Loads on offshore strucrures-otc-1741.pdf

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1/16

OFFSHORE TECI INOLOGY CONFERENCE

PAPER

6200 North Central Expressway

NUMBEROTC1741

Dallas Texas 75206 -

The Mean Wave W i n d and

Cu r r en t F o r c e s o n

O f f s h o r e

S t r u c t u r e s a n d T h e i r R o l e i n

t h e

D e s i g n

o f

M o o r i n g

S y s t e m s

BY

G

F M Remery and G. van Oortmerssen Netherlands Ship Model Basin

O Copyright

1973

American Institute

of

Mining Metallurgical and Petroleum Engineers Inc.

Offshore Technology Conference on behalf of th e American In s t i tu t e of Mining Metall urgical and

Petroleum Engineers Inc . American Asso ciation of Petroleum Geolo gists American In s t i t u t e

of

Chemical Engineers American Society of C iv il Engineers American So cie ty of Mechanical Engineers

I n s t i t u t e of El ec tr ic al and Ele ctro nics Engineers Inc. Marine Technology Society Society of

Explora tion Geoph ysicis ts and Soc iety of Naval Arch ite ct s Marine Engineers.

~

This paper was prepared fo r- pr es en ta ti on a t th e F if th Annual Offshore Technology Conference

he ld i n Houston Tex. Apr il 29-May

2

1973

Perm5.ssion t o copy i s re st ri ct ed t o an abs tra ct of

not more than 300 words.

I l lu s t r a t io n s may not be copied.

Such use of an abstract should con-

t a i n conspicuous acknowledgment of where and by whom th e paper i s pr esen ted.

A b s t r a c t

T h e mean f o r c e s i n d u c e d by wav es win d

a nd c u r r e n t o n t a n k e r s b a r g e s a nd o t h e r

s t r u c t u r e s are v e r y im p or t an t f o r t h e

s e l e c t i o n o f a n ap p r op r i a t e p a s s iv e o r

a c t i v e p o s i t i o n i n g s ys te m. I n t h e p r es en l

p a p e r t o o l s a r e g i v e n f o r t h e d e te rm in a-

t i o n o f t h e s e f o r c e s e s p e c i a l l y f o r

t a n k e r s ha pe d b o d i e s t a k i n g i n t o ac -

c o u nt t h e m ain i n f l u e n c e o f w a t e r d e p t h .

The way i n w hi ch t h e e s t i m a t i o n o f t h e

mean f o r c e s h a s t o b e u se d f o r a p r e -

l i m i n a r y d e s i g n o f

a

mo o r in g sy s t em w i l l

b e d e a l t w i th .

I n t r o d u c t i o n

o f t h e problem.

t

i s a p ro b lem o f d y n a -

m i c s a nd t h e m oored s t r u c t u r e m ay

be

r e g ar d e d a s a m a s s - s p r i n g s y s t e m . T h e

t o t a l l o a d e x e r t e d b y t h e en vi ro nm en t

c o n s i s t s o f t h e o s c i l l a t i n g wave f o r c e s

a nd o f f o r c e s w hi ch v a r y a t a f r e q u e n c y

much l o w e r t h a n t h e w av e f re q u e n c y : t h e

w in d c u r r e n t a nd

wave

d r i f t f o r c e s .

When d e s i g n i n g a n a n c h o r s y s t e m t h r e e

a s p e c t s o f t h e s e v e r y s l ow l y v a r y i n g

f o r c e s

a r e

o f i m p o r t a n c e .

1

A s w i l l b e i l l u s t r a t e d a t t h e en d of

t h i s p a p e r t h e a l m os t s t e a d y wi nd

c u r r e n t an d wave d r i f t f o r c e s a x e m o st

s i g n i f i c a n t f o r t h e f i n a l d e t er mi na -

t i o n o f t h e d ia m et e r o f t h e a nc ho r

l i n e s . T h i s i s du e t o t h e f a c t t h a t

m oo ri ng o r a n c ho r in g s y s t em f o r f l o a t i n g

o f f s h o re s t r u c t u r e s i s r a t h e r c o m p l i c a t e d

n o t

a t

l e a s t d ue t o t h e n on - l in ea r n a t ur e

T he p ro b le m o f d e s i g n i n g a n a d e q u a t e

a v er ag e p o s i t i o n . B a s i c l y t h e f o r c e

r e q ui r e d f o r t h i s s t a t i o n k e ep in g

e q u a l s t h e s t e ad y o r t h e s lo wl y

t h e m ai n p u r p o s e o f a n a n c h o r i n g sys

t e m

i s t o h o ld t h e s t r u c t u r e on

an


2/16

OTC L741

G .F .M.

REMERY AND

G . VAN

O O R T M E R S S E N

1 171

Description of steady forces and moments

Wind forces and cur re n t fo r ce s a r e f r e -

que nt ly pr esente d as being composed of a

d r ag f o r c e , i n t h e d i r e c t i o n o f t h e f lo w ,

and a l i f t f o r c e, p er pe nd ic ul ar t o t h e

f low di re ct io n. However, when des cr ib in g

th e dynamic behaviour o f a f lo a t in g ob-

j e c t , t he equa t ions o f mot ion a r e u su a l l j

r e l a t e d t o a s t r uc tu re bound sys tem o f

coo rd ina t e s , w i th

i t s

o r i g i n i n t h e mid-

s h i p s e c t i o n of t h e s t r u c t u r e . T h e re fo r e

it i s conven ien t t o de sc r ibe t h e s t eady

f o r c e s a s a l o n g i t u d i n a l and a transverse

component applying i n th e midship sec t io r

and a moment around th e ve r t i c a l a xi s .

F igure

2

shows a ske tch i n which th e s igr

of th e fo rc es and moment, and th e dir ec -

t i on o f w ind , waves o r cu r r en t a r e de f in -

ed.

The f or ce due t o wind

Like a l l environmen tal phenomena, wind

has a s t oc ha s t i c na tu re which g re a t l y de-

pends on

t i m e

and l o c a ti o n . f t

i s

usual11

c h a r a c t e r i z e d

by

f a i r l y l a r g e f l u c tu a -

t i o n s i n v e l o c i t y and d i r e c t i o n .

I t

i s

common mete orolog ical pr ac t i ce t o gi ve

th e wind ve lo c i ty i n te rms of th e average

o ve r a c e r t a i n i n t e r v a l o f

t i m e ,

vary ing

from t o 60 minutes o r more. The va ri a-

t i o n i n mean v e l o c i t y i s very slow com-

pared with th e wave per iod . The f luc tu a-

t i on s a round t h e mean va lue

w i l l

impose

dynamic f o r c es o n t h e s t r u c t u r e , b u t i n

gen era l the se aerodynamic for ce s may be

neglec ted i n compar ison wi th t he hydrody

namic fo rc es , when c ons ide r in g th e dyna-

t u d e and d i r e c t i o n , r e s u l t i n g i n con-

s t a n t f o r c e s and a constant moment ac t -

i n g on t h e s t r u c t u r e .

The ro l e which wind p la ys i n t h e de te r -

mina t ion of th e envi ronmenta l condi t ions

o f f l o a t i n g s t r u c t u r e s i s twofold:

On the p a r t o f t he s t r uc tu re exposed

t o t h e a i r , wind f o r c e s a r e e x e r t e d

due t o t h e stream o f a i r arou nd t h e

v a r i o u s p a r t s . F o r t h e d e t er m i n a t io n

o f t he se fo rc e s i n forma t ion

i s

r e q u i r -

ed abou t t he l o ca l w inds on ly .

The for ce s ex er te d by t he wind on th e

wa te r su r f ace cause d i s tu rban ces o f th

s t i l l w a t er l e v e l , t h u s g e n er a t i n g

waves and cur re nt , which induc e fo rc es

on th e submerged pa r t of t h e s t ru c t u r e

To de te rmine t h i s e f f e c t of t h e w ind,

in format ion i s r equ i r ed abou t t h e

wind

and s torm condi t ions i n a much l a r ge r

a r e a .

