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Page 1: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty
Page 2: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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UlUSJI •sQVIDi' PltOiiiCl'XLB ftP& c

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,.~ JWpoft ...... ......_ 'Nimd. wna • a J" dtaMII"Mr ....._ ol tM -a.-.• _. Bl'l.Ub fJ'pe --c• PI'03tiO*t1-. ,_.. ... _,. ........... t'O, .... pwpoH qt ..... ld ....... pWtom ... ~ .. lniu ot tbtl ,....,.-u ... 1N11 u .....s.w.u• dfieta wlUl ~ _._. ........... ~- •de -· .... ·- _. j4da., Nfi"'M" ~ .. Jt)>l~lo JAiii.Nl"Y oo•aa~ .- 1lbt a--. ot or.tuaM.

App .... ,. cs.w. ..... rlsY\l• ~ ,.... wn.~ .......... ~· __., .. 1111.1 u a ~J"ie.t UM•aaaU. ot ._ nqdai• ~iliAiiit ~· lltabU1~ ta a pro~t.-u•~ APP•tta "8• pwa • 4 .... 117'1• ~ ...... llu MID-...... the ttc~w c .... •. Tlata u -.ra.l iD UMftdadr"AI tJw rel•"-• ,_,...,., ... •~' ~ ~~-ia ..... l ..

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n..- 1, •· _. a .._. ....,1• or tbl _..1 et the P"­jeot.Ue with ._. •1&bb ._.. •u U-bl7• !'be •• Bftl d.S .... i.olall ot .__ .O.l ant

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Page 3: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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PMH&npha ot llo4el Bri~iah 'JP• •en Projeatile

Page 4: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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~·--- ,...e -..to Oil the ao••1 1n the 'alp Sp..ct at.r Twan•l ~ 4etefti1De ~ ctnc, oro•• .tone, Ul4 •••11 .tor -..luea of ,aw angle~~ ti'Oil- 10• 'to ..a.o•. 1'rclli 'th ... ••el'ftll 4ata -.n •lCNl&'\M 'fibe ~ U&l CWOU .tHM Mtftl.oleaisl aM tha ~ ooetts..t...-t iabout. t.he ..-.. ot pa'Yl•· For. -. •••n ...t­tiel.tillt 1lb.e on\er 01 ~YlV la ail' -.. ue4. ovw u.it, ncar. •, ahew ~ ... 1-..a ot the ooetti.oi•u azul ~P eoOIIIIiltriel~ "f8..'J'!Dc w1~ 'the ,.. aucle·

!be ~erlatlo OMI't, ~ 6 1 pw~ tb relati«W be-..a U.s ooett1oier:R; -11 o .. tt1o1eat 41~ by tM ,_ uel•• aD4 CP eoo.triol~. ,..._, th1a oh.it.i"t it t• ... that tbe projeotU.• hu & 1cw Aras eoettte1e:t (aot ~ 0.11 at 10• J&W) aa4 tbail the QP U•• a. little owr 1~ ot tM ln~ aft. o.t tho ca. tt 1a &leo ••• ~ 4:• "••rmc ~ iDonuO• at • ooutant rats. witb 1Mrau1ai 1M' U.Cle. 1"Uae oon41tlODI !Dtioato that the projeotUe hae a fair de~•• ot •1:&b1lit7•

X. Ol"d.er to ~Rpolate the 4S.ac;rtka •aaur.-nta Oil tM JDOdel to pi'O~l'Pe aeale, 4rac ooottielenta...,. 4neralno4 with :vel• ool tliu 1a tbt t.D.el fti'J'lng troa 10 to H toft ~r teooacl. TlMt ne\llte are ....... 4ot• - ~ •ben, J't,ave aa, ta. ftteh the 4n.C ooettiuaata .... plotted. aptu" JlO)'BD14• m.ber, I· xa 11bia oalo\lla't;ion R ia aei1Do4 us

.... •VL 7T

Y • V.l?olt7 ot projwttle 1D hot~ noODA

L • tArl&th ot projoot11• til ton v • Jt~t1o 'Y1eooai'b7 ~ wa118J" 1D ''CI ft. per 100

B7 ~ "he ourn, t1tto4 to the ~rmntal polDta, 1sba dfts ooe.l't1oltmta tor hlP.r Re,nol4a ILllli'b•r• u• obtau.d.

