Transonic aerodynamic characteristics of a tailless fixed-wing supersonic transport model

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TRANSONIC AERODYNAMIC CHARACTERISTICS

OF A TAILLESS FIXED-WING

SUPERSONIC TRANSPORT MODEL

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by Edward J. Ruy and Robert T, Tuylor

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Langley Research Center

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ff 663 July 65 W A S H I N G T O N , D . C. M A R C H 1966 NATION A I A E R 0 N A U T I CS A N D SPACE A D M I N I S T RAT I ON A ~ ~~ NASA TM X-1214 TRANSONIC AERODYNAMIC CHARACTERISTICS O F A TAILLESS FIXED-WING SUPERSONIC TRANSPORT MODEL By Edward J. Ray and Robert T. Taylor

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Langley R e s e a r c h Center Langley Station, Hampton, Va.

N A T I O N A L A E R O N A U T I C S A N D SPACE A D M I N I S T R A T I O N For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - Price $1.10 TRANSONIC AERODYNAMIC CHARACTERISTICS O F A TAILLESS FIXED-WING SUPERSONIC TRANSPORT MODEL By Edward J. Ray and Robert T. Taylor Langley Research Center SUMMARY An investigation has been made in the Langley high-speed 7- by 10-foot tunnel to determine the effects of wing planform and twist and camber on the aerodynaniic charac- teristics of a tailless fixed-wing supersonic transport model throughout a Mach number range of 0.40 to 1.14. To determine these effects, three wing planfornis with the same aspect ratios were investigated with and without twist and camber. The three wing plan- fornis were a modified delta having an ogee-shaped leading edge, a delta, and a trapezoid.

All three plane wings were equipped with trailing-edge elevons t o determine the control effectiveness of these devices.

The results of the present study indicated that the wing planform differences had little effect on the aerodynamic center variations with Mach nuniber and on the trimnied lift coefficients at reasonable landing attitudes. The wing twist and camber effects, how- ever, were signiticant ana the resuiis i i i u i L c L L c u A 2 - - - 4 - J &'.-* L I l u L +h- cllL L v-nnvnid c . y v - v - - . rniifiplr3tjOn- - _.-~ which had the highest values of pitching- moment coefficient a t zero lift, would exhibit the high- e s t triiiimed lift coefficients of the twisted and cambered wing coilrigurations near reason- able landing attitudes, The static lateral data indicated that the twisted and canibered wing configurations had positive directional stability and positive effective dihedral for all Mach numbers of the investigation. The directional stability, however, of the twisted and cambered delta and trapezoid configurations w a s considerably greater than the directionai sta'uiiiiy of the twisted and cambered ogee configurations.

INTRODUCTION The National Aeronautics and Space Administration has investigated a nunnber of configurations which niay be suitable for a comniercial supersonic transport aircraft.

These investigations have covered a variety of design concepts, including both f ked-wing and variable-sweep wing arrangenients. Results from investigations to determine the aerodynamic characteristics of fixed-wing supersonic transport models may be found in references 1 to 17. References 18 to 30 contain results obtained from investigations to' determine the aerodynamic characteristics of supersonic transport models having variable-sweep wings o r variable-sweep auxiliary wing panels.

The purpose of the present investigation was to determine the subsonic and tran- sonic aerodynamic characteristics of a fixed-wing, tailless, supersonic transport model designed f o r cruise at a Mach number of 2.2. Three wing shapes, an ogee wing, a delta wing, and a trapezoid wing, of the same aspect ratio and thickness ratio distribution were tested with and without twist and camber to determine the effects of wing planform and wing twist and camber on the aerodynamic characteristics of the model. In addition, the plane wing configurations were provided with flap- type trailing- edge elevons t o evaluate the conti.01 effectiveness of the three configurations. This paper presents the longitudinal and lateral results which were obtained f o r these configurations throughout the Mach num- ber range of 0.40 t o 1.14.

The study of this model has been extended to supersonic Mach numbers and the data resulting from these investigations are presented in references 31 and 32. The investi- gation described in reference 31 was conducted at a Mach number of 2.20 to determine the aerodynamic characteristics of the model at cruise speed. Reference 32 presents longitudinal and lateral data for the Mach number range of 1.80 to 2.86 and includes the effects of two forebody modifications.

SYMBOLS I

The longitudinal data are referred t o the wind-axis system and the lateral data are referred t o the body-axis system.

The moment center f o r all configurations is located on the model reference line at a point 61.77 percent of the body length behind the nose.

(See figs. l(a), (b), and (c).)

The units used for the physical quantities defined in this paper are given both in the U.S. Customary Units and in the International System of Units (SI). Factors relating the two systems are given in reference 33.