The wave and cu rr en t gen era t ing c ha ra ct e

of

t h e

w i n d

will

be

left

out

o f consider

a t ion . The e f f e c t s of waves and cu r re n t s

w i l l b e d e a l t w it h s e p e r a t e l y .

Local winds a r e ge ne ra l l y de f ined

i n

terns

of t he average ve lo c i t y and averag

d i r e c t i o n r e l a t e d t o

a

c e r t a i n

height

above the s t i l l wate r l e ve l . The s t an da r

he igh t above t he wa te r su r f ace fo r wh ich

g e n e r a l l y t h e wind v e l o c i t y d a t a a r e

giv en amounts t o

1 0

metres o r

3

f e e t . P

number of emp i r ica l and th eo re t i ca l fo r -

mulas i s a v ai l ab l e i n l i t e r a t u r e t o de-

t e rm i n e t h e wind v e l o c i t y a t o t h e r

h e i g h ts . An a de qu at e v e r t i c a l d i s t r i b u -

t i o n of t h e wind speed i s r ep re sen t ed b y

s e e r e f . 1)

m i c behav iour o f t h e f l o a t i n g body.

V Z )

s 7

Therefore ,

w e w i l l

con sid er t h e wind ve-

/G

E)

oc i t y a s a s t eady va lue , bo th i n magni-


3/16

1-170 T H E /LEAN WAVE WIND A N D CURRENTOR ES OTC

1 7 4 1

o s c i l l a t i n g wave w ind and cu r r en t

f o r c e s o n t h e s t r u c t u r e .

2 . The a lmos t s t ea dy wind cu r re nt and

wave d r i f t f o r c e s c a us e a s h i f t o f t h

n e u t r a l p o s i t i o n o f t h e moored o b j e c t

a ro un d w hich t h e o s c i l l a t i o n d ue t o

waves o c c u r s . S i n c e t h e r e l a t i o n s h i p

between t h e ho r i zo n t a l d i sp l acemen t

a

t h e a nc ho re d s t r u c t u r e and t h e r e s t o r

i ng f o r ce o f t h e anchor s ys tem

i s

a lmost a lways non- l inea r t h e s h i f t c

t h e n e u t r a l p o s i t i o n c a u s es a c ha ng e

i n t h e s p r i n g r a t e and c o ns eq u en tl y

i n t h e dynamic respo nse. However

g e n e r a l l y t h e n a t u r a l f r e qu e nc y o f

t h

ho r i zo n t a l mot ion o f t h e anchor ed

s t r u c t u r e i s cons i de r ab l y s ma l l e r tha

t h e wave f r eguency a l s o a f t e r an i n -

c r e a s e o f t h e s p r i n g c o n s t a n t d ue t o

t h e mean s h i f t o f t h e s t r u c t u r e b u t

t h i s has t o be checked f o r each spe-

c i a l d e s ig n . T h er ef or e t

i s

ver y i m -

portant to

study this

effect of the

wind cu r r en t and wave d r i f t f o r c es

a n e a r l y s t a g e o f t h e d e si g n t o b e

s u r e t h a t r es on an ce a t t h e wave f r e -

quency w i l l be avoided.

3

Sinc e th e wind cu r re nt and wave dxi f

f o r c e s a r e s lo w ly f l u c t u a t i n g f o r c e s

t h e

r i s k

e x i s t s t h a t r es on an ce o c c ur s

a t t h e v e r y low f r e q u e n c i e s a t which

t he s e f o r c es o s c i l l a t e . Low fr equency

o s c i l l a t i o n s i n t h e h o r iz o n ta l p la ne

l

have been observed i n model exp er i -

m ents a s w e l l a s a t f u l l s c a l e . The

na tu re of t h i s phenomenon i s n o t y e t

f u l l y u n de r st o od b u t i n ge n e r a l

t

c an b e a t t r i b u t e d t o t h e s l ow l y v a ry -

i n g wave d r i f t f o r c e a s a r e s u l t o f

t h e v a r yi n g wave h e i g h t i n i r r e g u l a r

s e a s . A t t e n t i o n h a s t o be p a id t o t h e

dynamic fo rc es due t o wind gu s t s

w h il e t h e v a r i a t i o n i n t h e c u r r e n t

ve l oc i t y occur s a t a much t oo low

f requency t o be of importance .

The f i r s t two a s p e c t s d i s c u s s e d h e r e

h av e t o b e ta k e n i n t o a c c o un t d u ri n g t h e

p r e l i mi na r y des i gn and

w i l l

b e o f s i g -

n i f i c a n t i m po rta nc e f o r t h i s d e s ig n . For

t h i s a s pec t t he w ind cu r r en t and wave

d r i f t may be reg arde d a s s te ad y phenom-

e n a i n d uc i n g o n l y c o n s t a n t f o r c e s . F o r

t h e i nv es t i g a t i on o f t h e dynamic char ac -

t e r

o f e s p e c i a l l y t h e wave d r i f t f o r c e

and

i t s

e f f e c t on t he dynamic r e s pons e

of th e anchored ob je c t model t e s t s a r e

s t i l l i nd i s pens ab l e .

F i gu r e

1

shows a f low diagram de pi ct in g

a p o s s i b l e d e s ig n pr o c es s f o r an anchor

s ys te m. I n g e n e r a l t h e p r o c e s s w i l l hav

t o b e re p e a t e d f o r a number o f d i f f e r e n t

c o nd it io n s. F or a d r i l l r i g f o r i n s t a n c

th e anchor sys tem must be s t ro ng enough

t o w i th s ta n d t h e e xtr em e l o a d s i n t h e

survival condition while for

the

maximu

ope r a t i on a l wave con d i t i on t he mot ion o f

t h e r i g may n o t e xc ee d a c e r t a i n v a l u e

I n a c e r t a i n c o n d i ti o n

t

may be neces-

s a r y t o cons i de r va r i o us combi na ti ons of

wave cu r r en t and w ind d i r e c t i on s .

I n t h i s pape r we w i l l d e a l w it h t h e de

t e r m i n a ti o n o f t h e st e a d y f o r c e s m a in ly

on t a n k e r h u l l s . The n a t u r e o f t h e wind

c u r r e n t a nd wave d r i f t f o r c e s w i l l be

b r i e f l y d i s cu s se d and d a t a w i l l be g i ven

f o r an e s t i m a t e o f t h e s e f o r c e s .

T h e

problem of th e choice of th e des ign en-

v i ronmenta l condi t ions

w i l l

be l e f t o u t

of c on si de ra t i on . An example how t o use

t h e s e d a t a f o r t h e d e s ig n of an a nc ho r

s y s t e m

w i l l

be g iven .


4/16

1 172 p p THE MEAN WAVE, WINDND CURRENT FORCES

OTC

1 7 4 1

l

i n which

V ( Z ) =

wind s peed a t he i gh t above t h e

w a t e r s u r f a c e

V ( 1 0 ) = wind speed a t 1 0 m e t r e s h e i g h t

above t h e wa t e r s u r f ace

The t o t a l f o rc e and moment exp er ien ced

by an obj ec t exposed t o wind,

i s

p a r t l y

o f v i s cous o r i g i n ( p r es s u r e d r ag ) and

p a r t ly due t o p o t e n t i a l e f f e c t s ( l i f t

fo rc e and moment). For b lu nt bodie s , th e

wind fo rc e may be reg ard ed a s independen

of th e Reynolds number -and pro po r t io nal

t o t h e s q u a r e o f t h e wind v e l o c i t y .

Wind l oad d a t a f o r t an ke r s

The f o rc e s and moment ex e rt e d by wind

on t an ke r s can be ca lc ul a t ed from:

2

C X W ( ~ )

Yw

= p a c ( a ) . AL

W2

NW = +pa Vw

Cnw(a) AL

L

i n which

Xw

= steady longitudinal

wind force

Yw

= s t eady t r ans ve r s e wind f o r c e

NW = steady yaw wind moment

p,

=

d e n si t y of a i r

Vw

= wi nd ve l oc i t y

= w i n d d i r e c t i o n

~ =

exposed t r ansver se a r ea

A~ = e xp ose d l a t e r a l a r e a

.

