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AD NUMBER

AD068959

NEW LIMITATION CHANGE

TOApproved for public release, distributionunlimited

FROMDistribution authorized to U.S. Gov't.agencies and their contractors;Administrative/Operational Use; MAY 1955.Other requests shall be referred toBallistic Research Labs., Aberdeen ProvingGround, MD.

AUTHORITY

BRL ltr, 22 Apr 1981

THIS PAGE IS UNCLASSIFIED

i t 1 11 -i

S~FC4- , r

REPORT No. 934

The Aerodynamic Propertie

Of A Simple Non RollinigFinned Cone-Cylinder

Configuration Between

Mach Numbers 1.0 And 2.5

L C. M•ALUSTER

DEPARTMENT OF THE ARMY PROJECT No, 5B0003-001ORDNANE. RESEARCH AND DEVELOPMENT PROJECT No. T&3.010S

BALLISTIC RESEARCH LABORATORIESW- 1.6 I 1,

ABERDEEN PROVING GROUND, MARYLAND

/

B A LLIST I C R SEA RO 1 1 'ARAT ORI ES

wo N~o. 934

MAY 1955

TE kM=YUMC PRP.*ES OF A SDL NO1 RO1LL19 FINNRM

OM-CY7flND CONEMI BBWT*W MAOR NUMWS

1.0 AM 2.4

L. C. Ma€Afliutm"

Deataa of the AMzi Plvect No, 5MO-03-00T1* 0itamca P49seanh and Dovelop~wert Primt, Nn ~Th.l-rnln

ABERDBEN PR VIV 0 R O0UND, MARYLAND

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F PALLISTI C RESEA R H LABORATORIES

m NO. 934

Wn~ac liiat /na,,

Abe'deen ftovizS Oround, Md.may 1955

TEE "RMZWAIC PRDPMES OF A SMIFLE. NON ROLLfM FINN=OMT,.=MMh~T OONIMUPATICN, BM~WEE W~H NU1MEM

The aeraot properties of a finned model " given for ataob bmmw ruge from 1 to 2.. The tegt vehiele io a ten-calibwrlong cono-.ylizder boc• with four rectangular fins, of 8% thick wedgeseation, set in a emciform configuration. The data wore determncdby firings in a wpark photograp2h range.

Ii

I' S•BOLS

",- lal momwt of inertia

Tranhsvere ?MOent af i.ne.aB -T curb I &l

rd 2

S - Rafe'reoe Area

V - Volooty

b -Fin pn

0 - Finc €rd

d - Model diameater (caliber)

k• 2- Axial radiw of gyration (calibr s2

k 2 - 07ruevcrao radius of gyration (calibers 2)

2

q - Tr ve"se angular velooit.

q - Dynamo presswea

2

- Anglo of 7w

p- Air demity

OOEFt•GZZ=S (a1vaar tmits-radilan)

aNormal force/ Zsa

w foa q =•xr:., ,,/ •(

INTRDUCTION

Free flight range testing piwvidos a roans of obtalning the s~ttioand LYa c properties of projectilea. Ridt~oricaly it has bee on% ofthe most aaourate means of determining the total drag of Spin or fiu-ntabi2lied proleotiloa in st~ersonio flight. Ptee flig),t testing mWalso be necessary to determine'the static farce and moment propertiesnear sonico peerie although tl•,s properties can nuaaI17 be adoquatel.7

datesrined at sasersonio and gubsonio speeds by other means. In thecase of the 67=mio forces and moments actin on the projectile onnyfree fliht testtig and some s•pocial wind tunnel instrmentations areavailable to yioiAl the desired informtion.

The Free Flight Aerodynaics ng azd the T so Range (1, 2)

of the Exterior Ball.stics Labcratory are instrrents for determn.ingdaba to yield the aercnazdio Oca.racteristics of moefls or fall sca1,missiles. The properUis of several classes of bodies of reolutioCn

have besz investigated (2, 4, 5, 6) amd also some of the charscteristitsof finned shells

An overall investigation of the motions of winged and finnedprojectilec of a aizlo type soared advisable. The ourremt report isconcerned with one phase of the larger pfogram: the parfomance of afilmed projectile as a funotion cf Mach n•Ibr. Inveztigations of the

axial (7) and the rolling nations (8, 9) of this model have alreadVbeen reported as haa anJ ±AItial stu* of the mcdel •1itb slight

(10)

It appeared that the detemtdatiom of static and dynamic character-istics, through utilization of the rang•i, c•ld be accoplisheC beat by a

sta of the angular motionI of a symmetric, non-rolling model.Acecordingly, a Ocrios of models vas designed and produced to have anlittle net deflection of the fin surfaces as was practical. The dataobtained from these cone-cylinder models with tail fins for a Kachnumber range of 1 to 2.5 art presented and some of the problems cn-countered in analyzing the observed mutiona discussed,

Aeo azically this motion is resolved in two campaentai pit-h,

vertical17, and yaw, laterally. In ballistics the vector sum of thecomonemta is tamed tha yaw, The t-m pitch will usually be usedhere to demote the we general ballistic yavirg motion for thesemodels Since they are pr flrk~Ir~~t~i +h(

The Aeoqdý eicv Rarge

The Rugq (Fig. 1) is an enclosed firing gallery containing 46individual spark shadowgraph stations which record horizomtal andvertical projnctions of the missile as it passes through the. Thetime of flight is recorded on chronograph countore.

