1、NASA TECHNICAL NOTEZI-ZNASA TN D-6142COPYVORTEX-LATTICE FORTRAN PROGRAMFOR ESTIMATING SUBSONIC AERODYNAMICCHARACTERISTICS OF COMPLEX PLANFORMSby Richard J. Margason and John E. LamarLa_lgley Research CenterHampton, Va. 23365NATIONAL AERONAUTICSAND SPACE ADMINISTRATION WASHINGTON, D. C. FEBRUARY 1971
2、Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-mProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1. Report No. 2. Government Accession No. 3. Recipients Catalog No.NASA TN D-61425. Report DateFebruary
3、 19714. Title and SubtitleVORTEX-LATTICE FORTRAN PROGRAM FOR ESTIMATINGSUBSONIC AERODYNAMIC CHARACTERISTICS OF COMPLEXPLANFORMS7. Author(s)Richard J. Margason and John E. Lamar9. Performing Organization Name and AddressNASA Langley Research CenterHampton, Va. 2336512. Sponsoring Agency Name and Addr
4、essNational Aeronautics and Space AdministrationWashington, D.C. 205466. Performing Organization Code8. Performing Organization Report No.L-726210. Work Unit No.126-13-10-0611. Contract or Grant No.13. Type of Report and Period CoveredTechnical Note14. Sponsoring Agency Code15. Supplementary Notes16
5、. AbstractA computer program has been developed for estimating the subsonic aerodynamic char-acteristics of complex planforms. The program represents the lifting planform with a vortexlattice. This paper is intended as a users guide and includes a study of the effect of vortex-lattice arrangement on
6、 computed results, several sample cases, and a listing of the FORTRANcomputer program.17. Key Words (Suggested by Author(s)Vortex latticeSubsonic speedsComplex planformsLeading-edge thrustLongitudinal aerodynamic characteristics19. Security Classif. (of this report)Unclassified18. Distribution State
7、mentUnclassified- Unlimited20. Security Classif. (of this page)Unclassified21. No. of Pages 22. Price“141 $3.00“For sale by the National Technical Information Service, Springfield, Virginia 22151Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provide
8、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CONTE NTSPageSUMMARY . 1INTRODUCTION 1SYMBOLS . 2BASIC CONCEPTS AND LIMITATIONS 8PROGRAM DESCRIPTION I0PART I - GEOMETRY COMPUTATION I0Section I. Reference Planform . IISection 2. Configuration Computations .
9、IISection 3. Horseshoe Vortex Lattice 13PART II- VORTEX STRENGTH COMPUTATION . 14PART HI - AERODYNAMIC COMPUTATION . 20Section 1. Liftand Moment Using Entire Horseshoe Vortex 20Section 2. Liftand Pitching and Rolling Moments Using Only SpanwiseFilament of Horseshoe Vortex . 26Section 3. Output Data
10、Preparation . 28EFFECT OF VORTEX-LATTICE ARRANGEMENT ON COMPUTEDAERODYNAMIC CHARACTERISTICS 32SAMPLE CASES 34CONCLUDING REMARKS . 34APPENDIX A - INPUT DATA 36APPENDIX B - OUTPUT DATA . 40APPENDIX C - SAMPLE CASES 45APPENDIX D - FORTRAN PROGRAM LISTING . 94REFERENCES . 122FIGURES . 124i!:=_111Provide
11、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-VORTEX-LATTICE FORTRAN PROGRAM FOR ESTIMATINGSUBSONIC AERODYNAMIC CHARACTERISTICSOF COMPLEX PLANFORMSBy Richard
12、 J. Margason and John E. LamarLangley Research CenterSUMMARYA FORTRAN computer program has been developed for estimating the subsonicaerodynamic characteristics of complex planforms. The program represents the liftingplanforms with a vortex lattice. These complex planforms include wings with variabl
13、e-sweep outer panels, wings with several changes in dihedral angle across the span, wingswith twist and/or camber, and a wing in conjunction with either a tail or a canard. Theaerodynamic characteristics of interest are lift and pitching moment for both the flatand/or twisted wing, drag-due-to-lift
14、parameter, leading-edge thrust, leading-edge suc-tion, distributions of leading-edge thrust and suction coefficients, distributions of severalspan loading coefficients, distribution of lifting pressure coefficient, damping-in-pitchparameter, damping-in-roll parameter, and lift coefficient due to pit
15、ch rate.This paper is intended as a users guide for program application and sample casesare included to illustrate most of the options available for use in the program. Alsoincluded is a study of the effect of the vortex-lattice arrangement on some of the com-puted aerodynamic characteristics along
16、with some recommendations for specifyingvortex-lattice arrangements for particular types of planforms.INTRODUCTIONIn recent years, some wings have become very complex because of the varied speedregimes in which they are required to operate. Such wings may have variable sweep,several changes in dihed
17、ral angle across the span, or even a variable dihedral angle nearthe wing tip. Computing procedures for predicting the aerodynamic characteristics ofthese wings become very involved if an adequate representation of the planform is to bemade. The problem becomes more involved when the body or body an
