Model and full scale motions of a twin hull vessel

REPORT No. 131 S

August 1969

(Sgo/ 187)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT

LEEGHWATERSTRAAT 5, DELFT

*

MODEL AND FULL SCALE MOTIONS OF A

TWIN-HULL VESSEL

by

M. F. VAN SLUIJS

Netherlands Ship Model Basin

VOOR WOO RD

Voor het onderzoeken van het gedrag van schepen in zeegang, hebben modelexperimenten bewezen van grote waarde te zijn. Een aantal onderzoekingen beeft aangetoond dat het aannemen van lineariteit en bet verwaarlozen van mogelijke schaaleffecten

voor de gebruikelijke rompvormen meestal tot bevredigende prognoses leidt. Of dit echter ook geldt voor ongebruikelijke

scheepsvormen is nog aan enige twijfel onderhevig.

In februari 1969 werd bet Scheepsstudiecentrum door de Nederlandse Maatschappij voor Werken Buitengaats N.y.,

eigenares van het als catamaran uitgevoerde motorschip ,,Duplus", de gclegenheid geboden orn voor dit, uit twee rompen opgebouwde, schip de geldigheid van de hierboven genoemde

aannamen na te gaan. De in dit rapport beschreven

onderzoe-kingen waren gericht op het veriliëren van:

de correlatie tussen metingen van de bewegingen van het

schip op ware grootte en modelexperimenten (schaaleffect), de mogelijkheid orn bet gedrag van bet schip in een onregel-matige zee te voorspellen met de resultaten van proeven in regelmatige golven (lineariteit en superpositie).

Tegeìijkertijd worden hierbij natu urlijk de zeegangseigenschap-pen van dit type schip bezien.

Hiertoe werden, in nauwe sarnenwerking met de rederij.

me-lingen uitgevoerd op het schip zeif gedurende een reis op de Noordzee en werden tevens modelproeven verricht, zowel in

regelmatige als in onregelmatige golven in de zeegangstank van

het 1'ederlandsch Scheepsbouwkundig Proefstation. AI deze

proeven werden uitgevoerd terwijl bet schip geen snelhcid had. De resultaten van de metingen en berekeningen die in dit rap-port worden weergegeven tonen aan dat zelfs voor deze oncon-ventionele scheepsvorrn de overeenkornst tussen ware grootte, modelexperirnentele en berekende waarden in bet algerneen zeer

hevredigend is.

De metingen van de scheepsbewegingen, zowel die op bet

schip als die in de tank werden uitgevoerd door bet Neder!andsch Scbeepsbouwkundig Proefstation. Gedurende de proeven op de Noordzee werden de golthoogten ter plaatse geregistreerd door

het Koninkhjk Nederlands Meteorologisch Instituut.

De vriendelijke medewerking van de Nederlandse Maatschap-pij voor Werken Buitengaats NV. zu hier met dank vermeld. Ook komt dank toe aan de auteur en alle erbij betrokken mede-werkers van bet Nederlandsch Scbeepsbouwkundíg Proefstation en bet Koninklijk Nederlands Meteorologisch lnstituut.

HET NEDERLAN 05 SCHEEPSSTUDIECENTRUM TNO

PREFACE

For investigating the seagoing behaviour of ships, model experi-ments have proved to be a very valuable tool. A number of in-vestigations have shown that the supposition of linearity and the neglect of possible scale effects mostly lead to satisfactory

pre-dictions for the usual hull shapes. Whether this will hold true

for unusual hull shapes, however, is still open to question.

In February 1969 the Ship Research Centre was offered an

opportunity by the Netherlands Offshore Company, Owner of the catamaran-type motorvessel ,Duplus' to check the validity of the above-mentioned suppositions for this twin-hulled vessel. The investigations described in this report mainly aimed at the verification of:

J. the correlation between full scale measurements of the mo-tions of the ship and model experiments (scale effects),

2. the possibility to predict the behaviour of the vessel in an

irregular sea from the results of experiments in regular waves (linearity and superposition).

At the same time, of course, the seagoing properties of this ship-type are considered.

For these purposes, in close collaboration with the Owners,

full scale measurements were carried out during a trip on the

North Sea as well as model experiments, both in regular and in irregular waves in the Seakeeping tank of the Netherlands Ship Model Basin at Wageningen. All experiments were performed at zero speed.

The results of measurements and calculations presented in

this report show that, even for this unconventional hull shape, in general the agreement between full scale, model-experimental and calculated values is very satisfactory.

The measurements of the ship motions both at full scale and in the tank, were carried out by the N.S.M.B. During the test at the North Sea the wave heights were, on the spot, recorded by the K.N.M.I. (Royal Netherlands Meteorological Institute).

