197oo25216 - nasa · nasa project apollo working ... characteristics of bluff reentry capsules with...

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t;_opy -"" NASA Project Apollo Working Paper No. 1021 PROJECT APOLLO INVESTIGATION OF NEWTONIAN STATIC LONGITUDINAL AERODIqXIAMIC CHARACTERISTICS OF BODIES OF REVOLUTION WI_H VARIOUS HEAT-SHIELD :i CURVATU}tES, AF'IERBODY ANGLES, AND CORNER-EDGE RADII -_ ICODE) _ t_ASACI_OR_MX ORAo NUM ) NATIONAL AERONAUTICS AND SPACE ADMINISTRATION SPACE TASK GROUP Langley Field, Va. : June 28, 1961 I https://ntrs.nasa.gov/search.jsp?R=19700025216 2019-01-25T23:01:30+00:00Z

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t;_opy - " "

NASA Project Apollo Working Paper No. 1021

PROJECT APOLLO

INVESTIGATION OF NEWTONIAN STATIC

LONGITUDINAL AERODIqXIAMIC CHARACTERISTICS OF

BODIES OF REVOLUTION WI_H VARIOUS HEAT-SHIELD

:i CURVATU}tES, AF'IERBODY ANGLES, AND

CORNER-EDGE RADII

-_ ICODE)

_ t_ASACI_OR_MX ORAo NUM )

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

SPACE TASK GROUP

Langley Field, Va.

: June 28, 1961

I

197OO25216

https://ntrs.nasa.gov/search.jsp?R=19700025216 2019-01-25T23:01:30+00:00Z

. - ..

tb.

NASA PROJECT APOLI/)WOFu_IG PAPER NO. lOO_l

PROJECT APOLLO

INVEZTIGATION OF NEWTONIAN STATIC

; LONGI_IrDINALAERODYNAMIC CHARACTERISTICS OF

<

_. BODIES OF REVOLUTION WIT_ VARIOUS HEAT-SHIELD1.

• i CI/RVA_UBES,_BODY ANL_/_S,ANDCOP_-EDGE RADII

f

_" Prepared by: _o_ _.

._ AST, Flight Mechanics

Tho_lasL. Blakemore U '"" AST, Flight Mechanics

_ Authorized for Distributinn:

N _[O_V_LAI_2,0NAUTICSAND SPACE AU'4INI_I_ATION

i, "_ SPACE TASK GROUP

I,angleyField, Va.

June 28_ ].9_i

1970025216-002

• TABLE OF CONTENTS

I_'T_OI_CTION ........................ '1

SYMBOLS............................. 2

D_S_SSIO_ASD_S]mTATIO_ OF RESULTS ............. 3

_, CONCLUSIONS ........................... 4

i

m

1970025216-003

liJ

LIST OF FIGURES

Figure Page

1 Configuration for heat-shleld curvature and after-

hod7 angle investigation .............. 7

2 Configuration for corner-edge radius investigation . . 8

3 Heat-shield curvature and afterbody angle investi-

gation ....................... 9

4 Corner-edge radius in_._stigation ........... 21

5 Summary of combined heat shield and afterbo_ aero-dynamic characteristics 25

t

6 Su_m_ry of corner-edge radius investigation ..... 27

7 Reference area ratio for combining corner-edge

• radius and afterbody contributions ......... 28

8 Reference distances for combining afterbody and

: corner-edge radius moment contributions ...... 29

A-I Geometric comparison of several configurations of

equal volume ................... 30

A-2 Comparison of aerodynamic characteristics for

several configurations with equal volumes.X

c.g_ o 24 3lD

A-3 Lateral c"nter-of-Eravity offset required to trim atvarious lJ Ct.to-drag ratios for several configu-

X

rations of equal volume, c._ = 0.24 33

1970025216-004

INVESTIGATION OF NEWTONIAN STATIC

LONGITUDINAL AERODYNAMIC _%PACTF_ISTICS OF\

BODIES OF REVOLUTION WITH VARIOUS HEAT-SHIELD

CURVATURES 3 A_BBCDY ANGLES, AND

CORNER-EDGE RADII

; SUMMARY

_. Newtonian aerod_vnamlc coefficients are presented for preliminary

,, prediction _f the static stability characteristics of bluff reentry

I, bodies _Ith various heat-shield curvatures, afterbo_y angles, an_ corner-; edge radii. An example of the usefulness of these design curves is

presented in the appendix where the aerodynamics characteristics are com-

!_ puted for several configurations of equal volume.

