Impact aspects in anchor chain cables and the speed when anchoring

I.'..I?:k:.ri, :1.;: :J'..L:Ly

:L::

:i: NIFr:iC:T fl:::::fc; 1 N th'K.O

I N LI:.I::

nND :;J::.J::::r : y

E:i.iil.

Ms':: , Li :):I. Ft::

Niv;.:L fl_l.iitpF

ti.str' M N

bOratorf urn vcor

CONTENTS Summary

1 Introduction

When ithpact oct±urs

3 Theoretical aspects of impact

4 Impact calculation

5 The speed when coming to an4hoP

Appendi> H.

References

8 10 19 23

Summary

p;per

.i:i:tri

tie 'i]ts

of

.t'dy

:i.ri:tIi

iI)1f)L .rid i.m.ic.t eriery i ri

ri rie±ior

b le when

..i

-h ip

is

;rit :iri':::hor'

;rici the nver.1cie speed whilst ari.:hoririçj

it

desribes the

ir!.Jn1st.rices

when in1p:t

o:ur's,

the

thec:r'et :i.

;ispects of

I mp;ct arid

Iiows how

the theoret :i.

:i

etmcnit

ri he used for ;.i ship .t

nichor

P.eca'..,se the sh:Lp

. s

1 r w.ter the. shi p s m:,....i. oil

:rd:i. rid

to the

Iieory

on si ip'

mnoe'Jvr :1. rii .nid

ortro 1

ic

:..ised

;irc1 ;cIdC/J

:. nic:.:'l:DIzt'J

:1. Ti tIi( c:r'rii'..i 3.

TIie

ve'.1:ie

çLIncI

;;ee.1

.I-eni .cr)i1i i niç

to .icl:oi

:1

w 1 U"i thC ;.ui. d of I 1 iw 0 f

OniSe:i'V;it1 Ofl of eniery

In

tJ"i :i.

:L

1.t :Lon :is used

the oi.jt come o

the

:i.mpit

iJ 1 t:L On

to

:ic)l..Irit fc r

:LvI:.T.1'.t wh:i. h czni ot:t::l..lr .,'Ieni

tte

.h :1. p

ieC? :(Dni.:: 3. ..1i:i.C)T :i thavt: 1 t :1 i.

e::t:ii .L.

:1. tc::' c)rii:v')i l:Iz.

ciid

iu:L c:r:I.y

F'oii

i:li

pc::irt of

I CTit1 /j./ )(i ( i C)I (I R I ii ,.lI\ I it I :4) I 'lii I.

of

the. wi rid 1;ss

des iri

ç

not

_{or :t.}

:

the

br; ke of

w :i.ndl .iss must

be ;.b:I. e to wi. thstinid

i.mt but z1 so the

ni:I when

the 1 o.d

:L s

.fpysj

.fsC)Fu1 the br';..ike to the

w I nidi ;.:.iss

Last

but riot

east...le

ti..idy shc:uw.s how I mpc:)rtnit

t

:L s

for'

n

proper des I çTI

of

;nr .nni:hor :i.nci

system

For

merhinit

sIi I :s

to

ta. ke :i. nito ...isi. der'.nt :i. or ni 1. 3.

ip.ts

ii J i Iii J iJ.fl I iC i

id

Ti J I iii 1 ui I Li i

h zt on the sIu : p

;ri.:

ni 'hor

:i.ni 3. Q1'i

:. i:onid it Loris

1

Introduction

Th 1 s

:p.ei'

do nil n :;. th

tio r?.SIJ its

ç .f sti_i:f.,. .1 Tit:C)

Iflif 1(_ iii I11j' 1 I nri

3 Li in hi Ii'.)l I

ii

I

iI

1 l p

u1 .nrii..Iior' ;irCI ti .n'..i.nic.;o :i. ini ior:L ni:i

It

:1 b.nsod

or

ni i:udy

:1. nio

the dos :1.

:Jri

of

)ri±ior :1 riçj ....

toiiis

or ('ier'':h.nnit sh :ij:s

by the

:i.jthor E]

The stuciy wnis

1 OflH L- I.)y ti i(

1'r

)Iu1Ii1C TirI.-i( I C)Ti ri I c iiie Oh J Ti(I 01 fliC 1 Ii liii l ii Iii 1 IC 'i II ic 1C1 '' liii L I( (1 I .Lni(? 1 i i L'JTi u I

.IC.l..I..jC.sI..)i.i(:fr. _{I:e rthe :1. ni:;i..i :1. ry :i. nito}

Iie di ;L?r' of the

ms ''Mi;iiss 1....I :1. ''

:1. ii wh :i.I"i 27 peric:ns :Lo

...ie:ir

]. i. Fe

ie :i. :)rI

ri'J'

:y

t!ie :'1i'iiriL...0

M.nir' i. ne: Ti' :1 biJTi.1:L

onIcer'n.

t:Ii:.?

'..o

o t.1O ''iiJ .1. os a f

thumb

to

itoi-ni :i. r:? tThe

:i. i':I 1 ?1i:1-I

':

f

.hii.IiC:'r' .:lin :i r

nini I i:st :1. c:it :1.

:i. ri(: to

c: 1 LIuo ::.roi;oTiI.: :I.T3y :(DZ11"

pi.iter' t:eIinio 1 oe ly

to&ns I tthe

sh :1. p s iite'

:i ri CiW

E TI tI-ic

oi.irse

a f tIe

:i. rivesti ft:i. c::'ris

:i. 1: be.me

qu:i. to

that:.

-

the ise

C) f the "ri_i]. es of thumb " shou :i

ci be. LrId0TIOd ± Ti

l)vour' a +

determiri :L,riçj

the

qui red

±;:Lri :L ericitf-

by

meris 0.1

the

E,teriry equtJ.oris;

tlie

des i gri ph:i. :LCDcpiiy

of

TihCDr 1 rici

systems for

'.tharit ships requires updatiricj,

it

i.at po I nt wh :1 Th

prompted the af:.ove

merit I oried

study. It showed that the

present desicjni philosophy,

h±Th

Is

based on

''E:qI..I:Lpm?nt number '',

omits to

take :i.nite

accijrj-ItIie f-ia]. d1.

OWO

0 t the

anr.hoi' arid the

orv ron....

mental torcel;

which

act

on the

sh :Lp

i :i st

iO

ii;

at

anchor .

Con :LJOrIt ]. y .ti

sr :i. p ' s master

iias TO

:L nis :i ciht...to

I h ip- 1

y o I

L- IC ri' i-mr Llm IC ti ii,i I rrm i ic_ I

pa mit

c: f view is l.JflSEit). s factory .

There fc:'ro a des:i. cir method

based on ti-ic holdirmq

power of the ane.:Iior arid

the eniviror....

Ic?nitZ)I

Ioi'cos

wh:i.ch

t

on the

ship at

archC::r was

pro"

poL d

Eli 11ie abr.)vc' mn L I. oried

p-j

t mp L mid m

energy

1.nm

the an.hc)v' cab]. o

arid the

avo1'.qe speed wh ± 1st

.T.iiicn'i. ncj wei'o

rierit:L: ...ed arid

s'.c.jciosted

that a

i;ep.

'ate.

sti_idy 1 nito

ti-u s

i.it: J oct ws

:ii' anted hence tN :1. s

2 When impact occurs

I niput: C)..ci..Irs w1uen sNm:i. p 1

si_irçj :i rig, siy rig arid

;nw

:1 nicj I)i.jr' :1. riji i:IiC

c:nis the sN :i.p

CDVOS around a ceri:a :1. ri

:l.c::.tiC:ni ZuTiCi c1'z)cs ...I"i? a:Ln oJ.C)riCJ

... jlt .

tIie

lia:i. ri

:1. sl::i :ht

t:::,e

:i.:

a

k that...

:sj...j n

hrPa i:;

c- Nhe zinidic'

L't;tccfraq .

'JIori

L1ie arilit:)r

I-c) :i 1

be ;j

sji.jdonu .:irre

I: 1. ni j:o :1. rit o

tE

niov :L r.ci

wh :1 ch

s

.1 C)teci

1. ni the

hawse p :1. pe entrance

arid the sti:i. p

w :1 :i I rotaLe arcurid ...po :1 nit

iiio

I::C:)ve

:lir' :i. :ect

ilt:)I. :1. c)ri :i. s 1;Ii(::'c.,'T r .:Ii..ire .(.(:)

':CDnie'TiS a :L2_:L . C)OO

tori

dwt t;.nik'

anicNioi'ecl in

itci' deptti

of 24. iiters

i:i :I.s of

Orestor' .

