The effect of cross-section distribution on the static stability characteristics of axi-symmetric bodies at Mach numbers of 5.35 and 6.71

< ~ H

lA) I\)

THHNlSCIlE

HOG~SCI~OOl DELFT VUEGTUIGSCUWKUNDE

BI

BLIOTHEEK

van KAR:MAN

INSTITUTE

FOR FLUID DYNAMICS

r

8

DEC. 1966

TECHNICAL HOTE 32

THE EFFECT OF CROSS-SECTION DISTRIBUTION ON THE STATIC STABILITY CHARACTERISTICS OFAXI - SYMMETRIC BODIES AT MACH NUMBERS

OF 5. 35 AND 6 0 71

by

J oF. REILLY

RHODE-SAINT-GENESE. BELGIUM

TECijNICAL NOTE 32

THE EFFECT OF CROSS-SEqTION DISTRIBUTION ON THE STATIC STAB~LITY CHARACTERISTICS OFAXI - SYMMETRIC BODIES AT MACH N,UMBERS

OF

,

5035

AND'

6071

by

JoF e REILLY

-1-TABLE OF CONTENTS

page ABSTRACT _{• • • • • • •}

_•

_{• • • • • • • •} 1i LIST OF FIGURES _{• •}

_•

_•

_{• • •}

_•

_•

_•

_{• •}

ii1 LIST OF SYMBOLS _{• • • • •}

_•

_{• • • • • •} viii

1. INTRODUCTION _{• • • • • • •}

_•

_{• • • • • •} 1 2. APPARATUS AND TESTS _{• • •}

_{• •}

_{• • • •}

_•

₃ 3. PROCEDURE. • • • • • • • • • • • • • • •

4

4.

DATA CORRECTIONS AND ACCURACY _{• •}

_•

_{• •} 6

5.

RESULTS AND DISCUSSION _{• • • • • • • •}

.

.

, 7

6.

CONCLUS IONS _•

_•

_•

_•

_{• •}

_•

_{• • • • • • •} 15

7 •

REFERENCES _{• • • • • • • • • • •}

_•

_{• • •} 17

ABSTRACT

An investigat~on has been made at hypersonic Mach numbers to determine the effects of cross-section distribution

on the statie stability eharacteristics of bodies of revolu-tion and to obtain the aerodynamic characteristics of these bodies.

All of the bodies tested had the same length and all were circular in cross-seetion. The bodies tested were conic, bi-conic, and tri-conic. The tests were performed at Mach numbers of

5.35

and

6.71,

and at unit Reynolds numbers from

1.5

x 10

5

to 3.2 x 10

5

per centimeter.

The results indicate that under certain test condi-tions a body with a foreeone followed by a frustum or frustum-flare combination exhibits, through the flow mechanism on the upper quarter of the body, an adverse center of pressure travel in the low angle of attaek region (0 to

5

degrees). For a

given moment reference point this yields both stable and unstable trim-points.

Figure 1 2

3

4 5

6

7

8

9 10. 11 -iii-LIST OF FIGURES Description Axes system

Model sketch: basic model: 4 degree cone-f1ares

Model sketch: basic model:

5

degree cone-afterbodies Model sketch: basic model:

5

degree nose-3 degree

frustum-long flares

Model sketch: basic model:

5

degree nose-3 degree frustum-short flares

Model sketch: pressure model:

5

degree nose-3 degree frustum -

4

degree long flare

Conic and bi-conic force model photographs Bi-conic force model photograph

Tri-conic force model photographs Pressure model pho~ograph

Insta11ation pnotographs

The fo11owing t ab1es list the aerodynamics coefficient data, schlieren photographs, shadowgraphs and loca1 pressure coeffi-cient dat~ presented in figures 12 through

45.

Cone half-angle, Flare half-angle Force coeffi- M Re Figures _{degrees degrees cients shown}

x 105/ cm 12-14 4 2, 4, 6 (long) C N ( a) 5.35 3.2 C N (CM) C.P.

( I

ai) Cone half-angle, Afterbody

half-degrees angle, degrees

15-17 5 2, 3, 4, 5 C_N ( a) _{5.35 3.2}

C

N (CM) C.P.

( I

al)

Figures Nose half- Frustum Flare half- Force coef- M Re angle, half-angle, angle, ficients

105/ cm

degrees degrees degrees shown x

18-21 5 3 0, 2, 4 C N ( a) 5.35 3.2 6, 8 C_N (CM) (long) CM (a) C.P.

( I

al) 22-24 5 3 0, 2, 4 C_N ( a) _{5.35 1.7} 6, 8 C N (CM) (long) C.P.

( I

(11) 25-27 5 3 2, 4, 6 C N ( (1) 5.35 3.2 (short) C N (CM) C.P. (11li) 28-30 5 3 0, 2, 4 C N ( (1) 6.71 1.5 6, 8 C N (CM) (long) C.P.

(I

al)

-v-SCHLIEREN PHOTOGRAPHS

Figures Nose half- Frustum Flare half- Angle of M Re angle, half-angle, angle, attack,

x 105/ cm degrees degrees degrees degrees

31-34 5 3 4 0,1,3,6 5.35 3.2

(side) (long) 2, 4

(side and top) Cone half-angle, degrees

35 4 4 (long) 0,3,6 5.35 3.2

Cone half-angle, degrees Afterbody half-angle degrees

36-37 5 2 0,1,2, 5.35 3.2

3,6

S HAD OW GRA PHS

Figures Nose half- Frustum Flare half- Angle of M Re angle, half-angle, angle, attack,

x 105/ cm degrees degrees degrees degrees

38-41 5 3 4(long) 1;3 5.35 1.7, 2.4

2.9, 3.2

Cone half-angle degrees .,

I _{42 4 4 (lon~) 0,3 5.35 3.2}

LOCAL PRESSURE COEFFICIENTS

Nose half- Frustum Flarehalf- Local pres- M Re Figures angle, half-angle, angle, sure coeffi- _{x lo5/ cm}

