ADVANCES m HYPERSONIC EXTRAPOlATION CAPABILITY -

WIND TUNNEL TO FLIGHT

J. A. Penland

NASA Langley Research Center Hampton J Virginia

and

D. J. Romeo

Cornell Aeronautical Laboratory, Inc. Buffalo, New York

PEN00218

Presented at the AIAA Ninth Aerospace Sciences Meeting

New York, New York January 25-26, 1971

ADVANCES IN HYPERSONIC EXTFAPOIATION CAPABILITY -WIND TUNNEL TO FLIGHT

J. A. Penland*

NASA Langley Research Center Hampton, Virginia

and

D. J. Romeo**

Cornell Aeronautical Laboratory, Inc. Buffalo, New York

Abstract

In the past, the limited Reynolds number capability of hypersonic facilities has prevented reliable extrapolation of data to flight Reynolds numbers. Recent results on a hypersonic cruise aircraft configuration obtained at Mach 8 in the Cornell Aeronautical Laboratory HYPersonic Shock Tunnel over a Reynolds number range from a completely laminar boundary layer to a predominantly turbulent one are presented. The significant factors which can affect extrapolation of wind­tunnel data at subscale Reynolds numbers to flight values are identified. The capability for predict­ing turbulent flight Reynolds number data from wind­tunnel data under laminar and transitional boundary­layer conditions are shown.

Introduction

The basic aim of complete configuration wind­tunnel tests is to determine the full-scale aero­dynamic performance of the particular concept. In the past,a major problem in the stu~ of efficient hypersonic airbreathing aircraft resulted from the limited Reyno~ds number capability of hypersonic wind tunnels.tl) The nature of the problem presented by this limitation is shown in Figure 1. Because of the relatively low Reynolds numbers then available on realistic configurations, the boundary layers over small subscale test modelS were mostly laminar and transitional, whereas, over full-scale aircraft (typically 100 meters long), a turbulent boundary layer will cover all but a small area of the vehicle near the wing and tail leading edges and the fuselage nose. This difference in wind tunnel and flight Reynolds numbers, of course, has always existed at lower speeds, but the problem has been overcome by adding small roughness elements to the model which artifi­cially produce a turbulent bO\Uldary layer. At hypersonic speeds, however, usable boundary-layer trips have not been developed.(2,3) Because of the inability to develop a predOminantly turbulent boundary layer over test models at hypersonic speeds, the viscous effects, not only on skin friction, but also on other important aerodynamic parameters, listed in Figure 2, that affect flight performance could not be determined. As a result, reliable

*

extrapolation of full-scale aerodynamics from wind­tunnel results could not be made.

In the meantime, several developments have occurred to increase the range of available Reynolds numbers. These developments include modification to existing conventional tunnels and improvement in shock tunnel capabilities. In particular, the cornell(t~ronautical Laboratory HYPersonic Shock Tunnel ) has been extremely useful in stu~ng high Reynolds number effects. As shown in Figure 3, by operating this tunnel at low stagnation temperatures (sufficient to just avoid air liquefaction) and high pressures, full­scale Reynolds numbers are available. Under these conditions, model boundary layers are predominantly turbulent without forced transition. On the other end of its Reynolds number range, the tunnel provides completely laminar model boundary layers. The Cornell Aeronautical Laboratory HYPersonic Shock Tunnel,then, provides the unique opportunity to stu~ hypersonic viscous effects on aero~c performance over the. complete boundary-layer spectrum.

Taking advantage of this opportunity, a stu~ has been carried out on the model shown in Figure 4. The configuration is representative of current ideas for a Mach 6, hypersonic transport aircraft. The full-scale version would be nearly 100 meters long and have about a 5,OOO-nautical­mile-range capability. The concept features a wide fuselage in relation to its height combined with strakes to improve the lifting capability of this predominant component. The fuselage is blended with the strakes and wing to reduce adverse component interference effects. The solid lines show the configuration tested. The vertical tail and propulsion system were eliminated during these tests to reduce the zero lift drag, and make the results more sensitive to variations of Reynolds numbers. The test model was about 2/3 meters long or 1/150 scale of the full-size flight vehicle. The investigation consisted of force tests over a Reynolds number range from about 0.5 million to 160 million, based on fuselage design length. Over this Reynolds number range, the Mach number varied from about 7.5 to 8.1.

Aero-Space Technologist, Hypersonic Vehicles Division

** Research Aeronautical Engineer

L-7479

The lift-to-drag ratio, Lin, as a fUnction of Reynolds number is shown in Figure 5. Notice that this is not a variation of the maximum Lin, but rather the Lin at an angle of attack of 30 • This is the angle of attack for maximum Lin at the highest test Reynolds number, and the model attitude is kept constant at this value for lower Reynolds numbers. Predictions of the data, assuming either an all laminar or an all turbulent boundary layer, are also shown. To obtain these predictions, inviscid theories (tangent cone on the fuselage, shock expansion on the strakes and wing) were applied to the isolated components through the computer program of reference 5. To these results skin-friction prediction given by the T', of reference 6, or Spalding-Chi, reference 7, theories were added. These theories were applied through the computer program of reference 5.

At the lowest Reynolds numbers, the model boundary layer is completely laminar. Transitional boundary-layer effects begin to emerge at Reynolds numbers of about 1.5 to 2 million. These effects predominate for about a decade in Reynolds number until the turbulent boundary layer exerts the major influence at Reynolds numbers between 15 and 20 million. This trend agrees with data obtained in the Cornell Aeronautical Laboratory Shock Tunnel on isolated cones and flat plates and from schlieren photographs of the present configuration. This is an interesting result for several reasons: (1) This range of Reynolds numbers is about the limit of conventional wind tunnels presently available, and (2) if the turbulent boundary layer predominates at these Reynolds numbers in these facilities (there are indications they do and additional tests are being made to confirm this) then flight extrapola­tions of wind-tunnel data can be made confidently since only small corrections will be re~uired. The ~uestion then, is what performance parameters have major effects on these extrapolations.

Consider first the normal force, CN, which is 'closely related to the lift force for low-drag configurations at low qngles of attack. This p~rameter could be sensitive to the nature of the boundary layer through the viscous effects on lee­side flows and component interference, and at the lower Reynolds numbers through the boundary-layer displacement effects. In Figure 6, the normal force is shown as fUnctions of angle of attack for various Reynolds numbers over the test range. Although there may be some viscous effects at the lower Reynolds numbers, this effect is very small. In any event, at Reynolds numbers above 10 million, there is no noticeable viscous effects at all. This result is further borne out in Figure 7 where the CN at an angle of attack of 30 is essentially independent of Reynolds number. This result implies that if viscous effects change the local characteristics 'of lee-side flows and component interference, their overall effect is negligible for this configuration, and the normal force parameter may be neglected in the extrapolation process.

Next consider the axial-force coefficient, CA. This parameter is, of course, strongly affected by viscous effects on skin-friction and boundary­layer displacement effects. The large variation of CA with Reynolds number is shown in Figures 8 and 9.

2

Most of the change in CA is prcbably due to skin­friction changes as boundary-layer displacement effects would be expected to be confined to the very low Reynolds numbers. The skin friction then, as it has always been, is a strong factor in extrapolations of wind-tunnel results to flight Reynolds numbers. It should be noted that the turbulent predictions for this blended wing-body configuration are superior to the laminar predictions.

The drag-due-to-lift parameter, dcn/CCL2, is the last one that will be considered. This parameter again would be most affected by viscous effects on both lee-side flows and component interference. The variation of ccn/ccL

2 with Reynolds number is shown in Figure 10. The slight increase with Reynolds number is approximately the same as the predicted trend which accounts for the effect of small variations in the tunnel Mach number with Reynolds number. For all practical purposes, Reynolds number has no effect en ccn/ccL2 which indicates again, as with the! normal force, that overall viscous effects on lee­side flows and component interference are negligible for this configuration. Considerations of the drag-due-to-lift parameter in hypersonic wind­tunnel data extrapolation are therefore not re~uired.

Of the parameters considered then, only the viscous effects on skin friction need be accounted for in correcting subscale hypersonic wind-tunnel data to flight values. Let us examine now how accurately we can predict the data at the highest Reynolds number by making these viscous corrections to the data at lower Reynolds numbers. The correction simply amounts to replacing the Skin friction in the data at lower Reynolds numbers with the skin friction at the high Reynolds numbers. For our estimates of the laminar skin friction, we used the T' method, and the Spalding-Chi method for the turbulent skin friction. The total axial­force coefficient to which these skin-friction corrections were made was obtained from a mean fairing through the data as shown in the top of Figure 11. The percent errors in predicting constant angle of attack (30

), values of CL, Cn, and Lin at the highest Reynolds numbers are shown at the bottom. For the curves shown, the skin friction, at a given Reynolds number, was assumed ei ther entirely lamirui.r or entirely turbulent. ,U Reynolds numbers below about I million and above about 15 million, where this assumption is nearly correct, the predictions are in error less than 10 percent. In between, large potential errors result because a mixed boundary layer (partly laminar, partly tranSitional, partly turbulent) predominates. It is encouraging to note that if conventional tunnels can achieve a predominantly turbulent boundary layer at the upper limit of their capability (Reynolds numbers of about 20 million), full-scale Reynolds number predictions on the order of 5 percent or less should be obtained assuming an all turbulent boundary layer. The accuracy of these predictions can be improved if the location of transition can be defined and the correct local skin-friction corrections are applied. The location of transition can be determined by using the phase-change-paint techni~ue.

\'

"-,

, , \

"j

These results, of course, apply to the constant angle-of-attack case, and are not necessarily representative of the optimum, or (L/D)max case. Because of the higher drag at lower Reynolds numbers, the angle of attack for (L/D)ma4 will be higher at these test conditions than unQer full-scale Reynolds number conditions, and this optimum angle of attack will not be known apriori. We consider finally then, how accurately the optimum case can be predicted. The results are shown in Figure 12.

Using the data at low Reynolds numbers (below 1 :nillion), where the model boundary layer is laminar, the high Reynolds number value of (L/D)max is well predicted, but the optimum values of CL and CD are not. These errors are partly due to the inability to accurately predict skin friction on a complete configuration, particularly in the laminar region and partly due to the critical nature of the determination of the optimum CL and CD from faired data. The tick marks indicate likely errors from the fairing of present data. By correcting data in the Reynolds number range from 15 to 30 million, however, where the boundary layer is predominantly turbulent, adequate optimum performance values at the high Reynolds numbers can be predicted.

Concluding Remarks

Studies in the Cornell Aeronautical Laboratory Hypersonic Shock Tunnel, at Mach number 8, of a blended wing-body configuration, representative of a hypersonic transport vehicle, have shown that the factor that significantly affects extrapolation of hypersonic subscale Reynolds number data to flight Reynolds number values is the skin friction. If wind-tunnel data can be obtained at Reynolds numbers where the turbulent boundary layer predOminates, simple turbulent skin-friction corrections to the data will allow good prediction of flight Reynolds number performance data. Further improvement should be possible by determining the location of transition and applying the correct local skin friction. The insignificance of the lift and drag due to lift factors indicates that overall viscous effects on both lee-side flows and component interference are secondary for the blended wing body used in this study. A different result may apply to discrete wing-body configuration types where the component interference effects may be more

3

predOminant. Furthermore, additional work is required to determine viscous effects on control effectiveness parameters over the Reynolds number range. An accurate knowledge of these parameters, of course, is required to predict reliable values of the tri=ed performance at flight Reynolds numbers, and because of possible flow separation over controls, viscous effects on these parameters could be significant.

References

1. Penland, Jim A.; Edwards, Clyde L. W.; Whi tcofski, Robert D.; and Marcum, Don C.: Comparative Aerodynamic Study of Two HyperSOnic Cruise Aircraft Configurations Derived From Trade-Off Studies. NASA TM x-1435, October 1967.

2. Morrisette, E. Leon; Stone, David R.; and Cary, Aubrey M., Jr.: Downstream Effects of Boundary-Layer Trips in Hypersonic Flow. Paper 16 of Compressible Turbulent Boundary Layers. NASA. SP-216, December 10-1l, 1968.

3. Whitehead, Allen H., Jr.: Flow-Field and Drag Characteristics of Several Boundary-­Layer Tripping Elements in Hypersonic Flow. NASA TN D-5454, October 1969.

4. Anon: DeSCription and Capabilities of the Cornell Aeronautical Laboratory Hypersonic Shock Tunnel. Cornell Aeronautical Laboratory, Inc., May 1969.

5. Gentry, Arvel E.: Hypersonic Arbitrary-Body Aerodynamic Computer Program, Mark TV Version, Volume I - "User's ManuaL" Douglas Report DAC 61552, 1968.

6. Monoghan,. R. J.: An ApprOximate Solution of the Compressible Laminar Boundary Layer on a Flat Plate. British R & M No. 2760, 1953.

7. Spalding, D. B.; and Chi, S. W.: The .Drag of a Compressible Turbulent Boundary Layer on a Smooth Flat Plate With and Without Heat Transfer. Journal, Fluid Mechanics, Vol. 18, Part I, January 1964, pp. 117-143.

CIRCA 1965

M~ FULL SCALE

(VDlmax 4

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o 00 o

TURBULENT

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21 L -~--l'--+4-'-76 1..L!1='=0--;t20~"-;40~60~~100;;--~200 x 106 REYNOLDS NUMBER

Figure 1.- Hypersonic wind~unnel extrapolation capability in the mid 60's.

1500

1000

ATMOSPHERES 500

Ol~~~~ __ ~~~~~_~~~~ 0.01 RL

2000

To' oK

1000

Figure 3.- 'Per~ormance o~ the Cornell Aeronautical Laboratory shock tunnel at M = 8.

10

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a • 3° 6 ",_ SPALDING CHI CF~

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. O:-~-~--:-3--:6~:';10:----:3';:-O -::60:-7.100:---:;;:300 x 106 .3 .6 REYNOLDS NUMBER

Figure 5.- Variation o~ li~t-drag ratio at 30 angle o~ attack with Reynolds number, M = 8.

PARAMETERS AFFECTING FLIGHT EXTRAPOLATIONS OF (L/Dlmax FRICTION DRAG CD

PRESSURE DRAG CD:

LIFT CURVE SLOPE CL DRAG DUE TO LIFT C a

DL CONTROL EFFECTIVENESS ACm ACL ACD

Figure 2.- Parameters a~~ecting Wind-tunnel data extrapolations to ~light.

.12

.10

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0

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Figure 4.- Hypersonic test model.

~ I

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ikJl' 0 153.2 X 106

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Figure 6.- Variation o~ normal-force coefficient wi th angle o~ attack at various Reynolds numbers, M = 8.

.(8

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Figure 7.- Variation of normal-force coefficient at 30 angle of attack with Reynolds number, M = 8.

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Figure 9.- Variation of axial-force coefficient at 30 angle of attack with Reynolds number, M = 8.

% ERROR

40

20 CD

FAIRED EXPERIMENTAL DATA & THEORY. M· 8

ASSUMED TURBULENT -----> o~~-_-_-__ ~C/~L~ ________ ~~ .. ________ _

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Figure 11. - Accuracy of extrapolation of performance" characteristics at a constant angle of attack to full-scale Reynolds number. .

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Figure 8.- Variation of axial-force coefficient with angle of attack at various Reynolds numbers, M = 8 .

6CD/6CL2, 0-;3· 2.4

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Figure 10.- Variation of drag due to lift with Reynolds number, M = 8. "

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REYNOLDS NUMBER

FigUre 12.- Accuracy 01 extrapolations of optimum performance characteristics to full-scale Reynolds "number.

Reprinted from JOURNAL OF AIRCRAIT, Vol. 8, No. 11, November 1971, pp. 881-884 Copyright, 1971, by the American Institute of Aeronautics and Astronautics, and reprinted by the copyright owner

,

Advances in Hypersonic Exploration Capahility­Wind Tunnel to Flight Reynolds Number

J. A. PENLAND*

NASA Langley Research Center, Hampton, Va.

AND

D. J. ROr.1EOt Cornell Aeronautical Laboratory Inc., Buffalo, N. Y.

In the past, the limited Reynolds number capability of hypersonic facilities has prevented reliable extrapolation of data to flight Reynolds numbers. Recent results on a hypersonic cruise aircraft configuration obtained at Mach 8 in the Cornell Aeronautical Laboratory Hy­personic Shocl. Tunnel over a Reynolds number range from a completely laminar boundary­layer to a predominately turbulent one are presented. The significant factors which can affect extrapolation of wind-tunnel data at sub scale Reynolds numbers to flight values are identified. The capability for predicting turbulent flight Reynolds number data from wind­tunnel data under laminar and transitional boundary-layer conditions are shown.

Introduction

T HE basic aim of complete configuration wind-tunnel tests is to determine the full-scale aerodynamic performance of

the particular concept. In the past, a major problem in the study of efficient hypersonic airbreathing aircraft resulted from the limited Reynolds number capability of hypersonic wind tunnels. The nature of the problem presented by this limita­tion is shown in Fig. 1. Because of the relatively low Reyn­olds numbers then available on realistic configurations, the boundary layers over a small subscale test models were mostly laminar and transitional, whereas, over full-scale aircraft (typically 100 m long), a turbulent boundary layer will cover all but a small area of the vehicle near the wing and tail lead­ing edges and the fuselage nose. This difference in wind-tun­nel and flight Reynolds numbers, of course, has always existed at lower speeds, but the problem has been overcome by adding small roughness elements to the model which artificially pro­duce a turbulent boundary layer. At hypersonic speeds, however, usable boundary-layer trips have not been de­veloped. 1,2 Because of the inability to develop a pre­dominantly turbulent boundary layer over test models at hypersonic speeds, the viscous effects, not only on skin fric­tion, but also on other important aerodynamic parameters, listed in Table 1, that affect flight performance could not be

Table 1 Aerodynamic parameters

PARAMETERS AFFECTING FLIGHT EXTRAPOLATIONS OF (L/Dlmax FRICTION DRAG CD PRESSURE DRAG C F

Dp LIFT CURVE SLOPE CL DRAG DUE TO LIFT C a

DL CONTROL EFFECTIVENESS ACm ACL AC

D

Presented as Paper 71-132 at the AIAA 9th Aerospace Sciences Meeting, New York, January 25-27, 1971; submitted February 26, 1971; revision received June 24, 1971.

Index categories: Aircraft Performance; Aircraft Configura­tion Design; Aircraft and Component Wind-Tunnel Testing.

* Aerospace Engineer, Hypersonic Vehicles Division. Mem­ber AIAA.

t Research Aeronautical Engineer.

determined. As a result, reliable extrapolation of full-scale aerodynamics from wind-tunnel results could not be made.

Shock Tunnel

In the meantime, several developments have occurred to increase the range of available Reynolds numbers. These developments include modification to existing conventional tunnels and improvement in shock tunnel capabilities. In particular, the Cornell Aeronautical Laboratory Hypersonic Shock Tunnel3 has been extremely useful in studying high Reynolds number effects. As shown in Fig. 2, by operating this tunnel at low stagnation temperatures (sufficient to avoid air liquefaction) and high pressures, full-scale Reynolds num­bers are available. All tests were conducted in completely unsaturated air where the lowest test static temperature was 71 OK thus, all data were taken well outside the supersatu­rated'region as defined by Daum. 4 Under these conditions, model boundary layers are predominantly turbulent without forced transition. On the other end of its Reynolds number range, the tunnel provides completely laminar mode bound­ary layers. The Cornell Aeronautical Laboratory Hyper­sonic Shock Tunnel, then, provides the unique opportunity to study hypersonic viscous effects on aerodynamic performance over the complete boundary-layer spectrum.

Test Configuration

Taking advantage of this opportunity, a study has been carried out on the model shown in Fig. 3. The configuration is representative of current ideas for a Mach 6, hypersonic

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Hypersonic wind-tunnel extrapolation capability in the mid-60's.

882 J. A. PENLAND AND D. J. ROMEO J. AIRCRAFT

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Fig. 2 Perforlllance of the Cornell Aeronautical Labora­tory Shoel< Tunnel at ~l = 8.

transport aircraft. The full-scale version would be nearly 100 m long and have about a 5000 naut mile range capability. The concept features a wide fuselage in relation to its height combined with strakes to improve the lifting capability of this predominant component. The fuselage is blended with the strakes and wing to reduce adverse component interference effects. The solid lines show the configuration tested. The vertical tail and propulsion system were eliminated during these tests. The test model was about i m long or Tto scale of the full-size flight vehicle. Additional model details may be found in Ref. 5. The investigation consisted of force tests over a Reynolds number range from about 0.5 million to 160 million, based on fuselage design length. Over this Reynolds number range, the Mach number varied from about 7.5 to 8.1.

~-=~ .. !

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Fig. 3 Hypersonic test uwdel.

Results and Discussion

The lift-to-drag ratio LID as a function of Reynolds num­ber is shown in Fig. 4. Notice that this is not a variation of the maximum LID, but rather the LID at an angle of attack of 3°. This is the angle of attack for maximum LID at the highest test Reynolds number, and the model attitude is kept constant at this value for lower Reynolds numbers. Predic­tions of the data, assuming either an all laminar or an all tur­bulent boundary layer, are also shown. To obtain these pre­dictions, inviscid theories (tangent cone on the fuselage, shock expansion on the strakes and wing) were applied to the iso­lated components through the computer program of Ref. 6. To these results skin friction C F predictions given by the T' theory of Ref. 7, and Spalding-Chi theory of Ref. 8, were added. These theories were applied through the computer program of Ref. 6.

At the lowest Reynolds numbers, the model boundary layer is completely laminar. Transitional boundary-layer effects

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Fig. 4 Variation of lift-drag ratio at 3° angle of attack with Reynolds nun~ber, ~l = 8.

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Fig.5 Variation of norlual-force coefficient with angle of attack at various Reynolds nuu~bers, 111 = 8.

begin to emerge at Reynolds numbers of about 1.5-2 million. These effects predominate for about a decade in Reynolds number until the turbulent boundary layer exerts the major influence at Reynolds numbers between 15 and 20 million. This trend agrees with data obtained in the Cornell Aero­nautical Laboratory Shock Tunnel on isolated cones and flat plates and from schlieren photographs of the present con­figuration. This is an interesting result for several reasons: 1) this range of Reynolds numbers is about the limit of con­ventional wind tunnels presently available and 2) if the tur­bulent boundary layer predominates at these Reynolds num­bers in these facilities (there are indications they do and addi­tional confirmation tests are planned), then flight extrapola­tions of wind-tunnel data can be made confidently since only small corrections will be required. The question then, is what performance parameters have major effects on these extrapola­tions.

Consider first the normal force CN which is closely related to the lift force for low-drag configurations at low angles of attack. This parameter could be sensitive to the nature of the boundary layer through the viscous effects on lee-side flows and component interference, and at the lower Reynolds numbers through the bourldary-layer displacement effects. In Fig. 5, the normal force is shown as functions of angle of attack for various Reynolds numbers over the test range. No viscous effects were included in the theoretical prediction of normal force. Although there may be some viscous effects at the lower Reynolds numbers, this effect is very small. In any event, at Reynolds numbers above 10 million, there are no noticeable viscous effects at all. This result is further borne out in Fig. 6 where the CN at an angle of attack of 3° is essen­tially independent of Reynolds number. This result implies that if viscous effects change the local characteristics of lee­side flows and component interference, their over-all effect is negligible for this configuration, and the normal force parame­ter may be neglected in the extrapolation process.

Next consider the axial-force coefficient CA. This parame­ter is, of course, strongly affected by viscous effects on skin­friction and boundary-layer displacement effects. The large variation of CA with Reynolds number is shown in Figs. 7 and 8. Most of the change in CA is probably due to skin-friction changes as boundary-layer displacement effects would be ex-

eN '06~ a • 30

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REYNOLDS NUMBER

Fig.6 Variation of norlllal-force coefficient at 3° angle of at tack with Heynolds nUlllber, ~1 = 8.

NOVEMBER 1971 HYPERSONIC EXTRAPOLATION SS3

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Fig. 7 Variation of axial-force coefficient with angle of attack at various Heynolds nun~bers, 1\1 = 8.

pected to be confined to the very low Reynolds numbers. The skin friction then, as it has always been, is a strong factor in extrapolations of wind-tunnel results to flight Reynolds numbers. It should be noted that the turbulent predictions for this blended wing-body configuration are superior to the laminar predictions.

The drag-due-to-lift parameter oC D/OC L 2 is the last one that will be considered. This parameter again would be most affected by viscous effects on both Icc-side flows and com­ponent interference. The variation of oC doC L2 with Reyn­olds number is shown in Fig. 9. The slight increase with Reynolds number is approximately the same as the predicted trend which accounts for the effect of small variations in the tunnell\1ach number with Reynolds number. For all prac­tical purposes, Reynolds number has no effect on OCD/OCL 2

which indicates again, as with the normal force, that over-all viscous effects on Icc-side flows and component interference are negligible for this configuration. Considerations of the drag-due-to-lift parameter in hypersonic wind-tunnel data extrapolation are therefore not required.

Of the parameters considered then, only the viscous effects on skin friction need be accounted for in correcting subscale hypersonic wind-tunnel data to flight values. Let us ex­amine now how accurately we can predict the data at the highest Reynolds number by making these viscous corrections to the data at lower Reynolds numbers. The correction sim­ply amounts to replacing the skin friction in the data at lower Reynolds numbers with the turbulent skin friction at the high Reynolds number. For our estimates of the laminar skin friction, we used the T' method, and the Spalding-Chi method for the turbulent skin friction. The total axial-force coefficient to which these skin-friction corrections were made was obtained from a mean fairing through the data as shown in the top of Fig. 10. The percent errors in predicting con­stant angle of attack (3°), values of C L, CD, and L/ D at the

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°.3=-" ........ 6,........J.-_1-..,...3 -'-'L..J6u..LI.lIO--'--3.L0..J-..... 6OL.LI..u100--'-~300 x 106 REYNOLDS NUMBER

Fig. 8 Variation of axial-force coefficient at 3 0 angle of attack with Heynolds nu=ber, M = 8.

2 ~CD/~CL 2'l ____________ .l~~cr~~END :::[111 111 1 IIIIII~ :1111'1 I

.3 .6 I 3 6 10 30 60 100 300 x 106

REYNOLDS NUMBER

Fig.9 Variation of drag due to lift with Heynolds nu=ber, M = 8.

highest Reynolds number are shown at the bottom. For the curves shown, the skin friction, at a given Reynolds number, was assumed either entirely laminar or entirely turbulent. At Reynolds numbers below about 1 million and above about 15 million, where this assumption is nearly correct, the predic­tions are in error less than 10%. In between, large potential errors result because a mixed boundary layer (partly laminar, partly transitional, partly turbulent) predominates. It is encouraging to note that if conventional tunnels can achieve a predominantly turbulent boundary layer at the upper limit of their capability (Reynolds numbers of about 20 million), full-scale Reynolds number predictions on the order of 5% or

.01Of CA

.008

a·3' .006

.004, I I 11 III I J

40 ACCURACY OF FULL SCALE EXTRAPOLATION AT CONSTANT ANGLE OF ATIACK

'I> ERROR

20 CD:-,... ~ L/ 0 ASSUMED TURBULENT

_--------- CL

-20 I ~S~yMIEPILAMI~R 1 I I !II! I I 111tll

.3 ,6 I 3 6 10 30 60 100 REYNOLDS NUMBER

Fig. 10 Accura'cy of extrapolation of perfonnance charac­teristics at a constant angle of attack to full-scale Reynolds

nu=ber.

less should be obtained assuming an all turbulent boundary layer. The accuracy of these predictions can be improved if the location of transition can be defined and the correct local skin-friction corrections are applied. The location of transi­tion can be determined by using the phase-change-paint tech­nique.