The kind cooperation of the Netherlands Offshore Company be gratefully mentioned here. Also thanks are due to the author and all staff concerned of the N.S.M.B. and K.N.M.I.

page

Summary 7

1 Introduction 7

2 Model motion measurements 8

2.1 Particulars of the twin-hull vessel 8

2.2 Model test procedures 9

3 Model test results IO

3.! Behaviour in regular waves IO

3.2 Behaviour in irregular head seas 10

3.2.1 Calculations from results of tests in regular waves IO

3.2.2 Measurements

il

4 Full scale motion measurements 12

4.1 Experimental procedure 12

4.2 Data reduction and results 12

5 Discussion of results 12

6 Conclusions 13

LIST OF SYMBOLS

aa

amplitude of vertical acceleration

aa

significant amplitude of vertical acceleration

AG

longitudinal center of gravity from aft perpendicular

BM

maximum breadth under water

BWL

breadth on waterline

g

acceleration due to gravity

GM

metacentric height

h

height of deck above water

KM

height of metacenter above base

KG

center of gravity above base

k

wave number = 2it/1

longitudinal radius of gyration

L

length between perpendiculars

area of spectrum

m1

first moment of spectrum

N

number of times

P

probability

amplitude of relative motion

Sa

significant amplitude of relative motion

S(w)

spectral density

T

draught

T

mean wave period

T..

natural period for heave

T0

natural period for pitch

T4,

natural period for roll

Y (w)

frequency response operator

Za

amplitude of heave

Za

significant amplitude of heave

V

displacement volume

wave amplitude

wave height = 2a

W3

significant wave height

Oa

amplitude of pitch

significant amplitude of pitch

wave length

A..

tuning factor for heave

A0

tuning factor for pitch

A4,

tuning factor for roll

wave direction

w

wave circulai frequency = J(2irg/))

MODEL AND FULL SCALE MOTIONS OF A TWIN-HULL VESSEL

by

M. F. VAN SLUIJS

Sumrnari'

The results of model and full scale motion measurements on an unconventional, twin-hull ship form are reported.

A correlation is made between the model motion responses to regular and irregular waves with those derived from sea trials with the prototype.

Three wave headings are considered. An adequate agreement has been established.

i

Introduction

Model testing techniques are commonly accepted as a

reliable means to predict the full scale behaviour and

performance of a ship in a seaway. For this purpose

the information derived from mode! experiments in

both regu!ar and irregular waves are uti!ized in

combi-nation with theoretical suppositions. Severa!

investiga-tors, as for instance Gerritsma and Smith [1], Aertssen

[2] and Canham et al. [3], found a satisfactory

agree-ment when correlating results of full scale sea trials

Twin-hull ,,Duplus" at sea.

with those obtained from model tests. The applicability

of the linear superposition principle to ship motions

was frequently

proved, whereas any scale

effect,

present during the model tests, was judged to be

insignificant.

These

findings

hold trite, however,

merely as far as the motions of single hull ships are

concerned.

The work described in this report deals with the

motion correlation of an unconventional vessel, being

the twin-hull unit ,,Dup]us" owned by the Netherlands

8

Offshore Company [4]. This vessel consists of two

submerged, submarine type hulls, each carrying a

slender superstructure. Under water the hulls are

interconnected by two hydrofoil sections: above the

waterline the superstructures support the box-like

maindeck structure.

The experimental

program conducted for

the

subject motion correlation can be subdivided into

three portions:

Model tests in uni-directional regular waves:

Model tests in uni-directional irregular seas:

Full scale motion measurements.

Since the main duties of the vessel under consideration

are to be performed when on station, solely the

condi-tions that the vessel is lying hove to in head, bow or

beam seas are examined.

The motion response of a 1/25-scale model to regular

and irregular waves is compared with that of the

prototype in open sea. Though the accuracy of the

sea trials is obviously a major restriction, it

is felt

however, that the results provide a sufficiently reliable

information. Eventually, predictions from the results

of the regular wave tests are made if and under what

circumstances the underside of the main deck is

touched by the waves. These predictions apply only to

the head sea conditions.

2

Model motion measurements

2. 1

Particulars of the twin-hull vessel

The vessel under consideration is composed of two

submarine shaped buoyancy bodies, interconnected

under water by two hydrofoils, each of 8 meters in

length.

Its main dimensions are given in Table I.

Table 1. Main dimensions and stability data of the ,,Duplus'

The hydrofoils are located at station 6 and 153- and

are adjusted at 3 degrees with the horizontal plane to

counteract the liability of the vessel to trim forward

when running ahead. A rectangular deck, provided

with a centerwell, has its lower part 8.2 meters above

the buoyancy body base line.

For the tests in waves a model scale ratio of I to 25

was chosen, a scale being mainly determined by the

capacity of the wave generator installed in the

Sea-keeping Laboratory of the N.S.M.B. A detailed

de-scription of this facility is given by Van Lammeren

and Vossers [5].

,,Duplus" model.

The model was constructed

of glass

reinforced

polyester except for the hydrofoils which were

manu-factured of wood. Bronze nozzles were fitted aft to the

underwater buoyancy hulls. Reproduction of the four

vertical axis propellers was omitted. The lines of the

model are given in Fig. 1.

The model was ballasted to an even keel draught

of 5.2 meters meeting hydrodynamic properties as

stated in Table I. These data correspond

approxi-mately to the actual ship condition during the sea

trials as summarized in Table II.

