A Jacket launch computerprogram compared with two full-scale launches

Behaviour of Offshore Structures,

Elsevier Science Publishers B.V,, Amsterdam, 1985 — Printed in Thfi Netherlands

325

A JACKET LAUNCH COMPUTER PROGRAM COMPARED WITH TWO FULL-SCALE LAUNCHES

Christian Aage', Poul Erik Christiansen' and Jakob Moller"

'The Technical University of Denmark, Dept. of Ocean Engineering, DK-2800 Lyngby, Denmark ^Earl & Wright L t d . , V i c t o r i a Station House, 191 V i c t o r i a S t . , London SWIE, U.K.

'Mïrsk Olie og Gas A/S, Esplanaden 50, DK-1263 Copenhacjc-n, Denmark

SUMMARY

A 3-dimensional mathematical model and a computer program able of simulating the launch of a jacket from a barge are described. The launch i s divided i n t o four dynamically d i s -t i n c -t phases, each charac-terized by -the de-grees of freedom. I t has been attempted to take a l l important parameters into account, such as the v a r i a t i o n of drag c o e f f i c i e n t s with respect to Reynolds' number and slamming on jacket members.

The computer results are compared with measurements of two d i f f e r e n t f u l l - s c a l e launches, the GORM C in 39m water depth and the BERYL B i n 119m water depth, both i n the North Sea. The f u l l - s c a l e launch photographic recording and analyzing methods are described and t e n t a t i v e conclusions are drawn as to the proper choice of hydrodynamic c o e f f i c i e n t s f o r launch c a l c u l a t i o n s .

1. INTRODUCTION

During the development of the Danish o i l and gas f i e l d s in the North Sea a need arose for launch simulation programs which could predict with great accuracy the minimum b o t -tom clearance of jackets launched from barges. The v/ater depth in the Danish f i e l d s is about 40m and the bottom clearance f o r the largest jackets during the launch i s only 3- 5m .

To obtain the desired degree of accuracy f u l l y three-dimensional mathematical models and computer programs had t o be developed, especially because unsymmetrical and damaged conditions ( e . g . a flooded buoyancy tube) had t o be considered. The computer programs should preferably be v e r i f i e d against f u l l -scale launch measurements.

To promote t h i s development f-tersk Olie og Gas A/S decided to carry out f u l l - s c a l e measurements of the GORM C jacket launch which took place on September 3 r d , 1980, The t o t a l mass of the jacket was 4000t and the water depth was 39m , In 1981- 83 a 3-D

mathematical launch model and a computer pro-gram were developed at the Technical Univer-s i t y of Denmark by two of the authorUniver-s. By the kind support of Mobil North Sea Limited the University had the opportunity to carry out f u l l - s c a l e measurements on the BERYL B jacket launch in the B r i t i s h sector of the North Sea on May 8 t h , 1983. The t o t a l mass of t h i s jacket was 14000 t and the v/ater depth was 119m . The two jackets represent nearly the lower and upper l i m i t s f o r launched jackets and so c o n s t i t u t e an excellent material f o r comparison with the computer program.

Several launch simulation programs are commercially a v a i l a b l e , but very l i t t l e has been published on the subject. Hambro (1982) describes a method of launch simulation by d i f f e r e n t i a t i o n of constraints and compares the simulation with model t e s t r e s u l t s . To the authors' knowledge, comparisons between computer simulations and f u l l - s c a l e jacket launches have not been published before. 2. LAUNCH DESCRIPTION

A jacket launch defines the event when a jacket s t a r t s s l i d i n g under i t s own vjeight down the s l i d i n g beams on a ballasted and pretriinmed launch barge. The s l i d i n g can be i n i t i a l i z e d by e i t h e r removing the l a s t sea fastening to the jacket i f the barge t r i m angle i s large enough, or by jacking the jacket to overcome the s t a t i c f r i c t i o n . The launch is completed when the jacket has come to rest i n a stable equilibrium p o s i t i o n . Normally the jacket/barge system w i l l go through four dynamically d i s t i n c t phases during the launch.

Phase 1. The j a c k e t slides down the deck of the barge towards the rocker beams. The jacket has only one degree of freedom r e l a -t i v e -to -the barge.

