Effect of thickness and sweep angle on the longitudinal ... · EFFECT OF THICKNESS AND SWEEP ANGLE ON THE LONGITUDlNAL AERODYNAMIC CHARACTERISTICS OF SLAB DELTA PLANFORMS AT A MACH

NASA TECHNICAL NOTE , NASA TN D- -- -

c .1 '3459 -

EFFECT OF THICKNESS A N D SWEEP ANGLE ON THE LONGITUDlNAL AERODYNAMIC CHARACTERISTICS OF SLAB DELTA PLANFORMS AT A MACH NUMBER OF 20

by Robert D. Witcofski and Don C. Marcnm, Jr.

Lungley Resedrch Center ' 7

Lung@ Stution, Humpton, Vu.

N A T I O N A L A E R O N A U T I C S A N D SPACE A D M I N I S T R A T I O N W A S H I N G T O N , 0. C. J U N E 1 9 6 6

-.

TECH LIBRARY KAFB, NM

EFFECT O F THICKNESS AND SWEEP ANGLE ON

THE LONGITUDINAL AERODYNAMIC CHARACTERISTICS OF

SLAB DELTA PLANFORMS AT A MACH NUMBER OF 20

By Robert D. Witcofski and Don C. Marcum, Jr.

Langley Research Center Langley Station, Hampton, Va.

NATIONAL AERONAUT ICs AND SPACE ADMl N ISTR AT ION

For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - Price $3.00

EFFECT OF THICKNESS AND SWEEP ANGLE ON

THE LONGITUDINAL AERODYNAMIC CHARACTERISTICS OF

SLAB DELTA PLANFOIWIS AT A MACH NUMBER OF 20

By Robert D. Witcofski and Don C. Marcum, Jr. Langley Research Center

SUMMARY

An investigation has been conducted at a free-stream Mach number of approximately 20 to determine the effects of sweep angle and thickness on the longitudinal aerodynamic characteristics of basic delta planforms. The sweep angles investigated were 450, 60°, 70°, 80°, 850, and 90°, and the ratio of thickness to root-chord length varied from 0 to 0.3. Reynolds number based on wing length varied from 1.4 X lo6 to 6.6 X 10 and the angle-of-attack range was approximately from 00 to 30°. Within the limits of the investigation, experimental estimates of the optimum sweep angles for obtaining maximum lift-drag ratio for a given thickness ratio were made. Also obtained were experimental curves for determining the slopes of the normal-force curves and lift curves at zero angle of attack. Maximum lift-drag ratio exhibited a nearly linear decay as thickness ratio and volumetric coefficient were logarithmically increased. Angle of attack at maximum lift-drag ratio increased nearly exponentially with thickness ratio. Increasing wing thickness from zero shifted the center of pressure forward from the 2/3-root-chord point. Newtonian impact theory and a modified Newtonian impact theory plus skin- friction calculations w e r e generally adequate for predicting trends only.

6

INTRODUCTION

The advantages in the ability of reentry or cruise vehicles to develop lifting capabilities at hypersonic speeds have been recognized for some time. capabilities tend to reduce entry deceleration and allow some range control, although some form of landing aid may be required. As lifting capabilities increase, deceleration loads are minimized, range control is greatly extended, and it is not at all unlikely that conventional landings could be executed. It was pointed out in reference 1, for instance, that the ability of glide vehicles to convert velocity to range is dependent to a large extent on their ability to develop sizable hypersonic lift-drag ratios. Increases in vehicle lifting capabilities tend to decrease the entry heating rate, but may also increase the total heat absorbed. Reference 1 has also indicated that if hypersonic reentry vehicles are to

Even small lifting

develop relatively high hypersonic lift-drag ratios and survive the high heating rates, the vehicles must have rounded noses and highly swept wings with rounded leading edges to reduce local heating problems while incurring minimum drag penalties. Of lifting configurations operating in high- speed ranges, the basic delta planform is of particular interest in that it has a relatively small movement of aerodynamic center with variations in Mach number (ref. 2).

The purpose of this paper is to present the results of an investigation conducted at a Mach number of approximately 20 to determine the effect of variation of sweep angle and thickness ratio on the longitudinal aerodynamic characteristics of basic delta planforms. Preliminary results of this investigation are presented in reference 3. The sweep angles investigated a r e 45O, 60°, 70°, 80°, 8 5 O , and 90°. Wing leading edges were hemicylinders and the noses were spherical segments. The ratio of leading-edge diam- eter to root chord varied from 0 to 0.3. Reynolds number based on root-chord length varied from 1.4 X lo6 to 6.6 X lo6, but for wings having thickness ratios of 0.034 or less a constant Reynolds number of 3.7 X lo6 was maintained to minimize possible Reynolds number effects. Angle of attack was approximately from Oo to 30°. Particular emphasis is placed on maximum lift-drag ratio, and the experimental results a r e compared with those obtained from Newtonian impact theory and a combination of modified Newtonian impact theory and skin-f riction calculations.

SYMBOLS

Measurements for this investigation were taken in the U.S. Customary Units but a r e also given parenthetically in the International System of Units (SI). To promote use of this system in future NASA reports, details concerning the use of SI units, together with physical constants and conversion factors, are given in reference 4.

