and horizontal-tail configurations for the 44°-swepttrapezoidal wing offered comparable performance.In both cases, a peak suction parameter of about0.91 was obtained for a moment coefficient of about

-0.09. There is, however, a significant variation ofaerodynamic performance with Cm, and Cm = ,0.09may be far from that required to trim the configu-rations with a realistic center-of-gravity location anda practical stability level. Figure 39 is a compari-son of the aerodynamic performance of the canardconfiguration with that of the horizontal-tail config-urations at equal stability levels. The suction param-eters shown here were obtained from figures 34 and38 using the relationship

dCm,cgdVm _ CL where SM =

Cm = SM 4- dC L ] dC L

where dCrn/dCL is the moment derivative given bythe code at CL = 0 for the wing without flap de-flections and with no incidence of the second sur-

face. For this example, dCm/dCL = 0.164 for thecanard, and dCm/dCL = -0.048 for the horizontaltail. Actual values of these derivatives at the opti-mized settings for CL = 0.6 and at the specified flapand second-surface settings are only slightly different.The derivatives listed above agree with the experi-mental data for near-optimum settings (as close asthe data provides) better than the full theory, whichincludes a vortex contribution that apparently does

not fully materialize. For comparison purposes, fig-ure 39 also shows similar data for a wing-fuselage

configuration (ref. 4).

11

Figure39indicatesthat thecanardconfigurationcanbecompetitivewith thehorizontal-tailconfigura-tion in aerodynamicefficiencyonlyif it canbeflownin a staticallyunstablemode. However,the pointto bemadefromthis exampledoesnot concerntherelativemeritsof the twoconfigurations,but rathertheusefulnessof the computercodein the conductof preliminarydesigntrade-offstudies.

The otherconfigurationstreated in this reportwerenot subjectedto the samedetailedtheoreti-cal analysis.However,an inspectionof the avail-abledata indicatesthat, for the mostpart, the ob-servationsmadefor the 44°-swepttrapezoidal-wingfighteraresupported,and are in no casecontra-dicted. In general,an optimizedcanardconfigura-tionwithnoappliedmomentrestraintshasacanardthat generateslittle or no lift with a surfacenearlyalignedwith thefreestream.Whentrim momentre-straintsareapplied,mostof the momentincrement(fromthe unrestrainedsolution)will besuppliedbytrailing-edgeflapsrather than thecanard.An opti-mizedhorizontal-tailconfigurationwith no appliedmomentrestraintswill havea horizontaltail thatgeneratesappreciablelift. Whentrim momentre-straintsareapplied,mostof the momentincrementwill besuppliedby a changein horizontal-tailinci-dence.For both the canardand horizontaltail inthe absenceof momentrestraints,suctionparame-ters aboutthesameasthosefor the correspondingwing-aloneconfigurationcanbeachievedfor a prop-erly optimizedcombinationof flap deflectionsandcanardor horizontal-tailincidenceangles.Also,theoptimumleading-and trailing-edge-flapdeflectionsarenotmuchdifferentfromthoseof the wing-aloneconfiguration.

Conclusions

An analysis of the subsonic aerodynamic perfor-mance of wing-canard and wing-horizontal-tail con-figurations which may employ wing leading-and trailing-edge flaps has led to the followingconclusions:

1. Linearized-theory, attached-flow, computer-code methods (with estimated attainable leading-edge thrust and an approximate representation ofvortex forces) provide a rational basis for the estima-tion and optimization of aerodynamic performance atsubsonic speeds below the drag-rise Mach number.

2. Optimization of aerodynamic performance re-

quires specified flap and canard or horizontal-tail

settings which can be predicted with reasonable accu-racy by numerical methods. Near-maximum perfor-mance, however, can be achieved over a fairly broad

range of deflection and incidence angles.

3. Generally, good prediction of aerodynamicperformance, as measured by the suction parameter,and reasonably good prediction of pitching momentcan be expected for near-optimum combinations ofcanard or horizontal-tail incidence angle and leading-and trailing-edge-flap deflection at a given lift coef-

ficient; these conditions tend to produce a predomi-nantly attached flow.

4. For canard configurations, maximum perfor-mance in the absence of pitching-moment restraintsis achieved with a canard that is nearly aligned withthe free stream and produces little or no lift. Whenpitching-moment restraints are applied, the most ef-ficient arrangements call for most of the moment in-crement to be supplied by the wing trailing-edge flap

rather than by the canard.

5. For horizontal-tail configurations, maximumperformance in the absence of pitching-moment re-straints is achieved with a positive horizontal-tail in-

cidence angle that produces a significant amount oflift. When pitching-moment restraints are applied,the most efficient arrangements call for most of themoment increment to be supplied by the horizontaltail rather than by the wing flaps.

6. For both canard and horizontal-tail configura-tions in the absence of moment restraints, suction

parameters about the same as those for the corre-sponding wing-alone configuration can be achievedfor a properly optimized combination of flap deflec-tions and canard or horizontal-tail incidence angles.Also, the optimum leading- and trailing-edge-flap de-flections are not much different from those of the

wing-alone configuration. These settings are a goodstarting point in the search for optimized canardor horizontal-tail configurations, even if pitching-moment restraints are applied.

Performance degradation brought about by lowReynolds numbers and high Mach numbers was notinvestigated in this study. The conclusions are thusrestricted to Mach numbers below the drag rise and

Reynolds numbers sufficiently high to avoid drasticflow separation at or near design conditions.

NASA Langley Research CenterHampton, VA 23665-5225October 18, 1989

12

Appendix A

Code Input and Output Data

The computer code

AERO2S - Subsonic AerodynamicAnalysis of Wings With Leading-and Trailing-Edge Flaps inCombination With Canardor Horizontal Tail Surfaces

used in this paper for the analysis of wing-canard andwing-horizontal-tail combinations that may employwing leading- and trailing-edge flaps may be obtainedfor a fee from:

COSMIC

Computer Services AnnexUniversity of GeorgiaAthens, GA 30602

(404) 542-3265

Request the code by the designation LAR-14178.This code is written in FORTRAN V for use on

the Control Data 6600 computer system and on theControl Data Cyber series.

The first record in the input is a code run iden-tification that accepts up to 80 characters. The re-mainder of the input is placed in NAMELIST formatunder the name INPT1.

The wing-planform information is specified by aseries of leading-edge and trailing-edge breakpoints

for a right-hand wing panel. Up to 21 pairs ofcoordinates may be used to describe the leading edgeand up to 21 pairs to describe the trailing edge. Theplanform input data in program terminology are asfollows:

NLEY number of leading-edge break-points (limit of 21)

TBLEY table of leading-edge y-values;beginning at y = 0; increasingorder of y from root to tip

TBLEX table of leading-edge x-valuesthat correspond to TBLEY table

NTEY number of trailing-edge break-points (limit of 21)

TBTEY table of trailing-edge y-values;beginning at y = 0; increasingorder of y from root to tip

TBTEX table of trailing-edge x-valuesthat correspond to TBTEY table

XMAX largest x-ordinate anywhere onplanform; includes second surfaceif present

SREF wing reference area for use inaerodynamic force-and-momentcoefficients

CBAR wing reference chord for use inaerodynamic moment coefficients

XMC x-location of moment reference

center

JBYMAX integer designating number ofelements in spanwise direction(limit of 41)

ELAR element aspect ratio

The size of the wing in code dimensions is con-trolled by the entry JBYMAX. The necessary scal-ing is done within the code by use of a scale factor2(JBYMAX)/_b). The number of complete wing el-ements N corresponding to a given JBYMAX maybe approximated as

N = 4(JBYMAX 2) (ELAR'_\ AR ]

The code has been written to accommodate 2000

right-hand panel elements. Generally, the JBYMAXinteger is much less than the limit of 41. Thenormal range is 8 to 20. Computational costs tendto increase as the square of the number of elements.

For flat and mildly cambered wings, an elementaspect ratio approximately one-half the full-wing as-pect ratio is recommended. For small chord leading-or trailing-edge flaps it may be necessary to use alarge element aspect ratio to place at least two ele-ments within the chord. The number of elements in

a given chord, CL or CT, may be approximated as

N = _ (JBYMAX)(ELAR)

or

N = _T2 (JBYMAX)(ELAR)

Because computational costs tend to increase as thefourth power of JBYMAX and the second power ofELAR, an increase in the element aspect ratio isthe more efficient means of providing for improveddefinition.

The wing mean-camber surface must be specifiedby exactly 26 chordwise ordinates at up to 21 spanstations. When fewer than 26 camber coordinates are

13

usedto definethesections,theordinatetablesmustbefilledwithenoughzerosto completethelist of 26.Thenecessarysectioninformationis asfollows:

NYC numberof spanwisestationsatwhichchordwisesectionsareusedto definemean-cambersurface(limit of 21)

TBYC tableof y-values for chordwisecamber-surface sections; begin-ning at y = 0; increasing order ofy from root to tip

NPCTC number of chordwise stationsused in definition of mean-

camber surface (limit of 26)

TBPCTC table of chordwise stations, in

percent chord, at which mean-camber-surface ordinates are

defined; increasing order fromleading edge to trailing edge

TZORDC table of mean-camber-surfacez-ordinates that correspond toTBPCTC table; the full 26 valuesfor root chord (including zeros forvalues in excess of NPCTC) are

given first, followed by similarinformation for all spanwisestations in increasing order

of y

TZSCALE multiplying factor appliedto TZORDC table to changecamber-surface ordinates, default1.0

The TZORDC table may be multiplied by a scalefactor TZSCALE. This factor may be useful if the

original tabulated ordinates are nondimensionalizedwith respect to a single measurement (e.g., the wingroot chord) or if it is necessary to evaluate the effectof a change in camber-surface severity.

The following wing-section information is re-

quired for the calculation of attainable leading-edgethrust and leading-edge separation forces:

NYR number of spanwise stationsat which information on airfoilsections is supplied (limit of 21)

TBYR table of y-values for airfoilsection information; beginning

at y = 0; increasing order of y-values from root to tip

TBTOC table of airfoil maximum thick-ness as a fraction of chord,

(t/C)m x

14

TBETA

TBROC

IVOROP

table of section locations ofmaximum thickness as a fraction

of chord,

table of leading-edge radii as afraction of chord, r/c

vortex location option as follows:

YAPEX

The flightfollows:

0 full vortex force acts normal

to wing reference plane at wingleading edge; does not contributeto axial force

1 vortex center given by empir-ical relationships derived fromdelta-wing experimental data(default)

2 vortex center given by methodof Lan (ref. 16)

spanwise location of vortex flow-field origin

For special planforms such asforward-swept wings or otherwings with an apex away fromthe centerline, this input can

help provide a better estimateof vortex-induced flow fields and

forces (default YAPEX = 0.0)

or test conditions are specified as

XM free-stream Mach number

RN free-stream Reynolds number

(based on _) × 10-6

NALPHA number of angles of attack to becalculated (limit of 19)

TALPHA table of angles of attack to becalculated, deg

NADRN number of additional Reynolds

numbers (default 0)

TADRN table of additional Reynoldsnumbers (limit of 3)

The commonly accepted practice of performingsubsonic calculations for a Mach number of 0.0 is

not appropriate for this code. Realistic estimatesof attainable thrust can be made only if both the

Mach number and the Reynolds number correspondto actual conditions. In fact, the code stops and

writes an error message when XM = 0.0 is input.

Thefollowinginformationmakespossiblethecal-culationof loadingsandforcesondeflectedleading-edgeandtrailing-edgeflaps.If flapdataarenotde-sired,simplyomit theseentries.

NLEFY numberof breakpointsin leading-edge-flapchorddistribution(limit of 21)

TBLEFY tableof y-values at breakpointsin leading-edge-flap chord dis-tribution; beginning at y = 0;increasing order of y from root totip

TBLEFC table of streamwise leading-edge-flap chords corresponding toTBLEFY table

TBLEFD table of flap deflections in degrees(positive for leading edge down)corresponding to TBLEFY table

NADLEFD number of leading-edge-flapdeflection multipliers other than1.0 (limit of 4) (default 0)

TXMLEFD table of leading-edge-flap deflec-tion multipliers (applied as amultiplier of tangents of inputflap deflections)

LEFTYPE type of leading-edge deflection

1 linear (default)

_L,s/

2 parabolic

NTEFY

TBTEFY

number of breakpoints intrailing-edge-flap chord distri-

bution (limit of 21)

table of y-values at breakpointsin trailing-edge-flap chord dis-tribution; beginning at y = 0;increasing order of y from root totip

TBTEFC table of streamwise trailing-edge-flap chords that correspond toTBTEFY table

TBTEFD table of flap deflections in degrees(positive for trailing edge down)that correspond to TBTEFYtable

NADTEFD number of trailing-edge-flapdeflection multipliers other than1.0 (limit of 4) (default 0)

TXMTEFD table of trailing-edge-flap de-flection multipliers (applied asa multiplier to tangents of inputflap deflections)

CLDES additional lift coefficient for

which flap-system aerodynamicperformance is to be specified;code aerodynamic characteristicsare given only for angles ofattack in input TALPHA tableunless CLDES is specified

Spanwise tables must begin with y = 0 andextend to y = b/2 (with chords of 0 where thereare no flaps). At spanwise positions where there arediscontinuities in either flap chord or deflection, itis necessary to make closely spaced tabular entriesinboard and outboard of the discontinuity.

