The role of model tests in the design of single point mooring terminals

OFFSHORE TECHNOLGCY CONFERENCE 6200 North Central Expressway Dallas, Texas 75206

THIS PRESENTATION IS SUBJECT TO CORRECTION

The Role of Model Tests in the.Design of Single

Point Mooring Terminals

_{TECHNISCHE UNIVERSITErf}

Laboratorium 'mar

ScheepshydromechanIca

Archief

Mekelweg 2,2628 CD Delft

By . TebO15-788873-FaxO15781838

J. A. Pinkster and G. F. M. Remery, Netherlands Ship Model Basin @Copyright 1975

Offshore Technology Conference on behalf of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. (Society of Mining Engineers, The Metallurgical Society and Society of Petroleum Engineers), American Association of Petroleum Geologists, American Institute of Chem.i-cal Engineers, American Society of Civil Engineers, American-Society of MechaniChem.i-cal Engineers, Institute of Electrical and Electronics Engineers, Marine Technology Society, Society of Explor-ation Geophysicists, and Society of Naval Architects and Marine Engineers.

This paper was prepared for presentation at the Seventh Annual Offshore Technology Conference to be held in Houston, Tex., May 5-8, 1975. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. Such use of an abstract should contain conspicuous acknowledgment of where and by whom the paper is presented.

PAPER

NUMBER OTC 2212

ABSTRACT

This paper gives a broad outline of model tests with single point mooring

systems. This includes the purpose of the model tests, the information necessary to set up test programs, the scope of

tests, the characteristics simulated,

measurements carried out, possible

-sources of errors and the analysis of

results. Furthermore, examples of test results are given which.show phenomena

characteristic of s.p.m. terminals.

Finally, some of the phenomena observed during tests and a source of uncertainty in existing methods to calculate the behaviour of s.p.mvship systems are

discussed. INTRODUCTION

Single point mooring terminals are,

as the name implies, facilities of small horizontal dimensions, to which large vessels are moored by means of a bow hawser or by any other means which allows the vessel to rotate 3600 around

the mooring point. Generally, the single point mooring terminal can have two

References and illustrations at end of

paper.

functions. Primarily, it affords a safe

mooting-to the vessels in question.

Secondly, it can form a link in the

chain for the transport of oil.

The single point mooring terminal

can assume many forms as is shown in Fig. 1. The most common is the Catenary Anchor

Leg Mooring system (CALM) consisting of a flat cylindrical shaped buoy which is anchored to the sea floor by means of up to 8 chains. This system employs the properties of the catenary to supply the elasticity required when holding large tankers in open seas. The Single Anchor Leg Mooring system (SALM) consisting of a cylindrical buoy attached to a heavy base on the sea floor by means of a sin-gle pre-tensioned anchor-chain, obtains

its elasticity from the angle between

the single anchor leg and the vertical.

Enlarged version of the single point

mooring terminal are the Exposed Location Single Buoy mooring (ELSBM) and the SPAR.

The second of these does not only

ful-fill the function of mooring point and link in the oil transport chain, but is also used as a storage

unit-The types of mooring system

30 _{THE ROLE OF MODEL TESTS IN THE DESIGN OF SINGLE POINT MOORING TERMINALS OTC} 2212

a correct interpretation is given of the results

Modern test procedures for single point mooring terminals are _concentrated

on the following aspects:

Behaviour and system loads in extreme environmental conditions when the ter-minal is unoccupied. During these tests

the so-called survival conditions _are

investigated. The system loads for

such a sea state combined with the pro-bability of occurrence of the sea state form the basis for determining the pro-bability of survival

or

_{system damage.}

Behaviour and system loads with the terminal occupied by a tanker. During these tests the upper limits (with

respect to environmental conditions)

for operating (transfer of oil) or the upper limits at which point the tanker must leave the mooring are

investiga-ted. The results of such tests combined

with the probability of occurrence of

limiting sea conditions form the basis for the evaluation of workability.

Behaviour and system loads under

envi-ronmental conditions which occur a large percentage of the time. These results, combined with fatigue and wear and tear data for the system components can form the basis for maintenance scheduling.

INPUT DATA FOR SETTING UP A TEST PROGRAM

In setting up a model test program

for a single point mooring terminal to be

placed in a certain location, the follow-ing environmental information should

preferably be known:

Water depth and tidal variation

Current: speed, direction, variations in speed and directions, de-pendence of speed and direc-tion on wind and waves

Waves : Probability of occurrence of a given significant wave height and period. Depen-dence of

significant

wave height on mean period. De-pendence of

significant

wave height on the direction of the waves

Wind : Speeds and the relationship

between wind direction and wave direction and between wind speed and wave height Ideally such information should be obtained by wind, wave and current mea-surements taken at or near the proposed site over a longer period of time; say a

year or more. Generally, however, few

designers can afford the luxury or time to have iich measurements carried out.

and the SPAR primarily used in water

depths of up to approximately 150 ft.

Some of the systems can with

modifica-tions be used for even greater water depths, however.

Rigid spar buoys connected to the

sea floor by means of a universal joint are at present being designed. These

consist of a buoy at the surface rigidly

connected to a frame work which extends

down to the base. This type of mooring

is intended for water depths of 300 ft.

or more. Finally, there are the mooring towers which consist of a slender open

frame work fixed to the sea floor.

Unlike all other systems, this type of mooring terminal does not contribute to

the total elasticity of the system.

Generally, the tankers are

connect-ed to the mooring terminal by means of large circumference synthetic ropes

which are part of the operating equip-ment of the terminal itself. In one case where the vessel is permanently moored

to serve as storage space, the connec-tion consists of a rigid arm.

Single point mooring terminals can be, as may be gathered from this brief

review, complex systems which present a formidable problem to those who are en-gaged in their design. In the design of such systems a number of aspects must be taken into account. Firstly, the system must afford a safe mooring for the tanker

in sea conditions prevalent in the area where it is located. Secondly, when

sub-jected to severe loads, originating

either from the tanker or, for the case that the terminal is unoccupied, from severe sea conditions, the construction must not fail. Thirdly, the combined behaviour of the terminal and the tanker must be such that the loading or

dis-charging operation may be carried out for the greater part of the year.