degrees degrees degrees cients shown *

43-45 5 3 4

r8c9~

5.35 3.2 [p8Ç p

goj

P cos ~ GO [P 8S -p

9~

I: P.. cos ~

CoP. 1 T M q T o

I

a

I

-vii;!~ LIST OF SYMBOLS

The aerodynamic force and moment data are referred to the body axes system (figure 1) with the moment

reference center at

60

percent of, the theoretica~ body lengtho Symbols used ~re defined as follows:

pitching moment coefficient, pitching moment/qSd normal force coefficient, normal force/qS

center of pressure location, percent theoretical length local pressure coefficient, PL/P~

reference "length, cm

model theoretical length, cm free stveam Mach number

2 local statie pressure on model, kg/cm stagnation pressure, kg/cm 2

2 free stream statie pressure, kg/cm

2 free stream dynamic pressure, kg/cm

-1 unit Reynolds number, cm

model reference area (~d2/4), cm 2

sta[gnation temperature, degree:s centigrade

angle of attack (of model centerline), degrees

absolute angle of attack (of model centerline), degrees meridian position angle, degrees

The following data point symbols have been used consistently for clarity to indicate either flare or afterbody angle.

0

0 degrees D 2 degrees

t>

₃ degrees

D

4 degrees (or

Q)

V

₅

degrees Ä 6 degrees 0 8 degrees

-1-1. INTRODUCTION

It ~s general practice to consider some angle of attack program for atmosphèric re-entry bodies and to develop acontrol system for them. However, the selection of some configurations can m~ke the control problem very difficult

under certain flight conditions. The cross-section ~istribution of an axi-symmetric body will determine the statie stability characteristics of that body about any given center of gravity, and will do i t by yielding a particular variation in center of pressure location (dcM/acN) with angle of attack. This variation, to insure stabIe trim-points, must be monatonic. For some

configurations, however, in the low angle of attack region (0

to

5

degrees roughly), i t is not monatonic but first moves forward and then aft as the angle of attack inc~easeso This

adverse center of pressure travel, with movement forward and aft, yields unstable trim-points and can thereby make control of

the vehicle difficult .

This investigation presents the effect of cross-section distribution on the statie stability characteristics df families

of conic, bi-conic and tri-conic bodies. Various configur.tions of cones, cones with flares, cones with afterbodies, and cone-frustum-flare combinations, were tested at Mach numbers of

5.35

and

6.71,

at unit Reynolds numbers from

1.5

x

105

to 3.2

~ 105

per. centimeter. The results provide guidance for configurat1on select10n wh10h w1ll not yield unstable trim-points and the1r attendant problems of anticipatory control system design.

This investigation was performed, under the supervision of Dr Jean J. Ginoux, in partial fulfillment o~ the requirements

-for the diploma of the von Karman Institute o This research was sponsored in part by the United States Air Force, European

-3-2. APPARATUS AND TESTS

2.1 Tunnel

•

Tests were conducted in the hypersonic wind tunnel H-l

of .the von Karman Institute for Fluid Dynamics. The tunnel is

a variable stagnation pressure, pebble bed heated, blowdown

facility (referen~s 1 and 2). The nozzle, ut±lized at Mach

6.71,

iS an adjustable two dimensfonal wedge nozzle which can be set

ta provide Mach numbers from

4

to

8.

At Mach 5.35 a two-dime~

sional contour nozzle was used which gives parallel flow in the test section. The test sections for both nozzles are about the same size (12 centimeters square).

2.2 Models

Sketches of the mode Is tested are presented in figures

2 through

6.

Photographs of the models tested and installation

photographs are presented in figures

7

through 11. The tests

were conducted on force and pressure modeIs. Configuratipns

tested were conic, bi-conic and tri-conic. All configurations·

had the same theoretical length (25.0 cm measured from the theoretical pointed nose to the model base) and were circular

in cross-section. The nose radius was

.5

percent of the

theoretical length for all models with a 5 degree nose cone

half-angle. For the models with a

4

degree nosecone half-angle,

the aótual model length was the same as that of the 5 degree

nose cone half-angle ·models thereby yielding a slightly smaller

nose radius. The coefficient reference length and reference area were selected at the body station 20.5 cm aft of the theoretical nose for all models for comparability.

3. PROCEDURE

3.1 Test conditions

•

The fo11owing tab1e presents the conditions at which the tests were performed:

M T ,degrees 0 P ,kg/cm 2 RE/cm centigraQie 0 5035 213 15.65 107 x 105 5.35 210 21.54 2.4 x 105 5.35 210 26.30 2.9 x 105 5.35 225 30.86 3.2 x 105 6.71 320 31.33 1.5 x lOB

3.2 Measurements and methods,

3.2.1 Foroe mode1s

Aerod1namdc forces and moments on the mode1s shown in figures 2 through 5 were measured with an interna1 three

component strain gauge balance '(reference 3). The ba1ance was attached to a sting support which was rigid1y attached to th:e tunnel sector aystemo Data were taken over an ang1e of attack

~ange from about -5 to +10 degrees. Mo4e1 base pressure and ba1ance chamber pressure was measured with a statie pressure

-5-orifice located Just at the exit of the balanoe oavity on the model base.

3.2.2 Pressure model

A model of one representative configuration

(5

degree nose -

3

degree frustum -

4

degree long flare) was constructed to measure local statie pressures (figure

6).

Twenty-two pressure

o~ifices were located axially along the modelo Data were taken

across an angle of attack range from 0 to +10 degrees and

around the body from windward to leeward meridian (by rotating the model)o The results were reduced to "local pressure coeffi-cients (CP

L) and integrated over the model to obtain the center of pressure location o

4.

DATA CORRECTIONS AND ACCURACY

Based upon balance calibration and repeatability of the data, i t i~ -estimated that at low angles of,.attack the various measured quantities are accurate within the following limits:

eN

• 0 0 0 0 0 0 .+ 0006

CM • • • 0 _{• •} 0 + '0006

-7-5.

RESULTS AND DISCUSSION

For the various models tested, aerodynamic charac-ter1st1cs in the body axes system were obtained utiliz1ng a three component internal strain gauge balance (reference

3).

