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Page 1: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Oot_o'b_r ]960WASHINGTON Declassifiea September i, ]-961

https://ntrs.nasa.gov/search.jsp?R=19980223615 2018-04-12T11:43:55+00:00Z

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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

TECHNICAL MEMORANDUM X-332

AERODYNAMIC CHARACTERISTICS AT MACH NUMBER 2.05 OF A

SERIES OF HIGHLY SWEPT ARROW WINGS EMPLOYING

VARIOUS DEGREES OF TWIST AND CAMBER

By Harry W. Carlson

SUMMARY

A series of arrow wings employing various degrees of twist and

camber were tested in the Langley 4- by 4-foot supersonic pressure

tunnel. Aerodynamic forces and moments in pitch were measured at a

Mach number of 2.05 and at a Reynolds number of 4.4 × lO 6 based on the

mean aerodynamic chord. Three of the wings, having a leading-edge

sweep angle of 70o and an aspect ratio of 2.24, were designed to produce

a minimum drag (in comparison with that produced for other wings in the

family) at lift coefficients of O, 0.08, and 0.16. A fourth and a fifth

wing, having a 75 ° swept leading edge and an aspect ratio of 1.65, were

designed for lift coefficients of 0 and 0.16, respectively.

A 70 ° swept arrow wing with twist and camber designed for an optimum

loading at a lift coefficient considerably less than that for maximum

lift-drag ratio gave the highest lift-drag ratio of all the wings tested -

a value of 8.8 compared with a value of 8.1 for the correspondlng wing

without twist and camber. Two twisted and cambered wings designed for

optimum loading at the lift coefficient for maximum llft-drag ratio gave

only small increases in maximum llft-drag ratios over that obtained for

the corresponding flat wings. However, in all cases, the lift-drag ratios

obtained were far below the theoretical estimates.

INTRODUC TION

It has long been recognized that because of their low zero-lift wave

drag and low drag due to lift, highly swept arrow wings have the potential

of allowing supersonic airplanes to compete successfully with the best

subsonic airplanes in the critical matter of range (refs. 1 and 2).

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However, if the maximumtheoretical benefits are to be approached, it isnecessary that a flat wing realize a high degree of the theoreticallypredicted leading-edge suction or that the wing be twisted and camberedto produce a theoretically optimum loading distribution.

The prediction of the leading-edge suction stems from the singu-larities in local velocities at the wing leading edge given by linearizedtheory. The existence of any large portion of the theoretical leading-edge suction has not been found in experiments.

It has been showntheoretically (refs. 3 and 4) that drag-due-to-lift factors slightly below those of the flat wing with full leading-edgesuction can be achieved by producing an optimum loading distributionthrough the warping of the wing surface. It is significant that in thiscase, no leading-edge suction is demanded. The present paper will beconcerned with the attainment of high lift-drag ratios through this latterapproach.

For this optimum-loading-distributlon method to succeed, it isimperative to avoid shocks and separated flow regions which would upsetthe balance between the local pressures and the slope of the surfaces onwhich they act. It is believed that in all the experimental work to date,these effects have been present to somedegree at the llft coefficientrequired for the maximumlift-drag ratios. Experimental results fortwisted and camberedwings have shownimprovementsover the correspondingflat wing, but have failed to reach the full theoretical benefits. (Seerefs. _, 6, and 7.)

As noted in reference l, the transonic flow phenomena(local shocksand regions of separated flow) may occur on the wing upper surface whenthe componentof flow perpendicular to the wing leading edge reaches theSpeedof sound, even though the total velocity is greater than the speedof sound. In order to keep the perpendicular componentof flow belowsonic speed for the design lift condition, the leading-edge sweepangle

must increase rapidly with Machnumber. At speeds approaching thehypersonic range, the required sweepswould result in impracticablyslender wings resembling bodies more than conventional wings.

Since at a Machnumberof 2 the theoretical advantages of twist and

camber are substantial and, at the same time, the planform restrictions

are not unreasonable, several wings were designed for this Mach number

to investigate the possibility of attaining the theoretical benefits.

The design procedure used was adapted to these purposes by using computa-

tion techniques developed by Clinton E. Brown and Francis E. McLean of

the Langley Research Center from the methods presented in references 8

and 9.

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Three of the five half-span wings tested in the Langley 4- by 4-foot

supersonic pressure tunnel at a Mach number of 2.09 had a leading-edge

sweep of 70o and an aspect ratio of 2.24. One of these wings was twisted

and cambered for a design lift coefficient of 0.16, a second wing employed

only half that amount of twist and camber, and a third wing had no twist

and camber. The remaining two wings had a 75 ° leading-edge sweep and an

aspect ratio of 1.69. One of these wings had twist and camber corre-

sponding to a design lift coefficient of 0.16 whereas the other wing had

no twist and camber.