In order to gain sufficiently reli-able data regarding the various aspects

pertaining to the total behaviour of

single point mooring terminals,

design-ers have frequently made use of model tests. These tests are carried out with

scale models of the terminal and the tankers in large basins in which the

environmental conditions expected in a

certain location can be reproduced. Such

model tests can provide information which may be inexpensible for an

effi-cient design, provided that:

- the correct parameters are investigated - the models and environmental

condi-tions are reproduced correctly

- the tests are carried out in a careful

In such cases, firms or institutes spe-cialized in collecting environmental

data on a world wide basis are often, 'consulted or published wave, wind and [current data are used. If environmental

data are totally lacking short term measurements are sometimes carried out

at the site or known data are

extra-polated

From the environmental data anum-ber of sea conditions with respect to wind, waves and current are selected

under which the tests will be carried out. At this stage experience gained from previous tests on single point mooring terminals or from experience gained with existing, similar

installa-tions is effective in reducing the

num-ber of different sea conditions possible

to a level which is acceptable: frOm the

point of View of limiting the number of tests while still remaining sufficient

to gain results representative: of the

particular systemin-that location. Besides information on the environ-mental conditions, the following

charac-teristics of the single point mooring must be known:

For instance for a CALM type system:

Buoy : dimension, weight,

centre of gravity, posi-tion of connecting point of bow hawser

Anchor chains rmumber, length, weight

per unit length, break-ing strength, elastic limit and elongation,, connecting point to

_buoy

and pre-tension

Bow hawser : length, weight per unit length, load Vexsts-elon-gation curve

Tankers moored to s.p.m.: size of tan ket(s), principal di-mensions

Loading conditions: transverse stabili-ty, period, of' roll,

lon-gitudinal Weight distri-bution, position of

bow

hawser connecting points

TEST PROGRAM

When the environmental conditions and the configuration of the terminal are known, the test program may be set up. Generally a limited selection of envi-ronmental conditions to be tested is made from the wide range of conditions

which may occur at the location. The selection is usually as follows: - For survival tests extreme

environ-mental conditions are chosen which have a probability of occurrence of

J.A. PINKSTER AND G.F.M. REMERY

681

once in 50 or 100 years. These

condi-tions are usually. with high winds,

waVesand current from the same

direc-tion.

- For tests in operating conditions with a tanker moored to the buoy, environ-mental conditions are chosen with a probability of occurrence of 1 to 10% or those conditions utder which it is expected that it will be possible to carry out operations or be able to remain moored to the terminal. Often those conditions will be selected which, from experience, are known to give high forces due for instance to the relative directions of wind, wave

and current.

- For tests under moderate conditions with the buoy occupied or unoccupied,

conditions are chosen which have a probability of occurrence in the region

of 50%.

The number of different sea states is

generally as follows:

Survival tests 'with buoy unoccupied: 1 to 3

Operational tests with a tanker moored to the buoy:.

3 to 6

Tests in moderate conditions:

1

The 'sequence of tests is often as follows:

One test in survival conditions and two

or three under operating conditions.

From the results of these tests it may be concluded that some characteris-tics of the system need to be altered for instance, the pre-tension

in

anchor .chains, length of bow hawser,

arrange-ment of underbuoy hoses etc. The first tests would then be followed by two or three tests in which the effect of the alterations are checked. This part of

the program, consists of, as it were,

quick look tests and preliminary

optimi-zation tests. After the first part, a series of tests

_Are

carried out under

operating conditions to investigate the influence on the behaviour and loads of

the following parameters:

- sea conditions with respect to wave

height and direction and. current and

wind speed and direction

loading condition tanker

underbuoy hose arrangement

etc.

These tests form the bulk of the program and may number from 10 to 30 tests..

Generally not all possible combinations

of parameter variations are tested,

however. After this part of the program, a number oftests are usually devoted to the optimization of some specific ele-ments in the system. These tests would

THE ROLE OF MODEL TESTS IN THE DESIGN OF SINGLE POINT

MOORING TERMINALS OTC 2212

Isually be carried out under both sur-,ival and operating conditions. The lumber of tests in this part would amount to 2 - 6 tests.

The above brief review gives an

outline of a possible test program. The following parts will discuss the actual information required and the procedures involved.

CHOICE OF SCALE

The choice of the model scale depends on a number of factors, the most important of which are:

water depth: each basin has a maximum

water depth.

accuracy of results: the larger the scale factor, the smaller the models, the lower the forces in the model and the accuracy with which for instance, pre-ten-sions may be adjusted. capability of generating the required

wave height and period at a particular scale in the basin. VM ,Vp = g ,g_{m p}

1m'1p

= Assuming that

ln

and that = where V it follows that: 12 =

/E

vm 1m V m and = -E = ic-aT 1

tm

_E

Vp

The scale factor for weight and force becomes:

where

_E

xa3 Fm

A = ratio between specific gravity

of sea water at the

s.p.m.-location and the fresh water in the model basin

The scale factor for frequency becomes: a velocity in the model or prototype acceleration of gravity in model or prototype a characteristic length in model or prototype

a= a

_1.rt

a = linear scale factor

= scale factor

of speed

= scale factor for

time

m

where w = frequency in radians/sec. or cycles/sec.

For tests in wind, waves and current it is normal practice at the NSMB to use scale factors ranging between 50 and 70. This range of scale factors allows accu-rate adjustment of such quantities as pre-tension in anchor chains, wave heights and current speeds etc. and assures model force and motion levels which may be accurately measured and

recorded.

SIMULATION OF ENVIRONMENTAL CONDITIONS Application of Froude's law of simi-litude results in the following scaling for the environmental conditions:

Waves:

For a given significant wave height -dw1/3 and mean period T the corresponding

values in the model are: -C1/3 _and

--f-a

ATt

Current:

If the current velocity in reality equals

V , thus the speed in the models equals: cp

Taking the above into account a scale factor a for the model tests is chosen. This means that if the linear scale factor is a, all full scale linear dimensions will be reduced accordingly. What are, however, the scale factors for weights, period of roll, inertia,

elasticity and all other quantities of importance? This depends on the princi-ple of similitude between prototype and

model which is to be adhered to. This,

in turn, is dependent on the phenomena which determine the dynamic behaviour of the prototype and of the model. In reality, the dynamic behaviour of bodies

located in or near the water surface are dominated by forces due to the action of waves and forces due to the inertia of the body. If the body is far removed from the water surface the motions are dominated by friction forces and inertia, The law of similitude between prototype and model for the case that the behav-ior is dominated by the action of waves and the inertia of the body has been

formulated by William Froude and hence is known as Froude's law. This states that for dynamic similitude the follow-ing condition must be satisfied:

known as the energy spectrum since the energy present in the waves is propor-tional to the square of the wave ampli-tude. The spectral density of waves in reality has been determined from full scale wave height records. From large numbers of measurements various inves-tigations have deduced formulae Which give the value of S(w) if the signi-wave height tw1/3 and mean period T

are known. One of these formulations

is given below: -5 -Bw

S(w) = Aw

e 7.-4 where.: A = 172.8

tw1/32

T B = 691.0 i7-4

This particular formulation is of

the Pierson-Moskowitz type which is applicable to fully developed seas.