•• th• pi'Ototypt proj~il• reao~• ita t•rai.Dal Teloo1v, ita •1&ht 1a •ter 1• equal to tiM clra~ toroo oa th• bocty. B7 ueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty tor 't~ pi'Oto~ ot 16.9 tMt t>W aOOOllCl wi1Jh a oono .. poncU.ng drq oooftiol•t of 0.2M. ,,_ R~lu !Mlber tor the tora1Jal ""looit}t of M1t teet per ... on4 ia to\81, blf t~ -.bow toftl\11&, to h• l·fil a 10 • ID theae oaloulatlaee the weipt of "h• b«**b iD aoa ••r ._. uel

Page 5: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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iild the t.wp•ature of the •• w.ter -.. ua\I!Md iio b • &bout: 70 "-1"*11 Jalarellheit. A.a the e:Rrapolat1oa ia l&o1J ~tl ancl the oba•n• uta cto _, ~·n :tmeh hoJa a iltft1&ht li.u, it l• ~liewd. tbat tu oaloUl&t4Kt ...U.u•• to.r the pro~n• U'e tatrl7 reliable.

CAVI'fATlC. HSTS

4 aeriM of pbftoeftpha-.. -.4• ot tM ... d.el b <the a'Mr Y\d'mel ehcnr11lg a w:lcle l'&ll&e ot M<fit&'bioD •«""•• The•• phfto­gapha a:Nt J'1~• 7 :W li iulqaift &114 haft btlell ur~e4, 'b)' l.Up"tio:a.. a e.ocol'4ano• ..nth the ••sre• ot oantatioD. cun• ,h .. t, ~· ao, ahowa the oaY1tat10A pareaetet, 1, oorreapoll41zl& to eaoh pJaotop-apb 1zl -tM JeJ"iea.

1'he kata were Mete by •tntai.Din& a ooaat .... water 'Yt1loo11Py ot 4.0 ten per eeoo¥ iJI the T\llm•l and ~ the •t•r prtaave b7 ....U blo~ta. A photo£1"&ph •• taken tor •oh ftlue ot 'the preaa\U'e afte.r 00J2141Uau b.._. dable.

It 1• 1n•~1Te to .-.s.a.e the. photocrapha !A relaticm to P11\lft U Diob pwa the nri&tion 1Jl 4rac WS.th 'the eaTitat1on par-ter. !!Mt --t ~ oantatlOA that OU H aeeA appara to be ftq aU.~, al~ 'the ett.O'\a an geat. Fi~ 21 ~• that the dn-5 au4cl•l7 1M,.....•• at • '81l01"110U. nte wl*l I baa dropped. below a nlqe ot 1.a&. 'fld.a potnt oorreapoAdt approxl­ll*tel,- to the ooild1t1on ahOn 1D Pigure 8 Where the oa·ri:ta:t1on eft.ot 1a hardly no,1o .. ble.

'rbe 'rlolc~ iMNue in ~ MUM b7 .... ~ appea,n 1zL \he p.hoto~u ~o be ali&h\ oa"d. te.tton u wll 1llna1:ratea b7 ._.. parii;lC Jl'ipna 10 aud 12 nth F1PI'• 1. l'A 'the eoncU. tton npr.­aente4 by FlpJ"e 10, 'the 4ng bU l>4MD 1Do,re.ued. ~ o'"r tha~ of FiCUH 7, the pobzt ot 1no1pleut oant&tlGD, Ud 1D tM OOD41t10D npreaenW4 by Pipre 12, 'the clrag baa beeD approx5aauly 40Qblecl.