The "variat1on of normal force coefficient with angle of attack", the "variation of normal force coefficient with pitching moment coefficient" and the "variation of c8nter of pressure location with absolute angle of attack" are pr~sented in figures 12

through 19 and 21 through 30j grouped according to configuration

and test conditions. In figure 20, a typical example of the "variation of pitching moment coefficient with angle of attack" is presented, in this case, for the tri-conic modele

All force data were reduced to coefficient form ,using the body cross-sectional area (S) and the body diameter (d), at the body station 200

5

cm aft of the theoretical nose, as

reference values o

501 Normal force characteristics

For all models the normal force coefficient is shown to increase with flare angle and afterbody angle, as would be expectede Comparison of figures 22 and 28 shows that the normal

force coefficient decreases with Mach number forthese configu-rations. The normal force coefficient is shown to increase with

ine~eased flare length in figures 18 and 250 For the configura-tions with expansion flares (0 and 2 degrees) increased unit Reynolds number is shown to bring a substantial increase in normal force coefficient (figures 18 and 22)0 For compression

flares

(4

to

8

degrees) increased unit Reynolds numQer also increases the normal force coefficient but not as noticeabl~.

5.2 Pitching moment characteristics

The pitching moment data for all models were reduced about the body station corresponding to 60 percent theoretical length. About this momen~ reference center increased flare ang1e or afterbody angle increases the static .tability for all models. Comparison o~ ~igures 23,and 29 shows that stabi1ity also increases with Mach number o F1are 1ength affects the

stabi1ity in that the incremental stability change due to flare ang1e varies directly with flare 1ength as shown by figures 19

an~ 26. The effect of unit Reynolds number, seen by comparing figures 19 and 23, is complex and is itself a key factor in this research. The pitching moment coefficient at any given normal force coefficient does not appear to be very diffe~ent from one unit Reynolds number to the other; the exceptions being the

o

and 2 deg,ree flare angles at high angles of attack,.·.whose

difference~~are present due to the behavior of the normal force

co~fficients. However, a c10ser examination of all data in the low ang1e of attack region shows very great differences. At the higher unit Reynolds number of 3.2 x 105/cm (figure 19), the data exhibits first, at zero normal force coefficient, a stabletnm-pomt (for any other suitably cho~en moment reference point); then as the normal force coetficientincreasea (inc~eased angle of attack) the data wil1 exhibit.an unstable trim-point. Further increasing the normal force cpefficient will again

yield a stabletrim-polnt. This peculiar behavior does not exist for the same configurations at the unit Reynolds number of

~9-1.7 x 105/ cm

(figu~e

23). Furthermore, i t can be shown with figures 16 and

26

thit this behavior occurs Qn all models with a forwa~d expansion shoulder (5 degrees cone with afterbodies,

5

degree nose -

3

degreéfrustum _with long or s~ort flares)

regardless of the configuration following the expansion shoulder.

One clarifying e~ampl~ of this behavior is pr~sented

in figure 20 inwhich the pitching moment coefficient is shown to vary erratically with angle of attack. It can be concluded from this figure (~ypical of the data from all models with expansion shoulders) in conjunction with the corresponding normal force variation ~hangle èf attack (figure 18) that in fact, this behavior is related to the center of pressure loca. tion on the model.

5.3

Center of pressure location

The variation of center of pressure location with

ab~olute angle of attack is, in fact, a representation of the statie stability characteristics of the bodies. For center of pressure location given in percent theoretical length (zero at nose) and with any arbitrary moment reference center, also in percent theoretical l~ngth, the trave~ of the center of pres-sure toward or away from the location of the moment reference center is a measure of the statie stability of the body. For monatonic travel of the center of pressure relative to the nose, trim-points will be either all stabl~ (travel away from nose) or all unstable (travel toward nose) for any given moment reference center about whieh the body is trimmed. Therefore, the figures (14, 17, 21, 24, 27, 30) presenting the "variation

of center of pressure location with angle of attack" show the characteristics of the trim-points for the various configura-tionso For example, figure 14 shows that the 4 degree cone with flares configuration has stable trim-points for the 2 and

4

degree flare angles and unstable trim-points for the

6

degree flare angle. The other configurations present much more compli-cated characteristi~s as described in the discussion of pitching moment characteristics o

The center of pressure moves aft for all configura-tions with increasing flare or afterbody angle o However, the

magnitude, of th~ adverse center of pressure travel is shown t o vary directly with the amount of expansion through which the

flow must pass over the shoulder (5 degree cone with afterbodies, figure 17)0 Flare length affects the center of pressure travel the same way i t affects the pitching moment characterist ics by increasing the incremental change due to flare angle with in-creased flare length (figures 14 and 17)0 Comparison of figures

'24 and 30 shows that the effect of Mach number is a multiple function of flare angle and angle of attacko For the

4, 6

and

8

deg~ee flare angles the direction of the center of pressure location travel with angle of attack is reversed (from movement aft at M

=

5035 to movement forward at M

=

6

071)0

Unfortunately, there 'is also an effect of Reynolds number in this comparison which is bette~ shown by comparing figures 21 and ~4e The conclusion ~hat all trim-points are stable for all configurations shown in figure 24 is invalid for the same configurations at a new unit Reynolds numbero In

-11-are shown to have both stable and unstable trim-points. The effect presents itself in the low angle of attack region, roughly 0 to 5 degrees, and tends to zero at higher angles of attack (the 2 degree flare angle configuration of figure 21 is a non-familial exception). It therefore becomes obvious that a given configuration can have both stable and unstable

trim-points at the same angle of attack and Mach number o Thus,

adverse center of pressure travel itself constitutes the primary difficulty in any control system design which might be applied to these bodies. For example, under the same test conditions, the conic bodies of f1gure 14 (4 degree cone with flares) do not have this adverse center of pressure travel, while the

bi-conic bodies of figure 17 (5 degree cone with afterbodies) do.

