Of Stall Characteristics

Home , Stall (fluid dynamics), Washout (aeronautics), Wing twist

NASACONTRACTOR REPORT

A DESIGNSUMMARY OF STALLCHARACTERISTICS OF STRAIGHT WING AIRCRAFT

by M. A. McVeigb md E. Kisielowski

Prepared by DYNASCIENCESCORPORATION SCIENTIFICSYSTEMS DIVISION Blue Bell, Pa. for Langley Research Center

NATIONALAERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. JUNE 1971 -__- TECH LIBRARY KAFB, NM

"" ~~ ~ ~~___ ~___. "" . ~ -~ ~ 00607b3 1. Report No. 2. GovernmentAccession No. 3. Recipient. rormluy I.u. NASA CR-1646 - -~ ~~ ~~~ -~ 4. Title andsubtitle ~ I 5. ReportDate A DESIGN SUMMARY OF STALL CHARAC!iTBISTICS OF STRAIGHT WING AIRCRAFT June lg7' 6. Performing Organization Code

~ ~~ .~ ~ .. ~ . ~-- -~ 7. Author(s) 8. Performing Organization Report No. M. A. McVeigh and E. Kisielowski DCR-705

~ ..~"" ~ ". .. . 10. Work Unit No. 9. Performing Organization Name and Address 126-13-10-06-23 DynasciencesCorporation I 11. Contract or Grant No. Scientific SystemsDivision I BlueBell, Pennsylvania NASl-8389 13. Type of Reportand Period Covered ~ ~~ 12. SponsoringAgency Name and Address Contractor Report NATIOW AERONAUTICS AND SPACEADMINISTRATION 14. SponsoringAgency Code WASHINGTON, D. C. 20546

"" " - ~______~ .. .- - . .. ~~ .~ 1-I 15. SupplementaryNotes

""___ ._. ." . - ~. 16. Abstract

A method of wing design using lifting line theory described in NACA Reports 865 and 1090 has beencomputerized and used tostudy the parameters which affect wing stall characteristics. The results of thestudy and the computerprogramaredescribed. The effects of airfoilsection variations,Reynolds number, aspect ratio, wing twist ad taper ratio are presented in design chart form.

- _i .- ~. - - ~ - 17. KeyWords (Suggested by Author(s) ) 18. Distribution Statement Subsonic Wing Design Unclassified - Unlimited Strip Theory Computer Program

~.-. . 19. Security Classif. (of this report) Unclassified I . Unclassified 226 ". " ~-

For sale by the NationalTechnical Information Service, Springfield, Virginia 22151 -. - SUMMARY Presented in this report is a comprehensivereview of the existing tech.nica1 literature and a design summary of stall ch.aracteristics applicable to light straigh.t wing aircraft. These characteristics are obtained with th.e aid of a digital computerprogram which. utilizes the most up to date analytical methodsemploying lifting line theoryand the available experimental test datafor wing sectioncharacteristics. The computer results are presented in th.e formof stall ch.arts suitable for preliminarydesign purposes. Based on th.e extensiveparametric studycovering a total of 331 different aircraft configurations, it canbe concluded that in modern airplane design satisfactory stalling characteristics can be readily built in with no apprecia- bleloss in airplane performance or handling qualities. A proper combination ofwing taper, twist andtype of airfoil sections with. minorpost-design fixes, if required, can in most cases providesatisfactory wing stall characteristics.

iii I - FOREWORD

This reportpresents a design summary of stallch.aracteristics ofstraigh.t wing aircraft.

Th.e workwas performed by th.e Scientific SystemsDivision (SSD) of the DynasciencesCorDoration, Blue Bell,Pennsylvania, for the NationalAeronautics and Snace Administration (NASA), LangleyResearch Center, Hampton, Virginia,under contract number NAS 1-8389during the periodfrom July 1968 through SeDtember 1969. Th.e NASA technicalrepresentatives were Mr. Robert T. Taylor and Mr. William J. Alford, Jr. The contributions of the NASA technicalpersonnel to this work are gratefully acknowledged. Acknowledgement is alsoextended to NASA computerpersonnel, especially Mrs. Belinda Adams, for their supportin this program.

Messrs. James C. Sivells and :Hartley A. Soul; were mecia1 technicalconsultants on this Drojectand Mr. Ron Anton was computerconsultant.

V l- CONTENTS Page SUMMARY...... iii

FOREWORD ...... V LIST OF ILLUSTRATIONS...... viii LIST OFTABLES...... xi LISTOF SYMBOLS...... xiii SECTION 1 INTRODUCTION...... 1 SECTION 2 BASICCONSIDERATIONS OF AIRPLANE STAUING...... 4 SECTION 3 THEORETICAL ANALYSI S...... 21 SECTION 4 COMPUTER PROGRAM...... 42 SECTION 5 PARAMETRIC INVESTIGATION...... 75 131 SECTION 6 SCALE MODEL WIND TUNNEL TESTING...... SECTION 7 DESIGN PROCEDURES...... 136 SECTION 8 CONCLUSIONS AND RECOMMENDATIONS...... 142 SECTION 9 REFERENCES...... 144 APPENDIXINTERNALA LISTING OF THE COMPUTER PROGRAM...... 149

vii

II I ILLUSTRATIONS

Figure Page

1 RepresentativeLift Curve(Reproduced from Reference 13) ...... 10 2 Th.e Low-Speed StallingCharacteristics ofAirfoil Sections Correlated With. Reynolds Number and theUpper-Surface Ordinates of theAirfoil Sections at the 0.0125-Chord Station...... 12 Wing Leading Edge Mofifications for Controlling Wing Stall ...... 20 Definition ofParameters for Transformation of Wing-Body Combinat ion...... 26 Typical Load Distributions for Obtaining Factors forAltering Two-Dimensional Data...... 37 Illustration of Meth.od for Correcting Two- DimensionalSection Data ...... 39 Extrapolations of Lift CurveSlopes at Low Reynolds Number ...... 51 Variation of SectionLift-Curve Slope with Thick- ness-ChordRatio at ConstantReynolds Number NACA 644 Sections ...... 54 9 Corrected LiftCurves for NACA 64-421 Airfoil at Low Reynolds Numbers ...... 55 10 Methodof Tabulation of Section Ch.aracteristics . . 57 11 Sch.ematic Representation of SectionData Storage in the Computer ...... 59 12 Nomenclature for DevelopingInterpolation Formulae 61 13 ComputerProgram Block Diagram ...... 62 1.4 SchematicRepresentation of the Computer Input Cards ...... 63 15 Experimentaland Calculated Characteristics for a Wing of AspectRatio 8.04 ...... 68

viii li- -

Figure Page 16 Experimental and Calculated Characteristics for a Wing of Aspect Ratio10.05 ...... 70 17 Experimental and Calculated Characteristics for a Wingof Aspect Ratio 12.06 ...... 72 18 Experimental and Calculated Characteristics for Wingwith. 60% Flap; Aspect Ratio 9.02; Taper Ratio 0.4; Washout 2O ...... 74 19 Typical Lift Distributions Along Wing Span..... 81

20 Variation of Clmax with Reynolds Number and Thickness-Chord Ratio ...... 83

21 Variation of CLmax with Reynolds Number and Taper Ratio ...... 86 22 Effect of Aspect Ratio on Stall Margin Distribution ...... 88 23 Effect of Aspect Ratio on Wing Stall Pattern....91

24 Effect of Aspect Ratio and Taper Ratio'Lmax. on . 94 25 Increment of Induced-Drag Coefficient Due to Washout, 230 Series Airfoil Section...... 98 26 Effect of Root Thickness-Chord Ratio on Stall Margin Distribution ...... 101 27 Effect of Root Thickness-Chord Ratio on Wing Stall Boundaries ...... 104 28 Effect of Root Th,ickness-Chord RatioCLmax on . , . 107 29 Effect of Tip Thickness-Chord Ratio on Stall Margin Distribution ...... 111

30 Effect of Tip Thickness-Chord Ratio on'Lmax ... 114 31 Effect of Reynolds Number on Stall Margin Distribution ...... 117 32 Effect of Reynolds Number on Wing Stall Pattern ...... 120

ix Figure Page 33Effect of Reynolds Number on Chax...... 123 34 Effect of Wing Camber on Stall Margin Distribution...... 127 35 Effect ofFuselage ...... 128 36 Effectof the Spanofa 20% Chord SplitFlap on the Wing Stalling Characteristics...... 130 37 Variationof WingMaximum LiftCoefficient with. Stall Speed ...... 138

X TABLES

Tables Page I Airfoil Section Data Available for Use with the Computer Program ...... 56 I1 Typical Computer Output...... 65 I11 Summary of Configurations Studied ...... 76

SYMBOLS

A non-dimensionalfuselage semil5eigh.t

A' fuselage semih.eight, f t .

Ai wing aspect ratio,

An coefficientsin trigonometric series a non-dimensionalaverage distance of point on wingfrom fuselage cross-section focI-1 al averagedistance of point onwing from fuselage cross-sectionfocii, ft. sectionlift-curve slope, per degree non-dimensionalfuselage semiwidth

fuselage semiwidth, ft. wingspan, ft. flapspan, ft.

total wing drag coefficient,- D qs

wing profile drag coefficient, qs

Di wing induced drag coefficient,-Di qs

wing lift coefficient, -L CL qs M wing pitching moment coefficient,

total section drag coefficient section induced drag coefficient section profile drag coefficient section lift coefficient, -I qc design lift coefficient two-dimensional, uncorrected value of lift coefficient maximum section lift coefficient maximum two-dimensional section lift coefficient section lift coefficient at end of flap section lift coefficient forth.at part of lift distribution involving no discontinuity in angle of attack section lift coefficient for partof c12 lift distribution due to discontinuity in angle of attack section lift-curve slope, per degree section lift coefficient with deflected flaps, calculated assuming linear lift curves section pitching moment coefficient section pitching moment coefficient about quarter-chord point

C wing chord at any spanwise station, ft.

C' wing mean aerodynamic chord, ft.

CR wing root chord, ft.

CT wing tip chord, ft. D total wing drag, lbs.

DO wing profile drag,lbs. Di wing induced drag, lbs. E edge velocity factor

e non-dimensional eccentricity of fuselage cross-section

xiv el eccentricity of fuselage cross-section, ft. F factor usedin altering two-dimensional lift curves Cf max FF y = y* Of (cf rnaxIo at taken at th.e flap side ofy*

Gmk coefficient of transposeof matrix Ghk

G&k coefficient of a matrix H non-dimensional wing h.eigh.t above fuselage centerline K section camberlevel measured in terms of section designlift coefficient coefficient of the inverse of matrixGmk

L wing lift, lbs. I section lift, lbs. M wing pitching moment,lbs. ft. dynamic pressure, lbs/ft.2

Re Reynolds number RB Reynolds number basedon mean aerodynamic chord

S gross wing area, sq. ft. T thickness factor

t wing section maximum thickness, ft. tr maximum wing root thickness, ft.

X coordinate parallel to fuselage centerline, positive forward, ft.

Y non-dimensional spanwise distance

YO non-dimensional coordinate of wing-fuselage junction - Y ,Y spanwise coordinate, ft.

xv A DESIGN SUMMARY OFSTALL CHARACTERISTICS OF STRAIGJTC WING AIRCRAFT By M. A. McVeigh, E. Kisielowski DYNASCIENCESCORPORATION

SECTION I

INTRODUCTION

Federal and military aviation regulations require th.at all aircraft possess stalling characteristics which.comply with the establishedspecifications. The finalevaluation of an airplane is made in flight tests in which. all factors influencing its stallingcharacteristics are integrated. At th.is stage, however, it may be too late or very expensive to make any alterations necessary to meet theestablished requirements.

It is highly desirable therefore, to predict th.e maximum lift and stalling characteristics ofan aircraft at an earlydesign stageand, on the basis of the predicted characteristics, to incorporate such modifications in the design as may givepromise of satisfyingthe FAA ormilitary stall requirements. With this end in mind,extensive research effort directed toward a compre- hensiveunderstanding of theaerodynamics of unswept wings has beenaccomplished in prioryears. This research effort was directed along lines of theoretical work,wind tunnelexperiments and flight tests. On the theoretical front substantial progress has been made. Prior to the World War I1 anadaptation of the lifting line theory in which the wing airfoil sections were assumed to possess a linear variation of lift with angle-of-attack was the only available method for predicting the maximum lift and stalling characteristics ofunswept wings. In theregion of maximum lift, however, the sectionlift curves are usuallyquite nonlinear. Consequently, predictions based on the method were quite unreliable in the maximum lift range.Shortly after the close of World War I1 Sivells (References 1 and 2) presented amethod for calculating unswept wing characteristics by lifting line theory utilizing nonlinear airfoil section lift data. The values of maximum lift and the point of initial stall predicted by thisapproach agree well with experimentalobservations, and the meth.od is regardedas a very effectivedesign tool. Other majortheoretical contributions were made by Theodorsen(Reference 3) andby Multhopp (Reference 4). Thesereferences provide valuable methods for developing improved airfoil sections and fordetermining wing-fuselage interference effects. Wind tunnelexperiments have provided extensive information in suchimportant areas as: two-dimensionalairfoil section characteristics (References 5 and 6); theaerodynamic characteristics ofcomplete wings at highReynolds number (Reference 7); the characteristics of a large number ofcomplete airplanes (Reference 8); andcompressibility effects on maximum lift (Ref- erence 9). Certainportions of the wind tunnel test datahave directdesign applications, oth.er portions provide a basis on which to evaluate the applicability of new th.eories,and still other portions provide information on which. to base empirical design guidance. The flight test results provide a comprehensiveevaluation ofthe integrated effect of all the factors that contribute to theairplane flying qualities. Measurementof the flight ch.aracteristics of many airplanes of differenttypes has permitted a definition of those characteristics which provide for good flying qualities.Additionally, the flight test results provide a reference base for th.e correlation of th.eoretica1 prediction and windtunnel experimental results. Much of the research. effort referenced above was accomplished andthe results were published in numerous isolated reports, during and shortlyafter the endof World War 11. Immediately after this period, interest in theproblems of straight wing aircraft was diverted to the pressing problems ofsupersonic mili- taryaircraft incorporating sweptwing configurations. In general, unswept (straight) wingtechnology is notapplicable to swept wingconfigurations. Consequently, the wealth of information pertaining to the maximum lift and stallingof unswept wing air- crafthas not previously been coordinated andhence h.as not re- ceivedadequate attention. Nevertheless, in the generalaviation field, interest st ill centers on ,subsonic aircraft incorporating unsweptwing configurations. A needtherefore exists for the application of available unsweptwing stall technology to th.e designof such aircraft.

This report presents a comprehensivebibliography of prior work in th.e field,and, insofar as practicable, presents the most pertinentinformation in a formsuitable for design application. In the preparation of this report a comprehensivereview h.as been conductedof all pertinent literature alth.ough.no attempt is made tosynopsize each. of th.e reportsunder one section. Effort h.as been made, however, toincorporate the information gained from thisextensive review into design guidance procedures, recommendations,cautions, etc. Basedon this comprehensivereview of pertinent literature a math.ematica1model was formulated and programmed forthe CDC 6600 digital computer. The computer which. employs available nonlinear wing section ch.aracteristics can be utilized to predict maximum lift and th.e spanwiseload distribution of a wing with. or with.out fuselage.

2 As a result of this study it canbe concluded that design for good airplane stalling characteristics is still part art and I part science. It appearsobvious, however, that application of i theavailable knowledge in earlydesign stage will greatly improve the probability of obtaining satisfactory stalling characteristics or, at least, may yield an airplanedesign wh.ose characteristics can be made acceptable as the result ofminor modifications during early flight test phase.

3 SECTION 2

BASICCONSIDERATIONS OF AIRPLANE STALLING

2.1 MINI" REQUIREMENTSFOR ACCEPTABLE STALL CHARACTERISTICS

The MINIMUM REGULATORY requirements for the stalling behavior of small aircraft are stated in theFederal Aviation Regulations, Part 23 "AirworthinessStandards: Normal, Utility andAcrobatic CategoryAirp1.anes'' (Reference 10). With. thelegalistic qualif- icationsdeleted, the regulations require that for specified power, gearand flap settings acceptable stalling characteristics bedemonstrated for two f1igh.tmaneuvers, one in straight flight withthe wings level andone in a coordinated turn. Inboth cases theprimary control manipulation is a steady progressive upward movement of the elevator until th.e airplane is stalled or the elevatorreaches its stop.

The demonstrationprocedures and acceptable stalling characteristics are defined as follows:

Forthe straight-flight maneuver, th.e airplane is trimmed at a speed fifty percent greater than the stalling speed before theelevator movement is started. With theusual three control system, it mustbe possibleto produce and correct roll by unreversed useof th.e rolling control and toproduce and correct yaw byunreversed use of th.e directional control up to the time when stall becomes apparent, i.e. when anuncontrollable downward pitchingmotion develops or until th.e elevatorreach.es its stop. Forthe two-control system airplanes, rolling motions must beproduced and corrected by unreversed lateral control with,out excessive yaw. Duringrecovery from the stall. it mustbe ossi- ble to prevent th.e occurrence ofmore than 15 degrees Of rofl Or yaw by normal use of th.e controls.

Forthe turning-flight maneuver, the airplane is placedin a steady,level, coordinated turn with. a 30-degreebank angle before thespeed is reduced. When stalloccurs, it mustbe possibleto regain normal levelflight with.out excessive loss of altitude or uncontrollable rolling or spinning tendencies.

Forboth maneuvers as stalls are approached, there must be a clear and distinct stall warningwhich begins at a speedabout 5 to 10 miles per hour higher than th.e stalling speed and continues untilthe stall is reached.For airplanes that cannot be stalled forthe two maneuversspecified, it mustbe shown thatif they canbe .stalled in steep climbs, then recovery shall not require excessivespeeds and/or accelerations. Multi-engine aircraft haveadditional single engine-out requirements pertaining to stalls in turning flight.

1111.1 111 I .. . I!" -

In summary, theregulations require that for gentle maneuvers the aircraft shallhave some stall-approachwarning, effective lateral control up to the stall, and sufficiently effective lateral control after the stall to restrict yawingand rolling dis- turbancesto small angles.Furthermore, recovery from the stall shallnot involve excessive altitude loss, speedincrease, or structural loading. 2.2 DESIRABLE STALL CHARACTERISTICS

For more safety, it wouldbe better if there were nouncon- trollablemotions during a stall and recovery. A 15-degreechange inthe angle of bank or heading could have serious consequences if it occurredclose to theground and off the end of the runway following a misjudgedlanding and thestart of the go-around climb. Since it is generallyconceded that there is nosuch. thing as a "good" stall (Reference 111, thesafest low-speed characteristics are those that do notchange noticeably to th.e limit of the up-elevatortravel. These are, of course,the characteristics sought by "stall-proofing"an airplane, such that the angle of attackfor maximum lift cannever be attained.This is noteasy to accomplishfor reasons which will be discussed later.

Forairplanes which can be stalled (i.e. aircraft angle of attack exceeds that for maximum lift), there is no unanimityof opinion on the least desirable type ofmotion that may result. Th.e consensus,however, is thatprobably th.e leastundesirable stall characteristic wouldbe for the nose of the airplane to drop ab- ruptly by a small butdistinguish.able amount beforethe occurrence ofexcessive rolling and yawingmotions requiring the use of either lateralordirectional controls. Also, under such. conditions,if the elevator control is eased forwardthe airplane should promptly returnto unstalled flight. Slight skidding or yawingmotions shouldhave no appreciable effect on these characteristics. The precedingare the more or less limitingconditions. Any- thingbetween the case of mild nosedropping and the stalling characteristics defined by the Federal Aviation Regulations (FAR) is a matter of th.e degreeof violence of the rolling andyawing motionsthat develop at th.e stall. It shouldbe noted that aside from the specified angular deviations in yaw and roll, th.e wording of theregulations is qualitative andopen to individual inter- pretation. 2.3 STALL-PROOFING Stall-proofing aircraft by limiting the up-elevator travel was suggested at least thirty-fiveyears agoand is a subject onwhich much research time and effort has since been expended. There are two major reasons why this solution has not been more widelyapplied.

5 The first, but not necessarily the more importantof these reasons, is the opinion that a stall-proof airplane may notbe completelyacceptable nor most saleable to the specific segment ofthe general public most interestedin personal flying. This group is considered to be composed largely of more adventurous persons(e.g. the buyers of sports cars, the water skiers) who want more thantransportation from an airplane. Therefore, the amount of effort that might be put into designing an airplane to be stall-proof depends on th.e purposeand th.e market for wh.lch. th.e airplane is intended. It is possibleto stall-proof an airplane forcertain flight conditions and notfor others. Fortunately thelanding approach. condition is oneof th.e simplest and one for which some effort may be warranted. The otherreason wh.y most aircraft are not completely stall- proofed is thetechnical difficulty of so doing. The elevator angle for a givenangle of attack varies with. a large number of interrelatedaircraft dimensional andmass parameters. Among the more importantnot under th.e control of th.e designer are the centerof gravity location ona given flight, the throttle, flap and trim settings; and theexterior surface condition, particular- lythe wingand horizontaltail surfaces. Added tothese are all those other parameters among which the designer normally has to compromise. The basiclongitudinal balance and, hence, the eleva- torangle for stall, depends on th.e relativeproportions of the wingand the horizontal tail surfaces, th.e taillength, vertical location ofthe tail, the orientation of the tail relative to the propellerslipstream, and theproximity of the tail to the ground duringtakeoff and landing. 2.4 STALL WARNING It is less difficult to obtain stall warning in the airplane as compared tostall proofing. Although it may notalways be possibleto provide for adequate stall warning in the design stage, it can in many cases be incorporated after aircraft construction. There are anumber of airplane characteristics which. can serve as ameans ofproviding warning to th.e pilot of h.is approach. tothe stall. Some of th.ese characteristics are largeincreases in th.e elevator force and in the control stick travel near th.e stalling speed, initially controllable rolling andpitch.ing motions, and vibrationsor ''buffeting" of th.e airplane and th.e control stick. The variation of control forces which are functions of elevator hinge moments are toodependent on the friction and elasticity in thecontrol system between th.e elevator and stick to provide th.e consistencyneeded for stall warning. On th.e oth.er h.and anappre- ciableincrease in the elevator control travel as stall is approached,airframe buffeting and initially controllable angular motions h,ave eachbeen found to give acceptable stall warning. The difficulty is to provide for the start of th.ese warningsin therequired speed range and to assure that the airplane angular

6 motionsdo not become toosevere in amplitudebefore the stallingspeed is reached. Althoughinherent stall-warnings are tobe preferred, stall warnings can be synthesized by detecting consistent changes in the airflow about the airplane and using th.e information to activate a mechanical or electronic device to alert the pilot of hisapproach to stall. The earliest formof a synthesizedstall warning was probablythe stall red-line on theairspeed indicator. The stall airspeed,however, is oneof thepoorer indicators of impending stall because it depends on aircraft weight andconse- quentlyvaries with passenger load and fuel consumption.Varia- bles wh.ich are directly related to the stall suchas the airplane angleof attack and surfacepressure differences give much more reliableindications ofimpending stallthan does airspeed.

Synthetic stall-warning devices can be designed to alert the pilot of his approach. to th.e stall th.rough. h.is sense of sigh.t, hearing or feel. Neith.er of th.e first twoh.ave beenfound very satisfactory. In th.e case of sigh.t, th.e pilot'sattention during takeoff and landing when unintentional stalling is most probable is requiredoutside of thecockpit. In the case of hearing, there is chance forconfusion as horns have long been used as a reminderto lower th.e landinggear. Th.e most satisfactorystall warningdevice would therefore be the one that would alert the pilot of his approach. tothe stall through the sense of feel. A description of the most common stall warningdevices and their principle of operation is presentedin Reference 12.

2.5 FACTORS~ AFFECTING WING STALL ~~ Th.e FederalAviation Regulations define the stall characteristics in terms of movement of the elevator andof the effective- nessof the aileron and ruddercontrols. Th.e wing,h.owever, is theprimary element of theairplane affecting th.e stalling characteristics. Its sizerelative to weigh.t sets th.e stalling speed,and its proportionsdetermine th.e location of th.e stall, its rate of propagation,and the violence of theresulting motions when thestalling speed is reached.

In thedesign of airplanes it is normal to start with th.e wingand select its dimensions bya series ofcompromises so as toassure good performance,acceptable stalling characteristics, andlow structural weigh.t . While not a tech.nica1factor a pleas- ingappearance must beconsidered because of th.e effect of style on themarketability of the design. The airfoilsection is fundamental to wing designand should be considered early in th.e preliminarystages. Th.e aerodynamicdata for th.e selected airfoil sections are then used in analysesto determine the spanloading of the th.ree dimensionalwing. It is on th.e basis ofcomputed span-load distributions that a decision is made on thefinal wing proportions.Sections 4 and 5 of th.is report

7 present a summary ofthe theory and a description of the computer program respectively for determining the wing span load distributions required for preliminary design purposes. 2.6 AIRFOIL SECTIONS The selection of the optimum airfoil sections for a wing is generally made after consideration is givento the following: a) Sectionprofile drag coefficient should be as low as possible-over a rangeof lift coefficients near the required cruise lift coefficient. b)Section maximum liftcoefficient should be as large as possible since this has a direct bearing on the maximum valueof the overall wing lift coefficient which in turn governs the stalling speed.

c) The chosensections should have sufficient depth to contain the wing structural members and other items such as landinggear.

d)Stalling characteristics of sections near the wing tip shouldbe gradual so as to avoid the possibility ofsharp wing drop. e) The section critical Mach number shouldbe as high as possibleto avoid transonic drag rise, if a highspeed aircraft is being considered.

All of theserequirements cannot be satisfied by anyone airfoilsection and some compromisemust be made. Forexample, theneed for sufficient structural depth, e.g. large thickness- chord ratios, conflicts with the requirement for high values of maximum liftcoefficient. Again, a sectionchosen for its high value of maximum lift coefficient mighthave undesirably sharp stalling characteristics.

While section maximum lift coefficient is of particular importance in regard to wing stalling characteristics, the section having the greatest value of maximum lift mightbe sensitive to small dimensionaldeviations and hence might not realize its ideal perfo.rmance. Wing stall characteristics can also be affected by air turbulence or gustiness. The sideslipping andyawing motions produced by gustiness can induce flow breakdown for certain wing sections thus resulting in large changes in wing lift. Much work has been done to correlate flow patterns at the stall withthe geometric properties of wing sectionsand the shape ofthe lift curve. There are threerepresentative types of

8 I

airfoil section stall generallyconsidered in thetechnical literature,e.g. Reference 13. Thesetypes are: a) Type 1 - Trailing Edge Stall b) Type 2 - Leading Edge Stall c) Type3 - ThinAirfoil Stall The lift curves for the three types (reproduced fromRef- erence 13) are compared in Figure 1 and a discussionof each type of stall is presentedbelow. 2.6.1Type 1 - Trailing Edge Stall The peakof the lift curve for this type of stall is charac- teristically rotlndedwith a maximum value of lift coefficient ofapproximately 1.5. Th.e loss of lift after the stall is gradualwhich is considered to be the least undesirable type of stall. The flowfor this type of stall is characterized by a progressivethickening of theturbulent boundary layer on the uppersurface of the airfoil as the angle of attack is increased. This is followed by aneventual flow separation which. starts at the trailing edgeand gradually moves forward as the airfoil angleof attack is increasedfrom about 100. Maximum lift is obtained when thepoint ofseparation reaches about the 50 per- centchord station. Beyond maximum liftthe forward progression of theseparation point continues at about the same rate as prior tostall. The trailing-edgetype of stall is generallyassociated withwings approximately 15% thick or greater. 2.6.2 Type 2 - Leading Edge Stall Airfoilswith the leading-edge type of stall usually have a sligh.tly greater maximum lift th.anthose with. a trailing edge stall. At thestall, however, th.ere is a large suddendrop in lift associated with an abruptseparation of theflow from theupper surface near its leadingedge. The separation is attributed to the behavior of theupper surface boundary layer. At an angleof attack well below that for maximum lift th.e boundarylayer, which is laminarat the time, separates from th.e uppersurface quite close to th.e nose, becomes turbulentand reattachesto the surface. The localizedregion ofseparated flow is referredto as a "laminarseparation bubble1', Up to the angle at which thebubble forms th.e boundarylayer behaves the same asfor airfoils having trailing-edge separation. The difference at higherangles is due primarily to th.e noseradius. As theangle of attack is furtherincreased, the laminar separation point moves forwardwhere the local curvature is greater. At stall the main flowcannot expand rapidly enough forreattachment and a suddenand complete disruption of the

9 J

I 0 4 8 12 16 20 24 28 Section angle of attack, cc

Figure 1. - Representative Lift Curves. (Reproducedfrom Reference 13).