A aspect ratio b span of wing, 19.25 inches (48.90 centimeters) C local wing chord, inches (centimeters)

-

mean aerodynamic chord, inches (centimeters) C reference chord of wing, 12.00 inches (30.48 centimeters) Internal axial force nacelle internal-axial-force coefficient, q s Drag drag coefficient, q s induced drag coefficient

lift coefficient, - Lift

qs

lift-curve slope near CL = 0, ac,/aq per degree

effective change in lift coefficient caused by unit angular change in ele von deflection, aCL/a6, per degree Rolling moment rolling-moment coefficient, qSb effective dihedral parameter, aCz/ap, per degree Pitching moment pitching- moment coefficient, qscr ef pitching-moment Coefficient at CL = 0 longitudinal stability parameter near CL = 0 Yawing moment yawing- moment coefficient, Cn qSb

c

directional Stability parameter, aCn/ap, per degree

"P

Side force side-f orce coefficient, CY q s C (L/D)m, maximum lift-drag ratio M Mach number dynamic pressure, pounds force/foot2 (newtons/meter2) q Reynolds number R wing reference area (includes body intercept), 1.665 foot2 S (0.1547 meter2) thickness- chord ratio t/c X distance from wing leading edge parallel to fuselage center line, inches e nt i m e t er s) (c spanwise station, measured perpendicular from model center line, Y inches (centimeters) z vertical distance from wing reference plane to mean camber line, inches (centimeters) L angle of attack, degrees control-surface-effectiveness parameter at CL = 0, effective change in wing angle of attack caused by unit angular change in elevon deflec- sideslip angle, degrees P 6 inboard and outboard elevon deflection, negative trailing edge up (measured from wing chord plane), degrees inboard elevon deflection, negative trailing edge up (measured from wing de, i chord plane), degrees outboard elevon deflection, negative trailing edge up (measured from 6e, o wing chord plane), degrees E angle of wing twist, degrees Wing notations: Ogee I plane ogee wing planform Delta I plane delta wing planform Trapezdid I plane trapezoid wing planform Ogee II twisted and cambered ogee wing Delta I1 twisted and cambered delta wing Trapezoid I1 twisted and cambered trapezoid wing Ogee III twisted and cambered ogee wing, modified MOOE LS The three wing planforms used in t h i s investigation were a modified delta having an ogee-shaped leading edge, a trapezoid, and a delta. (See figs. l(a), (b), and (c).) The The wings without twist and camber will be r e f e r r e d aspect ratio of the wings was 1.55.

to as Ogee I, Trapezoid I, and Delta I, and the twisted and cambered wings will be denoted The Ogee I1 wing w a s modified further t o provide as Ogee 1 1 , Trapezoid 1 1 , and Delta II.

additional wing twist and camber outboard of the nacelles, near the leading edge, and this wing will be r e f e r r e d to as the Ogee I11 wing.

Longitudinal and lateral control was provided by plain, flap-type, trailing-edge ele- vons iocaieci iibuii-d and o.~t5zarc! cf the nacelles. Onlv the plane wings were equipped with elevons. The elevons were attached t o the wings with brackets which embled the The location and dimensions of the elevons to be deflected to angles of Oo, -5O, or -10'.

elevons f o r each planform are shown in figures l(a), (b), and (c).

The two-dimensional inlet nacelles were fitted to the lower surface of the plane wings and positioned as shown in figures l(a), (b), and (c). The nacelles were located on the twisted and cambered wings so that the center lines of the nacelles were 3.65 inches (9.27 cm) f r o m the fuselage center line. De'taiis of tile i i ; r C d k arc s h a v ~ i n f i g x e l(d).

A s shown in A comparison of the various wing planforms is shown in figure l(e).

this figure, t h e r e w a s no difference in the projected planform a r e a between the twisted and cambered aiid the plaiiz ddtz wizgc e r hetween the twisted and cambered and the plane trapezoid wings; however, the planform a r e a s o f the plane and the twisted and cambered ogee wings differed slightly. The wetted wing area, excluding the area covered by the nacelles, is listed f o r each planform in table I. An approximate quartic equation for the curved portion of the leading edge of the twisted and cambered ogee wing is shown in figure l(f).

Ratios of wing thickness t o wing chord, as shown in figure 2, varied from 3 percent Circular-arc airfoil sections were utilized for all the at the root to 2 percent at the tip.

' wings. The twisted and cambered wings were designed for a lift coefficient of 0.1 at a Mach number of 2.20. (See ref. 34.) Airfoil sections of the twisted and cambered wings were sheared SO that the trailing edge of each wing was straight. The twist and camber distributions of the Ogee 11, Delta 11, and Trapezoid II wings are shown in figure 3. The leading edge of the Ogee I1 wing was modified to form the Ogee 1 1 1 wing by rolling down the leading edge of the outer 45 percent of the wing semispan an additional 0.10 inch (0.25 cm). A typical section and the twist distribution illustrating this modification are presented in figure 4.

The cross-sectional area distribution of the model, excluding the cavities of the engine nacelles, with the twisted and cambered ogee wings is shown in figure 5 and photo- graphs of this model are presented as figure 6.

TESTS AND CORRECTIONS The investigation was made in the Langley high-speed 7- by 10-foot tunnel at Mach numbers of 0.40, 0.60, 0.80, 0.90, 0.98, 1.02, and 1.14. The Reynolds number based on the reference chord of the wing cref and on the average temperature at each Mach num- ber is shown in the following table: M R 0.40

2.25 X lo6

.60 3.10 .80 3.70 .90 3.90 .94 3.95 .98 4.00 1.02 4.05 1.14 4.10 The model was sting supported and the f o r c e s and moments were measured with an internally mounted, six-component, strain- gage balance.

The angle-of -attack range varied throughout the Mach number range because of the load limits of the balance. At the low Mach numbers, the angle-of-attack range was generally about f r o m -2O to 20° and at the higher Mach numbers the range extended about f r o m Oo to 14'. Lateral sta- bility data were obtained at all Mach numbers throughout a sideslip-angle range of -12' to 17' at an angle of attack of Oo for the plane ogee configuration and at sideslip angles of 0' and *5O for all the twisted and cambered wing configurations. To insure a turbulent boundary layer, 1/16-inch-wide transition s t r i p s of no. 60 carborundum grains were appliedaear the leading edge of the wings, 1 inch (2.54 cm) behind the body nose, on the vertical tail, and outside and inside the engine nacelles.

