Motions and forces in anchor chain cables for merchant ships

Lëusderi1 3 November 1992

Vcor

lJe

D De!ft

MOTIONS AND FORCES IN ANCHOR CHAIN CABLES

FOR MERcHANT SHIPS by L.Brink Msc. (TU.Dift) Nv1 Arrthiteet Master MN(Ret)

Contents Summary 1 Mathematical model - 2 Computational Procedure 3 Inputdata 4 Results of cIculations

5 Conclusions and reofflmendationi

References 9 12 24 27 35

TIlE ANCIIORLINE CALCULATION MOI)EL . F w = Wind force Wave force F8 = Current force

Fa = Holding Power Anchor WaLer depth

F9

F a

Surnmiry

rIumEer of

'jthors !iave

dc;ait wxI::h the sub jt

The-re foThe-re the

tudy w.s

esti' :L

ted

to the wr k

L t

1. - -s..

arid Foi;:I.d

J Wi isori ;.rid

r;b,.::i.oL j

method

used

by Walton

arid F'ola±eck is

based

on a

d:i s.rete

mass

mo&1 .

This

cans that the - mass of

the abie is

replaced by a series of discrete

masses

concentrated at

a finite number

a-F points along

the cable.

Ti-c nsses

ire

1! i.

ned t.L:'ciLher

by we g

it3 ss st-ri riii

H

strings .-.ari be elastic or non elzstic, Walton

and Fala....

check use

riorr-eiastic strings, Wilson

uses a diFferent

mol-iiO d '.h i. c.h . b d i sm-uI L 1. om I- I-i-: :-ih 1

E.oth cal cu la ti on metho.ds

a;sume ti;jit

the fi'cs .wh :1.

act on the cable are ca'jsed by;

rio-t i. CDT

a:

i:ti:' n:J a -F

the cb. I e

water

r-Face;

'-'-ic

ra'-' of bhe cai:.].e throLic:J

the

water;

added moss a-I

ti--

:- _;

the

weioht of the

b.i_ici-'ani.cy

a-F tne cab I a

The calculation method

chosen for this paper is

mainl

or

this

..,ork

of

Walton and

F':j 1. Thak .snid wHeio

necessary

data from

Wi. J.sori are

used

The choice

was

!:ramptad

by ttie

pass Lb. :1 ii t ...n-its the

matha.::i :L

T..ir-bo 'F'. sca 1 arid

to make the reclu

:L

red cal ciii at Ions

far

i::ieirive ....Lgat:Lon

on

ha

avaiab.1

:.-'-s:::r.a L ..:smp.utar

(11 _o t: o fliC bho' j I ;i

'o'

i 1 Lu I '... I t hc

di sp icenient,

'ye :Loci ty,

.sccel erationi and

force of

sement in which

the cable is

div:L.dcd .

These

data can

U i hO I I. (i .1 i J I 'i ii . 1. i.iIi Ti in ir :i mi_mi V

J. 'J5

1--ia pai.er

w ± .1 1:1. rt dea I. w:i. -i.

this

dais . c:pmerb a f the

ma: a i.-t:Lcoi model ar.::

:onij:'..t.st:Lorai

:',::sdT.jre Uani the

I pi j-I i i ri - i-'-le rnofjaJ i ]

1 I _{_' __} r t

Fi.r.::L:Ly t is .:c:r..:L:..s:L::ns T:r-.: -i a-)rfi---mardat :f. or

1 Mathematical model

rhc. rizt ernst

:Lca I

odel is based

on ths

sh i.:.-

st anchor'

as is

si-own in

f :L<'.re rio , 1.

The any i ronmenita L

forces

qer:er-atsd by w:i.rd,

current and waves

a'c

:i.ri 's.c;ui. :Lbriurn

ti-ia hoi::l:Lr:i power

a-I the anchor

The length of this

cab i.e Is deter-rn i. ned

wi. th the ',..s 3. 3.

known catsnary

1i_r

Th

ui

1

Hr fl1J ILl

I ii - Ii

-.eriieTit,

'.e.l ac:. ti

acce]. crat i. oris

arid far:::e:s

in a. ser :1.

cD-

i.ocat:Lons

:Ln

t!-a .snchDr'

,.*ri:s,i::... ,,I:;.l_i_i

fIp

f

rnc-tNad c',i.ven !:

Walton arid Polacf-iek

3

It is riot the p.'..n-pose

Of this p.per to ci:Lvc

r

in depth

desriptiori

_-

of

the

method₂

For

thai

the

eider

is

u'eerred to the:.

ppi',

E

J Only

hos

p:ts

ihi-i

esseriti1

re ddresscd.

The

authors

in

La _onis:i.dered

the

_problem

_zis

gericri i.s:-jtiori of the alssii problem of

the ma ions

of vihrtire

strire.s zred w.rited

to dedj.e ivr

;ipp,roxi--moti. on

of ti-ic

b 1 e w :1 th':Dut beaom i. r :1. nva ived

in

the expl.:Lit

_{omuttiori of eist:i fcres}

whi'h

ct or

the ':blo

rILo

thoj

ri 1o'l ma o

rir1

o mL.1 I

of

the problem .

For th.:it pl..,i'i:.ce they set the fo 1 J. ow :1.

des:LeJrL ri Lcr i for the :1. r model

1 onçj i. tud. rIO 1 ,i _{j ]} ; ::

t'r'.:::i

cb loris of

the

line must b.c t.keri into crisider.t:ior

tIi

oc.in-'r'erae

o f I zir.:le? :i:L .;p ]. .:iiie.ribs frorii

tIe

eou:i 1 :i.bi':L'jm

aorf:Li..rot:Loni

of

the

.:ob.1c must: be

permitted;

tlie extrem :L t :. os a

ti-c

J. c

be ot

.d :

1 erert

lc'ic.:Ls

Lit-

H- _{.:obl na b,ct,1e:.:::ni ttc p.os :iticris}

a f 1'.:Ip:.c)rt . Th re<:1'_i :L resthot

tie rixs we :i. Tht

c: f

the

1 :Lnic mi.ist

be token

::.ritc:

o,:.o'rit

Thus, ever

when tluc aobJ.e

is

in

stoti.

c.qijilib-i.um,

the

tens ion

:1]. ].

rot

be 'Jne :i. iDrmror w i 1 1 t1e _{aol: 1 e. be}

stroaht;

si. r..e tho ...:

:i. s si..thmuaed

be

tot:. a

Ec:irae mi_ist

ruai.ujcie t:1e l:'.JL..; a :ie med :L urn .dynom :L..::

rupjst o]. I ow far

the

u rtu;;:i I ± T-i(:?rti .0 fl f

mcdii.jm Furthcrmori:.z, .;.l._

i

_rie.:essor

_{to m.ni ke pray}

si ons for

dornç: :. na

fra

dii::.

to the

f:ia or

ti

I :i re wherever ...orisve.rsc motion

is c:a..i rr :1 na

Fino]. ly

:L t .::l :i. red

to

suspend

aoncn.ote.d

loods

.ot once or

rnor'c paints

olania the

ao!:].'

oricJc the di omete' ;rnd

:1. reel doris :i a the aeb 3.

ot: sp.cea i f i ed paL ribs

c nu

I d:'ed th.Tj...t1e besL .0I::.j::.'cu.:

to t:-

. :i...1:1. or

j'i)l'iii

'L!ll

i n:?

"'i.I i

.i1i

11._I I

II'

.1

( ru I 3 Ich.

ijL

I Ciii I Ti Ii. I .?u 'Tu I

op,p,io< iot :L :L 11?Ort tIioi:: bIuCe i..I0e :) f ::I :i. F

:1. ri b,oti ti. me

ord .oe

:1 i. ens ...is crc rcequ 1 rei:I ?I1i11

th;:..rI:

it would

be simpler

to

introduce the

spocc,.;isc

:1 :i benc :.ntc.:'f: ho a' ± cii. iuo I

fórAiul ot ion 0 f

the

pro--b. 1cm . Ttie 1... :1 ..:.:i 1 stei:

wes then the

dci' :1 vet: :L on of

the

equsiti orus of rnat:Lor of .o s :i up.]. :1. f:i. ed made .1. ire wIi :1. e::h

the

d:i.

:1 butod mess of th:c

b Ic wesd :L

by ;

:i.

cf

discrete

mosses

etteal-ed

to

o we I atit less,

i ncxtcens i. b, 1 e 1...c

he op .roech

eo.::l eta

e system

I:: f

ordi ruery ci :i ffer'enti.e I :cqi..iet :i. ones They showed :i.

ti-c I

popert ho...,

ire the 1 im:Lh,

the rcsuitin

ce.q'ietions p055

over I rite

the aorrespc)T-ud i na pert 101 di f Ienut 101

eque....

The anchor ilne d.evid'ed into discrete _masses

Ei.gtire No.2

Numbering:

Stations I is 1 to n Station : .1 x(i) ,z(i)

Segments : i is 1 to n - 1

Segment : 3

DIVISION INTO SEGMENTS

Fi.gure No. 3

a z

DISC.ETE SZG4ENT STATION.I

4

Tiue

ppro.:I- ws idei

for'

_{purpose of th:Ls p.;pkr'}

_s

:it Wj5

the

.Lm

to

i. r c-?sti

te the fOreS

due to

the

moI Loris

I ri the

1 e .

s

tliere

er'e rio

1ods tt:hed to the

b1e

the opt:iori to

suspend

.ori-reritted loads

:.t one? or

two p.o i nits

I or

the

b. I e

w.s riot ijJ,

FI'i..ire rio .2

shows the

distribution oF isrete. msse;

LtI-ied

.

we :Lhti ess sb' :Lr

wh:Le.h

hs

I ly de'

veloped

teni.ry

sh:.e

ricfror

c:-3b,le of

: sh:Lp

nihor.

