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NASA TM X-372

TECHNICAL MEMORANDUM

X-572

INVESTIGATION AT MACH NUMBERS OF 0.20 TO 3.50 OF

BLENDED WING-BODY COMBINATIONS OF SONIC DESIGN

WITH DIAMOND,

By George H.

DELTA, AND ARROW PLAN FORMS

Holdaway and Jack A. Mellenthin

Ames Research Center,

Moffett Field, Calif.

NATIONAL AERONAUTICS

WASHINGTON

AND SPACE ADMINISTRATION

A_t 1960Declassified September i, 1961

https://ntrs.nasa.gov/search.jsp?R=19980235518 2020-02-27T05:49:51+00:00Z

NATIONAl. AERONAUTICS AND SPACE AD_Z_NISTRATION

TECHNICAL _MORANDUM X-372

INVESTIGATION AT _CH NUMBERS OF 0.20 TO 3.50 OF

BLENDED WING-BODY COMBINATIONS OF SONIC DESIGN

WITH DIAMOND_ DELTA, AND ARROW PLAN FORMS

By George H. Holdaway and Jack A. Mellenthin

SUMMARY

The models had aspect-ratio-2 diamondj delta_ and arrow wings with

the leading edges s_ept h_.O0 °, _9.04°_ and 70.82 °, respectively. The wing

sections _ere computed by varying the section shape along with the body

radii (blending process) to match the prescribed area distribution and wing

plan form. The wing sections had an average value of maximum thickness

ratio of about 4 percent of the local chords in a streamwise direction.

The models were tested with transition fixed at Reynolds numbers of about

4_000_000 to 9,000_000_ based on the mean aerodynamic chord of the wings.

The effect of varying Reynolds number was checked at both subsonic and

supersonic speeds,

The diamond model vras superior to the other plan forms at transonic

speeds ((L/D)max = ii.00 to 9.52) because of its higher lift-curve slope

and near optimum wave drag due to the blending process. For the _ing

thickness tested _ith the diamond model_ the marked body and wing contour-

ing required for transonic conditions resulted in a large wave-drag penalty

at the higher supersonic Mach numbers where the leading and trailing edges

of the wing were supersonic. Because of the low sweep of the trailing edge

of the delta model_ this configuration was less adaptable to the blending

process. Removing a body bump prescribed by the Mach number 1.00 design

resulted in a good supersonic design. This delta model with i0 percent

less volume was superior to the other plan forms at Mach numbers of 1.55 to

2,35 ((L/D)max = 8.65 to 7.24), but it and the arro_ model were equally

good at Mach numbers of 2.50 to 3.50 ((L/D)ma x _ 6.85 to 6.39). At tran-

sonic speeds the arrow model was inferior because of the reduced lift-curve

slope associated with its increased sweep and also because of the wing base

drag. The wing base-drag coefficients of the arro_ model based on the wing

plan-form area decreased from a peak value of 0.0029 at Mach number 1.55 to

0.0003 at Hach number 3.50.

2

Linear supersonic theory was satisfactory for predictin_ theaerodynamic trends at Machnumbersfrom 1.55 to 3.50 of lift-cu_-ve slope,wave drag, drag due to lift_ aerodynamic-center location, and maximumlift-drag ratios for each of the models.

INTRODUCTION

This report is a continuation of the investigation of a blendeddiamondwing and body combination reportec in reference i. The designmethod has been applied to models with delta and arrow plan forms. Thediamondwing, which is the best structural shape of the zero-taper-ratioplan fo_s, is generally considered to be aerodynamically the poorest,particularly at Machnumber 1.00. This concept was discussed in refer-ence I, which also illustrated how someof the transonic limitations ofthe diamondplan form could be overcome. The purpose of the present inves-tigation was to illustrate with experiment and theory the effects of wingplan-form variation on the aerodynamic performance characteristics ofblended wing-body combinations.

The diamondmodel _as designed with a body, wing sections, and areadistribution which resulted in near optimum zero-lift wave drag at Hachnumber 1.00 and in decreasing wave-drag coefficients for Machnumbersupto 1.20. An interesting feature of the diamond-_ing design was that thecomputedinboard wing sections _ere inderted. Similar analysis of arrowand delta plan forms with the sameover-sll model area distribution as thediamondmodel indicated that equally low wave drag could be obtained atH : 1.00, but there _ould be someincrease in wave-drag coefficient withincreasing Machnumber. Although differ(,nt area curves could have beenselected for the sonic design of the arr(,w and delta models_ the analysisincluded in appendix A indicated that using the samearea curve as selectedfor the diamond model would give essenti_lly the sametransonic wave-dragresorts. Using the samearea distributi,)n for all the models would permitan evaluation of possible plan-form effe:ts at M = 1.00. Eachplan fo=_mhad an aspect ratio of 2, and the complete models _ere designed so thatmost geometric items, such as volume, sp_n, and length, were equal. Thewing sections were computedfrom the sel_cted area distribution by assuminglinear spanwise thickness variation of e_ementsperpendicular to the centerline. The design procedure is described in appendix B of reference i. Theleadini_ edges of the diamond, delta, and arrow wings were swept _5.00°_P9.04°, and 70.os , respectively.

Experiments _¢ereconducted at Machnumbersfrom 0.20 through 3.50 atReynolds numbersbased on the meanaerodynamic chord of roughly 4,000,000to 9,000,000. Also tested at Machnumbersfrom 0.60 to 2.35 was a bodywith the samearea distribution as the design area distribution for thewin6-body combinations. The _ave drag cf the body alone served as areference or a reasonable goal for the ving-body combinations. As a check

on the experimental results 5 theoretical predictions were madeof thefriction drag, zero-lift wave drag, drag due to lift, lift-curve slope,maximumlift-drag ratio_ and aerodynamic-center position of the modelswith wings.

A limited investigation of the effect of sweepon transition of theboundary layer from laminar to turbulent flow _¢asconducted _ith the sub-limation technique to insure that transition was fixed on each model. Adelta model was tested at Machnumber 3.00 and a Reynolds numberper footof 2,000,000, with four different sizes of grit used as a distributedroughness to fix the boundary-layer transition. The tests of the differc _tsizes of grit were madeto evaluate the magnitude of the drag penalty ofthe grit itself above the drag change causedby fixing transition. Theseresults are discussed in appendix B.

