Motions and mooring forces of twin hulled ship configurations

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REPORT No. 162 S

December 1971

(Sgo/2 19)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT

LEEGHWATERSTRAAT 5, DELFT

*

MOTIONS AND MOORING FORCES

OF TWIN-HULLED SHIP CONFIGURATIONS

(BEWEGINGEN EN ANKERKRACHTEN VAN DUBBELROMP SCHEEPSVORMEN)

by

M. F. VAN SLUIJS

(Netherlands Ship Model Basin)

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Bu de uitvoering van werkzaarnheden buitengaats, op het water-opperviak, op of in de zeebodem, is het nauwkeurig handhaven van een bepaalde positie van het materieei onder invloed van stroorn, wind en golven vaak een probleern, dat bijaondere eisen stelt aan de werktuigen.

De krachten welke op een vaartuig werken bepalen de keuze van het ankersysteern. Dit kan zowel een dynamic positioning systeem zijn als een conventionele meer-punts verankering. Daar de krachten veroorzaakt door golven, wind en stroorn meestal overheersend zijn, is de keuze van het type vaartuig bijzonder belangrijk bij werken buitengaats.

Dit rapport behandelt de bewegingen en de ankerkrachten van drie verschillende dubbelromp configuraties in vierpunts ver-ankering. Hiertoe zijn modeiproeven uitgevoerd in de zeegangs-tank van het Nederlands Scheepsbouwkundig Proefstation te Wageningen. De modellen zijn bloot gesteld aan onregelmatige golven, stroom en wind. uit drie verschillende richtingen.

Twee ankersysternen zijn beproefd.

De resultaten maken een vergelijking mogelijk tussen de drie configuraties van dit type schip. voor wat betreft het gedrag in zeegang in verankerde toestand. De windweerstand toegevoegd aan de krachten in de ankerdraden ten gevolge van golven levert een totaalkracht welke goed overeenkomt met gerneten anker-krachten in golven en wind te zarnen. Het lineair superpositie beginsel is dus toelaatbaar. Dit is niet het geval bu golven en stroom, waar de krachten gemeten onder invloed van stroom en golven te zarnen aanzienlijk hoger zijn dan de sommatie van de afzonderlijke componenten.

Het zou interessant zijn orn de voorliggende resultaten te ver-gelijken met de karakteristieken van een conventioneel vaartuig van dezelfde grootte en onder dezelfde ornstandigheden. Tot op heden is echter op dit terrein nog zeer weinig onderzocht.

Dank zu verschuldigd aan de Nederlandse Maatschappij voor Werken Buitengaats, het Bureau voor de Scheepsbouw Ir. P. H. de G root en alle betrokkenen van het NSP voor hun welwillende samenwerking.

HET NEIDERLANDS SCHEEPSSTUDIECENTRUM TNO

The maintaining of a certain position at sea for all kind of floating equipment, exposed to current, waves and wind, carrying out all sorts of jobs on the water surface, the seabed and below, asks for very specialized equipment. The forces acting on the vessel govern the choice of the mooring equipment. This may be a dynamic positioning system as well as a conventional multi-point mooring, or a combination of the two. The forces induced by waves, wind and current in most cases prevailing, very much depends on the choice of the type of vessel used for the offshore operation. The present investigation deals with the motions of, and the mooring forces acting on, three different twin-hull ship configurations, each moored to four wires. To this end, model tests have been performed in the sea-keeping basin of the Nether-lands Ship Model Basin at Wageningen.

The models were exposed to irregular waves, current and wind, from three directions. Two different anchoring systems were investigated.

With the results obtained from the tests, it is possible to com-pare the different configurations of this type of vessel, regarding their sea-keeping qualities when moored. The component of the wind resistance added to the forces in the anchor wires induced by waves, is in good agreement with the anchor wire forces measured in wind and waves simultaneously. This means that linear superposition holds. The forces measured in the anchor wires in current and waves, however, were considerably higher than the sum of the components induced by current and waves respectively.

lt would be very interesting to compare the present results with the characteristics of a conventional vessel of the same size under the same conditions. Until now, however, very little has been investigated in this field, especially for smaller vessels.

Thanks are due to the Netherlands Offshore Company,

Bureau voor de Scheepsbouw Ir. P. H. de Groot and the author and staff concerned of the NSMB, for their kind cooperation.

THE NETHERLANDS SHIP RESEARCH CENTRE TNO

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page

List of symbols

6

Summary

7

Introduction

7

2

Motion and mooring force measurement

7

2.1

Hull configuration specifications

7

2.2

Anchoring systems

7

2.3

Model test procedure

9

3

Model test results

10

3.1

GeneraI

10

3.2

Motions

11

3.3

Anchor line forces

il

4 Conclusions 12

References 12

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LIST OF SYMBOLS

AG

Longitudinal centre of gravity from aft perpendicular

BM

Maximum breadth under water

BWL

Breadth on waterline

F

Anchor line force

GM

Metacentric height

h1

Depth to lower deck at station 10

h2

Depth to lower deck at station 20

KM

Height of metacentre above base

KG

Centre of gravity above base

kyy

Longitudinal radius of gyration

k

Wave number

L

Length between perpendiculars

M

Moment

N

Number of oscillations

Sa

Relative motion amplitude

S

Wave spectral density

T

Draught

T

Mean wave period

T:

Natural period for heave

T0

Natural period for pitch

T

Natural period for roll

T

Natural period for heave

T

Natural period for sway

T1,

Natural period for yaw

x0

Surge amplitude

Y0

Sway amplitude

z0

Heave amplitude

V

Displacement volume

Wave amplitude

.

Significant wave height

Pitch amplitude

&

Roll amplitude

o-

Root-mean square value

w

Wave circular frequency

(6)

i

Introduction

In the framework of studying the dynamic properties

of the twin-hulled m.s. "Duplus", of which the

correla-tion between full scale and model behaviour has been

reported in reference [I], further model investigations

were performed into the motion and mooring force

characteristics of various alternative configurations of

this ship. The objectives of the present experiments

comprised the examination of the effect of three hull

forms and two anchoring systems upon motions and

forces when moored to four lines at open sea.

For the purpose of the investigation the following

hull shapes and anchoring systems were considered:

- Hull configuration I

- without casings [1]

- Hull configuration II - with outer-casings

- Hull configuration III - with outer-and

inner-casings

- Anchoring system I

- low fastening points

- Anchoring system 2

- high fastening points.

The majority of the experiments were done in irregular

seas corresponding to wind force Beaufort 5 at the

North Sea, both with and without wind and current.

Three wave directions were simulated; wave and

wind directions coincided whereas current directions

deviated in particular cases from those of wind and sea.

In addition to this also the motions and mooring

forces caused by wind only, matching force 5 Beaufort,

and those resulting from force 7 waves were determined

for the hull configuration with outer-casings.

Throughout the course of the experiments the six

modes of motion, the relative motion amidships

be-tween the hulls and the four mooring line forces were

recorded.

All data were evaluated by spectral analysis. Mooring

forces were analysed in the usual way for obtaining

data about the anchor system design as regards

station-keeping. They were, moreover, expressed in their

resul-MOTIONS AND MOORING FORCES

OF TWIN-HULLED SHIP CONFIGURATIONS

by

M. F. VAN SLUIJS

Summary

Results of motion and mooring force measurements on models of three twin-hulled ship configurations are described. Experiments were conducted in irregular seas from various directions, both with and without wind and current. Two anchoring systems were investigated.

Comparison of the response characteristics of the ship configurations enables the assessment of the most favourable hull shape with respect to motions and mooring forces.

tant total longitudinal and transverse force and

mo-ment, so that information for the evaluation of a

dy-namic positioning equipment is available. In this

pro-cedure solely the force fluctuations having periods

larger than 20 seconds were taken into account, thus

avoiding forces with periods equal to, or smaller than,

the periods of the waves encountered by the models.

The experiments were conducted in the Seakeeping

Laboratory of N.S.M.B., which facility is described

by Van Lammeren and Vossers [2].

This present report intends to summarize the most

important findings of the experimental model

pro-gramme. Full information can be obtained from

reference [3].

2

Motion and mooring force measurement

2.1

Hull configuration specifications

Small-scale body plans of the three hull configurations

are given in the figures I through 3.

Principal dimensions and stability data are

summa-rized in Tables I and 11, which values apply to the full

scale. For the wave tests principally the same model,

scaled 1:25, was utilized as that described in [I]. In

addition a superstructure was reproduced, since the

wave experiments were to be done inclusive of wind

simulation. All model configurations were ballasted

such that for the free-floating condition a level trim

draught of 5.2 metres was obtained and their stability

matched the data listed in Tables I and II.