10 - y-.i'

flow takes place. As the nose radii of airfoils normally decrease with thickness leading-edge stall is more likely to occur with airfoils with thickness ratios of or 12% less. This type of stall is consideredto be the most undesirable. 2.6.3 Type 3 - Thin Airfoil Stall This type of stall occurson all sh,arp leading-edge airfoils (regardless of thickness ratio) and may also be encounteredon rounded leading edge airfoils with sufficiently low thickness ratios e.g. t/c49%. As can be noted from Figure1, the airfoils with Type3 stall have substantially lower values of maximum lift coefficients than those associated with the airfoil types discussed above. The type 3 stall is characterized by flow separation from the leading edge with subsequent reattachment further downstream. The exact mechanism of flow reattachment is not clearly understood. Experimental observations have shown that at low angles of attack the flow reattaches to the upper surface of the airfoil at a short distance behind the leading edge and stays attached up to the trailing edge without further separation. With increase in angle of attack, the point of flow reattachment progressively moves toward the trailing edge and the stall is fully developed when the reattachment point occurs approximately at the trailing edge. Figure 2, reproduced from Reference14, more clearly delin- eates the types of stall discussed above and indicates some basis for a correlation between stalling characteristics, Reynolds number and leading edge shape. 2.7 WING PLANFORM EFFECTS In the design of the wing for stalling characteristics, wing planform is as important as the characteristics of the airfoil sections. Probably the most important planform parameters are the aspect ratio, taper ratio, and the sweep and twist angles if either is used. They have an important influence on airplane performance and wing weight as well as the stalling characteristics. Therefore, effective compromises between these parameters must be made to obtain the required performance, handling qualities and structural integrity of the airplane. The aspect ratio for a given wing area will directly affect the wing span. Low aspect ratio and short span are conducive to maneuverability for an aircraft intended for aerobatics. High aspect ratios are attractive from the pointof view of maximum aerodynamic efficiencyor L/D. However, an increasein aspect ratio generally results in an increase of wing root bending moments and probably wing weight. One fact that should 31 I I I I I oThinLairfoilstall. Leading-edge stall. I I -I! aioo OI0 I A Combined leadingedge and.trailing- edge stall. o Trailing-edge stal I. I I

"railing-edge stall

Sombined leading-edg and trailing-edge stal "t-"

7 ?." 6 1 "-

5 I "I

"I 1.2 1.6 2.0 2.4 2.8 3.2 3.6 3.2 2.8 2.4.4 2.0 .8 1.6 1.2 Upper-surface ordinate at O.Or25 chord, percent chord

Figure 2. - The Low-Speed Stalling Ch.aracteristics of Airfoil Sections Correlated With Reynolds Number and the Upper-SurfaceOrdinates of theAirfoil Sections at the 0.0125-Ch,ord Station.(Reproduced from Reference 14).

12 be considered relative to the compromisebetween maximum L/D andwing rootbending moment is that the lift coefficient at which maximum L/D is attained also increases with aspect ratio. The performance characteristic most affected by maximum L/D is theaircraft range. For personal aircraft with relatively light wing loadings operating at altitudes below10,000 feet, the speed for maximum range may be too slow to make it an attractive cruise speed. The increase inthe value of the maximum L/D obtained by increasing the aspect ratio, therefore, may beof little practical use. In fact, if the L/D is much increased for the lift coefficients used in the approach glide, the effect may be to flatten theapproach path, make judgment of the landing point more difficult andgive the airplane a tendencyto "float" after the landing flare. This statement is intended only to imply that increases in aspect ratio do not necessarilylead to improvedaerodynamic performance. Improved performance may be better obtained by a reduction of fuselage, engineand landing gear drag. Taper is normallyemployed to increase the wingchord and spardepths at thewing root and, hence, offset the adverse weighteffects of increasing the aspect ratio. At the same time it increases wing torsional rigidity which is animportant structuralconsideration. Wings canbe tapered either in thickness or planform or in any combination of both. When COm- binedtaper is incorporated in the wingand straightline Surface fairing is usedfor structural simplicity, airfoil sections betweenth.e fairing stations may beslightly distorted.

Sweep shifts the aerodynamiccenter of the wingfore-and- aftrelative to the wing root.Small amountsof it cantherefore beused to adjust the longitudinal aerodynamic balance or to improve the position of the aircraft center of gravity relative to the main landinggear. Wing twist affects the span load distribution by changingthe local section angle of attack along the wing span. Negativewing twist or washout may be used effectively to move thestalling point inboard.

High-liftdevices such as leadingedge slots or trailing edgeflaps, if they are installedacross the full span, influence the wing stall only through their effect on the section lift characteristics.Rarely, however, are eitherleading edge slots ortrailing edge flaps used over the entire wing span.Leading edge slots over the tip portion of the wing were one of the first means tried for improvingthe wing stalling characteristics. Such slots increase theangle of stall ofthe tip sections of the order of tendegrees. Much experimentation wtth relatively simplefixed slots, as well as withthe movablcHandley-Page type, led to the early conclusion th.at neither the complexity

13 andcost of the automatic slots nor the drag penalty of the fixedslots were warrantedfor small personalaircraft. There hasbeen a recent revival of interest in movableleading edge devicesfor the tip portions of the wings of high-speed, swept- wingcommercial and military aircraft where their use can be economicallyjustified. Flaps are usuallyinstalled inboard of theailerons. They depress the angle of attack for zero lift of the airfoils to whichthey are attached while having only a secondary effect on the stall angle.Inboard flaps, therefore, have the effect of a discontinuous wing twist with wash-in starting at the flap end.

Application of the simple lifting line theory as described inReference 15 topredict the stalling characteristics of flappedwings will indicate a discontinuity in the spanwise distribution of maximum section lift coefficient andan assoc- iatedinitial stall at theend of the flap. Inasmuch asthis discontinuitydoes not exist in threedimensional flow, early attemptsto predict the stalling characteristics of flapped wings(Reference 16 and 17) by the methodof Reference 15, did notyield good correlationwith experiment. Subsequently, a far more reliable method of applying the lifting line theory was developed(Reference 2). The latter method predictsthe point of initial stall quite well and is described in detail inSection 4 of thisreport.

2.8 CONSTRUCTION TOLERANCES -@D SURFACE IRREGULARITIES- In most cases the final wingdesign represents a compromise among thebest dimensions for performance, stall characteristics and structuralweight, although occasionally some importance may begiven to appearance. Curved leading edges, taper and sweep canadd to the attractiveness of a designand givethe impression of speed. While suchfeatures so used may notnecessarily penalize the design, their impact on flight safety and construction costs should be carefully studied.

No adequatemethod of defining either the permissable deviations of the airfoil ordinates from their specified values orthe permissable degree of surface roughness and waviness has beendevised. Reference 5 gives some generalguide lines concerningthe surface conditions and constructiontolerances that mustbe adhered to in order to achieve extensive regions of laminarflow at low valuesof the lift coefficient. In general, it would appearthat i-f valuesof clmax comparable to thosepresented in Reference 5 are to beachieved, the surface conditionsand construction tolerances over th.e forwardupper surfaceof th.e airfoil(approx. 0 to 10% chord)should be at leastas good asthose indicated in the reference. As sh.own by the results of Reference18 "very small errors in airfoil

14 contour,particularly around the leading edge, could cause large changes in the stalling angle of attack and the resulting valueof maximum lift coefficient."

The advisabilityof applying the stall analysisprocedure in the early stages of the airplane design cannot be over- emphasized.This stall analysisprocedure relies on theuse ofpublished airfoil section data characteristics. The designer is warned,therefore, that unless the aircraft as finally constructedincorporates airfoil sections that are approximately equal in contour and surface condition to those utilized in obtainingthe two-dimensional airfoil section data, the calculated stalling characteristics will not necessarily be comparable to thoseencountered on the flight vehicle.

2.9 WING-FUSELAGE FAIRINGS One of the more importantstructural considerations affecting aircraft stall is the fairing between the wingand fuselage. Themethod of Multhopp used for calculating the effect of the fuselage on the wing liftonly accounts for changes in local flow anglesof the root sections due to presence of the fuselage. Neither this method nor any other method considered in the course of thisstudy adequately treats the modification ofthe surface pressures on the wingand fuselage as a resultof the mutual interference. Such changesseriously influence the boundary layer atthe junction and can cause premature separation of the main flow. The turbulencein the wake behindthe separated region may intersect the tail plane where it may inducevibratory loads which ifmild, can be used as stall warning. It may, however, result in vibrations severe enough toimpair the structural integrityof the aircraft. The violenceof the vibrations depends on theextent of th.e separatedregion and the location of the horizontal tail relative to wake. Wing fuselage flow interaction effects largely dependon the position of the wing relativeto the fuselage. For thehigh wing position, wherethe influence of the fuselage is confined tothe lower less critical surface of the wing theseeffects arequite small. Thelow wing positionwith the wingtangent to thefuselage introduces the largest wing-fuselage interaction effects which increaseas the angle between the wing-fuselage surfaces becomesmore acute. The wing-fuselageflow interaction can be to some degree controlled by theshape and size of theroot fairings associated witheach wing position. The high wing positiondictates a minimum amount of fairing fromaerodynamic considerations, whereas for the low wing position a considerable amount of fairing may be required to ensure proper flow conditions on the uppersurface of the wing closeto the fuselage. Also, careful considerationshould be given to the chord-wise shaping of

15 the wing rootfairing, since it effects the expansionof the flowover the after portionof the junction. The chord-wise shapeof the root fairing largely depends on thefore-and-aft position of the wing relative to the fuselage maximum diameter. Sincethe geometry of the wing-root fairings critically dependson detail design of the junction there are no established theoretical methodsby which the size and shape of the wing- root fairingscan be predicted. Some empiricaldesign rules, whichcan be employed for this purpose are presented in References 19. However, it is generally recommended that the final size andshape of the wing-root fairings be determined by anexperiment either in a wind tunnel or in flight. The fairingproblems discussed above are similar to those associatedwith the nacelles of wing-mounted engines.Location of thenacelles close to the fuselage may result in some additionalinteraction effects of the nacelle-fuselage flow fields. However, thepropeller radius requirements generally ensuresufficient spacing between the nacelles and the fuselage to preventserious interaction.

2.10 PROPELLER SLIPSTREAM -~CONSIDERATIONS____

Anotherimportant consideration of airplane stall is the effect of thepropeller slipstream in power-on flight.This effect is introducedthrough an increase of the local velocity overthe wing immersed in the slipstream and thechange of wing localangle of attack due to slipstream rotation.

The increased velocity tends to stabilize the flow over the wingimmersed inthe slipstream. The rotationwithin the slipstream tends to increase thelocal angle of attackof the wing sections behind the upgoing propeller blades and decrease the localangle of attackbehind the downgoing blades. The overall effect is usuallythat of promoting an asymmetrical stall. The stall of that portion of the wingbehind the upgoing blades is hastenedwhereas that behind the domgoing blades is delayed. Inthe case of a singleengine airplane the asymmetrical stall canpromote serious wing dropping tendencies when the airplane is operatingin the vicinity of CLmax. Reference 8 presentsthe results ofextensive experimental observations of the effect of propelleroperation onwing stalling. It is interestingto note, from theresults presented therein, that in the case of oneof thesingle engine airplanes investigated, the action of thepropeller in promoting an asymmetrical stall is more adverse atthe engine idle power condition (Tc = 0) than at the power-on conditioninvestigated (Tc = 0.2). Inthe case ofanother single engineairplane investigated, the effect of power was in the reverse orders The effects of the asymmetrical stalling in the case of multi-engine aircraft can not be clearly defined primarily due to the fact that these effects are largelydependent on a specific combinationof various geometric parameters related to each aircraft .

2.11 STABILITY~~ AND CONTROL CONSIDERATIONS

In the abovediscussion of airplane stall characteristics, it is assumed that the aircraft is in a steady unyawed trimmed flight, and that the stall is developedth.rough. a gradual increase of airplaneangle of attack. However, thesteadiness of actual flightdepends on thelongitudinal stability of the aircraft, th.e control effectiveness, the rate at which. the pilot moves th.e control stick andthe atmospheric turbulence. With referenceto atmospheric turbulence, little canbe done in designto reduce its effect on thestall. Even assuming that th.e airplanestability and control are adequate,severe tur- bulencecan upset any aircraft and therefore it shouldbe avoided where possible.In an unavoidable flight in turbulentweath.er, theFederal Regulations require the pilots ofcommercial airlines tofly the specific airplane at its designatedspeed low enough to minimizethe structural loads due to the gusts, but high enough to assurethat the angle of attackchange produced by the probable maximum upward gust will notstall th.e aircraft. The designer of theprivate airplane can only suggest that h.is cust- omers follow a similar practice. Inaddition to the angle of attackch.anges, gustiness will induce rolling andyawing motions that can result in premature unsymmetricalwing stall andsudden roll-off. The dangerdepends on th.e stall margin of the wingand on th.e lateral stability of theaircraft. One of therequirements for good lateralstability is anadequate finarea. The relation betweenth.e finarea and the wing dihedralangle determines wheth.er the yawing or rolling componentof th.e lateraloscillation predominates. The occurrence of light oscillations as stall is approach.edhas been suggested as anacceptable stall warning. This ph.enomenon is usually associated with a reduction of fin effectiveness at large wing anglesof attack and is caused by blanketing of the lowerportion of th.e fin by thefuselage or submersion ofth.e fin in alow- energy wing wake.

Th.e longitudinal stability and th.e elevatoreffectiveness combine to determine the stick movement required at different parts of thespeed range. In general, high.-wing positions result in more longitudinal stability at low speedsth.an at high. speeds. Low-wing positionsproduce the opposite effect. Th.e elevator effectiveness varies with the relative proportions of the elevator and stabilizer, and it decreasesafter the angle of the

I elevatorexceeds a critical angle. Hence, for an increasing rate of stick movement as the stall speed is approached, as suggested for stall warning,the high-wing configuration with. a small elevator is more desirable. There are, however, a considerable number of otherfactors affecting the stability and control characteristics which. in turn influencethe airplane stall. The subject is too complex for a shortcomprehensive treatment in thisreport. Among others,the aircraft stability and control is affected by thesize, location and type of flaps; the wing wake and its position relative to thehorizontal tail; theorientation of thepropeller slipstream relative to both the horizontal and vertical tails and the vertical, as well as thefore-and-aft, position of th.e center of gravity.These and other factors areadequately treated in the available technical literature, e. g.References 20 and 21.

2.12 FLIGHTVERIFICATION AND CERTIFICATION

The theoretical meth.odsand th.e designprocedures, presented in thisreport should reasonably well predict th.e stalling characteristics of unsweptwing aircraft, particularly for gliding flight such. as in th.e landingapproach. Since th.ese methodsand procedures are basedupon a number ofsimplifying assunptions, it is alwaysadvisable to verify the theoretical predictions by actualflight tests.

Th.e test proceduresto be followed are specified in the Federal Aviation Regulations for Certification Demonstrations cited earlier. If th.e tests showa need to improve theaircraft stalling characteristics, a flowvisualization tech.nique, utilizing tufts is often employed in gaining an understanding of'the flowdeficiencies. Th.e tufts which are normallyshort lengths ofstring attached at intervals on theupper surface of the wing and sometimeson the sides of th.e fuselage,can be observed and/ or photographedfrom within the test aircraft or the chaseplane. The flowpatterns indicated by the tufts will defineareas of attached and separatedflows and can show thespanwise or chordwise location of initial flow breakdownand th.e rate at which. separationincreases with. smalldecreases in speed.

Th.e tuftstudies, the motions after initial stall and the stall-relatedvibrations felt in the structure and the control system will generally indicate the design changes required for improving the stalling ch.aracteristics after the airplanehas beenbuilt. No attempt will be made to list or discussall the possibilities in this report.

One possibility is th.at a part of th.e wing will stall sudden- ly withalmost no warning. This typeof stall can occur with airfoils exh.ibiting leading edge stall and with wingproportions

18 yielding low stall margins at th.e sectionsclose to the point (11 of initialflow breakdown. Interferencebetween the flows over adjacentsections promotes separation which. can spreadacross the wing veryrapidly. Themeans most used for improvingthe stalling characteristics in such a case is the installation of a triangular-sh.apedprojection or spoiler,Figure 3 (a), for a short distance along that part of the leading edge over which an earlier stall is desired.Attainment of satisfactory stalling will generally require a trial-and-errorprocedure, varying th.e spanand spanwise location of th.e spoilerand its radial location at theleading edge. It may bedifficult to obtain a configuration of the spoiler which is effective with full power but nottoo effective when power is reduced.Spoilers of th.is type canincrease th.e power-off minimum speedby an objectionable amountand producelarge vibrations of the wing, stabilizer or fuselage. The otherextreme possibility is a root stall starting well above the minimum speed. The associatedth.ick turbulent wake, if it impingeson th.e tail, will produce stall warning,but may also make it impractical to fly the airplane in th.e speedrange requiredfor th.e landingapproach. If theroot fillet is prop- erly designed it may benecessary to modifythe wing leading edgeof the root sections to increase their forwardcamber and reduce th.eir effectiveangles of attack. One such. leadingedge modification is shown inFigure 3(b). It is frequentlynecessary to tailor th.e leadingedge modification such.th.at a smallvibra- tionremains for stall warning. Such modification may be utilized to control th.e asymmetrical stall that sometimes occurs within th.e propeller slipstream. Th.e actual cases are rarelyas clearcut as the two just discussedand the reason for poor stalling characteristics is oftennot clearly understood. During World War 11, many aircraft withconfigurations similar to thoseof current private owner designs h.ad to undergopost-design stall improvement testing. Many of th.ese cases are in the literature and h.ave beenincluded in the bibliography presented in this report.

19 (a) SharpLeading Edge Strip to Hasten Stall.

(b) Modified Nose Radiusand Camber to Delay Stall

Figure 3. - Wing Leading Edge Modifications for Controlling Wing Stall.

20 SECTION 3 THEORETICALANALYSIS Presented in this section is a brief review of the available theoretical analysis which formed the basis for developing the mathematicalmodel and the computer program contained in this report.Specifically, in selecting the most suitable theoretical approaches,due consideration was given to the past work in the fieldsof wingtheory and wing-body interference theory. The significant contributiorsin these areas and their applicability to the present program are discussed in the following pages. 3.1 REVIEW OF THE~______AVAIWLE THEORIES 3.1.1 Wing Theory

The simplest wing theoryinvolves th.e conceptof th.e lifting line whereby the wing is replaced by a vortex filament fixed in the wingand a systemof trailing vortices. The vortexfilament is known asthe bound vortexor lifting line. At eachpoint on thespan the strength of the vortex is proportionalto the local intensity of lift and is related to it throughthe Kutta-Joukowskf law, which is based on therequirement of smooth flowfrom the wingtrailing-edge. In accordance with the Helmholtz theorem of vortex continuity it is assumed thatwith each elemental change in the spanwise distribution of the strength of the bound vortices there is associated a free vortex which is shed at the wing trail- ingedge and which passes downstream with the general mass of the fluid. The strengthof this vortex is equalto the incremental change in spanwisecirculation. This system of free or "trailing" vorticesinduces velocity components (called downwash) at the wing andthus causes a change inlocal angles of attack of each wing section.

The problemof evaluating the downwash at eachpoint is difficultbecause of the interrelation of downwash, lift distrib- utionand wing planform. Using the lifting line theory Prandtl (Reference 22) obtained a solution for the case of a wing withan elliptical lift distribution.Glauert (Reference 23), using Fourieranalysis, developed methods for obtainingsolutions for wingsof any planform and twist. Thesemethods were usedby Anderson(Reference 15) to determinethe characteristics ofwings for a widerange of aspect ratios, taper ratios and linear twist distributions.

All ofthese approaches discussed above involve the assumption of a linearvariation of section lift with angle of attack. This assumption was not utilized in the iterative methodsdeveloped by Sherman, Tani,Multhopp, and Boshar (References 24 through 27) whichemploy nonlinear section lift data in thecomputations.

21 Based on these iterative methods Sivells and Neely (Reference 1) developed solutions which yield excellent agreement with the test dataup to angles-of-attack close to stall.In a later paper Sivells and Westrick (Reference2) extended the method of successive approximations to the calculation of the aerodynamic characteristics of wings with deflected or flaps ailerons. All of the above solutions and methods which are essentially based upon the Prandtllifting line theoryare known to be inadequate for wings of aspect ratio less than3. about For wings of this class the influence of the chordwise loadingcan no longer be neglected and resort mustbe made to the general theory of lifting surfaces to obtain solutions. Lifting surface theory involves finding a potential flow solution which satisfies the Kutta condition all along the span while at the same time satisfying the boundary condition that there is no flow through the wing surface. Solutions of varying complexity and accuracy have been advanced by many authors. Early attempts were made by Weissinger, Mutterperl, and Schlichting (References28, 29 and 30 to use simplifying physical models for the approach to the general problem, e.g. placing a lifting line at the quarter-chord point and satisfylng th.e downwash condition at the three-quarter-chord position. Falkner (Reference 31) proposed a vortex-lattice treatment of the wing thereby approaching a truly continuous lifting surface. Attempts to use a continuous lifting surface theory without resort to arbitrary physical assumptions or models are exemplified by the work of Garner (Reference32 and 33) and most notably by that of Multhopp (Reference34). When lifting surface theory is used to predict load distributions on high aspect ratio unswept wings at low angles of attack, the results do not differ significantly from those computed using lifting-line th.eory. However, to date, lifting surface theory has not been successfully modified to permit the use of nonlinear section lift data and hence cannot be expectedto give reliable predictions of load distribution at wing angles-of-attack near the stall. For this reason the lifting-line theory, as modified and presented in Reference2 has been chosen as the more appropriate method and the one which is better suited to the present task.

22 3.1.2 Wing-Body~~ Interference Theory Many methods exist for the calculation of air loads on wing-fuselagecombinations and these have been summarized by Schlicting(Reference 351, and by Flaxand Lawrence (Reference 36). In view of theforegoing selection of lifting-line theory to calculate essentially wing characteristics,the following discussion will be limited to those wing-body interference methods whichhave been developed for use with the lifting-line approach.

The spanwise lift distribution over a wing-bodycombination of minimum induced drag was first treated byLennertz (Reference 37) for a body consistingof a infinitely long circular cylinder. His solution was generalized byPepper (Reference 38) to include bodiesof any cross-section. Multhopp(Reference 41,using a conformalmapping technique, obtained a solution for the case of a highaspect ratio wing mountedon aninfinitely long cylinder of anyshape. This method may be applied if a functioncan be found which. maps the body cross-sectionconformally onto a circle or a straightline. The advantageof the method is thatthe transformed cross-section shapeautomatically becomes a streamline,thus satisfying the fuselageboundary conditions.

An alternativeapproach is that first used by Lennertz (Ref- erence 37) in which singularitiesin the formof image vortices are introducedwithin the fuselage cross-section to satisfy, approximately,the boundary conditions. Zlotnick andRobinson (Reference 39) applied this method to the case ofswept wing-body combinations with centrally placed wings. The use of the image vortex method in combinationwith the lifting-line methodof Reference 1 is restricted to wingswhich arecentrally mounted on circularfuselages. For wingsnot aentrally mounted theequations become extremelycomplex due to the fact that the image vortices no longer lie on theextended planeof the wing within the fuselage. For other thancircular cross-sections, the determinationof the number andlocation of the image vortices is difficult.

Weber, Kirbyand Kettle (Reference 401 havemodified Multhopp'sapproach to accountfor non-zero wing thickness and applied this method tolow-aspect-ratio sweptwings. In view of this success andbecause of its simplicitythe Multhopp formulationof the wing-body solution(Reference 4) has been adopted herein rather than the more complexmethod of images of Reference 37.

23 3.1.3 PropellerSlipstream Effects

As pointedout inSection 2.10, thepropeller slipstream exertsan important influence on wing load distribution which in turn affects the aircraft stall characteristics.

A reviewof the technical literature indicates that there are no adequatetheoretical or semi-empirical methods which canproperly account for the effects of propeller slipstream on thespanwise load distribution of the entire wing. Most ofthe availabletheoretical andexperimental investigations, e.g. References41through 47 predict wing load distributionssolely for that portion of the wingimmersed in the propeller slipstream. Thisapproach is consideredto be inadequate for predicting stall characteristics of wingsspanning the propeller slipstream because the portions of the wingoutside the slipstream cylinder are strongly influenced by the slipstream flow. On theother hand, development of a mathematical model for predicting the effects of propeller slipstream on wingload distribution within and outside the slipstream cylinder is rather complexand is considered to beoutside of thescope of the present work.

In viewof the above difficulties, it was decidedto temporarilyexclude the power effect fromwing stall analysis. However, provisionshave been made toinclude such effects at a later date, wh.en reliable theoretical methods for predicting the effects of propellerslipstream on the load distribution of the entire wing become available.Therefore, in developing the theorypresented herein, the methodof Multhopp (Reference 4) for wing-body interference effect and the methodof Sivells (Reference 2) for the isolated winghave been successfully cornfinedand are presentedin the following analysis.

24 3.2 FORMULATION.~ . OF THE ANALYSIS 3.2.1 ConformalTransformation ofWing-Fuselage Combination - "_ ." - ~ A wing in thepresence of a lifting fuselage(aB>o) is subjected to an upwashwhich decreases towards the wing tips. This upwash has the effect of a variable wing twist, which is a function offuselage and wing geometries,fuselage angle of attack and aircraftforward speed. The problemof fuselage-wing flow interacgion has been the subjectof numerous investigations in thepast. As mentioned previously,the approach selected in thepresent analysis is that based on Multhopp'sformulation. In th.is approach,the wing- fuselagecombination is conformallytransformed into an equivalent wingwith a vertical slit representing the fuselage. The vertical slit is aligned with. thecross-flow and is therefore automatically a streamline. The transformation is applicable tofuselage cross-sections which are approximately elliptical or wh.ich canbe transformed to such by the use of other meth.ods. If the wing is not centrally mounted on the fuselage it transformsinto a slightly curved trace whose curvatureincreases withan increase in the vertical distance of th.e wing relative to the center of thefuselage. This introduces an effective dihedral to th.etransformed wing, but its effect is considered to be small and is thereforenot treated in th.is analysis.

Figure 4 shows thegeometry ofa wing-fuselagecombination inboth the real (u) andtransformed (U) planes. The definition of real and transformedparameters is presented in th.e list of symbols.

The wing load distribution, c1 (Y) , inthe u-plane is a functionof the local effective angle of attack Qe (y) of the sectionunder consideration. This effectivesection angle of attackcan be expressed as follows:

Where UB,Q R , and E (y) are the body angle of attack, wing-root incidence relative to the bodyand thewing section geometric twist, respectively. Th.e angle due to body upwash. A a(y) and th.atinduced by the wing trailing vortex system ai (y) canbe determined from th.e followinganalysis.

