unclassified 2mi7 ad7*an attempt to study the «sefulneoa of the flat-plate coefficients in regard...
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UNCLASSIFIED AD
2Mi7 Tl o"7121 ■ Reproduced by \ £*
flrmed Services Technical Information Agency ARLINGTON HALL STATION; ARLINGTON 12 VIRGINIA
UNCLASSIFIED
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i « i
ok"'"»«»
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'^ REPORT NO. 7U0
J.ir iHt
ASTI A AflilMOTON CAlt STATION
«■LINatON II VIIGINI4
EFFECT OF APPENDAGE AND Hl'LL FORM
ON HVDB00TNAM1C COEFFICIENTS OF SURFACE SHIPS
ITMMI TUIMU
Oetittan LaboiaiO'i Slcran* mtit<iM of Ttinolog/
Hotott». WM Mrff
ASTIA
OAMOSON LABORATORY STEVENS INSTITUTE OF TEOWOLOCY
HoeOREN NEW JERSEY
EFFECT OF APPENDAGE AND HULL FOB«
UN HYDBODYNAMIC COEFFICIENTS OF SUBFACE SHIPS
by
mtrAHfO UNIXK SPOHSOMHIP
fl»«*MlNT*L MTOWMICMANICS MM»« CaMTIIACI RM« MMItl
TICXMICM.L* AOMINFSTHED ■ D*VID TAVLMt MODEL MUH
IDI PHOJEtl JU I)J*)
Report No. 740 Appro*«d by
Paul bplln
W
I-TkO - 1-
^
■* Teata mm made to detemlne tha hrdrodyiahlc coeffiolanta la the yaw pUn» of trr^MMl BU2 (of tho Tkylor Standard SorioB) with skago of vary- ing alia, shapa and position. Similar axporimonta wer« conducted wlLh flat platos haTlng the SUM profile area arid geanatrj mti tbe various conflfunt- ions. The static and damping hydrtxiynamic coeficionta wore detemlnsd for various angles of attack by neans of straight-course experiments md by In- terpolation of rotatlng-am data. Conparlson of the straight-cows a results with those derived by linear Interpolation of the rotatlng-arm data show ex- cellent agreeasnt^ This sucoesaful conparlaon confinns previous experience at the Davidson ^voratory that the rotatlng-am can be relied upon to give hydrodynamic c^nvatlves applicable to strai^it trajectories (infinite rad- ius of turn). ^Consequently, straight-course motion can be considered as an intermediate between a large turn to the right and an equally lirge turn to the lef t^, --'
^Investigation of varioia flat plates reveals a ilmilarlty between the hydrodynamlc characteristics of a model and those of a corresponding plate, These experiments show the same general trends in latersl Curcn and yuMlng moment, vlth the exception that lateral force is larger on the pUtes. 8» sons for this behavior are given. Compa-löcr. of experimental ronults with existing low aspect ratio theories substantiates the analogy believed to ex- ist between ship hulls and wings, __._—--^^^
7*An attempt to study the «sefulneoa of the flat-plate coefficients In regard to determining the stability indices for ■ ship model of the same pro- file area is included. fXon^arisons of the stability indices calculated for the ship model (with its^arlous skeg arrangements) with those obtained us- ing the flat-plate hydrod^wmlc coefficients (in lieu of the model coeffi- cients) show that this substitution cannot be made. It Is ooncluded that the disagreement in lateral forct. rates between the model and plate of the sane profile area is primarily responsible for the lack of agreement of the oon- puted stability indices. This Indicates that iimediate praotical use of the existing similarity cannot be made before a correction la applied to the mag- nitude of the lateral forna.
Since the length and draft of a ship are taken into account 1 n low as- pect ratio analogy, while the fullness or beam is completely ignored, an im- mediate problem of correlating the fullness with the lateral force express- ion available from the loir aspect ratio theories arises. The attempt to bring the results of experiments into agreement with tbe linear part of the low as- pect theories shows that a correction factor, k , linearly dependent on the affective aspect ratio, Ata , can be employed. It may also be seen that the factor k strongly depends on fullness of the hull, but no conclualonn could be drawn on its affect, since only two different beam-lengtli-imtlo configur- ations were considered.
Model designations applied prior to change from Experimental Towing Tank to Davidson Laboratory will be ratained.
Intrvduotloo..........*...........,.................,............•*•... 1
■oMnolAtura. .*...... ■>•••>.•■>■> ■•.■^^•■•■■■■■■. >>■■■■■■■■■■■■>.■ k
Dvaorlptlon of Modal and teat BqulpMmt................................ 6
Tost PrcgraM and Prooadwa...•■......,,,,.•,.,,...,....,,.,,,..,,...,.. 8
Prea«nt*tlon and Dlacuaalon of Data*«......>.....«.. ■■...■>.■...■.■(■■■ 9
Coneludli» Wwiajlia and ■aooHaandatlena....................■...*.. IB
Aolmowlad()«anta.•..•.•..••■....■.....................•,..-.•.... 20
Ilafannoaa............................................................. 21
Tiblaa 22
nc*u*B***«>>«••••••••••••••••>•«■*••••••••■••■■••■■••••••>•••* •••••■•■ 31
»ppwrrfl* (ncuraa 1-1. 1-2, 1-3J 6»
milODDCTIOII
Th« probX«« of turning «nd «taerln« of mirfac« ship« im of -rttal 1»- port»nc« In the flsld at n»«l ■rrW.tmjtur» ainco It la inti^Uily r»l*t»d to mrTOiTBi«blllt7 and aUblUty «nd la, nom-nr, a apaoial oaa« of tha 9*0-
aral problaa of tba motion of bodlas In fluid«.
Tiia problam of turning and oouraa-lcaoplng oLaraotarlatloa waa Inwat- igatod "by DaTldaon and Schiff1 «ho Introduoad orltari* for dynamic atabll- Ity baaod on tha follovlng ■SMunptionst
1, tho Idaal Inoavraoslbla fluid surrounding a ship la BiibnUntially still,
2. th« linaarlnad theory la used (oroaa-ooup- ling of varloua effeots are not aonslderod),
3^ fore and aft nsynaietry together with w«*e- tualttng effects «re omitted«
Eroluatlon of these criteria Is baaed on a priori knowladga of o«rtaln hydro- dynanlo coefflolonte which can be detemdnod exparljMntally for wrlous »oe- aels vlth dlfforsnt appendages and \arloua typoo of propulal*» dOTloaa.
It has bean aetabUstwd that the atudy of turning and »tearing of a Burfkoo ship oan b« restricted to tha horlanntal plane alone sod that, for length-Froudo nunbers less than 0,20, wave-making «ffacts oan bo naglaotad. Therefore, the hydrodynanio lateral force and Moment ooaffioiant» are tha essential parameters In turning and steering, «nl theae can ha ototalnad fn» roUtlng-a™ testa at ar^ spe«l irtjare F S 0.20 , but Urge anoutfi «o that Reynold- mitnber effeots are mitigated.
The requirement of opllinlaliig the maneurwraülllty and atablllty diar- ■cteriatlcs of a surface TOSBBI makes the question of Intarferance effects between tha hull and various appendages one of fundamental Importance, The- oretical work on intarferanc« of flows at vlng-body and tailrbody Juncture« has been done by aerodymmlaistB «nd to a mob more United extent by ra- aaarchar«2»3 in nawal arefaitactur« who han> approachad the ttmlogaam problm In regard to rudders in a propeller raoa.
Ttls report presents tha results of a modal study of the h^plrodynamlo oharmcteriatlcs of BTT Model BUZ of tha Taylor Standard Series, «.n oon- flgurations were InTestlgatad, ri.«., a bare hull and a hull with four dif- ferent skegs. Maasuremenba of longitudinal and lateral force* ma well «a
IM««) ntlo at 0.8.
•d olranlar p«th tavUg a 3»-foot radbw. «• ■ dMplnf fora« dwrlntlm Alan« wltt • t. .•««*■
L«t«ly, as att««* kH bM« wmdm u
t*m forcM and MMBta «otlj« V« • «^P * MU« »• t, ratla vine thMry (SM FOl—I^IJ ar MotoJ1 Mi I—a^) lbs aMp «all la UMtlfUd «Hk a win« »»Tint tfc- «d «atarUm «c Itc Avi and taiM ttia drwTt >• Its «pan. Xte pMpW «^ th« f ■«• rarflMa la OirHf ta*«a Into aeeowt. To datnvlM tka «ctai of «to wlUMr «f »1* ■—1—y «l- dltlowl vparlMntel «srtt «u oanrlw. «t M flat ptetos «Uk tfca nw v>*- fUa araa and iMMtxr ■■ **«»• rf t'- -unilwilM kall^fe^ aOTnpva«- lona. Uta oovatod UTt and ya-ln« » *nt eaaffiDlwd» ar* iTawi la Ik» praMnb raport «rltb aodaUag Urn aay ratio vim tkaorta», and ip^fc af tfaaaa oa^parlaona ravMl tka wlldlty .» tba akaaa odl^r-
Timlly an aaalMtlaa of «ba »v«afkla aaa of 4ka Hat-vlaW iaalig la undarUkoo to datandaa If tka atal lit» UaJloM an ka «ktaldad «itt aeomcr *r «in« tka plata oorffie: ea la iiao af tkaaa af tka kaU ^^ oonflcmtloaa. Ikia Mbatltatlan La fawd to ka laadaqaata wd tka —— for ita fallnra ara gi-rmu
In anaarr, tka lavMtlfatlan daaerikad karala la dlvidad lato two poi-Ui tka flrat daallas vltk axparlMBt tleo aa «ka akl* aadal flttad «itk mrlaua Aa^, and tka aaiaad vltk ao^arlawtal «aak intortaJ aa «to ftot- plat« eonflfaratlana.