Phase 2. The jacket slides on the rocker beams which r o t a t e r e l a t i v e to the barge.

hence the number of r e l a t i v e degrees of f r e e -dom f o r the jacket are tv/o.

Phase 3. As Phase 2 but the jacket s t a r t s l i f t i n g o f f one of the rocker beams giving one t r a n s l a t i o n a l and two r o t a t i o n a l degrees of freedom f o r the jacket r e l a t i v e t o the barge. For a jacket/barge system with l a t -eral synmetry t h i s phase w i l l normally not be entered. Both of the recorded f u l l - s c a l e launches went d i r e c t l y from Phase 2 to 4 .

Phase 4. The jacket has separated from the barge and the tv/o bodies move completely i n -dependent of each other, each body having six degrees of freedom.

The launch c h a r a c t e r i s t i c s have great im-pact on the jacket design. For shallow water jackets the a u x i l i a r y buoyancy configuration w i l l be determined solely to provide s a t i s -factory bottom clearance during launch. For medium and deep water jackets the launch loads become increasingly important and w i l l be the governing design loads f o r a s i g n i f i -cant number of jacket members.

Equally important are the behaviour and the loads experienced by the barge. Calcula-t i o n of barge bending momenCalcula-ts and deCalcula-termina- determina-t i o n of determina-the maximum barge keel immersion during launch are standard requirements f o r launch preparations.

For jacket designers the main information about the launch behaviour i s obtained by performing model tests and simulations with 2- or 3-dimensional launch computer programs. Model t e s t i n g involves a number of scale e f -f e c t s , where especially the overprediction of drag forces due to the low Reynolds number i n model t e s t i n g i s s i g n i f i c a n t . For that reason good c o r r e l a t i o n between model t e s t results and computer simulations can not be expected.

3. 3-DIMENSIONAL MATHEMATICAL LAUNCH MODEL The mathematical model used i n t h i s com-parison with the two f u l l - s c a l e launch record-ings i s a 3-dimensional model developed and implemented on a main frame computer by the authors.

3.1 Jacket/barge model d e s c r i p t i o n The mathematical representation of the jacket i s set up by a normal 3-dimensional s t i c k model, where jacket members are r e f e r -enced t o predefined nodes. The model operates with four d i f f e r e n t types of modelling e l ements: Cylinder, sphere, l i n e , and point e l -ements. Cylinder and sphere elements are used t o model real jacket members of the same types. Line and point elements are used f o r modelling e i t h e r mass, i n e r t i a , buoyancy, or hydrodynamic properties or any combination of these t o s u i t a r b i t r a r y j a c k e t members. The hydrodynamic properties can be s p e c i f i e d i n d i v i d u a l l y in the three local member d i r e c -t i o n s . The model accoun-ts f o r j a c k e -t framing as brace members are stopped a t the surface of chord members to ensure correct buoyancy of each node.

The barge model i s defined by l e n g t h , breadth and depth assuming the barge i s box shaped. Additional information about s l i d i n g plane and rocker beam location i s provided together with mass properties and hydrody-namic c o e f f i c i e n t s .

3.2 Equations of motion

Four reference co-ordinate systems have been adopted as shown in Figure 1 . A space-fixed global system with the Xo - yo plane coinciding with the sea surface. A j a c k e t -f i x e d system with the o r i g i n at the jacket CoG (Center of Gravity) and a s i m i l a r barge-f i x e d system also with the o r i g i n at the CoG. F i n a l l y a rockerbeamfixed system w i t h o r i -gin at the rocker p i n .

—

327 I n i t i a l l y the axes of the j a c k e t - , the

barge-, and the rocker-fixed systems w i l l be p a r a l l e l with the z-axis normal to the skid surface on the barge, and the x-axis i n the skid d i r e c t i o n of the j a c k e t , v/hich i s also the o r i e n t a t i o n of the global x - a x i s . The spacefixed system has been chosen as r e f e r -ence system f o r the equations of motion.