25 Trace of wing 7 "

.__ " "_ "_ "__. - ." 1 Transformed plane 6 (ii-plane1 2

Figure 4. Definition of Parameters for Transformation of Wing-Body Combination

26 UsingReference 4, the wing angleof attack due to body ti upwash for zero wing thickness is givenby:

where dij/du, is the real partof the derivative of the conformal function u (u) . For an elliptical fuselage, thisderivative can beexpressed as follows:

where,

For a circularfuselage equation (3) becomes:

dii A12( y2- h2 ) (5) R-=l+ du (y2 + h2)2

For wings of non-zerothickness, Reference 40 suggeststhat the upwash at the wing is decreased as compared to that for wings ofzero thickness. Th.is can beapproximately accounted for by reducing the wing angle of attack due to bodyupwash, Aa (y) , by a factor T taken as constantacross th.e wingspan. The factorcan be expressed as th.e ratio ofthe body cross-sectional area aboveand below the wing to the total frontal area of the body.Thus, ifthe wing is nottoo thick, there follows:

Thus, for wings of non-zerothickness, equation (2) can be rewritten as:

If, however, the conformal function for the th.ick wing ,(ea) couldbe determined, then equation (7) wouldbe du T

27 Comparing equation (7) and (8) there results:

Equation (9) representsan approximation to the real part of the derivative of theconformal function applicable to wings ofnon-zero th.ickness. This equation is thereforeused to relate the induced angle of attack at a point y in th.e u -plane to that at thecorresponding point 'i inthe J -plane,thus:

Finally,substituting equations (7) and (10) intoequation (1) the effective angle of attackfor wings of non-zero thickness is given by

The only unknown wh.ich remains to be determined in equation (11) is Cri (7) . The inducedangle of attack, in degrees, at a point 7, on thetransformed span is given by the familiar relation

where (Y) is thesection lift coefficientin the transformed plane at a point TJ. It shouldbe noted that since the transformation is conformal,the circulation r (9) aboutany wing section and th.e associatedsection lift coefficient El (y) in thetransformed plane are equalto the corresponding values in the real plane.Since the geometric quantities of ch.ord length. (C andwing twist at eachpoint in the real plane are also the same at thecorresponding points in the transformed plane then

28 Forwings with undeflected flaps, the spanwise lift distribution in the transformedplane can be expressed as an infinitetrigonometric series as follows:

where,

Usingequations (12) and (14) th.ere follows,according to Reference 23

- I80 a, a/ 4 IT sin S xnAnsin(n8) n= I

Thus, inorder to determine th.e inducedangles of attack the valuesof the coefficients An arerequired. Th.ese areobtained as follows:

The spanwise lift distribution is approximated by a finite trigonometric series of r-l terms corresponding to determining theload at an oddnumber, r-l , of points on th.e span. Th.at is, therange o<8

Usingharmonic analysis, equation (17) yields the coefficients A, of th.e trigonometric series, th.us

If equation (18) is now combined withequation (161, an expression is obtainedfor th.e inducedangle of attack, th.us

29 Sincethe induced angle of attack is to bedetermined at the pointsat which theload distribution is required, i.e. at the points a = then

where

It canbe shown th.atif k+rn is odd th.en

and if k-rn

finally, wh.en k+rn is evenand k+rn

30 3.2.2 SpanwgsgLoad Distribution for a Wing With No Flap or a Full Span DeflectedFlap Th.e method ofdetermining the lift distribution is oneof successiveapproximations. For a given body angleof attack a distribution of crc/ij is assumedand theinduced angles of attack are computed usingequation (21). Using equation (11) th.e effective section angles of attack are calculated and th.e correspondingvalues of lift coefficient obtained from airfoil data atthe appropriate values of thesection parameters. This process is repeated until the guessed values agree with th.e computed values to within th.e required tolerance.

Inorder to minimize th.e numberof iterations required to converge on the final distribution of lift coefficient a systematic method is requiredto generate increasingly better approximations. Such. a method is developedin Reference 2 and is herein presented in sligh.tly different notation. For a wing-bodycombination with zero thickness wingand no flap deflection, th.e basicequation to be satisfied during anycycle of th.e iterative process is the simplifiedversion of equation (111, i.e.

31 Assuming linear section lift-curves the relationship for one cycle of the iteration is

where Ak is the amount to beadded to theapproximate value cl c/~jto obtain the calculated value. Forthe following cycle a value A'k is chosensuch th.at the calculated values areequal to the guessed values thus:

then with

therefollows

[Gmk] (.'m} = (am}

32 ,y

I where Gmk is the transpose of Gmk . Thus, the valuesto be added to one set ofapproximate values to obtain a better approximation are given by:

The matrixof coefficients Kii is easilyobtained by th.e usual methods of matrix algebra. 3.2.3 Spanwise Load Distributionfor a Wing With a DeflectedPart-Span Flap The deflection of a part-span flap causes a discontinuity in th.e distribution of absoluteangle of attack at theend of theflap. In order to maintain a continuousspanwise distribution of lift a correspondingdiscontinuity must exist in the distributionof induced angle of attack. From Reference 2, th.e complete lift distribution may be expressed as th.e sum of two distributions,thus:

where F(c~c/b) is thedistribution due to a unitdiscontinuity in inducedangle of attack and cflc/b is th.e remainderof th.e lift distribution.Since the latter distribution is continuous the multipliers Pmk may be used directly to obtain the correspond- inginduced angles of attack.

Since tiii2k = 8 over the flapped span and ai2k = 0 over th.e unflappedspan, the total induced angle of attack is

33 Now, if the multipliers were used with. the total lift distrib- ut ion

and Ei2k were added to both sides, the result wouldbe :

Rearrangingequation (34) yields:

A comparisonof equation (35) with equation (21) shows that for a wingwith a deflected flap an additional term is required which is proportionalto th.e magnitudeof the discontinuity. This terms represents a correction factor to account for th.e inability of a limitedtrigonometric series torepresent adequately the spanwise lift distribution of a wingwith deflected flaps. Equation(35) may berewritten as:

34 [$! wh.ere th.e uncorrectedinduced angle of attack is expressed as

and the correction factor per unit discontinuity is

d 6 are in degrees.

The distribution of c12c/I;6 asgiven by equation (39) depends solely on th.e spanwiseposition of the discontinuity at th.e end of the flap, a_nd applies to outboard flaps wh.ich beginatzT/i = 1 and end at 2y*/b For a wing with. symmetrica_linboard flaps . " extendingbetween 2y/E = 2y*/b and 2y/jb=-2 Y*/b thedistribution is obtainedby-subtracting values of c12c/E 6 for 27% from those for - 2Y*/b . The correctionfactor per unit discontinuity ack/6, givenby equation (38) is th.erefore a functionof only thespanwise position of th.e discontinuity and Pmk.

It should be noted that two values-of_(z c/ 6 exist at the endof the flap, onecorresponding to 2y*/k j- 0 , (th.e flap side of 27*/E 1 and th.e oth.ercorresponding to 2y*/b - 0 , (theunflapped side). The values are related by: - (40) --0 -+O b b

35 Either of the two values ofcc/6 may beused so long as the value is used with the proper section lift curve.

3.2.4 Modification of the Two-DimensionalSection Lift Data If the two-dimensional section data were used directly discontinuities wouldbe found in the maximum lift distribution at theends of thedeflected flaps. Since the discontinuities do notactually occur, the two-dimensional data must beadjusted to reflect the fact thatsections in the vicinity of th.e end ofthe flaF exhibitvalues of CZ max. which. lie betweenthose for flappedand unflapped sections. Therefore, following the method ofReference 2 thetwo-dimensional data is modified to obtain so calledthree-dimensional section data.

Th.e root section of a wing with. a partial-span flaps deflected would act most nearly like that of a wing with. full-snan flaps.Similarly, the tip section wouldbehave asif it were on a wing with no flapdeflection. Now th.e loaddistribution for the wing with partial span flaps can be calculatedas long as eachsection is operating in thelinear range of its lift curve. A typical distribution, denoted by cl 8, is shown in Figure 5.

A lift distribution is now calculated for th.e same wing with no flap deflection and theordinates scaled so that the wing has a liftcoefficient of unity. Sucha distribution,denoted by cl , is a1so shown in Figure 5. This distribution is multiplied by a suitable constant factor k, to givethe same value at theroot as th.e distribution with the flap deflected andby anotherfactor k2 to give the same value as the flap distribution at th.e outermoststation usedin the computations.

The differences between Cz 6 and kt Cz I inboardof the flap end and between CZ 6 and k2 Ct1 , outboard of the flap end, are divided by thedifference between kl Cz1 and k2 ct 1 takenat the endof theflap. Thus, the resulting values or factors, F can beexpressed as follows:

and for 2- >: 2y * b b

36 1I.

Figure 5. - Typical Load Distributions for Obtaining Factors for Altering Two-dimensional Data. Thesefactors are relatively insensitive to lift-curve slope and may be used in the non-linear portions of th.e lift curves.

In calculating the abovementioned distributions, any convenientvalues of the discontinuity 8 andwing angle of attack may beused. Wing twist is omittedin th.ese computations. Havingobtained the factors F th.e values of maximum lift coefficient are thenaltered according to:

where (Clrnax lo is th.e two-dimensionalvalue of section maximum liftcoefficient and A ‘!%ax is theincrement in clmax due to flap deflection at the endof th.e flap.

Figure 6 illustrates the methodof obtaining the final correctedlift curves. At eachangle of attack (a,) th.e two- dimensionaluncorrected value of liftcoefficient ( ‘10) , as obtainedfrom the airfoil data, is factoredto give the corre- spondingvalue of lift coefficient corrected for proximity to theflap endth.us,

‘1 max ‘1 cor = ‘lo (44) (‘2 max)o

Th.is value of lift coefficient wouldcorrespond to a value of angleof attack a’ on thetwo-dimensional lift curve. Due to the fact that each wing section is not operating in a true two-dimensionalflow, but forms part ofa finite-span winga correction mustbe made toaccount for the fact th.at the air canflow around the wing tips.This extra degree of freedom impliesthat a section on a finite-span wingmust operate at a high.erangle of attack th.an the same section in strictly two- dimensionalflow in order to achieve the same value of lift coefficient.This correction was firstderived by Jones,Ref- erence 48, in the formof th.e edgevelocity factor given by:

Qe - Qto E= (45) a0 - QI 0

Jones originally derived the correction factor for a wing of elliptic planform and expressed it as,

38 Inboard of flap end

t 'i' I/

Uncorrected 2-Dimensional Characteristics

__ - Final Characteristics Corrected for 3-Dimensional Effects

QI a, a. a

Outboard of Iflap end

I I I

I ! i t .I ." ." \r a

Figure 6. Illustration of Method for Correcting Two-dimensional Section Data.

39 win g semi-perimeter (46) semi-perimeter wing E= wingspan

Reference 2 gives a more accurate expression,applicable to wingsof other than elliptical planform, in th.e form,

E =Jq (47)

Thus, theeffective angle of attack,ae , correspondingto th.e two-dimensionalangle of attack, a’ , is givenby,

and since a1 is related to the originalvalue a. by

then th.e correction which. must be made to QO to accountfor bothedge-velocity and flapproximity is obtainedas

Figure 6 shows the final corrected lift curves as compared to th.e original two-dimensionaldata for two stations, one inboardand the otheroutboard of the flap end.

The abovemethod of correctingthe two dimensionalsection datato account for flap discontinuity is substantiated experimentally by Reference 2.

It shouldbe noted that the Jones edge velocity correction applies regardless ofwh.ether th.e flap is deflectedor not. 3.2.5 Calculationof Overall Wing Characteristics Once thespanwise lift distribution of a winghas been calculated the determination of drag and pitching moment

40 I' coefficients is a simplematter since these quantities depend on the lift distribution. By theuse of Simpson's Rule, the integrated values of lift, induceddrag, profile drag and pitching moment coefficients are given by:

wh.ere

Inequation (55) the section lift anddrag forces are assumed toact through. the quarter-chord points. The multipliers Tm usedin equation (51) through (54) are defined by :

Step-by-stepcomputational procedures based ?n the preceding analysisare presented in the following sectlon.

41 SECTION 4

COMPUTER PROGRAM

The solutionof the mathematical model described in Section 3 was accomplished bymeans of a specially developed digital computerprogram. This sectionpresents a detaileddescription ofthe computational procedures, the requiredsection data, and the implementationof the computer program. The results of sample calculations are alsopresented.

4.1 COMPUTATIONAL PROCEDURES

The following is a mathematicaldescription of the individual stepsused in the computation of the wing spanwise load distributions. Th.e sequenceof the calculations is essentiallythe same as that set up in the computerprogram wh.ich. is described later. Thecomputational procedures cover three separatecases; wingswith no flaps, wings with full-span fLaps andwings with part-span deflected flaps.

4.1.1Computation of Basic Parameters

(a) Calculatethe following geometric quantities

e = JG2

2yo 2B’ 2h 2A’ 2e’ where Yo,B,H, A , e are, respectively, -b 1 -b >b’b’b

(b) Calculate a number of points y’ on the exposedwing spanfor even increments of 8 using

Yl= yo+ ( I-Y~1 cos e

42 where

e = ( ;- yo ) --Yo2

.. Y -Y = cos-' ( I -;)

where for the wing tip

(dl Transformfrom th.e u -plane to the 0 -planeusing th.e following relationsh.ips for an elliptical fuselage.

and

(65)

If th.e fuselage has a circular cross-section compute

(66)

I and

- y'= y' I- (67) [ Yl2+H2A2 1

where A is thecross-sectional radius (non-dimensional), (e) Calculate a new set of points Y on thetransformed spanfor even increments in th.e spanwise variable 0 as follows - Y = cos e (68)

where

(fUsing the relationsh.ip of Y' to y' obtainedabove, interpolate to find the points on th.e physicalspan, Y , corresponding to Y. (g) For an ellipticalfuselage cross-section obtain values for

where

or, ifthe cross-section is circular,use

RB=l+ A2 (Y2-H2) - du ( Y2+H2I2

44 (h)If the winghas a deflectedpart-span flap calculate 1, the location of the endof the flap in the E -plane using

where

(i) For a wingwith linear taper in both.ch.ord and thickness from fuselageside to wing tip calculate

(t/c) = I -1 (t/c), (75)

and

I where Re’ is th.e flight Reynolds number based on th.e exposed wing mean aerodynamicchord c’ which fs givenby

Note thatthe geometric wing twist,€ , is non-linearand th.at thespanwise distribution of wing section camber level is taken to be linear. For a wingplanform which. is not trapezoidal the foregoing quantities may bedetermined from a drawing or from a special calculation.

(j) Finally, calculate the multipliers Bmk, Tm, and the matrixof coefficients Kij usingequations (23) (56) and (30) respectively. Also, for part-spandeflected flaps obtain c12c/68 and ack 16 fromequations(38) and (39).

4.1.2 Wings With. No Flaps or With Full-SpanDeflected Flaps If the wing has deflected or undeflected full-span flaps th.e computations are simplifiedsince no correctionsare required for spanwisediscontinuities in induced angle of attack. In this case thecomputational procedure is asfollows: (a> For the desired body angle of attackcalculate the distribution ofgeometric angle of attackusing

(b)Obtain the corresponding Cl and (20 values by interpola- tionin the two-dimensional section data at th.e properReynolds number, thickness-chord ratio andcamber level.

(d)Calculate th.e correspondingvalues of induced angle of attack Ci usingequation (21) and determine th.e effective wing anglesof attack in the real plane from equation (11).

46 9 (e) Now computeequivalent the angles of attack, QO , for use withthe two-dimensional section data thus

(82)

where E is givenby equation (47).

. (f) Usingthe section data obtain the values of lift coeffic-ientcorresponding to QO and then calculate new values of cl c/b .

(g) Compare th.ese values to th.e guessedvalues of CI c/b and if agreement is notsufficiently close obtain a set ofvalues of Aj by applyingthe matrix Kij to th.e differencesbetween the calculated andguessed values as shown inequation-(30b). Add th.e results to th.e originalguessed values of cf c/b and obtain a new and better set ofapproximate values. Repeat steps (d)through (g) until satisfactory agreement is reached.

(h.) Havingdetermined the lift distributionobtain section valuesof profile-drag coefficient, induced-drag coefficient and pitching moment coefficient. (i) Finally,using equations (51) through (56),calculate th.e values of CL , CDO , CDi , and CM .

4.1.3 -Wings With Part-Span Deflected Flaps -. "_ (a) Determine the liftdistribution for the plain untwisted, unflappedwing-body combination at anangle of attack which is with,in the linearrange of th.e section lift curves.Scale the resulting lift distribution to give a value ofwing lift coeffic- ientequal to unity. Denote this distribution by cf, . (b)For th.e untwisted,flapped wing body combination, select a body angleof attack within the linearrange ofboth the flapped andunflapped section lift-curves. Obtain the value of section lift coefficient, clR , forthe root section from the airfoil data.

47 and

(dl Takingthe value of 6 as thedifference between the flapped and unflappedzero lift angles of the section at the end of the flap, determine the resultant angles of attack, ae ,at the real wingusing equations (11),(36),(37), (381, (39). Correct these angles for edge velocity and then use the section data to obtain new valuesfor the lift distribution. Repeat this iterative cycle until a convergence is obtained in the lift distribution.Denote this distribution by Cjs.

(e) Calculatethe correction factors F from equations (41) and (42).

(f) Usingequation (81) obtainthe first approximation of the final lift distribution andcompute the value of section lift coefficient at th.e flapend, c/ *, th.us

c/* = (F)(+) (+) (&) (85)

(g) Determine theuncorrected value of liftcoefficient at theend of th.e flapusing

where FF is thevalue of 1 + F A Cb* max / (CI takenat the flap side of T* .

(h) Obtainthe angle of attackvalue, Qo, whichcorresponds to cl ,, from the flapped section data and correct it to obtain the equivalent angle of attack, ae 8 thus

(5)In th.e same way find th.e equivalentangle of attack, “I 8 = o for the unflapped side of V*.

48 d, (j) The first approximatevalue of thediscontinuity in angleof attack 6 is thengiven by

(k)Again, use equations (111, (361, (371, (381,and (39) together with equation (88) to obtain values of th.e resultant angles of attack, Q, , at each station on th.e real wing. (1) The correspondinguncorrected angles of attack are then found using

(m> Use thetwo-dimensional section liftdata to obtain values of c! atthese angles of attack and factor th.em togive thecorrect values of lift coefficient, th.us

(n) Compare th.is calculatedlift distribution to the approximatedistribution and repeat the iterative process until th.e convergence is ach.ievedwithin the specified limits.

(0) Finally,obtain the overall wing-body ch,aracteristics usingequation (51) through (56). 4.2 SECTION DATA CHARACTERISTICS The accuracyof wing spanwise load distributions computed by this program largelydepends on the quantity and quality of theavailable section data ch.aracteristics. The sectioncharacteristics requiredin the computations are: Th.e two-dimensional sectionlift-coefficient versus section angle of attack,the section profile-drag and th.e quarter-ch.ordpitch.ing-moment coefficientsversus section lift coefficient. Ideally, th.e data shouldbe available for as broad a range of Reynoldsnumbers andthickness-chord ratios as is requiredto cover the range of theseparameters expected in actualf1igh.t. Oth.erwise, linear interpolation and extrapolation of the existing section data are requiredto perform the computations at the values ofReynolds number and/orthickness-chord ratio outside the available range.

I .. - .. The most reliable airfoil section data which. are now available are summarized in References 5 and 6.. Reference 5 presentg the data obtained for Reynolds numbersbetween 3x106 to 9x10 while Reference 6 extend8these measurements to values ofReynolds numbers down to 0.7~10 . 4.2.1 Correctionof the Section Data The seniorauth.or of Reference 6 hasindicated th.at errors exist in the values of lift curve slope for all airfoils tested at Reynoldsnumbers of less than3.0~106. These errors are attributed to an angleof attack change associated with. air leak- age at theintersection of the test airfoil and the wind tunnel walls. The evidenceof the inconsistencies at lowReynolds numberscan be noted by examining th.e behavior of the values ofsection lift-curve slope as a functionof Reynolds number, sh,own inFigure 17 of Reference 6. Since th.e values of lift coefficientsobtained from force measurements are known to be correct the irregularities in the trends of C~Qversus Reynolds number can onlybe associated with th.e errors in airfoil angle of attack. Therefore, a correctionprocedure based on extrapolation ofthe high Reynolds number lift-curve slope data was employed to generate approximate section data for low Reynoldsnumbers. Thisprocedure which was approved by the senior author of Refer- ence 6 is describedbelow.

For each airfoil section the variation of lift-curveslope withReynolds number was plotted as shown in Figure 7. A straight-lineextrapolat'on of th.e best fit to thedata for Reynoldsnumbers of 3x10' and greater was used to obtain values of lift-curveslope at low Reynoldsnumbers. Th.ese values were thenused to correct th.e quotedangles of attack at constant values of liftcoefficient. In making th.e extrapolations, account was takenof the variation of lift-curveslope with thickness-to-ch.ordratio at constant Reynolds number as sh.own inFigure 8. Furthermore,an effort was made toensure that the extrapolationtrends were compatible with. th.e trends of th.e highReynolds number data. The magnitude of thecorrection for a typicalsection is illustrated in Figure 9. Table I indicates which airfoil section data required this correction.

4.2.2 Preparation of theSection Data for Computer

The airfoil section data, corrected as requiredusing the previouslydiscussed procedures, are prepared in the form of specialtables, which are used in th.e computer.For a given airfoi2 th.ese data represent the relationships of c[ vs. tl ,Cdo vs. Cl , and Crnc/4 vs. C1 forconstant values ofReynolds number. Typicaltabulation of these section characteristics suitable for th.e use in the computer are shown in Figure 10.

50 .12

NACA 64409

.10

.12 NACA 64412

UI r .10

.12 NACA 64415

.10 .5 1 2 34 5 20 Reynolds number x 0 Data from NACA TN 1945

Figure 7. Extrapolations of Lift Curve Slopes at Low Reynolds Number NACA 64418

a, a 0

NACA 23012

e .rl0 c, 0 al m NACA 23015

Reynoldsnumber x 0 Data from NACA TN 1945

Figure 7. Continued Figure 7. Concluded " . . .. .- . "- . . -

Thickness-chord ratio, t C

Figure 8. Variation of Section Lift-.CurveSlope with Thickness-Chord Ratio at Constant Reynolds number NACA 644 Sections

54 1.

Angle of attack - degrees

Figure 9 - Corrected Lift Qrves for NACA 64-421 Airfoil at Low Reynolds Numbers TABLE I, - AIRFOIL SECTION DATA AVAILABLE FOR USE WITH THE COMPUTER FROG-

I I I 63- 4XX I I

I I 64-4XX

! 2 4XX

a Data correctedat Reynoldsnumbers below 3x10 6 . b No dataavailable for section with 60' splitflap. R ynold'-. -- . . . - . .. -o~-7". 1.0 1.5 1 2.0 ~ ~__._.. Cf -90.8 0 0 0 -14.0-0.34 -0.40- -0.50 -0.60 / li.6 1:37 1142- 1:48 1: 47 20.0 1.22 1:28 1130 1126 / 90.6 ___.10.0 Titi- 1.51 -" max I" d 13.4)

Table of Cd Values

. "" 0.7 1.0 ." 2.000 2.0002.000 2.000 0.011 0.0090.009 0.007

0.008 0.608 0.6070.607

0.50 0.640 0.620 0.619 "_2.000 "_ 2.000 2.000 2.000 0. -"-l-+o0. 0.-.

Table of Cm Values

"\ " . . ~ Reynolds Number x~O-~ J " \, 0.7 - 1.0 " t;\ 0. 0. 0.

C mc '4

* For computercontinuity only.

Figure 10. - Method of Tabulation of Section Characteristics.

57 The tabulationof section lift data is consideredto be most critical as compared to the two sets ofdata cited above. For a given airfoil thickness-ch.ord ratio, values of lift coefficient are carefully read at selected angles of attack for eachReynolds number so as to best define the lift-curves especiallyin th.e vicinity of Cl max.. Large scale plots of Cl VS.Q (e.g. NACA originals) are recommended for this purpose for improvedaccuracy.

Th.e valuesof lift coefficientth.us obtained are entered in an array as shown in Figure 10 with th.e first and last entries ofangle of attack being -90° and +900 corresponding to lift coefficientvalues of zero and 10.0 respectively. Th.e latter value of section lift coefficient is enteredonly for thepurpose of the computer in order to avoid computational discontinuity in the case of wings with. part-span fully deflected flaps. The bottom two rows of the arraycontain the values of maximum liftcoefficient (c[max) and the correspondingangles of attack at which these first occur (amax) . Th.is procedure is repeated for each value of airfoil thickness-chord ratio for which data is available.

Similarly,using the plots of cdo vs. cI and cmd4 vs.C~ th.e drag and pitching moment tablesare prepared and tabulated as shown inFigure 10. Inthese arrays of data th.e last two rows are entered as zeros. Thus, a libraryof section ch.aracteristics tables is prepared. The data is key-punchedand storedready for use in th.e computer. The families of airfoils for wh.ich datahas been prepared are summarized in Table I.

4.2.3 AirfoilData Table Look-up Procedures

The basic airfoil data are read into th.e computerrow-wise and stored on tape.During execution of the program the data is readfrom tape into core in the form of files. Th.e arrange- mentand designationof the files is sh.own diagrammatically inFigure 11. Each file must containat least two,but not more thanfive,levels or values ofthickness-chord ratio. Each level, or each tableof data, is limited to 25 rowsand 12 columns. Th.is file size is adequatefor most purposes,but may be increased if desired bychanging th.e specifications relating to file size in the program. Linear interpolation is usedthrough.out and is performed first for th.e requiredvalue of Reynolds number th.enthickness- ch.ord ratio and finallyfor the given value of camber. Wh.en th.e requiredangle of attack is outsidethe range of the maximum angles of attack listed in the table for the two bracketing

58 interpolates File 1 cc VS. Q

Subroutine 'ARC'

File 2 C,A vs. e1 "" . U

~, Eubroutine 'LOOK': interpolates ,- within each. level __

File 4 cf VS. Q File 20 CC vs. Q with flap deflected with flap deflected

Airfoildataforroot Airfoil datafortip camber level eg. 230XX camber level eg. 430XX Figure 11. - SchematicRepresentation of Section Data Storage in the Computer.

I valuesof the parameters under consideration, simple linear interpolation formulae are utilized with no special order of interpolation. A specialcomputational procedure is required to obtainvalues of lift coefficient when theangle of attack falls betweenthe tabulated values of arnax. Thisprocedure is briefly described in th.e followingparagraphs as an aid to understanding the program listing.

UsingFigures 12(a) and 12(b),the values of and ‘l max at the required value ofReynolds number, Re , are determined for each.of thebounding values of th.ickness-chord ratio,(t/c), and(t/c)2 . Thisyields values of liftcoefficients at the points , and m2 , respectively. Dependingon whether the given valueof angle of attack, Q , is greater or less thanthe values of Qrnax , appropriatevalues of Ct (denoted by XI , x2 1 areobtained for each bracketing value of thickness-chord ratio.

Knowing the values at points ml and m2 , new values of ctmax and amax arecalculated corresponding to the required value of thlckness-chordratio and aredenoted by the point m3 . Using thepreviously computed values at points XI (or X2 1 togeth.er withthe values atm3, th.e above interpolationcycle is repeated toobtain the value of ct at th.e requiredth.ickness ratio.

Th.is valueof Cl now correspondsto the required values of Reynolds numberand thickness-ch.ordratio, but applies only to the camber levelassociated with the tip airfoil series. The aerodynamicdata for the root airfoil series is thencalled into core andth.e process is repeated. Th.e finalinterpolation sh.own in Figure 12(d) is performedfor th.e correctvalue of camber level in the sameway asthat used for thickness-chord ratio.

4.3 DESCRIPTION OF THE COMPUTER PROGRAM The computationalprocedures described in Section 4.1 h.ave been programmed for use on the NASA CDC 6600 series computer locatedat LangleyResearch Center. Th.e program is writtenin theFortran IV machinelanguage. An internallisting of the program is presented in Appendix A and a block diagram illustra- ting the major logic features is presentedin Figure 13.

Th.e program is initiated by reading in the basic configura- tionparameters punchedon cardsas indicated in Figure 14. The values of either aerodynamic or geometric twist may be input. Whichever twist is specifiedthe column reservedfor the oth.er twist must contain 100. Columns 1 to 11 on card #2 containthe maximum allowabledifference between the calculated and approximatevalues of Cl ‘/b at th.e end of eachiteration. A value of.001 was used in the computationspresented later in this report.

60 1:) 1:) 1 (5)2

\ \'\ \ "Re

Re Re, t/c

(512

Q a

Figure 12. Nomenclature for Developing InterpolationFormulae.

61 CALCULATE YES TRANSFORMATION BEGIN f-"PARAMETERS c2+ CALCULATE READ CASE DATA OR READ IN NO TABLES ONTO -L n, ETc CONFIGURATION 1 - GEOMETRY

t CALC. FACTORS CALCULATE MULTI PLIERS 2 -DIMENSIONAL SECTION DATA Pmk- 7 i I + PRINT OUT CALCULATE DISTRIBUTION OF CHORD,TWIST acK/6, "i ETC.