2.2

Anchoring systems

The models were positioned in the basin by means of

four mooring lines fastened to poles, vertically

extend-ing under the towextend-ing carriage, enablextend-ing the simulation

of a waterdepth of 40 metres.

The angle between the lines and the horizontal plane

at the attachment points to the model amounted to

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8 Fig. 1. Body plan of Configuration I. Fig. 2. Body plan of Configuration II. Fig. 3. Body plan of Configuration III.

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15 degrees; the horizontally projected angle between

line and the vertical plane through the centreline was

60 degrees. For anchoring system 1, lines were attached

at 3.3 and 3.8 metres above base at the force- and aft

ship respectively. They were situated 8.7 metres from

the ceritreline at 3.5 metres from F.P. and 3.0 metres

from A.P. For anchoring system 2, lines were fastened

identically to those of system 1, except for the height,

which in this case was 11 metres above base, both fore

and aft. Throughout the experiments the lines were

pretensioned with 3 tons, with the exception that for

the Beaufort 7 test a I

ton pre-tension was applied.

The mooring lines were scaled to model size as

re-gards linear dimensions, submerged weight and

elastic-ity. Reproduction of elasticity was realized by inserting

into the steel model wires a system of 4 linear springs,

each of which had its specific stiffness and was bounded

into its permissible region of elongation. For the

pur-pose of the experiments only the portion of the

load-deflection curve within the 30-43 metre range was

reproduced.

An example of the actual and simulated mooring

line characteristics is shown in figure 4 of the appendix

which relates to the port bow wire, designated line 1.

The full scale data of the anchor lines are stated in

Table IlL

Table Ill. Full scale- hor line data

2.3 Model test procedure

WAVES: The models, moored to four lines, were

subjected to two irregular wave systems in succession

approaching from ahead, from the bow quarter or

from abeam. Both wave systems are considered to

represent North Sea conditions, having wave spectra

similar in shape to the Pierson-Moskowitz formulation

for fully developed seas, see also [I]. They correspond

to wind force Beaufort 5 and 7 respectively and are

shown in the figures 6 through 10.

The values for significant wave height and mean

period are equal to the average values of weathe:ship

observations,which have been compiled by Petri [41.

Irregular waves in the basin were produced by varying

the frequency of the paddles of the wave generator at

constant amplitude. Dispersion of the simple waves

results into irregularity at some distance from the

wave-maker. Generally the model waves are long-crested,

which means that every individual wave has the same

direction of propagation. Specific conditions, indicated

by an asterisk in Table 1V, V and VI of the appendix

were short-crested. This is to be attributed to the

manner of making oblique, irregular seas as is

de-scribed in [2]. In those cases the waves containing

maximum energy were approaching from the correct

direction.

Table E. Configuration specifications

Configuration

Designation Unit I Il Ill

Length between perpendiculars m 40.00 40.00 40.00

Maximum breadth under water m 17.08 17.08 17.08

Breadth on the waterline m 14.77 17.08 17.08

Depth to lower deck at centreline

at station 10 m 8.20 8.20 8.20

Depth to lower deck at centreline

at station 20 m 10.20 10.20 10.20

Draught level trim ru 5.20 5.20 5.20

Displacement volume m3 1147 1288 1453

Centre of gravity above base m 6.24 6.68 6.95

Centre of gravity forward of aft

perpendicular m 20.88 20.68 20.53

Metacentre above base m 6.71 9.41 9.92

Metacentric height m 0.47 2.73 2.97

Longitudinal gyradius %L 25.2 25.2 25.2

Table II. Natural periods

Configuration

Mooring system pre-tenSion 3 tons

Natural period in sec.

Motion Magnitude I Free Heave 10.8 Pitch 14.5 Roll 24.8 4 anchors Heave 10.8 Pitch 14.3 Roll 23.0 Surge 62 Sway 70 Yaw 51 EI Free I-leave 9.7 Pitch ILS Roll 9.5 H 4 anchors Heave 9.7 Pitch 11.5 Roll 9.5 Surge 60 Sway 67 Yaw 52

III Free Heave 8.0

Pitch 9.0 Roll 9.4 HI 4 anchors Heave 8.0 Pitch 9.0 RoIl 9.4 Surge 60 Sway 70 Yaw 50 Length of wire 500 n-1

Wire diameter 30 orn

Sectional area 3.75 cm

Modulus of elasticity 0.8x 106 kgf/cm2

(9)

'o

CURRENT: The effect of current upon the behaviour

of the various vessel configurations was simulated by

moving the carriage over the basin. The anchor wires

being attached to the carriage as described in chapter

2.2. The model and the anchor system thus were towed

through the basin.

Current speed was constant

throughout the tests, and corresponded to 2 knots for

the full size vessel.

WIND: For particular cases the models were exposed

to wind corresponding to force 5 Beaufort.

Conse-quently the wind velocity was 18 knots for the full size.

Wind was generated by a set of blowers mounted on

the towing carriage. Wind speed was adjusted and

calibrated by an anemometer, at the location of the

model, 0.40 metres above water level.

Wave, wind and current directions p are defined

counterclockwise as the angle between the

ship's

centreline and the direction of wave propagation or

wind and current direction:

p = 180 degrees for the head on direction

= 135 degrees for the starboard bow direction.

p = 90 degrees for the starboard beam direction.

This is shown in figure 5 together with the anchor line

designation.

During all experiments the following quantities were

simultaneously recorded on FM tape and on

light-sensitive strip chart:

HEAVE amidships, ROLL and PITCH angles,

RELATIVE MOTION amidships, see [1].

SURGE and SWAY, measured by a pantograph

system provided with potentiometer pick-ups.

YAW, recorded as the rotation of the heave rod by

a potentiometer.

- ANCHOR LINE FORCES, measured by strain

gauge equipped ring-shaped force transducers

locat-ed at the fastening points to the model.

- WAVES, sensed by a resistance wire wave probe.

- WIND, measured by an anemometer.

CURRENT SPEED, equal to towing carriage speed,

recorded by a slotted disk with photo-cell pick-up.

The duration of each irregular wave test corresponded

to half an hour for the full-size vessel in order to attain

a reliable statistical treatment of the observed

phenom-ena.

3

Model test results

3.1 General

All data of motions and mooring forces were evaluated

by reading the records at constant time intervals of

0.124 seconds for the model. This corresponds to 0.622

seconds for the prototype. When for instance the motion

Z is now considered:

N

where N is the total number of readings per test,

which is approximately 3000.

The root-mean square value a. follows from:

o.z - _J

_N

Significant values, denominated by index 1/3, were

obtained by averaging the one-third highest peak to

trough values, when double amplitudes are under

consideration.

The highest value occurring in the record is

desig-nated by "maximum".

Freq uency-response characteristics

were derived

from the motion response and wave spectra, e.g.:

(w)

/s(w)

\St(W)

Where S..(w) denotes the spectral ordinate of the heave

motion and S(w) the spectral ordinate of the waves

at identical frequencies.

Distributions of motions and forces are given as

histograms,

in which also a cumulative curve is

provided. These histograms indicate the percentage of

time that:

/

n

[+1]

2

in which n is an integer.

10 20 TIME In sec

(10)

Cumulative curves, shown by the dashed lines, were

obtained by integrating the area of the histograms in

successive steps. In the majority of all cases the hori-zontal translatory motions and henceforth the anchor line forces comprised a low-frequency oscillation upon which high-frequency amplitudes were superimposed. The period of the low-frequency motion corresponds practically to the long natural period of the horizontal

modes of motion of the platform; the periods of the

high-frequency motions correspond to those of the

waves.

Reference [5]

describes both the origin of this

phenomenon and the parameters by which it is

deter-mined.

A short mathematical

description

of analysing

irregular phenomena is given in the appendix.

3.2

Motions

Results of the motion measurements in long-crested

sea conditions are shown in the tables and figures

accompanying this report. Short-crested information

is only tabulated since a derivation of response curves is deemed arbitrary.

The motion response curves are given in the figures

11 through 41.

Histograms and cumulative curves are given in

figures 42 through 49.

Numerical results are represented in table IV.

In as far as possible, the present results are compared

with the data of regular wave tests from [1] for a wave height of 2.0 metres.

One may conclude from the results that fitting outer-casings does not result in an increase of ship motions as compared to the original configuration.

When also inner-casings are installed, heave, pitch

and roll, however, are enlarged by about twenty to

forty per cent.

In considering roll of the various configurations one must realize that due to the relatively large difference

in waterplane area and stability two modes of rolling

were observed during the experiments. Rolling of

con-figuration 1, being the original shape, comprised a

long-periodic motion upon which amplitudes were

superimposed having the same periods as those of the waves. Long-periodic phenomena diminished when the natural period became smaller. Therefore the response

data, given in figure 12, are not adequate for

dis-cerning the vessel with minimum roll. In order to

detect whether long-periodic phenomena took place,

the ratios between significant and root-mean square

values, derivable from Table 1V et al. are to be judged. When long-periodic rolling is present this ratio differs

from the factor of about 4.