The program requires flap deflection angles mea-sured in the x-z plane. Flap deflection angles mea-sured normal to the flap hinge line may be convertedto code input angles by

5L,s = tan-1 (cos Ah,L tan _L,n)

_T,s = tan-l( cos Ah,T tan 5T,n)

The code provides solutions for wing surfacescomposed of all possible combinations of leading-edge and trailing-edge-flap settings provided by theoriginal deflections (TBLEFD and TBTEFD) andby the flap deflection multipliers (TXMLEFD andTXMTEFD). Up to 25 pairs of leading-edge andtrailing-edge-flap deflection schedules may thus betreated simultaneously. Solutions obtained by usingthe multipliers (values other than 0 or 1) are deter-mined by a perturbation process; thus, they are notas accurate as solutions for the original or nominal in-put deflections. When increased accuracy is required,or when the change in performance with the changein deflection must be evaluated--as in the construc-

tion of suction-parameter contour maps--individualsolutions without recourse to multipliers may be re-quired. There is, however, a strategy that may be

15

usedto Obtainasetof datanearlyasaccurateasthecodeiscapableof providingwith theuseof onlytwocoderuns. Theprocedureis describedin detail inappendixB of reference4.

Thecodealsoprovidesfor an improvedaccount-ing of hinge-linesingularitiesin determinationofwingforcesandmoments.Thetechniqueusedis de-scribedin appendixB of reference4.

Todeterminelifting-surfaceperturbationvelocitydistributions,the codeprovidesfor a maximumof70 iterations. If this numberis reachedwithoutthe convergencecriteria beingmet, the resultsforthe70thiterationareprintedwith a warningof thefailureto meetthecriteria. Themaximumnumberof iterationsmaybe increasedor decreasedby theentry

ITRMAX maximumnumberof perturba-tion velocityiterations(default70)

The code convergence criteria are met when, forall four wing surfaces and for two successive itera-tions, the average difference in perturbation velocitybetween iterations is less than half of 1 percent of theaverage velocity over the wing. If the average velocityfor the camber surface or either of the flap surfaces is

less than the average velocity for the flat surface ata = 1°, the flat-wing surface value is used instead. Inmany instances, these criteria may be more stringentthan necessary. If desired, the convergence criteriamay be changed by the entry

CNVGTST perturbation velocity convergencecriteria (default 0.005)

The following set of input data is required for

the handling of wing-canard or wing-horizontal-tailconfigurations. If wing-alone solutions are desired,simply omit these entires.

ILS2 second surface identifier

0 no second surface (default)

1 canard

2 horizontal tail

If a second surface is to be employed (ILS2 --1 or 2) the following planform information must besupplied:

NLEY2 number of leading-edge break-points (limit of 21)

TBLEY2 table of leading-edge y-values;need not begin at y = 0;increasing order of y

16

TBLEX2 table of leading-edge x-valuesthat correspond to TBLEY2table

NTEY2 number of second-surface

trailing-edge breakpoints (limitof 21)

TBTEY2 table of trailing-edge y-values;need not begin at y -- 0 butinitial and final values must bethe same as the TBLEX2 initial

and final values; increasing orderof y

TBTEX2 table of trailing-edge x-valuesthat correspond to TBTEY2table

The second-surface, mean-camber surface mustbe specified by exactly 26 chordwise ordinates at upto 21 span stations. When fewer than 26 camber co-ordinates are used to define the sections, the ordinatetables must be filled with enough zeros to completethe list of 26. The necessary section information isas follows:

NYC2 number of spanwise stations atwhich chordwise sections are usedto define mean-camber surface

(limit of 21)

TBYC2 table of y-values for chordwisecamber-surface sections; increas-

ing order of y

NPCTC2 number of chordwise stationsused in definition of mean-

camber surface (limit of 26)

TBPCTC2 table of chordwise stations, inpercent chord, at which mean-camber-surface ordinates are

defined; increasing order fromleading edge to trailing edge

TZORDC2 table of mean-camber-surface

z-ordinates that correspond toTBPCTC2 table; the full 26

values for root chord (includ-ing zeros for values in excess ofNPCTC2) are given first, fol-lowed by similar information forall spanwise stations in increasingorder of y

TZSCAL2 multiplying factor applied toTZORDC2 table to changecamber-surface ordinates (default1.0)

Thefollowingcanardor horizontal-tail section in-formation is required for the calculation of attain-

able leading-edge thrust and leading-edge separationforces:

NYR2 number of spanwise stationsat which information on airfoil

sections is supplied (limit of 21)

TBYR2 table of y-values for airfoilsection information; increasing

order of y

TBTOC2 table of airfoil maximum thick-ness as a fraction of chord,

(t/C)

TBETA2 table of section locations ofmaximum thickness as a fraction

of chord, 7?

TBROC2 table of leading-edge radii as afraction of chord, r/c

YAPEX2 spanwise location of second-surface vortex flow-field origin

For special planforms such asforward-swept surfaces or othersurfaces with an apex away fromthe centerline, this input can

help provide a better estimateof vortex-induced flow fields andforces. The default is YAPEX2 =0.0.

DELTA2 incidence of the second surfacewith respect to the wing refer-ence plane, deg (default DELTA2

= 0.0)

The code is constructed so that successive runs

may be made with a given code entry. To make ad-ditional runs, it is necessary only to add an identifica-tion record and namelist data that are to be changed

from the previous run.The printed code results include the following:

1. An iteration-by-iteration history of the conver-gence parameters.

2. A listing of theoretical pressure distributionsfor the combined camber surface at a = 0° and forthe combined flat surface at a = 1°. For each of the

program spanwise stations (controlled by JBYMAX),interpolated or extrapolated pressure coefficients are

given for a set of chordwise stations.

3. A listing of the spanwise distribution of sec-tion normal, axial, and pitching-moment coefficientsfor the combined cambered surface at a -- 0 ° and forthe combined flat surface at a = 1°. The interferenceaxial-force coefficient caused by the flat-surface load-

ing acting on the camber surface and the theoreticalthrust parameters are also printed.

4. A listing of overall theoretical aerodynamic

coefficients CN, CA, Cm, CL, and CD with no thrustand with full theoretical thrust as a function of angle

of attack.

5. A listing of the spanwise distribution of theflat-wing, angle-of-attack range for full theoreticalleading-edge thrust (for wing-alone solution only).

6. A listing of overall estimated aerodynamic co-efficients, including CN, CA, and Cm for the ba-sic pressure loading, ACN and AC.4 for attainablethrust and vortex-force increments, and CN, CA, Cm,

CL, CD, and Ss for the total loading.

Additional tabulated output data may be selected

by using the following print options:

IPRCPD = 1 theoretical pressure distributionsfor each selected angle of attack

IPRSLDT = 1 theoretical span load distributionof Cy, C A, era, eL, and CD withno thrust and with full theoreti-

cal thrust for each selected angleof attack

IPRSLDA = 1 estimated span load distributionof CN, CA, Cm, CL, and CD withattainable thrust and vortex-forceeffects for each selected angle ofattack

IPRALL = 1 the preceding print control op-tions apply only to the first setof flap deflections. Select thisoption if the three precedingoptions are to apply to all flapdeflection combinations. Selec-

tion of this option could resultin a very large volume of printed

output.

17

Appendix B

Notes on Computer-Code Application

Table I presents sample input data for the flap-system analysis code for each of the test configura-tions studied. The wing lifting surface includes con-tributions of the fuselage planform as well as thewing planform. The canard or horizontal-tail lift-ing surface is restricted to span positions outside thefuselage to avoid overlap. The camber ordinates,TZORDC, were determined from the mean ordinatesof the wing and fuselage combination.

As with any numerical solution of mathematicaltheory, the problem is to find a sufficiently detaileddiscretization that provides accurate answers withoutincurring prohibitive costs. To sufficiently representthe flap geometry of the Study configurations, thenumber of semispan elements, JBYMAX, and theelement aspect ratio, ELAR, were chosen so that,for the most part, two or more elements would becontained in any given flap chord. This resultedin element aspect ratios ranging from 1.84 to 6.0and from 8 to 10 semispan elements. Generally, thewhole-wing-body planform was represented by 400 to600 elements.

To obtain estimates of attainable leading-edgethrust, Reynolds number, RN (R × 10-6), and Machnumber, XM, are both specified and the section geo-metric characteristics of t/c, r/c, and _ are enteredin the appropriate tables. For evaluation of the es-timated forces caused by leading-edge vortex separa-

tion, the vortex location option IVOROP = 1 was

chosen for all the wings with swept leading edges.Option 0 was used only for the unswept wing.

The wing evaluation program has a feature thatpermits simultaneous solutions for a number of com-binations of leading- and trailing-edge-flap deflec-tions by use of a perturbation process. This time-saving code option is sufficiently accurate for smalldeflection angles (streamwise angles of about 15° orless), but because of the large deflection angles of-ten considered in this investigation and the needfor a high degree of accuracy, this feature was notused to its full capacity. When required, individ-ual computer runs were performed for each pair ofleading- and trailing-edge deflections; however, a sin-gle computer run can be made to yield as accurate aprediction as the method is capable of for a setof four deflection-angle combinations which includezero deflections of leading- and trailing-edge flaps.The code input data of table I provide for flap de-flection multipliers, TXMLEFD and TXMTEFD, of0.0, which produce results for a leading-edge-flapdeflection with no trailing-edge-flap deflection, atrailing-edge-flap deflection with no leading-edge-flapdeflection, no leading-edge-flap deflection wi.th notrailing-edge-flap deflection, and the leading- andtrailing-edge-flap deflections in combination.

Also, some of the input data of table I provide

for a second computer run in which only the leading-edge-flap deflection and/or the trailing-edge-flap de-flection are changed. It is unnecessary to repeat theother data.

18

References

1. Carlson, Harry W.; and Walkley, Kenneth B.: A Com-

puter Program for Wing Subsonic Aerodynamic Perfor-

mance Estimates Including Attainable Thrust and Vortex

Lift Effects. NASA CR-3515, 1982.

2. Carlson, Harry W.; and Walkley, Kenneth B.: An Aero-

dynamic Analysis Computer Program and Design Notes

for Low Speed Wing Flap Systems. NASA CR-3675, 1983.

3. Carlson, Harry W.; and Darden, Christine M.: Applica-

bility of Linearized-Theory Attached-Flow Methods to De-

sign and Analysis of Flap Systems at Low Speeds for Thin

Swept Wings With Sharp Leading Edges. NASA TP-2653,

1987.

4. Carlson, Harry W.; and Darden, Christine M.: Validation

of a Pair of Computer Codes for Estimation and Opti-

mization of Subsonic Aerodynamic Performance of Sim-

ple Hinged-Flap Systems for Thin Swept Wings. NASA

TP-2828, 1988.

5. Margason, Richard J.; and Lamar, John E.: Vortex-

Lattice FORTRAN Program .for Estimating Subsonic

Aerodynamic Characteristics of Complex Planforms.

NASA TN D-6142, 1971.

6. Woodward, F. A.: An Improved Method for the Aero-

dynamic Analysis of Wing-Body-Tail Configurations in

Subsonic and Supersonic Flow. Part I--Theory and

Application. NASA CR-2228, Pt. I, 1973.

7. Magnus, Alfred E.; and Epton, Michael A.: PAN AIR--A

Computer Program for Predicting Subsonic or Supersonic

Linear Potential Flows About Arbitrary Configurations

Using a Higher Order Panel Method. Volume I--Theory

Document (Version 1.0). NASA CR-3251, 1980.