The

.zL-1e. is

tt.2hed

to

the ship

;nd

the

.inhar

on

the

bed . The

sh.ft

of the

.rihor

± s

:1 3. uded :Lni

the cz3. u l.iti on

Th

s

N'ip the

sh;nik

ót.tes .r'o'rid t!t

_..T:hor

_{p:Ln whi:!1 Is 1ob:.d :Ii}

tiG? .rEiTI'hOr' 1-cud.

By .onisider 1. c:i th: s-i;

w:L1.h u

di ffererit lerith .rd

d:ieter' it is oossii::ie

.:.f.Lne one ms s zt

the znihoi' point arid another m;:iss

:..t

t-ie ar:J-ior sa..kIe

io the bound.ry

.:ond:Lt:Lon at seabe.::t

is that

the unJ-or

point

:1. s stati oriary

:.i id the

shark

an rotate around the pin .

The

!:oss.i.b :1 L ltyto :Lrtod.:e

a movinic;

.urnor

point as

a

bcund.:iry

':::'ni::t:t:ion WS 1:e,.:;'.J3? l.1i .a:Lii cE t:ie :i F:.i:1

:i. r.r'ease

:1.

F"" due t1"ic

bo..' flcj....1 oii> .11..l::.T.i

thi

_{I p. ±}

at a:hoi' arid riot d'ag.:iri

The bo'..indary

onid± tier at

the other' end of the

ab 1 e :i.

at the.

water level.

E?.y emi tt:i.n.

the part

f

i--from

the water

_{sur F.:e to the ortrar,.:e}

_{o fThe,}

_hOWSe,

pipe M-

lculation

is s:Lmpl :1 fiud .a

only t1e unider'wa"

ter p;:irt

is I nil uded

1

.ji.jre no 3 s-iows the d:L Vi s :i cr

oF the,

r

o...3.

seqmerits arid

ives tl-ie

rii.mb::,rirc; oF

tI-c

eer;t:

015

bciideri.nicj the

s'grenit

.

Stat

. Or nuirber

1

i.atiori

of the archer'

hc.r.::I .ar<:1

staton 2 the

1 ocati on

el...e anche

. Fr'oii

tI-crc the cab 3.

Is

dlv :1. :Id:L to

ar

± rtec.ir'al r.jmber

el...I: :1C)1IS :rn

order

1:o s . rip. . i F L at :i. or tI-ic :1:1

nce

a 1 c:r

the

1 :

L.etecr b-c

bat :1 ons i. s e:eq.i :i.d :i....tart

-f::'c

i''..ibeïi

3. o I riii::t±:Di

Zi1 be

:;. ro

nc.es:.a'.,

i:: .'::ris :1. d?r

tIe

re i'L.i. 1.

r'j:.crt:L

oF

f.:j:I.::I In wh:L.:h

the c;.bLis:i.mri-scd,

It:I.:;

u'..imc<:I f:I-i.aI: t1c k :1 ret :1

ererijy

:i.mp..a'tc:J

....bhe

_{s...rs,_)iJT.l,:I}1 ....

_4. . ... ... ... ...2...

.2...I..f...

I ...2..,

ii

j

U fl 1... 1 I .1 _i... I I.., I . U . II ... U) II II .. I...2.

1 i.e 1 ti-le

cb i.e

_{whei'eas :L: var ± es as the}

qir'

of ti-ic velc:c:L ty component otr' :Loht an.1cs to

..he cab:Le

3 I ri ..ni .1 riie

b e

hi- i Li_ - 1. - i I - .1 1. or

:1 V rj hydrc)dynari j(

i'ec't

cm

OI..jiS but

..'IiTi tI

..a1::. 1 e :1.

i'c I ei'aI:ed

...;'.arrSVerSe I y :i. t i-.,Th::v...

it c:c:ic.u:

a.ck:Iibic:n;:I.1. :iniei'b:La

(...'crmj :Lno bc) :1 cure

no 4 the

trarisver'so.

ameononit

bi-:. .ac..o J. :c ':ab :1. or oF : :l:L s.:ioto _.::.

1

Dir X

-

_ein

-

2. cBe

\.1..

. J-' no

--

d i. ..roI '

3'rnnit

..f t1. iii 1 0 1

(1r2trcpJ1zir

cc-:.r-t:

system o-F ;ixis.

_is

usod Th

subs.:r ipt

0

indie.ts

thz

'f'h

_bound

oL)r'4 Lritc L-on TI

stt

with ro :s'..b ..

...' L

-'-1

t1 e lo ..1

s ; born wi i1 _. r r ₁

fe

ih lr

_.

J.otior

i

Both

systorn .s dfird :ibovo

used :i:r

this ppor.

Whr

Forrn'jI a CL)

is roso 1 vod

i rto

o )( id fTho Z

di rct :Lor the

_{.,orerl:s oF}

:e ier:ti on to wh :L

h

lie

I rerti 1

or wi 11 be propc:'rt I ori;i 1'

1si8 -21coee

:ir

Z0

t!e

huy,th'o.d.'rmi: re...:i::L or -:i:.d:. or ::::cri:,c:r?i!:s ':j-f

t7h-:' zi::e1er:tior

;.rid is

erei'.11'

r;c:: p.risJ.].e1 tc:

tle

a.::e1er.tioru

e:ept

w!r

th: tr::'r:v':i.r I

':imj::::ie.rt is

'rj - IL I I. I L.!I 1 fR.. - L R .1 ER I ': 1

:..st:c.ni :s L:ror's

'.1.h:r

I:i-z.T s:L;dpl :

I:

it

th.t

e

::..tiorIsfo

stst:Lor

:1 ::i:Lvi:ru :Lh

f:i...ii's, no

..jri L...or s f:j I I ows

!'

-LJ

i--;

L7j

[j

+ -

(e ejn2O + osin2O_)

= + - (e

co2O +

(4.)

TWO DISCRETE SEGMENTS

z

C

1

fl d 1

A.

1 'I m .. .-. i ..i i-i

= 0

. Cm

/ 1

=

-

/ 1

In

ti-

13i

lcrrJ.

d :i. t i OTis. ;nn,d din ':'rs:L Lis

1inie.r rnss

cnis t

.dcJd

isrt

LCiSO se.:t.iani.1

-;

;ib1.c

srs:;msnit .j :: . :.oa"d :. 't:±::iJ. .:ac:d:Lni.t-s 6 r...,. L m..j

1 'Jmpe.: I.iiS

ij

1i.TiS J'55T ;is

IiiiL.

.J

tI

JJlLII.... O I 1...

LITLi

al st;i:ioni

:1

SC orM 1 1 al thc,

:;uJviI snu

.rsvn-se niss

a a

!:hc.L

artr.ai

:1.

cl

tha

ts

is

:1. r.1i.jcjacj :i. Ti

iIi:

1 T1aY'i: :i.

c'sncii

INt:LTI 1 .jdact

:1 r

tha

uiñi'j 1. .na rc

t:hia m::

.n.: dad

mss al

:i. jii :L _{:i. Ti}

aria or mar-a

i I IL l' I ñ . I a fli .

rL i

nc:t

rJ I:h?'efc-.:

n:Yf. in i_i e:.cJ :i.r thi: :.njJcJJ;:.

I::L:)r

nIj..1

irrex':Lr

h: ::t.b

.:i:

ariL-israd

I _c t-'" I

is exp ::.. :. na.::I :i Ti I:

2

::

In 1d. nc: 5 shc'w:s tha si tuot 1 a...I

Tiie

Faa v':tor,

in

larmu 1. . ( 3: :sni ba axpri:s.sa....

t;!-a sUn c: I i? 1. rtarr.:L

.nnd axtarr.ü

_{frr'r... wh :i.}

d-Th': :Lrtarri.:n 1

f.:a:

..iv'a

this tansi crs

.:t:t r

ii /4

J I1CT L i IL I L -si i i

n II :: 1 '.v :L

I::..iy.ry

.n::! 'II _{.j:Ld ss}

iii- I i I I

r'i

I ni ic irs I- '

-7.

= +

-

-

t

Ii .r 1 S:

=

tension in

cmrt of 1:Lre

.'eer

sttiors i.

nid ± -J. EN:!

X

l-ci'izorit1

omporierii: oF rs:..:1tznt:

externi;1 For.

Et :Lc:T.1 -J. C

:L:.i1

:orp::rirt of r'i..I1 trti:

ext'1 force ;t

;itior

± NJ

=

- -

einO, +

=

+ -.CThcO,

+D4C$i

c.i.jb,ri:.<:i..d riiss , '.1 .:J.i.:J i. fc:1 3. - I -,

Iii i J _P - -.. i ,..tt ... i-i ..I

:,::c .1.:?rzi t: an

to ar:v :L tv

2

::!

I.: ;E::t

c±Lct:Lc)I

Li _ ii ..L I i. . .11 1

nt c i ii - R Ii R. 1 .i !c I

j. ni tti :1. . :L

1 .t tar

:.nII.Js:. it

;t

.:L1

:. owest RyrIói...ri'..iiiiI:eii.

vary

::iii;. 1.]. :::omp.or'ad to

roi-ni.i.1

!....:1_...s.i.IIT..:...

_F':'

_{.::r:i.c '..h:t:::I}

..i 1. .io .. 3. 1c'i r) . i. :Lor a F

Ibe

...I

Fith'zr

:i t

ks assuriad

taiL...IC !...art as

iii .

1 I D I I 1 - i I Ii i i I _7.

s 1:1-a man

v.:1 ua al

...:

aaI...

or

t::cidai' :i rIj ...:

.:F::ii

..i

iti';:i.c;!It

:L jir maTTt

h ,c I 1 I t- Ii LI

rt

1.7 t..h. c it '

I1a

i';.I

.a'z' IF ± art di2p.erds or f:Iie keyn':D .::!s

ni..':I'

t11a sacnarit .rrt::i 1 'i;r j. .s:: 3. c:'v'r

I:1a ai::ti

:1.