NOTATION

A

_b

Awb

AN

&

b

CD

CD i

CL a

CDo

c_

CL

aspect ratio

body base area

wing base area projected on a plane perpendicular to the conven-

tional x axis

area distribution of the approximate New%onion spindle shape (see

fig. 20)

coefficients determining the magnitude of the harmonics of aFourier sine series

semispan

drag coefficient

(All aerodynamic coefficients are based on the total wing area.)

slope of the curve of drag coefficient due to lift versus lift

coefficient squared_ taken at the lift-coefficient data point

nearest to that for 6_ 1\_/\ max

zero-lift drag coefficient

wing or body base drag coefficient

lift coefficient

4

c_

Cm

cR

k

Z

M

N

rl_

R

r

r o

r b

S

t

2

x

Y

x1

c R

lift-curve slope_ per deg

pitching-moment coefficient about body station 34.50 inches_

measured from the body nose_ except that when noted the body

station _as selected to produce lO-percent static margin at

M = 0.60

wing root chord measured along moc[el center line

mean aerodynamic chord of the wings

average height of transition grit based on at least i00 samples

maximum lift-drag ratio

model length

Mach number

total number of harmonics used to compute _CDo or to define anarea distribution

specific term or harmonic used to define an area distribution

Reynolds number

body radius

body maximum radius

body base radius

cross-sectional area

total wing area

wing semithickness

coordinate and body station_ measured from model nose

coordinate measured in a spanwisc direction

aerodynamic-center location_ whe_e xz is the station measured

from leading edge of wing center-line chord

V volume

VVA2

c_

_CD o

ALE

@

volume relative to a Sears-Haack body with minimum wave drag for

given volume and length

angle of attack

4M - 1

zero-lift wave-drag coefficient

roll angle of a cutting plane tangent to a Mach cone as measured

between the z axis and the intersection of the cutting plane

vith the yz plane

angle of wing leading-edge sweep

transformation of the length x to radians, cos-1Q_ - i_

MODELS AND TESTS

The geometric details of the H = 1.00 equivalent body and the three

wing-body combinations are presented in figures i and 2 and in tables I

through IV. The delta model was also tested without a rear_rard body bump

as sho_n in figure l(c) and in table I_ which lists the radii of the body

components of each model. The design area distribution derived in ref-

erence i is presented in figure 3, along with the modified area

distribution for the delta model without the body bump.

The wing coordinates are listed in tables II through IV for the three

plan forms. The wing thickness distributions are illustrated in figure 2

and were computed as described in reference i. The wing thickness in each

case is formed by straight-line elements perpendicular to the model center

line which form triangular spanwise sections as shown in figure 2. Note

that the rear portion of the arrow wing was designed with a blunt trailing

edge_ as suggested in reference 2_ to avoid wing sections with large rear-

ward slopes. For wing sections perpendicular to the body center line,

similar to the one shown in figure 2(c), the trailing-edge thicknesses of

the arrow wing were half the ridge thicknesses, except near the body

juncture_ as shown in table IV. The wing sections had an average value of

maximum thickness of about L percent of the local chords in a stream_ise

direction with greater thickness ratios inboard.

The models were tested at the Ames Research Center in the 12-foot

subsonic pressurized wind tunnel_ the 14-foot transonic wind tunnel and

in the 9- by 7-foot and the 8- by 7-foot supersonic test sections of the

6

Unitary Plan wind tunnel. Photographs of the models are presented in

figures 4(a) through 4(d). The ranges of the test variables in each

facility are show_ in the following table:

Tunnel I Modelsthroat (i)

12-foot 0/_ A

i2-foot A A14-foot A A A

AAAA

AA&A

14-foot

9- by 7-foot

9- by 7-foot

J_- by 7-foot

_i- by 7-foot

@- by 7-foot

$- by 7-foot

_- by 7-1"oot

_- by 7-foot <> &A

B

B

B

M

0.20

0.20

0.500.60 to 0.80

0._0 to 1.20

1.55

1.55 to 2.35

2.50 to 3.00

3.00 to 3.50

3. O0

2.5O to 3.50

3.00

3.50

R/ft

3,000,000

6,000,000

3,OOO_0OO

3,500_000to

4,000,000

4,000,000

4,000,000

3,O00_000

4,000,000

3_000_O00

3,0OO_000

2_000_00C2_O00,00C

2,000_0OC

deg-4 to 26

-4 to 26

-4 to 18

-2 to ii

-2 to

-3 to 6-2 to 12

-2 to 12

-2 to 12

-3 to 13

-3 to 15

-i to 15

Transition

Free

Fixed_ O.040-inch grit

Free and fixed with 4

sizes of grit

One _ing panel free

and the other panelsfixed with different

sizes of grit

iB M = i.OO equivalent body

<_ Diamond model

/k Delta model

• Delta model _Ithout buml0

Arrow model

Three-component aerodynamic forces and moments were measured and

corrected by standard procedures. For the model sizes and shapes_ the

force corrections for blockage and buoyancy were generally believed to

be negligible. Wall interference corrections _ere required for the angle-

of-attack and drag data obtained in the stbsonic wind tunnel_ and these

corrections were based on the theory of r(ference 3. At all Mach numbers,

the drag coefficients were adjusted by selting the body base pressure

equal to free-stream static pressure. A_If aerodynamic coefficients vere

based on the complete plan-form area of tlte wings of @00 square inches.

The pitching-moment coefficients were com],uted about a longitudinal center

34.50 inches rearward from the nose of ea(:h model. This position was

selected for approximately neutral longit_inal stability at moderately

supersonic speeds.

Transition was fixed near the nose of the bodies and near the leading

edge of the wings with distributed roughness composed of grit with an

average height of about 0.040 inch. The grit was located 1.13 inches

rearward of the wing leading edges (upper and lower surfaces) and of the

body nose in a streamwise direction so that a laminar-flow area of only

5 percent of the wlng area was allowed. A grit location farther rearward

could have been used at the higher supersonic Mach numbers; ho_ever_

natural transition would have occurred ahead of the grit location at

transonic speeds. The selection of the grit size was based on tests of

the diamond wing reported in reference i. The diamond wing with the

least sweep was considered to be the most difficult to fix transition on_

so the same grit is certainly larger than necessary for the other plan

forms. Subsequent to the tests with the diamond model_ the $- by 7-foot

test section was limited to lower Reynolds numbers; so additional tests_

reported in appendix B_ were made to check the performance of the grit in

fixing transition on each wing and to determine the drag penaltyattributable to the grit.

RESULTS

The basic test data are presented in figures 5 through i0. Notice

that the data from the subsonic wind tunnel are plotted to a coarser scale

than the rest of the data because of the greater angle-of-attack range.

For this reason_ and in order to illustrate the slight effects of doubling

the Reynolds number_ the data obtained on the three basic models havingdifferent plan forms at M = 0.20 are listed in table V. The delta model

was tested at transonic speeds both with and w!thout the rearward bump on

the body_ however_ only the basic data for the delta model as designed for

M = 1.00 (with the body bump) are presented at transonic speeds (fig. 6).

At supersonic speeds the delta model was tested only without the bump as

indicated by the results in figures 7 and $. A comparison at transonic

speeds between the delta models with and without the bump will be brieflydiscussed relative to cross plots of the data and will be considered in

more detail in appendix A. At supersonic speeds the effect of Reynolds

number is illustrated only for the delta model without bump and the arrow

model (figs. 7(d) and 7(e) at M = 1.55 and figs. $(d) and $(e) at

M = 3.00)_ because the Reynolds number effects on the diamond model data

have been reported in reference i. The M = 1.00 equivalent body was

tested over a small angle-of-attack range to clearly define the zero-lift

drag coefficients which are presented in figure 9.

Figure i0 shows how the wing-base-pressure coefficients for the arrow

model varied _th spanwise position and Mach number. Body-base pressures

were measured for each model and were used to correct the drag data. The

body-pressure coefficients shown in figure i0 for the arrow model are

representative of the values obtained for each model.