The wind fov'

was 7

0 + F..eai..ifort . The we]. 1.

was 2

meters

south

west

rho

tide WiS

:i ac k Ihfa

b-:L :Lt .

;i-in L.yrne

bay, 3.2

to 8 CDni the scale

tY'Ofli the 5c)i..tI"i tc:'

se

:1 nicf:Lc..)l:or

sI-iowod tI-iat...10 y;;:iw :i. riq ..vivera:jed m'Jre

than 2.5 dees :or

:i. iii.jt . Ii? in LiiC 1:1. i..iro I mote tl"me sef:Ii..ieruce C) 1

the

mc)t]. On . 1Ni

data wore

recoi'ded some

ye;:mv's a:jo by

(.pia :1 ni I-i. LJrm.Ci' . 'J:L t.1-i I :1. ; k :i. rid porm :1 s5:i.c.)ni

E !ave used this

f :i. cj m_ r' t?

1Iici.

?np].e

uC).Jt i:it

it

:i. Nc:) accc:)ijnit

for

:1 ric$ ni tIic: :L ci o .:)rm

;:11'"1ç). :i. ricj %\ii

f().' I)C'cIiDrmN

N:i. :;

3 Theoretical aspects of Impact

The

± mpact cai..ised

by

the sh :i. p' s

mat i on car

be assessed

a' _, /

-'-

'

"-

/

it / 7;__- / F / / b.

,

I6

.'

'

/ i

/

I,

/

/'

':'

'

"

I /

I

\

/

I /

I,'

'1

I ,

it

v

/

r _\ / IL 4

/'t

--t

/

I I

/

/

/

\f

'I

I '

/

'

/

/\

'1

I)'

B

'I

/

I \.

\I

I /

/I

fr I

\J

_\I /

//

_/

_/

_/'

/

\

H 2 CAL'ES 1 / r \ / ' / I / '4 I /

)/._

I

''

I-

\

_f-;\

-

I I _/ ___i \

/

/

I

'

\

/ I

r

\I

-

I

\L)

I -. I C '.

/

-I

/

/ S.---

5-MOTIONS TANKER AT ANCHOR

1 / I / I / L CABLE -, I QALES

scaLe 1: 200

Figure no.1.

Sudden Arrest of a Point i

a Body Moving in Plane Motion

4.

I:o:Iy movi. rig

:L ri p lane mat: ior arid is amoni:ist others

:j :1 yen by

(o Ld .m it iIi

H .J iw U

th&? sudden

onistra:i. nts on a

body aJ. te rtc :::Iiav'ater

L

in i Li

1

nnt i.Ui

ri'J p di jc( 1 flip' i. s

a

sudden arrest

of a

body In

a po itt

res Ll:L t

tcr'm :1 TIa mot:ioni wh :1 :h oris :i. si: :i c :i ': .1: a rotat :1 on

aba'....this point,

the f:ini.:i 1 ariji J.aY' ye 1 c)c: :i ty '..niri be .a 1 '..i 1 ated

rc:m the

L-w o

c.o ici v b iciri o I-

irici'l.-n mom'... ii

tcni a

iov:i.ni.:i body is sudden,]. y

i'r't:?/:I

:1. Ti a pc:i :i. nii Liic

111fllCT,t ) I 11)IiIii Ii Ifi)

)'iji it

ii \(.?TieI I II I ii

j i cij.iI

(Iii

:. 1 nv i t ii Li I iii I i

ttie

Th:i.s

f?rniii:s

?v.:L'j.T.:i,:r oF

nicessary I :jnc-ar'

I ripuJ. ses app :L i

t...ii

d :::d. nit

I .I,

:::;'.sce

I

:Lcr

ls.i:ini examp :i. h

vei: th

s'..iddv:ri

arx....i.: a

pa i nit: () a

body

of mas

M :L ru

t:i al ly

: rug p1 ma....1 cr wi t:h a

)u u L t II uIue I )Tici I I V' vcJ C)'1_ b i i ii

:1 ii

t:gi.ii'e.

ru

tie

is

iascnu i:.i'a:I.:Le:i I.i u arid

I-I . ciut ) Ji V LI V (.i Li I I 0 Imo ly 1 I I

oorcI I ruibes x2 arid y The 1 :1 run 1 mot :1. on Is a 'otat :1 or 0

I'oiii tue

:i. '.:i'..Irc :1. fu 1 1

( .... .- uj A1m

m, > :: _{A p :L )}

( _{- A ::}

y

Ey US 1 ri.:i

tI

)i...IS 0 .f: .iyi-ai: :i art :L 1: Ia 1:1. ows ...

2

.i:(...i.fliuj 1 ;:uc (I. ) ..inui.:J (2)

it

Ia...Lows that...0

nj. anuqu

lar vc10-ity :i.s

.2 2 2

(3

L .

iIi

I. v' a f . n

'vtL or

of i:r :1

eruc'' (Ii VOS

I iui:it

nuc:?f:iy '..F :i. I :i...e .:I-;inuç'e L:) 1 k :i. ii&b:i.

.iinid a fLer t:he

:Lm;::..ne:t

he abc:'.,e ':i :i. von tIie(:)ret:L ..aJ. t.iSeatmerut eanu

b.c i.jscd for the

requ:i. rIT th;..it

the

1 m'.i L rio

.re

le f :1. ned on 5l.A i t.b :i.

:ystem aF >cLs a f .

sh.i. p ;irid the

e.:orud that the

mati. on of

the ship :Lri water is

ssssed

For

the ship

ichthrid orthaçjor1. system of axis fixed

with its arid; :Lr

jr the

eritre of

cirav :1 ty is used

It :1s

IC)' Ui ii I n c No TIIC X- i - I LJ(Irl I c- t p1 1TIC?

a f the

ship arid

its pos :L t :1 ye

d :1 r'et an

:t. s

torwai'd

arid

:1. ridiates

...0 head:i nci a f...ie

ship .

500TId

r ic.jht"'harid

I IL)(JarI 1 Ic o I .. ' ' J 'I it I I

liii JJ.)I lii I .1 .

Ii

0/I Iii (.1 0 I i _{I '..} ii I'I I I0 _III

Tlie

.rid y

..;.; is ;;:Ire p.ava : : :i

to tI-o sii :ip

1 :Lxod

i. s XGY S iri..:e

or

.;:ir e twc:

Iu:iwi:e p i :es tIi:'

form'.jI ae are

iE F:i. nod

fa r tI"i

I::aIxii'tJ s ide wh 1. :I

:L s the j)O51 t :i. ye s :i.de C) I t ha Lom C.) I 1 I 0/I I Ti I.I IC? OTu I C? 1

'

i I o I

I io Ii I ou I. I ;o \or I. . i I I R- 'y OCfl I TI IO I ITI'I0 L ITI

The >'c.)cI'r :i.

uat,e fo ....h

hawse p :1. p:Ls a Lways pcs:i. t.... I2.:e Ic::- ::Ie f i ru .1. rig tluo formu .1:01....1. mp.ut ....e ::t I . 0.1:

p .i'e as1c1T.ecI

(C?Ti0rZ) 1 ]. y tIuO fc. 1 1 (:).' :L TI( nic:i::i. )Ti5 Ii;;:j..J tc)

I:e r.:ori:L del'e/.:I

the mat :i. on of Uie sh :1. i::. when she :1. s flU Ci'Cl

to ;nuhoi'

iheru her' CD :i. on w :1. 1 1 be

aver t:ie s:l'ri

arid 1h0

w :1. 1 1.

Fo.1. 1 ow

ii've.:i

path.

r::1t...0 same ti. me she. w :i 1.1

ave 's i:arbord du.ie to the aL....or of ftie proae :i.i.

tIu(: crt :1. c)ni. ieru

s at

uiuIic:'

Fcr tiiat

fl.

rut:) . :1.

I::

:i cjure rio . 3 shows the

m at :i. an when she :15 om :LriO tcD arichor

for pa ...anue'Iuor.