llb&t a.ppeua to be a •11p1: base abcma 'bhe ao4el t.a Plprea T 1:o 10 la aot 4ue to h&la'bion in 1=he plaotopoaph, bu-t ia •u.ae4 by tM tine bubblea of -yapor be~~ aw.y 1'I'Oa tho ea't'itat;ioa &one at the no•••

J)1 PiCUJ"O• 11 rbO 1• ~ •Ttta"oza e1'teot appeara to lJe OOD­tine4 to 'the upper paJ"t ot 'the aod.el. It 1• probable 1ohi.t thia 1• larPl7 cl\le to interf'erenoe a.-t up 'by t~t• aup,.n ahle14, althwp it; M\18t be 'bona 1D 11111cl, the ooDdit1ou tor oan'\atia beiJaC ao oritial, 1:b&t the ali&ht cl.ift~ 1A pre••ur• between the top ancl bottoaa of the model earmot l>e tpored.

It ia ob••rn4 that tlw -.oclel ia oa.pletely ez,:nlopecl ill tM oaT1\at1on bubble 1D P1CU"• 1'1, 18, ancl 1~. thia 'IIOulcl oor.rea­pond to ~ ataw ot :the pi'C)je~tile d.urlOc 1ohe tirat portiou ot 1'\a trajeotOry after •tftnoe.

Page 6: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

A ••ioa ot ten• ,.. MAlo ~ 4.wnd.De :nr1at1oa 1l'l t» 4ft& eoetf'ioient with dU'tor~ "f'al•• of' tho oa'rl.tatioa pu ... t•~• I, 1n all ouoa the -.tol" wlooit,' be1Ds -.s.nu1no4 " .a ren per ' aeooJacl. T~ r .. ulta of' ~oao iioda are liTeJl ill J'i~ 21. 1'bia oune ahDn tb&t 1na1p1.en1i ea'ri.tatle oooura at a nluo of X • 1. 'TO 1ri1ib a clrac ooett1•1et tor~· ao4el of 0.112 IU:Icl e. p.p pre••~ of: '·' polllld.t per lquar• il:f.oh. .At praoti.Ul7 &01'10 pge preaave tho 4r&& ooetf'io1•t a~cl to inorouo rapidl7 with redual!4 'ftluea flt I, ancl With a p.p pr .. auro ot •&.& po-.cta per eq_..• i.Mh aD4 a ftlue ot 1 • o.sa, the cb'ac ooottioioilt 1Mreato4 -to o.~o&. tn~ur thta o0ntit10Jl ~ oantation of'f'qt oxtw.tcled. about 1/2 1DO be.ok troa the :a.oao {1•••• t/4 cli.uaet••) or praot10al.ly aa ab()Wa in 'the pbo\opoapb, nsur• 10.

There ia Ori.Cl•t a utiD1 'toe, though --.11, deoreu• 1IL 4ft& With 4eoreaa1ng wl.uee of It 1!1 the •rly a"h:gee ot oa:rttat1olh .&ppvent1y tbia reaul ta traa a red.uotioa 1B U:1!1 tr1ot1on -.uaecl by th• •..elo~ ot 'ftpOJ' b•iJ:is 1'onae4 around t-he moclol. !hia b a ..,.11 lmOwa ph41Q01Maon that hu been obae~ in the teatillg of p~a and t1U'b1n••.

in .Uoh

P • l.baol\Ro •••t~ proa sure ln lbe per ~~q t1»

Py • Vapor preae\11"8, a~ th• oorFeepondiai water ~\.\IJ'O, ill l~a pezo aq ft

p • ..... dtllai'T of tho t'luid 1U du&• ~r ou tt • I . .

• • ·~1tio •1pt ot 'the t~uU in lbl per ou n ' 2

C • ,looeleratioa of ~'Vi ty' 1n tt per teo

V • v•lo.:i~ ot the pl"'jeotil• 1n til p&r aoo or nlooti;y ot the water, h ~1 wata.