Cross plots of the various aerodynamic parameters with Machnumberwill be presented when discussed in the following sections of the report.Figure ii is presented in order to summari_ethe differences in testReynolds numberswith Machnumber. Note t_at for Machnumbersabove 2.50the diamond model was generally tested at _igher Reynolds numbersthanthe other models; however, the effects of this Reynolds numberdifferencewere not very large, as maybe seen in figures 8(d) and 8(e).

DISCUSSION

In general, the discussion will makecomparisons between theexperimental results for the three models cf different plan form andbetween supersonic linear theory and experiment for each plan form. Thedelta model without the rearward body bumpis used for the comparisonsbetweenplan forms, because the body bumprequired for the sonic designwas too blunt to be treated by linear theory at supersonic speeds. Thisproblem is discussed more fully in appendi_ A, which contains an evalua-tion of the transonic zero-lift wave drag _elative to the design concepts.Except for the subsonic data from M = 0.2C to M = 0.50j the results dis-cussed are for transition fixed and have net been corrected for the dragpenalty which can be attributed to the gril. Appendix B presents ananalysis of theoretical and experimental results of the effect of the gritused to fix transition_ at M = 3.00. The analysis indicated a gritpenalty in CDo of 0.0003 separate from a_d above the effect of fixingtransition. The wave drag due to the grit appeared to be negligible.

The following discussion has two main divisions: the first part isan analysis of the zero-lift wave and base drags, and the second is ananalysis of the other basic aerodynamic tr(nds with Machnumber. Thearrow-model data contain the wing base drawl.

Zero-Lift Waveand Ba_e Drags

The zero-lift wave-drag coefficients for the three wing plan formsand the M = 1.00 equivalent body at Mach lumbers from 0.60 to 3.50 arepresented in figure 12. The theoretical w_e-drag coefficients were com-puted with the procedures of reference 4_ _d 49 harmonics were used todefine the derivative of the model area distributions. The variation ofthe body area distribution with Machnumber, used in the theoretical com-putations, was based on method i described in reference i.

The experimental zero-lift wave-drag coefficients (fig. 12(b)) _eredetermined from the basic data by removing the friction-drag coefficients.The friction-drag coefficients were assume<to be equal to the zero-liftdrag coefficient at M = 0.60 and were adjltsted at each Machnumberto

accom_t for the variation with Machnumberof the friction-drag coefficientfor fully turbulent flow over a smooth surface. This procedure was dis-cussed and justified in reference i. For the test models, the smallregions of laminar flow and of turbulent flow over a rough surface hadsmall and compensating effects relative to the variation in friction-dragcoefficient with Machnumber. The friction-drag coefficients used todetermine the wave-drag coefficients were also corrected for variationsin Reynolds number. The latter correction was not madefor the resultspresented in reference i_ because the variations in Reynolds numberwerenot as great in that case. The experimental results of figure 12(b) showedthat the diamondmodel had the lowest wave-drag coefficient at transonicspeedswith values which matched the H = 1.00 equivalent body data; thediamondmodel had higher wave drag than the other models at Machnumbersabove 1.7.

The comparison between theory and experiment can be more clearlydemonstrated by considering each model separately (see fig. 13). For thesimple body, the 49-harmonic solution is larger than the experimentalresults at supersonic speeds, although the variation with Machnumber issimilar. The diamondmodel data (fig. 13(b)) have been discussed previ-ously in reference i and are repeated here with the slight Reynolds numbercorrection used for all the data presented in this report. The reductionin wave-drag coefficient shownfor the computation identified as method 2(discussed in ref. i) would be less for the smoother body of the arrowmodel and almost negligible for the delta model without bump. In general_the experimental wave-drag coefficients for the three plan forms investi-gated are lower than the theoretical wave-drag coefficients near sonicwing-edge conditions. The one exception is for the delta model, whichhad perfect agreement between theory and experiment at sonic leading-edgeconditions. Note in this case that the theory did not indicate a wave-drag peak at sonic leading-edge conditions, and thus this better agreementbetween theory and experiment for the delta model is reasonable. As wasdiscussed in reference i_ the higher wave-drag coefficients for the diamondmodel at the higher Machnumbersare a result of the marked body and wingcontouring required for transonic conditions.

The experimental wave-drag coefficients shownfor the arrow model infigure 13(d) include the wing base-drag coefficient. The agreementbetweentheory and experiment sho_n at the intermediate supersonic Machnumberswould be poorer if the variation with Machnumberof wing base drag wereintroduced. The theory used to compute the wave-drag coefficients doesnot include viscous effects. The zero-lift base-drag coefficients for thewing and body bases of the arrow model, as determined by experiment andempirical predictions based on reference 5_ are presented in figure ik.The body base-drag coefficients include an effect of the sting_ so thecomparison madewith the analysis of reference 5 is only qualitative. Thebody base-drag coefficients are representative of the values for the othermodels. The _ing base-drag coefficients of the arrow model_ based on thewing plan-form area_ decreased from a peak value of 0.0029 at Machnumber

i0

1.55 to 0.0003 at Hach number3.50. The two-dimensional analysis ofreference 5 did not represent the three-dimensional results at transonicspeeds, but could be used to obtain slightl_ conservative predictions forMachnumbersabove 1.60. The individual pro ssure measurementsat differentlocations on the wing base varied as shown_y the basic pressure coeffi-cients in figure i0. The greatest different es in wing-base pressurecoefficients occurred where these coefficients were the greatest_ that is,from Machnumbers1.55 to 2.35.

Aerodynamic Trends With M_chNumber

Summaryplots of experimental values o _ maximumlift-drag ratio_lift-curve slope_ drag due to lift, and aer,_dynamic-center location arepresented in figure 15 for the three models of different plan form. Itshould be noted that the delta model withou_ the rearward body bump, usedfor the comparison between plan forms at s_0ersonic speeds_had about lO-percent less volume than the other models. Themodel with the greatestmaximumlift-drag ratio or the greatest lifZ-curve slope generally v_asthe one with the lowest zero-lift wave-drag coefficients. At transonicspeeds the diamond model was superior ((L/D)max -- ii.00 to 9.52); at theintezvaediate supersonic Machnumbersthe delta model without bumpwassuperior ((L/D)max = 8.65 to 7.24); at Machnumbers from 2.50 to 3.50 thedifference between models was not very great and the delta model withoutbumpand the arrow model were equally good ((L/D)max _ 6.$5 to 6.39).With an increase in Reynolds number_the maximumlift-drag ratios wouldbe increased_ as maybe determined from thc exampleplots presented infigures 7(d) and 7(e). For instance, in figure 7(d), which showstheleast effect, the increase in Reynolds numkerper foot from 3,000_000 to4_000,000_ for the delta model without bum_, resttlted in an increase in(L/D)max from $.69 to 8._6 (M = 1.55). T_e effect of zero-lift drag onthe maximumlift-drag ratio is as importan_ as the drag due to lift andshould be kept in mind whenone comparest_e data presented in figures 15(a)and 15(c). For Machnumbersfrom 2.50 to _.50, the arrow model, relativeto the delta model without bump, clearly h_s the lower values of drag dueto lift. However_at M = 3._0 an increas_ in zero-lift drag coefficient_from 0.0075 for the delta model without b_ to 0.0082 for the arrow model_was enoughto cancel a possible benefit in maximumlift-drag ratio due toa decrease in CDi/CL2 from 0.$13 to 0.72_. Less than half of the aboveincrease in zero-lift drag coefficient of (_.0007 (that is, 0.0003) couldbe attributed to the arrow wing-base drag_ but the remaining difference issmall relative to possible cumulative expe:'imental errors. These dataindicate that the effects of the plan-form variation considered are smallat Machnumbersabove 2.50_ and that the model with the lowest zero-liftdrag coefficients would probably have the _lighest values of maximumlift-drag ratio. The zero-lift wave drag of ea.:h of the test models could beimproved if specifically designed for the higher supersonic Machnumbers;however_ the greatest potential improvemen_exists for the model with the

