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Distribution authorized to U.S. Gov't. agenciesonly; Test and Evaluation; OCT 1976. Otherrequests shall be referred to Air ForceArmament Lab., Eglin AFB, FL.

USADTC ltr, 2 Apr 1980

AEDC-TR-76-111 AFATL-TR-76-79

OC.( :.:, ,, .,L,/G

J4:,/ ,. J984:

-S_EP 18 199Q_

STATIC STABILITY CHARACTERISTICS OF THE MK-82/84

AIR-INFLATABLE RETARDER HIGH DRAG MODEL

PROPULSION WIND TUNNEL FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER

AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE 37389

PROPERTY OF U.S. AIR FORC[- AF.DC TF.CHNI'CAL LLBP,~RY

October 1976

YlL Final Report for Period 26 - 31 March 1976

If~'~ ~o¢~mer, t l'Ja: ',...-. :, ~;p;;ro',,~d ~o~" publ;,c te[oas~ ~,~ ('1,%'~" its ~,~fri~)u|ion is unJimiled. ~ T~r/~ ~ D- I~

Distributio~imited to ~overn~t agencies on/~; this/~ report/~ntains inf/~ation on_~4es[t, and e,al/~tionz~" j ~ r e ~ / O c t o b e r 1.~6,. other req~'ts for/Xn,s I ~ ~ ~ , _ Fj__~. ,,~.~.n, I

-"".,d,.,.b- I'. -~ -" -,_

Prepared for

AIR FORCE ARMAMENT LABORATORY (DLJC) EGLIN AIR FORCE BASE, FLORIDA 32542

NOTICES

When U. S. Government drawings specifications, or other data are used for any purpose other than a definitely related Government procurement operation, the Government thereby incurs no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, or in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.

Qualified users may obtain copies of this report from the Defense Documentation Center.

References to named commercial products in this report are not to be considered in any sense as an endorsement of the product by the United States Air Force or the Government.

APPROVAL STATEMENT

This technical report ha.~ been reviewed and is approved for publication.

FOR THE COMMANDER

JOHN C. CARDOS! Lt Colonel, USAF Chief Air Force Test Director, PWT Directorate of Test

ALAN L. DEVEREAUX Colonel, USAF Director of Test

UNCLASSIFIED R E P O R T D O C U M E N T A T I O N P A G E

, REPORTNUMBERAEDC_TR_76_III 12 GOVTACCESS,ONNO.

AFATL-TR-76-79 t 4 T I T L E ( ~ d Subt i t l e )

S T A T I C STABILITY CHARACTERISTICS OF THE M K - 8 2 / 8 4 AIR-INFLATABLE RETARDER HIGH

DRAG MODEL

7 A U T H O R ( e )

R. A. P a u l k a n d C. F. A n d e r s o n , Ago, I n c .

9 P E R F O R M I N G O R G A N I Z A T I O N N A M E A N D A D D R E S S

Arnold Engineering Development Center (XO) Air Force Systems Command Arnold Air Force Station, TN 37389

If C O N T R O L L I N G O F F I C E N A M E A N D A D D R E S S

Air Force Armament Laboratory (AFATL/DLJC) Eglin Air Force Base, FL 32542

14 M O N I T O R I N G AGENCY N A M E ~ ADORESSt'J! d l l f e ren r I rom Con f roH tn~ O f h c e )

16 D I S T R I B U T I O N S T A T E M E N T (o f t h i s Repor t )

READ INSTRUCTIONS B E F O R E C O M P L E T I N G FORM

3 R E C I P l E N I " ' S C A T A L O G N U M B E R

5 T Y P E OF R E P O R T & P E R I O D C O V E R E D

Final R e p o r t , 26 - 31 March 1976 6 P E R F O R M I N G ORG R E P O R T N U M B E R

8 C O N T R A C T OR G R A N T N U M B E R ( s )

10 P R O G R A M E L E M E N T , P R O J E C T , T A S K A R E A & WORK U N I T N U M B E R S

P r o g r a m E l e m e n t 64602F P r o j e c t 5713 ' a s k 0 3

12 R E P O R T D A T E

O c t o b e r 1976 13 N U M B E R O ~" P A G E S

64 15 S E C U R I T Y CLASS (o f rhte repor t )

UNCLASSIFIED

15a D E C L ASSI FIC A T I O N ' DOWN G R A D I N G SCHEDULE N/A

Distribution limited to U.S. Government agencies only; this report contains information on test and evaluation of military hardware; October 1976; Other requests for this document must be referred to Air Force Armament Laboratory (AFATL/DLJC), Eglin AFB, FL 32542.

]7 D I S T R I B U T I O N S T A T E M E N T (o( the ebseract en te red Jn B l o c k 20, i f dJ f ferent from Repor t )

18 S U P P L E M E N T A R Y N O T E S

Available in DDC.

19 K E Y WORDS ( C o n t i n u e on reveres sede t l n e c e s s a ~ ~ d Iden fJ ly by bJock number)

MK-82 bomb o r d n a n c e MK-84 bomb p a r a c h u t e s s t a t i c s t a b i l i t y r e t a r d i n g B a l l u t e s

20 A B S T R A C T ( C o n l l n u e ~ reve rse s ide t t n e c e s s a r y end I d e n t i f y by b l o c k number)

An investigation was conducted in the Propulsion Wind Tunnel (16T) to obtain static stability characteristics of the MK-82 and MK-84 with air-inflatable Ballutes v and selected fin configu- rations. The )~-82 model was 0.442 scale and had slotted fins with 12.5-deg spin wedges. The MK-84 model was 0.264 scale and had two sets of cambered fins. Each model was equipped with a fuse, lugs, and a lanyard pack. The tests were conducted for various model and Ballute roll orientations at Mach numbers from