Rolling is, as a matter of fact, sensitive to the

loca-tion where the anchoring system is attached to the ship.

The maximum roll angle becomes about 20 per cent

smaller when the anchor lines are fastened in the lower

position. Measurement of the relative motion was

performed amidships in between the two hulls, which means that mutual interferences between the hulls and hydrofoils were directly taken into account as well as the deformation of the oncoming waves caused by the oscillating hull.

Relative motions for the various configurations do

not differ substantially from each other, though this

could be expected when especially the hull shape at

the inner side is considered.

Heave and pitch for the configuration with

outer-casings can be regarded to vary linearly proportional to wave height, since the response curves derived from the Beaufort 5 and 7 tests practically coincide, see the

figures 34 through 37. This also holds true for

con-figuration 1, see reference [I].

Figures 19 through 29 and 38 through 41 show that

generally the addition of wind and/or current to the

waves does not have an appreciable effect upon the oscillatory motions.

The distributions of heave, pitch, roll and relative

motion, given as examples in figures 42 through 45,

show that the normal Gaussian character is generally

confirmed. These figures apply

to

sea condition

Beaufort 5 without current and wind.

Largest surge

oscillations appear for

the bow

quartering heading, in

particular when the waves

combined with wind and current approach

simulta-neously from the 135 degree direction. When the moor-ing lines are pre-tensioned with 3 tons, maximum surge amplitudes amount to approximately twice the signifi-cant wave amplitude. This value is doubled when the

pre-tension is reduced to i ton for head seas. Maximum

sway excursions are about three times the wave

amplitude for the quartering and the beam direction.

Sway amplitudes are 25 per cent larger when a 2 knot broadside current is added, which also holds true as to

the yaw angles.

The distributions of the motions in the horizontal

plane deviate generally from the normal fit, as follows from figures 46 through 49.

3.3

Anchor line forces

Since the horizontal motions of the different platform

configurations comprised long- and short-periodic

components, these components must hence also be present in the line tensions.

The long-periodic part of the force is deemed to be

of importance for establishing a dynamic positioning

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12

when also the horizontal ship motions, having

frequen-cies corresponding to those of the waves, must be

counteracted.

Table V gives the information of forces occurring in

each separate line.

Table VI summarizes the resultant total longitudinal

and transverse forces as well as the moments of the

long-periodic part. The latter were evaluated by

com-bining the separate line tensions after which periods

shorter than 20 seconds were filtered out.

Distributions of the forces obtained are given in the

figures 50 through 62.

From Table V it appears that fitting of casings to

the original shape has hardly any effect upon the

maxi-mum anchor line forces that are to be expected. This

is also valid for the effect of moving the

attachment-point of mooring lines vertically. Largest mooring

forces occur in waves approaching from abeam with

or without current. When the mooring forces are

con-sidered in connection with the vessel's motions, mutual

trends appear to be consistent.

From Table VI, giving the total forces and moments

of the long-periodic portion, it follows that addition

of the mean forces due to wave action to those caused

by wind only, results in approximately the same value

as that obtained from the experiments in waves and

wind directly. Hence wind forces can be superimposed

upon wave forces in order to obtain the mean value

of their combined effects. Figures 50 through 62 show

clearly that force and moment distributions do not

follow the norma] character.

4 Conclusions

Results of a motion and mooring force study of var

ious "Duplus" configurations are presented in this

report. It is shown that the behaviour in a seaway of

the original design is not substantially influenced by

the fitting of either outer-casings to the hulls or of

both outer- and inner-casings. This is also valid as

regards the mooring forces. The casings will make the

vessel roll with periods that correspond to those of the

waves.

Long-periodic rolling

will then mainly be

avoided.

Mean horizontal motions and anchoring forces

originating from the action of wind may be

super-imposed upon those due to waves to obtain their

combined effect.

Vertical motion fluctuations are not affected by

wind. Low or high fastening points of the anchor lines

do not significantly influence the mooring forces and

motions, except naturally rolling.

Generally, motions are linearly proportional

to

wave height. The relative motion at the centreline

amidships is not, which may be explained by the

interaction and wave deformation effects of the hulls

and hydrofoils.

References

SLUIJS, M. F. VAN, Mode! and full scale motions of a twin-hull vessel. Netherlands Ship Research Centre TNO, Deift, Report No. 131S, August 1969.

LAMMEREN, W. P. A. VAN and G. VOSSERS, The Seakeeping Laboratory of the Netherlands Ship Model Basin. I.S.P.,

Vol. 4, 1957.

Siuiis, M. F. VAN, Motions and mooring forces of twin-hulled ship configurations. NSMB Report No. 70-052-ZT, June 1970.

PETRI, O., Statistik der Meereswellen in der Nordsee. Einzel-veröffentlichung Nr. 17, Deutscher Wetterdienst, Seewetter-amt, Hamburg.

VERHAGEN, J. J-I. G. and M. F. VAN SLUIJS, The low-frequency

drifting force on a floating body in waves. I. S. P., Vol. 17, No. 188, April 1970.

LONGUET-HIGGINS, M. S.. On the statistical distribution of the heights of sea waves, Journal of Marine Research 1952, Number 3.

PIERSON, W. J. and L. MosKowiTz, A proposed spectral form

for fully developed wind seas based on similarity theory of S. A. Kitagorodskii, Journal of Geophysical Research. Vol.

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Appendix

Thus a can be derived from experiments with:

General

A quantity x varying irregularly in the time t can be

described as:

The probability distribution in time that the value

of x is between x1 and x2

The probability distribution of extreme values of

x lying between x1 and x2

The spectral density of x.

Probability distribution of x

The probability x1 < x < X2 is given by the

proba-bility density function p(x):

P[xj<x<x2]

=

$p(x)dx

(1)

XI

Often a p(x) is found that almost coincides with the

normal probability density function:

p(x) .

e2122

(2)

where

= mean value of x

= root-mean square value of x

= standard deviation of x

The probability density is independent of the time in

the case of a stationary process. The standard deviation

can be estimated by measurements during a limited

time interval.

The duration of the measurement is assumed to be

sufficiently long so that the difference between the

standard deviation of the sample and the standard

deviation of the actual density function can be neglected.

P()

during the time interval T = t,t1.

The probability density functions actually found and

the normal distributions generally conform very well

at values of x in the vicinity of

.

Due to a limited duration of the experiment the

agreement between extreme values of x and the normal

distribution is hard to prove by measurement.

The probability

rï

(

n+1

+ ., 5) <X<

+

2

can be calculated with:

n+1

'\1

P

+

<

(

+

2

)] =

.+(fl+ 1)a/2

=

$

p(x)dx

(4) x + (n/2)

The theoretical distribution can then be calculated

with (2), (3) and (4).

The probability x, < (x ) < cc can be expressed

as:

<(x-5i) < cc]

₌

_$

p(x)dx

(5)

Equations (2), (3) and (5) being used the following

table is compiled:

Theoretical values of extremes

The above table can only be used when x is distributed

normally, whereas the reliability of extreme values

decreases when (x,,,)I is increased above 2a.

Probability distribution of extreme values of x

The character of the variable x can also be described

by the distribution of the extreme values (= peak

values) of x analogous to the description Sub. 1.

3o

99.87 0.13

.-2o

97.72 2.28

i. o

84.10 15.90

1+ a

15.90 84.10 2.28 97.72 1+3o 0.13 99.87

MATHEMATICAL DESCRIPTION OF

-

[x(t) ]2di

(3)

IRREGULAR PHENOMENA

probability percentage probability percentage

Xrn P[Xrn <x < 00] P[oo < x < x,1J

(13)

2[x:î]

= mean of the one-third highest peak values

of (xi)

= significant double amplitude of (x.)

The most probable maximum value 2(X)max (double

amplitude) of the variable (xi) depends on the

num-ber of oscillations N0 as is calculated by

Longuet-Higgins [6]:

=

with

O =

lnNo_ln[l _(l_e_0)]

For large values of N0 it can be shown that

2(X.)max

o/2 In N0

Spectral density of x

The quantity x, varying irregularly in time t (O < t < T

with T * cx), is assumed to consist of an infinite

num-ber of harmonic components with arbitrary, random

phase angles e,,.

n = w

x(t)

=

X,,,,CoS(flW1t+s)

with

X0aCOSCO

= mean value of x

X,,,, = amplitude of the nth component

with circular frequency w,,

(0,,

= flw1

wndw

dw

(9)

m0 = $ S,,dw = area

under spectrum

(10)

w

rn1 = $ Swdw =

first moment of spectrum

0 ₍₁₁₎

T = 2m

m1

S(w) = Aw5-e°'4

Where:

S(w) = spectral density of wave heights

(6) A

= 172.8(w113)2(T)4

B

= 691 (Ty4

w

= circular frequency

of x

(7) w =

T =T

= 4,/nI0

T

=

2mm0

m,

(14)

Irregularity of waves

Since it is known that the distributions of the wave

heights at sea are approximately normal, all

before-mentioned formulae are valid to describe irregular sea

conditions. To judge the behaviour of vessels at sea,

irregular seas are assumed to have power spectra that

can be described by:

Formula (15) represents hypothetical spectra similar

in shape to the Pierson-Moskowitz [7] for fully

develop-ed seas. In relating the spectra (15) to observations,

the average observed wave height

is assumed to

coincide with the significant wave height

being

the calculated mean of the one-third highest peak to

trough values; the average observed period T is

assumed to coincide with the average calculated

period T.

