https://ntrs.nasa.gov/search.jsp?R=19710007949 2019-03-26T15:31:37+00:00Z NASA TECHNICAL NOTE NASA TN D-6142 Z I-- COPY Z VORTEX-LATTICE FORTRAN PROGRAM FOR ESTIMATING SUBSONIC AERODYNAMIC CHARACTERISTICS OF COMPLEX PLANFORMS by Richard J. Margason and John E. Lamar La_lgley Research Center Hampton, Va. 23365 NATIONAL AERONAUTICSAND SPACEADMINISTRATION • WASHINGTON, D. C. • FEBRUARY1971 m 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. NASA TN D-6142 4. Title and Subtitle 5. Report Date VORTEX-LATTICE FORTRAN PROGRAM FOR ESTIMATING February 1971 SUBSONIC AERODYNAMIC CHARACTERISTICS OF COMPLEX 6. Performing Organization Code PLANFORMS 7. Author(s) 8. Performing Organization Report No. L-7262 Richard J. Margason and John E. Lamar 10. Work Unit No. 126-13-10-06 9. Performing Organization Name and Address NASA Langley Research Center 11. Contract or Grant No. Hampton, Va. 23365 13. Type of Report and Period Covered Technical Note 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, D.C. 20546 15. Supplementary Notes 16. Abstract A computer program has been developed for estimating the subsonic aerodynamic char- acteristics of complex planforms. The program represents the lifting planform with a vortex lattice. This paper is intended as a user's guide and includes a study of the effect of vortex- lattice arrangement on computed results, several sample cases, and a listing of the FORTRAN computer program. 17. Key Words (Suggested by Author(s)) 18. Distribution Statement Vortex lattice Unclassified- Unlimited Subsonic speeds Complex planforms Leading-edge thrust Longitudinal aerodynamic characteristics 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price" Unclassified Unclassified 141 $3.00 "For sale by the National Technical Information Service, Springfield, Virginia 22151 CONTE NTS Page SUMMARY ....................................... 1 INTRODUCTION .................................... 1 SYMBOLS ....................................... 2 BASIC CONCEPTS AND LIMITATIONS ........................ 8 PROGRAM DESCRIPTION .............................. I0 PART I - GEOMETRY COMPUTATION ...................... I0 Section I. Reference Planform ......................... II Section 2. Configuration Computations ..................... II Section 3. Horseshoe Vortex Lattice ...................... 13 PART II- VORTEX STRENGTH COMPUTATION ................. 14 PART HI - AERODYNAMIC COMPUTATION ................... 20 Section 1. Liftand Moment Using Entire Horseshoe Vortex .......... 20 Section 2. Liftand Pitchingand Rolling Moments Using Only Spanwise Filament of Horseshoe Vortex ......................... 26 Section 3. Output Data Preparation ....................... 28 EFFECT OF VORTEX-LATTICE ARRANGEMENT ON COMPUTED AERODYNAMIC CHARACTERISTICS ...................... 32 SAMPLE CASES .................................... 34 CONCLUDING REMARKS ............................... 34 APPENDIX A - INPUT DATA ............................ 36 APPENDIX B - OUTPUT DATA ........................... 40 APPENDIX C - SAMPLE CASES .......................... 45 APPENDIX D - FORTRAN PROGRAM LISTING ................... 94 REFERENCES ..................................... 122 FIGURES ....................................... 124 111 i!:=____ VORTEX-LATTICE FORTRAN PROGRAM FOR ESTIMATING SUBSONIC AERODYNAMIC CHARACTERISTICS OF COMPLEX PLANFORMS By Richard J. Margason and John E. Lamar Langley Research Center SUMMARY A FORTRAN computer program has been developed for estimating the subsonic aerodynamic characteristics of complex planforms. The program represents the lifting planforms with a vortex lattice. These complex planforms include wings with variable- sweep outer panels, wings with several changes in dihedral angle across the span, wings with twist and/or camber, and a wing in conjunction with either a tail or a canard. The aerodynamic characteristics of interest are lift and pitching moment for both the flat and/or twisted wing, drag-due-to-lift parameter, leading-edge thrust, leading-edge suc- tion, distributions of leading-edge thrust and suction coefficients, distributions of several span loading coefficients, distribution of lifting pressure coefficient, damping-in-pitch parameter, damping-in-roll parameter, and lift coefficient due to pitch rate. This paper is intended as a user's guide for program application and sample cases are included to illustrate most of the options available for use in the program. Also included is a study of the effect of the vortex-lattice arrangement on some of the com- puted aerodynamic characteristics along with some recommendations for specifying vortex-lattice arrangements for particular types of planforms. INTRODUCTION In recent years, some wings have become very complex because of the varied speed regimes in which they are required to operate. Such wings may have variable sweep, several changes in dihedral angle across the span, or even a variable dihedral angle near the wing tip. Computing procedures for predicting the