SYMBOLS

b/2

CA

CD

CD,o

CL

Cm

Cp

Z

L/D

M

q

S

wing semispan

wing mean aerodynamic chord

axial-force coefficient, Axial forceqs

drag coefficient, Dragqs

drag coefficient at zero lift for uncambered and untwisted

wings

lift coefficient, Liftqs

moment coefficient about 5 Pitching moment

K' qS_

pressure coefficient

overall length of wing measured in streamwise direction

lift-drag ratio, CL/C D

free-streamMach number

free-stream dynamic pressure

free-stream Reynolds number based on mean aerodynamic chord

wing area, half-span model

U free-stream velocity

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U_V

x,y,z

b ,_

c w

X I

y'

8'

A

perturbation velocities in x- and y-directions

Cartesian coordinate system with origin at wing apex, X-axlsstreamwise

coordinates used in defining mean camber surfaces (fig. 3)

angle of attack, deg

leading-edge sweepback angle, deg

Subscripts:

max maximum

min minimum

MODELS AND INSTRUMENTATION

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Photographs of the five half-span models (designated wings i to 5)

mounted on the boundary-layer bypass plate are shown in figure 1. The

first three wings had a 70 ° swept leading edge and an aspect ratio of

2.24. Each of the wings in this first series was designed to produce a

minimum drag (in comparison with that produced for other wings in the

family) at a certain lift coefficient. These design lift coefficients

are O, 0.08, and 0.16 for wings l, 2, and 3, respectively. (A design

lift coefficient of 0 corresponds to a flat wing.) The remaining two

wings had a 75 ° swept leading edge and an aspect ratio of 1.65. The

design lift coefficients in this case are 0 and 0.16 for wings 4 and 5,

respectively.

The all-steel wings were attached to a four-component straln-gage

balance housed within the plate. The plate was supported in a hori-

zontal position by the permanent sting mounting system of the Langley

4- by 4-f00t supersonlc pressure tunnel. During the tests, the wing and

plate moved through an angle-of-attack range as a single unit. A clear-

ance of O.010 to 0.020 inch was provided between the wing root and the

surface of the plate, except where the wing attaches to the balance.

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The layout of the wing planforms and typical wing sections areshownin figure 2. Thickness distribution for all the wings was deter-mined by a 3-percent-thick circular-arc airfoil section in the streamwisedirection. This thickness was added symmetrically to the mean camber

surface of the twisted and cambered wings. Ordinates of the mean camOer

surface based on the coordinate system shown in figure 3 are given in

table I.

TESTS

The tests were conducted in the Langley 4- by 4-foot supersonic pres-

sure tunnel with a free-streamMach number of 2.05 and a Reynolds number of

4.4 × 106 based on the mean aerodynamic chord. In an effort to insure a

turbulent boundary layer, transition strips were used on all wings. The

strips, composed of a sparse distribution of No. 80 carborundum grains

in a lacquer binder, were 1/8 of an inch wide and were located 1/4 inch

behind the wing leading edges. Wings i and 5 were tested over a Reynolds

number range of i × 106 to 4 x 106 to insure that the chosen test

Reynolds number would be well above the transition regions.

The measurements of aerodynamic forces and moments were supplemented

by a flow-visualization technique (re±. I0) which utilizes a fluorescent-

oil film painted on the wing surface. The oil-flow pattern during testscan be used to indicate the direction of airflow at the wing surface and

to indicate regions of detached flow.

Angle of attack was measured optically using prisms recessed in the

wing surface.

From pretest calibrations and repeatability of the data, the Mach

number and aerodynamic coefficients are estimated to be accurate within

the following limits:

M ................................ ±0.01

CD ............................... ±0.0003

CL ............................... ±0.0030

Cm ............................... ±0.0010

DESIGN CONSIDERATIONS

In order to minimize transonic flow phenomena at the design condi-

tions, wing-leading-edge sweep angles were chosen with consideration

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given to the prevention of a sonic componentof local flow perpendicularto the wing leading edge. The severe restriction this imposes can beseen in figure 4. Here the critical pressure coefficient correspondingto a sonic componentof flow perpendicular to the leading edge of a sweptwing has been plotted as a function of leading-edge sweepangle. Theupper curve does not take into account the sidewash on the wing uppersurface whereas the lower one does. The existence of this lower boundwas not realized until after the wings were tested. Since these curvesserve only as a guide and do not represent rigid requirements, it wasfelt that the chosen sweepangles of 70° and 75° would sufficientlyminimize the possibility of transonic flow phenomena.

For a uniformly loaded wing it should be possible to reach liftcoefficients equal to twice the critical pressure coefficient beforeencountering a transonic type of cross flow. In this case, a uniformload was not imposedon these wings so that the optimum loading mightbe more nearly approached. However, pressure coefficients in the vicinityof the leading edge were restricted to a value 1.4 times the average (or-0.7 times the design lift coefficient). The pressure coefficient of-O.112 that might be expected near the leading edge of wings designed forlift coefficient of 0.16 is shownin figure & for wings 3 and 5. Wing 2was designed to produce a minimumdrag at a lift coefficient of 0.08, andthus had only one-half the amount of camberas wing 3. At that lift coef-ficient the leading-edge pressure coefficient could be expected to be-0.056, which is below the critical, but additional lift must be generatedby increased angle of attack before the maximumlift-drag ratio is reached.Thus each of the twisted and camberedwings would develop pressure coeffi-cients near the critical value, but contrary to original expectations (asrepresented by the upper curve of fig. 4) none would be below. The addi-tion of thickness to the meancambersurface produces an additional camberin the upper surface which has somewhatof a relieving effect on the pres-sures over the forward part of the wing.

