Full report

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TECHNICAL Copy NASA TM X-525 CASE F I L C O R Y MEMORANDUM X-525 A SIMPLIFIED METHOD FOR ESTIMATING SUBSONIC LIFT-CURVE SLOPE AT LOW ANGLES OF ATTACK FOR IRREGULAR PLANFORM WINGS By Bernard Spencer, Jr. Langley ResearchCenter Langley Field, Va. DEC tiASSIFIED BY AUTHORITY OF NASA CLASS!CM ICATIQN CHANGE NOTICES BAT : ITEM NO. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON May 1961

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» • • • • ::•' •':! • • • : :' • NATIONAL AERONAUTICS AND SPACE ADMINISTRATION TECHNICAL MEMORANDUM X-525 ; \ PR o • SIMPLIFIED METHOD TOR ESTIMATING { H M O A IH EM £3 SUBSONIC LIFT-CURVE SLOPE AT LOW ANGLES OF ATTACK W H FOR IRREGULAR PLANFORM WINGS* By Bernard Spencer, Jr. v <J |M H SUMMARY i in Min & j <H V) A simplified method is presented for estimating the lift-curve ' slope of irregular planform wings at subsonic speeds and low angles of 0 0 attack. The present process is an extension of the.method derived in NACA Technical Note 5911 and enables quick estimates of subsonic liftcurve slope, to be made whereas more refined procedures require considerable time and computation. Comparison of experimental and estimated values for a wide range of wing planforms having discontinuous spanwise sweep variation indicates good agreement. A comparison of the present procedure with a 20-step vortex method (NACA Research Memorandum L50L13) indicated good agreement for a variable-sweep configuration. INTRODUCTION A major problem associated with supersonic aircraft, and hypersonic aircraft considered as possible reentry vehicles, is the fact that the configuration most desirable for the supersonic cruise or the atmospheric reentry is incompatible with subsonic flight and landing requirements. One method of alleviating this problem is the use of variable wing geometry. For high-performance supersonic aircraft, both military (refs. 1 and 2) and commercial (ref. 3)> variable-wing sweep offers a possible means of obtaining an aircraft which is efficient at both supersonic and subsonic speeds. With regard to hypersonic aircraft considered as possible reentry configurations, employment of variable geometry such as folding wing-tip panels allows a high-drag, high Mach number atmospheric reentry maneuver to be accomplished while still maintaining desirable glide angles in the approach conditions (refs. h and 5)- *Title, Unclassified.

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2 . CONFIDENTIAL ••• 4 Since one of the major purposes of variable geometry is to provide .' lift effectiveness at subsonic speeds, a rapid method of estimating the lift-curve slope at subsonic speeds for configurations having variablegeometry wing planforms would be desirable for preliminary design study purposes. For the most part the wings, when in the low-speed'position, are of unconventional planform and although various methods such as those of references 6, 7> -and. 8 can be used in estimating the lift-curve slope for these planforms, they are quite involved and laborious. The • method of -reference 9 provides a simple means for estimating subsonic • lift-curve slope at low angles of attack for wings with constant sweep . along the span. The purpose of the present report is to extend the . I method of reference 9 to include wings having variation in sweep, along 1 . the span. . '• , 1 ^ ' ' ' • " ' 1 . SYMBOLS . .A aspect ratio, b /S • ao section lift-curve slope, per deg ' '. b wing span, ft ...' . c wing chord, ft . " . c mean aerodynamic chord, ft - . . CL wing lift coefficient - . • ' CT wing lift-curve slope, per deg CC M . free-stream Mach number S - wing area, sq ft ' • ' x longitudinal coordinate of wing leading edge, ft (fig. l) y • lateral coordinates as referenced to wing root chord, ft A taper ratio . ' . . . ' A:/2 sweep of half-chord line, deg , ' AT-O sweep of leading edge of outboard wing panel, deg .