The ye ...)(::Lty vector

wIii.±u is ...u:iorut

tC;)

the path w :1. 1 1 ma

a dri ft

nig1 ç. (?.

with the headi ri

al the

ship

TI-ue dr :1 Ft and :i r

results

i

i ye 1oc: :i. ty omporuerit :1. rita the arid one :1. rutc: the. y di. re't :1.01 There .1:c:re the :L:ie must orita...i two vol.... :1. ty

vet.C)rs and

on':

rot;.r-tionu vector'

tI"ue sI :1. . moti CDnis are :1. Ti .nitoi'

ttie t:ieory a

sh :;.

uc:ei.jvr :1. rig arid c:)rib'(:) 1 ,

reF

d :i. .tritos ...at...o mass

of the sh

h;::i5 to

be .:orreted

.fy' added mass of sh :i. p

i. n

the

:i c:nio :1. tud :1. rial. , I Ti

the transverse y

di i'o.t ion arid

also tOr true rotat:ioru around th':

vert :Le:.a 1 six :15 throu:Wi the

entro o+ .cjravity

(:)

the ship

I i :Ls .1ssi.Jfl)0d ....i..:I...iO. added

msi-berms have the

form as

dos2r :1 bed in Ref ITh

They sire

SYTEM OF AXIS

V

q

L4)

Suden arrest in a point located

in the hawse pipe of a ship oving in plane motion

Figure no.4.

y

X-O . 05i71

(_L)(4.4+!)

(

f*. 11 ..i:i. c!

::; cIi.: :i. ty

in si :1.

T

'.:rfi

B b:;.uii

..IrL?r'

:kpt1i

:i.

iqLIi btweeri .erperid

. c'..

p.oi. Iti. OF

riti

cjr.v :1. ty

(7 )

ct:.

:or'ectd

nla!E5s Foi

rcjI:.t :1 or .rid

ricJ y i. :1. '.:)rl

;:is fo]. J.ows

rn=m -Xz

m7=m -1%'

=JgNt

:1. tti:.?

i:Li'.r i!yt

rd

f:i. e.. ic::'rnii.. 1 i +cr

:i.

it

I:.c ..r :1. ttc?ri

Ill ( - ) A

m ( v ) A p )

:i ... :::: .... >.. Ap..

E:i.ri.1 u':i'j1.v' v: 1. c-. : :7 :i.I::tie: .ii-,c-i _Z:-'

t7+mK.y. u-m7.x7. v

Jtc: 1rn,-y 1rn

TIie:L

rii'qy

b 1 1

F':m Llo

cl

r:rvzvL:i. on al

IuC'.. liii i1 c.Tiei ei .JTId 1 . t.I . c I v flL L Li....

rci ij

b fare ;nid

. FLi

est

i

k:i. ri?t i eT:y'cI.r

tIiE? s'jdder,

. rr

tI

I..'se p:i.piz

:i.s

1

ip:zct

rI?r'?1'f

[ri 1:1i :i.i; F':Drm'.J I r

iS

3C)

cied Fcr .:k:IaJ

1lie k:i..ri(: :. c

a

s'j.clan

;i'..t: 13

ori

c L 1 I ii )' 1 I I I IT I () I I 1 ) >1 _II11 I

11 Ti 1 diii .i i ic I .i my 1. lIc u' c I.I uc L

-al tl-ic

sIuip ha ...

ba co1'c:tad

d :L:: bctW0cTu

I hc cTu I c' I

r i'

Ly i ui I I I i I uci 1

Li Ii I

(11 so Il- i' Ic 11 _{ni - -} 1u I I ñ . i Ii tij I a

I I I

ot

.-u I IuloInL ut iH' iL 0 di iL. I o

l I

ct

₁₁ ii ii _i

posed a 1 fair tr m

For t10

pI..I1:a3a

al

:1 s ii.t'j.cIy t±ie i:',,.'u::

:!li

to ...ie

ia i.:1.

tiii'i'

fai'coi

;:ir':

1 atCI

(I 1sc) :1.1:

i.mi?.:I

fc)r

.'::Iie. III.11 ...u :LnuL 0 :i.i :I.

:i r 11u 1 ;:iic a 1 tlu ¶.1I 1 p 5c: '.' ti1 ( )

tI:'

cc:)i-1'ctCI ic)nIC?rul:: ': 1 :1. i :r'I :1 ..i :L

'7

J+ (4+y) .m -

It

£;1m

TI-.x. I. :1 rueL-:i. cTIc.:.1çJi ..1 ILO.'

t:la

..illani .e'r' aiL

.nd

tho

:1

cricr:iV ai'e

, 2

- t.J

yIrpac

rl-:i. tl-ueorc.i:,:L:a:L

of

impai:

(B)

.u.m+(-) .v.m+

2

9::

IMPACT AND ENERGY

k N s e

lOx

60

40

20

0

IMPACT AND ENERGY

TANKER

185

195

205

b in DEG

4

Impact c1cu1atior

With the

above ciive farrnul;ne

iomput?1

p'acJr'rn w.s

wr1t-I.-ri i LI I wit c h i.I i. ; N Lc t I ii t I u i rnp . .-rI I

1 I oiIC-I'IJy

ot

h .i p For v i' i

t. vc-]

'c .1

i c;

riri rO

b:i.ort

i;Eii:j.e ic: 1 c:i .ri

:Lii:>:iI

.T.T:I

:i.rI:e;t

ricrt3 ': 1 ':'i I - L- 1. on F or . I vic-d + i ii' r r

I or

t N ; _'.

'I

I

tie

'dci :i. i_i

of

yi';t t. cr

:1. s ;'..mci to

L: Ci, 24. X: L,0 TI

vi1'.ies in

ti-ic

tbic .rc

t a'it

:Lri ±:L..1l.Jr No Th:i.st.T:b.I.o

c.

fc:i::

c)i .1.

Y.1'

iTiC! ict:t::Lc)ri;i].

ye :1 :1 ty 1:cr .i

zonist.nit di' I f

.iTY. :.

on the :L;t

.iri.::I

ir

fiiur'

nO $

t1ic dri. ft

.ain.:1 e :Ls vEir led ini t:I I ± niei' .:ir.d c:t.rL:L or :. L :1.

:. '.e:i.cri fv'c:rii .... F:i.

!ji's I

c.i t:ii

1 :1 m ± c.::I

cnier'iy

.:oriti I ned in tiie

;nri':hor ha:L r :h 1 c,

both

ti-c 1 1 r:car .iricI i-ctzit :i Dni.:,1 ye 1o: :1 .y

i..L be kept

1. ow ;is J\C) I Ti LI i sj_ c . L cini ii . ii t Lt I. Ti

'I

I'i:L p

.irl-icr' ziiii

i:Iic, 5Ii :i: C(Dl)i :1. Ti 0 Fi iCDI'

si-i :1. p .t nor

lot :i. ors oF

tho i:ow depend or the

j Ci it L (I II I' I IV I I.) IL r L . 1. UT id L I ii. .'i it I LI I

nic:iL I irs wIi :1. ...Thi :1. nt....u::d..i

e I lç::.Tt

or, the

.:lI :1 r

I:.c me

to fi cir.e

or i'

bhL nici .i Fi:L p i b&x'i' ;iri dci

hc.ive:?:.ini: Ic- .T)n:I

Ii

WI-ri c:m:i. r14

to .iniho...e sh :i. p s

ni.t'

te ::; I

b :1 1 :i.by to koei:. N i. s ste n'ni speed. over

tIie .:iroijrd

:i c

:i.

;I

Iuri

bJw

ti(f'cI 1 cr

i .

I tted

1. so ...i y.T:..'

tilt) I til I

liii

I LI t si IIThjt I. _t I

:190.C)

0.20

2,5.00

5.63

:196:19.3 4396 S I C ti 0' 3U LI UU J 0 W 1 6 190 0

0 30

' 00 3 I

75' /

i9 I) J 90 0

U 30

I U DCI 'I '07 I .. S I'?u U i) 0 19 01.1 ID 351 9fl,O

0.30

?.fl(3O

5.12

23142.8

4462.2

190.0

030 25.00

.6.07

24844.3

5650.3

I 0 U (I iLl

0 1i

1

1/

35J0 /

fi..6V ') I

t) 0

tl 0 j I IL) '

/

'I_3 :1.90 . 0 '0 . 60 1.0; oc:: : .

499 ,

I i ) U U 0 1 Li iJ U 'i 6 36 5 ' 3 3 :I.90.0

0.60

20.00

s. s 28725.