C wing root-chord length, inches (meters)

FA axial-force coefficient, - q,s CA

CD

CL

drag coefficient,

Lift lift coefficient, - qms

lift-curve slope at a! = Oo, per degree cLa

lift coefficient at maximum lift-drag ratio 'L, (L/D)m,

2

I 1 . 1 ~ 1 1 1 = 1 1 1 ~ 1 1 1 1111 111 1111111111111111111 1111 II II I I

C m

P

P,

4,

r

rb

R

S

t

t/c

V

I l l I I 111 II II 11111111111.~111 II I I I

pitching-moment coefficient about a point two-thirds of model length rear- MY ward from nose on model center line, -

q,sc

r.N normal-force coefficient, - q,s

normal-force-curve slope at a = Oo, per degree

P - P, maximum pressure coefficient, - q,

axial force, pounds force (newtons)

normal force, pounds force (newtons)

lift-drag ratio, CL/CD

pitching moment about a point two-thirds of model length rearward from nose on model center line, inch-pounds force (meter-newtons)

free-stream Mach number

pressure

free-stream static pressure

free-stream dynamic pressure, pounds force/inch2 (newtons/meterZ)

wing leading-edge radius and nose radius, inches (meters)

base radius of balance-housing body, inches (meters) (see fig. 1)

Reynolds number, based on root-chord length

planform area, inches2 (meters2)

wing thickness, inches (meters)

thickness ratio

volume of wing or of wing and balance-housing body, inches 3 (meters3)

I I I

3

~ 2 1 3 1 s volumetric coefficient

X distance along wing longitudinal axis, measured from nose of wing, inches (meters)

location of center of pressure XCPp

a! angle of attack, degrees

angle of attack at maximum lift-drag ratio, degrees YL/D)max

Y ratio of specific heats

A

Subscript :

wing sweep angle, degrees (fig. 1)

max maximum

MODELS, FACILITY, AND TESTS

Models and Wind Tunnel

The basic configuration (fig. l(a)) consisted of slab delta planforms with sweep angles of 45O, 60°, 70°, 80°, 85O, and 90°. The thickness ratio t/c varied from 0 to 0.3. The models had either hemicylindrical leading edges and spherical-segment noses o r sharp leading edges and noses. A sketch of the basic configuration with a balance-housing body is shown in figure l(b). to simulate zero leading- edge thickness and of the balance-housing bodies associated with them. A photograph of the 80° sweep-angle wings is figure 3. Basic dimensions for all models tested a re given in table I.

Figure l(c) is a sketch of the wings used

All tests were conducted in the Langley 22-inch helium tunnel (fig. 2) by utilizing a contoured nozzle to obtain Mach numbers on the order of 20. A detailed description of the tunnel characteristics is given in reference 5. the present investigation was 20.3 for all but the zero-leading-edge-thickness wings, for which, to maintain a constant Reynolds number, stagnation pressures were selected based on the results of reference 5. Reynolds number based on wing length was approximately 3.7 X lo6 for wings which had thickness ratios of 0.034 or less and ranged from 1.43 X 106 to 6.60 X lo6 for the entire investigation. The free-stream Mach numbers and the Reynolds numbers a r e given in table I. Stagnation temperature decreased about 20° F (110 K) during each test because of decreasing reservoir pressure; however, an average stagnation temperature of 70° F (294O K) would be representative. The angle-of-attack range was approximately from Oo to 30'.

The free-stream Mach number for

4

Instrumentation

The optical system described in reference 6 was utilized to measure pitch attitude. Data were obtained by the use of five different strain-gage balances. Because of the physical size of the strain-gage balances used to measure forces and moments in this investigation it was impossible to house the strain-gage balances completely within the more slender wings, that is, wings having thickness ratios of 0.034 or less. Balance- housing bodies were therefore necessary on the leeward surfaces of the more slender wings. A sketch of the balance-housing body on the basic configuration and a table con- taining pertinent information on the geometry of the balance-housing bodies are shown in figure l(b). At the time the zero-leading-edge-thickness wings were tested, a new external strain-gage balance became available and made possible the use of a much smaller balance-housing body, as seen in figure l(c). The effect of the balance-housing body on the validity of the data was determined by retesting the wing having a thickness ratio of 0.01 and a sweep angle of 80° by utilizing the external balance which required a balance-housing body having only 18 percent as much volume as the balance-housing body used when the wing was first tested. housing body and the small balance-housing body, are presented in figure 4. As can be seen in the figure, the reduction in body size, as well as a reduction in the angle of attack at which the balance-housing body was hidden from the flow, resulted in only small changes in the basic force data and about a 3-percent increase in (L/D)max, which is believed to be within the accuracy of the data. As a result of these tests, it is believed, at least for the wings having sweep angles of 80° or less, that the balance housing had no significant effect on the wing characteristics.

Results from tests on both bodies, the large balance-

An additional test of the same wing with the large balance-housing body was made to determine the possible presence of Reynolds number effects. number of 6.60 X lo6 are compared with those at a Reynolds number of 3.66 x lo6 in figure 4. The data show that the change in Reynolds number produced only small differ- ences in the force and moment data.

These data at a Reynolds

Base pressures were not measured for the present investigation and therefore the data have not been corrected to a condition where free-stream pressures would exist on the base. However, base pressures were measured on delta-wing-half-cone bodies of reference 7, and from the results of reference 7 it is thought that base pressures in the range of three times free-stream static pressure should be realistic. When applied to the present data, base pressures of this magnitude would result in corrections to the axial force which were smaller than the inaccuracy of the strain-gage balances used for the present investigation.

5

Accuracy

Tabulated estimations of the accuracy of the data are shown in coefficient form in table I. These estimations were computed by using the quoted accuracy of static-balance calibrations.