The angles of attack and sideslip have been corrected for sting and balance deflec- tion under load. Jet-boundary and blockage corrections are negligible for the open- slot tunnel configuration and therefore were not applied to the data.

The internal skin friction of the two nacelles w a s calculated and the measured axial force was corrected at each Mach number by the internal axial-force coefficient CA,i in the amount shown in the following table: M cA, i 0.40 0.00141

.60 . 00132

.80 .00125 .90 .00122 .94 .00122 .98 .00121 1.02 .00119 1.14 .00116 Nacelle base p r e s s u r e measurements were made by using a manifold placed around the solid c r o s s section of the er,gine nacelle base. The data were cui=i-eeted tc c o r r e - spond t o a condition of free-stream static pressure at the solid portion of the nacelle base and at the base of the fuselage.

Some problems w e r e encountered with regard to the absolute level of the drag Although the exact magni- measurements on the plane delta and plane trapezoid wings.

tude of the resultant e r r o r s in minimum drag cannot, of course, be established, compari- sons w i t h sUbaoiiic theory based. nn flat-plate skin friction (ref. 35) and thickness-chord ratio (ref. 36) indicated that the measured minimum drag coefficients f o r the plane delta and trapezoid configurations were slightly high. In view of this, the drag coefficients f o r the plane trapezoid wing and plane delta wing configurations were reduced by 0.0010 and 0.0007, respectively, in a n attempt to reduce the c r r o r s assnciated with the drag measure- ment problems encountered on these wings. Because of this somewhat a r b i t r a r y correc- tion no comparisons of the subsonic or transonic lift-drag ratios have been made. No problems w e r e enc.ountered and no drag adjustments have been made, however, f o r the plane ogee wing, all the cambered and twisted wings, and all the supersonic data repro- duced f r o m references 3 1 and 32.

PRESENTATION O F RESULTS The basic longitudinal results of this investigation are presented in figures 7 to 15 and some of these results are summarized in figures 16 t o 23.

Lateral data are pre- sented in figures 24 to 25. An outline of the figure content is as follows: Figure Effect of inboard elevon deflection on longitudinal aerodynamic characteristics of plane ogee wing configuration at Mach numbers from 0.40 to 1.14 . . . . . .

Effect of inboard and outboard elevon deflection on longitudinal aerodynamic characteristics of plane ogee wing configuration at Mach numbers from

0.40 to 1.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Effect of twist and camber on longitudinal aerodynamic characteristics of

ogee wing configurations at Mach numbers from 0.40 to 1.14 . . . . . . . . . . 9

Effect of inboard elevon deflection on longitudinal aerodynamic characteristics

of plane delta wing configuration at Mach numbers from 0.40 to 1.14 . . . . . 10

Effect of inboard and outboard elevon deflection on longitudinal aerodynamic characteristics of plane delta wing configuration at Mach numbers f r o m

0.40 to 1.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Effect of twist and camber on longitudinal aerodynamic characteristics of

delta wing configurations at Mach numbers from 0.40 to 1.14. . . . . . . . . . 12

Effect of inboard elevon deflection on longitudinal aerodynamic characteristics of plane trapezoid wing configuration at Mach numbers from 0.40 to 1.14 13 . . .

Effect of inboard and outboard elevon deflection on longitudinal aerodynamic characteristics of plane trapezoid wing configuration at Mach numbers

from 0.40'to 1.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Effect of twist and camber on longitudinal aerodynamic characteristics of

trapezoid wing configurations at Mach numbers from 0.40 t o 1.14 . . . . . . . 1 5

Effect of plane wing planform on variation with Mach number of lift-curve

slope C and longitudinal stability parameter aCm/aCL . . . . . . . . . . 16

La Effect of plane wing planform on induced drag C D , ~ at M = 0.40, 0.90,

andl.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Variation with Mach number of elevon effectiveness parameter arg f o r plane ogee, delta, and trapezoid wing configurations 18 . . . . . . . . . . . . . . . . .

Effect of t w i s t and camber on variation with Mach number of longitudinal stability parameter aCnl/aCL f o r ogee, delta, and trapezoid wing configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Variation with Mach number of pitching-moment coefficient at z e r o lift Cm, f o r twisted and cambered wing confibwrations . . . . . . . . . . . . . . . . . .

9 Figure Effect of twist and camber on variation with Mach number of lift-curve slope

C for ogee, delta, and trapezoid wing configurations . . . . . . . . . . . . 21

' C Y Effect of twist and camber on induced drag CD,i of ogee, delta, and

trapezoid wing configurations at M = 0.90. . . . . . . . . . . . . . . . . . . 22

Variation of angle of attack with trimmed lift coefficient C at 'trim M = 0.40 and variation of maximum lift-drag ratio (L/D)max with Mach

number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Lateral aerodynamic characteristics of plane ogee wing configuration.

