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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
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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-
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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 .
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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 .
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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
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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 :
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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
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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
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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
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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
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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
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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 .
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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
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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
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8/18/2019 Loads on offshore strucrures-otc-1741.pdf
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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
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