The estimated pitching-moment accuracy includes the possible e r ro r incurred when pitching-moment reference center is transferred from the moment reference ten-

ter of the balance to the moment reference center selected on the models. This transfer introduces the inaccuracy in the normal-force component into the inaccuracy already present in the balance pitching-moment component. all wings was at a point two-thirds the chord length from the nose. Angle of attack is believed to be accurate to at least rtO.2'.

The moment reference center for

RESULTS AND DISCUSSION

The pertinent results from this investigation are shown in summary plots in figures 5 to 11 and in basic-data plots in figures 12 to 42.

Maximum Lift-Drag Ratio

Maximum lift-drag ratios obtained in the present investigation a r e shown in fig- u re 5 as a function of thickness ratio. The abscissa scale has arbitrarily been extrap- olated to zero to present the data from the wings used to simulate zero leading-edge radius. It is noted that (L/D)max exhibited a nearly linear decay as thickness ratio was increased logarithmically. Included along with the experimental results of the present investigation a r e the results obtained from both Newtonian impact theory and a modified Newtonian impact theory by utilizing the method described in reference 8.

The two theories a r e represented in figure 5, Newtonian impact theory (Cp," = 2) for wings having t/c > 0.04 and modified Newtonian theory plus skin friction for t/c < 0.04 (skin friction calculated by the method described in ref. 9). In the modified theory a maximum stagnation pressure coefficient given by reference 8 as

was used on the cylindrical leading edges and spherical- segment nose sections, whereas y + 1 was used on the flat-plate portions of the wings. The force and moment contribu- tions of the balance housings, as well as the dihedral on the leeward surface of the zero-leading-edge- radius wings, have been neglected and the theoretical calculations have been made on the basic wings only.

6

Wings having thickness ratios less than about 0.10 (fig. 5) were seen to achieve higher values of (L/D),, when the wings had 80° sweep angles, whereas wings having thickness ratios greater than 0.10 had higher values of (L/D),= when the wings had sweep angles of 70°. (L/D),=, for the basic type of configuration considered in this investigation, can be more easily ascertained from figure 6. increased from a value of zero the optimum sweep angle for maximum lift-drag ratio decreased from an angle slightly larger than 80° to 70° or less for the highest thickness ratio. The peak in (L/D)max for each curve suggests that as sweep angle decreases from 900, the increased lifting surface more than offsets the increase in drag initially; whereas at sweep angles less than optimum the converse is true. Unfortunately, the angle-of-attack range did not permit many of the higher thickness-ratio wings to obtain a maximum lift-drag ratio and the optimum sweep angles for the higher thickness-ratio bodies could not be ascertained. Newtonian theory is in fairly good agreement with experiment for the higher thickness-ratio wings and is thus useful in determining the optimum sweep angle for these cases.

The optimum sweep angles for obtaining maximum values of

Figure 6 indicates that as thickness ratio

Figure "(a) indicates the large penalty in l i f t coefficient at (L/D)m= that is accrued as thickness ratio is decreased. The angle of attack at which (L/D),= occurs is seen, in figure 7(b), to increase nearly exponentially with thickness ratio. Drag polars were useful in ascertaining lift coefficient and &gle of attack at (L/D),=. Included in figure 7(b) are the predictions reference 10 and expressed in

of angle of attack at (L/D)m= given by the method of degrees herein:

In the present paper experimental values of predict angle of attack at (L/D)".

(L/D)max a r e used in this equation to

. . 8 ." Volumetric Coefficient

In figure 8 (L/D),= is presented as a function of the volumetric coefficient V2/3/S. The solid symbols denote results in which the volume of the balance-housing bodies have been included. However, since the balance-housing bodies have very little effect on the wing characteristics (see fig. 4), the data a r e also representative of wing- alone data. alone by subtracting the volume of the balance-housing bodies and are shown in the figure as flagged symbols. When the wings alone (all open symbols) a r e considered, (L/D),= exhibits a nearly linear decrease as volumetric coefficient is increased logarithmically, the slope of this trend depending on wing sweep angle.

Therefore the volumetric coefficients have also been computed for the wings

This analysis

7

indicates that considerable volume may be discretely added to delta planforms without incurring serious losses in ( L / D ) ~ = .

Normal- Force- Curve and Lift- Curve Slopes

As can be seen in figure 9 the slopes of the normal-force curves and lift curves at zero angle of attack increase nearly linearly with thickness ratio. As sweep angle increases, CN, and CL, decrease, a trend previously obtained on slender wings at lower hypersonic speeds (ref. 11). Because the presence of balance-housing bodies would tend to introduce negative normal and lift forces at and near zero angle of attack, initial slopes for only the wings which had no balance-housing bodies were presented. Within the limitations of the data in figure 9, values of CL, may be interpolated for various combinations of thickness ratio and sweep angle. The following empirical expression was found for determining CN,:

CN, = O.O16667(t/c) + 0.00O24O(9O0 - A) + 0.000718

(0.08 5 t/c 5 0.30; 600 5 A 5 85O) (2)

The values of CN, as predicted by this equation a r e shown in figure 9 as straight lines. Equation (2) was found to be inadequate in predicting values of CN, at lower Mach numbers, when compared with data obtained on similar wings from reference 12.