CY=oo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Comparison of lateral aerodynamic characteristics of twisted and cambered

wing configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

DISCUSSION Longitudinal Characteristics Effect of wing planform on longitudinal characteristics.- The effect of plane wing planform on the variation with Mach number of the lift-curve slope C L , and the longi- tudinal stability parameter aCm/t3C, is shown i n figure 16. Figure 16 shows that the plane ogee wing configuration exhibited the largest degree of static longitudinal stability f o r the plane wing configurations at a given Mach i i i i i i i k z r as ;; result ef its mere r w r - ward location of centroid of exposed area. It should be noted here that the longitudinal stability p a r a m e t e r s f o r the three wings were based on a constant reference chord. The maximum variations of longitudinal stability parameters f o r the ogee and trapezoid wings when based on the mean aerodynamic chords (table I) were slightly l a r g e r than the varia- tion indicated f o r the delta planform. The results of reference 32 indicated that at super- sonic Mach numbers ranging from 1.80 to 2.86 the ogee wing configurations would exhibit the largest aerodynamic center variation of iiie three iviiig p!ad.,f=rrnS.

The lift-curve slopes for the plane trapezoid configuration, as shown in figure 16, w e r e considerably greater than the lift-curve slopes for the plane ogee and delta wing zoi-iiigdrati.,f=ns at Mach numbers higher than 0.40. This effect may be attributed to the lower sweep (fig. l(e)), and greater exposed a r e a of the plane trapezoid wing configura- tion. (It should be noted that all data were nondimensionalized by using the same wing reference area.)

The effect of plane wing planform on induced drag at Mach numbers of 0.40, 0.90, and 1.14 are shown in figure 17. The induced drag of the plane trapezoid wing configura- tion w a s slightly less than the induced drag for the plane delta and ogee wing configura- tions throughout the Mach number range of the investigation. This result is as would be expected since the induced drag of highly swept wing configurations with sharp wing leading edges is inversely proportional t o the lift-curve slope.

Figure 18 presents the variation with Mach number of the elevon effectiveness parameter a6 at a lift coefficient of z e r o for the three plane wing configurations. A s shown in this figure, deflection of the elevons produces the greatest effective change in wing angle of attack for the plane ogee wing configuration, particularly in the subsonic Mach number range. Reference 37 reveals that this effect might be expected since the ogee configuration has a generally higher flap-chord to wing-chord ratio than the trape- zoid o r delta wing configurations. Figures 8(b), ll(b), and (See figs. l(a), (b), and (c).)

14(b) indicate, however, that the change in pitching-moment coefficient at zero lift per degree of inboard and outboard elevon deflection was very nearly the s a m e f o r the three plane wing configurations as a result of the comparable elevon locations and areas.

Effect of twist and camber on longitudinal characteristics.- The effects of twist and camber on the variation with Mach number of the longitudinal stability parameter aCm/aCL f o r the ogee, delta, and trapezoid wing configurations a r e presented in fig- u r e 19. The maximum aerodynamic center shift occurring f o r the three wing planform Configurations throughout the Mach number range was very nearly the same f o r the plane wing configurations as for the twisted and cambered wing configurations. However, it will be noted f r o m figure 19 that the longitudinal stability parameters f o r the twisted and cambered and the plane trapezoid, and the twisted and cambered and the plane delta, wing configurations differed considerably near z e r o lift. The greater stability levels of the twisted and cambered trapezoid and delta wing configurations, relative t o the plane wing configurations, are presumed due t o maintaining unseparated flow conditions t o higher lift coefficients. The plane trapezoid and delta wing configurations apparently experience leading-edge separation at very low angles of attack in the wing apex region; this separa- tion would tend t o reduce the level o f longitudinal stability. For the ogee wing configura- tions, the difference in stability levels between the twisted and cambered and the plane wings is much less and is opposite in direction from that for the delta and trapezoid con- figurations. The similarity of stability levels exhibited f o r the ogee wing configurations suggests that the flow conditions at the leading edges of the plane and the twisted and warped wings were similar o r that the stability levels of the ogee wing configuration were much less sensitive to differences in flow conditions.

The zero-lift pitching-moment results shown in figure 20 indicate substantially at z e r o lift Cm, higher values of pitching-moment coefficient throughout the Mach num- b e r range of the investigation f o r the twisted and cambered trapezoid configuration than for the twisted and cambered ogee o r delta configurations.

Fi'gure 21 shows that the effect of twist and camber on the variation with Mach num- was not significant f o r the ogee, delta, or trapezoid ber of the lift-curve slope CL C Y planforms.

The effect of twist and camber on the induced drag of the ogee, delta, and trapezoid In addition t o wing configurations at a Mach number of 0.90 is illustrated in figure 22.

the experimental results, computed drag polars for zero and full leading-edge suction are shown f o r each planform. The close agreement between the experimental values obtained for the plane wing configurations and the values of drag for z e r o leading-edge suction might be expected due t o the sharpness of the leading edges of the wings. These results indicate that the wing twist and camber of the ogee and delta configurations resulted in some reduction in induced drag at a Mach number o f 0.90 but that only slight differences existed between the induced drag of the plane and the twisted and cambered trapezoid wing configurations. The results of the investigation of reference 31, however, indicated that the wing twist and camber of the trapezoid configuration resulted in substantial improvements in the drag characteristics at the design Mach number of 2.20.

Low- speed trimmed lift coefficients and supersonic performance. - The variations

of angle of attack with trimmed lift coefficient at a Mach number of 0.40 and of maximum lift-drag ratio with Mach numbers ranging from 1.80 t o 2.86 are presented in figure 23.

