VARIATION OF PITCHJNG MOMENT it LOCATION OF CENTER OF PRESSURf WITH REYNdLf)S NO. M=6'.B6

SLIDE.-6

PEN00055

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, ~ECEP/E!) NASA LANGLEY

OPE~ -(1I1RR 9 AM 10 : IS 1

'"' APPLIED PHYSICS LABORATORY

THE JOHNS HOPKINS UNIVERSITY 8621 GEORGIA AVE.

SILVER SPRING. MD.

,­

-- ----~-------

A SECTION T.CONTRAcT WITH. DEPARTMENT OF: THE. NAVY .

BUREAU OF ORDNANCE

CP .. 410.

, . TEf,EPHONE

~-'JNlp'~R9.:T700 (Wf,SHI¥rTON. D. C.)

'\ )'

NASA Langley Research Center Langley Field Virginia

6 March 1959 ,-':,

Attention: Associate Director for Mr. D.R. Lord for~ •. R.:W.Rainey . ..,.",::.,"'" .

. Gentlemen:

. I am pleased to advise you of the acceptance of your paper entitled "Aerodynamic Characteristics of Various Missiie Configura .. tions at Angles of Attack From 00 to 900 for Mach Numbers from 2 to 7" '.' '.' .

for presentation at the 40th Meeting of the Bumblebee Aerodynarnics Panel which 'fIorill be held on Tuesday and Wednesday,'I-lay12 and '13, 1959" at the Howard CoUnty Building of the Applied Physics Labo>ratbryof the Johns Hopkins University, near Silver Spring, Md. . '

The agenda will include approximately 20 papers on the general topic !'Hypersonic Aerodynamics!! ~ Presentations will be limited to 30 minutes, usually apportioned 20 minutes for the actual>presentation and 10 minutes for pertinent discussion.

DIREC ASSO II'.

ASST-II ASST~a ASST-$ T ASS1

RiD . EDIT " REC ,'.

V'COMP~ The organizations which will be represented on. the ,agenda for .,</ DLD

this meeting are as follows:- ,·,,---~-L---FRD

Aro, Inc. Convair Astronautics Convair/San Diego Cornell Aeronautical Laboratory General Electric/Philadelphia Lockheed Aircraft Corp. McDonnell Aircraft Corp. Hartin Company/Baltimore Martin Company/Orlando NASA/Langley NOL/White Oak Norair/Div. of Northrop Corp. North American Aviation, Inc. United Aircraft Corp. University of California Applied Physics LabQratory

You will receive in the near future notification of complete details concerning this meeting, including a copy of the agenda for your use in making the necessary arrangements for your attendance. You are reque~ted to be prepared to furnish one copy of the final rough draft of your paper to the Secretary of the Panel at the time of pre-

fSRD HYDR IRD PARD'

STAB STRue TMD u~wr

NACA eTS ENG S CA

FISC OF.' S

PHOTO PE,~S

p~oc

cYC1'-fl

APPLIED PHYSICS LASaRA Ton THE JOHNS HOPKINS UNIVERSITY

--~-~---Sll YERSPRING-~- -MAIYUND--

-2-

~ March 1959

sentation for inclusion' in the minutes of the meeting. ' A copy of these minutes wi11'be forwarded to you when published.

, If your presentation includes projection of slides, we suggest 'that you uti1:tz~ the standard 3!ux 4" size slide. If you plan to use.

"soitte other size,pie.aseadvis.~me oftbis fact in advance 'so that I might ".? make the nec~ssary arrangements for hanOling same. .... '. .

J ~ ~Jr \ " ' .. , It wi'll be 8pprE1ciatecl if you will agaiIl confirm (in duplicate) Cf

f!, ,/ } y-our willin.:gness to participate in the May 1959 panel m.eeting, indicating f~# J~ . th .. e exact t.it1e~f. yoUr p. ap.er (as noted above) .and stating wheth.eryou , y f"'~ ~ have obtained the necessary permi~sion to malGe the presentation from your

cogniz~t Sponsoring agericy. -.' ,

Yourqooperation in this matter is sincerely-appreciated and we are loo~ing forward to seeing you at the meeting.