6245.8

:L ::,o

0 40

25 '30 6 . 52 :3(33:1.0 , :1. 7437 :3 9 :1.90.0 :1.90.0

0.00

0.00

0.00

5.00

0.95

0.00

226(3. :1.

o.o

0.0

:1:39.6

19CJ 0 ci UU ILl OcJ .1 0

i5.(J

I 5)C.J

L0 11

0 Dii

S Oh - 6730 ' 190 . 0

0 . 0020 . oo

3 . 00 9060 . 2:3:3 . 5 190 0 (1 01.

5 00

'

/"

II 3i)1) ' 1 C)0 C) 0 1Li Ii uLi 0

3/V /

:190 . C) 0 . :L':3 S . 00 :1. 39 7181 . 4 39C) . 4 .1 '0 Ci L 10 i U 00 (30 79 I 190 0 0 .10

5 00

1 .1

'u

1 79 jQØ Ci 0 JO

0 00

'

J ti1

/I6

I :1.90 .0 c.(j T 0;, I) 10 ''(.) 5 . 00 i..j CII. I 5 LI . :19

'''

:1.4890 .I J 8 (j 3676 It I('JI . 4 'I 1 'O 0 (3 0

9 00

1 (3 I I I

V 0 0

0 .1i

UI 'iLl

I '.

I 1) I) (1 C) 1

jij

I '3

j

1 0 U Ci Li ) Ou ' I

' /

/'

TL.:L rio . :1

:r.MP(.c2T flND :I:MI::1CT ENER(W RIJlT3

Type sh ii::. :1.

L.cded tard'eP

Di. p 1 ;d rn.iss I

50.000000 0 kq

i..rigtti b

. p p.

i

ic .00 rn

I?krn I

. :32, 24 rn

C)rift is

. 1:1.62 rn

x .H I::i.l:e :is

77.00

rn

y

oord H pipe iii;

8.00

rn.

R.d:i.us .:jyr.t.:i.ori :i. o .

Deruity

;itcr

:i.s 1025 . 00 kçt/rui3

I,ij.VI:.V'

I.i:!:li

:1. . 00 i

::i?Lta I:

0 V z 0 ANCHC'RLINE SHAPES Ultimate slack W = q.l.f 0 Slack - ' -c Fully developed Figure no. c -I

V

F F V 0 p P F V F h

CATENARY SHAPES

5

The speed when coiuirkg to anchor

speec.i when

.om iniq to irhor

:::ini be

Fo'd w :i. th

the

.::. :Ld of ti

of

oriserv.it:Loni of ererçjy

FOr .

;ip

t

ri'tior this ciri be expl.iried ;üs foi.lows

The .ri'±ior

2hrJ in wi-i i h

oririets i:i-ue sh:i. p to the

.rihôr

:i.

represented by

;.i

dteni;iry .

The

ateri.iry

zissume ii. ye

Of

:i.:e 1:iv'ee ilii:es ;mi.

;hc',ri :i. Ti F:i. qi.ire

rio 7

I ni

t

f:i. 'st: pos 1 t i. on

rihor dh:ij. Ti

J. :'av? 't:i.

J..y do',,'ni

irid its

tipe is ::i. led

ii]. ti m..ite En second

position the

n:chor chain

is taricierit to the se;:,bed

at the

anici"ior su.nc ki e ;.irid

tlie

1h;3:IF:e :i.s

c. 1...ed fu I ly

deve loped

I sJ ._fr

.liipe

c.

I i'.

c. 'Ti t c'f Ii ihuv

init

ii

I

pos :1

:iors

:r ri th :i o jcs :i. 1:1 on pa ri: of

:iie

e:Tha:LTi :L3

C)T 5"

bed

The 1 ± miti niq taut

shape oc.'..irs when the ship.e

of the

"ii n I om

tti

.ri' I

o H o

hwse pxpo

. Li

'ii

1 ric I I ii< I iac i (IC) I i iowTi Nr i I

I II

.i t jut I i ii

wh:L..Thi is between Iie i.m:Lt:Lnct taut

;nnid the iijl :i.. deieioped

one

The. cateniary

can be.

J. ci..ilated with

the we]. .1. kno....

iteniai-y equai:::ionis wh :i.ch are, i :1 yen

i Ti the appnud Lx

nI c?.am:1e

of these

ciJ.cu_IIat1oTis is

iiveri in tab].e

ro 2

wh:L ch c; :1 yes the cha in

ienicjths wi" ch car t:e eected

for a

number of water' dej:ths

stab.1. e

shows ...iat for

70 meters water

depth the di

arice iy'cjm

the anchor'

p0:1 nt

to the

ocat :i. On

where the

Ti I i c '. I' I Iv 1cvcJ o; d . I.I I ' iiC.I. (f ii

:1 96 th :i.p

lenijti-is when

compar' :?d tOi:i

1 :?Cidh a

the

:1

:1. ch :1. $4 L!(J I... ::. cu 1 .nr's The

ircie

.

1 lows from both data

:i: t T I::.e

shown that...he enier':jy st ore<:i

:L ri the

e.itenar'

rc? lat mov :i. nic a str:L p,

from I:he

1 :1 m:i. ti. TId :t. k c:ase. :i.

tFe wc:'r per' Ic:)r'mex:1 a:ai.nisI...Ie hor:i. :onita L tenis .i. on :1 Ti the.

"n y '1 i'Ti LI I i)i rit it

ii

Ti' i Lrvi t i i ii

I i. /I].v( (i J (I I Cr1 liii I "i (it) i I ..iTifI

Ii

Ii' TiC) J

B? .=

I

(:1.:1. )

TI" :1 s q'.ia 1"...ie ::,c:)I:enit La Tiercly Lored :1 T; the e 1 CT

0.1: _tI"ie i1 oF

the

iteriar'y

ab.ve

the

id plus tFi

i I _ut I

ii

lIiLi

_J )i '. fi )i

Ii

Iii J I Ii i i ii ii I

I::ti:c; EvI:IIdI1 11"ie ::'.c)I:eritJ..TiJ. ui..ai :i. ...

Liiij lIi

iiu

iIi

iiiiII

iii

L IfIT'Qi I

;:i TiC 1 1 .zin i: L:

nc: the

::h'Yt

cTic'Jy 0

1::II}:z 1'S..L.L :nji .I:C)i.SE oF w:L rid,

c'.jrrerit

:ini:! Nii. cr

tic' ii:ij;

F.ri:.1. ruc

Type sh:Lp :1 c.lc:I T.nker

R.?ql.Jii'?d iri.tl 0 '.I';.i:L r

:1.

Type ruIior

M;i; irlc:3r :1. CJC:i (DC)

I_If.:

fz,toi'

1. ':1 :1. rig: yic:I0r 882. 90 kN

rflcIc.? Ii;1:Lri LJ3

C) :1. ic.ri :i..ri 0(J rum

1:u. e.::u:Lr 1 39 ,:(.J

k/ru

l) T i i. Li.' ru in i I 73 iD (10

ty

.;uL:.y" 1. S 00 k.:I/m3

I):Lt.ru.

L_rt.i, f:..rl).; ri ii ::.t..1.p:.> i' :. pc :L0,C)i::) 5.4.7 121.82 66..:T. :L22,.36 91 4.45 20OC) 10.96 :L72(J9 4..:i.0 :L7343 9.,94. 0 Oh 16 hO 2i0 '3 I I I L / /' no o

i: 7

i

ii

DU 011 _/ 4

', I.

Lc _o I I ') Ii ç) 60.00 32,81 2:96.75 162.27 304.69 166.61 :1.1 .08 70.00 %8 .28 32C) .18 :L75 .08 3%0 .17 :1.80.54 17 ...3:1.

6000

341.92

186.97

:s4.,l.o

:I.93.e2

12.88.

9'::) oo 49 2:1. 362 . 27 198 .09 :376 . 77 2(J6 02 :1.3 70 :1.00,00

5668

8i. .46 208.59 398,41. 217,85 .1.4,49

13y 13sl.jIl i. ri: t:Ii r?13i.J L.riL c)voy' :I :i.

= F

diri

(1:2)

sIii. p Iizs

ki T Ee1 i

rir'.y

:1. n :i. :i. c:ri1: tjj.:J :

tic

iri:jy

_:i.it:L:ri

r- ... c .... ....

pf kb pb

(? ' 13

E., k.:i. iit: :1.