The choice of the trailing-edge line was the result of a compromisebetween the desire for high aspect ratio and the need for structuralrigidity. Similarly, the 3-percent-chord thickness of the circular-arcairfoil sections is believed to represent a reasonable compromisebetweenlow wave drag and structural considerations.

The camber surface was designed according to the methods of refer-ences 8 and 9. The loading distribution was obtained by a superpositionof three types of loading combinedin such a manneras to produce a mini-mumdrag at a given design lift coefficient. The fundamental loadingsconsidered were a uniform load, a linearly varying span load, and alinearly varying chord load. The resultant loading was subjected to thepreviously mentioned restriction that the leading-edge pressure coeffi-cient not be greater than 1.4 times the average. The theoretical pressure

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distribution at design condition may be expressed in the following

manner:

For the upper surface

-CL,design iCp =.4 + 1.846

and for the lower surface

Cp = CL_design!'4+2 _ 1"8461b72- _I

The resultant theoretical lift-drag polars are as follows:

For the 70o swept wings

CD = CD, o + 0.230(CL,design) 2 - 0.425(CL,design)CL + 0._00CL 2

and for the 75 ° swept wings

CD = CD,o + 0.338(CL,design) 2 - 0.63](CL, design)CL+ 0.622CL 2

RESULTS AND DISCUSSION

In order to evaluate the effectiveness of the transition strips in

providing a fully turbulent boundary layer, two of the wings were tested

over a Reynolds number range. Wings 1 and 5 were chosen for this purpose

as being representative of a flat wing and a highly cambered one,

respectively. In figure 5, the minimum drag coefficients are plotted

against Reynolds number up to the _st Re_nolds number of 4.4 × lo 6 .

The variation of turbulent skin friction with Reynolds number according

to Van Driest (ref. ll) has been computed. The estimated minimum drag

coefficients shown in the figure were obtained by adding estimated wave

drag and drag due to lift to the skln-frlctlon values. For the flat wing,

transition from laminar to turbulent flow appears to take place at a

Reynolds number of about 2 × lO 6. The data for the twisted and cambered

wing follow the turbulent line over the Reynolds number range. Thus, it

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could be expected that turbulent flow would exist over all the wings atthe test Reynolds number.

The aerodynamic characteristics in pitch of the five wings aregiven as a function of llft coefficient in figure 6. Data for wings ofthe sameplanform are plotted on a single set of axes for ease in makingcomparisons. In figure 6(a), note that the presence of twist and camberdoes not appreciably change the lift-curve slope.

As shownin figure 6(c), for the 70o swept wings, the wing designedfor a llft coefficient of 0.16 produced a maximumlift-drag ratio of 8.3whereas the wing designed for a lift coefficient of 0 produced a maximumlift-drag ratio of 8.1. This rather modest gain is overshadowedby thevalue for (L/D)max of 8.8 attained by the 70° swept wing employing thesmaller amount of twist and cambercorresponding to a design lift coef-ficient of 0.08. Thesedata indicate that although there are sizablebenefits to be derived from the use of wing warping, present designmethods are not adequate to exploit this approach to the fullest possibleextent. There is no reason to believe that the rather arbitrary choice ofdesign llft coefficient for wing 2 has achieved the optimum loading.Similarly, for the 79° swept wings, the wing designed for a lift coeffi-cient of 0.16 showedonly a slightly higher maximumlift-drag ratio thandid the flat wing - a value of 7.6 comparedwith 7.4.

A comparison of theoretical estimates with the measureddata is pre-sented in figure 7. The failure of all the wings to match the theoreticallift-curve slope may, in part, be due to the flow separation present ineach case. Another factor is the aeroelastic deformation under load whichtends to produce a loss of lift in the tip region. The sketches in fig-ure 7 give an indication of the extent of separated flow on the wing sur-face. Observations and photographs of the fluorescent-oil film madeduring the tests were used in preparing the sketches. The photographs arenot presented in this paper because they were of poor quality and wouldtherefore not reproduce satisfactorily.

Note that for both flat wings (figs. 7(a) and 7(d)), separationoccurred at the leading edge and, from its inception, occupied a largeportion of the wing. On the other hand, for the twisted and camberedwings (figs. 7(b)# 7(c), and 7(e)), separation appeared first at theinboard region along the trailing edge, and the area affected grew moresteadily than that for the flat wings.