These results, of course, apply to the constant angle-of­attack case, and are not necessarily representative of the opti­mum, or (L/D)max case. Because of the higher drag at lower Reynolds numbers, the angle of attack for (LjD)max will be

~~~~~~r[ -,F==;=::::::?==::====*=-----40~ /ASSUMED LAMINAR

C~PT ro~~~--------~t==~~~(~A-S-sUTME--Dru--RB-U-LE-NT---SERROR 0 . 1

-ro

DOPT

ro C 40~ 'ERROROr----------~~L==~~==-T--------­

-20, I 1,,!l1 I I ""I ",,,,,1 .3 .6 3 6 10 30 60 100

REYNOLDS NUMBER

Fig. 11 Accuracy of extrapolations of opti=u= perfor­=ance characteristics to full-scale Heynolds nu=ber.

884 J. A. PENLAND AND D. J. ROMEO J. AIRCRAFT

higher at these test conditions than under full-scale Reynolds number conditions, and this optimum angle of attack will not be known a priori. We consider finally then, how accurately the optimum case can be predicted. The results are shown in Fig. II.

Using the data at low Reynolds numbers (below 1 million), where the model boundary layer is laminar, the high Reynolds number value of (LjD)m.x is well predicted, but the optimum values of eLand CD are not. These errors are partly due to the inability to accurately predict skin friction on a complete configuration, particularly in the laminar region and partly due to the critical nature of the determination of the optimum eLand CD from faired data. The tick marks indicate likely errors from the fairingJ)f present data. By correcting data in the Reynolds number range from 15 to 30 million, however, where the boundary layer is predominantly turbulent, ·ade­quate optimum performance values at the high Reynolds numbers can be predicted.

Concluding Remarks

Studies in the Cornell Aeronautical Laboratory Hypersonic Shock Tunnel, at Mach number 8, of a blended wing-body configuration, representative of a hypersonic transport vehicle, have shown that the factor that significantly affects extrapolation of hypersonic subscale Reynolds number data to flight Reynolds number values is the skin friction. If wind­tunnel data can be obtained at Reynolds numbers where the turbulent boundary layer predominates, simple turbulent skin-friction corrections to the data will allow good prediction of flight Reynolds number performance data. Further im­provement should be possible by determinillg the location of transition and applying the correct local skin friction. The insignificance of the lift and drag-due-to-Iift factors indicates that over-all viscous effects on both lee-side flows and com­ponent interference are secondary for the blended wing body used in this study. A different result may apply to discrete

wing-body configuration types where the component inter­ference effects may be more predominant. Furthermore, additional work is required to determine viscous effects on control effectiveness parameters over the Reynolds number range. An accurate knowledge of these parameters, of course, is required to predict reliable values of the trimmed per­formance at flight Reynolds numbers, and because of possible flow separation over controls, viscous effects on these parame­ters could be significant.

References

1 l\Iorrisette, E. L., Stone, D. H., and Cary, A. l\1., Jr., Down­stream Effects of Boundary-Layer 'l'rips in Hypersonic Flow, NASA SP-2Hl, Dec. 196H.

2 Whitehead, A. J., Jr., "Flow-Field and Drag Characteristics of Several Boundary-Layer Tripping Elements in Hypersonic Flow," TN D-.)4:i4, Oct. 1969, NASA.

3 "Description and Capabilities of the Cornell Aeronautical Laboratory Hpersonic Shock Tunnel," l\Iay 1969, Cornell Aero­nautical Lab. Inc., Buffalo, N. Y.

4 Daum, F. L. and Gyarmathy, G., "Condensation of Air and Nitrogen in Hypersonic Wind Tunnels," AIAA Journal, Vol. 6, No.3, ::'.Iarch 196R, pp. 4;i8-46;;.

5 Ellison, J. C., "Investigation of the Aerodynamic Character­istics of a Hypersonic Transport Model at l\Iach Numbers to 6," TN D-6191, April 1971, NASA.

6 Gentry, A. E., "Hypersonic Arbitrary-Body Aerodynamic Computer Program, l\Iark IV Version," User's l1[anual, Vol. I, DAC 61.5;)2, Douglas Aircraft Co., McDonnell Douglas Corp., Long Beach, Calif., 1968.

7 l\Ionoghan, H. J., "An Approximate Solution of the Compres­sible Laminar Boundary Layer on a Flat Plate," Hl\I 2760, 1953, National Physical Lab., Aeronautical Research Council, Ted­dington, Middlesex, England.

8 Spalding, D. B. and Chi, S. W., "The Drag of a Compressible Turbulent Boundary Layer on a Smooth Flat Plate with and without Heat Transfer," Journal of Fluid Mechanics, Vol. 18, Pt. I, Jan. 1964, pp. 117-143.

o AIM Paper No. 71-132

ADVANCES IN HYPERSONIC EXTRAPOLATION CAPABILITY - WIND TUNNEL TO FLIGHT

by J. A. PENLAND NASA Langley Research Center Hampton, Virginia and D. J. ROMEO Cornell Aeronautical Laboratory, Inc. Buffalo, New York

AIAA 9th AeroSpace SCiences Meeling

NEW YORK, NEW YORK / JANUARY 25-27, 1971

First publication rights reserved by American Institute of Aeronautics and Astronautics. 1290 Avenue of the Americas, New York, N. Y. 10019. Abstracts may be published without

permission if credit is given to author and to AIAA. (Price: AIAA Member $1.50. Nonmember $2.00).

Note: This paper available at AIAA New York office for six months; thereafter, photoprint copies are available at photocopy prices from Technical Information Service, 750 3rd Ave., New York, N. Y. 10017

.. NOTES ..

ADVANCES IN HYPERSONIC EXTRAPOIATION CAPABILITY -WIND TUNNEL TO FLIGHT

J. A. Penland*

NASA Langley Research Center Hampton, Virginia

and

D. J. Romeo**

Cornell Aeronautical Laboratory, Inc. Buffalo, New York

Abstract

In the past, the limited Reynolds number capability of hypersonic facilities has prevented reliable extrapolation of data to flight Reynolds numbers. Recent results on a hypersonic cruise aircraft configuration obtained at Mach 8 in the Cornell Aeronautical Laboratory Hypersonic Shock Tunnel over a Reynolds number range from a completely laminar boundary layer to a predominantly turbulent one are· presented. The significant factors which can affect extrapolation of wind­tunnel data at subscale Reynolds numbers to flight values are identified. The capability for predict­ing turbulent flight Reynolds number data from wind­tunnel data under laminar and transitional boundary­layer conditions are shown.

Introducti on.

The basic aim of complete configuration wind­tunnel tests is to determine the full-scale aero­dynamic performance of the particular concept. In the past,a major problem in the study of efficient hypersonic airbreathing aircraft resulted from the limited Reynotds number capability of hypersonic wind tunnels.l 1 ) The nature of the problem presented by this limitation is shown in Figure 1. Because of the relatively low Reynolds numbers then available on realistic configurations, the boundary layers over small.subscale test models were mostly laminar and transitional, whereas, over full-scale aircraft (typically 100 meters long), a turbulent boundary layer will cover all but a small area of the vehicle near the wing and tail leading edges and the fuselage nose. This difference in wind tunnel and flight Reynolds

.numbers, of course, has always existed at lower speeds, but the problem has been overcome by adding small roughness elements to the model which artifi­cially produce a turbulent boundary layer. At hypersonic speeds, however, usable boundary-layer trips have not been developed.(2,3) Because of the inability to develop a predominsntlyturbulent boundary layer over test models at hypersonic speeds, the viscous effects, not only on skin friction, but also on other important aerodynamic parameters, listed in Figure 2, that affect flight performance could not be determined. As a result, reliable

extrapolation of full-scale. aerodynamics from wind­tunnel results could not be made.

In the meantime, several developments have occurred to increase the range of available Reynolds numbers. These developments include modification to existing conventional tunnels and improvement in shock tunnel capabilities. In particular, the cornell(t~ronautical Laboratory Hypersonic Shock Tunnel ) has been extremely useful in studying high Reynolds number effects. As shown in Figure 3, by operating this tunnel at low stagnation temperatures (sufficient to just avoid air liquefaction) and high pressures, full­scale Reynolds numbers are available. Under these conditions, model boundary layers are predominantly turbulent without forced transition. On the other end of its Reynolds number range, the tunnel provides completely laminar model boundary layers. The Cornell Aeronautical Laboratory Hypersonic Shock Tunnel,then, provides the unique opportunity to study hypersonic viscous effects on aerodynamic performance over the complete boundary-layer spectrum.

Taking advantage of this opportunity, a study has been carried out on the model shown in Figure 4. The configuration is representative of current ideas for a Mach 6, hypersonic transport aircraft. The full-scale version would be nearly 100 meters long and have· about a 5,OOO-nautical­mile-range capability. The concept features a wide fuselage in relation to its height combined with strakes to improve the lifting capability of this predominant component. The fuselage is blended with the strakes and wing to reduce adverse component interference effects. The solid lines show the configuration tested. The vertical tail and propulsion system were eliminated during these tests to reduce the zero lift drag, and make the results more sensitive to variations of Reynolds numbers. The test model was about 2/3 meters long or 1/150 scale of the full-size flight vehicle. The investigation consisted of force tests over a Reynolds number range from about 0.5 million to 160 million, based on fuselage design length. Over this Reynolds number range, the Mach number varied from about 7.5 to 8.1.

* Aero-Space Technologist, Hypersonic VehicleB Division

** Research Aeronautical Engineer

The lift-to-drag ratio, Lin, as a fUnction of Reynolds number is shown in Figure 5. Notice that this is not a variation of the maximum Lin, but rather the Lin at an angle of attack of 30

• This is the angle of attack for maximum Lin at the highest test Reynolds number, and the model attitude is kept constant at this value for lower Reynolds numbers. Predictions of the data, assuming either an all laminar or an all turbulent boundary layer, are also shown. To obtain these predictions, inviscid theories (tangent cone on the fuselage, shock expansion on the strakes and wing) were applied to the isolated components through the computer program of reference 5. To these results skin-friction prediction given by the T', of reference 6, or Spalding-Chi, reference 7, theories were added. These theories were applied through the computer program of reference 5.

At the lowest Reynolds numbers, the model boundary layer is completely laminar. Transitional boundary-layer effects begin to emerge at Reynolds numbers of about 1.5 to 2 million. These effects predominate for about a decade in Reynolds number until the turbulent boundary layer exerts the major influence at Reynolds numbers between 15 and 20 million. This trend agrees with data obtained in the Cornell Aeronautical Laboratory Shock Tunnel on isolated cones and flat plates and from schlieren photographs of the present configuration. This is an interesting result for several reasons: (1) This range of Reynolds numbers is about the limit of conventional wind tunnels presently available, and (2) if the turbulent boundary layer predominates at these Reynolds numbers in these facilities (there are indications they do and additional tests are being made to confirm this) then flight extrapola­tions of wind-tunnel data can be made confidently since only small corrections will be required. The question then, is what performance parameters have major effects on these extrapolations.

Consider f1rst the normal force, CN, which is closely related to the lift force for low-drag configurations at low angles of attack. This parameter could be sensitive to the nature of the boundary layer through the viscous effects on lee­side flows and component interference, and at the lower Reynolds numbers through the boundary-layer displacement effects. In Figure 6, the normal force is shown as fUnctions of angle of attack for various Reynolds numbers over the test range. Although there may be some viscous effects at the lower Reynolds numbers, this effect is very small. In any event, at Reynolds numbers above 10 million, there is no noticeable viscous effects at all. This result is further borne ·out in Figure 7 where the CN at an angle of attack of 30 is essentially independent of Reynolds number. This result implies that if viscous effects change the local characteristics of lee-side flows and component interference, their overall effect is negligible for this configuration, and the normal force parameter may be neglected in the extrapolation process.

Next consider the axial-force coefficient, CA' This parameter is, of course, strongly affected by viscous effects on skin-friction and boundary­layer displacement effects. The large variation of CA with Reynolds number is shown in Figures 8 and 9.

2

Most of the change in CA is probably due to skin­friction changes as boundary-layer displacement effects would be expected to be confined to the very low Reynolds numbers. The skin friction then, as it has always been, is a strong factor in extrapolations of wind-tunnel results to flight Reynolds numbers. It should be noted that the turbulent predictions for this blended wing-body configuration are superior to the laminar predictions.

The drag-dlle-to-lift parameter, CfJn/CfJL 2 , is

the last one that will be considered. This parameter again would be most affected by viscous effects on both lee-side flows and component interference. The variation of CfJn/CfJL2 with Reynolds number is shown in Figure 10. The slight increase with Reynolds number is approximately the same as the predicted trend which accounts for the effect of small variations in the tunnel Mach number with Reynolds number. For all practical purposes, Reynolds number has no effect on CfJn/CfJL 2 which indicates again, as with the normal force, that overall viscous effects on lee­side flows and component interference are negligible for this configuration. Considerations of the drag-dlle-to-lift parameter in hypersonic wind­tunnel data extrapolation are therefore not required.

Of the parameters considered then, only the viscous effects on skin friction need be accounted for in correcting subscale hypersonic wind-tunnel data to flight values. Let us examine now how accurately we can predict the data a.t the highest Reynolds number by making these viscous corrections to the data at lower Reynolds numbers. The correction simply amounts to replacing the skin friction in the data at lower Reynolds numbers with the skin friction at the high Reynolds numbers. For our estimates of the laminar skin friction, we used the T' method, and the Spalding-Chi method for the turbulent skin friction. The total axial­force coefficient to which these skin-friction corrections were made was obtained from a mean fairing through tiE data as shown in the top of Figure 11. The percent errors in predicting constant angle of attack (30

), values of CL, Cn, and Lin at the highest Reynolds numbers are shown at the bottom. For the curves shown, the skin friction, at a given Reynolds number, was assumed ei ther entirely laminar or entirely turbulent • At Reynolds numbers below about 1 million and above about 15 million, where this assumption is nearly correct, the predictions are in error less than 10 percent. In between, large potential errors result because a mixed boundary layer (partly laminar, partly tranSitional, partly turbulent) predominates. It is encouraging to note that if conventional tunnels can achieve a predominantly turbulent boundary layer at the upper limit of their capability (Reynolds numbers of about 20 million), full-scale Reynolds number predictions on the order of 5 percent or less should be obtained assuming an all turbulent boundary layer. The accuracy of these predictions can be improved if the location of transition can be defined and the correct local skin-friction corrections are applied. The location of transition can be determined by using the phase-change-paint technique.

These results, of course, apply to the constant angle-of-attack case, and are not necessarily representative of the optimum, or (L/D)max case. Because of the higher drag at lower Reynolds numbers, the angle of attack for (L/D)max will be higher at these test conditions than under full-scale Reynolds number conditions, and this optimum angle of attack will not be known apriori. We consider finally then, how accurately the optimum case can be predicted. The results are shown in Figure 12.

Using the data at low Reynolds numbers (below 1 million), where the model boundary layer is laminar, the high Reynolds number value of (L/D)max is well predicted, but the optimum values of CL and CD are not. These errors are partly due to the inability to accurately predict skin friction on a complete configuration, particularly in the laminar region and partly due to the critical nature of the determination of the optimum CL and CD from faired data. The tick marks indicate likely errors from the fairing of present data. By correcting data in the Reynolds number range from 15 to 30 million, however, where the boundary layer is predominantly turbulent, ade~uate optimum performance values at the high Reynolds numbers can be predicted.

Concluding Remarks

Studies in the Cornell Aeronautical Laboratory Hypersonic Shock Tunnel, at Mach number 8, of a blended wing-body configuration, representative of a hypersonic transport vehicle, have shown that the factor that Significantly affects extrapolation of hypersonic subscale Reynolds number data to flight Reynolds number values is the skin friction. If wind-tunnel data can be obtained at Reynolds numbers where the turbulent boundary layer predominates, simple turbulent skin-friction corrections to the data will allow good prediction of flight Reynolds number performance data. Further improvement should be possible by determining the location of transition and applying the correct local skin friction. The insignificance of the lift and drag due to lift factors indicates that overall viscous effects on both lee-side flows and component interference are secondary for the blended wing body used. in this study. A different result may apply to discrete wing-body configuration types where the component interference effects may be more

3

predominant. Furthermore, additional work is re~uired to determine viscous effects on control effectiveness parameters over the Reynolds number range. An accurate knowledge of these parameters, of course, is re~uired to predict reliable values of the trimmed performance at flight Reynolds numbers, and because of possible flow separation over controls, viscous effects on these parameters could be significant.

References

1. Penland, Jim A.; Edwards, Clyde L. W.; Whitcofski, Robert D.; and Marcum, Don C.: Comparative Aerodynamic Study of Two Hypersonic Cruise Aircraft Configurations Derived From Trade-Off Studies. NASA TM x-1435, October 1967.

2. Morrisette, E. Leon; Stone, David R.; and Cary, Aubrey M., Jr.: Downstream Effects of Boundary-Layer Trips in Hypersonic Flow. Paper 16 of Compressible Turbulent Boundary Layers. NASA SP-216, December 10-11, 1968.

3. Whi tehead, Allen H., Jr.: Flow-Field and Drag Characteristics of Several Boundary­Layer Tripping Elements in Hypersonic Flow. NASA TN D-5454, October 1969.

4. Anon: Description and Capabilities of the Cornell Aeronautical Laboratory Hypersonic Shock Tunnel. Cornell Aeronautical Laboratory, Inc., May 1969.

5. Gentry, Arvel E.: Hypersonic Arbitrary-Body Aerodynamic Computer Program, Mark rv Version, Volume I - "User's ManuaL" Douglas Report DAC 61552, 1968.

6. Monoghan, R. J.: An Approximate Solution of the Compressible Laminar Boundary Layer on a Flat Plate. British R & M No. 2760, 1953·

7. Spalding, D. B.; and Chi, S. W.: The.Dragof a Compressible Turbulent Boundary Layer on a Smooth Flat Plate With and Without Heat Transfer. Journal, Fluid Mechanics, Vol. 18, Part I, January 1964, pp. 117-143.

CIRCA 1965

M~ LAM INAR-TRANS ITI ONAL B.L.

!TRI PS INEFFECTIVE)

FULL SCALE

TUR BULENT B.L.

-I@-o 00 o

(LlDl max 4 o

2!-1 -~-c..-:~-;'6 ..L.L';\IO;-:-· ---;2~0 ---'--4;';;0:-'-;6O~-';1*'00;--o',,200 x 106

REYNOLDS NUMBER

Figure 1.- Hypersonic wind~unnel extrapolation capability in the mid 60's.

1500

1000

ATMOSPHERES 500

SHOCK TUNNEL PERFORMANCE, M • 8

~ ;FULL; SCALE RANGE

I o 0 0.01 0.1 1.0 RL 1000

Figure 3.- Performance of the Cornell Aeronautical Laboratory shock tunnel at M = 8.

10

8 L/ D,

a • 3° 6 ,,_- SPALDING CHI CF~

LAMINA~~'6~ 0 --A Cl...!f.:fF~

6~O-(J.-:~ TURBULENT 4 -(J .-,,_..(J1 REFERENCE

TEMPERATURE CF

o !--1.-!--~--!----:l:----:::---f:--:-::-'-:""~300 x 106 .3 .6 3 6 10 30 60 100 REYNOLDS NUMBER

Figure 5.- Variation of lift-drag ratio at 30 angle of attack with Reynolds number, M = 8.

4

PARAMETERS AFFECTING FLIGHT EXTRAPOLATIONS OF (L/Dlmax FRICTION DRAG CD

PRESSURE DRAG C F Dp

LIFT CURVE SLOPE CL DRAG DUE TO LIFT C

DO

L CONTROL EFFECTIVENESS t.Cm t.CL

t.CD

Figure 2.- Parameters affecting wind-tunnel data extrapolations to flight.

I . b --

Figure 4.- Hypersonic test model.

.12.-

.10 f-

.08 f-

.06 f-

.04 -

.02-

0~,6

~ I

~/''-THEORY

~ ~ 1M REYNOLDS NUMBER

ittJ!' 0 153.2 X 106

)!' 0 32.31 tr 0 10.41 / l:l. 4.02

/' ~ 1.53 )J' 0 .597

-.02:1'C...._....L. __ L-r_...L-I_....II_---...JI

o 2 4 6 8 a, deg

Figure 6.- Variation of normal-force coefficient with angle of attack at various Reynolds numbers, M = 8.

.08

CN' .06

a - 30

.04 --~{3{)~04)~ooam~-8-0'C~---THEORY

.02

0.3!--&. .......... 6..u.J~-~:--'-...L.76..L..L..l:I:l::-0-....L...-:!3:-0 ..L..J.6-!:0~100~--L-:-!3oo X 106 REYNOLDS NUMBER

Figure 7.- Variation of normal-force coefficient at 30 angle of attack with Reynolds number, M = 8.

• 014

.012 \ \

.010 \~RENCE TEMPfRATURE CF

C·OO8 ,() 0 • A' LAMINAR, 0.., '--....

a - 30

•006 ' ........ ~o""'?:r.&...~ TURBULENT .... 0 <::)V U~~§a.a..

.004 ...... - SPALDING CHI cr

.002 .Lr-rL�.iC.!Jl ___________________ _

.6 3 6 10 .30 60 100 REYNOLDS NUMBER

Figure 9.- Variation of axial-force coefficient at 30 angle of attack with Reynolds number, M = 8.

% E~KOR

40

20 CD:-,...

FA I RED EXPERIll'lt:NTAL DATA & THEORY, M • 8

r J

ASSUMED TURBULENT _---Cir---O~~--~~----------~~----------

-20, ~S~yMIEPILAMI~ARI 1 I "" I I I I II II

.3 .6 1 3 6 10 30 60 100 REYNOLUS NUMBEK

Figure 11.- Accuracy of extrapolation of performance characteristics at a constant angle of attack to full-scale Reynolds number.

5

.016

o O ......... "'-LAMINAR 0'/ REF. TEMP. CF .012

0 .... °............. RL • 0.597 x 106

_-Q..8"'" AVERAGE REYNOLDS NO.

.004

O~-L--~~--~ __ ~~ -2 0 2 4 6 8 10

a,deg

o 153.2 x 106

o 32.31 o 10.41 t:;,. 4.02 b.. 1.53 ° .597

Figure 8. - Van.ac10n of axial-force coefficient with angle of attack at various Reynolds numbers. M = 8 .

6CD/6CL2, a; 3° 2.4

2.0 .LEXPfCTED TREND ----- ---

1.6 o

1.2

.8

.4

01,-l.l.J,..LJ.J~-L-l:_l..l...!,.llII:I:_-.l...-::I::-I~if_L!_!:::_-..I..._.::_!300 x 106 .3 .6 6 10 30 60 100

REYNOLDS NUMBER

Figure 10.- Variation of drag due to lift with Reynolds number, M = 8.

(L/DlMAX20

[ ~ %ERROR 0r--,F=~==~==::::::::::========~-------­

-20

40~ /ASSUMED LAMINAR C 20 ~ t 1- t

LOPT ! . :t-- I (ASSUMED TURBULENT %ERROR 0~-~----~~~~--;1-----------

-20

C 4O~ ----~ DOPT

20 r .. % ERROR 0 1= r

-20, f! I ! I II I!!' , , 11 , ! , ",,'

.3 .6 6 10 30 60 100 REYNOLDS NUMBER

Figure 12.- Accuracy of extrapolations of optimum performance characteristics to full-scale Reynolds number,

.. NOTES ..

6

CIRCA 1965 FULL SCALE

~~ LAMINAR-TRANSITIONAL B.L

ITRI PS INEFFECTIVEI

.-TURBULENT B.L...1 ~~" .

-~- ~} o DO o o ,~.

lliDl max 4

2~1--~--~4~~6~~IO~'~2~O~~~~00~~100~~2ooxl~ REYNOLDS NUMBER

Figure 1.- Hypersonic vind~unnel extrapolation capability in the mid 60's.

1500 SHOCK TUNNEL PERFORMANC£, M • 8

~ 2000 1000 'FULL:

~CALE TO' 0(( ATMOSPHERES RANGE

500 I 1000

0 0 0.01 RL

1000

Figure 3.- Perfornance of the Cornell Aeronautical Laboratory shock tunnel at M = 8.

10

8 UD,

a·3° 6

2

o .'----1---'------''----1~-IJ...n----....J">I\~-L~-,M'---~.j x 1n6

PARAMETERS AFFECTING FLI~HT EXTRAPOLATIONS OF (L/Dlmax FRICTION DRAG CD

PRESSURE DRAG C F Dp

LIFT CURVE SLOPE CL DRAG DUE TO L 1FT CD:

CONTROL EFFECTIVENESS toCm toCL toCD Figure 2.- Parameters affecting vind-tunnel data

extrapolations to flight.

I . -b-- --

I· 94.2 m. FLIGHT

Figure 4._ Hypersonic test model.

.12 ~ I

.10 ~/'-THEORY

~

..... -:...

.04 " ~ REYNOLDS NUMBER

._&p' 0 153.2 X 106

j5! 0 32.31 81 0 10.41 j!J A d. n?

.as

.02

~~~~~-L~....J....J~6~~IO~~~3~O~00~~100~ .6 REYNOLDS NUMBER

Figure 7.- Variation of normal-force coef 30 angle of attack .... ith Reynolds number

.014

.002 J.tfil.iClP ________________ ·

3 6 10 30 00 10 REYNOLDS NUMBER

Figure 9.- Variation of axial-force coef 30 angle of attack vi th Reynolds numbe

C ~:[ , FAIRED EXPER"ilvltN A & THEORY, M

a. jO .006 ....

LAMINAR...> .......... .004,1111'" I 11111:tn

An _ ________

CIRCA 1965

. 6 ~~

FULL SCAlf

fUROJ"", .c)/A­--~~ ~~

LAMINAR-TRANS ITIONAL B.L ITR I PS INEFFECTIVE)

ILlDlmax 4 o 00 o ' . o

2 LI _-L..---l'--14-l..-.L6 .LJ....LI,I,-0-.--f20:--.L......J40~60.J.:-I-.LJI~00:----:::!200 x 106

REYNOLDS NUMBER

Figure 1.- Hypersonic Yind~unnel extrapolation capability in the mid 60's.

1500

1(xx)

ATMOSPf£RES 500

O~~~~ __ ~~_~~_~~~~ QOI RL

2(xx)

To' OK I(xx)

Figure ). - Performance of the Cornell Aeronautical Laboratory shock tunnel at M = 8.

10

8 UD, a' 3° 6

, ...... SPALDING CHI CF:::'"

.'. LAMINA~~'a~~%-~ 4 ~6~~:~:::-- TURBULENT

, .,.,-a:J ~[FERENCE 2 TEMPERATURE C

F

~ 3~-. .J..6-~-~3--'6L-:-'::10---:30':---60-':-:"'100':--~300 x 106 REYNOLDS NUMBER

PARAMETERS AFFECTING FlIqHT EXTRAPOLATIONS OF (L/Olmax FRICTION DRAG Co

PRESSURE DRAG CO~ LIFT CURVE SLOPE CL DRAG DUE TO L 1FT Coal

CONTROL EFFECTIVENESS ~Cm ~Cl ~CO

F1;ure 2.- Parameters affecting vind-tunnel data extrapolations to flight.

I . .h

.12

.10

_02

I, 94.2 m. FLIGHT

Figure 4.- Hypersonic test model.

~ I

~/'--THEORY

~ rf

fM REYNOLDS NUMBER -.g,]l' .' 0 153.2 X 106

~ 0 32.31 f¥ 0 10.41

.' ~ 4.02

.(1

.OZ

3 6 10 30 ~ 100 REYNOLDS NUMBER

Figure 7.- Variation of normal-force coer 30 angle of attack vith Reynolds numbe~

.014

.012 \ \ .

.010 \~RENCE TEMPERATURE ~

CA, .008 LAMINAR '< o~ ............. a • 30 006 '"ce-o(j--~ TURBUlEI

. ' ...... o§Ou~ik....~

.004 .... ~ SPALDING CHI C

.001 l.f'£!I~ClP ________________ •

3 6 10 .30 60 HI REYNOLDS NUMBER

Figure 9.- Variation of axial-force coe!. )0 angle of attack vi th Reynolds numbe:

FAIRED EXPERIMtN' & THEORY, M

. 6

(lIDl max 4

CIRCA 1965

~<?-LAMINAR-TRANSITIONAL B.L.

ITRIPS INEFFECTIVEI D DO

D

TURBULENT

-~-o

21 L -~--''---!-4--1-~6 .L..J...1~10-·--:!:20;:--.L......;40~::60...L..L.':"!100:;:--~200 x 106

REYNOLOS NUMBER

Figure 1.- Hypersonic wind~unnel extrapolation capability in the mid 60's.

1500 SHOCK TUNNEL PERFORMANCE, M " 8

~ 2000 'FULL~ 1000 ~CALE To' 01(. RANGE ATMOSPHERES

I 1000 500

0 0 0.01 RL

1000

Figure 3.- Performance of the Cornell Aeronautical Laboratory shock tunnel at M = 8.

10

8 UD. I" 3° 6

~ .... _- SPALDING CHI CF~

/. LAMINA~~~6~ O---t3 C>...~~

4 -66 .-~O_Q_:-~ TURBULENT

~ .... .(J1 REFERENCE 2 TEMPERATURE C

F

PARAMETERS AFFECTING fliGHT EXTRAPOLATIONS OF (l/Olrnax . FRICTION DRAG Co

PRESSURE DRAG COF

LIFT CURVE SLOPE Cl P

DRAG DUE TO liFT COal

CONTROL EFFECTIVENESS bCrn bCl bCO Figure 2.- Parameters affecting wind-tunnel data

extrapolations to flight.

.08 c .

N .06

.04

~--=~.-

94.2 rn. FLIGHT

Figure 4.- Hypersonic test model.

~ I

~/'-THEORY

~

W~ REYNOLDS NUMBER

&i! 0 153.2 X 106

)!' 0 32.31 §' 0 10.41

I I

.O!

