The influence of a bulbous bow on the motions and the propulsion in longitudinal waves

&

_20

The Influence of a Bulbous Bow on th. and

the

ga

ulenngu"nal Waves.

B Pro.ir

J1 G.rr1tima end W. 1.uk.lasn.

!h;vbui]4jnt LsborstQp,

Teobomioa] Uiversiy

Delft.

January 19g.

Tb. propulsion and the motion. of two ebipsodels were measured in longitudinal regular bead wavs. Tb. first model is a parent

form of the B.ziss 8ixty and baa a block coffioi.nt 0.65.

The other model his the sass aftsrbody and block coitfioit but is

fitted with a 10% bulbous bow and a

correspondingly modified

en-trano e,

The eperim.fltal results in regular Waves wire used to predict the b.haviour in irregular waves. It is shown that the influence of the bulbou. bow on the motion. in longitudinal irregular waves is small. The increase in power, due to th. see waves is larger for the bulbous bow model

1. ntr91aotion,

tth regard to the general increase of speed of normal cargo

ship.,

shipowners sometimes consider th. use of a bulbous bow 'to take edvantag. of th. possibl, reduction ef wave resistance in still water, The bulbous bow is certainly not a new approach to th. resis-tance problem of a ship. In tact, many publications, which bgan to appear many years ego, discuss th. subject.

Well-known investigations on the merit, of th. bulbous bow were carried out by Taylor, lrsgg, Iggart, *1glsy, Weinbium and others. A reviaw presenting moss of their result. In a suitable way forrdemign work mae given by Lindblad [1]

-

.2-It was proved that for higher speed. -say )) 0.2k. a correot 17 constructed bulb can reduas the still water resistance. Th. beet results, how.,.r,-aocording to Lindblad.. will be obtained in the

sp..d rang. from - 0.30 to - 0.k2. Isp.oislly on over-driven

ship. a good r.eul.t say be expected from a bulbous bow.

Tb. improvement will be partly due to th. if feet of the pres-sure reduotios øauaed by the bulb in the region of th. bow wave. Aløo the reduction of the angle of entrance of the waterlines, as

coapar'ed with a conventional design of the ease main dimensions, can be advantageous in some cases. Douat [2] antions the faot that the reduction of th. total resistance seldom exceed. 4% when

F <0.30. For a trawler with a 5% bulb he found a 5% to 7$

reduc-tion in P in the speed range ?, 0.27 to - 0.32 when compared

with a corresponding conventional form. Du. to an increased propul-. liv. efficiency th. total reduction in power for' this particular model amounted from 10% to i%.

In the last few years Japan... investigators drew

the

atten. tion to th. usi of rather progressive bulbous bow constructions.

In this respect the work of Inui is very noteworthy. On. of the

examples in (3] is a ship form whiob has the same main particulars as model nr. N k2kO of the D.TM.B. Sixty Series (03 . 0.60). A 20% bulb is fitted and the EHP prediction for a 600 feet ship,

using model test results, showed that at the design speed _Fi.0.28_

an EEP reduction of th. order of 22% could be

obtained in

comparts

with the Sixty Series model. The effect of large bulb. is clearly shown by phot.grapha or .t.r'.ophotograph. of the wave formations f running ship models [3, k) . A notable decrease of surface el.-vation is obtained and in this respiot Japanese authors frequently us.

the

expressien "waveless bow".

A full-scale application of the "wave-less bow" priaeile was carried out with the high-speed passenger ship "iusnai )Jaru"a The bulb in this case has a maximum or.s.-s.etiea which is 17% of

the ship's

main section. In camparison

with

a conventional

sister

ship whiob has a 5% bulb, the "lurutat )4aru" needs 13% lea.

shaft-ivri.powerat t 033, the de.in epeed

[51.