Table II. Full scale trial conditions

Wind Wave

speed height Displacement

and and and

direction direction metacentric Area (estimate) (estimate) height

5242'N 16 rn/sec

2m

V = l,ll9m'

3 l6'E

180° 180°

GM=0.90rn

15m/sec

2m

135° 135° 18 in/sec 2m 90° 90 Draught aft and fore TA 5.00 ni TF = 4.55 m

Denomination Symbol Unit

Loaded condition

Length between perpendiculars L m 40.00

Maximum breadth under water BM m 17.08

Breadth on the waterline BWL m 14.77

Depth to lower deck at

center-line at station 10 h1 in 8.20

Depth to lower deck at

center-line at station 20 Ii m 10.20

Draught - even keel T m 5.20

Displacement volume V m3 1,174

Center of gravity above base KG ni 5.81

Center of gravity forward of

aft perpendicular AG m 20.88

Metacenter above base KM in 6.71

Metacentric height GM in 0.90

Longitudinal gyradius k55

%L

25.2

Heave period T1 sec 10.8

Pitch period T1, sec 13.6

Ap

Fig. 1. Lines of the ,,Duplus".

2.2

Model test procedures

The tests in waves were conducted with the model

lying hove to. To this purpose the mode! was

posi-tioned by four lines, each of which was inserted with

a linear soft spring having a spring constant of 1.12

kg/rn. The lines were attached to both hulls forward

and aft at waterline height each under a 45 degree angle

with the model centerline.

lt was realized that the

natural frequencies of the horizontal modes of motion

were well outside the range of wave frequencies

inves-tigated.

During the

tests

the following quantities were

recorded simultaneously (the values of the positions

where the various quantities were measured apply to

the full scale):

- Heave amidships and at 1.75 m aft of the fore

per-pendicular, measured by vertical light-weight rods

attached to the deck. The upper ends of the rods

were driving

potentiometers.

In

the following,

heave denominates the absolute vertical motion of

the vessel.

Pit ch and roll angles, recorded by a gyroscope

equipped with wire resistance potentiometers.

Vertical accelerations at 3 meters aft of amidships

and 2.75 meters aft of the fore perpendicular, sensed

by 2-g Statham accelerometers.

Relative motions (with respect to the wave surface)

amidships and at the fore perpendicular, obtained by

resistance wire wave probes. These probes consist

of two thin brass wires; the resistance variation

caused by the passage of electric current is a measure

for the motion of the ship relative to the waves.

Wave height, measured by a wave probe, identical

to those used for the sensing of the relative motions.

The waves were calibrated before the tests at the

location of the model.

L

All model testing was done in uni-directional regular

and irregular waves. The tests in regular waves were

run over a sufficiently large range of wave frequencies

to establish the motion response curves fairly accurately.

Three wave headings were investigated viz. head-,

bow- and beam waves. The wave direction p is defined

as the angle between the ship's centerline and the

direction of wave propagation - see Figure 2.

Fig. 2. Definition of wave direction.

p = I 80 degrees for head waves

p = 135 degrees for bow waves

p = 90 degrees for beam waves

Throughout the regular wave experiments the wave

height was kept constant at t/20L, corresponding to

2 meters for the prototype. For the head and bow sea

condition the effect of variation of wave height (/4

and 1/10L, corresponding to

i and 4 m ) upon the

model motions was studied for two specific wave

length- ship length ratios. Table III lists the tests in

regular waves.

To

investigate

whether

the

linear

superposition

principle to the motions of subject vessel is valid, tests

were carried out in two irregular sea states, of

which

the spectra are given in the Figures 28 and 29. The

irregularity of the waves in the basin was obtained

by varying the frequency of the paddles of the wave

generator at constant time intervals. Dispersion

of the

waves results in an irregular wave system

at some

distance from the generator.

The adjustment of an energy distribution according

to a prescribed wave spectrum is realized by trial and

error until the desired distribution is met as close as

possible.

During the irregular wave experiments all

afore-mentioned data were recorded simultaneously on an

U.V. recorder and digitized in punch paper tape.

Evaluation was performed by a C.D.C.-3300

com-puter analogous to the method described

by Walden

and Piest [6] and Korvin-Kroukovsky [7]; the number

of lags used was ni = 50.

3

Model test results

3.1 Behaviour in regular waves

Results of the tests in regular waves are given in

the

Table 1V. Motion response to regular bow waves (direction 35 degrees)

where a

is given in units of the acceletation due to

gravity.

Resonance conditions for heave, pitch and roll are

indicated by A.. = 1, A0 = I and A = 1 respectively.

The results of the tests in regular head waves were

used to predict the motions in irregular seas, up to

conditions corresponding to wind Beaufort 12 on the

North Atlantic.

In addition, the probability that the lower deck

amidships and fore is touched by the waves is

cal-culated.

3.2 Behaviour in irregular head seas

3.2.1

Calculations from results of tests in regular

waves

The behaviour of the vessel in irregular head seas is

calculated from the response to regular waves. The

motions of the vessel in ari irregular sea are determined

by the linear superposition of the response to

each

wave component in regular waves. For the significant

double amplitude of heave for instance holds

=

4,j

_f

(z)2.