OTiy sI

:1. ri

c:)(':rit.L;;:i.l. ::Ii;.:Lri :i.ru n IE kb :1. ii:t :i si p:i.T l:::PCb ::'::.?rIl:i. Ti l'fj'./ Iii:L ri :i.i B

By defi.n:Lri

tl;:

j:>Icio. of

'.ro

p.q1Tt1:I.

?ii('..J'

in

I:c)1%:.t::.c)ii c: ::lic:

Ei'.i1.r

::':

E:KO:::: E:kb± b (14)

iIi

:,Tu,rS:I

cf

:.lo 1li:i1:: ::.:'

Foi'm..i1.:

rio S

W . tI"i br' mi.J]. ( 14) : t:Ls :xDss 1. b 1 o

to

I

I

t:

rn ]. o: :1 ty w :L th whi Ii

the sii ip :n be rihored

To do

130 :1. t i_s ss'..imed th_r: zi Etc

tNc

.ini:hc_j...; dropped t!ie sh :1. p

; rr :i. yeS :1 ri the po :1 IitS i ;jrid

B w th ;

1 :1 :rIe.ii'

ye 1oi ty v

I v b el r(11 1 )fl1i _L

r

I b L

:i.Ti ' b ;.ni::l

r

b s :: :i.l: I. e 1.o 1 i..i 1. .!iO ,.L c.:

r

f:,c_.ri1I::LI.t.pi.s nlccle I wis wr :i.

t:eri to

:1. '..i 1 :itc Form'..i 1 .i ( :L 4)

Iu1)/lt I W 1 fl I C L. i 1 I I I

I (i 0 L L f' '1 Iii Oti1 1 it?'U c 1 0 I t , ii..) (Ii I I huh

ii

yw :1 TicJ to 1L-;.1rl:(:u;i1rd due

t

;::rope :i.:I. er' .T.1t :10Th t..kO13

;.Ft or' :o :1. rit: Thu.s moalnis

hut

i.s

iurt.i on of v

on :i Thie vor' stor'ni ye 1 OC :i. t:y V :i. sti wlieni

E.uib + 1::. pcb : o (:l.5)

r.:hTj:j _{I:eo;:i'_I13i3? :1 ti. 13 ::c:)s1th I. e}

thiti t

_.i.s

fi od

.0 1 Liv' 11 I Oc I.I. _' .1u 1 I) 1 I I I I I I I) Ill'I L) I)

zi fujrthior rc.qu_i I i'oIh1onit

for the

cxi. ston::o 0

V 1111.1St b.c?

(13) :L 2

TN Fc)i'('..:l. .i :Ltii

.jli :i.i

Ll:? L by be 1.

iL.:!

+ Vh2.1ZZ. - (2J+ 2.Eb-2.F1.dis

N

(:L?)

1:_ci Form'j 1 rio :L6 :1 t I. e;:ir

th.T.vb be pal: rit :

1

orv

tle

'osl..I J. 1.. .:rib

I'cT iribi 1

Fc:ui

jist

:i_1.Tl.

or

sm.1 .1. er'

t'Ii;ri

pcDerlt i.T.i 1 energy oF t1e

±iairi

rer'e for'e

1hj. Fc.i :i. . :1.

.ri

:1. rid :i o.Trb. on ,

the

nerg.' of

the

:i n '.zb. 1

± s krio.r

, a

:ic

'.irr

nv':L oi;inut

.1. i

..'h :i e.l :1

i...CI

:Ji_:r :Lnic vlc)v':Lnc

Tlie poI:crit:L:i :L a :1. r o fc: 1 1 ows

Earn the

CCi;Eib . or ;inc1 ;iTi e.T:ilrij:

e a f

v.:i :i i. :.

1:;:I::ie rio .

tI' v;].i..i

loiS the 73 mm

:Ii.im:er'

olv.:Lr ;st:.1.e

lrom t1i±s

.1ïJ

th:: vo:Lues For

onii of 78 mm

di. .T:moter

arid the

imo 1r:idc

;ire

sot a'..it

:i.ri I j ...o ro 9 IThuo energy

ourves ;.r'e

set out...tho ...i. c:n

i. ni

the

..i :i t iite tflut

shpo ;ir;d ttie foroc

ourves to ti

...:1 or... y

, i

'I I I I i h Ti I.) t I

t-I-ie erier'cy.,

oijr'vo

: ... io ;i'eT.l unu.::Ieï

th.

l:)' oe c:::l..Irvo :Ls

1. :wi. frc)I11 c)rini.J 1 rio :1. :1.

Bd OTI

Fc 'mu 1 .:.i rio :1.7 .nid the r'o.qi.J :L remorits :1 von ;M::ovo

oc:)mp'..Iter pI'ocjril wr :1 ttOTi w:i. th wIi :i.oh :1. .t.:l.:T. pass lb ].

to

c.T. 1. o'..i 1 te the speed when oam :L ri

to

iniohor

The phi. 1 osophy OT

wh :i oh the progri.im Is b;sed

f: _{.1. 1....)WS iOFii}

I: Ii.pI:.oris di..irinig ;:ni .nohoririi I.1ric:)?'..I\'r':?. r::?Tii ..1 lv wIieni ..i ]. 'CI: :i.

:iI'r' :1. yes .t...lo

niIio1'.T.1f.;ie the .T.urohor : s w:i 1 ked

oil: bo

ji..1.t:

obect ;.ri:I

I::Iio.ni .:I'(:)j:j:e.d I)'..ir :L.ni. l.:ii :1

j

::j :.

s . I

:ii l:i

ía i :i. c:w:L n<: .r

I i I' inc I y 'I if)

t)

>1

Ii I I i l 1 1 )i

I'JI-icni bi:i.ni :irc)i.Jnib cF iI.i:LT

J.TiVbi

:L

c:.jb:i.,:t

bIue

:i. j bhe

tv'ri

m..vomc:ril:: :i. TboI:l:.e.:t nici i.:lie b.r.n.

of

.inv.:Ii..i;

is

_cl:1:i?'J,. I"ioni

tIie I:i;.iIo

:i.s .iip.p1Ie.d b1e c.Ii;iiini

heooiies

t :L ghI: .nid .is 1re.n.:y oxp :i ;: seoF::1 an 2 ;.n

:i.j:,;:1o: o.ini oc.::i..r wlien

l:::.

.T:Ti..lic:'i' lic:1.:Is

ol l:Ii:?

r:i.sk

l::.:jt:Lr

... c':ri lc:

:1. rio 1. ucle th: Tier'gy rIiJc.? ba

i. mpt in

tli

1 t :1. an made

:Iici':i.ni

TIi1 s ini I::.e .cI:ii: by nisI..Irii:i. nic tI"i.T:it...ie i1i1c:)..ITi:

C) f erieIy

1. Ti

:Ly

;lii:::

of

l::io li;;:i:Lr ,:::;i::,

'sb

.LJJ.t:i.m.te T'zii..ih Cz:iso

I.r..i'sior

6;? ...9'K1. m

:i:c:.

:1C:iE:I.C) ,

T .b x

rio .

Type ship is Loaded

T.riker

For.e/E.nerçjy

'i's:i.

c:)ri 3. T.

:1 ,:I.?rI:I.

ri'.iev'

C]

richor'

M.ss iri.:hior'

:L s000. co

Co::tiori

niss irii.:tjor

:1 . 00

1.11::.

oIizi pC)wer'

rihc'

332 . 9C) RN

...f .1.... .j .. ..i i':LTi C) : riiei:. on :i. i

70 00

mm M.iss :1 ni :L39 . 20 kcj/m L) 1.. J Ii Ti it , )U oci fr :1. ty Lor'

:1025 00

k/ii3

',';.ter'

depthi 70 OC) m

RN ci.. 000 r L _0r

100.000

190 000

RN ii 0.. 000 r) C 1:110.2:14 :1. r.:1 m

0 oc:o

j

43 00666

::J

i)tJ C]OC' 21 i 9 1 ''9Ci 001)

5 o

'. I

0i

:oo 000

2926 266

53 . 3CJ4. :350.,

000

:$$oc) 5:10 56 . 45920

.000

3653. 752

55.403:15

r Or)C I . SaC) . C:)C)C) 4309 . C)74

so soo:

.550 000 46 5 , 524

57 45237

600 000

&r

Quo 4910 , 044 11 /

57 5o 504

'<

rrri

/00 000

9

'3

3 ' sc: . 000 ;:17z

₃₅₄

_{15° 19283} 800 , 000 5991 .