In «to flxat part, tto atatla nd «tnaada aaafflatoala far MM totMl fereaa aid anainta obUinad fm attaint-aaawa «rparlaaatc aa aaU aa % rotoWnf-ara faailltiaa ara praaawtad, 8«s^a faraa and aaBMd aaafflalaato obtalnad by IntarpeUtln« tka ratatlat ara «aato ar« aMparad wltfc toaaa ato talnad la tka atral^t-eaniva aapartaaata.
|b* «aoond part oeatalna tto aoparlaantal raaal'. a ^talaai altk Ika flat-plat* ooaflgomtloM. A papkloal eoaparlaoa af tkaaa data alto «daft- Xim lav aapaat ratio win« «kaorlaa la touin and naalto af toa atabiiity *»- alTvla daaarlfead abovt ara paaaaidad.
lad
Thim mtaOj bu bMa o*rrimt oat at tto DSTUMMI Ubontorr (foiwrly ttw ■«p«^««nua Towliif Tk*), 5tn«M IiMtltuU of f^ihnolflCT, nfpaeUA by ttM BUTMU of aiip»' rmdMMtr'^l ■ytrn—ntarim ■HOAT* Pragru, m>d«r Oen- troot fcnr 263(l£) «ad tMtaniOftUy «AanLitr.l JJ by tu David Taylor Ifadal BMIB (DL rro>Dt JO 2026).
- I ■■MMrf frtaiiiiMitniiiiiii iinwi i Jii
B-TUO - It -
CO.
-l'-i
oU».-wl«« teflnaa In th« t«t
DUUnc« at th» C.O, oT th« aodal fi» «»tow point, U» f»«*
Oiflwtrlc «apt et n^lo, H A
BrMJth of hull, In fMt
C«nt«r of gr«Tity oT mriou« oonfl««r«ti«>n"
Lift eo«fncl«ni
Honant oo*fflolint
Dr«ft of hill, in f««t
IhxlMw h«ight of Tmrlowfl »kmgf
Ha««nt of lUM^il* of M« huU «bout 'h« »-Ml»
Radlua of nr^tion of th« hull «bwit th« »-«xl»
Co«ffloUnt «pr«.li« th. «tlo of «F "^^^SfiS^ 1T0 to oorr.»pondln« <** of lln~r 1« "!«•• «t1» U,w» ltB
ttiwo of affoctiT« ■•p«et («tlo)
LowltudlMl, l*t«^l »nd roUtloml («^ A ••*• 00^"^«*' of »ccBoalon to ln«rtl*, rwp«Jtlwlj
Longth of hull. In twmt {lo«d imtorUn» :Unc«0
LonRtli of skoc, in Inohas
Maas of «rioua hull conf l(ur«tlonB, In olud«
Nftss of wrlo«B pl«t« eonflro-'tlo™» * ■lM«"
LonRltudlral «nd Ut«r*l nus corfflcl«nU, ««pootlT«!!
TkwLnc woiMnt, In Ib.-ft.
T«Ming mamiA coeff lcl«nt
SUtlo and dynwdc 7«*lng ■w*"1 dort«"« ««fflclÄit«, r»- •p«ctiT«iT
Tawln« «o—nt d«rl-«tlw oo«fflcl*trt In lto.1 llald
Hcawnt of liwrtl« eMrfflcisnt *boat th« ■-«!»
Profil« *r« of TOrteww alfge, in »qu»« r««t
- s-
I'.I'
V*rloM pl«t« oMifl*«r»tion«, wbar« the l*tt«r ■?• Btaad* fw plat« »iri th» MWl^ir d«not»B UM oorr««poi»llat lmU-«l»i oonflfuratioiw
Etadiua of taxnlng clrcl», la fa«t
Tarloui »V«« oonflgur«tlon»» MMI« ttm Utt«r »S" ttand« for sktg i«l tb« Miulnter d»not«« Uw wrtn»» typ«i of •)(•(•
Moclty of »dwnc«, In f»«t p*r Mcond
Lonirttudlml «nd Ut«r«l foro» Tmmp»eti.T*lj, In pound»
Longltudii»! «al Ut«r«l foro« oorfflol«nt«, rvspaotlTsly
Static *nd d7im«lc lat»rtl fero« IMMMH oo«fflcl»nt« r«- sp«otlT«ly
Taw aDgla
Maas dsnoity of watar. In sluga
Itoota of tha otablllty aquation, (aUbllity Indlcaa)
U mmt
DtSClIPIIM Or KBKL *» TVf wvxiw*
ft. «d.1 «- in thl. l«~Upti« «. ITT «o. BW, of «- W*
flU«Unl Sri«. -1th .11 d«*™* MMI. 1« o«flr«tl«. «.« «M* a ta« hull .«1 thl. bull flttl «ith fur dlfr.r«t «ta«. Wt^Wi U»
of t*. b«-hull «od.l .M m «riou. .PP-n-.^.. «i —«ofxl.tlo dl
MMlonP of «od.1 «nd «pp-nd.«» »r« fl»«> *»olfl,r-
»HnCÜIAIB OF ETT MOO«, M M APPMH»«S
Kodal Partloulan
Lsngth, I i ft. BrMdth, B , ft. Dr«ft, H , ft. Lanffth-Bo» rutlo, VB L«i«th-Druft r.tio, L/B B«WB-Druft i»tlo, B/H
Weight, lb». Profil« ur»«. * » 1« '<V>*™ f««* Poaitlon of CO. from bow. Inch«»
S.A. 3.B. S.C.
Inch«.
23.51l 16.33 12.73
9
Sims PurtlcuUr«
MX. h iMa.' I ft. 2
3.57 2.21
0.253 0.115 0.0« 0.116
16.5 7.S U.3 1,6
6.00 0»8T0 0.296 6.90
20.1 2.92
liS.iiO 1.53ll
37.UU
CO. of 8k«(t frw» CO. of hull, InehW
-27.15 -22.27 -19.88 ♦27.1lS
fc, pta W .nd Mi™. (-) -I«», indict. th.t «- CO. of M -f« U-
for« (♦) or ^t (-) of tho Uro-huU C.3.
Th. thin tmm u.«l in th« ..oond prt of th. tMtlng pro««-, «f.
jya-lnch MU. -HOT - >■* «• — P""1- •** •n,1 ',,•,,, "^ T" ^.pond^ mm conflation. fUM wltb th. r^^Z^Tw Zilm «M. .1- tb. p-tiouur. of tb. PUU -^tfTi. PH M. . to., 1*.« th. fir-t Utur d«.t- tb. pl-t. «i th. .«»-
-ÜJI« tail 1 . -H- .t«d« f« b«»*»ll p«fiX., '*- for otA th. oorroapondln« hull, I.... m ■!»>»■
hull pi«. AH *» o*0«
I
I
I
i;
Mjmcouis or PUBS COIUSPC»>INO TO rat »DBL
WITH VARIOUS J
put« Conflfurmtloiui ^v W.lRht,
pound. CO. tWi Of
Tow point, ft. O.oiwtric
»„»et Iktlo
P.H. l.S31i 9.M 0.335 0.0579
P.A. 1.787 10. U 0.223 0.0U97
P.B. 1.611» 9.82 C.W 0.0539
P.C. l.«0 J.73 0.313 0.0555
P.D. 1.6SO 9.69 0.386 0.0538
Taste MI« conducted using th» roUtln«-«"» 1" Ä Änk Ho. 2 wh«r« th« mod»l «B ooMti»lD«) to ww in a clrcuUr p«th tartnR » 32-foot «dlM, »nd la DL Tank So. 3 for th« etraight-cour«« wotlon.
In th« Pot«tln*-«r«i t«et«, th« modml mm *tt«oh«d to ■ "baUi»« b«««" on th« «rw by Man« of a alopinf plat« haTln« llrtt flwcur«« «t «aoh «nd coniMatln« to tb« b«««i and to th« d«ok of th« mod«!. Ttm d«n«otlon et th« balance b«aB (torqu« tub«) which va« «ttactwd to the roUtln«-«« *>? ■ •prlng, iwamirwd th« longltwlln«! and tr«n>f«r«« fore«« «otlng on th« mod«! and th« yawing mo»«nt«. Th« d«fl«ctlonB w«r« tranafomtd Into «Uctrioal signal« which w«r« trarwmltt«d to an «lootrle Mt«r "aahor«". * Saidiom •T^O" Sort«« oaolllograph w«" ueod to meaaur« th« tr*n««itt«d output«.
Th« «tralght-oour«« exp«rli»ont« w«r« conduct«! In Tank »o. 3. using the «am« towing ayotein «nd »«««uring d«Tio«a «o that additional «rror« at- trlbutabl« to InooMist.int ■schanlaM would b« a«id«d. Thu«, th« «tralgbt- oouim dat« w«r« obt«ii«d with th« «an« dagr« of «ocuraoy as th« rotatlnf-
ana data.
The ■xp«rljwntB w«r« conductad at aaro h««l angla by r«»tr«iniiig th« torque tub« and flwrur.-vl plat«« In rolling aotlen.
A strut of 0..09 Inch placed at an angla 20 d«gr««« to th« wrtioal and at a distano« four Indies in front of th« bow (at itutor «urTaoa) was u««d a« a turbulanc« stimulator throughout tb« «xp«rlN«ntal work.
Qsnsral >l«ws of the model and plat« configurations with th« tnring apparatus are glwn in Pig. A-2 and A-3 in App«ndlx A.
TEST PBOOWM AND PROCEDUIB
n» i.n-itrir "tio. v/yr , «.. i»u ri^i » ■ "i" " "■' thr.mil.out ti. lnw.tlg.tlon, »I.1J» til. .»p.rl»nt. wr. »ndMcrMd .t th.
following yw» anflMi
j - o0 ,? 2° ^u" .:6° ,*io° ,iiii°.
