dry transport of large semi-submersible units - 1987

12
7/21/2019 Dry Transport of Large Semi-Submersible Units - 1987 http://slidepdf.com/reader/full/dry-transport-of-large-semi-submersible-units-1987 1/12  y TRAN SPOR T AT I ON OF LARGE S EM - S UB M ERSI BLE UN I TS  . v an H oo rn : : ; ' . P. a ll i nga Wj smul l e r Tr anspo rt B. V . , IJmu i den , The Net her l ands Ma r i t i me Resea r ch I ns t i t ut e N et herl ands (M ARI N ) SUMMA R Y Dr y trans por t a ti on of sem - submersi bl e dr il li n g u ni t s h as beco me com m on pr a ct i ce in r ecent yea rs . The paper re vi e ws t he mer it s of t hi s mod e o f tr a ns por t at i on and t he t echn i cal probl ems whi c h hav e t o be over co m e in t he e ngi neer i ng of t he tr anspor t . I N TR ODUC TI ON A l t houg h heavy c a r goes have bee n d r y- = o we d s i nc e t he e ar l y s i xt i e s, t he f i r st s em - su b me r si b l e d ri ll i ng rig wa s not dr y- =r anspo rte d un t i l 1 983. T r anspor t at i on by se lfp r opel l ed heavy l i ft vessel s means : - r edu c ed t r ans it t i me, t hus a r edu ct i on of do wn t i me and speed-ups of re venues, poss i bi l it y t o avoi d st o rmya r eas, r e duc ed mo ti on r esponse, henc e reduced i n - e rt i a fo r ces o n t he c ar g o, m anoeuvr abi l ity in al l ci r cumstances, - i ncr ease d s af e t y , hence re duced i nsur ance p r em um D ry t r ans por t at i on of s em - s u bmersi bl e  r i l l i ng uni t s poses man y t echni ca l cha l- : eng eson t he t ra n s por t er [ 1 ]. St andar d ana Lca L m et hods m ay not b e a c c ur at e eno ugh t o mee t a ll of them i n an adequa t e  ay . I n t hi s r es pect mo d el t es t s have p r oven = 0 b e a n accept abl e means to ge nerate d at a on mo t i ons, s l am m ng, hyd r ody nam c l oads, et c . wh i ch ca n be us ed f or th e d es i g n of - ri bb in gs and sea f as t eni ngs. B ec aus e of t he l ar ge ove r han g of t he rig  o at er s a nd t he f ac t t hat of t en t he ou t er coLum n s ar e s i tuated out si de t he ca r r i er ' s  e ck edg e s, much at t en tio n mus t b e pai d to = be st rengt h of t he f l oat er s , over al l as el l as lo cal . S i nce t he net t s uppor t i ng a re a is r el ati ve l y small in r el at i on to the -- ei gh t of t he ri g, a l so the c ar r i er s t r engt h s t b e car e f ul l y check ed to a v oi d any st ru ctural member to become o verstressed . A  ni te e l ement mode l is us e d, i ncor porati ng - th rig an d shi p, as wel l as t he cr i bbi ng  or d er t o det er m n e t hei r mutu a l i nf l uence t he l oa d di st r i but i on. The s hape and = . ens ity o f t he cr i bbi ng la y er s can be pt imzed in t hi s wa y to a v oi d l oc al areas of hi gh st r ess. F ul l s ca le m easur em en ts s u ppo rt th e val ue o f t hi sme t hod. 2. B A C K GR OUN D Tr adi t i onal l y , t h e sem - submer si b l ed r i l - l i ng r i gs wer e t owed b y la r ge o c ean goi ng tu g s. T he t r ansi t s peed wa s l ow, of t en in the orde r of 2- 4k not s . Sometimes t hi s c ou ld be im p r oved b y havi ng t he r i g' s pr opul si on assi st i ng t h e t ug. Th i s is not a l wa y s eco- nom cal especi a ll y if t he r i g' s pr opul s i on s y s t e m was des i g ned f or st at i on k eepi ng. In t he m ean ti m e, j ack - up dri l l i ng rig s wt h t h ei r aw k war d hul l s h apes and f r agi le l egs wer e dr y -t owed on bar ges si nce t he ear l y sevent i es, and dr y - t r ans por t e d b y sel f propel l ed hea vy lift vessel s s i nc e 1979, t he year o f t he i nt r od uct i on of t he S UP ER SER V A N T 1 . N ot unt i l 1983, however , t he firs t s em - submers i bl e dr i l l i ng ri g wa s dr y- tr anspor t ed. W j smu ll e r t r anspo r te d its f i rs t sem -s u bmersi bl e ri g i n th e f ol l o w ng year , a n d s ucces sf u ll y in cr eased its m a rk et share s  n  : e see Tab l e1 . Tabl e 1 Sem - subme r si bl e r i gs dr y- t r anspo rte d by W jsmul l er t o dat e Da t e N am e W ei g ht Fr o m To ( t ) 6/ 84 B e nr e och 17 200 N. Z eal and Spai n 1 /8 5 Sedc o 60 1 7 000 Spai n U. S. Gol f 7 / 86 ROS S 19 200 Ja pan N or wa y 1 0/ 86 Shel f - 6 12 800 F i nl and Shaka fn 1 0/ 86 Bowdri l l 2 17 000 C anada Chi na  

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Dry Transport of Large Semi-Submersible Units

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Page 1: Dry Transport of Large Semi-Submersible Units - 1987

7/21/2019 Dry Transport of Large Semi-Submersible Units - 1987

http://slidepdf.com/reader/full/dry-transport-of-large-semi-submersible-units-1987 1/12

  y

TRANSPORTATI ON OF LARGE SEM - SUBMERSI BLE UNI TS

  . van Hoor n

: : ; ' . P.al l i nga

W j smul l er Tr anspor t B. V. , I J mui den, The Net her l ands

Mar i t i me Resear ch I nst i t ute Net herl ands ( MARI N)

SUMMARY

Dr y transpor t at i on of sem - submersi bl e dr i l l i ng uni t s has become common

pract i ce i n r ecent year s. The paper r evi ews t he mer i t s of t hi s mode of

t r ansport at i on and t he t echni cal probl ems whi ch have t o be over come i n t he

engi neer i ng of t he t r anspor t .

