Ship @!l!:s:F{n e#; 'iD\ ii Folloqrsedasddire s$ StabilityofShips G.$d ft bnoyinryldiig or rlt csrs or bLoy.nc) Bbc G lil Ih ro$r oi orlnuorgm!i! rh! cflter or bnoyoly B s rhc seol nll| rorc tr Nir mov.lo l Posfon B ldtrd or,!i'iy rllldnfl W aod!d YMi.xUI r on ldiig up\nt\ 'busl, B, Nlrcnft \ inryinerlE d sDhlo! ,5rlr lrnzonkldinun!! btr**r rhcft w b) rl)cnghthg LlkrGZ \$L$ , ' , ' eEmdeendJ'dhs[Mmhlhfuho8h' ",!\ Br rir'F\'rrn,JJr, d i,.ir r! rQpo,.i M rEr r, I't plr M rser rtu ndlcds M lod rhccsk of g.aliryGj t'q\' , h roh., f F,roiorG fi r.r i! n!e0 d,r.oGM '0 F r',,'0' 1' 'dGM p}'.rc!.hrvvl" r.,1 i heiehris kmw0.rhe g|liig mommr.ri b! foNd by mdiDtyingrh rishrif! hB Gz by Bighlinm g o m e nEl W G Z= W G M s l , Fig.4l rearE nlFnq d rc'reMc eish, of buoystrcyBM is iidjcdcd hy rhc for- BIM: K? E@ $"." n,,,, ".,d",,!,, Tli! Loieirudil iiulldq Mr of a iin b B l,N movcdronvxil rd B, nlhingrnonqrw.Gz s prodrsdiwlrr w is rh|di\rrkcor ofrhc\hDx Gz (rtE kuh ndr.fui.h.rskGMr i\ sLlLnlcry mushty m '.t: li t ',,'., ,.''.",,."', ', ' d, o.EorM3h,p3 ftrorrfviyGnfteddDnortr nrr'! dsitY.di(djoi c{ rLctqh!rz i'trt rbr x- y andzjc, posirilcb nir boirr 5jds lL!Zn,.poe \n!i Lm,ng lr l: ,t., F i ! J l \ , J ' , u , Eil@@@@ 1) - G I $,rH".d,",,"$",", @ BasicElem€nts of RcgularWrves rie+{ (r) ind FiFj ,l (b) dcpid hlmdni wloi l frcm ,vo ditreEd peBp€rives Fic.l l {r) sio*s rhl wlvc prcrik (wirh qav rnprin'de, a, 8id vM reu$ r ) ,s a iuncrion ordisrai Fis.l-l (b) shNs rinc ruryd or rhcu\r 0mfik (virh *rv ampli, tude,a ind Mve ffqlem, c) dbltflar r oncrocatron r A $rvcshichcnDotnrisrh€ sen.nd towsrsu {.poi ndcturgh om rhc $ill wdi lcd ro rhc fe$j o ro rh€ hl'gh) r H I Wryc hoichr(F]=2ajvEe anplrtodc) i wavercnerhlhor;odaldisrncebeNeninyr*osuNc$i[wlcrcnt Tw: trhve p.nod (rhesm dkr$.c ^ {avd.ngrh rroig rhe!'ne dis) G.c rig.{{-b) e vdociry (r /rw; vclociry d vhich rhewve prcflc Uiddgo* , n|lcb ]60ie3Ee yd ol phAe hsg.) k : w!*rumbu(k=rrl,\ Gid.h)) o crrtu|fi \qvc rEqulncy (o=? z/T! (nd./s)) d vave !c!pns! (d =H/,I, nho o q$cbcrkatlhenppslimilof H/,\=!|0 ) For pias velociq, cv, ir is in1libnad rheuverom movs *irh rhis ph,{ ycl€iq, rihe wvdom 'novB ii rbc posniv x diEdronj rhe*st p6ilc (rhc shrp ol rheldd (=a.cos(kr-@t) suftr) an qavs (roucr d(rwin gru!tuy {!Er) s mpk waw wtoctty(c,) a, = *51-1 ftn^l ellaneousitemsrehtcd to wav€e d!ron!of ,h ur F(tdr.,R(Eff F " p wrocily- 6- 5-4 "t.t\, -3 cs=+cw -2 E@ snp "-d,,"c,"$.