Amidships forces and moments on a CB = 0.80 series 60 model in waves from various directions

REPORT No. 100 S

BibLiotheek vande

Ocde rafde Ii jderSch eipsbouwkund e

_Technische Hogeschool, DeIt

DCUM ENTA T lE

DATUM:

2--

ioo5

10 MEl 1U2

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT

*

AMIDSHIPS FORCES AND MOMENTS ON

A CB=0.80 "SERIES 60" MODEL

IN WAVES FROM VARIOUS DIRECTIONS

KRACHTEN EN MOMENTEN T.P.V. HET GROOTSPANT VAN

EEN ,,SERIES 60"-MODEL

MET EEN BLOKCOEFFICINT VAN 0,80

BIJ GOLVEN UIT VERSCHILLENDE RICHTINGEN)

by

IR. R. WAHAB

Netherlands Ship Model Basin

DOCU k(NT TE

2 2_t.tL_

November 1967

VOORWOORD

Behalve de nadruk die de laatste jaren is gelegd op het

onder-zoek van de scheepsbewegingcn, heeft ook het hiermede nauw verbonden gebied der sterkte van schepen in zeegang meer aandacht gekregen. De ontwikkeling van nieuwe scheepstypen, het steeds maar groter worden van het schip en de invoering van nieuwe laadsysternen, die een nieuwe constructiewijze met zich mede brachten, hebben bijge-dragen tot de vernieuwde belangstelling. Uit het oogpunt van de berekening der sterkte, werd het belangrijk in kwali-tatieve zin te weten, hoe groot de invloed was van bepaalde veranderingen voor de maximum grootte van momenten en krachten. Een ander vraagstuk is de bepaling van de kans die bestaat dat een bepaald berekend moment of een zekere kracht overschreden zal worden en onder welke voorwaar-den, welk probleern nauw aansluit bij het onderzoek be-treffende momenten en krachten optredende in

onregel-matige golven.

Het buitengewoon uitgebreid onderzoek van zowel de bewegingen van bet schip in zeegang [7] als de momenten in golven [8], welke kort na de ingebruikstelling van de zeegangstank van het Nederlandsch Scheepsbouwkundig

Proefstation te Wageningen door VossERs, SWAAN en RIJKEN werd volvoerd, heeft veel gegevens opgeleverd voor de

regel-matige golven. De voornaamste parameters die toen werden onderzocht, waren de verhouding der hoofdafmetingen, de vormcoèfficiënten en de snelheid in samenhang met bet gedrag van het schip zowel ten aanzien van bewegingen als van de uitgeoefende momenten en krachten.

Wat betreft het hier beschreven onderzoek, is aandacht besteed aan de bepaling van de momenten en krachten in meer golfiengten dan de vijf in het eerder aangehaald

onder-zoek. Omdat het duidelik was geworden dat onder

be-paalde condities de buigende momenten een maximum ver-tonen voor cen golfiengte ter grootte van ongeveer L, wer-den kortere golfiengten toegevoegd aan bet te onderzoeken gebied. Na bet controleren van de geldigheid van het super-positiebeginsel, werden de in regelmatige golven verkregen gegevens gebruikt orn de momenten en krachten te voor-spellen in onregelmatige golven.

Omdat het niet geheel duidelijk was in welke mate de voorspellingen over de grootte van de buigende momenten n onregelmatige langkarnmige gol ven geldig zijn voor kort-kammige onregelmatige golven, heeft ook deze kant der zaak aandacbt gekregen. Vergelijking van de uitkomsten toont aan dat de verschillen klein zijn zowel voor golven op de kop als voor achter oplopende golven.

Omdat de meetinstrumenten sinds de eerder aangehaalde proeven [7] en [8] geleidelijk aan verbeterd zijn, werd bet rnogelijk om nu behalve de momenten in vertikale en hori-zontale richting, ook de vertikale en horihori-zontale dwars-krachten te meten, benevens het torsiemoment. Deze uit-breiding van mogelijkheden kan van veci belang worden, omdat ten aanzien van de laatste drie grootheden erg weinig

bekend is.

De grote hoeveelbeid gegevens, die dit onderzoek heeft opgeleverd, kan voorts een goede basis zijn, voor nader on-derzoek b.v. op het gebied van slamming verschijnselen of t.a.v. bet overnemen van water.

HET NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

PREFACE

Besides the emphasis laid during the last years upon the in-vestigations in the field of ship's motions in a seaway, also

the allied aspect of the ship's strength in waves has got more and more attention. The development of new types of ships,

the ever growing ship's size and the introduction of new loading systems, involving new constructions, have contri-buted to the renewed interest. From the point of view of the strength-calculation it became important to know in

quali-tative sense, what influence certain modifications could have for the maximum of forces and moments. Another as-pect is the determination of the chance to surmount a certain calculated moment or force and under what conditions, which problem is coupled directly to the investigations con-cerning moments and forces as found in irregular waves.