Di= -

_-

Cd d

± =

-

₊

_{- c)JsinO +}

_1*0

+ ±ceC

1.)JierC-?

is

Cd dr'zici

oefFiient

d =

Iimter sjrerit

i. =

ve1oityjrrert

Up I'

tti ± s po ±rt

_{n :?>q:. :L :L}

I

frmu :L.:1 .ss b

r.L vr fo.

LThe

ti.or

of

every term

of

_{formIJJ.Ej 3}

wi;h

ption of the

tensions

To determine t is

1: e

t.tij bi I I ty

Loridi t I or,

wi ± .± wss ;is

;:1f L:

outset

must be

irivo ke.:! .

It

.F:....Srl :.. .. ...-jriL or

moti. on of tie I me

.

It fj.j5.3..L.1....L.

p '

pi';t or

betweei- ..i onis must ri ..::

re w :L 1± t :L

I fY.'ztsnis i.:: :i. 1. i. : or

2 _.L .2 _...

..

'Si ,.t_i. .. . - t _..- .

i-i

I c. .I II C)

.:r)1_S :1. = 1. . mum z1L ors

Tb :L bo id-s

for

c-.s:li

mert: of

:zb 1. .snid .1..

reqr_i I red tbrL...e :ce.sporid± r'. set

:L c:rs T

)ii

j'IR

lhi.41 iii

'I

iII.(i

_)I

I. 1ij.s.j LJ(I _{C) I Iiii_} I .1.ui I _.

k. UT,.. I -.S. (I 1 I Ii U

:1. voi-i .:ond :L 1i rr

E'.s'jsC.

ç) :L mp 1 :1.. :L1 yuIlJi::. f

..Lon:L L :i. cr i.:. :i .d

.s syster

_{o 1 ieI::.'.: :1..:}

:::'..j;: iris

..jys

_'c.

_{n.T:it :L on u i}

_{the :..oper tens I}

,' I....I..

9 L LI J.. -.. JI . .I eI1i J... .1...: ...1. I') f .J... ...

,.j, ...

... ..

...

.. ...I...

:1. niC<i liCjn) tic.:.

I:::)I..Idr'y

cini.::I'i. I: :L on niI'.e 1 V

>..L :: (.:)

f ::::

(t),

_:

(t)

.i:i .ri:

f'ji..:t I

k:., F i.ci _:..:rm:i.

Lri LI /iIJf_ .)) I

ri,

Lr' u

I I uli..

:i.

.t

;iIiIC)

ti

b,o..i(.iiv'y _{f.2c)rf.:i :1. Li. oris} .Ji':' _L

n.:iior

rii::i

t!i

i i. p ,:ir:j. vi r. _{m:)I: I :r} :1 S _Is'

.irt:

,jtz'v

.i...

t:r

_ric;:iici

i

10 ''im. :1. ri sL;.i....i. ....i;:i' on

i.:i]. lv .:iset o

:i.n:LtI.s]. .0...dit:;.onis 1.1st

e ;iVen for

e;s.:h'st st :L or or

the .:;nb, ]. s

f,e..Is'f

IThe equst ± ons 0

ILL' L U r ii '1R r IL '- -; -'

'-:1. fy I:oth I:Iie

.:oor,:j :L nles;n,:

I:I-i. VOl :L L j

.s...

.1. .

I

:i ::i 1 tjc.:

iLri;sf: :L

1 s's :L by

I tori

nd Po 1 s.Th _k .srd 1: ,.sL-tert :L On

&.j .I . 1' :. cr.s .

Computati oraI

Proe.cure

This

sctior

addrsss. thr

impertrt

parts oii

:omi u LOu 1. p duri.. i. . i or

in

_

but .s cirieri

s .possib1 Th

p'ts

Jiir

tt:

f11-irig:.

toth

fir it di

fFrer.c?

method

i3

giver in setioris 2 rd 3 of this p.per:

:JeTr:LJ. cs.:r' :i.

c:ir o 1 ... on::.j1;iuI: :. or .

re;

th

rumeri

tEib i. 1 i ty c f th

Th fo 1 low :1 E:L n i d :1 f ior'er q' :1 v. I ents

Ti ::::

A=

4 -, 2 U U ni-i _if .1L4

2x

4

42

2ZL + 9

i.:i.

rirt.r'

:Lr I:

r.iTi-

.

r.;i 'ir

Steps

tini

step :].rt.'v;Ei].

C'

± rter:i.s t h:

:1.iTer:;.r

I I c:.::i. t'.

1

r!:::. s

.jsod :1 i

the i

Lb i. I :L t...:or::i :L

:t on <)

1:1 c:r :1...

f Fe:r :.t::'1

'.':i. :i.

fo 1. 1 ow . i.i ;

....t :i. onsi

F::.jrid

(x

x1_1) (.*

k._) +

(z1 z_1) .

(x1 .x_1) (.2 +

_{(zjzi_,L)}

(.2

t

(

-

1

-

sQ

::Fcr :i.

.

i:Lr:..n

:itici ic:)

Ti-c 'j ':

....orn

:. vol. :LtI ii vc a:::

aid

ac.1.c'at:.c:'r'

bc.i:jJsa

it

:L...'rvr crit

I :i. .d :L .i: .1...:.

.IuI:..4ti

p'::'s :L i: :L.c'n:

..

I I Li I II

It

JTI '

1'.i I(

Ii

j:,D i t: i ri i:inz. :L 1: :L . i::5 L ii L..:: c.:: :L f

:i:i

:e'.:Ei: :L

TI In-i - _{- -I}

j.Lijj

'r(

- Ui .11 I , j V.1 L

i:wo rc...i. 3.

toJetei

.s :ir.: thc foJ. l-cw:Lr::: cpc....

'ilat: aris

ard Id-c.

v'c L o it: at m I .d:.o :L

rts In

... fli. ti-z? V.I

ri'.nr :L:..i

:LrLtr:tioru

: f .q zvf±:Lor5 0 ffl''t1orr.

to predi.t th

oordirts ori

stip ated.

Th

sCor.

ttksc

irivo

th

.ztiori of

m.1 L

di

ir the

orstr.irt

ions from

whi.h ;j set

of First order

o

e:tioris is cbt:;:Lnied .nid

:Lrit'tiari

of tte equtioris a

se:on.dtme to

h.ts:Lni ;j::ur;ite

vnJu-"

es. of

the

oar'd ri.tes

(

sp.i.1

form of equ:tioris is

ise

for

oiputiig

the

firs!: time

step .

In the first

step it

is .ssumed th.t

tf-e iriiti:1, ve1o.ii..omponórits zr'e zev'o

nt

e.h;:t-on .rid

th.t the

iriiti.1 car 'din.te.s

nra c:t.n:Lria.c.

for

.1.._{LL1_.}- - _{qiJ...A :.l..lr:}1 .; .

....

£.. ... - .._ T. -. ...

-...

LJ L..? ..,L LV._.'fl _.J

tenitnt:Lve

v.n 1 ues For th ord :L ri.i:es

nt

:1

.ride

of Tzyior series xp.nr ..Loris

.nbo'.jt the po:Lr.t

.L.._: fr0

xl =4 +

+ +

= 2.c + (e)*+

j.(A)i?!

+

r.'.iIJse the ye ] O.. 1 tY C:Cmporier:tS Sire set

nt zero hr

fL rst stp.

the

ca I er.nt ± Or

frï'm. ...a vets : red

1!-e .nss'.mp: : L..ris

For' .ci_;t It ..:i:hef:Lrst:

:vteosc:

.

'

i

J ri ri - r ..)

1.a ux<

For ta c;I c_iL .nt J. or . Tf- :. wi .1

in tlia

next seci:ioni

Th: .ZjbCj',G. cc±'tcJ. 'ides .::j .mn

J.

nim;:irJ r)

the compjtnt :

1.

1 ast

:i t:ri of

th is se.t :L on d. 1 1

nd:r'sad ±

.1' _{'..iiiv' :i.} :. .

r:C)_.i_. ::::F ç::.C:

:Lfr!

:;..L?Tit

I I... ...1 ...I....

j. Li - ._ .. .L: Iii'..jt ,.. .) j... I? II1..iII.I :1:1. ....1. ..

;.mn::J :har

Va lie

:1.

E ri order l:

obt

.i. r . vri 1 id SC: :LLt LO 1

.I..:j...

_rcsss.nr

_t::j

ri I c. I Lho I 1__ ' _{I .}

cc.::,

'.ntions used

in

cri.tstioni

To .

:armina

tte

stzbi I of z

system o

fir ± ta

cI::i. f f 'zrcc:....c.zc;usit ± ons

tie

:F

sirs 11 di.sji-b,;r..e

r par''1:!...IsSt::.:Dr :i.s

11a' ::c:jni.dit::i.c:irin Fc:'v' t'b.:i. 1. ;:ii"c.. s.n:i.d l: ha

I F .smI:: I 1 tu::ia' o n !. .i : It!....t.Zin::S'.

:L.r-"-hi-c)''_I'.a': .nh

sri

:.ni

r:n' cF

nb las. does rot :Lr'a.nsa

a

oranti.n1 iv with

i.c.sass:Lve

3 Input date

This s .t-ióri addresses the :Lriput

data for the

omDuta--iorial

model

The fir'

part will deal wit-h the phvsi

a1 data suc.h as mass .rd the

I ;nst part with the Fc,r;s::

motion

t the end

1ie cable at

i-e water s'jrFa..:e

The tab. le

no . 1 or pacie no . 13 hows a..