ii

diamondwing which structurally could be madethinner than the other planforms. With transition free, the wing with the least sweepwould also havepotentially the greatest amount of laminar flow, as shownin appendix B,and thus lo_¢er friction drag.

The variation in aerodynamic-center location with Machnumber_assho_a_in figure 15(d), occurred primarily at transonic speeds, was notunduly large for any of the models, and was greatest for the diamond model.

The utility of supersonic linear theory in predicting the trends inthe aerodynamic parameters is demonstrated in figures 16 and 17 for thedelta model without bumpand the arrow model, respectively. Theoreticalcomparisons with experimental results were presented and discussed inreference i for the diamondmodel and will not be repeated here. Thetheoretical results presented in figures 16 and 17 were computedin thesamemanner as in reference i_ and, except for the friction and wavedrags required in computing the maximumlift-drag ratios, the theoreticalresults were computedfrom equations available in reference 6 or 7. Thetheory used assumedno wing leading-edge suction and no arrow-wins basedrag. Theoretical estimates of wing leading-edge thrust are consideredin later figures. The agreement shownin figures 16 and 17 betweentheory and experiment and between test facilities was considered to besatisfactory, because the differences shownare generally of the sameorder of magnitude as the slight nonlinearities in the basic data. Forinstance, the large difference in the trend of the lift-curve slopes forthe arrow model (fig. i7(b)) between the highest transonic data and theH = i._5 data obtained in the 9- by 7-foot test section occurred nearzero lift where the slopes were measured. At angles of attack of 2° or3° the lift-curve slopes for the arrow model are about the sameattransonic speeds as at M = 1.55. As was the case in reference !, theexperimental lift-curve slopes obtained in the 9- by 7-foot test sectionwere consistently higher than those of the theory.

Somewing leading-edge thrust is indicated in figures 16(c) and iT(c),because the experimental values of CDi/CL2 are lower than the theoreticalvalues based on no-leading-edge thrust. However, only a small amoun.tofthe theoretically possible leading-edge thrust was obtained for the arrowmodel. Figure i$ presents the theoretical values of the drag-due-to-liftparameter, CDi/DLa, with and without leading-edge thrust, as a function of_, for flat-plate wings of the three plan forms investigated. From super-sonic theory alone and assuming almost full leading-edge thrust_ one mightconclude that the arrow model would be superior at all MachnumbersandCDi/CL2 would approach the minimumvortex drag due to lift or a value ofI/_A at _ : 0 (or H = 1.00), as plotted in figure i$. The linearizedtheory used for computing the leading-edge thrust was developed in refer-ence 6, which states that no entirely satisfactory theory for this effecthas been developed. Thus, if one assumeslittle leading-edge thrust, thearro_ model vrould only be superior at the highest Machnumbersand there

12

only slightly superior. The experimental r_sults (fig. 19) indicatedthat there was little leading-edge thrust. Although the arrow model hadsomeleading-edge thrust at the lower value_ of _, it had a drag-due-to-lift part,meter as high as or higher than that for the other models atvalues of _ lower than 2.0.

CONCLUDING_3

The following statements apply to blenled wing-body combinations astested with transition fixed by distributed roughness.

The diamondmodel was superior to the other plan forms at transonicspeeds ((L/D)max = ii.00 to 9.52) because of its higher lift-curve slopeand near optimumwave drag due to the blending process. For the wingthickness tested with the diamondmodel_ th_ marked body and wing contour-ing required for transonic conditions resulted in a large wave-drag penaltyat the higher supersonic Machnumberswhere the leading and trailing edgesof the wing were supersonic. Possible advantages in supersonic zero-liftdrag are significant for the diamondmodei; because its structural rigiditywill permit a thinner wing section and its low relative sweepis favorableto laminar boundary-layer flow.

The delta model was less adaptable to the blending process because ofthe low sweepof the trailing edge. Removinga body bump, prescribed bythe Machnumber1.00 design_ resulted in a good supersonic design. The10-percent less body volume madeit superior to the other plan forms atMachnumbersof 1.55 to 2.35 ((L/D)max = 8.65 to 7.24). This delta modeland the arrow model were equally good at Msch numbersof 2._0 to 3.50((L/D)max _ 6.65 to 6.39).

At transonic speeds the arrow model was inferior because of thereduced lift-curve slope associated with i_s increased sweepand alsobecause of the wing base drag. The wing b_se-drag coefficients of thearrow model_ based on the wing plan-form a_ea, decreased from a peak valueof 0.0029 at Machnumber1.55 to 0.0003 at Machnumber3.50.

Linear supersonic theory was satisfac_ ory for predicting theaerodynamic trends at Machnumbersfrom i._ 5 to 3.50 of lift-curve slope,wave drag_ drag due to lift_ aerodynamic-center location, and maximumlift-drag ratios.

There was no apparent sweepeffect on the wave drag of the sharp-leading-edged wings at Machnumber1.00.

AmesResearch CenterNational Aeronautics and SpaceAdministration

Hoffett Field; Calif., March 23, 1960

13

APPENDIXA

EVALUATIONOFTRANSONICDATARELATI-V-ETOSONICDESIGN

The design area curve (fig. 3) was selected primarily for the diamondplan form as discussed in reference i (to seek a low wave drag at M = 1.00which was consistent with a decreasing supersonic wave-drag coefficient).This design curve is a modification (N = 25 fit of the derivative) of thepeak-shaped area curve presented in the upper left-hand corner of figure 20.Of the area curves considered in the preliminary analysis (fig. 20) thispeak type of area curve was also best for the delta plan form at transonicspeeds (_ cos @= 0 to 0.6633) and almost best for the arrow plan form asshownin table VI. In any case, it was decided to use the samearea curvefor each plan form so that a direct comparison could be madeof the effectof sweepon zero-lift wave drag at Machnumber i.O0.

Data points of transonic zero-lift wave-drag coefficients are plottedin figure 21 to showclearly howwell the diamond and arrow models matchedthe equivalent body at Machnumbernear one. Therefore_ there is no appar-ent sweepeffect on the wave drag of sharp-leading-edged wings at Machnumber one.