.a!

~~~~~-L~~~6~10,---1-'3~0~60~1~00 .6 REYNOLDS NUMBER

Figure 7.- Variation of normal-force coef 30 angle of attack with Reynolds number

.014

.Daz .lff!I1.ClP ________________ ·

3 6 10 30 60 10 REYNOLDS NUMBER

Figure 9.- Variation of axial-force coef 30 angle of attack with Reynolds numbe

NASA T .- 7() - q?~

NASA Technical Paper·

.2159

July 1983

NI\S/\

Wall-Temperature Effects on the Aerodynamics of a Hydrogen-Fueled ,Transport Concept in Mach 8 Blowdown and Shock Tunnels

Jim A. Penland, Don C. Marcum, Jr., and Sharon H. Stack

25th Anniversary· 1958-1983

NASA Technical Paper 2159

1983

NI\S/\ National Aeronautics and Space Administration

Scientific and Technical Information Branch

Wall-Temperature Effects on the Aerodynamics of a Hydrogen-Fueled Transport Concept in Mach 8 Blowdown and Shock Tunnels

Jim A. Penland, Don C. Marcum, Jr., and Sharon H. Stack Langley Research Center Hampton, Virginia

SUMMARY

Results are presented from two separate tests on the same blended wing-body hydrogen-fueled transport model at a Mach number of about 8 and a range of Reynolds numbers (based on theoretical body length) of 0.597 x 106 to about 156.22 x 106• Tests were made in a conventional hypersonic blowdown tunnel and a hypersonic shock tunnel at angles of attack of -20 to about 80 , with an extensive study made at a constant angle of attack of 30. The model boundary-layer flow varied from laminar at the lower Reynolds numbers to predominantly turbulent at the higher Reynolds num­bers. Model wall temperatures and stream static temperatures varied widely between the two tests, particularly at the lower Reynolds numbers. For the blowdown-tunnel tests, the wall temperature was about 860 0 R and the stream static temperature was about 100o R: for the shock-tunnel tests, the wall temperature was about 540 0 R and the stream static temperature was 200 0 R to 300 o R. These temperature differences resulted in marked variations of the axial-force coefficients between the two tests, due in part to the effects of induced pressure and viscous interaction variations. The normal-force coefficient was essentially independent of Reynolds number. Current theoretical computer programs and basic boundary-layer theory were used to study the effects of wall temperature, static temperature, and Reynolds number.

INTRODUCTION

The interpretation and application of aerodynamic test data from conventional wind tunnels and shock facilities in the determination of full-scale aerodynamic performance of a particular design are the primary goal of configuration testing. This is accomplished by selecting a design having sufficient volume to house the required fuel and payload, adequate wing area for a safe landing, and a shape based on available theory, published data, and experience. Such a configuration was the liquid-hydrogen-fueled hypersonic transport concept, figure 1, that was extensively tested through a wide Reynolds number range in a shock tunnel and reported in reference 1.

The purpose of this paper is to report the results of further free-transition tests on the same model of reference 1 in a conventional hypersonic blowdown wind tunnel at the same Mach number through a sufficiently wide Reynolds number range to allow the boundary layer to vary from essentially all laminar to predominantly tur­bulent, to compare the data from the blowdown tunnel with the data from the shock tunnel, and to analyze the results.

The major differences existing between tests in the two tunnels were the ratios of model wall temperature to stagnation temperature and the stream static tempera­tures. The shock-tunnel data were taken with a relatively low model wall temperature and a relatively high stream static temperature, whereas the conventional wind-tunnel data were taken with a high model wall temperature and a low stream static temperature.

Presentation of results includes a comparison between all experimental longitud­inal force and moment coefficients measured in a conventional blowdown hypersonic tunnel and those measured in a hypersonic shock tunnel: experimental data are then compared with theoretical predictions made with the Mark III Gentry Hypersonic

Arbitrary-Body Aerodynamics Computer Program (GHABAP). (See ref. 2.) The experi­mental data were obtained at a Mach number of about 8 through a Reynolds number range (based on theoretical model body length) from about 0.597 x 106 to about 156.22 x 106 • The model boundary-layer flow was laminar at the lower Reynolds numbers and predominantly turbulent at the higher Reynolds numbers. The angle-of­attack range was from -2° to about 8°.

The results of an extensive study of data at a constant angle of attack of 3° are presented. Included in the study is a comparison of experimental data with calculations from the GHABAP (ref. 2), an estimation of the inviscid pressure forces by extrapolation of axial-force data to very high Reynolds numbers, and an improved method of axial-force prediction under laminar-flow conditions by evaluating the induced pressure effects, including viscous interaction, through use of the calcu­lated displacement boundary-layer thickness distributions.

Blowdown-tunnel and shock-tunnel calibrations are presented in appendix A, a discussion of the boundary layer and laminar skin friction as affected by the wall and stream static temperatures is presented in appendix B, and a presentation of the effects of model location and test time on force data recorded in an axially symmet­ric hypersonic blowdown tunnel is presented in appendix C.

SYMBOLS

A reference area, area of wing including fuselage intercept, 70 in 2

C

axial-force coefficient

drag coefficient,

CF average skin-friction coefficient

local skin-friction coefficient

lift coefficient,

pitching-moment coefficient, q Ac

00

normal-force coefficient,

Cp pressure coefficient

CPA axial pressure coefficient

c wing chord

c mean aerodynamic chord

2

ccl wing centerline root chord

c r exposed wing root chord

D drag, FN sin a + FA cos a

axial force along X-axis (positive direction is -X)

normal force along Z-axis (positive direction is -Z)

L lift, FN cos a - FA sin a

L/D lift-drag ratio

t reference length (theoretical length of model fuselage), 25.92 in. (see fig. 1)

M Mach number

My moment about Y-axis

Npr Prandtl number

P pressure

qw free-stream dynamic pressure

R Reynolds number

Rt

Reynolds number based on theoretical fuselage length, free-stream conditions

RX Reynolds number based on distance from leading edge

T temperature

T' reference temperature (see appendix B)

V volume

X distance from beginning of boundary layer

Y/b percent exposed wing semispan

a angle of attack

0* boundary-layer displacement thickness

y ratio of specific heat

~ dynamic viscosity

~' dynamic viscosity based on reference temperature

3

Subscripts:

aw

B

IP

Inv

LE

max

min

o

P

TE

unit

VI

W

w

x

1

adiabatic wall

body

induced pressure

inviscid

leading edge

maximum

minimum

stagnation condition

planform

trailing edge

per unit of length

viscous interaction

wing

wall condition

local distance from leading edge or from beginning of boundary layer

local

stream condition

Abbreviations:

Cal.

GHABAP

Inv.

LRC

t.p.

calculated

Gentry Hypersonic Arbitrary-Body Aerodynamics Program (Mark III version)

inviscid

Langley Research Center

tangent point (see fig. 2)

Fuselage dimensions detailed in table II and figure 2:

X/\ body station, in percent theoretical fuselage length

X distance from nose of fuselage to cross section

4

H height of fuselage

A distance between reference line and top of fuselage

rad. B radius of fuselage bottom

rad. T radius of fuselage top

rad. US radius of strake upper surface

rad. LS radius of strake lower surface

rad. E radius of fuselage side

Sd distance" from bottom of fuselage to strake leading edge

SW distance from side of fuselage to strake leading edge

rad. W radius of fairing from fuselage to wing

TEST CONFIGURATION

The test model was the 1/1S0-scale hypersonic transport concept of reference 1 and is shown in figure 1. The fuselage cross-section design was semie~liptical with a width-height ratio of 2 to 1; the cross-sectional area was expanded from the nose to a maximum at the 0.66 body station according to the Sears Haack volume distribu­tion equations for minimum drag bodies of reference 3 and converged to zero at sta­tion 1.00. Strakes were added to improve the hypersonic lifting capability of this voluminous component. The fuselage was blended with the strakes and the wing to reduce adverse component interference effects. (Details of the configuration tested are shown by the solid lines in fig. 1.) The vertical tail and engine were not installed for the present tests. The fuselage cross-sectional design scheme is shown in figure 2. All design curves were circular arcs to facilitate fabrication. The overall geometric characteristics of the model are presented in table I and the detailed fuselage dimensions illustrated in figure 2 are presented in table II. The model was constructed entirely of 4130 steel to provide maximum strength in an annealed condition to withstand the high loads imposed on the model during the shock­tunnel tests. The model fuselage was machined to accept a three-component strain­gage balance and three accelerometers to measure aerodynamic forces, moments, and accelerations for the shock-tunnel tests. A six-component strain-gage balance was utilized for the blowdown wind-tunnel tests.

PRESENTATION OF RESULTS

The results of wind-tunnel and shock-tunnel tests at M ~ 8 on a wing-body model of a hypersonic transport concept are presented in the following figures:

Figure Computer drawing of paneling scheme of configuration for hypersonic

aerodynamic calculations ................................................... 3 Comparison of theoretical force and moment coefficients with experimental

data for various Reynolds numbers in the blowdown tunnel and shock tunnel ..................................................................... 4

5

Figure Comparison of normal- and axial-force coefficients with calculations from

the GHABAPi a = 3° •••••••••••••••••••••••••••••••••••••••••••••••••••••••• 5 Extrapolation of data to very high Reynolds numbers; a = 30 ••••••••••••••••• 6 Buildup of present laminar predictions of axial-force coefficient at two

wall temperature ratios and comparison with experimental data; a = 30 ••••• 7 Comparison of experimental lift, drag, and lift-drag ratio at two wall

temperature ratios with improved theory; a = 30 ••••••••••••••••••••••••••• 8

APPENDIX A - HYPERSONIC TUNNEL CALIBRATION: Mach number calibration on vertical centerline of the Langley Mach 8

Variable-Density Tunnel; Po = 2515 psia; To = 1460 0 R ••••••••••••••••••• 9 Test region and calibration scheme in the Langley Mach 8 Variable-Density

Tunnel •.•......••••••••.•....••••••••••••••...•.•.•..•....••..•••.••....• 1 0 Calibration Reynolds number and Mach number for stagnation pressure range

in the Langley Mach 8 Variable-Density Tunnel............................ 11 Test conditions for present study in the Calspan 96-Inch Shock Tunnel...... 12

APPENDIX B - LAMINAR SKIN FRICTION AND DISPLACEMENT BOUNDARY-LAYER THICKNESS: Variation of local flat-plate laminar skin friction with local Mach number

and local temperature .................................................... 13 Variation of laminar-boundary-layer displacement thickness on a flat plate

with Mach number for various Prandtl numbers ••••••••••••••••••••••••••••• 14 Variation of boundary-layer displacement thickness with temperature ratio

for various Prandtl numbers; M1 = 8 ..................................... 15 Variation of calculated boundary-layer displacement thickness by two

theoretical methods at M1 = 8 and ~ 1 = 0.384 x 106 •••••••••••••••••• 16 Variation of calculated laminar-boundary-iayer displacement thickness with

wall temperature ratio on root chord; M~ = 7.74; Rl = 1.4 x 106 •••••••• 17 Variation of the slope of boundary-layer displacement thickness with wing

root chord and resulting tangent-wedge pressure; Rl = 1.4 x 106 ; Moo = 8 ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 18

Typical calculated wing pressure distributions; a = 30 •••••••••• ~........ 19

APPENDIX C - EFFECT OF MODEL LOCATION AND TEST TIME ON FORCE-BALANCE DATA RECORDED IN LANGLEY MACH 8 VARIABLE-DENSITY TUNNEL: Schematic downstream view of test section with model at various vertical

locations in the Langley Mach 8 Variable-Density Tunnel.................. 20 Variation of lift and pitching-moment coefficients with vertical

test-section location at various Reynolds numbers; a = 30 ••••••••••••••• 21 Variation of lift and pitching-moment coefficients with blowdown-tunnel

test time for various test-section locations; Rl = 11.01 x 10 6 ; a = 3° ...•.....•.....•..•.••..........•.••.••.•.....••........••.......•• 22

APPARATUS AND TESTS

Langley Mach 8 Variable-Density Tunnel

The Langley Mach 8 Variable-Density Tunnel consists of an axially symmetri.c nozzle with contoured walls, has an 18-inch-diameter test section, and operates on a blowdown cycle. The tunnel-wall boundary-layer thickness, and hence the free-stream Mach number, is dependent upon the stagnation pressure. For these tests the stagna-

6

tion pressure was varied from about 128 to 2835 psia and the stagnation temperature was varied from about 1135°R to 14800R to avoid air liquefaction and the supersatu­rated region as defined in reference 4. The resulting Reynolds number varied from about 0.637 x 106 to 11.0 x 106 per foot. Dry air was used for all tests to avoid any condensation effects. The calibration of this tunnel for the present tests is presented in figures 9 to 11 and discussed in appendix A. The model was tested in the Mach 8 Variable-Density Tunnel on a sting-mounted internal six-component water­cooled strain-gage balance. This combination was injected into the hypersonic flow after the blowdown cycle had begun and retracted before the cycle was stopped. Tests were made with free transition at a fixed angle of attack, and the final data were corrected for sting deflection. The moment reference station was placed at 6.15 percent a, 0.566\. (See fig. 1.) Tests were conducted through an angle-of­attack range of about _10 to 70 at zero sideslip angle. The base pressures were measured for all tests, and the axial force was corrected to a condition of free­stream static pressure on the base.

Calspan Hypersonic Shock Tunnel

The Calspan 96-Inch Hypersonic Shock Tunnel, described in reference 5, employs a reflected shock to process air to conditions suitable for supplying an axially sym­metric convergent-divergent hypersonic nozzle. The shock-processed air is expanded through a contoured nozzle, having interchangeable throats, to the desired test con­ditions at the 24-inch exit diameter. Test time varied with conditions up to about 13 milliseconds duration. For the shock-tunnel tests the stagnation pressure varied from about 337 psia to 18 650 psia, and stagnation temperature varied from about 691°R to 3973°R to avoid liquefaction and to tailor the wide test Reynolds number range at a Mach number of approximately 8. The Reynolds number per foot varied from about 0.276 x 106 to 72.3 x 106 for the shock-tunnel tests. Some of the higher stagnation temperatures were utilized at the lower stagnation pressures to help obtain the lower Reynolds numbers by increasing viscosity. Stagnation pressure, temperature, and Mach number are plotted with Reynolds number in figure 12 and are discussed in appendix A for all shock-tunnel tests. Tests were conducted in unsaturated air where the lowest test static temperature was 127.8°R; thus, as defined in reference 4, all data were taken well outside the supersaturated region. The model was mounted on a three-component strain-gage balance just downstream of the contoured nozzle exit at a fixed angle of attack for all tests, and the final data were corrected for sting deflection. The free-stream Mach number was determined from pitot pressures measured for each test run by means of piezoelectric crystal pressure transducers mounted in the test section. Tests were made with free transition, and base-pressure corrections were applied as described in the previous section on the blowdown tunnel.

THEORETICAL METHODS

The theoretical studies made in the present report consist of, first, computer­ized calculations predicting the various longitudinal aerodynamic coefficients at appropriate flow conditions for angles of attack up to 100 and, second, a detailed investigation of the normal and axial forces with variation in Reynolds number at a constant angle of attack of 30, for which both the high-speed computer and desk-top calculators were utilized to evaluate the induced pressure effects on axial-force coefficients.

7

Inviscid Aerodynamics

The theoretical studies made major use of the Mark III Gentry Hypersonic Arbitrary-Body Aerodynamics Program (GHABAP). (See ref. 2.) The aircraft configura­tion was divided into approximately 800 elements, as shown in figure 3, for the cal­culation of both the inviscid and viscid aerodynamics. This program has available a variety of optional inviscid pressure-distribution calculation methods for both the impact flow and the shadow flow regions, which may be arbitrarily applied to indi­vidual model panels. Various methods and distributions were tried on the present configuration including the tangent-cone, tangent-wedge, and the shock-expansion methods for the impact flow regions while using the Prandtl-Meyer expansion from free stream to all shadow regions. The most successful combination was found to be the use of the tangent-cone pressure distribution on the forward fuselage and strakes ahead of the wing-fuselage junction and the tangent-wedge method on the wings and that portion of the fuselage aft of the wing-fuselage junction. This choice of pressure-distribution methods gave normal- and axial-force coefficients on the com­plete configuration that were essentially the same as those predicted by the use of the tangent-cone option on the fuselage and the shock-expansion option on the wings and strakes, as presented in reference 1, but gave much more realistic pitching­moment coefficients. The difference between the estimated pitching moments calcu­lated by the methods of reference 1 and those calculated by the present methods was in excess of 10-percent static margin. This compromise in selection of inviscid pressure-distribution calculation methods is reasonable when consideration is given to the flattened conical shape of the forward fuselage and to the relatively small average thickness ratio of the aft blended wing-body cross section. Wing and fuse­lage leading-edge axial-force contributions were assessed from the results of the circular-cylinder study of reference 6. A base pressure coefficient of -11M2

(ref. 7) was assumed to exist on the blunt-wing trailing edge.

Skin Friction

Laminar skin friction was calculated within the GHABAP by the T'-theory (the reference-temperature method of Monaghan in ref. 8). A discussion of this reference­temperature calculation is presented in appendix B. Although the magnitude of the laminar skin friction is relatively insensitive to variations of Prandtl number and Mach number, it is sensitive to wall and local stream temperatures. For a given local stream temperature of 100 o R, figure 13(a) shows that the skin friction may be expected to decrease somewhat with increasing Mach number but to decrease markedly with wall temperature. For the given hypersonic Mach number of 8, figure 13(b) shows that the laminar skin friction will decrease with increases in the ratio of wall temperature to local temperature or in stream static temperature or in both.

Turbulent skin friction was calculated within the GHABAP by the method of Spalding and Chi (ref. 9).

Induced Pressure

The buildup of a laminar boundary layer on an aerodynamic surface effectively alters the surface contour; consequently, the resulting airflow is rerouted and the surface pressure distribution is changed. Two methods of accounting for this laminar boundary-layer induced pressure were utilized.

8

The first method used the induced-pressure option available in the GHABAP to provide estimates for comparisons between theory and experiment with angle of attack, figure 4, and with Reynolds number at a constant angle of attack, figure 5.

The second, or present, method used detailed two-dimensional boundary-layer induced pressure estimates made for the exposed wing panels and for the fuselage and strakes at a constant angle of attack of 30 for the low Reynolds number laminar test region below R = 10 x 106 • This method is detailed as follows. The boundary-layer displacement thickness distribution was calculated for both the upper and lower sur­faces of the wing and the fuselage-strake combination, taking into account the wedge­slab-wedge airfoil section of the wing, the fuselage contours, and the resulting variation of local flow conditions by the methods of reference 8. (See appendix B.) The wall temperatures were taken as 540 0 R for the shock-tunnel tests and 8600 R for the blowdown tunnel tests, and a Prandtl number was assumed as 0.68. The variation of displacement boundary-layer thickness on a flat plate with Prandtl number and a comparison of calculations by the methods of reference 8 with a more exact method of reference 10 is presented in figure 16 and discussed in appendix B. The local slope of the displacement boundary-layer profile (figs. 17 and 18) was determined analyti­cally at longitudinal stations, and new pressure distributions were calculated from these boundary-layer displacement thickness contours on both wing and fuselage sur­faces using a tangent-wedge approximation based on stream Mach number. The differ­ence in the integrated pressure distribution obtained by this method and the inviscid value given by the GHABAP was considered the present induced pressure increment. As an example, a plot of the pressure distributions on the wing are shown in figure 19. The new induced pressure distributions vary for Runit = 0.66 x 106 per foot and Tw = 8600 R, from as high as 20 to 60 times the inviscid pressures immediately down­stream of the leading edge for the bottom and top forward wing surfaces, respec­tively, to only 1.2 to 1.5 times the inviscid pressures at the wing trailing edge. Similar pressure distributions were calculated for the fuselage-strake combination. No estimates of turbulent boundary-layer induced pressures were made.

Viscous Interaction

The large induced pressure gradient (falling pressures) discussed in the preced­ing section has an adverse effect on the laminar skin friction and is hereafter referred to as viscous interaction. As with the induced pressure calculations, two methods were utilized to account for this viscous interaction. The first method used the GHABAP which normally tabulates the laminar skin friction in combination with an estimate of the viscous interaction. For the present analysis, this program was modified to tabulate the skin friction without the viscous-interaction increment. The increment of viscous interaction was therefore the difference between the origi­nal and the modified computer-program results. These increments were used in combi­nation with the induced pressure increment and the leading-edge and trailing-edge drag in figure 4 and were shown separately in figure 5.

The second or present method to account for the increase in CF due to the induced pressure gradient used the methods of reference 11 which assumed a boundary­layer velocity profile similar to those of incompressible flow and a power-law dis­tribution of the self-induced pressure gradient. The variation of the calculated pressure distributions with distance from the leading edge was compared with the equation P« Xn to determine the value of n that would best match the pressure­distribution curve, and a skin-friction correction coefficient was obtained from a chart of the coefficient versus n for various values of wall temperature (ref. 11).

9

A further-required correction was a function of the ratio of local pressure to stream pressures at the trailing edge. As with the induced pressures, the differences in the calculated values of skin friction with induced pressures (favorable pressure gradient) on the exposed surfaces by the methods of reference 11 and those values from the GHABAP without viscous interaction were considered to be the present values of viscous interaction or the incremental skin friction due to induced pressure. The present estimate of the total axial-force coefficient for the configuration at any given flow condition is therefore the sum of the inviscid and skin-friction coeffi­cients provided by the GHABAP plus leading-edge bluntness drag, wing trailing-edge base drag, incremental values of induced pressure, and viscous interaction, i.e., the skin friction due to induced pressure gradient. Because these increments are depen­dent on the boundary-layer displacement thickness distribution, which (like the lami­nar skin friction) is a function not only of Reynolds number but also of the ratio of wall temperature to local temperature, there was a noticeable variation between data recorded in the shock tunnel with a cold-wall model and data from the blowdown tunnel with a hot-wall model. Leading-edge bluntness further contributes to the induced pressure effects, as pointed out in an early study (ref. 12), but these effects were not evaluated for the present configuration studies. No estimates of the viscous interaction were made for turbulent boundary-layer conditions.

RESULTS AND DISCUSSION

Comparison of Blowdown-Tunnel Data and Shock-Tunnel Data and Comparison of Data with Theoretical Estimates

Experimental longitudinal aerodynamics of a wing-body configuration through an angle-of-attack range from a conventional blowdown wind tunnel and a shock tunnel are compared in figure 4, along with theoretical estimates from the GHABAP. Tests were conducted in the blowdown tunnel through the widest possible Reynolds number range, and an effort was made to match those Reynolds numbers of the shock-tunnel tests. It was not possible to match the extreme Reynolds numbers (0.597 x 106 and 156.22 x 106 ) of the shock-tunnel tests because of the excessively thick tunnel-wall boundary layers at the lower Reynolds numbers and a design stagnation pressure limit at the higher Reynolds numbers. Therefore, there were four test Reynolds numbers from both facilities that were comparable with each other and with theory, and there were two extreme Reynolds numbers from the shock tunnel that were comparable with theory. Many tests were made in both facilities at a constant angle of attack of 3° and will be discussed subsequently.

Normal force.- It may be seen from figure 4(a) that the experimental normal­force coefficient varies only slightly between test facilities and/or with Reynolds number. Some scatter exists; but considering that each data point shown was the result of a separate wind-tunnel test made at a different time, it is not severe. The theory shows good predictions both for the trend and magnitude, particularly at possible cruise angles of attack, i.e., 2° to 5°. The small variations between normal-force predictions at the high and low Reynolds numbers are due to the variation in free-stream Mach number with tunnel stagnation pressure. At M ~ 8 it may be concluded that there was a minimal variation of normal-force coefficient with Reynolds number or with test facilities - although there were large variations .in model surface temperatures and stagnation temperatures between the blowdown tunnel and the shock tunnel. (See appendix A.)

Axial force.- The axial-force coefficients from the two sets of tests are pre­sented in figure 4(b). This figure shows not only a wide variation of axial-force

10

coefficient with Reynolds number - as expected within a given facility - but a marked variation of axial-force coefficient between facilities at approximately the same Mach and Reynolds numbers. A discussion of the variation of the axial force between the two facilities at similar flow conditions must be based on theoretical considera­tions because the identical model was used for both sets of tests. There were two main differences between the blowdown-tunnel and shock-tunnel tests. First, the model wall temperatures were nearly 60 percent higher in the blowdown tunnel where the model was subjected to about 10 seconds of hot hypersonic flow 1135°R to 14800R before data were recorded. The wall temperature of the model in the shock tunnel was at an ambient temperature of about 5400R before the run that lasted less than 0.015 second, thereby allowing the model walls little time to heat up. The estimated average model wall temperature for the LRC blowdown-tunnel tests was 860 oR, or about 3200R higher than the known model wall temperature during the shock-tunnel tests. The second major difference between the tests was the much higher stagnation tempera­tures for the shock-tunnel tests, particularly at the low Reynolds number. The dif­ference amounted to about 6400R at R t = 23.79 x 106 and 22400R at Rt = 1 .69 x 106 • The variation of model wall temperatures when combined with the widely different· stagnation temperatures produces values of TWITo' a highly significant boundary­layer parameter, as high as 0.64 for the blowdown-tunnel tests to as low as 0.16 for the shock-tunnel tests. Both laminar and turbulent boundary-layer theories are based on equations that have been derived in terms of the local Mach and Reynolds numbers and the ratio of wall temperature to stagnation temperature or the ratio of wall tem­perature to boundary-layer edge temperature; thus, variations of boundary-layer thickness and skin friction would be expected to exist between the two test facili­ties. The high stagnation temperatures of the calspan tests combined with an approx­imate constant Mach number resulted in high stream static temperatures which, as discussed in the theoretical-methods section and appendix B, were responsible for skin-friction coefficients nearly equal to those of the LRC hot-wall tests made with low stream static temperatures. The cold-wall conditions of the model during the Calspan tests contributed to the laminar boundary-layer stability which will be dis­cussed subsequently.

To facilitate a comparison between the data from the two tunnels, the same symbols were used for similar Reynolds numbers on the two parts of figure 4(b). Theoretical estimates were made assuming either all-laminar or predominantly all­turbulent skin friction. For consistency, therefore, only the lower and higher Reynolds number viscous estimates are presented, as the intermediate Reynolds number data are considered to contain a high percentage of transitional flow which cannot presently be predicted by the computer program. It may be seen that the experimental axial-force coefficients from the blowdown tunnel were consistently higher than those from the shock tunnel. This trend was predicted by Monaghan's laminar T'-theory, which as presented herein included skin friction, induced pressure, and viscous­interaction increments; but the turbulent Spalding-Chi theory predicted slightly lower estimates for the hot-wall blowdown-tunnel results. Predictions of the cold­wall shock-tunnel results by either laminar or turbulent theory were consistently superior to those for the blowdown tunnel at all Reynolds numbers. This was partly due to the lack of knowledge of the model-waIl-temperature distribution during the blowdown-tunnel tests and to the larger induced pressure effects at the lower Reynolds numbers. These induced pressure effects were only partially taken into account by the computer program and will be discussed subsequently. The overall trend of the variations of axial force with angle of attack was accurately predicted by the GHABAP. It should be noted (fig. 4(b» that the predicted increments of skin friction, taken as the difference between the leading-edge axial-force curves and the individual total axial-force curves (labeled "TUrbulent Cf " and "Laminar CF"), tend to increase with angle of attack. These increments of sk1n friction increase more

11

rapidly for the turbulent than for the laminar predicted by the GHABAP. The short curves at estimates made by the present methods and will

estimates, a trend that was accurately ex = 3° labeled "with <>*Cal." are be discussed subsequently.

Improvements of complex configuration axial-force prediction at hypersonic speeds depend on a better understanding of the model wall temperature distribution, a revision of computer programs to calculate pressure distributions and skin fric­tion along surface streamlines in lieu of the present streamwise or longitudinal flow assumption, and advanced methods of accounting for the laminar induced pressure effects on local pressures and skin friction. Local areas of boundary-layer transi­tion and/or separation must also be accounted for.

Lift.- The lift coefficients are shown in figure 4(c), along with theoretical predictions for the highest and lowest Reynolds number tests. It may be seen that there was little difference between the lift-coefficient data taken at different Reynolds numbers or between facilities. predictions of lift coefficient are con­sidered adequate for preliminary design, but the predicted slope of CL with angle of attack is slightly high. This is due in part to the buildup of boundary layer which tends to effectively distort the model surfaces in such a way as to decrease the experimental lift-curve slope. This observation stems from two-dimensional shock-expansion calculations made on wings having wedge-slab-wedge airfoils similar to the present model wing airfoil and an airfoil designed from the boundary-layer profiles discussed in appendix B. These calculations showed that the normal-force coefficient was decreased and that the axial-force coefficient increased on the wing having the boundary-layer-shaped airfoil when compared with the wedge-slab-wedge airfoil. Both of these forces contribute to a decrease in the lift coefficient at a given angle of attack, which results in a decrease in the slope of the lift curve with angle of attack.

Drag.- Comparisons of the experimental drag coefficients and theoretical esti­mates~ presented in figure 4(d) for the various test Reynolds numbers. Because the drag coefficients are determined from a combination of the normal- and axial­force coefficients and the predictions of the normal force were superior to those of axial force, the variations between the experimental drag and theory are primarily due to the errors in the prediction of axial force. Again, the shock-tunnel results are better predicted than the blowdown-tunnel results throughout the angle-of-attack range for all test Reynolds numbers.

Lift-drag ratio.- The lift-drag ratio versus the angle of attack is presented in figure 4(e), along with theoretical estimates. A maximum lift-drag ratio of just over 6 was measured on the present wing-body model at the highest average shock­tunnel Reynolds number of 156.22 x 106 • A loss of about 0.5 in L/D was recorded with a reduction of Rl to 32.59 x 106 and 24.32 x 106 for the two test facilities. These results compare favorably with the M = 6 data of reference 13 on a similar but not identical body-wing model at a Reynolds number of about 21 x 106 • Estimates by the present theoretical methods tend to overpredict the lift-drag ratios at all angles of attack for both laminar and turbulent conditions. This is again primarily due to the inaccurate axial-force predictions that, in turn, were due to a variety of reasons discussed previously, including the lack of knowledge of the model wall temperature distribution, the assumption within the computer program that the flow on the model is always streamwise for pressure calculations and longitudinal on the model with no cross flow for skin-friction estimates, and inadequate estimates of induced pressure effects. Also, local areas of transition and/or separation were not taken into account by the present computer program.

12

Drag due to lift.- The drag due to lift is presented in figure 4(f), accompanied by calculated estimates. Of interest is the more linear nature of the experimental data than the theoretical curves. With improved estimates of drag, particularly for the blowdown-wind-tunnel data, adequate estimates of drag due to lift may be expected at all Reynolds numbers and at angles of attack higher than that required for maximum lift-drag ratio. The slope with cL

2 of the inviscid drag curves and the laminar total drag curves are almost the same while the turbulent drag curves have a slightly higher slope, a variation due to the change in axial-force increments as pointed out previously.

Longitudinal stability.- The longitudinal stability is presented in figure 4(g) for the various test Reynolds numbers and may be seen to be approximately neutral about the 6.15 percent a moment-reference station. The GHABAP gives reasonable estimates of the longitudinal stability, but the underestimation in the level of the pitching moments which occurred in four out of the six tests could lead to poor esti­mates of trim. To obtain positive stability, the center of gravity must be placed farther forward than the present moment-reference station of 6.15 percent c, 0.5661. (See fig. 1.) However, such a forward location of the center of gravity could produce an overly stable condition at high subsonic and low supersonic speeds that could require excessive control power. A redistribution of planform ahead of the wing, or a shift of the wing on the present body, could provide a more favorable compromise.

Comparison of Experiment and Theory at a Constant Angle of Attack

An extensive study was carried out at a constant angle of attack of 3° over the complete range of experimental Reynolds number to assess the improvement in aerody­namic efficiency with increasing Reynolds number and to gain an understanding of the deficiencies of the available theoretical prediction methods. The angle of 3° was selected for the wide-range study because the angle of attack of 3° was approximately the angle of attack for maximum lift-drag ratio at the highest test Reynolds number of 156.22 x 106 (see fig. 4(e».

The normal-force coefficient is shown in figure 5 to be essentially independent of Reynolds number for both the hot-wall tests from the LRC wind tunnel and the cold­wall tests of reference 1 from the calspan shock tunnel. This conclusion may be better understood if consideration is given as to what happens with variations of Reynolds number. The primary effect of decreasing Reynolds number is a rapid thick­ening of the boundary layer, particularly under laminar conditions. The thickness of the boundary layer is dependent on the Mach, Reynolds, and Prandtl numbers, the local gas and model-wall temperatures, and the viscosity and specific heat of the test gas which, for the present tests, was dry air. This boundary layer forms on the upper surfaces as well as the lower surfaces and, as discussed in appendix B, alters the surface pressures in a manner that always increases the axial force but minimizes the variations in normal force at low angles of attack by inducing positive pressures on the upper surface as well as on the lower surface. Excellent predictions of the normal-force coefficient on the wing-body configuration with Reynolds number by the GHABAP are shown.

In contrast to the nearly constant normal-force coefficient with Reynolds num­ber, the axial-force coefficient may be seen to decrease as expected from theoretical considerations by more than 50 percent through the same Reynolds number range. Pos­sibly of more importance is the difference between the axial forces measured in the

13

two facilities. There was about a 16-percent increase in the axial-force coeffi­cients measured at low Reynolds numbers on the model mounted in the LRC wind tunnel compared to those measured on the same model mounted in the Calspan shock tunnel at about the same Mach number and Reynolds number. The major difference between the two tests was the average wall temperatures of the model and the test-gas temperatures, or more exactly the ratios of average wall temperature to stagnation temperature which were about 0.64 for the LRC tests and 0.16 for the Calspan tests. The average wall temperature of the LRC tests was estimated to be 860 0 R and the wall temperature of the model in the Calspan shock tunnel was measured at 540 o R. The comparative noise levels between the facilities were unknown, but the test section of the Calspan tunnel was 30 percent larger than that of the LRC tunnel.

At lower Reynolds numbers up to R\ = 3 x 106 where the boundary layer is pre­dominantly laminar, the GHABAP theory underpredicts the experiment for both sets of tests, but particularly so for the hot-wall LRC wind-tunnel data. The laminar theory presented on figure 5 included the sum of inviscid estimates made by assuming tangent-wedge pressures on the wings including fuselage-carry-through and tangent­cone pressures on the low-aspect-ratio nose and strakes. Added to this were viscous estimates made by using the Monaghan T'-theory to calculate skin friction, plus induced pressure estimates and viscous interaction corrections utilizing hypersonic similarity theory of references 14 to 16, all calculated by the GHABAP. The leading­and trailing-edge drag estimates were calculated separately and added to obtain the total axial-force coefficient CA,total. (See figs. 5 and 7.)

Predictions at Reynolds numbers above about 15 x 106 were only fair where an all-turbulent boundary layer was assumed and the Spalding and Chi turbulent skin­friction theory was used. This underprediction of the turbulent viscous effects was due in part to the lack of the addition of increments of drag due to either the boundary-layer induced pressures or the viscous interaction and the use of the nose and leading edge for the origin of the turbulent boundary layers by the GHABAP rather than the virtual-origin concepts of reference 17. The Reynolds number range from about 3 x 106 to 15 x 106 was a mixed flow region with a combination of laminar, transitional, and turbulent flow, the viscous aerodynamics of which could not be determined by the present GHABAP.

From these studies it may be concluded that the normal-force coefficient is essentially independent of Reynolds number and wall temperature and that the GHABAP predicts reasonably accurate normal-force coefficients over a wide Reynolds number range for the present class of configuration. The GHABAP predictions for axial-force coefficient leave much to be desired, and it was not clear whether the difference between experiment and theory was due to errors in the predicted inviscid axial force, the induced pressure correction, the estimated skin friction, or the viscous interaction correction. The next section presents a study of the experimental data to provide an insight into the prediction of the inviscid axial-force coefficient.

Estimation of Inviscid Pressure Forces by Extrapolation of Axial-Force Data to Very High Reynolds Numbers

The comparison of experimental axial-force coefficients with theoretical r.esults made with the GHABAP showed that the best correlation existed at Reynolds numbers where the boundary layer was thinnest. Thin boundary layers are generally associated only with high Reynolds numbers; however, cold-wall temperatures produce a thinner boundary layer than do hot-wall temperatures. It was the low Reynolds number cold­wall tests and those at high Reynolds number turbulent conditions that showed the

14

best correlation with theory. A study was therefore undertaken to gain a better understanding of what might be expected with the present test configuration under very high Reynolds number conditions where the boundary layer would be very thin; the results are presented in figure 6.

It is well-known that laminar boundary-layer parameters including laminar skin friction are functions of the reciprocal of the square root of the Reynolds number. To obtain an estimate of the laminar Reynolds number test range, the axial-force coefficients for all a = 30 tests were plotted against 1/~ and are presented in figure 6(a). Lines were faired through the lower Reynolds number data and extrapo­lated as a straight line to 1/{R; = 0 or effectively to a very high Reynolds number. Only minimal compromise was required to make the fairings converge to the inviscid value of CA = 0.0022 obtained from the GHABAP plus leading- and trailing­edge drag. From this set of data and faired curves it may be concluded that the GHABAP gives accurate predictions of axial-force coefficient at low angles of attack for this class of vehicle at very high Reynolds numbers or under inviscid conditions. The change in slope of the data from the faired curves gives an estimate of the Reynolds number where transition begins and where the turbulent boundary layer begins to dominate the model boundary-layer flow. It may be inferred from these faired data that the flow over the model was predominantly laminar at the lower Reynolds numbers and that the difference between the present laminar-theory predictions and the exper­imental axial-force data is a failure of the theory to correctly model the flow, not an error in the assumption of the existence of laminar flow conditions.

This relatively successful extrapolation of the low Reynolds number data to very high Reynolds numbers utilizing the assumptions of laminar flow theory suggested that a similar extrapolation effort be made for the turbulent Reynolds number range. A root of 1/5 was tried and found unsatisfactory. Therefore, to determine the root of the turbulent Reynolds number range of experimental data, a plot of the experimental axial-force coefficients minus the inviscid coefficient of 0.0022 was prepared. This plot, figure 6(b), was made on full logarithmic paper to best illustrate the varia­tion of the approximate skin-friction coefficient or net axial-force coefficient with increasing Reynolds number. As was expected from the results of an examination of figure 6(a), the net skin-friction coefficient at low Reynolds numbers plotted not only as a straight line but as having a slope of 1:2 which corresponds to the laminar square root of the Reynolds number. A careful fairing of the data at the higher Reynolds numbers produced a slope of 1:7 (i.e., 1/7 root) which historically has been associated with turbulent boundary-layer parameters. Figure 6(c) shows the experi­mental data plotted against the parameter 1/~; again, straight-line fairings of the data extrapolate to the inviscid value of axial-force coefficient of 0.0022 determined by the GHABAP. The abrupt change in slope of the data from the faired curves is more pronounced here in figures 6(b) and 6(c) than in figure 6(a), and transition appears to begin at about Rt = 3.4 x 106 for the LRC wind-tunnel hot­wall data and about Rt = 4.5 x 106 for the calspan shock-tunnel cold-wall data. A study of figure"6(c) provides additional evidence that the experimental data taken at Reynolds numbers of about 10 x 10 6 to 15 x 106 and above are predominantly turbulent and may be used to extrapolate the axial-force coefficient to very high flight Reynolds numbers. It may be concluded that the present tests were made under predom­inantly laminar flow conditions at the lower Reynolds numbers and predominantly tur­bulent flow conditions at the higher Reynolds numbers and that the GHABAP provides an excellent estimate of the inviscid axial-force coefficient.

The higher apparent transition Reynolds number of the shock-tunnel data may well have been due to the increased boundary-layer stability on the cold-wall model and a likely lower tunnel noise level. Laminar boundary-layer stability is that flow

15

quality which resists the progression to transition, and hence the development of a turbulent boundary layer, and can be affected by the Mach number, the ratio of wall to local temperature, and the noise emanating from the tunnel-wall boundary layer. As the present tests in both facilities were conducted under nearly constant Mach number conditions, it must have been the cold-wall condition of both the test model and the shock-tunnel walls and the larger test-section size of the shock tunnel that contributed to the observed higher transition Reynolds number. Cold-wall model tests, where the model walls absorb heat from the air, are known to delay transition; and larger test sections have been shown to have lower noise levels than smaller test sections at similar Mach and Reynolds number conditions. (See ref. 18.) It may be concluded that the observed higher transition Reynolds number of the shock-tunnel data was due in part to the cold-wall condition of the model and to the larger tunnel test section.

The next section will discuss the results of a study to improve the estimates of induced pressure effects on the axial-force coefficients.

AXIAL-FORCE PREDICTION USING PRESENT METHOD OF INDUCED PRESSURE EVALUATION

As summarized in the section entitled "Theoretical Methods," the laminar axial­force coefficients may be considered as a combination of the inviscid pressure forces including the wing and body leading-edge pressure force, the wing trailing-edge base pressure, the skin friction, the induced pressure due to boundary-layer growth, the variation of the skin friction due to the induced pressures (termed "viscous interac­tion" herein), and an increment of induced pressure due to leading-edge bluntness. The present study utilized each of the above factors except the bluntness induced pressure increment to evaluate the total axial-force coefficient of the present test configuration.

The buildup of the calculated laminar axial-force coefficients at a = 3° for the Reynolds number range from about 0.7 x 106 to 10 x 106 based on model theoretical length is presented in figure 7(a) for both the hot-wall and cold-wall test condi-tions. The inviscid body axial force ~C and the body and wing skin friction

AB,Inv

and !::CF W make up the largest portion of the total coefficient, with the

change in the body and wing viscous interaction and ~C Aw,VI

making the

next largest contribution (particularly for the hot-wall tests). The inviscid wing forces and the body and wing induced pressure increments are relatively small com­pared to the viscous forces. The increment of axial force ~C included a

AW,LE&TE

small estimate of drag due to the blunt trailing edge, as well as the leading-edge bluntness drag.

A comparison between the total calculated axial-force coefficients and the experimental data is presented in figure 7(b), from which it can be seen that consid­erable improvement has been made over the GHABAP predictions presented in figure 5. The major improvement appears to have come from the estimated increment of the change in skin friction due to induced pressure, particularly for the hot-wall case.

A comparison of the resulting lift, drag, and lift-drag ratio calculations util­izing the improved axial-force estimates and the experimental data are shown in fig-

16

ure 8. For the known laminar flow region below Reynolds numbers of about 3 x 106 , the lift-drag estimates were in error by no more than about 10 percent for the scat­tered data points. Future improvements in this combination of methods of axial­force prediction are possible by taking into account any variation in wall tempera­ture on the model, by using shock-expansion pressure-distribution predictions for the boundary-layer induced pressures, by making induced pressure corrections due to leading-edge bluntness, and by taking these induced pressures into account when estimating skin friction.

The final computed estimates of axial-force coefficient, drag coefficient, and lift-drag ratio, which are presented on figures 7 and 8, have been added to figures 4(b), 4(d), 4(e), and 4(f) at a: = 3° and are labeled "With o*Cal." A marked incremental improvement of the estimates is shown on figure 4 for the R\ = 1.68 x 106 and 1.53 x 106 hot- and cold-wall tests, but a somewhat poorer correlation is shown with the R\ = 0.597 x 106 cold-wall test.

It may be concluded that detailed calculations of the effects of induced pres­sure, particularly the variations of the skin friction due to induced pressures or viscous interaction, are required for accurate configuration performance estimates at low Reynolds numbers when the boundary layer is predominantly laminar.

CONCLUSIONS

An analysis of experimental data for a hydrogen-fueled, blended wing-body hyper­sonic transport concept from a conventional blowdown wind tunnel and a shock tunnel at a Mach number of about 8 through a Reynolds number range (based on fuselage theoretical length) from 0.597 x 106 to about 156.22 x 106 leads to the following conclusions:

1. There was a minimal variation of normal-force coefficient with Reynolds number, or between test facilities, although wide variations of model surface temper­atures and tunnel stagnation temperatures existed between the blowdown and shock tunnels.

2. The minimal variation of normal-force coefficient with Reynolds number is indicative of an immunity of normal force to the effects of viscous boundary-layer variations due to changes in the ratio of wall temperature to stream temperature.

3. Good theoretical predictions of normal-force coefficient with angle of attack and with Reynolds number were made with the Mark III Gentry Hypersonic Arbitrary-Body Aerodynamics Program, particularly at possible cruise angles of attack, i.e., 2° to 5°.

4. Very high Reynolds number axial-force coefficients, approximating the invis­cid values, may be estimated with the logarithmic extrapolation method presented.

5. The Mark III Gentry Hypersonic Arbitrary-Body Aerodynamics Program provides excellent estimates of the inviscid axial-force coefficients for the present blended wing-body configuration.

6. The low Reynolds number experimental tests were made under predominantly laminar flow conditions, and the high Reynolds number tests were made under predomi­nantly turbulent flow conditions.

17

7. Higher transition Reynolds numbers occurred in the shock tunnel and were due to greater boundary-layer stability on the cold-wall model and the apparent lower noise level in the larger test section.

8. For a given hypersonic Mach number, the laminar skin friction decreased with increases in the ratio of wall temperature to local temperature or in stream static temperature or in both.

9. Satisfactory estimates of laminar axial-force coefficients, and thus config­uration performance coefficients, can be made only when the effects of induced pres­sures have been taken into account, particularly the variations in skin friction due to induced pressure. Knowledge of wall temperature distributions, accounting for local areas of boundary-layer transition, and the calculation of pressure distribu­tions and skin friction along surface streamlines would further improve calculations.

10. Estimates of turbulent axial-force coefficients and performance were only fair, due in part to the need of drag increments from boundary-layer induced pres­sures and viscous interaction and a computer program that uses the virtual-origin concept for the initiation of the turbulent boundary layers.

Langley Research Center National Aeronautics and Space Administration Hampton, VA 23665 May 4, 1983

18

APPENDIX A

HYPERSONIC TUNNEL CALIBRATION

Langley Mach 8 Variable-Density Tunnel

The circular cross-section axially symmetric nozzle design of the Langley Mach 8 Variable-Density Tunnel and the rapid expansion of the wall contour downstream from the first minimum contribute to a region of varying dynamic pressure near the longi­tudinal centerline of the test section. This focusing effect produces spikes in the calibration amounting to as much as +1.24 percent to -3.2 percent, of the average stream dynamic pressure over a region about 2 inches in diameter. (See fig. 9 taken from ref. 19.) The present tests were designed to have the model remain between this central core and the thick 3.5-inch tunnel-wall boundary layer.

Figure 10(a) shows a frontal view of the model at a ~ 00, 30, and 60 mounted inverted in a region of undisturbed flow with the center of rotation at 2 inches below the tunnel centerline. The calibration of this nozzle consisted of a vertical and horizontal centerline survey at various longitudinal intervals through the test section at various stagnation pressures. A study of these data showed that the longitudinal average of measurements on the horizontal survey were approximately the same as average measurements on the vertical survey if they were made at the same radial distance from the nozzle centerline. This made it possible to estimate with confidence the Mach number on concentric contours about the nozzle centerline. These lines of constant average Mach number are shown in figure 10(b) superimposed on the frontal view of the model test region. The region shown was numerically integrated to obtain an overall average test Mach number for the various calibration stagnation­pressure levels. The results of this integration plotted as a straight line against stagnation pressure on semi logarithmic paper are presented in figure 11. The Reynolds number based on theoretical fuselage length (with boattail) and the average Mach number shown in this figure are also plotted as a straight line against stagna­tion pressure, but on full logarithmic paper.

Calspan 96-Inch Hypersonic Shock Tunnel