CALCULATE FIRST RE AD FIRST PRINTFIRSTREAD OUT APPROXIMATION TO VALUE OF QB CASE HEADING LIFT DISTRIBUTION

"I "I I I T I

READNEXT

+ I VALUE OF aB + CALCULATE CALCULATE INDUCED CALCULATE NEW ANDEFFECTIVE WING ETC.AND LIFT DISTRIBUTION SECTION ANGLESOF PRINT OUT - ATTACK A

CALCULATE BElTER APPROXIMATION TO LIFT DISTRIBUTION t1"' SELECT VALUES OF OB SO AS TO DEFINE EXACT STALLING ANGLE AND REPEAT CALCULATION I

FIGURE 13 COMPUTER PROGRAM BLOCKDIAGRAM

62 No. - 1% r bf I x b

No. 2j O=No 6 A A B H 4, Flap fXZEa l=Flap

No. --\

No. 4 Levels, Title options, etc. _. x-. .._ ,.~.. . ". -=..\./--... i "- ',// - .

No. 51 Angles of Attack

No. 61 Angles of Attack Normally the distribution of suchplanform parameters as chord, twist, localReynolds number, etc. are calculatedbut provision is made to read these in if the planform is not trapezoidal. The programperforms the computations using 10 controlpoints per wingsemi-span. This number of stations is usuallyadequate for most purposes, h.owever, if it is desired to increase (or decrease 1 th.e number of points th.e programcan easily be modified.

Having calculated,or read, th.e geometricparameters and computed theparameters governing fuselage transformation (if a fuselage is present), the values of the multipliers Prnk and 'I; are computedand stored.If the calculation is for a wing with. a deflectedpart-span flap the values ofthe parameters associated with a spanwisediscontinuity in angle of attack are computed. Th.e coefficients of thematrix Kij , given by equation(30b), @re now computed using a matrix inversion subroutine to obtain successiveapproximations to th.e liftdistribution. If the calculation is for a flapped wing the programbranches to compute the two load distributions required to obtain th.e factors used in alteringthe two-dimensional section lift data. Havingobtained th.esefactors the basic program iterativeloop is entered and executed until a lift distribution is calculated which. agrees with the guessed distribution to within the required tolerance. The computed distributions of section lift coefficient, etc., and thecorresponding integrated values are immediately printed out for each case run.

If,at anypoint on thewing, the stall is detected,i.e. the computed valueof effective section angle of attackexceeds that for maximum lift,the computations are th.en repeated for a value of angle of attackhalf-way between the last two values.If at this intermediate value the wing unstalls the program increases th.e angle of attack by 0.2 dggreesuntil stall again occurs or untilthe increments total 1 . Similarly,if stall is still detectedat the intermediate value, the angle of attack is decreased until the wing is unstalled or until th.e total decrease equals lo. Alternatively, if, for a given body angle of attack wing stall is notobtained, the computations are performed for th.e next inputedvalue of body incidenceuntil the value of aB = 99 is encounteredwhereupon the calculations are stopped. A typical print out of th.e final results is presented in Table 11.

The computerprogram described herein can be used to predict th.e distributions and the integratedvalues of lift, drag and pitching moment coefficients for wings of trapezoidalplanform withzero sweep in th.e presence ofa fuselage at all angles of attackup to andincluding stall. In addition, these computations

64 64 2 SERIES FLAP CASE

SPANWISE STATIONS ( 11 $.57711503E-01 ( 21 9.61459121E-01 ( 31 9.02092175E-01 ( 41 8.21185699E-01 ( 5) 7.20940345E-01 I 61 6eC4219115E-01 ( 71 4.74712490E-01 I 81 3.37573147E-01 9) 2.02203541E-01 I101 1.00000444E-01 (111 -2.02203541E-01 I121 -3.37573147E-01 (13) -4.74712490E-01 (141 -6004219115E-01(151 -7.20940345E-01 (16) -€.21185699E-01 (17) -9.02092175E-01 (181 -9.61459121E-01 I191 -9.97711503E-01 (

ALPHA MAX ( 11 1060889831E+01 I 21 1.61635207E+01 I 31 1.63227454€+01 ( 41 le66417263E+01 I 51 1.72603411E+Ol I 61 1.85084020EtOl 7) 2.37034870E+Ol I 81 1.25746196E+01 I 91 1.39745350E+Ol1101 1.43900028E+OL I I 1111 1*39745350E+Ol 112) 1.25746196E+01 (131 2.37034870EtOl t 141 1.85C84020E+01 115) 1.72603411E+OL 16) 1.66417263E+01 (171 1.63227454€+01 (181 1.61635207E+01(191 1e6088983 1E +01 (

CL MAX I 11 1~55000003Et00( 21 1.55650944Eb00 I 31 1.57042592E+00 ( 41 1.59829929E+00 ( 51 1.65222564E+00 I 61 1.76061569E+00 I 71 2.12708990€+00 I 81 2.55834961E+00 I 9) 2.6458441OE+OO 1101 .2.73499988E+OO 2.69584410E+00 112) 2.55834961Et00 113) 2.12708990EeOO (14) 1.76061569E600115) 1.65222 564E+00 ~ 1111 I161 1.59829929E+00 (171 1.57042592E+00 (181 I. 5565C944E+00 ( 19) 1.5500C003E+00 (

THICKNESS / CHORD DISTRIRUTION 1.38603977E-01 cn I 11 1.20152566E-01 I 21 1.22569392E-01 ( 31 1.265271RBE-01 41 1.3192C953E-01 ( 5) cn I 61 1.46385392E-01 ( 7) 1.55019167E-01 ( 8) 1.64161790E-01 ( 91 1.73186431E-01 110) 1.79999970E-01 I111 1.73186431E-01 (121 1.64161790E-01 (131 1.55019167E-01 (141 1e46385392E-01 15 1 1.38603977E-01 (16) 1.31920953E-01 11711.26527188E-01 (181 1.22569392E-01 (191 1.20152566E-01 I

SECT ION REYNCLOS NUMBER I ( 1) 6~00060006E+00 ( 2) 6~00060006E+00( 31 6.00060006E+00 ( 41 6.OCO600C6Et00 I 51 I I 61 6~00060006E+00 ( 71 6.000600C6E+00 I 81 6~00060006E+00 I 91 6~000600C6E+00I101 (111 6.OC060006E+00 (121 6.00060006E+00 113) 6~000h000hE+00(141 6.0006C006E+00 (151 1161 L~00060006E~001171 6~00060006E+00(181 6.00060006Et00I191 6.00060006E+00 I

CHORD DISTRIBUTION I 1) 1~00000000Ee00 I 2)1~00000000E+00 I 31 1~00000000E+00 ( 41 1~COOOOOOOE+00I 51 I 61 1.00000000E+00 I 711.00000000E~00 I 8) 1.00000000E+00 I 9) l~OOOOOOOOE+OO (101 (111 1~00000000E~001121 L~OOOOOOOOE+OO t 131 1~00000000E~00(141 1~CCOOOOOOE+00 115) 1161 1~00000000E+00 1171 1~00000000E+00(181 1~00000000E+00I191 1.000CCOOCE+00 (

GEOMETRIC TWIST 11 -4.92881352E+00 I 21 -4.72977270EtOO ( 31 -4.40382321€+00 I 41 -3.95561265E+00 I 5) -3.40922351E+00 I 6) -2.76837490E+00 ( 71 -2.05732909Et00 I 81 -1.30437645Et00 t 91 -5.61140405E-011101 -2.43856132E-06 1111 -5061140405E-01.1121 -1.30437645E+OO 1131 -2.05732909E+00 ( 14) -2.76837490E+00 (151 -3.40922351E+00 1161 -3.55961265E+001171 -4.40382321Et00(181 -4.72977270E+00 (19) -4.92881352E+00 I

TARLE 11. Typical Somputer Output 642SERIES FLAP CASE

.f..f..f..f..f..f..f..f~.f..f*.f..f..f..f~.f..f..f..f..f..f..f..f..f..f..f..f..f..f..f..f~.f../../.~/../../*./..

BODY AYGLE OF ATTACK, DEG. . = 16.00 VALUE OF OISCRICINANT. = .001000 BODY HEIGHT/SPAN. = .10 B3DYWIDTH / SPbN...... -= .10 ASPECT RATIO = 6.00 WINGHEIGHT /SPAh. . . 0 - 0.00 YING aoDY INCIDENCE, DEG . . = 0 .oo TIPTHICKNESS CHCRD. . 0 = .12 ROOT THICKNESS CHORD - .18 GEOMETRIC TWlSTr DEC - -4.94 NUMBER OF SPANWISESTATIOIJS. = 20.00 AERODYNAMIC TWIST, DEG = -5 00 FLAPSPAN f WINGSPAN. = .45 TAPERRATIO. o = 1.00 FLAPSETTING, DEC. = 60.00 REYNOLDSNUMBER...... = 6.00 COORDIYATES OF MOMENT REFERENCEPOINT X= 0.00 2= 0.00

./../..f*.f..f..fO.f..f..f..f..f..f..f..f..f..fO.f..f..f..f..f..f..f..f..f..f..f..f..f.~f..f..f../..f..~..f../*

OISTRIBUTION CF SECTIONLIFT COEFFICIENT cn 1) 3.42250509E-01 ( 6.30955940E-0121 ( 8.65952551E-0131 I 1.06170561E+0041 ( 5) 1.24114608E+00 cn I1*43723537E+00 6) 7) 1.82981852EtOD I 81 2.23042330Et00 ( 2.42268737Et0091 (1012.54358422Et00 (11) 2.42268686E+00(1212.23042074E+00 (13) 1.82985557E+001.43723226E+OO(14) 1.24114578E+00(15) (161 1.C6170626Et00117)8.65954479E-01 (1816.30959085E-01 (19) 3.42254744E-01 1

STALL MARGINDISTRIBUTION ( 1) 1.2C774952E+00 I 9.25553438E-012) ( 7.04473366E-0131 ( 5.36593679E-0141 t 51 4.11079557E-01 ( 3o23380322E-016) ( 2.97271378E-0171 ( 81 3.27926310E-01 I 9) 2.73156732E-01 (101 1.91415661E-01 (111 2.73157242E-013.27928873E-01(12) 11312.97234334E-01 (1413.23383436E-01 (1514.11079859E-01 (1615.36593023E-01 (17)7.04471438E-01 (18)9.25550353E-01 119)1.20774529E+00 (

BODY ANGLE OF ATTACK. DEG. = 16 e00 LIFTCOEFFICIENT . = 1.666010 ...... 0...... 0...... 0...... 0.0...... 0.'00*..~..~.*..**.,

TABLE 11. Concladed $1 incorporatethe effects of linearspanwise variation in section camber forunflapped wings. The effect of a deflectedpart-span flap on thelift distributions is included. However, drag and pitching moment results are notincluded for these cases because of thelack of section drag and pitching moment characteristics for flapped airfoils. The computerprogram described above constitutes a part of this report and is therefore available for public use through ComputerSoftware Management and Information Center (COSMIC), as stated in Appendix B. 4.4 RESULTS OF SAMPLE CALCULATIONS The computerprogram was used to calculate the characteristics of threeunflapped wings and onewing having a 60% span splitflap. Thesecomputer results were correlatedwith the correspondingtheoretical predictions ofReferences 1 and 2 and theavailable experimental data. Figures 15, 16, and 17 present computed lift, drag and pitching moment characteristics for unflappedwings of aspect ratio 8.04, 10.05 and12.06, and Figure 18, shows thevariation of lift coefficient with angle of attack for a flapped wingof aspect ratio 9.02,having a 60% span, 20% chordsplit flap. Included in these figuresare typical spanwisedistributions of section lift, drag and pitching moment coefficients.

The correlation of the computer results versus theoretical characteristics ofReferences 1 and 2 and the availableexper- imentaldata are performed, where possible on thebasis of the integratedvalues as well asthe spanwise distributions of wing characteristics.Unfortunately, measurements ofwing characteristics in the presence ofa fuselage,especially of thespan loading,are extremely difficult to obtainfor the class ofwing- fuselagecombinations considered herein, As a result,there is a lack of suitableexperimental data of thetype required for thepresent comparisons. Some experimentaldata exists for swept wingbody combinations but such data is notapplicable for correlations with the straight wing results. Examining Figures 15 through18, it canbe noted that the computer results are in good agreementwith the available experimentaldata. The slightdifferences between the present computations and those ofReferences 1 and 2 are attributed to hand versusmachine fairing of the section characteristics.

67 1.

1. .

, CD “CB Pitching-moment Drag coefficient Angle of attack, coef f iclent , Cm

Geometric Washout = 4.5’ Root Section 4416 Aspect Ratio = 8.04 Tip Section 4412 Reynolds Number = 4.32~10~ Taper Ratio = .4

Figure 15. Exp3rimental and Calculated Characteristics for a Wing of Aspect Ratio 8.04. 0 04 .6 .8 Fraction semispan 032

024

016

.008

Figure 15. Concluded

I I4 U

al u0

Drag coefficient, CD Angle of attack,oEB Pitching-moment coefficient , Cm Geometric Washout = 3.5' Root Section 4420 Aspect Ratio = 10.05 Tip Section 4412 Reynolds Number = 3.49~106 Taper Ratio = .4

Figure 16. Experimental and Calculated Characteristics for a Wing of Aspect Ratio 10.05 Fraction semispan .024

016

.008

- 080

- .090

- .loo

Figure 16. - Concluded

71 Pitching-moment Drag coefficient, CD Of attack,

Geometric Washout = 3.0' Root Section 4424 Aspect Ratio = 12.06 Tip Section 4412 Reynolds Number = 2.87~10~ Taper Ratio = .4

Figure 17. - Experimental and Calculated Characteristics for a Wing of Aspect Ratio 12.06. ~- Fraction semisDan

Figure 17. Concluded

73 Fractionsemispan (a)Calculated span load distribution €or LOo angle of attack.

Angle of attack

(b) Comparisonof experimental andcalculated lift curve.

Figure 18. Experimentaland Calculated!Characteristics for Wing with 60% Flap;Aspect Ratio 9.02; TaperRatio 0.4; Washout 2'.

111 II I I SECTION 5 PARAMETRIC INVESTIGATION The computer program was used to determine the effect of wing geometry on the spanwise lift distribution, the location of the initial stalling point and the corresponding of value the effective maximumwing lift coefficient,CLmax. A similar investigation based on a linearized formulation of the lifting- line theory is reportedin Reference 49. Th.e present results may be considered as an extension of this work in that a broader range of parameters was investigated and the more accurate nonlinear theory was employed. 5.1 RANGE OF PARAMETERS The range of parameters selected for this study is representative of that applicable to present-day 1igh.t aircraft. Computations were performed for wings utilizing the three basic airfoil series commonly encountered,NACA 64 series, 44 series and 230 series. These calculations were selected to show the effect of the three major geometric parameters, aspect ratio, taper ratio and section thickness, together with the influence of washout and linear camber variation from toroot tip. Varia- tions in flight Reynolds number, based on the wing mean aerodynamic chord, were also investigated as were the influences of a part- span deflected flap and the presence of a fuselage. The variation of wing thickness and ch.ord length. was linear in all cases but the distributionof washout was non-linear in contrast to that used in Reference49. Th.e non-linear wash.out distribution chosen ensures straight-line leading and trailing edges. Washout was aerodynamic which is defined as the angle between the zero-lift lines of the root and tip sections. All wings were of trapezoidal planform without rounded tips, and zero sweep. The investigation encompassed 331 different configurations which are summarized in Table111. The configuration defined anby aspect ratio of6, a Reynolds number of 6x106 and a root and tip thickness chord ratio of0.18 and 0.12 respectively was selected as a standard case for systematic variation of the parameters. These variations included the values of aspect ratios6, 8, of and 10, aerodynamic washout ofOo, 2%', 5O, and 7k0, taper ratios of 0.5, 0.75 and1.0; root th.ickness ratios 0.21,of 0.18, 0.15, and 0.12; and tip thickness ratios 0.12of and 0.15. The complete rangeof calculations were not performed for untapered wings having 7S0 washout since this amount of twist would not normally be used on wings of this planform. However, to assist in establishing trends, fewa computations were obtained for this washout.

75 TABLE 111 - SUMMARY OFCONFIGUMTIONS STUDIED (a> Wings of NACA 44XX Airfoil Section i Tip t/c \Aerodynamic e. Nob j Washout -Deg. 10- I I I " Comments I 1. .75 .5!6 8 10i.12 .15 .18 .21!.12.15 2.5 5.0 7.: 369 1 .18jO 1-.- x x x ;x X ;x IX x x X -i xxx~xj X 'X xx X Aspect x x X' X tx xx x X Ratio i xxx X ,x X X Variation x X' x x! X 'X I X X Ix X "_ . X "I x x x jx 'x x x X x x x Ix ix x x X Root (t/c> I x x ix 1 X X Variation 1I x x Ix ! X X I

.. . X -. . . t X xx X X X X xxxX X X X Tip (t/c> j X X X X X Variation Ix X X X X I Ix X X X X ." X I X X I i X X Reynolds NO. i X Variation ! x x x ]X I X x/xX x

Total number ofconfigurations = 106 TABLE I11 - SUMMARY OF CONFIGURATIONS STUDIED - Continued (b) Wings of NACA 230XX Airfoil Section

-. -- -- " I 1 Taper ; AspectRoot t/c 1 Tip t/c !Aerodynamic;Re. N0-I Ratio i Ratio ! i Wash.out-kg. I x lom6 I I ! ! Comments ' '1. .75.5 6 8 10/.12.15 .18 .21!.12.15 .1810 2.55.0 7.5( 3 6 9 I I I i ! ,x x x,x X ix ix x x 4 x: I

IX X ~ X x x x ;, 'x !x x x ! Aspect I !x x x; X ix /x x x ! X 1 Ratio I I x x ]x X x X / X j Variation j X X x. x X !x ! xj x j j ".. -. . . . ."_____ xxxx x :x I X /x :x x x I X IX !x x x ' XII Root (t/c) j I I X~X I x ~ x j , Variation I x x Ix I X /x XI x 1 I xxx X /x I x!-". XI - I xxxx X I X /x x x i x : Tip (t/c) I

xxx X I X ~ ""x x x :: :: :: +. . +- ."Variation ---. - xxxx X X 1 xxxx X jx x 1 Reynolds No. xxxx X !x X/X Variation xxxx X X XI X

Total number of configurations = 99 TABLE 111 - SUMMARY OF CONFIGURATIONS STUDIED - Continued (c> Wings of NACA 642XX Airfoil Section , .Taper "" Aspect 1 Root t/c Aerodynamic 1 Ratio Ratio : Washout-Deg. . .-. . . ". .. -.-. .- ... .. - .. -. . . Comments '1. .75 .5. 6 8 10,.12 .15 .18 .21! .12 .15 .18 0 2.55.0 7.: " . +"" -. -.- -. . .- - - .- . ,xxxx X X xx x x: .xx X' x X X xx x X Aspect :x x x X X X xx x I x I Ratio ~ xxx X X X x , Variation xx X X X X x: x x: X X X I X I ." ." ~__~- - " 1. Ix x x x x/x 'X x x ]x x x:x X )x !x x x xi jx x x x X IX x : Root (t/c> X ~ Variation \ xxx XIX jx x x x. I x x .x X !X I X x I X #X I X XI x x,x ___ ~ . .. -, ____" 'X x x.x X X 'x x x

Total number of configurations = 99 TABLE I11 - SUMMARYOF CONFIGURATIONS STUDIED - Concluded (d) Effects of Camber, Fuselageand Flaps on Wings of Various NACA Airfoil Sect ions. ~-~ I -7"" j Taper I Aspect!Root : Tipi Aerodynamic j Re.No i Wing/Body Flap Span ! ' Ratio \ Ratio 1 t/c t/c; Washout-Deg. ; x I Incidence,! Wing-Span i "___."" - ". - " -- - 000 Comments ! '1. .75 .5 : 6 1 .18 : .12. 0. 2.5 5.0 3 6 9 10 2 4 1-45 .go -75I Effect of ! 0.2 Camber 1 Increase FuselageEffect,l High Wing I L=1/10 SDan

I Flap Effect

, "

Total number of configurations = 27

Grand total of configurationsstudied = 331 5.2 METHOD OF PRESENTATION OF RESULTS

The effects ofvarious design parameters on the stalling ch.aracteristics of unsweptwing aircraft are h.ereinpresented in th.e formof plots sh.owing the stall margindistributions, location and movement of stall boundaries and the maximum values of integratedwing lift coefficient.

5.2.1Stall Margin Distributions

The stall margin,A Ct , is defined as th.e differencebetween the maximum section lift coefficient and the section lift coefficient when thestall first occurs on the wing.Figure 19 shows typical distributions of Cl ,Cf rnax andA CI computed for the conditionsindicated. The spanwiselocation of zero stall margin correspondsto the point ofonset of stall and the rate ofsepara- tionof the ACl curve from the horizontal axis indicates the rate of stallpropagation across the span. A wing is usually assumed to have sufficient stall margin if a valueof ACl = 0.1 is indica- tedat the 70% semispanstation.

Since it wouldbe impractical to present all th.ree distributions (i.e. Ct , Ct max , and Act 1 for each of the 331 cases computed, in the manner presented in F-igure 19,only the distributions of stall marginare given.

5.2.2 StallBoundaries

Ingeneral, th.e curverepresenting the spanwise lift distrib- utionat the onset ofwing stall is tangentto the section Clrnax curveat more thanone Doint. This implies that a few adjacent wing sections (i.e. a portion of the wingspan) can be stalled simultaneouslyat a givenoperating condition. The limiting valuesof spanwise locations encompassing these stalledsections aredefined as the stallboundaries. Using stall margin distributions, such. as shown inFigure 19, the inner and outerboundar- ies of th.e stalled wing areacan be estimated as the spanwise locations where ACl= 0.01. Furthermore, th.e movement of these stallboundaries affecting the growth and the propagationof wing stallareas can be expressed as a function of thebasic designparameters. For example,using Figures 19(a> and 19(b1 the stall areas for th.e unflappedand th.e flapped wing configura- tionsconsidered are defined by thestall boundaries 50% to 68% and 10% to 40% of the wingspan, respectively. 5.2.3 Maximum Lift Coefficient Maximum lift coefficient is an important criterion in assessing wing stall ch.aracteristics as affected by the variation ofbasic design parameters. Th.is liftcoefficient is defined asthe integrated value obtained from the spanwise lift distributions when any one of the wing sections is stalled. Such stall

80 .8

.1 0 0 .4 .6 .8 1.0 Fraction semispan (a) Unflapped wing - 230 series sections.

1. . 0 .2 .4 .6 .8 1.0 Fraction semispan (b) Flapped wing - 60% span flap - 642 series sections.

Figure 19. - Typical Lift Distributions AlongWing Span

81 is obtained when thelocal section lift coefficient Cf equals th.e maximum value (Cf max 1 of th.atsection. Th.is valuedepends primarily on sectionthickness-chord ratio, Reynolds number and theairfoil type. Typical variations of th.e maximum section lift coefficient (Cfmax 1 with th.ese parameters is sh.own in Figure 20. The effects ofvarious design parameters on integrated maximum wing lift coefficient are herein presented in the form of carpetplots. These plots facilitate linear readings ofnon- linear relationshipsbetween th.ree variables and th.us permit more accurateinterpolation (or extrapolation)for intermediate values oft'ne parameters. However, sincethis methodof data presentation is notas commonly usedas the familiar X-Y plot,an explanation of theuse of carpet plots is presentedin the followingsub-section.

5.2.4Carpet Plots

The procedurefor constructing and readingcarpet plots can bebest illustrated by th.e followingexample: The carpetplot shown inFigure 21 represents th.e variation of CLmax with Reynolds number and taper ratio for a wingemploying 230 series sections and a constantvalue ofwashout of 7%O. Curve (abc) on this carpet is a conventional(x-y) plot of CLmax v Reynolds number for a constantvalue of taper ratio of 0.5. The indicatedhor- izontalunit distance corresponds to a change in Reynolds number of 1x106.Thus, point (a) corresponds to Reynolds number of 3x106and poi t (b) which is 3 horizontalunits from (a), corresponds to 6x10' and point (c) to 9x106. The curve(def) presents a similar plot for a taper ratio of0.75. However, instead of plottingdata for x = .75 on the same horizontal scale as th.at for curve ( abc 1 a new scale is ch.osen whose origin is 2% h.orizonta1units to th.e right of th.e point (a), reflecting th.e change in taperratio from0.5 to 0.75. Thus, as regards changes in taper ratio, each. horizontal unit corresponds to a changeinXequal to 0.1. Similarlycurve (ghi) for X = L. 0 is plotted 5 units to th.e right of point (a) or 2% units to therigh.t from point (b). After a new origin is selected for eachtaper ratio (i.e. point(a) for X= 0.5,point (d) for X = 0.75and point (g) for X= 1.01, the plotting of th.eCLmox vs. Re curves for each taper ratio is accomplishedin th.e conventional way. If allpoints corresponding to the same valueof CL max Reynolds number are now joined,e:g. curves (adg) (beh) and (cfi), the resulting curves show the vanation of CLmax with taper ratio forconstant values ofReynolds number.

Reading the carpet is as simpleas constructing it. If theva ue of CLmax is required,say, for x = 0.62and Re = 5.3~10&= it canbe obtained as follows: For all three values of taperratio locate and joinpoints (j), (k) and (1) correspondingto Re = 5.3~106. This is accomplished bymoving 2.3

82 I

Reynolds Number x l@

Figure 20. Variation of Vmax withReynolds Number andThickness-Chord ratio - 230 series sections, i :

=In

1 i

Reynolds Number

Figure 20. Continued - 44 series sections 1. cf rnc

Figure 20. Concluded - 642 series sections 1

hax

1.:

1.1

Figure 21. - Variation of Chax with Reynolds Number and Taper Ratio.

86 horizontalunits towards the right from point (a) to locate point (j) on the X = 0.5curve, 2.3 horizontal units from point (d)to locate point (k) on th.e x = 0.75 curve and th.e same number ofunits from point (g) to locate point (1) on th.e x = 1.0 curve.Similarly, locate and join point (m) (n) and (0) moving 1.2 horizontalunits from points (a), (b)and (c) on th.e corres- pondingReynolds number curves,respectively. The point of intersection(p) of the curves (ihl) and (mno) yieldsthe required valueof CL~~~= 1.445 for X = 0.62and Re = 5.3~106.

5.3 COMPUTERRESULTS Presented in this section is a compilationof wing stall designcharts obtained from the computer program. These charts can be used in preliminary design of unsweptwing aircraft for determining optimum geometricparameters of a wing to yield good stallingcharacteristics. The effects of th.ese geometricparameters on stallingbehavior of straight wing aircraft are discussed in the followingpages. 5.3.1Effect of Aspect Ratio

Figures 22, 23, and24 show th.e effect ofaspect ratio on wing stall margins, stall boundariesand the values of maximum wing liftcoefficient, respectively. Each. of th.ese figures is presentedfor three different families of airfoilsections, i. e. 230,44 and 642 series, and for a rangeof wing taper ratios between0.5 and 1.0 andwing wash.out between 0 and 74O. Examining Figure 22 it canbe noted that an increase in aspect ratio results in a reductionof th.e stall margins atout- boardwing stations. This effect is minimized at highvalues of wash.outand wing taperratios. Furthermore, as can be seen fromFigures 23 and24, an increase in aspect ratio appears to h.ave little effect on the spanwiselocation of stall boundaries and yields only a smallincrease in wing maximum lift coefficient.

It cantherefore be concluded that although. wing aspect ratio is import ant from aircraft performance considerat ions, its effect on thestalling haracteristics is very small. Forthis reasonthe remaining stall results which. are presented in this section for aspect ratio of 6 onlyare considered to betypical and representativefor the range ofaspect ratios associated withpresent day 1igh.t aircraft.

5.3.2 ". Effect of Taper Ratio Figures 22 through24 also show th.at taper ratio is one of the mostdominant design parameters affecting wing stall characteristics. Forany fixed aspect ratio andwing washout an increase in taper ratio from x = 0.5 to X = 1.0 (rectangular

87 WASHOUT = 0 Deg. Deg. 2% 5 Deg. 7% kg.

0 2Y/b 10 2y/b 10 1 Taper Ratio = .5

0 Taper Ratio = .75

Aspect Rat io 6 "- 8 -.-.-.. 10 Root Section 23018 Tip Section 23012 Re = 6x106 0

L WASHOUT = 0 Deg. 2% Deg. 5 Deg. 7% Deg.