The higher wave drag of the delta model at Machnumber 1.00 was notpredicted by theory_ because all models had identical cross-sectionalarea distributions. This model illustrates that an area distribution madeup of a wing arid a body which individually have large slopes in area dis-tribution can result in wave drag greater than that for the equivalentbody. For the delta-type wing the problem is primarily confined to tran-sonic speeds and is a result of the low sweepof the wing trailing edge.The sonic design contour for the body of this delta model resulted in alarge body bumpwhich caused an increased thickening of the boundary layer,as indicated by the surface flow lines in figure 22. The fluorescent-oilfilm method used for the surface flow study is described in reference 9.The increased boundary-layer thickness would result in an effectiveincrease in the bumpsize over that prescribed by the design and thus inhigher wave drag. Removingthe entire bump_as indicated by the bodyradii of table I_ resulted in an increase in the drag coefficients nearMachnumber1.00, as shownin figure 23_ and a reduction in wave-dragcoefficient for Machnumber1.20.

The theoretical zero-lift wave-drag coefficients of the various wingedmodels at transonic speedsare comparedwith experimental results in fig-ure 24. The predictions for the diamondand arrow models are very goodfor 25 harmonics as well as for 49. The previously discussed problemswith the delta model affected the theoretical results as well. The deltamodel_ with the body bumpof sonic design_ obviously violated the slender-ness limitations for the theory_ as indicated by the poor wave-drag

14

coefficient predictions. _ithout the bump, the low sweep of the trailing

edge of the delta wing is responsible for nhe high wave drag and poor

predictions at Mach number 1.00. Also note that the use of the higher

number of harmonics for both of the delta models generally results in

poorer agreement _ith experiment. The _redictions for the delta model

_ithout the bump were satisfactory for Mac_ numbers above 1.20_ as show_

previously in figure 13(c).

The inferior aerodynamic characteristics of the arrow model at

transonic speeds were analyzed to insure that the reductions in maximum

lift-drag ratio were primarily due to the increased sweep (reduction in

lift-curve slope) and not due to the wing 0ase drag or to separated flow.

The effect of the w_ng base drag on the maximum lift-drag ratios at tran-

sonic speeds was not large relative to the differences between models_ as

shown in figure 25. The possibility that the arrow wing had separated

flow was investigated w_th the fluorescent-oil technique of reference 9.

At low lift coefficients representative of the maximum lift-drag ratios

there were no visible regions of separated flow_ and the surface flow was

uniform in a stream_ise direction. At an_les of attack greater than 4°

there was a faint indication of a leading-edge vortex amd a small

separated-flow region near the trailing e@ge of the arrow wing. The small

separated-flow region increased with angl_ of attack to that shown in

figure 26 for ii ° (M = 0.70). The separaled region may be identified by

the accumulation of oil which appears as a short curved line near the wing

trailing edge.

15

APPENDIX B

DRAG DUE TO THE GRIT USED TO FIX TRANSITION

Lift and drag coefficients for the delta model w!thout btnmp, w_th

transition free and fixed at Mach number 3.00 and a Reynolds number per

foot of 2,000,000_ are presented in figure 27. Runs with transition fixed

on the w_ng and body were made with four sizes of grit with average heights_

in inches, of 0.016_ 0.040, 0.062, and 0.089. The grit was located, as for

the basic investigation, 1.13 inches rearward of the wing leading edges

(upper and lower surfaces) and of the body nose in a streamwlse direction.

The drag due to lift for the transition-free run (figure 27) was greater

than the theoretical value of CDo + C L tan _ and corresponding values of

drag due to lift with transition fixed. This result was probably due to a

forward movement of natural transition (primarily noted on the lower sur-

face from sublimation pictures taken at (L/D)max) with an increase in angle

of attack. At lift coefficients above 0.30 the reason for the drag

coefficients of the model with the O.040-inch grit being lower than those

for the transition-free model is not known; however_ for the one run with

the O.040-inch grit, the model mountin_ holes were filled a little more

smoothly (painted and sanded condition as used for the results presented

in the body of the report). For the other runs presented in figure 27the holes were filled with wax.

The O.Ol6-inch grit did not quite fix transition at M = 3.00 and

definitely did not fix transition at M = 3.50, as show_ in figure 26

(R/ft = 2,000,000). Otherwise the larger grit (0.040 in. or greater)

fixed transition at the grit for all test Mach numbers and Reynolds num-

bers. Figure 28 also shows that there was a decrease in the length of the

laminar boundary-layer flow with increase in wing leading-edge sweep. For

each wing the white lines are spaced three inches apart in a stream_ise

direction. The most forward line shown in most of the photographs is where

the grit was located 1.13 inches from the wing leading edge in a stresmu_ise

direction.

The zero-lift data of figure 27 are plotted in figure 29 to show the

effect of grit size on the zero-lift drag coefficients of the delta model

without bump_ as determined by experiment and theory (M = 3.00,

R/ft = 2,000,000). The theoretical friction-drag coefficients were com-

puted by procedures discussed in reference i. The average length of the

laminar-flow region, used for the transition-free theoretical point, was

estimated from photographs of sublimation material to be 6 inches_ or

somewhat less than the higher Mach number pattern sho_n in figure 28.

The theoretical effect of fixing transition was computed at zero grit

size as the change from partially laminar flow over a smooth surface to

completely turbulent flow (rearward of the 1.13-in. station). The lack of

agreement between the theoretical and experimental drag coefficients shown

16

in figure 29 for zero grit size may be attrLbuted to errors in the

theoretical wave drag; however_ the experimental model may not have been

theoretically smooth. The important featur_ of figure 29 is that the

e_erimental increase in zero-lift drag wit _ increasing grit size was

predicted by a theory (M = O) which did not include the possibility of

wave drag attributable to the grit. Thus, the wave drag of the grit was

apparently negligible. The theoretical slooe of figure 29 (which involves

the average grit size squared) was extrapol_ted through the experimental

data points to zero grit size, which would _ive an indication of the

experimental zero-lift drag coefficient with transition fixed but without

grit. With this point as a reference_ the drag coefficient penalty of the

O.040-inch grit was 0.0003. Thus, the drag coefficients presented in this

report are high by an amount of at least O.DO03 (the theoretical penalty

of the O.040-inch grit was 0.0010) because _f the grit used to fix

transition.

17

REFERENCES

It

_e

So

B

5_

.

.

.

o

Holda_ay, George H._ Mellenthin, Jack A., and Hatfield, Elaine.W.:

Investigation at Mach Numbers of 0.20 to 3.50 of a Blended Diamond

Wing and Body Combination of Sonic Design but With Low Wave-Drag

Increase With Increasing Mach Number. NASA TM X-lOS, 1959.

Chapman_ Dean R.: Reduction of Profile Drag at Supersonic Velocities

by the Use of Airfoil Sections Having a Blunt Trailing Edge. NACA

TN 3503, 195_.

Glauert, H.: The Elements of Aerofoil and Airscre_ Theory. Cambridge

Univ. Press, 1937.

