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https://ntrs.nasa.gov/search.jsp?R=19660006100 2020-03-18T03:17:51+00:00Z

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REPORTNO. a&37

PAGENO. 2

No DISCUSSIOI QF m. . . . ... . . . . . . . . . . . . . . . . . . . . . . . . .14 A. kmx2-c StaCiUty laalyeie

1 . SPrary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2. Configuratioa.. . . .. . . . . . . . . . . . . . . . . . . . . . . . . .14

5 . Freeentation of Predicted Coefficients . . . . . . . 19

1. ~......................................215

2. Colriiguratioa Descrlptlam . . . . . . . . . . . . . . . . . . . -25 3. M S C U B ~ I ~ or 1i~~.....................25

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REPORTNO. CR-wn

PAGENO. 3

5. Resent;*ion of Finrl Predicted Pressure Coef'ficientr. . . . ... . . . . . . . . . . . . . . . . . . . . . . . . .33

1

c . - =eperei- study. 0 0 035

1. wnrary. 0 0 0 0 0 . . 0 0 0 0 0 038

8 I I P I 1

c. MsP-si- =w. . . . 0 0 0 0 0 054

t * 0 - o w 0 1

uNG-TEyco-IK)uQHT, m. REPORT NO. a-3

PAGENO. 4

VI. LIST c8 RmEmCEs. ................................. 56

A. her-c StabSllty Ma. ............... ......7 O

D. Trajectary m c e Analysis IMa........-......U? 0

I)(. ABsmncr. .......................................... *m

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REPORTNO. wU3A cR-66037

PAGENO. 5

1 5 Aerodyaapic data on a law fineness ra t io 25. half w e sphere-

cone reentry body are presented cld iurrctlozm of Bhch number, Reynoldr

mber md # of attack, and are used 88 inputs in a tmJectory analyst8

study. "he aerodymmic data presented include force and moment derivatives,

bee pressure snd skin f r ic t ion data, a d e a t i r k Of the dyrrcuic

rrtabillty for Mach numbers up t c (H) 26. Also imluded a detailed

prerrsure distribution psalyais for Mach numbers (M)? 4 and angles of attack

up t o 15 degnes. Thee data vere obtained from a compilation, comelotion,

and interpolation of rury data reports from several sources.

AB an aid in the selection of the mi- entry path &e I

copynaurate with impact range requiraKnts, mdnal Scout launch vehicle

performnce in the fonn of bumout range versus bummut f l ight mth w e is

preeented along w i t h iapact di8per8iOn as a function of entry m e . A

typical nollliml tra3ectory and an accuracy -lysis showing the burnout

azd Impact deviations attributable t o individual error sources are also

presented.

A d l g i t a l computer reentry traJectory otudy MB caducted t o

establi8h the mst farorrble center of gravity location ead t o detcrmlne

the individual effects of t ip-off, ~LBB uabalsnce mad center of gravity

offset. Tbe effect of c.g. location and of each of the imlirLdup1

disturbances on the angle of attack envelope is shovn.

offset vlii fo- t o have a pnz-ticululy dverrc effect on the angle of

Center of gravity

attack history.

b

0 - S O S B 1

REPORTNO. a-66037

PAGE NO. 6

C

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Tbt pitch frequency for the spinnlng body wa6 detedned for

the n-1 trajectory and reveral off-namirurl casee. Although roll-pitch

resonance was not experienced for any of the caeee considered (tbere wee no

roll lock-- or catastrophic yew) conditions are! identified vhich could

read+, io severe mgahr m;;tions b e to lock-in.

t

e

c LING-TEMCO-VOUGHT, INC.

IM'RODUCTI ON '

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REPORTNO. a-66037

PAGENO. 7

Among t h e conf'iguations most acceptsble for re-entry vehicles

are spherical ly t ipped conical frustruns. These a r e basic aerodynamic

shapes and a s such have been the cibject of extensive aerodynamic research

f o r a number of years. A considerable amount of data have accumulated f o r

a large range of parameters, but a survey shows t h a t many information

voids s t i l l exist.

An extensive l i t e r a t u r e survey was conducted t o gather a l l

avai lable infannation pertaining t o t h e aerodynamic properties of sphere-

cones i n an attempt t o present in t h i s report accurate aerodynamic

charac te r i s t ics of a 25. half angle spherically blunted cone. Thk data

presented w e r e obtained from a correlation and interpolation of data fran

many sources, including theore t ica l resu l t s .

A s an a i d i n t h e selection of nominal burnout conditions, an

estimate of i m p a c t range dispersion a s a function of nan ina l entry f l i g h t

p a t h angle was made using previously established "Scout" burnout e r rors -

On t h e basis of t h i s estimate, a nominal entry angle that was compatible

wi th t h e impact dispersion requirements was selected and a nominal boost

t r a j ec to ry was established.

was perfoxmed t o re-establ ish burnout deviations. On t h e basis of these

burnout deviations an improved estimate of t he impact dispersion was

established.

An accuracy analysis of th i s booster t ra jec tory

U s i n g t h e aerodynamic data established herein, a six-degree

of freedan d i g i t a l computer study was conducted t o invest igate t he e f fec t

of var ia t ions i n center of g,ravity locat ion on t h e dynamic behavior of

UNG-TEMCO-WHKIHT, INC.

I REPORT NO. m a 3 7

P A G E N O . 8

I I

1 I I 1 I I I I 8 t II 1 I 8 I

CA

o(-0 cA

cAf

0 C A

CM

c M t x

CN

REPORTNO. m-66037

PAGE NO. 9

LIST (3Br SYMBOIS

- Integrated forebody pressure drag coefficient measured along axis of symmetry, not including base drag or skin friction d=g,

Fzrebody I)resswe mi&/ -5 '?r Pm #s

- Integrated forebody pressure drag coefficient ab zero angle of attack, c A, - c% - CAP, or

- Bsse pressure drag coefficient, equal to [- cpb S b b ]

- Integrated skin friction drag coefficient measured abng axis of symmetry,

' Skin Friction Drag/' -5 8 Pa $S

- Total drag coefficient measured along axis of symmetry, cA + c% + cAf

- Pitching moment coefficient measure about the moment reference, Pitch Moment / .5 XP- J s D

- Pitching moment coefficient variation with angle of attack at a- 0 , i.e.

- Pitching moment coefficient variation with pitch velocity rate, i.e.

, per degree or per radian

- Normal force coefficient measured n nml to the axis of symmetry, Normrl Force / .5 Zf P, 2 s

% oc

C P

cP*

9, C

pb C

C P# = 0

p a = 0 C

C %

D

h

I

5 K

PAGENO. 10

- ~ase3 pressure coefficient, (Fb - P, )/q- .

- surface pressure coefficient presented as e function af 7 .

- Circuaferential pressure coefficient at a m r i d i a n engb m a sharp cow at angle of attsck.

- Pressure coefficient on win- meridian, = 0, at a?Igb of attack on sharp cares.

- sharp cone pressure coefficient at zero 8n&b of attack

- Pressure coefflclerrt at 618 and

given by tables of ibpal or Sims (Reference 4).

"Tangent Sphere-Cone" Ipethod vithaut the cross fluw modiflcatian.

obtained uSiLlg tbe

- Mfference betveen C st (s/R>r spd CP#, 1.e. pn:

- Reference Isngth, rmutiwmr diameter of Sphere-~one body, 2.5 ft. I

Q r

Ra R

S

6

1 S

sb

V

x

loc

BASA cR-6Cjon REPORT NO.

PAGENO. 11

- Free stream Mach number

- Msch IllllPber behind normal shock

- ~ e e stream s tat ic pressure, -/ft

- Pressure ert stagmtiosr point behind normal shock, lb/ft2

- Point, located on sphere-cow by coordiaates s/R and JI!

-surface pressure on sphere-ccme at polnt p(s/R,#), lb/ft

2

2

ar spin frequency

2 - Averaged base pressure over b8Se -6, lb / f t

- Free strewn dyncPaic pressure, l/2 XP, 8, U/f't2.

- %to or C- oi pitch gttitude with time, aeg/eec. - Axisymnetric radial body coardinate

- FkynoXds mrmber,

- Radius of spherical nose on sphere-cone bodies, ft.

- Reference mea, .-, ft

- Mstsnce alaag a meridian line (points o f constent I)

W L P

nD2 2

loeasured fran the intersection of the axis of symetry t o the p o w p(s/R, #), ft.

- Mstance along a nrerldlan path measured ~VCQ the stagnation point op a ~ ~ s p b r e to the point p ( ~ / ~ , f l ) 00 on the hemispkre, ft.

2 - Area of base wer which Fb a c t s , ft

- Tkxrmalized distance t o the tangency point where pressures l a the canlcal overexpansion region reach the sharp COLY value correspmdiog to a cane angle

- Free stream velocity, ft/sec.

- Distance measured alaplg ards of syraretry Frap m d e l baee t o the mapcnt reference center (center o f graety).

PAGENO. 12

- Distance measured a l w ruds of synretry Wan model base t o the Intersection of the integrated force vector and tbe axis nf sylametry, tt., positlve upstrecrpp.

- Mstunce measured fran the axis of symaaetry t o the inter- secticm point of the Integrated force vector and a llxm n d to tbe exis of‘ sgmpetry passing thraugh the mament reference, fi. ( ~ e e Fig. 1).

- Distance frau axis of s m t r y t o t k center of gravity alc~g the Z - s x i ~ .

- Angle of attack, deg.

- The angle of attack for oaxirmma pressure on the windward

- Included angle un hemisphere defined by s/R.

- Ratio UP specific heats considexed constarit (1.e. perfect

meridian of sharp cone, Reference 62.

w), X = 1.4 for air; orr, flight path angle, deg. .. - Angk & f m d by equation 6 , page 31.

2 - Pressure integration ordinate, ( r / R ) . - Cone semi-vertex angle, degrees car radians.

- Angle between the vertical Kindwssd m e r i d i a n plane and the

- Free stream air density, l b 8ec /ft

- ~bs0l.ut.e viscosity of m e stream air, ~b sec/ft

Illerldian p b n e passing thruugh the point p( s/R, # ) a

2 4

2

- Included angle betweten the stagn&ion velocity vector and the conrical ray rying along the meridian line definrrd by points cb canst- 6.

- Ratio of roll a r t i a t o pitch Ishrtia, I& = 0.762.

- Xon-spinning body pltah frequency divided by the spa A.eqUaWY,

I

P

- Spinniag body high pitch Frequency

-n2 - Spinning body low pitch frequency

- Correlation coefficient between velocity and altitude errors.

- Comelatioar coefficient betveea velocity and path angle errors. ?A"N

- Cmrehtiorr coefficient between sititude and path a n g h errors.