Both bodies are assumed to be r i g i d , hence Newton's second law of motion can be applied f o r each body at the CoG.

dt (m[E]{x}^ = ( n (1)

[ I ] { 6 } = {M} d

where m i s the mass of the body, E i s the 3x3 unity matrix and [ I ] i s the i n e r t i a m a t r i x . Neglecting wind and assuming calm water the forces {F} are composed of

(F) = (W) + {B} + (H) + { P } + I K ]

where

{W} = Gravity force {B) = Buoyancy force {H} = Hydrodynamic force

{ P ] = I n t e r a c t i o n force between the two bodies

(K) = External f o r c e s , i . e . mooring l i n e s , tugger l i n e s e t c .

(3)

{M} represents the moments of the same forces about the CoG.

For small displacements the buoyancy force can be l i n e a r i z e d by including the hydro-s t a t i c hydro-s t i f f n e hydro-s hydro-s matrix [S] , where ~ dehydro-s- des-ignates l i n e a r i z e d values:

(4)

Closed form expressions f o r f i v e fundamen-t a l d i f f e r e n fundamen-t locafundamen-tions of fundamen-tubes wifundamen-th respecfundamen-t to the water surface have been established f o r buoyancy, center of buoyancy, watorplane area and center of f l o a t a t i o n , from which the buoyancy force vector and s t i f f n e s s matrix can be c a l c u l a t e d .

Morison's equation i s applied to describe the hydrodynamic forces on the j a c k e t . L i n -earized they can be expressed as:

• I H H } r{x}^ ,{xj> f{Ax), Ak] - ( C D ] J . - [ A C J ••{AB}-! 10} (5)

The added mass matrix [C,„] i s estab-lished by the technique described by Hooft (1972), which e f f e c t i v e l y is an expansion of Morison's equation to the general 3-dimen-sional case using the projected acceleration perpendicular to the member method. The two damping matrices [CuJi and [CDI?. are con-structed in a s i m i l a r manner using the pro-jected v e l o c i t y method, however due to the v e l o c i t y square term in the Morison damping term the v e l o c i t y has been Taylor expanded which produces the additional [CDIS matrix. When c a l c u l a t i n g the damping matrices a l i n -early varying current v e l o c i t y can be included. The slamming forces are included by the

[AC,,,] m a t r i x , defined as:

[ACf.,] [ C J t - [C„] raJto

t - to (6)

The 3-component i n t e r a c t i o n force { P } can be expressed from the i n t e r a c t i o n force

in j a c k e t - f i x e d y- and z - d i r e c t i o n s .

I P ) = [R^] r 0

0 1

Cl

[R][U] (7)

where \iy is the f r i c t i o n c o e f f i c i e n t f o r a force in the y - d i r e c t i o n and Uy. is the f r i c t i o n c o e f f i c i e n t f o r a force in the z-d i r e c t i o n . [R^] i s the r o t a t i o n matrix that rotates a vector from the j a c k e t - f i x e d co-ordinate system to the space-fixed system.

D i f f e r e n t i a t i n g (1) and (2) with respect to time and i n s e r t i n g the force expressions (3) - (7) y i e l d s the f o l l o w i n g equation f o r the j a c k e t :

(

r{AX^}^ "[E] [Of

+ [S] . -J L ^ ] [ E ] _ J L ^ ] [ E ] _ [R^] [U] [ p • { f 4 }

}

A s i m i l a r equation e x i s t s f o r the barge. Note that the matrix [L^] contains the lever arms from the j a c k e t CoG to the point

and P are v/here the contact forces

assumed t o a c t .

Let us resume the problem of deterinining the motions i n 3-dimensions f o r the two bodies i n t e r a c t i n g w i t h each other. This i n -volves f i n d i n g 2x5 kinematic and 5 s t a t i c un-knowns:

{8^) 6 kinematic OOP's f o r jacket {x3}, {03} 6 kinematic DOF's f o r barge

• { M p } p p

• = -. 2 i n t e r a c t i o n forces 3 i n t e r a c t i o n moments { M ^ } = - v n p ;

The equations of motion f o r the jacket (8) and the s i m i l a r ones f o r the barge pro-vide a t o t a l of 1 2 simultaneous equations. Hence 5 additional equation of constraints w i l l be necessary to solve the problem. 3.3 Equations of c o n s t r a i n t s

The equations of c o n s t r a i n t s are unique f o r each phase of the launch as described

previously.