CSP~jm

c. S.Perry, Secreta.~ B~b1ebee Aerodynamics Panel

APPLIED PHYSICS LABORATORY

T~5~R-&---AM-10-~-UO . -TFIE-JOHNSHOPKINS-PNJVERSITY- -- - .. _--

OPERATING UNDER

8621 GEORGIA AVE.

SILVER SPRING. MD.

A SECTION, T CONTRACT WITH

DEPARTMENT,OF THE NAVY

BUREAU OF ORDNA!'ICI!

, TELEPHONE'

JUNIPER 9·7700

(WASHINGTON, D. c.)

April 3, 1959

National, Aeronautics & Space Adininistration Langley Research Center , Langley,,¥'ield, Virginia, '

Attention:MF.4'~aw.~ INFORMATION COpy, i

Gentlemen: .... ,",' ".

The Forliet,h'Meeting eftheBumble~e Ae~od~ies ,fanelwill be held on Tuesday andWednesday~Maf12' and 13;_1959~ttheHow~d", " County Building of the Applied Physics La:Dora1.9I'Yof tAe}JQhD.s "IIopk1D:s University. A copy of t.heagenda for t.his meeting is Em closed. herewith for your iito:rination. As indicated, papers Will be presentedor{:t;'he subject. of "Hypersonic Aerodynamics".. Ycrii'arecordially:tnvited'to'send a represeri.tativ~ 'to participate in this meeting.. ' ' ,

Af'orm :lsenclosed for your use in notifying, t,he ,seqretary of yOllr intention to be present at the meeting.. Pleasefillinand:return thiS form (whether you plan to attend or not). no laterthari ApriL 24, , 1959. ' • ',", "" ' "

, 'c-, "', "'~~ .

The meeting will be held in the auditoriumQf,the;H(>w~d County Laboratory beginning at 9:30 A.M. Transportatibn:tothe,How~d County Buildingwil~ be provided with bu~oh€duled'todepartfre.Jir ' the Applied Physics Laboratory, 862lGeorgia.:AVenue,SilverSpririg;Md~;, a~ 8i~O.A.M.Registration for, the meeting Will be held at ,the Howard County Mld:i.ngat 9':00 A.M~ At the conclusion of the m~et~, trans­portationfor the return trip to Silver Spring rllL"hepr:oVided.·

v-...,The security cl~ssification of t~s .meetirigw:q#-.• be-SEG~T. , Please forward your secur1 ty clearance specl.fl.callyforthl.smeetJ.ng

(whether or not you may have an establ:i.shed term-tyPe clearari6e) on or before.A,pril ,27, 1959 via yOur cognizant military secu,rity"·agency to the U.S. Naval Inspector of Ordnance, Applied Physics;LabOratory, the Johns Hopkins UniverSity, 8621 Georgia Avenue,Silveroppring, 'Md.

Gopiesof the minutes, :i;,ncluding transcriptsQi'a1.1 papers, will be distributed to all who attend as soon "!S possible 'aft'erthe meet:tng. ~.

CSP:jm Encls.

bH~l!t A!SO, ASSf~1 _>02 ASST-3 TAS(

Rli -R~ COf,fp ILB fRD fSRDl HYOO !Ru

PARD STAI ~TQ 11m' UPY« -as -~ .. me bft::s ..... fEllS .. i

I 1-

APPlIED PHYSICS LABORATORY _ TH[JOHNSJIO~KIIISUIlIVERSIlY__ __ SILVER SPRIIIG MARYLAIID FORTIETH MEETING

of' the

BUMBIEBEE AERODYNAMlCS PANEL

To Be Held At

APPLIED PHYSICS LABORATORY THE JOHNS HOPKINS UNIVERSITY

SILVER SPRING, MD.

AGENDA

TUESDAY, 12 MAY 1959,

8:30A.M. BUses Depart 8621 Georgia Avenue, Silver Spring.

9:00 A.M. - Registration at Howard County Laboratory.

