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Supersonic Wing •( «UK- SECTION THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY 8621 GEORGIA AVE., SILVER SPRING, MD. Operating under Contract NOrd 7S86 With the.Bureau of Ordrience, U. S. Navy 1 »V- ) AERODYNAMIC CHARACTERISTICS OF WINGS AT SUPERSONIC SPEEDS by R. M. Snow and E. A. Bonney . L •'. H i i« '-• » u o o • FOK FI D D < >>" "ralöfbfiehe';" •;< JUL111968 '#» 6.«.V ,«±J Bumblebee Series March 1947 Report No. 55 Copy No. 2 DISTRIBUTION OF THIS I DOCUMENT IS UNLIMITED •Y^»W>-**K 1* w«n«~--• * * * ^^i^Mj •L-4 'i ACCISIK f:r CFSTI DDG •ok I U:A ro - -: .- n THE JOHNS HOPKINS UNIVERSITY Ji3.!, !•;. ,ri.! APPLIED PHYSICS LABORATORY 8621 Georgia Avenue :Y ! Silver Spring, Maryland DKTH'DU-ir,::/.! ?.!L,u!Uf, .'• ^S DIST. A'./.iL ai/y *.'£. IL Operating Under Contract NOrd 7386 With the Bureau of Ordnance, U.S. Navy AERODYNAMIC CHARACTERISTICS OF WINGS AT SUPERSONIC SPEEDS by R. M. Snow and E. A. Bonney BUMBLEBEE Report No. 55 DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED MARCH 1947 1 1 1 <«taw^»»'-"j. " " «»" —/—-) :: -jw" •rrr» TABLE OP CONTENTS Introduction. , v Reference Table for Aerodynamic Coefficients vi I. Application of Busemann1o Conical Field Method to Thin Wings "by Robert M, Snow Introduction 1 Characteristic Cones, Boundary Conditions 3 Rectangular Wing * » 4 Raked Wing 8 Bent Leading Edge 11 Case of Intersecting Envelopes 13 Trapezoidal Wing. .... 15 General Symmetrical Quadrilateral 0 ...... 16 Wing With Dihedral 20 II. Aerodynamic Characteristics of Solid Rectangular Airfoils at Supersonic Speeds "by E. A. Bonney Summary ,23 Assumptions 23 Nomenclature „ ...» 24 Discussion 26 Derivations . e 27 Results 34 Conclusions , 34 111. The Reverse Delta Planform , 43 17. Lift and Drag Characteristics of Delta Wings at Supersonic Speeds by E. A. Bonney Abstract ..44 Assumptions 45 Nomenclature 45 Discussion 46 V. Sectional Characteristics of Standard Airfoils by E. A. Bonney 58 iii A^'""" —;»* *.*-'• '*-*^ ^ - ~MWC««n¥Q&Si*r? V II SB OF FIGURES I. Application of Busemann1 s Conical field Method to Thin Wings fe /jf Figure 1. Flow for Rectangular Wing, Section "by Plane X j Perpendicular to Stream , 3 .^tovj 2» Flow for Swept-hack Leading Edge. „ 4 3, Pressure Distribution Along Span for Rectangular Wing or for Raked-back Rectangular Wing 7 4. Wing With Dihedral, Section "by Plane Perpendicular to Stream , , . * , . .14 5; Symmetrical Trapezoidal Wing .15 6. Pressure Distribution Along a Span Line for Trapezoid 16 7. Pressure Distribution Along Span Line for Forward- pointing Triangle 17 8. General Quadrilateral 17 9. Wing With Dihedral. , 20 II. Aerodynamic Characteristics of Solid Rectangular Airfoils at Supersonic Speeds Figure 1. Pressure Loss Due to Flow Around the Tip 38 2. C3 vs M . 38 3. Aspect Ratio Correction to Lift and Wave Drag .38 4. Center of Pressure for Finite Aspect Ratio". 