Very large bulbs

on destroyer ship toras were investigated by Takezawa tb.

give an optLmum

solution and resulted in a 7% EP reduction. So*e at the bulbous bow research concerned the influence of

th. bulb on the ship motions in waves Dillon anti Lewis

_17]

ri.d out wive modal teats to inveetigat. the influence of bulb ate. on ship motions. Jour models of a passenger liner ware tested, with

bulb size. 0,

4%, 9%

and 131%. This wide variation in bulb *ii.

was found to have rather a small effect on the ship motions

and on

the resistance in waves. It was concluded that the abeto. of a

fsily larg. bulb can b. mad. on the

baeie

t calm water restBtancL

Tb. trawler model teate by Doust 12) indioat.& that the sps.A

loss in waves isleas for the bulbous bow form forJ> 0.22.

8,low this speed the speed loss is JArg.r than that of the oonven-tional tori. Depending on wave length ratio and speed the motions of the trawler in regular head waves are larger or less than for the ship wititout a

A useful approach in judgitg the performance in waYCs can be made by using regular wave test results for th. prediction of

aigni-fiàsnt motion amplitudes and the

mean

ncreaae of resistance,

thrust nd power in irregular

WaYCS [81

Takezawe ['9) used a similar method to investigate the p.rfor-manee of the destroyer model already mentioned with a 26% bulb. Neuam.nn spectra wez. used to defin, the sea. state. Zn comparison with the conventional form there is a fairly large reduction of the significant pitch amplitude, both in Moderate and. in high ass.. No data ott heave are given

itt

Take*w'i paper. A r.duoUon of the

significant bow acceleration is only attained at high speed and abort waves. The thrust increase

itt

wave. is slightly larger 'than for the convsntionei. hull and this is due to a larder resistance increase in way.. and due to a reduction cl the propulsive effi oi.noy' in waves which, following Takesawa, is csueed by a decrease of th. moan immersion of the propeller.

The total J8? in irregular waves is slightly lees or nsrly

equal to that of the conventional bull, except for var

)tigb waves

F4-In this paper

the performance, with regard to motione and

pro-pulaion in longitudinal ir'regular waves, of a

0.65 Seriea

sixty hull, will be compared with the performanøe of a modification

of this hull which has a 10% bulb and a correspondingly Eodifid

forebody. The construction of the bulb fora has been done according to the data in [1)

)'z'o the for.going t will be clear that for the uival service

speed F 0,24 of a 0.65 hull a conventional bulbuue bow will

only giv, a email inproveaerxt in the etifl water reaistanoe. The recent Japanese approach to new bulb forms was not known to the

authors when the modified S1xtr Series bull form was designed.

The main object of this paper, however, is to study'

the inflenoe

of the

bulb on

the performance in waves and the almost equal

chax'ao-teristic. in, still water could therefore be accepted. TABLE 1.

p1ode3. atioU]pis.

Ben.. 8ixty Modificatkn

Length

between perpendiculars.

2.26

a

2.26 a

Length on the waterline.

2.30 m

2.30 a

Breadth. 0.311

a

O.311 ii

Depth.

0.194 m

019k a

Draught .

-

0.125 a

a

Volume of displacement.

o . 057Oa

0,O57m3

8leck.'øotftoisnt.

O.6o

04650

Prismatic cofficjent. 0.661 0

0.661

Waterplane coifticteztt.

004 746

_0.733

Coffioient of midlength section.

0.982

0.982

Half angle of entrance,

9,'

40

_7,

lOB 0.30% 0,44%

Longitudinal radius of inertia. _{0.25 LBP} 0.25 Lap

Waterplane area,

)ioazent of inertia of waterplane area.

0,524 a2

0.142

a4

0.515 a

0.134

a4

Centre ofeffert of

waterplen. aft.+ Ia

2 _63%

_3.38%

Bulb are

in percent of ii&iip area

0%

Ltz-on-

pp.i1er diameter.

_8.73cm

Pitch ratio.

w

2. 5he mod&.

In table I the main particulars of the two ship modol are

givin. A bad)' plan Coy each of the two

bull forms is given in

figur. 1, Both models were mad. of polyeeter, reinforced with glees fibre.

U

3. 'rest proa)m..

The fsl.lowing tests were carried out with both ship models: A progressive propulsion test in still water &t the sIlf-propul

ion point of the model.

Propulsion and motion teats in regular

longitudilta]. head waves.