The authors were not involved in the calibration of the Calspan 96-Inch Hyper­sonic Shock Tunnel; this section is therefore limited to a description of the flow conditions for the tests reported in reference 1 and analyzed herein. As expected, the stagnation pressure was increased with required Reynolds number as presented in figure 12, but contrary to normal practice in a blowdown or continuous hypersonic tunnel, the stagnation temperature was increased at the lower Reynolds numbers to facilitate the production of low Reynolds number conditions by increasing the viscos­ity and decreasing the mass density. At the higher Reynolds number the total temper­ature was reduced to values just high enough to avoid air liquefaction, thereby mini­mizing the viscosity and maximizing the density to produce the nearly flight level Reynolds numbers. The variation of Mach number with Reynolds number (fig. 12) was somewhat less than that of the Langley Mach 8 Variable-Density Tunnel, had it been capable of being run at pressures sufficiently low and high enough to produce the same wide Reynolds number range. This was due to the use of interchangeable throats for the contoured nozzle which had an exit diameter of 24 inches.

19

APPENDIX B

LAMINAR SKIN FRICTION AND DISPLACEMENT BOUNDARY-LAYER THICKNESS

Laminar Skin Friction ,

The Gentry Hypersonic Arbitrary-Body Aerodynamics Program (GHABAP) utilizes Monaghan's T'-theory, or reference temperature method, of reference 8 for the calcu­lation of laminar skin friction. This method is a semiempirical modification of the classic Blasius incompressible laminar skin friction by making the calculations on the flow properties based on a re~erence temperature rather than either the local stream or wall temperatures. For a flat plate the equation for local skin friction is

where

and

since

and

T T' = _w __

T, -r,

T aw

0.664 Yc

o .468(N ) '/3 (Tw _ Taw) _ 0.273N (Y - '_1 M 2 Pr T, T, Pr 2 / '

equations (B3), (B4), and (B5) may be combined such that

20

T

T W

--+ T,

- 0.273N ~ + 0.273Npr Pr T,

T (N ) '/2 ~ _

Pr T, (N ) ,/~

Pr J

(B' )

(B2)

(B3)

(B4)

(B5)

(B6)

APPENDIX B

With the substitution of Prandtl number, equation (B6) yields the following reference temperatures. For Npr = 0.68,

T' (B7)

0.75,

T' (B8)

and for Npr = 1.0,

T' (B9)

The similarity of these equations shows the relative insensitivity of the reference temperature to Prandtl number and thus a similar insensitivity of the calculated skin-friction coefficient to Prandtl number.

Plots of the laminar flat-plate skin-friction parameter Cf~Rx,1 from equa­tion (B1) are presented in figure 13. Figure 13(a) shows the skin-friction parameter versus Mach number for a typical blowdown wind-tunnel stream static temperature of 100 0 R for various wall temperature ratios. This is the typical plot that is used to present hypersonic laminar skin friction; it shows a relative insensitivity of skin friction to Mach number but a considerable sensitivity to the wall temperature. From this plot it could be concluded that the laminar skin friction decreases with increased wall temperature; this is correct for a given stream static temperature. Because the present study concerns experimental data measured in two distinctly dif­ferent temperature environments at approximately the same Mach number, figure 13(b) was generated at a constant Mach number of 8 with stream static temperature as the variable. Data points are included at the appropriate wall temperature ratios and stream static temperatures for the present Langley and the Cal span test conditions. It may be seen that the skin-friction parameter is slightly smaller for the cold-wall test condition because of the twofold to threefold increase in stream static tem­perature and the nearly 80 percent lower wall temperature ratio. It, therefore, may be concluded that for a constant Mach number the laminar skin friction decreases not only with increasing wall temperature but also with increasing stream static temperature.

Displacement Boundary-Layer Thickness

The reference temperature method of reference 8 was also used to study the induced pressure effects of boundary-layer buildup on the wing surfaces. An example of the large change in the measured surface pressures that may be expected near the leading edge of a wing in hypersonic flow and the resulting large favorable chordwise pressure gradient was first shown by Becker in reference 20. These experiments were made in the first hypersonic wind tunnel, the NACA/NASA Langley 11-Inch Hypersonic Tunnel, at a Mach number of 6.9. Wing surface pressures were accurately predicted using the contour of the displacement boundary-layer thickness as the effective wing surface.

21

APPENDIX B

Monaghan's equation for displacement thickness was derived in terms of free­stream Mach number, local unit Reynolds number, local and wall temperature, Prandtl number, and the Chapman-Rubesin viscosity-temperature relation. After terms are collected, Monaghan's equation can be written as follows:

(N ) 1/3 Pr

(B10)

With the substitutions of Prandtl number, equation (B10) simplifies to the following equations. For Npr = 0.68,

O*~Runit = T

1)M 2 w 0.288(y -2.083 T + - 0.363 ex

1 1

(B11 )

For Npr 0.75,

0* JRuni t = T

1)M 2 w 0.298(y - - 0.275 1.995 T + CX

1 1

(B1 2)

For Npr 1 .0,

O*JRunit T 1)M 2 w

0.323(y -CX 1.719 T + 1

1 (B1 3)

It may be noted that for M1 = 0 and Tw/T1 = 1.0 each equation reduces to approxi­mately the classic equation of Blasius for low speeds, i.e.,

0* 1.73X (B14)

Plots of the three equations (eqs. (B11) to (B13» for Npr = 0.68, 0.75, and 1.0 are presented in figure 14 for local Mach numbers up to 10 and the ratios TwiT 1 up to 16. To examine more closely the effect of Prandtl number on 0*, a cross plot of O*VRunit/CX versus TwiT 1 is presented in figure 15 for a Mach num­ber of 8. It may be seen that smaller values of &*~Runit/CX are predicted for Npr = 1.0. To determine the difference between the prediction of 0* by this method and by the more rigorous method of reference 10, figure 16 was generated for a laminar boundary layer at M1 = 8 and a constant low Reynolds number of 0.384 x 106 • For the range of wall-temperature ratios considered, it may be seen that the varia­tion between the two dissimilar methods was no more than 5 percent for cold-wall test

22

APPENDIX B

conditions and about 3.5 percent for the hot-wall test condition. It was therefore concluded that the T'-theory of reference 8 was adequate for the present calculation procedure and the use of Npr = 0.68 would be the more realistic.

and

Equation (B11) may be written for y = 1.4 as follows:

* .JC -IX (Tw 2 ) o = I~ 2.083 T + 0.1152M1 - 0.363 V -'uni t 1

dO* dX =

which is the local slope, i.e., tan- 1 of the angle between the wing curved boundary of the displacement thickness contour at station X. tions (B15) and (B16) results in

dO* ." -­

do =~o* dX 0*

2- rp:--:-tVX V"unit 0*

VcVx VRunit

0* 2Vx 0*

= Yx = 2X

( B15)

(B16)

surface and the Combining equa-

(B17)

which provides the following simple relation between the local slope of the contour of the displacement boundary layer and its thickness or depth:

do* 0* --=-dX 2X

(B18)

Equations (B15) and (B18) were used extensively as discussed under the section enti tIed "Theoretical Methods."

Examples of the distribution of the displacement boundary layer are shown in figure 17 for the exposed wing root chord sections for both the hot- and cold-wall tests. These boundary-layer displacement thickness distributions were calculated by use of equation (B15) at a Mach number of 7.74 and a Reynolds number of 1.367 x 106

based on theoretical body length. The boundary layer is nearly twice as thick on the wing section from the hot-wall test than that from the cold-wall test; therefore, creating higher flow deflections just downstream of the leading edqe, and thus higher induced pressures than were created during the cold-wall tests. Figure 18 illus­trates the rapid variation of the slope of the displacement boundary layer which may be seen to decrease by about 95 percent in the first 10 percent of the wing root chord. An inset plot on figure 18 illustrates the variation of the tangent-wedge pressure ratio with the boundary-layer slope and the resulting flow deflection.

23

APPENDIX B

Although the forward surface of the boundary layer is blunt and may create a small region of detached flow and very high local pressures, the integrated pressure force is of little consequence due to the very small areas involved.

A typical calculated pressure distribution is presented in figure 19(a) for the exposed wing root chord of the model during the hot-wall test and for the variation of the integrated chordwise axial pressure distributions plotted with respect to the exposed wing semispan in figure 19(b). This figure illustrates the high calculated pressures at the leading edge on both the top and bottom wing surface for a = 3°, which contributes substantially to the axial force but negligibly to the normal force due to the similar upper and lower surface pressure changes. The axial pressure coefficient is shown to increase spanwise and is a planform effect of wing taper due to the lower local Reynolds number at the tip and the resulting increased induced pressures.

24

APPENDIX C

EFFECT OF MODEL LOCATION AND TEST TIME ON FORCE-BALANCE DATA RECORDED IN LANGLEY MACH 8 VARIABLE-DENSITY TUNNEL

In general, hypersonic blowdown tunnels with axisymmetric nozzles have central test cores of nonuniform flow compared to the average test-section calibrated Mach number, as discussed in appendix A. In addition, hypersonic tunnels designed for about M = 4 and higher that operate at pressures above 400 psia require additional heat to be added to the air to prevent air condensation (liquefaction) during the expansion to test Mach number. This heated air often distorts the contoured tunnel walls, particularly in the vicinity of the nozzle throat or first minimum, resulting in a variation with time of the average test-section Mach number and the stream dynamic pressure.

The Langley Mach 8 Variable-Density Tunnel is a blowdown facility, has an axially symmetric nozzle, and utilizes high temperatures to test at high Mach numbers and thus meets all of the above criteria. A specific test was designed to determine the magnitUde of the variations of these test conditions. It consisted of a series of tests at a constant angle of attack of 30 in which the model position was varied from 1 inch above the test section centerline to 2 inches below the centerline (fig. 20). The results of these tests are presented in figure 21 and show that the. lift coefficient varied up to as much as 6 percent at the lower Reynolds number and that the pitching moment varied more than 20 percent at the intermediate and higher Reynolds numbers. It was therefore concluded that all other tests would be conducted with the model in the more uniform air 2 inches below the centerline.

During the position tests, data were taken at approximately 5-second intervals, and the results are presented in figure 22 using expanded scales. It may be seen that there was a variation of coefficient with time at all model positions and that the lift coefficient decreased and the pitching-moment coefficient increased. Part of these variations was due to the heating up of the model nonuniformly and thereby contributing to variation in heat load to the water-cooled shield of the balance and possibly unsymmetrical heating of the strain gages. It was, therefore, decided to utilize where possible only those data recorded at about 10 seconds for analysis and inclusion in the present report.

25

REFERENCES

1. Penland, J. A.; and Romeo, D. J.: Advances in Hypersonic Exploration Capability - Wind Tunnel to Flight Reynolds Number. J. Aircr., vol. 8, no. 11, Nov. 1971, pp. 881-884.

2. Gentry, Arvel E.: Hypersonic Arbitrary-Body Aerodynamic Computer Program (Mark III Version). vol. I - User's Manual. Rep. DAC 61552, Vol. I (Air Force Contract Nos. F33615 67 C 1008 and F33615 67 C 1602), McDonnell Douglas Corp., Apr. 1968. (Available from DTIC as AD 851 811.)

3. Sears, William R.: On projectiles of Minimum Wave Drag. Q. Appl. Math., vol. IV, no. 4, Jan. 1947, pp. 361-366.

4. Daum, Fred L.; and Gyarmathy, George: Condensation of Air and Nitrogen in Hyper­sonic Wind Tunnels. AlAA J., vol. 6, no. 3, Mar. 1968, pp. 458-465.

5. Hypersonic Shock Tunnel - Description and capabilities. calspan Corp., Sept. 1975.

6. Penland, Jim A.: Aerodynamic Characteristics of a Circular Cylinder at Mach Number 6.86 and Angles of Attack up to 90°. NACA TN 3861, 1957. (Supersedes NACA RM L54A14.)

7. Mayer, John P.: A Limit Pressure Coefficient and an Estimation of Limit Forces on Airfoils at Supersonic Speeds. NACA RM L8F23, 1948.

8. Monaghan, R. J.: An Approximate solution of the Compressible Laminar Boundary Layer on a Flat Plate. R. & M. 2760, British A.R.C., 1953.

9. Spalding, D. B.; and Chi, S. W.: The Drag of a Compressible Turbulent Boundary Layer on a Smooth Flat Plate with and Without Heat Transfer. J. Fluid Mech., vol. 18, pt. 1, Jan. 1964, pp. 117-143.

10. Price, Joseph M.; and Harris, Julius E.: Computer Program for Solving Compres­sible Nonsimilar-Boundary-Layer Equations for Laminar, Transitional, or Turbu­lent Flows of a Perfect Gas. NASA TM X-2458, 1972.

11. Bertram, Mitchel H.; and Feller, William V.: A Simple Method for Determining Heat Transfer, Skin Friction, and Boundary-Layer Thickness for Hypersonic Lami­nar Boundary-Layer Flows in a Pressure Gradient. NASA MEMO 5-24-59L, 1959.

12. Bertram, Mitchel H.: Viscous and Leading-Edge Thickness Effects on the Pressures on the Surface of a Flat Plate in Hypersonic Flow. J. Aeronaut. Sci., vol. 21, no. 6, June 1954, pp. 430-431.

13. Ellison, James C.: Investigation of the Aerodynamic Characteristics of a Hyper­sonic Transport Model at Mach Numbers to 6. NASA TN 0-6191, 1971.

14. Bertram, Mitchel H.; and Blackstock, Thomas A.: Some Simple solutions to t~e Problem of predicting Boundary-Layer Self-Induced Pressures. NASA TN 0-798, 1961 •

15. White, Frank M., Jr.: Hypersonic Laminar Viscous Interactions on Inclined Flat Plates. ARS J., vol. 32, no. 5, May 1962, pp. 780-781.

26

16. Bertram, Mitchel H.: Hypersonic Laminar Viscous Interaction Effects on the Aero­dynamics of Two-Dimensional Wedge and T~iangular Planform Wings. NASA TN 0-3523, 1966.

17. Cary, Aubrey M., Jr.; and Bertram, Mitchel H.: Engineering Prediction of TUrbu­lent Skin Friction and Heat Transfer in High-Speed Flow. NASA TN D-7507, 1974.

18. Pate, Samuel R.: Effects of Wind TUnnel Disturbances on Boundary-Layer Transi­tion with Emphasis on Radiated Noise: A Review. AIAA-80-0431, Mar. 1980.

19. Goldberg, Theodore J.; Hefner, Jerry N.; and Stone, David R.: Hypersonic Aerody­namic Characteristics of Two Delta-Wing X-15 Airplane Configurations. NASA TN 0-5498, 1969.

20. Becker, John V.: Results of Recent Hypersonic and Unsteady Flow Research at the Langley Aeronautical Laboratory. J. Appl. Phys., vol. 21, no. 7, July 1950, pp. 619-628.

27

28

TABLE I.- GEOMETRIC CHARACTERISTICS OF MODEL

Wing: Reference area (includes area projected to fuselage centerline),

cm2 (in2 ) •••••••••••••••••••••••••••••••••••••••••••••••••••••••• Exposed area outboard of strakes, cm2 (in2 ) •••••••••••••••••••••••• Wetted area, cm2 (in2 ) •••••••••••••••••.••..••••••••••••••••••••.•. Span, em (in.) •••••••••••••••••••••••••••••••••••••••••••••••••••••

451.64 195.04 390.09

24.71

(70.00) (30.23) (60.42) (9.730)

Aspect ratio .........•......•..•..•.....•.........•......•.••.•••..••.••...• 1 .353 33.24 (13.086) Root chord (on fuselage centerline), cm (in.) ••••••••••••••••••••••

Tip chord, em (in.) ••••••••••••••••••••.••••••••••••••••••••••••••• 3.32 (1.308) Taper ratio ...•.......•••••.........•.......••••••••••••••••••.•....•..•...• 0.099 Mean aerodynamic chord, cm (in.) Sweepback angle, deg:

22.38 (8.810)

Leading edge •••••••••••••••••••••••••.•••••••••••••••••••••••••••••••••••• 25-percent chord line •••••••••••••••••••••••••••••••••••••••••••••••••••••

65.0 56.99

Trailing edge ••••••••••••••••••••••••.•••••••••••.•••••••••••••••••••••••• -15.4 Dihedral angle (airfoil mean line), deg •••••••••••••••••••••••••••••••••••••••• a Incidence angle, deg •.•••••••.•••••••••.•••••••••••••••••••••••••••••••••••••.• a wing airfoil section (see fig. 1):

Thickness ratio of Exposed root ••••••••••••••••••••••••••••••••••••••••••••••••••.••••••••• Tip ••••••••••••••••.••••••.••••••••.••••••••.•••••••••••••.•••••••••••••

Leading-edge radius, cm (in.):

0.03 0.03

Fuselage centerline chord ••••••••••••.•••••••••••••••••••••••••• 0.00762 (0.003) Tip ••••••.•••••••••••••••••••••••••••.•••••••••••••••••••••••••• 0.00762 (0.003)

Trailing-edge height •••.•••••••••••••••.••••••••••••••••.••••••••• 0.01524 (0.006) Center fin proposed ~vertical tail):

Area (exposed), cm (in2 ) ••••••••••••••.•••••••••••••••••••••••••• 79.99 (12.399) Span (exposed), em (in.) •••.••••••••••..•••••••••••••••••••.•.•••••• 9.33 (3.672) Aspect ratio of exposed area •••••••••••.•••••••••••••••••••••••••••••••••••• 1.09 Root chord (fuselage surface line), cm (in.) •••••••••••••••••••••••• 13.59 (5.353) Tip chord, em (in.) ••••••••••••••••••••.•••••••••.•••••••••••••••••• 3.53 (1.390) Taper ratio •••••.••••••..••••••.•••••••.••••••••.•••••.•••••••.•.••••••••••• 0.259 Mean aerodynamic chord of exposed area, cm (in.) Sweepback angle, deg:

9.55 (3.759)

Leading edge •••••••••.••••.•.••••••••.•••.•••••.•.•••.••••••••.••••••••••• 60 Trailing edge •••.•••••••.•••••••.••••.••••••••••••••••••.••••••••••••••••• -30

Fin airfoil section, variable: Thickness ratio of -

Tip trailing edge ••••..•.••••.•••••••..••••••.••••••••••••••.••••••••••••• Root trai ling edge .••.••••••.•••••.••.•••••••••••..•.•••.•••••••••••••••••

Leading-edge radius, em (in.) ••••••••••.••••.•.••••••••••••••••••••••••••.•• Fuselage:

0.06 0.06

0.003

Length, Length,

cm (in.)

cm (in.) theoretical model •••.•.••••••••••••••••.••••••••••. test model ••••••••••.•.•••••••••••.••••••.••••.••••

65.84 59.95

(25.92) (23.61)

Maximum height, em (in.) •••••••••••••••.•••••••••.•.•••...••.••••••• 3.63 (1.428) Maximum width excluding strakes, cm (in.) ••••••••••••••••••••••••••• 7.25 (2.856) Nose radius, em (in.) •••••••.••••••••••.•••••..••••••••••••••.•••• 0.00762 (0.003) Fineness ratio of equivalent round body (excluding strakes) ••••••••••••••••• 13.0 Base area, em2 (in2 ) ••••••••••••••.•••....•.•••.••••••.•••••.••••••.• 11.03 (1.710)

Complete model (excluding vertical tail and engine): Planform area of theoretical model, cm2 (in2 ) •••••••••••••••••••• Plan form area of test model, em2 (in2 ) •.•.••••••.••••••..•••.••.•

648.69 (100.541) 633.38 (98.268)

Aspect ratio of theoretical-model planform •••••••••••••••••••••••••••••••••• 0.942 Aspect ratio of test-model planform ••.•...••..••.••..•.•.••••.•••••..••••••• 0.963 Wetted area, approximate, cm2 (in2 ) •••••••••••••••••••••••••••••• 1451.70 (225.0)

Model scramjet engine (proposed): Frontal area, 2 percent wing area, cm2 (in2 ) ••••••••••••••••••••••••• 9.03 (1.40) Chord ratio of width to height •••.••.••.•.•••.•.•.•••.•.•••••••••.••••.••••• 4.8

Volume of test model, cm (in3 ) ••••••••••••••••••••••••••••••••••••• 896.46 (54.70) v2/3/Ap (test model) •••••••.•.............•••.•••••••••••••.••••••••••.••••••• 0.146

TABLE II.- CROSS-SECTIONAL DIMENSIONS OF FUSELAGE

[All values are in inches]

X/'l X H A rad. Brad. T rad. US rad. LS rad. E Sd SW rad. W

0 0 0 0.396 0 0 0 0 0 0 0 .067 1.728 .411 .194 1 .508 .465 .084 .632 .103 .101 .084 .133 3.456 .663 .083 2.436 .752 .389 1.264 .166 .163 .154 .200 5.184 .862 .025 3.164 .977 .457 1.897 .216 .212 .216 .267 6.912 1.022 0 3.751 1 .158 .533 2.529 .255 .251 .274 .333 8.639 1 .151 0 4.233 1 .304 .547 3.161 .288 .283 .332 .400 10.368 1.253 0 4.597 1.419 .590 3.791 .313 .308 .383 .467 12.096 1 .316 0 4.828 1 .491 .644 4.424 .329 .324 .429 .533 13.824 1.379 0 5.058 1.562 .634 5.058 .345 .339 .465 .600 15.552 1.426 0 5.234 1 .616 ". .522 5.234 .357 .353 t 1 .014 1.440 .667 17.279 1.428 0 5.242 1.618 ". .392 .357 .351 t1.819 3.870 .700 18.144 1.426 0 5.234 1 .616 ". .389 .356 .342 t2.224 4.320 .733 19.008 1.378 .007 5.058 1.562 ". .432 .345 .313 t2.676 1.800 .767 19.872 1 .316 .032 4.828 1 .491 ". .457 .329 .281 t3.141 1.080 .800 20.736 1.253 .076 4.597 1 .419 ". .529 .313 .245 t3.607 1.800 .833 21 .599 1 .151 .126 4.223 1.304 ". .601 .288 .198 t3.174 2.016 .867 22.464 1.022 .180 3.751 1 .158 0 .256 .117 2.485 2.808 .900 23.328 .862 .230 3.164 .977 .216 .933 24.192 .663 .284 2.436 .752 .166 .967 25.056 .411 .338 1.508 .465 .103

1.000 25.920 0 .396 0 0 0

* . . . Fal.rl.ng to wl.ng. tDistance to leading edge or tip.

29

w o

... , ,­L I 1-­I r­L_ I ~-

~~========~==~~ I-.--- c/ 3 ---.. +I·~- c/3 - __ ·+1· ___ - c/ 3 ~ ~C ~- -----ccl"Q5049 ---1 c=,n,,'l1

.3754

I Moment reference

-.j .0505 ~ Station 0 .133 .400 .566 .910 1.000 .700 ,

I ~ C:> ~ ~ ==-

'/7-1 ,," 1

7

I

Figure 1.- Details of wind-tunnel model. fuselage theoretical length \ = 25.92 in present test.

, " , , / , , , ,

- ·t-~ . -t------

I I , -- I , /

~l--------

l • 25.92 in. (65.837 cm)

All dimensions have been normalized by the in. Dashed lines show components not used

/ 1 /

1 1

1 1

-;/' -

Reference line

A

f / 2/3H y...... / rad. US

+

E 1/3H

SW ~--------------2H

FigUre 2.- Detail of fuselage cross section and strake design. Dimensions are listed in table II.

I H

31

Figure 3.- Computer drawing of paneling scheme of configuration as input for hypersonic aerodynamic calculations.

Hot wall

0 6 R

Z = I.68x 10

Cold wall

0 RZ = 0. 597 X 106

0 0 4. 37

{;,. II. 01

1.53

0 4.02 RZ = 0. 597 x 106- YI .14

~ 24. 32

-- Theory ref. 2

IL

D. 10. 41 f ~ 32.59

RZ

= 156.22 x 106_ hi D 156.22

~ Theory ref. 2 f I }I:::>

.12

/,~ RZ = I. 68 x 106

f-----II ~ If

/(~ .10

J ~ ~

R = 24.32 x 106- f---~l Z

1 ~D ~

. 08

J P' ./ ~ J r .A ~ ,

l/ r£

V .04

.1 /

~

) ~ V

/ . 02

L ~

/ ~ ) r

) V o

/' «( 8 o 6

-.02 -2 o 2 4 6 -2 2 4 8

a, deg a, deg

(a) Normal force.

Figure 4.- Comparison of theoretical force and moment coefficients with experimental data for various Reynolds numbers in the Langley Mach 8 Variable-Density TUnnel and the Calspan 96-Inch Hypersonic Shock TUnnel.

10

.016

.014

.012

.0lO

.008

.006

.004 t-

.002

Hot wall Cold wall

o RZ

= 1.68 x 106

0 4.37 0 R

Z = 0.597 x 106

0 1.53 t:. 11.01

0 4.02 ~ 24. 34

t:. 1Q41 -- Theory ref. 2

~ 32. 59

D 156.22 ,,~RZ = 0.597 x 106

-- Th eory ref. 2 I

Ir-f- With Ii '*' Cal.

'\~With Ii'*' Cal. 6 r RZ

= 1. 68 x 10 Laminar CF- t\\. \\ jV \ \,,\ \ '\ N::= V IY

\ Laminar CF- \

~b \ p l V 1\ f\ ./

(D -< b--r\-< I> \ <D '\ r-

b \( b~ g- P V < ~ h h [ .../ t\ \ \ h .;

~ V-

~ 6. V -- ~

\[ bJ! ~ V ~ -I- D 1V'6. V <I> ~ /"" ~ ~ r- 6. ~ ~ V )...-

~ <f> g. < IV' IV'

6. It:.~ ~ V t:. t:. ~ ./

-c> ~ V ~ t-RZ

= 24.32 x 106 .-.--l---

~ ~ ~ ~ <I> V

k-"i K-~( V -'I ~

\. f- Turbulent CF ~b ~ Jp-\ 1-\ I-RZ = 32. 59 x 106 ~

~ ~ p-

- Turblulent CF-j:!

---~ ~ F\ \. f-Inv. + C

A \ LE & TE L--:: 1--\

r-- 1\ \. Hnviscid 'C I nviscid

o 2 4 6 8 -2 o 2 4 a,deg a, deg

(b) Axial force.

Figure 4.- continued.

~ (D /'" V

~ V ty'

6 RZ = 1.53 x 10 /'"

1\ [ b ./ V /'

~ v ~

v ./

~ ./ V l/

~ V li

f\- RZ

= 156. 22 x 106

~ ~

~ ~

I-Inv. +CA LE & TE

6 8 10

W 111

.12

.10

.08

.06

.04

.0 2

0 /

.I~ V

Hot wall

0 RZ

= 1.68 x 10 6

0 4.37

6 H.Ol

~ 24.32

-- Th eory ref. 2

RZ = 1. 68 x 10 6

R = z

24.32 x 106_ ~

i! J ~

)~ l(

,/ ) P'

~~

o 2 4 a,deg

J

/; i'- i"'-. /

r( I/J~

~ ~ D

W f:.J

~

)

) If <r

6 8 -2

(c) Lift.

Cold wall

o R Z = U 597 x 106

0 1. 53 6

0 4. 02 RZ = 0.597 x 10 -

6 lU 41

~ 32. 59 6 C:§ D 156.22

RZ

= 156.22 x 10-

-- Theory ref. 2

l7 L rr

/

" o 2

E-A [D ~

4

a,deg

~ /) ~

/If

#<b A ~D ~ ~

6 8

Figure 4.- Continued.

~ If

10

.-032

.028

.024

.020

.016

.012

.008 t-

.004 t-

o -2

Hot wall

0 RZ

• 1.68x 10 6

0 4.37

C:; n.01

~ 24. 32

-- Theory ref. 2

I

I VI

RZ

• 1. 68 x 10 6 ~ j: l¥J

\ if / / r V

'\ -With 6* Cal. df j / ~ V ~ I

Laminar CF-

"" ~ ~ W I ~ ~~

V V h h 10 )

.-V< ~/ ~ ~RZ = 24. 32 x 106

h. b. ~ ~ ~ .-V ~ "t Turbulent CF

~ V ...... I-Inv. + C

A LE & TE

l'- I nviscid

o 2 4 6 8 a,deg

Cold wall 1 :-- 6 0 R

Z= 0. 597 x 10 Ii;

r-- 0 1.53

0 4.02 I /~ r--R

Z = 0. 597 x 106_ / Ilff J C:; 10.41

~ r-- ~ 32.59 \ VI WI I-- D 156. 22

- Theory ref. 2 I p /~ I / II II II

6 RZ = 1.53 x 10 ~ )) I 'ifl I>Z: ~/; I V ) )D WI!

/ II; '/ I ~

I-With 6* Cal. ) ~ I P£ II ~ J?' V/, ~7

Laminar CF- ~ 0 ~ / ~ V ( ~ ~ - I)-- 1M t- Jtl...-0 ~.~

<I> .-~ ~ t-\T- f( ~

-2 o 2

(d) Drag.

J) [12 iT I-RZ = 32. 59 x 106

~ ~ Df..... RZ

= 156. 22 x 106 ~~ ~ ~ V r'-I-Turbulent C

F

V ~ r--. ......... I-Inv. +CA LE & TE

~ Hnviscid

4

a,deg

6 8 10

Figure 4.- Continued.

LID

Hot wall

6 o R Z = 1. 68 x 10 o 4.37 I-----f--,+_-R-

Z "-=-2--J.

4.-32

-x

-"-I-=06,.....-i

6 11. 01 ~ 24.32 \ ,t-Turbulent CF

6 -- Theory ref. 2 /v:~~

I / / J / I ~ [P 4~~-+--H-~~~F-~-+--r-~

I/~ V ;fP / II j'f8/[b I / r- Laminar CF

31-----f--+-rr+--f-r+--H---f-------~ I <V I L RZ = 1. 68 x 106

-1 I, ~ -2 I I

-2 0 2 4 6 8 a, deg

Cold wall

o R Z • 0. 597 x 106

0 1. 53

0 4.02

6 10. 41 /

~ 32. 59

~L D 156.22

- Theory / ~ ref. 2 / !~

11< ~~ jl L V I II jL p~ fj / vv' / / Ili/

l fl / It--

fl tI'

} ~ d_

!J /II! (~I J -2 o 2

(e) Lift-drag ratio.

Figure 4.- continued.

6 / --R

Z = 156.22 x 10

Vi ~RZ = 32. 59 x 106

IG'I -/ V F r Turbulent CF

~-~/

? ~ ~ ~ <) ~ p ~ t> / p [ J-""" ~ ~~ r / lY '" ~ J r- --,...

L r j l P/() r--Y / V r-Laminar CF

/ L 6 RZ = 1. 53 x 10

/ R z = 0. 597 x 106

-With ()* Cal.

4 6 8 10 a, deg

Hot wall

0 6 RZ

= 1.68x 10

0 4.37

6- 11. 01

~ 24. 32

Cold wall

RZ • 0. 597 x 106 0

0 1.53

0 4.02

6- 10. 41 R Z = 0. 597 x 106 \

.02

-- Theory ref. 2

8

~ 32. 59 \ I- RZ = 1.53 x 106

D 156.22 1\ 'i

'\ f\ f-lami nar CF

IU -- Theory ref. 2 /'"

1\\ \ /V 6

\.. RZ = 1.68x 10

1\"' I-laminar CF

.024 \ \\ V V tV

./ ~ 1\\ / ~ V } .\ 8 k>/'

IJ \ V V .020 0/

!7 TI ~ ~ l7 /

V \/ ~ V V V

./

j) 16 V 6 ./

\ ~With Ii. Cal. 8 V / V V

.01 f- With [). Cal. / V I V ~ V V

~ ~ ./ /

\ I~ ).V n / A V V 1\ 8/

VOL V /' V

2 )y ~ .63' V V I'..

\~ V ./~J ~ Vf / V

P KQ 8 V ~ ~ lX ~ 6~

[ !/G. ty ~ k> V 18 I'..

V~ V V '" 1'-."'- r- R = 24.32 x 106 [0 z

~ K "" r- Turbulent CF ./

V '\. t-Inv. + CA / lE &TE

.008

.004

<!Y I~ ~ ty" / ~

"'" ""-l- R Z = 32. 59 x 10

6 [7

V1 :~ V k '" "'-I- RZ = 156. 22 x 106

c~ V """

'C I-Turbulent CF ./ p/ V I-Inv. + C

A LE& TE

.002 .004 .006 .008 .010 o .002 .004 .006 .008 .010 .012 .014

Cl 2 C 2

l

(f) Drag due to lift.

Figure 4.- continued.

'·~IIIIII T' 111111 '"'''' , Theory ref. 2 h Rl " 0. 597 x 106

0 IV

0 0 0

...... () () 0

----- \

' .• ~ t~~ III r Illo,,!" fr I Theory ref. 2 6

:\. R1

"1.68xlO

0 [ 0 ...... 0 n .,

--I-- ...

'·~I Hoill tlolffFI Illoll! 1+1°1 !lTr I .008

em .004

o

(:, (:, (:, l.

Rl " I100l x 106 \~

R[ " 10. 41 x 106

~ (:,

,.~ I~~ I j t f 1·11,'rrn R[ " 24.32 x 106

~ ~ ~ c, ~

...... ~

. '. ·~IIIIIIIIIIIII I ~*III ~ 101 ! I:fr~ -.02 0 .02 .04 .06 .08 .10 -.02 0 .02 .04 .06 .08 .10 .12

C CL L

(g) Longitudinal stability.

Figure 4.- Concluded.

39

40

.06

.02

.008

~6 1

Monaghan l' CF

Experiment Theory

LRC Calspan

o o

Figure 5.- Comparison of experimental normal- and axial-force coefficients with calculations from the GHABAP on the fuselage-wing configuration. a = 3°; Me:>" 8.

300

.010

.008

.006 <0 oe(JJ

8 ~r?o cA f93 BoB

a' 3°

.004

T.J To Experiment .002 lRC 0.64 0

Calspan 0. 16 0

00 2 8 12 14 16

(~) x 10-4

(a) Extrapolation of laminar data • . 010

.006

~ .004 Slope 1: 7

CA - 0. 0022 ~o 0 B

.002

. 00~6 3 300

(b) Reynolds number root determination.

.010

~ gO

0 0 I2J .008 0 0

0

.006 CA a' 3°

.004

.002

°0~----~----~----~6----~8----~~--~~--~~--~J6

(yifRJ x 10-2

(c) Extrapolation of turbulent data.

Figure 6.- Extrapolation of data to very high Reynolds numbers. a = 3°; ~ ~ 8.

41

42

.002 4

t:.C

96

.008

.004

.002

AB,lnv Zt:.CA B, If

3 6 10 .6 6

Rr x 10-6

(a) Buildup of laminar theory.

.....

Laminar CF

C A, total Monaghan T' CF

..... ..... ..... ..... ' .....

.............. -.-

-6 Rr x 10

o LRC Hot wall

---- 0 CalspanColdwall

Spalding-Chi CF

Turbulent CF

(b) Comparison of experiment and theory.

10

300

Figure 7.- Buildup of present laminar predictions of axial-force coefficient at two wall temperature ratios and comparison with experimental data. a = 3°; Moo ~ 8.

.06

.02

.004

6

UD a = 3°

4

0

2

(a) Lift coefficient.

(b) Drag coefficient.

-6 Rr x 10

(c) Lift-drag ratio.

Experiment Theory

Turbulent CF

Calspan o o

6ll

300

Figure 8.- Comparison of experimental lift, drag, and lift-drag ratio at two wall temperature ratios with improved theory. a = 3°; M"" .. 8.

43

M 00

44

8.4

8.2 (

0 u 0 0

0 8.0

0

7. 8

7. 6

7.4

-2 o

r ~ Tunnel core /

0 ,.,

,.., )0 UJ f-'oCO v ...

0

2 Inches

-OCo< ~

4

1 ) -0-< ru

6

Figure 9.- Vertical Mach number distribution (taken from ref. 19) through test-section centerline of the Langley Mach 8 Variable-Density Tunnel. Po = 2515 psia1 To = 1460 0 R.

8

__ \I--____ A_pp_ro_xi_m_ate_.~=+_ + __ )+-___ _

\ I

(a) Schematic downstream view of test-section area utilized for present tests.

1 nches

5.5 4.5 3. 5 2. 5 I. 5 . 5 .5 1.5 2.5 3. 5 4.5 5.5 r---~--~--~--'I----'I--'--'-----'------Ir---~r-----r---~

Calibration probes -=z:::=<r------.. Lines of constant Mach number

(b) Radial lines of constant calibrated Mach number superimposed on frontal view of model.

Figure 10.- Test region and calibration scheme in the Langley Mach 8 Variable-Density TUnnel.

45

46

R

6 30 x 10

20

10

8

6

4

/

2 // 3

/ V

/

V

/ /v L

/ £

.8

.6 /

8.5

/'

~ V ___

~

/ /

/ /

V

/ /

T9--

V V------

7.5 100 200 300 400

/ v / /

/~ V

/ /

v V /

{1m / / /

V / /Rr /

V /

/ V

.rR;ft

--"

1500

/'

../ V

/ 1400

V Vf.-'

V V ~ ----

1300

q" l-I--1----- 1200

1100

600 800 1000 2000 3000

Po' psia

Figure 11.- Calibration Reynolds number and Mach number for stagnation pressure range in the Langley Mach 8 variable­Densi ty Tunnel.

-2 x 10 •

8.5

7.5

40

35

30

OR 25

Po -3

x 10 ,

20

15

20

16

12

psia 8

4

o 0.3

~ ~ ~

<$ <0 ~ ..

& A0t$> - />,8;1 '0-

~ 7'~ o ~0 0

~

IZl

8 tZI fil .,;;1

'-;;" PI '" '§ ~ 0 ~ la U -, 0

IZl

"\ ~ ~ n

-~ ~

IZI IZI IZI

r:J ---~ 0 IZl

Flag indicates duplicate point

·1 Slash indicates a· 3° 0 ,",

,,,,is! / ~

~ \

/

/<- Data fairing ./ ~<\.

~0 ~(';0 0 0

~ .mI"L

1.0 3.0 30 100 300

Figure 12.- Test conditions for present study in the Calspan 96-Inch Shock Tunnel.

47

48

.68

.66

.64

Cf~ .62

.60

.58

.56

.54

• 520 2 3 4

(a) Variation with local

.68

.66

.64

.62

.60

Cf~ .58

.56

.54

.52

.50

.25 TwlTl I 2

16 18 20

5 6 7 8

Ml

Mach number. T1 100o R.

LRC hot wall 6 Rl • 1. 68 x 10

4. 37 11.01

Calspan cold wall

o Rl ' 0. 597 x 106

IZl 1. 53 o 4.02 /l,. 10. 41

10

.480 50 100 150 200 250 300

(b) Variation with local temperature. M1 = 8.

Figure 13.- variation of local flat-plate laminar skin friction with local Mach number and local temperature.

.r;>. ~

401 7 I 11

3611-------11-----,-

321 1 :::::> ---= 1

281 ::;;> <: 1

241 :;;> "'l

201 ::;> <f

"V~nit V () U- r-----:=:r ::;>

16

121 ~I ::lei A" /' 1/ / I

81 ----=1 /-P c :...I.e 7/ L/

41 ....-=t;? 1::><

00 2 4 6 8 10 o 2 4 6 8 10 o 2 4

MI MI MI

Figure 14.- variation of larninar-boundary-layer displacement thickness (ref. 8) •

Npr • 1. 0

6 8 10

50

6"tunit ex

40

36

32

28

24

20

4

.80

.75 Npr

.70

.65

Taw

I I I

0 1 2 3

T, oR x 10-3

Figure 15.- Variation of boundary-layer displacement thickness (ref. 8) on

14

a flat plate with temperature ratio for various Prandtl numbers and M1 8.

.5.------.------1I------------~------~----~ Npr C 0.68

O. 75 .4

• 3 ~. u , in.

· 2

· 1

2 4 8 10

Figure 16.- Variation of calculated boundary-layer dis2lacement thickness on a flat plate by two theoretical methods at M1 = 8 and Rx,1 = 0.384 x 106 •

12

51

U1 IV

??Z?ZZT/2/ V7J2ZZZ2222

I o

8. 1 in.

Figure 17.- Variation of calculated laminar-boundary-layer displacement thickness with wall temperature on exposed wing root chord. Moo = 7.741 R\ = 1.4 x 106 •

VI W

dO* dX

1.5 1.0

dO* dX Flow

.5 30 defl.,

deg

15

1.0 Shock detachment 80

0 40 60

P/Poo

Upper surface

Lower surface

TwlTo .5 LRC 0.64

Calspan 0.16 ----

-------- ------. 1 1 10

Percent wing root chord

Figure 18.- variation of the slope of boundary-layer displacement thickness with exposed wing root chord and resulting tangent-wedge pressure. R

t = 1.4 x 10 6; Moo = 8.

100

54

Cp

?ZZ77ZZZZ-~~/2ZZZZZ772Z

.15~---------------'r----------------.-----------------.

I I

.10

I I I I I I I

.05

\ \ \

0

\. ........ -

Lower surface

"" With 6 Cal. I nviscid

---Upper surface

"" With 6 Cal. I nviscid

----, ,-------

-. 050!-----------;!. 3~3--------.-766-;-----------:-I1. 0

(a) Variation of pressure coefficient on the exposed wing root chord.

Figure 19.- Typical calculated wing pressure distributions. Moo = 7.74; 6 R =1.4x10; 0:=3°.

1.

[ .15.-----------~------------~------------~----------~

. 10

---------

.05

.25

With 0 «: Cal .

5400R --------

.50

V/b

I nviscid

-

.75

(b) variation of axial pressure coefficient on the exposed wing semispan.

Figure 19.- Concluded.

1.00

55

/ APproXlm~t~c'nt'~c:~ _ __ ___ ___ ___ Mod,flocation, inc:" from c,nt,\n,

,------- -----------~~~

I ------- -- -- -- -- \ --- -----, r-

, --- ------ / 0 ---- ---, --/-- ----- --------

I C=-.=------" // __ ..J I --- -~-

-------4----------------~=-~~_--_--------~~----- -r ------+-~--------_--~---~--~----------------~r--------, r-L --~.:: / -1

\

- - - - - - - \. ~ ... -....... / T - - - - - - - - - - -=--:":J c~~:~~-- , / ------ I ------ / -----..... /' r-\ ....... -~~--+---~- ." \ 1-2

\ "' ........ - /// / - -\ /

"'" / V Approximate boundary layer /

--- -----Figure 20.- Schematic downstream view of test section with model at various vertical locations in the

Langley Mach 8 Variable-Density TUnnel.

CL

CL

CL

· 06 6 · 008 6 Rl = 1. 68 x 10 Rl = 1. 68 x 10

C

.04 g " g.. ---0

m · 004 Q Q Q e

· 02 a

· 06 4.37 x 106 • 008

4.37 x 106 R = R = l l

C m

.04 g g g g .004 Q- --Q-=

.....g g

· 02 0

.06 R l = 11. 01 x 10

6 · 008 R l = 11. 01 x 10

6

C ~ ~ 0 0 ~ m

~ ~ Q .04 · 004

• 021-.--_.1...2 ---.1.._

1-----1o----.1

1 0~--~2----~-1------~0----~1

Distance from tunnel centerline, in. Distance from tunnel centerline, in.

Figure 21.- variation of lift and pitching-moment coefficients with vertical test-section location at various Reynolds numbers in the Langley Mach 8 Variable-Density Tunnel. a = 3°.

58

C

Distance from tunnel centerline

o 2. 54 cm n in.} above o On centerline o -2. 54 em (1 in. ) below 6 -5 .. 08 cm (2 in. ) below

.006--------~------~--------~------~

m .005

.004

.050--------~------~------~-------,

.040

o 10 20 Time, sec

30 40

Figure 22.- Variation of lift and pitching-moment coefficients with blowdown-tunnel test time for various vertical test-section locations in the Langley Mach 8 Variable-Density TUnnel. R = 11.01 x 10 6 ;

'l

1. Report No. I 2. Government Accession No. 3. Recipient's Catalog No.

NASA TP-2159 4. Title and Subtitle 5. Report Date

WALL-TEMPERATURE EFFECTS ON THE AERODYNAMICS OF A July 1983 HYDROGEN-FUELED TRANSPORT CONCEPT IN MACH 8 BLOWDOWN 6. Performing Organization Code AND SHOCK TUNNELS 505-31-73-01

7. Author(s) 8. Performing Organization Report No.

Jim A. penland, Don C. Marcum, Jr. , and Sharon H. Stack L-15100

10. Work Unit No.

9. Performing Organization Name and Address

NASA Langley Research Center 11. Contract or Grant No.

Hampton, VA 23665

13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address Technical Paper National i'\eronautics and Space Administration 14. Sponsoring Agency Code Washington, DC 20546

15. Supplementary Notes

16. Abstract

Results are presented from two separate tests on the same blended wing-body hydrogen-fueled transport model at a Mach number of about 8 and a range of Reynolds numbers (based on theoretical body length) of 0.597 x 106 to about 156.22 x 106 • Tests were made in a conventional hypersonic b lowd own tunnel and a hypersonic shock tunnel at angles of attack of -2° to about 8° , with an extensive study made at a constant angle of attack of 3° • The model boundary-layer flow varied from laminar at the lower Reynolds numbers to predominantly turbulent at the higher Reynolds numbers. Model wall temperatures and stream static temperatures varied widely between the two tests, particularly at the lower Reynolds numbers. These tempera ture differences resulted in marked variations of the axial-force coefficients between the two tests, due in part to the effects of induced pressure and viscous interaction variations. The normal-force coefficient was essentially independent of Reynolds number. Analysis of results utilized current theoretical computer programs and basic boundary-layer theory.

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Laminar skin friction Unclassified - Unlimited Turbulent skin friction Boundary-layer induced pressure Hypersonic aircraft Computational aerodynamics Subject Category 02

19. Security Oassif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price

Unclassified Unclassified 59 A04

For sale by the National Technical Information Service, Springfield, Virginia 22161 NASA-Lang1 ey, 1983

-NASA Technical Paper. 2728

August 1987

NI\S/\

/

Effect of Rey:qolds Number ~ Variation on Aerodynamics . "of a Hydrogen-Fueled Transport. Concept at Mach. 6

Jim A. Penland and Don C. Marcum, Jr.

NASA Technical Paper 2728

1987

NI\SI\ National Aeronautics and Space Administration

Scientific and Technical Information Office

Effect of Reynolds Number Variation on Aerodynamics of a Hydrogen-Fueled Transport Concept at Mach 6

Jim A. Penland and Don C. Marcum, Jr.

Langley Research Center Hampton, Virginia

Summary

Two separate tests have been made on the same blended wing-body hydrogen-fueled transport model at a Mach number of about 6 and a range of Reynolds number (based on theoretical body length) of 1.577 x 106 to about 55.36 x 106 . The results of these tests, made in a conventional hypersonic blow­down tunnel and a hypersonic shock tunnel, are pre­sented through range of angle of attack from -1° to 8°, with an extended study at a constant an­gle of attack of 3°. The model boundary-layer flow appeared to be predominantly turbulent except for the low Reynolds number shock tunnel tests. Model wall temperatures varied considerably be­tween the two tests; the blowdown tunnel varied from about 255°F to 340°F, whereas the shock tunnel had a constant 70°F model wall temperature. The ex­perimental normal-force coefficients were essentially independent of Reynolds number. A current the­oretical computer program was used to study the effect of Reynolds number. Theoretical predictions of normal-force coefficients were good, particularly at anticipated cruise angles of attack, that is, 2° to 5°. Axial-force coefficients were generally underesti­mated for the turbulent skin friction conditions and pitching-moment coefficients could not be predicted reliably.

Introduction

The interpretation and application of aerody­namic test data from ground test facilities in the de­termination of full-scale aerodynamic performance of a particular design are the primary goals of configu­ration testing. These goals are accomplished by se­lecting a design having sufficient volume to house the required fuel and payload, adequate wing area for a safe ·landing, and a shape based on available theory, published data, and experience. Such a configuration was the liquid-hydrogen-fueled hypersonic transport concept (fig. 1) that was extensively tested through a wide range of Reynolds number in a conventional blowdown wind tunnel and a shock tunnel at a Mach number of about 8 and reported in references 1 and 2.

The purpose of this paper is to report the results of further free-transition tests on the same model of references 1 and 2 at a lower Mach number of about 6 in both a blowdown tunnel and a shock tunnel.

The major difference existing between tests in the two tunnels was the ratio of model wall temperature to stagnation temperature. The shock tunnel data were taken with a relatively low model wall tempera­ture, whereas the conventional wind-tunnel data were taken with a high model wall temperature.

Presentation of results includes a comparison of all experimental longitudinal force and moment coefficients measured in a conventional blowdown hy­personic tunnel and those measured in a hypersonic shock tunnel; experimental data are then compared with theoretical predictions made with Gentry's Hy­personic Arbitrary-Body Aerodynamics Computer Program (Mark III Version) (GHABAP). (See ref. 3.) The experimental data were obta.ined at a Mach number of about 6 through a range of Reynolds num­ber (based on theoretical model body length) from about 1.577 x 106 to about 55.36 x 106 . The range of angle of attack was from -1° to about 8°. The re­sults of a study of data at a constant angle of attack of 3°are also presented.

c

L

LID

M

My

Po

axial-force coefficient, q:% drag coefficient, q/},s average skin friction coefficient

lift coefficient, q;'S

pitching-moment coefficient,

q':,l$c normal-force coefficient, q~S

wing chord

mean aerodynamic chord of total wing

drag, FN sin 0:' + FA cos 0:'

axial force along X-axis (positive direction is - X)

normal force along Z-axis (posi­tive direction is -Z)

lift, FN cos 0:' - FA sin 0:'

lift-drag ratio

reference length (theoretical body length), 25.92 in. (see fig. 1)

free-stream Mach number

moment about Y-axis

stagnation pressure

free-stream dynamic pressure

Reynolds number based on theoretical body length at free­stream conditions

s

v

Subscripts:

LE

TE

cl

Abbreviations:

reference area, area of wing including fuselage intercept, 70 in2

planform area, in 2

stagnation temperature, oR

volume, in3

angle of attack, deg

leading edge

trailing edge

centerline

Exp. experiment

GHABAP Gentry's Hypersonic Arbitrary­Body Aerodynamics Program (Mark III Version)

HST Hypersonic Shock Tunnel

Inv. inviscid

LRC Langley Research Center

M = 6 LRC 20" Langley 20-Inch Mach 6 Tunnel

M = 8 LRC VDT Langley Mach 8 Variable-Density

TC

TW

t.p.

Tunnel

tangent-cone pressure distribu­tion method

tangent-wedge pressure distribu­tion method

tangent point

Fuselage dimensions in table II and figure 2:

A

H

rad. B

rad. E

rad. LS

rad. T

rad. US

rad. W

Sd

2

distance between reference line and top of fuselage

height of fuselage

radius of fuselage bottom

radius of fuselage side

radius of strake lower surface

radius of fuselage top

radius of strake upper surface

radius of fairing from fuselage to wing

distance from bottom of fuselage to strake leading edge

SW

x

x/I

distance from side of fuselage to strake leading edge

distance from nose of fuselage to cross section

body station

Test Configuration

The test model was the 1/150-scale hypersonic transport concept of references 1 and 2 and is shown in figure 1. The fuselage cross-section design was semielliptical with a width-height ratio of 2 to 1; the cross-sectional area was expanded from the nose to a maximum at the 0.66 body station according to the Sears-Haack volume distribution equations for mini­mum drag bodies of reference 4 and converged to 0 at station 1.00. Strakes were added to improve the hypersonic lifting capability of this voluminous com­ponent. The fuselage was blended with the strakes and the wing to reduce adverse component interfer­ence effects. (Details of the configuration tested are shown by the solid lines in fig. 1.) The vertical tail and engine nacelle were not installed for the present tests. The fuselage cross-section design scheme is shown in figure 2. All design curves were circular arcs to facilitate fabrication. The overall geometric characteristics of the model are presented in table I, and the detailed fuselage dimensions illustrated in figure 2 are presented in table II. The model was con­structed entirely of 4130 steel to provide maximum strength in an annealed condition. The model fuse­lage was machined to accept a six-component strain gauge balance to measure aerodynamic forces and moments during the wind-tunnel tests.

Apparatus and Tests

Langley 20-Inch Mach 6 Tunnel

This investigation was conducted in the Lang­ley 20-Inch Mach 6 Tunnel. This tunnel operates on a blowdown cycle through a two-dimensional noz­zle with a test section 20.5 in. high and 20 in. wide. Dry air was used for all tests to avoid water con­densation effects, and it was heated to avoid air liq­uefaction and the supersaturated region as defined by reference 5. Tests were conducted at free-stream Mach numbers of 5.799 to 5.994, stagnation pressures of 34.3 to 525 psi a, and stagnation temperatures of about 784°R to 912°R. These conditions result in an average free-stream Reynolds number based on body length of 1.577 x 106 to 18.20 X 106 (0.7303 X 106 to 8.426 x 106 per foot).

A six-component water-cooled strain gauge bal­ance was installed inside the model body and was

attached to the tunnel variable angle sting support system. The angle of attack was set for each test point by the reflection of a beam of light from a fixed­point source to a small mirrored prism/lens installed flush with the surface of the model to a calibration board. Thus, by setting the model at the desired an­gle of attack instead of the sting support, no sting deflection correction was required. Forces and mo­ments were measured through a range of angle of attack from -1° to So at an angle of sideslip of 0° . All screw and dowel holes and joints were filled with dental plaster before each test run. Base pressures were measured and the axial-force component was adjusted to correspond to a base pressure equal to the free-stream static pressure. All tests were con­ducted with natural boundary-layer transition.

Calspan Hypersonic Shock Tunnel

The Calspan 4S-inch leg of the Hypersonic Shock Tunnel, described in reference 6, employs a reflected shock to process air to conditions suitable for sup­plying an axially symmetric convergent-divergent hypersonic nozzle. The shock-processed air is ex­panded through a contoured nozzle, having inter­changeable throats, to the desired test conditions at the 24-inch exit diameter. Test time varied with con­ditions up to about 13 milliseconds duration. For the shock tunnel tests the stagnation pressure varied from about 259 to 4093 psi a, and stagnation temper­ature varied from about 1479°R to 22S9°R to tai­lor the wide test Reynolds number range at Mach numbers of 6.13 and 6.5S and to avoid liquefaction. These conditions resulted in an average free-stream Reynolds number based on body length of 1.64 x 106

to 55.36 X 106 (0.7599 X 106 to 25.63 X 106 per foot). The higher stagnation temperatures were uti­lized at the lower stagnation pressures to help obtain the lower Reynolds numbers by increasing viscos­ity. The model was mounted on a three-component strain gauge balance downstre~m of the contoured nozzle exit at a fixed angle of attack for all tests, and the final data were corrected for sting deflection. The free-stream Mach number was determined from pitot pressures measured for each test run by means of piezoelectric crystal pressure transducers mounted in the test section. Tests were made with free tran­sition, and base-pressure corrections were applied as described in the previous section on the blowdown tunnel.

Precision of Data

Estimates of the uncertainties in the measure­ment of force and moment coefficients for the individual test points are generally based on the

accuracy of the force balance system, which is ±0.5 percent of maximum balance loads with all components loaded simultaneously. During the present tests, only the normal-force, axial-force, and pitching-moment components were utilized and the balance was check calibrated at full, one-third, and one-fifteenth loads. Due to these precautions, an ac­curacy of ±0.125 percent of full load is considered a more reasonable estimate and is pre?ented as follows for the low Reynolds number worst condition:

±O.002

±O.0004

±O.0002

The stagnation pressure was measured to an accu­racy of ±0.003 to ±1.3 psia for the pressure range of 35 to 525 psia and the angle of attack was set to ±0.1O°.

Theoretical Methods The theoretical studies made in the present report

consist of, first, computerized calculations predict­ing the various longitudinal aerodynamic coefficients at appropriate flow conditions for angles of attack up to So and, second, an investigation of the normal and axial forces with variation in Reynolds number at a constant angle of attack of 3°. The computer program was also used to evaluate the induced pres­sure effects on axial-force coefficients under laminar boundary conditions.

Inviscid Aerodynamics

The theoretical studies make major use of Gentry's Hypersonic Arbitrary-Body Aerodynamics Program (Mark III Version) (GHABAP). (See ref. 3.) The aircraft configuration was divided into approxi­mately SOO elements, as shown in figure 3, for the cal­culation of both the inviscid and viscid aerodynam­ics. This program has available a variety of optional calculation methods for inviscid pressure versus flow deflection in both the impact flow and the shadow flow regions, which may be arbitrarily applied to individual model panels. Various methods and dis­tributions were tried on the present configuration including the tangent-cone, tangent-wedge, and the shock-expansion methods for the impact flow re­gions while using the Prandtl-Meyer expansion from free stream to all shadow regions. The most suc­cessful combination was found to be the use of the tangent-cone pressure distribution on the forward fuselage and strakes ahead of the wing-fuselage junc­tion and the tangent-wedge method on the wings and that portion of the fuselage aft of the wing­fuselage junction as discussed subsequently. This

3

distribution methods gave normal- and axial-force coefficients on the complete configuration that were essentially the same as those predicted by the use of the tangent-cone option on the fuselage and the shock-expansion option on the wings and strakes, as presented in reference 1, but gave much more realistic pitching-moment coefficients at M = 8 (ref. 2). This compromise in selection of inviscid pressure distribu­tion calculation methods is reasonable when consid­eration is given to the flattened conical shape of the forward fuselage and to the relatively small average thickness ratio of the aft blended wing-body cross section. Wing and fuselage leading-edge axial-force contributions were assessed from the results of the circular-cylinder study of reference 7. A base pres­sure coefficient of -1/ M2 (ref. 8) was assumed to exist on the blunt-wing trailing edge.

Skin Friction

Laminar skin friction was calculated within the GHABAP by the T'-theory (the reference tempera­ture method of Monaghan in ref. 9). A discussion of this reference temperature calculation was presented in reference 2.

Turbulent skin friction was calculated within the GHABAP by the method of Spalding and Chi (ref. 10). Adiabatic wall temperature was assumed for both laminar and turbulent calculations of vis­cous effects for the Mach 6 blow down tunnel tests. For the shock tunnel estimates, the measured wall temperature of 70°F (5300 R) was used.

Induced Pressure

The buildup of a boundary layer on an aerody­namic surface effectively alters the surface contour; consequently, the resulting airflow is displaced out­ward from the surface which changes the pressure dis­tribution. The boundary layer of some of the present tests was laminar, and due to the effective surface contour changes and additional effective blunting of the leading edges, there were marked local flow de­flections and, therefore, high local pressures, which decreased rapidly downstream to levels somewhat higher than would be expected for inviscid flow. (See refs. 2 and 11.) To account for this change in sur­face pressures on both wings and body, the induced pressure option available in the GHABAP was used to provide estimates for comparisons between theory and experiment with angle of attack. It is gener­ally recognized that turbulent boundary layers are equally capable of inducing surface pressure changes but little experimental effort has been made to un­derstand this important phenomenon. References 12 and 13 are some examples of comparison between

4

theory and experiment under laminar, transitional, and turbulent conditions. No configuration aerody­namics program incorporates pressure effects induced by boundary layers at this time, and no estimates were made for the present tests.

Blunted leading edges of the model may also be expected to induce surface pressure variations; however, no estimates were made for the 0.003-inch­radius leading edges or nose radius of the present test model. (See ref. 11.)

Viscous Interaction

The large induced pressure gradient (falling pres­sures) discussed in the preceding section has an ad­verse effect on the laminar skin friction and is here­after referred to as "viscous interaction." As with the induced pressure calculations, the GHABAP was utilized to account for this viscous interaction. This aerodynamic program normally tabulates the lam­inar skin friction in combination with an estimate of the viscous interaction. For the present analysis, this program was modified to tabulate the skin fric­tion without the viscous-interaction increment. The increment of viscous interaction was therefore the dif­ference between the original and the modified com­puter program results. These increments were used in combination with the induced pressure increment and the leading-edge and trailing-edge drag. No es­timates of the viscous interaction were made for tur­bulent boundary-layer conditions.

Results and Discussion Experimental results at Mach 6 for seven different

Reynolds number tests through a range of angle of attack from -1° to 8° from a conventional blowdown wind tunnel and a shock tunnel are presented in figures 4 and 5 for the wing-body hypersonic concept and compared with theoretical estimates from the GHABAP. Numerous tests were made at 0: = 3° through a range of Reynolds number from 1.577 X 106

to 18.199 X 106 in the blowdown tunnel, and two tests were made in the shock tunnel at R[ = 1.906 X 106

and 52.963 X 106 . These data are presented m figures 6 and 7, along with GHABAP estimates.

Normal Force

Experimental normal-force coefficients, presented against angle of attack in figure 4(a), show only a slight variation between facilities and Reynolds numbers. The largest variation occurred for the shock tunnel cold wall test at low Reynolds number. Each cold wall data point was the result of a separate shock tunnel test made during a period of several days on the same model; this may have contributed

to the data scatter. The change in the slope of the normal-force curve with Reynolds number was due in part to the variation of tunnel test Mach numbers with stagnation pressure. It is evident that the wide range of model surface temperature and stagnation temperature between the blowdown and shock tunnels had only minimal effect on the normal force. The GHABAP estimates are good at cruise angles of attack (2° to 5°) and adequate at higher angles of attack.

Axial Force

The axial-force coefficients from both the blow­down and shock tunnel tests are shown in figure 4(b) and are compared with theoretical estimates com­puted with the GHABAP. See the section "Theoret­ical Methods" for a description of the present ap­plication of turbulent and laminar skin friction and reference 2 for a detailed discussion of the effects of model wall temperature on the axial force. A study of the left side of figure 4(b) shows that the experi­mental data taken in the conventional blowdown tun­nel with hot model wall temperatures were generally underpredicted by the GHABAP, particularly at the lower angles of attack. For these predictions a tur­bulent skin friction was assumed although laminar­boundary-layer conditions would be expected to exist at the lower Reynolds numbers. This apparent early transition is discussed subsequently. The present turbulent skin friction estimates do not contain ei­ther induced pressure or viscous interaction incre­ments as included in the laminar estimates. (See sec­tion "Theoretical Methods.") Furthermore, it is not known with what accuracy the inviscid axial-force coefficients were calculated by the GHABAP. In ref­erence 2, the predicted inviscid axial-force coefficients at 0: = 3° were substantiated by extrapolation of ex­perimental data taken at low Reynolds number test conditions to very high Reynolds numbers. Such an extrapolation can only be done under laminar condi­tions where the skin friction parameters are propor­tional to (Reynolds number) 1/2. The turbulent skin friction parameter may also be considered to be pro­portional to (Reynolds number)n but in turn n varies with Reynolds number, thus making simple extrap­olation over wide ranges of Reynolds number unreli­able if not impossible (ref. 14). It should be pointed out that the turbulent skin friction varies much more with Mach number than does the laminar skin fric­tion; therefore, this contributes to the less than desir­able accuracy in predicting configuration axial force with codes that do not take into account local Mach number variations.

The right side of figure 4(b) shows the two avail­able angle-of-attack sweeps from the shock tunnel at