Center of Pressure

Figures 10 and 11 contain the center-of-pressure data as given in root-chord lengths from the nose and as plotted as a function of angle of attack. The initial forward shift of the center of pressure occurring at low angles of attack on some of the wings is attributed to the presence of the balance-housing bodies. representing Newtonian impact theory. For the sake of clarity, Newtonian impact theory is presented for only a representative number of wings. Also indicated on the plots is the location of the center of pressure for zero-leading-edge-thickness wings as predicted by Newtonian impact theory. In figure 10, each set of data represents a particular sweep angle and the data within each set represent the different thickness ratios investigated at these respective sweep angles. The experimental data indicate that as thickness ratio t/c increases from zero, the center of pressure moves forward from the 2/3-root-chord point. In figure 11, each set of data represents a particular thickness ratio and the data within each set represent different sweep angles. Center of pressure of the wings having higher thickness ratios is seen to move rearward as sweep angle is decreased. Center of pressure is also seen to move rearward as angle of attack increases from zero. The rate of rearward shift of the center of pressure increases with increasing sweep angle.

Included in figure 10 a r e curves

8

BASIC DATA

Presentation of the basic data (figs. 12 to 42) is made in order of decreasing thickness ratio and, for each thickness ratio, in order of increasing sweep angle. Arrows on the abscissa of the plots (figs. 30 to 42) indicate the approximate angle of attack at which the balance-housing bodies were geometrically hidden from the flow by the wings. The Newtonian impact theory calculations a re shown as solid lines (figs. 12 to 42) and the results of the modified Newtonian impact theory plus calculated skin friction (figs. 30 to 42) a r e shown as broken lines. In general, it will be observed that the theoretical predictions a r e good for predicting trends, but a r e inadequate for predicting experimental values.

CONCLUDING REMARKS

An investigation has been conducted to determine the effects of sweep angle and thickness ratio on the longitudinal aerodynamic characteristics of a ser ies of delta planforms having hemicylinder leading edges and spherical- segment noses. The sweep angles investigated were 450, 60°, 70°, 80°, 85", and 90°, and the thickness ratio varied from 0 to 0.3 for each sweep angle. The investigation w a s conducted at a Mach number of approximately 20 in helium flow and the angle-of-attack range was approximately from Oo to 30°.

Maximum lift-drag ratio exhibited a nearly linear decay as thickness ratio and volumetric coefficient were logarithmically increased. The angle of attack at which maximum lift-drag ratio occurred exhibited a nearly exponential increase with thickness ratio. to delta planforms without incurring serious penalities in maximum lift-drag ratio. Normal-force-curve and lift-curve slopes generally increased linearly with thickness ratio. Center of pressure moved forward from the 2/3-root-chord point as thickness ratio increased from zero. Center of pressure also moved rearward with decreasing sweep angle for the thicker wings. Newtonian impact theory and a modified Newtonian impact theory plus skin-friction calculations were generally adequate for predicting trends only.

The data indicated that it may be possible to discretely add a considerable volume

Langley Research Center, National Aeronautics and Space Administration,

Langley Station, Hampton, Va., February 8, 1966.

9

REFERENCES

1. Eggers, Alfred J., Jr.; Allen, H. Julian; and Neice, Stanford E.: A Comparative Analysis of the Performance of Long-Range Hypervelocity Vehicles. NACA Rept. 1382, 1958.

2. Fetterman, David E.; and Neal, Luther, Jr.: An Analysis of the Delta-Wing Hyper- sonic Stability and Control Behavior at Angles of Attack Between 30° and 90°. NASA T N D-1602, 1963.

3. Witcofski, Robert D.; and Marcum, Don C., Jr.: Wing Sweep and Blunting Effects on Delta Planforms at M = 20. AIAA J., vol. 3, no. 3, Mar. 1965, pp. 547-548.

4. Mechtly, E. A.: The International System of Units - Physical Constants and Conversion Factors. NASA SP-7012, 1964.

5. Arrington, James P.; Joiner, Roy C., Jr.; and Henderson, Arthur, Jr.: Longitudinal Characteristics of Several Configurations at Hypersonic Mach Numbers in Conical and Contoured Nozzles. NASA TN D-2489, 1964.

6. Johnston, Patrick J.; and Snyder, Curtis D.: Static Longitudinal Stability and Per- formance of Several Ballistic Spacecraft Configurations in Helium at a Mach Num- ber of 24.5. NASA TN D-1379, 1962.

7. Johnston, Patrick J.; Snyder, Curtis D.; and Witcofski, Robert D.: Maximum Lift- Drag Ratios of Delta-Wing-Half-Cone Combinations at a Mach Number of 20 in Helium. NASA TN D-2762, 1965.

8. Olstad, Walter B.: Theoretical Evaluation of Hypersonic Forces, Moments, and Stability Derivatives for Combinations of Flat Plates, Including Effects of Blunt Leading Edges, by Newtonian Impact Theory. NASA TN D-1015, 1962.

9. Bertram, Mitchel H.: Boundary-Layer Displacement Effects in Air at Mach Numbers of 6.8 and 9.6. NASA TR R-22, 1959.

10. Maslen, S. H.: Considerations in the Design of Vehicles Capable of Substantial Hypersonic Lift-Drag Ratios. Space Technology, Vol. 11, U.S. Air Force and Aerospace Corp., Aug. 1964,

Trans. Ninth Symposium on Ballistic Miss i le and

pp. 117-158.

11. Bertram, Mitchel H.; and McCauley, William D.: Investigation of the Aerodynamic Characteristics at High Supersonic Mach Numbers of a Family of Delta Wings Having Double-Wedge Sections With the Maximum Thickness at 0.18 Chord. NACA RM L54G28, 1954.

10

12. Olstad, Walter B.: Longitudinal Aerodynamic Characteristics of Several Thick-Slab Delta Wings at Mach Numbers of 3.00, 4.50, and 6.00 and Angles of Attack to 95O. NASA TM X-742, 1963.