I NTRODUCTI ON

Al t hough heavy cargoes have been dr y-

=owed si nce t he ear l y si xt i es, t he f i r st

sem - submer si bl e dr i l l i ng r i g was not dr y-

=r anspor t ed unt i l 1983. Tr anspor t at i on by

sel f pr opel l ed heavy l i f t vessel s means:

- r educed t r ansi t t i me, t hus a r educt i on of

downt i me and speed- ups of r evenues,

poss i bi l i t y t o avoi d st ormy ar eas,

r educed mot i on r esponse, hence reduced i n-

er t i a f or ces on t he cargo,

manoeuvr abi l i t y i n al l ci r cumst ances,

- i ncr eased saf et y, hence r educed i nsur ance

pr emum

Dr y t r anspor t at i on of sem - submersi bl e

 r i l l i ng uni t s poses many t echni cal chal -

: :  engeson t he t r anspor t er [ 1] . St andar d

ana  LcaL met hods may not be accur at e

enough t o meet al l of them i n an adequat e

 ay. I n t hi s r espect model t est s have pr oven

=0 be an accept abl e means t o generate dat a

on mot i ons, sl ammng, hydr odynam c l oads,

et c. whi ch can be used f or t he des i gn of

- r i bbi ngs and seaf ast eni ngs.

Because of t he l ar ge over hang of t he r i g

  o at er s and t he f act t hat of t en t he out er

coLumns ar e si tuated out si de t he car r i er ' s

 e ck edges, much at t ent i on must be pai d t o

=be st rengt h of t he f l oat er s, over al l as

el l as l ocal . Si nce t he net t suppor t i ng

ar ea i s r el at i vel y smal l i n r el at i on t o t he

- - ei ght of t he r i g, al so t he car r i er st r engt h

st be car ef ul l y checked t o avoi d any

st r uctural member t o become overstressed. A

  ni t e el ement model i s used, i ncor porati ng

- t h r i g and shi p, as wel l as t he cr i bbi ng

  or der t o det ermne t hei r mut ual i nf l uence

_  t he l oad di st r i but i on. The shape and

=. ensi t y of t he cr i bbi ng l ayer s can be

pt i m z ed i n t hi s way t o avoi d l ocal areas

of hi gh st r ess. Ful l scal e measur ement s

suppor t t he val ue of t hi s met hod.

2. BACKGROUND

Tr adi t i onal l y, t he sem - submersi bl e dr i l -

l i ng r i gs wer e towed by l ar ge ocean goi ng

t ugs. The t r ansi t speed was l ow, of t en i n

the order of 2- 4 knot s. Somet i mes t hi s coul d

be i mpr oved by havi ng t he r i g' s propul si on

assi st i ng t he t ug. Thi s i s not al ways eco-

nom cal especi al l y i f t he r i g' s pr opul s i on

systemwas desi gned f or st at i on keepi ng.

I n t he mean t i me, j ack- up dr i l l i ng r i gs

w t h t hei r awkward hul l shapes and f r agi l e

l egs wer e dr y- t owed on bar ges si nce t he

ear l y sevent i es, and dr y- t r anspor t ed by

sel f propel l ed heavy l i f t vessel s si nce 1979,

t he year of t he i nt r oduct i on of t he SUPER

SERVANT 1 . Not unt i l 1983, however , t he

f i r st sem - submer si bl e dr i l l i ng r i g was dry-

t r anspor t ed. W j smul l er t r anspor t ed i t s

f i r st sem - submer si bl e r i g i n t he f ol l ow ng

year , and successf ul l y i ncr eased i t s mar ket

share s

 

n :e see Tabl e 1.

Tabl e 1

Sem- submer si bl e r i gs dr y- t r anspor t ed by

W j smul l er t o dat e

Dat e Name

Wei ght

Fr om

To

( t )

6/ 84

Benreoch

17200 N.

Zeal and

Spai n

1/ 85 Sedco 601 7000 Spai n U. S.

Gol f

7/ 86

ROSS 19200 J apan

Norway

10/ 86 Shel f - 6 12800

Fi nl and

Shaka  f n

10/ 86

Bowdr i l l 2

17000

Canada

Chi na

 

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1 ..1

Fi g. 1. ROSS s em - s ubmer s i bl e dr i l l i ng r i g t r an spor t ed by   MI GHTY SERVANT 2 

f r o m J apan t o Nor way

Bec ause of t he gr eat s pac i ng of t he r i g

f l oat e r s , al l r i gs wer e l oaded at hwar t s hi ps

on t he car r i er . I n t hi s way max i mum s uppor t

ar ea i s achi e ved whi l e keepi ng t he over hang

at a m ni mum ( di agonal l y pos i t i oni ng of t he

r i g wi l l i nc r eas e t he s uppor t ar ea but al s o

t he over hang) . Fur t her mor e, t he r i g  s

s t r engt h member s mor e or l es s coi nc i de wi t h

t he car r i er s s t r engt h member s .

F i g. 2 i l l us t r at es t he over hang of t he

var i ous r i g f l oat er s . I t i s obvi ous t ha t an

ocean t r ans por t of t hi s t ype of car go can

on l y be done af t er ext ens i ve f eas i b i l i t y

s t udi e s .

3. TRANSPORT ENGI NEERI NG

3. 1 I n t r oduc t i on

Bef or e a heavy l i f t t r ans por t can be

r eal i z ed a s ubs t ant i al engi neer i ng ef f or t i s

r e qui r ed t o ens ur e i t s f ea s i bi l i t y and

s af e t y. Dependi ng on The t ype of car go

spec i al at t ent i on mus t be pa i d t o spec i f i c

a reas [ 1] . I n case of l ar ge sem - s ubmer s -

i bl es , l oaded at hwar t s hi ps on deck, t hes e

ar eas ar e:

- des i gn envi r onment a l c ondi t i ons ,

- mot i on r e spons es ,

- s l amm ng,

- f l oat er s t r engt h,

- deck s t r engt h car r i er ,

- c r i bbi ng des i gn

- s eaf a st eni ng ar r angement .

Dynam ca l s t abi l i t y i s i n gener al no

pr obl em gi ven s uf f i ci ent i ni t i al s t abi l i t y ,

because of t he buoyancy c ont r i but i on of t he

over hangi ng f l oat er s , s ee Fi g. 3. The ABS

1. 40 r at i o i s of t en eas i l y met .

3. 2 Des i gn envi r onment al   c ondi t i ons

The s hi p mot i ons ar e i nduced by t he waves

whi ch can onl y be pr edi c t ed by us i ng exi s t -

i ng wave dat a   The r es ul t i ng des i gn sea

s t at e i s of t en a poi nt of di s cus s i on bet ween

t he var i ous par t i es i nvol ved. W j smul l e r

j us t r ecent l y es t abl i s hed a new met hod f or

det er m ni ng t he l ong- t er m des i gn s ea s t at e.