38 5. Kfc's for Various Wing Sections (single taper) ...... .39 6. K^'8 for Various Wing Sections (double taper) 39 7. Aspect Ratio for Thin Rectangular Wings Supported Over Entire Base. , ?3 8. Optimum Lift Coefficient - Entire Base 39 9. Maximum Lift-Drag Ratio - Entire Base 40 10. Optimum Angle of Attack - Entire Base 40 11. Lift Curve Slcpe - Entire Base. 40 12. Thickness ZUtio - Entire Base 40 13. Optimum Aspect Ratios for Thin Rectangular Wings Supported "by a Huh 41 14. Optimum Lift Coefficient - Hub 41 15. Maximum Lift-Drag Ratio - Hüb , . .41 16. Optimum Angle of Attack - Hub 41 17. Lift Curve Slope - Huh 42 18. Thickness Ratio - Huh 42 IT , ,:rm •:,*t*.u*- '•^-!P^vvmfKmmm IV. Lift and Drag Characteristics of Delta Wings at Supersonic Speeds Figure 1. Lift Characteristics of Delta Wings 50 2. Form Drag of Delta Airfoils Whose Leading Edges are Inside the Mac'r«. Cone , 50 3. Lift-Drag Eatio of Delta and Rectangular Wings 51 4.» Maximum Lift-Drag Ratio - Delta Wings , 51 5. Maximum Lift-Drag Eatio 51 6. Optimum Angle of Attack - Delta Wings 51 7. Ratio of Maximum Lift-Drag Ratios of Delta and Reverse Arrow Wings , . , 52 8. Aspect Ratio of Delta Wings. , 52 9.'Planform Semi-vertex Angle of Delta Wings 52 10. Optimum Lift Coefficient - Delta Wings ..... 52 11. Optimum Lift Coefficient 53 12. Spanwise Center of Pressure Location - Delta Wings .... 53 13. (Nomenclature) . ....... 53 14. Delta Wing Drag vs Maximum Thickness Position, Swept Trailing Edge; a = 0.5 53 15. Delta Wing Drag vs Sweepback iLxgle., Swept Trailing Edge; a = 0 54 16. Delta Wing Drag vs Sweepback Angle, Swept Trailing Edge; a = 0.5 54 17. Delta Wing Drag vs Sweepback Angle, Swept Trailing Edge; b = 0.2 55 18. Delta Wing Drag vs Mach Number, Swept Trailing Edge; b = 0.2 55 19. Lift Curvs Slope - Delta and Arrowhead Planforms ..... 56 20. Lift Curve Slope - Delta and Arrowhead Planforms ..... 56 21. Spanwise Center of Pressure Location - Delta and Arrowhead Planforms . «, . 57 22. Chordwise Center of Pressure Location - Delta and Arrowhead Planforms * 57 V. Sectional Characteristics of Standard Airfoil* Figure 1. Drag Coefficient vs Stress ..... 59 2. Drag Coefficient vs Thickness Ratio. , 60 3. Stress vs Thickness . ? * . 60 (gpp .jtw^rr? ~ tr-^—•*-•^., •? '-^s^vSiu^ %>* INTRODUCTION Five paper« dealing with practical aspect» of theoretical work done at the Applied Physics Laboratory on the subject of the aerodynamic char- acteristics of wings in supersonic flow are presented in this BUMBLEBEE report. These papers, which hare appeared as internal memoranda of the Applied Physics Laboratory, represent the combined efforts of APL/JHU personnel and outside contributors as noted in the references. The first paper derives lift coefficients and center of pressure location for fiat plates of polygonal planform from fundamental consid- i T. erations, using Busemann1s conical field method. The other papers utilize Busemann** second order approximation formula to determine the aerodynamic characteristics of certain types of wings having finite thickness. Con- sequently