It ia uacl•atoo4 tbat thi a projl otile enter a the -~r at a TOlooit7 ot approzblat•l7 160 f'o.t per eeooncl a~ P an&).• ot •5•. B041ea wtth h.mtapher1oal no••• appov to haft an e.tt.niw cb'at ooetti9S.ont ot abo\3 0 .et at ent!"'UU..o, mel tor tbia ·cttaouaeioa it 1• ua~ that 'thie Talue applies to tlw •sq,ncl• aleo. Aes~ t'Urthw 'that the drac ooett1oict deor•••• linearl7 w1 th iiloreadn&

Page 7: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

Taluea of the oaTS.ta'bion ~or, 11, &Q4 -hat it. r•ohea a tonaS.nal ft.l• tor the pi'ft~ of o • .au When x • 1.26, the nlooi~ rolaislOilPS.p eaa be •lo111&._e4. fhe reaul ta of the•• o&loulatlon• are ah~ 1• Pl~re 22, 'tlb1oh &i"• tho rolatiOD botweq aubaerpue, ftleoi't7, u.cl X up to a ftl.ue of X • l.Te Whioh s.a ~• ~at of meipieat oari1;&tioa. 'the aba4e4 ar• 1D41oat .. the "gion in 11hiob oa-.1\atloa 4ooa aot take pl ....

ID Pipre U lo &lao abo'ldl a otll"ft of on~Wd prajeotUo perfo~o• bu.., em t;he aii&Plit'yiq aa~loa 'hat the ..._, .. tar7 naama at a •a• -~· d'ter entranM. It Will be ... ~~.trill tkia Ourft that P&ther Yiol•'\ 0& n:tatiOJl ia to be- kp4teft4t4 UQ\11 1fhe pl'o'jeot11• baa trawlle4 ·to & ct•pth 'Of 1'1 tnt (X • o.?) aut hU had a N4u0tion 1n ftltol't7 u 86 fen per a-.ona. tt 1a probable that thia -..na the ctiiaDM bubble Will not be ~ away •ttl at'tor thia poizlt ia reuMd, u the ~OJ'1&ati-on troll~ the •n­'tat.1ol'1 Will ·ktep f .. 4.1ng ~ to the YOt4.

J». o&lo..Ua~illg 11ho porto.nanoe ot 'the p,.joot1lo a.tt.r ..,. 'tnnoo., it w.a ua-.4 tha-t :tho p,..a&WfO 1D tM bUbble_. ~ual 1:;0 Wl• ft.por pl'o•AH• t' io probable that tho pr"oaau.re ie •'Uah .,._._r tbu. tbi.a dv.o :tlo t.b4t &1r entraiil84 at --... ••

It 1a 1DwJ'Oat1Dc to ~ the puw~phl 1D thou r•latt.e to the nrfta iD Fipr• 22. !he pbO'boarapla oorr•epomtlllc to ftr1oQ po1irh OD 'llbo do~ ourn ot projeo:tS.l• pwtoma .. O&D

bo 14on,1f1H by ..... ot t.be oa'rl't•iiiou paraaner. It •hl111.4 be r....abottld that tho pho~O&J"'t.PU J'Oproaoni= the •'Jii- aoDd.t;\10111 to b• ~·•4 u 41aouaa.._ in the toropSAc ptU"&Q'&ph•

Page 8: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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British Type ~C " Projecf/le

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Page 9: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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Page 10: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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Page 11: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

riG. 7 A-'= /. 6?8

riG. 8 I("" /.303

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FIG. 10 /(= 0.814

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riG 14 I{== l'lol ckl;mune

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/YOT£: Pholc?9rophs .hove- been orrr:mqed by msp:?c!i0/1 occordlh.J lo 1-?e de-9'ree or covt1afton .