; INTRODUCTIONt

The purpose of this paper Is to present Newtonlan aerodynamic

coefficients for preliminary prediction of the hypersonic static stability

characteristics of bluff reentry capsules with various heat-shield curva-

tures, afterbody cone angles, and corner-edge radii. As an example of the

_ usefulness of the design curves, the static stability characteristics of"' several configurations of equal volumes are calculated and compareO.

_,. PROCEDURE AND ACCURACIES

This paper consists basically ol two separate investigations: heat-

shield curvature and afterbody-angle investigation 3 and corner-edge radius

investigation. All aerod2namlc coefficients presented, except the after-

body contribution, were determined by numerically integrating the New-tonian pressure coefficients on an IBM 704 digital computer, utilizing a

program set up for bodies of revolution. The afterbody contribution was

co_puted ITom algebraic Newtoniau aerod_namlc coefficient functions. All

coefficients were computed for every ten-degrees angle-of-attack and woald

correspond to a maximl_ stagnation point pressure coefficient of 2,_ (M = _, 7 --i). Solne ide_ of the accuracy of the numeric.%l integration

,: procedure m,'_ybe obtained b_ comparing the integrated values for the

._ sphere (Rc/D = 0._0, fig. ,), with exact values. For the sphere at any

_ ,

1970025216-005

angle of attack, the exact Newtonian value of the lift coefficient is

zero and the drag coefficient I. The maximum deviation of the integratedvalues of the lift and the drag coefficients from these exact values is

0.005 and 0.013, respectively.

SYMBOLS

Axial force

CA axial-force coefficient, qS

force

CD drag coefficient, qS

Lift force

;: _L lift coefficient, qS

! L/D lift-to-.irag ratio

Cm pitching-moment coefficient, Pitchin_ momentqSD_n

pitching-moment-curve slope, per degree at m = 0o --m

Normal force

CN normal-force coefficient, qS

D configuration maximum diameter

D' configuration diameter at station of afterbod_-corner-edge

" Junction. (See insert figure, fig. 8.)

"_ free-st_ _m Mach number

q free-stream _ynamic pressure

RC corner-edge radius

heat-shield radius

S configuration cross-sectional area at station of maximumdiameter

x distance from most forward point of configuration to station

of maximum diameter. (See insert figure, fig. 9. )<

f

1970025216-006

x' distance from station of maximum diameter to station of

afterbody corner-edge Junction. (See insert figure, fig. 9.)

- = D sin @"" D v

t

. X all,Lance from most forward point of configuration to center-of-e.g.

_j. gravity location along axis of symmetry

i Yc.g. lateral distance from axis of symmetry to center-of-gravity

: location

_J _ angle of attack of model centerline_ deg

_27 ratio of specific heats

ev afterbody angle_ deg

DISCUSSION AND PRESE_2ATION OF I_ qT_TS

The effects of heat-shield curvature and afterbody angle on the

static stability characteristics are presented in figure 3 for an XCog.

" location at the configuration maximum diameter, angle-of-attack rangefrom 0° to 90°, heat-shield radius of curvature to diameter ratios of

,'. 0.8, 1.2, 1.6, _, and afterbo_v angles of 0°, I0°, 20°, 30°, _0°, _0°and 60°. (See fig. 1. ) The heat-shleld contribution and afterbo_y con-

tribution to the stability characteristics are presented separately in

j :"_ figures 3(a) and 3(b), respectively. The heat shield and afterbody• _ characteristics are combined in figure 3(c) and the maximum li_T,-to-drag