Other formulations have been given

among others, by Darbyshire,

Roll-Fischer, Bretschneider and Pierson Neuman and James. The choice of the

spectral density formulation to be

used for a particular test depends to a large extent on the location of the

prototype. For most investigations

where little is known concerning the

local conditions except the significant

wave height and mean period, the

Pier-son-Moskowitz formulation is often

used. The waves used in the model basin are generally long crested. This means there is no directional scatter in the waves. This is not the case in reality where waves of a particular frequency

may be progressing in a range of

direc-tions around some mean. This is

espe-cially true of wind driven waves. Long waves or smells generally tend to have

less directional scatter and to have

-longer crest lines: In model basin

long crested waves are usually gener-ated for the following reasons:

the directional properties of the waves at the proposed location are not known

- with uni-directional waves the In-fluence of variation in the wave

-direction on the behaviour of the s.p.m.-ship system are more prominent

and therefore give results which are more easily interpreted

In the model basins waves are adjusted by a method based on past experience

and a trial and error process. The

waves are measured by a resistance type wave probe placed in the position

V cp

/Tx

gind: the same speed scale as used for :he current speed applies.

Using these scale factors the

pre-?arations prior to the actual model :ests can be carried out- For the envi-:onmental conditions the preparations

mnsist of:

- adjustment of water depth - adjustment of current

- adjustment of wave generators - adjustment of wind

[these adjustments are carried out without

my models in the basin. later depth:

- the adjustment

of

the water depth in a basin is a straight-forward procedure requiring water to be added or let off. :urrent:

- The adjustment of current entails

measurement of water speed in a number of pointiin the vicinity of the

posi-tion in which the models will be placed in the basin. For the case that tests are to be carried out in waves combined with current, the area over which the current is adjusted; must be large enough to ensure that the waves enter-ing the test area of the basin are not distOrted. An example of the horizontal and vertical current distribution

measured in the wave and current basin

is shown in Fig. 2. Erregular waves:

- After the current, the waves are

ad-justed. For open sea conditions the

waves are of an irregular nature.. This requires that for a realistic

simula-tion the model waves also must be irre-gular. Irregular seas are generally

characterized

by

their significant

wave height and mean :period. The

sig-nificant wave height is defined as the

average of the one-third highest peak:

to trough values while the mean period corresponds to the mean time lapse between zero-up-crossings. The

signi-ficant wave height and mean period, however, give, only a rough description

of the sea state since the values give no indication as to the contribution of the various frequencies present in the irregular waves- This information

is given

by

the spectral density of the waves. The spectral density

Sr(w)

of the waves is defined as follow:

S (w) Aw _{= 15c a2}

w-½w < w < w+kAw

The spectral density-Sc(w) is also

212 J.A. PINKSTER AND G.E.M. REMERY

THE ROLE OF MODEL TESTS IN THE DESIGN OF SINGLE POINT MOORING TERMINALS OTC 2212

2 PC°

S (W) = j

R (T) COS

WT dt

7 C

An example of the spectral density of

the waves generated in a model basin is

given in Fig. 3. In this figure the

spectral density of the model waves is compared with the spectral density as

given by the Pierson-Moskowitz

formu-lation for the same significant wave

height and mean period. The agreement

is generally good except for the drop

off in the model spectrum at higher

frequencies. This is due to mechanical

limitation of the wave generator. In most cases this discrepancy is

accept-able since the distribution of the major position of the wave energy over

the wave frequencies is correct and

since, in general, the higher

frequen-cies have a negligible influence on the behaviour and loads in the systems

investigated. The failure to generate the very high frequency waves also

results in an increase of the mean period of the model waves, compared to

the required mean period. However, the fact that the spectral density of the

model waves matches the theoretical

formulation in the frequency range containing the major part of the total energy means that the mean period of waves within this frequency range is correct.

qind:

In the model basin, wind is usually

generated by means of fans placed some

distance away from the testing area. The wind speed is measured by means of an anemometer. The number, position and speed of the fans is such that the wind speed is reasonably homogeneous in the area where the models are to be located

The wind distribution is, however, not

up to wind tunnel standards since for instance the vertical distribution is not adjustable.

MODELS- OF S.P.M.''S AND TANKERS S.P.M's:

Models of s.p.m. terminals are

construct-ed of different types of materials:

wood, metal, synthetic foam, plastic etc. In practically all cases, components are

made as rigid as possible since the tests are aimed at the determination of rigid

body behaviour and not at the determina-tion of elastic behaviour of construcdetermina-tion elements. Centre of gravity of the models are determined and adjusted by means of

inclining tests in air while the mass distributions are checked by means of pendulum tests.

The model anchor chains for the buoy are

made to the correct length and weight.

The elastic stretch of the model chains

is smaller than is the case in reality.

To this end a small coil spring

compen-sating the lack of elastic stretch is

added. This method insures that both the

catenary characteristics and the elastic

properties of the chains are simulated

correctly. Tankers:

The models of tankers are generally

con-structed of wood. They are fitted with deck and superstructure. The longitudina3

weight distribution (mass moment of

inertia for pitch and yaw) is adjusted in air using the principle of the phys-ical pendulum. The transverse stability is adjusted by means of inclining tests. The adjustment of the natural period of

roll completes the preparations of the

ship model. In most cases stock models may be used and are available.

The bow hawsers of tankers moored to

single point mooring terminals are in

reality made of synthetic fibres which

have a distinctly non-linear load elonga-tion characteristic.

For the model tests the bow hawser gener-ally consists of a thin steel wire

attached to a system of springs which

provide the elasticity. The spring

pack-age consists of successively stronger springs mounted in series. Each spring

is fitted with a system which limits the stretch. As the load in the hawser is increased, the weakest spring first

reaches its stretch limit after which the stiffness of the hawser increases. This

procedure repeats itself as the second

weakest spring reaches its stretch limit. In this way the non-linear elastic

characteristics of bow hawsers may be closely reproduced. In Fig. 4 the elastic characteristics of a model hawser are compared with the full scale values. in the basin where the single point

mooring is to be tested. From the record of the irregular wave height measured in this point, the spectral density is computed in the following way:

If the wave height record is c(t), the auto-correlation function

R (T)

is cal-culated from:

R

1T

c(T) = liM ,y, f

ot).0t+T) dt

o

The spectral density S(w) is obtained by Fourier transformation of the

nderbuoy hoses, floating hoses:

n some test programs, models of

under-luoy hoses or floating hoses have to be

zed. These hoses in reality consist of

.trings of large bore flexible hoses,

ach string of hoses consisting of dements with lengths of 30 - 40 ft.

mcdted together. The bore of these hoses

aries between 12 and 24 inches in real-ty. A hose element consists of a flex-ble middle section made of steel coils

aibedded in rubber and rigid end section :riding in a flange. Models of such hoses Lre made in a manner similar to reality ind consist of coil springs covered with .atex. The extremities of each model ?lement ending in a rigid part with a flange to which the next section may be :onnected. In model hoses the following )roperties may be reproduced: length, liameter, underwater weight and bending ;tiffness. In Fig. 5 the bending stiff-less of a model hose is compared with full scale data for a 24" submarine hose. then modelling underbuoy hoses, addition-xl items such as buoyancy tanks, beads Ind tie wires etc. are also reproduced )n scale with the appropriate nett

)uoyancy and elasticity. A complete set-ip showing a CALM and SALM single buoy mooring fitted with chains and underbuoy loses is shown in Fig. 6. In Fig. 7 a lumber of different types of s.p.m.'s :ested at NSMB are shown.