PHOTOG,QAPHS oF CAVITAT/0/Y T£ST.:5

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Page 12: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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CAVITATION PARAMETERS AND PHOTOGRAPH NUMBERS

British rype ''C" Projeclile

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Page 13: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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CIT-1-//"'TL £JRt:-I'IIJ24- -1661!1-45

Page 15: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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Page 16: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

!JIB BIGB SPEBD W.l'tER 'rUJIDL a-t ~h•

C.ALIYOUIA IHS'frtOTE OF 'l'ECBNOLOGY

'fM an&l• Which 'the asi• flf the model Jlak .. with ~· 41reot10D o:t flow. :t.ookiDI 40111l on the liiD~l, ya.w aqlea 1D a ooQbte..-.loobiae 41nn1oa are neptiTe (-) and in a olook• wiae direoticm, poaitin (+)•

!foment. teudiuc to rotate the •4el ill a O<Nilte~oloGkwl•• clireotiea (1111• loo~q aowo. Oil the -~> are nep.tift (-). and thoa• Ru1nc oloObl•• rotat1oa, Pf)ait1w ( +).

Dll aooorianoo With tbia aip. oolmblt10n a ma..n~ baa a de­nab111s1n£ ot~ot Wha it haa tho aeae aip &8 the 'J&W angle •

na all M4ol toaw ~ JaOment ia meuure« about the po1.Dt Of aupport.

)fo11..-ta about the oenter of' ~Tity haw the ayabol, Jl01

DRAG -The tone, 11l poaDd.a, exerted. on the JI&Delel ~allel. with

the dU'eetion of now.

CROSS FORCE

Tho toroe, 1A poadll, exerted on t he m.odel nonial. to ._ direotioa ot tlcnr. A poaitin oroaa :tone ia defined u oM aoting 1D the aaae direotioD aa the diaplao-..nt of the projeotile noae tor a posit1Te ~··

t'lw aua o~ the oo:apcmenta ot the drag and oroe1 toto• aotinc noi'JDt.l to the uil ot the aodol. %he Tal ue ot 'bbo normal oa.­ponent ia ci......n by tho f'ol101li.D.&a

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Page 17: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

OElflD OF PUSS'OD

'l'~ pobrt 1n the il.xl.a et 'the llOUl ai; whioh the 1"••ult&Dt ot &1.1 tore•• ao1;in& oJl '\bit aotel ia applie4. Thla baa ~ a,abctl { CP) •

CBI!BR•OP•PRBSSUBE BOCEJ!RICI!T

r» cti~oo 'be1iweea the center ot p:ro .. ur• (CP) Nl4 tbt ee.ter ot c:ranty (CG) e.:preaeilt aa a 4Ms.al tn.otioa ot \he lenpll {L) ot ~ llOQl. The oen*er-ot-preaaure eooet:rieit7 (•) 1• do:r1,.. •• ~o11 ....

l ·-L • • • Cem~·ot•prea•~• eoo~trio1~

L • Lft&"h ot 110clel 1D teet

L • D1atanoe troa noaa ot p:rojeottlo to 00 tn toot cg Lop • Diataaoe tr• aoao ot projeotilo to OP 1a r.n

· comtclUTJ

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' • Aooolo.ra:tio». ot ga'Yl';y 1Jl ft/a•2

.4p • uea 1a tq ft ot a oroaa ••ot1on at tho oyU.Jl4rioal port1oa ot 'the pl"ojootilo takft aoNal to tho po­.nno &ld.a ot the proj .. tilo

T • .... :relatiw 'Nleoity DftwMil th* •t•r i.nd the projonile 1D ft/ '"

Page 18: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

• ~ la toot•lbl •uwe4 about M7 par1;1o•lar polJ:* on the peaevi.o u.ia ot the pnj•tilo

L • crql'&ll len~ o~ tho pr•jeotile 1D t~

OBlmWo DISCUSS Ial'