The model is fired from a gun through a blast chambor into therange gallery. In passing through the blast chamber the missile passesbotwevr electrovtatleaUy' charged plates and ami•es a t-i~gg•ing Oahvgs.As the charged model approaches each station 2) an antenna loop

before the station generates a signal which is amplified and dela~ed topermit hbe modol to cone to the center of tho station before the stationfires. The modol is shado-qraphed in two planes and the characteristicsurvq markd of the station imprinted on the photographic plates. Theseplates yield the basic data to deterr-dne the 1notantanecus spatialcoordinates of the rdaeile and its angular orientationj the7 also pro-vide a graphio view of the flow field about the model.

The firing progrnm vas carried out in two phases. The first phaacconsiated of the launohing of twelve models, four each of three centerof mss positions. The models with various mass center positiots

would pro'vido checks, through the c.m., tranaformationl (12) , forconsistemcy of the data and give a determination of the lift and dapingforaS. The basic Mach =umbar wan 1.8.

The second phase involved the launching of eighteen models of twocenter of mss positiaos in a range of MacL mmbars from about 1 to 3.

The model configuration was ten-calibers long with a 100 semi-angleconical nose. The crucifoz- tail section was Iccated at the base ofthe body and consisted of 8% thick wedge-airfoil sections with a ono-caliber cowdr and an overall span of three calibers (Fis. 3),

The models were launched from a special sooth bore gun with an "m"shape bore (Figs. L and 5). The model was accompanied by a sabot andobturating wafers to permit launching Csigs. 3 and S).

Some special reductions of the rounds, and also of comuted motionswere '.caer-d out t* assess the various reduction procedures which mghthe app~led to the motion of models of this tT"e and to evaluate the

problems were aggcsted by earlier programs and by current work n thepresent program. The mechanics of, and mzq of the suggestions for,

Appendix A

IA

this latter work veý'e done by ners of the Data Reduction Sectionand only the results are discussed.

It is a buic requirsmet of the free flight range tochaique thatin order to study thn AMdy'naaic proporties, other than drag, the modalrmst y=, At the incepUon of the Virst test phases one of the morePrmsifng mct)cq of inducing yaw with the rail 1un w~a by means ofthrowers inntalled in ti, grail extensicn " (Fig. 4). These devicesintercept tha followic sabot as it clear& t the =Ls the cc othe ex.tension and deflect it to the side. Zf at this momoL the sabo 1" iniontect vih the modell some of the ery of the thrown sabot will edelivered to the model. Since this force is delivered at the modal

base It should result in the madolt

a. yaving avn from the direction of the thrwn• sabot,b. attain, as a result of a., an sorodynado jw avfrom thAo abot,a. auquirign some directly trazsnitted lateral velocity in

the direction of the thrmi sabot.The latter two factors tend to nullify each other, and could con-oa.vaayb permAt ths production of reasonable yawing motions withoutprobbitive lateral deflections of the rodel.

A prelirdnary progran was fired to test the feasibility of thismethd for the prosent program. The rcoults indicated that if theamount of wezr' transferred fr'm the sabot to the model could beLimited by, se, a f'agile shear pin botwco the sabot and the model,the system could produce desirable yaws. It also indicated a markedsensitivity to rdror variations in pin manufacture.

A general survey of the firings is given in Table II. It appearsthat the sabot thrcevs, coupled with a shear pin, can produoe yawbut the system is very sennitive to several varlables.- Only onemodel had insufficient yaw to yield a reduction but, also, only abouta third of the models were at or near the most desirable yaw level,

A potentially better rethod was availablo for the second phase ofthe program. This methed cor-isted of enclosing a high strength !agnetin the model and launching it through the field of a powerful lectro-mapt. Since these firings consttuted the first test of a system of

-~ c:~:(~)vtii ationj Ln Pio s9trenith (a~fter the

large arount of machining necessary to reduce them to the desired sheararea) (b) probable variations in the separation of the model and sabotat the instAnt of contact with the throwerz.

7

thia nature some difficulties were encountered Lhat could be avoidedin future firinSs utilizing this syste. 1

The models contained four inch long, half inch diameter, Alnlic Vmagnuts and wero launched throeh amn armoured lectromagnet vitb ama~d.= field strength of 18,000 Gauss4 (?ig. 6). In the main it pro-vided a reliable source of yaw.

Table I gives the physical properties of the models and Table 1I thelauehi.g aemodtioins.

AEM0•NAC MTA

General Treatment

The r4anmge datA were processed by the usual reduction techniquesapplied Wo sinning shell and by special reduction teoohiques s$t up

for thia program (12). Tho test data of the first group were obtainedin a Haoh nwutar region of 1.734.M 1-1.84 and at an average 7aw levelvp to eight degrees. Primarily these models furnishud a check of the,vriaticn of the aerodnamic properties with canter of o:a poatti=n forone M&h number and secondaril the varia'ion of some of tho coeofficientswith yaw levol.

The second group wa tfired from 0.98 1- M /L 2-.5 and with average

yaws up to four degreca. These odels furnished data pri Arily as funotionsof Mach nbe'. Onl in tho case of the drag coefficient were corre-lationa with 7a level protio•at.