587

59. 5255o

850 000

6242. 035

59.82933

'Ju

'

03 'I C)

60 0

'

figure no.9.

FORCE / DISPLACEMENT AND ENERGY

I.

DISIPLACEMENT

kNm 1.0 0 00 8000 6000 4000 2000 0 0 15 20 30 40 50' 60 m horizontal displaCmeflt k.N 1000 80.0 6.00 '400, 2 00 0

me tt-

:i .:imu::'.irit a f erier':iy

i. r the

ha :1. ii aab 1 e Fo 1 lows From

the Ui ti mate

Taut shape

Ta

this amount

ar

be added the

strii ri enerçjy

:1. ri U it :i. mate ra'..it s?-aI::? :c n tt- :i. .. at:L or,

mc:e.:!e].

tra I ri enerciy

± s riot

I rid '..ided

It

:j. s

as'imed

that

approximately

50%

of

the

differeriae

betwer,

the

erier'cjy :1. ri

the ta'..it arc!

Fi..i 3. 1 y deve 1. aped shape :i. s used For

Lrnpa L rodlit1.rIi2 he o I..

l

mouri t c I c i 1 I I

:i t im.rte taut

aase by the

so found d:L Fiererice

the poter....

t:La 1 eniery avai 1 ab 1. e For arrdl-ior :L riq

the

S? :L: :i.s found F:rsc

the

_{:1. mpact 'a 1 ij3. ait :1. or, for}

t he ship

the

_{3. 1 near ari:I}

cDt-at-lanai veiodlty ji.it be fore :Lpadt

car, be Found

These

data in

then he entered into the ?.alculatlonI made]. as the

end ye :Lc)c :1 t :Les for the anichori nic speed

it

t?-ai_...

shi p .'ri.

itt-he

3. ocati or where the .iape

c:: F

tIie sn,i.'ho,'

cab 1 e :i. s fu 1 1 y deveL aped,

over's!oots

that pos it ion

arid

arrIves

at the

'..i3. t :i. r,i;:ite t:aut 1 ocat :1. or w i. th predeterm :1. red The

50 % difference is art::d.trary arid any value

car be entered :i ritc

...ie mode].

TI-ic Fc 11. o'.. I rcj ni: :L :1. 1...,;t:i'I:c ...:Ii :1. :i

Tab 1 e re 3 c :1. yes ...ie. d :i stance between, the u] t :i. mate ta'....

arid ..he

ILL

i

:Lcped shape

...2 479 m

and tite d :i. 1 fc:...

:i ni ener'cy 4107 86 kNm Thzt:d :i.

frerce ± s s.::?ed

:L

fl guro no 9

o :L

the

sh :i.p moves Fr'::m '

L tit

to

thc: fl]. 3. y deve 3. aped

shape tiiere

is

4107, 686 kNm

eniery

:Le ftiri

tThecha :1 n cab 1 e

over a d :1 stance

o

nieters

Compared to tie

3. enicith a FtI: sh± p

obv La'...hat the

amo'..init c:f .i.CJ7 686 kNm :L s carisume<:l kl.

arid tlieri

there

:1. s:i. risi_if fl dent erierqy

3. e ft for the

:i m;ct wi"i :i '.tu caf

fo 1 low when the I:x::nd bra ks. of 1li

w :L rid lass :i. sa:.j:. 1 :1.

F::) :i. 3. c:iw :L rci tIe i:?i :;. 3. (:).ic)p.I"y set

a_it above an

r:iruic:'..ir,t al 2Y7 kNm :1 ch

:is si :i.cittl y

shave the ci :1. 1 Fereni:::s al 5(J%, :t.s

3. c:'e:? 1 c:r

:i.iai.:t:

y. rrJs.. .:I"en

tlie

l;: :1. ni :1. '..]. t :i.r:t:: t:i'..ji:

Tab 1 rio 1.. ows ...st an

amour,!: al

i. npact

eniev':jy al

kNni a :l.io..'

fc:r

sri eri 3. :1. nea rYe]. oci ty al 0 20 rn/sec and

a

rot-at :1 aria : ye 1 oc :1. ty a f 1. 5 dedJi'ees

per

m :i. riute (1 dr :1. ft

;snicj 1 e oF :?. :1. s assure:?

r

it-is

assumei::l

that...e res'..i I i:ant

en,v:L rormerta].

ci", acts

ant-he sh:i p

1 s 40 RN Th :

Is

,jLIt c:.c:

:1 nij Fcjr':c: S on tI"ie sca 1 e al

Bea'.i fart

arid? ;, ci...'ent- el:

.r:ibout 0 :3 ;1,sec:

Tie

ïesi..i3;: c:'F t:?"ie s3..:'..i]..st:ic:ni .i,:id:I, :is ci:i'en .n, 1.s!::.].cr:

4.

siowstI",at...re

eric? ye 1....c :i. ti

ar':z reacIii

w :1 th a

:i. Ti,:I vS' iC)d :i. ty \ (D+ 0 5 :L in1' c circ:unid ecri:l

± s I?"at...i? iax :1. lium 1 0_ 1 :; _{J"j 3 3}

Fe...ie eneresy

con!:.eri: oF

the cha :i. Ti cab]. e

are ce*y

3. Ow

More

:1. mportarit...e Fttf-,at...e

ca 3. ci]. ated ye :tc::c :1 t:i. es

are

Oart-hl::.oi.in,d ! Tl"iere Fore w :Lth a cii rrenil: ye I oc :1 ty

al

o 50 m/sec

very

3. it-tie or no prope 3. 1 er act:i. on Is requ :1. red

to st-ta :L n the

:i ..:

:t:l cjrounid speed

.J.

ric ,

M(.XIMUM SF'EEI) .iF!ILS" iNcHoR:uNG

Type shi. p

:i.s

Loaded Triker

D::i. sj:.:I. .e:.ed m.ss is 500000C)0 . 0 k

Lericth b p. p

:Ls i.64 . 00 m

I2:;i

:1 s

32 26

m

:1:1. . $2 ii

oord

1 j: i. ± s 77 . 00 m

y

i.;

. . C)(J ir

.c.t:L'..is

s/'lI:.:)rI

:is

0.24

r)T1 1. 1."y'

is

1. c:) s

:o

k:j'in3

L.:itev' dc.pthi :1. . CJC)

:i. ru

eruei'CJy Ui t Tt

:i. 081. C) 00 kNm

CI-u;iru erery :i.

64-03 . 00 kNm

:::.-L -?rir..-

1 2227 . oo

1 t:rut rcv :1 r .

tC)i'e

5 40. DC) Kri

:190.0

is

0.00

0. 0(3

$2 49

Vs rii/ o . o :19C).'J

o.::o

2.0(3

0.48

0.9

:T.90.0 o.o':::'

4(30

'::i.3

0.9

:L90.C) c).13C1 .cjc:: (:).4 0,1.30

8.00

0.4-9

l.0

:190.0 0,0::) 10.C)Ci

0.49

IC)

:190.0

0.05

0.00

0.48

0.9

190.0

2.00

0.48

0,9

:190.0

0.05

4.00

0.48

:190.0

0.05

o,;.:

0.9

190.0

0.05

8.00

0.49

:LC

:19'O,u

U,Uj

:LLJ.0Li (.J,4-:'

1.0

:t.9C).C) 3,1(3

0.00

0.9

:19(1(3 0,1.0

2.00

CL4-:120.C) 0.1.0

4.00

.49

:1.0

190.0

0:1(3

6.00

C:t.49 :1.0 :190. C) 0. :1:3

8.00

0.49

: .0

190.0

(1.10

10.00

o.so

:1.0 :L90.C)

0:1.5

0.0(3

0.49

:L .0

190.0

0.15

2.C)0

0.49

1.0

190.0

0:15

4.00

0.SC)

1.0

:1.90.C)

0.15

.c1cJ

0.50

1.C)

190,0

0:15

8.00

(3.50 :1.0 :19(3.0

0.15

:1.0.00) 0.5:1.

1.0

190.0

0.20

0.00

0.50

:19(1.0

0.20

2.00

0.SC)

1.0

:19(1 0 o .20 , oci ci, :1. .1 :190.C) (3.2.0

.or

C).5:1.

1.0

1

't3

IJ U i) U )i, I I I 19C).C)

0.20

:10.00 0.51.