4EASUREMENTS

Measurements during model tests with

single point mooring terminals may

in-Forces in anchor chains and bow haw-sers. These are measured by means of transducers fitted in the appropriate

lines (see Fig. 8).

Motions of the buoy. These may include

surge, sway, heave, pitch and roll.

The linear motions are measured by means of a light pantograph system

(see Fig. 9) or a system of mutually

perpendicular thin wires connected to the top of the buoy and running to

fixed potentiometers.

The roll and pitch motions are measured by means of buoy-mounted potentiometers connected to a vertical taut wire which is used as a reference. The tension in the wire is held constant so that the buoy motions are influenced as little as possible. A new method of measuring linear buoy motions consists of a point light source fitted to the buoy and an optical tracking system which is homed on the point light source. In this way motions are measured without

applying external forces to the buoy.

-

Axial forces and bending moments in underbuoy and floating hoses. These are measured by means of transducers which

have been constructed so that they may be fitted at the points where hose

elements are flanged together. The length of the transducers is such that they correspond with the length of the rigid parts of the actual hoses. In this way the discontinuities in the curvature of the hoses are retained

(see Fig. 8).

- Motions of the tanker are measured by means of pantograph systems and gyro-scopes (see Fig. 9). When the horizon-tal motions of the vessel become large,

they may be measured by means of a remote tracking system based on laser

beams.

TEST PROCEDURE

After all transducers have been cal-ibrated the model of the s.p.m. is placed in the basin and the pre-tension in the anchor chains is adjusted. Tests in ir-regular waves, wind and current are carried out according to the following

procedure:

The static values of forces and mo-tions are recorded in still water (no

waves, current and wind).

The current is turned on when the speed has stabilized the values of

the forces and motions are recorded.

The wind is turned on and when the system has again stabilized the forces

due to wind and current are recorded.

The wave generators are put into oper-ation. The waves are generated for a period of time corresponding to 70 minutes in reality. For the first 35 minutes no measurements are carried out since the starting-up phenomena may influence the results. Measure-ments are carried out during the

second 35 minutes of the 70 minutes

period. The 35 minute test period is sufficiently long for phenomena with wave frequency to be considered

sta-tionary. As will be discussed later,

this test period may be too short when considering low frequency pheno-mena, sometimes observed in the

hori-zontal motions of tankers moored to

s.p.m.'s.

RECORDINGS AND ANALYSIS OF RESULTS

Signals are recorded by one or more

13 channel magnetic tape recorders and/or

one or more 24 channel Ultra Violet paper

strip chart recorders depending on the number of signals to be measured.

Signals recorded on U.V. paper strip J.A. PINKSTER AND G.F.M. REmERY

THE ROLE OF MODEL TESTS IN THE DESIGN OF SINGLE POINT MOORING TERMINALS OTC 2212

wave train with the same spectral

densi-ty, all averages connected with the

measured signals would be the same. This

is, however, not true for the maximum

value of a signal. If for instance, the test duration is increased, the probabi-lity that a signal may reach an even higher maximum value increases also. On the other hand, if the test is repeated

in another wave train with the same spectral density but with the same dura-tion, then a different maximum value will be found also. The problem is to know the

behaviour of the extreme value of which only one is found for each measured sig-nal from each test. What we are in fact

seeking is the distribution of the ex-treme values or the probability of

occur-rence of some extreme value. The proce-dure by means of which distribution

functions for extremes may be determined

from the results of model tests is given

in (11). Briefly the procedure.involves_

the determination of the ratio between

the maximum value and root-mean square

value of a signal for all tests. These non-dimensional maximum values are used to construct the required distribution function of extremes which is valid for test length of 35 minutes. Based on this distribution functions estimates can be made of the extreme values with arbitrary

probability of exceedance for test pe-riods greater than 35 minutes.

Besides records of forces and mo-tions, visual behaviour of the tanker

and s.p.m. is recorded by means of film

either taken at model speed i.e. pro-jecting at the same number of frames/sec.

as the film was made at or with a high

speed camera at a rate of

IE

times the

projection speed. In this case the

pro-jected film will show the motions in real time. Records of the motions of

underbuoy hoses etc. are made by means

of underwater television equipment. ACCURACY OF THE RESULTS

For a given set of model and envi-ronmental conditions, errors,

uncertain-ties and inaccuracies in the results of tests come from the following sources:

the duration of the test scale effects

the sensitivity of the measuring de-vices

errors made in reading off values on

the U.V. paper charts

errors introduced by sampling and

digitizing signals recorded on magnetic tape.

iart are used for quick-look and check-1g purposes. From these recordings

Lx mum and minimum values are read off.

gnals recorded on magnetic tape are

.mpled at a rate of up to 32 samples second by computer. These values are .gitized and stored for further

analy-s.

For signals recorded during tests

irregular waves the normal statistical lalysis consists of determining the

alowing quantities:

mean value

root-mean square value maximum value

minimum value

significant value: mean value of the one-third highest peak to trough values

significant positive value: mean value

of the one-third highest zero to peak

values

significant negative value: mean value

of the one-third highest zero to trough

values

required the following characteristics

in also be determined:

distribution function of all digitized

values

distribution function of peak values distribution function of trough values distribution function of peak to

trough values spectral density response functions

le following additional treatment of bgnals may also be carried out:

filtering

combination of signals

As can be seen from the above, one

bgnal measured during one test can al-. ady yield a large amount of data. Al-lough all these quantities describe the . .haviour of a signal, the amount of data

too wieldy when it comes to using such

.sults for design purposes. In many lses the designer only requires a reli-31e value for the extreme of a particu-ir signal on which he may base the imensions of a particular construction 1ement. One would be tempted in such ise to use the maximum value recorded iring a particular test. This would,'

wever, be incorrect since the maximum

lime of a particular signal is a statis-ically unreliable quantity.

