Simulation of the behaviour of a moored ship when passed by other ships

"0

5. JAO 1982

National Maritime Institute

Simulation of the behaviour

of

a

Moored Ship when

passed by other Ships

by

I W Dand

NM! Rill

August 1981

National Maritime Institute

Feitham

Middlesex TW14 OLQ

Tel: 01-977 0933 Telex:263118

Lab.

v. Scheepsbouwkunk

Tecknische Hogeschool

Deift

This report is Crown Copyright but may be freely reproduced for all purposes other than advertising providing the source is acknowledged.

SUT1MARY

A computational model to simulate the behaviour of a rroored ship whea passed by other ships is described. Comparisons are then made between

calculated and measiired behaviour using restilts from both model and full-scale experiments.

Bibliotheek van de

J Md&ng Scheepso.'-. en Schcpveartkline

Teh.ic

Deft

D)CtJi'iENiATlE

SIMrJLT1ON OF THE BEHAVIOUR OF A OORED SHIP WHEN PASS Y. OTHER SHIPS

1. Introduction

Page

2. The Simul/ation Model 2

2.1 General 2

2.2 Axis System 3

2.3 Equations of Motion 3

2.4 Added Mass and Damping 3

2.5 Overall Mooring Stiffness 5

2.6 Fenders 8

2.7 Sinkage and Trim 10

2.8 Steady External Forces and Moments 10

2.9 Numerical Methods 10

3. Exciting Forces and Moments Due to Interaction 12

3.1 General 12

3.2 Prediction of Exciting Forces and Moments 13

3.2.1 Non-Dimensional isation 13

4. Comparison of Simulation with Measurements 17

4.1 General 17

4.2 Comparison with Model Measurements 18

4.2.1 The Experiments 18

4.2.2 Results Obtained

4.3 Comparison with Full-Scale Measurements - the 'Daphne1

19

Trials 21

4.3.1 The Experiments 21

4.3.2 Results Obtained 23

4.4 Comparison with Full-Scale Measurements - Fawley Trials 24

4.4.1 The Experiments 24 4.4.2 Results Obtained 27 5. General Discussion 30 6. Conclusions 33 7. References 34 8. Acknowledgements 35 9. Nomenclature 36 Figures 1 - 1k

SIMULATION OF THE BEHAVIOUR OF A MOORED SHIP WhEN PASSED BY OTHER SHIPS

by I W DAN])

Project 252001

1.

Introduction

A moored ship is subject to many external influences from its environment

Its jetty and

oorings must be designed to keep the resultant

moVement of the ship w.ithifl prescribed limits while keeping the loads in

the mooting lines at an acceptableleVel.

The usual eiteriial influences are

those arising from current, wind and waves, but occasionally, when berths are

close to a fairway used by large ships, the forces an'onepts

üe to ship-ship

interaction assume some importance.

It is the latter case with which this repott' i

coflcErhed as it has an indirect

bearig on the fairway design -lOcal to the berth.

It is known that interaction

forces and thOthentVa

tith both the speed and :distañcë off of the passing

ship so that clearly the movethent and thOoring line

loads of the moored ship

are deendent on these two paratheters asociated with the passing ship.

Whilethédistance off of the passing ship is naturally related only to the

local fairway width, its speed is indirectly related to both fairway depth

(due to squat) and

idth (due to requirements for safe navigation)

As the movements Of some berthed ships are subject to certain constraints,

imposed generally by the cargo handling gear, it is possible in principle to

determine the approximate limits of speed and distance-off of the passing ship

from a knowledge, of these and the probable response behaviour of the moored

ship.

Movement constraints are particularly imporant on tanker berths,

where the cargo-handling manifolds allow a maximum movement of t3m in

surge

and 3fn in sway (ref.

I,)

and container berths, where the.operatioti of the

container crane

impose constraints more severe than those applicable to

tanker berths.,

Clearly a final constraint on the ship'movement is' that it

must not be ]arg

enough to impOse loads in the mooring lines 'àhich would

cause them to break.,

., ' . . ' ,

-The effect of the passing ship has' been studied by Remery (:ref. 2) using the

work of van Oortmerssen (ref. 3) while Lean and Price (ref. 4) describe a

comprehensive series' of rnodel experiments relevant to a tatker berth.

Although 'a VeriOnoI Rethery'Sméthod had been used at-N1'ff to study the

behaviour of a ship ,moored in a canal by-pass while ships passed in the main

canal, it became clear that a more comprehensive simulation, allotâng for

non-linearties and cross-coupling'effects,was necessary.

Such a simulation

could then be used to give suitable re.coendations concerning the behaviour

of the passing ship. Such a simulation should be as general as possible so

that, a wide range of passing and moored ship sizes can be accOmmodated.

This report describes the constructionof such, a simulation and

presents some comparisons of calculation and measurement made using model and full-scale experiment results. '

2. The Simulation Model'

2.1 General

The work described in reference 2 used an impulse response function technique tà solve the equations of motion in the'time, rather than the frequency, domain. Although this is an elegant method of solution, it is somewhat restrictive in that mooring stifnesses independent of' each other in surge, sway and yaw are assumed. In some cases this is acceptable, but' if cross-coupling between all the motions of interest, is, to be studied, another approach must be used.

Clearly a numerical technique is suitable for solving the equations,of motion, as this can deal with both non-linearities and cross-coupling (ref. 3).

In what follows, such a ethod is de'eloped sübjêct to the following main assumptions:

the motions of surge, sway and yaw are of prime interest, heave, pitch and roll being ignored.

SOe allOwe i

made boevt for the sinkage

and tflm induced On the moored vessel by the passing ship as shown below.

the behaviour' of the ship can bédCdüced from a 'solutioi of the appropriate equations of motion with the exciting forces and othents for those

motions being deduced from measurements made on 'rigidly-moored' models. In othEr words we assume that the motion"of the moored ship

is

sufficiently small

that

it does not affect the time Kitories of the forces induced by

the passing ship. '.

In some respects the method shown belO bears

_a

resémb lance to those of

refer-ences 3 and 5 'although it will, be noted that the basic equations of motion

2.2 Axis System

The axis systems used are shown in Figure 1. In one system fixed in the

ship, the positive x-axis is directed forward, the positive y-axis to starboard. The origin is taken to be in the water surface on the centreplane amidships and

the yaw angle, denoted by ij is positive as shown. The other axis system is

fixed in space and is co-incident with the ship body axes: at the start of a run.

2.3 Equations of Motion

Three simultaneous equations of motion are solved in the time domain:

(m+m)5 - (m+m)y

+ C() + S(x,y,W,t) + X(X,yY,t) = X(t)

..

(1)

(m+m) + (m+m) + C() + S(x,y,'1,t) + YF(x,y,\!,t) = Y(t) ... (2)

(I+I)'l + C() + S(x,y,Y,t) + NF(x,y,1',t) = N(t) ... (3)

where m

is the mass of the ship

I is the longitudinal inertia of the ship

m, m ,

I added virtual masses in surge, and sway and added virtual inertia in yaw

C(x), C(y), C('!)

are damping functions in surge, sway and yaw

S(x,y,W,t), S(x,y,,t), S(x,y,W,t)

are overall system stiffnesses

in surge, ssy and yaw

X(t), Y(t), N(t) are exciting forces in surge and sway and exciting

moment in yaw

XF (x,y,P,t), YF(x,y,I1,t) NF(x,y,W,t) are fender reaction forces and

moments

It may be noted that non-linear overall stiffness, damping exciting forces!

moments may be used in the above equations (ref. 3) with the main

cross-coupling effects assumed to arise within the overall stiffnesses and in the terms involving i and .