,OR. 1473 EO, T,ONOF ' NOV 6S ,S OBSOLETE D D , jAN ,3

UNCLASSIFIED

UNCLASSIFIED

20. ABSTRACT ( C o n t i n u e d )

0 . 6 t o 1 . 4 f o r a n g l e s o f a t t a c k up t o 20 d e g a n d R e y n o l d s n u m b e r s f r o m 5 . 1 x 105 t o 6 . 8 x 105 b a s e d on t h e c e n t e r b o d y maximum d i a m e t e r . Model a n d B a l l u t e r o l l o r i e n t a t i o n h a d o n l y s m a l l e f f e c t s on t h e n o r m a l - f o r c e , a x i a l - f o r c e , a n d p i t c h i n g - m o m e n t c o e f f i c i e n t s . I n s t a l l i n g t h e B a l l u t e w i t h t h e B a l l u t e i n l e t s i n t h e wake o f t h e f i n s d e c r e a s e d t h e r o l l i n g - m o m e n t a n d y a w i n g - m o m e n t c o e f f i c i e n t s a n d i n c r e a s e d t h e s i d e - f o r c e c o e f - f i c i e n t .

A F S C II, r ~ l d A F $ T * ~

UNCLASSIFIED

AEDC-TR-76-111

PREFACE

The work reported herein was conducted by the Arnold Engineering

Development Center (AEDC), Air Force Systems Command (AFSC), for the Air

Force Armament Laboratory (AFATL/DLJC) under Program Element 64602F,

Project 5713. The AFATL project monitor was Mr. Paul Shirey. The

results of the test were obtained by ARO, Inc. (a subsidiary of Sverdrup

& Parcel and Associates, Inc.), contract operator of AEDC, AFSC, Arnold

Air Force Station, Tennessee. The work was done under ARO Project

Number P41T-C7A. The authors of this report were R. A. Paulk and C. F.

Anderson, ARO, Inc. The data analysis was completed on April 29, 1976,

and the manuscript (ARO Control No. ARO-PWT-TR-76-63) was submitted for

publication on June 16, 1976.

AE DC-T R-76-111

C O N T E N T S

1.0 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . .

2.0 APPARATUS

2.1 Test Facility . . . . . . . . . . . . . . . . . . . .

2.2 Test Articles . . . . . . . . . . . . . . . . . . . .

2.3 Instrumentation . . . . . . . . . . . . . . . . . .

3.0 TEST DESCRIPTION

3.1 Test Procedures and Conditions . . . . . . . . . . .

3.2 Precision of Measurements . . . . . . . . . . . . . .

4.0 RESULTS

4.1 MK-82 Bomb . . . . . . . . . . . . . . . . . . . . .

4.2 MK-84 Bomb . . . . . . . . . . . . . . . . . . . .

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . .

5

5

5

7

9

10

11

I L L U S T R A T I O N S

Fisure

I.

2.

3.

4.

5.

6.

Q

8.

.

Schematic of Model Installation . . . . . . . . . . .

Photographs of Model Installation . . . . . . . . . .

MK-82 Model Details . . . . . . . . . . . . . . . . .

MK-84 Model Details . . . . . . . . . . . . . . . . .

Ballute Details . . . . . . . . . . . . . . . . . . .

Variation of Reynolds Number and Dynamic Pressure

with Mach Number . . . . . . . . . . . . . . . . . .

Axis System and Sign Convention . . . . . . . . . . .

Effects of Ballute Roll Orientation on the

Static Stability Characteristics of the MK-82,

~M = -45 deg . . . . . . . . . . . . . . . . . . . .

Effects of Model Roll Orientation on the

Static Stability Characteristics of the MK-84

with T2 Fins, ~B = -45 deg . . . . . . . . . . . . .

13

14

16

19

22

24

25

26

38

AEDC-TR-76-111

10. Effects of Fin Configuration on the Static

Stability Characteristics of the MK-84, CB and

CM = -45 deg . . . . . . . . . . . . . . . . . . . .

NOMENCLATURE . . . . . . . . . . . . . . . . . . . .

Page

50

64

AEDC-TR-76-111

1.0 INTRODUCTION

An investigation to determine the six-component static-stability

coefficients of the MK-82 and MK-84 bombs with fabric Ballutes ® ~ir-

inflatable retarders (AIR~ was conducted in the Propulsion Wind Tunnel

(16T), Propulsion Wind Tunnel Facility (PWT). The bombs were tested with

selected fin configurations and at various Ballute and tail roll orienta-

tions. Data were obtained at Mach numbers from 0.6 to 1.4 at a constant

total pressure of 800 psfa. The Reynolds number range, based on center-

body maximum diameter, was from 5.1 x 105 to 6.8 x 105 .

2.0 APPARATUS

2.1 TEST FACILITY

Tunnel 16T is a closed circuit, continuous flow, variable density

wind tunnel capable of operating at Mach numbers between 0.2 and 1.6.

The tunnel is equipped with a plenum evacuation system, and the test sec-

tion is formed by fixed, parallel top and bottom perforated walls, and

perforated variable angle side walls. The test section is 16 by 16 ft in

cross section and 40 ft long. (A more complete description of the wind

tunnel, its operating characteristics, and support equipment is given in

Ref. i.) The location of the test model and the model support system in

the test area is indicated in Fig. i, and photographs of the model installa-

tions are shown in Fig. 2.