8. Polhamus, Edward C.: Predictions of Vortex-Lift Char-

acteristics by a Leading-Edge Suction Analogy. J. Aircr.,

vol. 8, no. 4, Apr. 1971, pp. 193-199.

9. Feistel, T. W.; Corsiglia, V. R.; and Levin, D. B.: Wind-

Tunnel Measurements of Wing-Canard Interference and a

Comparison With Various Theories. SAE 1981 Trans-

actions, Section 2, Volume 90, 1982, pp. 2026-2039.

(Available as SAE Paper 810575.)

10. Gloss, Blair B.: Effect of Canard Location and Size on

Canard- Wing Interference and Aerodynamic-Center Shift

Related to Maneuvering Aircraft at Transonic Speeds.

NASA TN D-7505, 1974.

11. Nicholas, W. U.; and Naville, G. L.: An Evaluation of the

Relative Merit of Wing-Canard, Wing-Tail, and Tailless

Arrangements for Advanced Fighter Applications. FZA-

547, Fort Worth Div., General Dynamics, Apr. 19, 1984.

12. Lamar, John E.: Recent Studies of Subsonic Vortex

Lift Including Parameters Affecting Stable Leading-Edge

Vortex Flow. J. Aircr., vol. 14, no. 12, Dec. 1977,

pp. 1205-1211.

13. Mann, Michael J.; and Mercer, Charles E.: Forward-

Swept-Wing Configuration Designed for High Maneuver-

ability by Use of a Transonic Computational Method.

NASA TP-2628, 1986.

14. Yip, Long P.; and Parlett, Lysle P.: Low-Speed Wind-

Tunnel Tests of a I/lO-Scale Model of an Advanced

Arrow-Wing Supersonic Cruise Configuration Designed

for Cruise at Mach 2.2. NASA TM-80152, 1979.

15. Radkey, R. L.; Welge, H. R.; and Felix, J. E.: Aero-

dynamic Characteristics of a Mach 2.2 Advanced Super-

sonic Cruise Aircraft Configuration at Mach Numbers

From 0.5 to 2.4. NASA CR-145094, 1977.

16. Lan, C. Edward; and Chang, Jen-F_a: Calculation of

Vortex Lift Effect for Cambered Wings by the Suction

Analogy. NASA CR-3449, 1981.