Wave length Wave height

in m in rn r., Zarla Zarla OaIk,r cl'al' Sarl a Sa,/,, 0urlG1)a aa,/Gk)a

125 1.00 0.702 0.81 0.87 0.50 0.24 0.44 0.16 1.58 1.75 125 2.00 0.702 0.8! 0.83 0.44 0.23 0.4! 0.18 1.58 1.68 125 4.00 0.702 0.8! 0.81 0.40 0.22 0.40 0.21 1.57 1.66 175 1.00 0.593 0.73 0.76 0.61 0.31 0.55 0.30 1.38 1.50 175 2.00 0.593 0.81 0.80 0.52 0.31 0.45 0.27 1.58 1.63 175 4.00 0593 0.92 0.91 0.50 0.32 0.36 0.24 1.8! 1.90

Table IlL Mode! test conditions

Figures 3 through 21 and Table IV (figures on page 14

and further). All data are represented as dimensionless

amplitudes versus wave frequency; an additional scale

Wave direction Wave length ratio

L/2

Wave height ratio

180 1.143 0.05

proportional to L/)L is included:

0.800 0.025 0.05 - 0.1 0.534 0.05

heave amplitude

0.400 0.320 0.05 0.05

wave amplitude

0.229 0.025-0.05 -0.1 0.200 0.05 Oa

pitch amplitude

0.160 0.05 _k40

_{- wave slope amplitude}

90 0.800 0.05

0.534 0.05 _4'a

roll amplitude

0.400 0.05

ka

=

wave slope amplitude

0.320 0.05

0.229 0.05

0.160 0.05

amplitude

of

relative motion

0.107 0.05

wave amplitude

135 0.320

0.025-0.05-0.1

0.229 0.025 - 0.05 -0.1

aa

amplitude

of

vertical acceleration

Similar expressions are

valid

for the

significant

values of the other motions under consideration.

The results are given in the Figures 22 through 25

(on page 19 and further), whereas the wave spectra

used

for

these computations are

represented

in

Fig. 26. The wave spectra are similar in shape to those

analyzed by Pierson and Moskowitz [8]

for fully

developed seas. These spectra are formulated by

S(w)

AB_814

where

S.(w) = wave spectral density

w

= wave circular frequency

In relating the energy spectrum of the waves to actual

observations at sea,

it

is assumed that the average

observed wave height conforms to the calculated mean

of the one-third highest waves (= significant wave

height) and that the observed period of the waves

corresponds to the calculated mean period.

In accordance with the recommendations made in

[9] the mean wave period is based upon the first

moment of the spectrum which is as realistic as

circum-stances permit.

Consequently:

S S,-(w).dw

Observed period = T = 2ir

O

ÇwS(w).dw

Thence the following relation

exists

between the

significant wave height, the mean period and the

coefficients A and B

A = O.25()2

B =

(o.8i7.

T!

The values of the significant wave height and mean

period used are equivalent to the average values as

measured and observed by weatherships on the North

Atlantic and reported by Roll [10].

In Fig. 27 the frequency of occurrence of the various

wave conditions is shown. Wind Beaufort 5 represents

average weather in this area, whereas force 9 may be

considered as rather extreme.

Assuming that the motion amplitudes in an irregular

sea follow the Rayleigh distribution law, the

probabil-ity per cycle of wave encounter P that the underside

of the main deck is touched by a wave crest can be

calculated with

=

j

S

ds =

Ii ¿nos

where

lì

= local height of the deck above waterline

'nos = area under relative motion spectrum

= variance of relative motion

The number of times per hour N5 that the deck is

touched by the waves follows from

N

r2'

where

'r2, = 27r

2s

= second moment of relative motion spectrum

= variance of relative velocity

Table V shows the calculated number of times per

hour that the deck amidships and at the fore

per-pendicular is touched by the waves in head seas.

Table V. Number of times per hour that the deck is touched

by the wave surface in head seas

Beaufort number Midships Fore perpendìcuiar

3.2.2

Measurements

The model experiments in irregular head seas were run

during a time period corresponding to 30 minutes for

the full scale, being sufficiently lon.g in view of

statis-tical analysis. The one-third highest values of the

various motions are plotted in the diagrams, Figures

22 through 25. Amplitude characteristics were derived

from the recorded motion and wave spectra by taking

the square root of afore-mentioned ratio, hence

Y..(w) = --(w)

=

/°

where

S(w) = the spectral ordinate of the heave motion

S(w) = the spectral ordinate of the waves at

cor-responding frequencies.

Similar expressions apply to the other motion

re-sponses. In the Figures 3 through 9 the motion

am-plitude characteristics derived from the irregular wave

model tests are indicated by dashed lines.

Observed wave height =

₌

_S(w)dw

_{9 o}

li 9 o

12

4

Full scale motion measurements

4.1

Experimental procedure

The full

scale sea trials with the twin-hull vessel

,,Duplus" were run from February 17 till

20, 1969, on

the North Sea, approximately

50

miles west of

Ijmui-den. Trial conditions are summarized in Table 11.

During the sea trials the waves, the pitch and roll

angles of the vessel, and the vertical accelerations at

3 meters aft of amidships and

2.75

meter aft of the fore

perpendicular at the ship's centerline were

simulta-neously measured. In addition, the heave at

1.75meters

aft of the fore perpendicular was sensed by an

accelero-meter suspended in gimbals, of which the output

signal was double integrated. The instrumentation for

the full scale motion measurements was equivalent to

that used during the model tests.