2.2 TEST ARTICLES

2.2.1 MK~2 Bomb Model

Details of the MK-82 test model are shown in Fig. 3. The MK-82

bomb configuration was 0.442 scale and represented the MK-82 warhead and

the BSU-49/B stabilizer assembly. The model had a fuse, lugs, lanyard

pack, latch, and spring housing. The stabilizer assembly was fitted

with four slotted fins equipped with 12.5-deg spin wedges. There were

additional fin mounting holes to provide for testing with the fins in

the (+) or (x) positions. The lanyard pack, latch, and spring housings

AEDC-TR-76-111

were similarly rotated; however, the lugs remained in the vertical

plane. A "whisker"-type boundary-layer trip was located near MS 1.0.

The boundary-layer trip was attached to the forebody and consisted of

two rows of 0.007-in.-diam copper wires located approximately 0.1 in.

apart, protruding approximately one wire diameter. The wires in the

second row were staggered relative to the wires in the first row.

2.2.2 MK-84 Bomb Model

Details of the MK-84 test model are shown in Fig. 4. The MK-84

bomb configuration was 0.264 scale and represented the MK-84 warhead and

the BSU-50/B stabilizer assembly. The model had a fuse, lugs, and

lanyard pack.

Two fin configurations, differing in both span and airfoil shape,

were used during the test of the MK-84. The fins were cambered to

produce a positive static rolling moment. The entire afterbody of the

model had to be rotated for testing at different fin roll orientations.

The lugs, however, remained in the vertical plane.

The MK-84 and MK-82 had the same forebody, and, therefore, the same

"whisker" boundary-layer trip.

2.2.3 Ballute (AI R)

Details of the Ballutes are shown in Fig. 5. The Ballute was a

ram-air-inflatable spheroid and was attached directly to the model base.

In this application it was primarily a decelerator , but it provided some

pitch and yaw stabilization as well. In operational use, the Ballute

would be contained within the afterbody prior to deployment. However,

for these tests the Ballutes were already deployed.

The Ballutes tested were made of fabric and were scale models of the

full-size Ballutes, except that no closure plate was attached to the

models. Each Ballute was pear shaped, with four scoop inlets and a toroidal

AE DC-T R-76-111

burble fence near its equator. The Ballute attachment to model bases

allowed for rotation relative to the model base.

2.3 I N S T R U M E N T A T I O N

Model forces and moments were measured with a six-component, internal

strain-gage balance. The model angle of attack was measured with the

pitch sector angle-of-attack indicator and was corrected for sting and

balance deflections resulting from aerodynamic forces and moments on the

model. Electrical signals from the balance and tunnel instrumentation

were processed by the PWT data acquisition system and digital computer

for online data reduction. Balance outputs were also recorded on an elec-

trostatic recorder for monitoring model dynamic oscillations.

3.0 TEST DESCRIPTION

3.1 TEST PROCEDURES AND C O N D I T I O N S

Static force and moment data for the MK-82 and MK-84 stores with

inflated Ballutes were obtained for Mach numbers from 0.6 to 1.4 for an

angle-of-attack range from 0 to 20 deg. MK-82 data were obtained with

the fins in the (x) orientation and the Ballute at roll angles of 0

and -45 deg. The lugs were in the vertical plane and were on the

windward side as the model was pitched.

MK-84 data were obtained with the fins in the (+) and (x) orien-

tation and the Ballute at a roll angle of -45 deg. The lugs were in the

vertical plane and were on the windward side as the model was pitched.

The total pressure was held at 800 psfa, and the variation of

Reynolds number and dynamic pressure with Mach number is shown in

Fig. 6.

The data were reduced to coefficient form in the aeroballistic axis

system with the moment reference at MS 15.416 for the MK-82 model and at

MS 13.166 for the MK-84 model. The axis system and sign convention are

presented in Fig. 7.

AE DC-T R-76-111

3.2 PRECISION OF MEASUREMENTS

3.2.1 Test Conditions

The uncertainties in angle of attack and roll angle are ±0.06 deg

and ±0.10 deg, respectively. The estimated uncertainties in the tunnel

Math number and tunnel dynamic pressure are given in the following table

and are based on a 95-percent probability.

Mach Number

0.6 0.8 0.9 1.0 1.1 1.2 1.4

AM= 0.002 0.003 0.004 0.005 0.007 0.008 0.012

Aq= 1.230 1.930 2.540 3.200 3.960 4.680 5.700

3.2.2 Aerodynamic Coefficients

The estimated uncertainties in the aerodynamic coefficients for the

MK-82 and MK-84 bombs are given in the following tables are based on a

95-percent probability.

MK-82 Mach Number

0.6 0.8 0.9 1.0 1.1 1.2

AC N 0.184 0.125 0.115 0.114 0.124 0.123

ACy 0.149 0.101 0.089 0.081 0.075 0.071

AC A 0.252 0.173 0.179 0.223 0.267 0.257

AC£ 0,072 0.048 0.042 0.039 0.036 0.034

AC 0.242 0.173 0.200 0.257 0.332 0.331 m

AC 0.186 0,126 0,110 0.101 0.093 0.089 n

8

AEDC-TR-76-111

MK-84 Mach Number

0.6 0.8 0.9 1.0 1.1 1.2 1.4

AC N 0.183 0.123 0.109 0.102 0.097 0.094 0.083

&Cy 0.150 0.100 0.089 0.080 0.075 0.071 0.068

AC A 0.243 0.165 0.149 0.141 0.139 0.134 0.112

AC~ 0.071 0.048 0.042 0.038 0.036 0.034 0.033

AC 0.230 0.155 0.141 0.137 0.136 0.131 0.105 m

AC 0.187 0.125 0.110 0.100 0.093 0.089 0.085 n

4.0 RESULTS

4.1 MK~2 BOMB

The effects of Ballute roll orientation on the static stability

characteristics of the MK-82 model at -45 deg roll are shown in Fig. 8 for

all Mach numbers of interest. Normal-force and pitching-moment coef-

ficients had slightly larger absolute values for the ~B = 0 configuration

than for the ~B = -45 deg configuration. The axial-force coefficients

were nearly equal for both Ballute roll orientations for subsonic Mach

numbers. For M = i.i the ~B = 0 configuration had a higher axial-force

coefficient.