5.4 Schlieren photographs and shadowgraphs

Since ReynQlds number appears to be such a significant

parameter in these studies, the confi gurations were extensively

photographed with both schlieren and shadowgraph systems. Some typical examples of these sehlieren photographs are presented in figures 31 through 37. In fig 032 and 34 both side and top views are shown for the tri-conic model. Examples of the shadow-graphs taken are shown in figures 38 through 420

Unfortunately, the appearance of windward and leeward transition can be seen in these photographs at the unit Reynolds

number of

J.~

x lo5/ cm (admittedly with considerable difficulty

in the schlieren photograph dark side boun~ary layer), on a

tri-conic model (fi~s 31 through 34 and 38 through ~l), on a bi-cohie

model (figs 36 and 37) and on a conic model (figs 35 and 42). The shadowgraphs of figs 38 through 42 provide the location of

windward and leeward on a tri-conic model at angles of attack of 1 and 3 degrees for unit Reynolds number of

l.i,

2.4, 2.9 and 3.2

~ lo5/

cmo

The adverse center of pressure travel has been shown to be coupled with test Reynolds number and thereby with the local flow conditions o· However, comparison of figures 35 and 42 for the conic model with figures 31 through 34, 40 and 41 for the tri-conic model shoWS (with the exception of a slight arrestation of the forward movement of the leeward transition point 'with angle of attack, for tlie tri-conic modeIs, at the expansion shoulder) no definitive differences which would ac-count for the adverse center of pressure travel present on the tri-~onic bodies o

505

.

Pressure measurements

With a pressure model, representative of the tri-conic configurations which exhibit adverse center of pressure

travel, local statie pressure data were taken across the angle of attack range at twenty-two positions axially along the

body and at twelve meridians around the bodyo These results were integrated over the body to obtain the center of pressure

location for comparison with the force data. Figure 21 p~esents these results o Analysis of this figu~e shows that the friction

forces which could arise due to differences in local flow con-ditions between the conic and bi/tri-conic bodies, and thereby eause the adverse center of pre~sure travel, in fact play no part. The center óf pressure travel is shown to be due to pressure forces onlyo

-1}-The cross-section distribution of a body has thus far been shown to affect its statie stabi1ity chara~ter1st1cs through the appearance of adverse center of pressure trave1 when a forward expans10n shou1der 1s present ~n the

conf1gura-tion~ The resu1ts of the pressure measurements made 1n tp1s investigat10n show how and where. F1gure 4} presents the

"var1ation' of 1oca1 pressure coeffic~ent increment with ang1e of attack"0 Th1s increment 1s the d1fference 1n the pressure coefficient (PL/P~) at the last pressure tube on the nose,

(body station 85) and the first pressure tube on the frustüm (body station 90) and is therefore an indication of the effect of the expansion shou1dero Data are shown at meridians spaeed

45 degrees apart from windward to 1eeward and at two additional meridians (150 and 165 degrees) up from the windward meridian. The behaviorof~he data with angle of attack 1s as .woul~ be

expected except on the upper quarter of the body. The data for the upper three meridians (leeward, 15 degrees down, }O degrees down) exh1bi t a f luctuation wit h angle of attack which

can be shown to be keyed d1rectly to t he adverse center of pressure travel of this conf1guration •

The "variat1on of norma11zed local pressure coeffi-cient increment with angle of attack" 1s shown in figure 44. In effect, this 1s the data of figure 4} norma11zed by the eosine of the meridian angle ~, (0 degrees windward meridian, 180 degrees leeward meridian). These data now show the component, at each meridian, of local pressure increment which contributes to pitching moment and thereby, center of pressure location. The summation of these results, over all meridians, as a function of angle of attack can be considered as actlng at

the ~orward expansion shou1der on the configurationo This

summation then becomes representative of the variation of pitching moment with angle of attack due to pressure fprces.

Figure

45

presents the " var iation of the summed norma1ized

loca1 pressure c~efficient ihcrement with ang1e of attack".

This fina1 figure shows that tlie variation of the summed values has the necessary characteristics to yle1d the adverse center of pressure travel exhiblted by this configuration (when in fact the complete model integration is performed for figure 21). i t is therefore apparent that the behavior of the flow through

the expansion from the' conic nose to the frustum behind on the

upper quarter of the body gives rise to the adverse center of pressure travel.

, . . . . - - - -- - -

-

-15-6.

CONCLUSIONS

An investigation has been performed in the hypersonie wind tunnel H-l of the van Karman Institute for Fluid Dynamics

at Mach numbers of

5.35

and

6.71

to determine the effect of

eross-seetion distribution on the statie stability eharacteris-tics ofaxi-symmetrie bodies.

The results indicate that:

1. A given body may exhibit completely different statie stability eharaeteristics at the same Maeh number and angle of attaek, depending upon the test Reynolds number. Trim-points may be stabIe (monatonio center of pressure travel) and/or unstable

(advense center of pressure travel).

2. This phenomena is confined to the travel of the center of

pressure on the body due to pressure farces and is not a

friction effect.

3.

Whether or not adverse center of pressure travel exists on

a given mode~ at given test Reynolds number, depends upon

forebody shape. Flare length and angle (over the range of configurations tested) does not affeet the existence of the phenomena. Only those configurations with a forward expansion shoulder exhibit this phenomena.

4.

The amount of expansion through whieh the flow must pass

on a forebody shoulder is direetly related to the magnitude of the adverse eenter of pressure travel present on that body.

5.

Local flow characteristics do not appear_, · to be sufficiently different in the flow visualization photographs to account for this phenomena except for an arrestation of the forward movement, with angle of attack of the leeward transition point by the forward expansion shouldero

6.

The behavior of the local pressure coefficient on the upper quarter of the frustum (or afterbody) behind the e)Cpansion shoulder is the direct cause of the adve~se center df pres-sure travel exhibited on the models ~

7.

The phenomena mayor may not be due to separation on the top of the expansion shoulder, with the available data no positive statementcan be made for either case.

8.