- 2)sillifi cadwaveheigh(rlLt) sigtrinsd *Nc bcidl js dc[neds thc aEnge h.ighrof rhehishe$oE rhid (Lj) ofsll*avc5rc ualy esiDardi Mve h.ighr signilis wlE rreisir ish.dtrageren|ns$ndrniouchro$ r) N3tud nniigei'.hiis pcidls sd o@ud{wE pqiod I Fig,4-6 sar-u,-.h-!h e|n'gs,Thesfucisrcqchly6tr o88 VGM T P= [ Eicound wd tsdodtrE).As shownh Fis.{-7.a shrpmakingvs (m's) i ho{vlEsof rruep€ood,Tv(=0 3rtr).b'ah.,r,ridph6s{loclry.c\(= I 25fi) ship sp*d pc,pcidicurf rooc waE l Lodis cxpnscd by rhcfdlrowing.qudton: + f rtfnin8 b rh! rprib rcrirtomtlp Fig,,l-7 r-.,-,,.F r r,, it rt! l2 ,i,,t E@ sh,pH-d'r"s,"$.* Itangerous Encounter withHighWaveGroup cB=rD cw (sE Fslllt croupvdejty n nqny.qual ro ri! $*d 6hp.n!nt ol a shiph rhevind dierioi, dai3.6us d.ouitr *id hich *r sou! @q 'hi b i pl6on6d wh.Eby'i.shiphrdct.Jby,sn.Bsioo|hjgh u6 As m4riomd aboE,d' mainum !m hei$r -,*k7; $Enl dagemN phenmem,kigr'bing Ih dsk or Fi3,4-eshowsrh?d?finitionolcncounr.rrnsk Fis.4-c Dcinioid(rENbr4r! I hcdrnc@uszoneioi.i.ounbins r hisnvavegroup;ir x s.li d'cfrs!(, &n E io ot shiplped v (knob)rouvr psiod TG), vn, is sho*n as r $ffiim orhish*,B core ft.y win bins rh shiprob.M, *hi.h pob rdnw.d sbbiliry fddopingd'.&ig.ix-m' b'trshipsp dffn(6bi|ily Fig/-r0 Di4mfud€d4!q34ftd $,pH,.r,.a," $ ", @ Redudion or shbil'ty tnds ro be norc i'h i la'! flar (oib in (bnkds ad nshi,g { shfs rsdt md k$ siFincad i tuu-hun ships andburk canieB) laBqvave|olih.i'.hry(*i€hei rpsiziig docrd rdtrccd lrbiliry ship{sd shouldbc e\lu(d or cou6e red.o' bofi, in ordq ro pcnoJ.whm cr{urii! d aboveprcduE' dE shoutdbe s bsn ca rhd fuy !l&e rhed(k u.d( urr or 6u$ sF Synchronous RouingMotion h.n rrE n,tunr muiig pedod(rr) dincidd vnh de en$!n d lwc Fnod (TL)(riF1{) o a o \lft4 fufunrc|3'.dd.bd.nd€hlorudby$aid*a€' tu iimb or$ip! 'onmituid wirhrrrswaEcd (orrqh) n.krm*ne 4hreno6 Enheil{cddngdan!.b6 h.aryreriis.) tl! : "," , _._:i":r,:- ns toigs(i( rhc$LPbcom( cndei ) sdiis rd sFchroios ro mtr b obrriid ustngrhe co.,= r-TR 125rT l-TR 1.251[ HowloavoldsynchronoG rolllng ch.ns F€d{vF)O- O ch.ns.odE (') o - o (Fts sftdE mm *Mi drqr4 dm.) ,"",,-",,.,.,Lffi." \%, r a -r sh,pH*d,,,gr,,$,,., @ rEr\sc nabirity isrhcpmdd ohhcsiipt leishr(w) ind rishrins kE (cz) (cz-cM {ii )i i.e igL,lc.dclkcledc4eiicludfad s pir.h.d ftd doryn.cM lncEds duerorh inreae m eFer nr on theorherhind M deu*s dE