The very extensive investigation in the sphere of both the ship's motions in a seaway [7] and the moments caused by

waves [8] undertaken by VossERs, SWAAN and RTJKEN soon

after the inauguration of the Seakeeping Laboratory of the Netherlands Ship Model Basin at Wageningen has given many data in regular waves. The main parameters

in-vestigated at that time were the ratios of the principal

dimensions, the hull coefficients and the speed in relation to the behaviour of the ship in respect of both motions and excited forces and moments.

For the matter of this investigation described here, atten-tion has been paid to the determinaatten-tion of the moments and forces in more than the five wavelengths tested in the earlier mentioned investigation. Because it has become clear that under certain circumstances the bending moments show a

maximum for wavelengths of approx. L, shorter

wave-lengths were admitted in the range to be investigated. After testing the validity of the superposition principle, the results obtained in regular waves, were used to predict the moments

and forces in irregular waves.

Because it is not quite clear to what extent the prognoses about the magnitude of the bending moments in irregular long-crested waves are sound for the short-crested waves, this aspect has got attention too. Comparison of the results shows that the differences in outcome are small, in the case of both head and following seas.

Since the tests described in [7] and [8], the instruments for measuring in waves have been gradually improved and now the bending moments horizontally and vertically but also the horizontal and vertical shear forces and the tor-sional moment can be measured. This extension of the pos-sibilities may be of much importance, since data available about these last three items are very rare.

The great quantity of data that this investigation has

delivered may be a good base for further research, for

instance in the field of slamming, or shipping water, etc. THE NETHERLANDS SHIP RESEARCH CENTRE TNO

Summary

i

Introduction

page

7 7

2

Particulars of the model and the equipment

8

2.1 Model 8

2.2 Weight distribution 8

2.3 Strain gauge balance 8

2.4 Model arrangement 9

3

Behaviour in regular waves

10

3.1 Experiments 10

3.2 Results 10

4 Behaviour in confused seas

il

4.1 The superposition principle li

4.2 Calculations 12

4.3 Results 12

5

Concluding remarks

12

6 References I3

LIST OF SYMBOLS

B breadth

CB block coefficient

CM midship section coefficient prismatic coefficient

Cw waterline coefficient Cvp vertical prismatic coefficient

D1 horizontal shear force amidships, amplitude

D. vertical shear force amidships, amplitude

f

centre of gravity from O.5L55

fA centre of gravity of afterbody from O.5L,

Ip

centre of gravity of forebody from O.5L

fhh wave spectral density

Fu = Froude number

VgL

g acceleration due to gravity

metacentric height

water surface elevation, amplitude

H draught

significant wave height, mean of the one third highest wave heights, trough to crest

'L longitudinal moment of inertia about centre of gravity, total hull

'Li

longitudinal moment of inertia about O.5L, afterbody

'LF longitudinal moment of inertia about O.5L. forebody

'r

transverse moment of inertia, total hull

'TA transverse moment of inertia. afterbody

'TF transverse moment of inertia, forebody

LDP (= L) length between perpendiculars

horizontal wave bending moment admidships, amplitude

M0,, vertical bending moment amidship at zero speed in still water

M5, torsional moment amidships, amplitude

M vertical bending moment amidships

M5 vertical wave bending moment amidships, amplitude

Mw,, average increment of M0,,, due to forward speed and waves

motion of the bow relative to the water surface, amplitude

f

mean wave period

V speed

a angle between velocity vector of the ship and the (main) direction of

advance of waves

A weight of ship

AA weight of afterbody

AF weight of forebody

phase angle between horizontal bending moment and waves phase angle between vertical bending moment and waves

A wave length

w circular frequency of the waves

pitch angle, amplitude mass density of water

angle between direction of advance of a wave component and the main direction of advance of the waves in a short-crested confused sea

AMIDSHIPS FORCES AND MOMENTS ON A CB = 0.80 "SERIES 60"

MODEL IN WAVES FROM VARIOUS DIRECTIONS

by

Ir. R. WAHAB

Summary

This paper presents the results of experiments on a "Series 60" model with a block coefficient of 0.80, in regular waves acting from 9 different directions, viz, from 10 to 170 degrees. Amidships, at 0.5L the vertical and horizontal bending mo-ments. the vertical and horizontal shear forces and the torsional moment were measured, together with the ship motions. The tests were carried Out at a speed corresponding to Fn = 0.15.

The results were used to predict the significant vertical and horizontal midship bending moments in long-crested and short-crested confused seas, for ship lengths between 190 and 400 m. In this case the main direction of advance of the sea was

varied from O to 180 degrees.

i

Introducticn

Soon after the Seakeeping Laboratory of the

Netherlands Ship Model Basin at Wageningen

was put into operation, the behaviour of a family

of "Series 60" hull forms was investigated in

waves from various dii'ections. The purpose of

that programme was to study the motions, the

propulsive performance and the

vertical and

lateral bending moments amidships. The results

were published in

[7]

and [8].

It has become clear that for a proper insight

into the behaviour of a ship, the response functions

have to be based on tests in more than the five

wave lengths reported in

[7]

and [8]. This is

par-ticularly the case for the bending moments in

relatively short oblique waves. In certain cases the

bending moment has a maximum at a wave length

of about 0.5L. Very long ships frequently

en-counter waves of about this length at sea. Since

the above mentioned tests with the "Series 60"

models, the instruments for the measurements in

waves have been gradually improved. The bending

moment dynamometer was completely redesigned.