19

Table I. Sample Input Data for AERO2S Code

(a) Unswept wing with canard

RECTANGULAR WING-CANARD - FEISTEL, SAE 810575

$1NPTI XM=.2,RN=I.4,JBYMAX=IO,ELAR=3.0,1VOROP=O,IPRSLDA=I,

SREF=6.0,CBAR=I.O,XMC=I.2642, XMAX=2.5575,

NALPHA=I6,TALPHA=-6.0,-4.0,-2.0,O.O,2.0,

4.0,6.0,8.0,10.0,12.0,14.0,16.0,18.0,20.0,22.0,24.O,

NLEY=2,TBLEY=O.0000,3.0000,

TBLEX=I.5575,1.5575,

NTEY=2,TBTEY=O.O000,3.0000,

TBTEX=2.5575,2.5575,

NYR=2,TBYR=O.O00,3.000,

TBTOC=.I300,.1300,

TBROC=.OI30,.OI30,

TBETA=.4000,.4000,

NYC=2,TBYC_O.O,3.0,

NPCTC=I3,TBPCTC=0.O,2.50,5.00,10.O,20.O,30.O,40.O,50.0,60.O,

70.0,80.0,90.0,100.0,

TZORDC=0.0,.O07,.OIO,.OI3,.016,.OI8,.020,.021,.0215,

.021,.018,.012,-.005,13"0.O,

0.0,.007,.010,.013,.016,.018,.020,.021,.0215,

.021,.018,.012,-.005,13"O.0,

NLEY2=2,TBLEY2=O.O0,2.12,

TBLEX2=O.O0,O.O0,

NTEY2=2,TBTEY2=O.O0,2.12,

TBTEX2=.710,.710,

NYR2=2,TBYR2=O.00,2.12,

TBTOC2=.I30,.130,

TBROC2=.OI3,.OI3,

TBETA2=.400,.400,

NYC2=2,TBYC2=O.O,2.12,

NPCTC2=I3,TBPCTC2=0.O,2.50,5.00,10.O,20.O,30.O,40.O,50.0,60.O,

70.0,80.0,90.0,100.0,

TZORDC2=O.O,.007,.OIO,.OI3,.OI6,.OIS,.020,.021,.0215,

.021,.018,.012,-.005,13"0.0,

0.0,.007,.010,.013,.016,.018,.020,.021,.0215,

.021,.018,.012,-.005,13"0.0,

DELTA2=2.0,1LS2=I, $

2O

Table I. Continued

(b) 60°-swept trapezoidal-wing fighter with canard

CANARD LOCATION MODEL - GLOSS, TN D7505

$1NPTI XM=.70,RN=I.35,JBYMAX=IO,ELAR=2.5,1VOROP=I,IPRSLDA=I,

SREF=I60.O,CBAR=9.18,XMC=23.3,XMAX=38.0,

NLEY=4,TBLEY=0.O0,1.40,1.50,10.O,

TBLEX=O.O0,6.00,18.8,33.5,

NTEY=4,TBTEY=0.O0,1.40,1.50,10.0,

TBTEX=38.0,38.0,30.5,36.2,

NYC=2,TBYC=O.OO,IO.O,NPCTC=2,TBPCTC=O.O0,100.O,

TZORDC=52*O.0,

NYR=4,TBYR=O.O00,1.400,1.500,10.00,

TBTOC=O.O00,O.O00,0.060,0.040,

TBROC=O.O00,O.O00,.OO02,.O007,

TBETA=0.500,O.500,0.500,O.500,

NALPHA=I3,TALPHA=-4.0,-2.0,O.0,2.0,4.0,6.0,8.0,10.O,12.0,

14.0,16.0,18.0,20.0,

NLEY2=2,TBLEY2=I.50,6.79,

TBLEX2=II.8,18.5,

NTEY2=2,TBTEY2=I.50,6.79,

TBTEX2=IS.9,20.O,

NYC2=2,TBYC2=I.50,6.79,NPCTC2=2,TBPCTC2=0.O0,100.O,

TZORDC2=52*O.O,

NYR2=2,TBYR2=I.500,6.790,

TBTOC2=O.060,O.040,

TBROC2=.O003,.O014,

TBETA2=0.500,O.500,

YAPEX=I.5,YAPEX2=I.5,

DELTA2=O.O,ILS2=I, $

21

Table I. Continued

(c) 44°-swept trapezoidal-wing fighter with canard

44 DEG TRAPEZOIDAL WING FIGHTER - NICHOLAS, GD FZA 547 - DLN=I2,DTN=I2

$1NPTI XM=.40,RN=I.91,JBYMAX=IO,ELAR=2.5,1VOROP=I,IPRSLDA=I,

SREF=I60.0,CBAR=9.17,XMC=23.39,XMAX=38.03,

NLEY=4,TBLEY=O.000,1.400,1.500,10.O0,

TBLEX=O.O00,4.250,18.78,27.00,

NTEY=4,TBTEY=O.O00,1.400,1.5OO,IO.OO,

TBTEX=38.03,38.03,30.51,29.66,

NYC=2,TBYC=O.O,IO.O,NPCTC=2,TBPCTC=O.O,IO0.0,TZORDC=52*O.O,

NYR=3, TBYR=O.000,1.500,10.O0,

TBTOC=.O000,.0600,.0400

TBROC=.0000,.O025,.O011,

TBETA=.4000,.4000,.4000,

NLEFY=4,TBLEFY=O.O0,1.40,1.50,10.O,

TBLEFC=O.O0,0.00,1.80,1.80,

TBLEFD=O.O0,O.O0,8.70,8.70,

NTEFY=6,TBTEFY=O.O0,1.40,1.50,7.47,7.57,10.O,

TBTEFC=O.O0,O.00,2.32,1.04,0.O0,O.OO,

TBTEFD=O.O0,0.O0,12.0,12.0,O.OO,O.O0,

NADLEFD=I,TXMLEFD=0.O0,

NADTEFD=I,TXMTEFD=O.O0,

NALPHA=IS,TALPHA=-4.0,-2.0,O.O,2.0,4.0,6.0,8.0,10.O,12.0,14.0,16.0,

18.0,20.0,22.0,24.0,

NLEY2=2,TBLEY2=I.500,5.500,

TBLEX2=I3.22,17.10,

NTEY2_2,TBTEY2=I.500,5.500,

TBTEX2=I8.55,18.17,

NYC2=2,TBYC2=I.500,5.500,

NPCTC2=2,TBPCTC2=O.O00,100.O,

TZORDC2=52*0.O,

NYR2=2,TBYR2=I.500,5.500,

TBTOC2=.0600,.0400,

TBROC2=.0000,.OO00,

TBETA2=.5000,.5000,

DELTA2=0.0,1LS2=I, $

DELTA2=IO.O

$1NPTI DELTA2=IO.O, $DELTA2=-IO.O

$1NPTI DELTA2=-IO.O, $

22

Table I. Continued

(d) 44°-swept trapezoidal-wing fighter with horizontal tail

44 DEG TRAPEZOIDAL WING FIGHTER - NICHOLAS GO FZA 547 - DLN=I2 DTN=I2

$1NPTI XM=.40,RN=I.91,JBYMAX=IO,ELAR=2.5,1VOROP=I,IPRSLDA=I,

SREF=I60.O,CBAR=9.17,XMC=23.39,XMAX=38.47,

NLEY=4,TBLEY=O.O00,1.400,1.500,10.O0,

TBLEX=O.O00,4.250,18.78,27.00,

NTEY=4,TBTEY=O.O00,1.400,1.500,10.O0,

TBTEX=38.03,38.03,30.51,29.66,

NYC=2,TBYC=O.O,IO.O,NPCTC=2,TBPCTC=O.O,IOO.O,TZORDC=52_O.O,

NYR=3, TBYR=O.O00,1.500,10.O0,

TBTOC=.O000,.0600,.0400,

TBROC=.O000,.O025,.O011,

TBETA=.4000,.4000,.4000,

NLEFY=4,TBLEFY=0.O0,1.40,1.50,10.O,

TBLEFC=O.O0,O.O0,1.80,1.80,

TBLEFD=O.O0,O.O0,8.70,8.70,

NTEFY=6,TBTEFY=O.O0,1.40,1.50,7.47,7.57,10.0,

TBTEFC=O.O0,O.O0,2.32,1.04,0.O0,O.O0,

TBTEFD=O.O0,O.O0,12.0,12.0,O.O0,O.O0,

NADLEFD=I,TXMLEFD=O.O0,

NADTEFD=I,TXMTEFD=O.O0,

NALPHA=I5,TALPHA=-4.0,-2.0,O.O,2.0,4.0,6.0,8.0,10.O,12.0,14.O,16.0,

18.0,20.0,22.0,24.0,

NLEY2=2,TBLEY2=I.500,5.500,

TBLEX2=33.14,37.02,

NTEY2=2,TBTEY2=I.500,5.500,

TBTEX2=38.47,38.09,

NYC2=2,TBYC2=I.500,5.500,

NPCTC2=2,TBPCTC2=O.O00,100.O,

TZORDC2=52_O.O,

NYR2=2,TBYR2=I.500,5.500,

TBTOC2=.0600,.0400,

TBROC2=.O000,.O000,

TBETA2=.5000,.5000,

DELTA2=O.O,ILS2_2, $

DELTA2=IO.O

$1NPTI DELTA2=IO.O, $

DELTA2=-IO.O

$1NPTI DELTA2=-IO.O, $

23

Table I. Continued

(e) 60°-swept delta-wing fighter with canard

60 DEG DELTA GENERIC FIGHTER - NICHOLAS, GD FZA 547 - DLN=20,DTN=20

$1NPTI XM=.40,RN=2.52,JBYMAX=I0,ELAR=2.5,1VOROP=I,IPRSLD A'I ,

SREF=I81.94,CBAR=I2.13,XMC=23.74,XMAX=41.63,

NLEY=4,TBLEY_0.000,1.400,1.500,10.O0,

TBLEX=O.O00,4.250,17.53,32.25,

NTEY=4,TBTEY=O.000,1.400,1.500,10.O0,

TBTEX=41.63,41.63,33.00,32.25,

NYC-2,TBYC=O.0,10.0,NPCTC=2,TBPCTC=O.0,100.O,TZORDC-52_0.0,

NYR=3, TBYR=O.O00,1.500,10.00,

TBTOC=.0000,.0600,.0400,

TBROC=.0000,.0025,.O011,

TBETA=.4000,.4000,.4000,

NLEFY_5,TBLEFY=O.00,1.40,1.50,8.50,10.O,

TBLEFC=O.00,O.O0,1.37,2.62,0.O0,

TBLEFD=O.O0,O.O0,9.60,9.60,9.60,

NTEFY=6,TBTEFY=O.O0,1.40,1.50,7.00,7.10,10.O,

TBTEFC=O.00,O.O0,1.69,1.21,O.00,O.O0,

TBTEFD=0.O0,O.O0,20.O,20.O,0.O0,O.O0,

NADLEFD=I,TXMLEFD=O.O0,

NADTEFD=I,TXMTEFD=O.O0,

NALPHA=IS,TALPHA=-4.0,-2.0,0.0,2.0,4.0,6.0,8.0,10.O,12.0,14.0,16.0,

18.0,20.0,22.0,24.0,

NLEY2=2,TBLEY2=I.500,5.500,

TBLEX2-11.58,15.46,

NTEY2=2,TBTEY2=I.500,5.500,

TBTEX2=I6.91,16.53,

NYC2=2,TBYC2=I.500,5.500,

NPCTC2=2,TBPCTC2=0.O00,100.O,

TZORDC2=52_O.O,

NYR2=2,TBYR2=I.500,5.500,

TBTOC2=.0600,.0400,

TBROC2=.O000,.O000,

TBETA2=.5000,.5000,

DELTA2=O.O,ILS2=I, $DELTA2=I0.O

$1NPTI DELTA2=I0.0, $

DELTA2=-IO.0

$1NPTI DELTA2=-I0.O, $

24

Table I. Continued

(f) 60°-swept delta-wing fighter with horizontal tail

60 DEG DELTA GENERIC FIGHTER - NICHOLAS, GD FZA 547 - DLN=20,DTN=20

$1NPTI XM=.40,RN=2.52,JBYMAX=IO,ELAR=2.5,1VOROP=I,IPRSLDA=I,

SREF=I81.94,CBAR=I2.13,XMC=23.74,XMAX=41.63,

NLEY=4,TBLEY=O.O00,1.400,1.500,10.00,

TBLEX=O.000,4.250,17.53,32.25,

NTEY=4,TBTEY=O.O00,1.400,1.500,10.00,

TBTEX=41.63,41.63,33.00,32.25,

NYC=2,TBYC=O.O,IO.O,NPCTC=2,TBPCTC=O.O,IOO.O,TZORDC=52_0.O,

NYR=3, TBYR=0.O00,1.500,10.O0,

TBTOC=.O000,.0600,.0400,

TBROC=.O000,.0025,.O011,

TBETA=.4000,.4000,.4000,

NLEFY=5,TBLEFY=0.00,1.40,1.50,8.50,10.O,

TBLEFC=O.O0,O.O0,1.37,2.62,0.O0,

TBLEFD=O.00,0.O0,9.60,9.60,9.60,

NTEFY=6,TBTEFY=O.O0,1.40,1.50,7.00,7.10,10.O,

TBTEFC=O.O0,0.OO,I.69,1.21,O.O0,O.O0,

TBTEFD=0.O0,O.O0,20.O,20.0,0.O0,O.O0,

NADLEFD=I,TXMLEFD=O.00,

NADTEFD=I,TXMTEFD=O.O0,

NALPHA=IS,TALPHA=-4.0,-2.0,O.O,2.0,4.0,6.0,8.0,10.O,12.0,14.0,16.0,

18.0,20.0,22.0,24.0,

NLEY2=2,TBLEY2-1.500,5.500,

TBLEX2=36.24,40.12,

NTEY2=2,TBTEY2=I.500,5.500,

TBTEX2=41.57,41.19,

NYC2=2,TBYC2=I.500,5.500,

NPCTC2=2,TBPCTC2=O.000,100.O,

TZORDC2=52_O.O,

NYR2=2,TBYR2=I.500,5.500,

TBTOC2=.0600,.0400,

TBROC2=.O000,.O000,

TBETA2=.5000,.5000,

DELTA2=O.O,ILS2=2, $

DELTA2=IO.O

$1NPTI DELTA2=IO.O, $

DELTA2=-IO.0

$1NPTI DELTA2=-I0.O, $

25

Table I. Continued

(g) Forward swept-wing fighter with canard

TBTEX=37.77,22.35

NYC=9,TBYC=O.O00,1.740,1

FORWARD SWEEP FIGHTER - MANN,TP 2628 - DLS=O,DTS=O,C=O

$1NPTI XM=.60,RN=2.5,JBYMAX=8,ELAR=4.0,1VOROP=I,IPRSLDA=I,

SREF=216.0,CBAR=9.26,XMC=23.77,XMAX=37.77,YAPEX=I3.32,

NLEY=4,TBLEY=O.000,1.740,1.750,13.32,

TBLEX=O.000,12.75,23.75,19.48,

NTEY=2,TBTEY=O.O00,13.32,

.750,2.660,5.590,8.000,10.65,11.98,13.32,

000,5.000,10.00

000,0.000,0.000

000,0.000,0.000

000,.1368 2067

000,.1264 1916

000,.0927 1428

000,.0593 1012

NPCTC=IO

TBPCTC=O

TZORDC=O

0

0

0

0

0

0 000,.0403

0 000,.0355

0 000,.0307

NYR=4,TBYR=O.O00,1

TBTOC=O.000,O

TBROC=O.O00,O

,20.00,30.00,40.00,50.00,60.00,80.00,100.0,

,0.000,0.000,0.000,0.000,0.000,0.000,0.000,16_0.O,

,0.000,

,.2075,

,.3190,

,.2339,

,.1654,

0596,.0831,

0529,.0701

0.000,0.000,0.000,0.O00,0.000,0.000,16_0

.4812,.6205,.7367,.8091,.7814,.3670,16"0

.4418,.5671,.6721,.7374,.7074,.3213,16"0

.3146,.3948,.4636,.5061,.4686,.1739,16"0

.2101,.2434,.2685,.2802,.2289,-.029,16_0

.0915,.0920,.0875,.0710,-.015,-.247,16"0

,.0724,.0639,.0431,.0138,-.080,-.286,16"0

O_

O,

O,

O,

O,

O,

O,

0462,.0571,.0533,.0538,-.001,-.043,-.145,-.318,16_0.0,

.740,1.750,13.32,

.000,.0420,.0460,

.000,.0020,.0023,

TBETA=0.250,O.250,O.250,O.250,

NALPHA=I3,TALPHA=-4.O,-2.O,O.O,2.0,4.0,6.O,8.0,10.O,12.0,14.0,16.0,

18.0,20.O,

NLEY2=2,TBLEY2=I.750,6.660,

TBLEX2zI2.75,17.66,

NTEY2=2,TBTEY2=I.750,6.660,

TBTEX2=IS.06,19.09,

NYC2=4,TBYC2=I.750,2.000,6.000,6.660,

NPCTC2=6,

TBPCTC2=O.O00,20.O0,40.O0,60.O0,80.O0,100.O,

TZORDC2=O.O00,.0991,.IIII,.0892,.0485,-.042,20*O.O,

0.000,.0961,.I095,.0902,.O522,-.033,20"0.0,

0.000,.0483,.0845,.i060,.ii15,.0974,20"0.0,

0.000,.0453,.0829,.i070,.I152,.I056,20_0.0,

NYR2=2,TBYR2=I.750,6.660,

TBTOC2=.0510,.0510,

TBROC2=.O024,.O024,

TBETA2=.3000,.3000,

DELTA2=O.O,ILS2=I, $C=IO

$1NPTI DELTA2=IO.O, $

26

Table I. Concluded

(h) Arrow-wing supersonic transport with horizontal tail

SST-YIP,TM 80152 - LEFD=4.3,12.8,12.8,12.8,11.2,17.6,TEFD=30,DELTA2=5,-15

$1NPTI XM=O.O9,RN=4.19,JBYMAX=IO,ELAR=3.0,1VOROP=I,IPRSLDA=I,

SREF=I4400.,CBAR=77.76,XMC=220.91,XMAX=372.,

NALPHA=I6,TALPHA=-6.0,-4.0,-2.0,O.O,2.0,4.0,6.0,8.0,10.O,12.0,14.0,

16.0,18.0,20.0,22.0,24.0,

NLEY=4,TBLEY=O.000,7.0000,51.710,81.330,

TBLEX=O.000,104.70,234.55,280.20,

NTEY=4,TBTEY=O.000,7.0000,25.800,81.330,

TBTEX=372.0,277.70,277.70,294.97,

NYC=I5,TBYC=0.0000,4.4090,13.428,20.899,23.218,27.202,29.498,

38.294,47.061,49.819,53.701,56.458,67.509,76.399,

81.330,

NPCTC=IO,

TBPCTC=0.O00,5.000,10.00,20.O0,30.00,40.00,50.O0,60.O0,80.00,100.O,

TZORDC=I4.30,15.20,17.50,17.40,15.40,12.55,10.O0,8.000,6.000,10.O0,16*O.O,

13.20,13.20,12.79,11.24,9.250,7.380,5.700,4.250,2.000,.6000,16"0.0,

6.250,6.780,6.990,6.890,6.200,5.320,4.500,3.770,2.330,1.000,16"0.0

4.280,4.850,5.250,5.430,5.130,4.600,4.030,3.500,2.470,1.420,16"0.0

4.030,4.600,4.940,5.200,4.980,4.450,3.930,3.430,2.470,1.500,16"0.0

3.760,4.270,4.600,4.890,4.660,4.220,3.780,

3.530,4.000,4.370,4.650,4.430,4.100,3.660,

1.950,2.430,2.800,3.120,3.070,2.880,2.680,

0.660,0.960,1.200,1.480,1.600,1.630,1.660,

0.470,0.700,0.880,1.120,1.250,1.330,1.400,

0.330,0.450,0.580,0.760,0.900,1.040,1.130,

0.260,0.370,0.430,0.590,0.720,0.870,0.980,

3.300,2.380,1.560,16"0.0

3.200,2.350,1.580,16"0.0

2.450,2.000,1.580,16"0.0

1.630,1.570,1.480,16"0.0

1.420,1.430,1.430,16"0.0

1.210,1.300,1.340,16"0.0

1.070,1.200,1.280,16"0.0

0.300

0.270

0.280

NYR=7,TBYR=0

TBTOC=O

,0.310,0.320,0.350,0.410,0.470,0.550,0.620,0.790,0.930,16"0.0,

,0.270,0.270,0.280,0.290,0.310,0.330,0.360,0.430,0.520,16"0.0,

,0.280,0.280,0.280,0.280,0.280,0.290,0.300,0.330,0.400,16"0.0,

.00000,4.40900,20.8990,38.2940,51.7000,51.7100,81.3300,

.04000,0.02380,0.02870,0.03000,0.03000,0.03000,0.03000,

TBETA=0.50000,0.66000,O.55000,0.58000,0.60000,O.60000,0.60000,

TBROC=O.O0000,0.O0024,0.00050,O.00048,0.O0040,.O00003,.000013,

NLEFY=10,TBLEFY=O.000,7.000,7.010,17.59,17.60,44.42,51.71,64.00,64.01,81.33,

TBLEFC=O.O00,O.O00,18.84,18.80,18.80,18.78,8.370,6.770,6.770,4.510,

TBLEFD=O.O00,O.O00,4.300,4.300,12.80,12.80,11.20,11.20,17.60,17.60,

NTEFY=IO,TBTEFY=O.O00,17.00,17.01,25.80,25.81,36.59,36.60,61.00,61.01,81.33,

TBTEFC=O.O00,O.O00,15.93,15.93,0.O00,O.O00,14.50,9.650,O.000,O.000,

TBTEFD=O.000,O.O00,30.00,30.00,0.O00,O.000,30.00,30.00,O.000,O.000,

NLEY2=2,TBLEY2=2.0000,23.700,

TBLEX2=323.20,348.99,

NTEY2=2,TBTEY2=2.0000,23.700,

TBTEX2=361.00,355.39,

NYC2=2,TBYC2=2.0000,23.700,

NPCTC2=2,TBPCTC2=0.0000,100.00,

TZORDC2=52*O.0,

NYR2=2,TBYR2=2.000,23.70,

TBTOC2=O.035,0.035,

TBETA2=0.500,0.500,

TBROC2=0.O00,O.O00,

DELTA2=5.0,1LS2=2, $DELTA2=-15.0

$1NPTI DELTA2=-I5.0, $

2?

f_y

1I

2 3 4 5 6 7 8 9 10 11| I | i | | i I | i

r I_

IIItIIII

II

I I

I I I I I, , , +_,o', I I I_AT /Ir---+- .... _+- iI , _ ._" ! I,J ' ;4

....... -r .... r---1 .... r'--1----T-_'-ni , , i i i/__ +/ i/I I I I I _. 23 X 24 I/ 5

.,_t'____ ' ' , /_ ]! I i----+---q---L./. I ,/ " /i---_1 I | I ._I i/ I/ /I i

I ' I lI 19_20 / 21 J'/'22/ I lI i

I I

, ' ! I//i /i _ I ! , j(_)....... t.... _----+- ..... I----I

I /l/ i/ I1 t/ I II I I/;5J/m Y17 J/is II I II I '/ lJ A /] if i i

j_ I'iI I I/..l/'12 j/13 I 14Xt\ , , 2I I I/, /' 1 ,% ,

+/+ ,,/ ,f , ,-+---,

L I I I l I I I i • I I

0 1 2 3 4 5 6 7 8 9 10 11X

AX

(a) Wing alone.

f_y

8

7

6

5

4

3

2

1

0

fl'l

////ii ////////// ////////////i111111

I I I I S t _ , = ' 210 I I I I I • . ,.rJ I I I0 2 4 6 8 10 12 14 16 18 22 24 26 28 30 32 34 36 3B 40

X

.*,X

(b) Wing-body-canard configuration.