Q M i a

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REPORTNO. -31 I ,

PAGENO. 14

a..,.. PAGENO. 15

below according t o t h e i r content, i.e., whether the report contains ex-

p e h e n t a l data o r t heo re t i ca l results, o r a development of a theore t ica l

method.

a. Estp erimental Data Reports

A- s m m a ~ 0%' t he contents of reports containing experiment

force and moment data is presented i n Table I, Par t A. The table presents

i n semi-graphical fonn t h e experimental parameters presented i n each report. 0

A review of P a r t A of Table I w i l l show that t h e bulk of t he

experimental literature presents data f o r cone ha l f angles of 20 degrees

and less and bluntness r a t io s greater than 0.1.

panuneter is not presently available which w i l l correlate bodies of p i f f e r e n t

Since a unifying s imi la r i ty

cone angles and bluntness r a t io s , t h e use of much of t he experimental data

was severely restricted. Nevertheless, it was possible t o glean frcm t h e

reports suf f ic ien t data t o establish with reasonable accuracy the aero-

dynamic coeff ic ients .

b. Theoretical Data Reports

Park B of Table I br ie f ly outlines t h e reports presenting

r e su l t s of a theory with d i rec t application t o pointed o r blunt cones.

These r e s u l t s include nunerical solutions, closed-fom solutions, graphical

correlat ions, and empirical design charts

4. Discussion of Theoretical Methods

During t h e study, several theore t ica l methods of calculation vere

Most of t h e theories were found t o be applicable on a very investigated.

limited basis f o r blunt bodies of

were considered are as f o l l m :

small fineness m t i o s . The theor ies which

8 0 - some 1 LING-TEMO-VOUGHT, INC.

REPORTNO. CR-37

PAGENO. 16

a. L ighth i l l Slender-Body Theory

b. Von Karman - Moore Linearized Theory

c. Basic Shock-Expansion Theory

d. second-Order Shock-ltpansion Theory

e. Modified Newtonian Flow Theory

f . Method of Characterist ics

a . The Lighth i l l Slender-Body Theory was considered f o r application . below a Mach number of 2.0 i n t h e supersonic range. This method of calcu-

l a t i o n relates t h e loca l pressures t o the var ia t ion of cross-sectional area

and t h e slope of t h e body surface. The theory was actual ly developed for

pointed nose bodies, but reasonable estimates of aerodynamic charac te r i s t ics

may be made using t h i s ,method for some blunted nose bodies. I

The pressure

coefficients a t points far frm the stagnation point ( i .e . , not applicable

a t stagnation point) may be calculated with reasonable accuracy for sane

blunt bodies. For bodies having e fineness r a t i o of 3.0, t h e theory y ie lds

values within a f e w percent of experimental data points over t he a f t 80% of

t h e body.

mately 25'% a t t h e shoulder a t M = 1.8, and 13% f o r M = 1.4.

body investigated i n t h i s stud,y has a fineness r a t i o of less than 1.0;

therefore, t h e accuracy would not be sa t i s fac tory even for t h e a f t portion

of t h e body.

For a fineness r a t i o of 2.0, the e f rors a re much la rger - approxi-

The entry

b. The Van Karman - Moore Linearized Theory was applied t o t h e

body i n an e f f o r t t o es tabl ish the charac te r i s t ics et low supersonic Mach

nunbers.

with t h e i r strengths and d is t r ibu t ion being determined by t h e body shape,

The theory replaces t h e body of revolution by sources and sinka,

REPORTNO. RASA CR-66037

PAGENO. 17

and the surface local pressures are calculated “y a s tep by s t ep procedure

using the following general equation: fi

cp = +-- 2u ?I )z V

( R e f . 54)

where u and %f are t h e perturbation veloci t ies along and normal t o the stream-

l ines , respectively. The method proved inapplicable f o r bodies h a v i x small

fineness ra t ios , and t h e equations only valid f o r very slender bodies. . c . The Basic Shock-Expansion Theory was considered f o r use a t super-

sonic Mach nunbers. This method of calculation defines the flow a t t h e apex

of a body by conical flow relations, and expands the flow downstream of t h i s

point by t h e use of Prandtl-Meyer expansion relat ions- A p rerequbl te for

using t h e shock exptms,iorl method is t ha t t he bow shock must be attached, and

t h e flow downstream of t h e shock is assumed t o be two dimensional. The bow

shock m u s t be attached t o apply t h e conical flow relat ions a t t h e apex,

and the theory requires tha t the flow is supersonic o v e r t h e surface under

consideration. The entry body considered here would not s a t i s fy t h e above

requirements; therefore, t he accuracy of t h e values determined using t h i s

method is not acceptable.

d. Second-Order Shock-Expansion Theory

Th i s theory is similar t o the Basic Shock-Expansion Theory

except t h a t it is a higher order approximation. Generally speaking, t h e

theory cannot be used t o detennine t h e aerodynamic character is t ics of a

sphere-cone f o r t h e same reasons tha t t h e Basic Shock-Expansion Theory

cannot (i.e., t h e bow shock m u s t be attached, supersonic flow m u s t be present

over t he en t i r e surface i n question,etc.). An UPV IR4 computer routine (LV-

VC-13) was used t o test the appl icabi l i ty of the theory t o sphere-cones,

LI MG -1EMCO -VOUG+iT, INC.

R E P O R T N O . a-66037

P A G E N O . 18

and t h e data obtained were unsatisfactory. The only way t h i s routine

(Second-Order Shock-Expansion Theory) may be applied is t o input t he

aerodynamic charac te r i s t ics of t h e hemisphere nose in to t h e routine by

t h e use of a sub-routine, and then t h e theory w i l l only be applied t o t h e

portion of t he body i n supersonic flow. Of course, t h i s procedure is not

beneficial , because t h e flow character is t ics of the conical portion of t h e

body may be eas i ly obtained using several other methods. t

e. Modified Newtonian Flow Theoq was used t o calculate t h e aero-

dynamic charac te r i s t ics of t h e body a t high supersonic and hypersonic Mach

nmbers.

body are those which undergo co l l i s ion with the parts of t h e body facing

The theory assunes t h a t t he only pa r t i c l e s of a i r affected by a

t h e incident flow.

normal component of momentun and then slide along t he surface conserving

On, co l l i s ion with the surf'ace, t h e pa r t i c l e s lose t h e i r

t h e i r tangent ia l component of manentan. The a i r particles have no effect

on t h e portion of t h e body surface facing away fran the f l o w ( i - e . the

pressure on the surface lying i n t h e "aerodynamic shadow" is equal t o zero ).

The theory has proved t o y i e ld values of acceptable accuracy f o r blunt bodies

i n many previous studies. The charac te r i s t ics w e r e calculated f o r t h e entry

body i n t h i s study by t h e use of an Il34 7090 computer routine, W - L W C ~ ~

( R e f . 11) The r e su l t s agreed w i t h the values of experimental data obtained

i n t he l i t e r a t u r e survey and were used a s a reference on sme of the plots.

f . The Method of Characterist ics was a l s o considered f o r application.

Though t h e method is more exact i n t h e solution of t he f l o w over a body than

t h e previous mentioned approximation methods, the time required t o apply

the method is far grea ter than is allowed during t h i s contract period. It

would be unreasonable t o use t h e method without haviw an applicable computer

routine

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REPORTNO. m n P A G E N O . 19

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RCCORTNO. ]w1I 41.66031

PAGENO. 20

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REPORT NO. cR-66oJf

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REPORTNO.

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REPORT NO. CR-66031 I

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I 0 - 5059 1 LING-T€MCO-VOUGHT, INC.

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REPORTNO. HASA CR-660-37

PAGENO. 25

B. Pressure Distribution Analysis

. 1. surmaarg

A technique is developed to predict the pressure distribution over

a sphere-cone body at moderate angles of attack and supersonic Mach numbers,

M 34. The method is verified w i t h experimental data from various sources.

The technique herein developed is applied to the problem of a sphere-

cone with a 25* half angle conical skirt. The pressure distribution is

predicted along meridian lines which converge at the axis of symmetry.

Pressure coefficient variations are obtained at o( = 0, 5 , 10 and 15 degrees,

M = 4, 10 and 15, and along eight meridian lines using the so called "Modified

Tangent Sphere-Cone" method.

2- Confkuration 'Description

For the purpose of this division the configuration under study is a

semi-infinite spherically tipped conical frustrum.

are located by two coordinates, s/R and 9. identified in the sketch of Figure 13.

Points on the surface

The major symbols used are

3. Discussion of Literature

An extensive literature survey was conducted during this study in

search of pressure data, both experimental and theoretical, related to sphere-

cones.

majority of the theoretical d a t a were for zero angle of attack only.

A very limited amount of experimental data were available, and the

A

cmplete summary of the results of the survey is presented in Table 11.

(he of the most comprehensive pressure data sources found during

this study was Reference 61. These data were obtained from detailed

characteristics solutions on sphere-cones at various Mach numbers.

Pressure coefficients are tabulated as a function of normalized surface

REPORT NO. cR-66oJI

PAGE NO. 26 I

I

I obtain t h e final predicted pressure variations. a s i m i l a r canparison

is'made i n Figure 20 f o r a 40" cone a t OL 4".

values indicate t h a t t h e method used herein t o establish the pressure dis-

t r i b u t i o n of t he 25O sphere-cone i s va l id .

The c lose agreement of t h e I This method is discussed i n detail

1 i n t h e next section.

I n addition t o t he data obtained i n the literature survey, an at tempt

was made t o apply two Urv camputer routines (References 11 and b), but the

data did not prove sat isfactory, therefore, w e r e disregarded. . 8

4. Method of Pressure Prediction I a. Basic Tangent Sphere-Cone Method

.4s stated before, Reference 61 includes a very comprehensive

and detailed pressure d is t r ibu t ion analysis on sphere-cones a t several Mach

nunbers. It was decided t o u t i l i z e t h e data i n Reference 61 as much as

possible by interpolating the results t o include other cone angles.

of t h e interpolat ion are shown i n Figures 14 through 17.

interpolated data is t h e pressure dis t r ibut ion on a 2 5 O sphere-cone a t zero

8 I The r e s u l t s

Included i n t h e

angle of a t tack and four Mach nunbers.

A method very similar t o t h e "tangent-cone theory" was used t o

predict t h e pressure var ia t ion along a meridian l i n e a t angles of attack.

This method, i n i ts simplest fonn, is t o calculate the included angle be-

tween the meridian line on t h e cone surface and t h e free-stream velocity

vector ( c a l l t h i s angle thmugh 17

corresponding t o the angle

l ine .