I

data wh i.

are

entered ± rt-o

:omputev' model

_{arid ad::esssd in}

_this

sectiori

141 th _{IThe 50JJ. pmenit}

ri'jmb.er for

_a

part I

I...I

mass

of the

arid-or arid the tot:i I

_Ier:t--,

_d: .

st-er arid

i )IJ. t1 IL J . cd ...'i Cl .41.. 1L' iiiri.

z I .1. ... I i .. J i i

..J .. i.j '4 ? I I .._ L) .&. ..j t. . .. I I

tI on óï

the mass oF the

5IL.

. a . . :t

the

:::mputat:Loris

t-ie at'.ial

mass is

used .ari

.rri::;untl

I he

I

Io '

. U. . .. I k ' nI &

ari.:hor is e.xp,rsssed as

a fun:t:L or a

t-e ari.or' mass I

::jrd is

::al..'jIate,:: as 1:].

I-!u: 1::. :L rIc FCJ'fl" Mass .aiich&:

I.,'i5iX

:i. (1

TIe 1ic 1 cLL TIc

po.Jei' Is id

bc::

. ate the

ful :. y :eie-"

:i. cI:.J eIcrI1I'V

'a f the eIrI..hor' d:: 1 'a T!; :L a .!b et w:Ll.1.

i...1J.. .4.I.. I ...

L. & .1.&. Wi. L II .1.:4 .

The 1 eriqth

a f ..he

_{s"Ia ft Ia 1 :1. cs Ft-c:m}

t;

;arI:L:r d

:L;r--'a .i. ars wh :11 stt--

mass al

Th':c shari k . . F rot T'swn an

> :sil-;eri .C:

al

tis

ass al the

_{c::i ;. a :':oer....}

i:eI':Js. :i.a

irl

I irc

'.:i.I.1" c.)E ::..s1C;s:L

.rjt±ci ...:!.et\ rules

Ti

use i

te

.51 ac:

b's dealt w I

':h

later'

7iic' _{Ii::. ;ns :LriL-c)}

i'eInI.

arId l.ast c.ie amp 1 :L t'..,d'a wH :L

_{-:..niri be e>ce.:t-ed}

t1e ari.dic:)'.nj5e T I:i.s ::k:pf.iI :i.a ed .:;1..::..iJ.bez' Ic

I I

dev: ope: ::.rIbsrI.rLI'y

13

TO , i

I)yr;.m

ts o

I

Eq11 :i.pnierit riurnL-.?r tJTI k(.::WT

Typ.e

rli:h'

Ms

rihor

15000 000 kç.

Cor:tiori rn.ss rr:I-iai'

I 000

HF Fztor

6

Hoidirijj powr' zm.:hor

382 , 000 kN

L.rigth shjrk

3 950

)f

:f0itI

. s

:c,000

C'.jri:

'1a..:L t

:1 . 2 5(J0

nse:

Grzde hir

U3

Di

rs ± on ri

78 000

mm

is hz±r

139 , 200

k/m.

Drit; ±

ty

:I-i; :L r m;t 7850 000

k/ri3

i'

, ic..

u25 Ut:

J 1t.

: Oi :1

1

:1. CJ:.0E0

. k

I 500

fi:t'::r

ii

i

:i. c:oo

.4;rt:i.

Ti

is

c:, 0cc:: 0 iJ47

N'.jrnber'sto::s

:1. .s 1.

C;1.:I.Jit?d p.z'riod is

0 , 047

Irp.L;t .J. ? i'.it 1 C)iS .st

Sir

I :Lm

ri/se.2

coo ui , 00:J o , ooO

Its (::;tr.:ui'\? Cs I cl.J

..:1t :;. crs

0 :L

t:sio EDst rs;"

_y i s .i2C' I 84 n

r r...-- -

f) I ,. i... .I I.. r:' y .! .... .. c.:: ii :::ffl :: O0. ,

:.:

ri

L_i3t" (sI:orsI'v :L

: , :L 2 rn :i. r Cj C: , CiOO r :Ls 20,:186 rn

965 023 kN.

Cornp. ,

Li

ED Cst 39 1 , 592 kN

Hor:Lz ...tiJ FH:L

;is $82000 kN

Li rFrs Czit

:L s

965 023 kN

- . I .;

c. I . ) '

I

ij

I ii

14

Tho I.jrrertf:

vo1oity ..:r bo tho

_{vo1o::Lt' c:E tho}

Nori-ont;r 1 t :L ..!.

I st"'oom

tho .so:

::..nrort

_{om:. :. r;;:jtj 0TI}

of b.ot-u T1-o

f i

o :L s .iss:..;iod ::o

orstr,t

over-ti-to

tor

dopt-As merit ± oriod zbovo

the

i';ido

rr.d di moris ior-:.

t:i-

jr foLlow

from the

_{equ:Lpmorit riumb.er' The mess}

_per

urii

of

1 eri.:ith fo 3. J. ow fyQm

_{the m kors pirti. ...i1 irs}

_zirid

is

t-zri

i'.

Lhe

-e

_{tr.jd I in k chzi :L ri .nid}

1:ii

kles

TIie density

of the

_{ch. fri}

m:itoii ii

_.

t.keri from the ri.kers

.rtirj1 zrs or est:L mL-od

ti-ic density

the

o' doperids OTt tho I000t;.orr of the

;ini,:

be Fi'r-i

_{h.i':t: k I}

:'

.::

Tiro

_{iJc1cci ns coo ff:i .:;i OTit for the}

_{k .irie.:1 ch;:i LIt wore}

:d on

for_incj

fri

v.:.i :L oi.is p;.b. 1 :1 c..it :Lnts

i'ro ft :

Dot Nc-s!'e c'or'its

i:

sh;n k

Is

. sc 3. ± d b.;.i.... ii t11 ;

squiro Cr roct;i:ul

i an

rd there fo.-o

tiio "- 3

.0 Cm :L

:iprapr ± ito

The f"J n

c.l::. 1 e is

1ss'..m:I to

o so]. :L d :: 3. J. rdr :i c.r

1. omenit wi ti-I : :L rcu I :r _{'oi;s...:;'i- I art onid}

the sre msss

:or

r_jnit icr.e.itL .:is

...0 ablc

The v;.1'je cf

Cm := _{:1. ws}

Eo'jrd fr.j...to c.nb 1 o

dro.:j oco fFj(

ort

far...ft arid

th

ci"a 1 ni

basod on data found

r

var I ijs

;:...:b. 1. :1. cat:L or

Tonta-t:i. vo vs -

---'-'i

r

:

:

ar.i iJ

when no data cr

vol oc I fr i iv;ii ab. 10 F :1. 'are

Nc: 6!c.,th

drao

cooff:Lc:Lont'.ialje.

_{I_a-'}

as a function

of ttio kevriclds

nutl....

Decarjse the voIo..:Lt'

door aso

from

the 't or

_surfacs

tcD'..r.js

t-o b.tf:oni

t-:'

i....

'::

i: :. is

.1...Je.::ro.:isos arid cc:rrsoquerit 1. V the

::ra.: coo

± ci

r . i_i...-... _{1 - ._ .,}

.. ...

... .L.?:: ._ ii .. It.? t _l I'.' .L ..II: ...1 _{._j...}

I t mcj .1

iri

II1 i it n rio

:1. r.: 1. i :i '

I:i;t.

_{IC)' : .:D?}

erit

:1. ci tor'm:i rc.c . :i. S :i. s a atb :;. trsiiy di::::; I 51 Dii

1

...0 .ode,d mass a ft-o s-a fl:

s found in

_a

m ± 3.ai' ri rini(n i.

f c:'rtzo

c:! :1. r

;:r,c! Is

d or a so]. ± d

s. 1. : rdr .ca 1 e].emenit

I

o sta-t± ri,

t :1. mo i. s ricn-m.:3. . _.' en .1:5 Zorc) i:i..:t can

taker as sivnj:rrt

t::i.ii':c s .::: h. i.I.s...'].L.:z::! ...jj];

I:io s:j:

_-ti

f:Li'i:

.:.cir...

::r

'ie'

otiE.? 1:1. nc torsion

_{cur,d from. the rei.j:i.to of}

_{e cats....}

nisii'/ ,.].i..:l.:!.::Lci:i :Lrr

i:io

;1L:L:

_{.s':i::i:i;t::i.c)r} . TaL.1:. ric

I

'II

_..-... 4 r _...

1 '.:: :.i .. I .i :: L I I t 1 t '...:1 ...1 .:.i ... I.., .' .. . I I

f'cDn ;:si" I:: ii 1..,J.i:iy:s

':.-::c-e

:i.r

:iI

:::.n.c:::L,::i

4 a.

The

ri'.b.er a E

sti:..ps :L ;

it:e:.d .:ird

t

t!ie

s;.ne t i ;ie the a: 1.::u 3..rit:..f per :i. ad i. .

eritn'd wh. .Th

:L

the

ii'.ji:er' a f simr'r;

p.er:i. ad

The

np'..;t a f

:1. ors wi. 3. 3.

be de ]t I .ter .s Fl rs

it

:1

reaessry

to

ass the eqi..i :L 1. :iJ:.i urn pc:s :i. t : or oF

the aabie art the

rririg of the oonput.tiori

To do so

it is :importrit to raa I Isa thait the ;r :Lm of the

studs'

:L

to irvestiita the displaoemerits, veIoit:ias,

t:Lors

.rid the

for'es in

v.r:Laus

1o:tions ;ior

the

r:har' azb 1. a for a ship art

.ri:hor and when ShL

I

sub

J atad to

anvi. ronments I for'as

There fore the st.rt :Lria

point is th.t the ha1wsa

pipe

its

h:L:het eiavstior

.:.jove

se;b,ad

rd is F.jrthast s..;.y

From

tte 1a.tion of

the ard-or

This

pa ± ret determ :L res

the

3. erth oF

the

;rnohor

b la

wh I oh :L ri

th:L a osse

is

Eu 11 .

developed.

based or the

ho3.d±ni power' of the anohor and

depth wh :1 oh

tkes:Lnta a. :ounit the

imurn t :Lda L

ar..ia and wa..e .:no .E :E tude

f :Lnt':s: :a

a i. I

ti: .sr:hci'

be

exoeo1::ed when sh:i.p. :Ls..:it

pr I ro:L pie

there are

5 shapes of

ioh 4

...Owr

nc 7.