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R OS S

 98 

S H  L F -

98  

Typi cal cross- sect i ons show ng t he

over hang of var i ous sem - submers i bl e

dr i l l i ng r i gs

based on the Gl obal Wave Stat i st i cs

- npdLed and edi t ed by Br i t i sh Mar i t i me

- - l ogy Lt d. [ 2] . The dat a are presented

=erms of pr obabi l i t y di st r i but i ons of

  - ei ght s, per i ods and di rect i ons f or t he

  sel ect i on of

1 4

sea ar eas. An anal y-

=. echni quehas been used t o der i ve r el i -

= st at i st i cs of wave per i od by an anal yt -

 del l i ng of t he j oi nt pr obabi l i t y

__ ut i on of hei ght s and per i ods, t hus

- - '   : J gany use of vi sual obser vat i ons of

 

per Lod, whi ch ar e' known t o be ver y

Li ng. Fr om t he above l ong- t erm wave

- - ' - : i cs ,shor t - t ermdesi gn sea st at es ar e

. :   -  - ,a pr obabi l i t y of exceedance of 5%

  t o es tabl i sh the wave hei ght .

  -= l ong- t erm pr edi ct i on of t he desi gn

' ed i s based on t he U. S. Navy 1ari ne

- - =e dt l as of t he Wor l d ( Vol ume I X,

- -   de Means and Standard Devi at i ons) as

by t he Naval Oceanogr aphy Command

  --'= 

[3].

_- - desi gn w nd speed i s used f or t he

__- _-  check and w nd l oad cal cul at i on.

 -  g n sea st at es ar e used f or t he

- - response cal cul at i on.

- =- i onr esponses

- behavi our of t he vessel was cal cu-

  : -   N w th t he ai d of t hei r com

- __ gr am SHI PMO based on l i near sea-

3

Buoyancy rig

floaters

included

c:

 

s;

Q)

 

Q)

C l

c:

 

ind lever

 

en

 

Vessel's buoyancy

only

 

4

Angle of inclination in deg

Fi g. 3. I nf l uence of f l oat er s on dynam cal

st abi l i t y

keepi ng t heor y. W t hi n t he scope of such a

t heory t he pr obl em of de erm nt ng t he wave

i nduced mot i ons can be separ at ed i n t he

pr obl em of det erm ni ng t he wave i nduced

f or ces i n waves ( vessel f i xed i n space) and

det erm ni ng t he uni t mot i on r esponse r eac-

t i on f orces ( i n cal m wat er ) . The wave

i nduced f or ces, t oget her w th the react i on

f or ces and t he i ner t i a and geomet r i c charac-

t er i st i cs of t he vessel , r esul t , when appl y-

i ng Newt on  sl aw, i n t he mot i on r esponse.

The comput er pr ogr am used f or determ ni ng

t he i nduced wave and r eact i on f or ces i s

based on t wo- di mensi onal st r i p t heory. An

i mpor tant f eat ur e of t he pr ogr am i s t he

i ncor por at i on of f orwar d speed ef f ect s. The

sur ge mot i on i s negl ect ed. I n or der t o

  t une the cal cul at i ons, model t est s wer e

per f ormed. The mot i on r esponses wer e cal -

cul at ed f or beam bow quar t er i ng and head

seas.

The mot i on responses i n i r r egul ar waves

ar e cal cul at ed by mul t i pl yi ng t he squar ed

r esponse f unct i ons w t h a uni - di r ect i onal

( l ong- crested seas) Pi er son- Moskow t z wave

spect r um gi ven by t he f ol l ow ng f ormul a:

  _Bw 

SI; O = Aw

e

2 - 4

wher e A

172 8

( H

si g

) ( T

m

B 691  T

m

)-4

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4

The ar eas under t he r esul t i ng r esponse

spect r a and t hei r second and f our t h moment s

ar e cal cul at ed w t h:

m

n

 

wns

 w 

dw

 

resp

f or n

  4

Si nce t he ampl i t udes of t he mot i on ar e

not exact l y Rayl ei gh di s t r i but ed, a br oad-

ness par amet er i s cal cul at ed f or each

spectrumusi ng:

2

2 mOm4 - m

2

 

=

mOm4

Gi ven t he r esponse spect r a and t he br oadness

par amet er s, t he si ngl e si gni f i cant ampl i -

t udes ( mean val ue of hi ghest one- t hi r d) ar e

cal cul at ed us i ng:

Si ngl e si gni f i cant r esponse ampl i t ude

2/ mO CF

i n whi ch CF

correct i on f act or t o t ake t he

br oadness i nto account

V(l - E2 

The ext reme val ues of a r andom process

are dependi ng on t he number of observat i ons

or , mor e meani ngf ul , dependi ng on t he dur a-

t i on of t he pr ocess bei ng st at i onar y. Thi s

s tat i onary per i od i s t aken as si x hour s,

anal ogous t o t he desi gn sea st at e cal cul a-

t i ons. Gi ven t he r esponse spect r a, t he most

pr obabl e si ngl e ext reme ampl i t udes ar e

cal cul at ed :

Si ngl e ext r eme r esponse ampl i t ude

 

m V2

l n

(60)2

T

\   \

 

2lT

V m

i n whi ch T st at i onary st ormper i od

si x hour s.

For up t o f i ve di f f er ent poi nt s, f i xed t o

t he vessel , l i near accel erat i ons can be cal -

cul at ed i n t he t hr ee di r ect i ons of t he

shi p

I

saxi s. The l i near poi nt accel er at i ons

ar e composed of t he l i near shi p accel er a-

t i ons, t he angul ar shi p accel er at i ons and

t he ear t h- bound accel erat i on of gr avi t y. For

t he f ormul as, see Fi g. 4.

Convent i onal l i near mot i on theory assumes

smal l mot i on ampl i t udes and an i r r ot at i onal

and i deal f l ui d medi um Thi s means t hat a

number of phenomena, e. g. l ar ge mot i on

ampl i t udes and vi scous ef f ect s as vor t ex

sheddi ng at bi l ge keel s and bi l ges ar e not

accounted for . When cor r ect ed f or i n a

pr oper way [ 4] t hi s i mper f ect i on i s not

ser i ous, whi ch expl ai ns t he success of

l i near seakeepi ng t heor i es .

av erti cal   (x p-xG HH Yp -YG ) +i

G

  atransvers e   -x

 

)JI1 'YG-(z -zG) ¢; -g· sin  

PT  .

p.. p ..

alongitudina l   -(Y p-YG ) -(zp -zG )O-g.sin 0

G(XG ,YG ,ZG)

P( xP'YP'Zp)

Fi g. 4. Tr i - axi al poi nt accel er at i on

3. 4 Model t ests

For t he exper i ments use was made of a

1

t o 40 scal e model of t he M ghty Ser vant 2 .