L =

l e n g t h o f t h e s h i p

C

and Cnw a r e c o e f f i c i e n t s , de-

Cxw yw

pend i ng on t h e ang l e of i nc i dence o f t h e

wind.

I n l i t e r a t u r e t h e r e s u l t s o f wind t u n n e l

e x pe r im e n ts a r e g i v e n f o r v a r i o u s t y p e s

of ve sse l s . From se ve ra l paper s t h e wind

d a t a on t a n k e r h u l l s we re c o l l e c t e d , and

t h e f o r ce and moment c oe f f i c i e n t s Cxw,

C

and Cnw were expanded i n Fou r ier

Y

s e r i e s a s f u n ct io n o f - t h e a n gl e of i n -

c i dence

C

= a0

n COS nm

n=1

C

= 1

b s i n n a

yw

n z l

n

Cnw = 1

b s i n na

n=

n

From th e harmonic a na ly s i s i t was found

t h a t a f i f t h o r d er r ep r e s e n ta t i o n of t h e

wind da ta

i s

s u f f i c i e n t l y a c cu r at e f o r

p r e l i mi na r y des i gn pu r pos es.

I n Tab l e I1 th rough I V t h e F o u r i e r c o e f-

f i c i e n t s a r e g iv en f o r t h e l o n g i tu d i n a l

and t r an sv er se fo rc e, and t h e yawing mo-

ment, fo r a number of t an ker s . Par t i cu -

l a r s o f t h e t a nk e rs a r e l i s t e d i n Ta bl e

I where a l s o t h e r e f e r en ce numbers a r e

g i ven o f t he pu b l i c a t i o ns , from which

t h e d a t a w ere t a k e n . F i g u r e 3 shows, as

an example, t h e measured wind fo rc e s and

moment tog et he r wi th t h e Four ier approxi

ma t ion , f o r one o f t he t anke r s .

The wind forces and moments on other

t y pe s o f s t r u c t u r e s , a s f o r in s t a n c e

f l oa t i ng s emi -s ubmers ib le p l a t f o r ms , can

be appr ox ima ted by d i v i d i ng t h e s t r u c -

t u r e i n a number o f components , a l l w i t h

a more o r l e s s elem enta ry geometry, and

es t i ma t i ng t h e wind f o r ce on each ele

ment. Fo r a l o t o f s i mpl e geomet r i ca l

fo rm s s uc h a s s p h e r e s , f l a t p l a t e s and

c y l i n d e r s of v a r i ou s c r o s s s e c t i o n a l

s hapes , t h e d r ag and

l i f t

c o e f f i c i e n t s

a r e g i ve n i n l i t e r a t u r e . R efe re nc e

i s

made of th e publ i ca t ion s of Hoerner 61

and Delany and Sorensen

( 7 ) .

The t o t a l wind l o a d o n t h e s t r u c t u r e i s

t hen f ound by add ing t he con t r i b u t i o ns

o f a l l t h e component pa r t s .


5/16

1 173

OTC 1741 G F M REMERY AND G VAN OORTMERSSEN

The f o r c e d ue t o c u r r e n t

There are several independent phenomena

r e s p o n s i b l e f o r t h e o cc u r re n c e o f c u r -

r e n t : t h e o c ea n c i r c u l a t i o n s ys te m,

r e s u l t i n g i n a s te a dy c u r re n t , t h e c y c l i

c a l c hange i n l u n a r and s o l a r g r a v i t y ,

c a u s in g t i d a l c u r r e n t s , wind and d i f f e r -

e n ce s i n d e n s i t y . The s t e a d y v e l o c i t y a t

t h e wa t e r su r f ac e due t o wind amounts t o

a b ou t p e r c e n t o f t h e wind v e l o c i t y ( a t

3 0 f t h e i g h t ) . T i d a l c u r r en t s a r e of

main im p or ta nc e i n a r e a s o f r e s t r i c t e d

w a t e r d e pt h and c an a t t a i n v a l u e s up t o

L0 kn ots . However, t he se ext reme velo -

c i t i e s a r e r a r e . A 2 o r k no ts t i d a l

c u r r e n t s p e e d

i s

common. The prediction

o f t h e m ag ni tu de of t i d a l c u r r e n t s

i s

a

s p e c i a l s i e n c e . Some p r e d i c t o r s t a k e n o t

l e s s t h a n 60 p a r am e t er s i n t o a c c ou n t i n

t h e i r p r e d i c t i o n p ro ce du re .

Although f o r f l o a t i n g s t r u c t u r e s t h e

s u r f a c e c u r r e n t s w i l l b e t h e g o v e r ni n g

o ne s, t h e v e r t i c a l c u r r en t d i s t r i b u t i o n

may a l s o be of impor tance , e sp ec ia l l y

f o r t h e c a s e of r e s t k i c t e d w a te r d ep th .

For th e des ign of an anchor sys tem of a

f l o a t i n g s t r u c t u r e t h e d e s ig n e r i s espe-

c i a l l y i n t e re s t e d i n t h e p r o ba b i l i t y

t h a t a p a r t i c u l a r e xt re me c u r r e n t v e lo -

c i t y w i l l b e e x c e e d e d d u r i n g a c e r t a i n

per io d of t ime. Observa t ions obta ined

f rom cu r r en t speed measurements a r e in -

d i s pe n s a bl e f o r t h a t p ur po se . t may be

u s e f u l l t o s p l i t up t h e t o t a l measured

cu r re nt i n two o r more component s, f o r

i n s t an ce i n a t i d a l and a non- t i da l com-

p on en t, s i n c e t h e d i r e c t i o n of t h e v a r i -

ous components w i l l b e d i f f e r e n t , i n

g e n e r a l . The v a r i a t i o n i n v e l o c i t y and

d i r e c t i o n of t h e c u r r e n t i s very slow,

and cu r r en t may th er ef or e be cons idered

as a steady phenomenon.

The for ce s and moment ex er ted by cu rr en t

on a f l o a t i n g o b j e c t

i s

composed of t h e

f o l l o w i n g p a r t s :

A

v is c ou s p a r t , due t o f r i c t i o n be-

tw een t h e s t r u c t u r e a nd t h e f l u i d , an d

due

t o

p r e s s u r e d r a g . F or b l u n t b o d ie s

t h e f r i c t i o n a l f o r c e may b e n e g l e c t e d ,

s i n c e it i s sma l l compared t o t h e v i s -

cous p r es su r e d r ag .

A po t e n t i a l pa r t , w i t h a component due

t o a c i r c u l a t i o n around t h e o b j e c t ,

and an o t he r component due t o th e f r e e

w a t e r s u r f a c e (wave r e s i s t a n c e )

.

I n

mos t cases , t h e l a t t e r component i s

sma l l i n compar ison w i t h t h e f i r s t

The forc es and moment exe r te d by c u rr en t

on a t a n k e r hull c a n ~ b e escribed by:

= P VC2

a )

ATS

i n whi ch

Xc

= s t ea d y l o n g i t u d i n a l c u r r e n t f o r c e

Yc

= s t ea d y t r a n s v e r s e c u r r e n t f o r c e

Nc

= s t ead y yaw cur re nt -moment

Pw

= d e n s i t y o f w a t e r

VC = c u r r e n t v e l o c i t y

a =

ang l e o f i nc i d ence

S

= submer ged t r ansve r se a r ea

ALS =

submerged l a t e r a l a r e a

=

L

X

T

L =

l e n g t h o f t h e s h i p

T = d r a f t of t h e s h i p

C

and

Cnc

a r e c o e f f i c i e n t s , de-

C X C

yc

p en di ng on t h e c u r r e n t d i r e c t i o n .

t th e N.S.M.B., th e cu rr en t Loads have

been measured on se ve ra l t an ke r model s

o f d i f f e r e n t s i z e . From t h e r e s u l t s t h e


6/16

OTC

1741 G.F .M . REMERY

AND

G.VAN OORTMERSSEN

1-3-75

f rom the BernouLli e qua t ion f o r non-

s t eady f low:

i n w hich

p

=

p r e s s u r e

p

=

a t m osphe r i c p re s su re

s v e l o c i t y p o t e n t i a l

g

=

a c c e l e r a t i o n o f g r a v i t y

V =

ve lo c i ty o f water motion

I n t h e t h e o r y o f p e r i o d i c s h i p ' s m o tio n

i n waves t h e v e l o c i t y

t e r m

v2 i s ne-

g l e c t e d , s i n c e

i t

has on ly a second or -

d e r i n f l u e n c e on t h e o s c i l l a t o r y be ha -

viour. However, it i s t h i s t erm wh ich i s

r e s p o n si b le f o r t h e s te a d y d r i f t f o r c e .