Taper Ratio = .5

aJ W

0 Taper Ratio = .75 .8 Aspect Ratio -6 -" 8 .4 -.- 10 Root Section 4418 ACJ TipSection 4412 Re = 6x106 0 WASHOUT = 0 Deg. .8

Taper Ratio = .5

0 Taper Ratio = .75

.8 Aspect Ratio - 6 "- 8 .4 - 10 Root Section 64218 Ac, Tip Section 64212 = I Re 6x106 0 Taper Ratio = 1 ~4 ~IFP. 22. Concluded WASHOUTDeg. =2% 0 Deg. 5 Deg. 7% Deg-.

Taper Ratio = .5 10

AEZ

U Taper Ratio = .75

Root Section 23018 8 Tip Section 23012 Re = 6x106 Au

L Taper Ratio = 1 Figure 23. Effect of Aspect Ratio on Wing Stall Pattern. WASHOUT = 0 Deg. 2% Deg. 10

TaperRatio = .5 10

Root Section 4418 8 Tip Section $412 Re = 6x10 AR

6 TaperRatio = 1 Figure 23. Continued

WASHOUT = 2% Deg.

1.4

1.5 WASHOUT = 5 Deg. 'kax

1.4

1.3

1.5 WASHOUT = 7% Deg. Root Section 23018 max TipSection g3012 Re = 6x10 1.4

Figure 24. Effect of AspectRatio and Taper Ratio on Cbaxm

94 l1q- -

WASHOUT 5 Deg.

CLTlax WASHOUT = 7% Deg. 1.4 Root Section 4418 Tip Section 2412 Re = 6x10

1.3

Figure 24. Continued

~~ 1.5

CLmaX

1.4

1.3 1.5

'Lmax WASHOUT 2% 1.4

1.3 1.5

'r+nax

1.4 WASHOUT = 5 Deg.

1.3

1.5

'hax WASHOUT = 7% Deg. 1.4 RootSection 64218 Tip Section64212 Re =' 6x106

1.3

Figure24. Concluded

96 wing) results in a substantial increase in stall margin on theouter portfon of th.e wing.This increase in stall margin is associatedwith a shift of stall boundariestoward the inner portion of the wing. The advantageof the favorable stalling characteristics obtainable by increasing wing taper ratio is somewhat offset by a reduction of wing CLmax and hence,for a given wing loading, an increase in stallingspeed. This reduction, whichcan be as high as 12% based on the CL rnax values for a rectangular wing, depends on the airfoil sections and wingwash.out. 5.3.3 Effect of Wing Washout- Washout is oftenused to promote desirablestalling characteristics. For a givenvalue ofwing liftcoefficient, twisting the tip section relative to th.e root sectionreduces the values of section lift coefficient in th.e tipregions and increases sectionlift coefficient at inboard stations. Since the distribution of section maximum lift coefficient is unaffected by twist, thenet result is to increasethe stall margins in the tip region and to sh.iftthe stall boundaries inboard of the wing. Th.ese effectscan be seen from Figures 22 and 23.

Examiningth.ese figures it canbe noted that for a taper ratio of 0.5 washout exertsrelatively small influence on the stall marginsat 70% semispan. As taperratio increases, however, the effectiveness ofwash.out becomes greater and is most effective for a rectangular wing (1 = 1). However,a rectangular wing is unlikely to require wash.out since,as discussed previously, wings of thisplanform normally exhibit good stalling characteristics. The beneficial effect of washoutappears to be offset by the adverseeffect of thelinearly diminishing Reynolds number. There- fore,the use ofwash.out seems most justified for moderatevalues of wing taper ratio.

Furthermore,Figure 24 indicatesth.at for fixed values of aspect ratio and taper ratio, wingwash.out tends to reducethe value of CL max . The amount of this reductiondepends on th.e wing sections and thevalue of washoutused.

Inaddition to theeffects discussed above, washout may affect wingperformance through. changes in both wing profile and induceddrag. The increasein induced drag coefficient due to washoutabove th.atfor an untwistedwing is presentedin Figure 25 for two values of aspectratio 6 and 10. Th.e data is for awing h.aving 230 series sections with root and tipthickness- chordratios of .18 and .12, respectively. As canbe seen, at low values of lift coefficient th.e use of washoutcauses an increase in induced drag while at high. values of CL washout reducesinduced drag. Increased induced drag levels

97 001

A CDi

001

0 AcDj .75

- 001

-.002

0 AcDi

- 001 1

-.002

-.003 Figure 25. - Incrementof Induced-Drag Coefficient Due to Wash.out, 230 series airfoilsection - aspectratio = 6 , Re = 6x106

98 Taper Ratio .5

AcDj

-. 001 .75

-. 002

- 003

-.00 1

“002

-.00:

Figure 25. - Concluded - aspectratio = 10

99 at low lift coefficients may impair cruise perfonnancedepending on the amount of theincrease relative to the overall drag coefficient of theairplane. Changes in profiledrag due to washout were found to be sufficiently small that their effects onwing performance can be neglected.

5.3.4 Effect of Root Thickness-Chord~~ ~~ Ratio

The effect ofroot thickness-chord ratio onwing stalling characteristicscan be depicted from Figures 26, 27 and 28. Th.ese figures are presented for an aspect rat io of 6 winghaving the tip thickness fixed at a constantvalue of 12% and the root thicknessvarying between 12% and 21%. Threefamilies of airfoil sections are considered; 230 series, 44 series and 642 series.

Thesefigures sh.ow th.at for the wingemploying 230 series airfoilsincreasing root thickness-chord ratio results in an increase in stall margins for outboardwing sections, a general inboard movement of th.e stallboundaries and a decrease in wing maximum lift coefficient.

Similar effects of th.e rootthickness-ratio can be noted for the wingemploying 44-series airfoils, however, in this case the variation in the stalling ch.aracteristics is less pronounced.

For th.e wingemploying 642 series airfoilsections, an increase in root thickness-ch.ord ratio causes a reduction in th.e stall marginson th.e outboardportion of th.e wingand tends to move the stall boundariesoutboard in contrast to th.e trends indicated by theresults for the oth.er series. Th.is effect is primarily due to the variation of Ct max with. thickness-chord ratio forthis particular airfoil series. As canbe seen fromFigure 20 the amount by wh.ich clrnax decreases with. increasesin section thickness-chordratios above12% is greatest for the 230 series airfoils, less forthe 44 series and least for the 642 series sections.In fact, for Reynoldsnumbers greater than 6x106 the 642 series shows a small rise in Cl rnax wh.en thesection th.ickness chordratio increases from .12 to .15.

Furthermore,for a givenspanwise distribution of section Reynolds number and thickness-chordratio the curve of Cfrnax versusspanwise distance will be flattest for the wingemploying 642 series sections. Th.is h.as th.e effect ofpromoting stall further outboard than would be the case for the wings composed of either 44 or 230 series sections.

The fact thatthe dependence of cC rnax on (t/c) is least for the 642 series airfoils is again reflected in the results for wing maximum lift coefficient as shown inFigure 28. For this case increasing root thickness-chord ratio results in the

100 WASHOUT = 0 Deg. 2% Deg. 5 kg. 7%. kg.

1 Taper Ratio = .5

0 Taper Ratio = .75

Root SecYTon -23012 "-23015 "-23018 -.--23021 Tip Section 23012 Aspect Ratio = 6 Re = 6x106 WASHOUT = 0 Deg . 2% Deg. 5 Deg.

Taper Ratio = -5

0 Taper Ratio = .75

.8 Root Section - 4412 "- 4415 -.-.- 4418 .4 -..-.. 4421 Tip Section 4412 Aspect Ratio = 6 Re = 6x106 0 Taper Kat io = 1 Figure 26. Continued WASHOUT = 0 Deg. 2% Deg. 5 Jkg.

TaperRatio = .5

r 0w

0 Ratio Taper = .75

Root Section -64212 “64215 “-64218 -*%4221 Tip Section 64212 Aspect Ratio = 6 Re = 6x106 0 Ratio Taper = 1 Figure 26. - Concluded WASHOUT = 0 Deg. 2% Deg. 5 Deg. 7% kg.

a. - Taber Ratio = -5 "

Y WASHOUT = 0 Deg. 5 Deg.

TaperRatio = .S

TaperRatio = .75

Root Sectdon 44XX TipSection 4412 AspectRatio 6 Re = 6x106

TaperRatio = 1 Figure 27. .Continued WASHOUT = 0 Deg. 2% Deg. 5 Deg. 7% Deg.

r 0 b\

TaperRatio = .75

Root Section 642XX Tip Section 64212 AspectRatio 6 Re = 6x106

Figure 27. Concluded Washout = 0 Deg. 2% Deg.

1. 5 Deg. 7% Deg.

1. Root Section 230XX Aspect Ratio = 6 Tip Section 23012 Re = 6x106 Figure 28. Effect of Root Thickness-Chord Ratio on Chax

107 Washout = 0 Deg. 2% Deg.

5 Deg. 7% Deg.

Root Section 44XX AspectRatio 6 Tip SectionTip 4412 Re = 6x106

Figure 28. Continued

108 Washout = 0 Deg. 2% Deg.

1.5

1.4

5 Deg. 7% Deg.

Root Section 642XX AspectRatig = 6 Tip Section 64212 Re = 6x10

Figure 28. Concluded

109 smallest reduction in the value of maximum wing lift coefficient.

5.3.5 Effect of Tip Thickness-Chord~~ Ratio

Figures 29 and30 show theeffects of tip thickness-chord ratio onwing stalling characteristics. The results are presented for a winghaving a root thickness-chord ratio fixed at a constant valueof 0.18 and tip thickness-chord ratios of 0.12 and 0.15. Limitedcomputations were performed for tip thickness-chord ratio of0.18 primarily for the purpose of establishing extrapolation trends for the variation of wing maximum lift coefficLent.

Figures 29 and30 indicatethat the effect ofincreasing the tip thickness-chord ratio is to reduce the stall margins and the valueof maximum wing lift coefficient.This is due tothe fact thatan increase in tip thickness-chord ratio resultsin reduced valuesof section maximum lift coefficient in the vicinity of the wing tip,thus yielding lower stall margins. Also, the reductionin the values of maximum wing lift ccefficient is smallerthan that due to increasingroot th.ickness-chord ratio. This is becausethe major effect of changes in tip th.ickness is confined to the tip regions where the wingloading is least.

Althoughthe effect of tip thickness-chord ratio on stall boundaries is notpresented, it is expected to be similar to thatof the root thickness-chord ratio discussed in the previous sub-section.

5.3.6Effect of Flight Reynolds Number

Sincethe maximum lift characteristics of most airfoil sections are inftuencedby Reynolds number (see Figure20) this parameter vtent1ally represents an effective means of controlling overall wing stall behavior.

The effect of flight Reynolds numberon stall margindistributions, stall boundariesand wing maximum lift coefficient is shown inFigures 31, 32 and33, respectively. These figures indicate that for wingsemploying 230 and 44 series sectionsan increase in flight Reynolds number results in increased stall marginsover the outboard wing stationand a shift of stall boundaries towardsthe wing root. However, exactlyopposite trends are indicated for wingsemploying 642 airfoilsections. An explanationof this behavior can again be obtained using the results ofFigure 20.

It canbe noted from this figure that for the 230 and 44 series airfoils the rate of increaseof maximum lift coefficient with Reynolds number is larger for th.e tipsections (t/c = 0.12)than thatfor the root sections (t/c = 0.18).This produces larger stallmarginsat the outboard (thinner) wing sectionswith increase in flight Reynoldsnumber.

110 WASHOUT = 0 kg. 2% Deg. 5 Deg. 7% kg.

Taper Ratio = .5 .8

r r r e4

0 Taper Ratio = .75

Tip Section - 23012 “- 23015 Root Section 23018 Aspect Ratio = 6 Re = 6x106

0 Taper Ratio = 1 ~i~~~~ 29. Effect of Tip Thickness-Chord Ratio on Stall Margin Distribution. WASHOUT = 0 Deg. 2% Deg.

0 1 0 1 TaperRatio = .5

TaperRatio = .75 .a TipSection - 4412 ”- 4415 .4 Reot Section 4418 AspectRatio = 6 Re = 6x106

0 TaperRatio = 1 Figure 29. Continued WASHOUT = 0 Deg. 2% Deg. 5 Deg. 7% Deg.

Taper Ratio = .5

0 TaperRatio = .75

Tip Section - 64212 "- 64215 Root Section 64218 AspectRatio = 6 Re = 6x106

0 TaperRatio = 1 Figure 29. Concluded 111 I I i

WASHOUT = 0 Deg. 2% Deg.

5 Deg. 7% kg.

1.5

1.4

1.3

Root Section 23018 AspectRatio = 6 Tip Section 230XX Re = 6X106

Figure 30. -Effect of TipThickness-Chord Ratio on Cbax

114 WASHOUT = 0 Deg. 2% Deg. -

5 Deg. 7% Deg.

1.5

1.4

1.3

1.2

Root Section 4418 AspectRatio = 6 Tip Section 44XX Re = 6X106

Figure 30. Continued

115 WASHOUT = 0 Deg. 2% Deg.

5 Deg. 7% Deg.

Root Section 64218 Aspect Ratio - 6 Tip Section 642XX Re = 6X106-

Figure 30. Concluded WASHOUT = 0 Deg. 2% Deg. 5 Deg.

Taper Rat .io = .5

Taper Rat :io = .75

Reynolds Number - 3x106 ”- 6x1066 ”.- 9x10 Root Section 23018 Tip Section 23012 Aspect Ratio = 6 ‘Taper Ratio= 1 Figure 31. Effect of Reynolds Number on Stall Margin Distribution. WASHOUT = 0 Deg. 2% Deg. 5 Deg. 7% Deg.

TaperRatio = .5

TaperRatio = .75

Reynolds - Numbgr 3x106 ”- 6x106 -e-#- 9x10 Root Section 4418 TipSection 4412 AspectRatio = 6 TaperRatio = 1 Figure 31. Continued WASHOUT = 0 Deg. 2% Deg. 5 Deg. 7% Deg.

Taper Ratio = .5

0 Taper Ratio = -75 -8 Reynolds Number - 3x1066

-0- 6x106 -4 --- 9x10 Root Section 64218 Tip Section 64212 Aspect Ratio = 6 Taper Ratio = 1 Figure 31.Concluded

I WASHOUT = 0 Deg . 2% Deg. 5 Deg. 7% Deg.

Taper Ratio = .5

Taper RatTo = .7!5

Root Section 23018 6 Tip 23012 Section

" Aspect Ratio = 6 Re ~- 3 Taper Ratio = 1 Figure 32. Effect of Reynolds Number on Wing StallPattern WASHOUT = 0 kg. 2% Deg. 5 Deg. 732 kg.

6 Re 3 0 10 10 10 1 Taper Ratio = .5

6 Re 3 Taper Ratio = .75

Root Section 4418 6 Tip Section 4412 Aspect Ratio = 6 Re 3 Taper Ratio = 1 Figure 32. Continued WASHOUT = 0 Deg. 2% Beg. 5 kg. 7% kg.

'Taper Ratio = .5

TaperRatio = .75

RootSection 64218 6 Tip 64212 Section AspectRatio = 6 Re 3 TaperRatio = 1 FigureConcluded32. WASHOUT = 0 Deg. 2% Deg.

5 Deg.

Root Section 23018 Tip Section 23012 Aspect Ratio = 6 Figure 33. Effect of Reynolds Number on Chax

123

I WASHOUT = 0 Deg.

5 Deg. 7% Deg.

1.5

1.4

1.3

124 WASHOUT = 0 Deg. 2% Deg.

5 Deg. 7% Deg.

1.5

1.4

1.3

1.2

1.1

Root Section 64218 TipSection 64212 Aspect Ratio = 6

Figure 33. Concluded

125 However, for the 642 series sectionsFigure 20 indicatesth.e opposite effect, namely that the rate of increase of maximum section lift coefficient with Reynolds number is much larger for theinboard sections (t/c = 0.18) th.anthat for the outboard sections (t/c = 0.12). This produces a spanwisevariation of maximum lift coefficient which has an increasingly downward slope towardthe wing tips and, since the value oflocal lift coefficient at anywing section increases with Reynolds number, the stall margins at th.e outboardsections will bereduced. The effect ofReynolds number onwing maximum lift coefficient shows theexpected increase with increasing Reynolds number. For the 230 series wing the maximum lift coefficientincreases almostlinearly with Reynolds number between 3 and 6 million, but with a further increase to 9 millionthe rate of increase is reduced.This trend is predictablefrom the section characteristics where it canbe seen th.at thegreatest ch.anges in section maximum lift coefficient occurs below Reynolds numberof 6x106. For th.e wingserie.s 44 and 642 the variation of maximum wing lift coefficient with Reynolds number in the rangeof 6 to 9 million is more linear,again reflecting the trend of the airfoil section characteristics

5.3.7Effect of Wing Camber

Th.e effect of a linear root-to-tip increase in wingcamber on the stall margins is shown inFigure 34 for th.ree valuesof taperratio, three Reynoldsnumbers and zero wing wash.out. Th.e results are compared with thosefor a constant camber. Th.e camber variationchosen was 64218 root section and 64412 tip section.

As canbe seen from this figure the particular camber variation chosen is notvery effective in changing th.e stall margins on theoutboard sections of the wing.This ineffectiveness is attributed, in part, to the particularchoice of a linearvariation ofcamber. It is expectedthat a largerincrease in stall marginswould be obtained for a differentcombination ofcamber andwing airfoil sections.

5.3.8Effect of Fuselage

Figure 35 presents th.e computer results for a wingalone and a h.igh. wingmounted on a fuselage of elliptical cross-section. Thewing has an aspect ratio of 6 (based on the gross wing area) withzero washout, and root and tip thickness ratios of0.18 and 0.12,respectively.

The computations were performed for taper ratios of0.5, 0.75and 1.0 andwing-fuselage settingsof Oo, 2' and 4'. The spanwise distributions of lift coefficient at stall were found

126 6 Re = 3x10 Taper Ratio = .5 TaDer Ratio = -75 Taper Ratio = 1

Tip Section Root Section AspectRatio = 6 -Washout6421864212 = 0 Deg. 64412 64228-" 64412

Figure 34. -Effect of Wing Camber on Stall Margin Distribution. Taper Ratio = .5 TaperRatio = .75 TaperRatio = 1 2.

I WFraction semispan urnaction semispan\-/Fraction semispan

-Wing alone Root Section 4418

”- Wing with Fuselage Tip Section 4412 Washout = 0 Deg. AspectRatio = 6 Re = 6x106

Figure 35. -_Effect of Fuselage. fd to benearly identical for all thewing-fuselage settings considered, thus resulting in the value of maximum wing lift coefficient (CLmax) being unaffected by thewing-fuselage incidence. The effectof positive wing-fuselage setting is merelyto reduce the body angleof attack at which the stall firstoccurs. This reduction is approximatelyequal to the wing-fuselageincidence.

Figure 35 indicates that for th.e highwing configuration shown, the effect offuselage is to sligh.tlyreduce the wing loadingspecially in theregion close to the fuselage. A similar reduction is indicated by the experimental results of Reference 50 where the lift distribution ona high wing circular fuselage combination is presented. 5.3.9Effect of Partial Span FlapDeflection

Figure 36shows the effects of flap deflection and flap span on the stalling characteristics of a rectangular wing with 64-seriessections operating at a flightReynolds numberof 6 million. The resultsare presented for the winghaving a 20% chordsplit flap, deflected 60° and extendingover 45%, 60% and 70% of th.e wingspan.

It canbe noted from this figure that, the deflection of a part-spanflap lowers the stall margins on the outboardportion of the wingand causesthe wing to stall further outboard. Furthermore, for therange considered, increasing flap span moves thestall boundaries inboard and increases wing maximum liftcoefficient. It shouldbe noted that the stall point on a flappedwing does not always occur at the flar end as would be predicted by simplesanalytical methods th.an h.e oneused In th.is program.

A discussion of the above results and their influence on thedesign of an airplane for good stall characteristics is given in Section 7.

129

I .. WASHOUT = 0 Deg.

bf/b Root Section64218 -. “ 0 Section Tip 64212 Aspect Ratio = 6 -0 45 ”- Re = 6x106 .60 Taper Ratio = 1 A” .70 Flap Deflection = 6d Figure 36. Effect of the Span of a 20% Chord Split Flap on the Wing stalling Characteristics.

130 SECTION 6

SCALEMODEL WIND TUNNELTESTING

It haspreviously been shown that the stalling characteristics ofan isolated wing, with or withoutdeflected flaps, can be adequately predicted through application of existing theoretical methods. Inthe case of a completeairplane, however, the interference of thefuselage, engine nacelles, propeller slipstream, etc., onthe flow over the wing may be such. as to dras- tically modify the wing stallingcharacteristics. The interference effects of the fuselage and nacelles are predictable with a fair degree of reliability as long as potential flow conditions prevail.Unfortunately, the body interferenceeffects often precipitateflow separation and availabletheories are notcapable ofpredicting such phenomena. At thepresent time no theory is available to adequately predict the effect of the propeller slipstream onwing stalling characteristics.

Forthese reasons, it is highlydesirable to obtain exper- imentalinformation concerning the complete airplane stalling characteristicsbefore the airplane goes into production. In certain cases economicconsiderations may indicatethe construction of a prototype model ofthe airplane with subsequent flight testing to obtain experimental information uponwhich to predicate thefinal design. In other cases, it may be more feasibleto conduct a scale modelwind tunnel investigation early in the airplane design stage in order to obtain the desired information.

During the period prior to World War I1 wind tunnel tests were ordinarily made ofmodels without propellers and empirical methods were relied on to account for the effects of propelller operationon the observed characteristics. Such a procedure was shown tobe inadequate when quantitative flight test data became available.In consequence it is now consideredessential that wind tunnel model evaluationof airplane flying qualities, whetherth.ey be concerned with stalling or with stability and control,should involve the use of a poweredmodel. The followingdiscussion will therefore consider some of the factors involved in poweredmodel wind tunnel testing. 6.1 SCALEMODEL REQUIREMENTS The selection of the model scale will bedependent on the sizeof the wind tunnelto be utilized in the investigation. As a rough rule of thumb the scale shouldbe chosen such that the modelwing spandoes not exceed approximately 75% ofthe width, or diameter,of the wind tunnel test section.Larger values of model size result in excessively large values of windtunnel boundarycorrections (Reference 23).

13 1 It is essential that the model betruly geometrically similar tothe full scale airplane. In this regard,the leading-edge portionof the wing is particularly sensitive to deviations from contour.Caution must thereforebe exercised to ensure that the airfoil shape over the forward 10 or 15 percentof the chord are true tothe theoretical ordinates. Small deviations from true contour are not particularly critical over the aft portionsof theairfoil. Wood, metal, plasticor combinations thereof may be satisfactorily utilized as material for model construction. However, it shouldbe noted that composite wood and metal surfaces are notsatisfactory because the wood shrinksand swells with change in atmospherichumidity conditions and thus gives rise to undesirable surface discontinuities.If wood construction is to be utilized, specially selected mahogany from themainland of tropical America is suggested as beingthe most satisfactory. It hasbeen found that mahogany from the islands of tropical America is not suitable for model constructionbecause it shrinksand swells more and has a greater tendency to warp than mahogany from themainland of tropical America. SimilarlyrtPhillipine" mahogany is not suitable for model construction.

6.2 PROPELLER DRIVE SYSTEM

Speciallyconstructed, compact squirrelcage induction motorshave been utilized extensively as the propeller drive in poweredmodels. Such motors are usually water cooled in order toincrease their power outputrating. In recent years some preferencehas been given to theuse of compactpneumatic motors. The selectionof motor type will depend to a large extent on .availability of appropriate electric power supplyor compressed air supply at thewind tunnel facilities being utilized.

Propeller rotational speed can be measured through the use of a highprecision tachometer and the measurementof propeller torque may be accomplished using an appropriate strain gage balancesystem. If a squirrel-cageinduction motor is utilized it is possibleto obtain a straightline calibration of torque versus minimum current. The minimum currentpoint is obtained by varying the voltage-frequency ratio of the electrical power supply until the minimum current point is arrived at. The valueof dynamic pressure at whichpower-on tests of an airplane model canbe conducted is largely dictated by the torque rating of thepropeller drive motor. For this reason it is advisableto at least make anapproximate estimate of the critical simulationrequirements before selecting the drive motor.

6.3 SIMULATIONOFPOWER CONDITIONS

In orderto adequately simulate the effects of power in the wind-tunneltesting of models, it is essential that the axial and rotational velocity contributions of the propeller be in the

13 2 same ratio to the free stream velocity as that which prevails underthe free flightconditions being simulated. This requires that the values of the propeller operating thrust andtorque coefficients will change as the airplane flight speed or operating valueof the lift coefficient is altered. It is usually most convenient to investigate the wind tunnel model through its operating range of lift coefficients at a fixedvalue of dynamic pressure,(constant velocity, fixed Reynolds number). To simulate the flight operating conditions during the constant velocity tests in the windtunnel it is therefore necessary to provide a different operating condition of the propeller at each different value of lift coefficient or angle of attack investigated in the wind tunnel. Varioustechniques have been developed for satisfying the conditionsof power similitudein wind tunneltesting. It appears that each different wind tunnel staff has its own preference as to theparticular technique to employ. It is suggested,however. that the power matching technique described in Reference 21. is most appropriate for use in wing stalling investigations becausethat technique ensures a nearlyexact condition ofpower similitude at each test condition andhence no interpolation of observedresults is required.

6.4 IFLOW VISUALI ZAT ION-

Numerous methods of visualizingthe flow over the airplane model in the wind tunnelhave been utilized. The most familiar are probablythe smoke flowtechnique, some variation of the lamp black and kerosene meth.od and theuse of tufts. Of the varioustechniques that have been developed, tufting is theleast complexand is usually th.e most satisfactory.In utilizing this technique, numerous tuftsare attached over the upper wingand fuselagesurfaces by cellulosetape or by other means.The tufts shouldbe of flexible material such as wool ornylon yarn. The lengthof the tufts is notcritical. Usually a tuftlength of approximately 3 or 4 percent of the wingchord will befound appropriate.Tufts should not be located forward of 20% chord.

The nature of the stall can bedetermined by notingthe behaviorof the tufts during the test conditions. Violent fluctuations and reversal of the flow direction as indicated by thetufts provides evidence of separation of the airflow from thesurface under observation. The behaviorof the tufts should ofcourse be observed through a rangeof angle of attack from well below to well beyond the angle for maximum lift. The flowcondition as indicated by the tufts may berecorded photographically, using either a still camera or a movie camera, or it may berecorded manually on the basis of visualobservation. Eachmethod has its own particularadvantages. Attention is drawn,

133 however, to the fact th.at still phot0graph.s of the tuft flow pattern can bemisleading. This stems fromthe fact that in the case of some configurations th.e nature of th.e airflow as the stall is approached may bevery unstable and erratic. At one point in time, the tuft pattern may indicate the flow to be attachedto the surface, an instant later the tuft pattern may indicatelarge areas of separatedflow. If a still picture were obtained at the instant of attachedflow it couldlead to an erroneousconclusion.

6.5 REYNOLDS NUMBER CONSIDERATIONS Stalling behavior of an aircraft can not be reliably predic- tedusing small scale models in th.e wind tunnel. Th.is is primarily due to the fact that it is extremelydifficult if notimpossible to duplicate in the wind tunnel th.e valuesof f1igh.t Reynolds numbers unless recourse is made to a compressed air ,tunnel or to a tunnel utilizing a highdensity gas such as Freon as a test medium.

It hasbeen well established that th.e maximum lift characteristics, includingthe wing stalling characteristics can be criticallydependent on th.e valueof th.e test Reynolds number. Inconsequence, judgment must beexercised in interpreting the windtunnel stall test results in terms of th.e airplane flight Reynoldsnumbers condition.

As anaid in interpreting the wind tunnel stallobservations, it is suggestedthat the theoretical analysis described earlier in th.is reportbe applied to predict th.e stall at a Reynolds number corresponding to the wind tunnel test conditionand at a Reynolds number correspondingto th.e airplanef1igh.t condition. By takingaccount of the differences between theory and experiment at the test Reynoldsnumber, an improved estimate of the stalling ch.aracteristics at thef1igh.t value of Reynolds number may beobtained. This approach.sh,ould at leastgive an indication as to wh.eth,er th.e free flight stall condition will be more or less severeth.an the stall conditionobserved in the wind tunnel tests.