Linearized theory indicates a singularity at the leading edge oflifting flat-plate wings swept behind the Mach llne. Actual upwashangu-larities Just ahead of the leading edge are in all probability very high.The region of separated flow immediately behind the wing leading edgewould appear to be caused by the inability of the real flow to negotiate

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the sharp turns necessary for attachment. When the flow above the sepa-

rated region does return to the wing surface, it is redirected along the

wing surface and results in a recompression and a shock. This is the

type of separation experienced by the flat wings. The twisted and

cambered wings were designed to eliminate the singularity at design lift

coefficient and thus might be expected to avoid leading-edge separation,

at least near design conditions. The test data indicate that leading-edge

separation of the turbulent boundary layer did not occur on the twisted

and cambered wing within the angle-of-attack range used here.

At the trailing edge of a wing at an angle of attack, the flow along

the wing surface is redirected in a nearly streamwise direction causing a

recompression and a trailing-edge shock. If the pressure rise across the

shock is too strong, a turbulent boundary layer cannot pass through the

shock without separating. In that case the flow would leave the surface

just enough to reduce the flow angle and shock strength to the critical

value. From considerations of two-dimensional boundary layers, it would

appear that the pressure rise at the trailing edge predicted for these

wings would not cause separation. Nevertheless, flow separation in the

vicinity of the trailing edge of each of the twisted and cambered wings

is evident from oil-flow observations. _ Of course, there is quite a

departure from two-dimensional flow in this case. In addition, although

local flow in the free-stream direction is assumed in making the calcu-

lations, there actually is a considerable sidewash which in the case of

the twisted and cambered wings results in greater surface slopes and

higher negative pressures at the trailing edge than those given by the

theory.

From the oil-flow observations there was no evidence of local shocks

or transonic flow phenomena near the leading edge of any of the twisted

and cambered wings. Thus it appears that the restrictions on leading-

edge sweep angle and loading at the leading edge produced the desired

result of avoiding these effects.

In spite of the loss in lift, both flat wings (figs. 7(a) and 7(d))

showed a lift-drag polar in close agreement with the theory. This agree-

ment may result from the presence of some degree of leading-edge suction

or, perhaps, may result from an improve d loading distribution brought

about by aeroelastic twist. Although each of the twisted and cambered

wings (figs. 7(b), 7(c), and 7(e)) showed some improvement in maximum

lift-drag ratio over that obtained for the flat wings as previously noted,

they fail by a considerable margin to match the theory. A part of this

failure may be due to the separated flow. However, it may also be due to

the inability of linearized theory to provide a camber surface with the

proper matching of pressures and surface slopes.

It is possible that wings designed for optimum loadings at lift coef-

ficients somewhat below optimum may achieve a substantial amount of the

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theoretical leading-edge suction at optimum lift coefficient. It may,in part 3 be this factor which allows the wing designed for a lift coef-ficient of 0.08 to have a higher value of (L/D)max than that for thewing designed for a lift coefficient of 0.16.

An interesting analysis can be madeby comparing experimental axialforce with the theoretical value for the cases of no leading-edge suctionand full leading-edge suction. In figure 8, axial-force coefficient hasbeen plotted as a function of lift coefficient for all the wings. Notethat for regions on each side of the design lift coefficient, the experi-mental data generally follow the trend of the theoretical curve for thecase of full leading-edge suction. At high lift coefficients, only asmall portion of the predicted thrust force or leading-edge suction isrealized. The increase in the axlal-force level for the severely twistedand camberedwings maybe the result of the failure of linearized theoryto match properly pressures and surface slopes under these conditions.

The variation with design llft coefficient (degree of twisted camber)of the maximumlift-drag ratio and the corresponding lift coefficient isshownin figure 9. The optimumlift coefficients agree well with thetheoretical curve for the case of no leading-edge suction. For thisseries of wings, the amount of twist and camber that can profitably beused in developing high lift-drag ratios corresponds to a design llftcoefficient well below the lift coefficient for (L/D)max. The designlift coefficient of 0.08 maywell be near the optimumfor this family.Note that the v_lue for (L/D)max of 8.8 found for that wing, althoughconsiderably above the value of 8.1 for the flat 700 swept wing, is stillfar below the theoretical maximumvalue of 10.2. (See fig. 9(a).)

As the design lift coefficient is increased, the amount of leading-edge suction theoretically available is reduced, but the possibility ofachieving any large percentage of that available maybe increased.Another consequenceof high design lift coefficients is the increase indrag which mayresult from the inability of linearlzed theory to matchproperly local pressures and surface slopes when extreme camberand strongdisturbances are present. Camberalso influences the type and degree offlow separation. All these factors, and perhaps more, make the task offinding an optimum twist and camberdistribution very difficult.

L876

CONCLUSIONS

An experimental investigation at a Mach number of 2.05 of several

twisted and cambered arrow wings and the corresponding flat wings provides

the following conclusions:

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i. A 700 swept arrow wing with twist and camber designed for anoptimum loading at a lift coefficient considerably less than that formaximumlift-drag ratio gave the highest lift-drag ratio of all the wingstested - a value of 8.8 compared with a value of 8.1 for the corresponding

wing without twist and camber.