The waves were recorded by a wave recorder

sup-plied by the Royal Netherlands Meteorological

In-stitute. This measuring device consists of an

accelero-meter mounted on a raft, which is connected to the

ship by an electric cable. The signal of the

accelero-meter is integrated twice and recorded aboard the

ship. During the measuring runs the raft was positioned

approximately one ship

length, being 40 meters,

ahead of the vessel. Thus it can be supposed that the

wave recording was not affected by waves, emitted by

the oscillating ship. An extensive description of the

prin-ciple of the wave recorder is given by Dorrestein in [li].

The sea conditions in which the full scale trials were

conducted appeared from visual observations to be

reasonably long-crested though not precisely

uni-directional; a low swell was present which was

ap-proaching perpendicularly to the dominant direction

of wave propagation.

All data were recorded on a FM tape recorder and

on paper chart.

A measuring run lasted for about

25

minutes, which

duration is considered to be sufficiently long for a

reliable statistical treatment, the more so, since the

length of the waves encountered was rather short.

4.2

Data reduction and results

The data recorded on the magnetic tape were

trans-formed into punch paper tape which thence served as

the input in the C.D.C.-3300 digital computer. The

spectra of the waves met on the North Sea during the

trials are given in Fig. 30. In comparing the observed

and the calculated significant wave height, the

cal-culated values as given in Fig. 30 are somewhat larger

than those listed in Table II. From the motion and

wave spectra, the response amplitude operators were

derived analogous to the method described in

para-graph

3.2.2.

The results are plotted in the Figures

4

through 7,

11 through

14

and 17 through

21

comparative to those

obtained from the model tests.

5

Discussion of results

The results of the tests in regular waves with varying

height show a slight non-linearity in the motions of the

twin-hull vessel.

In general, the effect of wave height upon the motion

response agrees with what should normally be

ex-pected; the response to lower waves is higher than the

response to higher waves. At a ship length - wave

length ratio of

0.229

in regular head waves, however,

a discrepancy with the above occurs in the response

of the heave amidships and fore and consequently in

the accelerations. The slight non-linearities are expected

to be mainly caused by second order effects in the wave

exciting forces on the hydrofoils and by mutual

inter-ferences, in particular when large motions are

ex-perienced.

Generally the response amplitude characteristics

derived from the irregular wave tests fit those obtained

from the tests in regular waves with varying height

particularly well. Apparently the effects of second

order terms in the wave exciting forces are less

pro-nounced when the ship motions are either irregular

or small.

In order to arrive at an overall figure about the

motions to be expected in various irregular head seas,

use has been made of the linear superposition

prin-ciple and the motion response characteristics to the

regular waves. The wave spectra employed are valid

for the North Atlantic and resemble the

Pierson-Moskowitz formulation. In comparing these results

with the data direct measured in the irregular seas a

good agreement is found between the predicted and

measured motions. Especially for the lower seas as the

theoretical and the produced wave spectrum are almost

equivalent. The slight non-linearities are obviously

insignificant for practical purposes.

In the higher seas a somewhat larger difference

occurs, which is mainly to be attributed to the

differ-ence in energy content between the wave spectrum

produced in the basin and the theoretical spectrum,

see Fig.

29.

During the model tests in the irregular

Beaufort

9

head sea it was observed that the deck

amidships was touched by the waves four times per

hour, whereas the deck at the fore perpendicular

remained dry. In comparing these figures with the

theoretically obtained values as listed in Table V, the

difference in energy content of the wave spectra has,

however, to be allowed for.

The results of the full scale sea trials check

partic-ularly well with those of the model tests. As the waves

met on the North Sea during the full scale motion

measurements were rather short, the correlation could

only be made for the higher wave frequencies. Major

differences between model and

full scale

results

originate solely in heave and consequently in the

accelerations. These discrepancies are merely of a

quantitative character; the nature of both the model

and full scale response is identical.

Considering the difficulties and inaccuracies

un-avoidably associated with full scale motion

measure-ments, it can be summarized that, though there are

some slight discrepancies between the model and

prototype response, the mutual agreement on the whole

is truly good.

The more so, since these discrepancies can be

mini-mized when the wave dependence is removed: thus by

plotting, for instance, the non-dimensional heave-pitch

ratio on a base of wave frequency [12].

6 Conclusions

The prediction of the full scale behaviour of the

twin-hull vessel, based upon model test results in regular

and irregular waves, is in confirmation with what is

experienced by the prototype in open sea.

In general the vessel under consideration can be

assumed to react as a linear system as appears from

the model tests. Minor non-linearities may be present

but are not of a great importance for practical

pur-poses. The motions of the vessel in the vertical plane

are very moderate, which effectuates that the

under-side of the main deck is solely touched by waves in

relatively high seas. Under these circumstances the

deck amidships is more vulnerable to wave-slapping

than the deck fore. The effect of wave heading upon

the ship motions is such that the motions in bow seas

are generally equivalent to those in beam seas, except

evidently pitching.

Since the eventual object of this work was to

com-pare the motion response amplitude operators for

the actual ship and the model, it can be concluded

that a very good agreement is found.