11

TABLE I.- PERTINENT MODEL DIMENSIONSJ TEST PARAMETERS, AND ACCURACY

Figure

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

a30 a3 1 a3 2 "33 "34 a3 5 a3 6

4 and 37 a38

a40 a4 1 a42

4 and 37

t

a39

1

a4

-

A, dee

45 60 70 80 85 '9 0 45 60 $0 80 85 '9 0 45 70 60 80 85 90 70 80 85 70 80 85 70 BO 85 60 70 BO 85 BO BO

-

-

0.299 .299 .299 .299 .299 .299 .205 .205 .205 .205 .205 .205 .143 .132 .098 .083 .083 .083 .033 .033 .033 .020 .020 .020 .010 .010 .010

1 1 1 1 .010 .010

- in.

1.25( 1.25( 1.25C 1.25( 1.25( 2.00c

.8OC 1.25C 1.25( 1.25C 1.25C 2.ooc .59€

1.25: .60C

L.25C L.25C L.25C .333 .333 .333 .200 ,200 .200 . loo .loo . loo

1 1

1 1 .loo .loo

__

~

~

t

cm

3.175 3.175 3.175 3.175 3.175 5.080 2.032 3.175 3.175 3.175 3.175 5.080 1.519 3.188 1.524 3.175 3.175 3.175 .846 .846 .846 .508 .508 .508 .254 .254 .254

3 3 3 I .254 .254

in.

4.18: 4.183 4.183 4.183 4.183 6.693 3.902 6.100 6.098 6.098 6.098 9.756 4.183 9.500 6.098

15.000 15.000 15.000 .o.ooo .o.ooo .o.ooo .o.ooo .o.ooo .o.ooo .o.ooo 0.000 0.000 5.200 8.150 .1.340 .1.380 0.000 0.000

~~

C

cm

10.621 10.62: 10.62: 10.62: 10.62: 17.00C 9.913

15.494 15.48: 15.48: 15.48: 24.78C 10.62E 24.13C 15.489 38.100 38.100 38.100 25.400 25.400 25.400 25.400 25.400 25.400 25.400 25.400 25.400 13.208 20.701 28.804 28.905 25.400 25.400

M,

20.:

1

21.7 20.6 19.9 19.9 30.3 21.6 __

CN

t0.0026 f.0025 f.0032 f.0026 5.0031 5.0094 f.0031 f.0043 f.0017 f.0026 f.0032 f. 00 54 5.0027 f.0027 f.0022 f.0020 5.0031 f.0028 f. 0029 *.0054 f. 009 5 f. 003 1 f. 0059 f. 009 5 f. 0030 f. 006 1 5.0116 f. 0027 f. 0026 f. 0037 f. 0073 +. 0041 +. 0036

Accuracy of - CA

t0.0065 5.0025 1.0032 f. 0009 f. 0010 f.0013 ~ 0 0 7 9 f.0006 f.0017 f.0026 f.0032 5.0008 f.0067 f.0004 f.0056 f.0003 *.0004 f.0069 5. 0004 m.0008 f.0013 rt. 0004 +. 0008 5.0013 k. 0004 *. 0009 k. 0016 t. 0003 t. 0003 +. 0005 t. 0009 t. 0005 t. 0005

Cm

t0.62 x lo-: 5.37 5.48 f.45 f. 52 f.12 f.81 *.61 f.17 5. 27 f. 39 f.48 f.91 5.25 k 3 6 5.11 f. 18 f.31 f.36 f.67 :1.17 f.48 f.94 :1.20 f.48 ~ 9 8 1.06 2.20 f.96 f. 55 1.10 f.89 f. 57

aBalance-housing bodies are on model.

bHemisphere-cylinder.

12

(a) Basic configuration.

r/c = 0 1 h,deg . 2,/c C

in. cm 28.90 85 0.77 11.38

80 .65 11.34 28.80 70 .77 8.15 2070 60 .77 5.20 13.21 .

t = 2r for t/c > 0.08, h= t h t/c

0.0 I 0 ,020 033

~

1 , /C 1 L,/c h/c rb/c

0.88 0.46 0.081 0.037

(b) Wing balance-housing bodies.

(c) Wings used to simulate zero leading-edge radius.

Figure 1.- Model sketches.

13

E%? " . . .:. , . . . . - .-. . - .. .

. c

HYDRAULICALLY' MODEL-SUPPORT

Figure 2.- Perspective drawing of Langley 22-inch helium tunnel.

a

b

0

0

. . 1 8%

C d

i 1

.-

I

!

e Wing t/c a 0 b .OlO C .020 d ,033 e .08 I f .205

, 9 299

9

Figure 3.- Photograph of A = 800 wings. The balance-housing bodies shown on wing a and wing c were used on wing b. L-65-7778.1

~ . . __ . . . - . 0 3.66 x IO'

660 x IO' '

8

o

0

e-

-

0

o

n

(a) Variation of CN, CA, and Cm with a.

Figure 4. - Effect of Reynolds number and balance-housing bodies on aerodynamic characteristics.

04

02 c,

3

,

16

6

5

.4

3

CL

.2

.I

0

- I

6

4

2

L/D 0

- 2

- 4 -

lu R I I I I I I I I IT

0 3.66XlO" -------I 17 6.60~10~ '

0 3 . 6 6 x I e

3

~

n

~

(b) Variation of CL, CD, and L/D with a.

Figure 4.- Concluded.