Holdaway_ George H._ and Mersman, William A.: Application of Tchebichef

Fo_m of Harmonic Analysis to the Calculation of Zero-Lift Wave Drag

of Wing-Body-Tail Combinations. NACARMA55J28_ 1956.

Love, Eugene S.: Base Pressure at Supersonic Speeds on _o-Dimensional

Airfoils and on Bodies of Revolution With and Without Fins Having

Turbulent BoumdaryLayers. NACA TN 3819_ 1957.

Puckett_ A. E., and Ste_art_ H. J.: Aerodynamic Performance of Delta

Wings at Supersonic Speeds. Jour. Aero. Sci._ vol. 14_ no. i0,

Oct. 1947, pp. 567-575-

Donovan_ A. F._ and Lawrence_ H. R.: Aerodynamic Components of Air-

craft at High Speeds. Princeton Univ. Press_ 1957. (High Speed

Aerodynamics and Jet Propulsion, vol. VII, pp. i00, 197-226)

Sears_ William R.: On Projectiles of Minimum Wave Drag. Quart. Appl.

Math., vol. IV, no. 4, Jan. 1947, pp. 361-366.

Loving_ Donald L._ and Katzoff, S.: The Fluorescent-Oil Film Method

and Other Techniques for Boundary-Layer Flow Visualization. _ASA

MEMO 3-17-59L, 1959.

18

M = 1.C0

._quivalent bod_

x I r

0 I0

•3i9 i .075

.75o .Ik_ I1. >c< ._>_!a.e'cl .390].coo I ,_L9].SC'] ,'_4aa,.::co I .6±35.2.-0 I ..q93

6.CC:< I .71 1

. ,%0 ! . 5O l

E'.>Oc I .905

_ .2.0 .;)(i9.c_I:.oul

TABLE I.- COORDINATES FOR B(DIES; INCHES

Disamnd

model

Delta model

with bump

r x

Same as

delta model

with rear-

_ard body

tlm_

r x

3.150 --

t.O¢O

4.:CO

5 -_,00

<'.-%0

7,2c<)

, ",OC

).7[,0 I I.ii_

ic.5oo I 1.179

ll .aSol 1.-_3#-_L£.000 J 1.2 }e,

12.','b0 I I-3_3

12._> [ i. Sk:,

_3 p _Ir£[ . I 1 . _5 )

14.6< I 1._o9 Il>.g£ I _.>yo I

le.: i_ 1.6%5

1L'. CO I i. 7,'3

i_.OCO I 1,'>z

1!a, OOC: 1,<23 } 1.56019. i't: 1.95 19.5K0 -- --

Blended20.'2 I 1.0_, I tC.O_ !.?t'4

ll.J(t _ .000 E!.C'@] body 1.325

22.12', a.Oq4 22,000 _ 1.712o_ ._[ _. i;_! _4.000 1.47124.3 : £.2 i 14.:C:C 1.392

2!).125 2.2Ab 2t,oCC i .3h7

£i; .c_3, _.374 26.400 yon K&cm_-_n 1.SbC

2/-3 f5 _.1_2'8' _'J.COC oglve (2) 1.409

2: .12:: d.g¢4 29.t:00 1.44724. :2: -".h >> _;:.200: 1. I_:::7

3C.3 '_ I i.tC5 I 4±.@0 1.722

5l.l_[ I

js.<sp

33.37'

34.125

3 >.f_': i

40;.3 i'[

3 £. 5oc;

J" .ud5

39. J t'9

40.12}:

41.<2[

%. ie _ i

g4 g I

£, . iz'

4r. i%

4 f .t2_

L: ,0C,0 i

_!. ,t

L9. p

_C. (-i

51.J 'h

_2. 2b

5J.r25

94.j[9

%' _'. J: C

p (. _ OC,

57.9oo

54.2OO

b}.50C

5::'. <,0

59.1oo

_9 400

54.7o3

6C.0oc I

2._ 54

.O73

-977

_.94

_.oco

.9,4

-< 9S 7

_.:20

a. P4

.7u9

2 r(_

a. 555

d .9C').4i,4

._C

.400

2.37 k

2.320

._21

2. ii0

2 .C-A

2.000

1.9g

l.d�o, eT,

!. 747

1. TS

1.709

i. O92

1._77

1._ 42

i.( 4 9

l.<J7

1.529

I.{_S

.3J - i _00

3a. 4oo39.2CO

36.08¢

36 .e_

3 r. gCC

49.S O01_. COC --

1-539

zc,>a

1.909

1.594

1.6o51.614

l.viil

Cylinder

I51.0oo---- 1.625

52.0OO Blended 1.657

b3.OO0 body 1.730

I i.tJ271.7

---- I.J6C

(0

I

lO.tJ_3 -- 1.190

11.@0 [i ed 1.210

12.000 1.216

1_._ 1.099

h 057

15 - _0 1.0!9

16 • O_ 1.035i.o£616.8oo

van K_n

ldN_O0 opiw, (u)

20.000 1.140

_o._oo i.17_21. 600 i, 20!

23. 200

24. dOO !.3!i i

26.400 w. Jot' I

28i O@ l i" _5 ]

29.(:0C I Z._: I

jl.200 i._ [ !

32''!00 I i ._,Zi '

_3.6oo [ i .549

3_.4co 2 .pp4 i3>.aOC 1.5'39

36.000 !.5;_ [

5 .':oo . ] O941

37.600 | 1.60b

3!! "1_C</ 1 ] .g1439.20% 1.0-'i

_O.OOO- I.!_S5

Cy,[ '- nd,-, r

4_--033 --_-- i.625

43.O9c !tien_ed 1-993

44. OCK: body 2.206

47.coo 2.4j4a.47. sgi

(9

aO* 00 --

54.;co55 " )_l

56. )co

_7. >00

;'7. _co --

Cy 11 nde r

-- 1.6e5Fillet !.637

i.£,,_i. L,!!I

1.711

-- I. i'_s

(H

1

i0. ikOC

IS. 002

!4.600

15. -'--oc,

ii.800

1:!. 400

19.10C

2C. OCt

20. ,CC:

21._00

d3. 200_4. CO

2_ .4oo

2,:. sOO

_[).{ COl

31. L!CC

32.:00

J 3 - ¢CO

j_, .2jC ----

3 '' 1 8(_

57. SGi

3 hlSqC

3 9. ¢1£<,

_'3. 'ClO C'

40. R'_D

kl. C_C:

41.932

4_. 3<C

4_ .qC©

4[;. 013'0

47" &t;O

_9.COO

51l 0_:

55. OOC

56 .coo

5 Y • CICG

57.50l I

i> _,.{.co

model

Wing

alone

-- 0.3!1

van K4rm_:: • j t'l

og_,.,_ (a) .4::4.474

• t'.':%o

.<5'

-739

•<:1(

• 90 I

.9i;0 P

1.02i:

] . Ci:,9

1 ,i16

i. I£ a

1.17

!.Re:t)

1,2iC l

1.ill

1.5_t I

i. 40_

,h4_

kli' l J:) I

!,L}Ji

i. _, t'( [

!_lended 1.!20 IBOast " 1.( ,(]0

!. :iS

i. 705

1.,']5

I.','_Il.fj) I

!./51

] .'!'/6 I

i.:'21

i. 90':

1 i l?'[5

?.Oll

2.cooI

1042

1.:!7; I

1. '2%, 1

1 .[i7

] .7j;2

-- ]. [2q:

O)

isaac as M = l.OO eq'_Ivalent hod Z

apart of a von K_L,_n o<ive (_ = 40 in. and Dj :: 1.024 In.)