_.-! ratios and maximum lift coefficients for the combined heat shield andafterbody are presented in figure _. The values in figure 5 were read

from the faired curves in figure 3. Since the coefficients presented in"--" figure 3 were calculated in lO increm_nts, the conditions at maximum

i lift-3o-drag ratios and maximum lift e.renot accurately defined. There-fore, the grid was dropped from figure 5. From figure 5, it is seen that

an increase in maximum lift-to-drag ratio and an increase in maximum lift

is obtained by decreasing the heat-shield curvature (increasing

and/or by increasing the afterbody angle. This results in a decrease in

static stability as illustrated by the pitching-moment curves of fig-

ures 3(a), 3(b), and 3(c). For the heat-shield contribution shown in

figure 3(a), the norm_l-force coefficient _ncreas=_ "_hile the axial-force

coefficient decreases with d.ecreasing RNID (m < _o). Thus the orienta-

, oo tho ,oroovoo,o,increases with decreasing _._/D.

m

1970025216-007

.f

The effects of corner-edge radius on the static stability charac-

teristics are presented in figure 4 and summarized in figure 6 for an

Xc.g" location of D/33 angle-of-attack range from 0° to 80°, corner-edge

radius to diameter ratio from 0 to 0.5, and heat-shield radius to diameter

zatios of 1.0 and 1.5. (See fig. 2.) From figures 6(a) and 6(c), it is

seen that incre_si;_ corner-e0ge radius decreases the absolute value of

L/D, whereas, decreasing the heat-shleld curvature increases the absolute

value of L/D. For moderate corner-edge radii (Rc/D)_<0.2, increasing

the corner-edge radius decreases the static stability; whereas, for very

large corner-edge radii (Ro/D)_ 0.3 increasing the corn__r-edge radius% v) I

iucreases the static stability. (See fig. 6(b).) It is also seen from

:_ figure 6(b) that the flatter the heat shield, the smaller the effect of:' . : corner-edge radius on the static stability. Figure 6(b) also illustrates

(again) that flattening _he heat shield decreases the static stability.The orientation angle of the resultant force vector is _een from fig-

! ure _(a) to increase with increasing Rc/D.

..,_ The reference area ratio and moment reference distances for com-bining desired cozmer-edge radius and afterbody contributions are given

• in figures 7 and 8. An ex_.ple of combining these contributions ispresented in the appendix where the aerod_vnamlc characteristics are com-

. puted for several configurations of equal volumes.

CONCLUSIONS

, .-. 1. Decreasing the heat-shleld curvature and/or increasing the

• . • afterbo_y angle increase_ the maximum llft-to-drag ratio an_ the maximum

lift coefficient _hile decreaslr_ the static stability.

2. Increasing corner-edge radius decreases the maximum lift-to-drag

ratio. For moderate corner-edge radius3 increasing corner-edge radius

decreases the static stability; whereas, for very large corner-edge radius,

increasing the corner-edge radius increases the static stability.Decreasing the heat-shLeld curvature reduces the effect of corner-edge

radius on the static stability.

3. The orientation angle of the resulting reentry force vector

' increases _ith i_._reazing heat-shleld curvature and increasing corner-

! edge radius.

4. In comparing the aero_ynamlc characteristics of several capsules

'- .'! of equal volume with inerc_,r_Ingcorner-edge radius (resulting in,.! increasing afterbody at_,._.!c),the effects of the iDcreased corner-edge

and CL'; '] ra_diu_B _,rere dominnnt_ r::;1,] Ling in r,. de,creased (L/D)m_lx

,,, .;,] max

'C// ' -

, 4_,,4 ........

1970025216-008

As an example of combining the corner-edge radius and afterbody

contributions presented in figures 1 through 8, the aerodynamics of atypical lunar reentry capsule are presented. The capsule _ms designed

for a hypersonic lift-to-drag capability of 0.7.

i_' The minimum volume requirements for the crew and equipment fixed

,_ the afterbo_y angle at 30_. The afterbody angle resulting from the_! volume requirement was based on a 13-foot diameter capsule and a semi-

_! integrated module concept (lunar vehicle consisting of a command and an_ equipment module). The lift-to-drag ratio capability requirement fixed

•_ the heat-shleld radius of curvature to diameter ratio at 1.2. (See

fig. _. ) The center-of-gravlty location has been estimated as 0.24

diameter behind the heat shield. Since corner-edge radius is desired

_ for the configuration because of the high local convective heating rates

_ associated with the very large velocity gradients resulting from thesharp cornerj the basic _onfiguration reentry aerod_nsmics are comparedwith two other configurations of equal volume whose corner-edge radius

to diameter ratios are 0.05 and 0.1C. (See fig. A-I. ) The resulting_ afterbody angles to hold the volum_ constant are approximately 3_° and _0°_

respectively.

