July 1985 Experimental and Theoretical of the Longitudinal

NASA Technica I Paper 2433

July 1985 Experimental and Theoretical Study of the Longitudinal Aerodynamic Characteristics of Delta and Double-Delta Wings at Mach Numbers of 1.60, 1.90, and 2.16

Richard M. Wood and Peter F. Covell

NASA Tec hnica I Paper 2433

1985

NASA National Aeronautlcs and Space Administratlon

Scientific and Technical Information Branch

Experimental and Theore tical Study of the Longitudinal Aerodynamic Characteristics of Delta and Double-Delta Wings at Mach Numbers of 1.60, 1.90, and 2.16

Richard M. Wood and Peter F. Covell Langley Research Center Hampton, Virginia

Summary An experimental and theoretical study was con-

ducted to investigate the supersonic aerodynamic qharacteristics of delta and double-delta wings. Test- ing was conducted in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.60, 1.90, and 2.16. Supersonic data were obtained on six uncambered, blunt-leading-edge wings mounted on a generic low- fineness-ratio fuselage. Measured longitudinal aerodynamic characteristics showed that the wing planform is as important as its aspect ratio in deter- mining the supersonic aerodynamic characteristics. The double-delta wings exhibited lower zero-lift drag values than the delta wings having the same aspect ratio, whereas delta wings provided lower drag due to lift than the double-delta wings. Deflections of the trailing-edge flaps for pitch control revealed that the induced aerodynamic forces were only a function of the flap planform and were independent of wing planform. The supporting theoretical analysis showed that the Supersonic Design and Analy- sis System (SDAS) did not consistently predict all the longitudinal aerodynamic characteristics of the low-sweep, low-fineness-ratio wing-body configurations under investigation. The drag-due-to-lift and lift characteristics were reasonably well predicted; however, zero-lift drag and pitching-moment computations were inconsistent with experimental data. Theoretical computations also overpredicted the ef- fectiveness of trailing-edge flaps for pitch control.

Introduction The next generation of tactical aircraft will be re-

quired to have high levels of aerodynamic efficiency at both the cruise and maneuver conditions at Mach numbers above and below 1.0. The ability to satisfy the broad aerodynamic requirements associated with subsonic and supersonic flight is strongly dependent upon the selection of the proper lifting surface. In the design of a wing, the aircraft designer typically employs preliminary aerodynamic analysis methods to assist in the selection of airfoil shape, wing aspect ratio, wing planform, and control-surface ar- rangement. For supersonic speeds, methods based upon linear theory or slender-body theory are the primary preliminary design and analysis tools. How- ever, their application has traditionally been to high- fineness-ratio configurations that have highly swept, thin, sharp-leading-edge wings for which the small perturbation assumptions of the theories are not vio- lated. Selected application of linear theory methods to configurations with lower fineness ratios, representative of tactical aircraft, has produced mixed results. The purpose of this study is to experimentally inves-

tigate the effects of aspect ratio and wing planform on the longitudinal supersonic aerodynamic characteristics of delta and double-delta wings and to determine the capability of the linear theory prediction techniques to predict these effects.

The effect of wing planform discussed in this paper refers to a comparison between delta wing and double-delta wing data for a given aspect ratio. The effect of aspect ratio discussed in this paper refers to a comparison of the three aspect ratios for a given wing planform.

The present investigation is part of a cooperative wing design study between the National Aeronautics and Space Administration and the General Dynam- ics Corporation. The wind-tunnel model geometry consisted of a generic low-fineness-ratio body and six interchangeable uncambered, blunt-leading-edge wings (three clipped delta wings and three clipped double-delta wings) with aspect ratios of 1.75, 2.11, and 2.50. All wings were configured with a part-span trailing-edge flap which consisted of approximately 18 percent of the wing reference area. Experimental testing was conducted in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.60, 1.90, and 2.16. This paper contains the results of the supersonic tests with supporting theoretical analysis.

aspect ratio, b2/S wing reference span, in.

wing chord, in.

wing mean aerodynamic chord, in. corrected axial-force coefficient,

Axial force CA,unc - c A , c , gs corrected drag coefficient,

CD,unc - c D , c , 9 change in drag coefficient, CD - C D , ~

zero-lift drag coefficient

change in zero-lift drag coefficient due to trailing-edge flap deflection,

rolling-moment coefficient, Rolling moment

lift coefficient, +$ lift-curve slope at Q = 0' change in lift coefficient due to trailing-edge flap deflection at Q = Oo, C L I ~ E Z O - C L I ~ E = O

C D , ~ I ~ , # O - CD,OI~E=O

9Sb

pitching-moment coefficient, Pitching moment

longitudinal stability at (Y = 0'

zero-lift pitching-moment coefficient

change in zero-lift pitching-moment coefficient due to trailing-edge flap

9sc

deflection, cmIo16TE#o - C m , 0 1 6 ~ ~ = 0

yawing-moment coefficient, Yawingqsyment

normal-force coefficient, Norm$ force

side-force coefficient, Side

fuselage station

lift-drag ratio

free-stream Mach number

component of free-stream Mach number normal to wing leading edge, M COS ALE (1 + sin2 (Y tan' ALE)'/^ dynamic pressure, psf

Reynolds number, per foot

wing reference area, ft'

longitudinal distance from nose of fuselage, in.

spanwise distance from model center- line, in.

angle of attack, deg

= d m ; also angle of sideslip, deg

flap deflection angle, deg

taper ratio, c t / c r , p

sweep angle, deg

9

9

Subscripts: B leading-edge break C chamber LE leading edge max maximum r , e exposed root chord rr P projected root chord

TE trailing edge t tip

unc uncorrected

2

Apparatus and Tests

Wind Tunnel

The investigation was conducted in the low Mach number test section of the Langley Unitary Plan Wind Tunnel, which is a variable-pressure, continuous-flow facility (ref. 1). The test section is approximately 7.0 f t long and 4.0 ft square. The asymmetric sliding-block nozzle leading to the test section permits continuous variation in free-stream Mach number from about 1.5 to 2.9. Experimental force and moment results were obtained for all six wing planforms at Mach numbers of 1.60, 1.90, and 2.16, at a Reynolds number of about 2 x lo6 per foot, at angles of attack from -5' to 20°, and with control-surface deflections of O', - IOo , and -20'. A detailed description of the test conditions and a tab- ulation of the force and moment data are presented in the appendix.

Model Description

The six wings tested, three with clipped delta planforms and three with clipped double-delta planforms, had equal reference areas and were designed with a 3.5-percent-thick NACA 64A airfoil. The wing planforms each had a trailing-edge sweep of -20' and a tip chord of 2.97 in. Each delta wing was matched with a double-delta wing of equal aspect ratio and trailing-edge flap geometry. The double-delta wings designed for this study had a leading-edge break at 70 percent span and had a 23' sweep angle on the outboard panel. The trailing-edge flap for each wing comprised approximately 18 percent of the wing reference area and extended to 88 percent of the span. For testing, the six wings were mounted on a generic low-fineness-ratio fuselage.

Computer-generated solid-model graphics of each wing-body geometry are shown in figures 1 through 6. A sketch of the generic low-fineness-ratio fuselage is presented in figure 7, and sketches of the six wing planforms are contained in figure 8. The geometric characteristics of the six wing planforms are given in table I. Table I1 contains listings of the wave-drag input geometry (ref. 2) of the six wing planforms and the host generic fuselage.