17

. . . . . . . . . . . . . - 7

6

5

4

(L

3

2

I

I Mod Newtonian impact theory

plus skin friction -c

I I I I I I I I

0 0 0 A h

- + Newtonian impact theory

0 I I I I 1 l l l l l - 1 - _ = _ 1 - .o I .02 .03 .04 ' 05 .06 .08 .IO .20 .30 .40

Figure 5.- Maximum lift-drag ratio as a function of thickness ratio.

18

................... I

7-

6 '- I

5

4

(L/D)max

3

2

I

9

0 0

0 A h ts

0 n

0

t /C

,010 ,020 .033 .083 . I32

0

.299 ::E / - - - - Newtonian impact theory -- Mod. Newtonian impact theory

plus skin friction

i

t/c = 0

t/c 0.010

t /c = 0.020

t/c = 0.033

t/c = 0.083

t/c = 0.205

t/c = 0.299

I

cf I I I ~

‘L, 1 Y

L A

LY #

t/c

( a ) Lift coefficient at (L/D)max. Flags indicate presence of balance-housing bodies.

(b l Angle of attack at (L/D)max.

Figure 7.- Lift and angle of attack at (L/D)max as a function of thickness ratio.

20

I I I

6-

I I I

3

\

Po w Figure 8.- (L/D)max as a function of volumetric coefficient. Solid symbols denote inclusion of balance-housing-body volume; flagged symbols denote inclusion of wing volume only. Unflagged symbols denote wings which required no balance-housing bodies.

I L,

I

I Jp

/-

/---

4 1

A'

t /c

Figure 9.- Slopes of normal-force curves and lift curves at zero angle of attack as a function of thickness ratio.

22

.018

..016

..014

,012

,010

' a C

,008

,006

004

002

0

I .c

.E

.e xCP -

C L

L

C

IS

_I

xCP - C

I

0

e

28 32

t/c 0 0.299 0 ,205 0 .083 A ,030 n .020

.010 0 0

- - - ,299 .- - - - - ,205 ~ ,083 _ _ - - .033

I .o

.8

/- t'c=o 6

xCP - C

.4

.2

36 40

Figure 10.- Variation of center of pressure with angle of attack. Curves denote Newtonian impact theory.

23

t/c 0 0.299

,205 0 .I32 * ,143

.098 h ,033 0 .020 0 .010 0 0

-- - .299 -----. I43

- - - - .033 - .oga

-t/c =o

0

8

/- t/c=

6

CP

C

X -

1

?

1

t/c=O


24

1

'

0

' I ' I t/c 0.299

t/c = 0.205

t/c = 0.083

Ll 20

Figure 11.- Variation of center of pressure with angle of attack.

25

L xCP C

- xCP C

A

t/c = 0.033

t /c = 0.020

h h Q

t/c = 0.010

I I I I I I I I

i 20

0

0 A

32

I

A, deg 85 80 70

I I

I I I

I 36

I .o

.8

.6 - xCP C

.4

.2

0

40


26

.. .-.. -, ... , , , , .. .._. ._

.e

.7

.E

F .C

L

CN

7 ..

c .L

.I

C

-.I

01

0

-01

cm

- 0:

-.0:

- .OL

Newtorion impact theory

I

'I /L I I I 1 r i 1 I I --t

I 1

I L I I

Y I 1 I 28

1. -

\

\

32

Figure 12.- Basic aerodynamic characteristics. t/c = 0.299; A = 45O.

27

I I

I'

I

32

i

/-

I .4

1 .2

-lo I

I 36

.o

.8

6

CD


28

I

.8

.7

.6

.5

.4

CN

-A .I

.L

.I

C

-.I

a

01

0

crn -.Ol

-.0:

- 0;

/

L

I

7.-

1

I I

I I I

1 I I

BY

1- 1

6-L - 1 T-

I 1 I 8

/

\

3

/

~

L

>

\

4 28

Figure 13.- Basic aerodynamic characteristics. t/c = 0.299; A = 600.

29

CL

L/D

I I I /

I I 4 c

I I I I


30

7

.6

.5

.4

CN 3

.2

.I

0

- I

.04

03

0 2

Cm

0 I

0

-01 -4 0 4

I I I I I I I - Newtonion impact theory

Figure 14

8

I

k I L 4

I L

I I I 16

Basic aerodynamic characteristics. t/c = 0.299; A = 70°.

3 32

20

.I8

CA .I6

.I4

3

31

CL

L/D

I I I I I I I I -Newtonian impact theory


32

7

.E

E _"

.4

CN 3

.2

.I

0

-.I

.04

.03

02

.o I

0

-01 -, 4 8 12 16 Q, deg

..

20

'A

16

Figure 15.- Basic aerodynamic characteristics. t/c = 0.299; A = BOo.

33

I

I I - . ) I I I -Newtonian Lnpoct theory

6

4

CD 2

0

I


34

.6

.5

.4

.3

CN .2

. I

C

-.I

.oE

.Of

OL

.0:

ctn .0:

.o I

0

-.O -

0

0

0

4

I I I I I I -Newt& impact theory /

.

1.22

.20 cn

.I8


35

-4 0 4

I l l l l l l .Newtonian impact theory I

16 ' 20 0 , deg

I ;i-

I

I I/

-

I

----

I I I I I

. - 1 36


36

.E

C

L

CN L

. I

0

- I

.IC

.O€

.a

c, .OL

02

0

-.Oi -

0

a

! I J J -Newtotian impact

/

.

.

/

.

1 2(

28

26

24 Cn

22

20

Figure 17.- Basic aerodynamic characteristics t/c = 0.299; A = 900.