1(3

rolii ticz' :.I:. rio :i :1. :1.50 .f:j i :Lo',

thzit

ho

:Lrnpt

:i.

oos with tJ

i. :iot erir'.ciy o F

i si 5988

kN&

)Iri

tto

hi I U

ii

p L L lvi l' mi . I L iN 1)

w:i. tli th.t

i mp.t.t

The

ih ui

.oei Fort hose

i.tioris

:i:i of

450.0

Kri which

gives

3 . 55

(''OTid I nipi t

t rue

O from I ii 3 Tic.) I L pc.m.i N] c. o

determ i rio first

;r

:1 iii .ct arid

1 ast:i y w :1. th the

;ii :Ld of the

I nipict orierçjy the zirictior Irig speed

r1-ie :I.c..i]..t:i on

is cii ye rifor

itcv' depth

oF

'0 meters

For

water deptlis

1 ess thri utv:l. ue

the ch. i. ri

I.

iie .s

c;.iri Frorii

th:Le

rio 2. 1hiori the chi :1 ri

I ricith.

red'_io

I ho PTIC r' co(i :n nod

lhc _h . ii di i

;iis :i. :1 nd cc:.rseqi..ierit ly the gro'..irv.:l sp.oe'.:l m'.ist .T.i]. so 'edi..ice

Iri:reDse

oF

d.isLicemorit of

the

ship

ircreses

the

i. rie.rt:i. ;:

lso

'cqIl

:1 i'OS i'od..::t :1. Dii ...::eed

the

tTiL ni

() I l tO ji'Oi lTii ICO(1 I 1 1 I

L :1.

ilr

i. rive t I c.it :1. or :1. rito ITho of F ts C) F hor depth .T:irid di.

r 1

i 'i:n'ri I

Dr

hr

flii

nit im H 0 ITI u.) 1 I Di

si:ips . The w.i1ii'

doç:.t:hs wore bzsed. or .ird :1

:ime: the

dr.i Fl: of

Lhie hiip

For

each ship two

chai. ris were deter'

m :i. nod . ThcT 3. :i. cjhtest ch.T:j :1. ni was

be.d

or

the

eq....i. pmerit

riumbor . IL

csI

LTi 11 i oi o im hhnd 1] i

i coi

for

i..is I nici these two

methods were

q :i von :1. ri the ± nitrodu_....

or The . resu 1 t:s

of t-no

I nivest I get :1 or ai'e .

out

:i. ii

tib]c

Tic). c)

:i: ni :.octi. or o ti

te

: T

1c;thiit...lie

I...iosh care

re'.j :Li'c.,d Lc

.ii1icr' sh :i

oF I:hc s :i. zes

i

ni :1. ri

:!

TI::

The coric 1. us]. Ti

from this

study of

:L mpact _{:1. nii::ict}

erieiçly

aru.:i the speed w:i.th whicli

Ti

sh:i.p car anchor :i.s,

the!:: it

is

I y :L mportarit to conitro 3.

the

çrc.)uTid speed

rot on]. y

from the

point: of

v:Lew of coritenit:i;

of the

I.e bt..t a 1 sc.:;

From that of

the w :1. rid]. ass dos I çji

fls it

on Ly the

bra ho 0 f the.

w :i. rid 1 ass must: be

able ta wi. ttistenc

the I iripict bi.it

also the

qear I niq ',.,'lieri the 3. oad i.

..rrii"

Ferred from the brake

.i_!.h._ w :1. rid]. ass . 1...ast l::i..it rio!: .1. o.:ist

the sti..idy shio

low :Lnipc ...tenit :1.1: i_s For

a pro:er desicini of

ar aTichor :1 rig

system Iov' merchant

shIps to take

:1 nitc:) :Dr....

I Ici -it Oh

ill

ilc' l..

'hi

H Iii' JilL i tilL

i iid'

ii

.TIci'iLis

.:.irici tl"ic:? Fc:i':'e:: .jhi :1. hi

it:

:)ri L!ie iiii :Lj: .ii.: ini.hior :1. II

c:I:

c:J F c?ri, :1.rr...iriic?.nit.n .1 e.c:)nucJJ. 1: :1. ori:

M.;:1m'.jiii

2rc.Jrii::i s::d

.i -F.jrir.:t: :1 or o F

,j.l:i' clp.th

ci I

::i. .iirit

n'J ii :i ri ci :1 ;zmet&:'r

:L .

iti.<.i

it'.iti.ori

tbi: rio

5 Typ sh :1;::.

'.);I:P

deI:I±li i):Ls1i Mx:i. ri.im 1. '.im

c2hiri

d :L.. Chk1r

t:.z: I'

1 o..id

Ini-::.I::

Irnp/

r k

I od

m k::::L03

m/i

kriot

mm kN kNs mrs--

17 43

50k 0 . 09 (3 2 73

3990

226(3 0 . 57

0 II

0 /(3

YiU

7I

70.00

50l

o.

0.6

73

3990

:16362

:3.60

0 . 53

1 0

78

4500

:15988

3 55

Trr'

28.35

235k

0.

:16.

0.3

:1:14 8900.

32813

3,68

kr

0.2:L

0.4

:137 12:160 20:193

:166

IL 3

3i'

0 ' U 3 I I Oi 2 j

-0 D9

:1 . 1 :137 :L2:160

97522

8 . 02 8.j:Lk :19 20

87k

0. :l.6

0.3

84. 5:160 35(34

0.70

rr

0 . 20 0 . 4 :1:3(3

7060

5974. 0 76 . 80 B7 0 . 31 0 . 6 86 5:L60 22:1.05 6 . 28

U i6

.1 1 I Old

'J' ii

Co :19 50

49k

0:12

0.2

78

6500

2200

0,49

tiri

c

0.28

0.6

:1.05

7700

665:1

0.86

78.00

4.9k

0.37

0.7

4500

23888

5.30

ci. 1. 5 :105 77(311 3887:1.

5,05

6

Appendi<

FOr

th

reder

who :i. riOt

ited w Ui

th

:'.;iteriry

eqi.;it: :Lori. . br :Le 1

.i.rit:L)-i .rid s:.jmmry o1

ormu Lie

i.s cliveri l:-e1ow

The sh;.pe

of the

ricIcDr 3. 1TIC fc:Lr .i Si L p

t ;zr:hor

iri be

omp:ro.d to

of

terizr'y

The 'rterizry is the

shape ssume:d by j:er fe::t 3. y Fl Lb 3. e

11 i. ijrid Lht ii I I ILTI 0

ji

y I ITI I L .' _i

t:wo suppc.'....poi rits

:i: t . s LJIOJ ...;)t ti-to m;:iss per ..iii :i. t

1 orict-i is r.Oristrit

iCii'

ir

Du iO .-fl Ti I L ts I.I ic i u ni

iii

;.iriC:I I' 3. c.'e.r'

tIio

c:)In: 1. et:

J. (:TitIi a f

I"i.i ri

F..:L :L. deveioi:.ed

criry

is

::Fired

:1 , ret OTi rid

:1...cerit...o

:iihorsh.).

:iI(?cI Ii:I (D1:1or' CDii1O

Io

4:l.R

fl.i f 1. c.'jre ri::) 1. C)

ic:tI-o

;:ocD oF the

;toriu'y (Dr

its

coordirute

<_yI(fl

S :i.re the ':1ev' :1. v.T.ii.: 1 on a 1 tI-i

ritri;.iry

ei.:p_iret :i. ors :;.Dri Foi.jri:t :i. nu

Ili

v.rn' i. a'.Js .i:I:xDoks or tb :1 s sub .j e:1: _{cr 3. :/}

:1. vni

fli

Fc]. 1 cw :1. r.ci Fci'iij 3. ,

.lii

i i ri

Iie ripper

ci :i.x

.re '.sed

i ri

pper'

'.:p::: _ci x (rI-c

rI-ic) /rlio.

_J (1)

(Fh > :L03

/

q x g)

rsirh

(

q x

:x. :i. ) . : _:LC :::: _{(F X 1O}

/ ci

X

i)

_O5Ii

q x

_cj x- .' F., ::< :I.0

::.!.+.

d 4 (:j x :L03)

/

(q x

) (.3

:t (F, x

O3 /q x q

) x s:LriIi ( q /' F * ti::? (4)

0 ::::;'I

r sirib

( .x.

q X

"/ I:.x. :L03)

_:3 (5) :::: (f: c ₎

/

_{( .x.}

j)

<

:L),'lOoO.::: Fh xsjril

(

q ::

j x.