2.4 Added Mass and Damping

Van Oortmerssen shows (ref. 3) that added mass and damping in the time domain may be calculated from results in the frequency domain. This results in values of m , m and I which remain constant with time. Van Oortmessen

x y

gives the following non-dimensional values for added virtual masses and inertias for a depth!draught ratio of 1 .2 close to an open jetty:

Table 1

HOwever Kilner in reference 6 presents experimental results hch suggest that the added mass coefficient in surge is of the order of 010 for all depth!

draught ratios while the sway added mass coefficient ranges from a value of 4.0 at a depth/draught ratio of 1 .2 to a value of 1 .0 at a depth/draught

ratio of 2 0 No information on added yaw inertia is given in this reference.

But the essential feature of Kilner's work is that the virtual masses were Obtained over a narrow frequency band, rather than the rnuch wider frequency range of reference 3 For comparison, the non-dimensional frequency

parameter /L!g is about 0 35 in sway and 0 65 in surge for the reference 6 results whereas in reference 3 it covers the range 0.2 < /LIg < 6.0.

(In this context w is the circular frequeny of motion of the moored ship in suge, sway o yaw).

Early numerical trials Of the simulation model showed that, for the special case of the motions Of a moored ship when passed by another, the frequency

pa±netr mentioned above was confined to a narrow low-frequency band

in the region of w/L!g = 0.2 for surge and sway and wvt/g = 0.3 for yaw.

It wa therefore asste4 that mptions of a moored ship in this special case were dominated by low frequency added mass and inertias which are shown in references 3 and 6 to be large, particularly in the ase of sway motions.

It was decided therefore not to use the values Of Table 1 which take into accoufit frequency-dependent added mass and damping over the whole frequency

ange1

but

rathe to use vaj.ues from reference 3 appropriate to wv'L!g = 0.2 for surge and sway and 0.3 for yaw. The following coefficients were

obtained. Depth/Draught Surge Sway Yaw 0 033 -0.505 0.045 1.1 1.2 2.0 0.20 4.10 2.86 1 .0 0.15

5

These values were used in the simulations discussed below and the sensitivity of some of the results, obtained in a certain case, to variations in added mass and inertia is discussed in section 5.

For damping it is shown in reference 3 that in the time domain the damping force in surge has the form:

t

c() =

K(t-t)(T)dT

(4)

with similar functions in sway and yaw. The convolution integral in

equation (4) shows that the past history of the motion has to be taken into account when computing the damping force at any instant of time. This

'memory effect' has been shown in reference 3 to be significant over the last 25 seconds of the motion for a VLCC and tables of the retardation function

K(t) in surge (with similar functions for sway and yaw) are given in

reference 3. These were non-dimensionalised according to the scheme

K' Ct') = K (t) .L/(mg); K' (t') = K Ct) .L

1,/(n3g);

x x y y P.

K'(t') = K,(t)/(mg L)

= t/IiJ/g

(5)

Values of the non-dimensionalised retardation functions were stored and used in the subsequent simulation with the infinite lower limit of the integral

in equation (4) replaced by a non-dimensional time value -T where

T1 '(=T1//L/) is sufficiently large. A value of T1' of 4.447 corresponds

to the 25 seconds for a VLCC for which damping memory effects are important as mentioned above and this value was used in the simulation.

2.5 Overall Mooring Stiffnesses

Values of the overall stiffnesses of the mooring system in surge, sway and

yaw were computed from a knowledge of the stiffness characteristics of each mooring line and the geometry of the mooring system. Each mooring line was

assumed to deform elastically according to a law of the form

.I_ =(')

...

(6)

T L

where. T' tension

T = load at limit, of elastic behviOur or breaking load- -.

'-V

= extension = line length

, = constants

If 8=1, a linear law, it is easy to show

= AL/Ty

(7)

where AL is the 'solid' cross-sectional area of the mooring line and E is

Young's Modulus fpr the material of which the line is made.

The above assumption implies that catenary effects from the mooring lines are negligible compared to their elastic deformation In all the cases considered below this was so, althpugh. it would be quite possible to cater for

catenar effects in such a simulation .f or the

_study

of, say, behaviour when moored at anchor or to a buoy.

In computing the restpring force for each line it was assumed that the fairlead was at (x1,y1,z1) and the fixed end of the mooring line ashore was at

(x2,y2,z2). The length of each line was assumed to cOnsist of a constant and a 'variable' portion. In a line which is a combination of, say, a braided polypropylene hawser and a wire, it can be assumed that the wire is inextensible compared to he polypropylene so the 'constant' portion 2 is the length of

the wire while the variable portion is the length of the polypropylene hawser If however the line is a wire rope leading frOm a. mooring hook ashore to a fairleãd (especially one with low friction, such as a roller fairlead) and hence to a mooring winch, the constant portion of the line is from fairlead to winch while the variable portion is from fairlead to mooring hook

At the start of the motion we have the distance from fairlead to shore fi*ing point r1 given by . . '

(8)

The ship may now move a distance .x 'in surge, y in sway and ' in yaw;

-7-to a new position (X1t,y1t,z1t) relative -7-to the berth where x1' = x + x1 cos'Y - y1 sin

yl' = y + x1 sin1' + y1 cos'P (9)

z'=z+x1sint

Replacing (x,y,z) by (x1 ',y1 ',z1t) in equation (8), we obtain a value of r2.

The extension of the mooring c(r2-r1) is then related to the length of the mooring line to give

c/i = (r2-r1)/(r1-i) (10)

which gives a restoring force T' from equation (6). It is convenient in the simulation to define the constant portion of the mooring line as positive or negative depending on whether it is inboard (negative) or outboard (positive) of the fairlead.

The restoring force T' from equation (10) is then resolved to give the contribution to the total restoring forces in surge and sway and restoring moment in yaw from the mooring line in question:

T = T cosW + T

sin;

T = T cos'Y - T sin'Y;

x 1 2 y 2 1

N

= Tx -Ty

T

yl

xl

where T1 = T'(x2-x1 ')/r2; T2 = T'(y2-y1 ')/r2

If the mooring lines have an initial tension T, the corresponding extension

is calculated from equation (6) and this is allowed for in the subsequent computations of restoring forces and moments. Knowing the initial tensions in each line, we can also compute the 'out-of-balance' surge force, sway force and yaw moment that these represent and which the fendering system must counter-balance if the ship is not to pull itself bodily away from its

initial moored position.

It should be noted that no allowance has been made for possible hysterisis effects in the stiffness characteristics of the mooring lines as discussed in reference 7. However, it is normal to assume (refS I and 8) that after

a line has been in service a short while, a permanent lengthening known as constructional stretch results from a slight re-arrangement of the wires or fibres that comprise the rope. This causes the rope to behave in a more

or less elastic manner, albeit with a greater stiffness than a new rope

(tefs I and 8). Stiffnesses have therefore been assumed that are appropriate

to stab ilised, used ropes with the further assumption that hysterisis effects are negligible. The results from reference 7 suggest that this is not an unreasOnable assumption.

2.6 Fenders

Two fenders on one side of the moored ship were simulated These naturally resisted any sway and yaw motion directed toward the jetty, but also, by assuming suitable friction forces between the ship and the fender face, resistance to surge, sinkage and trim cOuld be sim lated.

Additional fenders would have led to the solution of a redundant set of

equations to find the initial fender deflect-ions f Or the initta] out-of-balance forces and moments, so that it was assumed that all fendering could be concen-trated at two points on the ship's side.