The fin spin wedges generated a positive rolling moment on the

MK-82 model, as is shown in Ref. 2. Adding the Ballute produced a nega-

tive model rolling-moment coefficient for both Ballute roll orientations

for M= = 0.6. For higher Mach numbers, only the ~B = -45 deg configura-

tion (Ballute inlets in line with fins) produced a negative model rolling-

moment coefficient.

The side-force coefficient generally tended to decrease with

increasing angle of attack while the yawing-moment coefficient increased.

Both side-force and yawing-moment coefficients generally showed a break

or change in slope at ~ = 9 deg. The reason for this change in slope is

9

AEDC-TR-76-111

not readily apparent; however, it should be noted that the Ballute

stayed approximately aligned with the airflow as angle of attack increased.

Therefore, the changes observed at ~ = 9 deg could have been produced by

the Ballute's moving into the vortices being shed by the forebody.

Rolling the Ballute to SB = -45 deg (inlets aligned with the fins)

generally reversed the side-force and yawlng-moment coefficients.

4.2 MK-84 BOMB

The MK-84 was tested with the ballute at -45 deg roll orientation

for all test conditions. The effects of fin roll orientation on the

static stability characteristics of the MK-84 with T2 fins are shown in

Fig. 9. The configuration with the fins in the (+) orientation had the

largest absolute values of normal-force and pltching-moment coefficient.

The axial-force coefficient was largest for the model with (+) fin

orientation for M = 0.6, 0.8, and 0.9. For M = 1.1, the axial-force

coefficients were nearly equal for both fin orientations. When the

Ballute inlets were aligned with the fins (~M = -45 deg), the rolling-

moment coefficient was either reduced or negative.

The side-force coefficient generally tended to decrease with

increasing angle of attack, whereas the yawing-moment coefficient

increased, as was the case for the MK-82. The slde-force coefficient

was generally larger and the yawing-moment coefficient was generally

smaller for the case with the fins and Ballute inlets aligned, ~M =

-45 deg.

The effect of fin size and camber on the static stability charac-

teristics of the MK-84 store is shown in Fig. 10. For ~ < 6 deg, the T3

fins produced slightly larger absolute values of normal-force and

pitching-moment coefficients than the T2 fins. For higher angles of

attack, the two sets of fins produced nearly equal normal-force and

pitching-moment coefficients. The axial-force coefficients were nearly

the same for both configurations.

iO

AEDC-TR-76-111

The T3 fins produced a larger side-force coefficient and a smaller

yawing-moment coefficient than did the T2 fins. The T3 fins produced a

larger rolling-moment coefficient than did the T2 fins.

I.

REFERENCES

Test Facilities Handbook (Tenth Edition). "Propulsion Wind Tunnel

Facility, Vol. 4." Arnold Engineering Development Center, May

1974.

. Anderson, C. F. and Carleton, W. E. "Static and Dynamic Stability

Characteristics of the Fixed-Fin and Inflatable Stabilizer

Retarder Configurations of the MK-82 Store at Transonic Speeds."

AEDC-TR-75-149 (AD-B007733L), November 1975.

I!

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AEDC-TR-76-111

21,770 (MK- 82) 13.OOO (MK -84)

e,

DIMENSIONS IN INCHES

~B = -45

Front view showing ballute dimensions and roll orientation Figure 5. Ballute details.

22

AEDC-TR-76-111

18.560 (MK-82) I 1.250 (MK -84)

DIMENSIONS IN INCHES

/ /

/ /

/ I

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b. Side view showing ballute dimensions Figure 5. Concluded.

23

AEDC-TR-76-111

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2

0 0.6 0 .8 1.0 1.2

Mo= 1.4

400

q=o, psf

500

200 f S

/

100

Figure 6.

0 0.6 0.8 1.0 1.2 1.4

M®

Variation of Reynolds number and dynamic pressure with Mach number.

24

AEDC-TR-76-111

CJA CAA

, _~LOW ,7

"~ CNA SlOE VIEW

ARROWS INDICATE POSITIVE DIRECTION OF FORCES, MOMENTS AND ANGLES

/ /

~ ~ C m A CYA

CNA

FRONT VIEW

Figure 7. Axis system and sign convention.

25

A E D C - T R - 7 6 - 1 1 1

5TH M. • 0.6 0 [] 0.6 -q5

Figure 8.

12 . . . . . . . . . . . i . . . . i i i

e !

. . . . . . . . . I . . . . . . . . . C~

0 i - T b

I

3O

Cm

2O

10

! ' ! 1 ' i ' !

! ) ~ i i

! i

-30

-2O

C,A

-10

i

i )

I

i F i

I I I

10 0 q 8 12 16 20

K R

a. M = 0 . 6 Effects of ballute roll or ientat ion on the static stabi l i ty characteristics of the M K ~ 2 , ~M = -45 deg.

26

A E D C - T R - 7 6 - 1 1 1

STM M. ® 0.6 0 B 0.6 -qS

C~

o,q : ' i

! i i i ; ........ = ' ..... i... i ........ ~ .....

- [ -

! -0.~

-0.8

-O.t~

0

0.~

0.8

1.2

i

I

I

- - - 7 - - - -

I

i

, i

C~A

Oi

-! 0

T I T T ! I

i I

I

i : ! , ! ,

u B 12 16 20 = R

a. Concluded Figure 8. Continued.