R e p re s e nt in g t h e v e l o c i t y p o t e n t i a l by a

p e r i o d i c f u n c t io n p r o p or t io n a l t o t h e

ampl i tude a of t he i n -c i den t

w a y e

s A

.

5,

.

s i n

w t

i n which

w =

frequency of waves

i t

f o l l o w s t h a t

2 a @

f p w V + pw

< a

s i n w t { 3)

x

By t a k i n g t h e a v e r a g e v a l u e o f t h e p r e s -

2lT

s u r e d u r i n g o ne p e r i o d (T -) it w i l l

b e c l e a r t h a t a l l pe r io d ic

t e r m s

v a n i s h

2

and o n l y t h e v e l o c i t y t e r m

kpwV

g i v e s

a con t r i bu t i o n . C onsequen tl y t h e s t ea dy

d r i f t f o r c e on a s t r u c t u r e i n waves i s

p r o p o r t i o n a l t o t h e s q u ar e of t h e h e i g h t

of th e in ci de n t wave. Maruo (8) shows

t h a t t he l a t e r a l d r i f t f o r ce

Y

p e r u n i t

l e n g t h on an i n f i n i t e l y l o ng c y l i n d e r

( 2 -d im e ns io n al c a s e ; no d i f f r a c t i o n ) i n

beam s e a s s a t i s f i e s :

Y I d pwg

car

i n w hic h

a r ampl i tude of wave re f l e c t e d and

sc a t t e r e d by t he body

He a l s o i n d i c a t e s t h a t t h e a m p l it u de of

t h i s wave i s p r o p o r ti o n a l t o t h e r e l a -

t i v e m otio n b etw een t h e o s c i l l a t i n g cy-

l i n d e r and th e wave.

Ogawa

( 9 )

app l i ed Maruo 's theo ry on

a

c a p t i v e ser ies 60 model (block co ef f i -

c i e n t

0 . 7 0 )

i n beam and bow qu at er in g

waves and he shows th a t

2

y T d +pwg car s i n 2

i n w hich

a

d i r e c t i o n o f waves r e l a t i v e t o s h i p

H e c a l c u l a t e d t h e a m p l i t u d e o f t h e

re

f l e c t e d and s c a t t e r e d

w v e

using the

s t r i p t he o ry f o r two wave d i r e c t i o n s

(90

and 120°) r e l a t i v e t o t h e c a p t i v e vesse l

and found a reasonable agreement wi th

th e measured r e s u l t s . For t h e beam wave

d i r e c t i o n t h e r e s u l t s g i v e n by Ogawa f o r

t he cap t i ve ve s s e l a r e com pared

i n F i g .

5

w i t h t h e e x p er i m en t al v a l u e s

of

t h e

wave d r i f t f o r c e on a f r e e f l o a t i n g ve s-

s e l h a vi ng a s m a l l e r b lo c k c o e f f i c i e n t

o f 0 .6 0. I n t h i s F ig u re t h e d r i f t fo r c e

I

Yd i s giv en i n a non-dimensional way by

div id i ng th e f or ce by 4pwg

;

. L and

t a k i n g t h e s q u a r e r o o t . c a ampl i tude

o f i n c i d e n t w a ve ).

T h i s no n- dim en sio na l d r i f t f o r c e c o e f f i -

i s

p l o t t e d t o a ba se o f non-d im ens ional

I

wave length k.T i n w hi ch :


7/16

1 174

THE

MEAN WAVE

WIND

AND

CURRENT

FORCES OT

74

c o e f f i c i e n t s Cx c , C

and Cnc w e r e c a l -

YC

c u l a t e d . F o r f lo w i n t h e l o n g i t u d i n a l

d i r e c t i o n a ta n k e r h u l l

i s

a r a th e r s l e n t

de r body, and consequen t ly co ns i s t s t h e

I

l o n g i t u d i n a l f o r c e m ain ly o f f r i c t i o n a l

r e s i s t a n c e . T he t o t a l l o n g i t u d i n a l f o r c e

was v e r y s m a ll f o r t h e - r e l a t i v e 3 y low

I

c u r r e n t s p e e d , a nd c o u ld t h e r e f o r e n o t

be measured very a cc ur at el y. Moreover ,

e x t r a p o la t i o n t o f u l l s c a l e d im en sio ns

i s

d i f f i c u l t , s i n c e th e lo n g it u d in a l

f o r c e i s a f f e c t e d by s c a l e e f f e c t .

For mooring problems, th e lon gi tud in a l

c u r r e n t f o r c e w i l l ha rd ly be of impor-

tan ce . An es t im at e of i t s magnitude can

b e made by c a l c u l a t i n g t h e f l a t p l a t e

f r i c t i o n a l r e s is t a n c e :

0 075

2

C ( ( l o g

Rn

2

) i pWs

*vc

COS

a

lcos a1

i n which

v cos

Rn

=

t h e Reyn olds numbe-r =

V

L

v = k i n e m a t i c v i s c o s i t y o f w a t e r

I

S = t h e w e tt ed s u r f a c e

E x t r a p o l a t i o n of t h e t r a n s v e r s e f o r c e an

yaw moment t o p ro to ty pe va lu es

i s

no pro

b lem. For f16w i n t he t r ans ve r se d i r ec -

l

t i o n t h e t a n k er i s a b lu nt body, and

s i n c e t h e b i l g e r a d i u s i s sma l l , f l ow

s e p a r a t i o n o c cu rs i n t h e model i n t h e

same way a s i n th e pro to type . The refore ,

t h e t r a n s v e r s e f o r c e c o e f f i c i e n t and t h e

yaw moment c o e ff i c ie n t a r e independent

the Reynolds number.

The c o e f f i c i e n t s f o r t h e t r a n s v e r s e f o r c

and t h e yaw moment were expanded i n a

I

F o u r i e r s e r i e s , a s was d one f o r t h e wind

l o a d c o e f f i c i e n t s :

m

.

C = bn s i n nci

Yc n=l ..

.

.

m

The aver age va l u e o f t he Four i e r co e f f i -

c i e n t s f o r t h e f i f t h o rd e r F o ur ie r se-

r i e s

a r e g iv e n i n T a bl e V. These re-

s u l t s a p pl y t o d ee p w a t e r . F or s h a l lo w

wa ter , t h e cu r r en t fo rc e and moment coef

f i c i e n t s h a ve t o b e m u l t i p l i e d by

a

coef

f i c i e n t , w h i c h

i s

g iv e n i n F i g u r e

4

on

a

b a s e o f t h e w a t er d e p th - d ra f t r a t i o . I n

t h e d a t a , g iv e n i n T a bl e V , t h e i n f l ue n c

o f t h e f r e e w a t er s u r f a c e i s i nc luded .