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• •• • • 'CONFIDENTIAL in sweep of inboard or fixed portion of wing as referenced from wing root chord, deg Subscripts: av average i incremental eff effective LE . leading edge r root - DEVELOPMENT OF THE METHOD The equation derived by Polhamus.(see eq. (A7) of ref. 9) for pre dicting the subsonic lift-curve slope of a constant-sweep finite wing is (for a0 = 2jt) cos 2 - (AM) This equation takes into account the effects of compressibility, wing sweep, and aspect ratio for wings on which the span loading is'approximately elliptical. Use of the half-chord line, as,-the sweep reference line, eliminates 'to a large extent, the effects of taper. (See ref. 9.) Equation (l) is a simple means for estimating lift-curve slopes for wings having constant sweep, but does not directly apply to irregular planform wings, such as variable-sweep configurations. An extension of- 'equation (l) to unconventional planforms appears to be possible by use of an effective value of cos-Ac/2> provided the span-load distribution is approximately elliptical. An effective value of cos A^, /2 which has been found to be satisfactory in predicting lift-curve slopes is a weighted average of'the local value of cos A,, AD in which the local chord length is used as a weighting factor. Standard procedure for obtaining the weighted average of a number of quantities is to multiply each quantity by its weighting factor and divide the sum of these' products by the sum of the weighting factors. Application of this rule to determine an

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Ij. ' CONFIDENTIAL * •* . '••; effective value of cos A/p may be done by dividing the wing into N sections, each section being assumed to have constant-sweep angles within its boundary. The span of section i is denoted by Ay-j> "the average chord of c section i, by av i> and'the cosine of the sweep angle of the half-' chord line of section i, by (cos AC M).• The weighted average or effective value of cos A~/o is therefore defined as - • - i=N (cos~A/PV =— c 2 . . :• (cos ACJ2\ cav .£ Ay.: (2) v ' / ;eff . i=N • ... . ' .' - ' : L—i^ y 1=1 '. . . • < The denominator of equation (2) is the total area of one wing panel S/2. Therefore, equation (2) may be written.as follows: i=N {cos A,,c 2 fo\ - — \ - / )eff S The value of (cos AQ/Z) • may be determined from the wing geometry and substituted into equation (l) for cos A /p. Equation (l) then UL a I A 2 (cos Ac/2) 2 157-3 - (AM) RESULTS AND DISCUSSION . In order to evaluate the accuracy of the present method in estimating lift-curve slopes at subsonic speeds, a comparison of experimental

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CONFIDENTIAL results with the method derived in this paper is presented for a wide range:of planforms having variations in sweep along the span. Figure 1 presents geometric characteristics for several low-aspectratio planforms which have-been considered as possible hypersonic or reentry vehicles. Data for wings 1, 2, 5> and 6 are .presented in ref-. erences h and 5> and data for wings 3; ^ and 7 are from unpublished results. Figure 2 presents comparisons of the experimental and estimated values of lift coefficient plotted against angle of attack for the wings of figure 1. Reasonable correlation between the experimental and the estimated values exists at low angles of attack for all wing planforms except wing 6. (This fact may be seen in fig. 3, which presents the correlation of experimental and estimated values of CT at . QC* a = 0°.) The method appreciably underestimates lift-curve slope above a = 6° to 8° for wings 1to 7-. Figure k presents the experimental and estimated values of lift- . curve slope plotted against Mach number for wings 1, 2, 5, and 6 at a. = 0°. Comparisons of experimental values of CL with estimates of 00 the present method indicate poorer correlation as the Mach number approaches 1.0 for wings 5 and .6 which are the higher-aspect-ratio v configurations. . Figure 5 presents the geometric characteristics of the airplane configuration of reference .10, herein designated as configuration I, and figure 6 presents the variation of lift coefficient with angle of attack for this configuration. Estimated values of lift coefficient were made by the present method and the method of reference 7. Good correlation with experiment at the lower angles of attack is noted for the present method with some improvement over the estimates of reference 7- Figure 7 presents the variation of lift-curve slope with Mach . number for configuration I, and this plot indicates underestimation by use of the present method of determining CL as the Mach.number approaches 1,0. Figure 8 presents the geometric characteristics of the basic " outboard-tail arrangement of reference 11, herein designated as configuration II, and figure 9 presents a comparison of the experimental and estimated values of lift coefficient plotted against angle of attack, for this arrangement. In determining the total aspect ratio and in estimating the lift-curve slope of configuration II, the horizontal tail was considered as part of the wing. Exceptionally good agreement at low lift coefficients between the experimental and estimated values is noted for this configuration. • .