1 I 8 8

) and t o use t h e data from Figures

as the pressure var ia t ion along the meridian

Fran spherical t r igonmetry t h e re la t ion between f , CC , 8 and 0 is

(1) s i n = cos oc s i n e + s i n = COB 8 cos 0 .

I I

s 1 8 I I I I I I I I I I 1 I

REPORTNO. CR-66037

PAGE NO. 28

This simp1 fied method assmes that ,he streamlines near t h e

body rad ia te fran t h e stagnation point along a meridian path t o t he sphere-

cone junction where they a r e abruptly turned t o follow a conical ray.

Consequently, t h e ci rclmferent ia l pressure d is t r ibu t ion around the conical

portion is established soieiy fran flow expansion over t h e hemispherical nose,

and t h e effects of cross flow a r e neglected.

method vary d i rec t ly w i t h angle of a t tack and inversely with Mach nmber.

The er rors involved with t h i s

In order t o reduce the errors a t high angles of a t tack a c o m c t i o n

was applied t o t h e basic tangent-sphere-cone method described above- The

correction essent ia l ly introduced a crossflow tern t o the conical portion

of t h e body suf f ic ien t ly f a r downstream of t h e nose and extended t h e correction

upstream t o t h e sphere-cone junction. #

A more detailed explanation of how

t h i s correction was derived and applied w i l l be given following a discussion

,of t h e pressure d is t r ibu t ion on the spherical portion of t h e sphere-cone body.

b. Pressure Distribution On Spherical Hose

A nuaber of authors have obtained solutions t o the hemispherical

blunt body problaa.

and 68.

Notable solutions are found i n References 61, 63, 65, 66

Figure 21 presents t he data fraa Reference 61 which is ident ica l t o

the solutions fraa t h e various other sources. These data are presented f o r

several Mach nuabers and a comparison is made with Newtonian theory.

The hemispherical pressure d is t r lbu t ion presented i n Figure 21

l a shown for zero angle of at tack, i.e. t h e stagnation velocity vector is

coincident with t h e longitudinal reference axis . (For a sphere-cone body of

revolution t h e longitudinal reference axis is a l s o the axis of synunetry).

1 0-sos91

I 1 11 1 I 1 t I I I 1 C 1 I 1 I I

e P A G E N O . 29

Thue strerrllnes at& mtridien lines are coincident at zero angle of attack,

end the prersure distribution le synnretricalabout the longltrpdirral reference

in locally sugersonic flow, hence the conical sklrt brre no effect on the pm66Ure

distribution overthe spherical portion up t o the sphere-cone juaction.

A t angles of attack (zero yaw) the stagnation point moves along

the vertical reridian 8 dietsnce

r o c (radian)' B Streamlines then redlate frcm the etagnation point i n a sylsPctrica1 pattern

about the stagnation velocity vector for a dieterre

(3)

vhlch is the arc distance fmm the stagnation point t o the aphen-cone Junction

at 0 = 0. m i c a 1 results were mt available t o predict a p r e i ~ ~ . r e variation

- 8 - # j arpd S l .I - lr -g(spbere- 2 R along the strwrrdlixrs path between 5 .I ( R

colle junct1on)for meridians ather then 4 = 0. Fbr the purpose of this report

it is asmwd that all streamlines follow exactly a leridirrr path between

the rtagrmtion point srd the sphere-cone Junction, ard tht the prea~eure variation

.ssumpticw

for lodtrrte angler of at- the sumpt ion ylcldr good accuracy.

rhould be Investigated further although it is believed tht

It now reprlm t o compute the pwrrurc dietribution aloag rrsridian

lisb8s cm thc hemlrpherical pose. The relation between tbh eider snd angles

of an oblique rpbcrical triangle i~

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REPORTNO. blAsA CR-66037

.

. .

can be found by first riding its distance from the stagnetion point, s1 ard K’ then take the pressure corresponding to this distance f’rom Figure 21.

Figures 22 through24 present the pressure coefficient muistion

along eQht wridisn 1-8 (@ = 0, 30, 60, 90, 180, 210, 240, 270) to - 1.1 fer a;rlj2ee ef atl*wk of 5, re, rg begreea apr? fvr xarg. mta fa= =the=

MBch numbers can easily be obteined using equation (4) and the method described

above, although as seen in Figure 21 tatre is little depedence on l&ch

nmber except the stagnation point.

C : -30391

E I B c 0 E E I I I E r I I t I I E

LlNG-TEMco-vouoHT. INC.

PAGENO. 31

c. M o d i f i e d Tangent Sphere-Cone Method

As mentioned before, the pressure dis t r ibut ion along a conical

ray of a sphere-cone body at angles of at tack can be determined approximately

using t h e tangent sphere-cone theory described earlier. This theory may be

hproved somewhat byobmining t h e actual c i r c w e r e n t i a l pressure dis t r ibut ion

on a sharp cone a t angles of a t tack and applying t h e results suf f ic ien t ly

far downstream fram t h e nose. . . Reference 62 presents a method of predictlng t h e c i r cmfe ren t i a l

pressure dis t r ibut ion on a sharp cone a t angles of attack. The method is

semi-empirical i n nature and the pertinent equations are reproduced here.

The circunferential pressure dis t r ibut ion is given by

3p + .00097f - .i5 cos3(ac+ e ) s i n 3 -0.1 4

(5) 5 8 = 1.1 cos3

cP$ = 0 where

and Cpwis the pressure coefficient on t h e ver t ica l windward meridian and

is given by

Equation (7) is modified sanewhat fmm tha t presented i n Reference 62 so that

Cp b = 0 will reduce t o t h e crxact cone pressure at o( = 0. Thus,

where Cpa=; is the exact cone pressure fran Reference 4 andOCP- is a

h n c t i o n of cone angle and Mmch nunber given on a chart i n Reference 62.

For 6 = 25' and M = -, 7, 4 and 3,mP- = 57.0, 55.9, 54.0 and 51.9

respectively. The cir-erential pressure dis t r ibut ion can lrpt be found from

1 E 1E I

c I ilc t

REPORTNO. HASA CR-66037 I

I PAGENO. 33 ~

obtained froa Figures 1h through 17. Predicted pressure cocf'ficient data

' on a 25. sphere-cone at angles of attack up t o 15' obtained by this rrethod

are presented in 28 through 39-

A check on the velidity of the acthod used is sbmm in Plaun 19

for a 15' sphere-cozw body.

t o the present nethod and t o the ' b e n t Sphere-Cone" mthod.

Experiwntal data from *farelre 62 is coapaFed

Unforturrately,

experirrental data on the leeward side of the body were aot svallnble.

Experimental data for a 15' sharp cone are also included as a check on

the predicted circumferential pressure distribution.

0 t I

Tht only other experimental data suitable for analysis were fouad

E I n Reference '(1.

camprison wi th the predicted results is shown i n ngure 20.

t h a t the dfscrepanciee are larg.ly due t o viscosity effects.

These data were for a 40' sphen-colle at M= 8' aad

It is believed

t I I I 1 Ili I I

5. Presentation of Final Predicted Pressure Coefficients

Figures 28 through 39 present the final predicted pressure

coefficient data on a 25' sphere-cone. These data were obtained uairrg the

%ified Tangent Sphere -Cone" ntthod described in section 4.c. Pressure

varations are presented along r r i d i a n llnes emirpat- -the axis of

sylwtry for severrl meridian lines, angles of attack, snd lbch numbera. \

Specifically, Figures 28 through 36 present the pressure variation

along eight mridian lirm~, each at K = 5, 10, d 15 degrees and Wrch

numbers 4, 10, snd 15.

meridian plant ( $ I 0 end 180 ), each at K r 0 , 5 , 10, srd 15 degrees

~ i g u r e e 37 through 39 present data in the vertical

.sd Mach numbers k , 10, and 15.

I'

REPORTNO. m a 3 7

PAGE NO. 34

6. ~ u r e e of Uncertainty

Although flow solutione by the method of characterietics are

considered the most exact solutions thue far obtainable, viscosity

effects are neglected. I n r>st cases these effects are -11 emugh

to neglect, but uder certain conditions these effects m y be consiberable,

for exaaple 8 I bo, pigure 15. Por large cone a,#es the shock wave lies

close enough t o the conical afterbody to induce a possible boundary layer-

shock wave interaction. Thus, the sccuracy of prediction is believed t o

suffer pDst along the w l n d v a r d meridian ( # 0 ) at high angles of attack.

Except in the vicinity of the sphere-cone junction where the

viscosity eifects axe most lzaticeable, the expected mean prediction

accuracy is % I iO.015. This accuracy figure is Wed upon a correlation

of experiment and theory and an intuitive appraisal of teot results,

va l ld l ty of assumptions, and anticipated viscosity effects.

e

' I IE 1 w I 11

I 8 E I 1 1 8

C. MPACT DISPERSION STUDY

-1

This division presents the results of an anlyeis uader-

taken t o define the re-entry path angles which produce, for a given

set of booster burnout deviation, om, two and three si- total

inrpact raqe deviations of n. mi. utilizing a standard NASA

Scout configuration, a Ilomiaal boost trajectory w a s developed which

satisfies each of the above derived re-entry path angles. The ncalrral

trajectory correapoxding t o the two

produces a range deviation of 400 n. m l . ) was then used as a basis for

an accuracy analysis.

upon the traJectory,and the burnout ard impact deviations s ta t i s t ica l ly

re-entry angle (which

a he boostex% errors were separately imposed

combined t o define the strzldard deviations in burnout and iplpsCt

conditions for this psrticular re-entry angle.

Scout booster vehicle configurstioa used in th i s

analysis consisted of the following rocket motors.

Stage One - Algol IIB

S-e Two - Castor I1

StageThree - ABL X 259

StageFour - ABL X-258

2. Impact Dispersion Study

The first part of this study was t o deternine the entry path

angle which, for a given re t of booster burnout deviations, would

produce one, two aml three si- impact range deviations of 400 n. m i .

The standald deviations and correlation coefficients wed In these

coaputetioas were defined in Reference 92 and are:

strudnrd Deviations Correlation Coefficients

v (velocity) - 62.3 ft./sec.

h ( a l t i t ude ) I 3.24 n. mi.

-81705

f!!VAU' = -*ln

(entry -le) I: .293 degrees P a f t A V I 0 7 0 6 I n p s c t range deviations were calculated on a three

degree-of -f'reedom t ra jec tory routine (Reference 93) which incorpomtes

t an oblate ro ta t ing spheroid ear th model ead a 1962 ARDC atmosphere model.

TIMZ marina1 entry velocity and a l t i t ude were a s e m t o

and 433,000 feet, respectively.

deviations 86 functions of velocity, a l t i t u d e apd f l i g h t path angle

deviations f o r s eveml mminal entry path angler (the angle between the

local horizon and the vehicle a i r r e l a t ive velocity vector).