Figure 1. Typical representation of lifting surfaces used for numerical solution of linearized theory.line indicates original planform; numbers used to identify individual wing elements.

28

Dashed

7

Actual planform

Code-input planf_

(a) 60°-swept trapezoidal-wing fighter with canard.

Actual planform %__

Code-input planform__

(b) 44°-swept trapezoidal-wing fighter with canard.

Figure 2. Numerical representation of lifting surface for selected configurations used in study.

29

Actual pranform

Code-input planform

(c) 60°-swept delta-wing fighter with horizontal tail.

Actual planform

(d) Forward swept-wing fighter with canard.

Figure 2. Continued.

30

Actual planform_

Code-input planform

_erated_

(e) Arrow-wing supersonic transport with horizontal tail.

Figure 2. Concluded.

31

• rrlT_

O Experiment

Theory

._,_.._.-. With attainable thrustand vortex force

...... Without thrust or vortex

CA

C N

.O8

0

-.08

-.16

-.24

2.0

1.5

1.0

.5

m'

_ ru _ _,_

" Cm ..-_

__ 0 O0 0 O0

/_,

,=,,,,rus,.-/'_ -- m 4

CD,0

/C D

+C L

.24

.16

.08

i ,_ , I 0-8 0 8 16

tan ( cL _.--..

,,0.,,,,.....7i/o/. i,i,#- CD, 0 + 7rA'-'--_

I I I I I0 .5 1.0 1.5 2.0

a ,deg C L

(a) Azle = O.

Figure 3. Theoretical and experimental data for unswept wing-canard configuration at three canard heights.M=0.2; R=1.4x10 6 .

CA

.O8

-.08

-.16

-.24

2.0

1.5

C N

1.0

.5

0-8

O Experiment

Theory

..___.._. With attainable thrustand vortex force

...... Without thrust or vortex

Full thrustI

0 8

a ,deg

Cm

.4-

0

-.4

CD, 0 + C L

.24

.16

C D

.08

I 016

J

__" O

tan / CL_

c.o, ,;/o//,,,,#

/,_/'/j_(___ CL 2- \ / CD'0+

.I I I I I0 .5 1.0 1.5 2.0

C L

(b) Az/_ =-0.5.

Figure 3. Continued.

33

.08

0

CA

-.08

-.16

-.24

2.0

1.5

C N

1.0

.5

0 I

-8

O Experiment

Theory

_._ With attainable thrustand vortex force

Without thrust or vortex

Fullhrust Jk _ -.4-

/0 #

\CD, 0 + C L

C D.08

x_0

I I 0 -I l i , I8 16 0 .5 1.0 1.5 2.0

a ,deg C L

(c) /Xz/e 0.5.

Figure 3. Concluded.

< - l

O Experiment

Theory

With attainable thrustand vortex force

Without thrust or vortex

.04 -

CA0

-.04

.1

o_ a..°-_ o_Cm 0 _.._

--.1

C N

.8 .24 -

0C D

-10 0 10 20

.16 -

.08

Co0_CL'aoI_)q,'c!L1

-.4 0 .4 .8

a ,deg C L

(a) Az/e = O.

Figure 4. Theoretical and experimental data for 60°-swept trapezoidal-wing fighter with canard at three canardheights. M = 0.7; R = 1.35 x 106.

35

-==-- I

O Experiment

Theory

-_--,---- With attainable thrustand vortex force

...... Without thrust or vortex

.04 .1

cA Cm0 0

-.04 -.1

C N

.8

.4

0

-,4 t, I •-10 0 10 20

a ,deg

CD

.24,

.16

.08

0

(b) Az/_ =-0.185.

Figure 4. Continued.

_'_..Q_ 5-6"o

CL2 /

CD,o, _,A--"_""_,/

-.4 0 .4 .8

C L

36

0 Experiment

Theory

--.-------. With attainable thrustand vortex force

...... Without thrust or vortex

.O4

CA0

-.04

Cm

.1

-.1

C N

.8

.4

-.4 L-10 0

I •

10 20

a ,deg

C D

.24

.16

.O8

- CD,o+CL tan[ C_L _-._ /

• \CL,a] 7,

,-.4 0 .4 .B

C L

(c) Az/_ = 0.185.

Figure 4. Concluded.

37

iO Experiment

Theory

._...-.--. With attainable thrustand vortex force

...... Without thrust or vortex

.08 .2

"04 I

CA _ Cm

0 0

-.04 -.1

.1

C N

.8 - .24 -

.4

0

C D

.16

!.08 -

-.4 L 0-10 0 10 20

a ,deg C L

C LCD, 0 + C L tan (._-) --k

L,a V/

C + !

• 1 I l

-.4 0 .4 .8

(a) _L,n =0°, _T,n =0°, _C =0%

Figure 5. Theoretical and experimental data for 44°-swept trapezoidal-wing fighter with canard. M = 0.4;R = 1.9 x 106.

38

O Experiment

Theory

._____.. With attainable thrustand vortex force

...... Without thrust or vortex

.08 .2_

.O4

CA0

-.04

Cm

.1

0

--o1 -

C N

.8

.4

0

-.4

/0 10

a ,deg

C D.08

0

C L

(b) 5L,n = 0°, 5T,n 0°, 5C =--5°.

Figure 5. Continued.

39

0 Experiment

Theory

_._._.._ With attainable thrustand vortex force

...... Without thrust or vortex

.08 - .2

.04

CA0

-.04

"o

%

Cm

.1

-.1

.8

.4

CN

-.40

#

d

I I

2O10

e ,deg

C Lcoo.c,,an_) _I #

CD,

!

-.4 0 .4 .8

C L

(C) 5L, n ----0 °, _T,n = 0°, _C = --10%

Figure 5. Continued.

40

w

O Experiment

Theory

.__..._. With attainable thrustand vortex force

...... Without thrust or vortex

.O8

.O4

CA0

-.04

%

Cm

.1

-.1

-.2

C N

.8

.4

0

-.4

I7

X

.24

.16

CD

.08

.I I ; 0-10 0 10 20

a ,deg

C L+ C L tan (_.-_L/"k #

CD'0 \_L,a/ _/I

. CD, 0+ __

I I t i-.4 0 .4 .8

C L

(d) _L,n ---- 12°, _T,n = 12°, dfC = 0°.

Figure 5. Continued.

41

w

O Experiment

Theory

. With attainable thrustand vortex force

...... Without thrust or vortex

.08 -

.04 -

CA0

-.04 -

Cm

.1

-.1

-.2

.8

.4

C N

-.4

I)

J

! I I-10 0 10 20

a ,deg

(e) 6L,n = 12°, _T,n

C D

.24

.16

.o8

0 I--°4

Co0 C,,an2 //

CL" -..-.., /

CD,0+ "trAR \/_/

I"t"_>" I I

0 .4 .8

C L

= 12°, _C = -lO°.

Figure 5. Continued.

42

!

O Experiment

Theory

.---.---. With attainable thrustand vortex force

...... Without thrust or vortex

.08 -

.04 -

CA0

-.04 -

O

Cm

.1

0

-.1

-.2

../.

.8

.4

C N

-.4 |

-10

7/S

J

/

I0 10

a ,deg

J2O

CD

.24 +C L tanIcC,_.L/.__CO'0 L,a \/

0,2_ _.o_°o,o+I_\/F/

-.4 0 .4 .8

C L

(f) _L,n ---- 12°, $T,n ---- 12°, tiC = l0 °.

Figure 5. Continued.

43

O Experiment

Theory

......,.... With attainable thrustand vortex force

...... Without thrust or vortex

.08

.04

CA0

-.04

\

Cm

.1-

_°2 D

O

C N

.8

.4

-.4 !-10

I I0 10

a ,deg

.24

.16

C D

.08

! 0 I20 -.4

coo.

CD'0+ _ /__/

0 ,4 .8

C L

(g) _L,n = 20°, d_T,n= 20°, 6C = 0%

Figure 5. Continued.

44

_-=:=.-- ]

O Experiment

Theory

_____ With attainable thrustand vortex force

...... Without thrust or vortex

CA

C N

.O8

.O4

0

-.04

.8

.4

0

-.4-10

ok',

//

I

0 10

a ,deg

(h) _L,n

.1

Cm

--1 D

--2 _- oo?/J

.24

.16

C D

.08

s 0 I20 -.4

CD, 0 + C L tan

CD, 0 +

/

0 .4 .8

C L

= 20°, tST,n = 20°, _C = --10%

Figure 5. Continued.

45

| --

O Experiment

Theory

_.,,,.--, With attainable rthrustand vortex force

...... Without thrust or vortex

CA

.08 -

.04 -

0

-.04 -

.8-

.4-

C N

0

-.4 - I-10

o -_O

/

Cm

CD

,1

0

-.1

-.2

.24

.16

.08

I I 00 10 2O

e ,deg

O

o/

+ C L tan { cL _.-_

CD'0 \CL,a) _///

/ Jo

CD'0+ ___

! !-.4 0 ,4 .8

C L

(i) _L,n = 20°, _T,n = 20°, d_C----10%

Figure 5. Concluded.

46

3

r"

_x

r"

!

I

%

IIC

II

l-.J

oo

! I

oo

(1) o

E e_

a) IIo. r-"

I I

%II

C

tX_

II

cJ

%II

0

I

o _ o

oo

II

I I

oo

I!

0

i I

o

I

II

I mo _ o

oo

I

II

! I o

oo

I

II

I I

o

I I

o X

0

_ °_

eN

°,-_

o _e_

_. _o'

°

"13

0 _ _

o,,_

47

Q)"0

II

--J

o

4B

i _

0 Experiment

Theory

._... --... Withand

attainable thrustvortex force

_c'deg _F"__

-10 L

Ss

1.0

.5

0 , i I I I0 .2 .4 .6 .8

CL

Figure 8. Optimum flap deflection angle, canard incidence angle, and maximum suction-parameter variationwith lift coefficient for 44°-swept trapezoidal-wing fighter with canard. M = 0.4; R = 1.9 x 106.

49

J

O Experiment

Theory

•-------.- With attainable thrustand vortex force

.08 - .2

CA0

.O4

-.04

..o-(Cm

-.1

8f.4

C N

.24 ./I

/0 10

.16

C D

.08

"o..-.4 - I, I 0 (.

-10 20 -.4 0

a ,deg

=o°, 6T,. =0 °, 6c=O °(a) 5L,n

I

I.4

C L

Figure 9. Theoretical and experimental data for 44°-swept trapezoidal-wing fighter with canard.R = 2.58 x 10 6,

O

/

.8

M = 0.8;

5O

.08

.04

CA0

-.04

J

0 Experiment

Theory

__.__ With attainable thrustand vortex force

Cm

-.1

-.2

-.3

O0 0 0000

o

C N

.8-

°4

0

-.4

/o

/oI

I-10

0.24

.16

C D.08

I 0 !0 10 20 -.4

e ,deg

0

0 .4

C L

(b) _L,n -----20°, _T,n = 20°, &C = -10°.

