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1-7267 HYPERSONIC PERFORMANCE ,STABILITY , AND CONTROL OF MANNED SPACE SHUTTLE CANDIDATES by William C. Woods, James P. Arrington, and David R. 'Stone NASA Langley Research Center Hampton, Virginia Presented at the 48th Annual Meeting of the ViTginia Academy of Science May 5-8, 1970 Richmond, Virginia PEN00065

PEN00065 - NASA · PDF fileblunt forebody and engine nacelles above the wing characterize this con- ... (Cp,max = 2) ... a = 40° to show the interference pattern at the initiation

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1-7267

HYPERSONIC PERFORMANCE ,STABILITY , AND CONTROL OF

MANNED SPACE SHUTTLE CANDIDATES

by

William C. Woods, James P. Arrington, and David R. 'Stone

NASA Langley Research Center Hampton, Virginia

Presented at the 48th Annual Meeting of the ViTginia Academy of Science

May 5-8, 1970 Richmond, Virginia

PEN00065

HYPERSONIC PERFORMANCE, STABILITY, AND CONTROL OF

MANNED SPACE SHUTTLE CANDIDATES

by

William C. Woods, * James P. Arrington, * and David R. Stone*

NASA Langley Research Center Hampton, Virginia

ABSTRACT

The results of analytical and experimental studies to determine

the hypersonic performance, stability, and control characteristics of

vehicles representative of three proposed space shuttle designs -- fixed

straight wing, fixed delta wing, and lifting body -- are presented. In

addition, summary results of flow visualization studies utilizing the

electron beam technique are presented, and, in one instance, an anomaly

in the experimental measurements is related to flow interferep.ce patterns

illustrated by these studies.

In general~ the results being presented indicate these configurations

are capable of achieving their design performance; however, both the force

and moment data &~d the flow visualization results indicate the existence

of flow interference problem areas which require more detailed study. Per-

formance predictions, particularly at angles of attack near CL,max are quite

sound, but trim and stability predictions are shown to be meaningless.

*Aerospace Technologist, Aerospace/Operations Analysis Section, Vehicle

Analysis Branch, Space Systems Research Division

-1-

INTRODUCTION

Analytical and experimental hypersonic performance, stability, and

control studies have for the last few years, focused primarily on high per­

formance configurations designed for some particular maximum range and

consequently operating at angles of attack near that required for (L/D)max

(refs. I and 2). However, the recent space shuttle studies, (refs. 3-6)

emphasizing system reusability for vehicles capable of moderate ranges,

have concentrated on relatively high performance vehicles which are capable

of hypersonic operation at CL,max to reduce configuration heating and its

associated proble~ (high insulation weight, high structural weight, short

material life, etc.). An on-going technology program in the area of space

shuttle operations is being conducted within Langley Research Center's

Space Systems Research Division. To date, a portion of this program has

been directed first toward experimentally evaluating candidate configura-

tions to gain confidence in the feasibility of the space shuttle concept;

secondly, toward flow visualization studies of all candidate configurations

to aid in directing more detailed studies of such problems as interference

flow fields; and thirdly, toward the evaluation of analytical prediction

techniques when applied at the relatively high angle of attack associated

with CL,max entry. This approach has been applied in obtaining aerodynamic

data at high Mach numbers on vehicles representative of three distinct con­

figuration classes being considered for space shuttle application, fixed

straight wing vehicles, delta planform lifting bodies, and fixed delta wing

candidates. Test models were configured to be similar to three orbiters which

were outgrowths of the NASA ILRV study effort - the MSC fixed straight wing

configuration (refs.3 and 4), a delta planform lifting body (ref. 5),

-2-

and a fixed delta wing vehicle (ref. 6), This status report covers

the more pertinent test results obtained as of March 1, 1970.