It now enables the measurement of 5 components

of the loads working in a cross section of a ship

model, viz, the vertical and horizontal bending

moments, the vertical and lateral shear forces and

the torsional moment.

The above

considerations have led

to the

decision to retest more extensively a "Series 60"

hull form with the following particulars:

Block coefficient

CB = 0.80

Breadth-Draught ratio B/H = 2.5

Length-Breadth ratio

LIB =

7.0

An insight into the magnitude of the shear forces

and the torsional moment amidships is of interest

since literature on these aspects

is

poor. The

experiments were followed by some analytical

in-vestigations, the results of which are also included

in this report.

A comparison was made between the measured

and calculated vertical bending moments and

shear forces. This was done because the

deter-mination of the bending moment demands rather

extensive testing and a fairly accurate calculation

method should be of great help for practical

pur-poses.

Another point of interest is to what extent

long-crested irregular seas may be used to predict the

midship bending moments at sea. Therefore a

comparison was made between the calculated

significant bending moments in a long-crested and

in a short-crested irregular head sea, both with the

same significant wave height and mean period.

In order to obtain an insight into the importance

of the horizontal bending moments, the significant

value of the horizontal bending moment in a

short-crested bow sea is compared with the significant

vertical bending moment in the same

short-crested head sea for a number of ship lengths,

for which purpose the model values were scaled

up to four different ship lengths.

The above investigations have an exploratory

character. All results apply to one weight

distribu-tion and one speed only.

With regard to the prediction of the bending

moments in irregular seas the linear superposition

principle was assumed to be valid for bending

moments due to waves from different directions.

To justify this assumption additional experiments

were carried out.

8

2

Particulars of the model and the

equipment

2.1 Model

The length of the model used during the tests was

4.289 m, somewhat longer than commonly used

in the Seakeeping Laboratory. Because of the

relative importance of the bending moments in

short waves, the model length was chosen in such

a way that tests could be performed in waves,

having lengths down to

The model was made of wood. It was cut

trans-versely at the middle of the length between

per-pendiculars and rejoined by the strain gauge

balance as indicated in figure 1. The gap between

WAVE HE!GHT TRANSDUCER

the two halves of the model, 8 mm across, was

sealed with a flexible adhesive tape.

To stimulate the turbulence of the boundary

layer, the model was fitted with two rows of studs;

one row at 7 cm behind the bow contour, the

sec-ond at O.O5L

abaft the fore perpendicular. The

distance between two studs in one row was 2.5 cm.

The model was equipped with O.4L

long and

1.72 cm (= O.004L) high bilge keels. The lines

of the model are given in figure 2.

AP

GAP

5 COMPONENTS STRAN GAUGE BALANCE

Fig. i Longitudinal section of the model

Fig. 2 Lines of the ship model

2.2 Weight distribution

The weight distribution of the model is given in

table I. It corresponds approximately to actual

ship conditions and

is

similar

to

the weight

distribution simulated during the tests reported in

reference [8].

2.3 Strain gauge balance

A sketch of the strain gauge balance is given in

figure 3. It was calibrated in the model by

ap-plying known bending moments or shear forces

on the hull. in this way the influence of the

flexible tape was directly taken into account.

The calibrations showed a satisfactory linear

relation between the force or the moment and the

record.

In the ranges of interest the instrument is free

from interactions for nearly all the components

to be measured. Only the shear forces may be

affected by the bending moments. A small

hori-zontal shear force was measured when a purely

vertical bending moment was applied and a small

vertical shear force was measured when a purely

horizontal bending moment was applied. In the

relatively few cases that the shear forces were

small and the bending moments large, the

devia-tion between the measured and the actual shear

forces is estimated not to exceed IO per cent. The

values given in the diagrams are not corrected for,

since a sufficiently reliable correction could not be

performed. The natural frequency of the strain

gauge balance, when fitted in the floating model,

5

Jable I. Particulars of the model Principal dimensions

Length between perpendiculars Breadth

Draught (even keel) Displacement volume Length-Breadth ratio Breadth-Draught ratio Form coefficients

Block coefficient

Midship section coefficient

Vertical prismatic coefficient Prismatic coefficient afterbody

forehody

total hull Waterline coefficient afterbody

forebody total hull LCB location forward of 0.5L». Bilge keels Length Heigth

was about 6 cycles per second for the torsional,

vertical and horizontal bending vibrations, being

well above the frequency of encounter of the waves.

2.4 Model arrangement

The experiments were carried out in the

Sea-keeping Laboratory of the N.S.M.B., of which a

detailed description is given in [2].

Weight distribution coefficients Afterbody weight

Forebody weight Afterbody moment Forebody moment Total hull moment Afterbody longitudinal moment of inertia Forebody longitudinal moment of inertia

Total hull longitudinal radius

of gyration

Still water zero speed bending

moment (hogging)

Afterbody transverse radius

of gyration

Forebody transverse radius

of gyration

Total hull transverse radius

of gyration

Transverse metacentric height

The experiments were carried out with the

self-propelled model connected by a small,

light-weight, vertical rod in the centre of gravity of the

model to a low mass sub-carriage. No appreciable

forces or moments are applied on the model by

this arrangement; it

is only used as a motion

pick-up.