These tests ware carried out with a constant wave height of

Six wava lengths were used, corresponding to

A-IL

0.6, o.8,

1.0, i., 1.4, and 1.6. Pitching and heaving motions, the phase

angles with regard to the waves and the

vertical .ovstszations at

0.131. frost the forward perpendicular were d.tewml.ned in the speed

range from 0.13 to F 0.30. Xn addition, the mean Values of

model speed, thrust md torque were m.aaur.d at constant revolutioM of the propeller.

Yinallj a visual, estimation waS made of the shipment of water across the bow by' using a high speed film camera.

4. Test results.

The results of the taste in still water and in regular waves

are given in the figures 2 and 3. Figure aa represents the

dimen-sionlase amplitude, of heave and

pitch as a function of speed and

wave length, wh.re

tob alitj4e_

CC maximum wave siope

bts ilitud

Tha phase ang2ea 2P (figure 2a),

and trz (figure 2b) are

defined in the following way:

P OO$)t

wave levation at the oroee'.e.ctio

through the centre of gravity.

W

W0001(t).t 4

- the pitching motion (bow up is

posi-ttvs).

S

z Coe(C

t

₊

the heaving motion (positive upward).

1#rq)

£

The acceleration asRpltu4e at O.155L from the forward porpen

dicu3er is given as

, where g is the ao.iaratien due to gravity.

The values for

are valid for the

wave height.

The natural priv

for heave and pitch were d.t.rstned by

dicay-teata mu a function of the jiod.l speed. There is a very small

v*riation with speed and this results in average values whi'oh are

summarized in Table

.

TABLE 2..

atqrai keriodu f

.ave1 and ,pitchtjtee,cond.

Resonance condition. for heave a6 pitch are indtoated by

I and Ap

I (i.e figure

a).

The wetness of the bow region of the models was studied with

the aid of high speed films. Three degrees of wetness were dafined

according to the ct.thod used by Newton 110), namely:

very wet

green seas break across the teok at any position

along the forecastle.

wet - height of wave formation at th. bow resohei higher than

the forecastle deck at any poeition in its length, but

with-dry - height of wave for*atton at tbe bow is below the eviI

of f*reoaetle.

-7,.

heave

_itob

No bulb

10% bulb

0.87,

0.947

Q9O

.1

-In

ab3.. 3 the three d.gree of wetnees are given ue a tuna.

tion of speed and wave length.

ABE 3.

f.11'

ritjg

ie!4 and wave 1SMt.h.

Vav. h.iht

4..

Od17

xw*t

cx

.ry wet.

The propulsive obarsoteriettos in still water arid in regular

wav-ae tot both models are rihown in figur. 3. In this figure the

mean values for apud, thrust, torqu. arid revolutione are plotted.

oonstant propeller revolutions at

the self-propulsion point oS the

odiI

Nobuib.

0.225

0.250

0.275

¶0% bulb.

Oi5O

0175

O200

₀₂₂₅

_025O

_0.275

1O

1,2

1,6

0

J

0

0

0

x

xx

0

x

xx

x

xx

xx

x

xx

*

0

0

0

0

0

o

o

0

5. 4a].sie of the reeult.

bow has some For the speed range

with the

from

X/L =

0.8 to quite cubstantial and

heaving motion on

is shown by the 1,2 a reduction is

at 1. For larger

motion. The result angles on wetness,

this wetness analysi8 differences between

of both models by Neumann apectra full scale sea conditions,

listed in Table k, bow model. influence on the

under oonside'

original model

X/L

= attains values the other hand

acceleration am-found for the

waves there of the

differen-as shown in is very the two models

in irregu.-were oompa.

which

k.

5.1.

he motions

n weg,

Figure a shows pitching and heaving ration pitching is

for wave length ratios In come oases the reduction of the order of 25%

is larger for the bulbous The difference

plitudee at O,1L.

bulbous bow form, is a slight increase ces in motion amplitudes Table 3 is hardly

qualitative

in

nature, can be detected.

'inally the mean ].ar longcrested head

red. The

main particulars were ueed for this

Sea stat.particu1ara

that the bulbous aap].itudee. reduced in comparison vaz'yirig is to 30%. The in bow motion For

X/L

particularly of the bow and phase

visible. Although

no major

motion amplitudes

waves, defined of the comparison are

PAL

çfullj developed seas).