The fender stiffness characteristic was ássümèd tO be of the form:

F=p

where F is the fender force is the fender dèflèôtion

p,

q are constants

This does not àllw £ or the effects.of auxiliary fenders, with the corresponding

stiffness discontinuity they má cause for the main fender (ref. 5)

The initial fender def.lections due to the initial out-of-balance sway force Y. and yaw moment N. are calculated from the solution of two simultaneous

1'

equationS which give the forces required from each fendet:

Y

=Y.-Y

1 i. 2

= (Y.)cfJ-Mi)/(

(13)

where the fenders ar,e at distances Xf1 nd Xf2 from the origin and and are the required, forces. .,

-9-Substitution in equation (12) yields the initial fender deflections and these are used as zero-offsets for subsequent fender deflections. These deflections are calculated from a knowledge of the position of the vessel at any instant thus enabling the deflection and hence the reaction force from each fender to be calculated. Each fender deflection is therefore calculated from

X

= X+Xf

cos'P - y.f S1flP

= Y+Xf sin'Y + Yf COS'1 (14)

= y+(x-xf) sin'Y Yfi

whete ô. is the initial fender deflection.

1

The reaction force for each fender is calculated from equation (12) which gives the total fender reaction in sway and moment in yaw.

As stated above, the fenders also provide a resistance to surge, sinkage and trim by applying friction between fender and ship. The simulation takes into account the static and kineintic friction between ship and fender by assuming that a static friction force opposing surge is given by

=

(15)

where is a coefficient of static friction and Y is the net sway force applied by the ship to the fenders at any instant. If the total surge force acting on the ship is less than f5 no motion is assumed to be

possible; if however the total surge force X exceeds f then X is

assumed to be diminished by the kinematic friction force _k where

= k

(16)

which opposes the motion,

11k

being the coefficient of kinematic friction.

It was further assumed that if friction was such that no surge motion was possible, then no vertical motion from sinkage and trim would be possible, and the ship would retain its vertical position until friction allowed motion

in surge. The ship was then assumed to 'jump' to a new vertical position determined by the time history of sinkage and trim induced by the passing

ship. Observations of ships alongside berths confirmed that such

discontinuous vertical motions could occur when a ship is 'tightly moored' alongside a berth.

2.7 Sinkage and Trim

That a moored ship sinks and trims when being passed by another vessel has been shown in reference 9. Results from this reference suggested that the mean sinkage and dynamic trim were in phase with the surge interaction force and that they could be approximated by functions of the kind:

Cs = As s + for 0 < üt < 2ir

... (17)

Cs = 0 otherwise

C = B sin (wt +c ) for 0 < 2t < 2ir

T S x

CT = 0 otherwise

where W1/t where tx is the period of the time history of the surge

force due to interaction

= 271/t

= the phase lag measured from the start of the interaction force/time history (see ref. 9).

As, B5 = amplitudes estimated from the experimental results given in reference 9.

2.8 Steady External Forces and Moments

Provisionwas made in the simulation model for steady external forces and moments to be applied to the moored ship in addition to the non-steady forces and moments arising from the passing ship. Such effects can arise from the wind and current prevailing at the berth before, during and after the passing manoeuvre.

Appropriate forces and moments can be calculated from reference I (or other suitable sources) together with a knowledge of the above-water and under-water shapes of the moored ship. They are then simply added to any other

exciting forces and moments generated within the simulation.

2.9 Numerical Methods

The equations of motion (I)-(3) were solved simultaneously using a numerical predictor-corrector method desribed in reference 10. This solves the

y'

= f(x,y.)

using the

scheme

= + t y'n (predictor)

= y + t(y' +y ')/2 (corrector) n+I n

It is also shown in this reference that if the third derivative of y remains constant in the interval tt, then the error in the corrector is given by

-(P-c)/5

...

(22)

where

P

is the

predicted and C

the corrected value at any instant.

This method was used in preference to the more usual Euler's method which was found to diverge unless a prohibitively small time step was used. The method was also used in preference to a Runge-Kutta method, as it was some-what less cumbersome to program and faster in use due to the smaller number of substitutions required in the somewhat complicated functions f(x,y ....) of the equations of motion.

The stability of the predictor and corrector is discussed in reference 10 and their combined use was generally found to be good in practice. For the simulations shownbelow a time step of 1.0 seconds was found to be satis-factory with no tendency for solutions to be unstable or to diverge.

Any instability which was found was in general amenable to a reduction in time step, but for the examples shown, reductions in time step below 1.0 second gave no significant change in the computed solution.

However, a note of caution should be sounded in relation to the choice of time-step when very stiff fenders are simulated. In a continuous motion, a ship will approach such a fender which will deflect a short distance

thereby generating a reaction force sufficient to stop the ship and possibly to push it in the opposite direction. In a discretised motion as occurs in the simulation, the ship at one instance of time t may be approaching and

about to touch the fender. At the end of the next time step at time t+tit the ship may have moved a distance y which is taken by the program to be the fender deflection. But, if tt is too large, y may be greater than

the value occurring in continuous motion and, for a very stiff fender, this excess deflection may give rise to a very large reaction force.

...

(20)

(21)

The simulated ship then behaves as if it had received a very large impulse which can have a major effect on the subsequent predicted motion. Clearly if the fenders are sufficiently soft then the errors from the discretisation of the motion are small and may be ignored.

Problems arise with the initial steps of a simulation of this type if the effects of an impulsive start are to be avoided. It is usual to overcome

this by allowing the motions to increase exponentially from the start of the motion so that they attain their normal values after some specified

time (ref. 3). In the present simulation this specified time was about 60 seconds after the start during which time it is clearly important that no major changes in exciting force occur. Clearly such a start is only important if the system of forces is not initially perfectly in balance; if it is,

no special starting procedure is required.

A problem also arises at the start of the simulation in the the computation of the integral in equation (4) when the elapsed time is less than that corresponding

to T1. _{This was done by progressively filling an array of ordinates with values}

corresponding to the most recently-calculated integrand, the other ordinates being set to zero. This array was then filled when the elapsed time t1.

corresponded to T. and thereafter was updated with the most recent ordinates

while ordinates obtained at a time t2<t-T1 were discarded. The integral of equation (4) was obtained using the trapezium rule at a time interval of

of T1 '/50. Values of the integrand were obtained from the ordinate

array mentioned above by linear interpolation to allow for the fact that At1 seldom coincided with the time step At of the main simulation.

3. Exciting Forces and Moments due to Interaction

3.1 General

It has been stated above that the prime purpose of this study was to investigate the behaviour of a moored vessel when passed by another ship. The exciting forces and moments induced by the passing ship are therefore of interest and

these have been derived from information contained in reference 9. In this reference, measurements made on one model when passed by another are

presented, the results covering a wide range of speeds, water depths and

separation distances with the proviso that the two ship models were on

13

-and it is the purpose Of this section to suest a èthod whereby they may be generalised to a wider range of ship-sizes and combinations and' then to test

this generalisaton with results frOm n unpublished study carried ou.t at NMI and from reference 2.

3.2 Prediction of Exciting Forces and Moments

An empirical method is described in reference 9 whereby, surge, X, and sway, Y, forces together with yaw moment, N, may be synthesised for the models used

in that. study. In essence thE method asSumes that the surge force can be

represented by an equation of the type

X B sit (w2t+c.) for. 0 < w2t < 2ff ... (23)

X = 0 otherwise .

and that the sway. force Y0-at a point on the axis of the moored ship can be represented by

= A sechIk(t-t)/c

sintut*(di,t) + c for 0 < ut < 3rr (24)

= 0 otherwise

where w3=3ii/t

and t, t,

1,c, c, A, B and other parameters are given

which allow time histories of X, Y and N, applicable to the passing Situation,

to. be generated.

An auxiliary computer program has been written to generate X, Y and N time

histOtiès in this way, the res1ts being dumped on to files for later access by the main simulation program.

3 2 1 Non-DimensionalisatiOn

The hon-dimensionalisat10fl 'scheme used in reference 9 has been in use cOnsistentl at NMIfor interaction studies and was of use when early compàriéOns with theoretical pre4ictions were being madC. Forces and

moments were non-dimensionalised with respect to the beam and draught of the ship, with no account taken of the length of the

However results given in reference 2 show the effect on a moored ship of passing ships of 41ff erent sizes, the moored ship size and water depth remaining constant throughout.