2. Two twisted and cambered wings designed for optimum loading at the

lift coefficient for maximum lift-drag ratio gave only small increases in

maximum lift-drag ratio over that obtained for the corresponding flat

wings.

3. In all cases, the lift-drag ratios obtained were far below thetheoretical estimates.

4. Proper selection of loading at the leading edge and of leading-

edge sweep angles for the twisted and cambered wings produced the desired

result of avoiding leading-edge separation and transonic flow phenomena

near the leading edge. However, regions of separated flow in the vicinity

of the trailing edge were present on each of the twisted and cambered

wings.

Langley Research Center,

National Aeronautics and Space Administration,

Langley Field, Va., June 22, 1960.

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REFERENCES

1. Jones, Robert T. : Estimated Lift-Drag Ratios at Supersonic Speed.NACATN 1350, 1947.

2. Brown, Clinton E., and McLean, Francis E.: The Problem of ObtainingHigh Lift-Drag Ratios at Supersonic Speeds. ,our. Aero/Space Sci.,vol. 26, no. 5, May 1959, PP. 298-302.

3. Jones, Robert T.: The MinimumDrag of Thin Wings in Frictionless Flow.,our. Aero. Sci., vol. 18, no. 2, Feb. 195l, pp. 75-81.

4. Jones, Robert T.: Theoretical Determination of the MinimumDrag ofAirfoils at Supersonic Speeds. ,our. Aero. Sci., vol. 19, no. 12,Dec. 1952, pp. 813-822.

5. Madden,Robert T.: Aerodynamic Study of a Wing-Fuselage CombinationEmploying a Wing SweptBack 65° - Investigation at a MachNumberof1.53 To Determine the Effects of Camberingand Twisting the Wingfor Uniform Load at a Lift Coefficient of 0.25 . NACARMA9C07, 1949.

6. Brown, Clinton E., and Kargrave, L.K.: Investigation of MinimumDragand MaximumLift-Drag Ratios of Several Wing-Body CombinationsIncluding a CamberedTriangular Wing at LowReynolds Numbersand atSupersonic Speeds. NACATN4020, 1958. (Supersedes NACARMLSiEll.)

7. Hallissy, Joseph M., Jr., and Hasson, Dennis F.: Aerodynamic Charac-teristics at MachNumbers2.36 and 2.87 of an Airplane ConfigurationHaving a CamberedArrow Wing With a 75° SweptLeading Edge. NACAEML58E21, 1958.

8. Tucker, Warren A.: A Method for the Design of SweptbackWings WarpedTo Produce Specified Flight Characteristics at Supersonic Speeds.NACARep. 1226, 1955. (Supersedes NACARMLSIF08.)

9. Grant, Frederick C.: The Proper Combination of Lift Loadings forLeast Drag on a Supersonic Wing. NACARep. 1275, 1956. (SupersedesNACA TN 3533.)

i0. Loving, Donald L., and Katzoff, S.: The Fluorescent-0il Film Method

and Other Techniques for Boundary-Layer Flow Visualization. NASA

MEMO 5-17-59L, 1959.

ii. Van Driest, E. R.: Turbulent Boundary Layer in Compressible Fluids.

Jour. Aero. Sci., vol. 18, no. 5, Mar. 1951, pp. 145-160, 216.

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i.

TAlkiE I

CAMBER-SUP/ACE ORDINATES

(a) Wing 2. A = 70o; CL,deslg n = 0.08

kO

cOI

y'

b' x' x' x'

Tr = o yr = o.o5 Tr = o.1o

o 0.032o .............

•05 .o2o9 .............zo .0125 ...... 0.0145

•15 .o077 o.o087 .0o94•20 .0043 .0055 .0061

•25 .0O25 .OO34 .0O4O

•50 .0O15: .0023 .0028•55 .00161 .0023 .0024.40 .0018 .0026 .0028

•45 .OOeO .0O30 .0O33•5O .0O23 .o054 .0o54

•55 .0O25 .0036 .0o37.60 OO27 .0037 .0039•65 .0O29 .0038 .0042

•70 .o031 .OO40 .0o_4

•75 .o033 .00%2 .0046

.80 .0035 .0o_2 .0047

•85 .O037 .0043 .0047.9o .0039 ....... 0o46

•95 .0O4_ ............1.0o .oc43 ............

Camber-surface ordinate z/_ at -

x' x' Ixt = 0.25 x' x' Ix' x _ x jTr : 0.15 _r = 0.20 Tr _-r = 0.50 _-r = 0.55 Tr = 0.40 _r = 0•45 Tr : 0.50

...... 0.0231 .................. 0.O249 ............