26,000 rt./sec.

Figures 40, 41 and 42 show Impact range

,

Range deviations obtained by separate s t a t i s t i c a l copbinetiane

of om, two and three si- velocity, a l t i t ude ard path angle errors

are shown i n Figure 43. Positive and negative range deviations were

combined separately t o show the non-symnetry of the impact d is t r ibu t ion .

Total range deviation wae plotted as a function of nominal

ent ry f l i g h t path angle and io shown i n Figure 44.

corresponding t o om, two srd three siep. total range deviation6 of

400 n. mi. were found t o be -3.14 degrees, -4.53 degrees aad -5.77 degrees,

Entry angles

respectively. A nominal Scout "gravity turn" boost t r a j ec to ry VIS

designed which achieved the 4.53O entry angle along with an entry

veloci ty of 26,500 ft/sec a t an a l t i t u d e of 433,000 it.

altitude p ro f i l e of this nom~pal t r a j ec to ry is shown in mure 45.

Gravity tu rn t r a j ec to r i e s for the -3.44. d -5.7'7. entry angles were

a l s o computed t o determine tbe variat ion of total range t o impact as

a function of aorinal -le.

A range

This variat ion is shown in Fim 46. -

I 0 '5W.l

REPORTNO. a-37

PAGENO. 37

3- Impect Dispersion A m l p IS

An impact dispelrrion anelyeis vas performed for the -4.53 degree

entry angle.

final burmut conditiane of the Scout booster as well as impact range

The effect of each significant booster error source on

of the payload WSB deterrined by traJectory calculations separately

IncorporatiDg each error source. These calculations w e r e combinations

of sir d three-degrees of fretdoaa traJectory simulations.

stage of the boost vehicle waa simulated in six-degreer of freeda in

Tbe first 0

order t o accurately sirnrlate the launch dynamlcs and the effects of

w i n d 8 clud thrust adsa l lpmnt . A three-degree of M a siwiLatiOn

w a s adequate for the upper &ages and was usdd in order t o conserve

machine camputation& tiare.

The results of these calculations are shown in Table 111.

The deviations from the rmainal value of the re-entry parameters of

velocity, altitude, flight path a w e , angle of attack and inrpact

m e are shoM for each error source.

both the plw and minus 3 si- values were run.

based on an average of the plus and a m u s deviations, since they

are essentially linear.

velocity errors are those produced by fourth stage mtor data, winds

and second stw deadbarn3 errors.

Is7 first aad mod-.-e motor data, drag variation6 apd secord stage

deedbed errors.

are most strongly a function of guidance, deadband end tip-off errors.

The lmpect w e deviations are iniluenced otaaergly by most of the

errors w i t h the exception of wILdo, thruet risrrlQpment and fourth

For most of the error sources

The RSS value is

It is of interest t o note that the largest

The significant altitude errma a m caused

Angle of r t w k and flight path angle deviations

8-e motor data. The bottom line on Table I11 shows the RSS vulue of the

average valucs.

I 0 - 56SP I

t

U N G - T E M C O - ~ , twc.

REPORTNO. NASA CR-66037

Staxnlard devlatione in each of the Important fourth stage

btvrrout pcuwaeters were c a p u t 4 iropr 'Rrble I11 using the RSS

technique a d are shown below.

Permeter Staxhrdl Deviation ~ -

Velocity

A l t i t u d e 2.70 n. rai.

PlQht path angle .25 aeg.

m e 2.60 n. mi.

Angle of a t tack .382 deg.

Correlation coefficients w e r e computed as described i n Reference (92)

aDd w e n found t o be

, fAMA& -0118

@ A ~ E = -.*e

ff&All' = .664

The "two sigus" total deviation i n impact range was computed by root

6- squaring the average deviation produced by each error source aJBl was

foumd t o be 374 nautical miles. Root 6u1p squaring positive ard negative

deviations separately resulted i n "two si-" devlationrr of W 5 n. ml .

and -169 n. m i . A n est i ra te of the "two sl@ma" range dispersion as a

rupctlon of napinal entry -le appears in pigure 47. This estimate is

baaed on the burnout deviations and correlation coefficients for the -4.53

degree entry angle rather than those from Reference 92.

0. Reentry Dyaaari C S Study

1. sunmry

This division presents the results of a study of the reentry

dynenics of the subject vehicle.

d e t e d n e tbe w e t aft center of gravity lirit which would cause -2e

Reentry trajectories w e r e computed t o

a - 0 -8080 1

REPORTNO. CR-66037

PAGENO. 39

of attack excurslone not t o exceed 2 degrees and t o investiwte the

effects of t ip-off, msee uabalance, atd center of gravity off-set.

A roll-pitch frequerrcy analysis VSB corducted t o determine the natural

fhqwncies of the vehicle and to derine regions of roll-pitch reso-e.

2. Tnrjectory Analyeis

A six (6) degree of freedom digi ta l computer study uae

conducted t o investigste the effect of center of gravity location on

the dynedc behavior of the spacecraft during descent through the

atmosphere. On the baeis of this study, a nominal center of EPgvity

we8 selected a d additional trajectories were computed to d e t e d n e

the individual effects of tip-off, mass unbehnee and center of gravity

offset on the angle of attack envelope.

effect of center of grcrtlty location and of each of the disturbances on

Data are presented which show the

the -le of a t tack envelope.

a. Simulation

he entry vehicle was simulated as a six (6) de-ee of

freedom rigid body using the U V lpEMAR trajectory routine. This routine

is described in deta i l in Reference 93.

MBIBS -lance was siwiLated as an Iru product of inertia.

Since the basic llEwlR routine does not have provision for includiq$ a

product of inertia term tbe equation for calculating body axis angular

'1 0 - S O B 9 1

R E P O R T N O . CR-37

PACENO. 40

1.

w h e r e Q, I$, HZ are the ccmponents of angular momentum of the vehicle

about its body axes in ft/lbs; I=, In, I,, are the moments of Inertia

of th vehicle about the body axes in nlugm -2;

of ixertla between the x and 2 body axes in slugs ft2-

i e the product

A center of p v i t y offset vas simulated as a dlspleceshnt

of the center of gmsvity along the negative z-axis f k a the

axis of symmtry, a8 defined in Figure 1.

narnt .of (ha ~ y ) and am d d i t i o m l y-axie moment of

introduced into the lfEMAFi tiPe rate of change of angular maepcntu

equations (equations 4.03, Reference 93).

Thue, an additional X 4 8 8

%) w e r e

The following vehicle characteristics were used in the

simulation. ,

Weight - 192 lbs. Pitch d O f imrtia - 4.2 SlUg i t2

Roll moment of inertia - 3.2 e l w ft2

Diemeter - 2.5 rt.

Base Area - 4.9 sq. it. Axial force coef'ficient v8. Mach no. - Figure 11 No-1 force derivative vs. b h no. - Figure 3

Center of pressure v8. Mach number - Figure 5 (M value)

Pitch damping derivative VB. WICh number - Figure 3.2

b. Effect of Center of Gravity Location

The purpose of this analysis is t o detexmine an acceptable

aft center of gravity l imit . The cr i ter ia f o r an acceptable l i m i t i8

1 that the angle of attack envelope not exceed two degrees, especially in

the regions of hi& heatil3g and hi& loads.

U N O - ~ - v M I G H T , INC.

REPORTNO. a-66037

PACENO. 41

A reference trajectory vae computed uiag the center of

gravity specified i n Reference 91, 0.3835 diareters forward of the

base.

speed regime to define an acceptable aft center of gravity 1-t sinee

In this region the vehicle exhibits the least stabil i ty.

Valws fraP this trajectory vere then used t o explore the low

Center of gravity locations of 0.20 D, 0.24 D ard 0.28 D ' w e r e selected and trajectories ccaputed using the follovirrg in i t ia l

corditions.

burnout as determined in tbe final nomirrrl trajectory.

Thse conditions correspond to a t i m e of 243.2 seconds after

l&h Number 1.16

Altitude 67909 ft. f

Relative Flight Path Angle -34.099 degrces

Spin Rate 3 CPS

The initial pitch ami y a w rates were zero as w e l l as tht

r o l l angle and aerodyneric angle of attack.

was included.

A 128s unbalance of 20 oz-in2

Angle of attack time histories for these trajectories are

shown i n Figure 48. The 0.20 I) and 0.24 D CG paisitions Vere fowl t o

cause divergence and were M o n e d . Thc 0.28 D p a i t i o n did lrtf diverge

but did reach a large m ~ ~ l m m angle of attack which appeamd upacceptable.

Consequently, th i s case was recomputed starting with burnout codi t ions

t o ipeun that results fro^ the short FUI~S, starting at M - 1.16, were

valid.

well vith the da ta of Figure 48 and shov that the short runs provide

valid results.

The results of th$e latter run, shown in Figure 49, correlate

1 1 1 8 I I 1 1 I I t I t I 1

REPORTNO. CR-66037

Unless otherwise specified, the in i t ia l conditione arc those

which exist at burrrout. There coxulitiono are listed below.

WBch number 16 . 42

Relative velocity, it/sec 26,500

Angle of Attack, degrees 1.15 (3 -=)

A tip-off of 1 lb-eec, acting at the eeparation plane, and

a m81 uabelance of 20 oz-inO2 were included as specified i n Reference 91.

!Fhe vehicle was initially oriented ( ro l l angle - 90') so t lmt bath the

rm)ra3e aml initial pitch rate (dm t o tip-off) teDd 00 in i t ia l ly

cauee a positivt angle of attack.

initial conditions were oriented or produce the largest posrible angle

of attack. The initial spin rate is 3 cps.

AB a result of these exploratory studies, a CG of 0.32 D

In other words, all di6turbances aad

wae selected as a probable aft l l m i t .

case, starting fraa burnout.

in Figure 49, uae considered t o be satisfactory. Consequently, a CO

position of 0.32 D was selected a8 the aft lirit and used for all of

the subsequent ~lrslyses.

18 1-15 degrees plus the effect of th 1 lb/sec tip-off @.pulse.

the tip-off Impulse produce6 a different raent for different CO positions

the initial angle of attack is d i f f e r e n t for tk two runs shown.

The initial -e of attack buildup (Figure 49) is due to a downward

rotation of the velocity vector that occur8 before tbe dymmic preeeure

A trajectory was camputed for t h i n

The angle of attack tire history, presented

Tbe i n i t i a l epglt of attack shown on Plgure 49

Sime

1 0 - soso 1

PACENQ. 43

attains sufficient -tude t o cause the aerodyn8mlcally stable

'vehicle t o terd t o follow the velocity vector.

hss very l i t t l e effect on the mgnAtude and damp- of t h i s initial

an@ of attack buildup. After a higher dynamic pressure is reached

the aagle of attack is reduc~d essentially t o zero.

angle of at tack buildup could be avoided by programmlrrg the booster so

t ha t hurnout occurs at a slightly negative angle of attack of

approxiPately 4.5 degrees.

would then reduce the angle of attack t o zero after .pprorirafely

80 seconds.)