References

GERRITSMA, J. and W. E. SMITH, Full scale destroyer motion measurements. Delft University of Technology. Report No. 142 of the Department of Shipbuilding, March f966. AERTSSEN, G., Service-performance and Seakeeping trials

on mv. Jordaens. Trans. RJ.N.A. 1966.

CANHAM, H. J. S., D. E. CARTWRIGHT. G. J. G0OnRICH and N. HOGBEN, Seakeeping Trials on O.W.S. Weather

Re-porter. Trans. R.I.N.A. 1962.

Holland Shipbuilding, Vol. 17, No. 12, February 1969,

pp. 54-61.

LAMMEREN, W. P. A. AN and G. VossEks, The Seakeeping

Laboratory of the Netherlands Ship Model Basin.

Inter-national Shipbuilding Progress, Vol. 4, 1957.

WALDEN, H. and J. PIEST, Vergleichmessungen des See-ganges. Deutscher Wetterdienst, Seewetteramt, Hamburg

1961.

K0RvIN-KRouKovsKY, B. V., Theory of Seakeeping.

S.N.A.M.E. 1961.

PIERsoN, W. J. and L. MosKowrrz, A proposed spectral

form for fully developed wind seas based on similarity

theory of S. A. Kitagarodskii. Journal of Geophysical

Research, Vol. 69, December 1964.

Proceedings of the International Ship Structures Congress 20-24 July 1964. Report of Committee No. 1 on environ-mental conditions.

ROLL, H. U., Die Grösse der Meereswellen in Abhängigkeit von der Windstärke. Deutscher Wetterdienst, Seewetteramt, Hamburg 1954.

DORRESTEIN, R., A wave recorder for use on a ship in the open sea. Proceedings Symposium on the behaviour of ships in a seaway, chapter 23, 7-10 September 1957, Wageningen, The Netherlands.

ABKOWITZ, M. A., L. A. VAssiLopouLos and F. H. SELLAR5, Recent Developments in Seakeeping Research and its Ap-plication to Design. Trans. S.N.A.M.E., Vol. 74, 1966, pp. 194-260.

14 a 1.6 12 08 04 o 1.2 0,8 04 0 04 08 W in rad sec'1 0.1 0.4 L/A

Fig. 3. Heave response amidships to head waves.

o 08

1.2 16

I t

12 15

Full scale sea trials

r'

04 0 01 08 W in rad 5ec1 0.4

Fig, 5. Pitch response to head waves.

i = I t i I i i I 08 12 16 1.6 12 08 04 a Regular waves , 1.00 rn

Regular waves, Ç=20Om

Regular waves . 400 m

Beaufort 1 98 m 75 sec

Beaufort 9 5.86 m T9.4 sec.

Full scale sea trials

0 01

a Regular waves, = 1.00 m

o--- Regular waves, 2.00 m

Regular waves . 4.00 rs Beaufort 5.,3=1 98m ,= 75sec. Beaufort 9, .,=586 m 94sec

\

1.6 £ Regular waves _____ Regular waves

.

Regular waves ,

-

Beaufort 5 Beaufort 9 i OUrs 2.00 m 400 m 198m, 5.86 m 7.5 sec ,, 94 sec 04 08 12 W ri rad sec

1111111 I

t I 04 0,8 1.2 16

Fig. 4. Heave response at 1.75 m aft of F.P. to head waves.

a s-n '-"J a a a 3.2 24 16 08 o o 04 08 1.2 16, a Regular waves = 1.00 m o Regular waves 2.00 re Regular waves 400 m Beaufort 1 98m ' 75 sec.

...._...Beaufort 9.,,3=586m.=94sec

16 -1C'J 'o 16 08 16 12 o o L Regular waves , 1 00m

o---- Regular waves 2.00 m

Regular waves . Ç=400 m

Beaufort 5 . WJ3 1 98m, = 75sec

Beaufort 9 586m f- 9.4 sec.

s Full scale sea trials

2.4

.\

a Regular waves , 1 00 m ___o____ Regular waves 200 m

Regular waves = 400 m

-

Beaufort 1.98m = 75 Beaufort 9, WV3=5.66 m ¶= 94 sec-.

:1?

04 08 W r rad sec1 a Regular waves - 1 00m Regular waves, =2.00m Regular waves, =400m Beaufort 5, ,13=1 98m,? 7.Ssec Beaufort 9, ,,3_586 m ¶= 9.4 sec

Full scale sea trials

o

-\

Fig. 8. _{Response of relative motion amidships to head Fig. 9. Response of relative motion at F.P. to head waves.} waves.

0 01 0.4 08 12 16

L/X

Fig. 7. Response of vertical acceleration at2.75m aft of F.P. to head waves.

(J) n rad sec

-o 01 04 08 12 16

Fig. 6. Response of vertical acceleration at 3 m aft of amidships to head waves.

04 0,8 1.2 6 W rc rad sec1 I I I 0 01 04 08 1.2 16 L/A 04 08 12 16 W n rad sec .1 0 0.1 0.4 0.8 1.2 1 6 L/x 12 16 12 08 04 0.8 'o ca a 04

16

12

O

-O---- Regular waves 2.00 m

Fig. IO. Heave response amidships to beam waves.

o---.- Regular waves Full scale sea trials

2.00 m

s

.