Thus:

(18) (19) (20) 14

In this case the following values are determined:

For a normal variable x is:

wheredw =

(DnWn_i

The following quantities can now be calculated:

Assuming that the wave height is a random variable

with a narrow band normal distribution, one arrives at:

ox =

(12)

When (xi) or (xx00 cos e,,) are considered to be

random variable having a narrow spectrum and zero

mean, it follows that:

4r =

=

2[xZ]113

(13)

= T

2ir/n (8)

T = measuring time.

The spectral density S can be written as:

(14)

Cumulative normal distribution

The cumulative-distribution function gives the relative

frequency with which the values of x are below any

specified value x1. This relative frequency is the area

under the distribution curve from minus infinity to

the specified value x1 (see figure A).

20

lo

o

100

F,g AI

The height H indicated in Figure A TI is numerically

equal to the area shaded under the normal curve in

figure A I.

The mathematical notation for the area between

x= candx=x1isgivenby:

Area =

-It gives the frequency with which values less than or

equal to any given value of x will occur.

(15)

Table IV.

Test review anil motion results

V . o .2 V

_

u -d * Short crested positive: heave

- ship up

pitch = bow down roll = starboard down

relative motion = ship down surge

= ship forward sway = ship to port yaw = bow to port rl) o 17

-

₉₀ 225

-

- -

135

-

90 135

-

-. -o V

a

a mean 2zk 2zmax mean 2 20rnax T mean 2 2Pmax 1 mean 2s 2smax 7 mean

24

Xmax

(+)

Xmax

(-)

7 mean 2 Ymax

(+)

Ymax

(-)

(J mean 2 Pmax

₍₊₎

V'max

(-)

0.42 0 1.66 2.7 0.17 0 0.62 1.2 2.31

-0.62

5.24 9.1 0.31

-0.02

1.20 2.4 0.09 0.09 0.05 0.5 0.1 0.78 0.64 0.97 3.4 1.0 0.44

-0.14

0.23 1.6 1.7 9.6

-0.46 0.07 1.78 3.5 0.22 0 0.82 1.4 1.48 -0.31 5.75 8.5 0.23

-0.05

0.90 1.9 0.05 0.15 0.05 0.4 0 0.97 0.80 1.34 4.0 1.5 0.36

-0.05

0.26 0.9 1.4

-O

-0.42

-O

-0.45 -0.01 1.75 2.9 0.20 0.06 0.73 1.2 1.46

-0.32

5.66 8.3 024

-0.01

0.95 1.8 0.06 0.30 0.03 0.4 0 0.91 1.25 1.25 4.8 0.6 0.35

-0.08

0.29 0.9 1.4 2 0.46

-0.10

1.81 2.7 0.32 0.05 1.11 1.8 1.12 1.02 4.05 6.6 0.34 0.10 1.26 2.7 0.23 0.73 0.19 1.5 +0.1 1.03 338 0.94 7.3 +1.5 0.67 0.14 0.31 1.6 2.4 2 0.44

-0.07

1.66 2.3 075 0.58 2,84 4.5 0.97

-0.59

3.47 6.1 0.33 0.12 1.27 2.2 0.48

-0.26

0.50 1.0 1.6 0.53

-3.36

0.79

-2.2

5.0 1.19

-1.90

1.11 2.6 4.9

-0.46 002 1.78 3.0 0.03 0 0.08 0.2 1.77 0.50 6.75 10.2 0.23

-0.06

0.93 1.7 0.11 0.31 0.05 0.7 0 0.85 0.52 142 3.2 1.4 0.29

-0.26

0.22 LO 1.8 0.30 0 1.15 2.3 0.79 0.06 3.12 5.5 1.00 0.01 3.92 5.9 0.26

-0.05

1.05 2.2 0.28

-0.06

0.4! 0.9 0.9 0.39 0.16 0.92 1.6 0.9 0.63 0.27 1.45 2.9 1.5

-O

--0.21

-0.25

-O

-0.30 0 1.14 2.2 0.79 0 3.09 5.6 1.03

-0.07

4.04 6.3 0.26 -0.01 1.03 2.2 0.27

-0.25

0.40 0.6 1.1 0.40 0.47 0.91 1.9 0.4 0.65 0.61 1.27 3.7 1.4 2 0.33

-0.07

1.24 3.0 0.81 0.45 3.12 5.6 0.69 0.54 2.50 4.8 0.31 0.08 1.25 2.5 0.52 0.68 0.48 2.0 1.3 0.39 3.18 0.64 5.2 +2.1 1.18 4.60 1.66 7.4 0.2

-0.22

-0.02

0.84 1.9 0.65 0.03 2.44 4.1 0.17 0 0.60 1.1 0.33 0 1.35 2.6 024

-0.04

0.61 0.8 0.9 0.03

-0.07

0.03 0.1 0.1 0.09

-0.03

0.15 0.2 0.4 2 0.23

-0.07

0.85 1.5 0.71 0.05 2.63 4.9 0.79 1.21 3.03 4.6 0.37 0.15 1.46 2.8 0.37 0.47 0.75 1.8 0.7 0.24 2.1 1 0.31 2.8 ±1.3 0.62 0.05 0.42 2.0 1.7 2 0.22

-0.06

0.84 1.5 0.70

-0.10

2.65 4.9 0.87 0.51 3.31 5.0 0.35 0.07 1.38 2.4 0.42 0.27 0.65 1.3 1.5 0.26 2.52 0.52 3.5 +1.7 0.72 4.10 0.69 5.9 +1.4

-0.65 0.03 2.47 4.6 1.44

-0.03

5.57 13.4 0.28

-0.10

1.02 1.8 0.51

-0.03

1.97 3.6 1.38 050 1.84 5.2 3.5 0.22 0.11 0.19 0.7 0.4 0.42 0.07 0.28 1.7 1.3

-0.41

-0.03

1.60 3.0 0.27 0.04 0.98 1.4 2.04

-0.22

8.18 12.9 0.31

-0.02

1.21 1.9 0.23 016 0.11 1.0 0.5 0.94 0.68 1.62 3.9 1.6 0.50 -0.11 0.35 1.9 2.1

-0.32 0.01 1.26 2.3 0.77

-0.05

2.93 5.7 0.15 0.05 0.50 1.0 0.38 -0.01 1.53 2.4 0.42 0.10 0.75 1.5 1.2 0.05 -0.03 0.09 0.1 0.2 0.14 0.08 0.15 0.4 0.6 1 1 I 3 90 5

-2 II I 3 90 5

-3 11 1 3

-90 18 4 II i 3 90 5 90 18 5 11 1 3 90 5 90 18 6 II i 3 270 5 270 18 7 II 2 3 90 5

-8 II i 3 135 5

-9 11 1 3

-135 18 Io II i 3 135 5 135 18 11 II i 3 135 5 135 18 12 II I 3 180 5

-13 II I 3 180 5 180 18 14* II I 3 180 5 180 18 IS 11 I I 180 7

-16 III i 3 90 5

-17 III I 3 180 5

-waves wind current heave pitch roll relative motion surge sway yaw z in metres o in degrees di in degrees s in metres X ifl metres y in metres cv in degrees

(16)

(17)

Table V.

Test review and anchor line force results

d force I in tons force 2 in tons c, mean 2F Fnìax o mean 2F 19 Fmax force 3 in tons force 4 in tons cc mean 2i Fmax (7 mean 2 Fmax * Short crested I I 3 90 5

-0.71 2.80 1.3! 5.1 1.51 3.83 2.82 13.6

I.7

4.12 2.86 11.6 0.7! 2.46 1.53 5.1 11 1 3 90 5 0.71 2.65 1.27 5.1 1.54 3.71 2.68 13.7 1.45 4.00 2.72 13.0 0.71 2.50 1.38 5.0 II I 3

-90 18

-2.55

.