Thi s i nf lu en ce , however, depends on t h e

wa te r de pth and on th e Froude number,

and consequen t ly changes i f t he c u r r e n t

ve l o c i t y o r t h e t anke r d imensi ons change

F or t h e c o n d i t io n t o which t h e s e d a t a

app ly, deep wate r and

a

pr o t o t ype

cur-

r e n t s pe ed i n t h e o r d e r o f k n o t s , t h e

e f f e c t of t h e f r e e w at er s u r f a c e

i s

ver y

smal l . Fo r a case o f a s ma l l unde rkee l

c l e a r a n c e a nd a c u r r e n t d i r e c t i o n o f 90

degrees damming up of th e wate r a t t h e

weather - s ide and a l oweri ng of t h e wa te r

l e v e l a t

t h e

l e e s i d e o f

t h e s h i p

o c c u r s

The c u r r e n t l o a d on o t h e r t y p e s o f f l o a t

i n g s t r u c t u r e s

c an b e e s t i m a t ed i n t h e

same way as was d es cr ib ed f o r t h e wind

l o a d i n a p r e vi ou s s e c t i o n .

ave d r i f t f o r c e s

A s t r u c t u r e f l o a t i n g i n waves e x p er ie n ce :

fo rc e s and moments which can be d et e r-

mined i f t he v e l o c i t y p o t e n t i a l o f t h e

wat e r mo ti on a round t he s t r uc t u r e i s

known. B y i n t egra t ing the component of

t h e p re s su re i n a p a r t i c u l a r d i r e c t i o n

o ve r t h e h u l l of t h e s t r u c t u r e , t h e

f o r c e component i n t h i s d i r e c t i o n c an b e

ca l cu l a t e d . The p r es s u r e can be ob t a i ned


8/16

1-176

OTC

f7K

k = - -T

wave number

X

wave length

l l r e s u l t s a pp ly t o d ee p w a te r . s il

l u s t r a t e d i n F ig .

5

t h e d r i f t f o rc e on

t h e f r e e f l o a t i n g v e s s e l c or re sp on ds

q u i t e w el l wi t h t h e f o r c e on an i n f i n i t e

l y l ong f l a t v e r t i c a l p l a t e ( s ee

10)

w ith a d r a f t e q ua l t o t h e v e s s e l s d r a f t

and o v er a l e n g t h t h a t e q u a ls t h e l e n g t h

o f t he ve s s e l be tw ee n pe r pe nd i c u l a r s .

The d r i f t f o r c e on t h e r e s t r a i n e d v e s s e l

i n de e p w a te r c a n be com pared q u i t e w e l l

w i t h t h e r e s u l t s g i ve n of t h e o r e t i c a l

c a l c u l a t i o n s c on du ct ed b y

e i

and Black

11)

f o r a r e c t a n g u l a r c a p t i v e c y li n d e r

e x t r a p o l a t e d t o t h e same beam o v e r d r a f t

r a t i o

B/T

2 .5) a s t h e v e s s e l h a s and

t o d eep w a t er . T h is i n d i c a t e s t h a t t h e

i n f l u en c e of d i f f r a c t i o n d ue t o t h e r e -

s t r i c t e d le ng th /b ea m r a t i o of t h e v e s s e l

prob ably may be ne gl ec ted .

The c o n s i d e r ab l e l a r g e r d r i f t f o r c e on

t h e c a p t i v e r ec t a n g u la r c y l i n d e r r e l a -

t i v e t o t h e f l a t p l a t e d em on stra tes t h e

i m p o r t a n t e f f e c t o f t h e beam o r t h e b o t -

tom o f t h e ve s s e l a nd c ons e que n tly o f t h

r e l a t i v e v e r t i c a l m o tio n betw een

the

ob-

j e c t and t h e wave motion. The ra t h e r go01

a gr ee me nt b et we en t h e f r e e f l o a t i n g ve s -

s e l and t h e v e r t i c a l p l a t e seems t o i n d i

c a t e t h a t t h e d r i f t f o r c e c o n t ri b u te d by

t h e r e l a t i v e h e a v e m o t i o n o f t h e v e s s e l

i

s m al l i n t h i s p a r t i c u l a r c a s e . The in -

f l u e n c e o f t h e w a t e r d e p t h - d ra f t r a t i o

i

i n d i c at e d i n F ig u re

6 ,

where some re su l t ,

a r e g i v en o f m ea su rem en ts c a r r i e d o u t a t

t h e N.S.M.B. on a se r i e s 60 model , b lock

0 . 8 0, be a m /d r af t r a t i o 2.5 Length/beam

r a t i o 7 . From t h i s f i g u r e t w i l l b e

c l e a r t h a t i n d eep w ate r t h e d r i f t f o r c e

i n beam waves on t h e b lock 0 .80 ve ss e l

c o r r es ponds a l s o r e a s ona b ly w e l l w i th thc

f o r c e on a v e r t i c a l p l a t e . However, a t

t h e ve r y r e duce d w a te r de p th o f 1 1

t i m e s

t h e d r a f t o f t h e v e s s e l , v er y h i g h

d r i f t f o r c e s a r e measu red f o r wave f r e -

q u e n c i e s n e a r t h e n a t u r a l f r eq u e n cy of

th e r o l l m ot ion . Th i s may be e xp l a in e d

by t h e much h igh e r r o l l dam ping ( t h e

d a m p i n g c o e f f i c i e n t

i s

approx.

t i m e s

l a r g e r ) a t t h i s w a t e r d e p th , w hic h means

t h a t t h e r o l l g e ne ra te d waves a r e h i g h e r

an d c on s eq u en tl y t h e s t e a d y d r i f t f o r c e

t o o .

F or a n a pp ro xi ma ti on o f t h e l a t e r a l d r i f

f o r c e i n d e ep w a t er i n r e g u l a r waves t h e

fo l low ing exp ress ion may be used:

2

yd 4pW9

L

s i n 2

a

i n w hic h

ca

a m pl i t ude o f i n c i de n t wave

R d r i f t f o r c e co e f f ic i e n t f o r a v e r t i -

c a l p l a t e w i t h d r a f t T . i s a func-

t i o n o f t h e d i m e n s io n l es s wave

le ng th kT

a w a v e d i r e c t i o n

F or t h e d e t e rm i n a t io n of t h e mean d r i f t

f o r c e o r t h e r e s i s t a n c e i n h ead

waves

r e f e r e n c e i s made t o t h e me thod de sc r i bed

by Gerritsma and Beukelman 12). T h i s

method i s b a se d o n t h e d e t e r m i n a t i o n o f

o f t h e r a d i a t e d e ne rg y by c a l c u l a t i n g t h e

ampl i tude of th e waves gen e ra t ed

by

t h e

r e l a t i v e v e r t i c a l mo ti on betw een s h i p and

waves. I n c a se o f a r a t h e r f l a t

b ow

a l s o

t h e i n f l u e n c e o f t h e r e l a t i v e s u r g e mo-

t i o n h a s t o b e ta k en i n t o a c co u nt

as i s

shown i n

( 1 3 ) .

Up t o now o n l y t h e d r i f t f o r c e on s h i p

s hape d bod i e s ha ve bee n d e a l t w i th .

F or t h e d r i f t f o r c e on s e m i s ubm e r s ib l e


9/16

t y p e s t r u c t u r e s no d a t a a r e a v a i l a b l e on

t h i s moment. Probably t h e be s t way t o

es

t im at e t h e d r i f t f o rc e

i s

t o s p l i t up t h

c o n s t r u c t i o n i n e l em e nt s c o n s i s t i n g of

c i r c u l a r o r r e c t a n g u la r c y l i n d e r s a nd t o

e s t i m a te t h e d r i f t f o r c e on e a ch e le me nt

s e p a r a t e l y . I n

14)

d a t a a r e g iv en f o r

t h e d r i f t f o r c e on a r e s t r a i n e d v e r t i c a l

c y l i n d e r .