3.3.1 Phase 1. The j a c k e t has only one degree of freedom r e l a t i v e to the barge, hence the jacket motions can be expressed by the barge motions and the r e l a t i v e motion:

{x^} = {x'^l + [R^]{x^} {x^} = {x^} + [R^'Kx^} + {x^} = fx''} + [ i ^ ] { x ^ } + 2 [ R ^ ] i ^ ^ + [R^'lix^ ( 9 ) ( 1 0 ) ( 1 1 )

v/here {xg} denotes the vector from the . barge CoG to the jacket CoG. Note t h a t (xg) d i f f e r e n t i a t e d with respect to t i m e , only has a component i n the d i r e c t i o n of motion, i . e . the barge x - d i r e c t i o n , hence only the f i r s t column of [R^l should be used, indicated by [ ] 1 .

Furthermore Phase 1 implies i d e n t i c a l r o t a t i o n s of the jacket and barge:

(AeJ) = {AB") {8^1 = {è^} {ö^} = {ë^} (12) (13) (14) By s u b s t i t u t i n g ( 9 ) - (14) i n t o (8) the jacket DOF's can be eliminated and the motion problem i s reduced to solving 9 simultaneous equations with 9 unknowns, which are:

6 kinematic DOF's f o r the barge 1 r e l a t i v e jacket DOF 2 i n t e r a c t i o n forces { x ^ l ( ? } {ë''}

The equations of constraints change when the contact moment about the rocker p i n be-comes p o s i t i v e and the j a c k e t enters phase 2.

3.3.2 Phase 2. The r e l a t i v e number of the jacket DOF's increases by one, as the j a c k e t s t a r t s r o t a t i n g r e l a t i v e t o the barge. The j a c k e t motions can again be expressed from the barge and the r e l a t i v e motions:

{x^} = {x''} + [R^][x.l] - [ R ^ K x f ] {x^} = + [R^]{x^} - [ R ^ ] { x ; } - [ R ^ ] ^ ; {k-^} = {x'^} + [ R ' ' ] { X ^ } - [ R ^ ] { x ^ } - 2 [ R ^ ] x - - [ R ^ l X j (15) (16) (17) where {xg} i s chosen to be the vector from the barge CoG t o the rocker pin i n barge sys-tem c o - o r d i n a t e s , and {x?} the vector from the j a c k e t CoG to the rocRer pin in j a c k e t system co-ordinates.

The j a c k e t r o t a t i o n s can be expressed by the barge r o t a t i o n s and the r e l a t i v e j a c k e t r o t a t i o n about the rocker p i n :

{A6^}= {A6^} + [R'^JzABg ( 1 8 ) {9^} = {6^^} + [k^],h(3l + [RhaAB^ ( 1 9 )

[P] = {6^} + [R^ljAB^

The s t a t i c condition which states t h a t the i n t e r a c t i o n moment around the rocker pin ( l o -cal barge y - d i r e c t i o n ) i s zero, is u t i l i z e d to obtain the l a s t equation of constraint necessary to balance out the number of un-knowns:

[RhT{M|} = [RhlfM^) = 0 (21)

As in Phase 1 equations (15) - (21) can be substituted i n t o (19) eliminating the jacket DOF's, giving 10 simultaneous equations with 10 unknowns:

{x''') , {ë^} 6 kinematic DOF's of barge x^ , 'él 2 r e l a t i v e jacket DOF's Pyj , P^j 2 i n t e r a c t i o n forces The jacket leaves Phase 2 and goes t o Phase 4 , separation, when e i t h e r the contact force between jacket and barge vanishes, or the end of the jacket launch r a i l passes over the rocker p i n , allowing the rocker beam to rotate to i t s maximum angle. Phase 3 can be entered i f the contact force on one o f the rocker beams vanishes.

3.3.3 Phase 3. S i m i l a r l y t o Phases 1 and 2 the jacket motions are determined from the barge and the r e l a t i v e motions:

( x h + [ R ' ' ] ( { X ^ ) + [R^lfx^^}) - [R^]{x^} (22) i x h . [ R h ( ( x D - [ R £ ] { X ^ } ) ^ [ R h [ R G l { x ^ - [ R ^ l f x ^ l - [R^]!);^ (23) {x'^} + [ R h ( { x ^ } + [RfaKx^}) + 2 [ R ^ ] [ R £ ] { X ? } + [ R ^ ] [ R £ ] { x ^ } - [R^){x^} - 2[R^]iX^ - [ R ^ ] X j (24)

{ x " } denotes the vector in rocker-beam-fixed co-ordinates from the rocker p i n , to the point on the skid r a i l which the j a c k e t r o -tates about, {x^} i s the vector from the jacket CoG t o the same point in j a c k e t - f i x e d co-ordinates. [R^] i s the r o t a t i o n matrix that rotates a vector from the rocker-beam-f i x e d system to the barge-rocker-beam-fixed system.