It» «l.tlng-.n. MM ..r. ran »llh . 32-foot r»!!". of torn. TM »«1.1 ... .« .t . D..!"«! J.« -ngl. Ml .t «ro h..l .ngl. tBroognotf, th. «cp.rlMent.tlon.
IK. roUtln«-.™ prortd.. i~.™ for «..urlng fore., «d «■«*. .ot- in, on . turtln, ~d.l .t «rlou. ™J11, .. "" .■ .I»«" *"' *" "jW*; Ho«.™r, 1« tl» pr...nt lnT.«lg.tlon onlj tl» WdM pmiMlVI» tumlnf radio, v.. «.«1 l»co.. on. obl.ctl« «. to .ho, th.t l,ylrodTi».lo oo.f- flcl.nl. o.o 0. obt.ln«l by oo,i.«.rlng .tralght-ooor.. «>tlo.. .. .n IntCT- mtUU b.t.-n . l.rg. turn to «.. rigM .nd . Lrg. turn U 1.". »• rang, of j.« ."tl«. '••■■ -iVS P S li" . u.«l throughout .1.1. lnT«tlo- tlon 1. th. ranp of th. lln~r b.h.Tlor of hjdroa7~-lo cl». .ot.rt.ao..
In thl. g.n.ral ..tup, t.o fora.., on. .long .nd th. oth.r p.n«™Ho- uUr to th. loogltudlnol pUn. of .j-.tr, of tl» .Mp, »r. ~«ui«l 0 - g.tlMr with th. y.wlng m<».nta.
ii n
"*
PMBMTfcTIOIl kW DISCUSSION OF MTfc
■Hi« tMt rwult» obUlnwl Inm this inwatlwtlön «™ pr«a«nt«l In Flf. 1 to 22.* Ih»M r«wilta «r» dl*ld«l into two p»rt«, ono roforrln« t« tha m&Wt «mflrj-aUon« tncl tho otiior to IM fUt-pUt. «xparlHont«.
For MM In working irtth tho d.t., TmbU I ll«te Uio Information
giimn In aach flgura.
TABLE I
Coriflpii-atlon
nOORE IltfOBttTIOH
npirm Ho. lnt0T%
Compariaon of rotatln(t-arpi daU with atralght-oourae axpartMnta
rut-plata ' configuration Comparlaon of rotatlnf-an« daU irtth
«tralght-courae oxp^rtMnta
! ♦ H 23 - 2l> T- and M' »a. ß at r' - 0
X « H ■( • 1« T' and N' T». p a* r' " 0.1875 j 4 jl 27 Stability ooafflol«nta and hydrodynnwlo
CMfflcianta TB. proflla ar«a
T . ri 28-29 Oraphlcal caaipaHaon of «p»rl*anUl 1 " lift ooafflclanta with that of low ••-
pact ratio thaorlaa for »arloua ahlp and plat* oonfliuratlona
; + n 30 Apparont omrtar of prwaaurw and proo«- ble trua eantar of praaaur«
, TT 31 Itatio of axparljawiUl lift dariyatiM ooafflclant to corraapondlng coaffld- ant of tha linaur low aapact ratio thaory TB. affootiTO aapact ratio
Tha fona data haw bMn corraotod for inartia and atnit foroa. (Urn
&bla. IT Uri T on pages 22 to 29) Tha yaviD« «omant OMffiolanta of tha .modal., ara aa naaaurad alnca tha point of attaohMnt (tow point) of th. flax- vnl plataa and baUnca bM« waa Mitlcally in lino with tha longitudinal
*A11 flpiKa ara niaAarod eonaaoutlTWly atartln« on paga 31.
po«ltlon of th« mrtml CO. Bowvvvr, In tbm O»M of th« flat-pUt« «xp-rU- MRta, »her» ttw tow point MB not In «llgrawnt ¥lth tbm rm^lc«! l±vm
through tha pl*t« CO , ■ correction had to h* »»d».
n* following g»Mnl fon»ul»« hrw b««n i»»d fcr th« hjdrodyn««!«
coefficients i K„(l • k,)
11 "W* t* aln ß
T No(1 + kl> co- p
h*
(I!
" MLV2* ipAL
the -»«aurwd forcoo {longlx dlnal «nd laMral) and yaw- ing moment, respectlTely, maoa of the hull conflpjrationa. *„ la kept oonatent in the ceae of the modal-a
•arlee fro« :onflf,urStlonf , inflKuratlone M'
»,*-*> naiiB of the Tartoua plate coi conflfturation to configuration, loi«ltudlnal, laterd, and rotational (about a-axla) coef- flcienta of acceaalon to Inertia, reepectlTely,
1.93V slugs. p - mass denelty of v p e yaw angle, R - radius of turning in feet, A - profile area of »ariouo eonflguratione in square feet, ä - dioUnca of the CO. «f the model frtei the tow point. Si
the present caea, » is positiTe- t-in« locate in front of the tow point,
T - velocity, fpa, L - length of configuration in feet,
the coofficienta of accession to Inertia ha»e been conalderad to be oqulvalent to thoae glten by LwA6 (pa»!e 155) for a prolate aUlpaoid aa
a function of the ratio of minor to major axes. In thie report the equlY«-
l«nt form la eoMld«r«d to tev* «a It« njor «is UM BMI l*nffUi and A«
Ita alnor «xlo tvltM tha draft, I.«., tvlM UM TOIOM of tt» avbmmrgtii part of tho «hip h«U. {■ tho prawnt =■■• UM foUcwln« nluoa «•« iModi
^ - O.Ot
k2 - 0.96
k1 - 0.68
The «Uta which tar« boon oorraotod (aaa T»bl. I) *ra praaantad aa
eoaf;<^>ani« af
1, hydrodynaBlc lenfitwiljial forea, I'
2, hTdrodrnanlo Litaral foroa, T1
3, hjdrodjnaMlo yawlnc mamnt, «'
plottad agalnat Taw angl-, P . <Saa PI«. 1 to 5 and U for shlp-aka« con- fifuratlona and 12 to 16 and 22 for tha oorraapondlnt fl*t plataa.)
By oroaa-plottln« tha rotatiiy-ana data, tha atatlo Utaral forca and moment ooafflolanta at r' - 0 ara detanalnad. Tha static and da^>lnc forca a«! Mtmmnt darltatlraa Tl , III » TJ. , and »J oan ba cowputart by croaa-plotting tha data at r' - 0 - 0 . thaaa ara a«aMrtaad In %bla n on tha followlnf paga.
Tho rasulta of Ut« at-aljht-couraa axparlnanta ara fraphlcally eo«- parad In Fl«. 6 to 10 and 17 to 21 with thoaa obtalnad by oroaa-plottlnc tha rot*tlng-am data, lha axcallant agraaawnt ahown (for both Modal and flat- pUto caaae), batwaan «tralcht-couraa axparlaanta and IntarvsUtlona of tha rot«tlr«-«m «cparljiants, laada to tha eoneloalon ttmt atralght-cour»« mo- tion can ba comldarad aa an Intaraadlata batwaon a Urga turn to tha ri(ht and a larfa turn to tha left, nierafore, tho darlTatlTaa of tha static hy- drodynamlc ooafficlanto oan bo d«tar«ln*d aquallj waU by althar rotatlnf- arm or atralght-coursa axparljaanta.
U
Static DarlmUiTH
1 »{ i; H-
•■.226 +.156 ^.337 ».087 ,283 *J&
■■.239 •.U3 ■■.516 ».261
-.032 -.OUi ♦.093 -.070 ♦.031 -.056 ♦,012 -.0ti9 -.158 -.060
TA8I£ II
HTDRCDTUKIC FOHCE AND WJWNT DFKTTATIVZS
B^ra Hull •< Hull ♦ S.A. < Hull ♦ S.B. * Hull + 3.C. t Hull ♦ S,D. ♦
PUUoi P.H. ♦.IjlS ».111? ♦•037 -,0ti0 P.A, +.Ii6U +.112 +.107 -.056 P.B, ♦.USB +.129 ♦.072 -.053 P.C. ♦,!O0 +.lli3 ♦.06U -.0lj2 P.D. +.630 +.206 -.027 -.078
Thm r«o'ilts of »n «tlawpt to corrvlat« the liydrodynamlc boharlor of
th« ahlp nodsl with that of the flat plate tikvlng Uia auw profile «r«« and
gponmtry «re shown in Fig. -3 to 26, where the static and dynamic ooeffici-
ente for lateral forcen and yawing moments are graphically compared. It ma;
be noted that the forces and moment« obtained from the flat-plat« experl-
ments have the same general trend as thoae of the corresponding modeLe, with
the exception that the forces show considerable deviation In magnitude, nil«
can be explained qualitatively, at least, by a study made by Cntbtre« who
found that the pressure distribution over a thin plat« (le«s than 12% thlck-
neas chord ratio) at vmrious incidence« shews a pronounced fiction peak near
the leading edge with a subsequent steep adverse pressure gradient. This
causes laminar boundary layer separation, since the particles near the re-
gion of auction peak do not acquire sufficient energy to overcon« th« large
pressure gradient and the existing friction lassos In the boundary layer.
The «lee and form of the separation region or "bubblo" has a considerable
effect on the pressure distribution atJ hence on the lateral force.
Th« variation of th« bubble formation with thlcknecs ratio, incidence
angle and local Reynolds number has been correlated with the pressure d.ts-
tribtuion, and it was found that a short bubble ha« very little effect on
th« pressure distribution as compared to the long bubble. Furthermore, as
the Reynolds number decrease« for a given Incidence or remains constant for
Increasing angle of incidence, the length of the bubble Increases and, con-
fcitt.-.. i
sequontly, the preusure distribution ±e «Xfacted considerably, Tt is ol«ar therefore, that, before reachlrg any oonolusion for the hQfdrodjmamio bahar- ior of th« thin piste, ■ detailed Investigation must be undertaken to study experimentally the lateral force wrlatlon with the Soynoldo number, «■igle of attack and geometry of the leading edge.