widely different Reynolds numbers. Correlation with the GHABAP shows that the lower Reynolds num­ber data may be considered to have been taken with a laminar boundary layer and the higher Reynolds number data with a predominantly turbulent bound­ary layer. The accuracy of prediction of axial-force coefficients for shock tunnel conditions was superior to those for the blowdown tunnel due in part to the knowledge of the precise model wall temperature. At Reynolds numbers of the order of 107 and above, the Spalding and Chi turbulent skin friction predictions are subject to considerable variation with wall tem­perature. This variation is sufficient to bring the the­oretical estimates up to the experimental points at the higher angles of attack for the blowdown tunnel data at R[ = 18.45 X 106 (fig. 4(b)) if the unrealistic low wall temperature of 80°F is assumed (ref. 10).

Lift

The lift coefficients for the present wing-body concept are presented in figure 4(c) with GHABAP estimates. Little difference may be seen between Reynolds numbers in the same test facility and/or between facilities except at the highest shock tun­nel Reynolds number. Predictions by the GHABAP tend to overpredict the lift, particularly at the higher angles of attack. This overprediction is partially be­cause of the inability of the program to accurately account for the effective airfoil geometry changes due to boundary-layer buildup. Two-dimensional calcu­lations have shown that the addition of displacement boundary-layer contours to a wedge-slab-wedge air­foil will not only increase the pressure axial force and augment the skin friction but will slightly reduce the normal force. Both of these forces contribute to a decrease in lift coefficient at a given angle of attack, which results in a lower lift-curve slope.

Drag

Comparisons of experimental drag coefficients and estimates by the GHABAP are presented in fig­ure 4(d) for all test Reynolds numbers. Because drag is a combination of normal force and axial force and the prediction of normal force was superior to axial force, the difference between theory and experiment was due primarily to the errors in the axial-force pre­diction. The shock tunnel results were better pre­dicted than the blowdown tunnel results, particularly at the lower angles of attack.

Lift-Drag Ratio

The lift-drag ratios for all tests are presented in figure 4( e) plotted against angle of attack. All es­timates by the GHABAP were higher than the ex­perimental data except the turbulent estimate for

5

the shock tunnel test at the lower Reynolds num­ber. This overprediction is again primarily due to the inaccurate axial-force predictions that, in turn, were due to a variety of reasons discussed previously, including the lack of knowledge of the model wall temperature distribution, the assumption within the computer program that the flow on the model is al­ways streamwise for pressure calculations and lon­gitudinal on the model with no cross flow for skin friction estimates, and inadequate estimates of in­duced pressure effects. Also, local areas of transition and/or separation were not taken into account by the present computer program.

Pitching Moment

Pitching moments are presented in figure 4(f) for the various Reynolds numbers. The experimental data exhibited a degree of stability at angles of at­tack up to about 4° where the configuration became neutrally stable and then showed a slight pitch-up at the highest test angles of attack. The theoret­ical estimates by GHABAP underpredicted the ex­periment at all angles of attack but did predict the correct slope at the lower angles of attack. Addi­tional experimental testing will be required to deter­mine the reason for the undesirable change in the slope of the pitching-moment curve with angle of at­tack. As mentioned in the section "Theoretical Meth­ods," the results obtained from the GHABAP are a function of which options for pressure versus flow de­flection were selected. Presented in figure 5 are ex­perimental pitching-moment data at various Mach numbers on the present wing-body configuration compared with inviscid estimates from the GHABAP using two different pressure versus flow deflection op­tions. The upper portion of figure 5 shows the results of pitching-moment calculations with the tangent­cone option on the fuselage and the shock-expansion option on the wings and strakes, and the bottom por­tion of figure 5 shows the tangent-cone option on the forward fuselage and strakes and the tangent-wedge option on the wings and aft fuselage. For Mach 6 the tangent-cone/shock-expansion option used in refer­ence 1 overpredicted the experimental data about as much as the tangent-cone/tangent-wedge (TC/TW) option underpredicted it. The TC /TW option was superior at M = 8 and was used in both reference 2 and the present report. The inset plan views show the regions of the model, both upper and lower sur­faces, covered by the respective pressure distribution options.

It may be concluded that the tailoring of a specific pressure distribution option scheme in the GHABAP can make possible the reasonable prediction of pitch­ing moments on a specific model under a given set of

6

flow conditions, but no assurance can be assumed for the same model under another set of flow conditions.

The GHABAP estimates, however, do show that the pitch stability is reduced with increasing Mach number. The present experimental data indicate that the change in pitching moment with Mach number is less than predicted. Reference 15 shows similar sta­bility results on the delta-wing X-15 concept tested in the same wind tunnels from which the data in fig­ure 5 were obtained. Additional experimental data at Mach numbers up to 6 may be found in reference 16, along with theoretical estimates, on a similar hyper­sonic cruise concept. These data were obtained on a larger cast aluminum model with less dimensional accuracy than the present machined model.

Comparison of Experiment and Theory at a Constant Angle of Attack

In parallel with the study carried out in refer­ence 2, a series of tests was carried out at a con­stant angle of attack of 3° through the widest possi­ble range of Reynolds number in the Langley 20-Inch Mach 6 Tunnel. Two data points were also avail­able from the Calspan Hypersonic Shock Tunnel at M = 6.13 and 6.58.

The normal-force and axial-force coefficients from these tests are presented in figure 6 and compared with theoretical estimates utilizing both laminar and turbulent skin friction generated by the GHABAP. The normal-force coefficient is essentially indepen­dent of Reynolds number, a conclusion also deter­mined at M = 8 in reference 2. The small decrease in normal-force coefficient with Reynolds number was due to the increase in test Mach number with stag­nation pressure. The effect of Reynolds number re­ductions is primarily one of the thickening of the boundary layer. As boundary layers tend to effec­tively alter the surface contours of the configuration, there is an accompanying variation in the surface pressures. These surface pressure variations always increase the axial force but show minimal effect on normal force at low angles of attack because pres­sures are induced on both upper and lower surfaces. Excellent predictions of the normal-force coefficients on the wing-body configuration with Reynolds num­ber by the GHABAP are shown. The tangent­cone/tangent-wedge pressure distribution options as illustrated in figure 5 were used for these estimates. The tangent-cone/shock-expansion options produced slightly lower normal-force coefficients.

As the Reynolds number was reduced during these tests, the aerodynamic forces were also reduced because of the decrease in dynamic pressure, which is a function of both the stagnation pressure and the

measured average Mach number. Plots of the tun­nel parameters for the tests at Q: = 3° in the Langley 20-Inch Mach 6 Tunnel are shown in figure 8. The Mach numbers shown were derived from the stag­nation pressures shown and a pitot pressure taken prior to the force balance measurements for each data point. The pitot probe was located in the test sec­tion at a point determined by wide range calibra­tions to give an average Mach number at all tun­nel stagnation pressures (ref. 17). Thus, there was about a 0.23 variation in Mach number from the lowest to the highest Reynolds number, which cor­responded to about an 8-percent change in dynamic pressure caused by Mach number variations alone. It is worth noting that the scatter in the measured Mach numbers with Reynolds number is greater than in the normal-force coefficients, which are sensitive to not only Mach number but to the accuracy of the measurement of pressures and of the setting of the angle of attack. This imparts additional confi­dence that the Mach number measurement was ac­curate and that the independence of normal-force co­efficient with Reynolds number is a valid conclusion. These observations indicate that the use of a stan­dardized model of known aerodynamic characteris­tics with Mach number might be used for wind-tunnel calibration where the average Mach number is de­sired and time is unavailable for customary lengthy pitot pressure distribution measurements and inte­gration procedures.

The axial-force coefficient at a constant angle of attack of 3° is shown in the bottom plot of figure 6. Theoretical estimates using the GHABAP are pre­sented for comparison with the experimental data. Estimates were made for the inviscid axial-force co­efficient which decreases slightly with Reynolds num­ber only because the tunnel average Mach number increased as the stagnation pressure was increased to make possible tests at higher Reynolds numbers. The increments in axial-force coefficient due to the wing leading and trailing edges were made as de­scribed in the section "Theoretical Methods." The curves for total laminar theory are the sum of the in­viscid, leading- and trailing-edge increments and the GHABAP estimates of laminar skin friction, induced pressure, and viscous interaction. A comparison of these program-generated laminar parameters and a more precise but laborious method may be found in reference 2. The curves for total turbulent theory are the sum of the inviscid, leading- and trailing-edge in­crements, and GHABAP estimates of turbulent skin friction by the Spalding and Chi method.

A comparison of experimental axial-force coeffi­cients at Q: = 3° with the theoretical estimates in

figure 6 indicates that the Mach 6 tunnel data were recorded on a model that was experiencing a predom­inance of turbulent-boundary-Iayer flow. The sin­gle data point at Q: = 3° from the Calspan shock tunnel at a low Reynolds number appears to have been recorded with a predominance of laminar flow. The data point at a high Reynolds number from the Calspan tests, on the other hand, appears to have ex­perienced turbulent flow. With the exception of the data point at a high Reynolds number from Calspan, all data were underpredicted. Part of this underpre­diction may well be an inaccurate estimate of the inviscid axial-force coefficient at Q: = 3°. As previ­ously discussed, there is no way that this estimate can be substantiated. The lack of induced pressure and viscous interaction estimates for the turbulent estimates and the simplified program estimates for the laminar estimates could also contribute to the underpredictions.

. The apparent early transition that occurred on the model during tests in the Langley 20-Inch Mach 6 Tunnel is a subject for future study and present speculation. It is known that the transition Reynolds number can be decreased by a variety of phenomena including

Tunnel noise emanating from wall boundary layer

Tunnel noise emanating from upstream turbulence in settling chamber

Tunnel size decrease Tunnel wall temperature increase Model wall temperature increase Unit Reynolds number decrease in

given tunnel Mach number decrease above M ~ 3 Leading-edge sweep increase Leading-edge and nose-diameter decrease Tests in the M = 1 to 3 region Surface roughness

Detailed discussions of transition at hypersonic speeds may be found in references 17 to 23. It is not known how many of these or other more obscure transition factors affected the present blowdown tun­nel data. Further, different Reynolds number tests on configuration-type models in a variety of facilities may be needed to resolve the question. The result­ing lift, drag, and lift-drag ratio obtained by resolving the normal and axial forces of figure 6 at an angle of attack of 3° are presented in figure 7. The estimates of lift and drag coefficients by the GHABAP follow the same trends as did the predictions of normal­and axial-force coefficients in figure 6. The prediction of lift-drag ratio tends to smooth out the variations between the experiment and theory such that the

7

overpredictions for the blowdown tunnel hot wall tests varied only from about 4 to 5 percent, and vari­ations for the Calspan cold wall tests were somewhat less.

Conclusions

An analysis of experimental data for a hydrogen­fueled, blended wing-body hypersonic transport concept from a conventional wind tunnel and a shock tunnel at a Mach number of about 6 through a range of Reynolds number (based on fuselage theoretical length) from 1.577 x 106 to about 55.36 x 106 leads to the following conclusions:

1. There were only slight variations of normal­force coefficients with Reynolds number through an angle-of-attack range of -1 ° to 8° in the blowdown tunnel with hot model wall conditions.

2. Gentry's Hypersonic Arbitrary-Body Aerody­namics Program (Mark III Version) (GHABAP) pro­vided good theoretical predictions of the normal­force coefficients with angle of attack and with Reynolds number, particularly at anticipated cruise angles of attack, that is, 2° to 5°.

3. All tests conducted in the Langley 20-Inch Mach 6 Tunnel and the high Reynolds number test in the Calspan Hypersonic Shock Tunnel appeared to have been made with predominantly turbulent boundary-layer conditions.

4. The accuracy of the GHABAP estimates of the inviscid axial-force coefficients could not be determined.

5. The GHABAP underestimated all axial-force data at low angles of attack when turbulent skin friction was assumed, except for the high Reynolds number cold wall shock tunnel data.

6. The GHABAP underestimated the axial-force coefficients of the low Reynolds number cold wall Calspan test while using laminar skin friction, plus the induced pressure and viscous interaction options.

7. Pitching-moment coefficients cannot be pre­dicted reliably with the present GHABAP methods, although the program does predict the trends with Mach number.

NASA Langley Research Center Hampton, Virginia 23665-5225 June 18, 1987

References

1. Penland, J. A.; and Romeo, D. J.: Advances in Hyper­sonic Exploration Capability-Wind Tunnel to Flight Reynolds Number. J. Aircr., vol. 8, no. 11, Nov. 1971, pp. 881-884.

8

2. Penland, Jim A.; Marcum, Don C., Jr.; and Stack, Sharon H.: Wall-Temperature Effects on the Aerodynam­ics of a Hydrogen-Fueled Transport Concept in Mach 8 Blowdown and Shock Tunnels. NASA TP-2159, 1983.

3. Gentry, Arvel E.: Hypersonic Arbitrary-Body Aerody­namic Computer Program (Mark III Version). Vol­ume I-User's Manual. Rep. DAC 61552, Vol. I (Air Force Contract Nos. F33615 67 C 1008 and F3365167 C 1602), McDonnell Douglas Corp., Apr. 1968. (Available from DTIC as AD 851 811.)

4. Sears, William R.: On Projectiles of Minimum Wave Drag. Q. Appl. Math., vol. IV, no. 4, Jan. 1947, pp. 361-366.

5. Daum, Fred L.; and Gyarmathy, George: Condensa­tion of Air and Nitrogen in Hypersonic Wind Tunnels. AIAA J., vol. 6, no. 3, Mar. 1968, pp. 458-465.

6. Hypersonic Shock Tunnel-Description and Capabilities. Calspan Corp., Sept. 1975.

7. Penland, Jim A.: Aerodynamic Characteristics of a Cir­cular Cylinder at Mach Number 6.86 and Angles of Attack up to gr!'. NACA TN 3861, 1957. (Supersedes NACA RM L54AI4.)

8. Mayer, John P.: A Limit Pressure Coefficient and an Estimation of Limit Forces on Airfoils at Supersonic Speeds. NACA RM L8F23, 1948.

9. Monaghan, R. J.: An Approximate Solution of the Compressible Laminar Boundary Layer on a Flat Plate. R. & M. No. 2760, British Aeronautical Research Coun­cil, 1953.

10. Spalding, D. B.; and Chi, S. W.: The Drag of a Compressible Turbulent Boundary Layer on a Smooth Flat Plate With and Without Heat Transfer. J. Fluid Mech., vol. 18, pt. 1, Jan. 1964, pp. 117-143.

11. Bertram, Mitchel H.: Viscous and Leading-Edge Thick­ness Effects on the Pressures on the Surface of a Flat Plate in Hypersonic Flow. J. Aeronaut. Sci., vol. 21, no. 6, June 1954, pp. 430-431.

12. Stollery, J. L.; and Bates, L.: Turbulent Hypersonic Viscous Interaction. J. Fluid Mech., vol. 63, pt. 1, Mar. 18, 1974, pp. 145-156.

13. Watson, Ralph D.: Characteristics of Mach 10 Transi­tional and Turbulent Boundary Layers. NASA TP-1243, 1978.

14. Bertram, Mitchel H.: Calculations of Compressible Av­erage Turbulent Skin Friction. NASA TR R-123, 1962.

15. Goldberg, Theodore J.; Hefner, Jerry N.; and Stone, David R.: Hypersonic Aerodynamic Characteristics of Two Delta- Wing X-1S Airplane Configurations. NASA TN D-5498, 1969.

16. Ellison, James C.: Investigation of the Aerodynamic Characteristics of a Hypersonic Transport Model at Mach Numbers to 6. NASA TN D-6191, 1971.

17. Goldberg, Theodore J.; and Hefner, Jerry N. (appendix by James C. Emery): Starting Phenomena for Hyper­sonic Inlets With Thick Turbulent Boundary Layers at Mach 6. NASA TN D-6280, 1971.

18. Stainback, P. Calvin (appendix by P. Calvin Stainback and Kathleen C. Wicker): Effect of Unit Reynolds Num­ber, Nose Bluntness, Angle of Attack, and Roughness on

Transition on a S' Half-Angle Cone at Mach 8. NASA TN D-4961, 1969.

19. Hopkins, Edward J.; Jillie, Don W.; and Sorensen, Virginia L.: Charts for Estimating Boundary-Layer 'ITan­sition on Flat Plates. NASA TN D-5846, 1970.

20. Cary, Aubrey M., Jr.: Turbulent-Boundary-Layer Heat­'ITansfer and 'ITansition Measurements With Surface Cooling at Mach 6. NASA TN D-5863, 1970.

21. Stainback, P. Calvin; Wagner, Richard D.; Owen, F. Kevin; and Horstman, Clifford C.: Experimental

Studies of Hypersonic Boundary-Layer 'ITansition and Ef­fects of Wind-Tunnel Disturbances. NASA TN D-7453, 1974.

22. Ashby, George C., Jr.; and Harris, Julius E.: Boundary­Layer Transition and Displacement- Thickness Effects on Zero-Lift Drag of a Series of Power-Law Bodies at Mach 6. NASA TN D-7723, 1974.

23. Pate, Samuel R.: Effects of Wind Tunnel Disturbances on Boundary-Layer Transition With Emphasis on Radi­ated Noise: A Review. AIAA-80-0431, Mar. 1980.

9

10

Table 1. Geometric Characteristics of Model

Wing:

Reference area (includes area projected to fuselage centerline), in2

Exposed area outboard of strakes, in2

Wetted area, in2

Span, in.

Aspect ratio . .

Root chord (on fuselage centerline), in.

Tip chord, in.

Taper ratio

Mean aerodynamic chord of total wing, in.

Sweep back angle, deg of-Leading edge 25-percent chord line Trailing edge

Dihedral angle (airfoil mean line), deg

Incidence angle, deg ...... .

Thickness ratio of wing airfoil section (see fig. 1) at -Exposed root ..... . Tip .................... .

Leading-edge radius, in., at -Fuselage centerline chord Tip .......... .

Trailing-edge height

Center fin proposed (vertical tail):

Area (exposed), in2 ... .

Span (exposed), in. . .... . Aspect ratio of exposed area . .

Root chord (fuselage surface line), in.

Tip chord, in.

Taper ratio

Mean aerodynamic chord of exposed area, in.

Sweep back angle, deg, of -Leading edge .......... . Trailing edge .......... .

Thickness ratio of fin airfoil section at -Tip ....... . Root ...... .

Leading-edge radius, in.

Fuselage:

Length of theoretical model, in.

Length of test model, in.

Maximum height, in.

Maximum width excluding strakes, in.

Nose radius, in. ........ .

Fineness ratio of equivalent round body (excluding strakes)

70.00

30.23

60.42

9.730

1.353

13.086

1.308

0.099

8.810

65.0 56.99 -15.4

o . . 0

0.03 0.03

0.003 0.003

0.006

12.399

3.672 1.09

5.353

1.390

0.259

3.759

60 -30

0.06 0.06

0.003

25.92

23.61

1.428

2.856

0.003

13.0

Base area, in2

Com plete model (excluding vertical tail and engine):

Planform area of theoretical model, in2

Planform area of test model, in2

Aspect ratio of theoretical-model planform

Aspect ratio of test-model plan form

Wetted area, approximate, in2

Model scramjet engine (proposed):

Frontal area, 2 percent wing area, in2

Chord ratio of width to height

Volume of test model, in3

V 2/ 3 / Sp (test model) . .

. . . . . . . . . . . . 1.710

100.541

98.268

0.942

. 0.963

. ·225.0

1.40

4.8

54.70

0.146

11

x/I x H 0 0 0

.067 1.728 .411

.133 3.456 .663

.200 5.184 .862

.267 6.912 1.022

.333 8.639 1.151

.400 10.368 1.253

.467 12.096 1.316

.533 13.824 1.379

.600 15.552 1.426

.667 17.279 1.428

.700 18.144 1.426

.733 19.008 1.378

.767 19.872 1.316

.800 20.736 1.253

.833 21.599 1.151

.867 22.464 1.022

.900 23.328 .862

.933 24.192 .663

.967 25.056 .411 1.000 25.920 0

aFairing to wing.

A

Table II. Cross-Sectional Dimensions of Fuselage

[All values are in inches]

rad. B rad. T rad. US rad. LS rad. E 0.396 0 0 0 0 0

.194 1.508 .465 .084 .632 .103

.083 2.436 .752 .389 1.264 .166

.025 3.164 .977 .457 1.897 .216 0 3.751 1.158 .533 2.529 .255 0 4.233 1.304 .547 3.161 .288 0 4.597 1.419 .590 3.791 .313 0 4.828 1.491 .644 4.424 .329 0 5.058 1.562 .634 5.058 .345 0 5.234 1.616 a.522 5.234 .357 0 5.242 1.618 a.392 .357 0 5.234 1.616 a.389 .356

.007 5.058 1.562 a.432 .345

.032 4.828 1.491 a.457 .329

.076 4.597 1.419 a.529 .313

.12G 4.223 1.304 a.GOl .288

.180 3.751 1.158 0 .256

.230 3.164 .977 .216

.284 2.436 .752 .166

.338 1.508 .465 .103

.396 0 0 0

bDistance to leading edge or tip.

12

Sd SW rad. W 0 0

.101 .084

.163 .154

.212 .216

.251 .274

.283 .332

.308 .383

.324 .429

.339 .465

.353 b1.014 1.440

.351 b1.819 3.870

.342 b2.224 4.320

.313 b2.676 1.800

.281 b3.141 1.080

.245 b3.607 1.800

.198 b3.174 2.016

.117 2.485 2.808

,..-, r­L_ I .­I r­L_ I ~-

.3754

I Moment reference

~.o~5~·l Station 0 .133 .4pO .566 .700 .910 1.000

I -= /'

/' /'

;'

/' /'

/' /'

/' /'

/' /'

"t ~ lSi --f---I - ---I I , -- I ,

~l--------..-

l' 25.92 in. (65.837 em)

Figure 1. Details of wind-tunnel model. All dimensions have been normalized by the fuselage theoretical length, l = 25.92 in., dashed lines show components not in present test.

-----7 /

/ /

/ /

/ /

14

/ 'f......

/ rad.

E

\

sw ~--------------2H

Reference Ii ne

A

f 1 H

l/3H

Figure 2. Detail of fuselage cross section and strake design. Dimensions are listed in table II.

Figure 3. Computer drawing of paneling scheme of configuration as input for hypersonic aerodynamic calculations.

.16

.14

• 12

.10

.08

.04

.02

o

-.02

-. G!4

Hot wall 71 R[ 6 if 0 1.60 x 10

0 3.33

j1~ 6.63

Cold wall /; R[ 6 1// 0 1.91 x 10

0 51.61 /; 0 {::, 11.47 ;,1(/

-- Theory,ref. 3

II ~ 18.45 jl~ -- Theory,ref. 3 II

/; II

f'~ ;)J 6 fir Rr :: 1.60 x 10 ~

6 If) Rr :: 1.91 x 10--~

II ff5 11 :: 18.45 X 10

6 -------.... j~ R7 :: 51.61 X 106_ ~ "d [ ,v ?) / j ~

if )6' HV /D

/ L )~ ~

LSJl ~( /

.I

/ t/ / /

/ j -2 o 2 4 6 8 10 -4 -2 o 2 4 6

a, deg a, deg

(a) Normal force.

Figure 4. Comparison of theoretical force and moment coefficients with experimental data for various Reynolds numbers in Langley 20-Inch Mach 6 Tunnel (hot wall) and Calspan Hypersonic Shock Tunnel (cold wall).

~

8 10

.020 Hot wall Cold wall

Rr 6 0 1.60 x 10

Rr 6 0 1.91 x 10

.018 0 3.33 0 51.61

<> 6.63 Theory,ref. 3

6 11.47 .016 ~ 18.45

- Theory, ref. 3

.014 Turbulent C F h

~ V

1-/1 r \ V .012

Turbulent CF ~ /V \- [Y

<D ..; V JV V V <D V IV< )/"< V fY ./'" > ..) /'

Laminar CF -1\ ./ V 1\ ~

(D l---[ hi P ( ~ V< Y k:: V l---- I>

ID P L

~ !>' k ~ V

L.---< ~ .008

\ V ty V V V

~ ~ V V V I-- 1\ \) .-J ./ ~ [l

~ k V V-I J b---1

-I--t:::: t::::-V ......-:

.006 ~ 8.-C-- ~

h I h ___ V

- ~I- l£y-V to- ./'

~ V ~

~ v ~ b

.004 L--~

j.:--

~ j::/"

........-::

~ V--~

.00 l--:: b::::: f::::::= 1\ 2

-:::: h I==-- '--- Inv. +(CA) - LE&TE

---1-:::;:::: l:::::::: F\ I-:::: r:::::=- '--- Inv. + (CAli

\ E&TE

f\- I-Inviscid IL Inviscid

Q. 4 -2 o 2 ·4 6 8 10 -4 -2 o 2 4 6 8 10

a, deg a, deg

(b) Axial force.

Figure 4. Continued.

.16 Hot wall II RZ 6 ~ 0 1.60 x \0

0 3.33

~',} 0 6.63

;::, 11.47 1/ t::. 18.45 jh

- Theory, ref. 3

~

J~

.14

.12

.10

Cold wall /11 RZ 6 II 0 1.91 x \0

0 51.61 j :;

-- TheorY,ref. 3

III /, II ::>

1/ /; .p

b 6 If 11 = 1.60 x 10 I--.. A

II .08

6 r--.. WD RZ

= 1.91 x 10"-

~8 11 = 18.45 x 106_

~ j~ Rz = 51.61 x 106_ ~ Ii K"

V Iff::>

/ )~

.04 j fP

)6'

2 ,V /

.0 1/15

/ 0

)~

J~ /itJ

V /

V /

-.02 V

1I J

-'~4 4 6 o 2 8 -2 10 /

-4 -2 6 8 10 o 2 4 a, deg a, deg

(c) Lift.

Figure 4. Continued.

.040 Hot wall 'lW Rr 6

0 1.60 x 10 ~ 0 3.33 9

<> 6.63

6 11.47 /~ ~ 18.45

i< if Theory, ref. 3

II / lib ~

.036

.032

.028

Cold wall II Rr 6 0 1.91 x 10 1/ 0 51.61 1//

Theory, ref. 3

~ II

III /1

Turbulent C F

" Ir fJ '\v.~ 'I

.024 Laminar CF - \ 1/

\ II f (jj II

II. W II j 1J

(/~ r .016 /;l

If )/J (jJ

"'- ~ ~ r .012 // \..- Turbulent C F

/I V ~ ~ -( )--1 ~ ~ ~ ~ s: ~ W--< ~ ~ -.008

, / V ~ I'--.. V fr/

-- :::::::: -..... I"--- l- ll..- /" .004

!!4 -2 o 2 4 6 8 10 -4 -2 o 2 4 6 8 10

a, deg a, deg

(d) Drag.

Figure 4. Continued.

~ o

8

7

6

5

4

LI D 3

2

o

-1

-2 -4

Hot wall Rr

6 0 1.60 x 10

0 3.33

0 6.63

6 11.47 .--

~ 18.45

- Theory,ref. 3 ~ V...d

1/;. ~ ~ 'fir /.

ffl< tic til 1" VI

~ V }h~ fJL V

J , J <,

I

fA -2 o 2

a, deg

I Turbulent C F

--LV d ~ ~ '?7r '--i ~ ~ .,-

~ ~ ~~ (~

r-......::: ~

4 6 8 10 '-4

(e) Lift-drag ratio.

Figure 4. Continued.

Cold wall Rr

6 0 1.91 x 10

0 51.61

Theory, ref. 3 ~ Turbulent C F

----f-(

L z p- a--" ..... 1--....

"'" ~/ D ~ ~ D ~

/ V p/ --.:...: ) "-~

1/ ~ '-..... '-.

"'-'I ~ ~ Laminar CF

II / II /

Jli 1/1 rl

b,

/~

j ~

j, /1/

-2 o 2 4 6 8 10

a, deg

Hot wall

.008 "r'-..

6 R{ = 1.60 x 10 "" ~

~ ( ( .004

'-----......, D

i'---.........

/---1------Theory, ref. 3 J r---

----Theory,ref. 3

-.004

.008

.004

-.004

.008

.004

-.004

.008

.004

-.004

.008

.004

-.004

"r'-..

f"-. [

~ 1-------

-

" ± 1---

t1=1=!

~

'-----

",-----i'---

"r'-..

",----- ~

"'---.

--- r------

Rl • 3.33 x 10 6

[ P

--------- --- ---r--- ;---... r---~

Rl • 6.63 x 106

< <

~

---- ----r------- ---I'--.

Rl • 11.47 x 10°

~ ---- --- ;---...

---- ----~

Rl • 18.45 x 106

-------- ---r---------- r---

.008~-~--r-'--~~~--~~~-.--~~-.~

_---L-l

"" f-- "{ --- -- -

-. OO!. '=-4 --'--_'72 ---'---:-----'----:---'---~-'----:6---'---::---'-----"1 0

-4 -2 a, deg

. (f) Pitching moment.

Figure 4. Concluded.

f--

~

r---

o

Cold wall

11 = 1.91 x 106

)

[7 ----r- p f--/ ------- t---..

-----.....

r--

Rl • 51.61 X 106

~ p CI

D !--- D

I - ----------

4 8 10

a, deg

21

C m

.020

.016

.012

.008

.004

o

.016

.012

.008

.004

o

-.004

-. 008

- 012 . -6

--...... -............. -r---

~ f\ 1\ \

I~ \

~ \

"" "'" \ \ r-...

~ "'" ,,\ ~ i'-.

r--. .............. ~ ~ r--

r-- -

-4 -2

Tangent ~

<:':IZijjjjj!::': Shock expansion M / V

8;!-/,/

1 / V --/ ~ V

/" ...-

v::: --r-- ./ V .-S 2-- P 0 tJ LJ ILJ I

0 o( D ~ I

( (~ ( ~ I

.. -

Tangent cone~ 0 M = 6 LRC 20· 0 M = 8 LRC VOT

(ref. 2) <8JZ?:::::E<:: ....... <.:-:-:.:::-:-:-::::::::::: - Theory

Tangent wedge

M ,I

\ 10 ---9 ~

)

~ ro- -I.. ILJ -o ( :a h--:::: ..:r

8 ~ """:::::;:;;-- 1)- ) ( -~ :::::- 7

\ 0 I--- r---r--. r--t--

\ "---, -~ ~ r--r--..

~ ~ "'-.... I'-............

"" '----...(

:---...

"" 'I""

"" '" ~

o 2 4 6 8 10

a, deg

Figure 5. Comparison of experimental pitching moments with estimates from GHABAP using different pressure distribution methods.

22

.08

.06

.02

. OlD

.008

.004

.002

TC/TW

l = 6.13

Exp. Theory o M = 6 LRC 20· o - - - - Calspan HST

...... ° 00 " COO<&,

............ '0

Total Turbulent Theory

T~ ooom

I ,,~ ""'tP061

Laminar C F --------e... Total Laminar Theory I 1 ~ rVi"O", Inte .. c~ T"bulent CF

_~ ic,nduced Pressures ~

Inviscid Z .. '(CA)

8 10

RZ

LE&TE

-.[]--

---

Figure 6. Comparison of experimental normal- and axial-force coefficients with calculations from GHABAP on blended wing-body configuration. a = 3°; M :::::: 6.

23

.06

-----o o .04

.02

.016~--------~----~--~~--~~~~--------~----~--~--'--T-'-'~~

.012

.008

.004

UD a = 3°

6

4

2

Exp. Theory o M ~ 6 LRC 20' o ------- Calspan HST

-_0 __

-----Laminar CF

-----o

Turbulent CF

Figure 7. Comparison of experimental lift, drag, and lift-drag ratio with calculations from GHABAP. a = 3°;M ~ 6.

24

1ooor---------.-----.---,--,,-,-Ir-r.-r---------,-----,---,

900

o o

o o

o o ~

o o 800

To' Q 0 00 oeo CD

Po'

pSia

Saturation curve 700

600L. ________ ~ ____ ~ __ -J __ _L-J __ ~~~ ________ ~ ____ ~ __ ~

600 I

r

400 r

r

200 r

r o 00 a') 0 ~

aP 0

I

00~ o 00 0

I I I J J J

& 0

oP OJ

0 ~

d'o 000

CQ:l

I

I

~ """ccptJ@ 60 -'Q 0 V-' o 0

000 Q)

I

-

--

-

-

I I

-

-

-

I I l I l i iii I I L---------~2----~~--~4---L~6~~~8~~1~0--------~2~0~--~----740x106

Rr

Figure 8. Stagnation conditions and resulting Mach and Reynolds numbers from present tests at 0: = 3° in Langley 20-Inch Mach 6 Tunnel.

25

Nl\SI\ Report Documentation Page National Aeronautics and Space AdmlnlslrallOn

1. Report No. 12. Government Accession No. 3. Recipient's Catalog No.

NASA TP-2728 4. Title and Subtitle 5. Report Date

Effect of Reynolds Number Variation on Aerodynamics August 1987 of a Hydrogen-Fueled Transport Concept at Mach 6 6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No.

Jim A. Penland and Don C. Marcum, Jr. L-16286

9. Performing Organization Name and Address 10. Work Unit No.

NASA Langley Research Center 505-62-81-01

Hampton, VA 23665-5225 11. Contract or Grant No.

13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration Technical Paper

Washington, DC 20546-0001 14. Sponsoring Agency Code

-15. Supplementary Notes

16. Abstract

Two separate tests have been made on the same blended wing-body hydrogen-fueled transport model at a Mach number of about 6 and a range of Reynolds number (based on theoretical body length) of 1.577 X 106 to about 55.36 X 106 . The results of these tests, made in a conventional hypersonic blowdown tunnel and a hypersonic shock tunnel, are presented through range of angle of attack from _1 0 to 80

, with all extended study at a constant angle of attack of 3°. The model boundary-layer flow appeared to be predominantly turbulent except for the low Reynolds number shock tunnel tests. Model wall temperatures varied considerably between the two tests; the blowdown tunnel varied from about 255°F to 340°F, whereas the shock tunnel had a constant 70°F model wall temperature. The experimental normal-force coefficients were essentially independent of Reynolds number. A current theoretical computer program was used to study the effect of Reynolds number. Theoretical predictions of normal-force coefficients were good, particularly at anticipated cruise angles of attack, that is, 2° to 5°. Axial-force coefficients were generally underestimated for the turbulent skin friction conditions, and pitching-moment coefficients could not be predicted reliably.

17. Key Words (Suggested by Authors(s)) 18. Distribution Statement Hypersonic aircraft U nclassified-U nlimited Turbulent skin friction Reynolds number effects Computational aerodynamics

Subject Category 02 19. Security Classif.(of this report) 120. Security Classif.(of this page) 21. No. of pages

J 22. Price

Unclassified Unclassified 26 A03 NASA FORM 1626 OCT 86 NASA-Langley, 1987

For sale by the National Technical Information Service, Springfield, Virginia 22161-2171

NASA TECHNICAL NOTE NASA TN 0-6191

INVESTIGATION OF THE AERODYNAMIC

CHARACTERISTICS OF A HYPERSONIC

TRANSPORT MODEL AT MACH NUMBERS TO 6

by James C. Ellison

Langley Research Center

Hampton, Va. 23365

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C.· APRIL 1971

1. Report No. I 2. Government Accession No. 3. Recipient's Catalog No.

NASA TN D-6191

4. Title and Subtitle 5. Report Date

INVESTIGATION OF THE AERODYNAMIC CHARACTERISTICS April 1971 OF A HYPERSONIC TRANSPORT MODEL AT MACH NUMBERS 6. Performing Organization Code TO 6

7. Author(s) 8. Performing Organization Report No.

James C, Ellison L-7478

10. Work Unit No. 9. Performing Organization Name and Address 722-01-10-04

NASA Langley Research Center 11. Contract or Grant No.

Hampton, Va. 23365 13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address Technical Note National Aeronautics and Space Administration 14. Sponsoring Agency Code

Washington, D.C. 20546

15. Supplementary Notes

16. Abstract

A wind-tunnel investigation was conducted at subsonic, supersonic, and hypersonic

speeds to determine the aerodynamic characteristics of a blended wing-body configuration.

Data were obtained for t~ ~ configuration with a single vertical tail, a flow-through inlet, and elevons deflected from 50 to -200. At a Mach number of 6 and a Reynolds number of

21.6 x 106, the configuration had a maximum lift-drag ratio of 5.0 with no trim penalty.

Based on the selected center-of-gravity position of 56.4 percent of the model length, the

configuration was stable in all directions over the Mach number range. Results of analytical methods agreed with the data at zero elevon deflection for the range of angle of attack from

00 to 60 at all Mach numbers.

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Blended wing-body Unclassified - Unlimited Wind-tunnel investigation

Aerodynamic characteristics

19. Security aassif. (of this report) 120. Security Classif. lof this page) 121. No. of Pages 1 22. Price"

Unclassified Unclassified 79 $3.00.

• For sale by the National Technical Information Service, Springfield, Virginia 22151

INVESTIGATION OF THE AERODYNAMIC CHARACTERISTICS

OF A HYPERSONIC TRANSPORT MODEL

AT MACH NUMBERS TO 6

By James C. Ellison

Langley Research Center

SUMMARY

A wind-tunnel investigation has been conducted on a model of a hypersonic transport

configuration at Mach numbers from 0.36 to 6 and at Reynolds numbers from 6.67 X 106

to 21.6 X 106 (depending on Mach number) based on model length. The model was

composed of a blended wing-body with strakes. The fuselage had a Sears-Haack area d.istribution, a width-height ratio of 2, negative camber over the forward portion, and a fineness ratio of 13.

Data were obtained for the model with the elevons deflected from _200 to 50 and for

the model without the inlet and without the vertical tail at zero elevon deflection. The

wind-tunnel results are compared with the results of several analytical methods.

Based on a fixed center-of-gravity position, the model was longitudinally stable or neutrally stable at all test conditions and could be trimmed at all Mach numbers. At a Mach number of 6 and a Reynolds number of 21.6 X 106, the maximum value of lift-drag

ratio was 5.0 with no penalty due to trim. The model was directionally stable and had

positive effective dihedral over the Mach number range of the investigation. Results obtained from analytical methods were considered adequate for preliminary design studies at zero elevon deflection for angles of attack between 00 and 60 •

INTRODUCTION

Preliminary optimizations of trade-offs between aerodynamic and structural design

interactions on hydrogen-fueled, hypersonic transports resulted in configurations with large-VOlume, low-fineness-ratio fuselages which aerodynamically dominated the remaining components of the airplane. (See refs. 1 and 2.) Conventional, distinct wing­

body designs, with small body width and large volume compared with the wing area, pro­

duce drag penalties which result in poor hypersonic maximum lift-drag ratio. (See refs. 3 and 4.) In an attempt to improve the overall performance under large volume restrichons~ a departure from conventional design was adopted to evolve a configuration

that features (1) a body width-height ratio of 2 to improve the lifting capability of the

fuselage, (2) negative camber in the forward fuselage to minimize trim drag penalties on

maximum lift-drag ratio, (3) strakes to retard windward pressure bleed-off at angle of

attack, and (4) wing-body blending to minimize adverse component interference effects.

The configuration has been the subject of preliminary weight and balance and structural

and aerodynamic studies similar to those reported in references 3 and 4. This report

presents the results of an experimental investigation conducted over the speed range

from subsonic to hypersonic.

SYMBOLS

Longitudinal data are presented about the stability axes and lateral data are pre­

sented about the body axes. The moment reference point was taken at 56.4 percent of the

body length.

b

CD,min

wing span (30.48 cm)

Drag drag coefficient, --qs

drag coefficient at zero lift

minimum drag coefficient

drag-due-to-lift parameter

lift coefficient, Lift qS

dCL lift-curve slope at zero lift,

da

rolling-moment coefficient, Rolling moment qSb

!:lCz C l{3 = A{3 , per deg

2

pitching-moment coefficient Pitching ~oment , qSc

dC longitudinal stability parameter, dC m

L

yawing-moment coefficient, Yawing moment qSb

.DoCn Cn{3 = .Do{3' per deg

Cy Side force side -force coefficient, qS

.DoCy Cy = --, per deg

{3 A{3

c wing chord, cm

c mean aerodynamic chord (27.56 cm) I 10· '8')0 tf ~ :

LID lift-drag ratio

(L/D)max maximum lift-drag ratio

l length of model (81.28 cm) / :3 ~ . 0

M Mach number

q dynamic pressure, N/cm2

R Reynolds number based on model length

r l e average leading-edge radius of strakes and wings (0.0204 cm)

S reference area, planform area of wing including body intercept (687 cm2) / O~.yr) k 2.--

tic wing thickness-chord ratio (0.03)

x,y,z longitudinal, lateral, and vertical coordinate, respectively, cm

angle of attack, deg

{3 angle of Sideslip, deg

Oe elevon deflection (positive, trailing edge do~n)

3

APPARATUS AND TESTS

Facilities

The data at M = 0.36 were obtained in the Langley low-turbulence pressure tun­nel; the data at Mach numbers of 1.50, 2.00, 2.36, and 2.86 were obtained in the Langley

Unitary Plan wind tunnel; and the data at a Mach number of 6.00 were obtained in the

Langley 20-inch hypersonic tunnel (Mach 6). Details of facilities are given in

reference 5.

Model Descr.iption

Details of the model and pertinent dimensions are shown in figure 1 (the dashed

lines indicate the afterbody shape prior to modifications necessary to accommodate the balances), and details of the inlet and vertical tails are shown in figure 2. The coordi­

nates of the cross sections shown in figure 1 are given in table I. All results are related

TABLE 1.- CROSS-SECTION COORDINATES

x = 5.418 em x = 43.35 em x = 48.77 em x = 73.15 em

y, z, y, z, y, z, y, z, em em em em em em em em

0.000 0.621 0.000 0.000 0.000 0.000 0.000 0.000 .161 .631 .341 .002 .410 .020 .480 .021 .251 .641 .761 .036 .750 .059 .839 .099 .352 .661 1.052 .084 1.149 .128 1.148 .186 .422 .681 1.383 .173 1.538 .218 1.495 .344 .492 .701 1.664 .251 1.865 .346 1.880 .603 .602 .750 1.905 .340 2.252 .506 2.165 .860 .712 .800 2.166 .459 2.588 .685 2.575 1.331 .823 .860 2.498 .627 2.963 .935 2.872 1.918 .943 .940 2.830 .856 3.278 1.173 2.976 2.201

1.033 1.020 3.101 1.055 3.620 1.502 3.059 2.544 1.144 1.150 3.343 1.274 3.903 1.819 3.092 2.825 1.234 1.290 3.635 1.553 4.147 2.106 3.096 3.106 1.324 1.411 3.897 1.862 4.320 2.391 3.295 3.180 1.444 1.481 4.129 2.171 4.573 2.708 3.543 3.276 1.645 1.550 4.301 2.460 4.759 2.863 3.792 3.332 1.475 1.631 4.543 2.699 4.956 2.998 4.032 3.377 1.355 1.681 4.774 2.899 5.154 3.103 4.382 3.405 1.224 1.721 5.005 3.017 5.344 3.137 4.110 3.459 1.124 1.761 5.206 3.116 5.603 3.184 3.628 3~508

1.044 1.782 5.477 3.205 7.772 3.396 3.174 3.629 .954 1.812 5.738 3.234 5.582 3.624 2.658 3.857 .864 1.822 4.838 3.579 5.069 3.722 2.365 3.991 .684 1.852 4.238 3.733 4.483 3.888 2.102 4.095 .574 1.862 3.528 3.907 3.738 4.070 1.607 4.274 .483 1.872 2.977 4.020 3.133 4.185 1.295 4.338 .353 1.893 2.257 4.145 1.966 4.387 .983 4.391 .253 1.893 1.506 4.259 1.323 4.451 .601 4.442 .133 1.903 .805 4.313 .631 4.474 .280 4.465 .000 1.903 .000 4.317 .000 4.489 .000 4.479

4

to the modified configuration and no attempt was made to account for the boattail of a

full-scale configuration. The model consisted of a fuselage having a fineness ratio of 1~. a Sears-Haack longitudinal area distribution (ref. 6) and a body width-height ratio of 2.

The fuselage was blended with negatively cambered strakes and a wedge-slab-wedge delta wing having leading- and trailing-edge sweep angles of 650 and _150 , respectively. A diamond vertical tail with 20 included angle was used for the subsonic investigation and a wedge vertical tail with a 40 included angle was used for the other test Mach numbers. It is anticipated that the flight configuration might have actuators that could change the

vertical tail to reduce the base drag at subsonic speeds. The propulsion package was

simulated by a flow-through inlet of constant area, 1.5 percent of the reference area. The model elevons, which had as area of 20 percent of the reference area, could be deflected from 50 to -200 at 50 increments to study the trim and control characteristics of the configuration. The relative proportions of the configuration were arrived at through sizing, weight and balance, and aerodynamic/structural trade-off studies and are representative of a vehicle with a gross weight of 226 800 kilograms capable of Mach 6 cruise and a range of 9260 kilometers.

Tests

The conditions under which the model was tested are presented in table II: 1\ ba1~ &...

M

0.36

1.50, 2.00, 2.36, 2.86

6.00

01'1 W,DU -4.11;'" ,.,A.:-.:z..I..~'.{f-.

R

9.4 x 106

6.67 X 106

21.6 x 106

5' .1 t 10;lt-

TABLE II.- TEST PROGRAM

Configuration

Complete, elevon deflected

Complete, oe = 00

No inlet Vertical tail off

Complete, elevon deflected

Complete, 0e = 00

No inlet Vertical tail off

Complete, elevon deflected

Complete, oe = 00

No inlet

Vertical tail off

a, fl, Transition deg deg

-6 to 21 0 Fixed -6 to 21 4 Fixed -6 to 21 0 Fixed -6 to 21 4 Fixed

-4 to 14 0 Fixed

-4 to 14 0, 8 Fixed -4 to 14 0 Fixed -4 to 14 0, 3 . Fixed

-2 to 12 0 Free

-2 to 12 -4 Free -2 to 12 0 Free

-2 to 12 0, -4 Free

A six-component strain-gage balance was used to measure the forces and moments on the model throughout the test program. For the tests at a Mach number of 6.00 the true angle of attack was set by optical means in which a prism mounted on the model reflected a point source of light on a calibrated screen. For the tests at the other Mach numbers the angle of attack was set by a calibrated counter and the data were corrected for changes due to load deflections.

5

Base pressure (M = 0.36 and 6.00) and balance cavity pressure (M = 1,50 to 2.86)

were measured and the axial force was corrected to the condition of free-stream static pressure.

Except for the tests at a Mach number of 6.00 the model had 0.159-cm-wide strips

of No. 60 carborundum grit located 3.05 cm from the nose and 1.02 cm (streamwise) from the wing, inlet, and vertical-tail leading edges to induce boundary-layer transition. Based on the· results of reference 7, no corrections were made for grit drag. At

M = 6.00 transition is estimated to end on the windward surface at a Reynolds number of

2 x 106 according to reference 8; this corresponds to about 7.6 cm from the leading edges

for the conditions of the present investigation.

The area distribution of the inlet was constant and the internal drag was assumed to be entirely skin-friction drag. An estimate of the skin-friction-drag coefficient (0.0009) was calculated and this correction was applied to the supersonic data. However, the estimates calculated for Mach numbers of 0.36 and 6.00 were less than the accuracy in

CD and were considered negligible.

The moment reference center for the model was located at 0.0613 (0.564l), which

is about O.le ahead of center-of-gravity position calculated for the full-scale air­plane, for all Mach numbers.

Accuracy of Data

The possible errors resulting from inaccuracies within the balances and uncertain­ties in measured quantities are estimated to be as follows:

M = 0.36 M = 1.50 to 2.86 M = 6.00

cy. ±0.05° ±0.05° ±0.1O°

CL ±0.02 ±0.004 ±0.002

CD ±0.003 ±0.001 ±O.OOI LID. 1.5 0.25 0.40 Cm ±0.005 ±0.001 ±0.0002

ANALYTICAL METHODS

The computer program described in reference 9 employs linearized potential flow concepts in the form of a vortex lattice and was utilized to calculate the lift-curve slope

(CLcy') and the longitudinal stability parameter (CmcL

) at zero lift for Mach numbers

from 0.20 to 0.80. Calculation of the total drag was predicted by CD = CD 0 + CL tan CY. ,

6

where the drag coefficient at zero lift (CD,o) was determined by the method of ref­erence 10 and CL tan ex was determined from the results of the computer program

(ref. 9).

A linearized supersonic-wing theory which has been incorporated into a computer

program (ref. 11) was employed to calculate the aerodynamic characteristics at Mach numbers of 1.50 and 2.00. (This program requires supersonic flow at the trailing edge

which limited its use to Mach numbers below 2.30 for the present configuration.) For

Mach numbers of 2.00 and above, three sets of results were obtained by adding tangent­cone-theory results for the fuselage, strakes, and vertical tail to results for the wing

obtained from tangent-cone theory (Method I), shock-expansion theory (Method II), and tangent-wedge theory {Method III). These methods were obtained by utilizing a computer

program presented in reference 12. All skin-friction-drag calculations (M = 1. 50 and

above) were obtained by the method of Spalding and Chi (ref. 13) for a turbulent boundary layer.

RESULTS AND DISCUSSION

Basic Results

The longitudinal aerodynamic characteristics for the complete configuration with elevons deflected from -200 to 50 are presented in figures 3 to 7. At the Mach number

of 0.36 no indication of stall occurred up to 200 angle of attack; and, in general, the con­

figuration showed no unusual aerodynamic characteristics over the angle-of-attack and

Mach number ranges of the investigation. In addition, the model was longitudinally stable

at all angles of attack, all elevon deflection angles, and all Mach numbers except 0.36 where the model was neutrally stable at the highest angles of attack for all elevon deflec­tion angles less than 50. The negative camber designed into the forward portion of the fuselage and strakes produced a positive pitching moment at zero lift at all Mach numbers

and elevon deflection angles except 50 at Mach numbers of 0.36 and 1.50. In general, at

all Mach numbers, the elevons showed good control power over the ranges of angle of

attack and angle of elevon deflection.

Effects of Inlet and Vertical Tail

The effects of removing the inlet and vertical tail on the longitudinal characteristics of the configuration with oe = 00 are presented in figures 8 to 11. The incremental

changes in CL, CD, and Cm due to removal of the inlet or the vertical tail were, in general, less than the accuracy of the data except at M = 6.00 where removal of the inlet and vertical tail produced positive and negative increments, respectively, in Cm . At all Mach numbers above 1.50, removal of the vertical tail increased (within the accu­racy of the data) the maximum LID more than did removal of the inlet.

7

Lateral Directional Stability Characteristics

The stability parameters Cl ' Cn{3' and Cy for the complete configuration and {3 {3

for the configuration without the vertical tail were obtained by taking the difference in

lateral coefficients measured at angles of sideslip of 00 and a nonzero angle (see table II)

and are presented as a function of angle of attack in figure 12. With the vertical tail the

model was directionally stable and possessed positive effective dihedral at all Mach

numbers. Without the vertical tail the model was directionally stable for angles of attack

below 100 and displayed positive effective dihedral for positive angles of attack at all

Mach numbers except 6.00. This behavior probably occurred because of the small side

area of the forward fuselage, compared with that of the rear of the fuselage, which

resulted from the noncircular cross section. A reduction in vertical-tail size could probably be made and a gain in maximum LID realized. (See fig. 10.) An unusual

phenomenon occurre9. at Mach numbers of 0.36 and 1.50 where the directional stability

increased with angle of attack. (See figs. 12(a) and 12(b).) A similar result occurred in

the study of reference 14 and was attributed to the effects of vortex flow from the wings.

Comparison of Analytical With Experimental Results

Analytical results of Cm , CD, and CL are compared with the experimental

results for the configuration (oe = 00) without the inlet in figure 13. At M = 0.36 and

angles of attack up to about 30 the calculated values of CL agreed with the data; .

however, at the higher angles of attack the experimental values were greater than the

calculated values. This result probably occurs because the analytical method used (ref. 9) did not account for vortex lift which occurs at these angles of attack. (See

refs. 15 and 16.) The calculated drag coefficient at zero lift agrees with the data; but,

because of the larger angle of attack required to obtain a given value of CL, the calcu­

lated drag coefficients at angles of attack above 60 were greater than the experimental

values. (See fig. 13(a).) The slope of the pitching-moment curve CmCL

obtained

analytically agreed with the experimental value, but the underestimated value of CL

suggests that this agreement is fortuitous.

The linear theory method of reference 11 was used for Mach numbers' of 1.50 and

2.00, and tangent-cone theory (Method I), tangent-cone shock-expansion theory (Method II),

and tangent-cone tangent-wedge theory (Method III) were used at Mach numbers of 2.00

through 6.00 to calculate values of CL, CD, and Cm over the angle-of-attack range.

All of the methods gave better results for Cv CD' and Cm at angles of attack below

60 than at the higher angles of attack. Since hypersonic transport configurations are

expected to trim around a. = 50, these methods are considered adequate for preliminary

design studies. Values of Cm calculated by these methods did not agree with the data

over the angle-of-attack range. At angles of attack above 60 none of the methods provided

8

adequate agreement with the data; and, in addition, the results of the various methods did not agree. The method which gave the closest agreement, although not always adequate,

over the angle-of-attack range was the tangent-cone shock-expansion theory (Method II).

Using Method II, the increments in pitching-moment coefficient due to elevon deflec­

tion were calculated for the configuration without the inlet and the results are compared

with experimental values (assuming the inlet has no effect on the increments) in figure 14. The comparison indicates that values of .6.Cm can be calculated to agree within

15 percent of the experimental values for the negative deflection angles investigated;

however, at . oe = 50 the calculated results deviated from the experimental results by as

much as 50 percent.

The experimental trimmed and untrimmed (oe = 00) characteristics for the complete

configuration are presented as a function of CL in figure 15. In addition, the analytical

values for the configuration without the inlet, calculated by tangent-cone shock-expansion

Method II for the trimmed condition are shown for comparison (assuming contributions due to the inlet are negligible, based on fig. 11) in figures 15(c) to 15(f). For the center­

of-gravity position selected, no trim penalties occurred at a Mach number of 6.00

(fig. 15(f)) where the trimmed (L/D)max == 5.0. At the Mach numbers below 6.00 signif­

icant time penalties occurred in CL and LID. The analytical and experimental values . of trimmed (L/D)max agreed within 10 percent, but the agreement between the values

of the other characteristics was inadequate.

Effects of Mach Number

Experimental and calculated values of the lift-curve slope, the drag-due-to-lift

factor, and the mininum drag coefficient for the configuration without the inlet are pre­

sented as a function of Mach number for oe = 00 in figure 16. The calculated values

of the lift-curve slope and drag-due-to-lift factor agreed with the experimental values at

all Mach numbers except 0.36 and the values of the minimum drag coefficient were within 10 percent of the experimental values at all Mach numbers.

Variations of (L/D)max, 0e, and CmC (static margin) with Mach number are L .

presented in figure 17 for the untrimmed (o~ = 00) and trimmed conditions. At Mach

num.bers below 6 significant trim penalties occurred in (L/D)max as a result of the

large variation in Cme (20 percent) over the Mach number range. A fuel-management L

program would be required throughout the flight Mach number range to reduce the varia-

tion in static margin and the corresponding trim penalties. The calculated values of

these parameters were within about 10 percent of the experimental values.

9

CONCLUSIONS

A wind-tunnel investigation has been conducted on a model of a hypersonic transport

configuration at Mach numbers from 0.36 to 6 and at Reynolds numbers from 6.67 x 106

to 21.6 x 106 based on model length and dependent on Mach number. Basically, the con­

figuration was a blended wing-body with strakes, an inlet, and a single vertical tail. The

fuselage had a Sears-Haack area distribution with a width-height ratio of 2, negative cam­

ber over the forward portion, and a fineness ratio of 13. The data have been presented

as aerodynamic coefficients and compared with the results of various analytical methods.

Based on the results of this investigation the following conclusions were made.

1. For the center-of-gravity location of 0.06 mean aerodynamic chord (0.564 model

length), the complete configuration was longitudinally stable or neutrally stable at all

test conditions.

2. The movement in the aerodynamic center with Mach number produced trim penal­

ties at all Mach numbers except 6 and reduced maximum lift-drag ratio by as much as 1.5

(at Mach 1.5). At Mach 6 and a Reynolds number of 21.6 x 106, the maximum lift~drag ratio had a value of 5.0.

3. The nonsymmetrical cross section and the high-fineness-ratio fuselage provided

a low side profile which contributed to the configuration being directionally stable and

having positive effective dihedral over the Mach number range.

4. Estimates of the lift and drag coefficients at zero elevon deflection and angles of attack below 6° over the Mach number range were considered adequate for preliminary

design studies.

Langley Research Center,

10

National Aeronautics and Space Administration,

Hampton, Va., February 23, 1971.

REFERENCES

1. Drake, Hubert M.; Gregory, Thomas J.; and Peterson, Richard H.: Hypersonic Tech­

nology Problems Identified in Mission Studies. Conference on Hypersonic Aircraft

Technology, NASA SP-148, 1967, pp. 1-19.

2. Gregory, Thomas J.; Peterson, Richard H.; and Wyss, John A.: Performance Trade­offs and Research Problems for Hypersonic Transports. J. Aircraft, vol. 2, no. 4,

JUly-Aug. 1965, pp. 266-271.

3. Penland, Jim A.; Edwards, Clyde L. W.; Witcofski, Robert D.; and Marcum, Don C., Jr.: Comparative Aerodynamic Study of Two Hypersonic Cruise Aircraft

Configurations Derived From Trade-Off Studies. NASA TM X-1436, 1967.

4. Small, William J.; Kirkham, Frank S.; and Fetterman, David E.: Aerodynamic Charac­teristics of a Hypersonic Transport Configuration at Mach 6.86. NASA TN D-5885,

1970.

5. Schaefer, William T., Jr.: Characteristics of Major Active Wind Tunnels at the

Langley Research Center. NASA TM X-1130, 1965.

6. Sears, William R.: On Projectiles of Minimum Wave Drag. Quart. Appl. Math.,

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

7. Braslow, Albert L.; Hicks, Raymond M.; and Harris, Roy V.: Use of Grit-Type Boundary-Layer-Transition Trips on Wind-Tunnel Models. NASA TN D-3579, 1966.

8. Whitehead, Allen H., Jr.; and Keyes, J. Wayne: Flow Phenomena and Separation Over Delta Wings With Trailing-Edge Flaps at Mach 6. AIAA J., vol. 6, no. 12,

Dec. 1968, pp. 2380-2387.

9. Margason, Richard J.; and Lamar, John E.: Vortex-Lattice FORTRAN Program for Estimating Subsonic Aerodynamic Characteristics of Complex Planforms. NASA

TN D-6142, 1971.

10. McDonnell Douglas Corp.: USAF Stability and Control Datcom. Air Force Flight Dyn.

Lab., U.S. Air Force, Oct. 1960. (ReVised June 1969.)

11. Middleton, Wilbur D.; and Carlson, Harry W.: A Numerical Method for Calculating the Flat-Plate Pressure Distributions on Supersonic Wings of Arbitrary Planform. NASA TN D-2570, 1965.

12. Gentry, Arvel E.; and Smyth, Douglas N.: Hypersonic Arbitrary-Body Aerodynamic Computer Program (Mark III Version). Rep. DAC 61552 (Air Force Contract

Nos. F33615 67 C 1008 and F33615 67 C 1602), Douglas Aircraft Co., Apr. 1968. Vol. I - User's Manual. (Available from DDC as AD 851 811.) Vol. II - Program

Formulation and Listings. (Available from DDC as AD 851 812.)

11

13. Spalding, D. B.; and Chi, S. W.: The Drag of a Compressible Turbulent Boundary

Layer on a Smooth Flat Plate With and Without Heat Transfer. J. Fluid Mech.,

vol. 18, pt. 1, Jan. 1964, pp. 117-143,

.14. Isaacs, D.: Tests at Subsonic and Supersonic Speeds on a Slender Cambered Wing With

Fin, Underwing Engine Nacelles and Trailing-Edge Controls. R. & M. No. 3593,

Brit. A.R.C., 1969.

15. Polhamus, Edward C.: A Concept of the Vortex Lift of Sharp-Edge Delta Wings Based

on a Leading-Edge-Suction Analogy. NASA TN D-3767, 1966.

16. Polhamus, Edward C.: Predictions of Vortex-Lift Characteristics Based on a Leading­

Edge Suction Analogy. AIAA Pap. No. 69-1133, Oct. 1969 ..

12

or 0 bS'fD" f ~ b~o c.) 7-= .'i'>-~Of 1rrz b.I)10 eel­

uHd ~ f);Y. ?

(0 rl.J,", ) () .

r1e •• 0204cm\

.54751 ------..,..-- I __ .. __ ._. _______ .. 39751 17.5;..'1 (~ll'4/1,~JJ4_&_"_)_'

12.,77. '1". .