!he OUJ"Wa o-f tore• ana ..,._t ooetttot•'• aacl of o~r­fd proaeure tinan" plotto.. u .fulaot1ena of ~· '18-• engle are uo:r.l to• a .U.aoual.a of the a1o&b1li"t)' of projeotil••• SinH thea• iamnel ;teau are md.e lmdor ll'ted7 now ooDdltiou • 1ohe reaulta will oal7 1a41oate the teJMltD07 of tho pnjeotile w rnun M or aoTO &W7 h'oa tho ~l1br1• poa1Uoa afWJ' a 418WI'baaee. A4op~1Jae uroquaie ua.p, a prejen1lo ie aa14 to 'be •na-t1ee.ll1" nul• it it -tend• •• retura to eqG111ln1.• whoa duturbetl. ])a i;ho 41aoud01l of natio ••btli't)r tho actual ~1cm t'ollowi».g tho ponlarliatun ia not ocma14a'ecl a't all. Ia h.n, a projenilo ...., oaoUl&t• about the equ111'brla poa1t1• witl:litut owr J"''lla•iniDC 1:A 11a. Ill thu oa•• the p~ jeotile w\al4 be na't1oa117 atabl• ft'ell 'tuuch ·~oallT' UDeta'blo. For a oc.plete diaouaaloa of tho DIDdo of .oU• te be a:pected hllo.ing a p4'.1"hrbatie, the "47Dui1•" atabU1'ty, uattioaal illton&tloa 1• AO ... •U7.

!he ooB41tlen tor oqu111brl• la ae.tlatiecl it c1, O&lealate4

abevb .. CG 11 equal to aero • Ill paeral 1 tor pl"'j otilea w1 th as1al. I) ·t17 tho ...-t ia sero e.t • • 0 , 10 that tor oqt.ii­l1br1- tlut projeotllo 1a ortonte4 with ita u:la parallel to the 41reo~101l or. ..tlOJa. If "h• projeo'il• 1a roV.'i4 :t...._ \\lie oqu111brl-. poaiti ao aa 15o Ci"f'' 1• a poaitln J&W ancl•, 11; ia DM .. Rl'J' ~tit baTe a nepti-.. .... llt oeett1oieut, aooorii.D& 'to the dp ooa'ftll151oa ~' 1n Order that it 'bo aV.t1Mll7 .-blo. '!'hila, a ~~:epflTO alepe of t.ho ourn, '!.• ••• ' ••n••­poncla 'tO aw:~io nablU.t,r, &D4 a ~a1t1-n elepe oorreapoa4a to tute:oilitT• tbt d.e&J'" o:t nabU1"Y or iilatabiltty is 1D41oato4 :b7 the •pltaclo of the alop•. !be ..... eoaeluaiou an obtained. b7 la:toJ'PI'niDc the .. n.._.r .. ot-pr•••u .. e oUI'TOa. Por a,_.tr1Ml projootiloa, 1t ~ eea'tJer o:t preaaure :talla behtid the oeater ot poant,r, & reatoriac .._.t GJ.ata IUl4 tho projH\1lo ia 1U.'MO&J.l7 ria'ble. If~ CP 11•• .-..cl of the CG, the ---.t la JWa-reatoriD& acl the prejeot1l• ia nat1oall7 'QUt&ble. 'the d.ogM ot •• bllity or iutabUi~ t• 1Dil1•W4 by the 41atiaaoe 'b.wea. tho oa.ter ot pw.Tit)' aDCl oentor o:t pre .. uro.

Page 19: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

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TYPICAL CHARACTERISTIC CHART

The California ln::>ttfufe of Technolojy---High c5peed Water l&nne/.

OR~-/tP2.tf.-/~ 71- L..

Page 20: ,,.-uueiJal 1»h1a rolati.Oilahlp, \he torSala tor the ea, ooett1o1ct IUI4 tba 4ril wn., Fipre 21• the 'MniDal velooity oan be Oaloula'Uct. 'fhil ealaul&tioD p.w a t81'J11Da11Rloo1ty

!JIB BIOII SPUD WATBR ftmnL ·---C.&LlPGlD.A DJ'lmrR (6 ftCJIIIC&.OG1'

APPDDIX 8

til• ati.uW nne a!UJ..t .-- 't;Jl»i-.1 ovw• tor ...._ _. •• 111\ Meftlo1.-ta aa.d, al.M, o.r.dHtr-of'•P"•••• ••..Wlel~ • all ft.J'7lzal with "he 7D Ull•• t'wo ou•• b&w beea •••.-4, 1ZMU.O&M4 1»7 •he .U•or1P'l• (1) aD4 (2). '!~abe •~• an ••1..-& •~'*17 to UluV&w .. thocl ·~ loilttq 1ihe u..n aDd cto net NpN••t M.W. • 'h• pi'Oj..Ule 41•eu•M 1D thl• "POrt.