19

o

17.5oo o

18.ooo .47o

18.5oo .685

19.ooo .525

19.500 .926 020.000 1.01020.500 1.047

21.000 1.070

21.5o0 i._9

22.0oo 1.098

23.000 l._q6

24.000 1.050

25.000 .996

25.500

26.000 .925

27.000 ._,}8

2_•000 •799

29.000 .795

29•500

30.000 .724

31.000 .7O2

31.900

32•ooo •68533.000 .677

33.50034.0OO •670

35.000 .661

35.5oo36.000 .640

36.500

37.000 .612

37.900 .594

38•OOO .6103_•5oo

39.000 .631

39.500

40.000 .643

41.ooo •649

41.5oo

42.000 .65o

43.0oo .649

43.500

44.0oo .655

45.000 .667

45.500

46•ooo •&_347.000 .710

48.000 .744

49.000 .757

49.500

50.000 .845

51.000 .924

51•500 .970

52.000 1.020

52.500 1.002

53.000 1.061

93.500 1.069

54.000 1.060

54.500 1.045

55.000 1.011

55.500 .942 o

56.000 ._142

56.5oo •712

57.0oo .50o

57.5oo o

TABLE If.- COORDINATES FOR DIAMOND WING, INCHES

Semithickness_ ±t/2

±2.000 ±4.000] ±6.667 ±8]000t±1£.00C ±15-335 ±14.000 ±16.000 ±lS.O00 ±19.000]±20.00C

I

o.054

.135

•19o

.230

o

.261 .o29 3o.833:0

.286 .o7i_

o

•307 •1_!] •055 .024

•328 .153 .066

0

•345 .183 •129 .102 .020

•359 .208 .132 .057

•363 .225 .179 •156 .0°6

•361 -235 .173 .iio

•356 .236 .196 .17q •119

•360 .235 .172 •1o9

•358 •222 .176 .153 .o95

•349 .202 .129 •095

•386 .334 .177 •124 .o98 •020

0

•315 .147 .063

•351 .291 .112 .052 .022o

•267 .o73 44.167=o

•311 .240 .027

o

.208

•259 •169

•117

.17o •01+6

50 •8.33=0 o

.202

.349

.459

•545 o.6101 .122

•691 .296

•727 .404 24.167=0

•730 .465

•707 .490 .199

•677 .496

•647 .495 .292

.624 .492

.6_ .492 •338

•598 .494

•591 •496 .370

•99o .5o2

•559 .5_3 .399

•585 .51o

•571 .5o2 .4o9

.549 .486

•539 .479 .396

•547 .45_

•563 .495 .404

•569 .496

•570 .492

.566 .482

•560 .47o

•5_8 .461

•560 .454

.564 .445

•_75 .440

•587 .431

•602 .417

.620 .394

.640 .396

•647 -323

•649 .27_

•629 .210

•59o .llS

•533 0

•4_4

.348

.202

0

•o17

o

.o47 .Ol,

•o57 .o3o

.047 .o16

o

• 01,'0

2O

TABLE III.- COORDINATES FOR DF_LTA WING, INCHES

x_ o +2.000

_. 7oo o

9•ooo •54o

9• 500 •'F_

lO•Coo .635lO.60o •92o

II• 000 •955

11•5oo •987

12•0oo i.oo0 12.o33=o

!2•500 1.000 .123

15•o0o I.OO0 .225

13.500 .992 •303

14.000 .960 •363

14. 500 •966 .411

15 .ooo .945 •447

15 •500 •930 •474

16 .O00 •910 •495

16.500 .b8 •5O8

17•000 .867 .519

17.500 •c_44 .525

IS •000 .122 •526

i_•5oo •_oo .525

19•000 •760 .528

19.5o0 .765 •529

2o.000 .753 •931

21.o0o .735 .536

_. oo0 •723 •542

25 •ooo .723 •554

24.ooo .721 •564

25.ooo .'(19 .572

26•oo0 .715 .577

27. ooo .71o .5s1

25.o0o •7o6 •564

29•ooo I .7o4 .5S630.000 _ •704 •594

31.OO0 •707 •601

32. O00 •716 .613

33 .O00 .730 •630

34•000 .739 •642

35 .O00 •742 .645

36.000 •739 .6£9

37.000 .721 •636

37.500 .706 •625

35 .ooo .688 .61o

39.0oo •643 •973

40•000 •593 •530

41.ooo •535 .450

41.5oo .5o6 •455

42.033 .47h .427

42.500 •439 •392

43. ooo •Aoo -353

43 •500 •365 .3ik-]