9:30 A.M. - Morning 'Session

Opening Remarks ••• ~ ........ o •••• o ..... o •• L. L. Cronvich, Cha.:irIlian, A,fL/JHtJ

Welcoming Address •••••••••• o •••••••••• R. E. Gibson, Director, . APL/JHU

-InVited Speaker

"The Sta.tus of Aero-thermodynamics of HypersoIl:ic Vehicleslf

................. " .. eo 0 •• ".00.0. " ..... R. E. Wi1son,Aerob8.liistic Program Chief, NOL, White Oak

10:45 A.M. - COFFEE

11:15 A.M. - 1. "Skin Friction and Heat Transfer Measurements at Mach Numbers From 8-10 ill Tllrbulent Boundary Layers" ....... ~ ............ ~ ...... .. • ~ ............. ~ ••••• 0 ." ••••• " ••••••• 0 of. K. 'H~rl~ AP~/~.

2.. "Experimental Investigation of the Hemisphere-Cylinder at Hypervelocitiesin Air'! •• ~ ............ J. C. Boison, Aro,Inc.

3. 'I1.Theoretical and Experimental Correlation of Shock Detachment Distances, Shock and Blunt Body Curvatures, and stagnation-Point Velocity Gradient in AXisynnnetric Flows" ................ .

·-~-~"o •••• 0.0 ••• 0'.0" •••• ~ 0 •• 0 ••••• 0 ~ o ••. S·. C. ",Traugott, The Martin Company/Baltimore

4. "The Shock~Layer Concept and The Three-Dimensional Hypersonic Bo'U:n.dary Layers'!.. 0 •• 0 •••• 0 ••• ". 0 ••• H. K • Cheng , Cornell

Aeronautical Laboratory

.11

APPLIED PHYSICS LABDRl TORY ________ lHUDHNUDI'KINUIl"ERSITL~

Sll VER SPRING MARYLAIID

1:30 P.M.

2:15 P.M.

3:15 P.M.

3:30 P.M.

4:30P.M.

5. "Integration Technique for StagnatipnPpint Jleat Transfer 'Problema" ......... o ••••••••• 0.0.0.;. o. oH. Bo. Moritague,The Martin

Company/Orlando

- LUNCH

- Afternoon Session

6. "The Thermal Degradation of Reinforced Plastics ,D-uring Hyper­sonic Re-Entry"' • ., ••• '. co 0 • " ~ • o •• " ...... • .. $.M .. Scala;~U,eneral Electric

~ , 'cOmpany/philadelphia

7. "An Engineeririg Approx:imation to Det.ermine Separation ofa Real Gas HyPelrsonic BOundary Layer Under Influence of an Incident ShockWave" ........................ .ooJ.J. Grant, Nor~dr/Div. of

, ,'. \, c ., Northrop Corp. ','

- BREAK

- 8.. ,fTheoretica.l and Experimental Pressure Distriblitions at Mach N"UITii:>er 5 in a Stream of High Density and Total Temperature of 4500~!,l~."." •••• o" •••••••• o •• ~o •• o •• H. 'A.WSllskog, APL/JHU

9. iten Mass-Transfer and Shock;"Generated Vorticity~ ..... H •• " •

• • • • • • eo"." 0.' ••• 0- ••• 0'.0 •• ' •• 0- •• 00-0' 0- ••• ~H .•. aoa;h1zak"i, ·.Lockheed Aircraft Corp.

- 'Adjourn - Buses Depart for Silver Spring.

WEDNESDAY, 13 MAY 1959

8:30 A.M.

9:00A.:M.

BuSes Depart 8621 Georgia Avenue, Silver Spring.

- Morning Session

10. "Comparison of Lift and Center of Pressure of Wing-~e1age Configurations as Calculated by Shock-Expansion and Linearized Super.sonic Theories" ••• o •••• 0 " • " 0' 0 .M. Fink ~ United Aircraft

Corp •

• "Aerodynamic Characteristics of Various Missile COnfigurations at Angles of Attack From 00 to 900 at Mach 'NUmbers From -2 to 1-n ~ •.••••••••••• ~ •.•.• 0 ~ • .,.0"0 ••• ·· •• 00 o'oD. ito "Lord, F. M~ Sm'ith, 4

R .. W. Rainey, NAS.A!Langley

12. it.A.nlnvestigation o'f Bulk Controls for Stabilization and' Control of Slender Bodies of Revo1utio"n at Hypersonic Speeds". 0 0 .~. ~ ~ ;; • 0 0'0.00-;' 000 • ~ 0 0 0 ••• R .. C~ .Brown, McDonnell

Aircraft Corp.