U 3. ti ma ..a

si

ex:L sts :L r des 1.

ai:. I ronmenta

oarditions .

are

Es no w:i.nd.

0...r'ert

or' wave

oi

The oha I ri 3. eads e1: :Eoa1 3. y dOWT

'I_{5]. so k '}

.

.c::moi....I

a::i. sb

En ::'sr .n:e

rv .

ron-meT tal

oc:ndit:Eo...The oha:Ln

l's.sds

d snd

.:ier' :L:!".: .n,r.l': .

s:t of

ta ..::".s:Lr

:::r:

Fu 3. I deve3. epe.c

sp.a

st.s ,.hisn

the any :i.

:

rs

-avc? :i. 1:o

.... .ir

at:rit

2.

oF ths. oHa:Lr

Es 1. :i. c.:f Eroii

.i::and this. e?id.

si:

!:ha .snoi-u...a,.k I a is tarcient

to the seabed.

brains. i

ti.

on 1 :: k arid

::'.:Dt .I....:ii.I.. _{... tIu:}

sn'.; :i 'rrereb.s 1

j1

aria

hiaie

fur-the.'

I nor'sasocf . The :

:-:..:

ad

.nc

]..s,::sar!:

t-s :r.sI-j...

..n:'si- sr

.sncils

',,:LI::1

Cansa.,::ja.nt ly .:j

''l:: I us 1

oomoornt of

the pj 1

L :L FcD

.sbt ho

.nn:hci'

ha: k .1. a

:o.jv's

.nri:i be p

sass

f b.ra k. :ici

be srs!ic:r

Fr oi the so I 3.

iss startd

:i:

.I_ i. I I I ni i - - ti

t:i.ciht.

:-:E.a':n

F.. 3. siv:i

this study

sisiok osise Es oF Er herest I::-.aoa..;a. it

Es

ob'..bus thsJ...to..;!:

...55

A:

c:roas 411 :.

ba

-s1o.:.

osse the

ins :-

nn'

: ....:

in

that

situation Era ioPt:

Ltd

I .1 . .1... _. .1...

I I -:. -. .. ... I.. j

...I

..; : .. :;. :: .. .. .. .. II

1.4. - I

IiiI

I i_i - - emeivroug, 1.0 with CD ñictrate "

-\::-0.5 0.4 Smcoth cvlinaar

Figire No.6

1 & 100 - -. -- 1o7 Reynods number

Figure 4.9a Orgcoefflalerir values recommended' by C/san, 7974

t) ,cJ U z ___I-_____,____,

-k

__

\ \\ \\\\ \

taut.-COORDINIV1'E SYSTEM 0 H

diff(1 -

1

dIstance 1

4

sh

distance

1

u'Iqiire No,. 7'

16

s :erihiored

above the

lerii!::ti of

lie

;Dricl-ior

h.iri

is

detcr'm:i. ied ',' :1.

:h :teri;Er'1,

c;i..izt:i oris The

i'5SOTI bj. r;

t!-.t

the spe of the .:cr

1 :1 ris

ar

be j::..r ed to

the shape

of

.

.:teri;ry,

The

:itcriy'y is

.ssurned by

;.

fcct1y Fle>dbie 1 inc

'..irdert he

:[nf1icr-f

p..i_y

whilst

hzriirici

b?twecri

two

suppc)'t

po:Lrits

It is .ss'..irned th;rb

the m;.ss per ur:it

ieriçtI-i

e.oristmt, For the ;ri,hor

_{ch.iri it is}

_{ver;çje v;lue}

mess of ch;ir arid shak1es o''bhc ea plet e leriçth

of

ti-ic

hirj

The fully developed :ntcri;ry is

_defined

c.:.teriry

which

.i

r

Liic

is t.nigent

_h,

_nid-ior

shck1e ;t

seabed

zrid

t the

other

_{lstenied to}

_the

ship

Fi.

'.irc

rio

7 shows the, c.tcr.ry or

±

coordi. ritc

system .

The -FiGure ;lso shows

t ht

_{tie fiji ly devel}

aped c;rL-eriry eqi.ii 1 :Lbrium

is

ar.riL-eed when the

hold----:LTIcJ

power 01

_ie

;DrcrC:r is equ; 1 but oppos :i

_{:L ni di}

'cc--t or 'cc--to 'cc--th

hor i zort. 1

_{ccpercrt Fh}

o t--i:

I ire i:'cs

Fo .st

the sur fe of

_{the w;.tsr}

_s

_for

_{fu I ly}

_{devc ....}

loped ct-cri-'y it isde f:iricd

::riovertj:L

c i st t the

ti-ors,-oc

!. e,

the verti

J.

compericrit

F.,

of the 1 :L re force

eqi.

Lst!-c

]. e.iith oF U-c .:JrC)jQyS csb Ic

from tc

.. cho...:h:ji::: ; J.

the w.ate;'

s:.jr ":1cc

ti is the

:iss ,..e i_

ht ...der' w.tci' ;:.er

'Jri 1. t I crçti C) 1

cNi :1 ri

c;ii_jse

e

dcr i vct:ioris o ( Ue

Lrcr'- eqi_lnt-jc-ns

csn

:': .f:oijri..-1 :1 ri

t:-ie v.r'i o.:; textbcx: 1<.:;

_{.iri.: pi...t:. I :L t:Lor} 1

: r

ci-:L, ie

fcrni.j3_e

.nie

iicz'i

in

t1i:Ls

p;.per' sr

iveri

1-ie si'irt

.. ni.:j pa i.rvt :i tc:

::etervi I re t-;.:

req..:

:L.edl?nit1-a F

:li.:Ln-Fo 'i:ie

o J. d : pD,.Ie' I:1ie :Ti.-iIJ

...srid

1qJ:j.l'ec

:icp.-t- T"I:i.s Ls,:1or;e

',it:...l:-:

].C)w1ni.c

t-:Dr'mij 1 .ne

.:l= q0 x.

( Nc:,

)./

u'!c : ::: _{(Fh :Li: ./ q x} ' :LO:-:L>

>:LI:;r;)

10CC::

:.::(

e:1).'i.C)CC:: .

T"e ii. riiIi :i. :....

k':i,'tr

....

.i ii -:

₃

W:.:::

.,

ii :1. ii :i. I'

rss ti±n :Lr

.:::ite:i

I I i Ti i:Di'c-: Dii .:-;;: :i. r

h

Hor :Lzonil::cJ. componi nit al F0

...-.1. ..: i .. ; C) liii- L) ) IL ii ._ LJ l i-.

(he

oiJtcoris

C) th :;. S c::i I cu I ;t i On _{1 3} i'cc... _{:i. r}

the

hcc.::I:ini

c,- Uc ;::ro2i-'cn

ss is sho'.. r

in tcb

ri:::

Ti-ic next ster.. I st

di 'i Ide the ieni,t!

:i rto

seçjmcnts a

thc memory a -F

ti

.:ornputsr .rd

w:srx:Lmum

30

Tl-1rith is

1so rs.or'dsd,

P.'.i'p th

.:am;:.:jtstiar

w:L 11

dors -For

sis.:k

I-p

ho-i--i zarit.1 for-.-? whi. :h rs.rsrts ther

u1 t:iart -Fo'.s

at

h-:

1on:r11

I .rc.- - r ii. .

-rioi-ior must h

rt'v'd

Ths v.:Lu

a-F ti-is

-For:.: wi .1 J. b

deit with lztsr

s:Ln's

it

t

th:Ls

point it

is mars

'.oriveriirit to dL

. .L1

LL a m.its

H oh .

.iori

th

ariohor I irie

rs .detsrmiried,

iJhsr

ths v.lue a-F

Fhj

is rird I rita

th

-Farmu J. :1.6) .

tn.ry 1 srtth

± s found wi-il oh

is

slio--ts'

t hri ti

Fu..iI Iv dsvs 1. opsd

os-L-erir'y

Tho di ffsrrios is or

ib.sd rirJ ths siiip hs

mavsd tc)w;ir',-:is tNs zroi"ai- Th :L s

15 s!owri

:i. rf :i

jjr-:

TiC) . S

T!-è s.vt1

svstsm is

rid i.o.i:sd with fThs

subsor :Lp!: o .nrd

th

tsrii : n I ol"

tis

;itsr.siy

is -:ls, irich

no s.bsor I pt

Ths rot-sti a T:3 ...-'rsspard to

ti-is arss ussd

in

i. i- ...-

t- ru ts

a-F tho otsni;ii'y

o;i J.

I :t ± ari

;.i's q lyon

To

.

oo.t1 on

a-F -: 11

.. ;t:rs

-For

eh di .to iss

;r row

bs dots-i :L rod, Fl çp_iro

No . S

I... ...__ - . 1 4.. -

...-I .J .. (Ii ..ii II .. I .1. I ..J I .1. .. ... llS ...1:: I... .,. I.l ...

I I I _II

'ii

IL H IL I I'I.. )r L. ILL

-: ":j-t- _{'._..F} -:ini

:1. -to.: -s I ri.jniborc-::torts, N.:L i:li'i'

:i 5

I ii tho

1 c...-t I or a-F

tho t.srort

zo I rt oTobsd

...:...I.. I.., ...-- .1--i...

:.,..I.J..:J..LIJII.i

-:I'

WL_ii L.y

.:.i.I:'iIl.Li.Lii

...I5 .1.1...