I.a ol'4.w to o'b'U.la .. ~ ... rti\a&l1u.151• or the pertoru.noe s.•t .. te41J7 .._ ._.... -•toned uow, tlwa •ChiJ'anertnl• CMJ-t", ahOwa a15 '\a• bot-. o'f the lb4Hitt, baa "M• a.-n..... Dl -thi• Obart 'M ctrac ... tttelent,. en, t• nr.t lnt.e4 apiM' ~ OP eooav1•1"7, •· oa 'bbia on oun. •• po'b.'t;a opp .. lw whio U"e ftC'~" a 11141ea111Jl& .. yaYanclo, • • '!hl• C OUJ"ft .... tM 'WU'iatlGD 1n 4ft& aD4 CP Moellt;rloit;r wS:bh iL IID&le • Alao, ~ pe•1111oa ot 1me e\U"'ft at 'the ri&ht or left ot tM ftl"\1oa1 .XU ( + • or - e) SMi•'-• w~r or ut 'the pnjen11• 1a •table or \ID8table, S.. cRher worcl•, whfth.r ~· CP 11•• aft or fe.....-4 of the eaiJer ot ga...S.'tJ'.

Ol 'thie ........ 1• plot"te4 ~ C}lllul1;1t7 ck.A wb1oll &1 ..... an 1DU•tiea ot ~ ~ i:A the ._. .... tt1of011t, c:11, Wl\h ~ 7U1 ucl•• ~· 1• dCIU 1fT 41Y14.bl the c 'bJ tu ~ '1a •..-..• uut pl-"Sa& the" w.lue•, ct./• , -. a Li~l• Halo, :Mr1aedallJ' troa ~. pol.At• r~•••'ilg 'bho pw aq,l•. (hi' eaoh .,... &Dil• ~· sen tor ~ cjt: eoale 1• at the CD o\lr'N) •

The "ChV&otel'ldi.o Cllllrtif 1• 'UeM u it P,u• a tdl'l7 DGF~Plete p1oture ot 'tlhe ftriatin ot tb:r" lllpol'klit • ...._......,. into• of the prej..tlle w1~ eliNlp• 1D yaw angle. I1: i• .... tha't can 1 •• ~ 1••• in•~• 1a ctac 1l.haD ca•• a • .11 .. , 'that tblt CP eeobtr1o1t)- 1a Cue 1 1Dorea••• w1 th the JU1 -.4 1• poifltiw, an4 taer•t••· t.U. to illor ... n&'bllit,... ra U41'b1• to th1•, .- cfi.L 1• 1norw.•blg a an iao!'eu~ raw, s..tloa1;1Dc a pNpertioan iaereue lD re•W.Oilii - -~ ia:aar••lnl ~· ansJ.u. fhle 18 an a4d1U08&1 •tabilisin& taotor.

xa cue 2 'the eppo11te ohal'Uteri•tie• ot cue 1 are iD­CU.oat«t. l!We, thel'• 1• a cr••t•r a.,..... ln cll"ac w1tb ill ...... 1D 7&"' alao, th• OP eooentrio191 :whloh 1• uept1w, iUJ'ou•• 'td:toh the ,...,, thua tea4'-D& to deo1'M.•• •t&b111t7• 'l'he •hUe• la .._,.. oOettiel-' .. ._.. at a 'Cleor••t;f rate, ia41oatiDI a pJ"Oponi.-1. U.reue in re•torin1mcaa'6 th lae:NUille J&'W• !l'hl• 1• a 4edabil111ng tao'bor.