2?

A E D C - T R - 7 6 - 1 1 1

S~M PL h ® 0.8 0 [] O. 8 -qS

12

8

C~ q

3 0

C m

2 0

1 0

- 3 0

-20

C~

-10

lO 0

! T ~ i i , ' ~ ~ t,

' i i ! I , I . ,

i "

---; ....... i ......... ' ......... ~ .....

. ~ ; . . . . . . . ~ . . . . . . . . ~ . . . . . . . . . . __ . . . . . . . . . . . .

i

j : ; b I

I----L-- i ,

t l q 8 12 16 20

e¢ A

b. M = 0 . 8 F i g u r e 8 . C o n t i n u e d .

?.8

AE DC-T R-76-111

SYM M. 0 0.8 0 m 0.8 -45

o.q

CvA 0

-0.4

-0.8

_0.41

0

C,.~

O.q

0.8

] .2

!

C,en

0

- I

I

. ° _ °

_ ° . _ .

/

_ / ~- - - c~ - - - - - -o - - - -~ - c c L

q 8 12 16 20

a( A

b. Concluded Figure 8. Continued.

29

AEDC-TR-76-111

SVM K, ez • 0.g 0 s 0.g -q5

12

8

Cm q

-[I

3O

Cm

20

!0

-30

C.m

- I 0

. . . . . .

L : - i -.-, T ~ , t

L ! t i I

L - - - - L - I _ - - t . . . . . . . . - - - , - -

: ,

' ~ - - ' F - ' - ---i I ~ "

r"

i

i T I

i I i

.Y

I0 0 q 8 12

~W

c. M = 0 . 9 Figure 8. Continued.

1 6 20

30

AE DC-T R-76-111

StM ~ h ® 0.9 0 m 0.9 -~5

- 0 . 8

-O.q

0

C~

o.q

0.8

! .2

i !

I i

i ' i

i .

~ J . . . . . . . . . , ~ . . . . . ~

i

;

i

i

I

I I

C jR I

Ol

-! 0

= , i

i

! t ! t q B 12 Z6

m R

20

c. Concluded Figure 8. Continued.

3]

A E D C-T R - 7 6 - 1 1 1

ST~ M. ** 1.0 -q5

8

Cm

3O

Cm 201

-2O

Cd

-10

12

~ 2 ~ "'1 . . . . . . . t- . . . . . . . O , r ~ I ! ,

, i i __._~_. _~_ ...... +__ I_.J__.

-, i ~ J

I I

i i l e

I

, - - T - - - - [

- ' I - - ° - - - - - - p - - - - - - - - - - , , , - - - - - -

i ,

t 10

-30

t ! l

I0 0 q

d ,

Figure 8.

i I

I

8 12 sA

M = 1.0 Cont inued.

16 20

32

A E D C - T R - 7 6 - 1 1 1

STM K, 13 1.0 -q5

- - - $ . . . . . . . . i . . . . . . . . ;I . . . . . . . . . . ~ . . . . . . . . . . . . I i i

-0.q a

- 0 . 8

-0.q

0

0.q

0 .8

1.2

I

l i

q

I

l

i I I

_ _ . |

I m

i

! ~ - G - . . =

i L_ 1 i

I

T

I B

I i

i

i I

1 I

C jR

0 ~ L I

0 q 8 12 ac R

16

d. Concluded Figure 8. Continued.

20

33

AEDC-TR-76-111

5TM M. o !.! 0 o I. 1 -q5

12

8

Cm q

O~

-q

. . . . . . . . . . . . !

i i

. . . . . . . . . . j . . . . . . . . . . . . . . . i . . . . . . . 4 .... ] l ! I

; I

' I

~ '

c. ---~ _I, ~ ...... ~__ _.~_=, ....

2o' ~~----~---,

- - , . . . . . . . . . . , ~ - i - ~ - l - ~ l -30

-2O

Cd

-10

m I

1

10 0 q 8 12 16 20

a A

e. M . = 1.1 Figure 8. Continued.

34

A E D C - T R - 7 6 - 1 1 1

STH R. O t . ! 0 B !. ] -q5

C~ I I !

-O.q

-0 .8

-o .q

0.~

0.8

1.2

. . . . . . . . . . . . - e -

• t

. . . . ! _ _ _ . t i

_ _ j . _ _ _ _ _ i

I ! ! !

i m J - - - -

J

i

i

i i

C~A

0

-1 t l L I i , 1

0 El 8 12 16

a¢ R

e. Concluded Figure 8. Cont inued.

20

35

AE DC-T R-76-111

STM A. h B 1.2 -q5

-q

'+ . . . . . . . . . . i ........ ! . . . . . . . . . . . . . . ! .... I 8

,.,rmn . . . . . . ---t . . . . 1

- ~ - . . . . . . L -

On I J ; 1 1 l , 1

I

3O

Cm

20~

10

+ i , i +i + i i . ( • ~ : T - - - -

: i i

- 3 0

-2O

C,,n

- 1 0

10 I 0 q

i _ _ _ L ~

; i 1 I ' 1

t 8 12 16 20

acFi

f. M = 1 . 2 Figure 8. Continued.

36

A E D C - T R - 7 6 - 1 1 1

$TM ~1. e~ m ! . 2 -qs

C~ O.LI _ . . . . . . . . . . . . . . . i ..... ! a

. . . . . . I

I i , . . . . ~ . . . . . . . . . . ,- . . . . . . . . . . . . . . . . . . . , . . . . . q - ~ - . 4 - ~ . -

- O . g ' ' '

- 0 . 8

-0.~

C,e

0

O.lt

0 . 8

1.2

I •

I

- - T - - r--- i I |

I E I !