The jacket rotations can be obtained from the barge r o t a t i o n s , the rocker beam r o t a t i o n A9g and the jacket rotations r e l a t i v e to the rocker beam AO^.

( A 6 ^ } = { A 6 ^ } + [R^l.Ae^ + [R^liAe^. (25)

+ [ R ^ l i A ü j + [R^lxAê^- (26) {ë^} - {ë''} + i R ' ' ] , A 9 ^ + 2 [ R ' ' ] , 9 ^

+ [ R ^ j C ^ + [R^liAoJ + 2tR^]ié^

+ [R^liö^. (27) The l a s t two equations of constraint are

made up of the s t a t i c moment c o n d i t i o n s , saying that the moment about the axis of r o -t a -t i o n f o r -the rocker beam, and -the momen-t about the point R on the launch r a i l v/hich the jacket pivots about are zero. Assuming the i n t e r a c t i o n forces act a t the point R the equations of moment can be expressed as:

[R^ljfM^} + t L j j p ^ ' H = 0 (28)

[R^]i{M^} = 0 (29)

where [ L R ] i s a 3x2 matrix containing the lever arms from the launch r a i l point R down to the rocker p i n .

The actual number of unknowns i n Phase 3, when equations (22) - (29) are incorporated i n ( 8 ) , can be summerized as:

{x'^l , {ë^} 6 kinematic DOF's f o r barge x^ , 0^ , 3 kinematic r e l a t i v e jacket

DOF's

Pyj , Pgj 2 i n t e r a c t i o n forces

3.3.4 Phase 4. As the jacket separates from the barge, the equations of motion f o r the jacket and the barge decouple, and the mo-tions f o r the jacket are governed solely by equation ( 8 ) , the barge motions by a s i m i l a r equation.

3.4 The time i n t e g r a t i o n procedure The launch problem i s determined by the equations of motion together with the equa-tions of constraint f o r each phase. The un-knowns comprise the kinematic DOF's f o r the barge and r e l a t i v e jacket DOF's, plus the dependent unknowns of i n t e r a c t i o n f o r c e s . Together they form a system of i n t e g r o d i f -f e r e n t i a l equations. The equations are highly n o n - l i n e a r , hence a numerical s o l u t i o n to the problem can only be obtained by a time step i n t e g r a t i o n procedure.

The Newmark 6 method, Nev/mark (1959), has been applied with ( 3 = 1/6, corresponding to accelerations varying l i n e a r l y over a time step. The connections between p o s i t i o n s , velo-c i t i e s , and avelo-cvelo-celerations are as f o l l o w s :

{x't ( X t ) = ( X t J + At{5^to) + | A t { A X t } (30) (31) ( X t l = ( X t , } + A t f X t o ) + l A t M x ' t ) + SAt-J/iXj,} (32) where Z\t = t - to .

Note the vector symbol { ) denotes an r-dimensional vector, r being the local num-ber of independent DOF's in each phase.

Assuming the p o s i t i o n s , v e l o c i t i e s and accelerations are known at time to , the i n t e -gration procedure of f i n d i n g the same quan-t i quan-t i e s aquan-t quan-time quan-t can be sumnarized in quan-these f i v e steps:

1. Guess the acceleration at time t , f o r instance assume them to be i d e n t i c a l with time to , i .e. lAx't) = { 0 } . 2. Update positions and v e l o c i t i e s using

(31) - (32)

3. Calculate a l l the motion dependent vectors and matrices on the basis of these v e l o c i t i e s and positions ( i . e . (B) , (K) . [R] , [R] , [L] , ICJ , [AC„] , [Cell , [CD]J , [ S ] ) .