APPLIED PHYSICS UID .. TDRY ---------lHUOHNSJlOI'KlIISUllIVERSITY-_

SIlVER SPRING lIaRYUIID

10:45 A.M.

11:15 A.M.

COFFEE

13 .nMissileWings and Bodies of Revoluticm'of'Minimum Drag in NeWtonian Flow" ......... 0 ••••••••••• T • Strand, Oonvili/San '-

Diego

i4. "Aerodynamic Stabiiity Coefficiep:ts ,ill Siip now" ....... ~ • ••• , •••• ~ ••• ·' ...... · •. ·~ .. ~ .... ·~ •••• · ......... ·..-.s-'o A .• S .. chaaf and 'G~ J.

-Maslach, University of California.

15. "Aerothennodinamies andPeirf6rmance of HyPersonic Giide Vehicles tf uo ....... ~ .... ~~ .. ~' •• ; ....... 0 .. G~ N. Hanley, Convair/

Astronautics

16. "The Flight En:rlronment of Long Range Ballistic Missiles, and Glide 'Vehicles" ............... .-. ~ ~ •• -.K. R. Enkenhus ,NOL/WMte

o.ak

17. "Afterbody Heating on Hypersonic Re-Entry vehicles" ••••• ~ ••• • ~ ~ • ••••••••• e"." ••• ~ •• ,o' •• ~: •• 0" •• 00'.0 .w- o. qaTlson". Ge.~eral

E1.ectricCo./PhJ.ladelphia

1~30P.M.

2:30P.M.

- Adjourn "':'-Lunch.

- Buses Depart for Silver Spring.

~'lIED 'HYSICS l, •• m., -

THE IDHIS .'I •• S i.E.SlTY -- --c- - ~ --Sll-V£I-S'I'IS---liln ••• --. --- ----- -------- ----- - --- ---- -.--.----------------

of the

13UMBIEBEE AERODYNAMICS PANEL

To 13eHeld At

APPLIED PHYSICS LABORATORY THE JOHNS HOPKINS UNIVERSITY

SILVER SPRING, MIl.

AGE N D A.

TUESDAY, 12 MAY 1959

8:3.0 A.M.

9:00 A.M.

9:30 A.M.

9:45 A.M.

10:45 A.M.

Iln5 A.M.

- Buses Depart 8621 Georgia Avenue,. Silver Spring.

Registration at Howard County Laboratory.

- .Morning Session

Opening Remarks ••••••••••••••••••••••• L. L. Cronvicn, Chairman, .. . APL/JHU .

Welcoming Address ••••••••••••• ~ ••••••• R. E. Gibson, Director, . APL/JHU

- Inn ted Speaker ,' ...... ~-

"The Status of Aero-thermodynamics of Hypersonic Vehicles" ••••••••••••••••••••••••••••• R.E. ·Wilson, Aerob~llistic

Program Chief, NOL, Whi~ Oak

COFFEE

- 1. -uSkin Friction and Heat Transfer Measurements at Mach Numbers From 8-10 in Turbulent BOundary·· Layers n •••• 0 • " 0 0 ••• 00 • ~ ••••• " •.•. ~ •••••••• ~ ~-••••••••••• ~. ~. ~ ••••••. F. "K'. Hill, APL/JHU'

2. "Eiperimental Investigation of the Hemisphere-Cylinder at Hypervelocities in-lir"~~ ••• ~ •••••• J.C. Boison,.A.ro, Inc.