Model tests are carried out suffi-iently long for the process to become tationary ergotic. This means that if ae length of the test had been increased r if the test had been carried out in a

irregular with sharp edges. This _means

that the points of separation of the air flovi are more or less fixed and the same

for model and prototype and that the scale effects will be small. They are estimated to be in the order of 0 - 10%.

Wave forces on the single point mooring

terminal:

If, the s.p.m. is constructed _{as a}

cylin-drical body, an Impression of the impor-tance of frictional effects in the wave forces in reality may be gained from Fig. 10, taken from (1). This figure gives an indicatioh of Whether friction effects will play an important part based on the values of ca/a and ka for

the s.p.m. in question

where.: k = wave number

Ca = wave amplitude

a. _{= radius of the s.p.m. body} If for instance it is required to know

whether frictional effects have, played

a part in results of tests on a 12.00 m

diameter buoy tested in. 8 second waves of 2.00 m amplitude,- then -this may be

checked. as follows: For 8 segond waves:

47r2 = 0.063 g

8.g

=.2 m Ca a = 6 m

c a/a,=

0.33 , ka'= 0.38

From Fig. 19 it is seen that the point

ka, c./a

is

in the region where inertia

effects are dominant:in.the wave. forces. In this case it means that although there may be scale effect in the friction

forces in the model, these will not in-fluence the total hydrodynamic force _to

any appreciable extent.

Current forces on the single point moor-ing terminal:

If the s.p,m. consists- of a .flat buoy,

the current flow around the buoy is three-dimensional, flowing under as well as around the buoy. That part of the flow which passes under the buoy, will

encounter.sharp corners which will re-sult in flow, separation in the model as well as in reality. This means that

ge-nerally the flow characteristics around such bodies match quite well with reality and consequently, scale effects due to friction will be small. They are esti-mated to be in the region of .0 - 10%.

If the buoy is of the slender, vertical

cylinder type, or if.parts of the con-struction consist of slender. elements, the flow around sudh- elementswill _{be of} Duration of tests:

If the. test has been carried out for a

sufficient length of time, then the

processes involved have' become

station,-ary. Tests repeated under the same con-ditions should then give the same re-sults. Normally, using a standard test period of 35 minutes all mean values

(mean, root-mean square and significant

values, distribution) will reproduce within one or two-percent Maximum val-ues may, however, differ as MuCh"as

20-30%.. Depending on.the terminal in

ques-tion and the sea States at that locaques-tion, reproducability maybe worse with appre-ciable shift in mean values and variation

of 100% or more in- maximum values. This

phenomena ismainly due to large ampli-tude low frequency horizontal motions of the tanker which may occur in some sea

states. The-nature of the phenomena in-volved will be discussed furtheron in this-paper. Such low frequency motions

will not become, stationary within the

standard testing time of 35 minutes. If this is the case, a test may be carried

out for longer periods of time. Scale effects:

'Tests are carried out according to

Froude's law of similitude. This means that scale effects will occur in pheno-mena mainly dependent on friction effects

since these are dependent on equality of

the Reynolds number.

All signals measured during tests in waves, wind and current are to some ex-tent influenced by friction effects. In the following a brief review of the mag-nitude of these effects on various mo-tions and forces measured during::tests

with single point mooring terminals is

given.

Motions of the tankers:

Motions of tankers, induced by waves,

are for the greater part induced

_by

hy-drodynamic Mass and inertia. forces. Scale effects: Negligible.

Current forces on tankers:

This depends on the direction of the current relative to the heading of the tanker. With current head-on the scale

effect is in. the order of 100%. The forces in thiscase are generally small,

however and not significant for the mooring problem. With current on the

beam, flow separation points are more orless

as they ate in reality. Scale ef-fects.: from 0 - 5 1.

Kind forces on tankers:

rhe above water shape of tankers is very

J.A. PINKSTER AND G.F.M. REMERY

8 THE ROLE OF MODEL TESTS IN THE DESIGN OF SINGLE POINT MOORING TERMINALS OTC 2212

--.11111111411111111111111 the two-dimensional type. In principle,

the model with these then show different points of flow separation to the full scale construction. In this case we must look to the local Reynolds

numberRe for model and prototype and determine the difference in the drag coefficients Cd' For circular cylinders

the drag coefficients are shown to a base of log Re in Fig. 11, taken from

(2). Model tests are practically always carried out at sub-critical Reynolds numbers. This means that the Cd values are always approximately equal to 1. Prototype Reynolds numbers are often in

the super-critical region. The Cd value in this region is, however, dependent on the roughness of the cylinders as shown

in Fig. 11. In the case of actual instal-lations, quite high roughness values may be reached due to marine growth

(bar-nacles etc.) and general deterioration

of the surface of the cylinders. This tends to increase the Cd values for the

i

prototype thus bringing t closer to the model values. In general, model values of the current forces will be somewhat higher with values being from 0 to 20% above those for the prototype.

Sensitivity of measuring devices:

Moments and forces: Bending moment and

force transducers are generally capable

of measuring forces with an accuracy

far in excess of the minimum accuracy required. They are accurate to approxi-mately 0.1%.

Motions: The accuracy of the measurement

of linear motions measured by means of

pantograph systems is dependent on the

frequency and amplitude of the motion, accuracy being less at higher

frequen-cies and smaller amplitudes. For the

normal range of frequencies with periods of 0.5 seconds to 3 seconds and ampli-tudes greater than a few millimeters in the model, accuracy of linear motions is approximately 1 to 5 %.

Angular motions measured by means of gyroscopes are accurate to approximately 0.1%.

Errors made in reading off U.V. paper charts:

2 - 5 cm. The error expressed as a

per-centage amounts to approximately 2 to

5%.

Errors induced by sampling and

digitiz-ing signals recorded on magnetic tape:

A signal recorded on magnetic _tape as a continuous signal is sampled _{at a} rate of up to 32 samples per _second. Nor-mal sampling rate: 8/sec. A _{sample read} off is digitized with _{an accuracy of}

1/256 _{of the maximum band width} avail-able for the signal. If the maximum value of a signal reaches the _{limit of} the available band width then _the accura-cy of each digitized sample equals

1

0.8% of the maximum value.

128

As may seen from the above brief _review

in which some estimates of the uncer-tainties, inaccuracies and errors in-volved in model tests _{are given, the}

major sources of uncertainty _{lies in the} reproducability of the tests and in

scale effects due to friction. With

regard to the first of these, it is

noted that they are in most _{cases due to}

low frequency phenomena. _{A longer test}

period is required when this _occurs. Friction effects have been estimated _for many phenomena to be in the order of 0

to some percentage. In all cases the

model test results will be the same or higher than prototype results.