'_ The aerodynamic characteristics of the configurations are presented_ in figure A-2 an_ the lateral center-of-gravity offsets required to trim

_ the configurations at various lift-to-drag ratios are presentea in

figure A-3 for the longitudinal center-of-gravity location to diameter

_ ratio of 0.24.

_ The forebody coefficients were obtained by interpolating fromfigure 4 for a heat-shield radius to diameter ratio of 1.2 and the after-

• body coefficients were obtained from figure 3(b). The combined coef-

i_ ficlents_ which are presented in figure A-2, were then computed withthe use of figures 7 and 8 as follows:

CA, CN, CL, CD = (CA, CN, CL, CD)forebody + (D') 2 (CA, CN, CL, CIlafterbody

Cm = C + - 0.333 CN + Cmforebody fo_ebod_ mafterbod_VU

_ afterbo_y

I

] 9700252 ] 6-009

It should be emphasized that small inaccuracies occur in combining

the comfit-edge radius and afterbody contributions in that a small portionof the corner-edge radius is shielded by the conical afterbody. For the

large ei_erbo_y angle and small corner-edge radd_ of the present investl-

gation_ the inaccuracies would be negligible.

The C_ I_ figure A-2 sho'_ that a ms_ximum llft-to-dre.g ret_o r_ngp

from -0.64 to -0.80 is attained for the conflg_ratlons at approximately50° angle of attack. The maximum llft coefficient ranges from -0._3 to

-0.69 and occurs at approximately 35° angle of attack. From figure A-5,

it is seen that the vehicle may be trimmed at a llft-to-drag ratio of

-0.9 by lateral center-of-gravity offset. Tri_ from an L/D cf -0._

(lower side of CLmax ) to (L/D)max could be _ccomplishedby augmentlr_the lateral center-of-gravity offset with an auxiliary flap. The change

in orientation of the resultant reentry for('evector !u _-_}_q_g the

Rc/D-- 0, 0.0_, and 0.10 vehicles from _ = 0 to _L is ap_ronimatelymgz<

&.0°, 6.5 ° and i1.5° respectively and in trin_ning Irom CL to (L/D)_;_

: is upproxi_tely 13.5 °, 14.5°, and ll._o, respectively. The comparison ofthe conflgurat_ons in figure A-2 shows that the effect of increasing the

; corner-edge radius was dominant over the effect of the resulting increa_

in afterbody angle and thus produced a d_rease in (L/D)max and CL

1970025216-010

1970025216-011

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1970025216-012

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._._, (a) Heat-shield contribution.

_ Figure }.- Heat-shleld curvature and afterbod_" angle investigation.

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1970025216-013

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l_gure 5.- Continued.P

1970025216-014

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1970025216-015

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Figure 3.- Continued.

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1970025216-016

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CI t deg

; (c) Heat shield and afterbody combined. RN/D = 0.8.

_"; FiE_re 3.- Cont,_ .... _,'_

1."t

1970025216-017

z4

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:i'""'..............._]: •i:: ; ' ''.:'.. .._:_.:_..........,".............,,.,,,,,........_;.:-"........0 I0 '20 30 4D 50 60 70 80 90-.

a t deg

(c) Heat shield and afterbody combined. EN/D = 0.8.

., Figure 3.- Continued.

1970025216-018

15

, deg

5O

o__._...._.._._ .-.-_ .... "._;--.-'-i,o'_

1J

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0 10 2C 3_ 40 50 60 71"/ 90 90,_ _, dog

g

\,' (c) Heat shield and afterbody combined. RN/D = 1.2.

._._:, Ftff, urc }.- Continued.