:n-'nu::or ;.id

tho

'-sot I or oF :i so. ini-t: C)

tho

marts on

ssbod

Tha

-Frsot ion a-Ft h's

socimsnt rot

or

ss-s1:.ad:. s- ti"ici-:'ri

js-:d

t:)

,-:::;:i I

I :to t"io

-:: rind

:: orrd:Lr;ts'

a -F

ta si: ;.t :i. on

'...' :i. th ts -Fc:rmi..L].

:i. van I1w

I -us

tha

.::c:::i:i. ri;;:tos tr-; ...-Fo...mod

to osrti

bound ooar.::l :1. n;tos .

Tvr Or'

Ti c: -F

thIs -systm is

:i r tha

:-.:L ....-o

tho

:!.:rc.ith - of

tha shrFt

...:' ba

zo..:)u-r-bac! -Far' . :L - w-rs mrjrc' :L ort _{-From ;s} pro....

irr1mini:i point

of vi'sw

tI-a n.mbsr:Lrci

a-F f±a

x ;srd

di rirts-s

strrt-r

i t-

:: :Lr

ti

or i çJ in Al so -For'

ras.c)r t1:'

'.ib.sor-J. r. : C:

-For tha s.r:-thbo.jrid

000rdi.----r:-- Fc)r'rI..J:i..r) ..,.i

';:1.'i]

i3O :. '::--c;.-::Lc:)-:r :-I

.:]_::Ini.:

-bI-is -:.rr:cii"'

-t:---:- :i_c..:L--i.;

-...----I...

- :I::.a. I, _i_,

X- o'::-s

(>/1)

. (I;:,)

- _i:j3:.._-- (

ijI:'I

bo I ':)o-rir:L c:'nis

;''-:

rv-s:L -.-.I

:iia

I ar<!:Ii C: -F

:. :-.-:::IC-? kod . :: -!: :L -s

: orr th;jt tiio 1 ry-i-:h

s-t

I f (i ii i. Ii i 1

_ I I II

os l.-.:. I ;t5.-j so.-r.srt- I oriçj!: I"

iïst:is:'v-

::-::j.-:.:-t::

:1. r:c ----1:-rn!.: ,

ti

p3. ri :i.---a

.-s:: :-s .rs n

--- :;.!.:

-:r

:Ir

T-o .;.s s-s :. e:, --o _-nos-. :-F

io' s1

:.

t-;b

c:--

ttz'

-1I;EjiT-i -rind !.his sp.r:Ln.

.::i!::-..::ni:i1T-.; :jr ':- -E :iE- -.:1.s .i...

0 z LOCATION O' STATIONS x x

N

x 4

_N

5 X6

'Nt.anqent pOini

jrn

diff

( 1

-1

₁₎

[?igure No.8

segm 5 1 2 4

0

₀₌ S

d: 1' 7'43 F OR CE E X C UR S 10 N: D jAG:fl AM

dla :78mm

U3 QUALITY

d: 30

d

70

0 8

16

24

32

40

48

56

E XCUIR.S 1 oN FIG LJiR.E No 9 kN

800

600

400

.20 0 U

The spririe; oorstrL- -Fal lows -ram the 'elation

,

.iiere

'F

is t!ie f

1.20

irit.:'emerit ::'a.:oed

by -e

IZC0I0Tit

Th

sprir

oonistarit

ari

be found

_{from the}

_foroc.

die--piaoemerit 11ot

This plot is

_{oonstruot.d with ttie}

_aid

of data from the. Fu1 3. y dove]. op.ed

teriary

arid the u it :i

-mat-e

s lack shape

See fiui-'e

_{no 7 .}

_{By di. vi. di. ri.z}

_rita

ecp_ial parts

the

di spiacenierit from

the

..ii ti mate

el ack

shape

_{to the}

-Eu I I y developed

0TIO, rL 1:

s

pose :L b I e to

oalcLllzat.e for 0.21- part

the force F

The result

for

78 diameter

U3 quality

oiair cable of

wh:ich the

pai....

tioulais are

qiveni

j

.L

rio

J...own

j ...

rio 9

The -Fi <iuv'e

shows i:at-e

spr t. ni

coo f f i ci erit

:L

nor...J. :1. near and var :i. Os w iti-I t:-G:

w-:tei'

e:t:-

1Th 'jo

como:ire-:i to

the mass

of

s:L;:- is

flLEl.L L

eTce

the

able

i.s a weak ..priri

iThiL.:;

... at the s-i:ip. car be

I_._ - ...1 ...- ...2-,

.2'..i1I::: .. .e .. . ..i :.A I ... J .J

'.':ih

t-...

;iiiij t_j.i.

tiie

(LiçJ

cc::eFfi..o:ieit...

ba ;: :1 ni.L - thO n,..rbLIra :. fre.q'..iency ) .: .-.-.

Jr. I - I I 1 I I I I

can bO WI' I ttri as

Wj

Nma

i1;s .s"ip.

:ir <cl

flia-

-i":i;: :Ln

spr'ini.:j coo ff:Lcier-b

1".::.,lI:1:.n,-,. - _. .::.C:i./f)

in

It -Eli -sc:

dote--rn I rest he

s'....e L:c)Ijndar I es

wN, i. c! -I rlf:'a:-Iljc.?d

_{i ri the}

coij:u-ber

rn

I

s obv I cue

that:

these bo'.iridar :1. es ar-:. on

_{the one -and the}

1' . ni-rite s] ac k

arid on the otiier Nanid the

Fiji iv

dove loped shape

. ')i. th :1. ii

.1..IJL...C I...I .._: .-j -i._'_i..)&..Ljji.' 1 ..._. -i__I...I ...

L) Iii_

1.001 ti. 05.,

0cO o1'at:L ...

far

-: si- :Lp

at

anchor makes sense as the

-Farces I

the

ul ti. mate

ac k

hope

wi 1 1 be

ti' lila land those.

:ir

the taut

case

which

lean

_{extr-aor'dlnary}

s:L-buat:i'::ni,

too

Nih

!ere -For

the p1 a-b

yes a

3. Ocal:: on

arid a

har : zont.a

ce ar-o'..ird wh:ioh the:- ship oar suroe

- :....:!-ite

p-.c;i.rr

i-q!..: :L;:-s

bci

:1

i:::

-F the ham :1 zorta I

an:f vert:i c-: :1

acoe3. erati onl

ai:z:!_e

_{1-owse pipe .}

o-.icu3.a-bi. an

is done

_{for t!-io}

_{urdc-:-r' water ::-nlrt}

_{a-F the}

)

Is

h.;Lri b1

ii:

i.s

;ssUri:l tizt. ttz

.

:r.1s.tic-i

':

F the

p ripe .:t

1: the '..tr

.1. sv.

Twa

i':r:s.

E

hoori

fD

the

.

"te

.e1er'tioris

The first

riiethod .sr-'..:mes tre ±nput

1np3L ho i.c'orL..

c L nL?t LI(I L. .

.:.scri,J

is

or

the

:Lsp:Leniert

of the

-wse p:i pe cu d by the

u

ion of the sh ± p

:ir ves

The first

method .ssumes

thai: the vrti1 motior

01:

t!ie h.wse

: p

fcI.

:r'o fri. I

of the

trc

±

o Tl

me rs

i : or ri U

epPessed D5:

-i ;;::,. :i...:.J

..r::

ir

t

teL re 1 Ti :L'.2OTiC!S

ri' i'.

::' ri. :vtv: I rIc:t: :. cr ci. :

ir.

u1c)i: irrr ..vi:: ...::j L,f:

:::.e..d b.

:. &:) :i.

ti.nR:' :.r

.(:r:i.i.s

:Er bi:i:1- ivI.v:!::;.cT , 2:. p.:i.i .i.].:L.::t

is

'..''r:

1 0.:ri

.1... .3... ...I... -. ... .1.. .3...3...- ... ...

..3.:::

.,.,...L)..:II.

L.: .3.!

...

cc' 1 :e..ivv:t ci. c:'r :L

i.;.:ri

:ecri:.'..it ri. I me stej::.

be

4

They were:

be

± ri

t i.

. ye I o-I.

op.orerits

.zire

set

zero

;t

eh stati':ri;

the

± ni t . 1

d:. rst±

nre

ob,t;:i. red

For

st..ziti

eq'i 1 ibr:Lum of the

..h.s:Lr L1e

the

e1ertiors ire rtirced,

:rt

Ls not

di ff:Lt..1t to

see

th:Ls

niethod

ampi ies

th

the three

sumotioris foi' the st..i

ic:r .t the wr

rs .t time

4:

= 0 the 'elo,ities re zoro

the

.00rd± riat.s znre

f:i. <sd

.zr.:f the s.00 er.st:. c::r

_{:L s rots}

whi..h is

the

orre.t po:edure to

st.sri: this

1.. 1

tioris

:Ls shown in

2 .,

The h.est 1oticri to sbr't the siI'jJ.stior

is when

h.ise p :ipe is st the

top of ...w.sv;s snd f...thest

sw.sy

from

the ri'.hor

.

This

hi

by ::c: ...

r

the

vei"bi,.-.:L .n.e:Lei.st:Lonis

sss:Jr .. ni.. <e.:j ;mr :J. :. _by

. I 1 .. .11) I iii L

:i.ri

th

.d.ni;:in1.. Fcie.C.. :ir h.s:i.ri .ss1e'.

v'os'.jIi:s will be d:Ee..::u

in

r ...h

riiI i.:hcji.: : lic:r:4

if"f:-bi o .

I !.. or

':hL: ;i:b:Lcr c)1...s iiI::.

ii

I,l::.j.

c: F pit:h,

rL:J. y.s.. ..p;:1..j. ..;Ji:. _.snd

sway. The d:s

p1a.:.omert

of

I.:1-o

swes

pipe

is

my

I ., . I

mots. o L. .. i:,e:;iIsc...o maTher;.nt:;. ca.... mode....;. ...': _{d :}

iiOn-s:Ljri;r1 :Lni .