'uU scale values.

Beaufort number,

Windspeed

*eters per second

Significant

wave height

meter.

Period of maz.

energy of spectrum

3econdl. Significant range of periods seconds.

5

6.

7

9.8

13.L,

14

a,i

'*.6

6.7.

7,7

10.5

11

2.8.-lo.6

k10-lk.5

11..716.7

.,9.

$

The dimenajo]ess tx'anefr; fanctiona and for' heave and

pitch are gjvsn in figure 14 _{uan squared values for' the heave}

and pitch amplitudes follow tore the following relations:

2

JOrJ.)

2

((&.)

fo,..(&).)

)e) dCe)

In these Sorulae2 G

corresponds to the Neumann spectrum viz:

4*

2g/UCJ2

20

a eeo.

whersi

C.) circular frequency

U windspe.d in meters per s.cod.

8 acceleration of gravity,

The means of the on-tbird highest values are ueSd to conpara the

motions of the two ship forms Th follow from:

*

a%J and

A ship length of 400 fs.t Was chosen or the full-cale coinpar

son. Th the figure the significant amplitudes for heave and pitch

are given as & function of the ship speed and the significant wave height. It is shown that the bulboue bow ha. a smaller pitching motion.

(0.2-o.k degrees), but heaving is increased in comparison

with the

parent modol (0,06"0,2k retez'e)1

AC the differences are .htt large,tt any be concluded that the chip *otion. in longitudina] waves are not very much influenced by the bulbous bow. The &tme holds for the wetneSs

characteristics,

as is ehon in Table 3. It is admitted that the wetness analysis i of a qualitative nature, but

there is as strong indication that the

bulbous bow ha. bettar' qualities than th. parent mod.l.

'4tf the radiu. of inertia have the same valø for

both model., the naturat

uidomatnty depend-on tha are&adth.

*oment of insrtia

of the watirplane

on tb. on. band and on the

10

-hydrodyn.iiiio mass and *oaent of inertia on the

other band. Using the

data of the T*bl.a I and 2 it is easily shown that the hydrodynamio male and moment of inertia have approximately th. ears values for both models at their natural period..

£ detailed analysis of the differ.noss in action amplitudes can only be aads by using forced osoiU.ation technique and by measuring the exciting force. and moments in waves. Buch an elabo-rat. kLlysis was not undertaken, since th. overail .ff.ot of the bulb on the actions appeared to be omall.

5.2. The roulev Dfornoe in wpss.

A power estimation in longitudinal longcr.sted head waves was

mad. for both modeli, in which the method given in reference _Ca)

was usd. In principle the resistance increas, due to th. seaway is a function of the motion aaplita4.s and the phases of the sotiom

with regard to the waves. aoh of these quantati.s ii influenced

by th. bulbous bow, a. can be seen in th. figur.e 2a and 2b, and some influence in waves could be expected.

The performanc. in regular

waves is the basis for the power

estimation in

irregular

waves. Figure 6 gives the dimensionless

transfer functions of the mean increase, of thrust, power, torque and revolutions, yjas

iç

p

_gr232/L.V

'

V

andi

a

Tb. scan iasr.ase of power

in a

particular way, spectrum G

folloWl frsa:

2J G(c)-(j) d,

where is the wave amplitude. Similar expressions arc valid for

thrüit.., -torqu. and rvolutio Increase.

-1he power increases for a IOO ft. ship were calculmt*d for the

see conditions given in

'abl. II. They us plotted on the basis of

ship speed in figure 7. It is shown that the power increas, is

lar-ger for the ship form with th. bulbous bow. £ similar picture holdi for the inoz'e*s.s of torque and revolutions, There is a r.lative ass].]. difference in thrust inoresse. ?or sp.eds smaller than

* 0.20 the buibsus bow is slightly better but for higher speed. the thrust inoreae., is higher than for the parent model. Tar speeds

higher than 0.2k the bulbous bow sod.]. needs about 3% lees

power in still water than the parent modal; below this speed the parent model is slightly batter.