I

i

I

I !

!

I

i i

I 1"

!

I

4 - - - - - - - -

i i !

C~ OI ' J j m ~

-1 q 8 12

~ A

f. Concluded Figure 8. Concluded.

16 20

37

AE DC-TR-76-111

SrMBOL M. oN 0 0.6 0 E] O.& -q5

Cm

I)

-2

Cm

8

6

i,==: =:~ ~,,- I--..,

-12

Figure 9.

-8

C,A

0

q I 0

. J . /

8 12 16 20

~R

a. M =0.6 Effects of model roll orientation on the static stability characteristics of the MK,94 with T2 fins, ~s = J,5 deg.

38

A E D C - T R - 7 6 - 1 1 1

STHBOL H. *. ® 0.6 0 0 O. 6 -q5

0.2

CyR

0

-0.2

-0.8

- 0 . q

C~

0

0.~

0 .8

0.2

CJn 0

- 0 . 2

l i i

l F

i i

i

r - T ~

- - 7 , !

. . . . . . . . • . . . . . . . . . 9 . . . . f

; I :

I

I

t T

I

i [

i

i

i i : I

I i

- - - !

L I

I 8 2

E R

a. Concluded Figure 9. Continued.

J

i

! I !

6 20

39

A E D C - T R - 7 6 - 1 1 1

StHSOL ~ em e 0.8 0 ra O. 8 -q5

q

2

Cm

O~

-2

8

Cm

-12

r

i

i t i

l

I

1 I

!

i

- 8

C,n -q

1

w •

I j ! I

, j

i i ' I

i

T

q 0 q

J

I

I

! 8 t2

=oR

b. M = 0 . 8 Figure 9. Continued.

16

I !

!

20

40

AE DC-T R-76-111

SVmOL K, e. e 0.8 0 m 0.8 -q5

0.2

-0.2

i

i , i

t I

, i

i I

-0.8

-0.~

0

0.~

0.8

i i

-+

i 4 i I

i

i

]

, ! , I

i

I i

i

i

i

I l

0.2

C jR

0

-0.2 0

J

i I

!

I

L_ Z i !

8 12 16 20

=R

b. Concluded Figure 9. Continued.

41

A E D C - T R - 7 6 - 1 1 1

StDeOL M. e. • 0.9 0 [~ O. 9 -45

Cm

-2

8

CM

- 1 2

- 8

C ~

-4

4 f

2 i

O' ~ I

I i '

I ~ . - $ .

i

i

I

I

I

i

f

i

i

I I

61 ;

I

i

l

i

i

X

. . . . ", ~ - . . . . . T--- , !

, l

0 4 8 12.

m R

c. M = 0 . 9 Figure 9. Continued.

i , - - - I ~

, i i i

. . . . | !

I

.... i 16 20

42

A E D C - T R - 7 6 - 1 1 1

SYMBOL H,,, e~ e 0.9 0 B 0.9 -q5

0 . 2 i ~ I i ,

o ' ~ ~ e ' - . . . - ' ~ _ , , , '_ , . . . - ~ ~

- - - - - - 4 . . . . . . * " 9 ,

I ! : ! - 0 . 2 i 1 : i 1 :

- 0 , 8

- O , q

0

O .q

0 , 8

i

- - - - 4 - - - i

' I

1

i

, i t

i E

1

i i , I

i

1-

'1 T

I

I i

t J

0 ,2 1

1 CM I

I

T

[ [

- 0 , 2 J 0 Y

....4 ~ - ~-

8 12

" A

c. Concluded Figure 9. Cont inued.

1 ]6 20

43

A E O C - T R - 7 6 - 1 1 1

STmOL ~. ~, o !. o -q5

q

2

Cm

0

-2

Cm

I

1

! r t i

i |

8

6

q

-12

. I

I

1

I i

- 8

Cd

01

1

i ~ ~ 1

- - i

i 1

•i " - °

i L i I

i

t t

i

f I

1

8 12 .c A

d. M = 1 . 0 Figure 9. Continued.

J

16 20

44

AE DC-TR-76-111

SVMBOt. K, B ! .0 -q5

C ~

- 0 . 2

0' . . . . ! . . . . . . . . . . T . . . . . . . . . . i ...... : i

i . . . . . 4 . . . . . . . . . . . . , . . . . : . . . . . . . . . . . . , . . . . . . . . .

i ! i ' I

- 0 . 8

-O.q,

0

O.q

0 . 8

I i r

! i ; B

. . . . ~ . . . . . . . . . . ~ . . . . . . . . . ~ . . . . . . . . ~ . . . . . . . i

=

i

=

. . . . - I 4 I ,

t i * i ' !

i 1 i

i I

• ? ~ -

J

, !

'- L

l I

I

I

t

F r

i

t I

0 . 2

CjA 0 (

- 0 . 2 0

i

L i

q T

8 12 16 20

=R

d. Concluded Figure 9. Continued.

45

A E D C - T R - 7 6 - 1 1 1

Q I . I 0 I~ I. ! -qs

2

Cm

01

-2

. . . . . . . . . i . . . . .

l

1 ' i

I

! l P

6a ~ : T

4 '

?

1

£ T - 2

l

I I

~ - T

1 I

r I .L

i !

-12

- 8

C,, -q

0

i I

I

r i

i i 1

/ " ! 1 I

' I I I

i i , q 8 12

g A

e. M . = 1.1 Figure 9. Cont inued.

16

I

20

46

AE D C - T R - 7 6 - 1 1 1

STm(]. ~, e, • I . I 0 S I. I -Y5

0 . 2

C~ 0

- 0 . 2

J I i - -

i ! ! I

! 1 I

i I

- 0 . 8 !