37

Figure 17

I I I impact theor)

16 i i i a , deg

.- Concluded.

i

6

4

CD 2

3

38

I

.8

7

.6

.5

.4

CN

3

.2

.I

0

- I

.o I 2

.me

004

cm C

-.004

-.008

-


39

- Newtonion impact

8

I I thew)

12 16 a , deg

/

.

/

8

6

‘D

2

0

)


40

I

.6

.5

.4

3

CN .2

.I

0

-.I

O?

02

0 I

Cm 0

-.Ol

-.02 -

I l l __ Newtonian

0 4 08 16 20

a, deg

I 28 32

Figure 19.- Basic aerodynamic characteristics. t/c = 0.205; A = 60°.

4 1

CL

L /D

4 -.2

-4 0

111 I 1-1 1- -Newtonian impact theory

8 12 16 a, deg

28 32 36

8

6

‘D

2

0


42

.8

.7

.6

5

.4

CN 3

.2

. I

0

- _ I

.O?

.Oi

.o I cnl

0

-.OI - 0


43

4

- Newtonian kpact

8 12

0 /

a

Q

/

/

Y

28 32 36

.6

.4

2

0


44

.7

.E

c .C

L

CN .?

.i

. I

C

-_I

.O?

.02

.o I

cm

0

-.01

-02 -

I l l - Newtonian

J I lpoct theor)

Q, deg

Figure 21.- Basic aerodynamic characteristics. t /c = 0.205; A = 800.

I4

12

32 36

cn

45

I 1 - 1 I I I __ Newtonian impact theory

i 0

-u

/

0

1

/

I

L

L

/'

,

-

.6

.4

% 2

0


46

.6

.5

.4

3

CN

.2

.I

0

-.I

.Of

.OL

.O?

c, .oi

.o I

1 C

h -.O!

r

I

I I I I I I -Newtonian impact thew)

/ 0

-

a

2.

I

Figure 22.- Basic aerodynamic characteristics. t/c = 0.205; A = So.

47

CI

L/D

4

3


48

c c

.4

.3

CN .2

.I

0

-.I

. I c

DE

.a

c, .OL

0;

0

-.a -

u -Newtonian impact theory

Figure 23.- Basic aerodynamic characteristics. t/c = 0235; A = 900.

49

. . - .. ---

CL 2

.I

0

-_I

1.2

I .o

.8

.6

LID

.4

.2

0

- Newtonian impact

0

,/

/

c

i

L

6

4

CD 2

0


50

7

.6

.5

.4

CN .3

.2

.I

C

-.I

,012

.mi

00

,

-.oo

-.oo

-4

0

D

c

0

l l l l l l l ~ 1 __ Newtonian impact theory 1

0 I

0

A

4 8

/ /

-

,

\.

4

/


51

, . ..

I H I I ~

Newtonion impact thea

/

/


52

.6 I

.5

.4

3

CN

.2

.I

0

-.I

.02(

.OIE

,012

.Go

.E

-.O(

/

-

i -r 24

0

. I I ~-

28 32 36


53


54

6

4

CD

2

3

28 32 36

‘I

1

.e

.7

.E

E

L

CN

L

_I

0

-_I

.0:

.0;

cm .01

0

-.O -

-Newtonian - impact theory

Figure 26.- Basic aerodynamic characteristics. t / c = 0.098; A = 600.

55

___ Newtonion impact theory(

0 /

?

i

I

-

/

I

.

e,

/

I

Q

24 28

6

4

CD

2

0


56

1

I I

6

5

4

3

CN i

I

C

- I

02c

016

012

OOE cnl

004

c

- OOf -

I I I I I I __Newtonian impact theory

/'

/

7gure 27.- Basic aerodynamic characteristics. t /c = 0.083; A = 80'

57

58

~~ l l l l l l -Newtonion impact thew

4


/

\

/

I

\

/

0

.4

.2 CD

0

.6

.5

.4

3

CN

.2

. I

0

- I

.04

.03

.02

cm

.01

0

-.Ol -4

0

0

0

0 4 8

! ! I / ! ! -Newtonian impact t b q

28

04

CA 02

0

32 36

Figure 28.- Basic aerodynamic characteristics. t / c = 0.083; A = 85O.

59

I

-4 0

I I I I I I - Newtonian impact thew

12 16 a, deg


60

..51

.4 I

.3 I cN 2 l

. I I

I

0

-.I

.07

.06

.05

.04

cm .03

.02

.o I

0

-4

I ! I I I I -Newtonion impact theory

20 24 28

CA

,006

04

36 I

32


61

__ Newtonian impact thew)

I 0

U

/

0

/ 0

CT

/

0

/

----

I

/ 0

IT

'- 0

/

I

\

/.

,

\

24 28 32 36


62

.7

.6

.5

.4

cN 3

.2

. I

0

-.I

.OOE

OOL

c, 002

(

-.oo;

I I I I I I I -Newtonian impoct theory ----Mod. Newtonian impact theory

plus skin friction

Figure 30.- Basic aerodynamic characteristics. t / c = 0.033; A = 70°.

63

11 I I 1 1 . 1 I --NewtoN'an impact fheory - - - - Mod. Newtonian irrpoct theory

plus skin friction

.6

.4

cD - 2

0


64

7

.6

.5

.4

'N

.2

.I

0

-.I

.OIE

.o I i

.OOt

Cm

,001

c

-.OOL -4

-Newtonian impact theory _ _ - - Mod. Newtonian impact theory

plus skin friction

9 I 3

l l i 7-

I

I

-L -7 I

Figure 31.- Basic aerodynamic characteristics. t/c = 0.033; A = SOo.