~~~-------====---·---~-------/~/~-r----r-~----,-,-------------------~--------i' ~--~

'"

.18751

.11 ---

~ - / / i i : ---T\'""=-:_::--_--

r-'~--~ ___ '_<_:=_=_. '-_'-_,=---:--___ -=-l-::.;;-~--=j=--:.:.--~-:=--~=---=_=_---~--~-=--.J---~~~~~~,,-~--Li

I I~ --"-r i 11

.106251

I .0275l

o . 06671 • 53351 i I I [-----6------- ----~-----_z=s

Lff bi:=. D)"O'l c..... ~- l' • 61 • 031251, .

=:C=s: n (a) Planform view 0

Figure 1.- Details of model. (All linear dimensions are given in terms of the model length l

h .37 S--L

L I. . G ~ 7 h

x t =- f(., '/ ~ =- It. Of"';'" ,

C- ::: I () 0 .,:;' f D,ll J (i I 0. ~- n ,:/-1 'I) lUI ,

v 1 C D"2 - s fV:V-'~ tv( ,

1/ b --- /2.DDD ---

7->.-.0551

I " . \ / \(-_/ '

of 81.28 em.}

01..,0 I YI '

;;.. ~ £~ -fi:.

(,11'17)

1---- . 333c --~·-it-·--- . 333c ~ _ ,Y2c --~~~~==~~~~~~~-.

c

t/ c •. 03

Wing section

Transition grit

I- .5641 .----- ~I , l __ ~===-----~----------------~----~----~~~~~~--- _ ... i -- - .02751

.0151 ~ ________ ~--~---.-:::-?:::=- _ T

.631 . ~I --~-.------:---~-------.--------

(b) Side view.

Figure 1. - Concluded.

1 10.80 c """"-

17. 09 c_~ ____ --4

C .1~'i! K

(a) M = 0.36 vertical tail.

Figure 2.- Vertical tails and inlet details. (All dimensions are in centimeters.)

1,.32

If 10.80

11.09 -----~

(b) M = 1. 50 to 6.00 vertical tail.

Figure 2.- Continued.