4. Solve the equations of motion (8) t o -gether with the respective equations of c o n s t r a i n t . The r e s u l t is a correction to the acceleration guess ( A x t ) . 5. Compare the correction with the r e

-quired accuracy. Are the corrections converging, update positions and v e l -o c i t i e s by (31) - (32) and g-o t-o the next time step. Otherwise use (30) with the improved guess and repeat from 2.

Figure 5. GORM C launch photogra recording (7 out of 27 p i c t u r e s )

The drag c o e f f i c i e n t i s calculated f o r each jacket member at each time step as func-t i o n of func-the momenfunc-tary Reynolds' number. As basis f o r the c a l c u l a t i o n a s i m p l i f i e d version of the curve in M i l l e r (1977) F i g . 8 has been used with t^oughness parameter 0,4>;10~' . For /iw>2xio'' the drag c o e f f i c i e n t is assumed con-stant C D = 0 , 7 .

The added mass c o e f f i c i e n t is assumed con-stant Cn,= 1,0 f o r the c i r c u l a r c y l i n d e r s . For other bodies such as f l a t plates standard values have been used.

As pointed out by Singh et a l . (1982) the s a c r i f i c i a l anodes may cause both an increase and a decrease i n the f l u i d loading depending on the flow d i r e c t i o n r e l a t i v e to the anode p o s i t i o n . In t h i s program the anodes are taken i n t o account simply as additions to the e f f e c -t i v e areas and volumes of -the respec-tive mem-bers.

During the inmersion of the members there w i l l even a t low speed be large time deriva-tives of the momentum of the added mass and hence a f o r c e , here called the slamming f o r c e . The program takes t h i s force i n t o account by c a l c u l a t i n g the time d e r i v a t i v e of the added mass m a t r i x .

The damping and added mass c o e f f i c i e n t f o r the barge have been taken from Vugts (1970) p.41. The c o e f f i c i e n t s have been doubled f o r the a f t end sections of the barge that are t o -t a l l y submerged, -t o provide f o r -the wa-ter on top of the deck.

Surface v«ves created by the jacket during the launch and thereby wave damping are not taken i n t o consideration.

5. PHOTOGRAPHIC RECORDING AND ANALYSIS A r e l a t i v e l y simple photographic record-ing and analysis method has been developed by one of the authors who also c a r r i e d out the two f u l l - s c a l e measurements. Two inde-pendent recording systems v/ere used, s t i l l photos and f i l m , both of which could y i e l d the desired information: j a c k e t p o s i t i o n as f u n c t i o n of time.

The photo system consisted of a motor-driven 35mm camera with zoom-lens, i n one case (GORM C) coupled t o another camera pho-tographing a stop watch, in the other case (BERYL B) with a b u i l t - i n clock as seen i n F i g . 2 . About 30- 40 photos w i t h i n t e r v a l s of 1 - 2s are s u f f i c i e n t to describe the launch. In both cases the observation platform was a stand-by boat, situated 200- 300m from the j a c k e t . Colour d i a p o s i t i v e f i l m was used f o r optimum r e s o l u t i o n .

The f i l m system was a 16mra colour f i l m camera with c r y s t a l c o n t r o l l e d f i l m t r a n s -portation clock-work set at 25 frames per second. So the f i l m i t s e l f i s a very accurate time reference f o r the launch.

system alone because the photographs have a s l i g h t l y b e t t e r r e s o l u t i o n than single frames of a 15mm f i l m . The f i l m , however, is a good supplement to the photo series because i t represents the dynamics of the launch more e f f e c t i v e l y than a series of s t i l l photos. The analysis was made with the aid of an ac-curate side-view drawing of the j a c k e t . The jacket positions were determined from the photos by i d e n t i f y i n g the c h a r a c t e r i s t i c nodes, beam ends, diagonal crossings e t c . close to the waterline and then p l o t t i n g the waterline p o s i t i o n r e l a t i v e l y to these p o i n t s . By using 4 - 5 p o i n t s , the waterline p o s i t i o n could be determined q u i t e p r e c i s e l y . Examples are shovm in Figs. 5 - 6 .

The v e r t i c a l , horizontal and angular mo-tions and the important bottom clearance were then p l o t t e d as functions of time. V e l o c i t i e s and accelerations can be found by simple d i f -ference methods but the u n c e r t a i n t i e s w i l l increase.