Bec~use transition is present on the top of the body at some angle of attack for all test Reynolds numbers, the process of elimination leads to the 'point of attack for future work. A study directed toward a definition of the leeward expansion-boundary layer interacti on, would,' i t is believed, provide the exact cause of the adverse center of pressure travel phenomenao

-17-7.

REFERENCES

1. KORKEGI, R o-H 0 g The intermi ttent hypersoni c wind tunnel H·l • .

T-CEA TM 15, March 1963.

2. TCEA Staff: Charapteristics of '~CEA hypersonic blowdown wind tunnels H-1 and H-2.

TCEA IN 1, September 1960.

3. CAPELLE. Bo: D~terminat~on des caractéristiques d'une ba1ance interrie à jauge~ extensomdtr1que~ pour la mesure des efforts normaux, axiaux et des moments de tanga ge des maquettes AGARD HB-1 et HB-2 à des nombres de Mach compris entre 5 et

70

T

I

_~

r

I

1~

s

It)

~

S

-.:

~

11') ~

i

~

~

,:

\

~

~

~

U

~

~ ~ I ~

I

~

..., I

"

0

I

~

_~

~

~

~

I..::

~

~

,

~

~~

~ I

~

- - - - ( 9 - - - r---~ r---~ " I ~ " ~

~ ~

~

<:

~

~ ~

~

8

~

~

fI)'t

~'ol ~

~~

~ Cl) ~~

~

~~

,~

~ ~

~

~ ~

Ç) ~~ I

~

~

,~ ~

~

~~

"

~

I

~

r

I

I

~

I ft) ~

~

~

~

I()

~

,:

~

L

~

I

~

I I l

I

I

+

I

I

I

~

I _I ( I

~

_lij "l I -.J

~

"

I

~

~

s

~

I

Ir)

I

~

~ I ~ _I ~ I .. I

~

"

~ 10 " ~

~

I

~

I

~ ~

I

~

\ti u

_s

-... <J 'I

~

I , ).. ~ I )".

~

_~

~ ~

~

_t

~

~

~

~

~

Iq I

~

~ ~

~

_~

~

~ ~

Ct) _I

~

~

...

~ ~

~

~

_"

I

"

S

Ic) " <:) ~

~

~

I

~

_~ "

~

~

~ ~

~

I

~

_~

~

I _~ ~

I

I \J

"

).,. ft)

~

~

~

0 I

~

I

~

~

~

~

~

s

"

~

,

~

~~

_~

_~

"

~

!;)~

_~

I IÖ

~

~~

_\

~

~ I ~

~~

I ~

I

~~

I

~ ~).. ~~ _I

,~

L..--+

I

L::-:'

r=~sc/'"'?

"I

-.

;..----

-

-

--

--A,U. ANfS,U:$ SNOWN AR4

8CXJY NA~F-ANfSJ..e$

---

-

~

2 .oE6'REE F~ARE BOE6REE FJ...ARE

r=",.5CM "I

r--=

.."..5 CI"1

--,

r---

---

-

-2 OE.IfIEE FLAJ'?E _{/"'1OMEII/7 Ct!NrER} ""O~6RE& "c:-.ul~~

I

,-

..,.5CH

----1

I

·1-I

I

-+-

~

-I:

J

I IJ. 'l'.5 C /'"f

I

I /SCN

.. I

o

~êE

FLAA'E

J

2!SCH

.27AS/C /'?~""-: !5 J)EG/?êE NOS~ .3 LJE'G/?EE FRVSTI//"1

FLA.Ré LEN<sTN: /8% T//EO/i'ET/CAL J..EN<$TH

ï

-".5CI"1--j

-

--,

-1' Pë6.1fEE rkAl'?E

--/100é.t... SKeTCH

ALL ANlfL&S SHO WN ARE

BO~Y NA.t...r-AN6.t...ES

~

'---6 LJEG~e,E F.t...A-f'E /'?ONE,Nr CENréR

I

!

,

I

~

~

I • 8. ?'.5C.I'-1 •

I

_I

ï

2 .SC

I'7""""1

I:

/5C~

.1

I

25 C/'-'1 .2 OEGR.FE rLA.lfE

-,

BAS/C ~OQE.t...: .5 LJEG/?éE NOSE, 3 DEGREE FRVSTVM

rLARE' LENGTH: /0 % THEORET/CAL .t...E/VG'TH

~

~ 10

~ ~

! o I - -

~ ~

~ I\..

~ ~

~

K-./

~ ~

10

~

i::

~

~ ~

~ ~

~ ~

10 ~ R ~ ~ ~ ~

.

~ _.... C') ~

~

~ ~~ "

Ó

~

"

_~

... ~

~ ~

(,j

~

~

~ ~

S

~

~

~

~ ~

~

~

~ t)

~

't

~

~ _~ ~

~

11)

S

v,

~

~ ~ ~ ~

~

_~

~ Ic\ ~ "

~

~ _~ "\

&\

q

~

~

~

~

2

_~

"

_~

R

_~ ~ 'l

~

~

_S

~

~

~

~

~

~

~

i~

!:)

~

~

0

.,

~~

~

~~

a)

~ ~

~

~~

~

u ~~

~~

0

+

~~

3èiVl.:! 830 Z - . -3NOJ 830 ., 3èiVl.:! 830

.,

~

ll:

~

\:i ~

~

q:

-...J 3èiVl.:! 830 9

~

Q ~

~

Q:

~

(J

~

\.J -!.. ~ 3NOJ 830 9

_~

I

'"

_~

~

(j 3NOJ 830 .,

À008~31.:!'V ~30 Z

AQOa ~31.:!'V 030

t

3S0N 030 g

~

~

'"

~

~

"

f)

~

~

~

:ti

~

~

~

"

~

CS

~

~

:b:

~

_(Ij ~,-"'" o DEG FLARE DEG NOSE ,3 DEG FRUSTUM 4 DEG FLARE

~

~

~ ~ ::::> I - w ~ W(/) a:: (/)::::>

_«

_Q

o

a:: ...J

~

ZIJ.. IJ.. (!)(!)

tB

_~

ww a a a ::s Lt>M -.J" ~ lij

ft

-' w

~

a 0 ~

~

w

_~

a:: ::::>

~

(/) (/) w a:: Q.