------======~======================,I~~

.I..--.--4.8.5---~----­L.---------- 12.90

II .(5)

·¢=t-~.-31-~3.4-8 -. -__ -_--., -:r: __ -_=-=----:-=--=IJ~}l J -1.3r+- 3.48:::::=:; L Parallel to fuselage

(c) Inlet.

Figure 2. - Concluded.

18

1.2 I,; Ii:.::! 1;;:11, ~ in::!; !I:: :,':::1'11:1 t81,::: "II I::; ;;:;I:~ I:;: ;~l::I:: 1;:d::;::i:fI~l~ " :'Ii, IHli Ill' IH' id' "i,li!lilli: i~1111 :'11 Htli,il:r' , : I" iii,: 1'"

1.1

1.0

.9

.8

ii" II ,IL" I:':' '" ':' 1'1 ',I': 1'1" ,. I lULl 1,r- '.',' ~ .:i Ii Iii i' " 'litH 1/11 Ii'i ,i"" IU ' ,I' " IJ ,i ,i,' .' Ii' ,1'1:', ,. ..17" L

" i': 'i 1'1' " . , , Il'll II 1

.7

,ii'" <,I HI II'! I Ii :11 I', ;'1 I:. ';.' '.i 14 I <: .'"

.6 ii, , .- ,~

: f.," ,i ,; , , , l

.5 :11:. .', .. ,,,' .. ,' ":::'iil" 'ill 1·11' I

CL .4

, .' , II 1,( II I -f-- __ ___ + ",'ii,' '1/'1/' ~--,--

.3

.2

.1

-.1

-.2

--,j-_1...

20 24

a, deg

(a) M = 0.36.

Figure 3. - Lift coefficient as a function of elevon deflection and angle of

attack for complete configuration.

• 7

.2

.1

o

-.1

: I; i I I I I'

I ! ii,

,i ,. I

:1 . i: !! :

)e deg +5 o

-5 -10

I I

i II . 1 ~: .

!I I', II I I' I 'II 1!0 li j,!' :1! l8.

I'L" 'lL' "

!I' 1,1';

ill· ,:'::! LJ.

" II -15 ffiittflHt!8t-ftSs:Hflftt+t1'i, Im,hti, H1lttt,i ItT, iitt,i!t, tt, ,I;\1,tfi'; 0 -20

I HI"

';',

I' I

-4

I! .

I ! ilii I' 'il

I" I 'I i,l'!

:','

:: :'. '

,i Iii

'I U " ",!! 'i I i !ill LL L

II: ij,:

Iii I'

, , , ,

I!: Ii ' I I> 'I ' ,:. rJ [j11l1 1Ji'8:, : Ii Ilil I: 'H:.k:' 1~I:j 1"1'

IJ ILL [,,1L • ' '~ I'

Kill! I

r·'

: I i ' lUi' ,!;i it:. il!tr::.l1. LbL. 'L

I ! :IP

,Ill

o 4 8 12 16 a, deg

(b) M = 1.50.

Figure 3. - Continued.

19

20

.5

.4 , '

-, '

I-+-H-+-+-+-+.JH-+-t-L-I-t+-H-I--+-+,'"- +-+++-l,L,f-V/--ltt1 t1{'I-ILl-- - -1--'- -~-.3 1 '/ rlf I: I'; ,.:. - ,- --- --- -- --\- - -- . -++- ~ -tf~!:1t~ - I- I -; ! r--~ --+-+-I--+-+--t-'+-t-+-+-+-+-+-+-t-+-+--+-,+-+-If:,1fc-7f.>I<-v //-V;jLI-'--t 1--, - --'---~=t--~ ----- --------i-----i---- "-17j/7f)~/-+- --)-1-+ -;1 i

~---- _ "- -l-+-I--+-j-I-+-+-t--c!'-+--l---'l--h,~~i/'-tI'-lIIi'-b',L l~v+! -+--1- -- -~-!- ~t~-: .2 ' ' i ~ )' I I'

-' --f---+ ' i //~~ljf~ri---!-- -+ + -1-:- -:--','/ ,- ciJ 'I I I , 1 i I :-

~- -t, ,-+-+-H-+-+-++-t-t-++,++II+t4,!~",,~ At'-I-i- -r-t-- -1- T ---, -:-:-

--- -1-- ---1- / /. /~/_'I::" __ I_ .L _L_I __ ~ __ -.1--1 -)/ _, tI l r ,i "

1- - ~ 1- - --'-- - - ':'-:-jl:/'7Ik -::. ~ -- - , i--i-l- -- -+ -+-r .1 _L __::.. .,--_ _ ' / J i ____ _ -,-__ 1 ~-- -~- --- -+ __ --rl __ 1,'___ !

, ' i'" " " , 'i , /,1/ -, j I

'1. ' '/ I I ' I--i ~ - ~ _~, - L" , r , : r;-+- -r~~I-LH-i -

-'-__ , ~ ~/~j: I - .' - ~j -Ii r:( /' /; -'i ' r-I- - - -

o 1-,+_ ,,--I-,-r, .. ,+,--1-":(,"'_ ,T.-_~" X--"'-f---l'~H:1I--t-'-b+"+-f'-+-+-+-+-+-,_,r, ,_+-t-t-+-t-t-+-t, -__ r~+I,,---Ij:::.-t-__ +. --1_ -__ H_

I " Jt, -'/' -,- 1',-,-" 'I ,,' :l:'", I',( ,'1. --, I J __

, " , :j' , ',;_ .. , ' --- 1 H+i-+-'lh-'+"+i'9'i':ii"cli"~" '~--b'-f' 'q" -"'+f'j'+""f',,-t-'--'c "'f-,''i+'t'-t-,,' +'+'+.'-+-+-+-I-o++-t~+-++~ '~j:::. -- + ±+'~+-+'~ii~_,~,~I--+-'4-'4'1--+~,I--,+,4:~i+i~'~'il--",+,4.1--.I--"+,4_"~,,,I--"+1:4:"~,'+,41-1-i ••• ,+-+-I-+-+~

-.1 -iii '1-' 1,- , .... -, i" , .. , -, ·'i' 'i,' ,,' -4 o 4 12 16

a, deg

(c) M = 2.00.

Figure 3. - Continued.

I', I,

H,oc+-t-'-t-cI-"--i I,'

a, deg

(d) M = 2.36.

Figure 3. - Continued.

21

22

.5 '11'1 ;1' RlllllllllliI ••• mll mw ii: 1 i !i I.

iii I i ii I'

I I Iii I I j Ii i t:'

': " I ' 1~-+ , iiii

'" .'jj1 I ":'

I

.4 I

i !,

, , , ! , , , : I !:

.3 ;1 , i :

iii!!!

i !

1: 1.

-2 -4

I: I i I

). 'ii i: i 1 Ii

1:1 'I! i! :I!I I I :1 'Ii! I II! I : i 1 . j d I, ::1 i il i[ i ,I t ,!

li.1 I 'j! il! I;

I

L I ,i I I II " , ;"1

'j i i

; , : i

I; 'II '!::i :!

1'.:,.: I:': i,:"

I':; .j; I' ,

I"~ ',' !i

i I' I Hi

.i ,- :IH

I I

0

i

I

,

i.

,

" i

11 ii i I'

4

:1

:! I

I!

ii'

ji

0 0 <) 8-0 0

11

,

,. , i: iii : db "'il I'

6e• de<] 'I

"I I I ;!li

:1 I ;:i:i , il:::" +5 Ii' Ii ,~, i::':':"

0 , , I'" : 0 -5 :i i'

, , I: !i'" -10 I, !

, Xl : , -15 -20

:i':I: I:

Ii ·'1';1': ,

;iil' " <H i I ,.,. :", I"

1"1>1,' :Ii' ,: It 1'.,)1"

': 1:1::'

I'i .~r~ rl~1 fl~,:I~I~I~I~I"1 . I:'j' Iii: • Iii Ii' 'IHi'

'I

8

I~:; , TG :: IjIG'YJiL : i,II;' :,1::1" '1'"

,I " ' II:;:: Ii ' '1'" :'IV';!' I'::: :

I I ; .. I

, , ; I

, Ii , ;

.. i ; " , ;

12 16

a. deg

(e) M = 2.86.

Figure 3. - Continued.

.24 ====rmm=ITTI,1T'"'IT, iITITTITICH"lTilii'TI:: ITTI:TTTm, T:,!"G,,1r, iSJT::,!., i=:IT1I:: ::TTr:.T" CJ7',11 :r,T,. '''"1'":'", '" .. :-'1. ,'1 ~'! -:)i l·i "IPili:1 ,'Iii'! iI"1 'it ".'1 'iii.', "':':;'J'/~

T 'il " i: :1 t ," i'!I:I! I I, ';:1,,':' :'i' ',:: [':: -:, ',' :!i'., ., .. 'i '.. 1y.~:~F~I . • 22 II:, " • ii' , i' i II 1:1' I,,' '., deg ') •• '.:. ". I. i'." '.' ..... :.,'; i .'. . I/-{J

IT I' 'I I I I, III i,1 I' - iii" .. ··!,',' t;,; ;: i i : I 'I i': I, i' ! I' ! 'i I :. 0 +5 ":.' , 'e.. L,c 7'!PI!'

H++*+++lJ!+jffiJ!#8H-1 '*' HtI-' +t¥f.IHji *"1'f+t++H'+H-i ',*PI!+o-' flttt+i"tI 0 O~" 'I: "I,i~·ilj .. : .20 , ! ,Ii: I I' ," I :,'1 <> -5 "~,~ .. ~~. f-< ... l~ . !.~'I' ;

H++r'ffi1mi/i+it' ttt! H+f't:'H'ft-ift'tti 'fit'IH' -'1:' -Hi:±' H+ti 6. - 10 ,I'."" I .' '.' :/'f. ' , ,! !, I Ii, I II 0 -15 ,'. / ~>j!'

.IS f+ic:ml+til;+j, +ti, *1Sli-H-:iii-:-n, ;tij;P;lii'It, m-lifi,ciI:I-r;:, ,*: ,'ii! m'THI 0 -20,'" ,. /'_C_I,,'

I [, ,Ii, ii, I' ii, 'II! ',i' ,'" ,'l·'i:. Y :.:" .': ':', :.' fJ. I; , ! I I, I,,: 'I ""I', i'i,' I'i . !,r-j',//. IV; I~L j,

~!1HH 11Ylf' f!lIl tlii I H~' +HHiffil#'+t'H-' *:' 'Wi Hi' '#4H1fLiilI ':: i ,,: i:' , .1 i:: "." f Nil' :. II I i I . 'i i 'I I' i:: ii, i " '·1 ,;1 '.' ,IT/, I,!_:'

.161,. ' ! I " ,. i1I'I!" . I ! :",': '//1., . .1 I '.' ! liii I . ,i ;, I; ': Ii';:: t, I ,. ~;I;,--: I',

" :, i Ii I; " ::,: i(' '" ,I "~"+: i : ,14 Hiiti-mlnlftl ittifmllltl~'*' TI/8, t+.tf: h, fit;tl,rI:i;tii, +t ;iffi: tti!:hl::!TI ,::.:,miS-h:iTtf:httT:tm'fu.+;ful1f![f.'i~ .. ,-rl .. ',.'.t -.' t.--!f-: -tl-t

i I i ~ I ;! I : i ; i ~ .!::! j I I :! lit"" I I '

, I I I I ' ; I ':'..:' i t i ! : i : : ~ I I .12

'I'i' I ,i, : t'i lii~ '~!ii: :"1'11" ""I'." "i':' ·1, 'I 'I I iii iP : . ! I I !' :: 11: \ ! ~ ! ; i i !!: : ' I : : :

I "':' 'I;:, i. ',i::: ;:I/""!:~--"·i+I. ++--':1'.+. f"

.10 ~llllli ~i '~I Ii::' j~'I~' '~i ~" I' Ii' Ilm~'I;;i,·ti'i·· ~'~"~'IJi' _II

,! I,', ,i i Ii 'I~IJ::::>: II I Ii i" Ii' Ii; ,. i Ii '''I' : ,.;" i'-

, I, , ' i!' "~'I ':i, -~ 1-' .• ": .08

i, ': I "~iii' I, ii,' ,I,·,:"'! .: .. 1"" ,I 'il i,:i .• ;I'Y"'., " 1".1,.

I+'+i i"-tP' '-ff+j+lbi fi;1 ~oht+l";'+""!.J.1 i:tt "+-'!H' -'Hi I ++;1 '*,*' mt' Ii,', .' :. .'... . .. !! I 06 ill:' .;" :.' . II" '.: I' i':' ,',' . 1. . i'i! [.: i,,:: ·'i,. Ti !'-.-"

',i !:: ,i,i: ,'i.: ""1" ,..,. , ... : .. I : .. , 'I ;' • i I!: ii ; •. ,', ,-.--'-;' i"

'1'" ... i ';,i,':'·,! 'i.;" ',I: . ,'" .. , .. I I

il~ ' •. ". i';.i:';"':::::I:'_:·:···'I·,i· P+i8tliffi,tt+

Ih'i fHttrrrr#Ht1f'+i!'!*! 1 ,!;I 'I: ,": !:! ,.: !_._I, .. , :.

f+iit+4i!'itliffiitiifrftftittttit'ttititi' ! i't "';"",." __ .:" : .02 H+*-rHl1ffi'ffi'l'tf;lilt1Mhl' . , ':" " .';, ..::. [-.-' .... c .!.

f+tt'tT'I+tt8H' tit' :H+ft!tH*'ttI%tl!' ,: iE":' :, -! i : ,:1 ,. . Ii' " i ,I! ,t·,·,. j: : ., ',~_...c_,,~ --'i--'''"';

, ' , I:' ~ :: 'i:! .i' .".,:.. . ,.. :

I'

Ii! :1:: r;!!: ;. ::, ' ,; i! : ,I' :i :. :;i: :I:i Ii': i: :::: ::;, . .' .: .. 1 'T

'I;'" i.,,; .'::;',:,;, '·:ii ',i "...... .

0 ! ,:

I --.02

-.04

! ii'!" JII i. , : ·'i:._ 'c "'~' " ", 'II ':",:,., ,I' •• : '. 't ' .. '~. ,,',',: i..:' ....

;; I.: i' ':"

I' I:: ~ I 't I 'r'~'!, ;'f .,' i ,'" .. '.

,I !. ,; 'I; [' i;i: '.;. " • :'1.,," Ii: "- .' Ii :i i' 'I' l'I':'i:·:'[I:: ·.i'.;:i ,." ....

': ::::, :,;;: ,:::;,I;:I::;;i. [' ••.•.. ' .. ' .. . i

:06_4 0 16

a, deg

(f) M = 6.00.

Figure 3. - Concluded.

23

.5 --:--,-------:---------"1-.- . __ .

----------.--.---.--~--'-----------------:------:...-- --0, ' .... -..•. ---- ._---::...-:;:---;----------- --

,2~.~'~~j '.' .~_ I __ rill h :tV '/ ·.1 I.· ' ........ ! ... ~. I ,T! . i .: v,:::: ..... ; ..• •• ! .• j'

...... ..:: ...: I ~ I i . I 17 / 7.. ,'/1/' .. ,. ! •.... Y. R"'+'+-+-f..-'i .. L.*"H"+++-H~.+i""'·' t--i-+~ .. /1--t-f" T' 1 . L ... :· .1 .' i/ r-;: 'fJ:'/ .I'~· <I· . i.e

§~.fc~:F.;+:~g;.F •• ~+:::..j •. F-f"~· P+++ •• +..t-l-++-i-1~+ Ii ++:..-t-I!. I,',. ~ ~! .. I .•.• 1. . r. : ••. t:l2.

~::ikj~:i ........ '. ... .1 I' I ••. V r ,/.' ft,Y,i ..... , .. , .J ".co ".1"" ·1" i ·····gl;..·-V·~T;;V .:'. ..I,,·'···, 'J.,."." .. COlC·.·

.1 ~~I~ ~~!;t~ ~~. :." .... .. ····.1 .' .• ' 1 • .'. I 'T '.,' Ir-VI, h'~f?1 ., .. I. ,I" c::: ..... 0: .,

,'" .i J+l'il ~:: :.;&. -:i: ... ". 1·1.1 'I.·· I··' .: .. VIr- :V' ~p . . ... 1·'''1'', I ! .. i" "i ..

0_8 -4 0 4 8 12 16 20 24

J a, deg

(a) M = 0.36:

Figure 4.- Drag coefficient as a function of elevon deflection and angle of attack for complete configuration.

~·t~ .~; -;r~ - .c'I~~· "'~, -c.-,,; ·-+~r:~. ~_I~ --d:~~ -'I;~~&'~+~ <t-r- ,~ hll~ .' ii' ,: , .', ., .. ;;; ',"., . '/~l4"· .... ".!

'·'L,·· .;, V~ I:::· .":.,, •

. 08~ '-r~ c,:l--~; -~ .. c~ {~.c:r-c~, ~I , I--J~ --~tt~~~:L, ~!':'.,~':, ' . ,:-.1-- ,;'. -' ~'~~r;:r-r-':~ -,' ., .. ~~~r2rtc-. -r-I::" j:"':I(i

o 4 8 12 16

a, deg

(b) M = 1.50.

Figure 4.- Continued.

25

a, deg

(c) M = 2.00.

Figure 4. - Continued.

26

:'1':':' 'I ::' .; o.

04 . .: ~:, .... ::' ,I!: I,:: .,', : _+ __ ,--1 .. _ . f-·tT.~ }h-~ l_~;, ' •• ; :~t.:j~ __ -j ..

:': :::l' :!:i ::i: !id\1~ .! I: I::! :

a, deg

(d) M = 2.36.

Figure 4.- Continued.

.' i /~f,: '. )l :!

i

i ! !.

I

I

I ··1

!

! ! .

! .

: .. ! I I i I

i I

!

16

27

.14

.12

.08

o

28

"

I

l' ,j. 'I ii.

: , :

T ,

ii.

I'

" ! i

i"l

i 1 , i " ."

, )' 1 ;

, i 111; i ~

, : !

, :" i I :!I

'I 1 lif! 11 " iii: i ,;j I,

'j 1; Ii !i:

II!, , 'ii;i: , i'"

iij :\ i' -i,i I

! ~ , ii:

I

be. deg

0 +5 0 0

<> -5 /:::,. -10 (] -15 0 -20

I'; , ~ ; : Ii!

i " Ii!

;b ! ~ i I:,' • ~ i :

i. :j li:<

iii , '::i: i'ii,

::' :"1:" .:. ',,, Ii ::1 i,

i' :L

Ii' .iji' .,. h~

:,i:S;::

!, I'i;ii:' i

!Ii' I. ','1 /111 : .,. i

!1,!,::,11,:, fIlii I: i :i:' ",'

I;:i :.: ':1'.' I'" , i',··· .. :~ , •. , .:.: I '!I;:IL i j; '{'/' ,i, ".' :>

Ii' 'li "iii, j'. I 1;1, I~F ,:. I·' ... ,,,.

I ! Ii'; ".i, liii; :il:' liii 'I" 'ii, i·'" i,"" i,:'

},i'iH,i .i1i i"" ,. ," I'; liii fl. 'i:ii; .i'.

" 1 'i.

. . ,

"'II" ." , , , '

• .' I

. , ' .'i'I', , ,. ' ;

'II

'" 1:

), 1

-4 o 4 8 12 16 a. deg

(e) M = 2.86.

Figure 4. - Continued.

008

c_._ -' _ -) I.· .1" _.- c.. tie. deg .. -:1 __ .. _L..j -II; ···1 . , 0 +5 .. VZ~ I

btc-j--·t-t-'-t--jr--j-- .. +-,-.",,:, J~ \-1--- - 0 0 l""-.l_ ... ~--l.. .. , -1: . I . I I

006 ~ ... _.~. --r-ct-c-, .+ __ Coo ~ 0'- '" ~.:, 2 ~~o •. •.•.. . ... t-\~~ 0011-, .j. . .. . . . . IL J * -15 •• ~W ' •.. ~ • ··1 ~ \i -20 ., lLaQ

l;t°. ~f'r. I .. . -::+":J<;;rl-:,~~ ..... ,' .... . .. tt~ ... ~hI' ... ',. . .............. ' ., ....

a. deg

(f) M = 6.00.

Figure 4. - Concluded.

29

! ; ______________ ._J ____ J 1_---'

.8 --------------~

r ~,

o ~ n f .:~ : .l ," c-t+-':- ~+-_+-"-+-H-~--l----+-+--f.-c!, +-H-',-+++.",-_,~ •• ~_-,:".!'-•. 4._ c"c __ -+'_:"'!~ "'"c_.+, .,_ •

--~ : 'i i I ~ : _Woe t--i-~~- f-~--+----i-i,---,. f--l--+-+I-+--\-c----1--'+-7~___,_'_\'_o____'r_+___'1=_'t==PcP---+, "4'-'-':'1'" "",'-:'f'-'-,':+"'-=1=: ~M --'---~' '\:, ; I, ! I'" : I ___ ._ ------·-"'c,"' .. __ .= ~.: \'.1; : I :1: iii

---~c:--. -r-'~--,- ----;---r- iii i i ~ ... j .- --~: - .... :~

--i-- -t-++ ~JI-l--'--'-+'-!'_-_ 1---_ ''-'':~.~-I--.---'+·I'''_.:+-.'4'}~;~ ~~ o .1 .2 .3 .4 .5

(a) M = 0.36.

Figure 5.- Lift-drag polar for complete configuration.

·6 ~r~ ••. ""T.,.-:-~i"co""T,!,-:->rITJ: ,.".. •• 'T"-cr':o.Tj-.,,,.T.j-:. ',:,Tt .. -r,T1'. ,-.. '".T:t-j:'",T, ,,..,, .r-r-rT! -.. "",."-,, '.,:'"'J.,.-:,'.""T.!,,-' •. T"""c'A.""", "",'":~:~.,',c""T·, .=,:",:""1"., ."""'::':,,,"': ,""':,'>'". ~."..:.r'o''"f-.:,F,~:"T, ,,,,,:,r-"c-r:=::r::~,",., ."-.,.r-f:='"':02=:"r.:_""T.~=.F~:."T::~:,, l~::·:l< ,! ,·!'r· co".,; .i "1' I ': .·1 .,. .. " <I·· :'.1 ... :,,: c:,: ::~: ", ,,: :':: 'o" ": :fH' .'. :::: .:,: :':.i:: cC:==;' :c' :c'c"= co:: ,,,::,. ·1.'.: ':,:'Y:' ., .... ·,',1· be. deg i .. , ',i':: ., ... ".:-::~"':':'C=':',:=:, .• , cr'" "". ",:~:~=. !,,,::,cI" I ':i" . ",+::: '~. . ,.. 0 +5 ,.,. ...1 :: .. ' .... :::r,.:· ..... C.t=o <." :::: ';~f=::~:': c., "': i-- .... '." ~.:I"'" : ... ~ ril ··i· .. · .....; .' .. l.'·T::"~~c. _':'<F':O":~c~~",,,~~i=o:;~,c=~ I·V!' j: "'::'!' "j ··8 0, ." 1 ,. .. , .F:,,···~ ."1''" ,::~ :::, ..... c -::C' :~~P'~ .~c ::. cc,;:~r~:'c =E'~ f',:,":f .... :. , •• ::;0:.' .j." Jo,,' 6 -5 .. T- ., . ,,,! .- .". . ... ,0+:::, R Coo', .• : •.•. :. :':.E" :'. __ S :.::

4 (: "1: .• 'f .. , ! 8 -10 ': , '.. ·,'10 .... . .... 0: #,;t; ~"'" .,. 2~':' ~t:3F ~" Co,. ,=.=o'~ :=== ,c ~ 1:·+:'·;: ,.. ! 0 -15" .. ", I:'~~!?~"P'-"-: ~;, 'c·.:~·<'~HY.· :=.;:':0=:: ',.o''='i r"'i~':::-i .; .' ':"'<i " .-~- , i" •..• 1 .• " .:.r:: ,. ~f"KIE:';;,;~::::c, ~.,j;;?'co :', ':.:1;;1r-CC .c, c'.·' ."c',. :,~='::O, ::c .::: fc:: ':L..;. ... c, ""1':1: .. :,:'r .,. kt::;::~ .,,~: :c:. ,,:?~.: c;"::: j.:-~t=Oj:,: ;,.:'~ Cc .,:; c'~c[.': :::. '~: ~~~ .co, ',; [:::<!.,: .J:.: ::H'·· .:: t<:: i . '..",'\: .,:- <w.. . -;.. :!::,~ .• ::,,:=i{.r:; .::~":'i2 ::: .• "'::: :'C: '.',,::=: ::c :::, co'::::!:' ==~ ::~ ·-F.:·,F b':,'i L ',',: <T, : :, .. :: :: .• ':: .,-1": .:.:. ·i':·"· .:';1.'" ~ --y .:.: , . ~"-'·l.:' P-:f'. ':.: .~:-;.t~ ~:, 'co . ... . .• ,.', ,:: ::" '.'" -.i: ~:: ~'i'~'. ::0: :::.: :ic~ :O~:if=i c:ce'. F C : , "I' '~'L . ,.'h :'2i:P" .:t;.:- •...• Ve, p,:: c,. ~,,~ ::' :'" :':: :.': ,<:,: >:,,,::,. ::~ ',,: ::;:",=~'t:~ .~".~. ",' '1': :'::U •.... ,j ':., :."1aP"7:co :,: 1s?1·""?T:· ..• k'L >.co ',:: ~::b:Or.: ~' .• c,; • ': ·'~.;'·E:Yj goo.

2·)"'t::.:r·::"b, :::t:" '.,. .:"":, •. :> ~:?'t%: ~~:7"~::" ~ttf": .:: ;:'l::~ '-C :i" ':', '''.0:=''. '= ,:. co:;' .. ~ c, ',,: . ~~:.[~t':.oot: '::.1':' ... i'c .:, i?'~j ,::: '" 7' ,:17 .1.'.:'. :. t'Vr':' ... .. . .................. :C:,,:'. ;,: '.:: • '.~ ;~ ,co , .. : ... == "': ..... " .,.:- ~!.

':~L':L.,::·:.,l,::: .c,t,,'::! ':'::: ;/' .": ~iV .:::;:: v.: :'j> .: V"/,: ..... .' ..... .... .:·:E· 'iC: "c' ", --. ,'0: ':.:: ::::/0=/':" co" ~ :::1.:1:.,:'.,:: >j ''''lo-.. <I'.::~ .. ,. i," 'l':., ','Y,:' ./ •. ,'. " '.e: ,'Or' ., ... 1' '.' , •.. :::~: ''':: :,:::~ :~': :'" ,:" :'i).:: .:":c :i: ;.~ .:::;:J::::'" "'F ·:::E ." :Z,I:"1/: .. t'·.'~:Ir.l"J: .il, j;':' > ",1.:. ,',: ..... .." ... ::: ,,:'···.'c=t:::- .. c ... · " "',4':'::: "r:.j, HI ...... ':i'HZL c;:ji'!' ,:+.y" "" ... ,. . :.co': :.:.0:, , .. , - - ..... .. .... ::.:E '~E:=: ,-:,:~ .,:: ;ol,,~ iT.<'T: :'Vi'Y~i .. .::'!7IYI"/VI' ,'II' II .. "'. .. ....>'c'::.:= ::: .?::.::: 2' co. ",E':F~~

·.>Y'~~: .:. ,,''':ic' !Hi ':,':;ci::',:::j,". "1':'1' !., il. 1 .. IJF' ...... : .... " ::. Co: .:. ::: = :::~' .. ~i8F-':1=' ~'.:" ,';: o ......... , "" "~,,, .::l,1!Sl' < ".",: ::: '. K·': ..... ·ol! .• ,·)·· . 'oj:'.. ":. J,oo:c, c· ....• ,,4::: c" E: :::: :~':O. :'.:;~::: ';0 .• :'.

"" :·'Y':·:'n!(;,oo·"t'::'·;,,·t'X .. : L'!: i "·1 'j··I' I". ,:' : .:::. ',,::

(b) M = 1.50.

Figure 5. - Continued.

(c) M = 2.00.

Figure 5. - Continued.

32

.4 ~~ :': jf: .~ ......... . t='.' c:: ,,'i :;;1 .'cC ~;.

§'==:.c:.,.,: ..... E ~ "= :, ~,,3:' :,. fE'~ c:':l§ ~. ~i:

.3 t=."" ~~ ''-:: ""

F! ;-~ ;,. ~~ ~ •..•• §. '=c co: ~" .. ~ c. Iii ~. :~8:i ::: •....

o [J

o £:,. o (>

.2 ~:: 8li ~~; ~~ :~~ ~f~ ::::~: ~ . -.-tr: f-l ~~i :1~ ~:~ ~~: :::> , ..

.•... ···1

:.1·

tiS '11"'8 gi'::' ,. ",. '"' 'UifrvV·· c .• 1/ ... ftll: ;t'1~ if :L;-; ~,; 'i~ ~:' '.C. ;;:iP,If:".I;";; 'f'-. c:7

' ..• _1: .:; ~ ;_:: _.: : .•

: Jif ;"'iSi 'j' ':".q ~J;:;Z'''il ... ;; '::' "} ~""' ...... . 1 '" :Hi" lili.~ ;:' ":',;:;; ., 'N 'rei J '.c:\/. ... .

';iti:: :Hi i'ti 'ii: 'i:ij7iJ';I+,: ,,; " "" .... .

o !ill; ~i; 'Hi". c~ H .

~t~ ~~! Si f~fi ~f~ ~L

!1:

-.1 II: ...• ::!:

o

q ... '.':;" ... 'Ii, ....... .

.02 .04

, ". "I

·.1.·

.06

CD

(d) M = 2.36.

I

Figure 5.- Continued.

... .. .... . ....... ". '0""': C-',.3 ...... ". " ..

? ~.~ .~:,;.'~ ~~~z. ~~t 2 ~~. ,~'

.. .,~ ."' .•. ;c.' ':;: :.,.". ,.:: "': :;;:1'-:= .:;: :;,·~"lic~t==.;.'.J,

.'. '" :c·i ..... "=c, ':";" :::; :;: ::;t 'c.: :"IsP':;I"" ,,;. ,"8=

. .. :" c'E'''~ ~ ,::: ~iil~l:=~' .~ ~ c •• ~ta,;; _'" '"- =, ~ ;"'1iE '~i . " "--; ""

. ... .... .. '" "C: ,'= ,." .::: '" "~ 'i:: .~J:~ :;: J.Jl~ • •• c: ,:c. c~ :~: :"~" ~~ ~~ .'" ~~' ,;': 8 ",' :;:~!c'1;2

. .... " .... ". .. ';U3 i~;:!: "';. :"' ;;,; ~:i/Si ,,:c ... :: ,," B;:' .~ c.!i ,,;iI~ 'j@ 'i'

.08 .10 .12

33

," ~",.. .. <:.1 .• . .• 1 •• .• . •. ktfl vV V , ...• '. 1 ···1 ' .' ; ::. ::.~ ._:. ~ . ... .. _- ...... .

~,: l~; .", t"" ..•. '''. . ". ,'f ji<17' /: V : / :.: ." ..... . :E J~ t,,, :C;. •.. .... . .. ... :,,; ..&17. .• co. . •..•• ," .•

'f!,.lt;U .; ,~ • .;}.r .,' •. , .••. .t' ". . .. ", ........ . .. . ' ···,'···· •... ~2 , .. . ...

". ::,' ... =.:.;....:."'--.c:..:.- .• ~:.: ... .:. .•.. c. •.• ~._ .. ', .• ::: .... :. .. '1'.

o .02 .04 .06 .08 .lD .12

(e) M = 2.86.

Figure 5. - Continued.

34

::~ 'f'; ~i'l;j' ,::' ';,~ ig;J\L/' , . I, r-" .,. I :", ". "

'W :~, JD Ii '::, •. : '.113 ' •• ''''ifi .,., ,., .,. , !.' •.• ,., "', ' ., ,. I ':' ",' <

"# ~~~ iii: hij ;~! ~i~~ ,i;it.\:ij\' Y: jl,k' ;,.i '" "i' .' .... , ,i,i,.:i ': , ... ,"" ' .. ,. ': ,.c , .. ,., , _... .. . Sl! 8i :ui ili. :li~ ~lP !~:l.r& :~:' ~~ttl! \:11 :~!; ::: :,': 'j .: ." .. " ... , .... ' .. "::: I": ., ': ::~~ >: ~:: <. :~;; ;~!; .:: ._. - '" :::! :: - :~:: ~~:: :]:, --"'J:OF. ~t' :'if eli 'ii, '.': ';'jru "" ',"'i" " ... ""I,." I" i" "'.' I'" '. ,." .... '::1 Co ............ . '.:' :ti if" 'lli if', ';i,:i 'LI::liV:I:'!i'N:'~ ,:,/y> ., .. , ;': ":.' " . ,,I " " :ii ,;: "',',, .. ,'" _ c ,~, 'ii; !![,j.;'i' ')i;! T :U:;"j',i i:' F :ri:'bJ. :. :.:' ...•. , •. '.t-.~ -:-.: ....•.. := .... , .. 1., ... ,.' ", .' .. <: ,., . ... ..... .... .... .. ........ '.. ,c:. i'C!

-.08 ~ .. ,. E "" .:L: ..... I;';' i" "" ' '',. ... ... . ... ' .. __ .. . .. ;;.; .'.' .....

o .01 .02 .03 .04 • 05 .06

Co

(f) M = 6.00.

Figure 5. - Concluded.

35

36

l D

a, deg

(a) M=O.36.

Figure 6. - Lift-drag ratio as a function of elevon deflection

and angle of attack for complete configuration.

L Ii

(b) M = 1.50.

Figure 6. - Continued.

37

38

l o

__ 1_ --Ti __________ p , I ill : (' :,!' , !, ,ii, ','I'~'i i', I

, / ',' ::\ 'I ',::"~ "" : - "I -- - 'J III! --/-- ~I~ I- .-,:'.'1-fH~*i '''!++i~ -~ •.

o +5 :LS: 1-" o 0 <> -5 i i,I'I: _ ,6 -10 I,";' : o -15 I' \:) -20 +1-

14:-+4+1---'-1+1--,1",4,

-2

- _. ,------~:

I '- ; --; - T f--r1:-:: -I ~ -'~-- -, -- ,- --HH-~I:_++,__f__,+'¥'H -4 :--- " - _J, -r T- -------t---1-+-+++--I---+----t-+-++++--+----t-+-++++--+----t-+-++++--+----tH

, , !'!- : - r+' + + +--~--' -'------- ~~---'

-, -: '-, : '-----,-~r~I-=+- -i-" ---:- .,' ,~-'.i-" ' -' 1 : i I ----1--- -. --- ---- - - --- -- ---"-,.- ,c- -.-c' ~,-":-~ '~,'- -,--":-" , ' , " r - i-- -r - ,- " j , _'L, __ <-:-1-- ---J-- i-+-H--i . --+++-++-I:"--'J--:j-":-I--+-:.ji--'--t--'

·6 -4 12 16

a, deg

(c) M = 2.00.

Figure 6. - Continued.

, D

-4 o 4 12 16

a, deg

(d) M = 2.36.

Figure 6. - Continued.

39

40

i h

o '

-2

-I,

-I, o 4 12 16

a. deg

(e) M = 2.86.

Figure 6. - Continued.

!. D

a, deg

(f) M = 6.00.

Figure 6. - Concluded.

41

. 16

.08 I o

-.08

-.16 -.4

" •• : •.• c '·:·r . r T' .' ......J' I .. ~ .. : '~';:: :.':'.'~ :~ • . r:'-... -"T··I.c.-··. . ".:.1 ·L •. !··/'·. '" •.. L·,·I.· Ic.:'·.r"·', •.

..... ... , ..• ,.'.1'1''''1'' ••• • .• ' ::.L. .' ':," .•..•..• c.. 6 deg .:::' .•..•..•..•. i •• • · •. >··!··I,· ... ;:::· .".,1::-.> •.• , I •••• :: •••..• ..I~~<-:J e~5~1~ . ....::I.~ ..... '.

-.2

... '[< -5 .: ••• .... .'.'I:C .'C' • tg 0', II;" "1"1:'

".:""" •. ~+". " .• ' •. ;::. ~'.'Ll." •••• -10 .... :::. .':. ::'1"" ++:" . •.. :. •. . •••• r::."I·· .. -cc'9 -15 ..•.•. ':. • .. · .. ·r.· . ::·l::·.::"'T.:·"I'.:·'·T~.:··.: . ';' -20 .. ::. ... . "I·' .,'

... :c •• : •. :::.. ,"·'1::::'·::I,,·,c.:+.: .:.: 1:::·'<. ::.:.... ....... ..... ...• .. :' .•• : :: :., .••. :::. '.:: • . I:.::f""·'.:' .' A' I·"TO:.. k::;::U. '''''' •. : .... : .' .. ' .... I'" '.' ::".

~~IA .~ 1=~F:::~~F0~1~~"~

!j:. :"':: :.... '··'T"· ::lA[ ••• " I.... '1 •• :.' •• ,"-1'" •• :: •• ~ '.: . "'" '" I.'. '::: ;'r' ... ·.. I:::: "''1''' ..•.•. ~',,:: .:

EI~C .... ~0: .. ". .~

~.. I..:: .. ~~~~= ".... ..... I •• ,I"',,':!':: ,,".: I,"

I'".. .I.·:~[:: j • . :"1" .-..• ''1'.': ... I',=~"

:c. "': •. t-'" . .... i'.': [c' • . : ...... ::. ur-: . ': •. ".r'''' ' .•. ::·f" .. ·.~J.:: .... I., ...

' .. ~ c:. ......: ~::?"I •• ,:~ . 0:;'"

:c.

. :'" c .•.. t"c'" .........:: .... I::': •. ':: ......... ~:.

l1"'<::I":I:"I'::" I :,::' :::~..: . I-"- ..... r..... " .. :':" ..

;';";;.'.:1"" , .• 1",. "~'"'?h -.:. ••

I=~F .. P~I;~ .. ~"::"~ iCc. . ". I ........ : ".: .• " ••• "~": •.• ' .c ....... ':'.::.1''''

!",:: '="~lc •• ,,'- •. ..r.y·:" :' •• :::' ••• I':" .... ~--k

::':'I'c·.:" '." :': '."-. " •.• ,.,,, .. . " ....... F·I .. I:::: .'1'[,,::::'::[ [..: .J.':' .::: •

I::.. ~1"'f=PI~I:"lc~~!::'

.2 .4 .6 .8

CL

.

(a) M = 0.36.

Figure 7. - Pitching-moment coefficient as a function of elevon deflection and

lift coefficient for complete configuration.

l.0 1.2

-.12 -.2 o .2 .4 .6 .8

(b) M = 1.50.

Figure 7. - Continued.