:.1.s-s

iictirs

nicit...3.i..jdd

F...the s:Lmp]. :1. fd.at:L or

is by

.sssum:Lni.i

that...

p :Lpe.

i

1. o:ahod : n 1:hie,

.itrs I i rio of

3. . neeci

ncj .:::::

to ken :L nbc:'

1s r es is

biot:

this

hior' i. zc ito 1 di ;;: :L siomsnit

si:!

,E1-b:i,.;n1 c:)n

i?55

ii.d p..hi

::T t::c.:.

:ibisr

;.rip.

.7

:

ii'is s!::

f 000r.d :i nib

sire .:..;se.d Tics :1. -st

st...earthi

bcjurid

the

otcs ...F:ue w :1. 1 1 rise I I

as; tto waves

55 ...

ship with

_{a Ic...word}

speed moves

with

':ssp.c..:i:

hc

t:hi . ...h; Ln<:l T1-i or(:l

soft

c:jvs Wi. th

ie

:d a f

lbs

...:L.;:Lri is

taken

st...i'.5

1 ood wobei- 1 ire

ob;ave .!...i

ertre

_{oF :1. by oF}

the shi;::.

The th:ird

set is

lo.:ate.J IT

the cent....e

of

<irsv:ty of .1.4...

ship .

This is

:1. r

Ii

ijris no

:L 0 . The

on

.s drowi

the

fac: ..._... .I_I..._

_{di rcsct ion}

rc)tst::Lor is hsfr.n up',,'ord

This co:Lric±des

with the dire....

.:::±:i on of rotot i. an whi :i

was to ken

fo...he:

coor.:Ii rate

syst:em used far

1:

.... boris....y equot ions

.. ... ... Il _..I

V I . .j .1. I I (.) ..J. II .J1 . I..)j. Ii . :: 1 .t '.' Ii _.. J , J I' .1. t:Iii:ri ::t':e i.nis:i JnI s ,;:L;;; cs-F

s heave

1:L :i'.jv' :L . v.v' :L.;bi cr

ir

.Ji.;p. I

mrt

f

p.1 p.' c.nr

w. ttE?r

= +

(:-c:ee)

-

+ x.e.nA

(1

(20)

T-rs

forrnuiz

b

'writteri

orsr.1.1

=

IZh

(2:L)

II . I I i .41 II. L. .... .J I I... l .1 -t . .

te horizorta I

ci

it:;Ii::

f'ai

rtr

of

p':v

:L I.i :1 I:cj o

ïd

i:i:.;rm..

::

Az -

D 2c.e

Th

:ci'

i:o

I',.o ci iazrs :L or.n L

od 1

1

bli.v 1 c:u'._:

4...

c: .Z....ç:,....L.:. p :.r ,j;:1:. '.rl b

td.c':d to

.

... ....4.; . . . .; .. .'

flJ L ..)I ..t . .1 I I I t it I I

W.flvE

ISt

i:i.ii1 .

:i.i: iz:Ic:kI: c:r].(

rs

1

iLc

t.o

1: :;.TJ

...I.:.c...

::L.:iir:J

I:.;.:;.i.rI

p . ) !i

!:.:cv'j'

:: nip. ..

r.:v . ty

t.-±c

.cp..i.

.I

-

cos (k1x-c,. t)

(23)

ir.:

!:.;J

::

!::.,t;i

. f ri: :L w :L

to

:i. p.

-. ...

. . !. ...

rtj IiiIg.

...:.-.I(; ,.fl .1. . .t:.(I :,

-

_{ce (k1 (x 1-}

_v.

_{w t)}

j

i.rt: Fo....Ij"c. t:u,I:n ci :1. Iuior :;.cir

I

:;. rI:c _Ic,I..Ii;:v Iz:I.:I

4. _:L

-

t

v

21

U

COORD I NATE SYSTEM

z

Hv

z 0 + x

= V.L + x

9

Figure No.10

0 z

A

'DISPLACEMENT I1AWSE PIPE

ZI

₀ z

0

G

Ps

t-

_shl:.

i:

.rR.licr

'cicis :roi.jrd

_ir

qiji I :U:rjjm

pos .t:.or te ship' s

:1. s

to. be:. Zi'O ;rid

,.=

a.

(26)

Wir

ob.'v'.:!

.t .i

fi.>':I po:f.rit i.tI

0 th:r

(23)

is

writtri

S

-(27)

Or :Li

Lh :.i'cF:L

s:'.did

0 thr (23)

:Ls

wi'ittri

;jv.

itde :Lri

k

vo ri'.inI::.:- 2 pi/ L..

L

w.v':: :Lr.t

jr matrs

:1. r &Z'.iJ:)TI::y ::: p:J.

/ T

..f. :er' :i. :L r;

p1 :.:h

rid mol: t.

oris

:r f:ro f:s

i c. i. ( i iii i... i i Iii ) I i. L (I _IL)

1 ;:i.s?...:L:L1-I

. otn'

z =

0 =

x U x coe (

t-'e,)

(

)h ,

th: ;itip

:i.

of

Ji"::;

ri:! p:Lt.:::!"i

ct:Lo-

;:.tid SE., E iri.: _e pFi.asi

. .... ,. .7 -. ...

1 - .- ...

I I '.iI iI I (I (I L & ii I I i I I Iii I ii

.

di 5I:-,.:: l:.t.sri to .n...grv :

_t:y

rd

th:

F:: I :: :i. s 1 tho fo I I o'.. :1. rig icrmiJ ]. a z)r'2 h::L;rid

v':Io..I!:.(

.rri.::

.:i,.:,zI:.i.::L::r

-... .;-. .1.. L ...

I...-.. ...I I Li ..I I I :. .. I.. .

-x..ain(p. +)

-

-x.w2.co(t. b+)

z.cos(c. +) +1. e.CO3 (c.

A±h-Z.c1).ain(rLt+) -1.e.ci.in(.t+)

-o

It

is riot dfi:u It to detev'm :1 r,e the bo'.jr,

;.i' :1 es ;.rd ttie

.r.ous pc ir,t

c I

tha

t -i

' Hc -1 u Fc'

r'

J

.:nr,d

;r,

I e

i.iver

:1 r,f:Li:.i.4v'e No :L2 Ti-jo

f

shows that the trk h

the shape of ;ar oIl ipso.

Irsp.00l:ior,

oF I±i

foniuI;e (3O)

a t!-i.t

the

ilerzit:Lor.r,rot

be .:..l .'3d

dire.:tiy :Lrput for

L"ie dyrt.mii. a.r.i1i.'j1z,t±or

'e,sor 1%

4iI:ii.5

o ± nt C)Ti

:e

'_n've

..'ere thc

. c:. t

. a src:' :L i

X

.3rc Z

. :L eat :Lor;

im..; 4:re..s ly as

e I

j

I I.. - t ,f--.

.4 ... ... ...

1 .1 .. 4 .. I

.i r. pc:. ± rt b.e.a.IJ3:...r.

.:jrensi'V

.acmputs: :L

paL nit of i :L ow :L t :L s best

ho do fire the st.nirt :L nc time

0 WhOTI the -zwso p ± 0 1S

nit the top

of the '..,;ao and

furthest

from the

1 si: :L on a... :r.ahc.j....Th:L s

e.as±ly

be dare

by

usin

a

aorrEot1or

jQ .

I ara...L ons

ii: nnv tiiat,

:L r tie

::.nise si"ó,..r :i. r

i.

t"e

eai: .ar.:

;:. :L :o iict:L c:r

:ir:%.

:L n arid

;Jv'ge ct:L or

:Lri t"o

tanl,jen. a.:: : rt B .

ho ,a,.iter

p. -o.c'r an w : 1 1 f1 I c:w

tho tancnit

''am

fd then

.a].cn:: sL ::. :Lp.::i..::; :r.ni.k .

1:1. r 1:)...cr:Ic.nic4

f:c

ti'.a:k. ::n,

v.a iue:3

entered

:L n the formu lao ZO) Hor..ae

I jjp di

a:Lor.:; thc: 1.... aar :.e

u.p site t a

the .d±re...

:L.:so'..n

: nf:L:;'.jre

... . .

In. tin4

:.aae

:ho eoj:..ior

p,o.nan

3 .L

--

; i.:c: C:

:j flI.JOS ar; 1:ie e 3. 1. :L .L i.::: !:ia. k. . L..oa :1 :' t: c f

. ::r f:!c 1. :L ntc

Farm. I :o ) .an:i

i.ny

.a;:ea .ao

pass :Lb. I ..

In the

::;.iso ti(:...::p.::...e: ::.J.Iipt:L.

t'.n.aI.:.is

fL.t it

ecie in

.n, 3. Lie

Fcj...y ELt

:Lt:Ls

:1. b le thaL...e 3. oaat ± on L..F the

tanerts p.::: :i. rjts

B .ari.d C

is so near

to

...,o :L rte'se.at :L on

(i that

t he a 3.au 1 ationi

,

..itic:'..:t

a much

ei'c:'I,

.a.:iii:,r1±r

.

In t'h;nt

:::.ase I,!. .. _{:L a} 1. i rear Pni

lo of a

aompi.ter aal a'...

:. .nited L....ni.ak : s c± von : ni

the nio>t

oat . or . In tti :i. a

aori--to::<t it should

be rioted

t:

nt

t he >(-

is

in the

h i.

motions

a.ala..i:i.L:_on...a.nteni.a1.

,:..aIj:L;at:LOTI ha'.,'e

Tj

:::L Fy tiiis

:'- e,aticn h:a. t::

T:j be aL. I e

use ti-c

c.... knu:::w I odoo c: .i-i..::. 1

Wave data arid

in, ::, 'b:Lau:L.ar on the

ro:Lat:ioni bG:teer the

wav':: amp 1. :itude .n

the

ho.n1ie, ... .