In general it is recommended _{to adhere} to model test results without _correcting

for possible scale effects.

EXAMPLES OF INFORMATION OBTAINED FROM MODEL TESTS

One of the most important results of model tests on s.p.m. systems is the

information that is obtained about the

general behaviour of a ship moored to a

single point in waves, wind and current. Ship motions:

In general the ship performs slow oscillating motions in the horizontal plane about a certain equilibrium posi-tion. This equilibrium position is deter-mined by the speed and direction of

cur-rent and wind and the height, period and direction of the waves. The equilibrium

position of the ship can be obtained from the mean forces which are exerted on the ship in a particular sea state and which

are dependent on the direction of waves, These are dependent on the width

of the trace of the signals in relation to the amplitude of the signal. The reading off error is in the order of

half the width of the trace which amountswind and current relative to the ship. to approximately 1 mm. With a signal - _{An estimate of the magnitude of the mean} amplitude in the order of magnitude of forces can be obtained from (3).

:n general the mooring loads are largest

then waves and/or wind are at more or

.ess right angles to the current. A

:ypical equilibrium position of the ship

.n those conditions is shown in Fig. 12.

:f the current is strong (e.g. 3 knots)

Lnd the vessel is loaded then this

equi-.ibrium position is very stable which

leans that the slow oscillating motions

7elative to the equilibrium position are

nmall. This equilibrium position is not

rery sensitive to small changes in wave

'eight, wind or current speed. Since the

Lngle between the current and the ship's

:entre line can be considerable (100-200)

:he athwart ship's component of the

cur-:ent force on the ship is large, which

nay result in large mean forces in the

)OW hawser. Superimposed on these mean

forces are the oscillatory forces due

:0 wave induced buoy motions and tanker

notions. When the current speed decreases

to for instance 1.5 knots or the vessel

'raft decreases during the

un-Loading operation, then the equilibrium

position changes considerably. The

tan-cer takes an average position more in

Line with the bow hawser and the angle

petween the ship's centre line and the

:urrent may increase up to 450. In the

mme time the ships often swing about

:he equilibrium position. The amplitude

)f these slow oscillating swing motion

:an be considerable. The position of the

XYW hawser may vary more than 900

be-:ween the two extreme positions. The

rariation in the heading of the ship

Luring the swinging motion is shown in

'ig.

13. High bow hawser forces

general-.y occur when the ship has reached her

mtreme positions during the swinging

uytion. Often large hawser loads. also

)ccur when the horizontal motion of the

;hip's bow is largest. This is normally

Lear the average position of the ship

Luring the slow swinging motion. The

winging motion and consequently the

Lagnitude of the largest loads in the

pow hawser can be reduced by a reduction

Pf the length of the bow hawser.

[ow the mooring loads of the ballasted

dhip compare to the mooring loads of

the loaded vessel depends on to

many

Parameters with respect to sea

condi-.ions, sea direction, ship's size and

ype of s.p.m. system, to be able to

ve a general trend.

luoy motions:

..11 case a relatively small mooring buoy

s used (CALM or SALM system) the

mo-Acms of the buoy, when occupied by a

:anker are, except the vertical heave

Lotion, mainly dictated by the loads in

the bow hawser. From the measurement of

the buoy motions the minimum and

maxi-mum distances between the suspension

point bf the underwater hose of the

buoy

and the pipe line end manifold (PLEM)

can be determined. These data are

in-dispensible for a proper design of the

underwater hose system. The horizontal

motions of the buoy are normally largest

in extreme operational conditions when

the buoy is occupied by a tanker; the

vertical motions are largest in survival

conditions without a tanker moored to

the buoy. An example of the envelopes

of motion of the hose suspension point

of a CALM buoy in extreme conditions is

shown in Fig. 14.

Up to now a proper explanation for

all phenomena that occur with regard to

the behaviour of the system

tanker-single point mooring is not available.

A systematic analysis of all data

avail-able on this type of systems is

there-fore not yet possible. However, much

'effort is being put into this subject.

A short description of the main problem

of slowly varying motions is dealt with

briefly in the next section.

MATHEMATICAL DESCRIPTION OF

ENVIRONMEN-TAL FORCES

In order to increase the efficiency

in the design of s.p.m.'s methods of

cal-culation are being introduced with the

aim of establishing, at an early stage

in the design, the behaviour and loads

of the system. These methods of

calcula-tion involve on the one hand a

mathema-tical description of the important

characteristics of the s.p.m.-ship

sys-tem including non-linear restoring

for-ces and the inertia and damping of the

buoy and ship for various modes of

mo-tion and on the other hand a

mathemati-cal description of the environmental

forces acting on the elements of the

system.

Due to the non-linearities of the

system equations of motion are

inte-grated on a step by step basis using

small increments of time. As has been

described before, the environmental

forces are due to:

wind

waves

current

Wind forces:

The formulations for the lateral and

longitudinal wind forces and yawing

moment are of the following type:

J.A.

PINKSTER

AND G.F.M.

REMERY

THE ROLE: OF MODEL TESTS IN THE DESIGN OF SINGLE POINT MOORING TERMINALS OTC 2212

2

Fw

= hp

V A C

w w dw

In this formulation the coefficient Cdw is determined from model tests in wino tunnels for different. angles between. the heading angle of the vessel and wind (3). Current forces:

The formulation for this type of force is similar to those for the wind forces:

F = 1/213 VAC

c

c

cdc

The value of the current force, coeffi-cient Cric is determined .by oblique towing rests or

by

tests in current for different angles between vessel and

cufrent,(3). Both wind and current for-ces are Constant values for a constant speed of wind and current..

Wave forces:

The forces due to waves may be split-up

into two components

wave forces and moments which are pro-portional

to

the wave height (1st or-der wave forces)

wave forces and moments which are pr&-portional to the square of the wave height (2nd. order wave forces or wave drifting forces).

The 1st and 2nd order wave forces in re-gular waves may in principle be

calcu-lated from the pressure distribution on the hull usingBernouilli's equation:

a(

p= -pgz -

pa -

kplvl.v

where cP is the 1st order velocity

poten-tial. The 1st order wave force is found

by integrating the pressures acting on

the hull whereby the 2nd order contri-butions of: the pressure components are neglected..The mean wave drifting force

in regular waves is found by integrating all second order pressure contributions. In determining the 1st order wave force

only the components pgz and acp

are taken into account..

All

three at

components of the pressure contribute to the mean Wave drifting force.

