Supersonic Area Rule and the Application to the Design of a Wing Body

8/2/2019 Supersonic Area Rule and the Application to the Design of a Wing Body

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"Ik

TECHNICAL REPORT R-72

A SUPERSONIC AREA RULE AND AN APPLICATIONTO THE DESIGN OF A WING-BODY COMBINATION

WITH HIGH LIFT-DRAG RATIOSBy RICHARD T. WHITCOMB and JOHN R. SEVIER, Jr.

Langley Research CenterLangley Field, Va.


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TECHNICAL REPORT R-72

A SUPERSONIC AREA RULE AND AN APPLICATION TO THE DESIGN OF AWING-BODY COMBINATION WITH HIGH LIFT-DRAG RATIOS 1

By P_ICI-IARD T. WfIITCOMB and JOHN R. SEVIER, Jm

SUMMARY

,is an exten,_.ion of the transonic area rule, aconcept for interrelath_g the wave drags off wing-bodycorobinations at moderate super,_onic speeds withaxial developments of cross-sectional area has beenderived. The wave drag of a combination at a givensupersonic speed is rdated to a number qf decelop-meats oj cross-.ectional area,q as intersected by .lIach})lanes. On the basis of this concept and otherdesign procedure*, a structurally .[ea_'ible, swept-wing-4ndented-body combbmtion has been. de,_ignedto have relatively high. maximum lift-drag ratios avera range o.f transonic and moderate ,_upersonie 3laehnumbers. The wing oJ the e_m_bination has beende,_'igned to have reduced drag associated with. l(ftand, when. used with an. indented body, to have lowzero-lift wave drag. Experimental results have beenobtained for this cot_figuration at .llach numbemJrom 0.80 to 2.01. 3Iaximum lift-drag ratio_' i_approximately 14 and 9 were measured at 3faehnumbers q{ 1.15 and 1.41, re._pectively.

INTRODUCTION

More recently, by considering the physical na-ture of the flow at moderate supersonic speeds, aconcept has been developed which should inter-relate qualitatively the zero-lift wave drag ofwing-1)ody combinations at these speeds with axialdevelopments of cross-sectional areas. This rela-tionship is basically the same as that arrived atindependently in reference 2 on the basis of theconsiderations of reference 3. On the basis of thisconcept and other design procedures, a structurallyfeasible, swept-wing -indented-body combinationhas been designed to have relatively high lift-dragratios over _ range of transonic and moderatesupersonic Mach numbers.

The present paper describes the supersonic arearule, the considerations involved in the design ofthe special configuration, and some experimentalresults for the configuration obtained ut Mathnumt)ers from 0.80 to 2.01. The results presentedfor Maeh numbers of 1.41, 1.61, and 2.01 wereobtained from reference 4.

bReference 1 showed that near the speed of o

sound, the zero-lift drag rise for a wing-body con> CLbimttion having a thin, low-aspect-ratio wing is cprilnarily dependent on the axial development ofcross-se('tion area normal to the airstream. Also, L/Dit was found that contouring the l)odies of wing- Mbody comt)inations to ol)tain improved axial ydevelopments of cross-sectional area for the con> abinations results in substantial reductions in the ACDdrag-rise increments at transonic speeds.

SYMBOLSwing span, in.drag coefficientlift coefficientwing chord, in.mean aerodynamic chord, in.lift-drag ratioMaeh nunll)erspanwise distance from center fine, in.angle of attack, (legincrement of drag coefficient for an

increment in lift coefficientSupersedes recently declassified NACA Research Memorandum L53H31a by Richard T. Whiteomb and Thomas L. Fiseheiti, 1953.


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2 TECHNICAL REPORT R-72---NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONa_juSet,script s:

mid

incremental drag coefficientMaeh angle, (legroll angle, deg

maximumminimum

CONCEPT FOR INTERRELATING WAVE DRAGWITH AREA DEVELOPMENTS AT

SUPERSONIC SPEEDSBASIS OF CONCEPT

The major part of the supersonic wave dragfor a wing-1)ody combination results from lossesassociated with shocks at considerable distancesfrom the configuration. Thus, the wave dragmay be estimated by considering tim streamdisturbances produced by a configuration at thesedistances. At moderate supersonic speeds, thesedisturbances may be considered in individualstream tubes, such as A in figure 1. If small

.- ...... _........... L- 812t2FIGt'ItE I. Geometric relations considered in developing

area rule for supersonic speeds.