The attractiveness of the idea of hydrodynamic Blmllartty between flat plates and surface ships of the same profile area led to the invsstlgation of the degme of applicability of such an analogy to the more practioal pro- blem of MtlmtlBg the dynamic stability of a hull using only flat-plate data. An analysis of dynamic stability of the Tarlous hull conf 1 (^urationB was therefore conducted, and stability Indices were compared with those ob- tained by using the mafla coefficients of the ship and the norreaponding hy- drodynemlc coefficients of the plates.
Heaults of this analysin are presented in Table III on the following page and in Fig. 27 where the stability indices and static and dynamic de- rivative coefficients are plotted versus the corresponding profile area, unfortunately this comparison shows that innediato practical use of this analogy is not possible as long as the lateral force on the plato behaves ao capriclouslj compared to the lÄteral force exerted on the surface ship.
The dynamic stability indices for various hull and plate configura- tions have been calculated from the stability equation Riven by Davidson and Schiff by means of
^ _ [n;T.-.w] ;{(n;^-.W);! . Uj.;^. (..-Tp»^]} ft)
where all the aynbols are according to the nomenclature adopted by the 3o- iety of Maval Architects and Marine Engineers.
Table III presents the mass (m! , ml) and inertial [n') coeffi- cients of the various configurations together with the stability indices.
In the non-ditienslonallBlng process for the mass coefficients nil , ml and Inertia coefficient n' , the quantities ip AL and Jp AL were re- opectively used. Furthermore, the moment of inertia of the hull abo\\t the
i is computed by means of the followliig «otpressiom
' M K' i0(f)2 . (5)
- Msa of th« hull conflgunitlon, I
- T»(J1II« of gyr»tlon, - load w*t«rlii» langth.
T»BI£ III
STÄB1LITT ISDICES
Haas ani Inertl* Coeffidenta of Hull
ConflFuratlona
subiutj Mio«. - st*bllitJ,571;c'*' Haa. and Hydradyna.lc «aaa Coafflcl.nt. Co.rflol.nta of Ship Ot Ship Configuration
Conflgoratlona And ajdrodjnajlo Coafflolanta of PlÄt.a
Ban. Hull .1723 .3301. .01967 Hull • S.A. .Ili79 .2836 .01705 Hull ♦ S.B. .160U .3075 .Oielt? Hull • S.C. .1652 .3167 .01905 Hull * S.B. .1602.3075.01817
* .207 • .»2 ♦ 1.02U
-3.876 -14.362 -li.'Ofl -3.823 -7.061t
♦ .1196 -1.261 - .Mb - .11.66 - .3392
-3.397 -3.79U -3.809 -3.375 -5.995
It 1. .rld.nl that .11 .hlp-ak.g oonflgunatlon. ar. «nafhl. axo^t th.
o„ Mtk am i.rg..t am, "•. s-»- *"•••'■ *• w«"""1 ■"•• """ m„ and ln.rU. oo.triol.nt, of ahlp-.k« oonfleu^tlon. »r. ua«. t.g.th.r .1th th. hjal»d™.lo oo.rflcl.nt> of th. oorr..pondln8 plaWa, aho,, ata- «llt, ror all oonriguratlona. IU., of oour... 1. not „rprl.lng alno.. a. ha. b..n ™ntl.n.d b.f.~, tha .Utlo and d,n..lo d.rl^ti™ oo.fflcl.nt. of
th. lateral foro, on th. plat., ar. oon.ld.r.Mj g^aWr than tho« of th.
oorr..pondliu. hull confleun.tlon.. (S~ Pig. 27)
In th. final .t»p of thl. lnv.atlgatlon, oorr.Utlon of th. .xp.rt-
»nUl roaulf with th. «rtatlng lo. a.p.ot ratio vlng th.orl.a «• undor- takan a. anoth.r fat of th. nOlMt» of th. hydrodyna.alc analog, bMM.
ahlp hulla and rial plat...
A. oo^arlaon la U-ltrf to th. folloring romula. of th. lo. a.p.ot
ratio thoorta. gl<«n by FUx and La.r.nca .
fclnlg. CL - n/2 « P ♦ 2ß2
Sohola. CL ^ n/2 « P • 3.6(>2
Flax-Lauroncoi CL * n/2 * P * P
H.™ th. lln.ar tan. 1. Id.ntlo.l In all oaa.a, .1»™.= tha ou.dn.tlc t.™ „rlou. oonaldornhly d.p.^lln« upon th. aa.u^Uon »d. and - In »o.t In-
.tue. - upon th. .xp.rl~..t. t.l»n Into oon.ld.r.tlon. Sohol. .t.«. tl»t hl. «v.Ma.l r.~lt M -»tlj HpW^ii to fUt pUt~ o! lo. «W-ot r.tlo. ■■ FU.-Uvr.no.8 formu 1. «Ud for * i O.S. «h». tl» oro..-rio. dr« oo.fflol.nt 1. MM to tl .^iltj. It ~>t .1.0 b. Wpt in rind th.t th. .Up. of th. l..dln« «1«. 1. of *lmmt ivort.no. In a.l.ctlnt th. qortrtM »rm, ,lno. th. fom.tlon of th. buhbl. .nd lt. «t.nt 1. Br..tlj ^f.o»d hj th. (MMtele condition of th. UMn ^«.. 1" «■ P~~»t lilWM»«* "» rounded tip .de. 1. oon.ld.r«J In oonfonütj «Ith th. »od.l oonflrir.tlon.
An .tt»»t to 0O1T.1.W th. «cp.rü.nt.1 r..!.«. with th. ■■• Wlt- «1 fomdl. .llUrt hl »,lok.r M F.hln.r' .ho»d . oon.ld.r.bl. dl.or^- „oj dn. to th. r.ot th.t th. non-U—r «MM «. jr..tlT «.«.m« b> th. pr...no. of th. ..poot »tlo In th, Hni.lWW, >■■■■■»» "" "'t,1°" introduo«! th.lr for^U on th. ...u«ptlon th.t th. ..p.ct ratio .hould b. gr..t.r th.n unit,, . f.ot Äloh U »Ud for control «nf.C.
M „,phlc.l c<»p.rüon m*W 1.. "«• «» f«- "» "" ".fflcl- .nt .how, th.t th. FUx-U«»nc. Wr...lor 1. In b.tt.r .g™,™« rfth th. WllmtU oonducfd rfth th. hoU-fc.« oonflrirmtlon, «h.r«. th. SchoU .xpr...lon l. in b.tt.r .p.«i.nt rfth th. oorr.w«ndln« fUt-pU» .«p.rl-
■wnta. Anothor f.ct of thl. corr.Utlon 1. th.t ..p.o«. r.tlo ™rl«tlon do..
not npUil th. lncr.».nt of lift co.fflol.nt d.T.lop.- on th. hull-.W« conflscratlon owr th. l»r.-hoU c... Althoocb "« »rUtlon of ..p.=t ratio do., not .otolly prodoc. .n .prracLbl. «rUtlon In th. lift oc.- p„„,„t of th. »rlo». pl.« confljuratlon. (Mt It- W, '" «• ■" <* th. hull-.k.B configuration, th. .«.. ..p«t ratio rarl.tlon ,1«. rl.. t« . con.ld.rabl. Incra... In th. corra.pondln« UXt co.fflcl.nt.. Ib. IMp gorafd tff.ct of th. ..p.ct raUo In th. huU-.fc.« configuration ~j b. •ttrlbut«! to th. h>ai-.k.g lnt.rf.ranc. .ff.c«, «.ich .ra b.ll.wd to d,p.nd .trangl, upon th. fulln... of IM .hip. It 1. th.rafora pUuhlbl. to conolud. th.t th. b.» .ffet (fulln... of th. .hlp) 1. ~lnU r..pon.l- bl. for th. .ff.etlran... of th. .fc.g. .Inc. <M Ml oth«- .hlp tMUttlU UM, mmU draft .nd l.ngth, h.™ .Ira.dj, b..n Ufc.« Into .coount, .nd ■oroorar, »Inc. th. .ddltlon of th. M> «M ■>" »• «- »'^ H*" ,,ld
not (.0 «tpoctod) inora... th. lift by .nj oo«p.rabl. «.ount. B.for. »fc- Ing u.. of th. lo. ..p.ct ratio th.orl.n, 1t ...u of pUMMrt taporfne. to .tt..pt to incorpora« th. b~. .ff.cl In tho «pra..lon. of th... lo.
aipoot uing thoorloa.
16-
rmmmm, m M —* ** 1- *> «»' "■ "*• "" "p*ct r*'1'' i^r, 1. in «MM •* «• «i •«—»1 c... — - W;~^ ,, B - 0 . In K,. 31 th. r.tl. k X «" »^1» •' «■• ■•«—" "» cJlcl.« ^ to «. o.™»^^ =1^ o, th. >M. "P-t ~"° '"^
,. „lott-d in t.™ of th. ..poet „tlo. ■ - «»/» ■ «■ ««" '"^ *
m.„, or th. i..«-.™.™ -»- *- «•♦ «- «»«»«« k "rt" 1'~'r- ö .1th th. ..p.ct ~tl.. • , •»■ If "t. of oh.»,. 1. m* pronounce In
th. hull oonfl^.r.tlon th.» In th. flat-pUt. o..... I««««., « — „otlcd .h.t th. «M 1.-3 for th. p^t. A ».., -hloh .ct„.Uy oorr.,-
po^. to . MM«., U im, .M to ^nd tunn.! »»»• for "» •••""- Hot r-tlo. (S.. ng. . of PUx-L—no.») TM. f.ct Indlo.«. th. » .,01« -.11- ~thod «nploy« 1» th. pr...nt .ort. 1» .cc.ntln, for th. tr..- .nrf.o. off«'- U cor-ct, .nd ^««T «^M (for 1« Proud. n™b.r.) thl. «ffot .« •• .tlrlb.t.bl. fetor to th. ob.or^d d.rt.tlon MM« pUt. „t oorr.-pondln, hull o.^l^tlon.. Fro. th. p^rlo.. dl.ou..l.n It 1.
w,ct,d th.t K .hould not onl, b. . function of « but .1.. • function of th. fulln... of th, -hip hull. »nfcrtun.t.lv, no ccnclu.l.n, or .t l...t fiction, could b. Mm fro. M .»1UH. ..t of .xp.rl».nt. .Inc. o^
t,o o.... -th v.rl.bl. b.», »«« (BA - 0 «d Cli,« .«. con,ld.r^.