1st order wave forces:

The first order wave forces induce ship

and

buoy

motions .with wave frequency. For ship S the, motions due to these for-ces may be calculated from first prin-ciples using strip-theory (4) or, in the case

of

Ships at zero forward speed,

a

method based

on

three-dimensional

poten-tial theory. (5').

Luoy motions may be calculated using the

potential theory method

or,

in the case:

the buoy is -slender or composed of slender elements which are small in

re-lation to the wave lengths,

by:a

finite element theory based on the, relative motion principle (6).

2nd order wave forces:

In irregular.waves the height of the incoming waves is a slowly varying quan-tity. Since the wave drifting force

is.

proportional td the square Of the wave height, this Will also show slowly

Vary-ing or low frequencTcomponents (see

Fig. 15). As may be seen from this figu-re, peaks in the wave drifting force are

associated with the occurrence ofgroups

of higher waves. In (7) it was shown that If the period of the wave groups

coincides with the natural period of the

horizontal, motions of the moored. vessel,:

large amplitude Motions- can occur. In principle the components of the 'wave drifting force in irregular, waves have frequencies from 0 to infinity, however, the :main components are concentrated between the frequency O'and the frequen-cy of the waves from Which the 'force

originates,

Moored ships generally Constitute mass-spring systems with natural periods for the horizontal.motions in the Order of magnitude of- 50 to 500 seconds. 'These frequencies are outside of the wave' frequencies and in the range of the frequencies of the drifting forces. Damping in the horizontal motions is generally low. These two characteristics combined with the frequencies of the slowly varying wave drifting forde can produce the large amplitude low fte-. quency motions in moored vessels..

These motions may

in

SOtecases

complete-ly dominate the loads imposed on the system as is Sh0wn

in

Fig. 16,

in

which results of the yawing motion of the tan-ker and force in the bbw hawser are

Shown. As may be seen, the force-fluctu-ation due to the ship and

buoy

Motion

with wave frequendy are small compared with the low frequency force and motion

oscillations.

CALCULATION OF WAVE DRIFTING FORCE

Under certain conditions with the

ship head-on,to Waves, it is possible to calculate the mean wave, drifting force in regular waves from. strip-theory -(8). In the general case with waves coming from arbitraryditectiOns,..cal-culations based on'three,dimensional potential theory,may be used (5).

UP to

the present the mean- wave drifting force in regular waves has usually been ob-tained from model tests

The equation for the mean wave drifting

fol-for these effects. This conclusion has been based on the undertainties which exist concerning the drag coefficients of the prototype. A brief review of the methods of analysis has shown how

re-sults may be used for design purposes

provided that the statistics of extremes

is applied. From the brief review of the

phenomena which determine the behaviour of moored vessels, it has been shown

that methods developed to calculate mo-tions and forces in s.p.m.-ship systems should include the influence of the low frequency drifting force in irregular waves. Methods to calculate these forces

are, however, not yet fully enough

de-veloped to yield the consistent results necessary for design purposes. At the present time, model tests are the most

suitable means to obtain quantitative results concerning the behaviour and

loads of Single point mooring terminals.

NOMENCLATURE

: linear scaling factor

: velocity

: acceleration of gravity : characteristic length : force

: ratio between specific gra-vity of salt water and

fresh water

: frequency

: mean period

: significant wave height

: spectral density of

irregu-lar waves

: small frequency interval : coefficient in theoretical

wave spectrum tormulation

: auto-correlation function : time shift : test duration : wave height : wave number : wave amplitude : radius of a cylindrical body : Reynolds number : drag coefficient

: specific gravity of salt

water

: specific gravity of air : characteristic area for

current force

: spectral density of the drifting force in irregular waves : velocity potential a 1 w,p T w1/3 S (w) Aw A,B Ca a Re Cd lowing form: 17(w) = kpg L R (w)a2

where R(w) is called the wave drifting force coefficient obtainable from calcu-lations or model tests. Based on certain assumptions the mean value and the spec-tral density of the oscillating part of the low frequency wave drifting force in irregular waves may be calculated using

equations of the following type: Mean value: co

f =

pg

f

S (w) R2(w) dw Spectral density: Sf(p) = 2p2g2

f

_{srmsc(w+p)R4(w+u/2)dw}

o

These expressions are derived using

ba-sic assumptions given in (9 ).

In the case of a rectangular barge moor-ed in head seas, the results obtainmoor-ed using the above equation4 have been

en-couraging (10).

Recent model tests have shown, however,

that with very large vessels moored in head seas, the mean wave drifting force in regular waves does not contain suffi-cient information to give an accurate

estimate of the low frequency behaviour.

This seems to be due, in part, to the fact that the mean drifing force in regular waves does not take into account the distribution of the force over the length of the vessel. At present re-search into these effects is being car-ried out at the Netherlands Ship Model

Basin.

In calculation methods used for

deter-mining the behaviour of the

s.p.m.-ship system, most of the above described components of the environmental forces

have been included. Generally, however,

the low frequency wave drifting force is conspicuous through absence. From the examples given above it may, however, be concluded that inclusion of this force

is a necessary requirement for insight into the behaviour of ships moored to

s.p.m.'s. CONCLUSIONS

In the aforegoing, the steps

in-volved in carrying out model tests with single point mooring terminals have been reviewed. Based on estimates of the errors due to scale effects, it has been shown that generally the results of model tests should be used without correction

co a

692 . .

,proto.type

-thOdel-.:

drag_

current

'-.force

Van OortsmerSsen, G.: "The'inter7,

action between :a vertical cylinder

..andregularwaves'"::PiOdeedinge'Sym-.

posiUM on Off

Hydrodynathics.-'

publication

No:I25.N.-S.M.:;Bage-hingen, 197-1;

FluiclDynamiO'brag".,

Published by the author,.. 1965

_ 3..Remevy,

,G;F:I.m,',andAran.-.0or,tmerssen,

-G'.:7The.reLein;-WaVe;.,Wind:'and

:FOkc07.5h,OfshOre.:StrUctuteearid.

their -role'lWthe'Designitihg

Sisteitts"4-0TC-paper-No.-:t741. OTC

,

4,':-Flokstral C.:-

"ShipmotiOh..inregu7,-iarWaVes" unpublished repOrtythe

..

THE ROLE OF MODEL TESTS IN,THE'DESIGNi OF"ISINGLE=POINT-MOORING -TERMINALS OTC

₂₂₁₂

. _,

vertiOal

-dietance,'below.

-In[P4tat*fiikcj'fdrd'

: IireSeure.

-

Nethe#linde_Ship Model

se:eih,

Van. Portmerssen, G:: Some aspects of

..;.very large Offshore' Structlires".

Ninth Symposium on Naval

Hydrodyna-..

:mibe.:Paris 1972.

.