The trimmed lift coefficients shown in figure 23 were determined f o r the three wing plan- f o r m configurations at an adjusted longitudinal stability level of 5 percent of the reference the trimmed lift data shown f o r tile twisted and zambcrcd *::icg c d i g u r a t i n n s chord and were obtained by utilizing the elevon control effectiveness of the plane wing configura- tions. These results indicate that the effect of wing planform on trimmed lift coefficient at landing attitudes of about 120 was insignificant. Wing twist and camber, however, are shown t o have a large effect on the trimmed lift coefficients of the three wing planform configurations. On the basis of the data shown in figure 23, it would be expected that sub- stantially higher trimmed lift coefficients would be expected for the twisted and cambered trapezoid configuration near reasonable ianciing attitudes than for the t.ivisted 2nd cam- bered ogee or delta configurations. This effect is attributed t o the higher lift-curve slope and higher values of zero-lift pitching-moment coefficient indicated for the twisted and cambered trapezoid configuration. In addition, the supersonic results contained in refer- ences 31 and 32 indicated that the trapezoid configurations exhibited larger maximum hit- drag ratios than the delta or ogee configurations throughout the supersonic Mach number range of 1.80 t o 2.86. The supersonic results of the aforementioned investigations also indicated l a r g e r pitching-moment coefficients at zero lift for the twisted and cambered trapezoid configuration than f o r the twisted and cambered ogee and delta configurations; these l a r g e r coefficients would naturally result i n lower trim-drag penalties f o r the trapezoid configuration at a given level of longitudinal stability.

Lateral Characteristics Variations of the lateral aerodynamic coefficients of the plane ogee wing with side- s l i p angle /3 a r e presented in figure 24. Figure 25 compares the lateral aerodynamic characteristics of the twisted and cambered wing configurations throughout the Mach num- ber range of the investigation.

Directional stability is evident for the three twisted and cambered wing configura- tions up to high angles of attack f o r Mach numbers of 0.40 to 1.14. (See fig. 25.) The static directional stability exhibited by the twisted and cambered delta and trapezoid wing configurations was very nearly the same and considerably greater than the directional The smaller values of stability of the twisted and cambered ogee wing configuration.

directional stability indicated f o r the ogee configuration are presumed to be due in part t o the comparatively forward location of the large twist and camber in the leading edge of the wing near the root section. (See figs. 3 and 6.)

The effective dihedral parameters indicate static lateral stability f o r angles of attack greater than zero degrees f o r the three twisted and cambered wing configurations throughout the Mach number range of the investigation.

CONCLUDING REMARKS A study was made at Mach numbers ranging f r o m 0.40 to 1.14 t o determine the aero- dynamic characteristics of three different wing planforms (ogee, delta, and trapezoid) both with and without wing twist and camber. The experimental results indicated that the wing planform differences had only small effects on the aerodynamic center shifts with Mach number and. ~n the t r i m x e d lift coefficiefits iit kiiidhig attiludes. The wing twist and cam- ber effects, however, were significant and the results indicated that the trapezoid configu- rations, which had the highest values o f pitching-moment coefficient at z e r o lift, would exhibit the highest trimmed lift coefficients of the twisted and cambered wing configura- tions near reasonable landing attitudes.

The static lateral data indicated that the twisted and cambered wing configurations have positive directional stability and positive effective dihedral throughout the Mach num- ber range of 0.40 to 1.14. The directional stability, however, of the twisted and cambered delta and trapezoid configurations was considerably greater than the directional stability of the twisted and cambered ogee configurations.

Langley Research Center, National Aeronautics and Space Administration, Langley Station, Hampton, Va., November 30. 1965.

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2. Sleeman, William C., Jr.; Ray, Edward J.; and Fournier, Paul G.: Low-Speed Effects of High-Lift Devices on the Aerodynamic Characteristics of a Supersonic Transport Model With Outboard Tails. NASA TM X-895, 1963.

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4. Morris, Owen G. ; Carmel, Melvin M. ; and Carraway, Ausley B.: An Investigation at Mach Numbers F r o m 0.20 to 4.63 of the Aerodynamic Performance, Static Stability, and Trimming Characteristics of a Canard Configuration Designed for Efficient Supersonic Cruise Flight. NASA TM X-617,1961.

5. Carraway, Ausley B.; Morris, Owen G.; and Carmel, Melvin M.: Aerodynamic Characteristics at Mach Numbers From 0.20 t o 4.63 of a Canard-Type Supersonic Commercial Air Transport Configuration. NASA TM X-628, 1962.

6. Spencer, Bernard, Jr.: Low-Speed Wind-Tunnel invesiigaiion of the Zffeets cf C a ~ x ~ r d Planform and Wing High- Lift Devices on the Longitudinal Aerodynamic Characteris- t i c s of a Supersonic Transport Configuration. NASA TM X-753, 1963.

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8. Whitcomb, Richard T.; Patterson, James C., Jr.; and Kelly, Thomas C.: An Investi- gation of Subsonic, Transonic, aiid Sqxrsmic ,A,erod.yna mic Characteristics of a Proposed Arrow-Wing Transport Airplane Configuration. NASA TM X-800, 1963.

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15. Fletcher, LeRoy S . : Static Stability Characteristics of a Delta-Winged Airplane Configuration With Nacelles, a Trapezoidal Canard and a Drooped Tail at Mach Numbers From 0.70 to 3.52. NASA TM X-780, 1963.

16. Fletcher, LeRoy S . : Dynamic Rotary Stability Derivatives of a Delta-Winged Configu- ration With a Canard Control and Nacelles a t Mach Numbers F r o m 0.25 t o 3.50.