A„ .tt^t >«. ~d. .Uo .t «.mUti« th. »..»r.d .o™.nt ocfflcl- .rt. .1«. tMorj. TU. - Ln^nc.- »plrloU-th.or.tlo.1 fo^ul. for lift ccfflcl^t ». -ultlplW b, th. dLfno. of th. .pp.r.nt o.nt,r ,1 pr...«ro
M. th. c.o., i.... *V«L • M= - ■,bt*1',=<1 ^ "'Tr n Tr. fllyobfln- »1 b, U,l...,th,.o..ntoo.fflol.ntd.rtr.tlv.byth.
lift -o.fflcl.nt ?.ri™tlPr.. ■» dC^/dO, d.ri™. In thl. »nn.r-- found
to b. «pM!.«» ccfnt ovr th. p. «ngl. »« t« »oh oonfl.u,.. « „.«.. (S., lit. 30) Th. coMp.rl.on of .xp.rl™nUl W* th.o,,tlo.l C U
gl^n on RC 21» ^r th. bar. hull, hull pi» Dm » «K "»« »»*' '«" •',,1
■I" (u.lnj; th. Schol. Uft fooiuU for th. plat«,).
Ih. WfUUt CnWr of pM>», of 00«., dl.r.g.rd. th. .ri.t.no.
of . pu™ coupl. «MM on . bod,. » I^M coupl. -ould .ot on th. hod. In „ ldc.l fluid in th. .b..noo of U«r.l fore. Foiling th. .tapllflrf Om th.or7 of Hunk10 .nd Alhrlns11 th. .o»nt corfflcl«,t could b. .^.r...»!
».-■v-n.'*!? <5,B ^ • (')
l-TljO
*twire iL la tb» daatablUilng noMnt oo«ffiolBnt d»rlwtlM In an ideal fiuld, (jt/2 m p) eqiuls CL In th« XinM^ low tapaot r«tlo th.ory, and #p ia th« dlatanoa fro« th« tru« center of praBaure to tba CO. m lonr fwrt of Fl«. 30 la a plot of axpartaontal Ni varaua Ti at p - 0 , Fit- ting th« thooratioal llnaar aquation (see nook10 and Albrti«11),
^ m\*^rh * f 10)
to the data polnta glvea an indication of both the ideal noncnt rate »i , tho ordlnate Intercept, and the actual center of preaeure ponition, 1
*p/L , the alope of the Una, Ttm wiuoa thus obtained aie eubstituted In Eq. 9 and the moment coefficient«, according to this foregolr« oijepllfiod flow theory, are plotted in Fig. 29 with the other experimental and theoreti- cal moment coefficient«.
It la «Tldent that the cowbiMtion of tba Flwc-Uwrenc« formula ulUi the apparent location of the center pressure (obtained from the erperimenta by mean« of dC^/dC^) give« oatlefectorr reeulta when compared with those obtained by experiments with the »arioua model configuration». In addition, Scholl' formula multiplied by the looatl on of the «pparent center of prea- aure, dcyd^ , dancrlbes clooely the plate oonflgurationa. If, however, more reaUotic procedure («Iwpllfled flow theory) 1« used for the determina- tion of the location of the center of preeBure, then the linear low aspect ratio expreBBlon well repreaent« the bare-hull case and fairly well the plate-lmll case.
COH0LIIDI1K1 XHLX3 UV HE00mi»O«IIOII3
o. m mm i m ummm mm «- '•^-1-,--4 ~-1«4- "■
.tr«Uht-«o»r»« »otloii (»n »• •«IW"i ""• """"«-
2 Ha .liriUrltj or result. oblmln«i for th. l»1;-''"«
SriTUiil^Sa ■< i» met)**. vi»r..0 th. SÜS SS! .ho» Ums* «• '""•,,ut ""M<"r- abl. d.Tlatlon In iMgültud«.
•, lubllltY iM-MtlT h.»"! on th. co.mcl.nt. of th.
for the of th. MOrttn .rr.nem.nt. »na1"" thlt no LmtMU pr.ctlcfi «M o.n 1» ™f »' g"
S i.t.^l"oSrit.rt.d on . thin ^t. I»"** SrtbS.bl. to th. U.ln.r bo»™l.rj ..p.r.tlon n«r t2 to^Ä' ««■ oorroctlon, th.r.for., .houU ta', ftSScTS th. loci ».ynold. nmt.r (b..«l on S. dl^"c...nt thlokn...), of th. InoWnc. .nj... and of th. l..dln. .dg. g.on.try-
1, Th. co«p.n.on of th. .»1>.rt..nt.l r..nlt. for th. lift ocSfflcl.nt Klth .»il.bl. lo. ..p.ct ""° iin« thcorl.. 1. .nothor Indlc.tlon of th. «xl.tlnj iSogj b.l-..n .urf.c. .hlp. «nd ..rofoll. of im ZSStritU. Th. Fl^-Uvr^c. •>£•""• 2,2 brtMr .Br....nt »Ith th. mirf.c. .hlp <"" "^r" „'„-lln.ar WM •>• not H pronome«!, .h.™.. th. Schol. «pr.o.lon 1= In b.tt.r MHUMt rith th. flat-plato dat..
S Tn Ib. c... of th. bar. hull onU, th. lli».r lo« 5- imet ^"."..or, clcU d..crlb.. th. «•■^"»n "Pth. Sft co.fflil.nt -Ith th. ..p-ct ratio -hm
I„ .11 th. oth.r »... ■ f.ct«-, «■• """g ". c.nd.nt on .8p«ct ratio, K , '■»« « n"«1 'n or SSlTteS, S. lln-r U*m 1«'° .jr—nt ^th mrperln.nt.1 ramilt..
«• sr-r^: ääTS srars sa^ s:
oth.r ranblneil »"H «» «PI«™"! loe.tion of «« c«n- t.r pr..mr. UCjMlJ !l"> ■«tUt»«*<»> r..nlt. ot»ip*rBd with the mod»! »M plito cnnfxgur«tlona, ro- apootlwly. If, how«»rf a more -«Uatlo [.rocwluro, l.o,. alJBpliflod flew t:«o.7 (imJi.. in the lineer re- flon onlj), ia uaed for the location of the center ol freoenre, the lo« •MM KMI H-'«' «T-reeelon ««11 reproaenta the l.re-hnll oe-o aä f«*.-ij ma the plate- bull
1. Iho failure of aapect ratio variation tu account fuV the ohaer^d «ri.tion in lift coeffloUnt fr«. the bare-hull confinuretion ^o the hnll-akeg ccbinati^n la an Important drawback to the uae of current theo- retical anal- ,'--- »ny approach baaed on low aapect ratio ia w' ..rito^ uae when the hull-akeg interfer- ence effect ic not taken into account. Jpocifically, it io believed that the fullneaa of a ship form should be inoorporatad in expressions of low aspect ratio win« theories, so aa to bring the aorodjnanic analogy into better agrsement with (ncperlmental results ob- tained on ship forms.
8. Tie agreement bo.woen the experimental results and those obtained in a wind tunn.l indicates that the fr.e-aurfaoe effect is well accounted for by the "solid wall »athod and, therefore, such an effect is oncluded as a possi- ble factor which contributed to the observod dlscre- psncloa between flat plates and hull oonliguratloi».
The effect of fullness and beam-length ratio en the hjd.-odyi.mlc corf- ficient. requi™. • systowtic study, particularly U, regard to the effect of
adding .kegs- The additional foroea and moment, produced by the hull whan skega are added must b. Isolated by measuring the force, and mo»«f on Of
skeg and hull separately.
«ore specifically it is rrcommemded that experi^mtal work .tallar to
that of the präsent investigation be undertaken usln„ a tmOg of forms of progreaaively incre.alng beam-K.ngth ratios. Ih. first member could be . plate of the same profile aa all other «n*ers of the family. The last «em- ber should be a form similar to . Serisa 60 design. Ihe effectl-»n.s. of adding a single skeg to each «ember could next be determined by .ep.rat. de-
termination of ekeg and hull forcee and momente.
rurthermore, the Umlnar .eparatlon -bubbl«" «»r the leading edge of the thin forms should be studied e*p.rl..ntall, for moderate value, of inci- dence to develop mean, of preventing the appsaranc. of such .ones of eepara- tlon. If this could be accomplished It ie anticipate that th. flat-plate
analogy would bo enhanced.
w .
-20-
*Mlytlo»l ■tudy within th« trmammrk at ti* IM trnfmat r»tto tbtory abould b» wKtarUlMn, »Ino» th» pr»««nt ln«Btl«»tloi> t»m Bham i-t» »Udltr
of %bm analocjf of «hip hull« «nd ulnga of low MpHl r«tlo.
AGOOWI£D(1MEITS
■n» tuthor wlBh«B to «tpi»DB hla Indobt^no»« to Dp. John Br«8lln for hla cotMtruoti™ BUgffBtioiui «od to MIBB Wlnnlfr«! J.oobs for her .BalBtmo«
during tho pi«p«r«tlon of thlB r«port.