....... o157 ...... o.17o ...... .o182 ...... 0.o19_

o.o10o .oio6 o.o111 .o117 o.oi.25 .o13o o,o154 .o14o

.0067 .o074 .o078 .0082 .oo85 .oo89 .0o94 .oo97,oo44 .oo49 .0053 .oo55 .0058 .o06o .0062 .0o62

.0050 .oo51 .0032 .0035 .oo54 .oo54 .0033 .0o35

.0023 .0022 .0021 .0019 .0016 .0013 .0011 .0010

.OO26 .0O20 .0014 .0008 .0005 -.0005 -.0007 -.0012

.0028 .0022 .0015 .0006 -.00O5 -.0013 -.0O22 -.0051

.0030 .0024 .0016 .0005 -.0008 -.0023 -.0035 -.0047

.0034 .0028 .0018 .00O7 -.0006 -.0O22 -.0039 -.0055

.0037 .0034 .OO29 .0021 .0011 -.0O00 -.0013 -.OO27

.0042 .0040 .0056 .0051 •0024 •0017 •0008 -•0002

.0045 .0044 .0o41 •0059 .0034 .0050 .0O25 .0O18

.o@+8 .00_8 .0047 .0045 .0043 .0040 .0036 .0052

.o050 .oo51 .oo51 .oo51 .0o5o .0o49 .oo47 .0044

.oo51 .oo55 .0054 .0054 .0054 .0O_ .o055 .0053

....... 0052 ...... .oo54 ...... .oo% ...... .oo57

....... 0o48 ................... oo94 ............

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

y_

V *' x, Ix,_T = 0.55 _T = 0.60 -- = 0.65C'

0.05 ...... 0.0260 ......

.lO ............ 0.0203

.15 0.0146 .0150 .0155

.20 .0101 .0105 .0108•25 .0064 .0065 .0067

.30 .o032 .0050 .0030

•3_ .ooo7 .0o02 -.0oo3.4o -.0019 -.0O24 -.0031

•45 -.0039 -.00_8 -.0057•5o -.0058 -.OO70 -.0081

•55 -.ooTZ -.oo86 -.oo98

.60 -.oo45 -.oo59 -.oo76•65 -.0014 -.oo25 -.OO38•70 .OOll .0003 -.0006•75 .0028 •0022 .oo16

.80 .00_2 .OO58 .0035•85 .0o52 .0050 .0O_9

•9o ....... 0056 ......

•95 ...... .0o57 ......

Camber-surface ordinate z/l at -

x' x' x' = 0.80x' x' x' x'= 0.70 _r = 0.75 _ _-T = 0.85 _-T = 0.90 _-T = 0.95 _-T : I•00

...... 0.0211

0.0159 .0163.0112 .0119. OO69 .0O70• 0029 .0026

- .0009 - .0o15- .0o59 - .o048- .0o67 -.oo78

- •0093 - .OLO8- .0111 - .0127

- .0090 - .OLO9- .0051 - .0067- .ool5 - .0026•OOlO .0o03.0032 .0028.0C_7 .0045•0o55 ......

0.0269 .................. 0.0273...... 0.0218 ...... 0.0225 .0226

.0166 .0169 0.0171 .0174 .0177.0118 .0120 .0122 .0124 .0125

.oo7o .0o71 .oo72 .0072 .0072

.0025 .0023 .0022 .oo2o .0O17-.0018 -.0022 -.0025 -.0033 -.00,_.2-.oo55 -.0O63 -.oo70 -.0O84 -.oio1-.0090 -.01o_ -.0115 -.0134 -.0162

-.0126 -.0145 -.0161 -.0185 -.0224-.0142 -.0161 -.0182 -.0208 -.0249-.Oll7 -.0131 -.0143 -.OLD7 -.0173-.0082 -.0097 -.0110 -.0124 -.0137

-.oo37 -.oo_8 -.oo6o -.oo72 -.0o85

-.00O3 -.o010 -.0018 -.OO27 -.OO36.0025 .OOZ8 .oo14 .o0o8 .0O05

.0043 .0041 .oo38 .oo56 .oo33

.oo5_ ...... .oo53 ...... .0O51•0o58 .................. .0o59

Page 16: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

14

TABLE I.- Continued

CAMBER-SURFACE ORDINATES

(b) Wing 3• A = 70°; CL,desig n = 0.16

y,b'

0

.05

.i0

.15• 20

.25

.30

.55

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95I.OO

K'c--r=O

o.o64o ............

•o417 ............

•0251 ...... 0.0286

.0159 0.0174 .0189

Camber-surface ordinate z/I

x' x f x I x Ic--r 0.05 x' = 0.19 = 0.20 = 0.;= _ = O.lO c-r _T 7

...... 0.0462

.0122

.OO_O

•oo_.0048

.OO97

.OO61

.0068

.OO74

•0078.0084

.0088

.oo91

•oo94

.oo99

0.02O0

.0135

.0089

.OO6O

.00_7

•0051

.OO56

.0061

•0067.OO76

.oo89

.OO9O

.0O96

.0099

: .0102

•008 .0Z06

.ooh_ .oo67

.oo51 .oo_7

.OO32 •oo_6

.oo57 •oo93

.oo41 .oo59

•00_9 •OO67

•0050 .0072

.oo54 .0073

.oo58 .oo76

.oo62 .oo8o

.0066 .0083

.oo7o .o089

•oo74 .0086

.oo78 ...... .oo92 ......