Experimental Results The objective of this test was to experimentally

determine the effect of wing planform and aspect ratio on the supersonic aerodynamic characteristics of the six wings. Test results are presented over the Mach number range for all configurations. All

moment data have been referenced to 35 percent of the mean aerodynamic chord for each configuration.

Since an infinite number of geometric configurations may be obtained in defining a double-delta wing planform, the results of the planform comparison presented in this paper are intended only to represent the aerodynamic options associated with the double- delta wing planforms of this study. The effect of wing planform discussed refers to a comparison between delta wing and double-delta wing data for a given aspect ratio. The effect of aspect ratio discussed refers to a comparison of the three aspect ratios for a given wing planform.

Longitudinal Aerodynamic Characteristics The effect of wing planform on the longitudinal

aerodynamic characteristics at M = 1.60 for aspect ratios of 1.75, 2.11, and 2.50 are presented in figures 9, 10, and 11, respectively. For a given aspect ratio, the double-delta planform consistently has lower drag than the delta planform at low lift conditions (0 < CL < 0.2); at the higher lift conditions (0.2 < CL < 0.4), the delta planform has the lowest drag. The crossover in the drag data for the two wing planforms results from the difference between zero- lift wave-drag and drag-due-to-lift characteristics of the two planforms. For a given aspect ratio, the more highly swept double-delta planform has more efficient zero-lift wave-drag characteristics but less efficient drag-due-to-lift characteristics than the delta planform. Further study of the drag data shows that as aspect ratio is increased, the crossover in the data occurs at higher lift. The lift and pitching-moment data of figures 9, 10, and 11 also indicate that increasing aspect ratio results in a merging of the data for the delta wing and double-delta wing planforms.

The experimental results presented in figures 9, 10, and 11 have been replotted in figures 12 and 13 in order to look at the effect of aspect ratio on the delta wing and double-delta wing planforms, respectively. The delta wing data presented in figure 12 show that for low to moderate lift (CL < 0.3), increasing aspect ratio degrades the aerodynamic performance and increases the lift-curve slope but does not affect the longitudinal static stability level. The reduced aerodynamic efficiency because of increased aspect ratio is due to an increase in the zero-lift wave drag. The double-delta wing data presented in figure 13 show results similar to those of the delta wings except that a change in the longitudinal static margin is observed.

A summary of the basic longitudinal aerodynamic characteristics of all wings tested at all Mach numbers is presented in figures 14 and 15. The longitudinal aerodynamic performance data, summarized in

figure 14, show that the double-delta wings outper- form the delta wings (i.e., have lower zero-lift drag and have higher lift-drag ratio) for all Mach numbers. The data show that both wing planforms expe- rience a nearly linear increase in zero-lift drag with increasing aspect ratio. The data also show that the double-delta wings have lower drag than the delta wings and have large decreases in zero-lift drag with increased Mach number. The drag-due-to-lift data of figure 14 show several interesting characteristics. The delta wing data show little effect of aspect ratio, whereas the double-delta data decrease nonlinearly. The decreasing drag-due-to-lift characteristics of the double-delta wings and the nonvarying characteristics of the delta wings result in a merging of the data at an aspect ratio of 2.50. In addition, the data also show that all wings are affected in a similar fashion by increases in Mach number. The merging of the drag- due-to-lift data with increasing aspect ratio results from all wings approaching the condition of having a supersonic wing leading edge ( M N > 1.0). For the delta wings, only the AR = 1.75 wing planform has a subsonic leading-edge condition, which occurs at M = 1.60. For the double-delta wings, the leading edge of the outboard panel is operating at MN > 1.0 for all Mach numbers tested. The flow condition of the inboard panel leading edge is subsonic for the AR = 1.75 wing at all test Mach numbers. For the AR = 2.11 wing at M > 1.90 and for the AR= 2.50 wing at all test Mach numbers, the inboard panel is operating at MN > 1.0. Experimental correlations (ref. 3) for delta wings have shown that for a given Mach number, increasing wing aspect ratio (i.e., decreasing wing sweep ALE) results in an increase in lift-curve slope for p cot ALE values less than 0.7. For values of pcot ALE greater than 0.7, the variation in lift-curve slope levels off to a constant value. For flat wings, the drag-due-to-lift characteristics are directly related to the wing lift-curve slope. As a result, flat wings with supersonic or nearly supersonic leading edges would have similar values of the drag-due-to- lift parameter.

The overall aerodynamic efficiency ( ( J ~ / D ) ~ = ) of a given wing planform is a function of its zero- lift drag and drag-due-to-lift characteristics. The maximum lift-drag ratio data presented in figure 14 show that the double-delta wing planforms outper- form the delta wing planforms at all conditions except for the AR = 1.75 delta wing, which has a subsonic wing leading edge at M = 1.60. The aerodynamic performance data summarized in figure 14 represent the aerodynamics at low to moderate lift (i.e., cruise range) and indicate the importance of a subsonic wing leading edge in obtaining low levels of

A

3

zero-lift drag and good overall aerodynamic efficiency at supersonic speeds.

A summary of the pitching-moment and lifting characteristics of all six wings is presented in figure 15. The pitching-moment data show that changes in aspect ratio and Mach number affect the stability level of the double-delta wing planforms to a higher degree than they affect the stability level of the delta wing planforms. The large variation in longitudinal stability for the double-delta wings is probably due to interference between the wing inboard and outboard panels. The lifting characteristics presented on the right-hand side of figure 15 support the drag- due-to-lift results of figure 14. These data show that increasing aspect ratio and decreasing Mach number increase the lift-curve slope. The characteristic merging of the lift-curve slopes as aspect ratio is increased is also evident. For the AR = 1.75 delta and double-delta wings, the data show large differences in the measured lift-curve slope. As the Mach number is increased, the lift-curve slope of the delta and double-delta wings begin to merge, characteristic of supersonic leading-edge wings.

Longitudinal Aerodynamic Control

Aircraft which are required to fly across the Mach number range will typically be statically stable at supersonic speeds and have neutral stability or slight instability at subsonic speeds. To provide the necessary pitch control for stable flight at supersonic speeds, a trailing-edge-up deflection is required. Aerodynamic forces and moments associated with longitudinal pitch control were investigated by de- flecting a single part-span trailing-edge flap on each wing. For a given aspect ratio, the matched delta and double-delta wings had the same flap planforms. Experimental results were obtained for trailing-edge flap deflections of O', -lo', and -20'. The data have been referenced to the 0.35C location for all wings and no attempt was made to provide a comparison of the trimmed performance characteristics. Instead the pitch-control data are presented in a fashion which allows for evaluation of the longitudinal aerodynamic characteristics based on trailing-edge deflection.

Presented in figures 16 through 21 are the pitch- control aerodynamic characteristics for all wings at M = 1.60. The experimental results show that pitch- control deflections produce significant increases in drag and pitching moment and reduce the level of lift for a given angle of attack. A survey of the data in figures 16 through 21 indicates that all wings ex- perience similar changes in lift, drag, and pitching moment. The resulting effect is a significant reduc- tion in the aerodynamic performance of all wings.