1. DuTldson, I.S., and Schiff, L, i "Turning and Course-Kaeping QualltlM'', Trana. SHAME, Vol. 5U, »oreBiber 19k6.
2. Okada, S. i "Investigation of the Effect of the Propeller Race upon the Performance of Rudders", Second Heport, Hydrodynamlc HBoearoh of Ship Rudders, Hitachi Shipbuilding and Ennlnaering Co., January 1959.
3. Roraahn, K., and Ihleme, H, i "On the Choice of the Balancing Areas of Rudders In the Propeller Slip Stream", Schiffstech nick. No. 21, April 1957.
U. Pedyaevsky, K.K., and Sobolev, O.V, i "Application of the Results of Low-Aspect Wing Theory to the Solution of Some Steering Problems", Proceedings of Netherlands Ship Model Basin Sympooium on the Be- harlor of Ships in a Seaway, WanRenlngen, Netherlands, September 1957.
5. Inoue, S.i "On the Turning of Ships", Memoires of the Faculty of Engi- neering, Kyushu University, Vol. XVT, No. 2.
"Hydrodvnamics", Dover Publications, Sixth Edition, New lorlc, , 19li5.
7. Crabtroo, L.F.i "The Formation of fiegione of Separated Flow on Wing Surfaces", Part II, Royal Aircraft Establlahmant, Report AEW). 25~8, July 1957.
8. Flax, A.H., and Lawrence, H.R,t "The Aerodynamics of Low Aspect Ratio Hings and Wing Body Combinations", Published by the Royal AerorAutical Society, Third Angl-j^American Aeronautical Conference, September 195l. Cornell Aeronautical Laboratory, Report 37, 1951.
9. Whicker, L.F., a«l Fehlnor, L.F. t "Free-Stream Characteristics of a Family of Low Aipoct Ratio, All-Movable Control Svrfaces for Appli- cation to Ship Iteslgn", DTMB Report 933, necomber 1958.
10. Hunk, M.M, i "Aerodynamic of Airships", Divi.-ion Q. Section 9, Vol. VI of Aerodynamic Theory. Durand, W.F., editor, 193«.
11. Albring, W.: "Stability and Haneuverabllity of Bodies with Control Surfaces", Translation by Dr. Arthur Kom, ETT Note 30, April 19li6.
■
TABULATION OF MEASURED AND CORRECTED RESULTS FOR LONGITUDINAL, LATERAL FOfiCES
AND YAWING MDkCNTS
Turning Radius R - 32 fa«t
Measured Corrected
Modal p° Spesd.V, fps
X-Force lbs.
Y-Forne lbs.
N-Moment lb.«.
X-Force lbs.
Y-Forc* lbs.
N-Nto merit lb.ft.
Ear« Hull 0 3.^6 -.2615 -.7101 -.8695 -.2615 -.0978 -.7749
2 3.2> -.2712 -.5976 -.2670 -.2347 ♦.0031 -.1742
3,34 -.3413 -.5334 ♦,2232 -.2634 ♦.1083 ♦.3225
0 3.29 -.3636 -.3895 +.6667 -.2499 +.2305 +.7650
10 3.25 -.',339 -.1277 ♦1.694 -.2445 + .4880 ♦1.791
14 3.29 -.5226 ♦.2781 ♦3.077 -.2597 +.8862 +3.174
- 2 3.32 -.2656 -.6772 -1.472 -.2336 -.2424 -1.374
- 4 3.23 -.2096 -1.002 -2.008 -.2827 - .4026 -1.915
- 6 3.26 -.2054 -1.216 -3,7» -.3210 -.6070 -2.671
-10 3.29 -.1634 -1.850 -4,667 -.3527 -1.235 -4.591
-14 3.32 -.0636 -2.560 -6.fi75 -.3515 -1,941 -6.777
-U 3.29 - .0985 -2.598 -6.761 -.3614 -1.990 -6.665
HuU*Sk«g A 0 0
3.38 3.29
-.2793 -.2678
-.3500 -.3268
-1.664 -1.558
-.2793 -.2878
♦,3067 ♦ .2965
-1.563 -1.462
2 3.26 -.3146 -.1265 -1.242 -.2774 ♦.4856 -1.147
3.26 -.3455 +.1743 -1.157 -.2711 ♦.7656 -1.064
0 3.29 -.3928 +.5345 -1.217 -.27 92 ♦1.154 -1.121
B 3,26 -.3912 ♦.9142 -1.191 -.2424 +1.D21 -1.096
10 3.29 -.4761 ♦1.342 -1.218 -.2867 ♦ 1.-957 -1.122
12 3.29 -.4718 ♦ 1.785 -1.201 -.2456 ♦2.3'Ä -1.105
14 3.29 -,5442 ♦2.315 -1.079 -.2813 ♦2.924 -.9814
- 2 3.29 -.2360 -.4966 -2.153 -.2759 +.1266 -2.057
- 4 3.32 -.1934 -.6485 -2.634 -.2711 -.2149 -2.536
- 6 3.26 -.1664 -1.127 -3.146 -.2774 -.6177 -3.052
-10 3.26 -.1254 -1.682 -4.465 -.3125 -1.277 -4.370
-IZ 3.29 -.1353 -2.391 -5.345 -.3614 -1.779 -5.249
-14 3,26 -.0670 -2.870 -6.059 -.3263 -2.273 -5.964
-14 3.29 -.1028 -2.954 -6.265 -.3657 -2.346 -6.168
Hull*SkBq B 0 2
3.32 -.2513 -.5334 -1.223 -.2513 +.1014 -1.125
3.32 -.2336 -.3802 -.6100 -.1951 +.2546 -.7119
3.29 -.2607 -.1612 -.3798 -.1850 +.4609 -.2835
0 3.29 -.2673 +.0801 -.1796 -.1742 -.7001 -.0833
10 3.32 -.3956 + .6656 + .3394 -.2028 +1.293 ♦.4375
14 3.29 -.4187 + 1.397 ♦1.019 - . 1547 +2.005 +1.116
_ j 3,32 -.2116 -.6910 -1.862 -.2502 -.0562 -1.764
- 4 3,26 -.1668 -.8961 -2.196 -.2393 -.3004 -2.104
- 6 3.32 -.1840 -1.300 -3.108 -.2997 -.6689 -3.01C
-10 3.29 -.1353 -1.991 -4.512 -.3246 -1.375 -4,416
-14 3.32 -.0804 -2.S09 -6.392 -.3493 -2.290 -6.294
H-TK) -23-
TABLE IV
C01TINUED
Weas-ired Corrected
Model p0 Spied,V. X-Forco Y-Force H-Moment X-Force Y-Force N-Moment
fpB Iba. lbs. Ib.ft. lbs. Ibe. Ib.ft.
Hull+Slceg C 0 2
3.32 -.2502 -.5962 -1.041 -.2502 •.0386 -.9433
3.35 -.2735 -.4708 -.4809 -.2343 ♦.1749 -.3811
4 3.32 -.2281 -.2931 -.1598 -.1521 ♦.3405 -.0617
6 3.29 -.2876 -.0866 ».1396 -.1742 •.5334 +.2359
6 3.35 --2B25 -.1199 •.1199 -.1662 •.5224 ♦.2197
10 3.35 -.3643 *.3924 ♦.8800 -.1682 ♦1.030 •.9798
14 3.29 -.4458 * 1.904 •1.742 -.1818 ♦2.512 •1.838
- 2 3.26 -.165S -.6973 -1.648 -.2030 -.0850 -1.553
- 4 3.29 -.1710 -.9967 -2.218 -.2467 -.3765 -2.122
- 6 3.29 -.1396 -1,282 -2.986 -.2532 -.6622 -2.890
-10 3.29 -.0995 -1.969 -4.631 -.2878 -1.354 -4.535
-Ii 3.23 -.0719 -2.740 -6.28. -.3261 -2.]55 -6.191
Hull+Sk«g D 0 2
3.29 -.22i-l -1.136 -1.655 -.2251 -.5129 -1.559
3.29 -.2597 -.7823 -.6600 -,2251 -.1591 -.5637
3.32 -.2402 -.5235 •.15°B -.1697 ♦.1102 •.2579
6 3.23 -.2553 -.2709 ♦.8338 -.1553 ♦.3261 •.9315
10 3.32 -.3295 *.3350 •2.711 -.1532 ♦.9620 +2.809
14 3.32 -.3582 •1.378 •5.312 -.1124 •1.997 •5,410
. 2 3.29 -.1872 -1.439 -2.608 -.2218 -.8158 -2.598
3.29 -.1363 -1.904 -4.133 -.2056 -1.282 -4.037
- i 3.32 -.17J9 -1.973 -4,199 -.2424 -1,339 -4,101
- 6 3.35 -.1906 -2.477 -5.527 -.2982 -1.835 -5.428
-10 3,32 -.1333 -3.526 -8.541 -.JÜ97 -2.899 -8.442
-14 3,29 -.1125 -4.609 -11.74 -.3538 -4.001 -11.64
Plate "H** 0 3.32 -.0551 -.0981 -.8465 -.0551 -,1135 -.7152
2 3.32 -.045? *.10S8 -.4507 -.0353 •,3174 -,3174
3.32 -.0496 •.4121 - .1895 -.0242 •,6237 -.0562
6 3.29 -.0801 •.7769 •.0995 -.oiye •.9835 ♦.2305
10 3,29 -.0595 •1.316 • 1.082 -.0087 ♦2,023 •1,213
12 3.29 -.1298 •2.424 •1.672 -.0692 •2*629 ♦2.003
14 3.32 -.1444 •3.306 •2.755 -,0672 ♦3.514 ♦2.887
- 2 3.32 -.0397 -.4077 -1.532 -.0496 -.1962 -1.398
- 4 3.29 -.0444 -.7466 -2.175 -.0682 -.5388 -,''.044
- 0 3.29 -.0206 -1.244 -3.224 -.0498 -1.038 -3.093
-10 3.32 -.0353 -2.457 -5.179 -.0860 -2.248 -5.046
-14 3.32 -.0562 -3,934 -7.163 -.1278 -3.726 ■ 7.031
Plati "A" 0 3.29 -.110" ♦.1645 -1,353 -.1104 ♦.3765 -1.232
2 3.29 -.0595 •.4350 -1.093 -.0467 ♦.6470 -.9727
4 3.29 -.1050 •.8364 -.9835 -,0801 +1.047 -.8634
6 3.29 -.0595 +1.369 -.9522 -.0281 ♦1.584 -.8321
10 3,32 -,12-15 •^,788 -.5257 -.0716 •3.002 -.4033
12 3.32 -.1201 •3.438 •,1047 -.0560 •3.652 +.2270
H 3.2« -.1052 •3.859 ♦.5528 -.0298 •4.063 '.6697
J
'.ABLE IV
COHTINUEO
Measurtd Correcttd
p0 Sp«ed,V, fps
X-Forc» Y-Forct N-Momant X-Foret Y-Forco K-Uanient lbs. lbs. Ib.ft. lbs. lb». lb.ft.