NOMENCLATURE

b reference length for lateral-directional characteristics, wing span for straight wing vehicles, fuselage length for lifting body and fixed delta wing vehicles

CD drag coefficient, Drag/qooS

CL lift coefficient, Lift/qooS

CL,max maximum lift coefficient

C~ rolling-moment coefficient, Rolling moment/qooSb

C~s effective dihedral, ~c~/~S~ S = 0° and 5°

em pitching-moment coefficient, Pitching moment/qooS~

Cn directional stability parameter, ~Cn/~S, S = 0° and 5° ~ S c~ maximum pressure coefficient -p,max

.Cy side-force coefficient, Side forcel q",S

Cys change of side force with sideslip, ~Cy/~S, S = 0° and 5°

L configuration length

~ reference length for pitching-moment coefficient, MAC for straight wing vehicles, L for lifting body and fixed delta wing vehicles

LID lift-drag ratio, CL/cD

(L/D)max maximum lift-drag ratio

MAC wing mean aerodynamic chord (applies to fixed straight wing configuration)

~ free-stream Mach number

qoo free-stream dynamic pressure

!\x"L

S

y

<5

-3-

free-stream Reynolds number based on configuration length

reference area, wing planform area for straight wing vehi­cles, configuration planform area for lifting body and fixed delta wing vehicles

angle of attack

angle of sideslip

ratio of specific heats

control deflection, positive for trailing edge down

TEST FACILITIES

No ground facility duplicates full-scale hypersonic flight(simu-

lates all free-stream conditions simultaneously). The results pre-

sented in this paper were obtained from two LaRC facilities capable of

simulating lifting entry conditions for space shuttles by duplicating

Mach number and Reynolds number. Figure 1 presents the facility capa-

bilities superimposed over the Mach number-Reynolds number ~nvelopes

generated by various shuttle candidates flying the proposed entry tra-

jectories for both high and low cross range (see, for example, refs. 4-6).

At M ~ 17 + 20, the 22-inch helium tunnel has the capability to duplicate

Reynolds number for all candidates. While the 20-inch tunnel does not dupli-

cate the complete range of Reynolds numbers at M = 6, it does cover enough of

the envelope to simulate expected conditions for low cross-range flight for

both the fixed straight wing and fixed delta wing configurations. The test

medium in both facilities is an ideal gas and, therefore, free-stream condi-

tions are known and test conditions repeatable; however, experience has

shown, as is the case with all ground facilities, that care must be used in

interpreting test results. Nonetheless, with careful analysis of the test

-4-

data and'treatment of the results in the proper perspective, data from

both facilities can be used to predict free-flight shuttle performance.

DISCUSSION

Fixed Straight Wing Orbiter.- During the initial planning stages

of the space -shuttle effort, the fixed straight wing concept was the base-

line design frozen in May 1969, shown on the left of figure 2. A very

blunt forebody and engine nacelles above the wing characterize this con-

figuration. Just prior to the initiation of hypersonic testing, the Aug-

ust 1969 baseline design revision, shown on the right of figure 2, was

completed and included in the test program.- Most of the design changes

were the result of low-speed tests conducted during the interim between

(ref. 7). Some of the more apparent alterations are a rounding of the

body corners (softening the chine lines) to improve high angle-of-attack

handling qualities and reduce buffet due to unsymmetrical vortex shedding,

a reduction of nose bluntness to move the center of pressure aft and in-

creased horizontal tail and control area to provide more longitudinal -,

stability and trim control. While configurationcE:nter-of-gravity location

is still subject to packaging studies, a range of from 0.525 L to 0.543 L

is being considered. The results being presented are based on a center of

gravity located at 0.535 L (0.25 MAC).

Experimental results obtained at Moo = 20, ~ L ~ 3 x 106 on both de-, signs are compared with Newtonian impact theory (Cp,max = 2) in figure 3.

In general, the May baseline configuration had undesirable stability char-

acteristics and did not trim in the test angle-of-attack range. The August

-5-

design revision for improving subsonic characteristics also greatly im-

proved the hypersonic stability and trim characteristics. The revised

design trimmed at a ~ 35 0 with 0 = 0 0, developed a CL,max Z 2.3 at

a ~ 50 0, and had an LID ~ 1.55 at a = 20 0

• Experimental results for

both vehicles agreed quite well with Newtonian theory up to an a ~ 40 0

where both designs experienced an anomalous behavior in pitch. Further

comment on the agreement between experiment and theory will be made later.