induced velocities arc assumed, the effeets ofchanges in the configuration arrive at points onthis tube along Mach lines which lie on conesegments, such as B. For reasonable distancesfrom the configuration (rouglfly 2 spans orgreater) and for conventional, relatively low-aspect-ratio wings, the surface of these cone seg-ments in the region of the configuration may beassumed to be the Math planes, such as C, tan-gent to the cone segments between the tube Aand the axis of sslnmetry.Consideration of the propagation of the local

effects of the configuration indicates that thevariations in the disturbances at the stream tubeA generally may be assumed to be approximalelyproportional to streamwise changes in the normalcomponents of the total areas of the cross sections,such as DD, intersected by these Math planes.Therefore, the wave losses in the stream tube arefunctions of the axial development of these cross-sectional areas. Obviously, tim losses in the set.of stream tubes along a given radial sector arefunctions of one axial development: of cross-sectional area, whereas those in tubes in cireum-ferentially displaced sectors arc functions ofvarious developments determined by sets of Mathplanes wit.it axes of tilt rotated about lhe axis ofsymmetry. Except for the substitulian of s_ream-wise changes of cross-sectional area for singulari-ties, these considerations are essentially the sameas those presented on page 93 of reference 3.

PROCEDURE FOR DETERMINING AREA DEVELOPMENTSFrom the foregoing considerations, the zero-lift,

wave drag for a wing-body combination at agiven moderate supersonic _lach number can beseen to be related to a number of developmentsof the normal components of cross-sectional areasas intersected by Maeh planes which are inclinedto the stream at the Math angle u (fig. 2). Thevarious developnwnts are obtained with the axisof tilt of tiwse Maeh planes rolled to variousposit.ions armmd lhe center line of the configura-lion. This procedure is illustrated in figure 2.For clarity, the position of the axis of lilt of theMath plane is maiutained a mt the configurationis rolh, d. For eonfigm'alions symmetrical abouthorizontal and w,rtieal planes, the area dew, lop-meats are determined for various roll angles 4,frmn 0 to 90 . The approximate wave drag forthe combination is an average of functions of anumber of area dew'h_pmenls so determined.

i_ Iil


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A SUPERSONIC AREA :RULE AND AN APPLICATION TO THE DESIGN OF A WING BODY 3

:!i:;i; _iiii:: /

L/ o0qAxial

F_GURE 2. Procedure for determining area developmet_ts

The area developments oblained for the con-figuration shown in figure 2 with the two repro-sentativc roll angles are presented at the bottomof the figure. As indicated by these curves, thevarious developments for _ given _X.[a(:h numbermay differ considerably. The partial end-plateeffect of the body on the field of the wing affectsthe applicability of this simplified concept. Formost practical combinations, this effect shouldbe of secondary importance. Obviously this rela-tionship reduces to the transonic area rule at a_I'tclt number of 1.0.

APPLICATION TO THE REDUCTION OF WAVE DRAGOn the basis of this concept, the approximately

minimum wave drag for a wing-body combinationat a given supersonic speed wouhl be obtained byshaping the body so that the various area de-velopments for this speed are the same as those forbodies of revolution with low wave drag. Ex-perimental result,s, such as those presented inreference 5, have indicated that body shapingsso designed usually provide substantially greaterreductions in drag at. moderate supersonic speeds

distoncerelated to wave drag at inodera(e super._onic M-ach numbers.

than do those shapes designed to improve thedevelopment for a _Xfach number of 1.0.

For most configurations, somewhat more satis-factory dewdopments can bc obtained by shapingthe body noncireularly rather than axially sym-metrically. Obviously, the body contours usedshouhl not cause severe local velocity _,n'adients orboundary-layer separation. In general, for com-binations of l)ractical wings wit ll l)odics withsufficiently conservative contours, the area devel-opments for tlle various values of 4) will deviatefrom the most desirable shapes. The possibilitiesof improving the various area developments at andoff the design conditions through the use of bodyindentation are strongly dependent on thegeometry of the wing.