Since the model was completely free to move in

H

Fig. 3 Strain gauge balance

TORSIONAL MOMENT 0.442 4F14 0.558 fA 1AIL55.4

0.095

fF.iF/LvD.4

0.120 0.025 /ILA/LSß2.4 0.160

/ILF/L2 .4

0.180 '1L/1-5221 0.240 M55/L55.4 0.0034 \/ITA/B2.AA 0.325 VIITFIB2 4F 0.325

1T/B4

0.325 GM!B 0.05 A E E *

b

173mm L55 4.289 in B

0.613 m

H 0.245 m 0.5152 m3 LJ,,/B 7.0 B/H 2.5 C 0.80 CM 0.994 Cvp 0.920 CPA 0.750 CPF 0.861 Cp 0.805 CWA 0.860 CWF 0.881 C 0.871

f

0.025L0 0.4L 0.004L5

Io

all six degrees of freedom course keeping was

pro-vided by an auto-pilot. The yaw angle, the yaw

angular velocity and the sway motion are used

as an input to control the rudder angle. Since

athwartship forces occur in

oblique waves,

a

correction to the mean rudder angle is given

auto-matically to compensate for the tendency to drift.

Hence the model is kept approximately in the

middle of the tank during the test runs.

3

Behaviour in regular waves

3.1 Experiments

The most important quantity for the judgement

of the strength of ships is the amidship vertical

bending moment. The model was run in sufficient

wave lengths for a fairly accurate determination

of the vertical bending moment curve. The curve

of the horizontal bending moment shows a more

fluctuating character. An accurate determination

of this curve would lead to a testing programme,

being too extensive since the range of wave lengths

was wide, viz, between

= 0.3 and 2/L9

=

1.8.

Throughout the tests the wave height was kept

constant at 0.02

In waves of this height the

model never shipped water. Slamming was not

observed either. To restrict the extent of the

in-vestigations the tests were carried out only for

one speed corresponding to Fn = 0.15. The wave

directions were a = 10, 30, 50, 70, 90, 110, 130,

150 and 170 degrees. The wave direction a is

defined as the angle between the direction of

ad-vance of the ship and the direction of wave

prop-agation (see figure 4). In oblique waves the model

travels with a leeway angle, hence the angle

be-WAVE SPEED

SHIP SPEED

tween the longitudinal plane of symmetry of the

ship and the direction of advance of the waves will

differ slightly from the wave direction a as defined

before. During the

tests this

deviation never

exceeded 4- degrees.

It

is

felt that the application of the transfer

functions for the wave directions mentioned may

lead to a fairly accurate determination of the

ship's behaviour in short-crested irregular seas.

Finally

it is

remarked that the designation

"vertical" and "horizontal" moment or force

refer to body axes of the vessel and not to a set of

axes fixed in space.

3.2 Results

In general, the forces and moments of a ship in

regular waves show a cyclic variation round an

average value. The water surface elevation varies

as

li CO5 wt

The instantaneous value

of e.g.

the vertical

bending moment M can be written as follows:

M

M0+M,+M5 cos

(wt+eVh)

M0 represents the bending moment at zero speed

in smooth water. (Mo5+M5) is the average value

at forward speed and in waves. M is the amplitude

of the oscillating part of the bending moment.

Analogous expressions can be written for the other

measured quantities.

In certain cases

may be relatively

impor-tant, as can be seen from the experiments by

VossERs, SWAAN and RIJKEN

[8]. During the

present experiments

was small. For this

reason an accurate determination of its magnitude

was not quite possible.

The amplitudes of the oscillating part of the

measured quantities are given non-dimensionally

in the diagrams 1 through 8 (see Appendix). The

measurements show that the curves should have a

rather fluctuating character. Vertical bending

moment curves with the same fluctuating

char-acter were also found by investigators as e.g.

MOOR [4]. In some diagrams the curves have been

faired in a rather arbitrary way, since sufficient

measuring points were not available.

In the diagrams la, lb, 2a and 2b the points

measured by \TOSSERS, SWAAN and RIJKEN [8] are

also plotted. It appears that these measurements

are in good agreement with the present results.

The diagrams 9a, 9b, 10 a and lOb (see

Appen-dix) give a comparison between the experimentally

determined and the calculated vertical bending

moment and vertical shear force respectively. The

calculations were based on the strip-theory. The

applied equations of motion were those described

by JACOBS, DALZELL and LALANGAS [1]. The

damping and added mass were determined

ac-cording to TA5AI [10].

The calculations confirm the fluctuating

char-acter of the experimentally determined curves.

The magnitude of the calculated and measured

values of the vertical shear force deviates strongly

especially for the shorter wave lengths; that of the

vertical bending moment corresponds somewhat

better.

The accuracy of the torsional moment is

some-what less than that of the other measured

quan-tities since it was affected by the fluctuations in

the propeller torque.