The dra coafficiert, %G. a given in Table I11 and in Graphs I

and I1 as a function of YMab number and yo.

The value of the drag coefficient descends fnirly sharply from apeak at about N - 1.O5 until Mach number 1,3 and thereafter decreamenmore slowly with izorouing Mach nurcer. "he portion of the curvenear sonic velocity Is not as well dotezmlmod as the rewan'der sincethere is only one Mata poitr belce H a 1.

The y drag coefficoent de:reases from about 15.O per rdiamn 5qeArodto 8.9 frcm a Mach numer of 1.4 to 2.4.

1 Primrv nzong these wae the extreme v•'iability in resictance todghstiszasion am the first lot of magnets procured. Laterlots appearO to be fre-r of this defect.

2 The theory of the Electroma.netic Yaw Inducer and the detailedresults will be the subject of another report and will not beconsidered here.

8

Several models of the second group had stable laminar b,3undaryt'• layers over the cons and part of the cylindrical body. Since the r•Jority• of the models had turbulent layers over the whole body, the friction~al

dr fh olso with 2A inar layer, were corrected to a full tur-bulezt condition and the curve drawn for this latter state.

Yaw Mom.ent and Cantbr of Pressure

The yaw mnoent derivative, CM., is given in Table Mi, in Graph IV

as a function of Mach number and in Graph V as a function of center ofmass position for M - 1.8. fhe movement of the center of pressure ofthe norrAl force as a function of Mach number is presmted In Graph I1.

The behavior of the noment coefficient appears typical above M - 1.4.A mzJim= value for the two center of mass posicns occurs near a Maohnumber of 1.2. Balw this speed the value of Iincreases slightly to a

m.rLun vilue betweaz M a 1.05 and 1 and appears to decrease sharplyssanhoically (althougbh this latter behavior hinges on one point belowN- * ).

The phaae I tests indicated a linear variation with center of masspooiticns for the three e.g. positions uned at M a 1.8. The elope ofthe curve (Graph V) yields IN for thisa Mach number,

The center of pressure appears to be in a maximum rearward positionnear X w I at about I-4/L calibers fror the base and moves for-ard forgreater or lesser speeds. As Mach number increases the c.p. movesformard urtil about M a 1.1, rearward until M - 1,4 and there begins tomove fomr d again steadily with increasing Mach number. A position ofabout 2.6 calibers forward of the base would be reached by M - 2.6.

Normal Force

The normal forclo coefficient could be determined by two methods inthis program. The Tariatiom of the yaw moment as a function of centerof mass position at a given Mach number determines the derivatiae ofthe normal force via thn o.m. transformation. 1 The transverse motionof the center of mans of the projectile in response to the lift forcecan also be used to determine the lift (hence normal) force through ananalysis of the swerv-ing motion. Both methods have advantages anddisadvatages. On the credit side the o.n. transformations involve onlyphpsiczl dimcwions and the well determined moment cofficients.Hawevr, two searate rounds are involved which cannot be exactly thesame shape. In addition, interpolation of the moment values withrepect to Mach nuber is usnally required to deterrire the rrnrn!1 force

dividual round through tho swerve reduction. However, this reductior is

App endix B

subJect to adverse conditionsr (1) the actual displacerent involved isemal, on the order of a tenth of an inch; (2) the swerve equations relyon the accu'rac of the yaw determination, and since this in-vulves adolible ilntep3= ol the yaw the eworve fitting is very sensitive toeven minwr anaozieo In the yawing motion. Both methods wore used and"are shown in Ursph V1.

Tim normal force ooefficient, O , appears to follow, qualitatively,

the trand of the moment coefficient. At about M n 1.1 a i' == Cn of

S- 25 is rm•baed and the value than increases to about - 14.9 atM s 1. It appears to decrease for the lower speed.

The dmping moment derivatives, (CMq ÷ .) are dotmm.nod from

thp total damping of the yawing motion once the lift force derivativeand the drag coefficient are Iciown, Pence the accurac7 of the deter-ninatLon of these coefficients hinges on the overall fitting accuracyof the yawing motion and the accuracy of the determination of the liftcoefficient 0

The damping moment derivatives are a quadratic function of centerof ass po•sitlon. This variation is given in Graph V1l for the firstgro1V of models (M - 1.8). The least daplc•g occurs for a a.m. positicn2.1 calibers from the base.

(CM + rr) values are given for twu center of mass positions as aq MI

fuMotion of Mach ncber in Graph WT. "The overall behavior is similarfor both om•m positions. The value increases from a large negativelevel near M - 1 to em ill-defined and possib2y positive value at aboutX M 105 and thereafter decreases ra±i.y to a maximum negAtive valueat M = 1.3. At higher Mach numbers there is a general -.9nd todecrease in magnitmue.

T he damzpin3 for C ' coefficients, (CM + CN.) can be detarrined bytwo methods, in minners analoous to those used to determino the Liftcoefficient., (C 4 C11) a be isolated by a compavison of the

Vq

10

dming1 moments from models wi5th two c.m. positions or from the swerveof the idividual model due to ý.e damping forces.