, - - - -

-F~CE /'?OD.t:L

.8

.10

-.2

B4S/C /'?O~EL: -4 ~E6"'l'T"éE C'ON'~ FL.4RE Fk;IIHE L..éN($TN: / 8 % rNFO~er/cA4. LêN67"N /"lACH:

5.

35

Rol!":

3.2 x IOo/cN FLA;&?E ANGLE, L)EG~Ee$

-o

0 o 8 l.e /10

.8 .6

V

h.'

~

."'1-Ö ~ 4: 4J

8

~ .2 V

~

"I 0

~

~

~

-.2

VA~/AT/ON OF /VO~.M'A.l FO~CE COEFFICIENT W/TH

PITCHING I'?OMENT COEF'F'ICIENT

BAS/C' /'-'10.!JE.l: ~ Oët5REE CONE, FLARE

FLARê ~ENG7'#.· /8 % T#EO,l?ET/CA~ LENGTN

/'1ACN: .5. .35" RE:

.3.2

X /05/C /"f I I F~AAE AN6LE, -ZJEGAEES

.

..,.

.2. o

o

Al!1S0LVTe ANGLE OF ATTACk

BAS/C /'-?OOëL,' "'iI OE6RGE CCYv'ë.l F~.ARE

.c'.i-AI'i'E LENtSTII: /8.y. 7"#EOI'i'€T/CA.t.. LëNtFTN

/"'lACH:

..5.

35

RE: 3.

Z

x /Os/C/"1

Nose

AT

OY.1r

/.0

.8

VAflIAT/ON OF NORI"1AL FOflCE CO.ëFFICIENr

w/r#

ANGLE OF ATTACK

BAS/C /"100EL: ,5L/,ê'6ReE CONE, A.c7ê/f'BOOY

A.e-reRBOOY LEN<STH: 65°,,", 7I1EoNE7'lCAL LEN67/1 /"IACH:..5.

35

RE: 3. 2 x /0

'l'

C/"1 AFTt=RBO~Y AN6'-E, ZJE(i",A?éES -~ 0

I~---~---~

~

~

o o o -8 o 8 / 2

PITCN/N6 /VOMENT COëFFICIëNT

a4S/C ;VOOEL: .5" ~E(5RëE COlVé" AFTêRBOOY

AFTé,l;'BOOY LENC5'TH: 65 % T#eO~ET/CAL ~/Vt5rH

I'1ACH:

S.

35

Re: 3.2)( lOS/CM /.0 .8 _ _ _ A,FTERBOOYAN5LE. L)EGREES

1

.2

o

-.2 -.4

~ 1& {,8

~

'I

,

~

~

'--9 ~ ~ ~ ~' ~o 0

i::

Û

0 "J 111 05(#

~

lIJ lIJ

~

~5.2

~

~

\.;: ~ 4 8

~

0

VAlrlA-7ïON 01= CENrE~ OF PRêSSV/'fE LOCATION

WITI-I

A

8S0LVTE

A

NtS.LE 0;:: ATTACI<'

8AS/C /'-100.!?" .. .5 LJE6"REë C'O"VE~ Ar=rEReo~Y

AFre/?so~Y i...ë/V6"r,l-/; 65"% T#Eo/?Er/C.4L L..ëN6TN

I'1ACI-/:

.5..35

RF: 3.2 X /O~CM /VOSE AT 0%1

_r

á A ~ A à à l'S: _{Cs ~ 6 b t s} A A ₅ tE tE is à 3

e-

₂ I!> CD

1

CD ArTE/?BOLJY A/V6.L.e; G:l _OEG';'?EES 0 Je ~

"

8 / 0

/.2

/.0

.8

.'-AN6~E o"c- ATTACK

BAS/C ~o,o~.t.: 5~G'.REE NOSE, .3OEG~Eé: ~RVSTU/"f~ r.!.A/fé F"-ARë .t.ENGTN: /8 % 7#EORET/CAL LENSTN

/1ACH: 5. 3.:5

Re: 3.Zx/O~C/"f

o o

o B

~

~

~

/.2 1.0 .8 .6

VA/E'/AT/ON o,c- NOR/'1AL. F~CE COEFF"/CIENr

WlrH

p/rCNIN6 /'?O/"'lENT COEFFICIENT

8ASIC /"fOOeL.: SOEG"I'?EE NO.s~ .30EtS'flEE F"/?VSTUH, ,&"~A'#?E

P~RE .l.ENGTN: /8 % THëO"'f'ET/CAL.. .l.êNGTN

F~AIf'~ AN6.l.E, .f)ëGR~E$­

o

2 /1ACN: .5.

35

Re: ..3.2x/O~cl"f ₆ 8

o

~I ______ -4 ________ I~~---_+---+_---~---~---~ ~.ë .z o ~B -/.0

-/'O

ANG4t 0"': ArrACK

BAS/C /'?OD.EL: .s/)e6R~ENOSE, 3D.:6REE FflUSTUM. FLARE

ri.ARE i.ENOrH: /8% TNEORET/CA.l. i.ENGrH /1ACH: 5. 3.5

R~: 3.2 x /05/C/'"f

FLA~E ANGLt,

l>ëGREES

~

~

~

~ ~

~

~

~

~

W4R/AT/ON OF CENT€~ OF PHESS(/.RE LOC"qT/ON W/TN

AeSOLUTE ANQ,(.E OF' ArrAC.K

&4SIC 1'10LUil..: SL>EG.I'?éE NOSE, .3L>EGIff'E.E F.R(/STU~ F,(.ARE FLARE LENGTN: /8 % THEO/?ET/CA4 LE/VGTH

/"'lACH: 5. 35

RE: 3. Z x /o6JC/"1

/VOSé A T

O701

_r /VOTE:

?.2 SYI'1'BOL-(J - L>ENOrES CENTE/? OF PRESSt/RE LOC'AT/O/V

bS

{,-f

o

o

2

oarA/NEL> W/TN P/?ESSU/?ë /"fOL>ëL

8 . 6 o 0

t

F.t.A/f'E ANtSLE, PEGREES /0

1.0

.B

.6.