The r i gs wer e r epr esent ed by l i ght wei ght

f l oat ers and st eel wei ght s, see Fi g.

The

connect i on between t he f l oat er s and t he shi p

model consi st ed of a si x component f orce

t r ansducer f or r ecor di ng t he hydr odynam c

l oads act i ng on the f l oat ers.

Al l t est s wer e per f or med i n t he Sea-

keepi ng Labor at or y of MARI N. They wer e

per f ormed i n l ong- crested i r r egul ar waves i n

or der t o get an i mpr essi on of t he st at i s t i -

cal pr oper t i es of t he hydrodynam c l oads.

Measur ement s compr i sed t he l oads act i ng on

t he f l oat er s, t he var i ous mot i on and accel -

er at i on l evel s and t he i mpact pr essur es

under t he f l oat er s. The i ner t i a l oads act i ng

on t he r i g wer e cal cul at ed ( i n t he t i me

domai n) f r om t he recor ded accel er at i on

l evel s. The t ot al l oads wer e obt ai ned by

addi ng t he hydrodynam c and i ner t i a compo-

nent s.

The t est s showed t hat t he over hangi ng

f l oat er s af f ect bot h t he wave i nduced r ol l

exci t at i on and t he r est or i ng r ol l moment i n

a ver y non- l i near way. The t ot al l oads act -

i ng on t he r i g i n beamseas exceed t he l oads

i n head seas by mor e t han a f act or of t wo

i ndi cat i ng t hat beam seas r epr esent a ver y

unf avour abl e wave di r ect i on.

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el t est r esul t s ver sus predi ct i on

or der t o check t he val i di t y of t he

r esponse pr edi ct i on ( i gnor i ng t he

=== of overhang) , a compar i son i s made

_ =he model t est r esul t s. The compar i son

 e f or t he f ol l ow ng desi gn sea st at e:

t i a l oads, t he t r i - axi al poi nt accel er at i ons

ar e used and t hese ar e i n gener al overest i -

mat ed ( hence on t he saf e si de ) compared

w t h t he model t est r esul t s. Especi al l y t he

ver t i cal and l ongi t udi nal accel er at i ons i n

head seas ar e appr oxi mat el y 150% of f . Thi s

can be expl ai ned t o some ext ent by t he di f -

f er ence i n f or war d speed ( zer o f or model

t est s, 6 knot s f or pr edi ct i on) and t he f act

t hat sur ge mot i ons ar e negl ect ed i n t he cal -

cul at i ons.

The measur ed and pr edi ct ed f or ces f or t he

desi gn sea st at e ar e gi ven i n Tabl e 3. The

measur ed f or ces i ncl ude al l hydr ost at i c

f or ces and t hei r phase r el at i onshi ps. The

measur ed val ues gi ven i n Tabl e 3 ar e t he

si ngl e ext r eme ampl i t udes, cor rect ed f or a 6

hour st orm per i od. Some of t hese l oads ar e

st r ongl y asymmet r i c, - due t o t he i nf l uence of

t he hydr odynam c l oads, see al so Tabl e  

si g   8. 5 m T

m

  10. 5 s

-  e compar i son of t he si ngl e ext r eme am

= es i n beam bow quar t er i ng and head

=   see Tabl e   I t shows that the angul ar

2ot i ons ar e si gni f i cant l y under est i -

because of t he l ong nat ur al r ol l

and t he f act t hat t he addi t i onal r ol l

 =. at i on i nduced by t he pont oons i s not

i nt o account , see Fi g. 6.

: - r cuna e

Ly

t he angul ar mot i ons ar e not

  par ameters. For cal cul at i on of i ner

Fi g. 5. Model i n head seas

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Tabl e 2

Compar i s on mot i o ns model t es t s - c omput er pr edi c t i on   ROSS   r i g

Headi ng, mode Uni t

Measur ed  P r e di c t e d

/ .  

Des i gn

Remar ks

val ue

 E K SEAS

Ro l l

de g

4. 6 0. 4

- 91

no

P i t c h

de g

1. 9

0. 4

- 79 no

Ver t i c a l ac cel e r at i on g

0. 31 8 0. 229 - 28 yes Under es t .

L o ngi t u di n al a cc el e r at i o n

g

0. 012 0. 012 0 no

T r ans ver s e ac c el er at i on g

0. 20 7 0. 192 - 7 yes Under es t .

 

W

QUARTERI NG SEAS

Rol l deg

3. 3 0. 2

- 94 no

P i t c h

de g 6. 5

7. 2

+11

no

Ver t i c a l ac c el er at i on g

0. 183 0. 22 7

+24

yes Over es t .

L ongi t u di n al ac c e L e r a

 

L on g 0. 10 6

0. 20 7

+95 yes

Ove r es t .

T r ans ver s e ac c el er at i on g

0. 131 0. 088 - 33 yes Under es t .

 

HEAD SEAS

Ro l l

de g

5. 6 0. 0 no

P i t c h deg 6. 8 8. 1

+19

no

Ver t i c al ac c el er at i on

g

0. 076 0. 19 7 +159

yes

Over est .

L o ng i t ud i n al ac ce l er at i on g 0. 09 5 0. 2 35

+147

yes

Over est .

T r ans ver se ac c el e r at i on

g

0. 107 0. 000 no

  Cor r ec t ed f or 6 hour s t or m per i od

Tabl e 3

Compar i s on l o ads model t es t s - c omput er pr edi c t i on ROSS r i g

Head i ng, mode Uni t

Measu red P r edi c t ed

/ .

Des i gn

Remar ks

v al u e

 E K SEAS 

Fx t ot al

t

26 8 228 - 15 no

Fy t ot a l t

6183 4251 - 31 yes

Underes t .

F

z

t o t a l t 6172 4351 - 30 yes Underes t .

 

W QUARTERI NG SE AS

Fx t ot a l

t 2050 3933

+91 yes Over es t .

Fy t o t a l

t 4317 1672 - 61 yes

Under est .

F

z

t ot a l t 402 6

4313

+7 yes

Over est .

 

HEAD SEAS

Fx t ot a l

t

1848 446 5

+142

yes Over es t .