-3.65

-3.67

-2.60

-II i 3 90 5 90 18

-0.56 2.20 1.02 3.9 1.89 4.48 3.27 17.3 1.80 4.63 3.28 16.1 0.57 2.13 1.19 3.7 II i 3 90 5 90 18 90 2 0.43 1.27 0.73 2.2 4.22 10.03 7.67 29.6 4.16 10.17 7.24 29.5 0.39 1.32 0.65 2.7 II 1 3 270 5 270 18 225 2 3.23 13.00 8.81 24.1 0.24 1.37 0.57 2.0 0.36 1.78 0.66 2.8 2.61 8.27 7.45 18.1 II 2 3 90 5

-1.01 2.72 2.20 6.5 2.01 3.74 5.45 13.7 1.83 4.13 5.13 13.4 1.11 2.65 3.09 7.0 II i 3 135 5

-0.44 2.92 1.05 4.1 0.86 3.37 2.29 7.9 0.43 3.14 1.21 4.8 0.64 2.75 1.91 5.0 II I 3

-135 18

-2.80

-3.72

-3.00

-2.61

-II I 3 135 5 135 18

-0.41 2.77 0.91 3.7 1.04 4.10 2.74 10.0 0.48 3.20 1.18 5.3 0.57 2.43 1.59 4.5 II I 3 135 5 135 18 135 2 0.19 1.54 0.34 2.3 2.72 12.30 8.20 24.2 1.50 7.20 3.60 15.0 0.47 1.74 1.16 3.1 II I 3 180 5

-0.53 3. 17 1.52 4.6 0.39 2.97 1 .12 4. I 0.35 3. I 1 0.90 3.9 0.39 2.79 1 .05 4.0 II I 3 180 5 180 18 90 2 0.28 1.60 0.74 2.3 1.37 6.75 4.05 12.3 0.91 5.91 2.08 9.6 0.28 1.61 0.64 2.6 II I 3 180 5 180 18 135 2 0.26 1,62 0.68 2.5 1.62 9.85 4.96 14.5 0.97 5.57 2.08 1 1.0 0,35 1.83 0.87 2.8 II I I 180 7

-0.32 0.97 0.72 2.0 0.26 0.84 0.64 1.6 0.32 1.26 0.62 2.4 0.38 0.91 0.89 2.3 Ill I 3 90 5

-0.91 2.83 1.55 7.3 1.71 3.95 3.25 14.5 1.68 3.96 3.34 14.3 0.96 2.54 2.09 7.0 III i 3 180 5

-0.51 2.89 1.50 4.4 0.43 2.94 1.28 4.3 0.40 3.1 I 0.95 4.4 0.47 3.00 1.16 4.0 waves wind current

forces in anchor lines

I ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉

(18)

Table VI.

Test review incl resultant forces having periods larger than 20 seconds

d I

F in tons

21 F5 in tons Mp in tons metre 2 3 ₄ 5 6 7 8 9 _lo _li 12 13 14* 15 16 17 * Short crested

a

mean

2i

2Fmax Fmax ( + ) Fmax

(-)

mean 2F 2Fn)a. Fmax ( ± ) Fmax

(-)

N a mean 2È 2Fniax Fmax ( +) Fnax

(-)

0.16 -0.01 0.58 0.8 1.0 0.5 41 302 2.02 9.68 17.2 3.9 16.1 31 3.4 7.2 12.4 20 24 6 0.11

-0.06

0.40 0.8 0.6 0.6 45 3.25 2.10 12.89 18.5 4.2 17.2 26 3.5 6.1 12.5 23 19 7

-0.03

--1.85

--. 1.4

-0.14

-0.04

0.50 0.8 0.7 0.5 49 3.36 4.02 11.63 17.2 0.5 18.6 33 3.9 6.0 13.4 18 20 5 0.34

-0.17

1.17 2.0 0.6 1.4 45 7.09 -15.01 22.63 31,9

- 5.4

41.5 33 9.2 12.6 26.8 47 55 8 0.77 2.08 2.78 3.9 4.5 0 44 3.79 15.28 1 1.37 13.5 27.2 -- 5.6 36 14.7 36.1 53.1 84 78 lO 0.19

-0.14

0.62 0.8 0.6 0.7 41 3.92

- 2.22

12.65 22.4 6.6 16.9 32 4.6 6.6 16.5 24 21 5 0.40 0.21 1.56 2.3 1.7 0.8 31 1.35 - 0.81 4.52 7.7 1.8 5.5 36 5.6 0.3 19.2 35 15 21

-0.40

-_

--1.10

-_

--4.4

-0.45 0.60 1.94 3.4 3.0 0.6 32 1.44

- 1.73

5.08 6.5 1.1 7.6 38 6.0

- 4.0

21.8 30 13 28 0.72 2.32 2.34 2.8 4.4 +0.7 37 2.82 -13.48 8.19 12.7

- 7.6

26.5 37 8.7

-39.2

27.4 34

-17

64 0.39 0.1 1 1 .37 2.0 I .2 1 .0 39 0.21

- 0.1 I

0.73 1.3 0.6 1 .0 44 1 .6 5.2 5.3 7 1 1 0 0.61 0.46 1.95 2.8 2.4 1.5 43 1.34

- 7.92

3.67 6.0

- 4.9

1 1.8 37 8.0 1.6 25.3 31 21 29 0.62 1.99 1.88 2.8 3.7 0 42 1.54 -10.02 4.36 6.9

- 6.5

16.3 43 9.6 -35.I 29.1 38

- 8

60 0.45

-0.18

1.22 1.7 0.9 1.3 44 0.23

- 0.18

0.68 0.9 0.4 0.6 44 1.8 4.8 5.5 7 9 I 0.28 0.13 1.09 2.4 1.2 1.2 35 3.59

- 2.08

1 1.59 20.5 4.9 18.8 33 6.0 4.9 22.4 38 32 14 0.47 0.08 1.63 2.1 1.3 1.3 33 0.26 0.05 0.91 1.5 0.5 .0 44 2.1 3.9 7.5 10 9 2 I II 3 3 90 90 5 5

-

--

-II 3

-90 18 II 3 90 5 90 18

-II 3 90 5 90 18 90 2 II 3 270 5 270 18 225 2 II 3 90 5

-U 3 135 5

-11 3

-135 18

-Il 3 135 5 135 18

-11 3 135 5 135 18 135 2 II 3 180 5

-II 3 ISO 5 180 18 90 2 II 3 180 5 180 18 135 2 II I 180 7

-III 3 90 5

-III 3 180 5

-waves wind current longitudinal force transverse force moment

(19)

15 10 O a) o o E C 3 '-n vr 0.4 02 o

Fig. 5. Definition of headings and anchor lines.

Fig. 4. Characteristics of anchor line.

04

25

-2

Wave spectr)Jm

Measured, 160m = 6 8 sec

Theoretical (Pierson-Moskowitz), i,3=l.7Q mur 6 Ose

23 DIRECTION

1i::t::C::hline

Wave elevation in m o =O.40m max= 1.3 m max.- = i i m Wave spectrum Measured, i 60 rn,7 = 6 6 sec. -Moskowitz ), w3= 1.70 m, '. 6,Osec Theoretical (Pierson I / / i il

\

s. s. Wave elevation in m a) C 04Om '-L C 4) max. 1.5 rn Co max-i 1.3 m J 25 O o C a) a)

u-o

E

C o o 30 35 40 45 Horizontal displacement ¡n m

Trou g h Crest Trough Crest

05 1.0 1.5 05 10 5

(L) In rad sec. W in rad.sec.

Fig. 6. Beaufort 5 wave spectrum. Fig. 7. Beaufort 5 wave spectrum for test number 6 and 14. 2 o -2 o 2 a) ru E C 3 vr 02

(20)

04 (C Cu E C 3 02 e e 25 o C C, e Q-0 -2 o Fig. 8.

Beaufort 5 wave spectrum for test number 5 and 11.

o 2 E C 3 LM Q, o o C, C e u 25 o e e Q-0 2 e Cu E C 3 04 u, 0.2 05 10 U) in rad SCcT1 e s 25 o e -2 o o 15 2 Fig. 9.

Beaufort 5 wave spectrum for test number 13.

Fig. O.

Beaufort 7 wave spectrum.

Wave elevation in m 0 -041m max 1,6 m max.-. 1,6 m

--Wave elevation in m O =0.41ro max.. 2.1 ro max-. 1.9 m

-Wave spectrum Measured 164m, = 6 6 sec wi3= 1.70 m, 60 sec Theoretical (Pierson-Moskowitz), f--.'.'

/

\ \ Wave spectrum Measured 164m. ?=71 sec

(Pierson- Moskowitz), .t70 m,. 6osec

, --Theoretical

--f"

\

N

Wave elevation in rs 0 .083m max.' 36 m max.-. 39 m Wave spectrum Measured, 32 m,'?.8,2 sec wV3=3.50 m,= 75 sec Theoretical (Pierson-Moskowitz),

Trough Crest Trough Crest

-5 - 2.5 o 25 5 Trough Crest 15 05 lO Ui in rad

'5

05 10 L,) n rad.Sec.