Wave d r i f t f o r c e i n i r r e s u l a r waves

When t h e d r i f t f o r c e on a s t r u c t u r e i s

known as

a

f unc t i on o f t he wave f r eq ue nc ~

e i t h e r from c a l c u l a t i o n s o r model

t e s t s

t h e l a t e r a l mean d r i f t f o r c e i n i r r eg u l a l

waves, desc r ibed by a pa r t i c u la r wave

spectrum, can be determined from:

A s an emper ica l approx ima ti on f o r s h i p

s haped bod i es t h e f o l l owi ng expr es s i on

m a y

be u s e d for

an

i r r e g u l a r se

d e s c r i b

ed by a narrow spectrum :

i n which

;

1 3

s i g n i f i c a n t wave h e i g h t c r e s t -

t rough)

R ( ) d r i f t f o rc e c o e f f i c i e n t f o r f l a t

p la te f o r mean wave f r e -

quency ~

Design of t h e anchor sys tem

I f t h e s te a d y fo r c e on a s t r u c t u r e i n a

p a r t i c u l a r se a s t a t e

i s

known and t h e

lay-out of th e anchor sys tem has been se-

le c te d th e minimum thi ck ne ss of th e an-

c h o r l i n e s i s dete rmin ed by t h e mean ex-

t e r n a l f o r c e a s

w i l l

be i l l u s t r a t e d

below.

S up po se t h e a nc ho r sy s te m h a s t o s a t i s f y

t h e f ol lo wi ng c r i t e r i a

1 . The maximum allowable excursion

max

o f t h e s t r u c t u r e from i t s i n i t i a l un-

l o a d e d e q u i l i b r i u m p o s i t i o n i s g i ven

a s a c e r t a i n pe r c en t a ge o f t h e w a t er

dep t h .

2 .

The maximum al low able te ns io n i n t h e

anchor l i n e s may not exceed a c e r t a i n

p e r ce n t ag e o f t h e b re a k in g s t r e n g t h .

The th i ckn ess of t he anchor cha in s i s

p r o p o r ti o n a l t o t h e w ei gh t p e r u n i t

le ng th sp e c i f ic we ig ht ) . The minimum

wei gh t r equ i r ed

w i l l

be a t t a in ed when

t h e p r e t en s io n i n t h e a nc ho r l i n e s i s

s uc h t h a t a t a n e x c u r s io n w hic h e q u a l s

th e maximum al low able exc urs ion a l so th e

maximum al lowable load i n t h e he av ie s t

l o a d e d a n c h o r l i n e i s a t t a i n e d .

From t h e non-dimensional ca te na ry cha-

r a c t e r i s t i c s t h e te ns io n i n t h e l i n e

To

di vi de d by w.ha and th e ang le between

t h e l i n e and t h e h o r i z o n t a l p l a n e

b o t h

measured at the attachment

p o i n t

of

t h e

l i n e t o t h e s t r u c t u r e , c an b e de te rm in ed

as a f u nc t i o n o f t he excur s i on x / ha o f

t h e s t r u c t u r e .

W submerged weight of anchor l i n e

per

u n i t l e n g th

ha he ig ht of a t t achment po in t above

bottom

S i n c e t h e b r e a k in g s t r e n g t h o f a pa r t i - -

c u l a r t y p e o f a n ch or l i n e

i s

propor t ion-

a l t o t h e s p e c i f i c we ig ht W , t h e e x cu r -

s i o n of t h e s t r u c t u r e c an be d e t er m in e d

a t which th e t ens ion To/w.ha equ al s

t h e

maximum allowable tension. Then the re-

q u i r e d p r e t e n s i o n a n g le 8 can be r ead o f

a t an excur s i on which i s

X

s m a l l e r .

max

The us ua l non- li nea r r e l a t i o ns h i p be-

tween t he excur s ion o f t he s t r uc t u r e and

t h e h o r i z o n t a l l o a d FH/w.ha r e q u i r e d f o r

t h a t e x cu rs io n c an b e c a l c u l a t e d f o r t h e


10/16

1 178

TEE

MEAN NAVE

WIND AND

CUXRENT FORCES

OTC

74

s e l e c t e d p r e t en s i o n .

Su bt rac t in g th e maximum expec ted f lu c t u -

a t i n g motion f rom th e maximum al lo wa bl e

e xc ur s ion X g i v e s t h e e x cu r si o n o f t h

max

s t r u c t u r e wh ic h c an b e a l l ow e d a s a r e -

s u l t o f t h e mean f o r c e d ue t o w in d ,

waves a nd c u r r e n t . The t o t a l h o r i z o n t a l

f o r c e F H r

=

FH/w.h, a t t h i s e x c u rs i o n

c an be r e a d o f .

Then t h e minimum re q u ir ed submerged

w ei gh t of t h e an ch or l i n e s h a s t o s a t i s f

~ h e ' a b o v e e s cr i be d p ro ce du re w i l l be

i l l u s t r a t e d by means o f a n exam ple .

Qu es ti on Determine t h e minimum wei gh t of

t h e a n c h o r - l i n e s o f a n an ch or -

i n g s y s te m f o r a t u r r e t mo orin g

of a drilling v e s s e l h a v i n g t h e

fo l low ing ma in d imens ions:

.

. .

.

1-ength

=

150 m

beam =

26

m

d r a f t

= 8

m

w ind e xpos e d t r a ns ve r s e a r e a

=

750 m

2

disp lacement

=

17500 m e t r i c t ons

w a t e r d e p t h = 7 0

m

lThe de s ign ha s t o be ba s ed ori a s e a s t a t e 1

de scr ib ed by a Pierson-Moskowitz spec trum

w i t h a s i g n i f i c a n t - wave h e i g h t o f 4 .5

m

a n d a mean p e r io d o f

8

s e c . The maximum

w i n d s p e s d . i s

4

k n o t s ,

the^

c u r r e n t s p e e d

2 kn ot s. The maximum all ow ab le ex cu rs io n

i s

9 % o f t h e w a t e r d e p t h . The f o r c e s i n

th e l i n e s may no t e xc ee d 50% o f t h e

b r ea k in g . s t r e n g t h . A lt ho ug h t h e v e s s e l

i s

e q ui p ed w i t h bow a nd s t e r n t h r u s t e r s t o

c o n t r o l t h e h ea di ng , s i n c e t h e t u r r e t i s

l o c a t e d a m ids h ips , t h e a nc hor s yst e m ha s

to be de s igne d f o r t h e combined a c t i on

of beam wave, wind and c u r re n t . The

s y st em c o n s i s t s o f

8

a n ch o r l e g s e q u a l l y

d i s t r i b u t e d o v e r t h e c ir c u m f e re n c e - o f

t h e t u r r e t . From model t e s t d a t a on s i -

m i l a r - s h i ps t he maximum os c i l l a t o r y e x -

c u r s i o n o f t h e v e s s e l i s e s ti m at e d t o

be approxima te ly4 .35

m

b e i n g

7 %

o f t h e

h e i g h t h a o f t h e a tt a ch m e n t p o i n t s o f

t h e a nc hor c ha ins a bove t h e bo tt om .

S o l u t i o n

The mean fo rc e on t h e ve ss e l d e te rmined

a cc o rd in g t h e d a t a g iv e n i n t h i s p ap e r

a r e a s f o ll o w s

:

due t o a 40 kn ot s beam wind 17 to n

d ue t o a

2

kno t s

beam

c u r r e n t

4 9

t on

due t o 4 .5 m s i g n i f i c a n t h e i g h t

waves

4 8

t o n

T o t a l

l14

t o n

From t h e c h a r a c t e r i s t i c s o f t h e c a t e n a r y

t c a n be de t er m ine d t h a t t h e a nc hor Leg

h av e t o c o n s i s t o f a p pr o x.