Analysis of these results suggested that for a given moored ship the exciting forces were related to, passing ship, size by

BT

V

P-P p

LTv2

ppp

'

NL2Tv2

ppp

(25)

at a constant distance off where the subscript p refers to the passing

ship. Such results seem not unreasonable becaUse intèractiOfl forces are known to vary roughly as as they arise mainly from normal pressure effects

so that one might expect forces to be roughly proportional to the projected underwater area of' the body producing them. Evidence for this is given in Table 2 where maximum values from reference 3 have been non-dimensionalised according to equations (25)

Table 2'

NB 1. X''= 1000 X/(B T /V ') Y' = 1000 Y/(L TV ) N' I000N/(L 2T V

2)

pp p

ppp

,

p pp

where V is in knots, X and Y in tonnef and N in tonnef metres.

p

-2. Moored ship 100,000 dwt.

It is clear from a comparison of values in Table 2 a.t a given distance off that the scheme of 'equations (25) applies reas9nably well with the exception of the

yawmomentnorr-dimenpnalisation for the allest passing ship. It is not clear why this should be so and it is not easy to speculate on reasons from the limited information about the model measurements and their acciracy given in reference 3 However it was decided, in view of its app4rent applicability over the rest of the range of passing ships, fotces and moments, to retain the non-dimensionalisation scheme of equations (25).

Passing Ship (dwt) Distance off Cm) 30,000 110,000 160,000 X' Y' N' X' Y" - N' 30 , 4.0i'4 2.394 0.850 3.770 2.967 0.547 3.602 2.463 0.332 60 2.408 1.639 0.533 2.492 1 .81 0.259 - 1 .656 0.238 120 1.168 0.859 0.274 - 0.795 0.101 1.277 0.931 0.102 200 = - - 0.672 0.503 O.O46 0.672 0.445 0.045

15

-Having established a method whereby the size of the passing ship culd be

allowed for, it became necessary to determine the effect of the size of the moored ship on the forces induced by a given passing ship. Again it seemed

rsohable to assume that the forces experienced by the moored ship should be

proportional to the projected underwater areas. in the surge and sway directions with the yaw moment again proportional to the lateral underwater area.

Therefore the following scheme was used:

x

x/(BT v

2) Y/( T v 2) N* _N/(L.2 v

oop- -,

oop

0

op

where the Subscript o refers to the moored ship.

Fortunately some unpublished results had been obtained at NMI relating to an experiment iü which the effects of a given passing ship model on two moor'ed

models Of different sizes were,studied, the water depth remaining constant throughout. The main particulars of the ship models tested are shown in Table 3.

(26)

Table 3

All models were of tanker hull forms and model 5182 was a fully radio-controlled

free-nnig model which could pass either of the other two at various

distances Of f and speeds. The experiments were carried out in the NMI out-door maioeuvring. tank and therefore the results were of necessity subject tO greater

error than occurs in the cont-rolled environment of an indoor tank. However, care was taken to ensure that measurements were taken in the best possible weather conditions.

Typical resu.lts are shown in Figure 2 where they have bêefl non-dimensionalised according to equations (26) with the following scheme (1):

X*. = X/PBTV

Y* =Y/L0T0v2

N* = NRL02T0v2

... (27)

Also shown for comparison in Figure 3 are the same result.s non-dimensionalised according to the following scheme (2), similar to that commonly used in

manoeuvring studies:

Model Length (pp) (m) Breadth (m) Draught Function

5182 4828 3.67.5 3.953 2.157 0.576 -0.656 0.334 0.212 0.249 0.128 Passing Moored Moored

X/pL

2 2

pp

A study of Figures 2 and accounts fairly well for in Figure 3. As stated to the small model 5335, the results obtained for good as could be expected

=

Y/pL2v2

N** = N/ pL3v2

(28)

3 reveals.that non-dimensionalisation scheme (1) the large differences in the original data shown above experimental error, especially in relation was probably fairly large and the agreement between each moored model shown in Figure 2 is probably as

Ideally all the results should collapse on to unique curves if the non-dimensiorialisation scheme accounts for all

differences between the moored ships, and it would appear that the simple scheme (1) gets close to this goal bearing in mind the quality of the available data.

It may be noted also in Figure 2 that the overlap parameter X/(L+L) used

reference 2 has been adopted rather than the simple X/L used in Figure 3.

It is seen that 'this effectively accounts for differences in phase and 'period' of the curves apparent in Figure 3.

The final non-dimensional quantit in Figure 2 and 3 is that Of distance off,

Y, which in this case has been non-dimensionalised with respect to th beam of the moored ship B as in referenc 9.' The comparison in Figures '2 and 3

i's made at approximately equal values of Y0/B0.

Sunmiarising the above argument, it appears that the exciting fOrce induced on a stationary ship model on moorings of infinite stiffness is proportional to

- the square of' the speed of the passing vessel

- the projected underwater areas of the passing vessel - the projected underwater areas of the moored vessel

while distance off should be related to the beam of the moored vessel and overlap to the mean length of moOre and passing vessels.

Itmay be noted that scheme (2) does not.üse any hull form parameters of the

moored ship and therefore shows the djfferences which existed in, the results obtained with each moored ship, the measured forces and 'moments being divided by a constant value, regardless of moored ship size.

17

-This information was then used with the synthesis method of reference 9 in the following way:

Compute non dimensional surge and forte and yaw rnômënt coefficients for the basis moored ship of reference 9uing the method of

ref.erenc9 and nbn-dirnensionalsation for the passing ship asth equations (25). ChOose a depth/draught ratiO and Y/B appropriate to the mOored ship..

Modify the fOrëes and moments thus obtained for variations in length from the basis ship (the effect of its beam and draught being already

taken into account b)V the Y/B and depth/draught ratio chosen)

Use X0/(L+L) as overlap parameter.

This method has been incorporated in an auxiliary program, the output of which is used in the main simulation program.

The simulations which follow in sections 4.2 and 4.4 have all used this

method and an example of the synthesied interaction forces and moments generated

by the program for the basis hip -i shpwn' in Figure. 4 where cputed results are compared with measured values.

4. Camparins of Simulations with Measurements 4.1 General

Having constructed a simulation of the behaviour of the moored ship due to predicted exciting forces and moments from a passing ship, it is necessary to

compare th.g results obtained with measured data. This will test not only the prediction of the behaviour of the moored ship but also, indirectly, whether the 'citing forces and moments,' estimated using the method ofsectiOn 3, are close to reality.

Three different sets of measurements were used for validation of the simulation:

(1) measuremants made at model scale as part of a comprehensive tudy

described briefly in reference 4 and in detail in reference 11.

full scale measurements carried oUt by in a canal by-pass while a convoy, of ships passed along the main canal.

full-scale measurements carried out by N on a VLCC moOted at an open jetty while passed by ships in a fairway adjacent tO the berth (reL 12)

:The.c0s0

are taken -i-n this order.as:it also represents the order-in which the corTarisons become less certain. This is because, with

full-scale measurements, inevitably less control can be exete4 over some

paatr in the expeient whose results must therefore

have a greater degree Of Un rtainty. Ths is particularly true, .hEre gqrig' line

stiffness characteristics and the behaviour of, the mooring winches under load conditions are concerned. Having- said this,:it must of course be admitted that controlled- model shidie are also ubject to' uncertainties. regarding

the scalingof- the' results to- full size.. It is usual to assume Froude

scaling for this and it has been shown (ref 13) that fo.r a moored ship

ectted by wave action, model and full-scale measurements agree well when

-Froude scaling is used.-- ' ' -. ., ' -"

--4.2 Comparison with MQdl Ne3s4.rents 4.2.-I The Experiments ' '

The-model study of refs 4 ad 11 concerned a. large -akr moored ata berth passed by other ship.s at various conditions of loading, speeds and distances

off. Particulars of the ships are given-in Table 4:

Table 4

Note: Passing ship (2-) is passing ship (1) in ballast draught.