b a dccN i effediv wder phne widrtl ilhelbendmc'bcsnclishlingmom I v.9|phHbdMd'3ighhdnqnrrEd ptriod(rE)n rppmr = ptriodof'hc ship(rr) (i rr t/2 rR) rhe aren for 'hisN .' ' ,, " ,,.' """., "' *" ";, " : E ,! l a'd" Fig,4l6 P.,1 , o L O b O ) b r r n dt r t r , ,]lc nd ofrol (o) ad rien incrcrs4(o b o) b siverhefrm slr dh nomotum * throushuprish (6), sd mi sussive ouNd gEdfflfunddFoiousone'Thntype uve pe od b(oncs lhon rn lo oNitr8 md quding sb, rhis can o(u panicdrly *hci i'iil ndrenhc heigr h sm,ll sd 'h ilruEl rcll penod k v.iy ldng (L' , r shlpvirh rn qrnsive b.w t tre ard r lotrgifld !.n i su$prihle ro panmeri rclliis lltrighlonbim|ionofw*.h.igh''Mrep.nod.miun|o||ingpenodmdshipsF.d udq wav Fddd (rE) ship sp.ed shoutdbe tuinbined iRbbi|ity'trd3f'\ou'dbrLrf'' e iear headss whei ofuin{ shlpsad Pccs vm $bjcr b sp4d Edudioi arordi0lty ior oily in ro[Niis sd qDdelrs sA @r a{, rc E@ *'r""anur"'t"- Sud-ridiDgmd Bmaching.to rllietr a shiph snured on rhe dirioN, me orbir,l v.lociry ot fiC.4J7 r!\ 'adai q di"e ri !trch I siturion (i.e shiphEnins dM.srdF), No is sisGd b m.on,o ,n Jd!0n.,ts Flg.4l8 tu !,oo h-hru , ",;,,",;" ' - hNn as brcachiigrd $d rheship n chrngeof hcadin! nbchmd*idl,snxr|mg|e.9y]0.r0d!!.bl|]erorc 'rdnd]snNlyovenikeiby'nc{av o| irl.ndi4 is oNideicd b be L'31, {hde L is ship L.ngrh.lr shouldbs norcd ) d , r cR : m n r r c m ( t r t s r i r h c o w l sped *hm I rars sulgefay ortr rhis * shiPeiss{fr) 9.81|ngh|gh.psd!|* ri{,.1.t9 v shF$sdfimD r: wsFdod (ec) Fi8 !t_20 S l r i p\ l o t i o Di n H c r d r n d B o $ S ( r t -l < shipLensrh wavelenqlh Fi!.1.:\ > shipLengrh wrverensrh = shipLength wruerensrh I r.l :5 E@sb+Hmd.!h$$N * shipplnsor warn cstro(n b.€u* rrre'ch Fig,4-26 Frd-r q,d(r&.sr,r$d., -" Propell.rRlcing iDd ReductionofShip Spe€d i.ausinsn b ra( Thisgrcdrid rbru ld loadrtsul\ in a suddennsese in propdlerreoturions,g.i.mins irros vihnrion Knosr B bB, n d.Jn shoutdh .l dtoz o2lw/4 "l ItD 101lTWo) Fig'l-27 a Fis.l1r rh! ou qrsim ir lLbjlar b qc$N E@ s h , pr ' * d h s h $ ^ ^ ShippingWaterForwdd The npacr rorc of $ipping N{cr has No etrebr dird dynamic pEstrE cEded by rh shirFd B shippins *rei Asdncd m ao adut shir ot (.oftspoidir3 ro B€.ufon $at r) Th! c! sidsshipspeeds.w$cmsubmglsmd nlioso|Mrleng'nbshipl.nglh' ilcEasswhenshielcne'rlkdru|bN[t srnppiig *fur Fig.,i.:0 fr$.i., deErsd i s.h wiln ib ovn anplltude,tensrhor rftqu.ncyfd dirce Th iitbdion olrhe$ ompon.nc on lc.d b itresuhnq Nedles ro sn il k impoilnr ro inw tl rig.4-30 by rcdlcitrs ;! o : "",Lt= F',;'; Fis l.ll n!qu.rrofdnl,pingtrj.