.a1d p:itah

amp.]. :L"

.L.j.:4ç:,....j ra:L .d :

ri.: tho

paso .ara Los :15 1e,qu ired

The wave

a-flOW MOTION TANKER.

Fiure no.12

tior Ie?r

.:nç'i :L i:.e rird

th

eave, :;;.jr.e arid

p it.h amp. I ± tudes

± r

1 udi. r:i te phase

ar:1esi t Is

rot

-

. . ... . . ....-1 ..

1..

_{.;._}

L) ' : a. I I .. I - I .. :) .1...I..! .. .1. C.) I .. Ffl .j ..j

desi.cr ö

a ship Where

the mu jar Lmehav:ia

is

part oF

the

work ther the phase ari

]. es should

.iva 1.1 able . I

ar

ro

] able thur

J

in

c

'eqIJ:L

red

For th :1

study use w;mae

of

data on the

series 60 :Lri

[7

J arid by i.e

a]

This.: cr1 ..id''s

e se

. or or data

4

Results of

1culations

.

!:

':;... I ;:t :;. ar.. _{'...'h I}

:-ited

In

th i. s sect j

r'e ar

rs I on

a f the '..:...dc:rae

or

esir oF

arc:cr .ng systems

tar iercart

ships .

:.. .. .11

k the .%Ir.aC)V' I

system far

mere.Tharat sh I p :1.

.

...t

i.

_{a.. ....a.,} ... I- _''.1..._a..,,

,: _.,Jave.

!'

kno',.ri :i;f:: :L

;:::s ]. a

.. :L-Cn

;i,.. _..

1

...c.:ii.o1-T.. ,d:i.rici...:Lc:ri

:F

thC

;'y,.ç)'

:;:ir

_tc)

.7....7... ...'j;.L ..LL,i ..)I .1

:i..)L1s.a

s.L::

..9!

.:i.::c.i'

:isrc..:

::

I:I-z. ii...L.jezr'u. i: F::-3.

;;::::ira ::(::;!v...

up:. 9-rI

he

,:--Ec

c;rjbi:. mI..3t .r:Lso

be

liCence t::.s s:.dy

iia

_.

::.x.... Jc ...i_ii'

si:

I..

....I

.1 I ... I... .7

..Il....ILJI LI..)

'(La ...

o..ii

....Iu::_.:.I.,._ _L..

E?.aai.Jfc)I't arid

a cLJar ...c:Lty

çf

misac .

.

.9...7

I

...

... _{... .}

I / ( I..I ...j ..-. aj.... .. ...

;.ir..d .

rtfc:d.:.

'..,'()Ie i

T1uxe ..t...i':riL

::.:i.t''

1,1:: _::,;i::.::! c: :.:ivb..::)av V .

10,

I at :;. or :e:L'..,aar

the

',.. I rd

ye cc

.1..:

±;e

_a.,'av

I .; .9..

..I ... ..

_.1.'... .7..,.. ... .7 .. ...1 ...t Ii.., I .... It...ji IIIJ..a.,...,,...:. a

'..l

...I....t.);I

...

:t ri t.-V . ::.aptc

.:1ta

_.. li.. _'3)1

the

2.C)r loiried _{.3a .1. .:a.. I at 1. L....}

I van

Far are CD

tVu) Fa.Jr sh :Lps . be :i. IIO

I aaded

.1.. ..I . I.;.,...7 ...I_{... ...} i

...

.j .. IJ ._{...J L.}...f.' .,..._ . .: ₍ .9_{.i. U U} I

anchored

:1. ra

:o .rd ;:'o

.

:i:

i

iG)Lit ..: i.:Liflt3:...j'

.1C:).1.)'ie ...re

l-cJ.cir<

_C) 3 :. ... l:.s : _ki'.! . The :1-a :i r C)

:LtJ o : .1:rC:!

:reak

C) u .. Li

3 in

:ebIe ru::

I

_a...1

the

l:ce3 ,

.r lid so].'..Jt::Loni

:i.t:;..

_{t:a c.rI.:::..iIaie:.}

.9..I...; ...I ...L.0...7_{... iL' .. 5- .} (.9

25 l:y i.

1 i:t1i a fl: ha

i , _in.c !.1,..

of lhe

par

?riqth

-i-iIi

t;bie

rio 1 in.

zid.i tiar tha fora

T !-s

to

data

ii :i;ried

It ws

by us :L ri 50%

parart a f

:J.

;L"j

_{.rib1a 1:5}

Found

arid the.

v.i1u

of

the t:Lme

ei

:aces

C 0262

iThiis

::4.5 th;t

Far .

w.va period of 10 20 se:orids

the

number oF

must be

(10 20 / 0 0262)

± :.

:iciure rio 9

± ridi aates l±i;it

surce

.mp. .1. ± t'..a c: :;.:: c:

ma

rs

i ri 70

meters depth

;.rid

Fav'a of

_{882 RN I}

:assib1e.

I ri

i'li

:)

c:'l:

tia

.1

;riaii:

a '.:I :L':l

çeriav'.:ad !:.!:ha

:npii.l: :L or

j: i'o''.n

i. f:l:ar

t:)

:;aek the

rii..<:Liiuri ;i.Lri±ni'_irii ;.i1i..;': oF e d:Lsp1..:....

merits ;rid fcr::es for

:y:.rih st.:L:Lon : d:Lv:L::ftj.:L r

:il IL For i 1.1 . ...L cn. .

:ri ....ha

:star;.iry .

...a

t:L),

_:F .:. rJ ... I - ....I..

- ...1.. ...

. _.,. ., : .. . .k.JI ii... Ij . I .) ii I .. IL _..I: I - vic 3

L...:.

II f-' .-...l.l_ ...I...I...,

... .. .) II ..i .. .i I.. .. I I ..j.J I .:.i _ .. I .-.:I .. i.:. .. II .; :.i .. ., ..

I . ...Ic -: .i I

:II

a:. ep.t :Lr

Ia

whei' a the verti.:;.I motions

El u:L...

1:-i :i. ,NII:1I :1. :: ...

..' I I_.. I_ ...- .; ...1 I-. .; ..' I.. .;. .... .I...- I.-...

LI II.I IlI1. .1(1 I I I ., I III

i i :1. '5 r:

I

c i _{'' :} :: Ti .j s a I 'cc c. ns a F :1. n a :1 1 ri a

i:ci...:i.sI'y' :':: T:;.t::i.J s ct:.sL:Lor

'

c.'l:L: .I..l... ..:...: ....

1 S:IIi:i I cci 'cctit :Lcirr:rv Th :i be ac::''ccetad

-::he :ter.ery st.nrt-'ccc.

t

th:Ls pa:;.rt

r: for

ful l:- deve

I

...1

... ...71...-f ._...

: (IS.

....

..':. e..:.ILi I It

f1..i.tu.te

:i ri .c ccc :Lm 1 1 ir .s..:i thT

:: :L S. I .Tiiit.

:i. ritarest: ci -5 the

:i ciTi5e

3. Ti the Li 'FL.

t

I e.vr 1

rij

a.:: uIri..ICJ .... sliT.cck : ..jrta ::.

the

. i.

ria'For''.:s...rn i ras1i

strrct

a F t ':h;i I Ti

'.'T:i:.Lri

t:is ...'hor p :Lr

te io1d:Lr:;

:iC)c.d'.I' oF the

I t

:is.;':.a i't..irit

tc:

'::.a I Isa that

,ha'ci :he

nl'ac3 c'ciri .c.c:.:2r.r: CIT

;rj I-s

f:L Iv ,'ji:'.':e:L"

oi::.acf I:: zi pc's:t::L)TI, :!i;s:i.ri ':1.]. 1 c:';" cccariba.d

:iF :1 :i..c:L'i...

liJ..1ri

:c'4a'' ct'i-i .:.rib1'as. ci: ':' .,ji..cs..i t:h rIrI::c:i.rnI..irI'I

1

i..ii.

c'

I.it::cl

i:c !::l"u: c3ri:i .1i'c ricul:

' t::. ce 'i:.I;;:il:c:::.cf ::l:i ii I: ri::I Fi.::I-.':::::

ic Jc'lj.c:i..I.:i1- ... i Ti"i:L'ccc :c.'c j.ii

.j.jji.i::.

4 ...I...I...-. ....

.:... .' ... ..:- ,.., ...

.. '..iL I . ::;. IL) ,.. ...I ..0 ..I I L I :.I ... ::: 1. I i_i ...I

::i.'::1 are::! s..ire

pa' i

a.::: -:;. .'::i..is

:. i. :;. .:rIe:: ;:::: .:ac'

'.h

;;irI:':

It

::.

'at .':..

'

.1...I_I .1.1...I_II I )I Iii

70 60 2000 a kN 1000 0 0

DYNAMIC MOTIONS TANKER

Method 1

figures are times in see.

. -7 325 rñ

/

5 _{10 sec} Line force Figure No.13 m 65 31 5 ₃₂₀ Track position 32

m 70 60

fiqures are time

Dynamic motions anchor line Tanker

2.193 310 3.15 320 325 rn

Distance from anchor

Track position 32'

Figure no. 1.4

65

kN

100;0

0

Built up period

Line Force at water level

1 I, U I II 4%

II

St

I,

'a I (\.I

/

I 'a I I I Figure n'o.15 I I I 'a I F 5 10 15 20 sec

Calculation period is tWo cycles of 10.2 sec.

'5 I _I 500 'a I' I 'a 'a I I I _I I 'a f I 'ci

it

I I S I / I g

Force increase on holding power anchor 150 1

St

methOd 2 nd method - U 100 Pynamic load in % of Break load chain water bow depth amp. m m 70

3570

70

-- 5207

30 -o- -5.207 0 200

DYNAMIC EFFECTS ANCHOR CHMN TAKR

10 m

0 _{5 10 ni}

surge amp litude Figure no.16