To provide a more detailed look at the pitch- control aerodynamic effects, the incremental changes in lift, zero-lift drag, and zero-lift pitching moment, referenced to the undeflected case, are summarized in figure 22. The data clearly show that the incremental forces and moment due to trailing-edge flap deflection are not affected by wing planform and were only slightly affected by aspect ratio. For -20' of pitch-control deflection, all aerodynamic characteristics show a slight nonlinear variation with aspect ratio. Separated flow and the near-field interaction of the wing and fuselage could be the cause of these nonlinear variations. The lift and pitching-moment data show a nearly linear incremental change due to trailing-edge flap deflections; in other words, a doubling of the flap deflection results in a doubling of the resultant lift force and pitching moment. However, for the drag data, the linear incremental change is not evident; a change in the flap deflection from -10' to -20' produces a 270-percent increase in the zero-lift drag. This extreme drag penalty is the predominate cause of the large drag increases and reduced aerodynamic efficiency observed in figures 21 and 22.

Theoretical Investigation A theoretical investigation was conducted on the

six study wings to evaluate the capability of the Supersonic Design and Analysis System (SDAS) to predict the supersonic aerodynamic characteristics of a parametric set of low-fineness-ratio configurations which had low-sweep, blunt-leading-edge wings. The SDAS code is a series of computational methods which are based upon linear or slender-body theory (ref. 4). The system of codes selected for analysis computes the inviscid zero-lift drag (wave drag) based upon the method of reference 5, computes the inviscid lift, pitching moment, and induced drag with the method of reference 6, and determines the viscous effects with the method of reference 7.

An initial theoretical study was conducted to determine the effect that geometric modeling of the lifting surface has on the computational capability of the method of reference 6. Three geometric repre- sentations were selected for analysis; these were the generic body with zero-thickness wing, wing-body planform representation, and a wing-only solution (figs. 23, 24, and 25).

Presented in figures 26 through 31 are representative comparisons of the computed longitudinal aerodynamic characteristics for all six wings with the three models at M = 1.60. Comparison of the theoretical predictions with the experimental results shows that the drag due to lift and the lift-curve slope are not consistently predicted by any of the

4

models investigated. In particular, the representation of the generic body with zero-thickness wing results in an overprediction of the drag and lift characteristics. The results for the wing-body planform representation and wing-only representation are very similar to one another. These models also result in an overprediction of the drag and lift characteristics, but to a lower and higher degree, respectively, than the generic body with zero-thickness wing. In addition, the pitching-moment results from all three models are similar. It was concluded from this study that the generic body with zero-thickness wing would be used for all subsequent theoretical analysis because it was more closely representative of the actual geometry.

Summaries of the predicted and measured performance results for the delta and double-delta wing planforms are presented respectively in figures 32 and 33. The delta wing and double-delta wing results indicate a general incapability of the SDAS code to predict the zero-lift drag for low-fineness-ratio configurations. These results were not completely unexpected; the far-field wave-drag code (ref. 4) is a technique based on slender-body theory, which assumes small disturbances and high-fineness-ratio configurations. The drag due to lift and the maximum lift-drag ratio for the delta and double-delta wings show similar results. The effect of aspect ratio and Mach number on the drag-due-to-lift characteristics is predicted by the SDAS code; however, the impact of the code's incapability to predict the zero-lift drag becomes evident in review of the maximum lift-to-drag ratio results, in which the predicted results vary erratically with changes in aspect ratio and Mach number.

Summaries of the predicted and measured lift and pitching-moment characteristics for the delta and double-delta wings are presented respectively in figures 34 and 35. The effect of varying aspect ratio and Mach number on the lift-curve slope for both the delta and double-delta wings is predicted by the SDAS code. However, the effect of varying aspect ratio and Mach number on the level of longitudinal stability is not predicted with any consistency. For the delta wings, the predicted results show incorrect levels and trends with changes in aspect ratio and Mach number. For the double-delta wings, the theoretical method does a reasonable job of predicting the trends associated with changes in aspect ratio and Mach number but incorrectly predicts the level of longitudinal stability in all cases. As expected with linear theory, the predicted stability level for a given wing shows no variation with Mach number once the wing leading edge becomes supersonic, a contradic- tion of the experimental work.

To complete the evaluation of the SDAS code, the capability of the theoretical method to predict the pitch-control aerodynamics was investigated. The predicted and measured incremental aerodynamics due to trailing-edge flap deflections are presented in figure 36 for the delta wings and in figure 37 for the double-delta wings. As with the basic longitudinal aerodynamics presented above, the analytic modeling selected was the generic body with zero-thickness wing. Comparing the predicted and measured results for the delta and dauble-delta wings reveals similar results. The SDAS code consistently over- predicts all the aerodynamics due to flap deflections. However, the trends associated with increasing Mach number and aspect ratio are predicted for all cases. For the lift and pitching-moment characteristics, the SDAS code does predict the proper linear incremental change due to flap deflection. Similar results are shown for the zero-lift drag data. The SDAS code does predict that a 270-percent increase in the zero- lift drag would occur when the flap deflection is increased from -10' to -20'. The overprediction of the pitch-control aerodynamics by the SDAS code for both flap deflection angles could be attributed to wing-thickness and boundary-layer effects, which would reduce the deflection angle and the resultant flap loading.

The results presented in figures 32 through 37 show that the SDAS code does not consistently predict all the longitudinal aerodynamic characteristics of the low-sweep, low-fineness-ratio wing-body configurations under investigation. The zero-lift drag results are inconsistent with the experimental data. These results clearly emphasize the importance of having an adequate zero-lift drag prediction technique in order to perform preliminary design stud- ies which would look at the effects of wing planform, aspect ratio, and various other aerodynamic parameters.

Concluding Remarks An experimental and theoretical study was con-

ducted to investigate the supersonic aerodynamic characteristics of delta and double-delta wings. Test- ing was conducted in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.60, 1.90, and 2.16. Supersonic data were obtained on six uncambered, blunt-leading-edge wings mounted on a generic low- fineness-ratio fuselage. Measured longitudinal aerodynamic characteristics showed that the wing planform was as important as aspect ratio in determin- ing the supersonic aerodynamic characteristics. The double-delta wings exhibited lower zero-lift drag values than the delta wings having the same aspect ratio, whereas delta wings provided lower drag due to

5

lift than the double-delta wings. Deflections of the trailing-edge flaps for pitch control revealed that the induced aerodynamic forces were only a function of the control-surface planform and were independent of wing planform. The supporting theoretical analysis showed that the Supersonic Design and Analy- sis System (SDAS) did not consistently predict all the longitudinal aerodynamic characteristics of the low-sweep, low-fineness-ratio wing-body configurations under investigation. The drag-due-to-lift and

6

lift characteristics were reasonably well predicted; however, zero-lift drag and pitching-moment computations were inconsistent with experimental data. Theoretical computations also overpredicted the ef- fectiveness of trailing-edge flaps for pitch control.

NASA Langley Research Center Hampton, VA 23665 March 21, 1985

TABLE I . GEOMETRIC CHARACTERISTICS OF WING PLANFORMS

Characteristic

Area. S. ftz . . . . . . . . . . . Span. b. in . . . . . . . . . . . . . Mean aerodynamic chord. 2. in . . . . Leading edge of 2: x. in . . . . . . . . . . . . . . y. in . . . . . . . . . . . . . .

Projected root chord. C7.p . in . . . . . Projected root chord leading edge: x. in . . . . . . . . . . . . . . y. in . . . . . . . . . . . . . .