The mooring scheme is, shown in Figure 5, each mooring line passing horizontally from fairlead to -shore initially,with no simulation of the inboard end of the mooring line The mooring lines were assumed to comprise used 9 Im long

72nnn diam nylon tails attached to steel wire mooring lines It was assumed that the elasticity of the steel wire was negligible

compared

to

that of the nylon tail so that the stiffness of each line was governed by that of the tail. It was found that the prototype stiffness curves given in reference 11 could be represented adequately by equation (6) with

-Ship Length (m) Breadth (m) - Draught (tr) -- . ---' -Displacement - - (m3) Laden Ballast Moored 348.0 51.8 19.8 269 000 - Passing (1) 304.8 - 1i8.7 20.1 - - 240 000 Passing (2) 304.8 48.7 - 'S.8F 12.5A 120' 000 -- Passing. (3) 159.4 - 20.1 - 9.8 - 22 270

m/pV = 0.20

19

-= 2.945 8 = 2.049 ... (29)

the breaking load being 90 tonnef.

Details of fender stiffnesses are not given in reference 11 and for the purpose of the simulation they were assumed to have an arbitrary stiffness with a

linear characteristic. Two types of fender facing material were used in the experiments giving two values of friction coefficients. One fender facing gave p

= k = 0.5 while the other gave = k = 0.12; only experiments

with the latter value were used for comparison purposes.

Following the arguments outlined in section 2.4 above, the following non-dimensional added mass and inertia values were used

m /pV = 2.86

I/pVL2

= 0.15

y

(30)

the subsequent motion of the moored ship being assumed to be one of low frequency only and the depth/draught ratio of the moored ship at rest being

in the region 1 .2 < h/T < 1 .3.

The jetty in the experiments was of the open-piled type and was not assumed to have any effect on the above added masses and inertias.

4.2.2 Results Obtained

Comparisons of computed and measured values are given in Figures 6 to 9 which concern parameters of interest in the approach channel design problem, being

a brief extract from a much larger body of computed and measured results. Comparisons are made by considering the maximum loads induced in certain mooring lines as well as the excursions of the origin of the ship body axes

(in relation to its initial position) while another ship passed. These are particularly relevant to determination of the appropriate speed and distance off of the passing ship which in turn are related to the width and depth of the approach channel near the berth.

The effect of speed and size of the passing ship is shown in Figure 6 where loads in one of the twin spring lines (numbers 4 or 5) are shown. It is

seen that for passing ships (1) and (2) both qualitative and quantitative agreement between measurement and calculation is quite good, with, in both cases, the calculated values being slightly greater than the measured

values. Agreement for passing ship (3) is not as good and this may be due to failure of the prediction method for a passing ship/moored ship size ratio so far removed from the experimental data which form the basis of the method.

Excursions of the mid-point of the moored ship for passing ships (1) and (2) are shown in Figure 7 where it is seen that in general the early part of the

excursion is well predicted. The latter part of the excursion is not so well predicted however, although it is of interest to note that fender impacts occur at approximately the same point in both the measured and computed excursions. This discrepancy may be due to the fact that one of the basic assumptions of the simulation, that the exciting forces measured on an immovable model are applicable to a ship which moves on a mooring, may be violated. Late in the excursion it is clear that the measured sway of the model is greater than that from the simulation which may be due to an increase in sway force experienced by the model as it moved closer to the passing ship. Such an effect is not

reproduced in the simulation.

It is also tacitly assumed in the simulation model that the jetty has no effect on the exciting forces, these being assumed to remain the same as those measured in open shallow water. This may not be the case and could cause some of the discrepancies in Figure 7.

It should however be noted that the excursions measured with zero preload on the mooring lines had not only zero preload but a simulated 0.3m slack in each line. This was not reproduced in the simulation model and may account for some of the discrepancy between measurement and calculation. In the latter part of the excursion for example the appropriate spring line in the simulation model will

'take up' earlier than the equivalent line in the physical model (as it has no slack) and hence surge would be curtailed over this part of the excursion.

Comparison of Figures 6 and 7 also reveals that the peak line loads for passing ships (1) and (2) are over-estimated by the simulation model at all speeds which may also cause reduced excursions.

- 21

-It is also possible that the discrepancies in Figure 7 are due to an over-estimate of the damping in the motion which would give rise to errors which would increase as the motion progressed.

The effect of a uniform pre-tension in all mooring lines is shown in Figure 8 for spring line 4 for passing ship (1). Again it should be noted that the

physical model had a simulated 0.3m slack in all mooring lines in the 'zero pre-tension' case. It is clear that qualitative and quantitative predictions are quite good for all speeds.

Finally in Figure 9 the effect of the distance-off of passing ship (I) is shown in terms of the maximum load in spring line 4 and breast line 7. It

is seen that agreement between calculation and measurement is good and that the effect of distance off at a constant speed is well predicted.

4.3 Comparison with Full-Scale Measurements - the 'Daphne' Trials 4.3.1 The Experiments

Full scale measurements of mooring line loads were carried out, with the involvement of NNI, on the 71,000 dwt tanker 'Daphne' moored in the El Ballah by-pass of the Suez Canal. (See Fig. 10) From the outset the

trials were beset with difficulties and the comparisons made below are included

here both as anattempted comparison with the simulation but also as an

illustration of the problems that can arise when one is attempting to obtain reliable full-scale data.

The ship itself was a single-screw all-aft tanker with the following principal particulars:

Length between perpendiculars 231 .76m

Breadth, moulded 33.53 m

Summer draught 13.24m

Block coefficient at summer draught 0.810

Number of screws 1

Number of rudders

Type of stern Closed

For the trial in question the ship was ballasted to a draught of 7.7m forward and 7.2xn aft with a corresponding displacement of 45877 tonnes. The depth of water in the by-pass was 13 metres at the ship giving a depth/draught ratio of 1.74.

The ship was moored as shown in Figure 11 with four safety lines (one 64 nun diameter braided polypropylene and one 6 x 36 36 nun fibre cored flexible

steel wiere rope at bow and stern) and two 'gauge' lines, each of 6 x 36 40 nun fibre-cored flexible steel wire rope.

In such a trial it is impossible to measure the stiffness of each mooring line at the time of the test so that a vital parameter in the subsequent comparison between measurement and calculation is unknown. A value has

therefore to be assumed, based on information given by the rope manufacturers and some assumptions about variations of stiffness with ageing. In this case the following values were used for each 'gauge' line:

limit of proportionality T 55 tonnef equivalent solid metallic cross-section area AL 0.001 257

Modulus, E 6.106 tonnef/m2

a (eqtns 6 and 7) 137.127

(eqtn 6) 1.0

The gauge lines were attached at the shore-mounted bollard end to 'Strainstall' strain-gauged shackles rated at 50 tonnef. Time histories of the loads in the two gauge lines (to the nearest tonnef) were sampled at 5 second intervals and recorded on a magnetic tape cartridge via a data logger on board ship. During each trial the safety lines were generally left slack so that all loads were taken on the two gauge lines.

After passing through Panama-type fairleads the gauge lines were led inboard to steam-driven mooring winches mounted close to the centreline of the ship giving a 'constant' portion of each gauge line of 17m.

The wind-speed for the trial in question was 15 knots from a direction of 3400. It was estimated that this produced an external constant exciting force of only 0.5 tonnef in the x-direction with no sway force or yaw moment. Wind effects for this trial were therefore ignored.