The phase angles between the vertical and

horizontal bending moments could not be

deter-mined with fair accuracy in some cases and are

therefore omitted in the diagrams 3a and 3h.

4

Behaviour in confused seas

4.1 The superposition principie

To investigate the validity of the linear

super-TIME

Fig. 5 Sample of wave height record

Fable II Results of tests in two component wave patterns

position principle to the bending moments and

forces due to waves from different directions some

simple tests were performed in a wave pattern

consisting of two waves with the same frequency

but with different directions of advance. Wave

patterns of this type can be generated in the

Sea-keeping Laboratory rather easily by giving the

paddles of the wave generator the appropriate

phase differences. Measurements were made on

the model running in three different two

compo-nent wave patterns. The wave height of the wave

components was 0.02

A characteristic record

is given in fig. 5.

The measurements were analyzed into their two

harmonic components. The results given in table

II, generally conform well to the results obtained

in single waves, diagrams 1, 2, 4 and 5, except for

the horizontal shear force in very short waves.

The agreement found in the results of these two

types of tests cannot he considered to be a

con-clusive proof, but it does support the assumption

of the soundness of the principle of linear

super-position.

Wave length

Wave

frequency directionWave

Vertical bending moment

Horizontal

bending moment shear forceVertical

Horizontal shear force w g degrees M1 Dl

gBL2h

gBL021l _gBL,9h

_gLB/i

0.4 3.96 30 0.0039 0.0040 0.0148 0.0390 70 0.0129 0.0197 0.0304 0.0170 0.6 3.23 30 0.0125 0.0089 0.0346 0.0444 70 0.0127 0.0096 0.0182 0.0091 0.8 2.81 30 70 0.0196 0.0095 0.0087 0.0064 0.0285 0.01 14 0.0323 0.0091 0.4 3.96 110 0.0140 0.0242 0.0079 0.0382 150 0.0047 0.0029 0.0230 0.0289 0.6 3.23 110 0.0032 0.0138 0.0347 0.012 t 150 0.0161 0.0087 0.0378 0.0282 0.8 2.81 110 0.0100 0.0082 0.0207 0.0072 150 0.0173 0.0086 0.0392 0.0168

12

4.2 Calculations

From the results of the experiments in regular

waves the bending moments were calculated for the

ship proceeding in a short-crested and in a

long-crested head sea.

(see diagrams 12 and 13 of

appendix). Both sea conditions are assumed to

have the same mean period and wave height:

Mean period = 10 sec

Observed wave height = 8.4 m

These values represent a very severe sea and this

wave height is very seldom exceeded, as appears

from the observations collected in [il].

The spectrum of the long-crested irregular sea

is given by:

A.B

-fhh(o-) =

e W5 (m2sec)

where:

= spectral density

U) = wave frequency in rad sec'

This spectrum is similar in shape to the spectra

analyzed by PIERSON and MOSKOWITZ [6] for fully

developed seas.

Tri relating this spectrum to the observations, it

has been assumed that the observed wave height

corresponds to the significant height (mean of the

1/3 highest as measured from crest to trough) and

the observed period to the average period.

Observed wave height =

direction of advance of a wave component and the

main direction of advance of the waves.

The coefficients A and

B

are equal for the

long-and short-crested seas.

The significant value of the vertical bending

moment in the long-crested sea was calculated as

follows:

=

Vait/2

S? 2 / ₍ V

dw d1

(tm)

Oa+,i/2 i

In which expression a = angle between the main

direction of the waves and the velocity of the ship.

The significant values of the horizontal bending

moment M11, as given in diagram 13 were

cal-culated in an analogous way.

4.3 Results

No significant descrepancies have been ascertained

in the vertical wave bending moments in

short-and long-crested seas as is shown in diagram

12,

the differences being smallest for very long ships.

The vertical wave bending moment varies

strong-ly with the wave direction. The largest value is

found in head seas, differing only slightly,

how-ever, from the values found for following seas.

Diagram 13 indicates that the horizontal

bend-ing moment varies not so much with the wave

direction. The highest value is found in beam seas,

while in the case of regular beam waves on the

contrary the response is smallest.

Finally it can be derived from the diagrams 12

and 13 that the importance of the horizontal

bending moment increases with increasing ship

length. For a ship of 200 m length the significant

horizontal bending moment is only 46 per cent of

the significant vertical wave bending moment.

For a 400 m long ship this percentage increases

up to 69.

5

Concluding remarks

The most conspicuous aspect found from the

experiments and calculations is, that the

re-sponse curves of the vertical and horizontal

bending moments and of the shear forces have

a very fluctuating character. This implies that

for an accurate determination of these curves

very extensive testing is necessary.

The validity of the superposition principle has

MV1 =4

(tm)

For the short-crested sea:

Hi13 = 41 fho)dW

(m)

Mean period

fhh(W) . dw o

T=2rc

(sec)

/ wfhh(w).dW

o

Then the following relation exists between the

mean period, the significant wave

height and the

coefficients A and B:

A =

O.25(I-Ii )2

3 (m2)

B ==

(O.8l7.2r/j4

(sec-4)

The spectrum of the long-crested sea is given in

diagram 11 and that of the short-crested confused

sea has essentially the same

shape:

2AB

fhh(w,/i) =

e .cos2u (m2sec)

where,

<t< +

been proved several times, hut only for head

waves of various lengths. The reported

ex-periments indicate that this principle holds

also for waves acting from different directions.