Exposed root chord. C+.e. in . . . . . Exposed root chord leading edge: x. in . . . . . . . . . . . . . . y. in . . . . . . . . . . . . . .

Break chord. c g . in . . . . . . . . . Break chord leading edge: x. in . . . . . . . . . . . . . . y. in . . . . . . . . . . . . . .

Tip chord. ct . in . . . . . . . . . . Tip chord leading edge:

x. in . . . . . . . . . . . . . . y. in . . . . . . . . . . . . . .

Inboard. deg . . . . . . . . . . Outboard. deg . . . . . . . . .

Trailing-edge sweep. ATE. deg . . . Aspect ratio. AR . . . . . . . . . Taper ratio. X . . . . . . . . . . Airfoil . . . . . . . . . . . . . . nailing-edge flap. percent span . . . Trailing-edge flap root chord. in . . . Trailing-edge flap tip chord. in . . . .

Leading-edge sweep. ALE:

Wing 1

2.379 24.488 19.355

14.477 3.963

30.396

4.878 0

26.902

7.928 1.219 5.830

26.324 8.571 2.927

27.891 12.244

68.22 23.10

-20 1.750

0.0963 64A0035

88 2.801 1.049

Wing 2

2.379 24.488 16.910

17.896 4.508

25.059

11.388

22.856

13.147 1.219

0

2.927

29.064 12.244

55.28

-20 1.750

0.1168 64A0035

88 2.801 1.049

Wing 3

2.379 26.878 16.934

16.366 4.518

26.436

8.509 0

23.802

10.698 1.219 6.114

25.407 9.407 2.927

27.127 13.439

60.90 23.10

-20 2.1083 0.1107

64A0035 88

2.777 1.044

Wing 4

2.379 26.878 15.271

18.677 4.994

22.570

13.195

20.788

14.533 1.219

0

2.927

27.947 13.439

47.67

-20 2.1083 0.1297

64A0035 88

2.777 1.044

Wing 5

2.379 29.268 14.933

17.886 5.113

23.056

11.624 0

21.074

13.162 1.219 6.397

24.554 10.224 2.927

26.427 14.634

51.62 23.10 - 20

2.500 0.1273

64A0035 88

2.391 0.992

Wing 6

2.379 29.268 13.902

19.319 5.488

20.488

14.731

19.024

15.750 1.219

0

2.927

26.965 14.634

39.90

- 20 2.500

0.1428 64A0035

88 2.391 0.992

I

7

TABLE 11. NUMERICAL DESCRIPTION OF WIND-TUNNEL MODELS

NASA/GD HYBRID FLAP STUDY WING 1 WITH FUSELAGE

342.65 16.934 21.251

50.0 60.0 70.0 80.0 90.0 100.0

26.324 8.571 0.244 5.830 27.891 12.244 0.244 2.927 0.0 .280 .341 .429 .591 .814 1.120 1.496 1.693 1.750 1.641 1.409 1.094 -735 .372 -013 0.0 .280 .341 .429 -591 .814 1.120 1.496 1.693 1.750 1.641 1.409 1.094 .735 .372 -013 0.0 .280 .341 .429 .531 .814 1.120 1.496 1.693 1.750

0.000 1.220 2.439 3.659 4.878 6.098 7.317 9.756 12.195 14.634 17.073 19.512 26.829 34.146 37.000

1 -1 1 0 0 0 3 16 1 17 15

0.0 -50 -75 1.25 2.50 5.0 10.0 20.0 30.0 40.0

7.928 1.219 0.244 26.902

1.641 1.409 1.094 -735 .372 -013


342.65 16.910 23.814 0.0 .50 .75 1.25 2.50 5.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 13.146 1.219 0.244 22.856 29.063 12.244 0.244 2.927 0.0 .280 .341 .429 .591 .814 1.120 1.496 1.693 1.750 1.641 1.409 1.094 .735 .372 .013 0.0 .280 .341 .429 .591 .814 1.120 1.496 1.693 1.750 1.641 1.409 1.094 .735 -372 -013 0.000 1.220 2.439 3.659 4.878 6.098 7.317 9.756 12.195 14.634 17.073 19.512 26.829 34.146 37.000

1 - 1 1 0 0 0 2 16 1 17 15


342.65 16.934 22.293 0.0 .50 .75 1.25 2.50 5.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 10.698 1.219 0.244 23.802 25.407 9.407 0.344 6.114 27.127 13.439 0.244 2.927 0.0 .280 .341 -429 .591 .814 1.120 1.496 1.693 1.750

1 - 1 1 0 0 0 3 16 1 17 15

1.641 1.409 1.091; a735 -372 -013 0.0 -280 -341 -429 .591 -814 1.120 1.496 1.693 1.750 1.641 1.409 1.094 -735 .372 -013 0.0 .280 .341 .429 .591 .e14 1.120 1.496 1.693 1.750 1.641 1.409 1.094 .735 .372 .013 0.000 1.220 2.439 3.659 4.878 6.098 7.317 9.756 12.195 14.634 17.073 19.512 26.829 34.146 37.000

8

GEOM 2 GEOM 3 GEOM 4 GEOM 5 A GEOM 5B GEOM 6A GEOM 6B GEOM 6C GEOM 8 A 1 GEOM 8A2 GEOM 8B1 GEOM 8B2 GEOM 8 C 1 GEOM 8C2 GEOM 1 0 A GEOM 10B

GEOM 2 GEOM 3 GEOM 4 GEOM 5 A GEOM 5B GEOM 6A GEOM 6B GEOM 8 A 1 GEOM 8A2 GEOM 8 B 1 GEOM 882 GEOM 10A GEOM 1 O B

GEOM 2 GEOM 3 GEOM 4 GEOM 5.4 GEOM 5B GEOM 6A GEOM 6B GEOM 6C GEOM 8 A 1 GEOM 8A2 GEOM 8 B 1 GEOM 8 B 2 GEOM 8 C 1 GEOM 8C2 GEOM 1 0 A GEOM 1 O B

TABLE 11. Continued


342.65 15.271 24.021 0.0 .50 .75 1.25 2.50 5.0 10.0 50.0. 60.0 70.0 80.0 90.0 100.0 14.533 1.219 0.244 20.788 27.947 13.439 0.244 2.927 0.0 .280 .341 -429 .591 ,814 1.120 1.641 1.409 1.094 .735 .372 .013

1.641 1.409 1.094 .735 .372 .013 0.000 1.220 2.439 3.659 4.878 6.098 7.317 17.073 19.512 26.829 34.146 37.000

1 -1 1 0 0 0 2 16 1 17 15

0.0 -280 -341 -429 -591 e814 1.120


342.65 14.933 23.112 0.0 -50 .75 1.25 2.50 5.0 10.0 50.0 60.0 70.0 80.0 90.0 100.0 13.162 1.219 0.244 21.074 24.554 10.244 0.244 6.397 26.427 14.634 0.244 2.927 0.0 .280 ,341 .429 .591 -814 1.120 1.641 1.409 1.094 .735 .372 .013 0.0 .280 .341 .429 .591 -814 1.120 1.641 1.409 1.094 .735 .372 .013 0.0 .280 .341 .429 .591 .814 1.120 1.641 1.409 1.094 .735 -372 .013