6.6 MACH NUMBER CONSIDERATIONS

The effect of Mach number on th.e maximum lift ch.aracteristics of airfoils has not been isolated’ and studiedas th.oroughly as the effect of Reynoldsnumber.

The results presentedin Reference 51 indicate that at a givenvalue of Reynolds numberan increase in Mach number causes a moderate decrease in maximum lift coefficient under conditions such. that the local velocities on th.e surfaceof th.e wing are somewh.at belowsonic speed. It has alsobeen clearly demonstrated bythe results ofReferences 9, 51 and 52, that when th.e free

134 9- -

1, stream Mach number is increased to th.e pointthat sonic speed is reached,locally onth.e wing, a large reduction in maximum lift coefficienttakes place. The same results show th.atcritical local velocities can occur at values of thefree stream Mach. number as low as 0.20. Therehave been instances in the past wherewind tunnelinvestigators have attempted to improveth.e test value of theReynolds number by conducting the tests at highvalues of the wind tunnelairspeed. Such. aprocedure can lead to quite misleading test results, particularly if the free stream Mach number is sufficiently h.igh to permit th.e attainment of critical local velocities over the wingsurface.

135 iI SECTION 7 DESIGN PROCEDURES The results presented in Section5 are intended to serve as a guidein the preliminary design phase an of unswept wing aircraft to determine the effects of wing geometric and aerodynamic parameters on aircraft stalling behavior. While this data does not cover all the possible combinations of taper, twist, etc. which may be encountered, it should provide a basis for the assessment of the relative effectiveness of different wing designs in promoting acceptable airplane stalling characteristics. In the early design stage of an airplane the values of wing aspect ratio, taperratio, and root and tip thickness ratios are usually chosen from considerations of performance, structural strength, etc. rather than stalling characteristics.In regard to wing performance, the computer program describedin this report can be of valuein providing data on wing lift, drag, and pitching moment characteristics through the complete angle of attack range, as wella information on the span load distributions. The stalling characteristics of the basic wing design can be assessed from the design charts presentedin Section 5, and if poor stalling behavioris indicated, the effectiveness of various methods for improving the stall can then be investigated. When awing design emerges which promises to fulfill the performance and stall requirements a final quantitative evaluation of its stalling characteristics can be made using the computer program which constitutes a part of this report. 7.1 APPLICATION OF THE RESULTS OF THE PARAMETRIC STUDY The use ofthe design charts presentedin Section5 is best illustrated by a sample calculation described below. Consider a light, single engined airplane having the following ch,aracteristics: Wing aspectratioWing 6 Wing taper ratiotaper Wing 0.5 Mean aerodynamic 5.4 ft. chord (m.a.c.1 2 Wing loading 17.2 lb/ft Root airfoilRoot section 23016.5 Tip airfoilTip section 23012

136 Cruise154 speed m.p.h.

Cruise altitude10,000 ft.,(standard day)

A likelystallYng speed for such. anairplane, flaps UD, is about 70rg.p.h.. or a Reynoldsnumber, based on the m.8.c. of 3.55 x 10 . A good estimateof th.e stallingmeed for the untwisted wing is obtained as follows: (a) A number of speeds in th.e neigh.borh.oodof 70 m.p.h. is selected and the corresponding Reynolds numbers are calculated thus

V ft/sec. - 90 , 95 9 100, 110, V m.p.h. = 61.35,64.76,68.17,74.98, Re - 3.11,3.80, 3.46, 3.28,

(b)Using Figure 33 for 0.S taperratio and a rootthickness ch.ord ratio of0.18, the following values of CLrnax are obtainedcorresponding to the Reynoldsnumbers calculated in step (a), - 1.47,1.45,1.435, 1.42, CLrnax+/~=. 18 (c> From Figure 28 the percentage ch.ange in CLrnax due to changingroot thickness-chord ratio from.18 to .165 is estimated tobe 2%. Strictly, th.e dataapplies only to Re = 6 x lo6, but the sectioncharacteristics, Figure 20, suggest that approximately the same changescan be expected at lower values of Reynolds number.

( d) The incrementsin CLrnax obtainedfrom step (c) are added to the CLrnax values from step (b) yielding:

Th.e results thus obtained are plotted versus stalling meed inFigure 37.

ship CLmax = 2 X W/S arecalculated thus: p v2 2w/s CLmax=T= 1.78, 1.445,1.60, 1.19 PV Th.ese results are also plotted in Figure 37.

(f) Th.e intersection of these curvesyields the values of 'Lrnax stall s eedand Reynolds number as 1.47.5,67.5 m.o.h. and3.42 x log, respectively,as shown inFigure 37.

137 1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1 Stall speed - ft/sec

Figure 37.Variation of Wing Maximum Lift Coefficient with Stall Speed.

138 At thisvalue of Reynolds number Figures 31 and 32 show that i:j the stall margin at the 70% station is only 0.02and that the stallbegins inboard at about 35% semispanand extends toabout 70% semispan.Obviously this is notacceptable and some means must beemployed to move the stall inboard and increase the margin at the 70% semispanstation. An acceptable stall pattern wouldbe the one in which the outeredge of the stalled area began,say,inboardof the 40% station andthe stall margin at 70% of thesemispan was at least 0.1. Figure31 shows th.at, forthe given taper ratio of 0.5, a stall marginof 0.1 at 70% semispancan be obtained with P4 degreesof washout. For this case thecorresponding stall boundaries lie between 15% and37% semispan. Since the use of washout influences the value of Cbax and hence stalling speed, steps(b) through (f) are repeatedusing the data presented for 7% washout. Ifthese computations are performedthe new values of CLmax , stallingspeed and Reynolds number are 1.4, 69 m.p.h. and3.5 million respectively. Using the new value of Reynolds number andwashout of 7?.5O, Figures31 and 32 indicatethat satisfactory stalling characteristics of the selected wing are attained with the safe stall marginof 0.1 at 70% semispanand inboardstall boundaries extending between 15% and 36%semispan.

If this amountof washout is used, a penalty may result in induceddrag at thecruise speed. The magnitudeof the increase in induced drag coefficient at the cruise lift coefficient of .38and cruise Reynolds number ofapproximately 6 million is obtainedfrom Figure 25 asA Coi= -0012. The significance of this dragincrease depends on thedrag coefficient of the complete airplane. For anairplane having a dragcoefficient equal to 0.02, anincrease in induced drag coefficient of 0.0012 represents a 4m.p.h. reductionin cruising speed at the cruise power setting.

An alternative to using a large amountof washout as highas 7% degrees is to incorDorate a tip section of higher camber than the root section with linear fairing in between,e.g. change the tipsection from 23012 to 43012. On thebasis of theresults presented in Figure 34, for awing employinglinear camber increase fromroot to tip, it appears that increasing camber alone will not result in any significant improvement inthe stalling characteristics. Combinations of linear camber increase with moderate amountsof washout may result in an effective compromise to yield satisfactory performance and acceptable stalling characteristics of th.e selected wing configurations. The parametricinvestigations ofsuch effects can be easily performed utilizing the computer program presented in this report.

139 If an effective combinationof camber increase andwashout cannotbe found the only remaining wing parameters which migh.t influencestalling characteristics are aspectratio, th,ickness distribution and taper ratio. On th.e basisof the results sh.own in Figure 23, ch.anging aspectratio is ineffective.Increasing root thickness-chord ratio from .165 tosay .18 is alsoof little value accordingto the results presentedin Figure 27. While an increase in wing taper ratio would represent a majorchange if th.e wing design were sufficiently far advanced, it migh.t be less expensive, in th.e long run to make such. a ch.angeth.an to try to solve badwing stall problems by other means during the flighttesting phase ofdevelopment.

An illustration of the stronginfluence which is exerted by taper ratio onwing stalling Characteristics is provided by repeating th.e abovecalculations for a taper ratio of0.75 with 2S0 ofwashout. The increasedtaper ratio is achieved by reducing the root ch.ordand increasing the tip chord by the same amount so as to maintain the same wing area as in the original design . By interpolationbetween these results.and results obtained for taper ratio of 0.5 it is found that anIncrease in taper ratio from 9.5 to 0.65 will produce a stall margin at 7/10th semispanequal to 0.1 with the stalled area extending between 10% and 40% semispan. The calculationsal$o show that the change intaper ratio and theincorporation of 2% ofwashout does not alter the stalling speed to any significantdegree. Furthermore, the induceddrag penalty due to washout for th.is taper ratio is negligible.

If all of the abovemeasures failto indicate acceptable stalling ch.aracteristics then it must be left until the flight test phase to try to improvematters by the use of the various "fixes"discussed in Section 2. Even at this stage the computer programshould prove valuable in assessing the relative rnerits of thepost design modifications. For example, if the installation ofsharp wedges over a portionof the leadingedge is beingconsidered,a precise evaluation of the effectiveness of such a devicecan be made by using the computerprogram if data is availablepertaining to th.e aerodynamic characteristics of sharpnosed sections. Some data on the effect ofsharp leading edges on section maximum lift coefficient can be found in References 53 and 54.

7.2 GENERAL CONSIDERATIONS

The designprocedures discussed in this sectionfogether with. the stall chartspresented in Section 5 are considered

140 7- - adequate for most practical casesin evaluating stalling character- #$\.? i istics of unswept wing aircraft. These procedures and charts should be specially valuable in the preliminary design phase in which numerous trade-off studies are required to obtain the best compromise in aircraft configurations. Once a given design has been frozen ensuring satisfactory aircraft performance, stalling characteristics, handling qualities, etc. it is recommended that the computer program presented as part of this report be utilized to more accurately predict the stalling behavior of the final aircraft configuration. As a by-product, the computer program will also yield valuable performance information as such distributions and integrated valuesof wing lift, drag and pitching moment coefficients, for cruise or any other aircraft operating condition.

141 SECTION 8 CONCLUSI ONS AND RECOMMENDATIONS Using the results presented in this report, thefollowing conclusions andrecommendations are made: 1. Based on good correlationsobtained between the theoretical results and theavailable test data, it is concludedthat the lifting line theorycan be confidently used to predict stall characteristics of wingshaving aspect ratios of 6 and larger. This theory is expected to yieldsatisfactory predictions of overallload characteristics for wings of aspectratios as low as4.0.

2. From the results of theparametric study it can be concludedthat taper ratio is one of the most effectivedesign parametersinfluencing aircraft stall characteristics. Increase in taper ratio results in an increase of the stall margins on the outboardsections of the wing and in aninboard shift of stallboundaries. This, however, is accompanied by a reduction of maximum wing lift coefficient.

3. Washout may beused to improve stallingcharacteristics of moderate to hightaper ratio wings. This improvement,however, may entail aperformance penalty associated with a reduction of wing maximum lift coefficient and an increase in winginduced and profile drag. 4. An increase in root thickness-chordratio and flight Reynolds number yields favorable effects on wing stalling characteristics associated with the 230 and 44 series airfoils. For the 642 series sectionssuch increases result in unfavorable effects.Increasing tip thickness-chordratio has an unfavorable effectfor all three airfoil series. For allcases the values of wing maximum lift coefficient are reduced.

5. For the wingconfigurations investigated in this report,deflection of part-spanflaps lowers the stall margins on theoutboard portion of the wing and shifts the stall boundariesoutboard. Increasing flap span moves thestall boundaries inboard and increases wing maximum lift coefficient. 6. The effects of aspectratio, linear camber, and fuselage on wing stalling characteristics appear to besmall and may be neglected for most present-day light aircraft. 7. The analysis and thedesign charts presented in this report apply strictly to unpowered flight, out of ground effect, as would be the case in aircraftapproach to landing.

142 8. Basedon the work accomplished in this program, it is recommended thatthe theoretical analysis be extended to include propellerslipstream and ground effects. Furthermore, additional flight test and wind tunnel test datashould be obtainedfor the purposeof verifyingthe theory.

143 SECTION 9 REFERENCES

1. Sivells , James C., andNeely , Robert H. : Method of Calcu- lating Wing Characteristics by Lifting-line TheoryUsing NonlinearSection Lift Data. NACA Rep. 865,1947.

2. Sivells, James C., and Westrick,Gertrude C. : Method for Calculating Lift Distributions for Unswept Wings With Flaps or Ailerons by use of Nonlinear Section Lift Data. NACA Rep. 1090,1952. 3. Theodorsen,Theodore: Theory of Wing Sections of Arbitrary Shape. NACA Rep. 411,1931.

4. Multhopp H.: Aerodynamicsof theFuselage. NACA TM 1036, 1942. 5. Abbott, Ira H., vonDoenhoff, Albert E., and Stivers, Louis S.: Summary of AirfoilData. NACA Rep. 824,1945.

6. Loftin,Laurence K., Jr. andSmith, Hamilton A.: Aero- dynamic Characteristics of 15 NACA Airfoil Sections at SevenReynolds Numbers from 0. 7x106 to 9 .0x106. NAC-4 TN 1945,1949.

7. Bollech, Thomas V.: Experimentaland Calculated Character- istics of SeveralHigh-Aspect-Ratio Tapered Wings Incorp- orating NACA 44-Series, 230 Series, and Low Drag 64-Series AirfoilSections. NACA TN 1677,1948.

8. Sweberg,Harold H. and Dingeldein,Richard C.: Summary of Measurements in Langley Full-scale Tunnel of Maximum Lift Coefficients and Stalling Characteristics of Airplanes. NACA Rep. 829,1945.

9. Fitzpatrick, James E. and Schneider, William C. : Effect of MachNumber Variation Between 0.07and 0.34 a d Reynolds Number Variation Between 0 .97x106 and 8.10~102 on the Maximum Lift Coefficient of a Wing of NACA 64-210 Airfoil Series. NACA TN 2753,1952.

10. FederalAviation Agency: AirworthinessStandards: Normal, Utility andAerobatic Category Aeroplanes. FAA Regula- tions,Part 23, Current.

11. Wimpenny, J. C.: Low Speed StallingCharacteristics. AGARD Rep. 356, 1961.

144 12. Zalovcik, John A.: Summary of Stall Warning Devices. NACA TN 2676, 1952. 13. McCullough, GeorgeB. and Gault, DonaldE.: Examples of Three Representative Typesof Airfoil-Section Stall at Low Speed. NACA TN 2502, 1951. 14. Gault, DonaldE.: A Correlation of Low-Speed, Airfoil- Section Stalling CharacteristicsWith Reynolds Number and Airfoil Geometry. NACA TN 3963, 1957. 15. Anderson, RaymondF. : Determination of the Characteristics of Tapered Wings. NACA Rep. 572, 1936. 16. Pearson, Henry A.: Span Load Distribution for Tapered Wings With Partial-SpanFlaps. NACA Rep. 585, 1936. 17. Pearson, HenryA., and Anderson, Raymond F.: Calculation of the Aerodynamic Characteristics of Tapered Wings With Partial-Span Flaps. NACA Rep. 665, 1939. 18. Sivells, James C., and Spooner, StanleyH.: Investigation in the Langley 19-Foot Pressure Tunnelof Two Wings of NACA 65-210 and 64-210 Airfoil Sections With Various Type Flaps. NACA Rep. 942, 1949. 19. White, James A., and Hood, Manley J.: Wing Fuselage Inter- ference, Tail Buffeting,and Airflow About the Tail of a Low-Wing Monoplane. NACA Rep.482, 1934. 20. Weick, Fred E.: The Behavior of Conventional Airplanesin Situations Thought to Lead to Most Crashes. NACA TN 363, 1931. 21. Phj.llips, WilliamH. : Appreciation and Predictionof Flying Qualities. NACA Rep. 927, 1949. 22. Prandtl, L.: Applications of Modern Hydrodynamicsto Aeronautics. NACA Rep. 116, 1921. 23. Glanert, H.: The Elements of Aerofoil and Airscrew Theory. Cambridge UniversityPress, Second Edition,1959. 24. Sherman, Albert: A Simple Method of ObtainingSpan Load Distributions. NACA TN 732, 1939. 25. Tani, Itiro: A Simple Method of Calcuating the Induced Velocity of a Monoplane Wing. Aeronautical Research Inst. Tokyo Imp. Univ. Rep.111, Vol. IX, 1934, page 3.

145 26. Multhopp, H.: The Calculation of the,LiftDistribution of Airfoils. Luftfahrforschung, Deutschland (R.T.P. Trans- lation No. 23921, 1938. 27. Boshar, John: .The Determinationof Span Load Distribution at High Speeds by the Use of High-speed Wind Tunnel Section Data. NACA ARC4B22, 1944 (Wartime Rep. L-436). 28. Weissinger, J.: The Lift Distributionof Swept-Back Wings. NACA TM 1120, 1947. 29. Mutterperl, William: The Calculation of Span Load Distribu- tions on Swept-Back Wings. NACA TN 834, 1941. 30. Schlichting, H., and Kahlert, W.: Calculation of Lift Distribution of Swept Wings. R.A.E. Rep. Aero. 2297, 1948. 31. Falkner, V.M.: The Calculation of the Aerodynamic Loading on Surfaces of any Shape. ARC &R M 1910, 1943. 32. Garner, H.C.: Methods of Approaching an Accurate Three- Dimensional Potential Solutionfor aWing. R & M No. 2721, Brit. A.R.C., 1954. 33. Garner, H.C. : Theoretical Calculations of the Distribution of Aerodynamic Loading on a DeltaWing. R & M No. 2819, Brit. A.R.C., 1954. 34. Multhopp, H:: Methods of Calculating the Lift Distribution of Wings. (Subsonic Lifting Surface Theory). R & M No. 2884, Brit. A.R.C., 1955. 35. Schlichting, H.: Aerodynamics of the Mutual Influenceof Aircraft Parts (Interference) Volkenrode & RT No. 171, Trans. 275, 1946. 36. Flax, A.H., and Lawrence, H.R.: The Aerodynamics of Low Aspect Ratio Wings and Wing-Body Combinations. Proc. Third Anglo-American Aeronautics Conference, Brighton, 1951, page 363. 37. Lennertz, J.: Influence of the Airplane Bodyon the Wings. Aerodynamic Theory; W.F. Durand, Editor,Vol. IV, Division K, Chapter 111, page 152, Durand Reprinting Committee, 1943. 38. Pepper, P.A.: Minimum Induced Dragin Wing-Fuselage Interference. NACA TN 812, 1941.

146 39 . Zlotnick, M., and Robinson, S.W., Jr.: , A Simplified Mathematical Model for Calculating Aerodynamic Loading and Downwash for Wing-Fuselage Combinations With Wings of Arbitrary Plan Form. NACA TN 3057, 1954(also NACA RN L52J27a, 1953). 40. Weber, J., Kirby, D.A., and Kettle, D.J.: An Extension of Multhopp's Method of Calculating the Spanwise Loading of Wing-Fuselage Combinations. R & M No. 2872, Brit. A.R.C., 1956. 41. Dynasciences Corporation: Effects of Propeller Slipstream on V/STOL Aircraft Performance and Stability. TRECOM TR 64-47, 1964. 42. George, M., and Kisielowski, E. : Investigation of Propeller Slipstream Effectson Wing Performance. USAAVLABS TR 67-67, 1967. 43. Laurence, H.R., and Flax, A.H.: Wing-Body Interference at Subsonic and Supersonic Speeds- Survey and NewDevelop- ments. J. Ae.Sc., Vol. 21, No. 5, page 289, 1954. 44. Ribner, H.S., and Ellis, N.D.: Theory and Computer Study of a Wing in a Slipstream. AIAA Paper No. 66-466, 1966. 45. Ribner, H.S.: Theory of Wings in a SlipstreamUTIAS Rep. 60, 1959. 46. Wieselsberger, C.: Contribution to the Mutual Interference of Wing and Propeller. NACA TM 754, 1934. 47. Yaggy, PaulF.: A Method for Predicting the Upwash Angles Induced at the Propeller Planeof a Combination of Bodies With an Unswept Wing. NACATN 2528, 1951. 48. Jones, RobertT.: Correction of the Lifting-Line Theory for the Effectof the Chord. NACA TN 817, 1941. 49. Soul&, H.A., and Anderson, R.F.: Design Charts Relating to the Stalling of Tapered Wings. NACA Report703, 1940. 50. Schlichting, H. : Report on the Special Field "Interference" to the Wind-Tunnel Committeein February 1945. NACA TM 1347,1953. 51. Furlong, G. Chester and Fitzpatrick, JamesE.: Effects of Mach Number and Reynolds Numberon the Maximum Lift Coefficient of a Wing of NACA 230-Series Airfoil Sections. NACA TN 1299, 1947.

147 52. Furlong, G. Chester and Fitzpatrick, JamesE.: Effects of Mach Number upto 0.34 and Reynolds Number up to 8x106 on the Maximum Lift Coefficienta Wingof of NACA 66-Series Airfoil Sections. NACATN 2251, 1950. 53. Jacobs, Eastman N.: Characteristics of Two Sharp-Nosed Airfoils Having Reduced Spinning Tendencies.NACA TN 416, 1932. 54. Weick, Fred E. and Scudder, NathanF.: The Effect of Lift, Drag, and Spinning Characteristicsof Sharp Leading Edges on Airplane Wings. NACA TN 447, 1933. APPENDIX A

INTERNALLISTING OF THECOMPUTER PROGRAM

L C C C C C C C C C C C C C C L C c C C C C C C

6) C 1E 2, 3 9' 4T 5L

149 L C: INTEKCHANGE ROWS C so, 30 30

40 C c I%TERCHAhGE CULUMNS

JK=kK+J .Il=.IP+.I

DIVIDE CIULCIMN BY t lNUS PIVOT (VALUE OF PlVOT €LFMENT 15 CONTAINEL) It4 BIGA) 80 90,909 lU0 90 100 1 LO 170 L

1 30 140 1 50 r

15 0 v-

PRODUCT OF PIVOTS D=D+b 1 GA E' REPLACEPIVOT BY RECIPROCAL

FINAL ROW ANDCOLUMN INTERCHANGE C K=N 190 200 2 LO

JK= Jdl+J HOLU=4(.JK) JI=JK+J ALJK)=-ACJI 1 220 A (.J I 1 =:i(?LD 230 J=Pl (K 1 IF( J-IO 240 KIz5-N DO 250 I KI=KI+h tlrlLd=A ( K

250 260

C C SUt>KC;Ul IN€ TO GET 1ALILE FFctlM DISK ANU PUT C I T IKTO ClJRE C

C C TAHLE PKtSFNTLY IN COKE IS INNOW C C IFr4BLE IS ALREAOY IN CUKE THEN RETUliN C IF XIIT Tt{€Pl GET TALLE I-RLtM DISK C IF( IFILt-I.~\INl;w) lUt90t10 10 II=l iZ E b; I "iIJ I I: I L C READ( IFILE) ARK.?Y t

20 30 40 L; )=O. \ 50 0 6 0

SUL3RTJUTIr

15 2 SUbROtiTIYE MAKESLIECISION BASED CiN THC StTr ING (jF THE SkI ICH SkT=l,NOT SET=O ICClr\lD=L IF SuITCtr IS SET ICflND=Z 1f SkdITCH IS NOT SET

IPJITIALIZELEVELS IN WHERE

LOOP TO READ IN LEVELS OF A SET OF EITHEK LIFT, DKAG,OR PITCHING MOMENT

FtEAO ANDPRINT NUMBEK OF KOWS,’ COLUMNS, TAU VALUES FOR A GIVENLEVEL

15 3 STORE NUMBER OF CCLUMNS MXCL.lL (.LVL 1 =NCOL c' C- STORE NUMBER UF RGWS C. MAXA(1VL )'=VC C C iif.49 AND WRITETITLE OF TABLE G KEA;) ( I I< ,70 1 NAME NR I TL ( I r) ,,ti0 NAK~',.L,VL C READVALUES FOR TABLE

M;ixX i

20 KLYlZ

15 4 v- -

L4 C PRIMARYCUBES AKF NIJMEERED 1,29394 SEC O NU AK Y CUBESSECONUAKY ARE NtJMi3EKED 5~10~~15~20 Lc NFW=LbF.i+5 C C STUAE XMAX C X?X=XE; AX . " C C DETEKHINE IF SINGLE VALUE IS TO BE USED OK C LIST OF. VALUES IS TO BEUSED IN LOOKUP

L C SET UP OFFOR VALUE CCINSTANT X C

c SET UP FOK VARIAHLE VALUE OF X

155 L s scr UP ALPHA VALUE

L c cL 260 2 70 2bO 290 C C C 300

.3 1o C C LOOK UI' C C C IIF TAU

15 6 SbbKi.:C,TINE TCj INTENPOLATE BETWEEN LEVELS OF C A GIVEN TAkiLL- C

C C IS TAL LESS THAN UK tOUAL TO LOWEST LEVEL c TAUVALUE C

C c C

C C C

15 7 IF(.ALPfiA-c)9 100 If (.KEYN-999 1.10 IFI.CVA.L-999 120 I-FLCVAL-999 L30 IF LCVAL-9YY 14 0 IF (.REYr\l-9YY 150 IF(.liEYN-999 160 If (.itEYON-99 170 IFLXKAX ): 22 180 If (.xl*;Ax 20 0 190 IFLP=l . so 1-0 210 200 I F.L P=2 2.1u IS=5 GO TO 270 220 230 240 250 260 270 xc ,.I t

9 1s ,280

2 90

300

3 10

320 3 30 340 358

C C c C

369

33 1.9 1.s :3 7 0 380 39u

15 8 420 CVAL=DUKY L-CLK A t UUW Y2r'ALR (*1 CVAL 1 KE.1 URN 430 CVAL=DUFiY 1-CLK A IJUh Y2 r'ALR(.2 c3 REFURN 440 If CALK (21 -ALR (< 60 450 IF (.ALPHA- DUMY 2 460 IF (.ALPHA- DUP!YZ 4.7 0 CLA=TtRP(.ALti ( 1 AICLR 'AL CLC=TERP (. K19K2 1) CVALZTEiiP( A L it (- 2 ,CLC )

.III-TLIRN . " . - . .. . 480 CLtj=TEKP(. 4Lk 2 1.. c 3) CLC=TERP( Klt CVAL=Tfi

530

C 540 cv fiL GKE ATFK. . .. . THAN. .. . . b:AX,. ... VAL 1 TAR LEVALUE/37Xv41HIf 3 AL 2 3tlI I- 0 TAUVALUF CANI'GO T HE 3 / 10 X,8tiC-VALUk=,F!0.2v 5x9 (4 t 5x ,6tIREYON=,flO.L,5Xt SHXM

c LKOW IS Th5LAST dC!d CflNrAININGINFOKMATI(1N L 1c.l ANY TAHLE.THt LAST TWfl RLIWS IIF ANY lA9.LE CUNTAIa\I MAX OA.IA.' 1.c

IS I

159 I5 THtREYNCJLDS NUMdER iJE ARE LOOKING FOR GKEATLKTHAI\ OR EQUAL TU THEREYNGLDS .'JUM:!EK SIVkN kLUhuG THE FIRST KUW ~JF THE TAb1.E

'LCRMAL CASL.. IF KLYNCJLOSNUMBER IS LESS Third MAX REYN WJX~FR 1'4 TABLE THEN WE,- CkECK 10 SEE IF IT IS GKEATEK THAI\; Tht IVI'VFPUK KLYNOLDS NUKBkK LISTEC) Il\j THETAHLE

If- LESS THAN CiAXIPUI*iAI49 GREATER THAN MIi\cI.PUC, he hANT TC SCAKCH TABLEUi\TIL WE FI:\IO A R€vh@LUSNUVBER GKEATER THAN THE <;IVF:\IHEYIdLILDS NUI.:B€R If- K€YNLESS THAN KtEPLOOKING IFKCYN GKtATER THArJ SkT lip KlpK3 FOR INTEKPULAT IWd

SECTI(JN FIIK !.IORI"IAL LOClK UP OF ALPHAAND CVAL. A VALUE OF 999 SPECIFIESTHAT THIS VARI-ABLE IS THE 0;Vk ShLISt VALUE IS TCI BE FC1IJ;dI) 1.a TtltTAULE

StCTIUN FOR LOOKINLUP MAX VALUES C 150 If (.XMAX 1 5801 8301 589 StCTIClNTO LOOK UP ALPHAFOR GIVEN CVAL BY I'ITEitPCILATI:\IGBETWEEN COLLMIVS WHERE KEYIVOLOS !dUMl3tKS BRACKETGIVEid REYN