there will "be some overlapping of results, hut no material is deleted inaiimuch as the two methods are quite different. Attention is called, however, to differences in nomenclature "between the first and the remaining papers. A short discussion of the sectional properties of various airfoil shapes and the optimum type is given at the end of this report. It is believed that these papers cover most of the unclassified engineering work on the effect of wing planforms available at this time. The work is by no means complete, there being many practical planforms for which no theory has been developed, particularly in the case of wings with finite thickness. Accordingly the table on the following page has been constructed to indicate the types for which information can be found in this report, to show where it can be found, and to indicate the mist- ing data. In this table the Roman numeral refers to the paper in this report as indexed in the Table of Contents, whereas the Arabic numeral refers to the page ©a which the expression for the particular coefficient may be found. An X indicates that the exact information is not yet known. vii • W il. 1 '* .Iti fi-JTmt - © pH M o> tef ^ 0 •3.2° « M H M K H H Jd <H N O ^ crt •H 00 CO 00 • 2-, VI H H • • 00 1 1 1 it >A M M HI W £< ^\ H H K / 4 r -d I »0 «0 IS \ © ja IO IO IO Pi r- ig <! Yi K M K \ > *» 5 \ \ IÄ i£ >l ^ 1M 4* 0 ^ M M M \ \ '^ © \ O Ä < 001^ C0l> to 10 ^- 43 ^ \\ • «> e» p \ NV. HCO tfl HW i~»tf *UJ- toio 10 IO • s ^\ ^T H f 1 I ( 1 1 1 • t I A \ ^ 1 > M*» H»> 0 •• • 0 • M M M M M MIß »-« M 3 a u cd <--N *H «H © 0 0» H M to *«. i^ <o N P- © M^< © cd J3 IO IO IO so IO !0 W) El CO Ö <o "O CVi VA 1 1 1 1 H 1 1 •H P. 0 «H c Nv t- J» • • t» > g, > -P 0 0 0 >J M M M M M M U U A •d « 0 •H F3 \ A t f- e^ •a a 0 o V^ 9» «O 0> fr. Ott- «to to IO crt H «! O to 0 — <\ H «ZJ H 10 t-HC • J J 1 S *> ^N\ • J » J • J 6» H • • ö M PS 43 ^V Ml* «>» M> »-* M M 0 ß -H © Ö M M t* •H ce -d A © +» •H CO •p O TO u © 43 J3 ^v in *8 8 IO IO % «M m CM to O cd M »1 H ^^ M M M M M O H © +> CO -3, N •P cd W •H as N i too «© to f-i © © 0 ^ a H e 8 IO IO © O ^•^ U { J <H <H -P © P in M M ^ 9 C9 0 CO >j *-» M M Hi 1 U •d © •H co X- ffl -p rH • © -a* « a In * CO ^ H P O © -d © P< • • « to A © «}• • » • • s Ä 03 CO cd 43 ß «H > 01 A 43 43 M O # B? > K *H M M M 3 © PH 0 Üb c •3 to Jd »d © J-) v A at -p •P co © to > cd t>r. © 43 & «H H J3 Ä Ö -O or \i t © 0 43 © 2 •H V* to s J3 = CO •d 0 s s H M H H > <H 4» U © u Tip s M O ie >H 43 0 1 M 0 u zoidal 4 H T>CJ \ ; OS u S 53 «M crt «H 0 IO u CC Tl 0 •^^ o ©a X l • •^ a P,H © •d -d to ^ « Ö CO P 3 © / 3 1 (A © © 1-4 0 ö § M w K M CD O A flS •H •H A 4 A rl u •H 43 >> v_^ s H CQ a •P ^ cd > a) -d O © ß cv B P* c O © M ä •p •H 43 0 <M fr- to Nt! ^ to £ to P4 Pi 0 43 q) •H .3 1 1 1 1 1 1 1 » 1 1 ^x c to S <D •d CO 01 M M M M M »• M M M M CO © CO •d ß as M M »- M M M M tJ a> fit O fi © © © H M •0 (3 rH $ CO O CD •H '•fir O W) = 0 **• H ^ 0 •d r* u.
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