-O .q

0

O.q

0 . 8

i

1 i

i

l ! :

~ 1

l , i i

~ T I

L

1

cam o13==~.. ~ .

- 0 . 2

1

----.~ )_..__ . ._.~

8 12 ]6 20 E A

e. Concluded Figure 9. Continued.

47

A E DC-TR-76-111

Sm8~ H. e. B ].~ -qS

q

1 i

0

~ - - - L . - . . . . . . . . t °

J

- 2

I

I

i

. . 4 . .

i

Cm

8

6

i !

q

w

-12

- 8

Cd -q

J . :

~ - - . .4

' I

i i

I i

z 1 I

- 7 I I 1

t

' I i q

] i

L - . _

I t '

I t i

J

8 [2 ]6

f. M= = 1.2 Figure 9. Continued.

20

48

A E D C-T R - 7 6 - 1 1 1

SmB~. P,. eM B 1 .2 -qS

0.2

C~m

0

-0 .2 t

I ! i |

. , . . . . & . . . . . . . . . t . . . . .

I

- 0 . 8

-O.q

C ~

0

O.tt

0 .2

Cjn Oi

-0 .2

i I

: T Y

r . . m ~ .

!

I

' I

i i ! • ±

/ i

i

L

t ;

t i

1 ' !

i ! I

~.....~ ]-.-..<

!

t

0 q 8 12 , E n

f. Concluded Figure 9. Concluded.

] 5 20

49

A E D C - T R - 7 6 - 1 1 1

S T ~ L C0flF H. G T2 0.6 -q5 G T3 0.6 -q5

Cm

t

i . . . . . I . . . . . . . . . . ?, "

2 i

0; r , ~ ' ~ i !

- T .. . . . . . . . i ...... -2

i I

_J, . . . . . . . . . ;,

j i •

T . _ _

I I

J

/

a !

. . . . - 4 . . . . .

i

Cm

8 I " I

i ;

q - - M

1 i

t

= w i

Figure 10.

- 1 2

- 8

C ~ - q

I I

i I i

i

I J I

I

! p

q L 0 q

! t I t

I 8 12

E A

a. M = 0 . 6

1 i

1

"i

16 20

Effects of fin configuration on the static stability characteristics of the M K~4 , ~e and ~)M = -45 deg.

50

A E D C - T R - 7 6 - 1 1 1

ST~BOL CONF ~1. e. e T2 0.6 -q5 B T3 0.6 -q5

0 .2

C ~

0

- 0 . 2

t I

...... l ........... i ......

1 I I

r i

i

- 0 . 8

-O,q

C~

_ I

i I

i

i

T . . . .

I J i

) i

O.q - - ' ~

t 0.8

J

I

i i

0.2

CM

o ~

-0 .2 0

W E E q 8 12 16 20

= R

a. Concluded Figure 10. Continued.

5]

A E D C - T R - 7 6 - 1 1 1

SmBO~ CONF H. e, o 12 0.8 -qS 0 T3 0.8 -qS

q t 1 )

!

2

C.R

O,

-2

I

I T

- t - I

i

i

i

I

) I

J - ~

!

J

. - . , j . . . .

/

- - - - 4 - - * - -

• !

Cm

q

-12

-8

C,~

e

--J I

. i

6

w

Oq

0

i I

I

I I

- - - T - - - - I

q

L m

: T

! n

)

t

k T

! i i

8 12

az A

b. M = 0 . 8 Figure 10. Continued.

T

I . . . - - - . - ~ - ~

I

° ~

i i I •

1

t

t

i 16 2 0

52

AE DC-T R -76-111

STHB01. ¢0NF H. e. • T2 0.8 -qS B T3 0.8 -qS

0.2

C1fl

0

-0.2

J . . . . . . .

. . . . . . . . i . . . . .

j

t ~. i . . . . . . . . . . . . . . . i - ° -

i • !

I ]

~ " ~ . . . .

I

-0.8

-0.q

C ~

0

0.q

0.8

. . . . . i _ _ ~ . . . . . . . . . ! . . . . I z t •

I [

I ~ - . . . . 4.

i

I t

i i

i I i i t *

i i I , I i

0.2

Cj l t

0

-0.2 0

I

q 8

I

1 A

12 16 20

b. Concluded Figure 10. Continued.

53

A E D C - T R - 7 6 - 1 1 1

$rM00L (:fie" R, em • fZ 0.9 -q5 B T3 0.9 -q5

2

Cm

0i

-2

Cm

-12

-8

C,m

1 I

,~r.~~l ~ I

, m . ~ - - o .

t i

- - 4 . . . . . . . . . ~ ~ . . . . .

I I 1

i

8 1

i i t

- - t , i 1 q I T l i

Y

0

! i

, r

q 8 12 acll

c. M= = 0.9 Figure 10. Continued.

16 20

54

A E DC-TR-76-111

S'mBOL CONF ~ e. • 1'2 O. 9 -q5 m T3 O. 9 -q5

e 2 i •

i i

o il: . . . . . . . . . . . . . . . i . . . . . . . . . . . . I . . . . .

-o .2 i

i i

i

- 0 , 8

-0.q

CNt

0

0.q

0 .8

i

i I I

I i

! i

I

I i

i I

~ - ° - _

B

II 1

0.2

CM

01 msdia, I m l ,m

-0 .2 0 8 I2

"It

c. Concluded Figure 10. Continued.

16 20

55

A E D C - T R - 7 6 - 1 1 1

sre~OL CONF ~1. e 1'2 I . 0 -qS m T3 ! . 0 -q5

q

2

Cim

0

-2

8

Cm 6'

q

-12

-8

Cd -q

I f I

t

- I . . . . . . . i ....