17.073 19.512 26.829 34.146 37.000

1 - 1 1 0 0 0 3 16 1 17 15

0.000 1.220 2.439 3.659 4.878 6.098 7.317

NASA/GD HYBRID FLAP STUDY W I N G 6 WITH FUSELAGE 1 - 1 1 0 0 0 2 16 1 17 15

342.65 13.902 24.185

50.0 60.0 70.0 80.0 90.0 100.0 0.0 .50 .75 1.25 2.50 5.0 10.0

15.750 1.219 0.244 19.024 26.965 14.634 0.244 2.927 0.0 .280 .341 .429 .591 .814 1.120 1.641 1.409 1.094 .735 .372 .013 0.0 .280 .341 .429 .591 .814 1.120 1.641 1.409 1.094 ,735 .372 .013 0.000 1.220 2.439 3.659 4.878 6.098 7.317 17.073 19.512 26.829 34.146 37.000

GEOM 2 GEOM 3 GEOM 4

20.0 30.0 40.0 GEOM 5A GEOM 5B GEOM 6A GEOM 6B

1.496 1.693 1.750 GEOM 8 A 1 GEOM 8A2

1.496 1.693 1.750 GEOM 8 B 1 GEOM 882

9.756 12.195 14.634 GEOM 1 0 A GEOM 1 0 B

GEOM 2 GEOM 3 GEOM 4

20.0 30.0 40.0 GEOM 5A GEOM 5B GEOM 6A GEOM 6B GEOM 6C

1.496 1.693 1.750 GEOM 8 A 1 GEOM 8A2

1.496 1.693 1.750 GEOM 8 B l GEOM 8 B 2

1.496 1.693 1.750 GEOM 8 C 1 GEOM 8 C 2

9.756 12.195 14.634 GEOM 10A GEOM 10B

GEOM 2 GEOM 3 GEOM 4 GEOM 5A GEOM 5B GEOM 6A GEOM 6B

1.496 1.693 1.750 GEOM 8A1 GEOM 8A2

1.496 1.693 1.750 GEOM 8 B 1 GEOM 8B2

9.756 12.195 14.634 GEOM 10A GEOM 10B

20.0 30.0 40.0

9

TABLE 11. Concluded

0.000 0.000 0.000 0.000 0.000 0.000 -.725 -.725 -.725 -.725 as725 -.725 0.000 .235 .404

.340 .279 .230 -1.115 -1.071 -.989

-a345 e.306 -a286 0.000 .321 .617

.565 .496 -396 -1.240 -1.188 -1 -056

-a004 -055 -094 0.000 .384 .720

.693 .594 .495 -1.260 -1.229 -1.068

.282 .341 .389 0.000 .446 .764

.602 ,513 -422 -1.273 -1.200 -1 008

.651 -690 -719 0.000 .416 -713

.750 .651 .531

.841 .909 .968 0.000 .475 .e29

.692 .593 .483 -1.216 -1.142 -1.001

1.094 1.142 1.171 0.000 .381 .854

.855 ,667 -567 -1.206 -1.191 -1.096

0.000 .491 .857 .810 ,660 .532

-1.216 -1.184 -1.081 1.102 1.140 1.168 0.000 .491 .857 .810 .660 .532

-1 -216 -1.184 -1.081 1.102 1.140 1.168 0.000 .491 .857 .810 .660 -532

-1.216 -1.184 -1.081 1.102 1.140 1.168 0.000 .491 .857

.810 .660 -532 -1.216 -1.184 -1.081

1.102 1.140 1.168 0.000 .491 .857 .810 .660 ,532

-1.216 -1.184 -1.081 1.102 1.140 1.168 0.000 .491 .857 .810 .660 .532

1.102 1.140 1.168 0.000 .491 .857

-1.243 -1.180 -1.029

1.108 1.165 1.203

-1.216 -1.184 -1.081

-810 e660 -532 -1.216 -1.184 -1.081

0.000 0.000 -. 725 -.725

512 .191

-.a80 -.276

-813 .287

-.a74

.986 365

-.739 .439 .961 .303

-.778 .758 ,980 .391

-.789 1.027 1.045

.384 -.a01 1.199 1.030

.400 -.995 1.231 1.074

.422 -. 969 1.187 1.074

.422 -.969 1.187

.422 -. 969 1.187 1.074

.422 -.969 1.187 1.074

.422 -. 969 1.187 1.074

.422 -.969 1.187 1.074

.422 -.969

-132

1.074

0.000 0.000 -. 725 -.725

561 .121

-.770 -. 257

.88? ,187

-.675

1.044 ,255

,467 1.087

.233 -. 479

.777 1.117

.272 - ,540 1.046 1.153

.236 -.632 1.218 1.168

.290 -.a74 1.249 1.201

.273 -.a48 1.214 1.201

.273 -.a48 1.214 1.201

.273 -.a48 1.214 1 .201

.273 -.a48 1.214 1.201

.273

1.214 1.201

.273 -. 848 1.214 1.201

.273 -. 848

151

-a510

-.a48

0.000 0.000 -.725 -.725

.570

.070 -.719 -.256

.889

.088 - .566

.159 1.054

.147 -. 342

.497 1.125

.134 -. 230

.787 1.165

.172 -.330 1.065 1.191

. lo8 -. 483 1.227 1.219

.172 -. 726 1.257 1.219

.143 -.729 1.222 1.219

.143 -.729 1.222 1.219

.143 -.729 1.222 1.219

.143 -.729 1.222 1.219

.143 -.729 1.222 1.219

.143 -. 729 1.222 1.219

.143 -.729

0.000 0.000 -.725 -.725

.571 0.000 -.661 -.258

.879 0.000 -.477

.169 1.043 0.000 -.272

.496 1.094 0.000 -.032

.796 1.174 0.000 -.013 1.066 1.176 0.000 .011

1.233 1.219 0.000 -. 002 1.264 1.219 0.000

.005 1.220 1.219 0.000

.005 1.220 1.219 0.000

,005 1.220 1.219 0.000

.005 1.220 1.219 0.000

,005 1.220 1.219 0.000

-005 1.220 1.219 0.000

005 1.102 1.140 1.168 1.187 1.214 1.222 1.220

0.000

-. 725

.540

-. 582

.847

-. 359

1.003

-.134

1.013

.196

1.153

.187

1.192

.436

1.219

.759

1.219

.764

1.219

.764

1.219

.764

1.219

.764

1.219

.764

1.219

.764

1.219

.764

0.000

- .725

.509

-. 503

.767

-.220

.943

.005

.902

.365

1.071

.425

1.120

.702

1.144

.924

1.170

.898

1.170

.898

1.170

.898

1.170

.898

1.170

.898

1.170

.898

1.170

.898

0.000

-.725

.449

-. 424

676

-. 102

.833

.143

.761

.523

- 950

.642

.910

.958

.995

1.030

.950

1.034

.950

1.034

.950

1.034

.950

1.034

.950

1.034

.950

1.034

.950

1.034

GEOM 14

GEOM 15 1

GEOM 14 2

GEOM 15 2

GEOM 14 3

GEOM 15 3

GEOM 14 6

GEOM 15 4

GEOM 14 5

GEOM 15 5

GEOM 14 6

GEOM 15 6

GEOM 14 7

GEOM 15 7

GEOM 14 8

GEOM 15 8

GEOM 1 4 9

GEOM 15 9

GEOM 14 10

GEOM 15 10

GEOM 14 11

GEOM 15 11

GEOM 14 12

GEOM 15 12

GEOM 14 13

GEOM 15 1 3

GEOM 14 14

GEON 15 14

GEOM 14 15

GEOM 15 1 5

10

Figure 1. Computer graphic of wing 1. AR= 1.75.