Figure 9. Concluded.

!.8

51

O Experiment

Theory

_..._=_ With attainable thrustand vortex force

...... Without thrust or vortex

CA

.O8

.O4

-.04

I Cm

.1

--.2--

-..CJJ

C N

.8

.4

0

.24

.16

CD

.08

-.4 I, J 0-10 0 10 20

-co,o+ci, nCD,

-.4 0 .4 .8

a ,deg CL

(a) _L,n = 0°, _T,n = 0°, _H = 0°"

Figure 10. Theoretical and experimental data for 44°-swept trapezoidal-wing fighter with horizontal tail atM = 0.4 and R = 1.9 x 106 .

T"

52

<.

0 Experiment

Theory

_._._ With attainable thrustand vortex force

...... Without thrust or vortex

.08 -

.04 -

CA0

-.04 -

Cm

.1

-.1

-.2

--oo

0

C N

.8

.4

-.4

?-|-10 0

/

10

a ,deg

I2O

.24

.16

CD

.08

0 I--.4

(CL'_ ,,6

cD,o÷CLtankC--'_'.)4:)

CL 2 ///_t//

CD,0+ W-'EF'--'_ /

I ,.__,

0 .4 .8

C L

(b) _L,n = 0°, _T,n = 0°, 5H = --5°"

Figure 10. Continued.

53

0 Experiment

Theory

,,,-----.-- With attainable thrustand vortex force

...... Without thrust or vortex

.08 .1.

.O4

CA0

-.04

Cm0

-.1

-.2

._3c

.8

,4

C N

0

-.4- I !-10 0 10 20

a ,deg

C D

.24 -

.16 -

.08

0

coo. 'aoJ /o,

co

I I |-.4 0 .4 .8

C L

(c) 6L, n=O °, 6T,n=O °, 6H =5 °.

Figure 10. Continued.

54

O Experiment

Theory

----.---- With attainable thrustand vortex force

...... Without thrust or vortex

.08 .1-

.04

CA0

-.04

%

--(5

O

Cm

0

-.1

-.2

.8

.4

C N

0

-.4 _!-10

,#

/

.24

0 10

a ,deg

.16

C D.08

I I 0 I20 -.4

CD,0

CD, 0 +D

!/ I

CL2 / / _,

0 .4 .8

C L

(d) 6L, n = 12°, _T,n = 12°, 6H = 0%

Figure 10. Continued.

55

O Experiment

Theory

_.....,.-- WTth attainable thrustand vortex force

...... Without thrust or vortex

.08

.04

CA0

-.04

0\_

\

o \0

Cm

.1--

--o1 --

--.2"

C N

.8

.4

-.4-10 0

I I

10 20

o ,deg

.24

.16

C D

.08

coon/////

,., CL 2 _;//_/C)

L,D,0 + _ "_,/_ /

, ,-.4 0 .4 .8

C L

(e) _L,n = 12°, _T,n = 12°, _H = --10°"

Figure 10. Continued.

m

56

<.

0 Experiment

Theory

--.--.--... With attainable thrustand vortex force

...... Without thrust or vortex

.08r .I-

.O4

CA0

-.04

---t

J ..... 0_%%%o\

Cm0

-.1

--.2'°'(7 "0

C N

.8

.4

-.4-10

/ C D

.08

i I 010 20

a ,deg

C L

CD'O - -L,e "--'k/

+ C L tan/C'E_.I

./,,;;,Oo,o __,/,.,¢"

-.4 0 .4 .8

C L

(f) 6L,n = 12°, 6T, n ----12o, 6H = 10°.

Figure 10. Continued.

5?

<

0 Experiment

Theory

. With attainable thrustand vortex force

...... Without thrust or vortex

.08 -

.04 -

CA0

-.04 -

%

o Q,

ok

Cm

.1

-.1

--,2-

" _c_:). O_.__ ° t- v O-o'6

C N

0

-.4 I-10

///

I I0 10 20

C D

a ,deg

.24 -

.16 -

.08 -

o+CL tan(_C_L/-_k_

CD' . \'-'L,e / /

CD, 0 +

I _-"_" I I

-.4 0 .4 .8

C L

(g) 5L,n = 20° , 6T, n=20 ° , 5H =0 °.

Figure 10. Continued.

58

<.

O Experiment

Theory

._.,.._. With attainable thrustand vortex force

...... Without thrust or vortex

.08 .

.04

CA0

-.04 -

0 _\

0 kk\

\\

0 _k

0

Cm

.I

-.I

-.2

00.. _"---......

UOOOoo

C N

.8 --

.4-

0

--.4 |-10

J

,o/°

0 10

a ,deg

.24

.16

CD.08

I 0 I.20 -.4

" CD,0+ CL tan/c_,a)'--_/

.I

Co,0+ ,_AR-'X /0

0 .4 .8

C L

(h) _L,n----20°, _T,n = 20°, d)H =--10%

Figure 10. Continued.

59

<Z

O Experiment

Theory

......._ With attainable thrustand vortex force

...... Without thrust or vortex

.08 -

.04 -

CA0

-.04

Cm

.1

-.1

--,2 -

"'-O

C N

.8

.4

0

-,4

/S

I i I-10 0 10 20

e ,deg

C D

.24- CD,0+ CL tan(CL /._k

.16 - I \"L,el 7

ocooo

-.4 0 .4 .8

C L

(i) _L,n ----20°, 5T,n = 20 °, _H = 10°.

Figure 10. Concluded.

60

L,.0

C"I-

I.. II

Q

-_- %

C:: x II"__ c*-'_- I..3

C_g j

0 I I

., %E ,--

_ CQ.x _

IIr-

.3

I I

..,on

%

I| c

I|

C

I0 _ 0

%II

A I

oQ

I I

o0

II

L0 U') Q

0")

oQ

I

II

"r

tX)

O

%I

]2

I o

oL_I

II"1- O_

¢.<:)

qD

n 0

=

0

.o ,_o_.-i

bO

_'-

_N0

°,-,u

°,-_

g___

._ N_"

61

"0

82

0 Experiment

Theory

..__...__ With attainable thrustand vortex force

_L,n & _T,n

'deg20f4.._..._10 oo..-I0

. X3---'_.._ °..-0"

10

_H'deg f,,.,.,.,, _5 ...I....O--0

S s

1.0

.5

-- O

0 I I I l0 .2 .4 .6 .8

CL

Figure 13. Optimum flap deflection angle, horizontal-tail incidence angle, and maximum suction-parametervariation with lift coefficient for 44°-swept trapezoidal-wing fighter with horizontal tail. M = 0.4;

R = 1.9 × 106.

63

-- - ""-"I--0 Experiment

Theory

With attainable thrustand vortex force

.O8 .2

.O4

CA0

-.04 -

Cm

.1

--°1 --

---.Ou

0

0

C N

.8

.4

0

?

/oS

-.4 I i I-10 0 10 20

a ,deg

CD

.24 -

.16

.08

0

m

I ""0_

--°4

0

0

o/-"0"0(

0 .4 .8

C L

(a) 5L,n = 0°, 'ST,n = 0°, _H = 0°.

Figure 14. Theoretical and ex_)erimental data for 44°-swept trapezoidal-wing fighter with horizontal tail atM = 0.8 and R = 2.58 x 10%

64

<

0 Experiment

Theory

.--,...-_ With attainable thrustand vortex force

.08

.04

CA0

-.04

Cm

0

-.1

-.2

-.3L

C N

.8-

.4-

0

-.4

/o

O

.1 I

-I0 0 10

a ,deg

.24

.16

C D

.08

O

I 0 .I I I20 -.4 0 .4 .8

C L

(b) 6L, n = 20 °, 6T,n = 20 °, 6H = 10°.

Figure 14. Concluded.

65

J

_._--3--

_====-

O Experiment

Theory

..__.._.. With attainable thrustand vortex force

...... Without thrust or vortex

CA0

-.04

Cm

.1-

o --------_o

CN

.8

.4

2

.24

.16

CD.O8

I J 0_L-10 0 10 20

a ,deg

CD,0 + C i tan IC_,a/ !>

CL

=0 ° =0% 6C=0°'(a) thL,n , _T,n

Figure 15. Theoretical and experimental data for 60°-swep t delta-wing fighter with canard. M = 0.4;

R = 2.52 x 106 •

66

l

O Experiment

Theory

-_..,..._.. With attainable thrustand vortex force

...... Without thrust or vortex

.08

.04

CA0

-.04

"o

Cm

-.1

-.2

C N

.8

.4

-.4 -L

-10 0 10

a ,deg

CD

.24

.16

.O8

I 020

C L

c!LY. oo _-_-x_f/

i I I-.4 0 .4 .8

C L

(b) 5L,n -----0°, ST, n = 0 °, 5C = --10 °.

Figure 15. Continued.

{}7

O Experiment

Theory

.__.__. With attainable thrustand vortex force

...... Without thrust or vortex

.08

.O4

CA0

-.04

Cm

.1

0

-.1

-.2

C N

.8

.4

0

-.4 I-10

C D

.24

.16

.08

I I 00 10 20

a ,deg

coo_c_,,oC_/_t

/CL2 /L

k_ I !

-.4 0 .4 .8

C L

(C) 5L,n = 0°, 5T,n = 0°, (_C ----5°.

Figure 15. Continued.

68

O Experiment

Theory

.__...__ With attainable thrustand vortex force

...... Without thrust or vortex

C A

.O8

.O4

0

-.04 -

._O

O _-,.O

OO

Cm

.1-

0

C N

.8

.4

0

-.4- t-10 0 10

a ,deg

.24

.16

C D.08

020

- CD,0+ CL tan/C-_n)-'_/

CD, 0 + -----7tAR

L "_ I I

-.4 0 .4 .B

CL

(d) 6L, n = 10 °, (_T,n----10°, 6C---- 0°"

Figure 15. Continued.

89

T-

w .mr-...._ j

O Experiment

Theory

_..,--_ With attainable thrustand vortex force

...... Without thrust or vortex

.08 - .1-

CA

.04

-.04 -

.8

,4

C N

-,4 .!

-10

Cm

*b

% "_

O

O

-.1

-.2

^ oO

f//

//!0 10

e ,deg

CD

.24

.16

.O8

| 0 I20 -.4

Co,o'C , n/,,'

2 /,'_CL I/A .

_ CD,O+ _ -'-_./,,/° V

0 .4 .8

C L

(e) 6L, n = 10°, 6T, n ----10°, 6c = --10 °.

Figure 15. Continued.

70

]-- 0 Experiment

Theory

•,.--,----- With attainable thrustand vortex force

...... Without thrust or vortex

.08

.O4

CA0

-.04

Cm

.1

0

0 -.10

-.2

0 10

a ,deg

C D

J 0_.120 -.4

CD'O +_/

I0 .4 .8

C L

(f) _L,n ---- 10°, _T,n = 10°, dfC = 10°.

Figure 15. Continued.

?1

T-0 Experiment

Theory

_.--.--- With attainable tnrustand vortex force

...... Without thrust or vortex

CA

.08

.O4

0

-.04 -

O

Cm

-.1

-.2

C N

.8

.4

0

-.4 _1-10 0

a ,deg

.24

.16

CD.08

i I 0 .I10 20 -.4

CD, 0 + C L

CD, 0 +

0 .4 .8

C L

(g) 6L,n =20 °, OT,n -_ 20°, _C =0%

Figure 15. Continued.

72

O Experiment

Theory

--..--,,.-, With attainable thrustand vortex force

...... Without thrust or vortex

.08 .1-

.O4

CA0

-.04

)

%.O

Cm0

-.1

-.2

C N

.8

.4

u

I/ Co

.O8

_1 i i 0-10 0 10 20

a ,deg

!

" I

C 2

CO, 0 + _/

.1_ I l

-.4 0 .4 .8

C L

(h) _L,n = 20°, $T,n = 20°, _C = --10°.

Figure 15. Continued.

73

0 Experiment

Theory

With attainable thrust--'-- and vortex force

...... Without thrust or vortex

CA

.1

_ Cm 0

.04

O_ °O "-- -'2

-.04

/ / .24 CD, O + C L tan. I

.16

°08

• -10 0 10 CL(z ,deg

(i] _L,n = 20°, 5T'n "" 20°' 5C = 10°"

Figure 15. Concluded.