For th. present purpose, vim, the comparison of the power in

waves, these differences are negl.ated'and an equal performance in

still water is assumed. An eatimati*n

f th. still water power was

made by using the dat* in [i 1]. ly adding the power increases in WaveS a comparison of the total power oould bC mad. for both modela

a.. figure 8. it is shown that the bulbous bow

8bip

eds more p'

to maintain a certain speed.

In terms of speed loss, assuming for instance a constant

maxi-sum owar of 600 hp, the xtr speed loss in 2.1 meter waves is

negligible, in 4.6 meter waves th. speed be, is about .3 knots

larger for the bulbous bow and in 6.7 meter waves the difference is about 0,6 knots.

0

It is quite certain, however, that th. ship will reduce power

tn 6,7 a head waves and therefore thi. condition

may net be signi*

ticsnt for the comparison. Also th. various assumptions which have been. usda fox' this analysis say be quenstionable in such rather

extreme cniitione

(significant wave height/ship length *

Based on average weather conditions th. differenc. in propulsive performance between the two ship forms will be very small. A]]. that can be said for this particular case i. that the bulbous bow does not have superior us].itiea in a seaway. Thi. result may seem sur pricing because of the smaller pitching vaotion.

whob were found for

th bulbous bow modøl. It has to b. remarked, however, that the

change

on the phase of the motions can result in a reduotVon of the

propulsC!rid]enco- uobreduotion. wa

found by Takimawa

This could be a posibl. explanation for the larger pow.r lniziai.

of the bulbous bow htp.

- 12 *

EflENCES.

N

Lindblad, A.

Expsrients with bulbous bow..

Publication of the Swedish stats 8hipbuilding Experimental Thc

Gtsborg 19½k.

[a]

Douat, DJ.

Trawler forM with bulboue bowe.

Tubing boats of tb. world

2.

London 190.

['1

Xnui, T4

Wave..asking resistance rf shipe.

Transactione of the Society of Naval Architects and Marine

Engineers.

1962,

[i1

Takahet, T. and Xnui, T.

The ways*oanuefljng .ff.cts of wavleee bulb on the high speed

passenger coaster a... "Kurenai Maria", Part III

Pbotograiias.

trioal oba*rv*ttone of abip

waves.

Journal of the Society of Naval Architats of Japan, Vel, 110.

1961.

[5] Shig.mitstt,

t. and )Cai,

.

The wa'vs..oanc.11ing effect. of wavel.as bulb on th. high speed

passenger coaster a.s. 'Kurenai Naria", Part XI - The full-seals

eZp.zis.4t.

Journal of the floci.ty of Naval Arcbitáote of Japan, Vol. 110.

1961.

t6J Takesawa, S.

A study on the large bulbous bow of a

high speed

displacement

ship, Part X - R.si.tsnce in still water.

Journal of the Society of Naval Arehitoots of Japan, Vo3.. 110.

1961..

E ,V.

Ships with butbotu,

T;hsandaveaaL

Transection, of. The $peiety of Naval Architicte end Marine

- 13

Osrritaaa, J. flosoh, J.. van den and 8eukalsan, W.

Propulsion in. regular and irregular waves.

International Shipbuilding Progress.

1961,

Takesaw.,S..

A study on the large bulbous bow of a high epsed displaøø*nt

ship, Part tI

Perforsanas in waves.

Journal of ih. Sociity of Naval Architects of Japan, Vol. 111.

1962.

Newton, R.N.

Wetness related to freeboard and flail,

Thsns*otiea of the Xn.titution of Ncv*l Arohiteot5.

I p59.

Todd, P.R. and Pi.n, P.C.

3srise 60

Thl effect upon resistance and power of variatiozi in

L.C.1. positio*.

Transactions of the Society of Naval Architects and Menus

Enginears.

LIST QF 8iBOLS.

axiatua wave slopø.

it, ii.

tuning tutor for pitch.

- tuning factor for

h.ay.

ph aug10 between wave *rtd pitch.

£

- phase angle between wave and heave.

phase angle between pitch and heave - wave length.

- d.nsiti at water.

W

pitch angle.

pitch amplitude.

aignificaut pitch amplitude. circular tr.uency.

= circular fz.queno of encounter.

a aco.lu'ation amplitude.