The accuracy with whi.h the lamping moments are deternined is loverthan that of the yaw moment henc, the daping force determination fromtwo momewtu is weaker than the si~ilar process for t he lift. In theoases of determination from the sew-ving motion it should be noted thatthe displacenent due t o the damping forces is considerAbly less thanthe displacement due to lift. In view of tnis it is gratifying that thebotter deturmlod values from the swerve are in reasonable agreement withtho curwv dotormined from the damping m=ment.

(a +. CNe), evaluated at the centrold, is given in Graph IX as a

fw.otion of Maoh rnmmei.

0esevable Phenomen an = 7aration of the A odyer aio Prportios

A seriou of shadvwraphn Showing the flow field at different FAchn=bera is given in 7i4. 7 & 8, The relation of the cbsw-,m drag andthe state ; Lbe boudary lgTer has been disoussod. Other propertiesof the obanginJ flow pattern with Mach numer also seem to be reflectedin definite cbnqes of the various force and =iant properties, Acorrelation i xivcn in Table IV. In general two major oharges in theflow, the atta0chmet of the boc' shock and the attachnent of the finshock system, appear to influence all the coefficients. The Macbnumbers associated with the interaction of the fin tip Mach cone withthe bod and with the one•t of fin-on-fin interference also ;npprto be points of changn =or -- o4 parsawters,

In the ,ase of the better determined properties, the generalbehavior is valitativey explainable from corsideration of the model asa su of the propeties or the body alone and the tail alone. The momentcoefficient may be considered as an -alpe.

The moment coefficie~t decreases with decreasing Fach number fromX - 2.5 to 1.4 in a manner suggeng n the theoretical variation of win&lift with Mach number. The value continues to decrease until H a 1.i1but with a decareing rate as the three dimensional tip effects influencemore end more the neighboriM surfaces. At M a 1.15 the fin chocksystem detaches and the tail suffers a loss of lift.

As toted in Appendix A the variation of the damping moment, coefficiamtsis a quadratic fuction of center of mass position and involves %,C %

and 4 %.) This comlic~tes the determination of the latter

Lcoefficients. tithever, a function of (%n+ C14*) and Ch can be

constmieted so that the fmetion varif- llnoarly id~th c.m. with aslope directly related to + %

The body, however, is still supersonic and its destabilizing momentis still increa•sing with decreasing Mach nurbor. Hence tLe momentcoefficient increases from M w 1.15 until M - 1.05 when tho body shookdetaches and equalizes matters. Below M - 1.05 the moment decreases inmagnitude.

The use of models designed, and carefully manufactured, to producea p•e pitching motion in the firing range is a feasible methnd fordetermining the static and dynamic aerodyrardc properties of a finnedmissile. Antually however, a considarable nmbsr of the projectiles somanufaotured will not be perfeot enough and will exhibit a rollingmotion azd/or trinmed flight. In order to yield th9 best Iata thesemcdols must be treated by reduotions that permit roll and asy etry,or must be discarded. As is noted in the Appendix B these defectsintroduce errors in the determinations of the yaw damping and of thelift and daMing force from the swerving notion if only qvmetricreductions and/or non-rolling reductions are us•td.

In the present program prAotical accuracy could have beenobtained by syrmetric-non-rolling reductions on all but two rounds aslong as it was not ucýasarý tu rbly nu the fit of thA Rwervi._nZ motionto deturmine the lift. Approxdmately a third of the models requiredasymmetric reductions to yield good lift coefficients from the srweuve.

~c YzAZaca21L. C. MacAllister

tI

/

L

1. Rgoers, •.K., The Transonic Free Flight RAnge, BL 8L5.

2. Charters, A.C.-, ome Sal.istio Contributions to Aerodynarcs, JASOVol. 1,4, No. 3, 1947.

3. Hupk, C.H., Sohr'dt, L.E. Effect of 1Leith on tho Aaeý411U;Idc

Characteriatics of Bodies ;f' Y97 =on inSpronic Fiit, M876 (C).4i. Murpv '.H., S0=dt, LE., The Ao=.4ao Pro ertivu of the 7-Caliber ,AN -21nner Rocket In Tran.one k-11gt, EMLM 775.

5. hrddt, L.E., The Dynamie Properties of Pure Cones and Cons-

6. Marten A.C. Thomas, The Aemotnady o Performnoo of Small .heresSSubscn~o to Aupson-••t JMassVol, lei NO. 4, IF45.

7. MacAllister, L.C., The Dr-• o' Leg Arrow Projectiles, NW 600.

. oolaiden, J.D., Boltz, R.E,• The foterrination of Some AerocynamiaCoeftci;a .fro S..upersonic r-ee'W 712.

9. Nleolaid•a• J.D., Boltz, R.E., On the Pure Rol1ing Motion of Winsadand/or Finned X.asiles in 7 ieqocklet M79

10. Nicolaide, J.D. On the Iree Flight Motions of Projectiles withSlight Configupaticm-l Asymn-,2 ML d5d,

21. Kelly, MoShane, Reno, Exteor Sllistice, Denver Press, 193.12. Hu'plp, C.P., Data Faduction for the Fnee FYliht S ark Ranges I 900#

23. NHiolaides J.D., VTafitin of the Aemrtamlo F7rce and Moment Caeftf-

114, "u.p, C.R., On the StabUilZt Criteria of the Kelly4-aShdne LinearizedThw7 of Y-vi o M 53.