Figure 2. Computer graphic of wing 2. AR = 1.75.

11

Figure 3. Computer graphic of wing 3. A = 2.11.


12



13

-r I

I

I I

I 1 I

I I

I I

I I

v

I I I

I i - I I

I I

81

v, LL

0 d W d cu I1

v, LL

-

0 0 cu N 4

0 0 m h

0 0 09 d

0 0 b. cu 0 0

0 9

I I

I I

I I

A A A L A t

14

I a ) a w

l-4 l-4

(v

II

Q

.r( z 3 .zi m W

Y

1s

0 0

P

.04

8

7

6

5

4

3

2

1

o L/D

-1

-2

-3

-4

-5

-6

-7

-a

01 1 I I I I 1 I I 1 I

CL

-.4 -.3 -.2 -.l 0 . 1 .2 .3 .4 .5 .6

Figure 9. Effect of wing planform on longitudinal aerodynamic characteristics at M = 1.60 for AR = 1.75 wings.

.10

-.05

20

18

16

14

12

10

8

d e g 6

4

2

0

-2

-4

-6 -

I I I I I I I I I I -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

0 Doubl e-del t a p lan form

0 Del ta p lan form

P

_1 .6

Figure 9. Concluded.

17

.20

.18

.16

.14

.12

c, .10

.08

.06

.04

.02

0

0 0

Double-del t a pla Del t a planform

P

I I I I I I I I I 1 .2 .3 .4 .5 .6 .1

CL

a

7

6

5

4

3

2

1

o L/D

.1

2

3

4

5

6

7

a


18

20

18

16

14

12

10

8-

d e g

-2

-4

0 Doubl e-del ta planform 0 Delta planform

-

-

-

-

-

-

6 -

4 -

2-

0-

-

-

-6 I I I I I I I I I 1 I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL


19

.20

.18

.16

.14

.12

c, .10

.08

.06

.04

.02

0 -

0 0

I I 1 I I I I I I

CL -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

8

7

6

5

4

3

2

1

o L/D

-1

-2

-3

-4

-5

-6

-7

-8


20

crn 0

-.05

-.lo L

2c

1 E

1 E

14

1 2

1c

E

d e g 6

4

2

a

-2

-4

-6

0 Doubl e-del t a planform 0 Delta planform

I I I I 1 1 I I I ' -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

A


2 1

AR

0 1.75

0 2.11

0 2.50

.20

. i a

.16

.14

.12

c, .10

.oa

.06

.04

.02

- -

-

-

-

-

-

-

-

-

01 I I 1 I I I I I I -.4 -.3 -.2 -.l 0 . I .2 .3 .4 .5 .6

C L

Figure 12. Effect of aspect ratio on longitudinal aerodynamic characteristics of delta wings at M = 1.60.

22

.10

-.05

2c

1E

16

1 4

1 2

10

8

a.deg 6

4

2

AR

0 1.75

2.11

0 2.50

-6 I I 1 I I I I I I I I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL


23

.20

.18

.16

.14

.12

c, .10

.08

.06

.04

.02

0

AR 0 1.75

0 2.11

0 2.50

P

8

7

6

5

4

3

2

1

o L/D

.1

.2

3

4

5

6

7

8

I I 1 I 1 I I I I I

CL

Figure 13. Effect of aspect ratio on longitudinal aerodynamic characteristics of double-delta wings at M = 1.60.

24

.10

-.05

18

16

14

12

10

8

c d e g 6

4

2

0

-2

20

-4 t

AR 0 1.75

0 2.11

0 2.50 P

-6 I I I I I I I I I I J -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

cl.


26

I / I

I / 11 d

0 0 0

1 I I I W m e m

I I I I I

X

aJ h W

X 5 E

h

n \ 1 v

- 9 9

0 m 0 N d d 0

26

E

-09 N

- . * N

lx =I

- . 0

N

- . W

c

0 0 0

I I I I I

N

5 N

lx =I

9 N

N 4

I

-1 V Q

a - 9

I

27

.20

.18

.16

.14

.12

c, .10

.oa

.06

.04

.02

a

7

6

5

4

3

2

1

o L/D

-1

-2

-3

-4

-5

-6

-7

-a

-

-

-

-

-

-

-

-

-

-

01 1 I I I I I I I 1 I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL

Figure 16. Effect of pitch-control deflections on longitudinal aerodynamic characteristics of AR = 1.75 double- delta wing at M = 1.60.

28

.10

-.05

18


29

.20

.18

.16

.14

.12

c, .10

.08

.06

.04

.02

0 I I I I I I I I 1

CL

I

a

7

6

5

4

3

2

1

o L/D

-1

-2

-3

-4

.5

.6

.7

.a

Figure 17. Effect of pitch-control deflections on longitudinal aerodynamic characteristics of AR = 1.75 delta wing at M = 1.60.

30

.10

-.05

-6 I I I I I I I I I I I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL


31

.2(

. I f

. I t

.14

.li

c, .1c

.08

.06

.04

.02

0

1

o L/D

-1

-2

-3

-4

-5

-6

-7

-8

I I I I I I I .2 .3 .4 I .5 I .6 I .1


32

.10

-.05

2c

18

16

14

12

10

a a d e g

6

4

2

0 ’

-2

-4

-6 I I I I I I I 1 I .2 .3 .4 .5 I .6 I -,4 -.3 -.2 -.l 0 .1


33

8

7

6

5

4

3

2

1

0 L/D

1

2

3

4

5

5

7

3

01 I I I I I I I -.4 -.3 -.2 -.l 0 . 1 ,2 .3 .4 I .5 I .6 I

Figure 19. Effect of pitch-control deflections on longitudinal aerodynamic characteristics of AR = 2.11 delta wing at A4 = 1.60.

34

-.lo L

20

18

16

14

12

10

a a,deg

6

4

2

0

-2

-4

-6 I I I I I I I I I

cl.


35

8

7

6

5

4

3

2

1

o L/D

-1

-2

-3

-4

-5

-6

-7

-8

01 I I I I I 1 I I I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

C L


36

.10

-.05

20

18

16

14

12

10

8

a,deg 6

4

2

0

-2

-4

-6 I I I I I 1 I I I I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL


37

Figure 21. Effect of pitch-control deflections on longitudinal aerodynamic characteristics of AR = 2.50 delta wing at M = 1.60.

38

- . l o -.05:

20

18

16

14

12

10

4

2

0

-2

-4

-6 -.4 -.3 -.2 -.l 0 .1 . 2 .3 . 4 .5 .6

CL


39

1" m

E 0 0 0 0 0 0 0

.) d d d N N N + W I I I I I I S I- 5

Lc) - - n~ W

I I

- ? N

- . 0

N

0, n

V a

I I I I I 1 I I I I Ln d m CJ F-4 0 N 0 0 0 0 4 9

I

co 0

I

Kt 0 0

I

0. E

V a

40

hil d

'B

x

P %

41 '

42

rcc 0

V .- Y

43

.20 -

.18 -

.I6 -

.14 -

. I 2 -

c, . l o -

.08 -

.06 -

.04 -

Mea s u r e d Zero- th ickness wing Wing-body planform Wing o n l y

8

7

6

5

4

3

2

1

o L/D

-1

-2

-3

-4

-5

-6

-7

-8

01 I I I I I 1 1 I I .2 .3 .4 .5 .6 .1 -.4 -.3 -.2 -.I 0

Figure 26. Effect of geometric modeling on predicted longitudinal aerodynamic characteristics of AR = 1.75 double-delta wing at M = 1.60.