Fy t ot a l

t 3994 0

no

F

z

t ot a l

t 1795 3743

+108 yes Over es t .

  Cor r ec t ed f or 6 hour s t o r m per i od

  I nc l udi ng 6. 6 deg s t at i c wi n d heel

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Tabl e 4

Tr ansver se l oads on sem - submer si bl e i n beam seas

Fy total

Uni t Maxi mum st ar boar d

Maxi mum por l si de Doubl e maxi mum

Measur ed

t

2228

6183 8411

Pr edi ct ed t

4153

4153

8306

 o  

o n t

 o  

o n t

 

oaputer c lcul t ions

 od el tests

  6. Compar i son of r ol l moment s:

comput at i ons and model t est s

  St r engt h r i g/ shi p

The st r engt h of t he car go i s i n gener al

  r esponsi bi l i t y of t he car go owner but

; st r engt h cannot be checked w t hout t he

=?

char act er i st i cs and vi ce ver sa. Cl ose

per at i ons bet ween bot h t he car go owne r s

= neer s and t he t r anspor t at i on - engi neer s

essent i al . I n or der t o st udy bot h t he

  engt h of t he r i g and t he shi p, a FEM ( Fi -

=e El ement Met hod) beam model of a t ypi cal

=ss+s ec I on i s made, see Fi g. 7 [ 5] .

nce al l desi gn l oads have been estab-

3  ed t he st r esses i n al l member s ar e

l at ed and checks are made t o see i f any

chese member s ar e over st r essed. I t i s

  r

t hat t he i nt er act i on between t he r i g  s

=zcer and shi p s mai n deck i s cr uci al .

: ne cr i bbi ng wood i s model l ed as a set of

  : :   i nearspr i ngs. By changi ng t he st i f f -

and/ or t he l ength of t he spr i ngs, t he

_ t r ansf er can be cont r ol l ed and op

t

 

- e r esul t i ng i n t he l owest possi bl e

=sses i n cr i t i cal spot s of t he f l oat er /

st r ucture. Of cour se, t he r esul t i ng

=sses f r om t he 2- D anal ysi s must be

- :   ned w t h st r esses f r om ot her sour ces,

  s

t he l ongi t udi nal bendi ng moment i n

at er and i n waves. The opt i mum set of

_ Lng spr i ngs must be t r ansl at ed i nt o an

=cL  v e cr i bbi ng ar r angement .

  r i bbi ng ar r angement

:   adi t i onal l y, car goes on boar d heavy

vessel s ar e pl aced on wooden cr i bbi ng

- - whi ch ser ve t he pur pose of absor bi ng

 

Fi g. 7. 2- D FEM of transver se sect i on

of f or war d f l oat er

any unevenness bet ween t he bot t om of t he

car go and t he shi p  s deck. I n case of t r ans-

por t i ng l ar ge sem - submer si bl e r i gs, t he

cr i bbi ng must al so ensur e even l oad di st r i -

but i on between f l oat er and deck. Thi s can be

achi eved by t r ansl at i ng t he cal cul at ed

opt i mum cr i bbi ng spr i ngs i nt o a cr i bbi ng

ar r angement i n whi ch t he hei ght ( i . e. t he

spr i ng l engt h) and t he densi t y ( i . e. st i f f -

ness) i s var i ed over t he w dt h of t he shi p  s

deck, see Fi g. 8.

I n cr i t i cal cases, a sandw ch cr i bbi ng i s

used ( t wo or mor e l ayer s cr oss- w se com

bi ned) . The cr ossi ngs can t hen be desi gned

so t hat t he wood st ar t s t o def orm excessi ve-

l y j ust bef or e t he f l oat er of t he r i g and/ or

suppor t i ng st r uct ur e become over st r essed.

The i ncreased l oad i s t hen absor bed by t he

sur r oundi ng suppor t s, see Fi g. 9. I f a

cr ossi ng st ar t s t o def orm excessi vel y t hi s

does not mean t hat i t col l apses and l ooses

i ts l oad bear i ng capaci t y. Af ter t he def or -

mat i on t he t r ansf er r ed l oad w l l i ncr ease

onl y l i t t l e, i n spi t e of l ar ge compr ess i on.

The r esul t s of t he cr i bbi ng anal ysi s ar e

st r ongl y i nf l uenced by t he pr oper t i es of t he

pr oposed cr i bbi ng wood. Especi al l y t he pr es-

sur e at whi ch t r ansm ssi on f r om l i near t o

non- l i near behavi our t akes pl ace i s an

i mpor t ant par ameter .

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  n l orr n c r

ibb

inq /

  \  

\ I

_  ' 

1   ' I SPeci,'ccibbiogde go

C ; 1 :   /

1 ; ;:  j J

8

F i g. 8. I nf l uence of c r i bb i ng des i gn on l oa d

di s t r i but i on '

Because of t he l ar ge bi l ge r adi us of s ome

s em - submer s i bl e r i gs t he ef f ec t i ve suppor t -

i ng ar ea i s i ns uf f i c i en t t o absor b al l t he

l oa ds . I n s uch cases , a s ol ut i on can be

f ound i n i nc r ea s i ng t he s uppor t i ng ar ea by

i nc l udi ng t he bi l ges , s uppor t ed wi t h cus t om

shaped c r i bbi ng bl ocks , s ee F i g . 10. W t hou t

t hes e s uppor t s bot t om of t he f l oat er s and

webs t r u c t ur e may s u f f er f r om l ar ge t r ans -

ver s e s t r esses . The bi l ge s uppor t s may

i nc r ease t he suppor t i ng' ar ea as much as 30

Measur ement s on t he f ul l s cal e behavi our

of t he c r i bbi ng ar r angemen t of t he  Shel f - 6 

dur i ng t he t r ans por t f r o m Fi nl and t o

Shakal i n wer e' made. The met hod us ed and

\fh =T

P r e s s u r e i n c r e a s e c e n t e r b l o c k

\ I

  i

P r e s s u r e i n c r e a s e s i d e b l o c k

Comp r e s s i o n i n mm m

F i g. 9. Pr i nc i pl e of l i m t i ng maxi mum l oad

by exc es s i ve def or mat i on of c r i bbi ng

c r os s i ng

r es ul t s ob t ai ned wi l l be di s cus s ed i n

Sec t i on 4. 3.