A

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diiii

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;l HITT! Hij: ill, Hit

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2-6

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30

APPENDIX A

Fittmj Equations and Trons±ormtioun

The equations utitmad in processing firinw range d•t are repeatedhere for convom:enoe. Further details may be obtained fro the indicatedref erenoo.

Tayl=~ Hatlanz

The eqaatomI usuall7y wed for fittir the observed motion of spi~tri(1) to-• tote

vhere p is ds~tanmo a•ong the tra.eotoor In oalUborm, X. and MrsIrd tl &I cenattaeto The za~ pars~utera rs eae t h itpaaimeters U followva

and

, £g ( S .2 ,) 2 2(foot-

md S~er~l.yv with spinning shell 1

(~) 2

1Red7otUo Symboli, t Corplex 7nw %a ilk

03 - Swrerve x + ±y, motion transverse to the mean, raject-orySpdyelit turning rates

S=picyclic damping rates

2 A -2"NOrmA1y7 IT _~ k, IT (I In +)rr-? of tl'-' b'nl ',tic i:c aS

6i - vP the spin in radians per caliber. Hence tkho term should

be sero or vem small for the present ease.

S|1

Squa•tl (1) involve-0 10 okn aly dj, eOs 0, Ojos 0J) 0 a for j w 1, 2.V•, cax be shown that if tho spin is zero and Mach numbr variation is neg-

ligible for the oberved a•iagt thAt it iu poatlble to reduce equation (1)to 6 unm simae

I I ty it

61 re2a11n Ai 0ý 1 i k

( • - 4 1." (01 + 0z 1 'P) -K20' V + : (020 "•P)

Ifw t dem tl the model as ivuvy tha a third codf entmustd be

added to iaeld, (10P c c) , t

Tia e oitting, equ tons as trei.•= derve (3# 11 U) aad asuvan.,3 utbli±ed f a te a tnurbat= on ad the rstatt Mof aent solutheof the dffeteontf a p qnathae , Tits plrturbatiemon ta is vaioeo

tv feioienatop vit ahnvolving Th aoti~sa~.= proa o hep'tw

•4 -,a (2 - H(- .)

ithout detls the =3 tae involves tho Momfs t Co e nte and the ePsn,Sthe danpin8 mment et ffie tets, T the Xagaw moman t s oelfl ent and 1is a rate of Ghange of esp i term. . e

AotuaLly in prog:wo imolvJing mo-dln with esseatialk. zar apin

vaaw e " to ed for the pantae bation and the rate of haMne of thelrate term• 0) 1 v'Atoh seem signiicat.Aam and do not apper• hM~ eable othe offe"t of spiAn. The most lqrical i-acom r•luan is vwa~tionof coefficients with Mach numbr. The a~twa yrnen of the parurUtian does not se cif what the varatic s are# but the tiviatg

the spi is evaluated as the major one for epiwndM sam tlMMMA•T

ane neglig•,1 indicates that the rate of change of the momentcoefficlent' wtb Mach nnbsr Is probably the mjor remning tamPraetical.., 'thi tam o=old be of signiflicat alms only in the transonioreon--but obtaining data in this region is one of the fortes of freeflight, rang. testin3 . The total pertabatlom terr (for spin - 0) is

f ~i2[./F-

of the om

of wkdoh the ao vod- eem to bu

1 41k'- L - 1- ( ;

from th data of tle present progrm the coefficient terms in thedenom.nator arc neligible with roepect to 1 and hoee

Cionnidt1g that rate chaong~e ce Is the prir.ary futot', thenin tarm of the it• follow thtt

S. • it •.v-

k -2

11 -k2 M

T ki

-A

(9)8 0 i 2K o j +0 p1 n)md also from the relation of the

let f

then (10) becoes

=d kh a % c emlt

?be eq=u=, fitted to the observatiae of tbo meigales mtiontravn•e to its basic tftajto17 Is of the following foa vhie£87st37 is ma~idereds

(3-1) 17,zO a 17aso so

0 p

The last Utzn ts oi.tted foruyoio ,e uetiona, and rednotioae mitbkWlo tayizvokJvý Lhu ripL~ ooi. cuaulJ to aci7- aiko al.o uULIcd.~ C4iuothe y fit haa beem established the intesral m be eiLluated bySeverml men u disneo d in •ef. 12. Tz, subseript %"- to s a e

gr/fty oatlow, the la abhcript to a Corioli correctiona.