23

-All three trials yielded measurements, but of these we concern ourselves with the first only. _{This is because it was known for the third trial that the} ship was hard aground on the canal bank and there was strong evidence to suggest

that this was the case in the second trial. Indeed with the gauge lines deployed as shown it is hard to see how the ship could not have been on the bank, for any tension in the gauge lines produces a sway force in the direction of the bank; _{without a counterbalancing force from a cross-wind, say, the} bank must have acted as a 'fendert. However for the first trial, it appeared that the ship was clear of the bank for some or all of the trial.

For this trial the mooring winches were manually-braked with the winches left in gear and the steam on. Exciting forces were provided by pressure waves transmitted along the bypass past the moored ship by a convoy of ships passing along the main canal. Excitation was therefore confined to surge forces only. However before the arrival of the pressure wave from the first ship in the convoy, loads were seen to be excited in both gauge lines as the trace in Figure 12 shows. _{Ultimately some activity was noted in the mooring lines at} about the time the first pressure wave was due to arrive at the moored ship, but shortly afterwards the winches started to render and heave, thereby inducing large loads in the lines as well as causing the ship to move in the by-pass. Ultimately the ship was run firmly aground on the bank and the trial

terminated.

4.3.2 Results Obtained

Measured loads in the two gauge wires, obtained when the ship was

_thought

to be

substantially clear of the bank and prior to the rendering of the winches are shown in Figure 12. The loads noted prior to the arrival of the pressure pulse from the first ship of the convoy could have been due to

- pressure waves moving down the main canal ahead of the convoy

- movement in the bypass generated by the positioning of the ship for the

trial

calculated results from the simulation program were obtained, making the following assumptions:

- virtual mass and inertias could be represented, at the depth/draught ratio in question, by

Mooring line

0.20

m/pV = 1.0

,

0.15 (.31)

- the effect Of the bank could be approximately accounted for by means of soft linear fenders with an unknown face friction

-the exciting pulse in surge could be represented by model test data

obtained from modelling a similar situation and suitably adjusted for variations in ship, canal and passing ship size.

Results of simulations of the first few osculations of, loads in the gauge lines are also shown in Figure 12 for values of

= k 0.0 and 0.075.

It is seen that agreement is poor when bank friction is neglected, but improves when a small amount of 'fender'friction is incorporated.

Measured

Maximum load (tonnef) Calculated

M_=O! 0

Of course good agreement between easurement and calculation would be unlikel.y due to the representation of the assumed batik contact by the. action o a soft

spring. The behaviour of a ship in motion while partially grounded on a

bank would involve soil mechanics and is beyond the scope of this report

However, in spite of the problemS wfth the full-Scale measurements some

apprOximate quantitative agreement between measurement and calculation can be

obtained, albeit with some possibly gross assumptions regarding mooring line stiffnesses and the effects of grounding.

4.4 comparison.w.ith Full-Scale Measurements - Fawley Trials 4.4.1 The Experiments

Measurements Of.. mooring line loads and ship movements were made. by NMI on a VLCC moored alongside Berth 5 of the Marine Terminal at the Esso refinery at Fawley. The techniques used and results obtained are described in reference 12

Forward 24.0 38.2 30.2

Aft 26.0 29.7 20.1

and involved the use Of gauged mooring hooks installed on the berth together with movement-monitoring equipment developed by NMI.

The results used below were obtained in relatively ç,aim-weather while the moored ship was passed by a large outward-bound passenger, liner. _The

experiment was essentially one of a preliminary nature as boh. themeasuring

system and simulation thethod were under test at the time of the expetiments. Therefore some parameters which were subsequently found to be required for comparison between measurement and calculation were not measured while others, in particular rnooring line stiffnesses, were unknown, arid required 'certain assumptions to be made.

Preliminary calibrationsof tie gauged mooring hooks were not encouraging as some of the hooks gave low readings for known applied loads An attempt to improve this was made. before the trial descripd below, but some doubt still, remained

regarding the ultimate accuracy of the loads measured on the, mooring hooks.

Particulars of the moored and.passing ships are given in Table 7.

Ship Type .- -..VLCC: .. Passeiger. liner

Table 7.

The .separation dist-anceY

was esim.td to be

04m and the passing -speed through

,the wat

was msured'a

6.75 nots ( 3.476..m/s) assuming a 0.3 knotheading current. . - -. . ..

The mqorjng' geometry of -the ship on the berth was as shwn in Figure. 13 with

lines I and14 being the 'First Lines Ashore' (see ref.8) and theregqre of

braided polypropylene. The other lines were flexible wire rope assumed to be of 6 x 36 42 steel cored construction with a breaking load of 115 tontef and an elastic limit of 65% of this value or 74.75 tonnef. No synthetic

tails were used. The mooring line stiffness was therefore calculated from

Moored Ship-' Passing Shi Length (PP) . ' ' ' 304.81m. 225.5'6m

Breadth (moulded) ' :47.1'7m 31.09

Draughts during measurements Fwd 4.27m 9.45m

Aft IQ.59m . 10.97m

Weight/rn

Metàlliô cross-section area Young's modulus, E a (eqtns 6 atid. .7) (eqtn6)

7.185kg

0.000910 m2 206.8.1O N/ 251 .82

10

a linear characteristic being assumed....he polypropylene lines were assumed

to be of 64 diameter, to hae a breaking lOad of 45 tonnef and tO obey a law, deriad ftO thanufactur.érs' data, for which a 6.36, 1.79 j

equation 6. . .

All thooiñg lities were assume4 to end ãtbor-ing wihche On deck, inbOard line...lengths beiñgestiate4 ftom a deck plan of.the ship mAking óertain assumptions about the orientation of the mooring lines over the decks

A wind Of 7.2 knots at an angle of 52.2° in the ship body axis system was recorded. this, and an assumed 0.3 knot: curenon'the bow -:,

-and parallel tp the berth produced the following ?xternal constant exciting forcesandrnoments, estimated using reference 14 and assumed lat-eral and longitudiflal above-water ateas of 7530 rn2 and 221

x

-6.76103N

4..46.104N Nc = I.031.lO6Nm

These were incorporated in the simulatTion model.

i-n the aence Of other information, the fen4ers were assumed to Mi,e a linear

stiffness of 1 575 1O7 N/rn (Ref 3) with friction coefficients between the fender

faces and ship of k's°

and

Acrbss-ectionOf the fairway at the bèth is giveñin'refereflce 12 which shows

that there was a dredged trench at the berth beneath the OOted ship some two metre deeper than the iediatel-.y adjacent fairway. As the program to predict interaction forces and moments assumes a flat sea bed, a mean water depth as obtained fromthe data in ref êeflce 12 and this was used in the

subseqüént sithul'ation. This depth gave a deth/meah draught ratio or the

27

-4.4.2 Results Obtained

Measured results obtained at the berth during the passage of the ship in

question are given in reference 12. Loads in all mooring lines and movements of the ship relative to the berth are given in full, but the comparison between measurement and calculation is illustrated here by means of results from a few mooring lines. It was noted in the full-scale measurements, and confirmed in the computations, that the first lines ashore (lines I and 14) played little

part in restraining the vessel. This is not surprising as their purpose is simply to aid in the initial phase of mooring; their elasticity is so much greater than that of the wire moorings that the movement of the tightly-moored ship, governed by the behaviour of the wire moorings, is generally insufficient to generate any appreciable loads in the first lines ashore.

Computed values of line loads and motions were made using the added masses and inertias of equation (31) above and line loads are shown in Figure 14 together with values measured at full-scale. Results are shown for mooring lines resisting predominantly sway and yaw motions (lines 5, 10, 11, 12, 13) and

those resisting predominantly surge motions (lines 6 and 7). Furthermore certain pairs of lines were chosen (lines 6 and 7, 10 and 11, 12 and 13) to

illustrate some differences in the behaviour of computed and measured results.