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• •«• CONFIDENTIAL Extreme cases of irregular planform wings are those involving • variable-sweep geometry. These configurations essentially have fixed portions of the wing inboard and employ sweeping of the outer portions as a method of combating off-design penalties encountered at subsonic speeds. Figure 10 presents the geometric characteristics of one of the . models of reference 1, which is referred to herein as configuration III, and figure 11 presents a comparison of the experimental and estimated values of lift, coefficient plotted against angle of attack for three of the wing-sweep positions tested. Figure 12 presents comparisons of the experimental and estimated values of lift-curve slope plotted against leading-edge sweep angle of the outboard portion of the wing of configuration III at M = 0.25. Good prediction of CL is noted throughout the sweep 'range, except for the case of- 0° leading-edge sweep, where the experimental value is lower than the estimated value. - Geometric characteristics of the variable-sweep configuration of reference 12, herein designated as configuration IV, are presented in figure 13 • Figure 1*4- presents the variation of lift coefficient with angle of attack for this configuration. Figure 15 presents a "comparison between"the present method and the 20-step method of reference 6 in predicting lift-curve slope for configuration IV. The present method is seen to overestimate CL • for the configuration throughout the sweep range except for the maximum sweep condition where good correlation is obtained for the low-aspect-ratio configuration. The present methodindicates good agreement with the 20-step method throughout the sweep range. Figure l6 presents a correlation of experimental and estimated values of lift-curve slope for configurations I to IV. This correlation essentially provides a comparison for 11 different planforms having sweep variations across the wing span. The present method is seen to predict the lift-curve slope within ±3 percent for all-the configurations presented. - . . ' ' • • DESIGN CHARTS It has been determined in reference 9. that CL /A is a unique A ' function of ' when the section lift-curve slope an is concos Ac/2 ° sidered equal to 2rt. Consequently, CL /A is also a unique function QL>/ A of r , and design charts, similar to those of reference .9, V2 )eff

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*• •••• CONFIDENTIAL . 7 are presented herein for convenience in determining lift-curve slope. A : Figure 1? presents the variation of CT, /A with - — - r - for a/ COS A ( c/2)ff the case of incompressible flow. In order to correct CL for the CL effect of Mach number, correction factors are presented in figure 18 as functions of the effective sweep of the half-chord line for a wide range of aspect ratios. L ~ " CONCLUDING REMARKS L . • 5 • . . . - 2 A simplified method is presented for estimating the subsonic lift- 1- curve slope of irregular planform wings at low angles of attack. The present process is an extension of the method developed in NACA Technical Note 39H- Comparisons of experiment and estimates for a wide range of configurations having wing planforms with discontinuous ' t ' spanwise sweep variation indicated good agreement near zero angle of attack. Comparisons' of the present method with other existing methods for predicting lift- curve slopes of irregular planform wings generally indicated. good agreement. ' . Langley Research Center, 'National Aeronautics and Space Administration, Langley Field, Va., February 10, 1961.