I1

Cciter of Mass Transformation

In order to determine the force coefficients from ==fmt data or to

apply the data partainirng to one centor of =ass position~ to V 3there aro roltions betwean tho ceofficents for tho cases. 10-1

As~teisks repro•nen tho val.u" of a, given c-officient at a now egg.position in terms of those at another position equrated by a diot=:o q(in 64.1bers, positive if the mtooion from the old Wth %5 now is nos.uard)

(aN -CN.) a % * .>q IN q %

:1~9 aM in M QC

(Cp~q CN)V(a

Modified damp••g relation

2(Ci.+qCx;)

'15

ft'o atb iab"'annovir poitU U progra of tbfb naturi LBtý,'ost~nt ap~re of iall and trim that indicate that the model Is not

a;4the simle vyet- reduotlcuorw htotba It is eesaryto

Tal Vgvea a cagwazibn of *a 'qyes of qxaet reductionsaontva'*Wdrounds and 'tobzrve acptmd actions. The aiLz-unkOrovn reduatiozpoaikltesnospin vle tMe ten- m ovn pmvlt8 sfpin ani variAtion ofsi.7ot the two actui4 'Wo=01 tbve VWa little. or co uigni.ficant

differece betweem the two reduticas?. The spin leval itvolied wasnall (39dogper foot), In the eue oftbe omutmd motionsaen

act4'effAof L bWjt IS error 1z the d~ping inop inaw'i'ed b7 applyingth x=nf ~utc p oarl ~t f1/t (Rofll ates onthe afr'diz 6 two dzegre per foot ha~ preiously ouaed trou~bl1e so tkatit was a queftion of wh~at lowe vilve.. tvul do.)

Rffeet of TrimIn orider to evaluate the effeat oft varimous trim on the rGaultan frm8y~t~i~~edut~oa c'the yuwift =d'Wsrvin viotions,'reductions of

A&~n with gad vithotrt kiln trim iwe tried. A yuing motion vuacomuted from the symmetric equatiom sad reduced and a asielaw motionuith trim vaa campu ad sad reduoad ±gmoring the trim. A aver±Mg wtionwas comp ad fromi the sym~etrio sqztions for this Pntion and for thrudiffeenttr-In levels an treated by wymetzio rsductionse

TAble 7rT shows the affect of voz'Ioun levels Of iny~tz" an the4ampiW mozent det-4 7dzatiou and on the Lift and du~ping, for'ce deate-mination from t.m &werve, Cen.ide,~r4 the yaving motions trim iqlaswhich might be jUft visible in tIha data C1002$ radians) produced an cacwrin tse da~ing maxet detarairtion of anbout I4%. A tris of .OQ0rendangs

I'which abould be quit& avielmtj prdtnc-ed about a 13% error. Tho 7=amooit coefficient war not sa iccaly affected. The caue of the swiervingmotion in nub 'we aswtit70. A t~la argle of .002 zadi~s yielded asatLt&tUol w'rrr of 10l% forr the lift c'ffilent from the fit (theactual diff~'ece, betWe ±zqut and cownted van of the order of 2%

but W Lh b't iitu The sim tztn gave an OrTdr for the'dx*W tt'f i-6ifflciEftt of 35% (actual difference 11$), H owever,

it Gvpean' that emon in the Utt dcatersiticon of up to %~ and in thedamping tbooe vp to 10% zdgbt rwuat frow aseyaetries that are not4 030 ate]y evidint in the rv- dat~a and idebt evon ho ot= d in a

daring force detunnation from tka nrserre and rkij introduce signiflez--te~rrr in the Ianping Mofa det~erdxizAtAon9

[3

Ii

AMINM 0

TA EU I

FW md Mach MA cAg.Nog NQ. p gm in gm-in in from

base

2588 1.82 104.65 13. 14 551.46 3..122589 1.827 10.73 13.52 552.53 3.n4259c 1.103 17.68 13. 5 552.06 3.1122595 1.7814 31.4777 13.72. 552-73 3.2.092596 1.81 255.95 26.69 664.84 2.2522598 1.79 255.95 25.88 859.61 2.2582599 1.788 2 eL. 65 27.02 8614.1462.02591 1.801 255.39 39.80 896.31 .4.0022593 733 2494.8 19.87 896.67 3.999259L4 1.7145 249.60 19.914 897o99 L 80013246 1,398 227,02 20,02 013.57 3.0453247 1.264 227.-25 1.978 81.152 3.0563248 1.077 228.18 20.43 816.14 3.035

3 sý00227.1.4 19.99 813,72 3.0513252 l.0oon 227.38 20.04 811.1a 3.0443253 1.047 227,57 28.18 812.41 3.0433254 1.506 313.82 2.60 1053.2 2.5923255 2.032 313.11 28.90 1054.5 2.5883256 1.993 312.03 28.45 10149,2 2.588.257 1.390 31.2.46 28.33 1050.3 2.59825 1,9 311;95 28.09 1050.3 2.599

S3259 1084 313.00 28.49 1050.8 2.5903260 10017 313.38 28.49 1059.2 2.597

3261 0.975 3 n,1 .4 28.21 101459) 2.595S3242 1.,044 31•2,38 28s42 1047.7 2.590

32614 2,1465 227.26 19.91 819.02 3.076

31

Row~d TA=~ I-

?e.L. viII &ve Yaw Yothod _

25 1,80 0.7 Sheir Fin

8 1 1,83 0.990 1.80 0,395 1,78 0,8

1 1.,81 1.298 1.80 2.4 a

99 1.79 1.291 1.50 0.5 "93 1.73 7.4 "