18、d tail are includedin the representation. In order to solve this problem for preliminary designs or forparametric evaluations, a computer program has been developed for estimating the aero-dynamic characteristics of these complex planforms.Provided by IHSNot for ResaleNo reproduction or networking p
19、ermitted without license from IHS-,-,-In this FORTRANcomputer program, the planform in steadysubsonicflow isrepresented by a vortex lattice. Althoughthis type of representation is not newforexample,refs. 1 to 12), the present program hasseveral useful features that are notfoundtogether in other gene
20、rally available programs of either the vortex-lattice orpressure-doublet type (refs. 13to 15).The program usesa minimum of input datato describe relatively complex plan-forms. Theseplanforms may be described by up to 24line segmentson a semispan.They may havean outboardvariable-sweep panelor they ma
21、y have several dihedralanglesacross the span. In addition, two planforms maybe used together to represent acombinationof wings and tails or wing, bodies, and tails. The analysis in the presentpaper hasbeenextendedto handle planforms in a sidewashfield. Thesevelocities occurwhena planform has dihedra
22、l or whena secondplanform is placedat a different heightfrom the first planform.The program described in the present paper was developedfrom a basic programwritten several years ago,which has had considerable useat the Langley ResearchCenter. In recent years this basic program has also been used in
23、industry. The resultshave shown good correlation with experimental data.The present paper is intended to serve both as a description of the program and asa users guide for its application. This paper describes in detail the program input data(appendix A) and output data (appendix B) and provides exa
24、mples and typical running timesof various types of configurations which can be handled (appendix C) along with aFORTRAN program listing (appendix D). In addition, the results of parametric applica-tions of this program are presented to provide guidance in specifying vortex-latticearrangements which
25、can be expected to give acceptable results.SYMBOLSThe geometric description of planforms is based on the body-axis system with theorigin on the planform center line. (See fig. 1 for positive directions.) The planform isreplaced by a vortex lattice which is in a wind-axis system with the origin in th
26、e planformplane of symmetry. (See sketch (d) in text for details.) The axis system by which thegeometric influence of a given horseshoe vortex is computed is wind oriented and referredto the origin of that horseshoe vortex (fig. 1). The units used for the physical quantitiesdefined in this paper are
27、 given both in the International System of Units (SI) and in theU.S. Customary Units. For the purpose of the computer program, the length dimensionis arbitrary for a given case; angles associated with planform are always in degrees.The symbols used for input data in the computer program are describe
28、d in appendix A.The symbols used in the description of the program are defined as follows:Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ABkbCD,iaspect ratio; listed as AR in computer program outputelement of boundary-condition matrix, 4_0 kwing spa
29、n, m (ft)induced drag coefficient, Induced dragq_SrefCD,i/CL 2CD ,ii/CL2CLCL,_-CLqCL_ClC/pCminduced drag parameter based on Munks far-field solutioninduced drag parameter based on near-field solutionlift coefficient, L/qc_Sreflift coefficient based on additional loading and actual planform areaBC Ll
30、ift coefficient due to pitch rate, 8/qcref_/ per rad2u /lift-curve slope, _o per deg or per radrolling-moment coefficient,Rolling momentqooSref bdamping-in-roll parameter,8C/8-_b_per rad2u/pitching-moment coefficient about Y-axis, Pitching momentqooSrefCref8Cm/SCLCmqCnlongitudinal stability paramete
31、r8C mdamping-in-pitch parameter, 8(_qCref._,per radelement of circulation term matrix, Fn/U3Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Plower “ Pupper = A_ppaCp incremental pressure coefficient,CSC TcCavC cCd,iiclCrefa Sc tdiiFFGn,kLl4leading-ed
32、ge suction coefficient,leading-edge thrust coefficient,qoo qooSuctionqooSrefLeading-edge thrustqooSrefchord, m (ft)average chord, S_/b, m (ft)chord along left trailing leg of elemental panel, m (ft)section induced drag coefficient based on near-field solutionsection lift coefficientreference chord,
33、m (ft)section leading-edge suction coefficientsection leading-edge thrust coefficientsection induced drag based on near-field solution, N/m (lb/ft)influence function which geometrically relates influence of single horseshoevortex to a quantity which is proportional to velocity induced at a point,m-1