44.000 •332 .2_4

44.5oo •295 •248

45 .ooo .261 •214

45.500 .225 •17t_

46. ooo .191 .144

46.500 .155 .]_o8

47• ooo _ •12o •073

47.500 .o63 •037

46.ooo •o5o .oo2

45.500 •008 49,.033=0

40•70o 0

Semlthlckness _ +±/2

15 •922=-O

•O10

.066

.113

•Z51•i_4

•211

•233

.254

•272

•303

•330

•358

•381

•400

•416

•430

•442

.454

.465

•478

•494

•513

•52'_

•53_

.544

•537

•529

.5_!}

•490

•456

•4i5

•395

.371

.337

.299

.264

•230

.194

.159

• 123•089

•053

•o16

47. 256=0

±6.667

19 ._{ii=o,

.012 ,

• o7i i•ii9.i61

•197

.229

•256

•279

•300

•319

.337

.355

•374

.396

•414

•429

• 450.43d

•434

•427

.4O7

.3_3

.351

.335

•316

.2_2

•244

•209

•175

•139•1o4

.o69

•o3446. 478:C

±!0.000

25.367=O

•o26

•063

•096

•126

•153

•179•204

.229

•252

• 272•258

.296

•297.297

•289

•277

• 259•249

•237

•203

• 166

.131

.097

.061

•026

45 •367=0

±13.333

30.922=0

•002

.033

.062

•090

.m15

• 13,'3

•155•162

.166

•172

.172

•167

.163

.158

•Z24

.08_

.053

.01_

44. 296=0

±26.667

.o13

•025

.o36

•054

.o67

•075

•077

•079.046

•olo

43.144=-o

21

TABLE I-_.- COORDINATES FOR ARROW WING; INCHES

x'-£O•000

•500

i. OOO

1•5oo2. 000

2.900

3 •000

3 •500

4.0oo

4.5oo5.ooo5•5005.75o6.ooo6•5oo7.ooo7.5oo8 • 000

9• oo0

i0.0o0

ii. 000

12.000

12. 497

i3• ooo14 •ooo

1_ •ooo16. ooo

17. o0o

z7.50013•ooo18•5oo19. ooo

19.16719•90020. 000

21. 000

22•000

23.000

24.ooo25.ooo26.000

27.000

28.000

28• 750

29.000

30.000

31.000

32•0OO33.00033 •333

34. 000

34• 500

35.ooo39 •_3o35.75036.ooo

36.5oo

iRidge

0

O. 000

.O_ 6

•171.2o7.237•270.3o4.337

•360

•380•395

.402

•408•414

•426

•443-467•505.534

•552•567

•957•61o

.64o

•669

•696

•704

•71_•7z_

•725.731

.746•764

•7_9

•824•833

.852

.864

-677

•590

•906

•925•9_.977

•956

• 959

.932

• 905

•89_

.852

.315

±2.000

0. 000

.o17

.048

•076

•lO3.i3i

•182

.227

.263

• 295

• 327

•359

•395

•429

•495.467•479

•491

.5o1

•5ii

• 521•542.564

.592

•619

•641

.663

•6_o.697

•724

.732

•753

•778,

._07

._16

.,%3_

•849

.c53

•_355

:.d53

• !339

.8o5

Semlthickness, +t/2

El dge

+4.333 +-6.667 +I0.000 +-13.333 +-16.667-+%/2 +y

O. 000

•025

.067

.108

.148

.164

•201

.217

.233

•247

O. 000.262 •012

•276 .030

• 303 •065

• 331 .09<!

.362 .131

• 391 .164

.41_! .194

•443 .224

•465 .251

.t57 .2770.000

•508 •302 .0o__

•530 •327 .03

•553 •393 •067

•579 •380 •096

.608 •410 .126

.6i7 .4i9 .i36

•635 .437 .155

.64_ .450 .169

•657 ,462 .12

.661 .466 .1,:!, _

•665 •476 •205

•666 ._30 .215

3.9d6 0.000

-955 -95_

• 952 •966

.905 1.379

.Spi 2.570

.838 2.2o7

.802 2.621

Trailin_ edge

±t/2 +-y

22

TABLEIV.- COORDINATESFORARROWW::NG_INCHES- Concluded

37.ooo37.50038.ooo3o.33338•5oo36•56939.00059.50o40.ooo40.5oo4:.ooo41•3g,941.53241•75o42.ooo42.5oo43.ooo43•791_•oso

45.ooo

45.417

45.333

46 .ooo

47. ooo

47.91.o

Lq. oo0

_>. 750

49.0oo

49.444

5O .0oo

51.ooo

51.667

52.OO0

53 •OOO

53 •473

54.000

54.5c_4

55 •000

55 •5OO

56•000

56• 500

57.0oo

57.500

ZRidge

Semithlckness -+t,2

Ridge

0 -+2.000 +4.333 -+6.667 +lO.OOO ±13-335 ±16.667 -+t12 ±y

0.765 0.769 0.668 0.486 0.225 0.770 3.034

•710 •725 .668 •489 •233 •756 3. 448

.642 •674 .668 .492 .242 .703 3 .$62

O. OO0

•576 .620 •667 •495 •250 .004 .671 k. 276

:.667

•565 .632 •499

•509 .584 -499

•45_S .540 .5O2

•397 .493 .505

•33c_ .441 .508

1.513

.265 .386 .504

.251

•35o .4&S

.314 .432

•277 .395

•21d

•371

•247

•5_{ .258 .o17 •642 4.690

.445 •264 •029 .6o9 5.1o3

.587 .271 .040 .5!s£ 5.5:7

.280 •052 .55 _ 5.931

.285 .062 .530 6•345

•295 .074 •509 6.7:'5

Trailing edge

-+t/2 ±y

0.367 0

•339 .571

•300 1.143

•306 ._9 .X94 7•172 •247 2.2_6

.318 .096 .478 7.566 •239 2.$37

•329 .lOS .462 !!:.000 •231 3.429

• 215 4•571

•199 5.714

.342 .177 .367 io.4t3 .153 6.857

.268 •200 .335 11.31o .167 8.000

o. ooo

.194 .223 .002 .3o3 12.13_ .151 9.143

•139

.247 .025 •271 12.966 .136 io.2_6

z .257

.216 .o_ .239 13.793 .12o 111.429

.143 .o71 .2oy 14.621 .lO4 112.571

.093

•094 •175 15.4_3 .ot¢ 13.714

•117 .143 16.276 .o72 14._;57

z. 12J

•o9o .112 17.103 .o56 16.ooo

.046

.o_so 17.931

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.o]_! 15.759

.o52 19.172

•o16 19.586

.ooo 2o.ooo

.040 17.143

.032 17.714

.024 18.286

.016 18._57

.O0!J 19.429

.000 20.000

23

TABLE V.- EFFECT OF DOUBLING THE REYNOLDS NIIMBER AT H = 0.20 ON THE

AERODYNAMIC CHARACTERISTICS OF THE THREE MODELS HAVING DIFFERENT

PLAN FORMS (TRANSITION FREE)

(a) Diamond Model

..R/ftxlO "e

0

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0

2.034.o4

4.06

6.098.12

i0.1512. i_5

12.19

14.22

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13.25

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24.34

26.36

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2.03

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6.1o

8.14

lO. 1712.21

14.25

15•26

16.20%

18.31

20.35

22.3924.41

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0

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2.02

4.06

6.098.12

io• 15

i2.i914• 22

16.86

18.30

20.34

22.3724.41

26.42

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3.0 6•o

-0 •004 0 •002

-.iF6 -. 164

- •073 -.082

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• 083 •O85

.... 167

• 167 ---• 2_3 •25i

•330 •337

•413 .422

•496 ---

--- •5e_•589 •598

.6{56 .6135

•756 .767

.831 .837

•885 .9oi

•926 .938

•965 •971

O. 005

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•176

•272

•366

•460

-565

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•761

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I.128

I. 199

0.007

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- •067

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•156.240

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•092

•177

•278

•376

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•566

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3.0 6.0

o.oo59 o.oo64

.o172 .o154

.0090 .oo81

•o063 .0o63

.0o91 •0057

.... o155.o161 ---

.0252 .0282

.o461 .o469

.0702 .o719

.lOLl

.lo56

• 1412 .1431

.191o • 19o5

•3027 .3053

•3604 •3663

•4177 .4226

• 4764 .45oo

(b) Delta Model

0•0075 0.0065

•0174 •016,9

•o099 .009i• 0073 .0069.0101 ---

•0179 .0170

•0327 •0325

• o539 .0546

.o!_i!} .o825

•1194 .1191

.1627 .1652

.1869

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•2708

.3389•4203

•4934

.5740

(c) Arrow Model

6•0o85 o.0081

•oi92 .0176

•Olli .OlOi

.0o55 .o084

.Olii .OlO5

.o19o .o178

.0326 .o318

• 0536 .o517

• OBl9 .0772

• 1130 .2219--- • 1546

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.2666

•33 78

•4166

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3.0

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•01i9

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- .o163

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•o178

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•o362

.o799

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•1278

•i505

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• 2183•2442

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.1600

.i919•2282

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.2976

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•0527

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.0827

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.o683

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•o185

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