This and the response curves given in the report

enable to predict the loads acting on the

in-estigated ship at sea. The results of such

cal-culations which are presented in the report have

only an exploratory character and lend

them-selves to extension.

.

Finally it is remarked that the strip theory may

be used with fair accuracy to predict the

vertical bending moments and shear forces in

head seas, which is the most severe condition

met by a ship. This may prove to be a

con-venient basis for further investigations into the

forces acting on a ship.

6

References

JAcoBs. W. R.,J. DALZELL and 1'. LALANGAS: Guide to

computation procedure for analytical evaluation of ship bending moments in regular waves. Davidson Laboratory, Stevens Institute of Technology, Re-port no. 791, October 1960.

LAMMEREN, W. P. A. VAN and G. VossERs: The

Sea-keeping Laboratory of the Netherlands Ship Model Basin. International Shipbuilding Progress, Vol. 4, 1957.

Lawis, E. V.: A study of midship bending moments in

irregular head seas, Journal of Ship Research, Vol. 1,

no. 1, ApriI 1957.

MOOR, D. I.: Longitudinal bending moments on models

in head seas. Trans. Royal Institution of Naval Ar-chitects, Vol. 108, 1966.

NUMATA, E.: Longitudinal bending and torsional mo-ments acting on a ship model at oblique headings to waves. Davidson Laboratory, Stevens Institute of Technology, Report no. 777, February 1960.

PIERSON, W. J. and L. MosKowlTz: A proposed spectral

form for fully developed wind seas based on

simil-arity theory of S.A.

Kitaigarodskii. Journal of Geophysical Research, Vol. 69, December 1964. Vossits, G., W. A. SWAAN and H. RIJKEN:

Experi-ments with "Series 60"-models in waves. Trans. Society of Naval Architects and Marine Engineers, 1960.

International Shipbuilding Progress, Vol. 8, No. 81, May 1961.

VOSSERS, G., W. A. SWAAN and H. RIJKEN: Vertical

and lateral bending moment measurements on

"Series 60"-models. International Shipbuilding Progress, Vol. 8, no. 83, July 1961.

ZUBALY, R. B. and E. V. LEwIs: Ship bending moments

in irregular seas predicted from model tests. Webb Institute of Naval Architecture, December 1963. TASAT, F.: On the damping force and added mass of

ships heaving and pitching. Report of the Research Institute for Applied Mechanics, Kyushu Univer-sity, Japan, Vol. VIII, 1960.

Report of Committee no. I on environmental condi-tions. Proceedings of the International Ship Struc-tures Congress, July 1964.

IO T n a 2 15 na IV 08 07 ØDDo

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Spectrum of the irregular long crested sea

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amplitude amplitude NO IDO 150 ZOO 200 H 0005 ODIO H 0005 O-DI O-Hl RE H 000

PUBLICATIONS OF THE NETHERLANDS SHIP RESEARCH CENTRE TNO

(FORMERLY THE NETHERLANDS RESEARCH CENTRE TNO FOR SHIPBUILDING AND NAVIGATION)

M = engineering department S = shipbuilding department

C = corrosion and antifouling department PRICE PER COPY DEL.

IO.-Reports

i s The determination of the natural frequencies of ship vibra-tions (Dutch). H. E. Jaeger. 1950.

3 S Practical possibilities of constructional applications of alu-minium alloys to ship construction. H. E. Jaeger, 1951. 4 S Corrugation of bottom shell plating in ships with all-welded

or partially welded bottoms (Dutch). H. E. Jaeger and H. A. Verbeek, 1951.

5 S Standard-recommendations for measured mile and endur-ance trials of sea-going ships (Dutch). J. W. Bonebakker, w. j. Muller and E. J. Diehi. 1952.

6 S Some tests on stayed and unstayed masts and a comparison of experimental results and calculated stresses (Dutch). A. Verduin and B. Burghgraef, 1952.

7 M Cylinder wear in marine diesel engines (Dutch). H. Visser, 1952.

8 M Analysis and testing of lubricating oils (Dutch) . R. N. M. A. Malotaux and.J. G. Smit, 1953.

9 S Stability experiments on models of Dutch and French stan-dardized lifeboats. H. E. Jaeger, J. W. Bonebakker and J. Pereboom, in collaboration with A. Audigé, 1952.

1 0 S On collecting ship service performance data and their analysis.

J. W. Bonebakker, 1953.

i i M The use of three-phase current for auxiliary purposes (Dutch). J. C. G. van Wijk, 1953.

12 M Noise and noise abatement in marine engine rooms (Dutch). Technisch-Physische Dienst TNO-TH, 1953.

13 M Investigation of cylinder wear in diesel engines by means of laboratory machines (Dutch). H. Visser, 1954.

14M The purification of heavy fuel oil for diesel engines (Dutch).