(21)

15 10 05 o o 05 W in rad.sec.1 1.0 1.5 6 4 2 o 15 10 05 o o 05 1.0 W in rad. sec.1

Fig. 14. Sway response to beam seas, anchor system 1. Test no. I, 2 and 16.

1.5 25 O Cor1figuraton Configuration I L 1) I

I

III / f / Configuraton Configuration t

I'

I .

__,I//!

o

/

f k\

\\

o o o I' 'f 't \'

t'

N. o Con Con iguration I [1 1 iguraton L iguratlon I guration IlL

-

- Con Con o t, Configuration I Configuration 2 Configuratiot III / \. \

i

I f

\\

\

\\ \

N. \\

\

o Configuration Configuration I I

I

IlL Configuration Configuration

Li]

o N

"è/i \\

/

/0

/

oc

O 'o

/

i'f/I

W in rad.sec.1 W in rad sec:1

Fig. I L Heave response to beam seas, anchor system I. Fig. 12. Roll response to beam seas, anchor system 1.

Test no. 1,2 and 16. Test no. 1, 2 and 16.

o 05 1.0 15

Fig. 13. Response of relative motion to beam seas, anchor system. Test no. I, 2 and 16.

05 10 1.5

15

1.0

0.5

(22)

15 10 05 0 0 o 0.5 1.0

Fig. 17. Response of relative motion to beam seas, Con- Fig. 18. Sway response to beam seas, Configuration II.

figuration 11. Test no. 2 and 7. Test no. 2 and 7.

1.5 15 10 05 o o o o Anchor system 1 system 2 -- Anchor Anchor system 1 System 2

-

Anchor Anchor system 1 system 2 Anchor I,

//

/

-Anchor system 1 system 2 Anchor I,, I

t'

j

\\

\'

's'

_\\

\

.5

\\

05 1.0 1.5 W ¡n rad.sec W ir rad,sec.

Fig. 15. Heave response to beam seas, Configuration 11. Fig. 16. RoIl response to beam seas, Configurat on IL.

Test no. 2 and 7. Test no. 2 and 7.

05 1.0 1.5 (D n rad.sec.1 05 1,0 1.5 W in rad.sec. 6 4 2 15 10 05

(23)

15 10 05 10 0.5 15 o W in rad sec.1

Fig. 21. Response of relative motion to beam seas, Con- Fig. 22. Sway response to beam seas. Configuration II,

anchor system 1. Test no. 2, 4 and5.

figuration II, anchor system I. Test no. 2, 4 and5.

6 4 C o 05 1,0 W inrad.sec 27

Without wind and current

and current With wind With wind

\

N

N.

and current

-

With wind With wind

/

_\

J1/'

\\\

\

N

Without wind and current With wind

With wind and current

r'

/

\,

\

/

\

/

_\\

/\(\

/

05 io 1.5 05 10 1.5 W in rad.sec. ti In rad.5ec.

Fig. 19. Heave response to beam seas, Configuration II, Fig. 20. Roll response to beam seas, Configuration li,

anchor system 1. Test no. 2, 4 and 5. anchor system 1. Test no. 2, 4 and 5.

o 05 10 1.5

15

10

(24)

a 15 1.0 05 o 6 4 2 o o 05 10 (U ¡n rad.sec.-1

Fig. 23. Heave response to bow seas, Configuration Il. anchor system 1. Test no. 8, 10 and H.

1.5 a -n

o

15 10 05 o o 05 1,0 (U in rad.sec.1

Fig. 24. Pitch response to bow seas, Configuration II, anchor system L Test no. 8, 10 and 11.

1.5 Without wind and current

and current With wind

With wind

and current With wind With wuid

/

-\.

_\\

\\

t N

\

/

\

J

'J

-\

\

J

/

f.' L

i

I"

/

j

/

05 1.0 15 (U inrad,sec.1

Fig. 26. Response of relative motion to bow seas, Config-uration 11, anchor system 1. Test no. 8, 10 and Il.

o 05 1.0

(U in rad.Sec.

Fig. 25. Roll response to bow seas, Configuration 11, anchor system 1. Test no. 8, 10 and U.

1.5 o

15

10

05

(25)

15 to 05 o o o 05 05 1.0 W in rad. sec.-1

Fig. 27. Surge response to bow seas, Configuration II, anchor system 1. Test no. 8, 10 and II.

Fig. 29. Yaw response to bow seas, Configuration 11, anchor system I. Test no. 8, 10 and Il.

15 15

to

05 o 15 10 0.5 o o 0.5 W in rad sec1 1.0

Fig. 28. Sway response to bow seas, Configuration II, anchor system 1. Test no. 8, 10 and II.

05 1.0

W i rad.sec.1

Fig. 30. Heave response to head seas, anchor system 1. Test no. 12 and 17.

1.5

15 29

and current With wind

With wind

/!I\\\,

and current With wind With wirid

\

t-

-/

o Configuration Configuration I (1) t in Configuration

/

o o

\\

o\ o o Without wind and current

and current With wind With wind o o 05 10 1.5 W ri rad.sec.

(26)

15 10 a

0

0.5 1.5 10 o o 05

--

05 o 05 1.0 W n rad,sec.-1

Fig. 33. Surge response to head seas, anchor system 1. Test no. 12 and 17.

15 15

lo

0.5 o

lo

o 15 0.5 10 W in rad

Fig. 34. Heave response to head seas, Configuration LI, anchor system 1. Test no. 12 and 15.

1,5 o Configuration Configuration I t1J 1f 1f Configuration / I I \ \ I C I i 'O o I \ \.__ .___, C 0 7' / / / o Configuration Configuratìon

I [1]

it 1 Configuration o I o Beaufort BeaufOrt 5 7

-

..

I u' u' 's s. I I I I_I Configuration lt Configuration

\

/' \\

u'

_u'

_I

\\

_u'

\\

_\

's

_-=.----.

Fig. 31. Pitch response to head seas, anchor system I. Fig. 32. Response of relative motion to head seas, anchor

Test no. 12 and 17. system 1. Test no. 12 and 17.

o 05 1.0 1.5

(j) in rad,sec»

1.5

05 1.0

(27)

'-M eD 15 10 0.5 1.5 10 05 o o o o 0.5 1.0 U) inrad,sec.

Fig. 35. Pitch response to head seas, Configuration Il. anchor system I. Test no. 12 and 15.

05 10

W irr rad.Sec.'

Fig. 37. Surge response to head seas, Configuration II, anchor system I. Test no. 12 and 15.

1.5 1,5 15 10 05 o 15 1.0 0.5 o o o 05 W ir, rad.sec.1 10 1.5

Fig. 36. Response of relative motion to head seas, Con-figuration II, anchor system 1. Test no. 12 and 15.

05

W in rad.sec1

1.0

Fig. 38. Heave response to head seas, Configuration II, anchor system 1. Test no. 12 and 13.

1.5 31 BeaufOrt 5 BeaufOrt 7

-'r Beaufort 5 7 Beaufort

-,/

__--_,

Beaufort 5 Beaufort 7 'S., r N'.,

_\\

\

Without wind and current and current (beam) With wirid

(28)

1.5

1.0

0.5

o

o 05

(i) in rad sec.

Fig. 39. Pitch response to head seas, Configuration II, anchor system 1. Test no. 12 and 13.

15 10 0.5 o o 1.0 05 1.5 a 1.5 10 0.5 o o j) in rad.sec.

Fig. 41. Surge response to head seas, Configuration II, anchor system I. Test no. 12 and 13.

10

05

1.5

W in rad.sec.1

Fig. 40. Response of relative motion to head seas, Conflg-uration II, anchor system 1. Test no. 12 and 13.

10 1.5

Without wind and current arid current (beam) With wind

Without wind and current and current (beam) With wind

t

(29)

loo 50 o loo 50 o o 33 HEAVE in m 042 1

i

--1____

r

RELATIVE MOTION ¡n m G 0.31 max. 1.6 max. - r 1.0

/

I

f--ROLL in degrees G r 2.31 max. r r 91 max. - r 9.6

/

I

I I

j,'

,1

-/

/

I---L.

100 50 o PITCH in degre,s G

.017

max. r r 0.7 max. - r 0.5 F

I.

1k

-5

o S o

Fig. 42. Beaufort 5 beam seas, Configuration I, anchor system 2. Test no. i.

-2 o 2

100

50

(30)

loo o loo 50 o loo 5° o PITCH n negrees G 0.22 max..

08

max. - . 0.8 i' HEAVE in ri, G 0.46 max, r 1.8 max.- l.