6. RESULTS AND CONCLUSIONS

Two f u l l - s c a l e launch measurements, the GORM C of 4000t and the BERYL B of 14000t, have been compared with computer c a l c u l a t i o n s as seen i n Figs. 7 - 8 . Generally the agreement i s very good.

For the GORM C jacket the calculated deepest draught curve, which gives the import-ant bottom clearance, comes very close t o the measured values whereas the computer c a l c u l a -t i o n is abou-t 4m on -the safe side f o r -the BERYL B.

The c a l c u l a t i o n s seem to have a somewhat contracted time s c a l e , more pronounced f o r the small GORM C than f o r the larger BERYL B j a c k e t . An explanation to t h i s phenomenon has not yet been found. Increased added mass co-e f f i c i co-e n t s of 1,5 or 2,0 improvco-e a b i t on thco-e time s c a l e , but the v e r t i c a l and angular mo-tions become less accurate. The t h e o r e t i c a l value of Cm= 1,0 gives the best o v e r a l l r e -s u l t -s .

For both c a l c u l a t i o n s the damping seems to be too s m a l l . I t has been attempted to use a constant drag c o e f f i c i e n t equal to 0,7 instead of the Rt-dependent Co. S u r p r i s i n g l y , t h i s means only a very i n s i g n i f i c a n t change i n the r e s u l t s . The explanation must be t h a t , the dominating part of the damping forces on the jacket are created at s u p e r - c r i t i c a l Reynolds' numbers.

The added mass and damping forces on the barge are calculated i n a rather simple way. A b e t t e r d e s c r i p t i o n of the hydrodynamic be-haviour of a p a r t l y submerged launch barge would undoubtedly improve the c a l c u l a t i o n s .

335 V e r t i c a l pos. of j a c k e t CoG r r r t i , J a c k e t t r i m angle P o i n t of d e e p e s t draught y ^ ^ ^

Figure 7. GORM C launch computer

simulation and f u l l - s c a l e measurements. Figure 8. BERYL B launch computer simulation and f u l l - s c a l e measurements.

The authors are grateful to the manage-ments of f'tersk Olie og Gas A/S and Mobil North Sea Limited f o r t h e i r help and support during the f u l l - s c a l e measurements, f o r the access t o a l l necessary data, and f o r per-mission to publish t h i s paper.

Special thanks are given to Mrs. G i t t e Bruun and to Mr. L e i f Stubkjser f o r excellent f i l m and photographic work under d i f f i c u l t conditions.

The work has been supported f i n a n c i a l l y by the Danish Council f o r S c i e n t i f i c and I n -d u s t r i a l Research.

8. REFERENCES

Hambro, L. (1982), "Jacket launching simula-t i o n by d i f f e r e n simula-t i a simula-t i o n of c o n s simula-t r a i n simula-t s " . Ap-plied Ocean Research, V o l . 4 , No.3, pp.151-159. Hooft, J.P. (1972), "Hydrodynamic aspects of semi-submersible p l a t f o r m s " , NSMB Publication No. 400, Wageningen, Netherlands, 132 p. M i l l e r , B.L. (1977), "The hydrodynamic drag of roughened c i r c u l a r c y l i n d e r s " . Transactions of RINA, England, Vol. 119, pp. 55-70.

Moller, J . and Christiansen, P.E. (1983), "Matematisk model f o r sositning af jacket f r a pram", ( i n Danish), Dept. of Ocean Engineer-i n g , The TechnEngineer-ical UnEngineer-iversEngineer-ity of Denmark, Lyngby, 218 p. + App.

Newmark, N.M. (1959), "A method of computation f o r s t r u c t u r a l dynamics". Journal of the En-gineering Mechanics D i v i s i o n , ASCE, Vol.85 , No.EM 3 , Proc. Paper 2094, U.S.A., pp.67-94. Singh, S . , Cash, R., H a r r i s , D. and Boribond, L.A. (1982), "Wave forces on c i r c u l a r c y l i n -ders with large excrescences at low Keulegan and Carpenter numbers", NMI Report 133, Eng-l a n d , 63 p.

Vugts, J.H. (1970), "The hydrodynamic forces and ship motions in waves". D e l f t , Nether-lands, 113 p.