74

7S

o}

"1:3

II,..I

0

T6

0 Experiment

Theory

..--...--_ With attainable thrustand vortex force

_L,n & _T,n,deg

2O

-10

S s

1.0"

.5

9

0 I I I I0 .2 .4 .6 .8

CL

Figure 18. Optimum flap deflection angle, canard incidence angle, and maximum suction-parameter variationwith lift coefficient for 60°-swept delta-wing fighter with canard. M = 0.4; R = 2.52 × 106.

77

-'--T-O Experiment

Theory

_--_ With attainable thrustand vortex force

.08. .2

.O4

CA0

-.04

Cm

.1

0

-.1

- t

C N

.8

.4

0

J .24

#,

.16

/

0

C D

.08

-.4 | I I 0 -I-10 10 20 -.4 0

l

?,0

/_00"

._|

.4

e ,deg CL

!

.8

(a) _L,n = 0°, _T,n = 0°, 5C = 0°.

Figure 19. Theoretical and experimental data for 60°-swept delta-wing fighter with canard.R = 3.4 x 106.

M = 0.8;

T8

]--O Experiment

Theory

.._..._. With attainable thrustand vortex force

.08

.O4

CA0

-.04 -

.1

Cm0

--.1 --

--.2 --

O0 0 000 o 0

C N

-.4 |-I0 0 10 20

a ,deg

C D

.24

.16

.08

0 I--.4

i I I0 .4 ,8

C L

(b) 6L, n = 20 °, 6T,n = 20°, 6c ------10 °.

Figure 19. Concluded.

79

-= =._ -.==..J

O Experiment

Theory

__.--. With attainable thrustand vortex force

...... Without thrust or vortex

.08 .1

.O4

CA0

Cm0 ",c

C N

.8 .24.

.4

C D

s'

//

0 10 20

e ,deg

.16 -

.08 -

-! 0 --.4-.4 -10

-,- tar,( Ct_

CD,0 CcI \CL'a Jr/_

, CL2 ..._, //

l -1"- I I0 .4 .8

C L

(a) _L,n = 0°, _T,n = 0°, _H = 0%

Figure 20. Theoretical and experimental data for 60°-swept delta-wing fighter with horizontal tail.M=0.4; R=2.52x108 .

80

O Experiment

Theory

___.._. With attainable thrustand vortex force

...... Without thrust or vortex

.08

.O4

CA0

-.04

Cm

.1

0

-.1

--.2 "

O

C N

.8

.4

-.4 I-10

/o,o,/"

0 10

a ,deg

I20

.24 CD, O+ C L tan C(C._,o) /_/0/

co coo,0 I 1- I I

-.4 0 .4 .8

cL

(b) _L,n = 0°, 6T,n = 0°, 6H------5°"

Figure 20. Continued.

81

O Experiment

Theory

,_,,,,,__, With attainable thrustand vortex force

...... Without thrust or vortex

.08 .1_

.04

CA0

-.04 -O

Cm

-.1

-.2

"E

O"O

C N

.8

.4

0

-.4 .!-10

J

0 10

a ,deg

I20

.24

.16

C D

.08

0

C L- +ct. tan(_._._._.L'___,/CD, o \CL.a) _/

I //

L-.4 0 .4 .8

Ct.

(C) _L,n -_ O°, _T,n ----O°, 5H----5°-

Figure 20. Continued.

82

O Experiment

Theory

._..-_. With attainable thrustand vortex force

...... Without thrust or vortex

.08- .1

CA

C N

.04

0

-.04 -

.8-

.4

0

-.4

7.Q

%

0

0

0 o

.I,,

-10

t_ I I

0 10 20

a ,deg

Cm0

--o1 -

--.2 --

.24 -

.16 -

CD.08 -

-,,,,

O

CD, O

I-.4 0 .4 .8

C L

(d) _L,n ----10°, 6_T,n= 10°, _H ----0°.

Figure 20. Continued.

83

O Experiment

Theory

_....-- With attainable thrustand vortex force

...... Without thrust or vortex

.08

.O4

CA0

-.04

O

OO

Cm

.1

-.1

-.2

O_..O

C N

.8

.4

0

-.4 .I-10

I

0

C D

.24

.16

.O8

i i 010 20

e ,deg

i/coo+_Ltan/_l_co

I I I

-.4 0 .4 .8

C L

(e) _L,n = 10°, 8T,n = 10°, 8H = --10°.

Figure 20. Continued.

84

_=-- -'=-I

O Experiment

Theory

...=_.=..._ With attainable thrustand vortex force

...... Without thrust or vortex

.08 .1_

CA

C N

.04

0

-.04

vO

OO

/

/

JO

Cm

m.1.,

-.2

.24 -

.16 -

CD

.08

-.4 - I i ! ! 0-10 0 10 20

a ,deg

O

CD0+C,,anC@/--qi 4"s

/,,,fcD,O+_ _/

I I !-.4 0 .4 .8

C L

(f) _L,n ----10°, _T,n ----10°, _H = 10°-

Figure 20. Continued.

85

-._____ _=_

O Experiment

Theory

.---.-.--. With attainable thrustand vortex force

....... Without thrust or vortex

.O8 .1

.04

CA0

-.04

%

O

O

Cmo

no1O '_

OO

hi2 m

.8

.4

CN

-.4 -!-10 0

.24

10

a ,deg

.16

C D

.08

I j 020

" CD,0+C L tan _'/CIc---_-n/-.._

, ,-.4 0 .4 .8

C L

(g) &L,n = 20°, 5T,n = 20°, 5H = 0%

Figure 20. Continued.

86

--=-t

O Experiment

Theory

,__,__..._ With attainable thrustand vortex force

...... Without thrust or vortex

CA

.O8

.O4

0

-.04 --

%

0 _,,

0

0

0

Cm

o1 -

0

--o1 -

--,2 "

v 0 ,_ "_

O O""O

C N

.8

.4

-.4-10

.24

.16

CD

.08

I I 010 20

a ,deg

/\/C L- + C L tan / e--_)'-'_, _

CD'0 ,- -L,a lJ

I I I I-.4 0 .4 ,8

C L

(h) _SL,n = 20 °, _T,n = 20°, _H = -10°.

Figure 20. Continued.

8T

O Experiment

Theory

__..._. With attainable thrustand vortex force

...... Without thrust or vortex

CA

C N

.08 -

-.04 -

.8-

.4

0

-.4 I-10

"%%.

O

10

e ,deg

Cm

CD

I20

.1

0

-.1

-.2 0"0

.2,co.o .16 I

.08 CD'0 + _,A

o-.4 0 .4 .8

C L

(i) 6L, n = 20 °, 6T,n = 20°, 6H = 10°.

Figure 20. Concluded.

88

2 ; _

E x II E --

m_

f- I i I ,

•- _

II E

I|

E

dI I |

%

I|r."

II

E

.

CO

%II

| I

%

| !

%

! !o u') o

r._

!

c)

%T--

III

"I"

oo

I

c0

_o

i o

II

co

I o

oLoI

III eo

gO

o4

i o

_Jo

_Jo

_Jo

bO¢'_

o II

o __

o___

= =

8_

o "_

a_

89

gO

O Experiment

Theory

.----.i With attainable thrustand vortex force

20_ .I

& _T,n,deg _ 010 .,._"

0

_H,deg

5 ..

0

.

SS

1.0

.5

-"--O- - -----Q__ ----O-- - --"O"

0 I I I I0 .2 .4 .6 .8

CL

Figure 23. Optimum flap deflection angle, horizontal-tail incidence angle, and maximum suction-parametervariation with lift coefficient for 60°-swept delta-wing fighter with horizontal tail. M = 0.4; R = 2.52 x 106.

91

_=- -=-I

O Experiment

Theory

_.,_ With attainable thrustand vortex force

.08 -

.04 -

CA0

-.04 -

Cm

.1

-.1

--°2 --

OO

C N

.8 .24 -

.4

0

O

to

/0

CD

.16

.08

//

/.J

I

.4-.4 • I I 0 I I

-t0 10 20 -.4 0 .8

a ,deg CL

(a) _L,n ---- O°, _T,n ---- O°, _H----0%

Figure 24. Theoretical and experimental data for 60°-swept trapezoidal-wing fighter with horizontal tail.M=0.8; R=3.4x106 .

92

<. -----_ -=-t

0 Experiment

Theory

----.,,--,- With attainable thrustand vortex force

.08 - 0

.04

CA0

-.04 -

0

,%\

Cm

-.1

-.2

-.3

00

.8-

.4-

C N

0

-.4 _L

-10

/

0_0 .24J

J .16

C D.08

I I 0 I10 20 -.4

(z ,deg

(b) _f/;,n = 20 °, 5T, n = 20°, _H ----"10°.

Figure 24. Concluded.

0

O

oo/ .o Oy

I 1.4 ,8

C L

g3

-_- -rO Experiment

Theory

,---.---- With attainable thrustand vortex force

CA0

-.08

.08. .2 -

Cm

0 o/°S

C N

1.6 .24

.8

,,/

/ .16

C D

.08

-.8- I i I 0-10 0 10 20

a ,deg CL

" CD,0+C L tan _'C(..z-.--_

\_L,a]/ J#

/ i/p

"n'AR ,X.,,'-'

Co,o /_

..l I i I

0 .4 .8 1.2

(a) _L,s = 0°, _T,s = 0°, _5C = 0%

Figure 25. Theoretical and experimental data for forward swept-wing fighter with canard. M = 0.6;R = 2.5 x 106.

94

<J ---=='

O Experiment

Theory

.__....-- With attainable thrustand vortex force

.08 -

CA0

-.08 -

Cm

.2_

Joo- -

_12 m

C N

1.6

.8

-.8 -!

-10

J,d°"

f-

!

0 10

a ,deg

.24

.16

C D.O8

I 02O

CD,0+ CL tanlc_a 1).

• I I

0 .4 .8

C L

!1.2

(b) _L,s = 0°, _T,s = 0°, _C = 10°.

Figure 25. Continued.

95

/

O Experiment

Theory

--,,-..,,.-- With attainable thrustand vortex force

.O8

CA0

-.08

\%

Cm

.2-

-.2

/

o o,.O_J

C N

1.6

.8

O[-.8 I

-10

/<o-

0I I

10 20

a ,deg

C D

.24 -

.16

.O8

CD,0+ C L tan C/C-_,a/

/

- / ,

coo

_-I I I J

0 .4 .8 1.2

C L

(C) _L,s----0°, _T,s = 0°, _C------10°.

Figure 25. Continued.

go

O Experiment

Theory

_--_--.-- With attainable thrustand vortex force

CA0

-.08

.08 -

Cm

.2

0

-.2 O

09-oj

OOJf

C N

1,6 -

.8-

0

-.8 - I-10

C D

.24

.16

.08

I I 00 10 20

a ,deg C L

- CD,0+C L tan C(C--.._,a/

• _

,. CL2 // p/_

I I _ J0 .4 .8 1.2

(d) _L,s ---- 0°, _T,s ---- 10°, _fC = 0°-

Figure 25. Continued.

g?

O Experiment

Theory

_.,_.,__ With attainable thrustand vortex force

.08

CA0

-.08

ob

\O',

Cm

.2-

O

C N

1°6 -

.8-

0

-.8 - I-10

I

S

0 10

a ,deg

.16

C o

.08

.24 .

J 020

CD,0+C L tan C/C.._,al

" o,2,/o:f/

.I I I I0 .4 .8 1.2

C L

(e) 6L,s = 5°, 6T, s = 10°, 6C = 0°.

Figure 25. Continued.

98

O Experiment

Theory

-.-,------ With attainable thrustand vortex force

.08

CA0

-.08

%

o_ \o_,

Cm

.2-

O i

-.2O O

O

C N

1.6

.8

-.8 - | I I-10 0 10 20

(x ,deg

.24 -

.16

C D

.08 -

0

CD,0+ C L tan/c_Lal

/

o"o--/-y-_ I I !0 .4 .8 1.2

C L

(f) _fL,8= 10°, _fT,s = 10°, /fc = 0o.

Figure 25. Concluded.

99

0 Experiment

Theory

,,.-,,-- With attainable thrustand vortex force

coo,r0

C D

C D

C D

08f.04

0

.12

"08 I.04

0

.20 r"

.16

.12

.08 "

.04

CL=.4

C L

!

_!

-_:0

C L

0 | ! I-10 0 10 20

(_C ,deg

--.6

-.8

C L = 1.0

Figure 26. Variation of drag with canard incidence angle for selected lift coefficients for forward swept-wingfighter with canard. _fL,s = 0°; _T,8 = 0°; M = 0.6; R = 2.5 × 106.