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CONFIDENTIAL REFERENCES 1. Alford, William J., Jr., and Henderson, William P.: An Exploratory Investigation of the Low-Speed Aerodynamic Characteristics of Variable- Wing-Sweep Airplane Configurations . NASA TM X-1^2, 1959. 2. Polhamus, Edward C., and Hammond, Alexander D.: Aerodynamic Research Relative to Variable-Sweep Multimission Aircraft. Ch. II of Com- ' C pilation of Papers Summarizing Some Recent NASA Research on Manned Military Aircraft. NASA TM X- 420, I960, pp. 5. Toll, Thomas A. : " 'Variable Geometry for Transports. Ch. VIII of The Supersonic Transport - A Technical Summary. NASA TN D-42J, 1960, pp. 71-79- . . ; k. Spencer, Bernard,. Jr. : An Investigation at Subsonic Speeds of Aerodynamic Characteristics at Angles of Attack. From -k° to 100° of a Delta- Wing Reentry Configuration Having Folding Wingtip Panels. . 'NASA TM X- 288, I960. ' 5- Spencer, Bernard, Jr.: An Investigation at Subsonic Speeds- of the Longitudinal Aerodynamic Characteristics at Angles of Attack From -k° to 100° of Delta-Wing Reentry Configurations Having Vertically Displaced and Cambered Wing-Tip Panels. NASA TM X-Ul+O, 1961, ' _ . . • ' • ' • • 6. Campbell, George S. : A Finite-Step Method for the Calculation of u. Span Loadings of Unusual Plan Forms .. NACA RM L50L1J, 1951. 7. McLaughlin, Milton D.: Method of Estimating the Stick-Fixed Longitudinal Stability of Wing-Fuselage Configurations Having Unswept or Swept Wings. NACA RM L5U2J, 1952. : 8. Brebner, G. G.: The Calculation of the Loading and Pressure Distribution on Cranked Wings. R. & M. No. 29*4-7, British A. R.C., ;1955. . 9. Lpwry, John G. , and Polhamus, Edward C. : A Method for Predicting Lift Increments Due to Flap Deflection at Low Angles of Attack in Incompressible Flow. \NAGA TN 3911, 1957- X_> . • ' 10. Fournier, Paul G. : Wind- Tunnel Investigation of the High-Subsonic Static Longitudinal Stability Characteristics of Several Wing- Body Configurations Designed for High Lift-Drag Ratios 'at a Mach Number of lA. NACA TN kjh-O, 1958.

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• •• • CONFIDENTIAL 11. Hayes, William C., Jr., and Sleeman, William C., Jr.: Low-Speed Investigation of the Effects of Wing Flap Deflection and Horizontal-Tail Configuration on the Longitudinal. Aerodynamic Characteristics of an Airplane Configuration Having Tail Surfaces Outboard of the Wing Tips. NASA TM X-333, I960. 12. Spencer, Bernard, Jr.: Stability and Control Characteristics at Low Subsonic Speeds of an Airplane Configuration Having Two Types of Variable-Sweep Wings. NASA TM X-303, I960. L 1 3 2 1

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10 CONFIDENTIAL r H >04 ro " O £> ^ "•*. .

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. • • • • :•* : :• :«•••••: CONFIDENTIAL 11 Wing. Aspect ratio Experiment Estimate 3 75 4 1.33 . 7 1.67 & H Jl , .5 - 4 O 4 8 1 2 1 6 2 O 2 4 Angle of attack,a,deg (a) Wings 3, U, and 7; M = 0.12. Figure-2.- Comparison of experimental and estimated values of lift coefficient plotted against angle of attack for'wings presented in figure 1. :'• C

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12 CONFIDENTIAL Wing Aspect ratio Experiment Estimate O 8 12 16 20 24 A ngle of at tack,a, deg (t>) Wings 1 and 5; M-= OAO. .. Figure 2.- Continued.

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.• ••• • •• : .• • ••• t. ••• •••«•• • • • • >• •« CONFIDENTIAL 15 Wing Aspect ratio Experiment Estimate 2 .69 6 1.49 0 8 cr * ——- 12 16 20 24 Angle of attackta,deg (c) Wings 2 and 6; M = OAO. Figure 2.- Concluded.

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CONFIDENTIAL Wing no. Experiment Estimate Aspect ratio Mach no. 0 1 OI75 .Ol 75 .69 .40 a 2 .0170 .Ol 68 .69 .40 O 3 OI90 .0195 A 4 .O32O .O330 75 .12 1.33 .12 k 5 .0369 .0361 1.49 .40 Q 6 .O374 .O359 1.49 .40 •> 7 0355 .0360 Estimated CL 1.67 .12 .02 Figure 5-- Correlation of experimental and estimated values of lift-curve slope for low-aspect-ratio -wings at a = 0°.