DESIGN OF WING-BODY COMBINATIONThe wing of the coml)ination has been designed

to have reduced drag associated with lift and,when used with an indented body, to have lowzero-lift wave drag on the basis of the conceptdescribed in the preceding section for a range oftransonic and moderate supersonic Math mmlbcrs.In particular, the parameters of the wing generally


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4 TECHNICAL REPORT R--72--NATIONAL AERONA'UTICS AND SPACE ADMINISTRATIONhave been selected so that it is possible to obtainwith a given body indentation relatively smootharea developments for the various wllues of (fig. 2) at the Mach numbers under consideration.Therefore, the area developments for the wingmust be similar for the various Maeh numbersand wdues of 4,.

DESCRIPTION OF CONFIGURATIONThe configm'ation is shown in figure 3. The

wing, which is eaml)ered and twisted, has 60 ofsweep, an aspect ralio of 4, and a taper ratio of0.333. It has XACA 64-series airfoil sectionswhich vary in tlfickness fi'om 12 percent chord atthe root to 6 percent chord at the 50-percent-semispan station and then remains constant at6 percent chord to the tip as shown in figure 4.The coordinates of the wing sections are listed intable I.

The body shape used as a basis for the design ofthe indented eonfiguration discussed herein isthat for tile body described in reference 6. Forthe primary configuration, the body has beenindented axially symmetrically to obtain rclativelysmooth area


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ASUPERSONIC AREA RULE AND AN APPLICATION TO THE DESIGN OF A WING BODY 5

c 4o

4

4--"

_2"5F


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6 TECHNICAL REPORT R--72_NL&TION'AL AERONAUTICS AND SPACE ADMINISTRATION

Wing aspect ratio and structural character-istics.--With the wing swept behind the Mathline, the drag due to lift is reduced by increasingthe aspect ralio (refs. 7 and 8). Because of therela.tively thick wing sections allowed with bodyindentation, aspect ratios significantly higher thanthose previously used for practical configurationscan now be considered. An actual wing of therelatively high-a_pect-ratio configuration proposedherein appears to be structurally feasible. Thedeflection of the wing of this configuration undera given load at the 70-percent-semispan stationwould be approximately half of tha.t for thehigldy swept wing discussed in reference 6.

Body contours and area developments,--Withthe primary body indentation used, the axialdevelopment of cross-sectional area for the com-bination for the median value of (45 ) at thedesign Maeh number of 1.4 (fig. 5) is approxi-nmtely the same as that for the body used as abasis for the design. At the extreme values of (0 and 90 ) the dcvclopnwnts differ somewhatfrom those for the basic unindentcd body alone;lmwever, the estimated drag increment for thecombination associated with su('h variations inthe area developments is negligible. The areadeveh)pments for Ma('h mmlbers between 1.0and 1.4 are all relatively smooth as indicated bythe developments for the extremes of tlfis rangepresented in figure 5. At Maeh mmlbers greaterthan 1.4, the devclopmenls become relativelyirregular as indicated by the developments for aMaeh number of 1.6 (fig. 5). The fuselageindentation desi_led for a Math nuniber of 1.4is very similar to that for a Maeh number of 1.0(table II). Tiffs similarity results from des@ringthe wing of this particular configura.tion to havesimilar area developments at all Maeh numbers.

The area developments obtained for this eom-t)ination at Maeh numbers uI) to 1.6 arc con-siderably smoother than those obtained for thesame condition._ for unswept, moderately swept,and delta wings _qth approximately the sameaspect, ratio and mean seetion-thiek,wss-to-ehordratios in combination with indented bodies. Asexamp]es of such developments, those ol)tained fora 45 swept wing with an aspect, ratio of 4, a taperratio of 0.3, and NACA 65A006 airfoil sections incombination with a body indented axiallysymmetrically to improve the area developmentsfor a ._Iaeh nuinber of 1.4 are presented in figure 6.

IO Basic body _one9 Wing-body configurationfor _ (dog) of:

9ot

_, |1 [

!J !41_

--Basic body alone

JLt

7-Iii0 2 8 I0 12 14 16 18 20 22 24 26 28 313 32Distance of model sfation from nose, in

(a) M 1.4.(b) M-- 1.0.

FIGURE 6, Representative axiql (tevelopmenls of cross-sectionM area for a 45 swept wing in combination witha body indented for 3[--- 1.4 at 31=1.4 and J.0.

Wing twist and camber. Results obtained atlow supersonic speeds (l'ef. 9) indicate that thefavorable cffeels of twist and camber on the lift-drag ratios can be added to those of body indenta-tion. The basis for the twist and camber used isthe mean surface form theoretically required for auniform load at a. lift coefficient of 0.25 at a Maehnumber of 1.4 fief. 7). This theoretical form hasbeen modified by redu('ing the camber near thex_-ing-body jmwture. (See fig. 4.) An analysisof the effects of the body on the induced field dueto lift at supersonic speeds has indicated that sucha modification should improve the drag associatedwith the lift.