44

20

18

16

14

12

10

8

d e g 6

4

2

0

-2

-4

-6

Me a s u red Ze ro - th i c kness w i ng Wing-body planform Wing o n l y

I 1 I I I I I I 1 I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL


45

Measured Zero-thickness w in Wing-body p lan form Wing o n l y

.20

.18

.16

.14

.12

c, .IO

.08

.06

.04

.02

0 I 1 I I I I I I I I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL

8

7

6

5

4

3

2

1

o L/D

-1

-2

-3

-4

-5

-6

-7

-8

Figure 27. Effect of geometric modeling on predicted longitudinal aerodynamic characteristics of AR = 1.75 delta wing at M = 1.60.

40

.10

.05

crn 0

-.05

-.lo

2c

l e

16

1 4

12

10

e a.deg

6

4

2

0

-2

-4

-6

- Measured Zero-thickness wing Wing-body planform Wing only

- _ - - - _ _ --- ----

1 I I I I I I I I I -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6

CL


47

- - - _ _ _ _ _ --- - _ _ -

.20 -

. i a -

.16 -

.14 -

.12 -

c, .10 -

.08 -

.06 -

.04 -

Measured

01 I I I I I I I I I _I

CL .2 .3 .4 .5 .6 .1 -.4 -.3 -.2 -.l 0

8

7

6

5

4

3

2

1

0 L/D

-1

-2

-3

-4

-5

-6

-7

-8


40

.10

-.05

1 8 t - Measured

--- Wing-body planform Zero-thi ckness wing

Wing only

- - - - - - - - - - -

14


49

Measured Zero-thickness wing Wing-body p lan form Wing o n l y

.2(

.1 E

.1 E

. 1 4

.12

c, .10

.08

.06

.04

.02

0

a

7

6

5

4

3

2

1

0 L/D

.1

,2

3

4

5

6

7

8

I I I I I 1 I I 1

CL

I - .4 -.3 -.2 -.1 0 .1 .2 .3 .4 .5 .6


60

.10

-05

crn 0

-.05

-.lo

12

10

-2

-4

2ol 18

-

-

8-

6-

4 -

2 -

0-

-

-

__O__ Measured

--- Wi ng-body pl anform Zero-thickness wing

Wing only

- - _ _ _ _ _ - - - - t

-6 1 I I I I I I I I I 1

CL -.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6


51

l 8

0

.20 -

.18 -

.16 -

.14 -

.12 -

c, .IO -

.08 -

.06 -

.04 -

.02 -

I I I I I I I I I


62

20

18

16

14

12

10

8

d e g 6

4

2

0

-2

-4

-6

__O__ Measured Zero-thickness w i n g W i ng- body pl an form Wing only

- - _ _ _ _ _ --- - _ _ -

I 1 I I I I I I I -.4 -.3 -.2 -.l 0 .I .2 .3 .4 .5 .6

CL


__O__ Measured - - _ _ - _ _ Zero-thickness wing --- Wing-body planform

. Wing only

.20

.18

.16

.14

.12

c, .10

.08

.06

.04

.02

0 I I I I I I I I I -.4 -.3 -.2 -.l 0 . I .2 .3 .4 .5 .6

CL

8

7

6

5

4

3

2

l

o L/D

.1

.2

.3

.4

-5

-6

-7

-8


64

-.05

cm -.lo L

l 8 t - Measured --- Wing - body pl an form

Zero - t h i c knes s w i n g

Wing only -___ 14

12.

10.

a .

6 .

4

2

0

-2

-4

-.4 -.3 -.2 -.l 0 .1 .2 .3 .4 .5 .6 C L


5s

P io i,

10 I I I I

I I I J o

10

0

0

In

v - c, lu

a

4 I

0 N

9

66

In 4 0

0, a

u

co N

* N

w

9 N

u3

4

“9 N

7 N

w

3. N

9

0 -

0 4

I” ? I

I I I

1 0 / o /

I I I 1 P) ? ID In

0

0

X IU E h

n \ -I v

ID

0 In N d 0 9

0. n

V

0 - d

9

57

k 0

0 0 0

0 I

I I ’ I I

I I

0

i I P I

m * 0 0

u W L 3 m 5 W E

n

u W L 3 m 5 W E

d Q

--?i u u

(? 0

I I , 000

ro 4

I

N 4

I

03 0

I

“9 N

d

cv

CY 4

0

N

ro d

“9 N

* cu

CT 4

0

N

a d

5 3

58

\ E u u

I I ' I I

0 0 0 I I

\O P I

1" b. cu

K i

9 N

3 U > V -0

I I I N a - 4 0

I I I I

Ip d

e N

59

.06 r

*01 t - .16

- .12

ACL -.08

- .04

1 - /--- d d d ---r--- - /

_c-- - ---- 4 / - d

-- _e----_

e- 0

0 - ----4

0 0

0

1.6 2.0 2.4 2.8 AR

I I I I

Measured Predicted M 6TE, deg

0 1.60 - 10 0 ------ 1.90 - 10

0 --- 2.16 - 10 d ---- 1.60 - 23

d ----- 1.90 -20

------ 2.16 -20

.040 r c /----- \

- 6 6

- L I I J

1.6 2.0 2.4 2.8 AR

Figure 36. Effect of aspect ratio and Mach number on predicted and measured incremental aerodynamics of delta wings due to trailing-edge flap deflections.

-. 1 6

- . 12

- c L - . o e

- . 04

I I

I

0

------ d d

---- r - - - d d

&--- w--- - - -~

L--- -----8- -0

e- o 0 - - -

0

,----m----- r-7- -3 0

I 1. 6 2.0 2 . j 2.8 F R ~

%,I?

.010

. 0 3 2

. c23

.016

. oog

Measured P r e d i c t e d M f i T E , deg

0 1. 60 -10

0 ------ 1.90 -10

0 ---2.16 -10

d - _ _ - 1. 60 -20 d 1.90 -20 0 ------2.16 -20

0---\

'\ /'

---I \

/ d 'u d d . e /- ---- ---.d

d d

1 I I 1 . 6 2.0 ? .J 2 . c

A 2

I ~

Figure 37. Effect of aspect ratio and Mach number on predicted and measured incremental aerodynamics of double-delta wings due to trailing-edge flap deflections.

I

61

Appendix

Test Description The wind-tunnel test program was conducted in

test section 1 of the Langley Unitary Plan h'ind Tunnel (ref. 1) at Mach numbers of 1.60. 1.90, and 2.16 The tests \ v u e conducted under the following conditions:

St agnation 1 Reynolds 1

125 125 2 x 106

2 x 106 1 1 .90

2.16 1349

The dew point was maintained sufficiently low to pre- vent condensation effects in the tiinnel. Strips of No. 60 sand grit were applied aft of the leading edge of all wings as shown in the sketches of figure A1 and

W i n g 1

62

W i n g 3

1 . 2 in. aft of the fuselage nose to induce bouridaiy- layer transition. The grit size and locations were x- lected according to the method of reference 8 t o en- sure fully turbulent flow over the model. Forcc. and moments on the model were measured by means of' d six-component electrical strain-gauge balance, which was contained within the model and connccted through a supporting sting to the permanent model actuating system in the wind tunnel.