S t ee l s u p p o r t

S t e e l c l i p

 

F i g. 10. Bi l ge s uppor t

3. 8. Se af as t en i ng a r r angement

I n or der t o pr event t he car go f r om s hi f t -

i ng, i t has t o be s ecur ed t o t he s hi p' s

deck. Thi s i s done by pl ac i ng s t eel br acket s

( s o- cal l ed s eaf as t eni ngs ) agai ns t s t r ong

poi nt s of t he car go and wel d t he s e s ea-

f as t e ni ngs t o t he mai n deck, s ee F i g. 11.

  u l k h e a d

S t r i n g e r

C r i b b i n g

F i g. 11. Seaf as t eni ngs s ecur ed aga i ns t

s t r ong poi nt car go

Re l a t i ve mot i on bet ween car go and s ea -

f as t e ni ng i s s t i l l pos s i bl e, t hus al l owi ng

f or di f f er ences i n f l ex i bi l i t y . Becau s e t he

f l oa t er s of a s em - s ubmer s i bl e r i g pr ovi de

no s uppor t s f or t he t r ans ver s e s eaf as t en-

i ngs , s o- cal l ed s t r ong boxes ar e necessar y.

I n s ome cas es t hes e s t r ong boxes ar e de -

s i gned and cons t r uc t ed s o t hat t hey al s o ac t

as l oad s pr ea di ng devi c es agai n t o i nc r ease

t he s uppor t i ng ar ea of t he f l oat er s . For a

t ypi c al s t r o ng box , s ee F i g . 12.

The l oads ac t i ng on t he car go ar e:

- i ne r t i a l oads due t o s hi p mot i on s ,

- wi nd l oad,

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 2 s i t Y. l oads due t o wi nd hee l and

  gul ar s hi p mot i ons ,

_ Cr odynam c l oads ( s l amm ng, s ubmer gi ng) .

  t r i n g   r

12. Typi cal s t r ong box

: a case of l i t t l e or no over hang and t he

of model t es t r e s ul t s , t he ext r eme

- " s on t he car go ar e cal cul at ed f r om t he

== i a l oads ( i nc l ud i ng t he s t at i c par t due

angu La r mot i ons ) and t he wi nd l oad ( i n-

·   ng s t at i c par t due t o wi nd heel ) ,

ng s t a t i s t i cal i ndependency. Si nc e

 

mot i ons and wi nd f l uc t uat i ons can be

- :   de r ed t o be i ndependent event s , t he

=j abi l i t y t ha t t he ext r emes of bo t h event s

_ s i mul t aneousl y, i s smal l . As sum ng al l

=e e l oads t o be i n phas e woul d l ead t o

s er va  Lve r es ul t s . Thi s i s al s o c l ea r l y

s t r at ed wi t h t he model t es t r es ul t s .

  or ement i oned l oads on t he car go ar e

_ : er ac t ed by:

== ct i on bet ween car go and c r i bb i ng wood,

c : 2a f as t eni ngs ,

  r odynam c l oads .

: he l at t er ar e of t en 180 degr ees out of

e

wi t h t he i ner t i a l oads , i . e. l oads due

=011 mot i ons .

  ae f r i c t i on bet ween wood and s t ee l i s i n

- or der of

30-50  .

Bar nac l es , r us t , et c .

even i ncr ea se t hi s per cent age.

-   j smul l er Tr anspor t B. V. i ncor por at es

of f r i c t i on i n i t s s t andar d sea f as t en i ng

- zn.Iat

 

ons

h t he s t at i s t i cal i ndependenc y of t he

- ; - and t he deduc t i on of f r i c t i on f or ces

_ _ t he t ot al s ea f a s t eni ng l oads , ar e of t en

_   nt of di s cuss i on bet ween t he t r ans po r -

o n engi neer and t he war r ant y s ur veyor s .

; : - -a t er , r ep r es ent i ng t he i ns ur ance com-

- :   S 

t end t o be mor e cons er vat i ve, r es ul -

 

i n s upe r pos i t i on of al l ext r eme l oa ds

. " no r educ t i o n f or f r i c t i on. I t mus t be

e c t hat t he t r ans por t company has t he

" ' goal , namel y t o pr ovi de a s af e t r ans -

9

por t . Exampl es her eof ar e gi ven i n t he

f ol l owi ng chapt er .

4. THE TRANSPORTS

4. 1 I nt r oduc t i o n

Once al l engi neer i ng i s f i nal i z ed and t he

number s conf i r m t he f eas i bi l i t y , t he ac t ual

t r ans po r t can be ef f e c t ed.

Be f or e l oad- out , t he cr i bbi ng ar r angement

i s l ai d out and s ecur ed ont o t he mai n deck.

The gui de pos t s ar e po s i t i oned and wel ded t o

t he deck and t he s e af as t en i ngs ar e pr epar ed,

as wel l as t he s t r ong box es ( i f not al r eady

i n pl ace) .

The l oad- out wi l l t ake pl ace wi t hi n a

s ui t abl e wea t her wi ndow, wi t h t he s ubmerged

vess el pr ef er abl y weat her vani ng behi nd one

bow anchor . The s em - s u bmer s i bl e r i g i s

s l owl y appr oachi ng , under con t r ol of 3 or 4

hi ghl y manoeuver abl e ha r bour t ugs . Once over

t he deck, t he r i g wi l l be hook ed up t o t he

s hi p' s t ugger wi r es whi ch wi l l ac cur at el y

po s i t i on t he r i g agai ns t t he gui de pos t s ,

t hus ens ur i ng an exac t pos i t i on over t he

c r i bb i ng ar r angemen t . The s hi p t hen s t ar t s

debal l as t i ng and l i f t s t he r i g out of t he

wat er af t er whi ch t he s eaf as t e ni ng

commences .

4. 2 Obs er vat i ons dur i ng t he t r ans por t s

Upon compl et i on of t he sea f as t eni ng t he

s hi p wi l l depa r t . Al l navi ga t i onal aspec t s

of t he t r ans i t ar e l ef t t o t he r es pons i bi l -

i t y of t he mas t er . He has at hi s di s pos al

weat her f ac s i m l e, t el ex and r adi o equi pment

whi ch enabl es hi m t o ga t her al l av ai l abl e

wea t her i nf or mat i on f or t he ant i c i pa t ed

r ou t e. Somet i mes add i t i onal weat her r out ei ng

i s r equi r ed by t he war r ant y s ur vey or . Th i s

may be he l pf ul i n r emot e ar ea s wher e l es s

weat her i n f or mat i on i s r ea di l y av ai l abl e.

W t h t he avai l ab l e wea t her i nf or ma t i on t he

mas t er dec i des on t he opt i mum cou r se and

s peed t o ensur e mot i ons t o s t ay wi t hi n t he

c r i t i c al l i m t s .