/

¡It

/

I-/

RELATIVE MOTION in m G 0.23 max r r 1.2 max. - . 1.0

/

7 ii

-t

1-.

it

i

ROLL in degrees G r 1.48 max. * r 4.4

max.-.

45

¡ /

i

-I o -2 o 2

-5

o S o

Fig. 43. Beaufort 5 beam seas, Configuration II, anchor system 1. Test no. 2. loo

5°

(31)

loo 50 0 100 50 o loo 50 o 100 50 o PITCH n degrees G r 0.03 max r 01 max. - r 0.1 35 HEAVE in m G r 0.46 max r r 1.6 max. - r 1.4

,/_

/

i

A-/

/

f,

-RELATIVE MOTION in n,

'i

ROLL n degrees G r 1.77 max. r r 6.6 max. - r 5.1

/

I / F /

I

¡ I I I Ii A

f'

t

/

'L

i

F

rL

-2 o 2

-5

o o

(32)

loo 50 o loo So o 100 50 o o

Fig. 45. Beaufort 5beam seas. Configuration III, anchor system 1. Test no. 16.

HEAVE ¡Ti m G 0.41 max * 1.5 max - 1.6

/

I

I.

L_

-RELATIVE MOTION in m 0.31 max * i.o max. - 1.0

f

/

If'

Ij/I

ROLL in degrees G r 2.04

max.. r

63

max.-.

66 /

/

Ii,

I

/L

/Th

100 5° o PITCH in degrees G 0.27 max. r 0.9 max. - 0.7

JA

1. o -2 o 2

-5

o 5

(33)

loo 50 o 50 o

o

loo 50 o loo 50 o

Fig. 46. Beaufort 5 beam seas, Configuration I, anchor system I. Test no. I. Fig. 47. Beaufort 5 beam sea, Configuration II, anchor system I. Test no. 2.

SURGE in m d 0.09 max. r 0.5 max. -r 0.1

/

I' _f

ti

f

_il

m t SWAY ri m 6 r 0.78 max. r r 3.4

lo'

YAW in degrees

r:

044

max 1 6 max. -r 1.7

I----

_II

_I,

_Is

p, L

-YAW ri degrees r 0.36 max r r 0.9 max. -r 1.4

/

₍

I

I,

II

'I

Il I:

_'i

SWAY in m 6 r 0.97 max. r r 4.0 max. -r 1.5 1 J

_/

t

1

/i

-1 o loo SURGE in m lOO max. = max. -0.05 0.4 O -2 2 -2 o -2 o 2 -2 o 2 50 o loo 5° o

(34)

loo 50 o loo 50 o 100 50 o ₁₀₀ 50 o SWAY in ni G t 0.65

max., r

3.2 max -1.4

/

_/

/

f

YAW in degrees G 0.29 max., 1.0 max. -1.8

f

'I

_/i

N-

L

SURGE in m G r 0.11 max. r r 0.7

max-r

O J'

_/

.1

_il

T I

IlL

SWAY in m G , 0.94 max. r r 3.9

max.- r

1.6

/

_I

li/i

-

--i1i

YAW in degrees G , 0.50 max. r 1.9 max. -2.1

/

(

_/

ii

I-rrn

SURGE in m G r 0.23 max. * r 1.0 max -, 0.5

f'

g V 1

r-j

I

1.I

o -2 o 2 -2 o 2 -2 o -2 o 2 100 50 lOo 50

(35)

loo 50

o

loo So o

loo 50 o

Fig. 50. Beaufort 5 beam seas, Configuration I, anchor system 1. Test no. 1. Fig. 51. Beaufort 5 beam seas, Configuration II, anchor system 1. Test no. 2.

LONGITUDINAL FORCE in tons

G r 0.16 max. r 1.0 max. -0.5

/

¡

-í

TRANSVERSE FORCE in tons r 302 max. , r 3.9 max.-r 16.1

t

_/

--

1L[-MOMENT in tm r 3.4

max,, 24

max. -6

/

-mm

MOMENT in tm r 3.5

max.,,

19 max. -7

/

i

_i

TRANSVERSE FORCE in tons

G 3.25 max. . 4.2 max. -17.2 11f

f

ii

G 0.1l max.. r 06 max. -0.6 ¡

/

i

-2 o 2 - lo o lo -20 o 20 - 20 o 20 - lo o 10 -2 o 2 loo 50 o loo so o mo 50 o

(36)

loo 50

o

100 50

o

loo 50 o

TRANSVERSE FORCE in tons

G 3.36 max. 0.5 / max. -18.6 J

f

13 0.14 max.. 0.7 max. -0.5

¡

MOMENT in tm G 3.9 max. 20 max. -5

i

A

j-LONGITUDINAL FORCE in tons G 0.34 max r 0 6 max. -. 1.4

/

ILm

TRANSVERSE FORCE n tons r 7.09 max.. r -5.4 max. -r 41.5

,'

I

_I

I

// /

/

_/

/

MOMENT in tm G 9.2 max r r 55 max. -8

--¡I

_/

f

/

A

1

I -2 o 2 -lo o Io - 20 o 20

-2

2 -30

-20

-10 - 20 o 20 loo 50 o 100 50 loo 50

(37)

loo 50 o loo 50 o

Fig. 54. Beaufort 5 beam seas, Configuration II, anchor system 2. Test no. 7. Fig. 55. Beaufort 5 bow seas, Configuration II, anchor system I. Test no. 8.

TRANSVERSE FORCE in tons 3.92 max. * 6.6 max. -16.9

i'

/

1 _/

,,i/)

r 0.19 max.. r 0.6 max -z 0.7

/

f fi

11k

MOMENT in tm G z

46

max., 21 max.-S II

À'

LONGITUDINAL FORCE n tons C 0.40 max. , 1.7 max. -. 0.8

7 _/

I

t

-

_i

MOMENT in tm G r 5.6 max., * 15 max. -21

7 'I

_r,

_I

-I-

¡

-TRANSVERSE FORCE in tons * 1.35 max. * , 1.8 max. -z 5.5

/

_¡

-2 o 2 - lo lo -20 o 20

-5

o s -2 o 2 - 20 o 20 100 50 o 100 50 o loo 50 o 100 so o

(38)

loo 50 o loo 50 o -2 loo 50 o loo 50

-lo

loo 50 o o -5

Fig. 56. Beaufort 5 bow seas with wind, Configuration II, anchor system I Fig. 57. Beaufort 5 bow seas, with wind and current, Configuration II, anchor system I.Testno. 11.

TRANSVERSE FORCE in tons 1.44 max.. r 1.1 max. -7.6 J

/

_/

r

--MOMENT in tm

.60

max., 13 max. -, 28

'r-f

1 -I

i,

L

i-

/-LONGITUDINAL FORCE in tons G 0.45 max. r r 3.0 max -, 06 MOMENT n tm 8.7 max. r r -17 max. -r 64

I

/

'f

g

i

I/li-

r

-TRANSVERSE FORCE in tons G r 262 max.. -7.6 max. -r 26.5

Ic

_/

/

_//

j!'

1/I

I

-J

I

I LONGITUDINAL FORCE in tons

:::

I

À"

-60 40 -20 o 2 4 -20 -15 2 o -2 -5 o 5 o 20 - 20 100 So

(39)

100 50 100 o 50 o 50 o TRANSVERSE FORCE n tons

i:

100 50 o

Fig. 58. Beaufort 5 head seas, Configuration II, anchor system I. Test no. 12. Fig. 59. Beaufort 5 head seas with wind and broadside current, Configuration II, anchor system 1. Test no. 13.

MOMENT in tm G 1.6 max., 11 max. -O 'T _¡ I LONGITUDINAL FORCE in tons

ma.

0.39 max. -1.0 í'1 J

I

-MOMENT in tm G 8.0 max., 21 max. -, 29

/ /

G 0.61 max. . 2.4

max.- 151

f

_/

TRANSVERSE FORCE ¡n tons G 1.34 max.. -4.9 max. -, 11.8

/

_/

!

f

loo G 0.21 max. * 0.6 max. -1.0 -2 2 -15 -10 -5 - 20 o 20 -20 o 20 -2 o 2 5 -5 o 100 50 o loo 50 o

(40)

loo 50 O loo 50 o 50 o ₁₀₀ 50 o TRANSVERSE FORCE

i

i;

Â

MOMENT in tm

i

_i

G 0.45 max. r r 0.9 max. -1.3

7 _/

/

II

ii

_I,

J1h

MOMENT in tm G 8.0 max. , 32 max.-14 74

--ifl

TRANSVERSE FORCE in tons G 3.59 max. . r 4.9 max. -. 18.8 f

_/

I

_/

k1

G 0.28 max,. 1.2 max. -1.2

/

_/

_f

i

in tons 100 50 G max. max. -. o loO G 0.23 max.. . 0.4 max. -0.6 -10 o Io -2 o 2 - 20 o 20 -5 o S - 20 o 20 o 2 -2 100 50 o

(41)

loO 50 o loo 50 o TRANSVERSE FORCE in tons max.. max. -1.0 G 0.26 -5 o 5 lOo 50 o MOMENT in tm G 2.1

max.,.

g max. -2

f

i,

i

_i 1.