100

O Experiment

Theory

--.-,._ With attalnable thrustand vortex force

.O8

CA0

-.08

(_(3D%

\Cm

.2

-.2

,x5,_

f

C N

1.6

.8

0

-.8

.24

JS

/

I0 10

a ,deg

.16

C O

.08

J#

/

_| I 0 t I I I-10 20 0 .4 .8 1.2

C L

(a) M = 0.8.

Figure 27. Theoretical and experimental data for forward swept-wing fighter with canard at transonic Mach

numbers. 5L, s = 0°; ST, s = 0°; 5c -_- 0%

101

0 Experiment

Theory

m.------ With attainable thrustand vortex force

.08.

CA0

-.08

000 000

%

\Cm

.2,

-.2

C N

.8

0

-.8 !

-10

/ /

10

a ,deg

.24 _

.16

C D

.08

I 0 u20 0

o/I

o/

I I I.4 .8 1.2

C L

(b) M = 0.9.

Figure 27. Concluded.

102

O Experiment

Theory

With attainable thrustand vortex force

...... Without thrust or vortex

.2-

.O4

CA0

-.04

Cm

.1

-.1

_x

O

C N

.8

.4 f

f-.4 .I "" I i I

-10 0 10 20

C D

2, c_)___,CD, 0 + C L tan

.16 -

/'

oc0 t _" t i

-.4 0 .4 .8

o ,deg C L

(a) Wing-body configuration; _L,n = 0°; _T,n = 0%

Figure 28. Theoretical and experimental data for arrow-wing supersonic transport. M = 0.99; R = 4.19 x 106.

103

<,./

O Experiment

Theory

._..._..- With attainable thrustand vortex force

...... Without thrust or vortex

.2-

.O4

CA0

-.04

Cm

.1

0

-.1

O0 C

0 °

.8

.4

C N

0

--,4

-10 0 10 20

C D

.24

.16

.O8

CD,0+ C L tan IC_.a/-'_//

I - "P'_" I I-.4 0 .4 .8

a ,deg CL

(b) Complete configuration; 5L, n ---- 0°; ST, n = 0°; 6 H = 0%

Figure 28. Continued.

104

O Experiment

Theory

_.--._.-- With attainable thrustand vortex force

...... Without thrust or vortex

.O4

CA0

-.04

Cm

-.1

.2.

Ooo

O o

.8

.4

C N

o

-.4 l , I I

-10 0 10 20

a ,deg

C D

.24

.16

.O8

(c) Complete configuration; _L,n -_ 0°; 5T,n

Figure 28. Continued.

¢CD,0 + CL tan (c_La)-_/

-.4 0 .4 .8

C L

= 0°; _H = -5°.

105

O Experiment

Theory

,. With attainable thrustand vortex force

...... Without thrust or vortex

.04

CA0

-.04 -

Cm

.2

.1

0

-.1

O0 o

0 o

0 0 ./

oY

.8

.4

C N

0

--,4

-10 0 10 20

a ,deg

C D

.24

.16

.O8

0

Co0tCL,an /

I C

-.4 0 .4 .8

C L

(d) Complete configuration; _L,n = 0°; 6T,n = 0°; 6H = --10°.

Figure 28. Continued.

106

<,j O Experiment

Theory

.__.._ With attainable thrustand vortex force

...... Without thrust or vortex

.3-

.04

CA0

-.04

i .2

.1

0

Ooo

0 °

0 o

0 0 II

.8

.4

C N

_.°-10 0 10 20

C o

.24

.16

.O8

0

"CD,0 + C L tan {' cL ,_._,//¢,/IM

. \Ck'aJll__ I

co .

-.4 0 .4 .8

a ,deg C L

(e) Complete configuration; 5L,n = 0°; ST, n = 0°; 5H = --15 °.

Figure 28. Continued.

107

_J O Experiment

Theory

• With attainable thrustand vortex force

...... Without thrust or vortex

.04

CA0

-.04

O 0o>/

.8

.4

C N

0

-.4

S

-I l-10 0 10

a ,deg

C D

.24

.16

.O8

| 02O

CL2 _ /

I 31 "'_- i J-.4 0 .4 .8

C L

(f) Complete configuration; 6L, n = 0°; 6T,n = 0°; 6H = 5°.

Figure 28. Continued.

108

.08 -

0 Experiment

Theory

.._...__ With attainable thrustand vortex force

...... Without thrust or vortex

CA

.04

-.04

0 n'_,_" Cm

0 o

.I

-.I

oo.0 ¢3si

C N

.8 .24

.4

0

L/.16

CD

.08

-.4 _1 I I 0-10 0 10 20

a ,deg C L

" tan [ cL \ /CD, O+ CL tC--'_,e)-' _ ,

, I-_'7, ,-.4 0 .4 .8

(g) Complete configuration; _L,n = 13°/34°/35°/35°/19°/29°; _T,s = 30°; _H = 0°.

Figure 28. Continued.

109

.08

.04

CA0

-.04

Cm

O Experiment

Theory

With attainable thrustand vortex force

...... Without thrust or vortex

.1-

0

-.1

OO

[.__°OOooooO°

C N

.8

.4Is7

C D

.24 -

CD, 0

.16 -

.08

0

CL 2 / __CD, O + "rrA"-"-R

I t I-.4 | I I-10 0 10 20 -.4 0 .4 .8

a ,deg CL

(h) Complete configuration; 5L,n = 13°/34°/35°/35°/19°/29°; 5T,s = 30°; 5H =--5°-

Figure 28. Continued.

110

.O8

.O4

CA0

-.04

O Experiment

Theory

._.____. With attainable thrustand vortex force

...... Without thrust or vortex

.1-

Cm

-.1

O °

Ooooooo. /

C N

.8 - .24

.4

LI

.16

C D

.08

-.4 I I 0-10 0 10 20

a ,deg C L

_ - CL

CD,0+ CL tanIc'_,al-_t/( _

-,., CL 2 /,(_ /

- _"D,O + ,_"_-R' --_//

-.4 0 .4 .8

(i) Complete configuration; _L,n = 13°/34°/35°/35°/19°/290; _T,s = 30°; _H = -10%

Figure 28. Concluded.

111

L/O Experiment

Theory

With attainable thrustand vortex force

fCD .04

0

.12 -

.08 -C D

.04

0

.20 -

.16

.12CD

.08 "

.0"4

0 I-20

.___.__ 5L'n = 0°; ST,s = 0°

5L, n = 13°/34°/35°/35°/19°/29°; ST,s = 30°

o

(3L,n = 0°; (3T,s = 0°

(3L,n = 13°/34°/35°/35°/19°/29°; (3T,s = 30°

(3L,n : 0°; (3T,s : 0°

(3L,n = 13°/34°/35°/35°/19°/29°; ST,s

= 30°

I I-10 0 10

(3H, deg

CL=.2

CL =.4

C L =.6

Figure 29. Variation of drag with horizontal-tail incidence angle for arrow-wing supersonic transport.M=0.09; R=4.19×106 .

112

0 Experiment

TheOry

With attainable thrust_'--'"_ and vortex iorce

5L, n = 0°; 5T,s = 0o= 13°134°i35°135°/19°/29°; _T,s = 30°

Cm

Cm

CL=.2

= 30°

CL =.4

= 30°

CL--,6

-'_ 100

-.2 -10

- 20 5H , deg

w

Figure 30. Variation of pitching moment with horizontal-tail incidence angle for arrow-wing supersonic

transport. M = 0.09; R - 4.19 × t06"

113

a)t-

a)

E.I

o_xLU

E

,_ t.3 ,_ oo oJ

o o o o T-

i" \ \ \

t I I

Eo,1

o o _-

,x'N "_ ". •

I"

i

t ' .t,l"tX./', l,.1,,I',I"I Io ooJ ,r-

l:

v-"¢,o

c

J

_ o

\ ,-

o,r-

l

0

0

oI

o

"I:Io

o

o¢,4)

<_

_O

"0 o

_×

II

N.N

.,_

N?

114

I" o o _ "_.

_q:_

_a

E ," o ° q • o _

,,- "0II 0 "

oo

II

f-

li

. ', \?t41I Io o

o')

Io

o

o

o

I

"o

0c,O

.o

d _

_"_ X

o _ II

._

115

S$

(_T,n ,deg

1.0

.8

.6

.4

.2

0

20

15

10

5

0

10

5

0

-5

-10

m

1

I, I I I I0 5 10 15 20

_L,n ,deg

Figure 33. Theoretical maximum suction parameter for Cm = 0, required trailing-edge-flap deflection, andrequired canard incidence angle for 44°-swept trapezoidal-wing fighter with canard as a function of leading-edge-flap deflection. M = 0.4; R = 1.9 x 106; CL = 0.6. Arrows indicate maximum performance.

116

Ss

1.0

.8

.6

.4

.2

0

20

15

10

5

0

Y

15

10

_T,n ,deg 5

0

10-

gc ,deg0

-5

-10v

I I I I J-,12 -.08 -.04 0 .04 .08

Cm

Figure 34. Theoretical maximum suction parameter, required trailing-edge-flap deflection, and required canardincidence angle for 44°-swept trapezoidal-wing fighter with canard as a function of moment restraint.

M = 0.4; R -- 1.9 x 106; CL = 0.6. Arrows indicate maximum performance.

117

I I I

0 o 0cd T-

r-

oN

0

"_r2

_x

II

I °o _

k

118

.-- _ o

i.J

t I I T _=.o

o

..- -- '--

E E ° _ o ' "_

01

Io

E_

"o

e-

!

o

o

I

o,--_

.,-_ °_

E:)

,=[_ _X

_?",,=,1

119

S$

1.0

.8

.6

.4

.2

¥J

u

20-

_T,n ,deg

15

10

5

0

10-

_H ,deg

5

0

-5

-10

IL -- = .i

" 0 5 10 15 20

_L,n ,deg

m suction arameter for Cm = 0, required trailing-edge-flaP deflection, and_,re 37 Theoretical maximu P • • "_ , - "-- _.+er with horizontal tail as a function

required horizontal incidence angle for 44 lPo v ,P6. _, - (_6 Arrows indicate maximum performance.of leading-edge flap deflection. M = u.a; zt = ...... , v, .....

120

7

/II

I , i I i

u'}CO

o,.-..

LC}0

0

I

0

L_

I

OC_J

I

L_

I

QC_

I

E

I..

E

.w..,

o_oN

!

_×

o li

0_

u

122

Report Documentation PageN ational Aeronaul_CS and

SPace AdrnlnlslraI_on

l. ReportNAsANO.TP_2961 12. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

Validation of a Computer Code for Analysis of Subsonic Aero-dynamic Performance of Wings With Flaps in Combination Witha Canard or Horizontal Tail and an Application to Optimization

7. Author(s)

Harry W. Carlson, Christine M. Darden, and Michael J. Mann

5. Report Date

January 1990

6. Performing Organization Code

8. Performing Organization Report No.

L-16611

10. Work Unit No.

505-68-91-02

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Paper

[14. Sponsoring Agency Code

i

9. Performing Organization Name and Address

NASA Langley Research CenterHampton, VA 23665-5225

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, DC 20546-0001

15. Supplementary Notes

Harry W. Carlson: PRC Kentron, Inc., Aerospace Technologies Division, Hampton, Virginia.Christine M. Darden and Michael J. Mann: Langley Research Center, Hampton, Virginia.

16. Abstract

Extensive correlations of computer-code results with experimental data are employed to illustratethe use of a linearized-theory, attached-flow method for the estimation and optimization of thelongitudinal aerodynamic performance of wing-canard and wing-horizontal-tail configurationsthat may employ simple hinged-flap systems. Use of an attached-flow method is based on thepremise that high levels of aerodynamic efficiency require a flow that is as nearly attached ascircumstances permit. The results of this study indicate that linearized-theory, attached-flow,

computer-code methods (modified to include estimated attainable leading-edge thrust and anapproximate representation of vortex forces) provide a rational basis for the estimation andoptimization of aerodynamic performance at subsonic speeds below the drag-rise Mach number.Generally, good prediction of aerodynamic performance, as measured by the suction parameter,can be expected for near-optimum combinations of canard or horizontal-tail incidence and leading-and trailing-edge-flap deflections at a given lift coefficient (conditions which tend to produce apredominantly attached flow).

17. Key Words (Suggested by Authors(s))

AerodynamicsNumerical methods

Flap systemsCanardsHorizontal tails

18. Distribution Statement

Unclassified--Unlimited

Subject Category 0219. Security Classif. (of this report)

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NASA-Langley, 1990