NASA T M X-781, 1963.

17. Koenig, David G. ; and Corsiglia, Victor R.: Large-Scale Low-Speed Wind-Tunnel Tests of a Delta Wing Supersonic Transport Model With Various Canard, Horizontal- Tail, and Wing Modifications. NASA TM X-857, 1964.

18. Henderson, William P.: Selected Results From a Low-Speed Investigation of the Aerodynamic Characteristics of a Supersonic Transport Configuration Having a n Outboard-Pivot Variable-Sweep Wing. NASA TM X-839, 1963.

19. Jernell, Lloyd S.: The Effects of Conical Camber on the Longitudinal Aerodynamic characteristics of a Variable-Sweep Wing- Fuselage Configuration at Mach Numbers From 0.50 to 3.50.

NASA TM X-804, 1963.

20. Ward, Robert J . ; and McKee, John W.: Low-Speed Aerodynamic Stability and Control Characteristics of a Cambered Fuselage, Variable-Sweep Supersonic Transport Configuration. NASA TM X-632, 1962.

21. Vogler, Raymond D.; and Turner, Thomas R.: Exploratory Low-Speed Wind-Tunnel Stability Investigation of a Supersonic Transport Configuration With Variable-Sweep Wings. NASA TM X-597, 1961.

22. Vogler, Raymond D. : Low-Speed Wind- Tunnel Stability Investigation of a Supersonic Transport Model With Variable-Sweep Wings Equipped With High-Lift Devices.

NASA TM X-728, 1962.

23. Sleenian, William C., J r . ; and Robins, A. Warner: Low-Speed Investigation of the Aerodynamic Characteristics of a Variable- Sweep Supersonic Transport Configura- tion Having a Blended Wing and Body.

NASA TM x-619, 1962.

24. Sleelnan, William C., Jr.: Low-Speed Investigation of the Effects of Horizontal Tail Height and Extension of the Wing-Root Leading-Edge Sections on a Variable-Sweep Supersonic Transport Configuration. NASA TM X-681, 1962.

25. Henderson, William P.: a Super- Low-Speed Longitudinal Stability Characteristics of sonic Transport Configuration With Variable-Sweep Wings Employing a Double Inboard Pivot. NASA TM X-744, 1962.

26. Shaw, David S.; and Henderson, William P.: Wind-Tunnel Investigation at Mach Num- b e r s From 1.60 to 2.86 of the Static Aerodynamic Characteristics of a Supersonic Transport Configuration With Variable-Sweep Wings Employing a Double Inboard Pivot. NASA TM X-745, 1962.

27. Alford, William J., Jr.; Hammond, Alexander D., and Henderson, William P.: Low- Speed Stability Characteristics of a Supersonic Transport Model With a Blended Wing-Body, Variable-Sweep Auxiliary Wing Panels, Outboard Tail Surfaces, and Simplified High-Lift Devices. NASA T M X-802, 1963.

28. Robins, A. Warner; Spearman, M. Leroy; and Harris, Roy V., Jr.: Aerodynamic Characteristics at Mach Numbers of 2.30, 2.60, and 2.96 o f a Supersonic Transport Model With a Blended Wing-Body, Variable-Sweep Auxiliary Wing Panels, Outboard Tail Surfaces, and a Design Mach Number of 2.6. NASA TM X-815, 1963.

29. Driver, Cornelius; Spearman, M. Leroy; and Corlett, William A.: Aerodynamic Characteristics at Mach Numbers From 1 . 6 : to 2.86 of 2 Scpersnnlr Transport Model With a Blended Wing-Body. Variable-Sweep Auxiliary Wing Panels, Outboard NASA TM X-817, 1963.

Tail Surfaces and a Design Mach Number of 2.2.

30. Lockwood, Vernard E.; McKinney, Linwood W.; and Lamar, John E.: Low-Speed Aerodynamic Characteristics of a Supersonic Transport Model With a High-Aspect- Ratio Variable-Sweep Warped Wing. NASA TM X-979, 1964.

Si. Foster, Gerald V.; ax! Cwlett, William A.: Aerodynamic Characteristics of a Tailless Fixed-Wing Supersonic Transport Configuration at Mach Number 2.20.

NASA TM X-960, 1964.

32. Corlett, William A.; and Foster, Gerald V.: Aerodynamic Characteristics of a Tailless Fixed-Wing Supersonic Transport Model at Mach Numbers From 1.80 to 2.86. NASA TM X-992, 1964.

33. Mechtly, E. A.: The International System of Units - Physical Constants and Conver-

sion Factors. NASA SP-7012, 1964.

A Numerical Method for the Design of 34. Carlson, Harry W.; and Middleton, Wilbur D.: Camber Surfaces of Supersonic Wings With Arbitrary Planforms. NASA TN D-2341, 1964.

1 5 Free-Flight Measurements of Tufiulentl 35. Sommer, Simon C.; and Short, Barbara J.: Boundary-Layer Skin Friction in the Presence of Severe Aerodynamic Heating at Mach Numbers From 2.8 t o 7.0. NACA T N 3391, 1955.

Fluid-Dynamic Drag. Publ. by the author (148 Busteed Drive, 36. Hoerner, Sighard F.: Midland Park, N.J.), 1958.

37. Lowry, John G . ; and Polhamus, Edward C.: A Method f o r Predicting Lift Increments NACA Due to Flap Deflection at Low Angles of Attack i n Incompressible Flow.