ANGLE' 0':- ATTACK

84S/C /'?OOEL.: S.tJE6REE /IlOSE. 3.tJéGREE FRVSrUI'f, PL..ARE rL.ARE LENGTH: / 8 " TNEO~ET/CAL LENGTH

/'1ACI-/:

5. 35

RE: /.?x IOs/c/'"1

,FLARE AN6LE,

OEtSREES

J

1-...'

~

Û ~

~

a

~

~

l\

~

~

~

/.0 .8 .'-.AI .2. -:2

VAR/AT/ON OF /'VO/{"I'1'A.l FO/'?C'E COEFFIC/ëNT

W/TAI

PITcH/Ne /'1onëNT COEFF/C/ENT

L!JASIC MOLJêL : 5 LJëG~EE NOS':J 3 /)GG~E~ F.RVSTVI"1, FL.A~E

FLARE LENGTH: /8 % THEO~Er/CAL LENGTAl

/'1ACH: 5.

35

R,!": /.?x /O~CI'1

F~A~E ANGLE.

8 _ _ LJE6REES

12

~

~ ~ ~B "I ~ IJ :....

~ ~~

~

"

~ 60 ,

~

~

0

0 ~ 5~ ~

~

~

~

~ SZ

~

~

I.;:

~

-118

\3

0

ABSOLUTE ANtSLE OF A7TACK

Ll4S/C /'-fOLJEL: .s LJEG/?êE NOSE • .3 OEGA'EE FA'VSTVrf. FLARE

~L.ARE L.ENQTh': 18 % TNêORêT/C'AL. L.ENQ7N /"1ACH: 5.35 Rt": J. '7 x /05 /C/'1 ·/VO.sé AT

OYo1

_r

-G G G Q 8 ~ G t:I G 6 2 · 0

f

F~ARe AIVISLe; ,t)EG/?EES 0 2.

.,.

6 8 /0 /-I!

ABSOLVTé ANGL~ OF ATTAC.k; /e></, DEGli'éES

/.0 .8 ~ .6

U

h.'

~

~ .-1

~

~

0 (; _.2. ~

~

~

'-I 0 I

~

~

---~

VA.R/~T/ON OF NO/eI'?A.l ,.cORCE COE,t:"F/C/ENT

W/T#·

ANGi..E OF ATTACK

8/1S'/c ~o,oe.l: .sL)EG~EE NOSE, .30EGri?Ee F~V.sTI./H~ FLARE

PLARE i..ENGTH: /0 % T#EORE"T/CAL LENGTN

I

o 0 o I'1ACN: 5. 35 RE.' 3. Z X /05/cl"1 8 /.2 6

8-4S/C /'-fOLJëi..: .5 OEG/i'ëE /VOSt:" .3 L)EG,.<i'EE FRVSTV/"1, ,cL-'lRE FLARE LENGTN: / 0 % T#EO.RëT/cAL LE/l/qTN

/.0 .8 '" 0 1 1

-~

~

~

.2

o

/'1ACH: 5. 35 R~: 3. Z X /Os/C/"1 -.2 FLARE AN<5i..E. ____ LJEGREES -.+ PlrCN/NG /'1onENT COEF"cICIENr; C_H

7.2

~

~

<:;8 lij '\J

~

~

~

6~

~

"

~ ~' (;0 ~

~

~ 4J 5G

~

~

~

~

.52

~

~

~

-

a

'1'8 0

VAA/AT/ON OF CENTlY? OF PAESSURE LOCAT/ON W/TN

A

BSOi..VTE ANGLE OF ArrACf<

.BAS/C /"10LJEL: 5 DElS;,?EE /VOSEJ .3 L>E6.REE FRVSTUM, FL.A,If'E Fi..A,If'é '-ENtSTH: /0 % T#EOREr/CA"-. LENtSTN

0 /"'lACH: 5. 35 7?e-:

3..2

X lOs/cM /VOSé A T

OYo..R

_r

2. 8 FL.,<9RE ANGLE. .DéG,If'€ES /0 /2

/.0 .8

.,

û

~'

~

.

.,

~ ~

~

~

.2

~

~

\(

~ 0

~

~

~-.Z

-.'"

/'9N<:;..LE o.&" ArrACK

BAS/C' """"oo~ "-: .5 L)E6R~é NoSe_J .3 af"~é "cRu.sru",,",,~ F..LA/i'e

F-'A~E ~EN6T;I/.· /8 Yo rh'EO;f'ëT/CA"- "-ëNGTN'

o

o

/"1ACN: 6.?/ RE: /..5 x /0 ~Cff F~A/i'E AN&L~ LJEGREES - -0 o

o

-.,

o

8

ANt!U.E OF ATTACK., oc::., CJEG/f"ees

1.0 .8 .~

U

k.'

~

.-9

0

K

~

₀ (j .2 lij

~

~

~

0

~

~

-:2 -."1

VA~/Ar/ON OF NOR.I'1'A~ rO.RCE COEFF/C/ENT

w/rN

ArCH/1V6 ~O/'?ENr COEI=FIClëNT

BAS/C HOPE,,: .50EtGr?EE NOSE, 3t>EGrr'ée FRUSTUM, FLAfiE

F~ARe ~ENGrll: /8 % TNEORET/CA'- LENGTN

I ."1 .L.

o

/'1ACN:

6.71

Re.'

/.5x/O'lcl'? 6 -.2 -.4 _ _ FLARE ANG1..E, DEGREES

o

Aa..so.L.ure AN6L..e OF ATTACK

BAS/C /"'IOtJéL..: $I:)éGREE NOSE, .3 bEG'RêE FRVSrVr" F.t.A/'f'E F.t.A/'f'E ,eNtSrH: /8 % TNEOHET/CAi.. LENGTH

/1ACH:

6

.