W h number is lpsched Sild the center of pressure shift reduces the

s tab i l i ty of the vehicle t o the exten€ thet the vehicle cannot follow

a rapidly pitching velocity vector.

the velocity vector reduces and the aerodynamic s tab i l i ty w i n reduces

the angle of attack t o a sarll value.

angle of at tack buildup is deperdent on the aero$yxmm.ic s tab i l i ty d

thus, I s obviously very strongly related t o the cog. po6ltlO~.

Tbe c.6. p i t i o n

(TUB ini t ia l

s

The 110-1 rotation of the velocity vector

Tbe angle of attack then rerpains very small un t i l a lower

Subsequently, the pitch rate of

The e t u d e of th i s low speed

The Mach number axul dyxmmlc pressure for these trajcctoriee

are presented in F'igUFe 50.

The Faxrges of acceleratians at the CG d body axla an&ular

rates as deternined fra~ theae trajectoriea 8re shwn belov,

&g - = .28D xcg- *3=

Accelerations (g's)

bngitudirral 0 t o 11.4 0 t o 11.4

Mom1 ard traverac +.85 t o -.e5 +.k5 t o -.15

Xcg - **

PAGENO. 44

Pitch a& Yaw 4 5 t o -65 A0 to -40

m s e trajectories Incorporated the! 1 lb-eec tip-off Impulse and

20 02-19 -6 unbalance di&urbancer. e

’ Q. mnal Tns3cctox-y

In order t o deternine th effects of individual disturbences

on t h -le of attack envelope, a trajectory w i t h no dleturbam2es is

required 88 a reference. A M.jl no=dieturbarrce trajectory vcld caputed

ulng tht burnout initla1 ca l t ions except that the Initial angle of

attack V L L ~ zero. Tbe angle of attack emreloper for the m m i m l

trajectory ard disturbance trajectories are shown in Figure 51, 52, ard

53. It l e interemting to note that the Mach number and dyaerpic preesure

tiPe histories for these cases e h w no significant variation fran

those presented in Figure 50.

I n the following peragmphe, which discuee the effect8 of

lmllvldual dIsturbcuree6, al l coodltioncl are the 8epe ae for the n a l n a l

case except as noted.

d. Bffec% of Tip-off

The effect on the angle of attack envelope of e tip-off

Impulse of 2 lb-sec. acting at the separation plane is ehom In Flgure

51. The 2 1b.-rec. tip-off Impulse was sirulated t u an initial pitch

rate of -21.8 degrees w i t h tbe vehicle In i t ia l ly rolled 90 degrees to

came the dlsplaceperrt of the cone center t o be upward arpd thua haw the

PAGENO. 45

greatest effect on angle of attack. !Fhe nearly constant irrlcawnt in

angle of attack seen In Flgure 51 I s due to the coning motion aml the

upuaml dleplacenenf of the cone center. When the region of hie d-c

preaaure I s reacbcd the coning lotion l a clamped and tbe angle of attaek

I 8 radueed t o zero. The -lnlmg portion of the angle of attack

envelope I s not affected by the lnitlal tip-off irpulre.

e. Effect of )lur Unklance

The effect of a 50 o t . ln.2 m s unbalance (In I .OOO 675

81ua rtS2) is 8bcnn in Figure 52. The 1.5 degree deviation f r a -1

tbst occurs at 118 ZKC. I 8 due t o r o l l pitch resonance. This rotion

u n h a l e t o produce a alight c o w motion which lncreaecr the angle

of attack ewelope by appmxiaekly 0.8 degrees.

f. Effect of Center of Gravity Offset

Prelirilvvy traJectmy calculat lone w i t h center -of -epavifg

offsets of 0.1and 0.2 laches Indicated that a vehicle with a cog. Offset

vould rather cloaely follow the nadrrs l angle of attack histories except

In region8 of roll-pitch re8-e which occur at approxWtely 120 m-8

and 235 eecomirr. During theae reglone the prelirirrrry traJectarles in-

dicated tbst lnrge dhvlatlons In angle of attack occurred; bovemr, due

t o the amplitude arrd frquency of the Potion Involved the Integration

error control used in there prelimirury celculatlonr was t o be

Inadequate for accurately defining the amplitudes of the= devistlom.

It i r lnterertllyl t o r d e tbrt the lntegratioa error control thrt m

dequste for c a l c u l d a the mtlon rcsultlBg fra the other di8turbmee8

I . 0 -101.1

REPORTNO. ma37

PAGENO. 46

was not suit-ble for calculating the motion resultlng from a cog. offset.

TUB is so because for a given error control (truncation error control)

=re IntegFatiOrr steps are required for a cg offset run than for esy

a PMB lmbelapce run. Tkrefore, for a given period or trs;)ectory tlme

the cg offeet pup will require mre integration steps.

number inteepation steps prodme a larger accrued build-up int-*im

The larger

error in the variables of Integration. To control this accrued error

the erior control aret IX tightened (allow a slasller truncation error)

but this process requires snaller integration steps and hence longer

computational times result for the same period of trajectory tire.

Since tightening the error control t o a suitable level resulted in em

alroet prohibitive 6aputer tirr requirement for an entire traJectory,

traJectories werp coprputed only in the region of roll-pitch resonance.

Trajectories starting a t 80 seconds and ending at 160 seconds were run

t o define the response t o the roll-pitch resommce that occurs at a high

W h number and trajectories b e g i ~ i n g at 220 secods a d e d i n g a t 280

seconds w e r e run t o define the response t o the law speed region or ro l l -

pitch resnnae. The i n i t i a l co&dltlons for the law speed region

tnrJectoriee were based on prellmlmsry computer runs. Trajectories

o? this ty-pe were run for c.8. offsets of 0.1, 0.2 and 0.3 inchee.

Results of theee crlculatiosr, are shown in Figure 53. ' It can be seen f r a

Figure 53 tbet the response to roll-pitch r e s w e in tbe high speed

region is very nearly linear w h i l e the nsponee in the low speed region I s

obviously very non-llnear. Tbe non-linear response that occur@ in this

region is evidently due t o a reduction in spin rate tbnt accapenles

the large amplitude deviation in angle of attack. Spin rate reduction

I '

8

REPORTNO. a & 3 7

PACENO. 47

is shown i n Figure 54. This spin rate reduction is due t o the rolling

aroment produced by the side forces acting at the offset c.g.

nmintaine a coning rate approximately equal t o the spin f'reqwmce

so that the vehicle x ard y axes nsintain the ~ a m e general orientation

relative t o the angle of a t t a c k plane (plane fonned by the vehicle

X body axis and the relative velocity vector). For t he three cases shown

the vehicle maintained an orientation with the negative y body axis lying

near the angle of attack plane eo that a negative rolling morent w a 8

produced by the side force.

w h e t h e r or not the vehicle will always settle into t h i s orientation so

that the spin rate is always reduced or if it is possible for the

vehicle t o renmin with the positive y axle oriented within the angle

of attack plane so that the spin rate w i l l be increased.

The vehicle

Further work needs to be done t o detemine

t

1

t 0-80501

8 . 8 I 8 8 8 II 8 8 I 8 8 I I 8 1 i

REPORTNO. ma37

PAGENO. 48

- 3. Roll-Pitch Frequency Analy sis

Roll-pitch frequencies have been computed for the numbel trajec-

tory and for several off-naminal cases.

will appear on the body axes.

of gravity off-sets of 0.2 and 0.3 inches and a center-of-pressure loca-

tion which is more aft than that used in the nominal case.

These frequencies are those which

The off-nominal cases considered are center

a. Method

The method used for calculating the roll-pitch frequencies is

a modification of the equations developed by Phillips in Reference 95.

Phillips developed the equations for a case where the nmss could be

assrrmed to be distribyted in a plane, as for em airplane.

approach, equations have been derived for the case of the m8s distributed

symmetrically about the longitudinal axis of the body.

Usingthe Bame

Since the reentry body being analyzed herein is both aero-

dynamically and inertially sylPPuetriu about the spin axis, the equations

can be further simplified by cambining the terms containing the aero-

dynamic moment.

body fixed frequencies.

These conditions result in the following equation for

t

REPORTNO. ]IIcLsA a-66037

PAGENO. 4

where: fl = the high body frequency f

= the low body frequency

= the non-spinning pitch frequency divided by the spin w

p = the ra t io of roll inertia t o pitch inertia = 0.$2

p the spin frequency

. Before proceeding t o the numerical analysis of this spinning

body 8- of the characteristics of the above equation w i l l be discnssed.

When: W = 0 (corresponding t o no aeroaynsmic maments) the equation

reduces t o

A,= P f

A2= (1 -e) P a (o+ - 1) P These are the spin frequency and the coning frequency for a

spinning body In a YSCUZBP.

When c3 -t 43 (corresponding to a case of zero spin rate)

both frequencies approach w , indicating that only the non-spinning pitch

frequency is present.

Roll-pitch resonance can occur when either of the ircquencies

beccme equal t o zero. Since the high frequency is alvrys

equal to, or larger then, the spin frequency, this can only occur for the

low frequency. A

It can be shown that the low frequency can never be lese

than zero but it can equal zero.

resonance and occurs when ~3 = d Y 7 The latter case represents roll-pitch

I I . O - S O 8 S l

8 I 8 I 8 8 8 I I 1 1 1 8 8 8 1 8 I

REPORTNO. EASA CR-37

PAGENO. 50

Substltutlng the inertia ra t io into the f’requency eqrrstion

prwldes a n-cal eqrrstion for the two frequencies as followe

A plot of this eqmtlon I s presented in P l p r e 55. ’Ihe lov

frequency goes t o zero at W - 0.486 indicating roll-pitch resonance a t

t h f s Of r3.

b. Result8 for H m Case

Figure96’preeents a time history of c3 for the trajec-

tory (~igurese) and for em- ~ii-noppinsl coaditi-. F ~ X the a trajectory, a spin rate of three cycles per second WLS used.

cases with a CO off-set, the spin rate a s taken f k m m s & b For

For the

these cases the spin rate stesdily decreased af te r 220 seconds.

The frequency ratio for the nomlnnl trajectq pasees through

roll-pitch resonance a t 120 secoslds and win a t 236 seconds.

spent near the resonant cosodition is short and the buildup in angle of

attack is acall as shown In Figure% For the cases with mss unklrnce

a u increase in angle of attack is noted pcar resmance (pieurr 5&).