aerodynamic characteristics of these wings become very involved if an adequate representation of the planform is to be made. The problem becomes more involved when the body or body and tail are included in the representation. In order to solve this problem for preliminary designs or for parametric evaluations, a computer program has been developed for estimating the aero- dynamic characteristics of these complex planforms. In this FORTRANcomputerprogram, the planform in steadysubsonicflow is representedby avortex lattice. Althoughthis typeof representation is not new{for example,refs. 1to 12),thepresentprogram hasseveral usefulfeatures that are not foundtogetherin other generally available programs of either thevortex-lattice or pressure-doublet type (refs. 13to 15). The program usesa minimum ofinput datato describe relatively complexplan- forms. Theseplanforms maybedescribedbyupto 24line segmentsona semispan. They mayhaveanoutboardvariable-sweep panelor theymay haveseveral dihedral anglesacross the span. In addition, two planforms maybeusedtogetherto represent a combinationof wingsandtails or wing,bodies,andtails. The analysis in the present paper hasbeenextendedtohandleplanforms in a sidewashfield. Thesevelocities occur whena planform hasdihedral or whena secondplanform is placedat a different height from thefirst planform. The program describedin the presentpaperwasdevelopedfrom a basicprogram written several years ago,whichhashadconsiderableuseat the LangleyResearch Center. In recent years this basic program has also been used in industry. The results have shown good correlation with experimental data. The present paper is intended to serve both as a description of the program and as a user's guide for its application. This paper describes in detail the program input data (appendix A) and output data (appendix B) and provides examples and typical running times of various types of configurations which can be handled (appendix C) along with a FORTRAN program listing (appendix D). In addition, the results of parametric applica- tions of this program are presented to provide guidance in specifying vortex-lattice arrangements which can be expected to give acceptable results. SYMBOLS The geometric description of planforms is based on the body-axis system with the origin on the planform center line. (See fig. 1 for positive directions.) The planform is replaced by a vortex lattice which is in a wind-axis system with the origin in the planform plane of symmetry. (See sketch (d) in text for details.) The axis system by which the geometric influence of a given horseshoe vortex is computed is wind oriented and referred to the origin of that horseshoe vortex (fig. 1). The units used for the physical quantities defined in this paper are given both in the International System of Units (SI) and in the U.S. Customary Units. For the purpose of the computer program, the length dimension is arbitrary for a given case; angles associated with planform are always in degrees. The symbols used for input data in the computer program are described in appendix A. The symbols used in the description of the program are defined as follows: A aspect ratio; listed as AR in computer program output Bk element of boundary-condition matrix, 4_0k b wing span, m (ft) Induced drag induced drag coefficient, CD,i q_Sref induced drag parameter based on Munk's far-field solution CD,i/CL 2 CD ,ii/CL2 induced drag parameter based on near-field solution CL lift coefficient, L/qc_Sref lift coefficient based on additional loading and actual planform area CL,_- BC L CLq lift coefficient due to pitch rate, 8/qcref_'// per rad \2u / CL_ lift-curve slope, \_]o' per deg or per rad Rolling moment Cl rolling-moment coefficient, qooSref b 8C/ damping-in-roll parameter, C/p 8--_b_'per rad \2u/ pitching-moment coefficient about Y-axis, Pitching moment Cm qooSrefCref 8Cm/SCL longitudinal stability parameter 8C m per rad Cmq damping-in-pitch parameter, 8(_qCref._, element of circulation term matrix, Fn/U Cn 3 Plower " Pupper = A__pp aCp incremental pressure coefficient, qoo qoo Suction CS leading-edge suction coefficient, qooSref Leading-edge thrust CT leading-edge thrust coefficient, qooSref c chord, m (ft) Cav average chord, S_/b, m (ft) Cc chord along left trailing leg of elemental panel, m (ft) section induced drag coefficient based on near-field solution Cd,ii section lift coefficient cl Cref reference chord, m (ft) aS section leading-edge suction coefficient ct section leading-edge thrust coefficient dii section induced drag based on near-field solution, N/m (lb/ft) F influence function which geometrically relates influence of single horseshoe vortex to a quantity which is proportional to velocity induced at a point, m-1 (ft- 1) F 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 on right half of wing, m-1 (ft-1) Gn,k element of influence function matrix, "Fw,n,k - _v,n,k tan 4_n L lift for entire wing, N (lb) l lift per unit length of span, //(2s cos _), N/m (lb/ft) 4