71

RE: /..5x/O~C/"f /Vose A r

OYo1

_r ----e---GI--~. 8 m C!J tol

o

t

r.t.AHe AIVGi..e, OëGREëS

o

2 6 8 /0 hûVflE

.30

oe

= 0 L>EGREE

oe:

= /

LJéG-'?éé

8AS/C nOLJEL.: 50EGl'féENOSE- 3LJEGFlee FI'fUSTU/"1-~PEG~Ee LONS FL.ARE

/"'/ ... 5. 35

RE

Q 3. Z X /o~CI"'f

oe

=

.e

LJEG'I? EES.I TOP VIEW

&SIC MOiJEL:.5' OE6/'fEENOSe-30E6/ftfE',FRUS7UH- 4iJé"6RIiE LONG' ,cLARE

/"'7

:-.s.

3S

RE ::

..3 .

.e

x /O'lcrr

cJ: :: to; OEG'REes'

BAS/C /"70.oJ!?,4 : 5bE<SRJ!?J!? NOSe--30EGRéé ):'~U$rVM-"'flOJ!?t$/i'ée- L.o/YG I=LARë

/"'1 :: .5. .3 5 RE': 3. Z x

/orc

N

oe = 30EGREES

ex: " 6 Dé"GREES .

BASIC /"fODEt-: "fOé(;!?EE CONE-40eaREt: LONG FLARE

. {J

/"1= ..5.35 ~ '" 3.2 x 10 /en

0 < : / L>EGr?EES

... oe = -ê DEGRIE ES

BAS/C /'0'1001:"-: 5LJeeREE CONE-Z LJéGREE ArréR800Y

,/"?= 5.35 /?E ::3.Zx /OYcr?

oe

=

6~EGREéS

.BAS/C /"'?oOé.L:

..5

oe&~ee CON4'

-.e

P56,qeE A;:re~80PY

/'-'7 =.5. 35 /?E =.3.

.2

K /0 o/CM'

/"1

=

5. 3 5 ex: = / L>E6REE

~

=

3

.

2

X

/O/C/"f

BASIC /'?OL)ë,{.: SLJEGRéE /VosE-3.LJEGREE FRUSTUI'1- ~L)EGNéE L.O'V6 PLA/fé

/-1 ::

5. 35

oe

== /OE6REE

Re

=

2.

-?

X

/O"YC/"1

BASIC /'?OOEL: 50EGRéë NaSt: -

3

Z;éc;Rëë FRUSTUH -

--!

OEG/?EE LON6 F-i.ARE

/1

=:

535

oe

=

3

LJëGREES

RE

=Z.9x

/O~C/'"1

Re

=3.2x/O~cn

BASIC /'100EL:

5

DéGREE NOSé- 3Dé6REE FRUSTI./M-

-<f

OEáR~E LONG F.t..ARE

1'1

=

5.

35

oe.

=

30EGRéES

oe = 3

LJêGREl!S

BASIC /'"'100EL: "10étiREE CONE- 4LJéáRéé LONá .. LARF

~:: 5. 35 RE = .3.2 x /05/ C/'1

.7 1-,,"'

~

~

.5

~

~

~

."1-~ ~

~

8

.3 lI,J

~

VJ ~ .Z

~

'l '\ \J () .1 ~

VAR/ATION o r LOCAL P/?ESSU/?é COErr/C/éNT INC/?éI'1ENT

WITH

ANGLE 0;: ArrAcK

B/iSIC MODEL: S.oE6/?EE NOSE, .3.oEGREE FRUSTU/"1, ~OEGREE rLARE

rLARE LENGThl: /8% ThléO-RéTICAL LE/V6ThI

/1ACH: 5. 35

RE: 3.2 x /O;/crr

/VOTE:

P85 - .L.AST Tt/BE ON NOSé

P..90 - F/,.qST TUBE ON FRVSTUM

o 2 8

AN6L..E Or ATTACK, oe, LJE6R.EES

·Xé/?/OIAN LOCATlOhj LJEGREES ( 0 A///VLJWAR4 /BO LEEWARLJ) ~ . 0 90 lBO /35 /0

~ .~ 11) 0

u

~

ct

.S I 'll

~

~ L - - - J -.3

BAS/C /'-70.oEL: 50~TG.ReE /VOSê, 3.oEGREE

.FRVSTO/"1, ~ LJE6REE FLARé

o

FL.ARE LENGTH: /8% TNEo/'i'ET/CA'-LENGT/-!

/'"1ACf/: 5. 35

RI!.:

.3.2

x I07cn

/VOTE:

Pas - LAST TUBE ON /VOSé

~o -F//?ST TUBE ON FA'é/STt//'1

·~--~--~r---fl--~.r---;r--,~---tr---D---~r---U 90

o 6 8

AN6LE OF ATTACK, oe , .oE6REES

/35 /80 ""1E/?/.oIAN LOCAT/atY, LJé'G,.e(EES ,0 W//f/tJIt/AAOJ /80 LEEWAR.o) /0

~ 11) 0 V

~

I ~

c:e

.8 L--...J

W

"

... ~ \tj _.7 t

~

~

~

"- .Co

~

~ ~

~

.5

(;

\4

~

~

'-IJ 4

~

~ 't ~ \) .3 ~

~

~ .2

t

Q;:

~

~ .I ~

t

~

Cr)

VAR/AT/ON OF SV/"1/"1EO NOR/>-1AL/ZEf) LOCAL. PRêSSURe COEPFIC/ENT INCRE/'"1ëNT WITII

o

ANaL.E OF ATTACK

,BASIC /YfOLJE,L..: S .oEGREE NOSE,..3 OEGRt::-E ÇRt/ST(.//"~J

-1f..DEGREE FLARE

F.L..ARE LENGTH: /8 Y. Th/EORETICAL LENGT#

/'v/ACII: 5.35

RE:

3.2 x /O~CM

/VOTE:

Pes - .t..AST TOtJE O'V NOSE

P!Jo- F/,.<?ST rOBE ON FROSTO/'"1

B /0