EXP ERIM ENTSAPPARATUS AND METHODS

Experimeninl results for 5[aeh numbers from0.80 to 1.15 were obtained in the Imngley 8-foottransonic tunnel. Those for Maeh ]mmbers from1.41, 1.6I, and 2.01 were obtained in the Langley4- by 4-foot supei_onie pressure tunnel (ref. 4).

1


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A SUPERSONIC AREA RULE AND AN APPLICATION TO THE DESIGN OF A WING BODY 7

The 60 swept wing was tested ,lot only incombination with the body designed to obtainsmooth area developments at a Math numberof 1.4 but also with a basic unindented body anda body indented so that the axial developmentof cross-sectional area for the combination for aMach number of 1.0 is the same as that for thebasic body alone. Axial developments of cross-sectional area for the configuration indented fora Mach nunlber of 1.0 are presented in figure 7.

[

?_

0 4 8 12 16 20 24 28 32Disfonce of model sto lion from nose, in.

(a) 3[= 1.0.(b) 3I- 1.4.(c) ,'it= 1.6.

Fmr_v_ 7. -Rcprcscntalive axial dcvt'lopmcnts of cross-sectional area for the 60 swept wing in combin/ttionwith the body indented for M--1.0 at ,1I=1.0, 1.4,and 1.6.

These developments are presented for variousvalues of at. Math numbers of 1.0, 1.4, and 1.6.The model dimensions are shown in figure 3.

Lift and drag data were measured by meansof a sting-supported internal strain-gage balance.All data presented are essentially free of theeffects of wall-reflected disturbances. The maxi-mmn errors of the drag coefficients at transonicspeeds are of the order of :L0.0005i those of thelift coefficients, _0.002. These limits include, theeffe('t of l)ossible errors in the measurements ofangle of attack. The results have been adjust('dto the condition of stream static pressure on thebase of the body.

The Reynolds number per foot: was approxi-mately 4.0X 10 '_for the t('sts in the S-foot transonictunnel and 3.7X106 for thosc in the 4- by 4-footsupersonic pressure tunnel.

RESLrLTS AND DISCUSSIONLift and drag coeiticients.--The variations of

the angle of attack and drag coefficient with liftcoefficient for the various test Maeh numbers arepresented in fi_lre 8. The coefficients arc basedon a wing area of 1 square foot.Minimum drag coei_cient.--The variations of

minimum dra.g coefficient with Maeh number arepresented in figure 9. The increment between thecoefficients at Mach numbers of 0.S0 and 1.41for the configuration indented for a Mach numberof 1.4 is approximately 0.0035. This value isappro_mately 0.0007 greater than the incrementmeasured for the basic hody alone. The differenceis associated with the small variations of the areadevelopments for the configuration at this Mathnumber from the development for the basic body,as indicated in fignre 5. At. lower supersonicM_wh numbers, the drag eocIIieients for this con-figuration are approxinmtely the same as that fora Maeh number of 1.41. At the higher test Maehnumbers, the drag coctticients _re considerably_eater. These varia.tions are consistent with thechanges of the area developments with Mathnumber, as shown in figure 5.

Because of the similarity of the fuselage inden la-tions designed for Math numbers of 1.0 and 1.4,the mininmm drag coefficients measured for thetwo configurations at the various test Maeh nmn-bcrs are roughly the same. The smaJ1 vari_tionsin drag are consistent with the differences of thearea developments for the two configurations


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S TECHNICAL REPORT R--72---NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Wing-body configuralionBody indented for M =1,4Body indented for M = 1.0Basic body

!I!l

.I 0 .I .6

(a) Angle of a_t,_lck.FIGURE 8.--Variations of angle of attack and drag coefficient with llft co_,Mcient for configur'_tions tested.

At a Maeh number of 1.0, the drag coefficient forthe configura.tion designed to have smooth areadevelopment at this condition is 0.002 less thanthat designed for a Maeh number of 1.4, whereasat a Maeh number of 1.41 the drag coefficient ofthe configuration desig3_ed for this condition is0.001 less them for the configuration designed fora Maeh nmnber of 1.0.