([lhu$jn tr.hip'$j)6 n.uG!F$abirrl Trbk4 I r".,-,, i,r ir rir* crri.rr rLr.sr.tu\Pondhs ro rhc B{ufon sdd 1ra$ hcishr) irc sho{r :"""" ," ti I2 @i,,,,",.,,,,,,\, rr !r' b qn r trL( i! bi Li'Dcsrs g i, Trhhr r rr n ns\!Drr udN,ion Slamning 60flom 3rammrns o!q$ $hLD.duL !,e rins wavelmp.cl -6-fis.l:1,{ @ $,p h,,d,,,sr"$., Apprcpnre r€dndLonot spcd i5 trTcdilc ii d Figrl-39 ae ; $ilc l0(asagcryalchcishremdcft)liLl$l: 11 Fi3"l_40 r o rn o d i a u \ i s ' h n " r l + n [...]...cnonoflnrafl Slrhilir! cau\ed bl Ridingon$,,eCr6r al Midship -r ir Loj'g*('idr rd ^ srrnr r a nd( orrcdrcd ni : $,pH,.r, .a, " $ ", @ Redudion or shbil'ty tnds ro be norc i'h i la'! flar (oib in (bnkds ad nshi,g { shfs rsdt md k$ siFincad i tuu-hun ships andburk canieB) laBqvave|olih.i'.hry(*i€hei rpsiziig docrd rdtrccd lrbiliry ship{ sd shouldbc e\lu(d or cou6e red.o' bofi, in ordq ro pcnoJ.whm cr{urii! d aboveprcduE'... qrnsive b.w t tre ard r lotrgifld !.n i su$prihle ro panmeri rclliis lltrighlonbim|ionofw*.h.igh''Mrep.nod.miun|o||ingpenodmdshipsF.d udq wav Fddd (rE) ship sp.ed shoutdbe tuinbined iRbbi|ity'trd3f'\ou'dbrLrf'' e iear headss whei ofuin{ shlpsad Pccs vm $bjcr b sp4d Edudioi arordi0lty ior oily in ro[Niis sd qDdelrs sA @r a{ , rc E@ *'r""anur"'t"- Sud-ridiDgmd Bmaching .to rllietr a shiph snured on rhe... loadrtsul\ in a suddennsese in propdlerreoturions,g.i.mins irros vihnrion Knosr B bB, n d.Jn shoutdh .l dtoz o2lw /4 "l ItD 101lTWo) Fig'l-27 a Fis.l1r rh! ou qrsim ir lLbjlar b qc$N E@ s h , pr ' * d h s h $ ^ ^ ShippingWaterForwdd The npacr rorc of $ipping N{cr has No etrebr dird dynamic pEstrE cEded by rh shirFd B shippins *rei Asdncd m ao adut shir ot (.oftspoidir3 ro B€.ufon $at r) Th! c! sidsshipspeeds.w$cmsubmglsmd... orbir,l v.lociry ot fiC.4J7 r!\ 'adai q di"e ri !trch I siturion (i.e shiphEnins dM.srdF), No is sisGd b m.on,o ,n Jd!0n.,ts Flg.4l8 tu !,oo h-hru , ",;,,",;" ' - hNn as brcachiigrd $d rheship n chrngeof hcadin! nbchmd*idl,snxr|mg|e.9y]0.r0d!!.bl|]erorc 'rdnd]snNlyovenikeiby'nc{av o| irl.ndi4 is oNideicd b be L'31, {hde L is ship L.ngrh.lr shouldbs norcd ) d , r cR : m 4 n r r c m ( t 4 r t s r i r h c... rars sulgefay ortr rhis * 6 shiPeiss{fr) 9.81|ngh|gh.psd!