34、 (ft- 1)sum of influence function F at a control point on wing caused by two sym-metrically located horseshoe vortices, one on left half of wing and one onright half of wing, m-1 (ft-1)element of influence function matrix, “Fw,n,k - _v,n,k tan 4_nlift for entire wing, N (lb)lift per unit length of s
35、pan, /(2s cos _), N/m (lb/ft)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-imyNDNcNsPqqooSrefS Tlift per unit length of vortex filament, N/m (lb/ft)lift generated along a finite length of vortex filament, N (lb)pitching moment for entire wing about
36、 Y-axis, m-N (ft-lb)free-stream Mach numberpitching moment about _r-axis due to lift developed on elemental panel, m-N(ft-lb)maximum number of elemental panels on entire wingnumber of elemental panels in a chordwise rownumber of chordwise rows of elemental panels on wing semispanroll rate, rad/sec;
37、also, pressure, N/m2 (lb/ft2)pitch rate about Y-axis, rad/secfree-stream dynamic pressure, N/m2 (lb/ft2)reference area, m2 (ft2)actual planform area, m2 (ft2)VVUhorseshoe semiwidth in plane of horseshoe vortex, m (ft)(lb/ft)backwash velocity, m/secresultant velocity, m/secsidewash velocity, m/sec(ft
38、/sec)(ft/sec)(ft/sec)ST= Sref/(2s n cos Car )t section leading-edge thrust per unit span, N/mU free-stream velocity, m/sec (ft/sec)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-wX,Y,ZX,Y,Zx,y,zx,yc/4X3c/4x =YcpTFAF6downwash velocity, m/sec (ft/sec)
39、axis system of a given horseshoe vortex (see fig. 1)body-axis system for planform (see fig. 1)wind-axis systemdistance along X-, Y-, and Z-axis, respectively, mdistance along X- and Y-axis, respectively, m (ft)distance along _:-, _r_, and 7.-axis, respectively, mmidspanmidspan(ft)(ft)_-location of q
40、uarter-chord of elemental panel, m (ft)T-location of three-quarter-chord of elemental panel, m (ft)fractional spanwise distance from root chord to center of pressure on leftwing panelangle of attack, deginduced angle of attack, radPrandtl-Glauert correction factor to account for effect of compressib
41、ility insubsonic flow, V1 - Moo2vortex strength, m2/sec (ft2/sec)c/cnondimensional lift, F_ orbU 2bnet vortex strength along left trailing leg of elemental panel, m2/sec(ft2/sec)nondimensional spanwise coordinate, _/(b/2)Provided by IHSNot for ResaleNo reproduction or networking permitted without li
42、cense from IHS-,-,-PAdensity, kg/m3 (slugs/ft3)dihedral angle, in Y-Z plane, degplanform leading-edge sweep angle, in X-Y plane, degquarter-chord sweep angle of elemental panel; because of the small angleassumption, also used as sweep angle of spanwise horseshoe vortex fila-ment, in X-Y plane, deg_
43、= tan-l(tan g/)/i3)Subscripts:BbdklowerOradditional; or angle of attacktwist and/or camber at C L = 0twist and/or camber at C L = 0desiredradfor chordwise row of elemental panelsfor elemental panelindex for elemental panel in chordwise rowmaximum number of elemental panels in chordwise rowindex for
44、control pointleft half of winglower surfaceindex for elemental panel on wing semispanvalue taken at C L=0right half of wingper radian angle of attack7Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-s spanwiseboundvortex elementchordwise boundvortex e
45、lementtc twist and/or camberu backwashupper upper surfacev sidewashw downwashBASIC CONCEPTS AND LIMITATIONSThe vortex-lattice method is used in this computer program to determine the aero-dynamic characteristics of planforms at subsonic speeds. This method is an extensionof the finite step lifting-l
46、ine method originally described in reference 16 and applied inreference 11. This method assumes steady, irrotational, inviscid, incompressible,attached flow. The effects of compressibility are represented by application of thePrandtl-Glauert similarity rule to modify the planform geometry. Potential
47、 flow theoryin the form of the Biot-Savart law is used to represent disturbances created in the flowfield by the lift distribution of the planform. It is assumed that in any plane parallel tothe X-Z plane the vertical displacements which occur in the wing or wake are neglected,except when the bounda
48、ry conditions at the control points are determined.The planform is divided into many elemental panels. Each panel is replaced by ahorseshoe vortex. This horseshoe vortex has a vortex filament across the quarter-chordof the panel and two filaments streamwise, one on each side of the panel starting at thequarter-chord and trailing downstream in the free-stream direction to infinity. Figure 1shows a typical horseshoe-vortex representation of a planform. The boundary conditionfor each hors