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•• •• I • • CONFIDENTIAL Wing Aspect ratio Experiment Estimate 2 .69 5 1.49 6 1.49 .07 .04 5 «HJig ; 'La .03 .02 a O A • ' / ^U j 1 1 B| IJg j : 1: 1 11 1 II. . 1 . .01 \ \ ' 11 ' i ! • •••••••iyHfiiii o .2 .34 Mach number, M .5 .6 7 .8 .9 10 Figure 4.- Comparison of experimental and estimated values of lift-curve slope plotted against Mach number for wings 1, 2, 5, and 6 at a = 0°.

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• • . . •• • . * • • ••• i • • • « , • • • • • • • « • • :T 16 CONFIDENTIAL T H ro Configuration I Wing Characteristics Sweep Inboard Outboard A reaf sq ft Aspect ratio Taper ratio LE T.E 0 6 7.OI 19.65° 0 6I.7O 53.61° 1.375 2.91 .167 Mean aerodynamic chord, ft .895 Figure 5-- Details of model of reference 10 (designated herein as configuration I).

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: :.. :. 17 o Experiment (ref.lO) ——Estimate (ref.7) Estimate (present) 12 1.0 .8 .6 4 .2 0 -.2 -4 0 4 8 12 16 20, 24 Angle of attack,a,deg Figure 6.- Variation of lift coefficient with angle of attack of configuration I. M = 0.60.

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••• »« • • • . .' • • ••. ' • • • • I ! • • • J. • • s: ••••••:•:..:„•" .::•:•: 18 CONFIDENTIAL 0) & H w O • ±°0 <H •H II H d ^ ^ ^ §•H rd -P 0) n5 -P M IS ^ tt) O I o Td ill S3 fn OJ O H ^ 05 h' -P 0) o a c a ,H a - (U ^1 ft o x a ' (U S =H -P' O W c 5 o cd CQ bO •H a S -d' ft 0) 0 -p °5 1 ft • D- •H fe

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• • • • • • e • • CONPTDENT1AL* "* ' * 19 Configuration R Wing geometry. A rea Root chord Tip chord Span A s p e c t ratio Tail geometry Area (one tail) Root chord Tip chord Panel span 784jOOsqin. 34.25 in. 21.75 in. 28.0Oin. I.OO IOO.66 5(7/77. 16.08 in.. 5.11in. 9.5Oin. Figure 8.- Details of model of reference 11 (designated herein as configuration II).

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• • • 4>'• • • • •• >• • •• • • • • • • • • • • •a '••• •• *« «.; 20 CONFIDENTIAL O Experiment (Ref. II) Estimate 1.2 1.0 .8 i .6 I m I -4 0 4 8 12 16 20 24 Angle of attack^,deg Figure 9-- Comparison of experimental and estimated values of lift coefficient,plotted against angle of attack for configuration II, M ~ 0.

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21 CONFIDENTIAL Configuration HL Geometric Characteristics . Airfoil section normal to leading edge NACA 63IOAOI4 Camber and twist Aspect ratio For ALE=2O° ALE=80° Area , sqft For ALE=20* ALE:80* IQ55 05 . '- 268 265 Reference chord(c for ALE =80°),ft l-865_ Moment reference point O.234 c Figure 10- Details of variable- sweep (designated Herein as co III)

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22 CONFIDENTIAL A L E Exper /men t Est ima te 2O° 60° 80° 1.0 .6 4 .2 -.2 n A b. '•— -5 0 5 IO 15 2O 25 Angle of attack ,a ,deg Figure 11.- Comparison of experimental and estimated values of lift coefficient plotted against angle of attack for.configuration III at three positions of the outboard wing panel. M = 0.25-

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• • • • CONFIDENTIAL 23 Experiment (Ref. I) Estimate 30 4O 5O 60 70 80 Leading-edge sweep, deg Figure 12.- Comparison of experimental and estimated values of lift-curve slope plotted against leading-edge sweep angle of outboard panel of configuration III. M = 0.25.