160 LCOKUP CVkL FOR GIVkN ALPHA. CHECK. TCI SEE c IF hE HAVE A LIFT OK DRAGTAt3LE IN AT [HIS L TIME. DRAG TABLESHAVE ZkKO VALUES FUfi ALL C

FOR LIFTTABLE. CJUKY 1 AND DUMYZARE THE C fJAXi.P"JKIhTEKP3LATED VALUES FUR GIVEN c RtYPJCLCiSUllk5€RS IIF ALPHAMAX AND CVALMAX a 210

L ,'MAX!? 9 LOCR ,250 70 9 260 9 260

270 280 230 300 10 310 LPHZ)) 320,55095 50 32CI 340,330 330

340 Hl-ALPHZ)+( ALPHA-DUhY 35L' 50 360 3'iC

3 t;. 0 / (ALPH2- ALPHA-DUPY s 3 3 03, 4 00 (.AL 550 9 550 4 10 420

4 30 ALPHZ-AL PHA-DUMY1) 440 550,550 456 460

161 GO ra 600 4 70 Cl=A(LVL,d,.LCCR CVAL=DUPV2+ (A(.L ,Cl)/(ALPHZ-AL .PHl)*(ALPHA-DUMYl GO TO 600 48 0 IF (.ALPHA-DUMY L 1 49 0 DO 500 J=3tlLRC;t\ If(.ALPH 1-A (.LVL, 0 500 CONT I lLUE I E=3 GO TO 600 5 LO C L=A LLVL 9.J ,.LO.Cil C3=A ( LVL J ,'LOCK C1=TERPiRL,s?EYN CVAL=TEKP(ALPtil I)UI.!Y 2 ): GO TCI 600 520 DO 53U J=.j,.LR@W IF(.ALPt!2-,~2*LVL, 0 530 CClNT INUC

54 0

5 50

: C C C L C C C

C:: C C C

162 ZtIERE MLCOL MA ZL Y:HEKE MYCOL MAYY XHEKk MwCOL HAWW AHERE MACOL MAAA BHEKE MBCOL MAD0 CHERE MCCOL MACC DHEKE MDCUL MADO

C C RkADFK(IR) AND PRINTER (IP) LOGICAL UNIT C 'dlJKBEKS C

C C C

c C LAYOUT OF FOURTH DATA CARD C C FIkLI: 1 I1 NlJMUtK OF rAllVALUES PER 1'ABLt L C FIELO 2 I1 1 F 0 R TAlJ 9 KEYqETC. c 0 FflR C C FIELD 3 11 1 Fllti DUMP OF COMPUTED ARRAYS C o FIIR NO DUMP C C F ItLI; 4 I1 1 FOR DUKPOF 8E TA ARRAY C U FUK N1.1 OLJMP C C F IELI) 5 1'1 1 KEADCUBE 1 FKUMTAPE, LOAD C TLI DISK, COPY CLJBt 1 1 O CUHE C Z Git DISK. c 2 KtAil CUBE 1 FROMTAPE, LOA@ C TUDISK, YEA0 CUBE 2 FROM C TAPErlLU4D TO 111 SIC. C 3 KEAD CUBE 1 FROM CARDS,LOAD C TOTAPE 9 LOAD TO UISK, COPY C CUBE 1 TU CU13E 2 Oid DISK C 4 I

163

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TO TAPE I LOAD TI7 DISK,IiIiAU CUaE 2 FRUKCARDS9 LOAL) TU TAPLT' LOAD T13 DISK FIE.LC h 25A2 FIFTY COLUkINS OF IUENTIFING I-I\IFOKKATIOIU. THIS IS PRINTED AT 7HE TOP OF EACH PAGE OF OUTPUT

4u 50 60 70 80

IK=IK+l

L 9'4 READ ( ARRAY KK= Ik: IK=IK 110 WRITE DO 12 AHE%k AHEKt BHERE t5HEhE CHE:',E CtiEKE DHEKt DIiEiit

164 120 130

L4 0

150 7 I=L 9 I= 1 =1*r\l * 1=1

1bU

170

1ao LYU

165 $- ELLIPTICAL FUSE

L C CCIKFC.CN 1Ci ELLIPTIC A;JD CIKCULAKFUSE C 250 DCI 2hC' I'L,.JPP C C Y FIAP (.I 1

166 SPECIAL CASE IF VALUESHAVE BEEN READ IN C DO NOT SANT rc1 COPPUTE CKB. WILL NOT COMPUTEVALUES ALKEADY READ Iq cL

450 460

470

480 R 4 '3 0 ,'!> 0 0 4 90

500

54 0 550

167 5 70 580 590 6 00

C C FO? XPAX=lOCI, ARC bILL LUGKUP ALPHA VrAX c FOh XF(AX=O. ARC WILL LOOK UP CL PAX

C C CCNTIPJUkT ION OF SbPRGUTI'VE,VAIN C 19

.T.4UT. TAU&;

20, )=1 Y (.AK* K-P 4 0 )=1 N ( AK* K 1. 3.141

,K)'*lR *TRANS

168 Ct!tCK

160

190

ZGL 210 220 2 30

240

i5U 26'3 270

2 H 0 C C CkECK C

2-90

169 300 CONTINUE 310 IBTA=1 C C STORE -BETA TEMPORARILY ON DISK SO WE CAN CWPUTE THE TRANSPOSE OF TRIX L:c REh IND 44 WRI- rE (441, RETA REWIND 44 C C STORE TKIX IN BETA c,

c NOW TRANSPOSE BETA LOLD TKIX) C

RESTURLH€TA C r RfAu(44)dETA L IN V ER T TKIX INVERT Lc CA.LL P, Mk CALL C GCI TLi WK 1.1 t ( CCILL S If (.YkL WRI.TE ( h'K I.TE ( CALL R WSITE( CALL A C C LL VAXLOOK UP C.

C LCJClK UP CL KAXVALUES cL

3 70 380

C C

170 C 390 4011 4.1 0

4- 420

1x1 / 1x 1. SE STATIONS)

171 LBOPINGPAkAMkTER. Ik IK (THELOGICAL UNIT XLKHEK OF 1 tlt RtAC:EK 1 IS SETPROPtRLY AT Il.!IS I'IMt: THEN THIS IS THEFIRST ENTRY INTO Tt!ISSUBKOUTINE. IT- IF: IS 100 THEIJ WE WISt-I rCi I.lEkA1E AGAIN ill F-INU CONVERGENCE.

INPUT OF ALPtiAVALljES TO BE USED FOR TtiIS RUN. A LIST OF ALPtIAVALULS MAY HE TFKMIr'JATEG IN ThU IrAYS. (1) INCLUDEALPIiA VALUESLARGE EhiOUGH T1J CAUSE A STALL. (2) END LIST nF VALUES lu'~TH A 99.

IF IR IS ZtRU THEW 'nF hISk TO TAKE THENEXr ALPHAVALUE

SlvI TCh INUMBER 3 IS USEDFOR AN INTERNAL DUMP C1F ARRAYS CUKPlJrEG DUkINGITEkATION PROCESS

172 q- -

c LGUK UP ALPIiA VALUE FLJK ZkKU LIFT

LUUK UP CLVALUES FOR A LIST OF ALPHA VALUES

v A L 70 9 170 P 1bO

173 I 111 I I 111111II 11111 1111 I I

CHECK FOR DUMP

c KEPE4 C CYCLE

IF UNABLE TO CONVERGE AFTER 30 ITERATICNS DUMP OELTA VALUES, C VALUES,AND TABLE PgESENTLY IN CURE bEING USEU FOR LOOK UP

174 SUBROUTINEMAIN4 t c. CUNTINIJATIONOF SUBROUTINE HAINZ c 1 tREY ( TAU( 19 ALPG ( 1 9 1 (DEL L(6)VM

rC f AXX DGE

COMPUTEPKT)FILE DKAG COEFFICIENTS CLL=Y9?. REYLlN=9YY. XMAX=G. Ch.LL U~.IDC(.CGO,~,I~P~~~I.Z,I~T~~Y,TAUTCA~BTCL,~TNP,CLL) DU 20 K=l,NP 20 CL (.ti)=CVAL (.K) CCMPUTECUAKrEFi CHLlKU PITCHING MOMENT CGEFFICIENTS CLL=999. iiEYCN=93Y. XMAX=O. CALL t3R1OG(.(;i\?~ltNPt 39 IWT~E,KEY~TAU,'CAMB,CL,~~TNP,CLL) LO 59 K=l,NP CIIECK IFSECTION STALLED

" . ISS=IS IKT=1

1 50

ChtCK F(JK UUKP

I CCMPIJTEOVEKALL LIFT, DRAG9 AND PITCHING KOMENT COEFF IC 1 ENTS

+SUP12

YO UM4

IFT,CDP

DEFIWE EXACT STALL ANGLE CF ATTACK L 100 I AGN= I AGNt 1 112 120 130 140 1.50 IOT=Z 160 IY=l 170

180 190 2 OD

2 LO

220

230 24 0

260 FOR~~T~L~XT~~HSTALLEO('1.3~32HAT POINT SECTION ANGLE OF ATTACK =9 lFl0.39LOXy30HMAX.SECTI*ON ANGLE OF ATTACK 'TF10.3)

176 NG FnOMEi\lT CUliFFICIENT)

ATT ACK NT NTI FICIENT) ACK,DEG 0.2 'X 9 3CHL IF CIE .. F ICI ENT 0.6 IIC 1X 9 30HrOT c OE

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190

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188 q-

APPENDIX B

AVAI+-ILITY OF THE COMF'IJTER PROGRAM

The computerprogram developed for the CDC 6400and 6600 series computershas been stored in the COSMIC Computer Center and is availablefor public use. All inquiriespertaining to availability and use of the programshould be directed to:

COSMIC Computer Center Barrow Hall University of Georgia Athens,Georgia 30601

Telephone: (404) 542-3265

189

" BIBLIOGRAPHY Presented herein is a compilation of a total243 technicalof reports related to the state of theof artwing, and wing-body aerodynamics. For convenience, the following papers are arranged in an alphabetical order by authors within the subgroupsof each of the three main groups; Theoretical Methods, Wind-Tunnel Tests, and Aircraft Flight Tests. 1. THEORETICAL METHODS (a) Wing Theory 1. Allen, H. Julian: Calculation of the Chordwise Load Distribution over Airfoil Sections with Plain, Split or Serially-hinged Trailing Edge Flaps. NACA Rep.634, 1938. 2. Allen, H. Julian: A Simplified Method for the-Calculation of Airfoil Pressure Distribution. NACA TN 708, 1939. 3. Allen, H. Julian: General Theory of Airfoil Sections Having Arbitrary Shape or Pressure Distribution. NACA ACR 3G29, 1943. 4. Allen, H. Julian: Notes on the Effect of Surface Distor- tion on the Drag and Critical Mach Numberof Airfoils. NACA ACR 3129, 1943. 5. Anderson, Raymond F: Determination of the Characteristics of Tapered Wings. NACA Rep. 572, 1936. 6. Anderson. Raymond F.: A Comparison of Several Tapered Wings Designedto Avoid Tip Stalling. NACA TN 713, 1939. 7. Boshar, John: The Determination of Span Load Distribution at High Speeds by the Use of High-speed Wing Tunnel Section Data. NACA ACR 4B22, 1944 (Wartime Rep.L-436). 8. Weissinger, J.,: The Lift Distribution of Sweptback Wings, NACA TM 1120, 1947. 9. Crabtree, L. F., Kuchemann, D., and Maskell, .C.E : A Survey of Some Research on the Stalling of Wings of Contemporary Design in Progress at the R.A.E. R.A.E. TN Aero 2331, 1954.

190 10. De Young, John: Theoretical Symmetric Span Loading Due to Flap Deflection for Wingsof Arbitrary Plan Form at Subsonic Speeds. NACA Rep. 1071, 1952.

11. De Young, John & Harper, Charles W.: Theoretical Symmetric Span Loadingat Subsonic Speeds for Wings Having Arbitrary PlanForm. NACA Rep. 921, 1948. 12. Diederich, Franklin W. & Zlotnick, Martin: Calculated Spanwise Lift Distributions, Influence Functions, and Influence Coefficients for Unswept Wingsin Subsonic Flow. NACA Rep. 1228, 1955.

13. Furlong, Chester G. & McHugh, James G.: A Summary and Analysis of the Low-Speed Longitudinal Characteristics of Swept Wingsat High Reynolds Number. NACA Rep. 1339, 1957. 14. Glauert, H.: Theoretical Relationships for an Aerofoil with Hinged Flap. R & M No. 1095, British ARC, 1927. 15. Glauert, H.: The Effect of Compressibilityon the Lift of an Aerofoil. R& M No. 1135, BritishARC, 1927. 16. Glauert, H. & Gates, S.B.: The Characteristics of a Tapered and Twisted Wing With Sweep-Back. ARC& M R 1226, 1928. 17. Goldstein, Sidney: Low-drag and Suction Airfoils, Eleventh Wright Brothers Lecture,J. Inst. Aeronaut Sci., Vol. 15, No. 4, 1948, pages 189-214. 18. Harper, CharlesW. & Maki, Ralph L.: A Review of the Stall Characteristicsof Swept Wings. NASA TN D-2373, 1964. 19. Jacobs, Eastman N.= Preliminary Report on Laminar Flow Airfoils and New Methods Adopted for Airfoil and Boundary-layer Investigations. NACA ACR, June, 1939, (Wartime Rep. L-345). 20. Jones, Robert T.: Correction of the Lifting-Line Theory for the Effect of the Chord. NACATN 817, 1941. 21. Kus, Yung-Huai: On the Stability of Two-Dimensional Smooth Transonic Flows. J. Ae. S., Vol. 18, No. 1, (19511, page 1.

22. Lippisch., A.: Method for the Determinationof the Spanwise Lift Distribution. NACA TM 778. 23. Martina, Albert P.: Method for Calculating the Rolling and Yawing MomentsDue to Rolling for Unswept Wings With or Without Flaps or Ailerons by Use of Nonlinear Lift Data. NACA Rep. 1167, 1954. 24. Muggia, Aldo: Remark on the Theory of Lifting Surfaces. NACA TM 1386, 1956. 25. Multhopp, H.: The Calculation of the Lift Distribution of Airfoils. Luftfahrforschung, Deutschland (RTP Translation No. 23921, 1938. 26. Multhopp, H.: Methods for Calculating the Lift-Distrib- ution of Wings (Subsonic Lifting SurfaceTheory). R.A.E. Rep. No. Aero 2353, 1950. 27. Munk, Max. M.: The Determination of the Angles of Attack of Zero Lift and Zero Moment, Based on Munk's Integrals. NACA TN 122, 1923. 28. Munk, Max. M.: Elements of the Wing Section Theory and of the Wing Theory. NACA Rep. 191, 1924. 29. Munk, Max M.: Calculation of Span Lift Distribution (Part 21, Aero Digest,Vol. 48, No. 3, 1945, page 84. 30. Naiman, Irven: Numerical Evaluation of the E -Integral Occurring in the Theodorsen Arbitrary Airfoil Potential Theory. NACA ARR L4D27a, 1944 (Wartime Rep. L-136). 31. Naiman, Irven: Numerical Evaluation by Harmonic Analysis of the E -Function of the Theodorsen Arbitrary Poten- tial Theory. NACA ARR L5H18, 1945 (Wartime Rep. L-153). 32. Nitzberg, GeraldE.: A Concise Theoretical Method for Profile-drag Calculation. NACA ACR 4B05,1944. 33. Pankhurst, R.C.: A Method for the Rapid Evaluation of Glauert's Expressions for the Angle of Zero Lift and the Moment atZero Lift. R & M No. 1914 British ARC, 1944. 34. Pearson, Henry A.: Span Load Distribution for Tapered Wings with Partial-Span Flaps. NACARep. 585, 1936. 35. Pearson, Henry A. and Jones, Robert T.: Theoretical Stability and Control Characteristics of Wings with Various Amounts of Taper and Twist. NACA Rep. 635, 1938.

192 36. Pearson, HenryA. and Anderson, Raymond F.: Calculation of the Aerodynamic Characteristicsof Tapered Wings With Partial-Span Flaps. NACA Rep. 665, 1939. 37. Reissner, E.: Note on the Theory of Lifting Surfaces, Proceedings of the National Academyof Sciences, Vol. 35, No. 4, 1949, pages 208-215. 38. Roshko, A.: Computation of the Increment of Maximum Lift Due to Flaps. Douglas Aircraft Rep. SM-23626, 1959. 39. Sherman, Albert: A Simple Method of Obtaining Span Load Distributions. NACA TN 732, 1939. 40. Sivells, JamesC.: An Improved Approximate Methodfor Calculating Lift Distributions Due to Twist. NACA TN 2282, 1951. 41. Sivells, James C., and Neely, RobertH.: Method of Calculating Wing Characteristics by Lifting-Line Theory Using Nonlinear Section Lift Data. NACATN 1269, 1947, Also NACA Rep. 865, 1947. I 42. Sivells, James C.and Westrick, Gertrude C.: Method for Calculating Lift Distributions for Unswept Wings With Flaps or Aileronsby Use of Nonlinear Section Lift Data. NACA Rep. 1090, 1952. 43. Soule, Hartley A. and Gough, V., Melvin N.: Some Aspects of the Stalling of Modern Low-Wing Monoplanes. NACA TN 645, 1938. 44. Squire, H. B. and Young, A.D.: The Calculation of the Profile Drag of Aero foils. &R M No. 1838, British ARC, 1938. 45. Tani, Itiro: A Simple Method of Calculating the Induced Velocity of a Monoplane Wing. Aeronaut. Research Inst. Tokyo Imp. Univ. Rep. 111, Vol. IX, page 3, August 1934. 46. Tetervin, Neal: A Method for the Rapid Estimationof Turbulent Boundary-layer Thickness for Calculating Profile Drag. NACA ACR L4G14, 1944 (Wartime Rep. L-16). 47. Theodorsen, Theodore: On the Theory of Wing Sections with Particular Reference to the Lift Distribution. NACA Rep. 383, 1931. 48. Theodorsen, Theodore: Theory of Wing Sections of Arbitrary Shape. NACA Rep. 411, 1931.

193

I 49. Theodorsen, Theodore: Airfoil Contour Modification Based on€-Curve Method of Calculating Pressure Distribution. NACA ARR L4G05, 1944 (Wartime Rep. L-1351. 50. Theodorsen, Theodore, and Garrick,I. E.: General Potential Theory of Arbitrary Wing Sections. NACA Rep. 452, 1933.

51. von Doenhoff, AlbertE.: A Method of RapidlyEstimating the Laminar SeparationPoint. NACA TN 671, 1938. 52. von Karman, T.: Turbulence and Skin Friction, J. Aeronaut. Sci., Vol. 1, No. 1, 1934, pages 1-20. 53. von Karman,T.: Compressibility Effects in Aerodynamics, J. Aeronaut. Sci., Vol. 8, No. 9, 1941, pages 337-356. 54. Walz, A.: Theoretical Calculation of the MaxYmum Lift Coefficient of WingsWith and Without Lift-Flaps. ZWB Research Report No. 1769, 1943 (Translated by Frank, Richard and Fahle, John, Cornel1 Aeronautical Laboratory, Inc., 1951). 55. Weich, Fred E., Flanagan, L.E., Jr., and Cherry, H.H.: An Analytical Investigation of Effect of High-Lift Flaps on Take-Off of Light Airplanes. NACA TN 2404, 1951. 56. Weich, Fred E. and Abramson, H. Norman: Investigation of Lateral Control Near the Stall. Analysis for Required Longitudinal Trim Characteristics and Discussion of Design Variables. NACA TN 3677, 1956. 57. Wimpenny, J.C.: Low-Speed Stalling Characteristics. AGmD Rep. 356, 1961. (b) Interference Methods 1. Ch.ester,D. H.: The Lift of a Propeller-Wing Combination Due to the Slip-Stream. Israel Journal of Technology, Vol. 3, No. 1, 1965, page 102. 2. Dynasciences Corporation: Effects of Propeller Slipstream on V/STOL Aircraft Performance and Stability, TRECOM TR 64-47, 1964. 3. Ellis, N.D.: A Computer Study of aWing in a Slipstream. UTIAS TN 101, 1965.

194 4. Flax, A.H. and Treanor, C.E.: A Variational Calculation of Subsonic Wing-Body Interference According to Lifting- Line Theory, Cornell Aeronautical Laboratory. (To be published.) 5. Franke, A. and Weinig F.: The Effect of the Slipstream on an Airplane Wing. NACA TM 920, 1939. 6. George, M. and Kisielowski, E.: Investigation of Prop- eller Slipstream Effectson Wing Performance. USAAVLABS TR 67-67, 1967. 7. Lawrence, H.R. and Flax A.H.: Wing-Body Interferenceat Subsonic and Supersonic Speeds- Survey andNew Develop- ments. J. Ae. Sc., Vol. 21, No. 5, Page 289, 1954.

8. Lennertz, J.: Influence of the Airplane Bodyon the Wings, Aerodynamic Theory;W. F. Durand, Editor,Vol. IV, Division K, Chapter 111, Durand Reprinting Committee, 1943.

9. Low, L., and Stone, H. N.: The Subsonic Aerodynamic Characteristics of Wings in Combination with Slender Bodies of Revolution, Cornell Aeronautical Laboratory, Bumblebee ReportNo. CAL/CM-679, 1951. 10. Matthews, ClarenceW.: A Comparison of the Experimental Subsonic Pressure Distributions About Several Bodiesof Revolution with Pressure Distributions Computedby Means of the Linearized Theory. NACA Rep. 1155, 1953. 11. Multhopp, H.: Aerodynamics of the Fuselage, NACATM 1036, 1942. 12. Munk, Max M.: The Aerodynamic Forces on AirshipHulls, NACA TR 184, 1924. 13. Pepper, P.A., Minimum Induced Drag in Wing-Fuselage Interference, NACATN 812, 1941. 14. Pitts, WilliamC., Nielsen, Jack N., and Kaattari, George E.: Lift and Center of Pressure ofWing-Body-Tail Combinations at Subsonic, Transonic, and Supersonic Speeds. NACA Rep. 1307, 1957. 15. Ribner, H. S. and Ellis, N.D.: Theory and Computer Study of a Wing in a Slipstream. AIAA Paper No.66-466, 1966. 16. Ribner, H.S.: Theory of Wings in a Slipstream. LITIAS Rep. 60, 1959.

195 17. Schlichting, H., Monograph on theAerodynamics of Mutual Interference Between the Componentsof the Airplane,National Research Council of Canada, Tech- nical Translation No. TT-92,1949.

18. White, RichardP., Jr.: VTOL Periodic Aerodynamic Loadings. TheProblems-What is Being Done and What Needs tobe Done. Paperpresented at the Symposium on theNoise and Loading Actions on Helicopter V/STOL Aircraftand Ground EffectMachines, at University of Southampton,Hampshire, England, Aug. 30 to Sept. 3, 1965.

19.Wieselsberger, C.: Contributionto the Mutual Inter- ferenceof Wing and Propeller. NACA TM 754,1934.

20.Yaggy, Paul F.: A Method forPredicting the Upwash AnglesInduced at thePropeller Planeof a Combination ofBodies with an Unswept Wing. NACA TN 2528,1951.

21. Young, A.D.: Noteon theEffect of Slipstream on BoundaryLayer Flow.Rep. B.A. 1404,British RAE, 1937.

22. Young, A. D.: FurtherNote on theEffect of Slipstream onBoundary Layer Flow. Rep. No. B.A. 1404a,British RAE, 1938.

23. Young, A.D., andMorris D.E.: Further Note on theEffect ofSlipstream on Boundary Layer Flow.Rep. No. B.A. 1404b,British RAE, 1939.

24. Zlotnick M., andRobinson, S.W., Jr.: A Simplified Mathematical Model for Calculating AerodynamicLeading and Downwash for Midwing Wing-FuselageCombinations with Wings ofArbitrary Planform, NACA RN L52J27a,1953.

25. Zlotnick, Martin andRobinson, Samuel W., Jr.: A SimplifiedMathematical Model for Calculating Aero- dynamicLoading and Downwash forWing-Fuselage Combina- tions With Wings of ArbitraryPlan Form. NACA TN 3057, 1954. (c)Total Aircraft Analysis

1. Goranson, R. Fabian: A Method forPredicting the Elevator DeflectionRequired to Land. NACA WR L-95 (Originally issued as ARR L41161,1944.

2. Graham, Ernest W. & Luskin,Harold: The Determination of the Stalling Speedand the Maximum Lift Coefficient in Flight. J.A.S., page95, Feb., 1946.

196 Howe, JohnT.: Some Fluid Mechanical Problems Related i. 3. to Subsonic and Supersonic Aircraft. NASA SP-183,1968.

Lovell, J. Calvin & Lipson, Stanley: An Analysis of the Effect of Lift-Drag Ratio and Stalling Speed on Landing- Flare Characteristics. NACA TN 1930, 1949. 5. Pinsker, W.J.G.: TIZero Rate of Climb Speed” asLow a Speed Limitation for the Stall-Free Aircraft. ARCC.P. 931, 1966. 6. Priestley, E.: A General Treatmentof Static Longitudinal Stability With Propellers, With Application to Single- Engined Aircraft. ARC R & M 2732, 1953. 7. Staff of Langley Research Center: A Preliminary Studyof V/STOL Transport Aircraft and Bibliography of NASA I Research in the VTOL-STOL Field. NASATN D-624,1961. ! 8. Zalovcik, JohnA.: Summary of Stall Warning Devices. NACA TN 2676, 1952. 2. WIND TUNNEL TESTS (a) Section Characteristics 1. Abbott, Frank T., Jr.,and Turner, Harold R.,Jr.: The Effects of Roughness at High Reynolds Numbers on the Lift and Drag Characteristics of Three Thick Airfoils, NACA ACR No. L4H21,1944 (Wartime Rep. L-46). 2. Abbott, Ira H., and Greenberg, Harry: Tests in the Variable-Density Wind Tunnelof the NACA23012 Airfoil With Plain and Split Flaps.NACA Rep. 661, 1939. 3. Abbott, Ira H., von Doenhoff, Albert E., and Stivers, Louis S.: Summary of Airfoil Data. NACA Rep. 824, 1945. 4. Abbott, Ira H. & Sherman, Albert: Flow Observations With Tufts and Lampblack of the Stalling of Four Typical Airfoil Sections in the N.A.C.A. Variable-Density Tunnel. NACA TN 672, 1938. 5. Aeronautics Laboratory, Cambridge: An Experimental Study of the Stalling of Wings. ARC &R M 1588, 1933. 6. Bullwant, W. Kenneth: Tests of the NACA 0025 and 0035 Airfoils in the Full-scale Wind Tunnel. NACA Rep. 708, 1941.

19 7 7. Cahill, Jones F.: Summary of Section Data on Trailing- Edge High-lift Devices. NACARM No. L8D09, 1948 (Also NACA Rep. 938, 1949). 8. Cahill, Jones F.: Two-dimensional Wind-tunnel Investiga- tion of Four Types of High-lift on Flap an NACA65-210 Airfoil Section. NACA TN 1191, 1947. 9. Cahill, Jones F., and Racisz, Stanley: Wind-tunnel Development of Optimum Double-slotted-flap Configurations €or Seven Thin NACA Airfoil Sections. NACARM No. L7B17, 1947, alsoTN 1545. 10. Clay, William C.: Characteristics of theN.A.C.A. 23012 Airfoil From Tests in the Full-scale and Variable-Density Tunnels. NACA Rep. 530, 1935. 11. Fischel, Jack, and Riebe, John M.: Wind-tunnel Investiga- tion of a NACA 23021 Airfoil with a 0.32-airfpil-chord Double Slotted Flap. NACA ARR No. L4J05,1944 (Wartime Rep. L-7). 12. Fitzpatrick, James E. & Schneider, William C.: Effect of Mach Number Variation Between0.07 and 0.34 and Reynolds Number Variation Between0.97 x 106 and 8.10 x 106 on the Maximum Lift Coefficientof a Wing of NACA64-210 Airfoil Series. NACA TN 2753, 1952. 13. Fullmer, Felicien F., Jr.: Wind-Tunnel Investigation of NACA 66(215)-216, 66, 1-212, and 65,-212 Airfoils With 0.20-Airfoil-Chord Split Flaps. NACA WR L-140 (Originally Issued as CB L4G101,1944. 14. Fullmer, Felicien F., Jr.: Two-dimensional Wind-tunnel Investigation of the NACA 641-012 Airfoil Equipped With Two Types of Leading-edge Flap. NACATN 1277, 1947. 15. Furlong, G. Chester & Fitzpatrick, James E.: Effects of Mach Number and Reynolds Numberon the Maximum Lift Coefficient of a Wingof NACA 230-Series Airfoil Sections. NACA TN 1299, 1947 (Originally issued MR as L6F04, 1946). 16. Gault, Donald E.: Boundary-Layer and Stalling Characteris- tics of the NACA 63-009 Airfoil Section. NACA TN 1894, 1949. 17. Goett, Harry J.& Bullivant, W. Kenneth: Tests of N.A.A.A. 0009, 0012, and 0018 Airfoils in the Full-Scale Tunnel. NACA Rep. 647, 1939.