Fig. 62. Beaufort 5 head seas, Configuration III, anchor system

i. Test no. 17.

0.47 max.. . 1.3 max. -1.3

/

_¡

'f

o 20 -20 2 O -2

(42)

PRICE PER COPY DFL. lo.- (POSTAGE NOT INCLUDED)

M = engineering department S = shipbuilding department C = corrosion and antifouling department

Reports

57 M Determination of the dynamic properties and propeller excited vibrations of a special ship stern arrangement. R. Wereldama.

1964.

58 S Numerical calculation of vertical hull vibrations of ships by discretizing the vibration system, J. de Vries, 1964.

59 M Controllable pitch propellers, their suitability and economy for large sea-going ships propelled by conventional, directly coupled engines. C. Kapsenberg. 1964.

60 S Natural frequencies of free vertical ship vibrations. C. B. Vreug-denhil, 1964.

61 S The distribution of the hydrodynamic forces on a heaving and pitching shipmodel in still water. J. Gerritsma and W. Beukel-man, 1964.

62 C The mode of action of anti-fouling paints : Interaction between anti-fouling paints and sea water. A. M. van Londen, 1964. 63 M Corrosion in exhaust driven turbochargers on marine diesel

engines using heavy fuels. R. W. Stuart Mitchell and V. A. Ogale, 1965.

.54 C Barnacle fouling on aged anti-fouling paints; a survey of pertinent literature and some recent observations. P. de Wolf, 1964. 65 S The lateral damping and added mass of a horizontally oscillating

shipmodel. G . van Leeuwen, 1964.

66 S Investigations into the strength of ships' derricks. Part I. F. X. P. Soejadi, 1965.

67 S Heat-transfer in cargotanks of a 50,000 DWT tanker. D. J. van der Heeden and L. L. Mulder, 1965.

68 M Guide to the application of method for calculation of cylinder liner temperatures in diesel engines. H. W. van Tijen, 1965. 69 M Stress measurements on a propeller model for a 42,000 DWT

tanker. R. Wereldsma, 1965.

70 M Experiments on vibrating propeller models. R. Wereldsma, 1965. 71 S Research on bulbous bow ships. Part II. A. Still water perfor-mance of a 24,000 DWT bulkcarrier with a large bulbous bow. W. P. A van Lammeren and J. J. Muntjewerf, 1965.

72 S Research on bulbous bow ships. Part II. B. Behaviour of a 24,000 DWT hulkcarrier with a large bulbous bow in a seaway. W. P. A. van Lammeren and F. V. A. Pangalila, 1965.

73 S Stress and strain distribution in a vertically corrugated bulkhead.

H. E. Jaeger and P. A. van Katwijk, 1965.

74 S Research on bulbous bow ships. Part I. A. Still water

investiga-tions into bulbous bow forms for a fast cargo liner. W. P. A. van Lammeren and R. Wahab. 1965.

75 S Hull vibrations of the cargo-passenger motor ship "Oranje

Nassau", W. van Horssen, 1965.

76 S Research on bulbous bow ships. Part I. B. The behaviour of a fast cargo liner with a conventional and with a bulbous bow in a sea-way. R. Wahab, 1965.

77 M Comparative shipboard measurements of surface temperatures and surface corrosion in air cooled and water cooled turbine outlet casings of exhaust driven marine diesel engine turbo-chargers. R. W. Stuart Mitchell and V. A. Ogale, 1965. 78 M Stern tube vibration measurements of a cargo ship with special

afterbody. R. Wereldsma, 1965.

79 C The pre-treatment of ship plates: A comparative investigation

on some pre-treatment methods in use in the shipbuilding

industry. A. M. van Londen, 1965.

80 C The pre-treatment of ship plates: A practical investigation into the influence of different working procedures in over-coating zinc rich epoxy-resin based pre-construction primers. A. M. van Londen and W. Mulder, 1965.

81 S The performance of U-tanks as a passive anti-rolling device. C. Stigter, 1966.

82 S Low-cycle fatigue of steel structures. J. J. W. Nibbering and J. van Lint, 1966.

83 S Roll damping by free surface tanks. J. J. van den Bosch and J. H. Vugts, 1966.

84 S Behaviour of a ship in a seaway. J. Gerritsma, 1966.

85 S Brittle fracture of full scale structures damaged by fatigue. J. J. W. Nibbering, J. van Lint and R. T. van Leeuwen, 1966. 86 M Theoretical evaluation of heat transfer in dry cargo ship's tanks

using thermal oil as a heat transfer medium. D. J. van der

Heeden, 1966.

87 S Model experiments on sound transmission from engineroom to accommodation in motorships. J. H. Janssen, 1966.

88 S Pitch and heave with fixed and controlled bow fIns. J. H. Vugts, 1966.

89 S Estimation of the natural frequencies of a ship's double bottom by means of a sandwich theory. S. Hylarides, 1967.

90 S Computation of pitch and heave motions for arbitrary ship forms. W. E. Smith, 1967.

9 1 M Corrosion in exhaust driven turbochargers on marine diesel engines using heavy fuels. R. W. Stuart Mitchell, A. J. M. S. van Montfoort and V. A. Ogale, 1967.

92 M Residual fuel treatment on board ship. Part II. Comparative cylinder wear measurements on a laboratory diesel engine using filtered or centrifuged residual fuel. A. de Mooy, M. Verwoest and G. G. van der Meulen, 1967.

93 C Cost relations of the treatments of ship hulls and the fuel con-sumption ofships. H. J. Lageveen-van Kuijk, 1967.

94 C Optimum conditions for blast cleaning of steel plate. J. Rem-melts, 1967.

95 M Residual fuel treatment on board ship. Part I. The effect of cen-trifuging, filtering and homogenizing on the unsolubles in residual fuel. M. Verwoest and F. J. Colon, 1967.

96 S Analysis of the modified strip theory for the calculation of ship motions and wave bending moments. J. Gerritsma and W. Beu-kelman, 1967.

97 5 On the efficacy of two different roll-damping tanks. J. Bootsma and J. J. van den Bosch, 1967.

98 S Equation of motion coefficients for a pitching and heaving des-troyer model. W. E. Smith, 1967.

99 S The manoeuvrability of ships on a straight course. J. P. Hooft,

1967.

100 5 Amidships forces and moments on a CB = 0.80 "Series 60" model in waves from various directions. R. Wahab, 1967. 101 C Optimum conditions for blast cleaning of steel plate. Conclusion.

J. Remmclts, 1967.

102 M The axial stiffness of marine diesel engine crankshafts. Part I. Comparison between the results of full scale measurements and those of calculations according to published formulae. N. J. Visser, 1967.

103 M The axial stiffness of marine diesel engine crankshafts. Part II. Theory and results of scale model measurements and comparison with published formulae. C. A. M. van der Linden. 1967. 104 M Marine diesel engine exhaust noise. Part I. A mathematical model.

J. H. Janssen, 1967.

105 M Marine diesel engine exhaust noise. Part II. Scale models of exhaust systems. J. Buiten and J. H. Janssen, 1968.

106 M Marine diesel engine exhaust noise. Part III. Exhaust sound criteria for bridge wings. J. H. Janssen en J. Buiten, 1967. 107 S Ship vibration analysis by finite element technique. Part I.

General review and application to simple structures, statically loaded. S. Hylarides, 1967.

108 M Marine refrigeration engineering. Part I. Testing of a decentraI-ised refrigerating installation. J. A. Knobbout and R. W. J.

Kouffeld, 1967.

109 S A comparative study on four different passive roll damping tanks. Part I. J. H. Vugts, 1968.

110 S Strain, stress and flexure of two corrugated and one plane bulk-head subjected to a lateral, distributed load. H. E. Jaeger and P. A. van Katwijk, 1968.

111 M Experimental evaluation of heat transfer in a dry-cargo ships' tank, using thermal oil as a heat transfer medium. D. J. van der Heeden, 1968.

112 S The hydrodynamic coefficients for swaying, heaving and rolling cylinders in a free surface. J. H. Vugts, 1968.

113 M Marine refrigeration engineering. Part II. Some results of testing a decentralised marine refrigerating unit with R 502. J. A.

Knob-bout and C. B. Colenbrander. 1968.

114 S The steering of a ship during the stopping manoeuvre. J. P. Hooft, 1969.