.

O

s

o---- Regular waves . w

Full scale sea trials

2.00 rit

s.

04 08 12 16 W nrad.sec I t t I 01 0,4 08 1.2 16 LIA

Fig. Il. Heave response at 1.75 m aft of F.P. to beam

waves. 04 08 1.2 1.6 W in rad sec o 04 08 1.2 16 W inrad 5ec1 o 0.1 04 08 12 16

Fig. 12. Roll response to beam waves.

I i i i I

¡iii

O 0.1 0.4 L/X 0.8 1.2 16 16 16 12 08 04 16 12 08 04 o o o 08 e -a e 04

32 2 08 16 12 08 o o o

o.---

Regular waves 2.00 m

Full scale sea trials

04 08

W irt rad 5ec

L/A

L/A

Fig.15. Response of relative motion amidships to beam waves. 0---- ReguLar waves 2.00 m 32 24 08 12 04 o 1.6

-0----

ReguLar waves m

/

04 08 1.2 16

W irr rad sec.1

r

I muni I

i ml

01 04 0.8 12 16

L/A

Fig. 16. Response of relative motion at F.P. to beam waves.

Fig. 13. Response of vertical acceleration at 3 m aft of Fig. 14. Response of vertical acceleration at2.75 m aft of

amidships to beam waves. F.P. to beam waves.

04 08 1.2 1.6

W irr rad sec1

01 04 08 12 1.6 o 01 04 0.8 1.2 1.6 1.2 1.6 1.6 o 0.4 08 12 W irr radsec

lint lin,!

01 0.4 08 1.2 1.6 L/A o (t '-n 04 08 ro o o o

18 1.6 1.2 O o W in rad sec.1 0.4 04 0.8 W 5 rad sec.1 08 12 16 L/X

Fig. 17. Heave response at 1.75 m aft of F.P. to bow waves.

Regular waves. 2.00 m

.

Full scale sea trials

o o s s . 1.2 16 16 12 o ¶'l o Regular waves

Full scale sea trials

200 rol s

.

s o o s s s s s o Regular waves,

Full scale sea trials 200m

o

O.

o O 04 0.6 1.2 16

Fig. 18. Pitch response to bow waves. Fig. 19. Roll response to bow waves.

o 04 08 1.2 i e, W n rad sec i t i t I r

il

0 0.1 o 01 04 0,8 12 16 o 01 04 08 12 16 06 t, lo 04 08 'n n e 04 08

o

0.4 o

ro (N 32 24 16 16 12 o o o s s

. s

3 5 7 Beaufort number 'o LO o 16 12 o

Fig. 22. Significant heave amidships and at 1.75 m aft of Fig. 23. Significant pitch in head seas. F.P. in head seas.

0.8 12 1.6

Fig. 21. Response of vertical acceleration at 2.75 m aft of

F.P. to bow waves.

o Regular waves,

Full scale sea trials 2 00m

5

o

.

.

s

.

.

s

.

Heave 1 Heave 2 Measured

Calculated from response to

regular waves . ., 200 m £ s

-o Regular waves =

.

Full scale sea tnals

2.00 r,, s s s 3 5, 9 Wave helgllt In m -J 3 5=. 7 9 Wave heIght n rn 7 g 11 12 Beaufort number 0 04 08 12 16 W n rad sec o 01 04 0.6 12 16 L/A

Fig. 20. Response of vertical acceteration at 3 m aft of

amidships to how waves.

o 04 0.8 W n rad secT o 0.1 04 L/X 12 16 9 11 12 5 V (o V

I

o 32 24 16 Measured

Calculated from response to

regular waves, 2.00 m

20 032 024 016 008 4, C, 4 o 16 12 4

ships and 2.75 m aft of F.P. in head seas.

Wave height in rn

the North Atlantic.

8 6 E 5e Sm Sm Cu o o E 2 u co u o 20_

Fig. 24. Significant vertical acceleration at 3 in aft of amid Fig. 25. Significant relative motion amidships and at F.P. in head seas.

3 4 5 6 7

Windforce Beaufort scale

Fig. 26. Theoretical Pierson-Moskowitz wave spectra for Fig. 27. Frequency of occurrence of wave conditions on the North Atlantic.

Acceleration 1

Acceleration 2

Measured

Calculated from response to regular waves .

_L=

2.00 m

-r

A A

p

--r

r

r

r

r

/ ii1

,A'

r--/

a,

/

/

9elative motion 1 L

---

elative motion 2 a Measured

Calculated from response to regular waves . 2.00 m Beaufort Beaufort 12 3 1.40 5.9

IA

5 215 65 7 375 78 9 620 90 11 840 10.0 12 925 105

Li

L'

3 7 9 3 5 7 Beaufort lumber 7 g wave height L113 in m 9 11 12 7 Beaufort number 3 5 9 11 12 o 0.4 0.8 bI n rad sec.1 1.2 1.6

048 16 12 04 o Measured 1.98m.=75sec

- Theoretical Pierson M0skOwtz) 2.15 m ' 65 sec

t \ 3 -M 6.4 48 Q) 3,2 E u, 1,6 Measured.,,, 5.86 m 94 sec

Theoretical I Pierson-Moskowitz ). ,,- 6.20 m 9Osec.