TN 3911, 1957.

TABLE I.- GEOMETRIC CHARACTERISTICS O F MODEL k c a l e 1 / 4 4 Ogee wings: Aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.55 Span . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.25 in2 48.90 cm2) Plane wing wetted area (excludes nacelle area) . . . . . . . . . . . . . . 325.18 in2 (2097.93 cm2) Twisted and cambered wing wetted area (excludes nacelle area) . . . . . 329.98 in2 (2128.90 cm2) Reference area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239.76 in2 (1546.84 cm2) R o o t c h o r d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.78 in. ( 70.56 cm) Reference c h o r d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.00 in. ( 3 0 . 4 8 ~ 1 ~ ) Mean aerodynamic chord . . . . . . . . . . . . . . . . . . . . . . . . . . 16.81 in. ( 42.70 cm) Delta wings: Sweep of leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68' Aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.55 Span 19.25 in. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 48.90cm) Wetted wing area (excludes nacelle area) . . . . . . . . . . . . . . . . . . 335.94 in2 (2167.35 cm2) Reference a r e a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239.76 in2 (15.46.84 cm2) Root chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.87 in. ( 63.17cm) Reference c6ord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.00 in.

( 30.48 cm) Mean aerodynamic chord . . . . . . . . . . . . . . . . . . . . . . . . . . 16.56 in.

( 42.06 cm) Trapezoid wings: Sweep d leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . 65' Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i . 5 5

I

Span . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.25in. ( 48.90cm) Wetted wing a r e a (excludes nacelle area). . . . . . . . . . . . . . . . . . 344.90 in2 (2225.16 cm2) Reference area 239.76 in2 (1546.84 cm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Root chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.30 in. ( 59.18 cm) T i p c h o r d 1.84 in. ( 4.67 cm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Reference chord 12.00 in. ( 30.48 cm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Mean aerodynamic ci1ui.i: . . . . . . . . . . . . . . . . . . . . . . . . . . 15.46 in. ( 39.27 cm) Fuselage: Length 42.50 in. ( 107.95 cm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.40 in2 ( 15.48 cm2) Balance chamber area . . . . . . . . . . . . . . . . . . . . . . . . . . .

Vertical tail: Root c h o r d . 7.64 in. ( 19.48 cm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.40 in. ( 6.10 cm) Tip chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A r e a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.64 in2 ( 139.61 cm2) Nacelles: Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.25 in. ( 26.04 cm) Capture area (each) 1.04 in2 ( 6.71 cm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B a s e a r e a (each). 0.96 in2 ( 6.19 cm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-7 c \ h ' , I - 1 ~

a

- I I I I I I I I I I I I I I I I I I I I I I I I i I I I I I I I I I 1 I I I I I I !

I I I I I I I , I I ' !I , I 'I

\r II

L - - - - - - l I .

.

%P

+ x

d

+

cu x k q

+

6-3- X I1 h

-

n -3- cu cu J cu W c- M Ln o?

VI I h k I

.02

.o/

Figure 2.- Spanwise thickness distribution of wing planforms.

* 4 - 4 b E T - 5 0 .2 I .6 .8

Chord s t o t ion, Vc

Trapezoid lT S p a n station, y/62 b b

e

.22 .39 \ .67 ' 0 .O/ 0, C P -98 "0 .2 I . 6 .8 LO 0 .2 .4 . 6 .8

C h o r d station,?c Ogee Zr S p a n s t o t i o n , 4/2

Y W 2 0 0 P

--

cr

0 .20 b * i 2 4 !

- 0 b k .61 .r, 0 Q o L F \ .82 0 -2

Z o

el . 01

- - 4

.93 -6 0 .2 4 .6 .8 10 0 .2 .4 .6 .8 LO C h o r d stotion,x/c De1to Z S p a n s t o t i o n , ' / b / 2 Figure 3.- Camber and twist distributions for ogee, delta, and trapezoid wing configurations ( w e e I I, Delta 1 1 , and Trapezoid I I).

L 3 u l .- L c .- W W U c m U W c u) .- C c B Q (F, L

-

c 0 ._ L U W u) J VI E n m L B c a h c

x

E

,e

c U 0 0 0 c m c 0 ._ c m cn c ._ a , a , E ?

a , c m - n c YI U .- c m .- L m

-

U m c 0 L m .- c m . c U .- L m U ._ >

- 5

m c

-

H a , m c 0 c 0 ._ c U a , - L a , U c 0, - a , v L s n c ._ c c U m c L W a , L cn .- Y 0 0 0 F c, eh * .

a 000 4 t ' h * . '.

a

m

i m

m I .

0 Ogee I 0 OgeelT o OgeeRZ (a) Variation of a with CL.

Figure 9 . - Effect of twist and camber on longitudinal aerodynamic characteristics of ogee wing configurations at Mach numbers from 0.40 to 1.14.

, o Ogee r ogeen' 0 Ogeel7Z ..- 12 0 .2 I .6 .8 -.4 : 2 0 .2 I .6 .8 IO -2 0 .2 I .6 (b) Variation of C m with CL.

Figure 9 . - Continued.

o O g e e 1 O q e e l T o Ogee m - 2 0 2 4 6 8 -2 0 .2 4 .8 CL (c) Variation of CD with Ck Figure 9.- Concluded.

x

E e L 0 0 0 J Z V i c m '9 co i 5 .- s c c 0 .- c m .- ? !