The indented configurations provide _pproi-nlately a one-ttiird reduction in drag coefficientin comparison with the configuration with thebasic body at supersonic Macli numbers up to1.41. (The relative improvement wouht liave

been slightly less if the size of the basic body hadbeen decreased to have the same volume as thatof the indented bodies.) At the higher test. Maehnumbers, the improvements progressively decreaseuntil at a Maeh number of 2.01 die reductionsare only roughly 5 percent.

lgaximum lift-drag ratios.--Variations of themaximum lift-drag ratios with Maeh number areshown in figalre 10. At a Maeh number of 1.15,the ratio for the configuration with the body in-dented for a. Math nunlber of 1.4 is approximately14. This very high value results not only fromthe small minimum drag coefficient sllm_m in

] j]i


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A SIEPERSONIC AREA RULE AND AN APPLICATION TO THE DESIGN OF A "WING BODY 9

m =

M=(

.5 ,co -,I 0Lift coefficient, CL

(b) Drag coefficient.FIGUaE 8,--Conchtdcd.

Wing- body configuration '_j_Body indented for M=1.4

Basic body

..... __..Li 2

figure 9 but ulso from the relatively low drag-due-to-lift factor, as sho_aa in figure 11. (The drag-due-to-lift values presented in fig. 1I are for tJ_elift coefficient range between 0.15 and 0.25.)

The maximum lift-drag ratio for the configura-tion indented for a Mach number of 1.4 decreasesto a value of approximately 9 at a Mach number

o[ 1.41 (ref. 4). The relatively low ratio for thiscondition is associated with the large drag-due-to-lift factor shown in figure 11. The measuredfactor is approximately 90 percent greater thanthe value predicted on the basis of linear theory(ref. 7) for this _'[ach number. In reference 6,similar excessive drag-due-to-lift factors are shownfor a body combined with a highly swept wing.


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]0.05

TECHNICAL REPORT R--72--NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

.8 l.O

I

Body indenled for M: 1.4Body indented for M: 1.0Bosic body

,.2 ,., ,.! ' ,'8 2.oMoch number, M

:FI(;I:RE 9.--Varitttion of minimum d.rag coefficient, with ,_,Iach ]_umher.

2.2

07

i

I2.0

I2.1

171GWRE lO.--Variations of maximum lift-drag ratios with 3hch number.


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A SUPERSONIC AREA RULE AND AN APPLICATION TO THE DESIGN OF A "WING BODY 11.4f

Jri

Body indenled for M: L4Body indented for M : 1.0

-- Bosic b ody _ .__Lineor theory (ref. 7) [J J

i i i i / I

.I

ti ' I! I.O L2 [.4

1Moth number,

jf/J

1.6 2,0M

FIGURE 11. Variations of the drag-due-to-lift factors with M,tch nmnber.

iJ

2.2

These large drags probably result primarily fi'omboundary-layer separation and nonlinearities ofthe field above the upper surface of the wing.Boundary-layer-flow observations made for thewing of reference 6 indicated such separation.This boundary-h_yer breakdo_m probably resultsfrom a shock wave above the wing in an actionsimilar to tlmt for configurations with less sweepat subsonic Maeh numbers.

At lhe lest, Math lmmbers gwealer than 1.41, themaximmn l ift.-drag rat los progressively decrease.These reductions are caused primarily by the in-creases of the minimum drag shown in figure 9.

The maxinmm lift-drag ratios measured for theconfiguration with the body indented for a Mathnumber of 1.4 (fig. 10) are slightly greater thanthose with the body indented for a Mach numberof 1.0 at X[ach nunlt)ers higher than 1.15, but aresomewhat less at. lower supersonic speeds, aswouhl be expected. The lift-drag ratios for lheconfiguration designed for a Math number of 1.4at subsonic speeds are substantially less than forthe configuration designed for a Math nmnber of1.0. This difference is caused by 't higher drag-due-to-lift factor for the configuration designedfor a Math mmlber of 1.4 (fig. 11).