Balance chamber pressure was measured through- out the test with a pressure transducer mounted ex- ternal to the model and connected t o pressure tubing located in the balance cavity. Force and moment data were corrected to free-stream static pressure at the balance chamber. All angles of attack have been adjusted for tunnel flow misalignment and sting deflect ions.

Table AI contains a listing of the symbols corre- sponding to the headings which appear in the tabulated data. Table -411 is an index to the tabulated data. which are presented in table AIII.

AR = 1 . 7 5

AR = 2.11

AR = 2.50

W i n g 2

W i n g 4

W i n g 5 W i n g 6

Figure A1 Location of wing leading-edge transition grit. All linear dimensions are in inches.

TABLE AI. TABULATED DATA SYMBOLS

Tabulated data heading

Both axes:

Definition

ALPHA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a BETA P CM Crn CY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c y MACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Body axis: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CL C A

CLB e1 CN C N CNB c n

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CAC c A , c CAUNC CA,unc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R/FT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R x ~ O - ~

Stability axis: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CD CD

CL CL CLS CL CNS c n LID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LID

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CDC CD,c CDUNC CD,unc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

TABLE AII. INDEX T O TABULATED DATA

Page 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109 110 111' 112 113 114 115 116 117 118

Run 149 152 153 155 156 157 158 159 160 94 98

101 102 103 104 105 106 107 51 54 55 57 58 59 60 61 62 66 69 70 72 73 74 75 76 77 15 18 19 21 22 23 26 24 25 36 39 40 42 43 44 45 46 47

~- ~

Configurat ior Wing 1

Wing 2

_ _ ~ Wing 3

Wing 4

Wing 5

Wing 6

~ T E deg 0 0 0

- 10 - 10 - 10 -20 -20 -20

0 0 0

- 10 - 10 - 10 -20 -20 -20

0 0 0

- 10 - 10 - 10 - 20 - 20 - 20

0 0 0

- 10 - 10 - 10 - 20 - 20 -20

0 0 0

- 10 - 10 - 10 - 20 -20 - 20

0 0 0

- 10 - 10 - 10 - 20 -20 - 20

Mach numbei

1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16 1.60 1.90 2.16

64

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ....................

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N N N N N ~ N ~ ~ ~ N ~ N ~ N ~ J J ~ J N m o o o o o o o o o o o o o o o o o o o ~ o ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 l 1 1 1 1 1 1 1 1 0 1 1 1 1 I

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I I I 1 1 1 1 I I 1 I I I 1 1 1

d d d ~ ~ ~ ~ w ~ m ~ 0 ~ ~ r l ~ m ~ m 3 m a o o o 3 o o o o o o u ~ 9 W ~ ~ ~ g g g o v ~ r l ~ ~ d r l ~ o o 3 0 o o o o o o o o ~ . - l 3 ~ 0 3 0 0 0 0 u ~ 0 3 0 3 3 0 0 0 0 0 0 .....................

v 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0. 0 c 0 ...................

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u o o o o o o o o o o o o o o o o o o o q q ................... m m m m m m m m ~ ~ 0 ~ d ~ u r 9 ~ o o ~

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0 3 0 3 0 0 0 3 0 0 3 0 0 0 0 3 0 0 0 0 0 ..................... 1 1 1 1 1 I I I 1 1 t

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N N N N N ~ N O N ~ N N N ~ ~ N U J . ~ J ~ ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a000000000000000000300 vooooooooooooooooooooo ..................

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References 1. Jackson, Charlie M., Jr.; Corlett, William A.; and

Monta, William J.: Description and Calibration of the Langley Unitary Plan Wind lbnnel. NASA TP-1905, 1981.

2. Craidon, Charlotte B.: Description of a Digital Com- puter Program for Airplane Configuration Plots. NASA TM X-2074, 1970. Love, Eugene S.: Znuestigations at Supersonic Speeds of 22 Ifiangular Wings Representing Two Airfoil Sections for Each of 11 Apez Angles. NACA Rep. 1238, 1955. (Supersedes NACA RM L9D07.)

4. Middleton, W. D.; Lundry, J. L.; and Coleman, R. G.: A System for Aerodynamic Design and Analysis

3.

I

of Supersonic Aircraft. Part 2-User's Manual. NASA

5. Harris, Roy V., Jr.: An Analysis and Correlation of Aircraft Wave Drag. NASA TM X-947, 1964.

6. Carlson, Harry W.; and Miller, David S.: Numerical Methods for the Design and Analysis of Wings at Super- sonic Speeds. NASA TN D-7713, 1974.

7. Sommer, Simon C.; and Short, Barbara J.: Free-Flight Measurements of nrbulent-Boundary-Layer Skin Fric- tion in the Presence of Severe Aerodynamic Heating at Mach Numbers From 2.8 to 7.0. NACA TN 3391, 1955.

8. Braslow, Albert L.; Hicks, Raymond M.; and Harris, Roy V., Jr.: Use of Grit-Type Boundary-Layer-lkansition P i p s on Wind-lbnnel Models. NASA T N D-3579, 1966.

CR-3352, 1980.

119

. Report No. NASA TP-2433

. Author(s)

Richard M. Wood and Peter F. Cove11

2. Government Accession No.

. Performing Organization Name and Address

NASA Langley Research Center Hampton, VA 23665

19. Security Classif.(of this report) 20. Security Classif.(of this page) 21. No. of Pages Unclassified Unclassified 120

2. Sponsoring Agency Name and Address

National Aeronautics and Space Administration Washington, DC 20546

22. Price A06

5 . Supplementary Notes

3. Recipient’s Catalog No.

5. Report Date

July 1985 6. Performing Organization Code

505-43-23-02 8. Performing Organization Report NO.

L-15899 10. Work Unit No.

11. Contract or Grant NO.

13. Type of Report and Period Covered

Technical Paper 14. Sponsoring Agency Code

6. Abstract An experimental and theoretical study was conducted to investigate the supersonic aerodynamic characteristics of delta and double-delta wings. Testing was conducted in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.60, 1.90, and 2.16. The double-delta wings exhibited lower zero-lift drag values than the delta wings having the same aspect ratio, whereas delta wings provided the lower drag due to lift. Deflections of the trailing-edge flaps for pitch control revealed that the induced aerodynamic forces were only a function of the flap planform and were independent of wing planform. The supporting theoretical analysis showed that the Supersonic Design and Analysis System (SDAS) did not consistently predict all the longitudinal aerodynamic characteristics of the low-sweep, low-fineness-ratio wing-body configurations under investigation.

7. Key Words (Suggested by Authors(s)) Supersonic aerodynamics Linear theory Experiment Delta wings Double-delta wings Trailing-edge flaps Aspect ratio Wing-body configuration

18. Distribution Statement Unclassified-Unlimited

Subject Category 02

For sale by the National Technical Information Service, Springfield, Virginia 22161 NASA-Langley, 198:

Documents

July 1985 Experimental and Theoretical of the Longitudinal