The anomaly in the pitching moment is of concern, since it could influ-

ence the vehicle's ability to achieve the hypersonic design trim point of 60 0,

and could be indicative of a flow interference problem area. Flow visual-

ization studies using the electron beam technique (ref. 8) were conducted

in the helium tunnel in an attempt to identify the cause of the pitch

anomaly. Some selected photographs from these studies are shown in fig-

ure 4. A distinct bulge in the bow shock is evident forward of the hori-

zontal tail at a = 40 0 which becomes more prominent with increasing angle

of attack. Figure 5 shows the result of applying photographic printing

techniques to the photographs in figure 4 to bring out the flow details

interior to be bow shock. These prints indicate that the protrusion in

the bow shock is due to a bow shock-wing shock intersection. Hypersonic

studies conducted on simple flared bodies of revolution (ref. 9) showed

expansions originating from body shock-flare shock interactions reduced

flare pressures causing pitchup. Although not visible in figure 5, it is

speculated that a similar phenomenon occurs on this complex shape, that is,

expansions generated by the intersection of bow and wing shocks and reflec-

ted back into the flow field impinge upon the horizontal tail and generate

the anomalus behavior shown in figure 3.

-6-

Additional views of the vehicle were taken to clarify the shock

interaction pattern. Three of these views - bottom plan, front top,

and top rear- are shown in figure 6. These views were obtained at

a = 40° to show the interference pattern at the initiation of pitchup.

Of particular interest~a1:"~_ the shock\intersections crossing beneath the

fuselage forward of the empennage, and the body shock crossing the wing

inboard of the wing tips. Stability and heating problems have been shown

to result from these types of interactions. But it should be pointed out

that complex flowfields of this type are extremely sensitive to model

attitude and free-stream conditions. In the low cross-range attitude

(a "" 60°), the vehicle I s flow pattern differs considerably from that shown

in the figure. In addition, flow patterns at full-scale--free-flight con-

point is that, while ground facility data pinpoint possible problem areas,

the extrapolation of tunnel data to free-flight--full-scale conditions for

configurations generating complex flow fields is not as well understood

as similar extrapolations for configurations with simple flow fields.

The results of control effectiveness studies conducted on the August

baseline design at ~ = 6 are presented in figure 7. These data indicate

the vehicle has the capability to trim to the high attitudes required for

low cross-range operation, even though the aerodynamic trim control

(elevator) was not as effective as impact theory predicted. The anomaly

in pitching moment noted at Mb = 20, a = 40° was not apparent during

these tests; but as mentioned earlier, these complex interference flows

are very sensitive to model attitude and free-stream conditions. General

-7-

performance levels (CL versus a, CD versus a, and LID vs a) for <5 = 0°

were not only predicted by impact theory but were essentially identical

to the Moo = 20 helium test results.

The results of configuration component buildup studies at Moo = 6

are shown on figure 8. As was expected, the fuselage was unstabte, but

the horizontal tail provided the required stabilizing influence. The

most unexpected result was the independence of LID from configuration com­

position at angles of attack above 20°. Past studies on high-performance

configurations had shown fuselage fineness ratio and volume distribution

to be the big performance drivers for entry vehicles. But these previous

studies were on shapes with only minor protuberances, if any. For this

fixed straight wing orbiter, the unswept wing and tail might have been

expected to reduce performance, particularly near a = 20°, by contri­

buting large drag increments. However, these surfaces increased lift and

drag by the same factor such that the fuselage performance potential was

unaffected by the addition of these large areas.

Lateral-directional stability studies (M = 6, fig. 9) showed the

vehicle to be statically stable at the design angle of attack (a = 60°).

Static directional instability was indicated at angles of attack less

than 55°, but analytical studies indicate that the magnitude of the effec­

tive dihedral and vehicle inertias are sufficient to maintain dynamic

stability at angles of attack as low as 40°. Newtonian theory does not

predict the lateral-directional characteristics.

Delta Plan form Lifting Body Orbiter.- Basically, the lifting body

studied has a double delta planform having tip fins rolled out 30° and

toed in 5° for lateral-directional stability, and base elevons for

-8-

longitudinal stability and trim control (figure 10). Configuration

center of gravity, based on vehicle packaging and realistic weight

and balancestudies" is at 72% of the fuselage length referenced to the

virtual origin of the planform.

Control effectiveness tests conducted at Moo = 19, Roo,L .~ 1.2 x 106

in helium (figure 11) indicated the delta planfbrm lifting body orbiter

had a trim capability of at least from CL,max' (a~ 55°, CL ~ .8, L/n ~ .6)

to L/Dmax (a :::: 18°, CL ~ .35, L/D '" 1.8) for the 72% center-

of-gravity location. While this trim capability does satisfy one of the

design goals for this particular candidate (both high and low cross-range

capability) it cou~d also introduce some difficulity. From the ILRV

studies this vehicle was sized to have an overall length of approximately

160 feet with~!~!<>'I1:~_£-? __ ~E':~t long ..... For control~1!!Jacesthis la.r.8-e~,~j;;.his~ .. _. _~_ ... __ . __ . __ . __

system may be overly sensitive (2.8 degrees trim per degree control deflec-

tion) and in the presence of structural deflections due to the high

heating, high loading conditions of entry, it could become difficult to

accurately control trim angle of attack with this degree of control

sensitivity.