43

44

E u

-' u

0 ~ C'J

II

:g ......... U ......,

'ri U) ::s ~ ...... ..., ~ 0

U

C-

U) I-t

~ ~

~:-=_-___ -__ -------1------------'----'---------_-__ -_ ~ ________ ,__ ____ ___ I ! -~t.- !:r , __ -._-- --- - ~-~- :---:-,

-.08 ----------

.2 .3 .4 .5 .6

c.

(d) M = 2.36.

Figure 7. - Continued.

-.1 o .1 .2 .3 .4 .5

(e) M = 2.86.

Figure 7. - Continued.

.012

"A::t .... ..' ..._. ...... ..>: .•.. .... ' .... ,~ ~: ?>t:i.

CL

(f) M = 6.00.

Figure 7. - Concluded.

.8 y M = .36 / i

IJ .7 ,

a complete If cnc inlet

/ Onc vertical tail .6

? M = 1.50 ~

.5 II ;r / /

j V l / M = 2.00

1 V ?

.4

Ip 7 / .3

/ / I' j I

~ ! V .2

/ J / J V }

/ /

.1

! I AI / V' / fi

(/ , Ji I W-

I

(M=2.00) 0

I!t l ' ;/

-.1 1/ -4 o 4 8 12 Hi

u, deg

(a) M = 0.36, 1.50, and 2.00.

Figure 8.- Lift coefficient as a function of angle of attack. 0e = 0°.

48

.5 I I I M = 2.36,

o complete o no inlet

~ ¢ no vertical tail

/ .4

/ /Itf

M = 2.86 , V V

i¥ .3

/" / /

) ~ /

.2

/ ~6 A /

d ~

L ~

(M=2.36 ) 0

, /( M = 6.0

P L

J1 hV ~ GY

(M=2.86) 0 01

c: ~ / V ~ ~

~

A ./

.{

"" ~ V ~

o

-.1 -4 o 4 8 12 .16

a, deg

(b) M = 2.36, 2.86, and 6.00.

Figure 8. - Concluded.

49

50

.24

.20

.16

.12

.04

(M=O.36) 0

(M=1.50) 0

(M=2.00) 0

-4

..

1':'1

0...::::

I I I ° complete o no inlet <> no vertical tail

/ J

V ~

/ V / ....-11'1 vr ~ / ~ b ,...

V' IV' ~ ~ ~

~ ~ (y

v

o 4 8

a, deg

(a) M = 0.36, 1.50, and 2.00.

I J3 K z: .36

/ /

~ / K '" 1.50

/ , ! /

1M = 2.: / I

/ J ;/ ~

/ ,~

12 16

Figure 9.- Drag coefficient as a function of angle of attack. De = 0°.

.16

.14

.12

.10

.08

.04

.02

(M=2.36) 0

(M=2.86) 0

~

(M=6.00) 0 -4

f.t::: .......

f};

o complete o no inlet o no vertical tail

j I

j i if J/

~ ~ h IJ .r. ,.,..-a::: ~ gf ~ ~

~ ~ ~-

:::£6 ~ / / ~

~ r;:r

~

L:t

o 4 8 cr., deg

I M = 2.;36

If_ /

/ 1. /= 2!6

P l L !

/ / $ I

'/ Ii

L If

M = 6.00 I".,. P'"

1 ~

/ ~

.01..

12 o

16

(b) M = 2.36, 2.86, and 6.00.

Figure 9. - Concluded. \

}2, ~ -: 2-/ . b Ai 0 f-

51

8

LID

~ Ill( ff .~~ !p fl Iff. I~

(M=O. 36) 0 1---1-----11/ =-+I1:..-t-+~--t--+--+---+---:::~~7'C" -1----1

!~ IJ ~

! ~ ~ : J ~

(M=l. 50) 0 I---I---i,'+-1/-fIt-/fH--+---t- 0 complete I /1 C no inlet I J <> no vertical tail

'/~

1//16 . 'i / P

(M=2 .00)'0 I----,-J \:'~-IHt-J-+---t---t---t--+--t---t---l

~H r;

'8 -2 ~~~~-~-~-~-~-~-~-~-~

-4 o 4 8 '12 16 eL, deg

(a) M = 0.36, 1.50, and 2.00.

Figure 10.- Lift-drag ratio as a function of angle of attack. oe = 0°.

52

2 LID

(M=2.36) 0

~IJ /I "" 0 complete

); / IT 0 no inlet

(M=6 .00) 0 Icpjl htt7~7J,t--+_+_+--+_--.;¢:.....:n=-o~v~ert-=i=ca:l..:.t=aiJl ~~ /j

-

p

cr., deg

(b) M = 2.36, 2.86, and 6.00.

Figure 10. - Concluded.

53

54

.04 I

M = .36

o l~

~" "-., K

o complete -C no inlet <> no vertical tail

~ J'b

~'" ~

-.04

M = 1.50 ~ r-...

~ Q....,

i'o .04 -.08

~ ~ 'B: ~

o

M = 2.00 ~ :\. "" ~ ~ ~ ~

.04 -.04 em

~ ~ ~ ~ ~ ~ "€ ~:t

o -.08

V'

~ ~ Fe ~ ~ ~ ~ f-..a

-.04 -.12

~ FB -.08

-4 o 4 8 12 16

cr., deg

(a) M = 0.36, 1.50, and 2.00.

Figure 11. - Pitching-moment coefficient as a function

of angle of attack. Be = 00 •

.04

~ (M=2.36) 0

~~ ~ ~

~ 0 ~ v

~ ~ ~ ~ k- M = 2.36 ~ ~ ~ W

~ ~

~ ~ ~ """""- ~

v ~ -.04

M = 2.86

- .08

.016

II I o complete

~ [] no inlet <> no vertical tail

~\R .012

\ f\\ R ~

.008

Om .004 ~"" ~ "~ I~ ~ P--

~ ~ ~ M = 6.00

h 0.. ~

~ ~~ p o

~ ~ ~ g

-.004

-.008 -4 o 4 8 12 16

eL, deg

(b) M = 2.36, 2.86, and 6.00.

Figure 11.- Concluded.

55

56

·004 I ji 'ij ll'lillJllilll!illilijUiliULjli,!!ii 'i

I I I ! :

, " , ' ' , , 1:': l4l I , 1.'1," \ I \ill ,. i, , " , ,. i,i.i iii "I: -.004 1 ! I j! 1 i i H ' , I IT"! , !l " :i I

I! I: II 'I '''' I I ,I I

j: I I \ I I ' I iii!. i I' II i Ii " I I Iii II: II

Ii I: I ' , II i !I II r ~ I, ~ : i -.008 fLH.H+li!+,,!!J; l:Jll.:i!+ljll4l11lif: Hft, 11, ll+I'+' fi!!1j+.t.tJlH+f+lf1f!8i-rl11:ffit,f,Htilm, 8tt1i*H+tftl1tmlHHm:mi:$li *: mT!jH, *'1; 7t1[ 'l:±iifH,ITI ~#f,'iliH±t7±t7ifl

11 \.1 i'l 1: '!I I:! 'I 'II ,: :

I I I!il III jjl

,ii. .1 I 1 i !: ii! j ,.

,I:' II ;" ,I:, i 'i! ;ii I'

II

: :

,I Ii 'I ,. "

: i

,! ;" 'I! i: Iii i ! MfH4P'~ii~!~I~I~ld~!!'~I~~1!.I4'~~I.~rl~,~i ~~~8¥~~~~~~~~~~"~jj4+~~,i,*b.'*i~' *R~~~f.I*rl .012

.004

o

I, il,'ll ' I 'i ", J :: " I

!' I:' :! Ii, J

j' ::, Ii

II

Iii

i,

'I ii,

1'1 I', " , i Ii:

Ii i 'il I ,i I jl :q

1: ..

I! I! p: i'

III' II'

1 :

j l

I

ll'

"

II!: I

,I

1111 11:1

H' Iii'

iI·

. i !. ; i ~ :1.

i!! .,' .004

:, ii I

II ! I

o

Cy~ -.004 1'Ill1'll1lJ+4f4'Wti'ltBfl-lH

-.008

-.012

- .016 -4

: "

"

, '

-2 o 2 4 6 8 10 12 14

a, deg

(a) M = 0.36.

Figure 12.- Experimental lateral-directional stability parameters for configuration without inlet. Be = 00 .

16

C n~

.008

.004

Cl 0

~

-.004

-.008

.004

0

Cy~ -.004

-.008

-.012

-.016 -4

I

I

-2 o

I I

'II I

I: : t I

i: i i !

, ! , I

i!

2

!

i

I I

i , I I I ! I ,

, !

: :

, I I :

I I : !

4 6

a. deg

(b) M = 1.50.

; _illLiliLltli:l~ rliilflllilHliliUllJlJHtllliili I, 'l'I!i

I I

I

I

,

,i

,

Ii

8

-------I;

i

, I I I I

I

I

, I

I I , , Ii il

! i

I

I

10

,

ii

I , II

I I I

I II

i!

I I

! ,

,

I ! , " 'I

i

i: 'I

I

Vertical tail on Vertical tail off

i ilil Ii! ! il IUiiliJ I. "I 'I, i lJj lllJ II il' I il

i: i i I!' I! II I I it II

II! I lul,

I i'lili , i I I Illlli , Ii i ! i !i

i i I Ii , I !i ,I , Ii II!I

Ii I' !i I: ii',

:;1 I; ~ ! I li

~ I i ,II ,:1 ill I i il I

:j II Ii I i :11

iii I '! ii

I " ~ :Ii , II II! 'Ii' 'I , I;; ;1; I ~ i : "

1 II

" I. I I

I I

I , I

: ,

12

Figure 12. - Continued.

! II~ I;

I .ill ii

I I I I , , I

1,1 II i i

!l

il i i , 'I I I' ,I

it!: :! I i .020

i

i Ii' ii I :!I

! i' !I I! ! I'! i I' .016

iiii! ii:

,ii: .012 :::.

.j! ! ,

Cn i,1 , ~ I I il! .008

It'

I ;L

I i!' .004 " .I:

I II 'I' ,I

I I!: 0 , !

14 16

57

.008

.004

Cl~ 0 I i

-.004 ,

-.008

i I

I ! ! ,i !

II I

I! i I I

i I I' "

I I:

II i : 'II

! I t ! I i : i i !l:

" ; ,il i

:1: PI 1'1

:1

III Iii ;1' ,T; " I:

.008 II'

Iii i , i ,

i .004 !! i !' i ii:

Ii II' I:! ii ,I

+: I

0 I :i i , i i

, 1

Cy I, Ii:

-.004 'I

~ T q

ii' ,! i 'I, -.008 i iii

jI I:

'ii ii' -.012

I ,

! I ili I

, 'I ! 'il: I! 'il:

-.016 , i 'i! i

-4 -2 0 2

58

if I

I': .n

, !

i ! , i

i I

:1.

JI:

I i I ,

: , I

I I I i , i I I !

I 1 •.

I I

I I , I , I , I'

, , , I ,

i J I

I , il! II'

I J ii. 11:

j : : !' i I L I

j

4 6 8

a, deg

(c) M = 2.00.

Figure 12.- Continued.

'I , 1: ,J

':1:

.. , ,:;

, i

d:

ii'

iii

10

Vertical tail onllilim Vertical tail off

I'

i I

:1'

i , !

i;

, , !" I :1 "1:

T 1;1 ,

I

I ; i ,j

,I

I it

! I

:i' t ,

: i ;1:

i ,

.012

.008

.004

0

-.004

12 14 16

C n~

·008 : II I I IllllliJ I !I I I lllillllilDl I I ! iii i i 11111111 Iii 1111 'I: I11I :11 , ' I ; , ,I I I I 1IIIIIIilllll!lIllillillill!lili!l!llil!l!llillliillllill II

---.-- Vertical tail on I I

.004 ,I I: i --- Vertical tail off

I ill I II Iill ! I

I j I, I I, i! I Ii ! i

" !

Cl~ 0 I ,I I I. I' . i I i I ! Ii i ~

i I I I ! : , I,

! , i I II j I ' , -.004

, , II 11 I , : :1

i i I 1 : 'I: II:

'I I ::1 : , , ;

-.008 ' ! ri IIi

: ! : I i i!

, I I ! I i ' 1!1i i i'

.008 : I ~ : i

II I ' I , I i I i I I' 'I ; :

I, .004

I!

; ,

0 C

i l n~

, ,

: ~ , q -.004 ':: ' ! , ,

, , :

.008 -.008

.004

0

Cy -.004 ! ~

-.008

-.012

-.016 -4 -2 0 2 4 6 8 10 12 14 16

a. deg

(d) M = 2.36.

Figure 12.- Continued.

59

Cy ~

60

.008 iIIi iii' i llii I; nil, I iii 1!1i iI~lliJi I !! i. I 'UI i J • I ! i1 I fl! Ii II iHiI!IIIIFlllIlHlliI'IilllnUllillllliill1i!lilIIIPi ", Ii!! i I I i : i dill! 1 I; ii I ':: •. Iii Iii! ! !lilt! • i I. 1" in, .. ; 1 I I , !I i! 'i I~i iilllllillHllliiUfIlllilillilllll!1 IIIJ1HiHiI i ! Iii; i i: iii Ii • ill. Ii Ii i! I ;i Ii I I I II!I " i I Ii': 1 ,II' Ii ill! I I I! Vertical tail on! i ,I iiil i Ii Ii! I! !' .. !lI. Illi ' J! i I ii, ·I!., II I t if :. if . ~' II!' I,ll ___ Vertical tail off . I I H,' "III I

.004 I'i 1)1 il ": I : I ili , I' i ! I "i i 'Hi Ii' I 'fli I: i'i' 'I, I ~. Ii; ....... . III Wi l.ill iill I I I); Iii Ii 11 II Iii i Ii U,' I ii, Ii 'iI!! I L I iiF'j • i I " .. :1' ,i ;iii iii! . L I ii 'Illi i I I . 'iii iii 'lii·l 'Ii Ii! ii i Iii! II: I iI 'ii :[1 I!' I qi !iii Iii 1 II !ilTI Ii ill II Ii' ii! ! . i:ll !Hi! ii ,IIIH: I i'l1: I Iii II!II II il'! ii I d 'Iii' i ' '".4. IiI ililill III iii ijlt il!! I !' i! lid' i! II. II! I!!' " '1)1 i1l I II : I, • Ili!i! I il/i 'ii IIi ! i ill: I I

o ',!';, :,".', '1!III'i iiJ'jii:!I il!::I'!ii' .;,;'~ !"liiillil IJI !iii!1 l:!iiilJiITII' IIii. ilill!I! 'Iii iii ,!i!'!i;1 II: !Ii' i' i 1.1 illl "" ';;,;;:.: .' ", . "' ,i' i, i. i '/ii! !I': 11 liilll 11""ii 1",1 ; I ,,; ': .. '. ~! ~"I i 'll.! ill I • I. jlil i i i:il

i.i: i I illl 11 I il Ii i!i' iili !!i i'l Ii'! iii In iii • I ill "'';: :,~,"" il i,I'!111 Ii. i! II' iUi ill! "F 'm. i ilii I' i Iii I [ [II iillll!i' i I' • il liJi iill II!! Ii' I. '1 1 iii! liil d I i !ii ,i! !II! ji iii iii ill'li. ,j!lllii iii: iill I,IUI! II il! Ii iii: 11'i. I Ii!

-.004 . I, .', i'li I I iili :1 iii Iii : ' iii! 1111'; • '1 i W! iii jii' I ijf, iii iili [iii Ii! 1m iii' "II iii '!iiilil Ii . 'iii ill !i'! 'i!I!1 i'l 1',' I Iill Ii! \' i'i !il .TII!1i I!! Li "j ',I Iii', !':iill,! I 'Ii! "i, iii iii!! iii li!J!iI' II Uil:\\1 i',' hil Ilitli l.l',i! T! t!

t i II iii II 'Iii iii iii' •• Iii I II ii Hli ,Ii Pi 'I iii Iii I!! I' !ili :Ii,ii! 'i iii i!IITW: iI! ill .Ii Ii! II.

-.008 , .' • '! iii iii ii'i I' I lilil' iH!Ii' Ilil Ii! iJi i ' 'fiil: 'Il!!i Ii ill. ilii 'U' ill 'I' 111" '11'il!i!: 'Ii I'i '11,,;1 iii .008 i" i, ill .• , ,:: ., '!dlli Ii:: jiii '. II, ;'il il1il'· IHi 'II' I 'Hi I,ii !I. I.lii Iii 1'1 'ill iii ill iii. I ill III Ii 'I'll if .,"I'illlililfilii ., .;.; ......... ,",.,. '.il il jiiili 'li'l!I ;il i'l: 'ii' • ill Ii, i ... ,i,1 ill i I;;i ! I !: it ilii/ilili ii' liiiillill ill II • Hii i iLl iii i:li rl'l '.Ii h"'" 'iq"lli ill iii i !! !Ii iiil !I ' t illl il! "I! Iii 'I' Ilil ilii :fl! ill' EL;; : H Ii; iii; liii iiilit Iii I: illii'!?" III !i iii .004

ii 1III • :1 Ii II .I!!' !! iii Ii!il li,I11 !I'I'II PI! Ii' I!; ;!i ill! ,1 l!!i!1 Ii lii:!ii'i!!ij::i!i !i;;!!!!i 'I' ii, 1!1'I'iil:' III tii iiil dn': Ii iiil!i il\1 1'.1 ;,!I .1 i! !il,!! !! iiii ::I! 'i'l !ii ::1,\,%1 i;!ili I,ll U i'il il ''1i!!I' I "1' ! i 1J ,I: , .,".11 .. ::, '" !. • ii' '!I,] ii! i::' UL ill I 11! S ,I); '!I' iiiilij I I :ilill : ill: II I iiij: 'i i!il llji J iii 'i UI . ',iiT • 'I~i 7CI ." .• :.:.:: iT

o :II !'II, il illiiil.I, Ii P,I II i ":I:j Iii! iii!/l i! I!'.' !i,i iiiililii Ii ''1i ilili/lilil I!II Iii II 'I I! ji i "! TI III {iiU' H' 1:: !iI: il 'Ii II. 'i 'ii Iii il/iiJl! I!!ii iii ,'Iii i' iii' liilll !;li ,'.'.,' .'.1,;' i,:. ,'! ,.:i .••••. , i:i :,LI,.: .. '., ,.i .• II.I,II.il'lli :ii, Ii ':\li il'll il! i:lil' .,.1 •••. , .. ".". !1.il.I"II':! ,I,I!I., .'.:,·',.I.I'.'!:""'IIII"I.il',.H.""!,,,lilii -.004 ~ I j'ii iiii j:: jT j:: '::;: q; !1' qli ~ij~ iIi! ij~' fjr~ T~ i j ~ttj iif! liP ili:i i 1:1:: :1: I:

jlli I I.i i! J Ii ill ili !IIi' II !'!il !I!!I ill il; 'ii';; il'l iii! il '!nl ill' !Iii!'!' iHi Ilii':li t iii iii i! I"ili;; I!i ,ii ilil. ,Iiiill '11111 liil Ii: ii '1I: 'H!:i iiii .! illl! iii! :i'.I' ii IT ill'H;il

·008 'Ii .: Iii Iii il l\idliji.'ili. '\Ii ill:' Ii.! '.!' :;1.1,1 ,~ IiI/ ill :'i'iF il iii ,i\ ii!' '!iii] Iii ,I'.' i\!jii, II! ij • PI lii l liPliiii'ilH Ii iii ,iii! li'i 'i:.;;u iili!'1 I!'I ii! iii 'iill'iiiil;":: Ii" Ii"! iii: -.008 iii !j iii!! I'!i • i I, lill! TIII!i !I '1 'ii! ;i !II'!' i!ili! liili ii iilii,ii !i!!il iii!! ii; iii I! l'llliji! j il!i ilii il! IlIiI'lli Iii Iii I: ii' : I! '.ii/I'ii! ii! I Ii i! iii 'ii! III !II'] III! lit ii/il .I.I! I!i

.004 !li.11 1t':I"I: II li!III' :llil: il':!! I i Ii :iii I!! il i II!I ,II Jill! il'l I: iiii 1I11'1i Ii

I] m tHl~ liE '~~~l it -Ifl ~ ~ 1 ~ 'H m: t'lft 'j: Hh i Ii .Itl H Ihlll if :li ·Iilliii 1m H im m] 1m 1:11 iii! m 1m, i • "iii 'iiili; iYilj'i .j I ill. 1,1 i I di liiHd i' i it. i • II i'! I'i! iii i .: iiii Ii iilil iii! j;:i hi !'I' ii! 'ii iii

0 'I" .! 'III iiii Ikl!/! ii i III Ij I il ! i il ilP lili!! '. ,I jili 1.1' 'i!i iii. Ii II I I I III:! iili Ii Il!!i!l: !'" ~" , ,::, i " iiiilil:' il!llil!::I'i!ii Ii'i!liilliiill! :Ilil' .i !iJl 1i'''I..,',",'!' 'jiPl'jj':i!II,iifj"'ji liit Ii!' i! li,'iI' '; • I. Ii! l!'ill~!i ! li:1 ,i i';'~. '. q ,iii ii'i Pii 'i I iT iii' I !i d. i'li:li:"! ii'li liii 11 ! Ii' Iii i , , ;I,i 'Ii " ,;;TIll 'jliii ii' II i! jdii; dil jill 'iii ill: Ii i 'liji Ii!" i. lllili'HHi iii

-.004 il !II i I,i il' if ill! II! Ii:i ! I i!'ill ',Ii/I'i. Ii I iii iiii! i! iii! 'iIi ill pli ~" I lli!I!1 :ii! iii i. 'iii I Iii ii'I :t !'!i liii!1 Ii" 'iT!! 'ii! l!j iiili!; ii': ~11i l8 :;1 iii' i itil Jili iHiji:1n ~:. ii,.

!ji " il,ilil!.! II! .1 iii ill! l!ii in II! .,i II Ill' !'i' '.il ! i end P: 111 ill'I.· :i1! ill Ii • i\~ 'i'lliii :1\ ill i!I'ili! WHli li'lidi I", • i! i d III! I. II Iii. PUJ ' .. , .1Iii,.:' iii iii; iifil'i ili iil'i'! iliilH Ii!! iii' I'll

-.008 jl I iii iii!: iii "ii! I : Iii '!' il" lip "II "n ii, Hi ill. II'l.1" ,Ii! It i : iti! "Ii n, !i i ilj!I!~ 1;;,: ii: iill iii II ill i'! 'Ii [ Iii " ,.,' :tii iii I' l'n!I: illl" II! iii II:iii, 'ii! !III 'iii liliWi ii'!i I'j [jEI;' ,'! ij!1 II '.'lliil~' H, • I !iii'ii :Il i iii L : I,' II, r,:' i ir'! lli iff!: I'W I';i '! Ii! i i lifl 1'1.::; I,fi' il i,1 !~ lin !: ; ii' i in Iii! illl'l' il'l • iii! ' jljli ,Ii! .1 I'il!' '! It' I;i iti II . if I ilii "I i! ii I it I II I if ;', U!:' •• [ ill ~; ill Ii • II I

-.012 ! • Ii/Hi Ii 'iii , .• ill! I • :'iiil i!ll , ii il ill; il 'i~ Ii 'Hi :i.' It iii i I n Ii ii! i!: ! I I iii' I. i ;: I. Iii f: ! i I! I 'Ii III ii': Iii il' IJ !I' il il • iIi! i I I ii Ii; : j! :iii i, it i ti ' fj f', Lit' I '. Iii • I iii IJ iii iii p: ~,'; fill ;,' 'p, Ii i Ii:;: iii) : :~i;: ~H II i 11 j i;~ 1 1;' 'j in !W [!Ii ~ . lW I r I j; t iH d; i ~ ;: 1Ii g: i Jj H iH ~ ill r;l !g; l!

11Ll !IUlii Iii ii Ii !! IU iii I' I' Ii! i!: I iii lin.li i i'i !'i' i 11+ iii U '.' HIW H'; ',I! I if Pliii\\1! !i -.016 i ill.llljllli!1 ! , "I!ilili .!JI! iii ,1;1 iil!li'li H Ii Ijil'iH .,i i iI!, Hi ,'i ,'i li !!Ij!HH 1" !I'! i!I!' i1.'ri " I,,' 'I';. II

-4 -2 o 2 4 6 8 10 12 14 16

a, deg

(e) M = 2.86.

Figure 12. - Continued.

C n~

·0008 IlmIHNHtIHIIIIIIIIIlI,IIIIIIHlllllIlIllfllll!lll! '''' til II

---- Vertical tail oni-ttlt1JlIfIIIlIfIIIttttttl - - - Vertical tail off

o I,

I' i' I i I, I, I,

,I ii,'" II ! l Iii,' ill 'I I 'I ,," 11 i: I!' I il: II !j ,

1 Ii! '11 , iill i I! II Iii I -.0008 iii i: n iii 'I iii I: i!: I I, i I

. I , j: ! ! 1 j '! I I Ii" ~, Ii: I ii' iii! , I i 1. I; ! ~ I I l' I i j' li. ,I q!! I \.1 11

I ! I i 'I: Ii'. iii Ii' ! ,: I,;' Ii i 'HI I, , ,I,: ',i. I,' I' : L ,I I ! i : I ! : II Ii 'II Ii, iiI: ill! ill; iI:'

I, :,; 'I ::':;1, II': WII',!! II I jiil:1 !: ,i'IIl'i·P·iJi!il!!I!li!i I I j ! i I ! 1 H 1 I 1. I!: I i'!! L Ii ! !nrlll 1 .:: il/:'

i ! ' ! 1 I ,I . I I ' I ; : fui" ! Ii ,ilT!,i i ' iii ',' ,; i,.'", '! ;! il P,II!I:; Iii il,illil 'iJ i

'I . ! I Hi" Ii il I:! 'I': I !; Ii 'I iii iii ,: lii!l!illi I I!! " I " il Ii:! i.i iI,!1 1,1 j 'I I. ,II i (Ii Iii I II, !il'!.1i iT ill Lil ij

,I , iii ,,' i,' Ii! I! ; II i i II, i! 'I Ill! Ii jll' i!il I'll l'iil! 'if : , II I II! I Iii I! i! I !! I ! i,ll ! '!I .' iii I; 'iii!!!i III

o. deg

(f) M = 6.00.

Figure 12.- Concluded.

.004

.002

o

C n~

-.002 .

61

Cm

el, deg

62

.02

0

-.02

-.04

-.06

_u ~ ~b

--------I'Z 0 Present data

r-..... -- Refs. 9 and 10

--K ~ ,., ~ r---- [":-...<:

~. V C

/ Va W

"./

---.-J,:J-p--

16

V V--

~ C:

~ v--- ()

8

l-if V

~ o ~

v---

-8

-.1 o .1 .2 .3 .4

CL

(a) M = 0.36.

Figure 13. - Comparison of longitudinal characteristics

for configuration 'Yithout inlet. 0e = 0°.

.12

I

.08

o

.5

.04

o

-.08

-.12

16

8

ct, deg

o

-8

o Present data -- Ref. 11

r---. G

~ r-~---+---+--~---4---+---~~~~---+--~--~.12

f----t-----t--t-+-----+---+---I---/-+

V-----:,lL-I7:---If7I

..:.LI---+--'--+ .08

/,/0 r--r-+--+-+--4~-(~-L-~-~~-+--+~.04

---r.l----' I~

o

-.1 0 .1 .2 .3 .4 .5

CL

(b) M = 1.50. {No /11 l-ef

Figure 13.- Continued.

63

.02

o

C m - .02

-.04

-.06

16

8

Ct, deg

o

64

~~ o I

Present data Ref. 11 Method I r---t-+I~~:nl~,~_~~. -l------l-----t--1 -_--_-

~ - - Method II ,~ Method III

~------~ !---r--

i

I

CL

(c) M = 2.00. (/lit? /~ /~r) Figure 13.- Continued.

.12

I

I .08 l I

CD

.04

I i

1 : 0 I

nJ-

.oz

0

- .02

Cm - .04

- .06

"~ 0 Present data

~ -- Method I r,. -- Method II ~

~ - - - Method III

~ t---~ f::--::9-. --I---''''::::::: ~ b :----t-

~ :Z r-~

D

"--- t---.12

~b

/ [;;~

/ ~~ .08

l&2Vf" 'I~

~

~ IP'

~

.04

--=-u i'J=C F-0'"

16 o

~i=)

0, deg

~ ~~ j:;-

~ k--~

b-= V' ~ ......-<

~ p.:r

J-V

8

o

-8 I -.1 0 .1 .2 .3 .4 .5

CL

(d) M = 2.36. (#o Iw/.d) Figure 13.- Continued.

65

.04 D':::--.. 0 Present data I ~ ],. Method I , -- Method II -

--- Method III

"-..,0 ~ ~ ~ "-::: ~ - ---,-..

-.04

~'::':::::::. ::-0- -----... --0. ----...,J :)

------I

.12

~ p V

~ t:(/ .08

k# ~ i ,

.h # I

~ I

.04

--C ro-c ~ ~-16 o

I ~ :r-::

0', deg

~ ~ :.-

~

~ ~/

~ ~

?

~ I

V I

A"~

8

o

<lr/

I -8

-.1 0 .1 .2 .3 .4 .5

CL

(e) M = 2.86. (;10 /~1 &'1)

Figure 13.- Continued.

66

.016 r-----r::-i--r-,-i-T--r---,------r----,;----..--------. FiJHf"f ~ 8-~ Sh7k<s~ I ....... ,q 0 Present data V~Tr. T;J/ •

. 012 I-t--f>-;~+-+----+--+-J --- Method I - -- - - la-h. to ... ..( - - Method II- " - - - Method III f- /'

.004

o

-.004

16

8

Ci, deg

o

-8 ~ __ ~ __ ~_~ __ ~ __ ~ __ ~ __ _L __ _L __ _1 __ ~ __ ~_~

-.1 -.05 o .05 .10

(f) M = 6.00. ()/o 1\\ l[t-)

Figure 13.- Concluded.

.15 .20

06

.04

.02

,0/

o

T71-'" c"M .... SI1()</c E",. 73M. w~Jte

67

68

.07

~ \) ") \) o () r----~

------I-- \) --!-------' r-.06 <

\) A

0 v

~ f-iZ- p 0 0 0 ~

V--r-- J:\ --.05

( 0 0

0 .04

I:::. 1:::.£ ::. I:::. ~I:::. I:::. - -A -E r--I:::.

.02

0 0< > <> Po <) <? 0 ~ ~ -Method II

.01 Del deg

(:) +5 /' v -5 6- -10 0 -15 0 -,20 o

-.01

0 p 0 0 ( 0 0 0 0 ~ --t---.02

-4 o 4 8 12 16

a, deg

(a) M = 2.00.

Figure 14.- Effect of elevon deflection on pitching-moment-coefficient

increment at angles of attack for contiguration without inlet.

.06

K .05

.04 ~

.03

"

<> .01

o

-.01 0

-.02 -4

0 0 0 0 I-- A --r---~

U o 0 0 t----- r--'--- n

[

A A A A A

v IVV i V <) <

0 uv IV U '-

o 4

a, deg

(b) M = 2.36.

Figure 14.- Continued.

f.-.--~ -~ 0 l)

0

- ~ b--p 0 0

..;r-~ ~ A

..c:. () b r>

v

f-.---i--

Method II r-

oe' deg r-0 +5 0 -5 r-l~ -10 [) -15 0 -20

10 u p

----8 12 16

69

.048 Method II

() De' deg

~ <) <) '7 +5

~ <) 0 -5 .6. -10

~ ::l -15 I--- 0 -20 ~------r---. --

.040

f) <)

<) A A

---0 v <)

~ r--o. --------~

.032

(- - 0

.024 b r., 0 0

1'1. J',. ~ p

~ -!::::..~ 8 ~ ~ ~ L:J.

.016

A 0 0

_ (> O<t <> 0 v f----<> < ) --.008

r., (.) C o CD :) 0 0 (.) ~ v 0

o

- --t--- ---r----.008

-4 L---.

o 4 8 12 16

0', deg

(c) M = 2.86.

Figure 14.- Continued.

70

.032

0

~ '"

.024

I~ .016 '.

.008 ~

tv

o h

-.008

-.016

-4

~ MetJod II De' deg

0 0 +5 0 -5 2. -10 , 0 -15

(.) \) -20 "-

~ I" ~ "" k::: to-- V --I'"'"' ------.

~ 10 rz; 10 l--' V r::- --~ V 11\ 0 ~ -&- r-'-' -~ ~

~

p ~- iZS" b-V lA.----

tv tv V K>- p- RJ IV

h !Q P 0 P b h - t-- I"" P P r----r---t- -r---

o 4 8 12 16

0, deg

(d) M = 6.00.

Figure 14.- Concluded.

71

72

l D

6

4

2

o

o

-4

-12

-16 o

,::. p--

j ~/

I

-.

/ / V

'"

I--f-.--'" _V

-

V r""--l- I--,,-~ --

... v V V

/'

/~ V V/

r-... ~ r-....

r----.. l"-

.2

v ,/

-V o

l---~ .----~-

..-.

- .2

1-r-- -------- ---r- -- t------r-- - ----

24

.-/' ../

/ ./"

---

20

/ ,/'

V --,./'

y

------

. .-/'....-- 16

/ V V

./

V ./ ....--

./

12 a. deg

. .-/'

------8

4

-- - be' 0° DATA -- TRIMMED DATA

o '.

I---r-----~ t---

.4 .6 .8 1.0

(a) M = 0.36.

Figure 15.- Trimmed and untrimmed aerodynamic characteristics

for complete configuration.

L D

6

4

2

o

20

10

-10

-20 -.t

p ./' ~

II

k::: ~ --=

I'-- r-.....

o

I--~ ~ I-- --r- ---

.-r-1-,- t-. i- -/'

V /" t--

/ V r--t--t--r-V

V ,/ V --

V V .-..-k-::

,/ ~ ..... - V

~ .-~ V

--- De' 0° DATA -- TRIMMED DATA

........... 1--- r--

r--. r--. r-. --r---I'-- --l"-I---

.2 .3

(b) M = 1.50.

Figure 15.- Continued.

o

I--.- e -.2 me L

-.4

-

16

V 12

V 8

a,deg

4

o

-4

..... .4

73

74

l D

4

2

o

20

10

-10

-20 - .I

= p-

fl , j

I'

~ V --

............ i'-..

.........

o

o

-----

-.4

~ --r-- --~ '---, i'"-. r---# '--

b ,/ f-" --- - :--;- r--~

V

16

" "../

,..,.. "

12

~ V ." "..- ,-

l.---:::: ~ ::..-v ~ ~~ V V'

~ ~

a,deg

4

p".

o

-4

--- be' rfJ DATA -- TRIMMED DATA ---- METHOD II !TRIMMED)

"" i'-.. r-.. -......... ~ r-----......... ~ t::: t:--- --r------:--r--

.2 J .4

(c) M = 2.00.

Figure 15.- Continued.

l D

6

4

2

o

20

10

-10

-20 -.I

~

1.1' A

II!

~ ~

I~ ~ --,

o

o

---- -

-.4

~f--r--- I--~-

,~ -- t--~ r:--t-- I-

~ V 1---I'::::::: I-r-

16

12

/ t:.-~ ~ ~ 1---....

~ r:::/ v ~

, ~ ~- ....

A ~ V~

8

a. deg

4

.... -o

-4

-" -- 6 _0° DATA T~'MMED DATA

---- METHOD II !TRIMMED)

~ r-...... 'r" .............. r--...... , r-- "-t--.... r---_

1'--""'" ~ F::::: .2 .3 .4

(d) M = 2.36.

Figure 15.- Continued.

75

76

o

6 t--t----t-----t-t--+---+-t---t--t--l-+-_+_j-+_-+_+--+--+----l-_1 -.4

l o

- -II 2~_T-r~/T-~_+-+~~+_~-+~~+-~

"

r--t--t-----t-t--cl--t-+--+-_+-l---+-_+_--- be: 0° DATA ", -- TRIMMED DATA

be' deg 0 r--t--t-----t-t--;:l-......... ~::--+--+-_+-l---+-_+_--- - METHOD II (TRIMMED) ................ ~,

,~" -10 t--t----t-----t-t--t---+-t---t-~~~l-+-_+_j-+_-+_+-+--I----l-_1

........... ~-

(e) M = 2.86.

Figure 15. - Continued.

16

12

8

4

0

-4

a,deg

L D

6

4

o

-5

.04

I-

--I-

.......-

'" 1-

I-'----~ ~

I-- --

~ ~

~ -"-

.08

o

---

r--

-.08 r--1--

- -t-t-- -- I--r--

I 6

-~ I---" !=

V I---V 1-- 1-- -..... 12

V I-' V r-

--- --~ ~-

f--.

8 cr, deg

4

o --- Oe = 0° DATA -- TRIMMED DATA ---- METHOD \I (TRIMMED) - --t--"- I--- '-

'~ 1-- '-t-- _

"" r---r---"I'---.

...........

I'----.......

I'---'I'---I--.

I'---

.12 .16 .20 .24

(f) M = 6.00.

Figure 15.- Concluded.

77

.04

.02

o

.024

.016

cD,min

.008

o o

78

0 I ( ~--'( I I I

..::::-VRef.9 ~(:) 0 Present data "- ---- Ref. 11

''-- -- Method II 0 1:--- --r--~-1---c--1

- l---A I--- ~

Ref. 9 1-- 0 I--- -~-__ -7' ().

0 (

<"'-, "'--0-

"< P'ci-Ref". 10 ~

G 1'--- ......... ~ --- - r- _

f- ---JD

1 2 3 4 5 6

M

Figure 16. - Summary of aerodynamic characteristics for

configuration. without inlet. 0e = 00 •

2.0

o

Be' deg

8 I I I

0 Be = 00 data C Trimmed data

-- Ref. 9 ---- Ref. 11 .

0 -- Method II ./

()

0 ( ~Q 0 - -::::; --- -- -- = [ 0 G r---[P - r--L----

4

5

/ 0

/ [J ./

-5

-10

( [ /

0 ~ V

---- -

-15

0 -= -= @ =-

-8 (~g f-Ef p-

r

t ---

-.4 o 1 2 3 4 5 6

M

Figure 17. - Summary of performance and stability characteristics

for configuration without inlet.

NASA-Langley, 1971 - 2 L-7478 79

II/if) -. Dls~

~~

tD 67 )r-,

. Diy' /"' , D L I...,

{;) I C '--'I'LI' (

,D );;:;>

~ ·[)tfJ s-

·OI2--~

.0 DI ~ ~o)O

t}:;;2 5 -

-,,0 1..- 50

.00) t)

~ 0/ 75""

··End of Document