The tipre

I p.sw.1

PAGENO. 51

I -heme llsking the eyetar st iffer. Wing the af't center of -8- does

8 8 B 1 8 8

not produce Cafsetropbic ro l l -p i tch Faearraoce; however, it can be roe11

tbst the aft CP In conJutwtlom with a CO --ret could c a w I, mr-t

c d i t i o n for a cop.idemble pcriod after about 260 recorda.

T h effects of CO oil-set on t h e frequency ra t io are profound

et the lou s p e d e& of th tmJectory.

reduct.ion in epin rete after 2 ~ ) e e c d r .

This is duc t o e algalflcaut 0

~ h d epin rete at 280 secoda

is 2.1 c p for the O.? -e end 0.23 cp. ror the 0.3 came. Altkmgh

WWer of the case6 6hovn bcreln reem t o have a roll-pitch res-e

very wel l produce a resarrat condition for all or pest of the period after

260 ~econde.

Tbe reduction in epin rate is caused by a rolling r n t dw

t o eideellp. An the a#.e of attack bttIl.de up after 220 eecoode, tht

angle of sideslip tellde t o be b-ed in a poaitivc direction.

ducer a eidc rorce which cauclci a rolling raent since the force doer mt

'phir pro-

act through tbc center of gravity. Positive btrs of the riderllp angle

O C C ~ far all Of t h C U ~ I with I, CO off-.& U m y be ~n

charrcterietic of the body in the low opead flight regim. * Tbt body iraquhnciee am preeentsd in Fi4prms 57 srrd 58 for the

nmiml tnr3ector-y w i t h a epln rate of 3 cps.

obtained f ra the data prerented in Flguras 55 and 56. As diecuesad

There frequencies were

uNG-TEyco.vwoHT, INC. REPORTNO. a-66037

PAGENO. 52

above, roll-pitch resonance occur6 when the low frequency (Figure 57) goes

to zero. rLlre high frequency can mver produce rescmance although it i o

near ths apln freqwocy for a ccmiderable portion of the flight.

is aat a problem for the c88ca considered. Bnwavcr, there l e a potential

problem area at tbe low speed end of the fU@rt. Roll-pitch resonance

could'develop in this area If the static rsrgin Is too large or for same

0

cabination of static rargin and CG off-set w l t h l n the range cauldered.

I

uNG-lEMabwn#HT. I w c .

8 8 I I 1 8 8 I 8 I 8 1 8 I I I

REPORTNO. HASA CR-66037

PAGENO. 53

I n keeping with the major divisions of th i s report the following conclusions

are drawn:

A. Aerodgnemi c Stabil i ty Analysis

1. Aerodyaamic s tabi l i ty coeificients have been predicted for a 25.

blunt and sharp cone using data available from technical l i terature.

2. The accuracy of prediction is considered t o be generally good for

Mach n\mibers greater than mtr.

3. A marked discrepancy was discovered between data of References 1 and 8

for Xcp and CN, a t subsonic Mach nlmbers.

an a c c m t e prediction.3mpossible based on these data.

This lack of correlation renders

4. The most notable information void exists for dynamic s tabi l i ty data

at all Mach nmbers a d Wles of attack.

5. Although much data are available f o r a wide range of sphere-cone cOnilgurstlons

and flow parameters, much additional data are needed before these parslneters

can be cuupletely correlated t o allow accurate interpolations.

B. Pressure Distribution Analysis

1. Complete pressure distribution data have been predicted for a 25*

spherically blunted cone a t Mach numbers 4, 10 and 15 and at angles of attack

0, 5, 10 and 15 degrees. %

2. A general method of pressure prediction at angles of attack VLLS

developed usiag exi-synmnetric sphere-cone characteristics solutions and an

adjustment for cross flow.

3. The accuracy of t h e "Modified Tangent Sphere-Cone" method of pressure

prediction is considered good.

c I 8 8 i I 8 I II 1 8 8 I 8 8 I 8 8 1

O-?rO1)01

REPORTNO. EASA CR-66037

PAGERO. 54

c. T.lqlrc t Dispersiorr S t a y

1. The entry an&les which correspotd t o om, t w o and three

total rsrr~p deviations of 400 nomi. were dete-

t o k -3.44, -4.53 e9d -5.7'7 d-6, respectively.

These w e e are based on typical Scout booster vehicle

bumout devlat lorn .

D.

2- The accuracy ~ s l s perfomed on the -4.53 degree entry

nnnl.c trajectory produced burnout dev3atione vhich are

very sirilar t o the deviations u e d in tbs impact dlsperrrion

study which were derived in an earlier Scout n-eatry

accuracy analysis for an entry -le of -7.0 (Reference 92).

For entry angles in tbe rmqp investigated the impact range

devistioas are not symetrical epd the down range or

positive range deviation io larger t k n the up-range

or oegative mmge deviation.

.

3.

Reentry Dylrui C. s t a y

1. A center of gFsvity located 0.32 diareters foward of tbc

brrse is a eatisfactory art l i m i t ,

2. Tip-off affects only tbc initial, low dynepic pm86-,

f l i & x t regime. A 2 lb.-6ec. tip-off produces an urglm of

attack of 3 dcgnes which to zero 160 recoIlds after

burnout.

Tbe effects of rses unbalsBce appear near the roll-pitch

resozmmt point. A 50 oz-in2 mu8 *lance caums a 1.6

degree incream in a q l e of attack 1r8 seeds after b\rraout.

3.

1 . 0 - S O 5 9 1

REPORTNO. a-66037

PAGENO. 55

I . A center of gravity located off the axis of 8y.#trY c(u1

b.re a profound effect on ths body rotloru in the law

aped flight reghe. An o f f - m t of 0.2 in. appcare

acceptable but a valw of 0.3 in. C B U I C ~ very large

excursions In angle of attack.

REPORTNO. a-66037

PAGENO. !j6

LIST OF REPERENCES

1. Owens, R. V.: Aerodynamic Characteristics of Spherically Blunted MSFC-KPP-AER~-~~-~~, Cones at lkch Numbers Pram 0.5 to 5.0.

m y 1961.

3. Hammer, R. L.: Linear Aerodynamic bads on Cone-Cylinders at ME& Numbers From 0.7 to 2.0. INSC/HREC/U289-1, March 1965.

4. Sims, Joseph L.: Tsbles for Supersonic Flow Around Right Circular Cones at Zero Angle of Attack. NASA SP-3004, 1964.

5. Foster, A. D.: A Compilation of bngitudinal Aerodynamic Character- istics Including Bessure Information for S h a r p and Blunt Nose Cones Having Flat and Modified Bases. SC-R-64-1311, January 1965

6. Sims, Joseph L. : ' Tables for Supersonic Flow Around Right Circular Cones at Snnsll Angle of Attack. NASA SP-3007, 1964.

7. Murray, Tobak; and Wehrend, W. R.: Stability Derivatives of Cones at Supersonic Speeds. NACA TN 3733, September 19%.

8. Geudtner, W. J., Jr.: Sharp and Blunted Cone Force Coefficients and Centers of F'ressure From Wind Tunnel Tests at Mach Numbers from 0.5 to 4.06. C(rJVAIR Report ZA-7-017, June 1955.

9. Penland, J. A.: A Study of the Stability and Location of the Center of Pressure on Sharp, Right Circular-Cones at Hypersonic Speeds. NASA TN D-2283, MY 1964.

10. Ward, L. K.; and Urban,'R. €I.: Dynamic Stability Tests of Three Re-Entry Configurations at bbch 8. AEDC m - 6 2 - u , January 1962.

11. Smith, D. E.: Computation of the Aerodynamic Characteristics of Arbitrary Bodies at Hypersonic Velocities by the Use of Modified Newtonian Impact Theory - Computer Routine No. LV-VC-26. ILFV Astronautics Report No. 00.447, May 1964.

12. Solomon, G. E.: !l!ransonic Flow Fast Cone Cylinders. NACA TN 3213, September 1954.

13. Bertram, M. H.: Correlation Graphs for Supersonic Flow Around Right Circular Cones at Zero Yaw in Air as a Perfect a s . I'?ASA TN D-2339, June 1964.'

REPORTNO. I(AsA a-66031

PAGENO. 57

14. Uehrcnd, W. R.: Changes i r i Base Coritcur on the Damping-in-Pitch of a Blunted Cone.

A Wind Tunnel Investiijation of the EfZects of

NASA !LTq D-2062, November 1963.

15. Webrend, W. R.; and Reese, hvid E.: Wind Tunnel Tests of the Static and Dynamic Stability Characteristics of Four Ballistic Re-Entry Bodies. FASA "?l X-369, J x e L(36'3.

16. Keyes, 3. 7 . : hngitudinal Aerodynamic Characteristics of Blunted Cones at hch Numbers or' 3.5, 4.2 and 6.0. February 1964.

NA.SA TN D-2201,

17. Shaw, D. S.; Fuller, D. E.; and Babb, C. D.: Effects of Nose Bluntness, Fineness Ratio, Cone Anglz, and Model Base on the Static Aerodynmic Characteristics of Blunt Bodies Rt Mmh Numbers of 1.57, 1.80, and 2.16 and Angles of Attack up to im". msfi m D-1781, k y 1963.

13. iJehrend, 'rlilliam R;: An Experimental Evaluation of Aerodynamic Damping Moments of Cones with Different Centers of Rotation. NASA TN D-176.3, March 1963.

19. Van Driest, E. R.: Turbulent Boundary Layer in Compressible Fluids. J. Aeron. Sci., vol. 13, no. 3, March 1951, 2p. 145-160.

SO. Penland, J. A.: Aerodynamic Force Characteristics of a Series of Lifting Cone and Cone-Cylinder Configurations at a Mach Number of 6.33 and Angles of Attack up to 130". June 1961.

NASA TN D-:?dtO,

21. Technical Staff Menibers: A n Empirical Method For The Determination of the Zero-Lift Drag Coefficient of Sharp and Blunt Nosed Conical Exit/Entry Configurations at Subsonic, Transonic, Supersonic and Hypersonic Flight Speeds. Space/Planetary Entry Systems, Inc., Technical Note - 641, August 1964.

22. Whitfield, J. D.; and Wolng, W.: Hypersonic Static Stability of Blunt Slender Cones. AEDC-TDR-~~-S~, August 1962.

23. Mmics, A. S.: Normal Force, Pitching Moment, and Center of A.essure of Several Spherically Blunted Cones at Mach Numbers of 1.50, 2.13, 2.31, and 4.04. AOMC/ARGMA/OML Report 6R3F, April 1958.

24. Merz, G. H.; and Pritts, 0. R.: Static Force Tests at Mch 8 of Sharp and Blunt 20-Deg. Half-Angle Cones and a Blunt 7O-Deg. Swept D e l t a Wing. AEDC-m-62-187, October 1962.