1970025216-019

" 16

:.... ..... -:...... : .............. ... = .............. :

I ........... -S."I

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: : .. :. = • : = [...... i " n ................................. !

• : " .i " ; ' : _ ! " i..4. • . . ..... ....._. :.... . ........... ;............................ -_.-::_.;_..• ... . ! .... • . ...,---,';,;;".._.__1 _. : L..-.. -,=-"=;_,_ "- :,---" .'_i _

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-" "0 10 20 30 4.0 50 60 70 80 90

, dog

(c) Heat shield and afterbody combined. RN/D = 1.2.

Figure 3.- Continued.

" .;4

1970025216-020

1y

Or, deg

- /50

LLLA___L____L___ I____I__L,_I ....

c_ -'_.L..Ik._ ,_! 1....i ]"._-_S _ " .--._ ! ' , ! _"- L_ _i _" ' lO

i_I . '_

1.6

i .... : .........

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0 lO 20 30 ¢0 50 60 7U 80 90

(Z, deg

:".,, (c) Heat shield and afterbody combined. _/D "-"L.6.

:'. Figure 3.- Continued.

• .wq'. _ ._ JI.,L _ I

1970025216-021

18

i ! . r-'--- I • ;'" ; T; !',r; 4 ,,,• ' .. i - '. , i ...... _ ... .-.-J ..... L-__ "'..............,...........,...............................:_ I-:L_ - ,__

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

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o4 ............................................... _.."_,_,,,' "40,;.• _._" _'p.4-'- I _,.=r"_ L,,"' g'[I

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• . . -..._,,.,,.-..--._;.r _ , , • : .. ,

-.8 ......................................................................!.0 20 30 40 50 60 70 80 J90

(;I, deg

(c) Heat shield and aftez'bo_2 combined. _JD = 1.6.

Pigure _.- Cor_ti-ued.

?

1970025216-022

19

i

e. deg

.,........ ,........,.-:':i .50t" ' "'_" -40

....,..'T." 20,, t.___... . : • L,._=_. " : '

-------- _. ,. .... . -10u

I./D • • '-'_

.,' ..........

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i- ........ " '_.. ,, .... ."% .. ,,..,

l_i_ II

o. Pl! " ":,, '" ,, ,,,"'

i

i I

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o.,ti,.o. .

c_ , f,..'

41..... " ._'i ,.,. _....... . . '';''>''''"_:-..,. ._oL .....• l'j I' " "'_...... 60 70 F?O 90

0, deg

(c) Heat shield and afLerb,_,dj (;ombined. IL,/D.= _.

';_ FLcLtr_ _ ._.• .'-.',_'_" _.z_,_ed.

1970025216-023

.4

5U

0 10 20 30 ¢0 50 60 70 80 90

•, dog

(c) Heat S]"Liel_ 8z_d afterbody cc_ined. 9_TP : _o. (Concluded)

Figure }.- Concluded.,7

#

1970025216-024

21

-.84. , . i :"'IT ,, " : I'" : ! --•..-.-: ". r..LL I. : ,_ .I .": : |._:._j_. "....... I •

Cm -. 08

-.12

0 10 20 30 40 5Q 60 70 80

deg

_, Figure 4.- Corner-edge radius investlgatlon.

] 970025216-025

22

%4 10

152025

0 .50

1.6

1.2

: C9 .5L.

•s i ......I

• 25• 20

"_ .15: 10

05

0

-.8

CL

-.4'

0 10 20 30 $0 50 60 70 80

deg

(%) RN/D = l.O.

Figure 4.- Continued.

J

4v ._

1970025216-026

23

-.12

-.15 .50

-.20

o

1.2

,50

,11

CN ,25.4, .20

.15

.10

.OS0

0 10 20 30 40 • ) 60 70 80

_, deg

L (b)N/D=1.5.,;, Figure _.- Continued.

t_L

I

]9700252]6-027

24

ttc/I1

12 , 6 ................. : .................. ; l l .

.... _. i i i i i !.... ".-i ......... :-.. = ...................

-2.4 ............ ."......": : -'": .... : ....... : "'" : ........ 7 "-: . .... i : , : /

..........i ........................ _ .... /-

..................... _i --': .--.