B breadth of ship or model.

bloek.00iffici.nt.

D propeller diameter.

EMP = ff.otIvs horsepower.

wave spectrum

acceleration due to gravit7. aignificant wave height.

L length between perpendiculars.

LCB centre of buoanoy.

n propeller revolutions per second.

P = power, Q torq)l.. r wave amplitude, T = thrust. V model speed. V5

ship speed.

a w heave. heave amplitude.

o 1/3 significant heave amplitude.

Tn

= Troude

number,

iflC?iaI Of

rvoluttons.

= increase of power.

-1-'4 increase of torque. increase of thrust. - dia.n.ionl.0 inorease - dta.nsionl..s increase -

4iae*sionl..s increase

- dia.nuionlas increase

- 15

of revolutions. of power.

of torque.

of thrust.

REPORT No. SOS

April 1963

(S2/44b)

STUDIECENTRUM T.N.O. VOOR SCHEEPSBOUW EN NAVIGATIE

Netherlands' Research Centre T.N.O. for Shipbuildingand Navigation

SHIPBUILDING DEPARTMENT MEKELWEG 2, DELFT

*

THE INFLUENCE OF A BULBOUS

BOW ON THE MOTIONS AND THE PROPULSION

IN LONGITUDINAL WAVES

(De invloed van een bulbsteven op scheepsbeweging en voortstuwing in langsscheepse golven)

by

Prof. Jr. J. GERRITSMA and W. BEUKELMAN

Shipbuilding Laboratory, Technological University Deift

REFOT -20-F

Issued by the Counsil

This report is not to be publish.1l unless verbatim and unabridged

CONTENTS page Summary S 1. Introduction S 2. The models 6 3. Test programme .6 4. Test results 8

S. Analysis of the results 10

5. 1 The motions in waves 10

5 2 -The propulsive performance in waves 12

References 13

THE INFLUENCE OF A BULBOUS

BOW ON THE MOTIONS AND THE PROPULSION

IN LONGITUDINAL

WAVES*)

1. Introduction

With regard to thegeneral increase of speed of

normal cargo ship, shipowners sometimes consider

the use of a bulbous bow to take advantage of the

possible reduction of wave resistance in still water.

The bulbous bow is certainly not a new approach to the resistance problem of a ship. In fact, many publications, which began to appear many years

ago, discuss the subject.

Well-known investigations on the merits of the bulbous bow were carried out by Taylor, Bragg, Eggert, Wigley, Weinblum and Others. A review

presenting some of their results in a suitable way for design work was given by Lindblad [1].

It was proved that for higher speeds - say

Fit > 0.24 --- a correctly constructed bulb can

reduce the still water resistance. The best results, however - according to Lindblad - will be obtain-ed in thespeobtain-ed range from Fit = 0.30 to Fit = 0.42. Especially on oer-driven ships a good.result may

be expected from a bulbous bow.

The improvement will be partly due to the effect of the pressure reduction caused by .the bulb in the

region of the 'bow wave. Also the reduction of the angle of entrance of the waterlines, as compared

with a conventional design of the same main dimen-sions, can be advantageous in some cases. Doust [2]

mentions the fact that the reduction of the total

resistance seldom exceeds 4 % when Fit < 0.30. For

a trawler with a 5 % bulb he found a 5 % to 7 % reduction in EHP in the speed range Fit = 0.27 to Fit = 0.32 when compared with a corresponding conentional form. Due to an increased propulsive

efficiency the total reduction in power for this par-ticular model amounted from 10 % to 15 %

In the last few years Japanese investigators drew the attention to the use of rather progressive bulbous bow constructions. In this respect the work of Inui

[31 is very noteworthy. One of the examples in [3]

') Publication no. 20 Delft Shipbuilding Laboratory.

by

Prof Ir. J. GERRITSMA and W. BEUKELMAN

Summary

The propulsion and the motions of two shipmodels were measured in longitudinal regular head waves. The first

model is a parent form. of the Series Sixty and has a block coefficient C1 = .0.65. The other model has the same

afterbody and block coefficient but is fitted with a 10 % bulbous bow and a correspondingly modified entrance.

