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, EFFECTOF OUTBOARDVERTICAL-FINPOSITION

AND ORIENTATIONONTHE LOW-SPEED.:

AERODY_'AMICPERFORMANCEOF HIGHLY

SWEPTWINGS

Vicki S. Johnson and Paul L. Coe, Jr.

VEPrlCAL-FI'_ POSI_[_ N _?;D OPIFS, TA_ION ON Tqm,

LOW-SPE_D _F,_ODYN_,_/C PEPFOP_A_C_-OF '=IqELV

SWFPT WINGS (NASa) ]_ p HC A"I,IMF _.'_I "_r.cl_;CSC/ t_IA q_/r'2 _5_Iu

September1979

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Na(_onalAeronaul,cs dlldSpace Admm_:;lral_on "

tLangley Research Center jhf'/f,[_:

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Hampton, V_rgm_a23665

1979023987

https://ntrs.nasa.gov/search.jsp?R=19790023987 2020-07-09T00:53:46+00:00Z

J,

SU_IARY

A theoretical study has been conducted to determine thepotential low-speed performance improvements which can beachieved by altering the position and orientation of the out-board vertical fins of low-aspect-ratio highly swept wings• Asexpected, the results of the study show that the magnitude ofthe performance improvements is solely a function of the span-load distribution. Both the vertical-fin-ehordwise positionand toe angle provided effective means for adjusting the

• overall span-load distribution•

INTRODUCTION

The National Aeronautics and Space Administration iscurrently investigating the aerodynamic characteristics ofadvanced aircraft concepts which are intended to cruise effi-ciently at supersonic speeds (see refs. I and 2). Such con-figurations employ a highly swept planform, which is twistedand cambered to achieve the desired high level of cruise aero-dynamic efficiency. These configurations typically includeoutboard vertical fins which are intended to provide direc-tional stability, but which (when properly aligned in thecruise condition) can be shown to produce a forward componentof force which is in excess of the additional skin friction

drag, and hence the inclusion of the outboard vertical finsprovides a net supersonic performance gain.

The necessary emphasis on optimizing these conceptualwing--outboard-vertical-fin designs for the supersonic cruisecondition has resulted in aircraft concepts which would exhibitrelatively poor low-speed performance in typical takeoff andlanding situations. Previous efforts directed towards pro-viding these concepts with improved low-speed p_rformance havebeen limited to studies of the leading-and trailing-edgesystems (see, for example refs. 3 and 4).

The present study, which utilizes a planar vortex-latticetheoretical mode] of the highly swept-wing vertical-fin configu-ration, is intended to determine the effect on aerodynamicperformance of changes in vertical-fin chordwise position andtoe and cant angle.

J

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S_IBOLS

Force coefficients are referred to the wind system of axes.

A wing aspect ratio, b2/S

b wing span, m (ft)

c local wing chord, nl (ft)

Cavg average wing chord, S/b, m (ft)

. CDi induced drag coefficient, Induced drag/qS

C L lift coefficient, Lift/qS

c_ section-lift coefficient

Cy section side-force coefficient

e span efficiency factor, CL2/_ACDi

M Mach number

q free-stream dynamic pressure, Pa (Ibf/ft 2)

S wing area, m2" (ft2)

x chordwise distance of the leading edge of the finbehind the leading edge of the wing, m (ft)

y spanwise distance measured from wing centerline, m(ft)

z vertical fin ordinate, origin at wing vertical-finintersection, positive upwards, m (ft)

angle of attack, deg

_f trailing-edge flap deflection, positive trailing edgedown, deg

o sidewash angle at vertical fin, positive outwards, deg

T toe angle of vertical fin, positive toe-in, deg

cant angle of vertical fin, positive outwards, deg

Subscripts:

o indicates condition without vertical fin

,- 2

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CONF [GUllAT IONS S IMULATED

The study was conducted for the two configurationgeometries shown in fig',ure 1 and defined in referenees 5 and 6.These geometries (referred to as configuration A and eonfigura-tion B) were simulated using, the planar vortex-lattice computerprogram described in reference 7. Configuration A includedboth twist and camber (see ref. 5) end a planar fuselage repre-sentation. Configuration 13was untwisted and uncambered anddid not incorporate a fuselage. Figure 2 depicts schematicallythe vortex-lattice paneling schemes used to represent theconfiguration geometries.