....... i ....... _ , =L/'; -Z.." ..... i ..... r ................... -: ........................ 7":'-.""-"" : ""

-:-i ...=.: ":......:i.._:. _: ......:_..,:_ ;.::' .....-;-.4...i-.--:-i............!-% ..... *-::-'

• • : : : • . : " " : • " _ : • _ ' ;

- R ._ • l_--_. :_#__. ! .... ._ ...... :_.,,,E....-::,,_ ........ :.L.. -.-...-_ ..-..%, ..:

• : : ': I , . " . ,,,_'." " . .r.-._..,.l...,...... .,---:- _"3-_r ,.. •N .ot....... • •

. I -""'_ ! : • i •.,.l.,_....,r_..:....,,._,• " ,_ • _ ".'.,.-I.".q r-_-_- _.- • _.;_r%;_ _ "".a--'F--__--__--__--__--__--___ "" I"---';"" ,"I"-_,".--',_ ,.-..--_-I

I :'" ..d_.._._E-_.._." ._._.._..a.-._ , "1.__ : _ _ -._

._. : • . , , lll_l__j_ ,rl, , . • ._-. • • , , • _ ".. .1,;._.,_._&', .,..._L.......................,.." I:-.:j,/li_-':-_. :..i. ""i ...... ! : =.-.I ..:! :.. • ."-+-..._ _._

• " , . ,, . "'" ! = i ! " i : ........ L. ,__ ..... :," : i'-"o_-.-..-:_.' !:-"! -'-'--:..... • • : : r,o! ": �-.// " : -,i " " i : "............... " ""' " : .....' " • "'' " • , :'". .... i """ ',

• • • :. : v . ..2.0 ,;.=.i.-"........ ""- I '"'" .......... .'--" "-'. ........: ....... "!."" : -'i ...... "-'"

• _ i i i . • : . : = • • . ••." •.- l .... ,-"'" : • I ":" ': I ........ • " " / ' : ! : "1

_..'--_._---..:, .--,-_-:- :.,-'-:. --,----..--. -!,.....i :-i -_- '_,.__<! _. :f:! !! : I ;i. i _

L_6 i_:"_'_",,IL'_'i l....... i ...- ..... ".. :..... I• I ''i I , " i,__...l__,,__.....!l" " " : "__, _._-,_..-=,__.-,,_.._....____._._...._+_.. ...........-_

_ __' __. _'_._i.-- -, _...." • / ".i _'"'!":"_ • ii...........

I'--_ .... _ .... '.... r" I • ! • •' Co I--.'__" ; .-_! , . _ , : 15G

I ! i :. I " , "ill,._ '": ;" =....... ,. • i ! ,, •o_ ......]..-j.:/ : _i . , . .. ,/:.:.-...:. i. "., / .... !: : _, "_..'___',--,,.,..,: .. i _ :r...__.._-r.:_.L......-i.....--___:--_ ..........,,. / ; _ . 1" : . • ! ._kT,_.-'--._".;_"_' , _-_-'-.-- ?5/'' • " I " " " • " i-I_'l-..'_l,_i.-_..*.,,. "r'-',..--. _ _

• / . , . _ .. I • ...:• i :"_,L_-_,..-;,.,."-!..i';/'""_ I. ";" / ; • , . -- _ ,"-;._-'_.._.i-_---.,i ..I--.:-.:._'.--.- :-.---t---_--" I .... + " "'1-'_-. "_. ............. ! ': _'-'.._"'-_''_

.... I " ' i " " " "_. ',i ' . i , • i . : . i • : i " _'U: • I • . ; i . / - . • I • i....: .:. , ! -, ; ", • ; '.: ...... " l" : [ .... ,i

• i _ l • i : ! i • i . = i

• : • .05"-L u- j : ' . : ! _. !'".'" .. ",..i._-._" I • , . ! =

........I....... _.:.'_. .-.ii'__. _:.'. '.............'...............•: . _. -;,.._..i-,_ . " ' l " " ! i

CL -., ..'_- ........ ' ....... -'"i"-"!...,r..__

0 10 20 30 4.0 50 60 70 8I'}

deg

(b) RN/D = 1.,_.