5 0 0 m 8 h )

a nchor c ha in (U-3 q ua l i t y ) o r

1050 m 17

h ) s t e e l w i r e ( h = w a t e r d e p t h - d r a f t =

62

m

i n o r d e r t o be s u r e t h a t t h e t a n-

g e n t of t h e l i n e a t t h e a nc ho r c o in c id e s

w i th t h e bo tto m a t

a

t e n s io n wh ic h e qua l

h a l f t h e b r ea k in g s t r e n g t h .

he p r e t e ns ion a ng l e

O

r e q u i r e d t o ob-

t a i n a t e n s i o n w hich e q u a l s h a l f t h e

b r e a k ing s t r e ng th a t t h e maximum a l l ow -

a b l e e x c u r s i o n o f 9 % of t h e he igh - t ha ,

am ou nts t o t h e f o l l o w in g v a l u e s

for 500

m

U-3 q u a l i t y s t u d l i n k c h a i n :

Opre t .

= 26.2 degrees

for 1050

m

s tee lwire : Opre t ,

=

10.7 de-

g r e e s .

The non-dimens iona l r e la t i o ns h ip s be -

tw een t h e e x c u rs i o n o f t h e v e s s e l a nd t h

l

h o r i z o n t a l f o r c e r e q u i r e d ha ve b ee n c a l -

c u l a t e d f o r b o t h t y p es o f a n ch or l i n e s .

l F or U-3 s t u d l i n k c h a i n t h e r e s u l t i s


11/16

1 179

RTMRRSSRN

l

shown i n Fi g.

6 .

A t an excurs ion of 9

o f t h e h e i g h t h a, t h e t e n s i on i n t h e

h e a v i e s t l o ad ed an ch or l i n e a t t a i n e s

h a l f t h e b r e a ki n g s t r e n g t h

Tobr

f o r U-3 qu a l i t y ch ain Tobr

4 X

f o r t e e l w i r e

Tobr

17500

X

W

Su btr ac t in g t h e maximum expected os ci l -

l a t o r y e xc urs ion from t h e maximum allow-

a b l e e x c u r s io n l e a d s t o an e x c u rs io n of

2

of th e he ig h t ha , t h a t may be al lowed

a s a r e s u l t o f t h e mean f o r c e of 108 t o n

on th e vess e l . The d imens ion less hor i -

zon ta l load on the sys tem cor responding

t o t h i s

2

exc urs i on amounts t o :