• RESUI,TS AND DISCUSSION

In the present study, a relative span efficiency factor,e/co, is introduced where

e__ = span efficiency factor - wing with outboard vertical ..[injeo span efficiency factor - wing without outboard vertical fin

This factor is introduced in an attempt to reduce thedependence of the numerical results on the particular panelingscheme and vortex spacing used. It is acknowledged, however,that changes in either the paneling scheme or the vortexspacing will affect the values of e/e o to some extent.Therefore, values of e/e o should be considered as a qualita-tive figure of merit, which is introduced to assess the rela-tive effect on performance of changes in vertical-fin chordwiseposition and vertical-fin toe and cant angles.

Effect of Vertical-Fin Chordwise Position

Figure 3 shows the effect of varying the chordwise positionof the vertical fin on the relative span efficiency factor, e/e o.As can be seen, changes in chordwise position result in modestchanges in span efficiency; however, the most interesting pointto be noted is the different trend exhibited by the results for

i

configurations A and B. For configuration A, the results indi-cate an inerease in span efficiency factor can be aehieved by

, moving the outboard-vertical fin forward relative to the wing.By contrast, the results for configuration B indicate that themaximum span efficiency can be achieved by moving the outboard-vertical fins rearward to approximate_2 x/c = 0.2. It shouldbe further noted that e/eo is a reasonably smooth function ofx/c, indicating that the computational results are fairlyinsensitive to the relative alignment of the bound vorticesrepresenting the wing and vertical fin.

3

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9

Inasmuch as the span effieieney factor is a funetion ofthe span-load distribution, some insight into the _reeedingdiffering trends of e/e o can be afforded by considering thisquantity. Figure 4 presents the calculated optimum span-loaddistribution for configuration A. The optimization seeks aminimum induced drag using a Trcfftz plane far-field drag compu-tation (see ref. 7). Although for a planar wing this result isaccomplished by obtaining a uniform downwash at downstreaminfinity, the present nonplanar solution utilizes Lagrange

multipliers to minimize the induced drag. Also presented infigure 4 are the calculated span-load distributions for eon-figuration A having vertical fins located at x/c = 0 and +0.2.The results show that for this configuration moving theoutboard-vertical fins forward produces an increased inwardload op the vertical fins, a slightly increased span load onthe portion of the wing inboard of the vertical fins, and aslightly reduced span load on the outboard wing panel. The netresult being that, for the values of x/e investigated, the con-dition with x/e = -0.2 results in a span-load distribution,particularly the vertical-fin side-force load distribution,which is closest to the optimum, and hence, exhibits the higherspan efficiency factor as shown in figure 3.

Figure 5 presents the optimum span-load distribution andthe span-load distribution for the condition of x/e = 0 and_0.2 for configuration B. As can be seen, moving the outboardvertical fin of configuration B aft to x/e = 0.2 results in areduction of the inwardly directed load on the vertical fins, areduction in the span load inboard of the vertical fins, and anincrease in span load on the outboard wing panel. This trendis in complete agreement with the results for configuration A,however, in this ease the reduced vertical-fin loads result ina condition which more closely approaches the optimum.Therefore, it can be concluded that the eff +t of vertical-finchordwise position on the span efficiency factor is simply afunction of how closely the optimum span-load distribution canbe approximated, i

Recognizing that the load on the vertical fin is a func-tion of the local angle of attack (e.g. sidewash in the ease ofa vertical surface) leads to an understanding of the fluid tmechanism responsible for the preceding results. Figure 6 pre-sents the calculated sidewash distribution along the vertical .

fin. As can be seen, moving the vertical fin forward would !produce an increased resultant angle of attack and hence an !increase in the inward vertical-fin load. Correspondingly, :moving tee vertical fin aft would produce a reduction inresultant angle of attack and a reduction in the inwardvertical-fin load. The change in the span-load distribution ofthe wing, which is observed to accompany the change invertieal-fin load, simply results from a change in circulation

. 4+

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(see fig. 7). An increase in the inward vertical-fin loadwould occur with an increase in the circulation around the vet--tics1 fin. As shown by the sketch of figure 7, the increasedcirculation would tend to reinforce the circulation (andincrease the span load) over the inboard portion of the wing,while tending to oppose the circulation (and reduce the spanload) over the outboard portion of the wing.

Effect of Vertical-Fin Toe Angle

The effect of vertical-fin toe angle, _, on the relativespan efficiency factor of configuration A is presented infigure 8. As can be seen, an angle corresponding to approxima-

• tely _= 2° results in a maximum span efficiency. This resultis simply related to the span-load distribution as previouslydiscussed and is totally consistent with the preceding resultwhich showed an increased span efficiency achieved for thisconfiguration by moving the vertical fins forward. (Both toe-in and forward placement of the vertical fin result in anincreased angle of attack for the vertical fin.) The result isfurther illustrated by the span-load distributions presented infigure 9 for several values of vertical-fin toe angle. Aswould be expected, T = 2° , which results in the highest spanefficiency factor, also results in a span-load distributionmost nearly approaching the optimum.