Newtonian impact theory (Cp ,max = 2) adequately predicted performance

for 25°<a<55°). Prediction of (L/D)max was considerably high which is to be

expected since no approximations to account for viscous effects were added

to the theory. Trim angle 'of attack was underpredicted consistently by 15°.,

The results of lateral-directional stability tests(fig. 12) indicate

no apparent static instabilities for the lifting body concept throughout

the design operational angle-of-attack range (18° <a<55°). Newtonian

-9-

theory overpredicted stability for high angles of attack (8 = 0°,

ex> 30°). Correlation between theory and experiment was not expected,

but past experience on high performance vehicles had shown a general

trend of underprediction of lateral direction characteristics, as seen

in figure 12 at the lower angles of attack (8 = 10°). Therefore, the

degree of overprediction shown here was not expected.

Flow visualization studies on this configuration revealed a fairly

typical lifting body flow field characterized at ex > 20° by a strong·

detached shqck wave with no apparent internal flow field shocks.

Fixed Delta Wing Orbiter.- Figure 13 presents a three-view sketch

of fixed delta wing orbiter being studied. Longitudinal stability is

provided by the delta wing having swept leading and trailing edges. Wing

. tip fins toed in 5° and rolled out 13.5° furnish lateral-directional sta­

bility and trailing edge elevons provide trim and roll control. Stability

data are referenced to a center of gravity located at 66% of the fuselage

length (nose to base).

Hypersonic control effectiveness tests (figure 14) indicate this

\ configuration, like the lifting body orbiter, can be trimmed from

{L!D)max (ex "" 19°, 8 = 20°) to the design entry angle of attack (ex "" 45°,

8 = 5°). Preliminary heating analysis indicates the 20° flap defle.ction

required for trim at {L!D)max could cause excessive wing and flap heating

for high cross-range operation. The design high cross-range entry tra-

j ectory and accompanying heating conditions were based on pitch modulation

of a vehicle with a theoretical (L!D)max of not less than 2.4. As shown

on the figure, M= 19 tests indicate a maximum L!D capability of 2. To

meet the l500n.m .. high cross-range requirement using the present mode of

-10-

operation,either the vehicle would need redesign to increase LID or

the entry trajectory would have to be modified.

The comments made about the theoretical predictions of lifting

body performance apply here except trim angle of attack was overpre­

dieted by as much as 8°. The fickle nature of trim predictions by

impact theory is exemplified when these results are compared with the

lifting body results where trim was underpredicted by 15°.

Directional and lateral stability characteristies are presented

in figure 15 for the control deflections required for trim at both the

low and high cross-range attitudes. The vehicle possessed lateral sta­

bility over the .test angle-of-attack range, but above a = 20° neutral

stability is experienced. This is no real problem since, in the verna-

cularof . con t rol~s_y_,$_t_ems~t_e_chnQJ,Gffibj,==U---=£-aa..be.~4a~k--.b~~~~utcc..r-e.!l~· .~. ~ .. --.--_ .. ~--.--.-

control tests show this configuration develops adverse yaw due to roll

control. While directional stability and yaw due to roll control are two

separate and distinct parameters, these quantities are tied together in

consideration of vehicle dynamics and handling qualities. Inherent direc-

tional stability, when· it exists, tends to counteract adverse yaw due to

roll control. High angle-of-attack neutral static directional stability,

however, in the presence of this adverse control effect,could lead to con-

trol and handling problems during entry.

Flow visualization studies on the fixed delta wing concept revealed

some interesting interference effects at angles of attack near zero.

This area was not pursued further since it is of no consequence for space

shuttle operation. At the attitudes of interest (a ~ 20°) a two-shock

-11-

system appears to exist but these shocks merge without any interference

effects being generated.