.: Pigure j'.- Concluded.

i-%

1970025216-028

";_' 25

-2, i

-2.0

/_l 1"6

.i_" .8

:}_'., - .S ;_0°

_o," -.4.

• 0 ' , i I I i ,i !

g/; -T "c°

f_, -. 6

" CL ;;orL_x

Sv: O"

' ' ! I I I I I I

,_ 0 10 20 30 4,0 50 60 70 80a, de9

FAgure _.- Sum_Lry of combined heat shield and afterbodyaerodynamic characterlstics.

1970025216-029

26

-.8- D

1.6

1.2

-.8- \\ e///_-_'_, ._CLm x -.4 - j_//20o

-'.2- /8v: 0°

0 I i , I I I I I I

Re-.8 D

_6 y/_20° , 60°

L/D "For

CLmax -.2-"4. / 2009v: 0°

I I I l I I , I I

0 10 20 30 40 50 60 70 80

, deg

Figure _.- Concluded.

i

" "Ill II

1970025216-030

2?

"': 0 .2 .4. 6 0 .2 .4. .6

•" no,m R,:/.

'_;_ Figure 6.- Summary of corner-edge radius investigation.

1970025216-031

28

= . _ _ : ........... .....

..........i..... _ :llll;lll___............• R P._. •

i [ CLY% __. •

.... __. -:, .........I:" n P,,_ h n pI V .... A ,¢ 4. n. _ ,_ ,,,I ,_

_oo___::,__ .....__ ...... _0-",_¢___._._.!."._.-",,..,._'_.... .....-.--,_....... -.90 i -:. "_--_'_'_"-%.--_'-'_ ......._ ...... "-'-_ ......

I l _ l _ ..... _ 2 O

i_;\\k'x_.-'_%,.._..-_.._........

" 8 O _ -l_ __ll "____ _ _" lllI " ' _ _ .... ' l !....... ,i il """ ";5 .........

.'qiS(_ I ill l : I_]

_ _: : "_ __.'' , " i " i4-5 .

i_O i"". ................ii'" i ill • .......I. 50

,_oI-. i........ _.

, 2 0 ........ _ ...... i l "--

l n n : _ .... I _n n _ nn_ n

i in _ n n m l

" _ 0 I j' ] " "" l--l_ ............. _ _ ............ _ i; ............ I

n n n : J" ' _ I i I_ n _ i n I

0 nn_ .......

0 ,1 ,2 ,3 ,4. ,5

Ro/D

Figure 7.- Reference area ratio for combining corner-

edge radius ar:d afterbody contributions.

............._-_......_. m_.._um_ _

1970025216-032

29

3o

0

0I °_

0

oo

o

_ o

%

?

] 9700252] 6-034

31

0

CN

.2 1 • - " _.-.'-'_" .-

i ' _......':-'-'=....... "I . ,*"_'"'='_1 ...........I_._--'" ...... ..

0 10 20 30 4-L, 50 60 70 80OL, deg

i', Figure A-2.- Comparison of aerodynamic chaz-ac_e_risticsfor sevez'al

_: configurationswith equal v°lum'_s" _D = 0.24

,_:.

:.j:

'<i

,_, ,%

-- --',"" ",,."-_ _-'" -- _ '"= _,;" .... _._ L -___ "-..;

] 9700252 ] 6-035

32

-" _............ ................... +"-.""'--: ......... -- ......-_- !.... i-..-

.---: _-:................. "...... !........ i ........ i • :/,.4_-- --_ .... _ ................. 7--.--_-_ -_--.-----_,,

":-_ -. i- - - " :- :--1 ! " :_i i " -- - !

-.4 i-............... "<,_., -.............. via'.-- : - • " •/ ..... .'_ L'.._

://

................... ":'? :"::....... _'@' ....... i_.'-:.: .-; ..._._.: • ,.........

• .... _ - _ ..

i ._ o2.0 ......_--..-.:........... ---: .......