198 Graham, DonaldJ.r The Development of Cambered Airfoil Sections Having Favorable Lift Characteristics at Supercritical Mach Numbers. NACA Rep. 947, 1949. Harris, ThomasA.: Wind-tunnel Investigation of an NACA Airfoil With Two Arrangements of a Wide-chord Slotted Flap. NACA TN 715, 1939. Harris, ThomasA., and Recant, IsidoreG.: Wind-tunnel Investigation of NACA 23012, 23021, and 23030 Airfoils Equipped with 40-percent-chord Double Slotted Flaps. NACA Rep. 723, 1941.

!' 21. Harris, Thomas A., and Lowry, JohnG. : Pressure Distribution Over an NACA 23012 Airfoil with a Fixed Slot and a Slotted Flap. NACA Rep. 732, 1942.

\ 22. Hood, Manley J., and Gaydos, M. Edward: Effects of Propellers and of Vibration on the Extent of Laminar Flow on the NACA 27-212 Airfoil. NACA ACR, October 1939, (Wartime Rep. L-784). 23. Jacobs, Eastman N., and Abbott, IraH.: Airfoil Section Data Obtained in the NACA Variable-density Tunnel as Affected by Support Interference and Other Corrections. NACA Rep. 669, 1939. 24. Jacobs, Eastman N., and Pinkerton, Robert M.: Tests in the Variable-density Wind Tunnel of Related Airfoils Having the Maximum Camber Unusually Far Forward. NACA Rep. 537, 1935. 25. Jacobs, Eastman N., and Pinkerton, RobertM.: Pressure, Distribution Over a Symmetrical Airfoil Section With Trailing Edge Flap. NACA Rep. 360, 1930. 26. Jacobs, Eastman N., Pinkerton, RobertM., and Greenberg, Harry: Tests of Related Forward-camber Airfoils in the Variable-density Wind Tunnel. NACA Rep.610, 1937. 27. Jacobs, Eastman N., Ward, Kenneth E., and Pinkerton, Robert M.: The Characteristics of 78 Related Airfoil Sections from Tests in the Variable-density Wind Tunnel. NACA Rep. 460, 1932. 28. Kelly, JohnA. & Hayter, Nora-LeeF.: Lift and Pitching Moment at Low Speeds of the NACA64A010 Airfoil Section Equipped With Various Combinations of a Leading-Edge Stat, Leading-Edge Flap, Split Flap, and Double-Slotted Flap. NACA TN 3007, 1953.

I 29. Kruger, W.: Wind-tunnel Investigation on a Changed Mustang Profile With. Nose Flap. Force and Pressure Distribution Measurements. NACA TM 1177, 1947.

30. Loftin, Laurence K.,Jr.: Theoretical and Experimental Data for a Number of NACA 6A-Series Airfoil Sections. NACA Rep. 903, 1947. 31. Loftin, Laurence K., Jr.: Airfoil Section Characteristics at High Angles of Attack. NACA TN 3241, 1954. 32. Loftin, Lawrence K., Jr.: Aerodynamic Characteristics of the NACA64-010 and 0010-1.10 40/1.051 Airfoil Sections at Mach Numbers from0.30 to 0.85 and Reynolds Numbers from 4.0 x LO6 to 8.0 X lo6. NACA TN 3244, 1954. 33. Loftin, Laurence K., Jr.: Effects of Specific Types of Surface Roughness on Boundary-Layer Transition. NACA ACR L5J29a, 1945 (Wartime Rep. L-48). 34. Loftin, Laurence K., Jr. & Bursnall, WilliamJ.: The Effects of Variations in Reynolds Number Between 3.0 x 106 and 25.0 x 106 Upon the Aerodynamic Characteristics of a Number of NACA 6-Series Airfoil Sections. NACA Rep. 964, 1950. 35. Loftin, Laurence K., Jr. and Cohen, KennethS.: Aerodynamic Characteristics of a Number of Modified NACA Four-digit- series Airfoil Sections. NACA RM L7122, 1947. 36. Loftin, Laurence K.,Jr. & Smith, Hamilton,A.: Aero- dynamic Characteristics of 15 NACA Airfoil Sections at Seven Reynolds Numbers From 0.7x lo6 to 9.0 x 106. NACA TN 1945, 1949. 37. Loftin, Laurence K., Jr.& Smith, Hamilton A.: Two- dimensional Aerodynamic Characteristics of34 Miscell- aneous Airfoil Sections. NACARM L8L08, 1949. 38. Lowry, John G.: Wind-tunnel Investigation of an NACA 23012 Airfoil with Several Arrangements of Slotted Flap With Extended Lips. NACA TN808, 1941. 39. Maki, Ralph L. & Hunton, LynnW.: An Investigation at Subsonic Speeds of Several Modificationsto the Leading- Edge Region of the NACA 64A010 Airfoil Section Designed to Increase Maximum Lift. NACA TN 3871, 1956.

200 ".I,. 40. McCullough, GeorgeB. & Gault, Donald E.: Boundary-Layer Iti and Stalling Characteristics of the NACA006 64AAirfoil Section. NACA TN 1923, 1949. 41. McCullough, George B. & Gault, Donald E.: Examples of Three Representative Types of Airfoil-Section Stall at Low Speed. NACA TN 2502, 1951. 42. Peterson, RobertF.: The Boundary-Layer and Stalling Characteristics of the NACA64A 010 Airfoil Section. NACA TN 2235, 1950. 43. Pinkerton, RobertM.: Calculated and Measured Pressure Distribution Over the Midspan Sectionof the NACA Rep. 563, 1936. 44. Platt, Robert C., and Abbott, IraH.: Aerodynamic Characteristics of NACA 23012 and 23021 Airfoils with 20-percent-chord External-airfoil Flapsof NACA 23012 Section. NACA Rep. 573, 1936. 45. Purser, Paul E. Fischel, Jack, and Riebe, JohnM.: Wind- tunnel Investigation of an NACA 23012 Airfoil With a 0.30-airfoil-chord Double Slotted Flap. NACA ARR No. 3L10, 1943 (Wartime Rep. No. L-469). 46. Purser, Paul E., and Johnson, HaroldS.: Effects of Trailing-edge Modifications on Pitching-moment Characteristics of Airfoils. NACA CB L4130, 1944 (Wartime Rep. L-664). 47. Quinn, John H.,Jr.: Summary of Drag Characteristics of Practical-Construction Wing Sections. NACA Rep. 910, 1948. 48. Recant, I.G.: Wind-tunnel Investigation of an NACA 23030 Airfoil With Various Arrangements of Slotted Flap. NACA TN 755, 1940. 49. Sch.uldenfrei, MarvinJ.: Wind-tunnel Investigation of an NACA 23012 Airfoil With a Handley Page Slot and Two Flap Arrangements. NACA ARR, February, 1942 (Wartime Rep. L-261). 50. Sherman, Albert, and Harris,T.A.: The Effects of Equal Pressure Fixed Slots on the Characteristicsof a Clark-Y Airfoil. NACA TN 507, 1934. 51. Stack, John, and von Doenh.off, AlbertE.: Tests of 16 Related Airfoils at High Speeds. NACA Rep. 492, 1934.

2 01 52. University of Southampton: 'Determination of the Forces Moments on an Airfoil Oscillating Through the Stall. A.A.S.U. 252, 1964. 53. von Doenhoff, AlbertE., and Abbott, FrankT., Jr.: The Langley Two-dimensional Low-turbulence Pressure Tunnel. NACA TN 1283,1947. 54. von Doenhoff, AlbertE., and Tetervin, Neal: Investiga- tion of the Variation of Lift Coefficient With Reynolds Number at a Moderate Angle of Attack on a Low-drag Airfoil. NACA CB, 1942 (Wartime Rep. L-661). 55. Weick, Fred E., and Shortal, JosephA.: The Effect of Multiple Fixed Slots and a Trailing-edge Flap on the Lift and Drag ofa ClarkY Airfoil. NACA Rep. 427, 1932. 56. Wenzinger, CarlJ.: Wind-tunnel Investigation- of Ordinary and Split Flaps on Airfoils of Different Profile. NACA Rep. 554, 1936. 57. Wenzinger, CarlJ.: Pressure Distribution Over an Airfoil Section With a Flap and Tab. NACA Rep. 574, 1936. 58. Wenzinger, CarlJ.: Pressure Distribution Over an NACA 23012 Airfoil With an NACA 23012 External-airfoil Flap. NACA Rep. 614, 1938. 59. Wenzinger, Carl J., and Delano, JamesB.: Pressure Distribution Over an NACA 23012 Airfoil With a Slotted and a Plain Flap. NACA Rep. 633, 1938. 60. Wenzinger, Carl J. & Gauvain, William E.: Wind-Tunnel Investigation of an N.A.C.A. 23012 Airfoil Witha Slotted Flap and Three Types of Auxiliary Flap. NACA Rep. 679, 1939. 61. Wenzinger, Carl J., and Harris, ThomasA.: Wind-tunnel Investigation of an NACA 23012 Airfoil With. Various Arrangements of Slotted Flaps. NACA Rep. 664, 1939. 62. Wenzinger, Carl J., and Harris, ThomasA.: Wind-tunnel Investigation of NACA23012, 23021, and 23030 Airfoils With Various Sizes ofSplit Flap. NACA Rep. 668, 1939. 63. Wenzinger, CarlJ., and Harris, ThomasA.: Wind-tunnel Investigation of an NACA 23021 Airfoil With Various Arrangements of Slotted Flaps. NACA Rep. 677, 1939.

202 64. Wenzinger, Carl J., and Rogallo, FrancisM.: Resume of Airload Data onSlats and Flaps. NACATN 690, 1939. 65. Wilson, Homer B., Jr. & Horton, Elmer A.: Aerodynamic Characteristics at High andLow Subsonic Mach Numbers of Four NACA 6-Series Airfoil Sections at Angles of Attack From -20 to 31O. NACA RM L53C20, 1953. 66. Young, A.D.: A Review of Some Stalling Research. ARC R & M 2609, 1942. (b) Wing Alone Tests 1. Bollech, Thomas V.: Experimental and Calculated Characteristics of Several High-Aspect-Ratio Tapered Wings Incorporating NACA 44-Series, 230 Series, and Low Drag 64-Series Airfoil Sections. NACATN 1677, 19 48. 2. Cahill, JonesF.: Aerodynamic Dath for a Wing Section of the RepublicXF-12 Airplane Equipped With a Double Slotted Flap. NACA MR No. L6A08a, 1946 (Wartime Rep. L-544) . 3. Greenberg, Harry: Characteristics of NACA 4400R Series Rectangular and Tapered Airfoils, Including the Effect of Split Flaps. NACA WR L-493, 1941. 4. Hamilton, WilliamT. & Nelson, Warren H.: Summary Report on the High-speed Characteristics of Six Model Wings Having NACA 65-Series Sections. NACA Rep. 877, 1947. 5. Hood, Manley J.: The Effects of Some CommonSurface Irregularities on Wing Drag. NACA TN 695, 1939. 6. Jessen, Henry, Jr.: A Summary Report on the Effects of Mach Number on the Span Load Distribution on Wings of Several Models. NACA RM A7C28, 1947. 7. Neely, Robert H. Bollech, Thomas V., Westrick, Gertrude C., and Graham, Robert R.: Experimental and Calculated Characteristics of Several NACA 44-Series Wings with Aspect Ratios of 8, LO, and 12, and Taper Ratios of 2.5 and 3.5. NACA TN 1270, 1947. 8. Nonweiler, T.: A Resume of Maximum LiftData for Symmetrical Wings With Various High-Lift Aids. College of Aeronautics, Cranfield CoA NoteNo. 5, 1954. 9. Noyes, Richard W.: Wind-tunnel Testsof a Wing with a Trailing-edge Auxiliary Airfoil Used asFlap. a NACA TN 524, 1935.

2 03 10. Palme, H.O.: Summary of Stalling Characteristics and Maximum Lift of Wings atLow Speeds. SAAB Aircraft Company, Sweden, TN15, 1953. 11. Pearson, E.O., Jr., Evans, A.J., and West, F.E.: Effects of Compressibility on the Maximum Lift Characteristics, and Spanwise Load Distributionof a 12-foot-span Fighter- type Wing of NACA 230-series Airfoil Sections. NACA ACR L5G10, 1945 (Wartime Rep. L-51). 12. Platt, Robert C.: Aerodynamic Characteristics of a Wing With Fowler Flaps, Including Flap Loads Down-wash, and Calculated Effect on Take-Off. NACA Rep.534, 1935. 13. Platt, Robert C.: Aerodynamic Characteristics of Wings with Cambered External-airfoil Flaps, Including Lateral Control With a Full-span Flap. NACA Rep. 541, 1935. 14. Platt, Robert C., and Shortal, JosephA.: Wind-tunnel Investigation of Wings With Ordinary Ailerons and Full- span External Airfoil Flaps. NACA Rep.603, 1937. 15. Sherman, Albert: The Aerodynamic Effects of Wing Cut-Outs. NACA Rep. 480, 1934. 16. Sivells, James C.: Experimental and Calculated Character- istics of Three Wings of NACA64-210 and 65-210 Airfoil Sections With and Without 20 Washout. NACATN 1422, 1947. 17. Soule, H. A. & Anderson, R.F.: Design Ch.arts Relatingto the Stalling of Tapered Wings. NACA Rep.703, 1940. 18. Stack, John& Lindsey, W.F.: Characteristics of Low- Aspect-Ratio Wings at Supercritical Mach Numbers. NACA Rep. 922, 1949. 19. Sweberg, Harold H. & Lange, RoyH.: Summary of Available Data Relating to Reynolds Number Effects on the Maximum Lift Coefficients of Swept Back Wings. NACARM L6L202, 1947. 20. Wallace, Rudolf: Investigation of Full-scale Split Trailing-Edge Wing Flaps With Various Chords and Hinge Locations. NACA Rep. 539, 1935. 21. Weick, Fred E., and Harris, ThomasA.: The Aerodynamic Characteristics of a Model Wing Having a Split Flap Deflected Downward and Moved to the Rear. NACA TN 422, 1932.

204 22. Weick, Fred E., and Platt, Robert C.: Wind-tunnel Tests on a Model Wing With Fowlerand Flap Specially Developed Leading-edge Slot. NACA TN 459,1933. 23. Weick, Fred E., and Sanders, Robert: Wind-tunnel Tests of a Wing with Fixed Auxiliary Airfoils Having Various Chords and Profiles. NACA Rep. 472, 1933. 24. Wenzing, Carl J.: Wind-tunnel Tests of a ClarkY Wing Having Split Flaps With Gaps. NACA TN650, 1938. 25. Wenzinger, Carl J. & Harris, Thomas A.: Pressure Distribution Over a Rectangular Airfoil With a Partial- Span Split Flap. NACA Rep. 571,1936. 26. Woodward, D.S.: On the Errors Induced at Tunnel Reference Pressure Tappings by High Lift Models. R.A.E. Technical Report No. 66049, 1966. (c> Complete Model Tests 1. Brewer, GeraldW., & May, Ralph W., Jr.: Investigation of a1/7 Scale Powered Model of a Twin Boom Airplane and a Comparison of its Stability, Control, and Performance with Those of a Similar All-Wing Airplane. NACA TN 1649,1948. 2. Goodman, A.: Effects of Wing Position and Horizontal-Tail Position on Static Stability Characteristics of Models With Unswept and 45O Sweptback Surfaces with Some Reference to Mutual Interference. NACA TN 2502, 1951. 3. Hagerman, JohnR.: Wind-tunnel Investigation of the Effect of Power and Flaps on the Static Longitudinal Stability and Control Characteristics of a Single-Engine High-wing Airplane Model. NACATN 1339, 1947. 4. Harper, Paul W.& Flanigan, Roy E.: Investigation of the Variation of Maximum Lift for a Pitching Airplane Model and Comparison With Flight Results. NACATN 1734, 19 48.

5. Harper, Paul W. & Flanigan, Ray E.: The Effect of Rate of Change of Angle of Attackon the Maximum Lift of a Small Model. NACA TN 2061, 1950. 6. Hartshorn, A.S., Hirst, D.M.,& Midwood, G.F.: Tests on Model of "Wapiti" Including Effect of Slipstream. ARC R & M 1419, 1932.

205 7. Hopkins, Edward J. & Carel, Hubert C.: Experimental and Theoretical Studyof the Effects of Body Sizeon the Aerodynamic Characteristics ofan Aspect Ratio 3.0 Wing- Body Combination. NACA RM A51G24, 1951. 8. Hopkins, Edward J. & Carel, Hubert C.: Experimental and Theoretical Study of the Interference Low at Speed Between Slender Bodies and Triangular Wings. NACA RM A53A14, 1953. 9. House, Refus 0. & Wallace, Arthur R.: Wind-Tunnel Investigation of Effectof Interference on Lateral- Stability Characteristics of Four NACA23012 Wings, An Elliptical and a Circular Fuselage, and VerticalFins. NACA Rep. 705,1941. 10. Jacobs, Eastman N. & Ward, Kenneth E.: Interference of Wing & Fuselage from Tests of209 Combinations in the N.A.C.A. Variable-Density Tunnel. NACA Rep. 540,1935. 11. Johnson, Harold S.: Wind-tunnel Investigationof Effects of Tail Length on the Longitudinal and Lateral Stability Characteristics of a Single-Propeller Airplane Model. NACA TN 1766,1948. 12. Jordan, Gareth H. & Cole, Richard I.: The Effect of a Simulated Propeller Slipstreamon the Aerodynamic Characteristics of an Unswept Wing PanelWith and Without Nacelles at Mach Numbers from0.30 to 0.86. NACA TN 2776,1952.

13. Letko, William & Tr7illiams, James L.: Experimental Invest- igation atLow Speed of Effects of Fuselage Cross Section on Static Longitudinal and Lateral Stability Character- istics of Models Having Oo and 45O Sweptback Surfaces. NACA TN 3551,1955. 14. Letko, William: Experimental Investigation at Low Speed of the Effects of Wing Position on the Static Stability of Models Having Fuselages of Various Cross Section and Unswept and 45O Sweptback Surfaces. NACA TN 3857,1956. 15. Martina, Albert P.: The Interference Effects of a Bodyon the Spanwise Load Distributions of 45'two Sweptback Wings of Aspect Ratio8.02 From Low-speed Tests. NACA TN 3730,1956. 16. Muttray, H.: Investigation of th.e Effect of the Fuselage on the Wing of aLow-Wing Monoplane. NACA TM517, 1929.

2 06 17. Pitkin, Marvin: Free-Flight-Tunnel Investigation of ,q-, the Effect of Mode of Propeller Rotation Upon the Lateral- Stability Characteristics of a Twin-Engine Airplane Model With Single Vertical Tails of DifferentSize. NACA WR L-354. (Originally Issued asARR 35181, 1943. 18. Prandtl, L.: Effects of Varying the Relative Vertical Position of Wing and Fuselage. NACA TN 75, 1921. 19. Ribner, Herbert S. & Mac Lachlan, Robert: Effect of Slipstream Rotationin Producing Asymmetric Forces on a Fuselage. NACA TN 1210, 1947. 20. Robinson, Russell G. & Herrnstein, William H., Jr.: Wing- Nacelle-Propeller Interference for Wings of Various Spans. Force and Pressure-Distribution Tests. NACARep. 569, 1936. 21. Sandahl, Carl A. & Vollo, Samuel D.: Wind-Tunnel Invest- igation of theAir Load Distribution onTwo Combinations of Lifting Surfaces and Fuselage. NACA TN 1295, 1947. 22. Schlichting, H.: Report on the Special Field "Interfer- ence" to the Wind-Tunnel Committee in February 1945. NACATM 1347, 1953. 23. Sherman, Albert: Interference of Wing and Fuselage from Tests of 28 Combinations in theN.A.C.A. Variable-Density Tunnel. NACA Rep. 575, 1936. 24. Sherman, Albert: Interference of Tail Surfaces and Wing and Fuselage From Tests of17 Combinations in the N.A.C.A. Variable Density Tunnel. NACA Rep. 678, 1939. 25. Sivells, James C., and Spooner, Stanley H.: Investigation in the Langley 19-Foot Pressure Tunnelof Two Wings of NACA 65-210 Airfoil Sections With Various Type Flaps. NACARep. 942, 1949. 26. Sleeman, William C., Jr. & Lindsley, Edward L.: Low-speed Wind-Tunnel Investigationof the Effects of Propeller Operation at High Thrust on the Longitudinal Stability and Trimof a Twin- Engine Airplane Configuration. NACA RM L52D04, 1952. 27. Stuper, J.: Effect of Propeller Slipstream on Wing and Tail. NACA TM 874, 1938. 28. Teplitz, Jerome: Effects of Small Angles of Sweep and Amounts of Dihedralon Stalling and Lateral Character- istics of a Wing-Fuselage Combination Equipped With Partial-and Full-Span Double Slotted Flaps. NACA Rep. 800, 1944.

207 29. Wallace, Arthur R., Rossi, Peter F., and Wells, Evelyn G.: Wind-tunnel Investigation of the Effectof Power and Flaps on the Static Longitudinal Stability Characteristics of a Single-Engine Low-Wing Airplane Model. NACA TN 1239, 1947. 30. Weil, Joseph & Sleeman, William C.,Jr.: Prediction of the Effects of Propeller Operationon the Static Longitudinal Stability of Single-Engine Tractor Mono- planes With Flaps Retracted. NACATN 1722,1948. 31. Windler, Ray: Tests of a Wing-Nacelle-Propeller Combina- tion at Several Pitch Settings Upto 42O. NACA Rep. 564, 1936. (d) Full-scale Wind-Tunnel Tests 1. Davis, Don D., Jr., and Sweberg, Harold H.: Investigation of Some Factors Affecting Comparisons of Wind-Tunnel and Flight Measurements of Maximum Lift Coefficients for a Fighter-Type Airplane. NACATN 1639,1948. 2. Fink, Marvin P. & Freeman, Delma C., Jr.: Full-scale Wind-Tunnel Investigation of Static Longitudinal and Lateral Characteristics of a Light Twin-Engine Airplane. NASA TN D-4983, 1969. 3. Kayten, Gerald G.: Analysis of Wind-Tunnel Stability and Control Tests in Terms of Flying Qualities of Full-scale Airplanes. NACA Rep. 825, 1945. 4. Roberts, John C. & Yaggy, Paul F.: A Survey of the Flow at the Plane of the Propeller of a Twin-Engine Airplane. NACA TN 2192, 1950. 5. Sweberg, Harold H. and Dingeldein, RichardC.: Summary of Measurements in Langley Full-scale Tunnel of Maximum Lift Coefficients and Stalling Characteristics of Air- planes. NACA Rep. 829, 1945. 6. White, James A. & Hodd, Manley J.: Wing-Fuselage Inter- ference, Tail Buffeting,and Air Flow About the Tail of a Low-Wing Monoplane.NACA Rep. 482, 1934. 3. AIRCRAFT FLIGHT TESTS 1. Anderson, Seth B.: Correlation of Flight and Wind-Tunnel Measurements of Roll-Off in Low-Speed Stalls on a 35O Swept-Wing Aircraft. NACA RM A53G22, 1953.

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Barnes, F. W. & Newman, B.G.: The Effectof Leading- p1 2. ?.? Edge Wedgeson the StallingBehavior ofthe Wirraway. R.A.A.F. Aircraft Research and Development Unit TN Aero/8, 1951. 3. Bicknell, Joseph: Determination of the Profile Drag of an Airplane Wing in Flight at High Reynolds Numbers. NACA Rep. 667, 1939. 4. Donely, Philip & Pearson, HenryA.: Flight and Wind-Tunnel Tests of anXBM-1 Dive Bomber. NACA.TN-644, 1938. 5. Gadeberg, Bernett, L.: The Effect of Rate of Change of Angle of Attack on the Maximum Lift Coefficient of a Pursuit Airplane. NACA TN 2525, 1951. 6. Gray, William E., Jr.: NASA Flight Research Center Hand- ling-Qualities Program on General-Aviation Aircraft, NASA TM X-56004,1964. 7. Hunter, Paul A.: Flight Measurements of the Flying Qualities of Five Light Airplanes. NACATN 1573, 1948. 8. Hunter, P.A. & Vensel, J.R.: A Flight Investigation to Increase the Safety of a Light Airplane. NACA TN 1203, 1947. 9. Huston, Wilber B. & Skopinski, T.H.: Measurement and Analysis of Wing and Tail Buffeting Loads on a Fighter Airplane. NACA Rep. 1219, 1955.

10. Kayten, Gerald G. & Koven, William: Comparison of Wind- Tunnel and Flight Measurements of Stability and Control Characteristics of a Douglas A-26 Airplane. NACA Rep. 816, 1945. 11. La Plant 11, Porter & Johnson, AlbinusP.: Evaluation of the Giannini Dual Stall Warning System and Stall Margin Indicators Installed in a C-133B. FTCTR-67-5, 1967. 12. Nissen, JamesM. & Gadeberg, Burnett L.: Effect of Mach & Reynolds Numbers on the Power-Off Maximum Lift Coefficient Obtainable on a P-39N-1 Airplane as Deter- mined in Flight. NACA ACR 4F28,1944.

13. Nissen, James M., Gadeberg, BurnettE. & Hamilton, William T.: Correlation of the Drag Characteristics of a Typical Pursuit Airplane Obtained from High-speed Wind-Tunnel and Flight Tests. NACA Rep.916, 1948.

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I. 14. Phillips, W. H. & Nissen, J.M.: Flight Tests of Various Tail Modifications on the Brewster XSBA-1 Airplane. I-Measurements of Flying Qualities With Original Tail Surfaces. NACA WR L-412 (Originally Issuedas AEtR 3F071, 1943. 15. Rhode, Richard V.: The Influence of Tip Shape on the Wing- Load Distribution as Determined by Flight Tests. NACA Rep. 500, 1934. 16. Silverstein, Abe, Katzoff, Samuel, and Hootman, James: Comparative Flight and Full-scale Wind-tunnel Measure- ments of the Maximum Lift ofan Airplane. NACA Rep. 618, 1938.

17. Sjoberg, S.A., Crane, H.L., & Hoover, H.H.: Measurement of Flying Qualities of a DouglasA-26 B Airplane. Part 111-Stalling Characteristics. NACAWR L-607 (Originally issued asMR No. L5A04a), 1945. 18. Soule, HartleyA. & Wetmore, J.W.: The Effects of Slots and Flaps on Lateral Control of a Low-Wing Monoplane as Determined in F1igh.t. NACA TN 478, 1933. 19. Spreiter, John R. & Steffen, Paul J.: Effect of Mach and Reynolds Numbers on Maximum Lift Coefficients. NACA TN 1044, 1946. 20. Stokke, Allen R. & Aiken, William S., Jr.: Flight Measurements of Buffeting Tail Loads. NACATN 1719, 1948. 21. Weick, Fred E.: The Behavior of Conventional Airplanesin Situations Thoughtto Lead to Most Crashes. NACATN 363, 1931. 22. Weick, Fred E. & Abramson, H. Norman: Investigation of Lateral Control Near the Stall. Flight Tests With High- Wing and Low-Wing Monoplanes of Various Configurations. NACA TN 3676, 1956.

23. White, M.D. & Reeder, J.P.: Effect of Wing-Tip Slots on the Stalling and Aileron Control Characteristics of a Curtiss SB2C-1 Airplane. NACA MR L4K13, 1944. 24. Zalovick, John A.: Profile Drag Coefficientsof Conven- tional and Low-drag Airfoilsas 0btained.in F1igh.t. NACA ACR No.L4E31, 1944 (Wartime Rep. L-139).

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