L1NG-TEMco-votJGHT, INC.

REPORT NO. HASA CR-66037 I

P A G E N O . 9

2 5 . Fisher, L. R.: Equations and C h a r t s f o r Determining t h e Hypersonic S t a b i l i t y Derivatives 02 Combinations of Cone Frustrums Computed by Newtoniafi Impact Theory. IVoveribsr 1959.

NASA 'I" D-149,

26. Gray, J. Don: Drag and S tab i l i t y Derivatives of Missile Components According t o the Modii'ied Newtonian Theory. Kovenber 1960.

AEK-'I"-60-191,

c -7. Shantz, I.: Cone S t a t i c S tab i l i t y I n v e s t i G t i c n a t Mach Numbers 1.56 through i t . 24. I?A'JOWD Report j5&, December 1'5 j .

23. Jilkinson, D. B.; and Harrington, S. P . : Hypersonic Force, Pressure, and Heat Transfer I n v e s t i s t i o n s of Sharp and Blunt Slender Sones. ~EDC-~R-63-17~ , August 1963.

29. Saltzman, E. J.: Base Pressure Coefficients Obtained From t h e X-15 PAqlane f o r Mach Kznbarz u;) tc 6. XASA TR D-'420, August 1964.

39. 'Yhitfield, J. D.; and Potter, J. L.: On Base L-Tessures a t High Reynolds Numbers and Hypersonic ,%ch Numbers. March 1960.

!LEE-TN-60-61,

31. Gabeaud, Ingenieru: Base R ~ s s u r e s a t Supersonic Velocit ies. J. Aeron. Sci., vol. 10, no. '7, July 1343, p. bj8.

32. Arnold, J. W.: S t a t i c S tab i l i t y and Control Effectiveness Testa on B i%i;c,Jwring Re-Entrj Vehicle i n the Mach P?umber Range of 9.; t o L L . >. Chance Vought High Speeci Wind l'wulel T e s t %, December 1$2.

33. Love, E. S . : Base Pressure a t Supersonic Speeds on Two-Dimensional Ai r fo i l s and on Bodies of Revolution 'Ji th and Without Fins Having Turbulent Boundary Layers. 'IT $19, 1?57.

34. Brooks, C. X.; and l h s c o t , C. D.: Transonic Investigation of t he Effec ts of Nose Bluntness, Fineness Rat io , Cone Angle, and Base Shape on the S t a t i c Aerodynarr?:? Character is t ics of Short, Bhmt Cones a t Angles of Attack t o l&". August 1% 3.

NASA TN D-1926,

35. hraca, R. J. : Aerodynamic Load Distr ibut ions f o r t h e Project FIRE Configurations a t Mach Numbers From 0.25 t o 4.63. D-26014, Feburary 1965.

NA-SA TN

36. Neal, Luther: Aerodynamic Character is t ics a t a h c h Number of 6.77 of a 9" Cone Configuration, With and iJithout Spherical After- bodies, a t Angles of Attack up t o 1%" Vith Various Degrees of Hose Blunting. KASA TN D-1606, March 1963.

o.sous1 1 REPORT NO. a-66037

, PAGENO. 59

I

37. Wolng, William: B l u n t Cone Force Tests a t M=CO. AEDC-TDR-6?-)+:, h r c \ 1969,.

33. I n t r i z r i , P. F.: F'rce-Fliirjit Measurements of the S t a t i c and Djrnainic S t a b i l i t y and Drag of a 10' B l u r t e d Cone a t Xach Xmbcrs 3.5 and 5.5. R P . 3 T3 D-1293, May 1962.

39. :;ells, Y. E.; and Arustr~n~;, i. 0.; "abies oZ AeroGjmadc Coefficients Obtained ROE Developed Neirtonian Exyrcssions r"or Conpl-te and A F l r t i F i l Conic And Spheric Bo4it.s a t Combind Angles of Attack and Sirl-sl ip with Some Co:imriaon; with Hj?>ersonic Experimental DRta. NASA TR R-127, 126; .

119. Eamtro%, E. J.; and Dye, F. E.: LocRl Flo:: Conditicjns and Aerodynamic Pameter ; b y B Seconci-Or3 :r Shock &.pinsion Method Applicable ic Bcdies of Revolution I'e-Rr Zerc Lift, RnS! a t Su-prsonic Syeeds - Et" Comgxter Routine Kc. LV-7!C-13. LTV Report Fo. 00.33, Sqternber lcx2.

41. Eggers, P. J.: Generalized Shock Expansion ;kthod. J. .e ron . .hi., vol. 72, no. I+, ?.?ril 1355, pp ;'3l-F33.

42. Eggers, A. J.; m d Savin, R. 2.: ,". Unified 3m-Dimen;ional C.pproach To Th2 Calculation of Tiirce-Dixnsicnal €I;r:?ersonic Flows, J i t h Application tc, BoCies ci' R e V G l l l t i C r i . p?.!Pc~', Rc?ort 1249, 1955 . (Supersedos R!-C?a TI: 2 Ll)

43. Sper-Lson, C. P . . ; and Dermis , D. H.: Seccaa Order Shock ExAmnsion Method fipplicable to Bo6ics of Revolut ion Kmr Lerc L i f t . Np,GA Report 1325, 1957. (Replaces NA3. m' j527)

44. Ecgers, A . J.; and Savin, R. C.: Approximate Methods For Calculating t h e Flow !'bout Nonlifting Bodics of Revclution a t High Supersonic Speeds. NACf! ?T! 2579, 1951.

45. :lard, G. IT. : Linearized Theory or' Steady High Speed Flow. Cambridge University Pres. , :.355.

46. Van Dyke, M. D.: A Study of Second-Order Supersonic Flow Theory. HACA TR 1031, 1952. (Su9ersedzs NAC!. !IT! T O O )

47. Van Dyke, M. D.: F i r s t and Second Order Theory of Supersonic Flow Fast Bodies of Revolution. J. Aeron. Sci., vol. 18, no. 3, March 1351, pp 161-173.

REPORT WO.HASA CR-66037

P A G E N O . 60

48. Van Dyke, M. D.: Agctical Calculations of Second-Order Supersonic F l o w Past Bodies of Revolution. mAcA TN 2744, July 1952.

49. Lighthill, M. J.: Supersonic Flow Past Bodies of Revolution. Bri.t;ish ARC R and M no. 2003, 1945.

50. Lees, L: Hypersonic Flow. IAS Preprint No. 554, 1955.

51. Hayes, W. D.; Roberts, R. C.; Haaser, N.: Generalized Linearized C o n i c a l Flow. NACA TN 2667.

52. Ferri, A.: The k thod of Characteristics for the Determination of Supersonic F l o w Over Bodies of Revolution at Small Angles of Attack. NACA Report 1044, 1951.

53. Isenberg, J. S.; and Lin, C. C.: The Method of Characteristics in Compressible Flow, Part I (Steady Supersonic F l o w ) , Air Materiel Command Report, No. F-TR-117U-ND, December 1947.

54. Kennedy, E. D.: Methods or" Calculating the Pressure Distribution on Various Nose Sbapes at Zero Angle 02 Attack in the Range of Mach Numbers F r o m 0.9 to 7.0. Inc., Scientific Report NO. 1, 1957.

Gruen Applied Science Iaboratories,

55. Kennedy, E. D.: Methods of Calculating the Pressure Distribution on Various Nose S h ~ p e s at S r r r a l l Angle of Attack in the Range of AYrch Embers Frm 0.9 to 7.0. Inc., Scientific Report No. 3, 1957.

Gruen Applied Science Iaboratories,

56. Cherngi, G. G.: Introduction t o Hypersonic Flow. Academic Press, New York, 1961.

57. Shapiro, A. H.: The Dynamics and Thermodynamics of Compressible Fluid Flow, Vols. I and XI. The Ronald Press Co., New York, 1954

58. Hayes, W. D.; and Probstein, R. F.: Hypersonic Flow Theory. Academic Press, New York, 1959.

59. Keuhn, D. M.: Experimental and Theoretical Pressures on Blunt

NASA TN D-1979, November 1963. Cylinders for Equilibrium and Nonequilibrium air at Hypersonic Speeds.

60. Jorgensen, L. H.: Aerodynamics of Planetary Entry Configurations in Air and Assumed Martian Atmospheres. AIAA -per No. 65-318, July 1965.

R I I I I I I B I I I

REPORTNO. llA6A m-64037 I

PAGENO. 61

I 61. E U e t t , D. M.: Pressure Distribution on Sphere Cones. SC-RR-64-1796,

J a n u s 4 1965.

62. Amick, J. L.: Pressure Measurements on Sharp and B l u n t 5" and 15" Half-Angle Cones at mch Number 3.26 and Angles of Attack t o 100". NASA TN D-753, February 1961.

63. Van Dyke, M. D.; and Corden, H. D.: Supersonic Flow About a Family of Blunt Axisymmetric Bodies. NASA TR R-1, 1959.

64. Id, Ting-U; and Gieger, R. E.: S t a p t i o n Point of a B l u n t Body i n Hypersonic Flow. IAS Preprint No. 629, 1956.

65. Inouye, hkmoru; and -, Harvard: Comparison of Experimental and Numerical Results f o r the Flow of a FerTect Gas About B l u n t - Nosed Bodies. XdSp, "E D - 1 ) + 2 6 , Septenber l S 2 .

66. Cravalos, F. G.; Edelfelt , I. H.; and Ermnons, H. LJ.: 'Rie Supersonic Flow About a Blunt Body of Revolution fo r Gases a t Chemical Equilibrium. Froc. M Int . Astron. Cong., Amsterdam, Vol. I, August 1958, pp. 312-322.

67. Storer, E. M.: A Method f o r the Prediction of the Pressure Distribution on the Conical Portion of a Sphere-Cone. G. E. Pero. Fund. Memo. No. 131, Mnrch 1962.

68. Vagl io-hurin, Roberto; and Trella, Massimo: l! Study of Flow Fields About Some Typical B l u n t -Nosed Slender Bodies. No. 6?3.

PIBP.L Report

69. Conti, R. J.: Iaminar Heat Transfer and Pressure Measurements a t a Mtxh Number of 6 on Sharp and Blunt 15" Half-Angle Cones at Angles of Attack up t o 90". NASA T'N D-962, October 1961.

70. h e r , A. L.: Pressure Distributions on a Hemisphere Cylinder a t Supersonic and Hypersonic hbch Numbers. August 1961

AEDC TN-61-96,

71. k c h e l l , R. M.; and O'Bryant, W. T.: An Experimental Investigation of the Flow Over Blunt-Nosed Cones a t a Mach Nurdber of 5.8. GAICIT Memo No. 32, June 19%.