Effect of Vertical Fin Cant Angle

The effect of vertical fin cant angle, \, cn the relativespan efficiency factor of configuration A is presented infigure I0. The results are presented for the configurationwith the vertical fin located at x/c = 0 and T = 0°. The

results presented show that there is a modest effect of cantangle on performance and that the effect is favorable for posi-tive cant angles and unfavorable for negative angles. Thisresult is simply related to the inward direction of the force

acting on the vertical fin. For positive values of _, a eom- Iponent of the vertical-fin load is acting in the positive liftdirection and, hence, results in an increased span efficieneyfactor. Correspondingly, for negative values of X, a com-ponent of the vertieal-fin load is directed in the negativelift direction and, as expeeted, reduces the span efficiency

' factor•

'_ Effect of Trailing-Edge Flap Deflection

The results of the preceding sections have shown that theimprovements in span efficiency, which are provided by {vertical-fin chordwise position and toe angle, are a direct 1result of such configuration variables providing a more

favorable span-load distribution. In order to more clearly

1979023987-006

illustrate this point, the trailing-edge.flap system sketchedin figure II was subjected to _ continuously variable deflectionin an attempt to approximate the optimum the span-load distri-bution. The trailing-edge deflection schedule selected forstudy is presented in figure 12, and the corresponding span-load distribution is presented in figure 13. As can be seen,the scheduled trailing-edge flap system provides the configura-tion with a load distribution which is a reasonable approxima-tion to the optimum. With the trailing-edge deflection incor-porated into the theoretical model, the effect of vertical-finehordwise position and vertical-fin toe angle on the span effi-ciency factor is reconsidered. The results are presented infigures 14 and 15, respectively, and show that variations inx/e and z (from the condition of x/c = 0 and _ = 0°) result inrcduetions in the span efficiency factor. These results are,

of course, expected as the span-load distribution for the con-figuration with the scheduled trailing-edge flaps (and havingx/c = 0 and _ = 0°) has been shown to be nearly optimum.

CONCLUSION

A theoretical study has been conducted to determine thepotential low-speed performance improvements which can beachieved by altering, the position and orientation of the out-board vertical fins of low-aspect-ratio highly swept wings. Asexpected, the results of the study show that the magnitude ofthe performance improvements is solely a function of the span-load distribution. Both the vertieal-fin-ehordwise positionand toe angle provided effective means for adjusting theoverall span-load distribution.

D

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REFERENCES

I. Robins, A. Warner; Morris, Odell A.; and Harris, Roy V.,Jr.: Recent Results in the Aerodynamics of SupersonicVehicles. J. Aircraft, vol. 3, 1966, pp. 573-577

2. Robins, A. Warner; Lamb, Milton; and Miller, David S.:Aerodynamic Characteristics at Mach Numbers of 1.5, 1.8,and 2.0 of Blended Wing-Body ConfigurAtion With andWithout an Integral Canard. NASA TP 1427, 1979

3. Coe, Paul L., Jr.; and Weston, Robert P.: Effects of WingLeading-Edge Deflection on the Low-Speed AerodynamicCharacteristics of a Low-Aspect-Ratio Highly Swept Arrow-Wing Configuration. NASA TM 78787, 1978

4. Coe, Paul L., Jr.; and IIuffman, Jarrett K.: Influence ofOptimized Leading-Edge Deflection and Geometric Anhedraion the Low-Speed Aerodynamic Characteristics of a Low-AsDcct-Ratio Highly Swept Arrow-Wing Configuration. NASA_,I 80083, 1979

5. Staff, Hampton Technical Center, LTV Aerospace CorporationtAdvanced Supersoni-c Technology Concept Study ReferenceCharacteristics. NASA CR 132374, 1973

6. Manro, Marjorie E.; Manning, Kenneth J. R.; Hallstaff,Thomas H.; and Rogers, John T.: Transonic PressureMeasurements and Comparison of Theory to Experiment for anArrow-Wing Configuration--Summary Report. NASA CR 2610,1976

7. Tulinius, J.: Unified Subsonic, Transonic, and SupersonicNAR Vortex Lattice. Rep. TFD-72-253, RockwellInternational Corporation, 1972

. 7

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Outboard vertical fin

2 = 0.726 I

(a) Planform geometry for wing of reference 5 (Configuration A)

Outboard vertical fin

(b) Planform geometry for wing of reference 6 (Configuration B)

Figure 1.- Planform geometries of configurations simulated.

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Figure 3.- Effect of vertical-tin ehordwise position on relativespan efficiency, a = 10°, M = O.

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