94 1.714 6.0

324~6 1.s0 14.24~7 1062.5

Y&V lato148 3.08 0.510 2.05 2.3

S1.Lm 0.553 1.05 0o,6

A• :1.5 1,9 a55 2.03 0 a Model Mgnet de-56 1.99 2.6 , =notzed

57 1.39 0.758 1,1L 2.3

1.01106 Modea Magma% do-1.02 m ,) upgnot4.ed

61 0.08 403

62 1.04 0.363 2.42 1.7 U

6L• 2oh7

I1TJ07 ION VALUES

No@ No. , a-____2- MOBp or ri) -(PaRZ

2588 L.812 o.L 0,66 8 (2%) 22.61. (0.7%) 266 (W4).9 1.827 0.7 0.614 = (16%) 21.95 (0.6%) 3 LO ( 8%)

90 1.803 o01 0-.6U9 1•.784 o.6 0.624 22.27 (0.6%) 238 (W4)

96 1.8• 1.5 o,629 U (2W) 9.12 (0.6%) 163 (2W)98 1,798 5.6 0.621 15 (114) 9.81 (o,4) 216 (8%)99 1-.788 1.5 0.6U ,5 (,9%) 9.56 (1.0%) 178 (22%)91 1.801 0.2 0.604 5 (93%) 36.58 (0.6%) 508 ( 8%)93 1.733 53.14 0.873 1.3(05%) 39.69 (0.14) 1466 ( 7%)914 1.714536,2 0.777 12.6(3%) 39.29 (0.05%) 518 ( 7%)

32.46 1.318 17.8 0,789 16,3(3,3%) 3o9 (1,2%) 326 ( 4%)147 1,2614 6,2 0.753 16-7(14-4%) 141.2. (0.2%) 3149 ( 3%) -108 (149%)148 1.07 0.2 o .895 19,0(19#5%) 40.0 (0.9%) 173 (43.%)

49 2.050 5.0 0o,56 10o3(1-3%) 16.8 (0.2$) 304 (%)

52 1.0= 0.2 0.889 9.3(56.5%) 37.7 (0o0%) 51( %)53 1•,047 0.3 0.883 15.7(22.3%) 38.0 %) 283 ( ) -289 (2c0%)`4 1.506 3.7 0.710 10.2(20.2%) 21.8 (0.3%) 333 (8%)5 2.032 0.56856 1.993 6.6 0.584 11.2k 1.4%) 10.8 (0.0%) 165 (%)57 1.390 0.5 0.706 25.9 ( %)58 1•139 5.4 0.850 17.9( L.1%) 27.8 (0.0%) 191 (%)59 1.c84 0.884 26.9 (0.0%) 138 (%)60 1,017 .0 0.900 27.8 (5.1%) 177 (35%)61 0.975 18.14 0.893 19.6( 5.0%) 32.6 (1.3%) -92 (115%)62 1.044 0.1 0.905 31.;(27.4%) 30.1 (1.7%) 170 (11%)63 2.4.23 29ý0 -on2 .7( rU";

614 2.1468 0.2 O.1419 21-7

2V

TABU IV

'UWUT=A!~ OF A ONAMIC PRMMESX AND OWMVAM PHMMLNA

mash liv ehoeo., d

-Douahrmt of Body shock"-etacbont of 7MShock

lSlmd of tinteact atin fin tip fu, d an bad$2.14 fof ntactlu of aug fin cm its no •baolA

Pz~w~ IHub R~m* o

_______ .04 2, O

,ulm Lppzo•maty ino of

of 1r4~&5iM z~id ilb?8em"3op witb de-. witb d4oai'ang

Vow' Ucal3 Nua mi~ Ayprcozmte3J* ~ w point of 0"-

Inia dwre~ewlth duwrcaaW~x

?ossib2l' lacal awe, L@.a9 SUIRM wona "0fbeim aft wo fmvays~d aft poigitlan rsts of forwa.rdpositLou psi mation wIth I.n-

cieue of Xdurgame

* Lcal pa.L Nin±d

Kai=LOWa w~p~m~ loael mu

ILI/= RIO m O~lMA

TATq.1P V

O ARt MN Or JUJTION TYPED

OaC D -V12 k( Cý cm

Compuedt 0 0/ft Spin 12.27 7.32 6 unknovrw

Oow~ut ed sO f./ft Spin 12.21 7.Lj1 6 uw'im~wn1.0 % .%

ft~utod t 1.C)0 /ft Sprin 12.21 7.140 6 uxm)on u%a 1.3%

Rv~uld 2.94 39.29 $5.21 6 unkn=m 7(spin '1/2 /tt 0.05% 0.6 %

39.2 .5,1, 19.510 uimov~ne0..o08 0,7%

Rou d 2598 9,80 30.81 6 unIawro(Gpin -1/2 */ft 0.J42% L.9 %

10,01 31-58 2n0,76% 8.0

I_=

TA~ MS

CPW TW ON~ OUCET OMAIN1M FlXM BMW=1 YAW AN~D WMV

c D )C-2 +CH

1. Cu-- ted yn-zUg mtin with 20. L 25-9Lme'o trim 0 0

2, OuVutod yawing rn@tlem with 20.062690. CC25 r.A trim o.3 3.6

3. YaIn rati" ofz or 258 9.80 30.90.4 4.9

Stim1.2 7

Computed wur,1" intLM with f.~1.a•ar tri 0 0o patw With .IoM5 trim U.48 .0o.?