For t he r ecor ded wi nd/ s ea s t at es and cor -

r espondi ng mot i ons and s l ams dur i ng t r ans -

po r t at i on of t he " ROSS" r i g f r om J apan t o

Nor way, s ee Tabl e 5.

Tabl e 5 i ndi cat es t hat t he envi r onment al

condi t i ons wer e m l d t h roughout t he compl et e

voyage ( maxi mum wave hei ght 4.0 m) and as a

r es ul t , t he shi p ha r dl y moved at al l . Onl y

l i t t l e s l amm ng agai ns t t he over hangi ng

pon t oon was obs er ved ar ound J ul y 9.

Recor di ngs of t he ot her dr y t r anspor t s of

s em - s ubmer s i bl es s how s i m l ar number s ; m l d

sea s t at es , l i t t l e mot i ons , no r epor t s of

s l amm ng. St or my ar eas i nc l ud i ng t yphoon

ar ea s wer e succes s f ul l y avoi ded.

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10

Ta bl e 5

Recor d of   ROSS  t r an s por t at i on

Dat e

Spe ed

W nd s peed

Se a Swel l

Ro l l Pi t c h

Sl am

i n kn

i n kn

Hei gh t Per i od Hei ght Per i od

i n deg

i n de g

 

23/ 6

Depar t ur e Hi r os hi ma

24/ 6

11 . 5

10 0. 5

1

 

-

25/ 6 10 . 5

10

1. 0

3

2. 0

6

 

26/ 6 12 . 9 13 0. 3

1  

27/ 6 12. 5

8 0. 5 2

1. 0

5

 

28/ 6

11. 8

7

0. 5 1

1. 0

5

 

0. 5

 

29 / 6 12. 5

6 0. 5 1

1. 0

6

 

30 / 6 12 . 0

10 0. 5

2

1. 5

6

 

1/ 7

9. 8

20

1. 0

3

2. 5

8

 

2/ 7

10. 0

22

1. 0

3

3. 0

7

 

3/ 7

11 . 0

10 0. 5

1

1. 5

4

 

4/ 7

Bunker s t op Si ngapor e

5/ 7 1 2. 0 10

 

6/ 7

14. 9

10

 

7/ 7

12 . 3

6

0. 5

2

 

8/ 7

10 . 0

15

1. 0

3

3. 5

 

0. 5

 

9/ 7

9. 0

20

1. 5

2

4. 0

8

 

1. 5

Sl i ght

10/ 7

10. 0

20

1. 5

3

3. 5

7

 

0. 5

 

.

11/ 7

 

»

12 0. 5

2

2. 5

7

 

0. 5

 

12/ 7

11 . 0

10 0. 5

1 2. 5

7

 

0. 5

 

13/ 7

12 . 6

5 0. 5 2 2. 0

7  

14/ 7

12. 8

10 0. 5 1 2. 0

8

 

0. 5  

15 / 7

12. 5 10 0. 5

2

1. 5

8

 

0. 5  

16 / 7

12 . 5

16

1. 5

2

1. 5

5

 

0. 5  

17 / 7

12. 5

20

1. 5

3

2. 0

7  

0. 5  

18 / 7

14. 5 20 2. 0

4 2. 5

7

  0. 5  

19 / 7

15. 5 34 2. 0

4

3. 5

8

 

0. 5

 

20 / 7

12. 0

15 0. 5

3

2. 0

7

 

21/ 7

9. 0 10 0. 5

 

22 / 7

1. 0

12 0. 5

2

 

23 / 7

8. 5 20

1. 5

3

1. 5

6

 

24 / 7

12. 5

5  

25 / 7

7. 0

18 0. 5

2

0. 5

4  

26/ 7

Suez Canal passage

27 / 7

Suez Canal passage

28 / 7

Suez Canal pas sage

29 / 7

Suez Canal pa s sage

30/ 7

12. 5

10

0. 5

3

 

31 / 7

13 . 0

 

1/ 8 13. 0 5

 

2/ 8 13. 3

10 0. 5

3  

3/ 8 12. 5

5  

4/ 8

10. 5

20

1. 0

3

1. 5

6

 

5/ 8 12. 5

10 0. 5

3

  0. 5  

6/ 8 12 . 0

10 0. 5

2

1. 5

10

 

7/ 8

11 . 3

6 0. 5 2

2. 5

10

 

1. 0

 

8/ 8

13 . 0

 

9/ 8

13 . 0

 

10/ 8

13. 0

 

l l / 8

Ar r i val Sa nde f j o r d

  I ndi cat es ni hi l

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?ression measurements on cribbing

cribbing arrangement of the  Shelf-6 

rt from Finland to Shakalin was

studied and some simple measure-

-ere taken during several stages of

==ansport, i. e. before and after load-

  after arrival, before unloading of

 

[6] .

-- 13 indicates the location of the

- eaents under forward floater.

_-- transverse shape of the cribbing was

_=--=iaed by Wijsmuller Engineering B.V.

:he aid of a 2-D finite element beam

; :

rig and ship. Before load-out, this

shape was checked by measuring

-e:'ght at various locations, see Fig.

:= is clear that the shape is correct,

- = e complete cribbing is a little too

343  147

neasuremcnts

before and after the voyage

2  Additional

  sur  nrs

after the voyage

_  . Loacation of measurements

Measured

T e ore tic al

 

_

Port 10 c.l . 10 STBD 20

Transv . pas.  m fro m c.l . 

Cribbing height before load-out

load-out, the distance between the

the floater bottom was measured

the same locations. The results are

=

 ig. 15.

11

--o--o-- -

Before load-out

A fter load -ou t

440

E

E

 

T -

en

  l J

::c

40

Compres sion

o  

20 PORT 10 c. l. 10 STBD 20

Transv . pas.  m from c. l . 

Fig.

15.

Cribbing height before and after

load-out

As is shown the resulting compression is

fairly uniform with the exception of the

outside blocks. This is in accordance with

the intentions to have the centre blocks

absor b most of the sta tic load and have the

outside blocks absorb the dynamic loads (due

to roll, sway and wind forces on the rig).

The cribbing height was again measured

53

days later, prior to the unloading of the

rig. During the time span of the transport

the rig settled itself a little deeper in

the cribbing as a result of its dead weight

and some dynamic loading, see Fig. 16.

Fig. 16 shows that the plastic compres-

sion due to dynamic loads is relatively uni-

form along the width of the deck. The fact

tha t the outs ide blocks are not more

deformed than the centre blocks can be

explained by the lack of rolling during the

transport. The maximumroll angle observed

was in the order of 1.