f o r U-3 cha in 8.7

f o r s t e e l w i r e

5 9 1

The r e s u l t i n g minimum req ui re d submerged

w e ig h t o f t h e a n ch or l i n e s i s g i v e n i n

Table VS . The corresponding approximate

d i am e te r s o f t h e l i n e s a r e al s o mention-

e d i n T a bl e V I

The method de scr i bed h er e has t o be

adapted fo r each sp ec ia l case . However,

t h e example i l l u s t r a t e s c l e a r l y t h e im -

po rt an t r o l e which t h e mean f or ce may

p la y f o r t h e d e t e r m in a t i o n o f t h e a nc ho r

system.

~~~

- -

Nomenclature ..

.

F o u r i e r c o e f f i c i e n t s

dept h of water

he ig ht of a t tachf t ient po in t of

anchor l i n e above bot tom

wave number = 2x/X

p r e s s u r e

a tmospher ic p ressure

t i m e

submerged weight of anchor l i n e

e x c u r s io n

max

maximum allowable excursion of

l

s t r u c t u r e

X , y , z r i g h t handed sys tem of coord i -

n a t e s

z v e r t i c a l c o o r d in a t e , u pward pas-)

i t i v e

l

~

l a t e r a l a r e a above w at e r s u r f a c e

s u b m e r g e d l a t e r a l a r e a

c

t r a n s v e r s e a r e a ab ov e w a te r s u r -

f a c e

A~~

submerged t ransverse a rea

B b r e a d th o f s h i p

nw

yaw wind moment coefficient

nc

yaw cur re nt moment co ef f i c ie nt

Cxw

l o n g i t u d i n a l wind f o r c e c o e f f i -

c i e n t

l o n g i t u d i n a l c u r r e n t f o r c e c oe f-

f i c i e n t

C

t r a n s v e r s e wind f o r c e c o e f f i -

yw

c i e n t

C t r a n s v e r s e c u r r e n t f o r c e c o e f f i -

Y

c i e n t

-

F t o t a l mean loa d on anchored

s t r u c t u r e

F~

ho r iz on ta l load on anchor sys -

t e m

I

yaw c u r r e n t moment

Nc

yaw wind moment

R

n on -d im en sion al d r i f t f o r c e

c o e f f i c i e n t

l d r a f t of s h i p

To

t e n s i o n i n a nch or l i n e

V

ve lo c i ty o f wa te r mot ion

vw

wind ve loc i ty

c u r r e n t v e l o c i t y

c

l o n g i t u d i n a l c u r r e n t f o r c e

.

x

l o n g i t u d in a l win d f o r c e

Y c

t r a n s v e r s e c u r r e n t f o r c e

I

t ra n sv e rs e d r i f t f o r ce

mean t ra n s v e r s e d r i f t f o r c e i n

i r r e g u l a r w aves


12/16

1 180

THE: MEAN-WAVE,

WIND

AND

CURRENT

FORCES

OT

174

a a n g l e o f i n c i d e n c e

a

a m p l i t u d e o f i n c i d e n t wave

c a r

a m p l it u d e o f r e f l e c t e d an d s c a t -

t e r ed wave

W 113

s i g n i f i c a n t wave h e i g h t

a n g l e be tw e en a n c h o r l i n e a nd

h o r i z o n ta l p l a n e a t t h e a t t a c h -

ment p o i n t t o t h e s t r u c t u r e

e p r e t

p r e t e n s i o n a n g l e = a n g l e

8

f o r T

0

i s e q u a l t o p r e t e n s io n

cP

v e l o c i ty p o t e n t i a l

P

a

d e n s i t y of a i r

PW

d e n s i t y o f w a t e r

W

wave f requency

mean wave frequency of an i r r e g u -

l a r s e a

w

mean t r a n sv e r se wind f o r c e

L i s t o f r e f e r e n c e s

7 . Delany,

N .K .

and Sorensen , N.E.

Low sp e e d d r a g o f c y l i n d e r s o f

va

1

B r e t s c h n e i d e r ,

C.L.

Wave and wind l o a d s

S e c t i o n 1 2 of Handbook of ocean and

u n d e r w a t e r e n g i n e e r i n g , MC Graw-Hill

Book Company, New York (1 9 6 9 ) .

2 . R es ea rc h i n v e s t i g a t i o n f o r t h e

i m -

r i o u s s h a p e s

NACA, Te chn ica l Note 3038.

8. Maruo,

H.

The d r i f t o f a body f l o a t i n g o n w ave s

J .

o f sh i p r e se a r c h ( De c. 1 96 0 ) V o l .

9. Ogawa,

A

The d r i f t i n g f o r ce and moment on a

s h i p i n o b l i q u e r e g u l a r w aves

P u b l i c a t i o n n o. 3 1. D e l f t S h i p b u i l d i n

L a b o r a t o r y . . I . S . P . V o l .

1 4 ,

no. 149

January 1967 .

1 0 .

Wehausen, J . V . a n d La i t o n e , E.V.

Handbuch der Physik

1 96 0, s e c t i o n 1 7 , B e r l i n : S p r i n g e r -

V e r l a g

11. M e i , C.C. and Black, J . L .

S c a t t e r i n g o f s u r f a c e w av es

J . F lu id Mech. (1969) Vol. 38 P a r t 3.

1 2 . G e r r i t s m a , P r o f . I r . J and

Beukelman,

W.

A n al ys is o f t h e r e s i s t a n c e i n c r e a s e

i n w aves o f a f a s t c a rg o s h i p

I .S .P . Vo l . 1 9 , Sept. L972 no. 217.

3 Remery, G F M and Hermans, A J

p ro ve me nt o f s h i p m oo ri ng m eth od s The s lo w d r i f t o s c i l l a t i o n s of

a

Report No. A-3 of t h e Hydro- and Aero-

dynamics L ab or at or y, Denmark, May 1971

5 . Gould, R.W.F.

B.S.R.A. R eport NS. 256 .

3. Wagner, B

Windkrz f t e an Ueberwasse r sch i f f en

Schif f und Hafen, Hef t 12/1967.

4 . Aage, C .

Wind c o e f f i c i e n t s f o r n i n e s h i p

models

Measurements of t h e wind fo rc e s on

a

se r i e s

of mode l s o f merchan t sh ips

N.P.L. Aero Re port 1233, A p ri l 1967.

6 . Hoerner , Dr . Ing . S .F.

Flu id-dynamic drag

moored o b j e c t i n random s ea s

S o c i e t y o f P e t r ol e u m En g i n e e r s Jo u r n a

(1972) Vol. 12 , no. 3.

1 4 . Oor tmer ssen , G . van

The i n t e r a c t i o n b etw ee n a v e r t i c a l

c y l i n d e r a nd r e g u l a r w a ve s

Symposium on O ffs ho re Hydrodynamics

i n Wageningen. August 1971.

P u b l i c a t i o n n o. 375 o f t h e

N S M B

P u b l i s h e d b y t h e a u t h o r i n 1 9 65 .


13/16

T BLE -

DATA OF TANKERS

TABLE

-

COEFFfCfENTS

FOR PHE

LOEiGIlVDINAL FORCE ON TANKWS

m

To

w

TABLE

COEWIZ:E iTS FOX THE TRANSVERSE

FORCE ON

TABLE

4

COEFFICIENTS

FOR THE YBW

MOhEXT

X TANKFRS

DUE

TO

KIXiJ

TANKERS DUE TOWITD

.

S h i p

No.

2

4

5

7

8

9

1 0

NO.

- 0 . 131

0 . 738 - 0.058 0.059

0 . 108 - 0 . 001

- 0.079

0 . 6 1 5

0.104 0.085 0.076 0 . 0 2 5

-

0.028 0.799 0.077 0.054 0 . 018 0 . 018

0.014 0.732

0.055 0.017

0 . 018

5 - 0.074 1.010 0.017

0 . 062 0 . 080 0 . 110

L e n g t h

-

225

m

1 7 2

m

150

m

' Type

b r i d g e a n i d s h.

b r id g e a f t

b r i d g e a m i d s h .

6

b r i d g e

a f t

p

I

6

7

8

9

1 0

TABLE COEFFIClEaPS FOR TFE

TRANSVERSE WZCE

Am YAW

MOK3NT

ON TANKERS DUE TO

CVRRENT FORCE

FOR

THE

LOADED

CONDITION

I N DEZP WATER -

l

t r a n s v e r s e 1 y a w

C o n d i t i o n

'

D a t a t a k e n

f r o m

r e f .

~.

0.055

-

0.038

-

0.039

0 . 042

0.075

- 0 . 051

b 5

- 0.019

0.003

- 0 . 023

0.020

0.044

0.025

0.040

0.017

- 0.003

- 0 , 0 3 2

0.029

loac led

.

b a l l a s t

l o a d e d

b a l l a s t

l o a d e d

b a l l a s t

Loaded

b a l l a s t

l o a d e d

l o a d e d

b a l l a s t

S h i p

NO.

2

4

5

6

7

8

9

10

TABLE

6 -

THE

MMPUM

REQUIRED

8UBMERGED W IGm

AND TXE

APPROXIMATE DlRMETERS OF TH ANCIWR LINES

2

2

2

2

3

'

3

3

3

4

5

5'

0.748

0 . 830

0 . 646

0 . 487

0 . 7 1 1

0.577

b2

0.039

0.004

0 . 036

0.014

0 . 013

- 0.014

0 . 032

0 . 003

0.037

0 , 0 5 1

0.026

b l

0.786

0.880

0.697

0 . 785

0.707

0 . 7 3 1

0.718

0 . 735

0.764

0.819

0.879

S h i p

NO.

2

3

4

5

6

7

8

9

1 0

0 . 018

0 . 0 3 1

0.034

0 . 072

0 . 082

0 . 058

bl

0 . 0451

0 . 0338

-

0 . 0765

0.0524

0.0216

0 . 0059

0.0526

0 , 0335

0 . 1025

-

0 . 0881

-

0.0644

b3

0.003 0.034

U-3 s t u d l i n k c h a i n

s t e e l w i r e

0.003-

0.018

0.014

0.028

0.016

0.010

0.004

0 . 052

0.023

0.014

-

0 . 012

0 . 012

0 . 024

0 . 109

0 , 0 4 3

0 . 051

b2

0.0617

0.0800

0 . 0571

0.0738

0 . 0531

0.0730

0.0596

0.0722

0 . 0721

-

0 . 0681

0.0726

0.004

0.028

0.015

0.007

0.001

-

0 . 0 0 1

0.005

0.016

0.032

0.031

s u b m er g e d w e i g h t

p e r m e t e r l e n g t h

2 1 1 k g

3 1 . 2 k g

0 . 015

0 . 021

-

0 . 031

0 . 075

0.064

0 . 062

b3

0.0110

0.0080

0.0166

-

0.0175

- 0.0063

- 0.0035

0 . 0111

- 0.0090

0.0345

-

0.0202

0.0244

d i a m e t e r

107

P

4 1/4

0.151

- 0 . 072

-

0.090

0 . 047

0 . 038

0 . 0 0 6

-

b4

0.0110

0.0096

0.0146

0.0089

0 . 0073

0.0017

0.0113

-

0.0047

0.0127

0.0145

0.0076

92

mm

3 5,'s

b5

- 0.0010

0 . 0013

0 . 0021

0.0021

0.0024

0 . 0 0 1 3

0 , 0099

0 . 0067

-

0 . 0022

0.0039

0.0024


14/16

OBTAIN ENVIRONMENTAL DATA

I

ESTABLISH DESIRED WORKABILITY

l

I

DETERMINE DESIGN CRITERIA

SELECT DESIGN CONDITION

WITH RESPECT TO:

LOADING CONDITION

WATER DEPTH etc

I

DETERMINE SURVIVAL

ENVIRONMENTAL CONDITIONS

CALCULATE STEADY FORCES

OF STRUCTURE WlTH RESPECT

o

CHECK AND OR

ADAPT

ANCHOR SYSTEM

DETERMINE DlMENSlONS

AND PRETENSIONS O F

VARIOUS ANCHOR SYSTEMS

SELECT PROP R

ANCHOR SYSf E M

no

FOR SURVIVAL

DESIGN CONDITION

ADAPT ANCHOR

SYSTEM FOR

ARE ALL

WORST

CRITERIA

CONDITION

SATISFIED

y s

4 INALIZE DESIGN

Fig The design

of

an anchor system

CHECK DYNAMIC BEHAVIOUR

IN IRREGULAR SEA CONDITIONS

BY M ODEL TEST


15/16


16/16

DRIFTFORCE COEFFICIENT R=

DEEP WATER

VERTICAL PLATE

RECTANGULAR CYLINDER

.T

Fig. - Drift force coefficient in

be m waves

A OGAWA SERIES 6 0 C g= 0. 70 CAPTIVE

2.5

1.2

0 8

0.4

b / w h a = T NSION

I N

HEAVIEST

LOADED

L I N

/

\

I I

6

I

EXCURSION

X/ h

LALANGAS SERIES 60 Cg=0 .60 FREE

2.5

MEASUREMENTS ON A SERIES 60

MODEL IN BEAM WAVES

Cgs0.80

;

L16.7

;

B/T=2.5

WATER DEPTH = 4

X

DRAFT

m = 1 1

x

DRAFT

. FLAT PLATE theory)

2 Pw g 5

L

Fig. 6 Influence of water depth on

the

drift force Coefficient.

Fig. 7 Characteristics of the eight leg anchor system.

/

/

//

/'

/'

I

I

l

I t

I \

I

I

I

l

0.5

1

O

-

.T

RECTANGULAR

CYLINDER

/

/

;/i

"0'

0.2 0.4

0 6

0.8

1

O

Loads on offshore strucrures-otc-1741.pdf

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Transcript of Loads on offshore strucrures-otc-1741.pdf