It is clear from Figure 14 that large discrepancies exist between measured and computed line loads. The computed line loads show far greater variation

with time and reach much higher levels than the measured values. The computed values are often reduced to zero while the measured values never dropped to

zero in the measurement period. Also computed values for the various pairs of lines show distinct similarities indicating a sharing of the load while the same cannot be said for the measured line loads. (The behaviour of lines 12 and 13 is a noteworthy example, initial tensions being the same for both computed

and measured results).

It is of some interest to list possible reasons for the observed discrepancies and the following points may be considered:

1. Error in measurement of passing esel speed and distance off

It is Seen in Figure 6 and 9 that the speed and distance off of the passing

veSsel have a large effect on measured line ladS, with speed having the

greater èffect. Therefore it migh be considered that errors in determining

the passingessel's Speed might cause some Of the diScrepancy noted above. However some fürther simulation runssuggested that a passing speed of 4.8 knots

rather than 6.75 knots would be required to give reasonable agteèment and it

ses un]4kely that an arror of thismagntidue could have occuted.

Hoever

as vessels have to slow as they approach Fawley it. is 'conceivable that the passing

vessel was still reducing speed when the meaürement was obtained thereby giving an effectively lOer (but unknown) passing speed. The interaction forces, and moments from an accelerating or decelerating ship are also not allowed for in the

simulation.

'2. Errors in simulation

It" has been Shown in section 4.2 and 4.3 that the. simulation tehds to over-stimate line loads, but agreement between measurement and calculation with the

comp±ehensivelydocumented experiments Of section 4.2 is ingenerel good.

This suggests that if errors do lie in the simulation they occur in -thd various s'Sumptions bade regarding line and fender stiffnesses etc.

Clearly a major unknown is the effective friction between feder and ship;

this is discussed in reference 11 and the effect of a large change in

"k and

is shown fot some lineS in Figure 14. As might be expected this change has its greatest effect on the line resisting surge motion, line 7. However little change in the magnitüd'eof the line loads ocCurred.

The 'pre'dict exciting forces and moments may also be in. error, but again the results of section 4.2 suggest that for experiments in controlled conditions, exciting forces are reasonably well predicted. .

It is however of interest to note that the model results. from reference II for a moored ship in ballast draught (i.e. similar to the Fawl,ey

show that maximum line loa4s of the order of 30 to 40 tonnef (as predicted) would be expected at a passing speed of 6 knots at a . similar .though

- 29

Errors in Line Load Measurements

The behaviour of the strain-gauged mooring hooks was less than satisfactory in their initial calibration.- As'a reult of this së. hooks were chedked

and a' repair. attempted, but coniderable- doubt remained regarding the validity of measurements from many of the hoOks. Trouble was experienced during the trials with zero drift on the gauges and the suspicion must remain

hat ome Of.thehOoks were giving unealistic.:(and probably- low) readings. This ay explain..aparent anomalies iti the 'measured. loads in some Iinepairs. For ep.lèwithl.inds12 .and'1.-3,line '13 -has the higher ..initiál tension and

the meãuements indièate that- it .responds.ore,w-ith line 12 apparently unresponsive. Howevèrqith lines 10 and 11 it. is. the linewiththè lower

initiaL tension,. line 11, that, appears to- respond more than line 1,0.

Condition of Mooring Lines

In all simulations the ageing of the mooring lines has been assumed to be uniforth for all wireropes. this of course may not be. the case so.- that

different. lines have dif-ferent tiffnesses and hence-resppnd- differently

to thir neighbours..-.- -It.is difficul- to- ee hqw. this could b,eallowc4

for adequately without knowing the stiffness of- 'each line o, at.. l,east its

age and work.ng life history.

Scale Effects in Exciting Forces and Mments

If significant scale effects are likely in interaction forces and moments thenclearly' the predicted''exc-it-ing forces.used in the simulation could be

ser iously in error, derived as they are from model measuremens.- Thi,s - woUld al-so account far the good agreethent with the model- results obped in

section 42 but the relatively poor 'agreement ith- fuLl-scale measurements.

However, as interaction forces '.and momeits.' arise predominantly from normal

pressure' effects over and .beteen the hulls of 'adjacent- Ships it is

generally assumed :that,'scale effects are small'., ,-Indeed, the. relatively

successful attempts to calculate' interaction forces and rnoients from potential flow theory have capitalised on this assumption and indirectly. shown it to be reasonable. . (RefS. 15 and 1.6) Furthermore, scale effects in the related

topic of ship-bank interaction have: been shown to be-. small in. reference 17,

well with model ptedictJion5..:

It is not considered therefore that scale effects. are a ajo ontribu.tion

toward the. discrepancies between prediction, and full-scale measurement.

6,. . Moo±ing LinFixings on the Ship .:

It was assumed inthe simulation -that the inboard end Of. each mooring line was attached. to a winch andthat no slippageoccurted.. Ref etence.8 lists several reasons which might invalidate this assumption ranging from 'winch.brake slippage

due to lack of maintenànce,-.Or too many turnsof wit.ë On thewinch.dr, to the winh'rendering at too low a value. Winh, tendering caused problems in the

"Daphne' trials as mentioned in section 4.3, but its effect was tocaüse large

transient loads in the mooring, lines, a featutê that was. not present in the Fawley results.

. : .

There seems little..reaso. to::suppose that line fixity.at the winches was anything less tha satisfactory, for' the. moored ship was. owned by a large and reputable company and .the features suggesting .slippàge'ereabsent from. the time histories of the mooting line forces. - . .

5. Genetal Discussion

It is clear from. the comparisons made. in section 4 that agreement between

simu-latiot arid measuremthlt ranges from reasonably good to poor. It is,

gratifying that the better agreem,ent was obtained with experiments made under controlled conditions where. the unknowns were few, but it-. must be admitted that agreements with ful.lscale measurements'. is less than satisfactory. This is probably largely due to the major problems of carty-ing out a satisfactory full-scale trial, especially when. conditions of ship and berth operation as well as weather '- are. not under the control of the experimenter. I.t is also a

rnàjor problem- of full-scale tria1s that a major parameter, the .itidivi4ual stiffness of-each mooring line, must remain unknown.

Problès also arise at .fu.11scaie with measurement of the behaviour of. the pässiñg ship which. may not be .pass-ing at a. constant speed on a straigh.t cours.e as as-sumed 'in the simulation. . The: experimenter's prob'iems.'are multiplied if

he can place less thati total reliance on the adequacy of the force measurements obtained from sttain-gauged mooring hboks; it is of course difficult to check

their calibration close tO the time of the trial on a berth which may be in continuous use.

31

-However it has become clear from the above discussion that in future trials, the following information would be of use in the comparison between

measure-ment and calculation

mooring line sizes, construction and if possible, stiffness mooring line geometry, both inboard and outboard

ship movements in relation to the jetty related to the origin of the axis systems of Figure 1

passing' ship speed, distance off and overlap on a time base before, during and after the passing manoeuvre

fender type, stiffness and facing material

wind and current speed and direction during the trial

recent 'before' and 'after' calibrations of any strain-gauged mooring hooks used to obtain line loads.

Many of the above items were logged during the trials mentioned in sections 4.3 and 4.4 while others had of necessity to be assumed.