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» * * • • * * • • •• • • • * > » • • •• * * • • ••• » » • • • • • • • CONFIDENTIAL . ra d •ti •H <U M d)'-^ ^ ^ •g^ -P ° . cS fl .a- (U w M -H ^ g —' Q)& OJ -P H ° 0) CQ O tQ S3 <U- •4) H ** % 0) P CH <1J CO fn -0) rM CH o O CJ •H .fel § « •rl -H. Id <u &.S CQ a o O M c ft OJ ggsa ^v a 10 QO Q> *"•-. ts. fc ITJ ^ tT) ^ ly . O O O O •H 'f -0 CQ I H ^^ •3^ •H IP. H <(H O C O CO -H H -P •H cd cd M- -p & <H '. 8 rn o 0) & bD •H fe

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CONFIDENTIAL ALE Experiment Estimate Aspect ratio 25° O 75" D OJ rH J. 1.0 ' i l l iiiiiiilj; iililiililiiliiiiiiiiiil tiiiiiiii; ; - .8 i^ iiiiiii iiii iiiiiiiiijiiiiiiiiii * iiiiiiiji C : : /L -° :;:: ;;;: ;;;;:;;:: ;;;; ;;;;;;;;;;;;;; :'; ;;; . 4 i i ; ; ; : : - ijii ; i i i i = i i i i = i = i iiii:i|i i ! .2 iiiiiiliiijiiii liii iliiipSiii iiijijii iii iiiii iiii ;;;;;;;•;;;; ;|i \ \ \ } ^ \ \ \ \ \ \ I ;;;;;;; ;;;;; _^MNHIIHIHHIIIHIIIIIIII!IIIIIIHIIHIIIIIIIIIIIIIIIII 8 12 16 20 2< - 4 0 4 5.148 1.894 J' ;;;;;;;:;;:; ;;;;;;;;::::;;;;; ; ; ; ; ; ! ;;:;;;;;;;;;;;; ;;;:; iiiii Angle ofattack,a,deg Figure 1*)-.- Comparison of experimental and estimated values of lift coefficient plotted against angle of attack for configuration IV at two positions of the outboard wing panel. : M ~ 0.

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26 CONFIDENTIAL

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CONFIDENTIAL Configuration ALE,in ALE Aspect ratio 0 UL 80° . 8O° 1.05 D -OT 6O° 75° 1.69 0 2L 6O° 6O° 2.24 A Z 67OI" 61.7" 2.91 k ET 60" 6O° 3.O5 b TSL 6O° 45° . 4.15 Q 2Z 6O° 25° 5.15 O 2ZT 80° 6O° 5.26 0 ur 8O° 40" 8.81 o 2ZT. 80° 2O° 10.35 > 2ZT 80° 0° IO.84 CM kj .04 .06 .08 Estimated C, Figure 16.- Correlation of experimental and estimated values of lift-curve slope for configurations I to IV. a = 0°. '

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28 CONFIDENTIAL o H <H ft •H W W 0) ^- ' ->n CM W O O O •H ' •H fc OS t- H

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• •• ••• • • •• CONFIDENTIAL 29 M-0 IO 2O 3O 4O 5O 60 7O 8O 9O Effective sweep of half-chord line ,deg Figure 18.- Ratio of compressible to incompressible lift-curve slopes for subsonic speeds.

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'•- • • • . * ; • • • . . . . , • ! • • •• • . 30 - 2O 1.7 // I.O /(? JO : M=O.9O.-\ 5O 6O 7O 80 9O Effective sweep of half-chord line.deg Figure 18.- Continued.

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: « .. • • • • • • • • • • « • : : : *"- :I : * : ... • • • • • • • • : :"• '• "• •• *•• * • " * * " 'CONFIDENTIAL H CM 'M=O 3O 4O 50 6O 70 8O 90 Effective sweep of half -chord line, deg Figure 18.- Concluded. NASA - Langley Field, Va. L-1J21

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» ••• •••* •• •• •» - » * * • • * * •

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