65

I I I. I I I I I -Newtonim impact theory - - - - Mod. Newtonian impoct theory

plus skin friction

i

/

t

20 28 32 36

6

4

CD 2

0


66

.6

.5

.4

.3

CN .2

.I

0

-_I

.02c

.016

,012

c, .cot

.m<

(

-.oo

! I I ! . . - I ! I I __ Newtonion irrpOct thewy

_ _ --Mod. Newtonian impact theory

28 32 36


67

1 I I I . I . I. I I -Newtonion impact theory _- - - Mod. Newtonian impact theory

plus skin friction

8 4

5

4

3

CD 2

I

1


68

.7

.6

.5

.4

cN 2

.L

.I

C

-.I

.ooc

.OOL

c, 00;

c

-00; 0

I I I I - - ! & U I

-Newtonion inpoct theory - - _ _ Mod. Newtorion impact theory

plus skin friction

Figure 33.- Basic aerodynamic characteristics. t / c = 0.020; A = 70°.

69

Newtonicn impact theory .Mod. Newtonian irrpact theory

plus skin friction

/

,’

c /

\

6

4

CD

2

1


70

I

.7

.6

.5

.4

c, 3

.2

.I

0

-.I

.008

,006

.004

cm 002

0

-.002 - 8 0

I I I I I I I ! __Newtonian impact theory - _ _ _ Mod. Newtonian impact theory

plus skin friction

4 12 16 20 a, deg

24

Figure 34.- Basic aerodynamic data. t / c = 0.020; A = &lo.

71

.6

.5

.4

.3

.2

_ I

0

- . I

6

4

2

0

- 2

- 4

-6 -4 0

-Newtonion impact theory ----Mod. Newtonion impoct theory

plus skin friction

8

I

/

/

I /

/

//

I .

4

6

4

CD 2

0


72

.8

.7

.6

.5

.4

CN

.3

.2

.I

C

-.I

,016

,012

.WE

cm .OOL

C

-.OOL -

I L I 1 1 . 1 I -Newtonion irrpact theory -Mod. Newtonian impact theory

plus skin friction

1

11 li: I

1 I 20

6 32

Figure 35.- Basic aerodynamic data. t/c = 0.020; A = 85O.

73

I I 1 1 - 1 I I I __ Newtonian impact theory -_--Mod. Newtonion impact theory

plus skin friction

20

-

-

/ /

b

b

/

/

. I

/

/

/

/

.

24 28 32 36

6

4

CD 2

0


74

.7

.6

.5

.4

cN .3

.2

.I

0

-.I

.oo:

.ooi

,001

cm C

- .001

- ,002 -

-Newtonian irrpact ihewy Newtonian inpact theory

plus skin friction

06

04

CA 02


75

6

4

CD 2

0


76

.E

F

1

CN

(

-

.oo

00

00

cm

-00

-.oc

~Newtonim impact theory ----Mod. Newtonian impact thecry

plus skin friction

32 36

Figure 37.- Basic aerodynamic characteristics. t lc = 0.010; A = 80°. Flagged symbols denote use of small balance-housing body; unflagged symbols, of large balance-housing body.

77


78

.7

.6

.5

.4

CN .3

.2

. I

C

-.I

,008

.006

004

cm ,002

0

-.002

-.OO?

I ! ! I ! . . ! ! I -Newtonion irrpOct theory _ _ - - Mod. Newtonion inpoct theory

plus skin friction

24 28 32 36


79

I IT I I . - . I I I I -Newtonion inpoct theory ----Mod. Newtonian inpact theory

plus skin friction

4

‘D

0


ao

L

L

,004

002

crn 0

-.002

-004 -

-Newtonian impact theory _ _ --Mod. Newtonion impact theory

plus skin friction

I

5 0

/

i

32

04

3

81

Figure 39.- Basic aerodynamic characteristics. t/c = 0; A = 60°.

_ _ __Mod. Newtonian irrpoct theory plus skin friction

24

4

'0

0

I


82

I

.5

.4

3

CN .2

. I

0

-.I

,008

.OOE

004

Cm 002

C

-.002 -

/

/’

-Newtonian impact theory - - - - Mod. Newtonian impact theory

plus skin friction

Figure 40.- Basic aerodynamic characteristics. t/c

I

tH 24 28

0: A = 70°.

04

02 c*

0

I2 36

83

CL

L/D

84

a , deg


11 I I 1 1 I I t h y

friction .4

* 'D

0

.OO(

001

cm 00;

(

-00; -

-Newtonion impact theory - - - - Mcd. Newtonian impact t h e w

plus skin friction

Figure 41.- Basic aerodynamic characteristics. t / c = 0; A = 800.

85

CL

L/D

I _ _ -Mod. Newtdon impact theory

plus skin friction

a

.


86

.5

.4

.3

CN .2

. I

0

-.I

.o I 0

.OOE

.ooc

OOL

00;

(

-00; 8

/ /

,/

/

/

/ /

-Newtonion impact theory - - - - Mod. Newtonian impact theory

plus skin friction

32 36

Figure 42.- Basic aerodynamic characteristics. t / c = 0; A = 85O.

87

8

/’

- - --Mod. Newtonian impact theory plus skin friction

- -

‘.

l


88 NASA-Langley, 1966

4

‘D

0

>

L-4 520

“The aerozautiral and spare activities of the Uizited States shall be conducted so as to cotitribute . . . to the expansion of hriman knowledge of phenomena iz the atmosphere and spare. T h e Administration shall provide for the widest practicable aiid appropriate dissemination of information concerning its actioities and the resiilts thereof.”

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