- 2 3.29 -.0649 -.1894 -2,099 - .0757 ♦.0227 -1.979 - 4 3.36 -.D84B -.6565 -2.949 -.1107 -.4362 -2.624
• 0 3.29 -.0595 -1.114 -3.452 -.0898 -.9013 -3.331 - 8 3,29 -.0454 -1.639 -4.177 -.0876 -1.426 -4.056 - 9 3.29 -.0747 -1.937 -4.642 -.1212 -1.726 -4.522 -10 3.29 -.0649 -2.251 -5.280 -.1158 -2.041 -5.160 -10 3.34 -.0747 -;'.252 -5.765 -.1271 -2.036 -5.641 -10 3.32 -.0937 -2.413 -5.620 -.1455 -2.200 -5.496 -12 3.15 -.0500 -2.920 -5.800 -.1080 -2.726 -5.669 -14 3.32 -.0595 -1.133 -6.645 -.1212 -3.920 -6.524 -.14 3.32 -.0551 -4.133 -6.667 -. 1278 -3.920 -6.546
0 3.29 -.0898 ♦.0249 -1.169 -.086« ♦.2337 -1,041 2 3.23 -.0855 -■.2968 -.6988 -.0751 •.4861 -.5757
3.29 -.0400 *.6708 -.6384 -.0151 ♦.6797 -.5118 4 3.32 -.0595 -.6832 -.6061 -.0342 ♦.6959 -.4761 0 3.32 -.0595 •■1.102 -.4507 -.0287 ♦1.315 -.3207
10 3.29 -.0896 •2.164 ♦.4691 -.0357 •2.372 •.6157 10 3.32 -.1003 •2.226 ♦.3802 -.0474 ♦2.438 ♦.5091 14 3.32 -.1047 •3.758 •1.741 -.0276 •3.967 •1.670
- 2 3.32 -.0353 -.2942 -1.796 -.0309 -.0815 -1.730 • 4 3.32 -.3694 -.8375 -2.645 -.0948 -.6246 -2.515 - 0 3.32 -.0595 -1.311 -3.449 -.0904 -1.099 -3.318 -10 3.32 -.0694 -2.535 -5.455 -.1212 -2.323 -5.326 ■14 3.29 -.0703 -4.058 -7.099 -.1407 -3.652 -7.772
0 3.32 -.0804 -.0165 -.9312 -.0804 ♦.1962 -.8001 2 3.32 -.0452 ♦.2215 -.6301 -.0353 ♦.4342 -.3969 4 3.29 -.0400 ♦.5259 -.3603 -.0151 ♦.7347 -.2315 fi 3.32 -.0253 ♦1.014 -.1906 •.0055 •1.225 -.0595
10 3.32 -.0452 ♦2.226 ♦.7646 ♦.0066 ♦2.437 ♦.8959 14 3.32 -.0551 ♦3.626 •2,204 •.0220 •3.835 •2.334
- 2 3.29 -.0400 -.3192 -1.612 -.0496 -.1104 -1.463 - 4 3.26 -.0404 -.7698 -2.392 -.0648 -.5847 -2.265 - 6 3.29 -.0303 -1.336 -3.246 -.0595 -1.129 -3.117 -10 3.29 -.0454 -2.424 -5.334 -.0952 -2.217 -5.206 -10 3.32 -.0595 -2.562 -5.444 -.1102 -2.345 -5.313 -14 3.29 -.0303 -5.BCJ -Ö.ÖOS -,0995 -3.787 -6.537 -14 3.26 -.0446 -3.976 -7.in -.1137 -3.774 -6.986
0 3.29 -.0151 -.2867 -1.645 -.0151 -.0768 -1.507 0 3.3Ü -.0195 -.2951 -1.714 -.01S6 -.0646 -1.577
3.30 -.0903 •.0488 -1.172 -.0694 ♦.2593 -1.034 4 3.30 -.0998 -.3895 -.3396 -.0749 •.6000 -.2016
1-71* -25-
TABLE IV
CONTINUED
Heasurad Corractad Spaad.V, X-Forc» Y-Forc» N-ltoment X-Forc» Y-Forca N-M>Mnt
fp« lbs. lbs. lb.ft. lbs. lbs. Ib.ft.
3.3Ü -.0445 ♦.6705 *.4666 -.0130 «.8799 +.6033 3.21 -.0453 •1.319 *1.272 -.0062 ♦1.538 ♦1.403 3.18 -.0641 •■1.837 «1.912 -.0160 «2.029 ♦2.038 3.23 -.0604 ♦3.1B5 ♦3.71C - .0125 ♦3.384 ♦3.848 3.1C -.0250 -.7157 -2.49^ .0390 -.5215 -2.365 3,24 -.0347 -.7035 -2.56^ ■ .0?4ü -.4996 -2.429 3.23 -.0094 -1.161 -3.591 -.0333 -.9588 -3.459 3.33 -.0599 -1.874 -4.S46 -.0909 -1.660 -4.70/ 3.26 -.0553 -3.056 -7.452 -.1052 -2.852 -7.316 3.27 -.0203 -4.376 -9.940 -.0699 -4.172 -9.805
H-7llO -26-
TABUUTION OF MEASURED AND CORRECTED RESULTS FOR LONGITUDINAL, LATERAL FORCES
AND YAWING MOMENTS
Straight Course r' ■ 0
Measured ', X-Force Y-Forc» N-Mamen
lbs. lbs. lb.ft.
Corrected X-Force Y-Force N-Moman
Iba. lbs. Ib.ft.
3.24 -.366 0 -.0567 -.273 0 -.1145 3.22 -.406 • .122 ♦.395 -.327 •.122 ♦.338 3.24 -.663 •.284 •1.071 -.597 ♦.284 •1.013 3.19 -.454 •.337 •1.122 -.371 ♦.337 •i.0Ö6 3.23 -.636 + .441 •l,i8C -.547 •.441 + 1.532 3.25 -.578 •.572 ♦2.247 -.577 *.572 •2.189 3.20 -.561 •.755 ♦3.091 -.463 *.755 ♦3 .035 3.1Ö -.474 ♦.659 ♦3.006 -.378 •.659 '2.951 3.26 -.637 •1.126 ♦3.667 -.530 •1.126 '3.829 3.26 -.589 •1.380 •4.669 -.481 ♦1.360 ♦4.613 3.21 -.425 ♦1.444 4.911 -.312 •1.4-14 + 4.752 3.16 -.499 '1.466 •4.683 -.344 •1.466 •4.629 3.24 -.568 -.102 -.536 -.519 -.102 -.593 3.23 -.595 -.267 -1.107 -.532 -.267 -1.163 3.24 -.567 -.389 -1.659 -.508 -.389 -1.717 3.25 -.625 -.943 -3.180 -.577 -.943 -3.238 3.26 -.656 -1.604 -5.098 -.621 -1.604 -5.144 3.17 0 -1.658 -4.995 0 -1.656 -5.050
3.22 -.655 0 -.114 -.562 0 + .172 3,20 -.561 •.224 ♦.270 -.504 •.224 *.ai4 3.21 -.530 ♦.459 ♦.709 -.446 ••459 •.653 3.20 -.602 ♦.663 ♦.908 -.514 ♦.663 + .852 3.30 -.709 • .741 '1.036 -.615 + .741 + .976 3.20 -.663 •1.377 ♦1.510 -.585 +1.377 ♦1.464 3.31 -.662 ♦1.617 •1.782 -.576 •1.617 +1.722 3.19 -.683 ♦2.346 ♦2.305 -.575 •2.346 +2.2*9 3.19 -.683 •2.448 '2.407 -.575 +2.448 +2.351 3.35 -.516 -.224 -.516 -.442 -.224 -.577 3.20 -.632 -.571 -1.040 -.575 -.571 -1.097 3.20 -.643 -1.377 -1.907 -.596 -1.377 -1.964 3.35 -.617 -1.659 -2.051 -.571 -1.659 -2.113 3.35 -.527 -2.959 -3.072 -.■18:: -2.959 -3.133
3.37 -.536 -.0226 ♦ .091 -.456 -.0228 + .02B5 3.38 -.559 •.182 ♦.570 •.472 + .182 •.507 3.41 -.580 ♦.499 •!,056 -.486 + .499 + .992 3.30 -.545 •.610 '1.428 -.451 ♦ .610 ♦1.368 3.31 -.550 ♦1.140 •2.230 -.454 U.I40 +2.175 3.26 -.647 •2.332 '3.805 -.534 +2.332 +3.747 3.30 -.719 -.251 -4.579 -.647 -.251 •3.979 3.26 -.625 -.466 -.996 -.561 -.466 -1.055
mk
TABLE V
CONTINUED
Measurad CorroctBd Sp««d,V, X-Forco Y-Forc« N-fcbuant X-Forc« f-Force
fpB lbs. lbs. Ib.ft. lbs. lbs. Ib.ft.