RN R,!'..-...__ • " -- ' : -';" ' : -" "-" _v, ,leg .tL--_T : : ' ......... _ r, 0 I

1, 6 F "" r7"--_7...'_i_ ........ "..... : 1.2 0 30 "I- -:. _ "",,s,.,_ ,,,,, • . . :

• .. :"! "--"i ...... _t.'_-"_%,..:" ; ' - .... I 2 05 35 ,]:_.'_'_ "--'-"2_._'",_'%-'"_".... "+" " " 'I,'-'+-= i .-: i.:"_'q'.' ., - ..... ,_.2 .lo .lo t

- _.2,-_---::-...... -_-_t_ " '" : .......... _." .......... t

, ..:_4-4_ • •__i-._. ]...iI" . : , ..-. : ................ t

,.-- "'"_""._'-g.-.:.--:-." ..--....... : -.- : . • : -........... 4-: I ...... ! "-[=:.'. [_ :i ..:. :...=. ._.. i. : ".....-....; .. : .... i . •

._:_.-...._..-:_...._.....i...i:-..._ ...-_ •....i.: ......-!.-.-.---:_.,.:._- . .... " _.L:_.._ _._i__'%___• . , ,

" % .....:":..i.. '" "-7-7_--77--.7-.i;-77-.--..-_.'_,,_. : .,.j: ., ....--..i.-..-. _...... ! ....-......".......__---_

.... ,. . .- : .... - , , ! -

--. -__._.'..._" ................................ -"'r--. ........

... ! .... • . :, :.... !0 "r-- .:_ .....

•" : ; . _. . : : • : . ... ,/

[-i i :::.1":.-:. i- .-.--4-_- :-= ! . 1: :_ :-i--_q,-' _:" ; !--J__ '__- ;.__-=__L_._A.-"- 11__=___ ____.: ,_"; .t_ _:L:-:.4. 4, : : "7-._ . -t _" !.':"_I'-.: ' 4- : _7 "£-

• ' _:Tq' -='::'_:-::--: ] :-- i. ' : " 7: " _ -:--_ ' --' ~ -- : ........ ,+---4-----

_=_-.::-=--":- _--"-.'.-,-.-, ,. • i _71." :•:i .... : • " '. - .'" ' .... " ...... _',,. ..... --':---. 2 --q-..-'. ":."-- -. 4--- .... -....... ;....... :...... -. -,---b..---_.... ,.......

..... .,,..: .|, _, .... ,, .............. , . . ..L ........ : .... =.-- ._°< L..,........ .......... .i£ _.. i "" " .. % _, I . ! • • : ___ :,_.....a.... "-

"" "':.-'f---!':-. ",: -'"--_ ........ ;......... '"" : • "_.... L i ..... : _7. - "-I• "L,. ".. ,J.......... ."-.,_.."_',,,_......... ,.u,,.,,._ ._ ._" _ -" ......... J • - " .... i ........... II", ,. !-.--X _ .... . ,. Da_ 'p-;--! • !

i:':-.'.+."'i'---P- ..'',,_ '"':-'. .. :-.*'_ :t'i"- _" !" "" ....... I-.6hH.._,:,,:_.,_.b_.:._±_-.i ......!........._,,--._--(

I" ":'.i.'-.:'.-!','ff":i" """! ...... r..... . , .-:.-.:.. : - I........... .: .... ,... :i....'.-g4.'_.."_."'-':_.-I..:...-.'.-_-.,. :......!-':':.'-.-.."-I--_-..:.-.• i ...':..-"...1:_:....:..'...iI :..".: :l -: • : ! • • i • . • l . l, . i : I . • : : I I

I".....i"?'"i''i-'!'":!........i:":":"ii":......v-:._.....:..!.- : •"I'"'_":""-,Ol ' ' " ' I.....'. ;--_.:_-..,: ........ ..J-:. "._--...J. " ' ..

0 10 20 30 40 50 60 70 --,0

d , de9

: _i_ure A-2.- Concluded.

II

1970025216-036

r

•-/ 33_-°

_" .12

0

0 .04. .O0 . 12

Rc/D

Figure A-3.- Lateral center-of-gravity offset requ_.'ed to trim at

_.: various lift-to-drag ratios for several configurations c' equal

volu_..e. _ = 0.24D

" " I " m m n qm

1970025216-037