2.14 8Co:•,ted with .OMl tri .11 143.6

14.8 16

9.7 35

.42

Attni -DITR•I~JTZ• ZXSTNo. of Nof

Qla of oidnanco 2 CowmdarDepartrwnt of' the A Naval Odnanco Tont

Attni O - Ba Boo 04na Lako CaliforniaAttnu ToK Library

Arnold Rn noortnSDevolopment Centc3 Cef Buzeau of Ordnanoo Tulah~o Tonooosee

ea t of- the 'Navy Attn: Deputy Chiaf ofuhia~ngton 25 P.C. Bu~iff 0 R0

AttnI Ra3

ro S r,, •aC.•o or

ANMI Pr.in Ground Dovedelopet os TO•

1 eiermnt endmt Knott BuidingNabal. Pontgrads, School Dyton 2, OhioMtor, C i fcrBia Attni 3 "lan

2 Co dar Ai1ttA Raferenco CDeterRval Air Missile Test Tech Infornation Di==sion

Center Library of ConresSlPoen'r Srnu, Y.lforni• W ngton 2, D.C.

1 Ccttzndn Officer .3 D' eovt:oramd Mrecto.V Nationrl Advisory ognc ttee

David H. Taylor for AeronauticsMo~g •.i 112 B Street, N.W.WNah gton ?s D.C. WaShnglston 25, D.C,

Artt AerCalif.or nab.Commandmg Oficer Dretor

1 C O iecaor National Advisory Coonittee

Naval Air Development for AeronauticsCent er Ames LaboratoryJohn"_• Ile, Penns. Moffett Fields Ca~lifoimia

Ittnt Dr. A.C. ChartersMr. H.J. Allen

DZ97~1M ION

¢Cmvdttee for Xn atallat.inAgeonata Dpo'martm oft heAn

Umg;•w HawrW L800 Oa Go.ve Di•-vo

AwuiuUoi. Lab. Paoadema 2, Califorya,uvlt7 Fe l ~d, Viz¶1nr.u Attna Mr. Izr1 Be WewLan* .,. 3, . .' Reporte Gou.

0, 0, B. B"mWe k4olf Ra u I Diroctor, Op'-,-tiow

Rhearch Oft'oo1 Hati~lmml &dv m 7100 Coneo•tio-t AvenueComdttea for Obew' Chue mmpaz.ndhatinauiztdo wash.ngtAor 15, D.C.

Labwatury 2 Amour Rearo- Fomdation01,•mean, AOrpct ;, W. 33rd , StreetWmey.1ando 0oto Chicago 16, l11±nis£ttni ?.1. Youwe Attni Mr, W. WialerDiretor

Nat.. �, Ma il of 1 Aem1rbo a• oae D olt

0oinneutiou Avenue & POO. Box 657vanz eag 1• t NoW. Pacific P.liaiedest Q1lif.

ifobim..w Jea • 25 Atnso Dr.• Wliam 1e

-Ar&r4tr Ow&O 1 Calif.±ornia 1atiuto of

-=1o Alm Norman Bridge Ltosratoryi.,:of IQ A•btn of pkui.ea

Fpsudsm, Galiazwira3 Onnwz ftmgOffoar Attnt Dr. Levevatt Daviss are

Plost~wi' ArsenalDover, Now Jej I. 1 Co.aol.idated V1uteeAttnt smuel YOU= A Lirora ft Corp.

kmantJ.m Labarat~orlea Ordnmca Aervpt'ajos Lab.DaingsrfiOld' Tema

ommmdmn OGaileS1 Attni vý%. J!E. Airnold7?mkor'd Ar1imalPbiladealpb.rh 37 Pwmia. 1 Comeu.l AeronauticalAttnt Reports 6=%p Laborat=•, Inc.

COmmMMng Officer 9falo, eov TY'k

Radiologicsl Laborntory Librarian

CrcV Cbe!4cal Cemttw, Md.

J44

(.

DISThIB3T'ON IeSTNo. of

Calitfornita Institute of I Dr. A. ". Fxkett11Tehnology Huhes Airteaft Oo4,ron

OGgg~ aoim Aero•autical Florence A--u.-ue atPazsadona, California Teal Str.Attn: Professor H.W.Liepmn COulv' Cit;, California

2. Ooval Sl'ctivto Co. I. Prcfessor Osorge Car•ierProject M Division of AppliedSoheetad~y IVhw York Soiences"Attr.1 Mr. J.C-- offtan Fhrvard Univorsity

Ccbridze 38, AMss.2 Sandia Corporation

USn&na BhO I Prof93or Francis H, OlauEr

P.O. B= 5800 rWaetent of A�roauticoAlbuqu.z uo, Now MeXdo John sHpkins 7niversityattnt ;4. Wye K. C= Baltimore 18, Kirylan

Uzdvermit7 of F40higanWillow Fbm Rop-e=aeh Cen arS'Al.ow Fb= Airport'iqbilantis Michigani,., t t n t M r. J , E . Co r e y

1 Unite Airrmoft Corp.flo e.rh partment-

Saut •-atford 8, Connect-i,+Attri 1r. 0. H. King

1 University of South CALix-niaDhrinemring CenterIQo9 Xn~eles 7a Cali~fm-dabttni Mr. B. R. Saffell,

Z•.recte~r

1. Profesaor Clark B. XillikanGuggenheim Aeronauticr,.

asd oratory

N..