At a Mach number of 1.14 the maximum lift-drag ratios for the configurations with indentedbodies are approximately 50 percent gTeater thanfor the configuration with the basic body. Thisimprovement results not only from the reducedminimum drag (fig. 9) but also, in part, from somelessening of the drag-due-to-lift factor (fig. 11).At a Math number of 1.41 the body indentationdesigned for this condition improves the maxi-mum lift-drag ratio by 20 percent, whereas thebody indentation designed for a Maeh number of1.0 increases the ratio by 15 percent. Theserelatively small improvements of the lift-dragratios, in spite of the pronounced reductions of theminimum drag coefficient (fig. 9), result primarilyfront the fact that at this condition the indenta-tions substantially increase the drag-due-to-liftfactors (fig. I1). The exact reason for this effectis unknown. IIowever, it may be conjectured thatthe adverse pressure gradienls produced by theindentation in the region of the wing aggravatethe boundary-layer separation which is probablypresent 'tbove the wing for this condition.

With an increase in Maeh number beyond 1.41,the favorable effects of the indentations on the


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12 TECHNICAL REPORT R-72INATIONAL AERONAUTICS AND SPACE ADMINISTRATIONmaxinmm lift-drag ratios continue to decreaseuntil at a Mach number of 2.01 they provide nofavorable effects. At these higher speeds, thedecrease of effectiveness is due primarily to thereductions of the improvements in the minimumdrag.

CONCLUDING REMARKS

A supersonic-area-rule concept has been pre-sented whereby the wave drag of a wing-l)odycombination is related to a number of develop-ments of cross-sectiomd areas as intersected by

Maeh planes. This concept has been applied toa special wing-body configuration, which has beentested at Mach numbers from 0.80 to 2.01. Therelatively high lift-drag ratios for the supersonicspeeds of the investigation suggest that judiciousapplication of the proposed supersonic area ruleshould result in considerable improvements ofthe possible performance of airplanes designedfor these speeds.LANGLEY RESEARCH CENTER_

. 'N'ATIONAL AERONAUTICS AND SPACE ADMINISTRATION,LANGLEY FIELD, VA., August 18, 1953.

REFERENCES

1. Whitcomb, Richard T.: A Study of the Zero-Lift Drag-Rise Characteristics of Wing-Body CombinationsNear the Speed of Sound. NACA Rep. 1273, 1956.(Supersedes NACA RM L52It08.)

2. Jones, Robert T.: Theory of Wing-Body Drag at Super-sonic Speeds. NACA Rep. 1284, 1956. (Super-sedes NACA RM A53HI8a.)

3. llayes, Wallace D.: Linearized Supersonic Flow. Rep.No. AL-222, North American Aviation, Inc., June18, 1947.

4. Sevicr, John R., Jr.: Investigation of the Effects ofBody Indentation and of Wing-Plan-Form Modi-fication on the Longitudinal Characteristics of a 60 Swept-Wing --Body Combination at Mach Numbersof 1.41, 1.61, and 2.01. NACARM L55EI7, 1955.

5. Loving, Donald L.: A Transonic Investigation ofChanging Indentation Design Maeh Number on theAerodynamic Characteristics of a 45 _ Sweptback-Wing -Body Combination Designed for IIigh Per-formance. NACA RM L55J07, 1956.

6. II,dl, Charles F., and tteitmeyer, John C.: Aerody-namic Study of a Wing-Fuselage Combination Em-ploying a Wing Swept Back 63.-Characteristics atSupersonic Speeds of a Model With the Wing Twistedand Cambered for I?niform Load. NACA RMA9J24, 1950.

7. Jones, Robert T.: Estimated Lift-Drag Ratios atSupersonic Speed. NACA TN 1350, 1947.

8. Carmel, Melvin M.: Transonic Wind-Tunnel Inves-tigation of the Effects of Aspect Ratio, SpanwiscVariations in Section Thickness Ratio, and a BodyIndentation on the Aerodynamic Characteristics ofa 45 Sweptback Wing-Body Coml)ination. NACARM L52L26b, 1953.

9. Harrison, Daniel E.: The Influence of a Change inBody Shape on the Effects of Twist and Camber AsDetermined by a Transonic Wind-Tunnel Inves-tigation of a 45 Sweptback Wing-Fuselage Con-figuration. NACA RM L53B03, 1953.


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A SUPERSONIC AREA RULE AND AN APPLICATION TO THE DESIGN OF A WING :BODY 13

TABLE IAIRFOIL COORDINATES

Ordinate, percent chord

10-pereent-scmispan 20-pereent-semispan 40-pereent-_emispan?herd statio station (c=-8.40 in.) station (c 7.80 in.) station (c=6.60 in.)