It is argued in section 2.4 that the motions of the moored ship due to the effect of the passing ship are of such a low frequency that added mass values relating

to the frequency parameter wIL/g -' 0 could be used. This is justified by a study of the frequencies of surge, sway and yaw motions of the measured and

simulated trials of section 4 which show that in general wv'L/g is close to

0.2-0.3 and seldom exceeded 0.5. From reference 3 it is seen that the constant added mass values used roughly correspond to these values. In the event, the choice of added mass did not appear to be critical if the sway added mass

coefficient was changed while keeping those in surge and yaw constant. For

example, comparisons

the simulation of the Fawley trial of section 4.4 gives of maximum line loads in tonnef for some lines

the following Line 5 6 7 10 11 12 13

m/pV2.86

35.8 24.8 22.3 47.6 45.0 42.0 47.9

m /pVl.0

y

m/pVO. 5

36.2 25.0 22.4 36.2 25.0 22.4 48.5 48.9 45.9 46.1 43.0 48.8 43.3 49.1

Note: 1. Passing ship speed = 6.75 knots

2. Fender friction

3. Fender stiffness = I .575.10 N/rn

This shows the peak 'liie loads to be insensitive to assumptions regarding added mass in sway over wide range Of virtua1 mass coefficient values, provided ad4ed masS in surge and added inertia in

yaw rain constant.

Similar results are obtained when surge added itass and yaw added inertia are varied, (the other vãlue remainin constantas shown in Tables 9 and 10.

Notes 1-3 as for Table 8

Table 9

Notes 1-3 as .f or Table 8

Table 10

It is clear frOm these Tables that large errors in peak line loadS in the

Fawley tial are unlikely to arise from an error in the choice of added mass or

inertia for given fender and mooring line characteriStics

This suggests a further benefit o sc a simUlation. in that it can show the relative importance of various parameters ma moored ship system when excited

by a passing ship The copaatiiely large effect of changing the, initial

tension in the mooring- lines for example has been. shown in sectior 4.2 agreeing with trends noted in reference 11. The effect of many of these par.eter changes

has been discussed in reference 11 and will not be repeated here, but it is of interest to note that prediction.of tren4s. is appaertly satisfactory.

Line 5 6 7 10 11 12 13 IpV=Q.,5 36.1 24.1 22.1 49.8 47.5 40.7 46.9. .0..2 .36.2 25.0 22.4 48.5

459

43.0 48.8. 0.03 36.1 24.1 _24.5 48.0 45.3 44.0 49.7 Line 5 6 7 10 11 12 13

IjPVLpp2030

37 0 25 1 22 4 46 2 43 7 40 2 46 1 0.15 36.2 25.0 22.4 48.5 4.5.9 43.0 48.8 0.O45 35.8 24.1 21.7 48.6 46.0 42.8 48.6

- 33 -,

6. Conclusions

A computat-ioñal model has been devised to simulate the beháViötitof a moored

ship being passed byanother. The main conclusions arising from thif study areas follOws:

(I) Reasonable agreement between computed and meaured thooring line peak

loads and moored ship movement is- obtained uing the

siulation::an4

a

comprehenively-documeited seris of model experiments.

The interaction fb±ces exciting the mOtioi can be generalised

by

suitable ñon-dimensionalisation assuming that interaction forces and moments are proportional to the square of the speed of the passing ship and the lateral and longitudinal projected underwater hull areas. A suitably-chosen parameter

will also make some allowance for phase

Full scale measurements can be made but suffer from the fact that a major: .par4meter - the stiffness, of individualoqrng liies - is.generãlly

Uñlthô'wn.

The itboard as well as the outboard mooring line 'eoëtry is required,

especially for ships with low-frictin, roll fairleads.

Changes in fender friction affect sujrge notions and consequently have a larger effect on thopritig lines resisting such motions.

In one case studied, ch4nges in assumed values Of added virtual basses and inertias. made only small differences to computed peak loads ma sample of mooring lines.

-7. References

I. ' 'GUidelines and Recoendations fr the Sale Moóing of Large

Ships at Piers 'and Sea Islands' Oil Companies. International

Marine Fort, London, 1978

REY C F- M:

'Mooriig Forcs Induced b Passing Ships" ' Paper 2066, Offshore Technology Conference, Houston, 1974, p.351 van OORT1ERSSEN G: 'The Motions of a Moored Ship in Waves'

Publication number 510, Netherlands Ship Model Basin,

Wageningen, 1977 LE11Q C 'and PRICE W A WILSON B W: '6 KILNER F A:

1.

WILSON B W: DAND I W:

'The 'Effect of Passing Vessels on a Moored Ship'

Dock and HarboUr Authority, \tol LVIII no. 684, November 1977

'Progress in the Study of Ships Nooed in Waves' NATO Advanced Study Institute on Analytical Treatment of Problems of Berthing and Mooring of Ships, Wallingford, May 1973

'Model Tests on the Motion of Moored Ships Placed on 'Long Waves' 7th Conference on Coastal Engineering, The Hague,

1960, p.. 723-745

'Elastic Characteristics of Mooring. Ropes' . NATO Advanced

Study Institute on the Analytical Treatment of Problems of Berthing and Mooring of Ships, WaI'lingford', May 1973

'Effective Mooring' Shell International Marine, Revised

Edition, '1978

'Some Measurements of Interaction Be'tween Ship Models Passing On Parallel Courses' NMI TM32, April 1979

HAING R W:

'Numerical Methods for Scientists and Engineers' McGrai Hill Interhätional Student Edition, 1962

WILLS A E.:

'Prediction of Wind and Current Loads' on \TLCC's Oil Companies International Forum, London 1976

TUCK E 0 and 'Hydrodynamic Interactions Bet4een Ships' 10th ONR Nava]r

NEWMAN J N': Hydrodynamics Symposium, NIT Nassachussetts, 1974

"Effect of Passing Vessels on a Moored Shi:p, PartS I and II' Report EX566, Hydraulics Research Station, Wallingford July 1971

'The Measurement of the Mooring Forces and Movements of Moored Supertankers' NMI unpublished TM, 1980

'Port of Acajutla 'El Salvador, Central America - Random Wave Model Study' Hydraulics Research Station, Wallingford, report EX739, July 1976

- 35

YEUNG R W: 'On the Interactions of Slender Ships in. ,S.hallowWatr' Ournal of Fluid Mechanics (1978), vol 85; part 1, p.143-159

DANDI W:

'Some Measurements of Interaction Induced by

Surface-Piercing and Flooded Banks.! .Nl'ff TM45, December 1979

8. AcknOwledgements .

The study described above was carried cut as Part of he Ship Behaviour Study for the UK Department of Transport under the iidance of the National Ports

:Nenclature

effective 'solid' cross-Sectional area of mooring line

B moulded breadth - -:

C corrected value (equation 22)

CC) damping functiOn

Cs sinkage coefficient = (SFP+SAP)

.1OO/2.L

CT trim coefficient

(Sp_S).lOO/Lpp

E Young's modulus

F fender force

g gravitational acceleration

I longitudinal inertia of moored ship

L ship length

length between perpendiculars

P. mooring line length

length of 'constant' portion of mooring line

m

ship mass

m,m ,I

added virtual masses in surge and sway, added virtual inertia in yaw

p,q cOnstantS

predicte.d value (equation 22)

SQ

overall stiffness

SFP,SAP sinkages at forward and aft perpendiculars

t time

tension in mooring line

T

load at limit of elastic behaviour or breaking load

y

T,T ,NT

contribution to overall restoring forces in surge and sway and

moment in yaw

T draught

V speed of passing ship

vessel mOvent in surge, sway and yaw

(x1,y1,z1) co-ordinate of fairlead of ship

(x2,y2,z2) co-ordinate of shore fixing of mooring line

X.,Y.,N.. initial out-of-balance surge and sway forces and yaw moment

X(t),Y(t),N(t) exciting forces in surge and sway, and moment in yaw

37

-constants

6 fender deflection

6. initial 'fender deflection

1

extension

coefficient of kinatic friction

coefficient of static friction water density

V volume of displacement

circular frequency f moored ship in surge, sway or yaw

Subscripts

o own ship

p passing ship

SPACE AXIS SYSTEM

SHIP BODY *:xis SYSTEM

AXIS SYSTEMS

SHORE FIXING

-vi