3,30 -.447 -1.363 -2.572 -.397 -1.^63 -2.632 3.28 -.659 -2,473 -3.877 -.621 -2.473 -3.915
3.35 -.381 O -.056 -.303 0 -.1:8 3.36 -.493 *.202 • .594 -.406 ♦ .202 • .532 3.34 -.526 '.459 •1.019 -.436 •.459 • .958 3.29 -.464 ♦.421 •.994 -.377 ♦.421 ♦ .934 3.35 -.594 *.560 ♦1.568 -.4 97 • .560 *'.506 3.3« -.563 ♦1.222 ♦2.892 -.475 *l.2?2 •2.831 3.36 -.628 •2.242 •4.361 -.sor ♦2.242 +4.2P9 3.36 -.617 -.202 -.594 -.543 -.202 -.656 3.34 -.571 -.336 -1.098 -.503 -.336 -1.159 3.28 -.535 -.524 -1.562 -.475 -.524 -1.621 3.26 -.541 -1.113 -2.756 -.492 -1.113 -2.814 3.27 -.599 -2.236 -4,408 -.562 -2.236 -4.467
3.24 -.503 -.096 -.171 -.428 -.096 -.230 3.28 -.572 ♦ .400 •.853 -.490 ♦ .400 + .794 3.26 -.604 ♦.784 •1.940 -.518 •.784 •1.862 3.28 -.518 ♦1.145 •3,208 -.426 •1.145 •3.348 3.32 -.594 ♦2.167 ♦5.500 -.488 •2.167 +5.440 3.30 -.578 ♦3.074 •8.360 -.462 ♦3.074 +8.300 3.30 -.643 -.319 -1.112 -.571 -.349 -1.172 3.30 -.600 -.850 -2.278 -.533 -.650 -2,338 3.28 -.464 -1.274 -3.456 -.404 -1.274 -3.515 3.2B -.583 -2.268 -5.962 -.534 -2.268 -6.021 3.28 -,670 -3.283 -8.651 -.632 -3.283 -8,710
3.30 -.2834 -.0327 0 -.2071 -.0327 -.0600 3.30 -.1744 ♦.2616 ♦.4251 -.0916 ♦.2616 +.3652 3,28 -.3024 ♦.7452 •.9828 -.2149 ♦.7452 +.9234 3.30 -.3161 •1.199 ♦1.700 -.2224 •1.199 +1.640 3.22 0 ♦1.842 ♦2.484 0 •1.842 +2.427 3.24 -.3045 ♦2.436 •3.308 -.2037 +2.436 +3.250 3.24 -.2100 •2.226 ♦3.297 -.1092 •2,226 +3.239 3.16 0 •2.540 •4.350 Ü •2.540 +4.295 3.2'! 0 •3.108 •5.355 0 •3.108 +5.297 3.17 0 ♦3.454 +5.353 0 •3.454 •5.297 3.28 -.2365 ♦3.859 •5.354 -.1226 •3.859 +5.294 3.26 -,2014 -.2968 -.3922 -.1314 -.2968 -,4505 3.30 -.?39B -.6976 -.9919 -.1733 -.6976 -1.052 3,34 -.4256 -1.266 -1.613 -.3629 -1.266 -1.674 3.30 -.3161 -2.376 -3.183 -.2660 -2.376 -3.243 3.26 -.3010 -4,214 -6.773 -.2634 -4.214 -6.832 3.18 0 -3.366 -5.192 0 -3.366 -5.246
-28-
TABLE V
CONTINUED
Measured Correctec
p0 SpMd.V. X-Forc« Y-Force H-Homnt X-Forct Y-Forc« N-Moiwmt
fpa Iba. lbs. lb.ft. lbs. lbs. Ib.ft.
0 3.36 -.2486 0 -.0565 -.1695 0 -.1187
2 3.37 -.2659 *.3311 ♦.2825 -.2000 +.3311 +.2203
4 3.32 -.3333 ♦.8416 ♦,7051 -.2442 +.8416 +.6446
0 3.30 -,3085 •■1.297 +1.221 -.2147 ♦1.297 •1.161
10 3.34 -.4301 »2.576 +2.520 -.3226 •2.576 ♦ 2.156
14 3.32 -.4240 ♦4.345 •4.279 -.3080 +4.345 •4.219
14 3.36 -.3447 ♦4.351 ♦3.978 -.2248 ♦4.351 •3.915
14 3.32 -.3443 ♦4.345 •3.982 -.2277 +4,345 •3.922
- 2 3.32 -.3465 -.3234 -.4499 -.2739 -.3234 -.5104
- 4 3.32 -.3300 -.8745 -.9295 - .2629 -.8745 -.9900
- 6 3.29 -.2899 -1,286 -1.417 -.2289 -1.286 -1.477
• 10 3.24 -.3077 -2.604 -2.814 -.2594 -2.594 -2.872
-14 3.26 -.2968 -4.081 -4.325 -,25^7 -4.081 -4.383
0 3.36 -.1827 0 +.0343 -,1026 0 -.0286
2 3.37 -.1596 ♦.3192 ♦,4560 -.0730 +.3192 +.3933
4 3.37 -.2394 ♦.9006 +.991Ö -.1471 ..9006 + .QC91
6 3.37 -.2166 ♦1.505 +1.562 -.1186 +1.505 +1.499
6 3.21 -.247? ♦■1.164 •1.478 -.1586 •1.164 •1.421
3.26 -.2024 ♦1.619 ♦2.194 -.1054 ♦1.619 +2.155
8 3.26 0 •1.717 ♦2.333 0 •1.717 •2,273
10 3.32 -.1998 •2.486 ♦2.964 -.0932 •2.486 +2.903
12 3.19 0 •2.77^ •3,662 0 ♦2.774 •3.606
14 3.34 -.2464 ♦4.211 ♦«,906 -.1277 ♦4.211 •4.844
- 2 3.30 -.3815 -.2965 -,3728 -.3096 -.2966 -.4327
- 4 3.34 -.2600 -.8512 -.9106 -.2117 -.8512 -.9722
m 0 3,28 -,2376 -1.307 -1.501 -.1771 -1.307 -1,561
-10 3.28 -.3888 -2.614 -3.143 -.3391 -2.614 -3,202
-14 3.25 -.3074 -4,102 -4,908 -.2703 -4.102 -4,966
0 3.30 -.1962 0 0 -.1853 0 -.0600
2 3,30 -.2943 ♦.3161 +.4035 -.2115 +.3161 +.3434
4 3.29 -.2170 •.6138 +.9982 -.1291 +.6138 ♦.9385
0 3.30 -.2616 ♦1.286 ♦ 1,537 -. 1679 •1,266 ♦1.477
8 3.34 -.2352 •1.646 +2.386 -.1333 +1,646 +2.324
8 3.32 -.2775 +2,198 +2,442 -.1765 +2,196 ♦2.381
a 3.34 - .2464 ♦1,646 +2.307 -.1445 •1.646 •2.246
8 3.39 -.2415 •1.829 ♦2.438 -.1369 •1.829 •2.376
10 3.28 -,1935 ♦2.569 ♦3.236 -.0903 ♦2.569 +3.177
10 3.37 -.1938 +2.645 •3.386 -.0844 ♦2.645 •3.323
12 3.29 -.2705 •3.019 ♦4.025 -.1612 '3.019 ♦3.966
14 3.22 -,2331 ♦4.040 ♦5.028 -.1154 +4.040 +4.967
- 2 3.36 -.1921 -.3164 -.4294 -.1175 -.3164 -.4916
- 4 3.36 -.1695 -.7345 -.8814 -.1006 -.7345 -.9436
- 0 3.36 -.2147 -1.254 -i.537 -.1514 -1.254 -1.599
R-Jlfi -29-
TABLE V
CONTINUED
Plat« "D"
MMSurad Conrecttd Speed,V, X-Forc« Y-Forc« N->to»»nt X-Forc» Y-Forc« N-Moment
fp» lbs. lb«. Ib.ft. lb*. lb«. Ib.ft.
3.39 -.1725 -1.725 -2,300 -.1139 -1.725 -2.363 3.3« -.2490 -2.735 -3.345 -.1966 -2.735 -3.407 3.3B -.2396 -4.248 -5.139 -.1999 -4.249 -5.202
3.26 -.2908 ♦0.594 ♦0.842 -.205? + .0594 +.0248 3.31 -.3520 ♦.4620 ♦.0803 -.2694 +.4620 +.7425 3.3i -.3080 *1.056 +1.760 -.2169 ♦1.056 +1.700 3.26 -.2438 +.9010 +1.791 -.1579 +.9010 +1.723 3.32 -.2886 ♦1.687 +2.786 -.1931 ♦1.687 +2.725 3.32 -.2331 ♦2.964 ♦4.595 -.1265 +2.9r ♦4.534 3.32 -.1996 +3.0*5 •5.228 -.0932 ♦3.0/5 *5.167 3.30 -.3052 »4.578 ♦7.783 -.1997 +4.^78 +7.723 3.30 -.2834 ♦4.251 +7.706 -.1679 ♦4.251 ♦7.646 3.30 -.2299 -.3815 -.7630 -.1570 -.3815 -.8230 3.31 -.1700 -.8030 -1.672 -.1099 -.8030 -1.733 3.30 -.2299 -1.373 -2.747 -,1679 -J,373 -2.807 3.2B -.2484 -2.786 -5,054 -.1987 -2.786 -5.114 3.20 -.2226 -4.113 -9.116 -.1944 -4.113 -9.174
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