Upper Lower Upper Lowersurface surface surface surface

0.5. 751. 252.5510152030405060

708090100

Upper Lowermtrface surface

0. 061.091.291.662. 072. 523. 093.353. 453.142.411.05--. 74--2. 68--4. 77--6. 88--8. 82

O.06--. 70--. 84--1.09--1.74--2. 56--3.93--5. 22--6. 20--7. 71--8. 829.42--9. 64--9. 61--9. 40--9. 18--8. 94

0.121. O01.181.4-[1.932. 593. 363. 774. 674. 043. 532. 491.05--. 64--2. 53--4. 5O--6. 48

0.12--. 67--. 82--1, 05--1.50--2, 12--3. 16--3, 98--4. O0--5. 80--6. 64--7. 04--7. 16--7. O0--6. 826. 68--6. 50

O. 29 921.051.261.672. 232. 963. 463. 793. 973. 823.272. 381.11--. 30-1.80--3. 26

O. 29--. 30--. 36--. 58--.91--1.33--1.91--2. 32--1, 70--3. 35--1.79--3. 89--3. 85--3. 70--3. 58--3. 4,1--3. 28

Chord station

0.5. 751.252.5510152030405060708090100

Ordimtte, percent chord

60-pereent-semispanstation @=5.40 in.)

Upper Lower_urface surface

O. 65 O. 651. ll .241.28 . 171.45 0I. 78 --. 262.20 --. 612. 85 -- I. 043. 33 -- 1.283. 72 --1. 464.07 --1.724.02 --1.913. 78 --1.873. 24 --1.742. 39 --1.431.35 -- 1. 15 21 -- 1. ll--. 09 --1. O0

80-percent-semispanstation (c 4.20 in.)

Up,per LowerSllri_te_ surface

0. 95 o. 951, 55 591.67 501.86 362. 21 142. 7(; -- 073. 52 -- 314. 19 -- 434.62 -- 485. 22 -- 575. 36 -- 625.12 -- 554.62 -- 193. 88 .092. 91 .361.93 .59 88 .83

100-i)crcen t-semispanstation (c=3.00 in.)

Upper LowerSllrfacc sllrfac('

1. 97 1.972, 50 1.502. 57 1.432. 83 l. 333.20 1. 173. 77 934.56 635. 10 535.60 506. 34 476. 53 536. 40 776.00 1. t35. 36 l, 504.53 2. O03, 70 2. 402, 83 2. 83


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14 TECHNICAL REPORT R--72--NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

(a) Forebody

Fus_,lagestation Radius, in.

0 0 5 t65

1.0 2821.5 3782. 0 ,t602. 5 5403. 0 6123. 5 6804. 0 7434. 5 8065. 0 8625. 5 9176. 0 9696. 5 1. 0157. 0 I. 0627.5 1. 1068.0 1. 1508. 5 1. 1879. 0 1. 2229. 5 1. 257

10. 0 1. 29010, 5 1. 32011. 0 1. 35011.5 1. 38012. 0 1. 40512. 5 1..13013. 0 1. 45213. 5 1. 475

TABLE ITBODY COORDINATES

(t)) Afterbody

Fiist!ag(_station

14.014.515.015.516.016.517.017.518.018.519.019.520. 020. 521.021.522. 523.524. 025. 026. 027. 028. 029. 030. 031.031.7

Radius, in.

Basic body

1. 4931. 512I. 5261. 5401. 552I. 5651. 5751. 5851. 5901. 5981. 6021. 6061. 6061. 6041, 602I. 6001. 5871. 5701. 5601. r_32I. 5011. 4601. 4141. 3641. 3051, 231I. 185

Body indentedfor 3I-- 1.4

1.46 l1..t401.4t01. 3651. 3181. 2701. 2261. 1951. 1101. 1501. 1401. 1401. 1601. 2001. 2501. 2801. 3101. 3351. 3451. 3501. 3501. 3301. 3101. 2711. 2301. 1801. 150

Body indentedfor 3I - 1.0

1. 4701. 4601. 4401. 4001. 3601. 3201. 2601. 2201. 1901. 1701. 1501. 1401. 1401. 1601.2OO1. 25O1. 2991. 3281. 3401. 3501. 3501. 3301. 3101. 2801. 2301. 1801. 151)

US GO VE RN ME NT P m_ NTI NG OF FI CE: I9f _

Documents

Supersonic Area Rule and the Application to the Design of a Wing Body