CONCLUDING REMARKS

These results, obtained prior to the Phase B space shuttle effort,

indicate each of the three shuttle concepts satisfies its performance

goals for center-of-gravity positions based on realistic packaging studies,

but both force data and flow visualization studies indicate there are

possible problem areas and expose a need for more detailed studies. In

fact, extensive ground facility testing of all types (force, pressure,

heating, flow visualization, etc.) will be required throughout the Phase B

activity. With this future effort in mind, there are two points which

should be made very clear. First, throughout the presentation, reference

has been made to whether or not Newtonian theory predicted longitudinal

trim and lateral-directional stability. The force and momen~ data pre­

sented on these three different configuration types graphically illustrate

the inadequacy of impact theory for predicting trim, stability, and design­

ing aerodynamic controls for hypersonic entry. This conclusion is not new

nor startling, but space shuttle designers are relying on impact theory,

which does an adequate job of predicting vehicle performance over most of

the operational angle-of-attack range, to design these vehicles. No theory,

simple or complex, will provide an adequate knowledge, a priori, of the

static stability and control of the diverse space shuttle candidate config­

urations. All design judgments concerning hypersonic aerodynamic control,

as well as all static stability and control derivatives for determining

hypersonic dynamic stability and handling qualities, must be based on

-12-

ground facility data. Second, tunnel data does not simply stand alone.

For instance, as flow field complexity increases, aerodynamic charac­

teristics become more sensitive to conditions which cannot be simulated

on scale models in ground facilities. Results must therefore be care­

fully analyzed and treated in the proper perspective to reliably predict

free-flight, full-scale vehicle behavior.

-13-

REFERENCES

1. Arrington, James P.; Ashby, George C., Jr.: Hypersonic Aerodynamic Characteristics Associated with the Evolution of a Maximum Lift­Drag Ratio 3 Entry Configuration. NASA Proposed TM, L-72ll.

2. Lloyd, J. T.: Preliminary Design and Experimental Investigation of the FDL-5A Unmanned High LID Spacecraft. AFFDL-TR-68-24, March, 1968.

3. Faget, Max: Space Shuttle: A New Configuration. Astronautics and Aeronautics, pp. 52-61, January 1970.

4. Final Study of Integral Launch and Reentry Vehicle System, Final Report. Space Division, North American Rockwell, SD 69-573-3, MSC 00192, December 1969.

5. Final Report - Integral Launch and Reentry Vehicle. LMSC Space Systems Division. LMSC-A959837, December 22, 1969.

6. A Two-Stage Fully Reusable Space Transportation System Phase A Final Report. Martin-Marietta Corporation, Denver Division, MSR-69-36, December 1969.

7. Decker, John P. and Spencer, Bernard, Jr.: Low-Subsonic Aerodynamic Characteristics of a Model ofa Fixed-Wing Space Shuttle Concept at Angles of Attack to 76 0

• NASA TN X-1996, April 1970.

8. Weinstein, Leonard M; Wagner, Richard D., Jr.; Henderson, Arthur, Jr.; and Ochettree, Stewart R.: Electron Beam Flow Visualization in Hypersonic Helium Flow. Presented at the 1969 IEEE Third International Congress on Instrumentation in Aerospace Simulation Facilities, Farmingdale, New York, May 5-8, 1969.

9. Fitzgerald, Paul E., Jr.: The Effect of the Bow-Shock-Flare-Shock Interaction on the Static Longitudinal Stability of Flare-Stabilized Bodies. at Hypersonic Speeds. NASA TM X-664, 1962.

24 I "\/'_ . r~'\\" 22" Helium Tunnel ~ ~ High Cross Range

20 I-~ . Test Range Capability

~ L .,-,,'\.'\,l,A. ~ ~ ~ Low Cross Range

, 16 !.... CJ.) ...c E ::::l Z 12 .c u ru :2:

8

4

,//////////~~ o 5 10 115 2'0 25 3b 3~ lo x 106

Reynolds Number, Roo L ,

Figure 1.- Mach number - Reynolds number range of candidate space shuttle orbiters.

May D69 Baseline August D69 Baseline

s s

~C ~ 1-A- --~---: ~ I

Figure 2.- Fixed ~traight wing orbiter.

4

Co 2

o

4.

Cl 2

o

Moo :3 20, Y :3 5/3, RooL ,. 3 x 106

2

em 0

-2

2

~~

~'I4!...o 0 c::tl!fJ ............... ,

Exp. Theory o May bas eli ne

o - - - Aug. bas eli ne

LID I

20 40 J

60 0 1 I I

20 40 60 a, deg 0, deg

Figure 3.- Fixed straight wing orbiter - performance and stability.

a

Figure 4.- Fixed straight orbiter - external shock structure.