6. nooft,"J=1).:."HydrOdynamic aspects

_ _

Of Semi-Submersible Platforms".

Ph .b Thesis. Technical U. of Delft.

G.P.M. and Hermans, A.J.:

"The- SlOw Drift oscillations of a

M6Ored Object in Random Waves". OTC

Paper No..1500. OTC 1971,

Gerr.itsma, J: and Bedkdiman, N.:

"Ahilysis%of the resistance increase

in-Waves:of a Fist Cargo Ship".

Re-port No

334, LabOtatorium voor

Scheepsbouwkunde, Technical T. of

Delft.,1971.

9. HsU,.F:H. and Blenkarn', K.A.1

"Analysis of-peak-Mbbring'Farce

Caused by Slow Vessel Drift

,Oscilla-ti6ns in Random Seas". -OTC Paper No.

1159', arc 1970.

10.'Pinkster,

Frequency

Pheno-mena associated With Vessel e moored

at-Sea"

SPE paper No..V 4837. SPE

Spring Meeting Amsterdith 1974:

11. Remeryi'G.F.M.: "Model testing for

the design of off shore structures".

Proceedings Symposium on offshore

hydrodynamics. Publication No.

325,

\ \ \

\

1

\

%

\\

`...,

/r

\/

,....,"

I ,

/

---./ -.... . .-,...

..-\\\\NN\\\\\\\\\\-\\\NN\N\NN\ \\

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

EXPOSED LOCATION S.B.M. SPAR

Fig. 1 - Examples of s.p.m. terminals.

":" , / .

/

. .., c\-\ C". \ N. \--. \\.N.

\\\ \ ... \ N.\\ \\\\NN\

RIGID ARM MOORING

ARTICULATED MOORING TOWER SPAR BUOY

-

Er"

/

_,

...\\\.\\\\"\\\\.\\\-\\\\\NANANA

\\ N \

\ \\ \ \ \ \ \AN \\ \\ \\N \\

CATENARY ANCHOR LEG MOORING

HORIZONTAL DISTRIBLIIT.IPN-.Rosit.ion buoy

- ,

r:-: 0 ,. 500'-: ' ..-15.00.

:DISTANCE_ IN .LON.Q)JUDINAL. DIR:E-CT,If_.:t1IFT'TH.,,--;BAI.N^ i,tyrii

-'C'PERPEN[5:1COL:?tol.- .1..6 cuiRk6.14.90.0i'ECA-0.0-.:..:=

,

... . --.. _{..--:.,,,,*4,-,,.:-,._...-..2,-,:i!,:...,... .}

..

.

Fig. .,,- Eiample o!' n current distribution ad,'.usted. _model*bAsin.

sdale Ve.Iues. -'

,...,.,,

- Compri'son of _{:.pectral density of model waves}

-0.75

600 40 20

2.5

ELONGATION in metres

Fig. 4 - Comparison of the load-elongation properties of a model bow hawser

and of an actual bow hawser.

Full scale values.

20 1

z.

MODEL PROTOTYPE

PROTOTYPE

2 x16" NYLON LINES LENGTH 40m

MODEL BENDING TEST

/

/

_/

/

-______ 1 2290 lb. 12500 lb.

---1 i I I I i 10 20 30 DISTANCE in feet

Fig. 5 - Comparison of hose bending stiffness in model and prototype

;f4,71 ,'"74 ..,#.:*7.1". 27 t'32.4.. 41917 1r"

0

:c

-

,

' - ...orTm="1"!?rC4114k*":"' --t. '

Fig. 7 - Examples of

'

.m. ' s tested at thèNS

,OV

=,

-Fig...

8--

_{Transducers for the}

measurement of hose and ...anchor chain toads..

Fig-

9 -

_{Pantograph systems for the measurement of linear.}

motions.

1.5

1.0

0.

CD

0.2

0.1 1 C-

)

0

U. DU

'Ka

Fig. 10 - Wave forces on cylindrical bodies (Ref. 1).

k.= SAND-GRAIN SIZE

d= DIAMETER

7

Viscous effects

become important

---T- a L

Line of maximum

wave steepness

_

_01

A% I ,2 I, A.

I Gravitation

I effects

! become

1

important

_

nl

/

= 9/10- .

INlemsonoursion...-2/10

21.1111111WriMOo

.4

kid =7/103

kid =

4/103

k/ d=

2/103

kid= 5/104

k/d= 0

k/d=

11111.11-111=

k/d

_Miketaiii

NI

NI 0

/ A

=. A A . ,-,

A 2

34 5 6 6

1,

10

C. RE

Fig.

8 -

Transducers for the measurement of hose and

anchor

chain loads. --k., -

,

'+.4.. .. ' .,..=.-. 3a; .. :-17., r4 . _-,7 I tr. ak -.;;; ' ... if '':,,z`'''''-'."-, -tJe..r.,"'"?,:yr 3 ''" ..-,,,, ,... ',tr,_ .14, "4.4.':- '''.."`4:42" 11;11+- ,":* _

L.

inkkaP

0.2 0.1 a 10 5 RE

74- 11 - Influence of surface roughness on the drag coefficient of cylinders (Ref. 2).

I .

Viscous effects

become important

( )

--a-- a L

Line of maximum

wave steepness

A

'Gravitation

I effects

I become

I important

I

_

i

kid =7/103

kid=4/103

k/d= 2/103

k/d=5/104

k/d= 0

- I

I =

.1 Ilik..-" ...

kid =2/102

=

9/103

`1111-1111111.111,

Ig.

kid

1111111M1

irt

in4

2 3

4 5 6 Bin5

2

3 4 5 6

81(16 2

3 4 5 6 8

i

0.25

0.50

0.75

'Ka

Fig. 10 - Wave forces on cylindrical bodies (Ref. 1).

k.= SAND-GRAIN SIZE

d = DIAMETER

1.5 1.0

0.5

CD

' . . :. ,.. .. , , . . .... ., .

),?.. r:Me.:nn rtisi Lion -tr.:1 cal, of n':.'?adecl,tarker in wind

woven

8n!

current. when il.nore:i. to O -s,r).01,,,

;;.}.

.':

. ' . .. CURRENT MOORING POINT -typical. 'Of

WAVE

DIRECTION

2

E0

-2

OPERATIONAC

_\

-...,

\

....

\

SURVIVAL' -*N.

1 --..---- )

Fig. 14 - Motions of the suspension point of the underbuoy hoses of a CALM buoy.

WAVE HEIGHT

SQUARE OF WAVE HEIGHT

time

Fig. 15 - Record of an irregular wave and the square of the wave height.

,-

--Yawing m6ti2ns and bow hawser loads typical

- .

RREN