A. Bremer, 1953.

15 S Investigations of the stress distribution in corrugated bulk-heads with vertical troughs. H. E. Jaeger, B. Burghgraef and I. van der Ham, 1954.

16M Analysis and testing of lubricating oils II (Dutch). R. N. M. A. Malotaux and J. B. Zabel, 1956.

17 M The application of new physical methods in the examination

of lubricating oils.

R. N. M. A. Malotaux and

F. van

Zeggeren, 1957.

18 M Considerations on the application of three phase current on board ships for auxiliary purposes especially with regard to fault protection, with a survey of winch drives recently ap-plied on board of these ships and their influence on the gene-rating capacity (Dutch). J. C. G. van Wijk, 1957.

19 M Crankcase explosions (Dutch). J. H. Minkhorst, 1957. 20 S An analysis of the application of aluminium alloys in ships'

structures. Suggestions about the riveting between steel and aluminium alloy ships' structures. H. E. Jaeger, 1955. 21 S On stress calculations in helicoidal shells and propeller

blades. J. W. Cohen, 1955.

22 S Some flotes on the calculation of pitching and heaving in longitudinal waves. J. Gerritsma, 1955.

23 S Second series of stability experiments on models of lifeboats.

B. Burghgraef, 1956.

24 M Outside corrosion of and slagformation on tubes in oil-fired boilers (Dutch). W.J. Taat, 1957.

25 S Experimental determination of damping, added mass and added mass moment of inertia of a shipmodel. J. Gcrritsma, 1957.

26 M Noise measurements and noise reduction in ships. G. J. van Os and B. van Steenbrugge, 1957.

27 5 Initial metacentric height of small seagoing ships and the inaccuracy and unreliability of calculated curves of righting levers. J. W. Bonebakker, 1957.

28 M Influence of piston temperature on piston fouling and piston-ring wear in diesel engines using residual fuels. H. Visser, 1959.

29 M The influence of hysteresis on the value of the modulus of rigidity of steel. A. Hoppe and A. M. Hens, 1959.

30 5 An experimental analysis of shipmotions in longitudinal re-gular waves. J. Gerritsma, 1958.

31 M Model tests concerning damping coefficient and the increase in the moment of inertia due to entrained water of ship's propellers. N. J. Visser, 1960.

32 S The effect of a keel on the rolling characteristics of a ship. J. Gerritsma, 1959.

33 M The application of new physical methods in the examination of lubricating oils (Contin. of report 17 M). R. N. M. A. Malotaux and F. van Zeggeren, 1960.

34 S Acoustical principles in ship design. J. H. Janssen, 1959. 35 S Shipmotions in longitudinal waves. J. Gerritsma, 1960. 36 S Experimental determination of bending moments for thre

models of different fullness in regular waves. J. Ch. de I)oes 1960.

37 M Propeller excited vibratory forces in the shaft of a singl screw tanker. J. D. van Manen and R. Wereldsma, 1961 38 S Beamknees and other bracketed connections. H. E. Jaege

andJ.J. W. Nibbering, 1961.

39 M Crankshaft coupled free torsional-axial vibrations of a ship' propulsion system. D. van Dort and N. J. Visser, 1963. 40 S On the longitudinal reduction factor for the added mass s

vibrating ships with rectangular cross-section. W. P. Joosen andJ. A. Sparcnberg, 1961.

41 5 Stresses in flat propeller blade models determined by th moiré-method. F. K. Ligtenberg, 1962.

42 S Application of modern digital computers in naval-archites turc. H. J. Zunderdorp, 1962.

43 C Raft trials and ships' trials with some underwater pai systems. P. de Wolfand A. M. van Londen, 1962. 44 S Some acoustical properties of ships with respect to nois

control. Part I. J. H. Janssen, 1962.

45 S Some acoustical properties of ships with respect to nois control. Part II. J. H. Janssen, 1962.

46 C An investigation into the influence of the method of applic tion on the behaviour of anti-corrosive paint systems in se water. A. M. van Londen, 1962.

47 C Results of an inquiry into the condition of ships' hulls i

relation to fouling and corrosion. H. C. Ekama, A. M. va Londen and P. de Wolf, 1962.

48 C Investigations into the use of the wheel-abrator for removiil rust and millscale from shipbuilding steel (Dutch). interi report. J. Remmelts and L. D. B. van den Burg, 1962. 49 S Distribution of damping and added mass along the length

a shipmodel. J. Gerritsma and W. Beukelman, 1963. 50 S The influence of a bulbous bow on the motions and the pri

pulsion in longitudinal waves. J. Gerritsma and W. Beuke man, 1963.

51 M Stress measurements on a propeller blade of a 42,000 t. tanker on full scale. R. Wereldsma, 1964.

52 C Comparative investigations on the surface preparation shipbuilding steel by using wheel-abrators and the applicati. of shop-coats. H. C. Ekama, A. M. van Londen and J. Re

melts, 1963.

53 S The braking of large vessels. H. E. Jaeger, 1963.

54 C A study of ship bottom paints in particular pertaining to tl behaviour and action of anti-fouling paints. A. M. van Lo den, 1963.