3. "Theoretical arid Exper:imental Correlation of Shock Detachment Distances, Shock and ffiuntBody· CUrvatures, and Stagnation­Point Velocity Gradient in AXisymmetric .Flows"" •••••••••••• "" •••••••• ~ .••• ~ ••••• " ••••••• ~' •••••• " ~ ~S.- "·c. :Traugott,. The Martin

Company/BaJ.t~ore

4. "The ShoCk-Layer Concept and The Three-Dimensional Hypersonic Boundary Layersu •••••• ~ •••••••••••• Hi. K.Cheng, Cornell

Aeronautical Laborator,r

--\ (

/ :l;l-G

'--__ 0

A"LlED PHYSiCS U •• IATDlY THE IDHiiS "PillS tIltEISI"

----- ---iIt"I:SPIIIC--IIIYU.'- - -- ----- -------- ---------2-----------

1:30 P.M.

2:15 P.M.

3:~5 P.M.

3:30 P.M.

4:30 P,.M.

5. "Integration Technique for stagnation Point Heat Transfer , Problems" •••••••••••••• ' •••••••• ' •••• H. B. Montague, The Martin 'Company/Orlando

.. LUNCH

- Afternoon Session

6. "The Thermal Degradation of Reinforced Plastics During Hypersonic Re-Entry" •••• ~ ~ ••••••••• S. M. Scala, General Electric

. ,Company/Philadeiphia

7. "An Engineering Approximation to Determine Separation of a Real Gas Hypers'onic' Boundary Layer Under Influence of _ An Adverse P.ressure Gradient" •••••• ;; ••••• ~' ~ •• ~J~.'J ~" Grant, Norair/Div. of

. Northrop Corp.

- BREAK

- 8. ,"Theoretical and EXperimental Pressure Distributions at Mach Number 5 in a Stream of High, Density and Total Temperature of 4500on.n;. ••••••••• ~ •••••••••••••• ; •• H~ A. Wallskog, AP.L/JHU

9. i10nMClss-Transfer and Shock,-Generated Vorticityn~ •••••••••••• •• ' ••••••••••.•••• e" ••••••••• ' •••••• ~ e' .'H. 'Hoshi~aki, Loclqle~d' .' . . . . . . .

Aircraft Corp.

- Adjourn - Buses Depart for Silver Spring.

WEDNESDAY, 13 ~1959

8:,30 A~M.

9:00A.M.

/-.l P [." / ' ,

,.1.--. ,~

V') ;;-'I';:..v .. / I '

C:;L,~:)0 -;:-;;:

- Buses Depart 8621 qeorgia Avenue, Silver Spring.

- M9rriing ,Session

10. "COmparison of Lift and Center of Prel?su.re of Wirig':"Ftiselage Configtlrations as Calctllatedby shock~Expansion and. Linearized SUpersonic Theoriestf ..... ~ ••••••••• M. Fink, United Aircraft

Corp.

"Aerodynamic ch.aracteristics,of,VariotlS M:tssile ConfigUrations at Angles of Attack From 0° to 90° at Mach Numbers From 2 to 7" •.•. ~ •••••••• ~ •••••••••••••••••••• ~.' :R. Lord, F~. H. S~th,

J. A. Penland,NASA/Langley

12. nAn Inves~igationof BUlk Controls for Stabilization arid Control of Slender Bodies of Revolution at Hypersonic Speeds lt .' ••••••••••• '~ ............... R. "(;. 'Bt-o~" McDonnell

Aircraft Corp.

APPLIED PHYSIcs. U, .. IT., TH IDNNS .PIlIIs .EISin

._-- _._- ·-1It,tl-SPlIIIC-.c..-IAIItAU-·-- -_. -3-

10: 4.5 A. M. ' COFm

l.i:15 A.,M. - 13. "Missile Wings and Bodies of Revolution of Minimum Drag in Newtonian F1ow" •• ~ ••••• ',q.:t~ • •••••• or. Strand, Convair/San . &., f (' l-\rl ....... ..N'- S' t..-.~ ~c..:~, Diego, ",

1:30 P.M.

2:30 P.M.