|* ri{,.1.t9 v shF$sdfimD r: wsFdod (ec) Fi8 !t_20 S l r i p\ l o t i o Di n H c r d r n d B o $ S ( r t -l < shipLensrh wavelenqlh Fi!.1.:\ > shipLengrh wrverensrh = shipLength wruerensrh I r.l :5 E@sb+Hmd.!h$$N 9 * shipplnsor warn cstro(n b.€u* rrre'ch Fig ,4- 26 Frd-r q,d(r&.sr,r$d., -" Propell.rRlcing iDd ReductionofShip Spe€d i.ausinsn b ra(... rLr.sr.tu\Pondhs ro rhc B{ufon sdd 1ra$ hcishr) irc sho{r 3 :"""" ," ti I2 @i,,,,",.,,,,,,\, rr !r' b qn r trL( i! bi Li'Dcsrs g 5 i, Trhhr r rr n ns\!Drr udN,ion Slamning 60flom 3rammrns o!q$ $hLD.duL !,e rins wavelmp.cl -6-fis.l:1,{ @ $,p h,,d,,,sr"$., Apprcpnre r€dndLonot spcd i5 trTcdilc ii d Figrl-39 ae ; $ilc l0(asagcryalchcishremdcft)liLl$l: 11 Fi3"l _40 r o rn o d i a u \ i s ' h n " r l + n ... cr{urii! d aboveprcduE' dE shoutdbe s bsn ca rhd fuy !l&e rhed(k u.d( urr or 6u$ sF Synchronous RouingMotion h.n rrE n,tunr muiig pedod(rr) dincidd vnh de en$!n d lwc Fnod (TL)(riF1{) o a o \lft4 fufunrc|3'.dd.bd.nd€hlorudby$aid *a ' tu iimb or$ip! 'onmituid wirhrrrswaEcd (orrqh) n.krm*ne 4hreno6 Enheil{cddngdan!.b6 h.aryreriis.) tl! : "," , _._:i":r,:- ns toigs(i( rhc$LPbcom( cndei ) sdiis rd sFchroios... ptriod(rE)n rppmr = ptriodof'hc ship( rr) (i rr t/2 rR) rhe aren for 'hisN .' ' ,, " ,,.' """., "' *" ";, " : E ,! l a' d" Fig,4l6 P.,1 , o L O b O ) b r r n dt r t r , ,]lc nd ofrol (o) ad rien incrcrs4(o b o) b siverhefrm slr dh nomotum * throushuprish (6), sd mi sussive ouNd gEdfflfunddFoiousone'Thntype uve pe od b(oncs lhon rn lo oNitr8 md quding sb, rhis can o(u panicdrly *hci i'iil ndrenhc heigr... r-TR 125rT l-TR 1.251[ HowloavoldsynchronoG rolllng ch.ns F€d{vF)O- O ch.ns.odE (') o - o (Fts sftdE mm *Mi drqr4 dm.) ,"",,-",,.,.,Lffi." \%, r a -r sh,pH*d,,,gr,,$,,., @ rEr\sc nabirity isrhcpmdd ohhcsiipt leishr(w) ind rishrins kE (cz) (cz-cM {ii 3 )i i.e igL,lc.dclkcledc4eiicludfad s pir.h.d ftd doryn.cM lncEds duerorh inreae m eFer nr on theorherhind M deu*s dE b a dccN i effediv wder phne widrtl... sidsshipspeeds.w$cmsubmglsmd nlioso|Mrleng'nbshipl.nglh' ilcEasswhenshielcne'rlkdru|bN[t srnppiig *fur Fig.,i.:0 fr$.i., nay 6 deErsd i s.h wiln ib ovn anplltude,tensrhor rftqu.ncyfd dirce Th iitbdion olrhe$ ompon.nc on lc.d b itresuhnq Nedles ro sn il k impoilnr ro inw tl rig .4- 30 by rcdlcitrs ;! o : "",Lt= F',;'; Fis l.ll n!qu.rrofdnl,pingtrj.([lhu$jn tr.hip'$j)6 n.uG!F$abirrl Trbk4 I r".,-,, i,r ir rir* crri.rr