55 S Fatigue of ship structures. J. J. W. Nibbering, 1963. 56 C The possibilities of exposure of anti-fouling paints in Curaça

Dutch Lesser Antilles. P. dc Wolf and M. Meuter-Schrii 1963.

57 M Determination of the dynamic properties and propeller e cited vibrations of a special ship stern arrangement. R. W

reldsma, 1964.

58 S Numerical calculation of vertical hull vibrations of ships i discretizing the vibration system. J. de Vries, 1964. 59 M Controllable pitch propellers, their suitability and econo

for large sea-going ships propelled by conventional, directl coupled engines. C. Kapsenberg, 1964.

60 S Natural frequencies of free vertical ship vibrations. C. Vreugdenhil, 1964.

61 S The distribution of the hydrodynamic forces on a heaving ax and pitching shipmodel in still water. J. Gerritsrna and

Beukelman, 1964.

62 C The mode of action of anti-fouling paints: Interaction tween anti-fouling paints and sea water. A. M. van Lond-1964.

63 M Corrosion in exhaust driven turbochargers on marine dic engines using heavy fuels. R. W. Stuart Mitchell and V.

Ogale, 1965.

64 C Barnacle fouling on aged anti-fouling paints; a survey pertinent literature and some recent observations. P. de W.

1964.

65 S The lateral damping and added mass of a horizontally os. lating shipmodel. G. van Leeuwen, 1964.

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

68 M Guide to the application ofMethod 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. lIB. 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 bulk-head. H. E. Jaeger and P. A. van Katwijk, 1965.

74 S Research on bulbous bow ships. Part. l.A. Still water inves-tigations 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 l.B. The behaviour of a fast cargo liner with a conventional and with a bulbous bow in a seaway. R. Wahab. 1965.

77 M Comparative shipboard measurements of surface tempera-tures and surface corrosion in air cooled and water cooled turbine outlet casings of exhaust driven marine diesel engine turbochargers. R. W. Stuart Mitchell and V.A. Ogale. 1965. 8 M Stem tube vibration measurements of a cargo ship with

special afterbodv. R. Wereldsma 1965.

9 C The pre-treatment of ship plates: A comparative investiga-tion on some pre-treatment methods in use in the shipbuild-ing industry. A. M. van Londen. 1965.

0 C The pre-treatment of ship plates: A practical investigation into the influence of different working procedures in

over-coat ing zinc rich epoxy-resin based pre-construction primers.

A. M. van Londen and W. Mulder, 1965.

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

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

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

4 S Behaviour of a ship in a seaway. J. Gerritsma, 1966. :5 S Brittle fracture of full scale structures damaged by fatigue.

J. J. W. Nibbering, J. van Lint and R. T. van Lecuwen, 1966.

6 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.

7 S Model experiments on sound transmission from engineroom to accommodation in motorships. J. H. Janssen, 1966. 8 S Pitch and heave with fixed and controlled bow fins. J. H.

Vugts, 1966.

9 S Estimation of the natural frequencies of a ship's double bottom by means of a sandwich theory. S. Hylarides, 1967. W S Computation of pitch and heave motions for arbitrary ship

forms. W. E. Smith, 1967.

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.

2 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.

Remmelts. 1967.

95 M Residual fuel treatment on board ship. Part I. The effect

of centrifuging, filtering and homogenizing on the unsolubles

ini 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. Beukelman, 1967.

97 S On the efficacy of two different Roll-damping tanks. J.

Boots-ma and J. J. van den Bosch, 1967.

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

99 5 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 of steel plate.

Conclu-sion.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.

104 M Marine diesel engine exhaust noise. Part I. A mathematical model. J. H. Janssen, 1967.

Communications

1 M Report on the use of heavy fuel oil in the tanker "Auricula" of the Anglo-Saxon Petroleum Company (Dutch). 1950.

2 S Ship speeds over the measured mile (Dutch). W. H. C. E.

Rösingh, 1951.

3 S On voyage logs of sea-going ships and their analysis (Dutch).

J. W. Bonebakker andJ. Gerritsma, 1952.

4 S Analysis of model experiments, trial and service performance

data of a single-screw tanker. J. W. Bonebakker, 1954.

5 S Determination of the dimensions of panels subjected to

water pressure only or to a combination of water pressure and edge compression (Dutch). H. E. Jaeger, 1954.

6 5 Approximative calculation of the effect of free surfaces on transverse stability (Dutch). L. P. Herfst, 1956.

7 S On the calculation of stresses in a stayed mast. B.

Burgh-graef, 1956.

8 S Simply supported rectangular plates subjected to the

com-bined action of a uniformly distributed lateral load and

compressive forces in the middle plane. B. Burghgraef, 1958.

9 C Review of the investigations into the prevention of corrosion and fouling of ships' hulls (Dutch). H. C. Ekama, 1962.

10 S/M Condensed report of a design study for a 53,000 DWT-class

nuclear powered tanker. Dutch International Team (D.I.T.) directed by A. M. Fabery deJonge, 1963.

11 C Investigations into the use of some shipbottom paints, based

on scarcely saponifiable vehicles (Dutch). A. M. van Londen

and P. de Wolf. 1964.

12 C The pm-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. Knob-bout, 1967.