14. "Aerodynamic Stability Coefficients in 'Slip Flowft.·~ ••••••• • !,.;"o ••••••• ,r ••••••• ~ .,I! ••••• ••••••• S., A.:!3chaafand G. "'~. l~MfL~,'l eM ~C< r,.J'"1,~c I Ma,'s~ach,.~ University of

, " I !7 Call.form.a

15.~Aerdtherm()dyna.mics and Performance of Hypersonic Glide Vehicles" ••••••••••••••••• ~ ........ G,.' M.' Hanley, Convair/

Cf):,w",y'l· j7;7J fS ~. ---r7A< ,Astronautics "

16. "The Fl.ight Environment of Long Range 13allisticMissiles and . . Gl.ide Vehicles". ~ •••• ~ ••••••••••• ~K.R;;Enkenhus , NOL/White

Oak

17. "Afterbody Heating on Hypersonic Re~Entry VehiC1es" •••• ~'~ ~ •• • ' ....... " ~. ~ • e". ';' ."' ~ • -~ ••• " .:".'~ ~ .~ .• , -•••••••• 'W~. : 0.·,· Carlson, ~ne~a~

Electric Co./Philadelphia and

- "A~ourn -- Lunch.

, Radio Corporatiollof America/ Moorestown

Buses Depart for Silver ,Spring.

(J ~ .. / Lt_<I::t . ~.s· • 1

--------- -"--

/

L. :: 17. Lf r __

-\(' . - Xd? +-

,._- "'--- \. '. ~

- Project Code' 'numbers:

~. M = ~8 helium force tests techniques

3. (Pre~iminary) M = 9.6 ~wing heat-transfer studies, NACA Models ~,2,3.

4. Martin-Bel~ Booster-glider force tests ~109

5. Martin-Bell Stage III-glider force tests

6. Boeing Heat Transfer, M= 9.6, BAC Models 4, 5, 6

7. Boeing M = 18, BAa Models 4;5,6,7

Balance 1110

9. X-15 Final Program tI 1110

10. Higb.-a. 1111' tI 1110

11. BW P.D.and flow study

12.

Unscheduled projects waiting:

'PARD HBG

-¥.lIB"· L ?plc'( &s0" (7(,'J.-,..,

HRV 00 , 100 flare ~Oo j flare

Engineer: Fetterman

It

"

"

Balance·

1114

1110

1110 2406

" Close

Armstrong Bernot

Engineer

Smith

Smith Fetterman:

Bernot, Fetterman

Shifts: 4 It

II

"

20

3

10

3

1

4 3

Bell model movies Ladson 2

Missiles Systems Section Cmq and Cmoc

WADC Short range glider

*High-a. flat plate Llwings ~

1110

1109

NAcA Heat-Transfer Models 8, 9, 10, M = 9.6

*To be inserted.

Bernot 1

Close 2

Dunavant 15

(

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Theadditi~n 9f stability devices such as flared skirts or { ! , '

cone frustrum aft~:rbodies to cylindrical missiles gives rise to a

considerable increase in the drag coefficient along with the desired

increase in stability. The next slide presents the drag at an angle

of attack of zero for a cylindrical missilewi-tQ.-three different

nose shapes, for various flare angles on the upper portion of slide,

and for various flare lengths on the lower portion of the slide.

These configurations were tested at M = 6.86 and a R.N. =~ X 106

~':'.7M1.~ ~wc-a)? based 'on~bod.y length,and were a pan of the 1-17 development progtaJJ.

made at the Langley ll-inch hypersonic tunnel. Calculations are

presented using the inviscid shock expansion theory with the exper-

imental spbere drag coefficient added for the tip hemispheres.

An estimate of the losses through the nose shocks vas made through

~~d~"£ON (ref~~;;;-~.h~mi;Ph;~.-";~;;·b~;:~-' Lo; $dy~ /I. /' .. /' / ", \ ~.A-""'(' ~

. /' ", 0.-" ,." \ Mechell )r€f. 2) f0r.>~lre/ 60 blUB:', dinical ,,~9ae body, a~.::~

.~s"'{ref. 3) fort~~_16~,,::?~.d:C~1 nO~~ __ ~odxJNO estimate was included to account for either skin friction or change

of flare effectiveness due to boundary layer buildup ahead of the,

conical afterbody.