1

! l

. . . . t . . . . . . .

; ]

% r

t

t

J i

j

I

~ . . - . e . - - ~ - . , ~ _ . . _ , , ,e . , ,_ . ~

! !

i

I

. . . . F _ _

Z

I I

I

, - ' T - - -

t !

I

8 12 ez R

d. M. = 1.0 Figure 10. Continued,

16 20

56

AE DC-TR-76-111

STNBOt. CONF e,,. q~ • T2 1.0 -tlS • 13 I . 0 -qS

o.2 i

ul i ; i

I i

. . . . t . . . . . .

C~

- 0 , 8 !

-0.~ I

o i

I 0.q

0 , 8

i ! i I

t

i

I , I

v "(' I

I

0.2

Cm 0

-0.2

I ±

m

w

r

0 q 8 12 16 20 ~R

d. Concluded Figure 10. Continued.

57

A E D C - T R - 7 6 - 1 1 1

sn~oc CONF ~. • ,T2 !. ! -q5 13 i'3 I. I -q5

Cm

2

O;

-2

8

Cm.

q

-12

- 8

C~ -q

T

. . . . . . . . . . . i _ . o

t

I

! i

J

t

l I ' © l L - . . ~ , l a i -

r

I L

O,

J T ~ _ ~ . I ; i

I

J

I

f

!

I "1

P t t

4 I i

q l [ I I I 0 q 8

0. M . .

Figure 10.

ml

12

4z A

= 1.1 Continued.

16

-t

20

58

AE DC-T R-76-111

STHB01. CONF H, e, • 12 t. I -~5 • T3 I. i -~5

0.2

C~

0

- 0 . 2

- 0 . 8

-0.q

C ~

0

0.~

0 .8

0.2

I

I

"i i

t * ° . . . .

t 1

P i

t !

t 1 i ! i

Cm

0

- 0 . 2 0 8

! 12 16 20

~A

e. Concluded Figure 10. Continued.

59

A E D C - T R - 7 6 - 1 1 1

SrMBOL (9 B

CONF T2 T3

1.2 1.2

-q5 -q5

i

0 i :

,+

- 2 L

l i . . . . .

1

i

[

t *~ l - - "

~ . . j . . . .

i

I

. . . . . i . . . .

i i i

i

i i

C~

-12

8 i

--4 !

61 L

i t

i

! ~ L v

p o - !

1

-4

w • I i

~ - J L . . . . . . . .

i

I

i

V

- 8

C I A

[ q

0 I

I

8 E A

1 I

. . . .4

16 20

f. M . = I ~ Figure 10. Continued.

60

A E D C - T R - 7 6 - 1 1 1

SYI,IBOL CONF' II. q~ • T2 ! . 2 -tJS rn T3 1.2 -MS

0 .2

0

- 0 .2

-0.8

-o.q

C~

O,q

0.8

0.2

EIA 01

-0 .2

I i I I ; I I

i

. . . . . . ), . . . . . . . . . - . ~ . . . . . . . . . 6 . . . . . . . . . . . • . . . . . i

I i - - m . t ~ - - ,

t l

i

i

4. . . . . .

,+

i

i

i I 1

L - - - - - - - - 4 -

I t

t

. . ~

l

I i

L

- - - - - !

0 q

I

I

8

f. Figure 10.

l

i I

12

T

I 1 I

i i t

6 " R

Concluded Continued.

20

61

A E DC-TR-76-111

STM~t. C~IF ~ 0 T3 I .q -qS

q

2

Cm

O,

-2

8

Cm

q

-12

-8

Cd -q

0

I

i I

Y J

J I

i i I l

]

I ....

i

.. L ......... 4- ....

; I

r r

I .._+ . . . . . . . I' ~ -

i I i

i i

tl 0

I

u - T ~. ....

b I

!

J

J

I t

~ t

I

I

i I

t t i

t

i I I

I l

8 2

~R

g. M =1.4 Figure 10. Continued.

I ! L ! i L I I

l

i

16 20

I

62

AE D C - T R - 7 6 - 1 1 1

STHBOL CONF H, *m m T3 !.~ -qS

0.2

C~ 1 I ~ . . ~ . . 4

0

-0.2

. . . . . . . . . i

| I

I t I

] i i

- 0 , 8 r

-O.q

C,~

0

O.q

0 . 8

, I

[ t

- t - I I

b ! J

I ! I ! |

!

i '

I I

q I i

Cjm

0.2

0 } - . . ~ . - - . (

I . . . - . ( p - - -

~ L

-0.2 0 q 8 12 16 20

~R

g. Concluded Figure 10. Concluded.

63

AE DC-TR-76-111

CAA

C£A

CmA

CNA

CnA

CyA

d

F A

F N

Fy

M£

M m

M n

M O0

MS

q~

Re

S

~A

*B

OM

NOMENCLATURE

Axial-force coefficient, FA/q=S

Rolling-moment coefficient, M~/qSd

Pitching-moment coefficient, Mm/q=Sd

Normal-force coefficient, FN/q S

Yawing-moment coefficient, Mn/qSd

Side-force coefficient, Fy/q S

Reference length, maximum diameter of model centerbody, 0.3958 ft

Measured axial force, ib

Measured normal force, ib

Measured side force, ib

Measured rolling moment, ft-lb

Measured pitching moment, ft-lb

Measured yawing moment, ft-lb

Free-streamMach number

Model station

Free-stream dynamic pressure, psf

Reynolds number based on d

Reference area, 0.1231 ft 2

Model angle of attack, deg

Ballute roll angle, deg

Model roll angle, deg

64