0

degree. The unif orm

deformation is caused by the heave and pitch

motion experienced en route. The maximum

observed pitch angle was 3.4 degrees, when

the transport was going through the tail of

typhoon  ELLEN (swell of 4.5 metres).

The measurements as discribed above are

not very accurate and were hampered by im-

perfections on the ship's deck and marine

growth on the floater of the rig. However,

the measurements do indicate the behaviour

of the shaped cribbing which is in line with

its design helping to avoid high loads at

the deck edges.

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  _  __ __ Dynam ic co m pre ss io n

440  T otal co m pre ss ion

 

12

4. 4 Seaf as t eni ng s

Seaf as t eni ngs ar e al ways vi s ual l y ob -

s er ved dur i ng and af t er t he t r anspor t . I n

gener al , t hey ar e never l oaded t o t hei r

des i gn l oads , i ndi c at i ng:

ac t ua l exper i enced envi r onment al condi -

t i ons ar e l es s s ever e t hen t he pr e di c t ed

des i gn condi t i ons ;

f r i c t i o n bet ween t he c r i bbi ng wood and

t he car go count er ac t s t he i ner t i a l oads

t o a l ar ge ext ent .

The l at t er was c l ear l y proven dur i ng t he

f i nal phas e of t he   Shel f - 6  t r anspo r t .

Af t er r emoval of al l s e af a s t eni ngs , t he

wea t he r s uddenl y s t ar t ed t o det er i or at e f as t

and wi nd pi c k ed up, exceedi ng Beauf or t 10.

Waves s t ar t ed t o gr ow t o 6 met r es . I t was

t hen dec i ded t o l ea ve t he s chedul ed unl oad-

i ng ar ea and t r y t o f i nd s ome shel t er c l os e

t o t he s out her n poi nt of Shakal i n I s l and.

The r i g was s t andi ng l oos e on deck, onl y

kep t i n pl ace by f r i ct i on, f or t wo day s

be f or e i t was s af el y unl oaded .

The ac t ua l l oads on s eaf as t eni ngs need t o

be meas ur ed s ys t emat i cal l y over a l ar ge

per i od of t i me. A f ul l s cal e meas ur ement

pr oj ec t i s pr es ent l y be i ng s t udi ed.

 

f   l

  -  

A fter

 

l

 

r

.. 0 ..•.. O   1  •..__

PORT 10 c. 1 . 10 STBD 20

Transv . pas.

 r 

from c.l. 

F i g. 16. Per manent compr es si on dur i ng. t r ans -

po r t

f i ve l ar ge

di s t ance of

t he i nf or -

W j smul l er

ex per i ence

5. CONCLUSI ONS

Af t er dr y t r anspo r t at i on of

s em - s ubmer s i bl es over a t ot al

52000 m l es , compl ement ed wi t h

mat i on f r om model t es t s ,

Tr anspo r t B. V. gai ned va l u ab l e

and know- how i n t hi s f i el d.

The model t es t s wer e concent r at ed on t he

ef f ec t of t he l ar ge ov er hang caus ed by t he

at hwar t s hi ps or i ent at i on of t he s em -

s ubmer s i bl e uni t s on t he deck of t he car r i -

er . The f l oat er s caus ed non- l i ne ar ef f ec t s

i n t he s hi p mot i ons and s uf f er ed f r om s l am-

m ng, espec i al l y i n beam s eas . I n pr ac t i c e,

howeve r , s l amm ng aga i ns t t he f l oat e r s

( ove r hangi ng up t o 26 met r es each s i de )

cou l d be m ni m zed by t he mas t er by car e-

f u l l y r out ei ng t he shi p ar ound s t or my ar eas

and s el e c t i ng opt i mum cour se and speed i n

cas e of i nc r eas i ng s ea s t at es .

Us i ng a 2- D f i ni t e el ement anal y s i s , bot h

t he s t r engt h of t he car r i er and t he r i g  s

f l oat er can be chec ked, i nc l udi ng t hei r i n-

t er ac t i on. Thi s i nt er ac t i on can be cont r ol -

l ed by changi ng t he cr i bb i ng des i gn. The

shaped c r i bbi ng r esul t s i n a dec r eas e of

peak l oads near t he deck edges . Ful l s cal e

meas u rement s on such a cr i bbi ng ar r angement

conf i r med t he comput er c al cul at i ons .

The s eaf as t eni ng ar r angement s eems t o be

over - des i gned i n pr ac t i c e. Vi s ual checks

af t er ar r i va l r ev eal ed t hat t he s eaf as t e ner s

had never been l o aded up t o t hei r des i gn

maxi mum Fr i c t i on bet ween t he bot t om of t he

r i g and t he c r i bbi ng wood i s of t en under -

es t i mat ed and, as a r ul e Mar i ne War r an t y

Surveyors do no t al l ow f or any r educt i on of

s eaf as t eni ng l oads due t o f r i ct i on. Ful l

s cal e meas u r ement s ar e r ecommended.

REFERENCES

1. Van Hoor n, F. ,   Tech ni cal Cha l l enges

Assoc i at ed wi t h Dr y Tr anspor t at i on   ,

Mar i ne Techno l ogy, Vol ume 24, No. 1,

J anuar y 1987.

2. Hogben, N. e  a l ; ,   Gl obal Wave St at i s -

t i c s   , Br i t i s h Mar i t i me Technol ogy L t . d. ,

Sur r ey, 1986.

3.   U. S. Nav y Har i ne Cl i mat i c At l as of t he

Wor l d  , Vol ume I X, Wor l d- W de Means and

St andar d Devi at i ons , Naval Oceanogr aphy

Command Det ac hment , Ashevi l l e, D. C. , May

1981

4. Aal ber s , A. B. and Dal l i nga , R. P. , Model

Mea sur ement s and Des i gn Cal c ul at i ons f or

t he Tr ans po r t of a J ack- up on a Bar ge ,

RI NA s ympos i um on Of f s hor e Tr ans por t and

I ns t a l l at i on, 1984.

5. Ri j ke, R. J . and Zaat , L . , A F . E. M.

Model of a Mi ght y Servant 2 t r ans ve r s e

Web

- ROSS Ri g t r anspor t - , Weng Repor t

85. 507, Mar ch 1986.

6. Heydr a, J . , Repor t on Compr es s i on

Measur ement s of Shaped Cr i bbi ng , WT

Repor t 4242- I N/ MVR, I J mui den , Febr uar y

1987.