The data as expected show that tbe drag is highest for the kt"""1'IS~ 'M>S~ ~1'c;J ~ blQDteet body and lowest for the least e±~ body no Eatter which

al~~ flare was used on the afterbody. Of importance is that-,\ the drag

increased with both flare angle and flare length for all nose shapes/

_ this increase was more pronounced for the sharp conical body.

!his is an indication of the b3s in dynamic pressure that takes

place through the nose shock on the blunter bodies aDd the l'esulting

lo~s ~n flaze effectiveness at low angles of attack. The calculated

values of drag are in excellent agreement with the experiment81values

-\

S~ide 6

Missi~e configuratiGns such as these, particu~arlY those with

the ~ong cylindrical bodies, bave consid~rable boundary ~ayer separation ahead of the flared afterbOdY UDder certain Beyuolds naober

conditions. On the next .~~ide is shown the variation of pitching

moment and the location of the center of pressure 'Wi th Reyno~ds number for a simi~ar missi~e configuration. This missile JIflkes use

of a von Karsan nose with a 10° balf angle conical tip, a cylindri8al

body and a 100 flared skirt afterbody. The data are presented for

a range of Reyno~ds numbers from 6.5 mil~ion based on total le~h ~ to .878 mi~~ion. At the high ReynoldS numbers where there was

. .

little separation ahead af the flare the change in pitching mOlllents of-was essentially linear with angle of attack through the range~ang1ss teS"teq, and the location of the center of pressure which- is at

about one diameter behind the moment reference is relatively constant.

A . study of the schlieren photographs indicates that as the Reynolds

number is reduced, the laminar bouDdary layer thickens and the

region of separated· f~ow becomes more extensive. Under such

conditions a noticeab~e non ~inear trend of pitching moment with

angle of attack occurs in the low angle of attack reg:l.oa

• su.cb steP

like variations of the pitching moments are due to a cambiantion of

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the asimetric variations of the separation of the flow on the

windward and leeward sides of the configuration, and a hysteresis . ~h --tIv ~ ~ ~ ~~..J.1, ~~;~

of the boundary layer while going i:rom aga:t:i:lJe 1;e peea.:M:¥e 8B@J:es

The exact magnitude of the respective contribution of

the windward and leeward surfaces to the pitching moment can be

evaluated only through extensive pressure distribution studies.

This trend continues with the reduction of Reynolds number until

the flare is completely blanketed by the separated flow, at such

time the curve of pitching momenn again becomes nearly linear throogh

this low angle of attack range. This trend gives rise to a rearward cit ~

movement of' the -center of pressure With~S number down to

some value of Reynolds number where a reversal occurs and the cente r

of pressure moves forward. In fairing the curves of center of' pres­

sure location the value of the slope ~N us used at an

angle of' attack of zero degrees as indicated by the darkened lines.

~~ __ ._~_"L. ______ ,_

ihift occurs is'probably not only dependent on the particular

configuration under study but also on the length of' the laminar ~

boundary ahead of the f'lared afterbody. /\ .

Slide 7 "

To provide more understanding of this variation of pitching ". ~ s-;;;wJ

moments in -the intermediate Reynolds number range of this diacussicn w~ "'tht }1It.'d-tI<~ ~~.e..:s ~ o-k/,e..- ()a.0AtA-

A the next slide presents the variation of pitching moment forll "-

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conical nosed miSSile at a M = 6.86 and a Reynolds number~ 1.8 million based on the length of' the unaltered cylindrical body.

The upper set of data shows ant with

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angle of attack for the configuration with flare angles of 0°, 7~:4° and 14.80 and the lower set of curves the variation of pitching

o moment with flare length for a constant flare angle of 14.8. 2nese

data iDdicate that the flare has a marked effect on the separation.

along the body and the configuration with no flare exhibits a linear

pitching moment curve. Increasing the flare angle notoDly increases

the average slope of the moment curves in a negative direction but

the non-linear nature of' the curves becomes more exaggerated with

the larger angles and the ensuing forward movement of the sepprated

flow region. !he lower set of data indicate that for the given

. 0 flare angle of 14.8 that same separation is present regardless

of' flare length and that the degree of stability for a conf'iguration~

is a function of flare length.

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