)'F

x :L:' (7)

F (q x d) ,':LOOO + F h (8)

:. (I2xq*

Ix:I.)/:1cjCi'J..t2.>.Fh.:*

( (2)

)t

Fcjrmij1 (9) :Ls i.JsodtcD

1':Lfto

tIi

p_;.t....:r.h::..i

a IiO i'..:l 3. y dave 3. aped ;.Dtar;.v'y

wi-iereby the

zero

:i. OvO 1. E 0 nc :L dos w :1

the

or :1 :1 r

a F tie system

of

I J.l IL Ti thc V( i Ci 3 V( I .)1 ..C.)tC(i1J iJ

L (ii

Iv .J I ii' ii IC.)

I C

IIi

iI

liii iiC' I'

li

tIiTi

Iii'.

i

Ii!( I X A X

z

The catenary

I /

Figure: no.10

F

F + dF

V F0

2c:

::, L::L ricj

tli? pctceritinJ.

o f tHc? :i

.LJ.TctI

of

.-i L)I, I

-o I.o

;ijht r'_t-k?'i

ñ

II

i

1

'' irid

I 1

or m'..i J.

(9)

Ihi d :1 nris:Loris

ire

dris :1. ty :1 I'ci/m

Iic..

dris :L ty

ntr

k.i/ii

::::

rnzss '.li:Lr

1Ti .1i'

k:j/m

:: I1Zic.S CIi.) i ri :i. Ti tEy'

d =

wter depth

m

::::

Tct.3. for'ee OFI

_{CIi.T.J. 1i kN}

VE-rt 1 iz]. component of F0

RN

:::: Ilj' I zorit.T.J. _{F0 RN}

F F'oi:eritri. . 1 eTer'':;y kNm

flJ :i.

3 ::::

.i.eritii c.iri

_m

iLie tot.J.

1 ericjtli of

cIi.:i. ni wli:i.

teeds ::o

be t.keni

Into

.co'.irf: consists of

-ie

i..Iri::Ierwter' :r't

ini<:I

trie

p.T.irt bov':x

rt...I":' br.i e c 1

w i. ïi.i Ls.s ei'

TI st:):per clepe...

di ri'. on :i

c.tic)r

.i'e

the

eriCh a 1 t _{:i. ri} :1.

eci..ire':l

lh iS

1enis

ciii. .T.t :i. ri ch;!J. ri :J. eniChth compr :1. s triq

two

Itie uri:!rw;itev' pert is

co

ected Fo rt:he (rcIi :i.med:s

Face ziricl the

.T.thOVC

iter pii

is

rat

i t.

pc±ti. e. to

: i: 1c)ri

ic:r

i. r 'ni. tl"i twc:

n1isses

For tti :i. s

:pei'

i tis. riot

qiji ed

:is

It

. i..i ff1

dent

to caicij:Lke

i't er.'y

:I.er-iju...am the

anchor

iiac k 3. e

to

....

f

rci

a

; I m!: 1

ca:Lc'..c1.aL:Lor for the part above

;iiter car be

:i. riciijded

.I.TipEi:t i. on

of the

Fcm'mu 1 ae

,' ...e

:LmJ::.0)tanid&:? a F

tss I::-i'

'jr :1 :i.

oF tlie

Tha in

Fore ii:

:i S c:.5S0...

t:i...i1 tc:'

r.'..ii'

:

hi:t...,c.. c(:))):ct

,.:jsJ

:LT

Orit(.?':d

:Lri

ti(?

ion

() f

1 Tt1st arE

_ti-

var I oi

_sI,ai

a F the

Tchor ch

:i Ti

w1i I cI"i can be

e<pected when

a sii I p

:L s

at anchor

Lisua 1 1

15 _{c)F iLC}

(" in F:i.ci..n'C

TiC)

The, Il

L.I iL :1.

;it:e s 1 ac k'

I.sl: :i. r :1. dea 3. erv :1. 1cinimeniI::a 1 conidri.

t :i.oris

There

:i. sno w i rid. cuSrnt or '.ve act :1 on

The cha i ri

3. eads vert :i. cal ly down

''S :J. i'. 1< '' . '.OfifllC)Ti .1. 1:: e:i. s...luiC)IE);.ii.:C? :'iiv :1. 3.

cc)ni.d :i. ij :nis

chaIn

!. .I:c:)1S;fli:I

an:i

cijwr '..inider

a

:i i It ;iT-iCj :i. l::ir.b c: f t1ie

Ii:,i Ti rets Ci...

tIi:,

iii

iev: L ;buI:C Ls

te :ri'J :1

'':ninieniI.aJ.

.:Dri.:l:i. is

have

:1. iu.:reased

tc:u such ar

extort...

:i. i. C) .:

tli

cI-,ai ri :i.s i : .FIf:l .i.Sc)fli

seabed

arid tIi

end

at seabed is

tari.jlerit....C)

the

anchor

shackj.e

:i:t...:

t:inis 1 ti or

21

?.ctii

sIipes CDc.i.Jr

.ziieri the eriv :1

' rinierit.n L .or:i :i t:L c:rii;

I .ve Fur 1h

r' r. i'i

1h

e'ItcAl ii y

pu]]

oil I. iih t rid

:Leds ..L...ieri:hor

end under'

ni .:ri:t e w :1

Conisei.:jijerut]. y vert :i. 1 (on1porIE?rut of the pu].]. i niçj

foie .it

thiC DTi l-uor

iil' 1. e CD'I

fl'S iT i/i IC.) CCCD5 0 I I'

r

I' T .1 t ii

;ridior

tram th:c_?

soJ hzs ...In

the i..iit:iit

t;.D'..It

1i.pe

the :htiri is st'.:i..ciht .rid ti.ht

fl drigg :1 riq ;zirur.hor ni

J::e e petee.:l l::.etweeni tiie

1 1 y deve :i.

hped .inid

i..il t :Li.te tzut siipes

ror'

the '.:leterminizitiori

of 1ti

i_i red

].erucith oF

nihor

t-iz :1 ri ti-ic Fi 1

1:hrcc sIij:es

.re CDI

.

nterest s :1 rice

they

cni

es:i ly I:e'

c1.ci..i1ted

The

i_iltimte. slack

sape

is

tr:i. v:i. a 1

.rid

botii otluers can

b :Lated w :i. th

tlie

i

Forni_i1 c 1iie 'i:i'..it

_ii:Ii13

eTi:lTi.i'(i

Ii:1. par<:i '..I13f.

be

avo :1 ded by qoad scamanush :1 p Formu L . ava :1 1 ab :i. e tC)i'

:hese :ses but' ;:re

riot cj :1. Yen because they arc

riot niecdczd

Fort he pu rSrSoc oF this paper'

LCD

ti-e

u]...1 m;:ite

sl ac k

shape it

:i. S

easy to

unide'tarici

tliat,

s :irce

is rio

bar :1. zonita I

Fo'ce at

se;.:i level

oriJ.y a

vertica]. Force at

J.eve]. :Ls

reqi.:i.red for

equi-:1 br :ium

That vn't :ica 1 force ef.:ii.Ja is

< x (:I.CL

FiiC

:LenitIi c)i

ia:i.n :1;

::q::. t:: t:i::: ' (:L:.)

i-.:r'

tIie

1 cu L at:Loni

CDt the

l. ac k

arid ..he

Ii]. 1 y ::Ieve Loped

shapes the

cziteriary ei'.jat :1 onis

are i'equ :1 red

Th Isis

riot

d :1. 11:1. c..i ]. t

ani:l can b

done wi. th ttie

aid o

a s:i. mp L e c.:i 1

J. ator

or In a

more sopu is....1. cateci

maTunier w :1. th

the

.h :1. p

comp.ut:er

For

new :Ly b.i..i :1 :i. t:

ships ti-ic

L

u 1 ;t Ions :ani

be

dcn

ii t1 i( I 'lii 01 I 0 iii I Ii I I ii i I ru

i-:i:ii..n'c ru::) 2

:l"ic)ws tivat

fo...uc Fi..u]. :l.y deVeI.C)pCed catcni;Dr'y

equ . ]. :1. br i_ui :1 s ' qi..ai'anL d c.,'I"ini tiuc ho]. di. niq power' C) 1

tIc

anicIuor

:s eqiJa 1 but appas :i. te

:i. r

di re'± :1. oh to tlue Iuor zo ....

:i.

component

Fh C)

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