00

a

a a '"

Figure 5.- Fixed straight wing orbiter - internal shock structure.

Figure 6.- Fixed straight

=20,y=5/3 PLAN VIEW

orbiter - shock interference pattern.

4

Co 2

o

3

2

CL I

o ...

-I

Moo :8: 6. 0, y lIS 1/5, Rool ~ 3 x , 106 2

/~

/

20 40 60 a, deg

Cm 0

-2

I. 6 '

. I. 2

LID . 8

.4

., 0

-.4 20 40

a, deg

Exll Theory • o o

60

Figure 7.- Fixed straight wing orbiter - hypersonic control effectiveness.

Flap Off 0°

-40°

Moo '" 6. 0, Y '" 7/5, Rool .. 3 x 100

2

f:::. o 0 000

f:::.D 8800000

f:::.°O em 0 j~g 0 Co 2~ e 08 0

f:::.vo . ~8S -I

f:::.f:::.g

e$~~ -2 OQ! e V y! . ! • I, • ,

0 FUSELAGE o FUSELAGE + WING·. . o FUSELAGE + TAil (0 • ~ 1.6[ ~ ~ &I

3 A FUSELAGE + WING + TA'IL (6 • 0) f) S r [1.2 () ~

~ 2~ . L\flL\L\ ..!:.-.st St o £l 0 0 0.0 ~

CL I ~ . ~ ~ B 8 8 88 .4 ~ ~~~

~t : ,I",,, "4 - 0 20 40 601 -. o. 20 40 60

a,deg a,deg

Figure 8. - Fixed straight wing orbi;ter - effect of configuration components.

Moo • 6.0, '1 '" 1/5, Rool :;::: 3 x 106

.002 I

0\ Exp. Theory Flaps

0° ----- 0

Cl~ -.002 ~ em --o to 0 0 e 0 - - -40°

~3 9 0

-.004 I 0

.. 02

.004 I 0

0_ CnP. °l-~fj

I'" 0 0 C .t I I I

-. 004 6 20 40 60

01 L -----:===:=~~ Cy~_ 02 1_

o

-.040

CO c a @I ~ 8 B

2(} 40

a, deg. a, deg.

Fj.gure 9. - Fixed straight ,\ling orbiter - lateral-directional stability.

3

2

UD

0 " 10

-I .05

Cm 0

-005

I.. 0 -. 10

,,5 CL

0

- 5 '0

0

Moo .. 19, r" 5/3, RooL ~ I.. 2 x 106

•••••• e e Ex T -t'.J.---!- _ :=---- - - - ..! J Po heory

,0 0 __ --QJ--n--o ° 0 0 e·---_ 0 0

---'Lo ~' .0.0 _0 0 -_ 0 .0 0 --Q..Q ° 0 - ----

..Q..-o- ..0.... '0 -

l_~l __ -L.._---I __ -'-____ J..-_--J

5 10' 15 20 25 30 35 40 45 50 55

0, deg

Figure 11.- Lifting body orbiter - control effectiveness.

Flap

Off 00

100

.002

Cn 0 ~

Cz ~

- .002

.002

o

-.002' 0

o

--0 00000-0

10

n 19, Y 25/3, RooL ~ 192 X 106

Exp. Theory Flaps 0 0°

0 -- 10°

o 0°00000

° 0

30 40 50

a, deg.

Figure 12.- Lifting body orb~ter - lateral-directional stability.

60

IV\

Ct' .. 5

o o 5 I 0 15 20 25 30 35 40 45

Cl, de90

Figure 14.- Fixed delta orbiter - control effectiveness.

~ ~ I

J .... <0

2l

Cn .~

Cz ~

Moo • 19 •. Y .. 5/3,· RC»L .. Cs x 100

Exp. Theory Flaps

o 5°

o -- -- 20°

.002

o rtT - -0-0 0- 0-~::n 1 I-d~ 0 ---0--0--0

".002

. 002

0 cJ"OOOODo

0000000 0 000 0 0

- .002 L _ _ _________ i ____ ..l

0 5 10 15 20 25 30 35 40 ·45

0, deg.

Figure 15.- Fixed delta wing orbiter - lateral-directional stability.