.oo82 ......i ......

.oo85 ............ I ......I

• O314 ......

.0212 0.0223

.0147 .0156

• oo98 .OLO6

.OO62 .0064

.oo_4 .oo42

.00_O .0028

.0C44 .oo_9

•oo_9 .oo31

•0055 .0036

.oo69 •0097

.oo8l .OO72

.oo87 .0o83

.oo96 .oo94•0102 .0102

•0106 .0108

.0103 ......

•0097 ......

at -

!5 XI xt_T = 0.30 _T = 0-39

0.0340 ......

.0234 0.0246

.0164 •o171

.0110 .0116

•oo65 .0068

.O037 .oo31

•oo 17 .o005

.0011 - .ooo9

.OOIO - .0016

.0014 - .0013

.00_2 .OO22

.oo61 .oo48

.0077 •0069

•oo91 .oo86

.0102 .Oloo

.0109 .0109

•0 lO9 ......

x I x rE.r 0.40 x' = 0.45 = o.5o= E-r

o .o_96 ......

.0026 0.0389•0259 0,0269 .0281

•0179 •0187 .0193

,0120 •0124 .0129•OO67 .0068 .0066

.oo26 .0023 .ooz9

- .o006 - .OOl& - .0025

- .0026 - .0045 - .0062- .oo_6 - .oo7o - .0O94

-.oo_3 -.0077 - .o109

- .0001 - .0026 - .0054,0033 ,0015 - •0005

•oo59 •00_9 .0036

.0080 .0072 .0064

•oo98 •0O94 .oo89.OlO8 .oio7 . OlO6.o112 ...... .0114

•0107 ............

IOO-4Oh

yl ........

).o5 ...... I 0.0520.1o ...... I .o_o7• 15 0.0293 I .0301

.20 .o2o3 1 •o21o

.29 .oLe8 l .o13o

.3o .oo64 I .oo61•35 .oo14 1 .00o5.4o -.oo37 1 -.oo_7

.45 -.oo78 I -.oo96

.9o -•o117 1 -.o139

•55 -.o142 I --o171.6o -.oo_ I -.0118

•69 -.OO27 1 -.OODO• 70 .0021 I .0006

•75 .oo55 1 .oo_3.80 .0o83 1 .oo77

.85 .OlO_ I .oloi

.9o •OlOl I •o113

•95 ...... I .o113

X =

: o.65 =0.70 o.75

...... 0.0_22 ......

0.o310 .o318 0.0326

.0217 .0225 .0230

.0134 .0i56 .0139

•oo59 .OO58 .oo53

- .0009 - .oo18 - .OO29

-.oo62 -.oo79 -.oo96

- •oo76 - •o155 - •o155

- .o162 - .o186 - .o216

- .o197 - .0222 - .0294

- ,0152 - .0181 - ;0210- .oo75 - .0102 - .0134

- .OOll - .oo30 - .oo51

.0032 .0019 .ooo6

.0070 .0o63 .0055

,o098 .0093 .o090

...... .OllO ......

Camber - surface ordinate

e_ = 0.80

o.o_,1.0435

.o333

.0237

.0141

.o05o- .OO37

-.0110

- .o181- .0251

- .0289

- .0237- .0165

- .0073

- .0006

,00_6

.0086

.0108

.o117

z/Z at -

o.4 =o. ol :o

0.0338.0240.o_2.oo_6

-.0043

-.0_9-.0206

-.02_-.0322-.0262

-.01_

-.OO96

-.OO21

.oo37

.oo_

............ I o.o_60.0_45 ...... I .0_93

.o3_3 o.o3_9 1 .o354

.o2_3 .o248 1 .o251

.0143 .0144 I .Ol_J_

•oo_5 .oo_o I .0034- .0o51 - .0066 1 -.oo83

-.0140 -.0168 1 -.0202

-.0230 -.0269 I -.0324

-.0323 -.0371 1 -.0_8

-.0365 -.0_16 1 -.0_97

-.o286 -.o315 I -.o345

-.0221 -.02_8 I -.O275-.0120 -.01_4 I -.0169

-.oo56- .oo9_ I -.oo72.OO27 .0016 l .ooo6

.oo76 I .OOTI I .0069

.olo5 ] ................... ------- I .0119

Page 17: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

15

TABLE I.- Concluded

_ -SURFACE ORDINATES

(c) Wing 5. A = 750; CL, desig n = 0.16

43t--COI

Camber-surface ordinate z/Z at -

b_, x' 0.05-- x' x' x' x' x'x.__'= O-- = x' = 0.i0-- = 0.15--= 0.20--= O.25 = 0.50--= 0.35 x_.['= 0.40c' c t c I c I c' c' _T c' c T

0.00 0.0789 ................................................