L ~" > m

-

- l u c ._ U 3 c m c 0 - c 0 c 0 .- I V a , -

-

a , u r_ > a , - a , Q F F 0 0 0 '9 W w. c m - a L UI " ._ c i VI ._ V I W c U m I m c U U U c .- 0 c L m c 0 c x ._ c n m ._ e L m W m > c 0 c 0 ._ c U W - L OI n Y

z 3

n c m Y m 0 n f .- c U W L c W W I 3 131 ._ 0 0 0 i V c c E u L c 2 0 .2 4 . 6 -.? 0 .2 4 . 6 CL (a) Variation of a with CL.

Figure 12.- Effect of twist and camber on longitudinal aerodynamic characteristics of delta wing configurations at Mach numOers from 6.46 i o 1.14.

i u .- E V L c 0 ._ c a J m ._ L L m 3 u l ._ > LL

-

F c, 4 7 4.

h c B

s

0- 0 ' 000 E 4-

-

w L al n E c c U

0 0 0 z

-

m c 0 ._

-

h m .- c c 0 U m c ._ V ._ 0, al a .

m L c al c m i = 0 - 0 v) 5 .u

3 z

L * a , - 0 o h c m o c ._ c u .E u L .-

; E

m = - - H a l m - m c .- V 3 c ._ m c 0 - c 0 c 0 .-

-

U a -

-

al V c > al - al E lv 9 c ._ c c U al I I c L Y zi E 3 m .- L L 0 0 0 i . _ E P) L a m ._ Y 0- E 's e L 8 u '4 i c m 0 0 0 c 0 ._ I m L m ._ L c G u E a a , cz m L k '4 i 5 ._ ?J V ._ L 0 5 c x c G .- I H m ._ L a , m s

-

m c 0 c 0 ._

-

u a , - L a , -0 c > 0) - W e m G 3 d

z

m E m 0 n c ._ c a , L m ._ L L 0 0 0 i f ._ n m L 3 =?

._ Y c VI L al a E o n 3 c E U i c m VI c 0 .- c m L Q 3 m .-

-

c m c .- .- al i n m L I L r c rn U ._ c VI U ._ L L al

-

U c 0 ._

-

m m ._ c U L U ._ x

z

al m c 0 L a J a U c m c VI .- b ' i V 5 ._ E L c 0 c “J .- L s

-

e

per deg

VQ

M

Figure 16.- Effect of plane wing planform o n variation with Mach number of lift-curve slope C b and longitudinal stability parameter dCm/dCL.

I 3

0 .6 .8 io 1 . 1

A 4

Figure 18.- Variation w i t h Mach number of elevon effectiveness parameter ab for plane ogee, delta, and trapezoid wing configurations.

0 .2 .6 .8 LO LZ

M

Figure 19.- Effect of twist and camber on variation w i t h M a c h number of longitudinal stability parameter bCm/bCL for ogee, delta, and trapezoid wing configurations.

fi

.L .V .- R I. 2

M

Figure 2 0 . - Variation w i t h Mach number of pitching-moment coefficient at zero lift Cm,o for twisted and cambered wing configurations.

0 .2 .6 .8

M Figure 21.- Effect of twist and camber o n variation w i t h M a c h number of lift-curve slope C h for ogee, delta, and trapezoid wing configurations.

0 Plone Warped Figure 22.- Effect of twist and u m b e r o n induced drag C D , ~ of ogee, delta, and trapezoid wing configurations at M = 0.90.

._ 5 E E .- x m E

P co

L - c 0 .- c m .- L m > V c m

x

I I I c m E .- L c -- s/ c c a l ._ U .- E s .- f P Y u m c c m c 0 .- c m .- L M 0 .40 .60 0 .80 M .40 .60 .80 .40 .60 .40 .60 .80 (a) M = 0.40, 0.60, and 0.80.

Figure 24.- L i t e r a l aerodynamic characteristics of plane ogee wing configuration. a = 0 ' .

M 0 .90 0 .94 o .98 M .90 .94 CY .98 .90 .94 .90 .94 .98 -/2 -8 -4 0 4 8 /2 1 6 20 B, ( b ) M = 0.90, 0.94, and 0.98.

Figure 24.- Continued.

I I . .

M 0 1.02 / I 4 M 1.02 CY 1.02 L 14 .I- -I2 - 8 - 4 O 4 8 I2 I6 ZO 8, deg (c) M = 1.02 and 1.14.

Figure 24.- Concluded.

-4 0 4 8 /2 /6 20 24

Q, deg (a) M = 0.40.

Figure 25.- Comparison of lateral aerodynamic characteristics of twisted and cambered wing configurations.

.

- - --- Tropezoid l 7

---

Delta I7

- 4 0 4 8 I2 1 6 20 24

(b) M = 0.60.

Figure 25.- Continued.

Ogee fl

--_-- Trapezoid LT

---

D e l l D D

-. 004

-.008 -.012 -004

.m3

.002 .OOl .002 -. 002 -. 004

-. 006

-4 0 4 8 12 1 6 20 24

a, deq (c) M = 0.80.

Figure 25.- Continued.

(d) M = 0.90.

Figure 25.- Continued.

(e) M = 0.94.

Figure 25.- Continued, .

- 4 0 4 8

(f) M = 0.98.

Figure 25.- Continued.

Q, deg (gl M = 1.02.

Figure 25.- Continued.

C ( h ) M = 1.14.

Figure 25.- Concluded.

NASA-I.angley, 1966 L-4703 75