Head

Full scale wave spectra S6sec 60 sec 5.7 sec sea, sea sea , w113201 rs, 232 re . w13 2 24 rs -T Bow Beam

r

04 08 12 W n rad sec

Fig. 30. Full scale wave spectra on the North Sea.

04 08 12 16

W in radsec.

Fig. 28. Beaufort 5 wave spectrum measured in basin.

04 08 1.2 16

W n rad sec1

Fig. 29. Beaufort 9 wave spectrum measured in basin.

4)

032

E

3

PUBLICATIONS OF THE NETHERLANDS SHIP RESEARCH CENTRE TNO

PUBLISHED AFTER 1963 (LIST OF EARLIER PUBLICATIONS AVAILABLE ON REQUEST)

PRICE PER COPY DFL.

10,-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. Wereldsma,

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 Michell and V. A. Ogale,

1965.

64 C Barnacle fouling on aged anti-fouling paints; a survey of perti-nent 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. 1. 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 mode] 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. 11. B. Behaviour of a

24,000 DWT bulkcarrier 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. 1. 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 indus-try. 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, !966.

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 5 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 5 Computation of pitch and heave motions for arbitrary ship forms. W. E. Smith, 1967.

91 M Corrosion in exhaust driven turbochargers on marine diesel en-gines 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 of ships. H. J. Lageveen-van Kuijk, 1967.

94 C Optimum conditions for blast cleaning of steel plate. J. Remmelts,

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 S 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 S 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 ofsteel plate. Conclusion.

J. Remmelts, 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 mod.l.

J. H. Janssen, 1967.

105 M Marine diesel engine exhaust noise. Part H. 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 1. J. H. Vugts, 1968.

110 S Strain, stress and flexure of two corrugated and one plane bu1k

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.

ll2S 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.

115 S Cylinder motions in beam waves. J. H. Vugts, 1968.

116 M Torsional-axial vibrations of a ship's propulsion system. Part 1. Comparative investigation of calculated and measured

torsional-tanks. Part II. J. H. Vugts, 1969.

118 M Stern gear arrangement and electric power generation in ships propelled by controllable pitch propellers. C. Kapsenberg, 1968. 119 M Marine diesel engine exhaust noise. Part 1V. Transfer damping

data of 40 modelvariants of a compound resonatorsilencer. J. Buiten, M. J. A. M. de Regt and W. P. H. Hanen, 1968. 1 20 C Durability tests with prefabrication primers in use of steel plates.

A. M. van Londen and W. Mulder, 1969.

121 S Proposal for the testing of weld metal from the viewpoint of brittle fracture initiation. W. P. van den Blink and J. J. W.

Nibbering, 1968.

122 M The corrosion behaviour of cunifer 10 alloys in seawaterpiping-systems on board ship. Part 1. W. J. J. Goetzee and F. J. Kievits,

1968.

123 M Marine refrigeration engineering. Part III. Proposal for a specifi-cation of a marine refrigerating unit and test procedures. J. A. Knobbout and R. W. J. Kouffeld, 1968.

125 S A proposal on noise criteria for sea-going ships. J. Buiten, 1969. 126 S A proposal for standardized measurements and annoyance rating of simultaneous noise and vibration in ships. J. H. Janssen, 1969. 127 5 The braking of large vessels II. H. E. Jaeger in collaboration with

M. Jourdain, 1969.

128 M Guide for the calculation of heating capacity and heating coils for double bottom fuel oil tanks in dry cargo ships. D. J. van der Heeden, 1969.

129 M Residual fuel treatment on board ship. Part LII. A. de Mooy,

P. J. Brandenburg and G. G. van der Meulen, 1969.

130 M Marine diesel engine exhaust noise. Part V. Investigation of a double resonatorsilencer. J. Buiten, 1969.

131 S Model and full scale motions of a twin-hull vessel.

M. F. van Sluijs, 1969.

scarcely saponifiable vehicles (Dutch). A. M. van Londen and P. de Wolf, 1964.

12 C The pre-treatment of ship plates: The treatment of welded joints

prior to painting (Dutch). A. M. van Londen and W. Mulder,

1965.

13 C Corrosion, ship bottom paints (Dutch). H. C. Ekama, 1966.

14 S Human reaction to shipboard vibration, a study of existing

literature (Dutch). W. ten Cate, 1966.

15 M Refrigerated containerized transport (Dutch). J. A. Knobbout,

1967.

16 S Measures to prevent sound and vibration annoyance aboard a

seagoing passenger and carferry, fitted out with dieselengines (Dutch). J. Buiten, J. H. Janssen, H. F. Steenhoek and L. A. S. Hageman, 1968.

17 S Guide for the specification, testing and inspection of glass

reinforced polyester structures in shipbuilding (Dutch). G.

Hamm, 1968.

18 S An experimental simulator for the manoeuvring of surface ships. J. B. van den Brug and W. A. Wagenaar, 1969.

19 S The computer programmes system and the NALS language for numerical control for shipbuilding. H. le Grand, 1969.