•O5 .05_2 .................. 0-0596 .................. 0.0636

.I0 •0345 ...... 0.0387 ....... 0&24 ...... 0.0462 ....... Oh91

.15 .0209 ....... 0264 ....... 0505 ....... 0358 ....... 0368

.20 .0129 0.0159 .0180 0.0196 .0212 0.0227 .0243 0.0258 .0273•25 .OO81 .0107 .0126 .0142 .0155 .0167 •0177 .0188 .0197

.30 .0062 .0086 .Oloo .0109 •0118 .0126 .0131 .0156 .o159

•35 .0072 .0098 .010_ .0106 .0105 .0102 .0099 .0095 .0091

.4o .O081 .01o6 .Oil5 .0115 .0105 .0092 .OO77 .O065 .0054

•45 .0091 .0123 .0131 •0129 .0118 .01o2 .0078 .oo51 .0030

.90 .0099 .o131 .0140 .0138 .0126 .oi07 .0o83 •0052 .0019

•55 .OliO .OlA4 .o155 .Olh9 .0136 .oi15 .0088 .oo_ .oo16

•60 .0120 .o157 .0168 .0163 .O151 .o151 .0105 .0072 .0032

•65 .0128 •0163 .0176 .0176 .0170 .O157 •0141 .0120 .0095

•70 .0137 .o17o .0184 .0189 .0187 .0182 .0172 .0157 .o139

•75 .0147 .0171 .0185 .0192 .0195 .019_ .0192 .0185 •0176

.80 .0155 .0180 .O199 .020_ .O210 .0211 .0211 .0208 .0204

•85 .O163 .O182 .0196 .0205 .0211 .0216 .0220 .0221 .O221

.90 .0171 ....... O195 ....... 0210 ....... 0219 ....... 0229

•95 .0179 ................... 0206 ................... 0222

1.oo .o187 ................................................

x_i= 0.45 x'e' _ = 0.50

...... 0.0518

....... 03970.0286 .o299.0206 .0216

.O143 .oi_6

.OO86 .0O80

.0043 .0032

.0010 - .OOlO

- .0011 - .00_2

- .0027 _ .0o69

-.0013 -.oo61• 0067 .0032

.o118 .0093

.o163 .0l_,9

.0198 .0190

.O221 .0218

....... 0229

Camber-surface ordinate z/_ at -

y'-- X' X T X vb o55i :o6o1 :0.65 _-: 0.70

o.o5 ...... I o.o66_ _ .............i0 ...... I .O539 i ...... 0.0556

.15 ...... I .Oh25 ! ....... 0_46

.20 0.0312 I .0323 I 0.0333 .03h3

•25 .0224 I .0251 I .0239 .02_6

.30 .0149 1 .0150 1 .o152 .o153•35 .0076 1 .ooTO I .0067 .oo62._o .OOl9 1 .ooo8 1 -.ooo5 -.OOl6•_5 -.oo29 1 -.oo_8 1 -.oo67 -.ooss.Do -.oo71 I -.OlOi I -.o129 -.0195

•55 -,OLO5 1 -.o139 I -.o178 -.o217

.60 -.OZl4 I -.o161 I -.o2o5 -.o2_5

.65 -.o008 1-.0050 I -.0096 -.0z_6•70 .0068 1 .00_0 1 .OOll -.OO22

• 75 .0132 .O119 .0096 .0074

.8C .0182 .0172 .0161 .Olh9

•85 .O216 I .0211 I .0206 .0200

.9C .0217 I .0229 I ....... 0229

-9_

x _ x= o.751-- = o.8o_- : 0.85T;

...... I 0.0683 - .....

...... I .o57o -.....

...... I .0_69 ......

0.0552 I .0360 0.0367

.0251 .0256 .O259

.o1_ I .015_ ' .0153.0057 I .0050 i .00_2

-.003o -.oc45 i -.oo6o-.OliO I -.o133 -.o157-.018_. I -.0213 -.0245-.0249 I -.0283 -.0325

-.0282 I -.o32o -.o36o

-.0193 1 -.0235 -.0274-.0056 [ -.0094 -.o134

.o0_ I .0o25 i -.ooo3

.0136 I .0122 ' .0104

.019_ I .0187 .0179...... I .0227 ......

...... I .0232 , .................. I .0238 1

c_-: 0.90 _ : 0.951 x-.[ = 1.00c Ii

............. 0.0693o.o582 ........ 0590.0_80 ........ 0_89.0373 0.0376 1 .o378.0261 .0265 I .026h

.o1_o .Ol47 , .Ol_

.o03h I .002_ i .00_3 1-.0077 -.0096 I -.0117-.OlSt_ -.0216 I -.0256

-.0283 -.0557 1 -.0_02

-.0387 -.O_5_ I -.0558

-.o_o8 -.o_66 _ -.o96o i-.OSlh , -.0350 1 -.o5_9-.Ol77 -.0220 I -.02_ i-.0032 -.0061 I -.oo9_ !•0085 i .OO67 I .OO_9 !

.Ol7O .o162 I .o152

.0223 - ..................!...... o.o2_i

II

Page 18: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 20: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 21: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 22: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 25: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 26: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 27: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 28: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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Page 29: Aerodynamic Characteristics at Mach Number 2.05 of a Series of ...

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