72 . Oliver, R. E.: A n Experimental Invest imtion of Flow Over Simple B l u n t Bodies a t a Nominal Mach Number of 5.3. No. 26, June 1955.

GAUIT Memo.

r /

REPORTWO. SASA CR-66037

PAGENO. 6Q

I I E 1 I I 1 I I I I E P I 1

73. O l i v e r , R. E.: An Experimental Investigation of Flow About dimple Blunt Bodies a t a Roninal hbch Number os' 5.';. vol . 1 3 , no. 2 , February 1356, g. 177-17).

J. Aeron. Sei.,

75. Lo=, Harvard; and Inouyc, hplmoru: 1:luncrical Analysis of Flow Properties About Blunt Bodies Moving a t Supersonic Speeds i n an Equ i l ib r im Cas. IVSP. TR R-704, J u l y YXb.

76. Gapiaw:, R.; and K a r c h r , L. : Flov Past Slender B l w t Bodies - A Review and Extension. IAS Paper No. 61-210-130b.

'(G. Jul ius , Jerome D. : on a 20° Cone a t Pnglcs of P.ttack ilp t o :?Oo fo r R Mach Ntmber of 11.95.

Measurexnts G: Pressmc and Icrcal H e a t Transfer

NASA TN D-179, December 1953.

79. Bertram, M. H.: Tip Blunzncss Sfi'cct; LL Cone Pressures a t W 5 . 3 5 . J. k r o n . Sci., vo l . F j , no. 2, ScptzXbcr 1356, pp. 293-900.

''50. Tewfik, 0. K.; and G i e d t , W. B.: Heat Transfer, Recovzrj Factor, and Pressare Distributions 'round A Circular Cylinder IJormal t o a Supersonic Rarefied :.ir Stream. Janwry 1sO.

L G Paper 110. 60-46,

31. Tewfik, 0. K.: Heat Trans;'er, Recovay Factor and Pressure Distributions Around A Circular bylindcr Normal t o a Supersonic Rarefied A i r Stream; Part I1 - Comparison of Experiment with Theory. University of Cal i fomin TR HE-150-169, b y 1959.

82. k h n e r t , R . ; and Schermerhorn, V. L.: dalce Investigation on Sharp and B l u n t Nose Cones R t Supersonic Speeds. NAVORD Rep. 5668, January 1950.

63. Ropal , Zdnek: Tables cr' Su2crsonic Flow Around Cones of Iarge Yaw. ! I T Tech. Rep. No. 5, 1349.

&- Van Dyke, M. D.; Young, G. B. :J.; and Siska, Charles: Proper U s e of t h e MIT Tables f o r Supersonic Flow Past Inclined Cones. Aeron. Sci., vol. la, no. 5, h y 1951, pp. 355-356.

J.

REPORTNO. m a 3 7

PAGENO. 63

35. Rolt, k u r i c e ; and Blackie, J o h : Experiments on Circular Cones a t Yaw i n Supersonic Flow. J. Aeron. Sci. , vol. 2 3 , no. 10, October 1356, pp. 931-96.

86. Harris, E. L.: Determination 03 Streamlines on a Sphere-Cone a t Angle of Attack From the Measured Surface Pressure Distribution. N A V m NOL 7% 63-37, 1363.

87. Ferr i , Antonio: Supersonic Flow Around Circular Cones a t Angles of Attack. EACA TR 1945.

3 3 . P a e s Research Staff : Equations, Tables, and Charts f o r Compressible Flow. NACA TR 1135, 1953.

83. Burke, G. L.: Heat Transfer and Pressure Distributions About Sharp and Blunt E l l i p t i c Cones a t Angles of Attack and High Mach Numbers. AFFDL ‘JX-64-172, hhy 1765.

90. Gregorck, C. M.; Nark, T. C.; and Ire , J. D.: A n Experimental I n v e s t i s t i o n of the 3urSace Pressure and the Iaminar Boundary Iayer on a B l u n t Flat Plate i n Hypersonic Flow. March 1963.

ASD-TDR-62-792,

91. Bean, J. M.: Statement of Work, Entry Body Aerodynamic Performance Study. LTV Memo 3-50000/5~-265 Rev. P., J u l y 1965.

3‘2. Yanowitch, S.; Kilpatrick, P. D.; and Miller, ;i. T.: Mission Accuraey Analysis f o r t he Scout hunch Vehicle. November 1962.

EI’V Report No. 23.41,

73. Everett, H. V.; and Dobson, W. T.: The Near Earth ?.lission Analysis Trajectory Routine, LV-VC-?7. LTV Report No. 00.251, October 1%3.

94. Rolf’e, B. P.: Nominal , Plus and Minus Three Si- Motor Performance. UY DlR No. 23-DIR-$2 Rev. B, September l(J65.

95. Phillips, W i l l i a m E.: Effect of Steady Rolling on bngitudinaland Directional Stability. M A TN l627, June 1948.

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Report 100. BfAsA CR-66037 psge Bo. 64

REPORTNO. a-66037

PAGENO. 65

TABU I - PART B S\osarrry of Reports Preeentiw Theoretical R e s u l t s

Tbe following references include a development of an applicable theory for Various types of bodies. theoretical approach, data presented, ard lirritstions of th theory is

A short 6- incl~&lng the

presented here.

Ref. 3 - An empirical collrpilatlon of aerodylrarnic loads on sharp cones m cone-cyllnders i n the trsnsonic W h number range are presented in des- chart form.

R e f . 4 - A solution of the !Faylor-)lsccoll sharp cone equation6 for cor& angles up t o 30' and supersonic W h numbers.

Ref . 5 - This report presents l i t t l e new inforration but d a e compile The rapge of material raqy reports together for comparison.

covered is very broad.

This report presents a solution of the equations derived by A. E. Stone which applies an a q l e of attack perturbation t o the Taylor-MBccoll equations. erne the sam 8s in Reference 4. angle of attack depeadcnt variables BFC presented in derivative form.

Ref. 6 - The nmge of parameterr

first order e o l u t i o ~ far

Ref. 7 - Closed form solutions for force and ropent derivatives for cones i n supersonic flow were obtained fran an Integration .of the potential flow equations . are presented.

c First and secoad order theorlee

Ikf. 11 - A computer routipe for the computation of aerodynamic cbaracteristlce of arbitrary bodies us- Eewtonian Impact theory is presented.

Ref. 12 - An approximete solution of the axtally e y r e t r i c tr8n8onic equations, valid for 8 s e d - I n f l a t e COLT, is preseakd.

Ref. 13 - The bypersonic similarity parereter is employed t o correlate sharp cone solutioas for all supersonic lbch numbers and cone m e s up t o 50.. fram Reference 4 and Reference 6.

The sharp cone solutions were obtaincd

Ref. 19 - A anaerica1 solution to the compressible turbulent boundary layer equations are presented for adiabatic a non-adlatmtic flat plates.

W e f . 21 - Base pressure drag axl forebody drag data are presented for rhfirp end blunt cones for all )lath numbem. obtalned f m m a correlation of nmny test r e ~ u l t r . e s t a t e is not incl&ed.

The data were An accuracy

I ' 0 - S O 5 9 1

Ref. 22 -

Ref. 25 -

Ref. 26 -

R e f . 40 -

LING-TEMCO-VOUGHT. 1%.

REPORTNO. l#ASA CR-66037

PAGENO. 66

S i s i h r i t y parameters correlating norvrl force and pitching ppapcnt coefficients f o r many sphere-cone coniig\uatione are presented. flov equations, hence are good only for hi@ mch numbers.

These parepeters were derived from Newtonian

C h e r t s for detelrmining aerodyaeraic coefficients on basic missile cmponents ere presented. based on lkwtonian flow theory am3 can be cocbined for coprplex miesile shapes.

The coefficients are

Thirr report I s similar t o Reference 25 except that characteristics for ephere-cones are presented 88 a carplete body.

This report develops a computer routhe using the second order shock urpaneion theory of Ref. 43 for use w i t h the L!FV 7090 computer. the routine allows camputations t o begln at 8n arbitrary pofirt by inputtbag local conditiane from another ~ource. RCason8bl.y accurate results m y be obtaintd by inputti- eetlmated corditiane at the sphere-cone junction and adding aerodyIlepic coefficients for the hemispherical nose.

Although th theory is inapplicable for blunt bodies

other reports, up t o Reference 61, mt included in either pert of t h f e Table contain special Inforpation which did not warrant a special discussion but VEIS neverthleus applicable in some degree t o the problem.

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REPORTNO. NASA CR-66037

PAGENO. 68

TABU I1 - PART B

S\1pllrary of Reports Present- Theoretical Preesure Distribution Dsta on Sharp and Blun t Cones

The following references Include a developeent &/or reeulte of an applicable theory for predicting pressure distkibufion on a sbarp or blunt c w . presented kre.

A abort describing the report contents is

Iter. 61 -

R e f . 62 -

Ref. 63 -

Ref. 64 - Ref. 66 -

Ref. 67 -

R e f . 68 -

R e i . 75 -

Ref . 83 -

Ref. 07 -

lhbulated data for spherecanes with colpc half anglee up t o bo' are presented for Mach numbers of 3, 4, 6, 10 ard infinity.

A seml-empirical Pethod of predictiw the c i m w e r e n t i a l pressure distribution on sharp cones l a developed.

Preseure distrfbution on a hemisphere is cauputed for several Mch numbers esd specific heats. one wherein a shock shepe is ass& and the flow equations are solved for a body shape that yields the ass- shock shape.

The nethod is an "ipvertm"

An approxinuate solution t o the pressure dietribution on a hemlsphere is presented.

A combiaation of relaxation methods, numerical integration, an3 method of characteristics are ccmbined t o developaunified theory for capputlng the flow f i e ld about 8x1-symetric blunt bodies in eupereonic flow.

A pzlppber of flar field solutions uehg ths mthod of Reference 68 are presented far spbre-carrss. using the r s t i o of specific bsts b e W a normal shock wave.

had &rs eolutioxui a m cum8lrt.d

A Pethod of correlating characterlatics solutions for perfect a d dissociated -see is presented for sphere-cones.

An "inveree" method IS employed t o capUte f l o w field solutions about hemisphems i n pcxfect and equilibriu gaeees.

H w r order t e r n a r e retained in Stonee' angle of attack pertubation of the Taylor4bccoll equations eo that accurate flow field solutions about a CODC at large y a w can be c q t e d .

A firet-order solution t o the circumferential pressure distirbution on a sbarp cone at sad1 angles of at tack l e presented.

Other reports, ug t o Reference 91, not included i n either part of this Table contain special informetion which did not warrant a special diecussion but was nevertheless applicable in some degree t o the problem.

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