The experimental results in regular waves were used to predict the behaviour in irregular waves. It isshown that

the influence of the bulbous bow on the motions in longitudinal irregular wavesis small. The increase in power, due to

the sea waves is largerfor the bulbous bow model.

is a ship form which has the same main particulars as model .nr. M 4240 of the DT.M.B. Sixty Series

(GB = 0.60). A 20 % bulb is fitted and the EHP

prediction for a 600 feet ship, using model test

results, showed that the design speed Fit = 0.28

-an EHP reduction of the order of 22 % could be

obtained in comparison with the Sixty Series model. The effect of large bulbs is clearly shown by photo-graphs or stereophotophoto-graphs of the wave formations

of running ship models [3, 4]. A notable decrease

of surface elevation is obtained and in this respect

Japanese authors frequently use the expression

"waveless bow".

A 'full-scale application of the "wayeless bow"

principle was carried out with the high-speed pas-senger ship "Kurenai Maru". The bulb in this case has a maximum cross-section which is 17 % of the

ship's main section. In comparison with a

cOn-ventional sister ship which has a S % bulb, the

"Kurenai Maru" needs 13 % less shaft-horsepower at Fit = 0.33, thedesign speed [5]. Very large bulbs on destroyer ship forms were investigated by

Take-zawa [6] in .the speed range up to Fit = 0.50 At

high speed a 26 % bulb appeared to give an optimum

solution and resulted in a 7 % EHP reduction

Some of the bulbous bow research concerned the influence of the bulb on the ship motions in waves. Dillon and Lewis [7] carried out wave model tests

to investigate the influence of bulb size on ship

motions. Four models of a passenger liner were

tested with bulb sizes 0, 4.%, 9 % and l3

_%.

This wide variation in bulb size was found to have rather a small effect on the ship motions and on the resistance in waves. It was concluded that the choice

of a fairly large bulb can be made on the basis of

calm water resistance.

The trawler model tests by Doust [2] indicated

that the speed loss in waves is less for the bulbous bow form for Fit> 0.22. Below this speed the speed

loss is larger than that of the conventional form.

Depending on wave length ratio and speed thç

motions of the trawler in regular head waves are

larger or less than for the ship without a bulb. A useful approach in judging the performance in

waves can be made by using regular wave test results

for the prediction of significant motion amplitudes

and the.mean increase of resistance, thrust and power

in irregular waves [8].

Takezawa [9] used a similar method to investigatc

the performance of the destroyer model already

men-tioned with a 26 % bulb. Neumann spectra were

used to define the sea state. In comparison with the

copventional form there is a fairly large reduction

of the significant pitch amplitude,, both in moderate

and in high seas. No data on heave are given in

Takezawa's paper. A reduction of the significant

bow acceleration is only attained at high speed and short waves. The thrust increase in waves is sligthly

larger than for the conventional hull and this is

due to a larger resistance increase in waves and due to a reduction of the propulsive efficiency in waves which, following Takezawa, is caused by a decreasc of the mean immersion of the propeller.

The total EHP in irregular waves is slightly less

or nearly equal to that of the conventional hull,

except for very high waves where the EHP of the

bulbous bow ship is larger.

In this paper the performance, with regard to

motions and propulsion in longitudinal irregular

waves, of a C,1 = 0.65 Series Sixty hull will be

compared with the performance of a modification

of this hull which has a 10 % bulb and a

correspond-ingly modified forebody. The construction of the bulb form has been done according to the data in

[1].

From the foregoing it will be clear that for the usual service-speed Fn = 0.24 of a C8 = 0.65 hull

a conventional bulbous bow will only give a small improvement in the still water resistance. The recent Japanese approach to new bulb form was not known to 'the authors when the modified Sixty Series hull form was designed, The main object of this paper, however,.is to study the influence of the bulbon the performance in waves and the almost equal

charac-teristics in still water could therefore be accepted. The models

In Table 1 the main particulars of the two ship

models are given. A body plan for each of the two

hull forms is given in figure 1. Both models were

made of polyester, reinforced with glass fibre. Test programme

The following tests were carried out with both

ship models:

A progressive propUlsion test in still water at the

self-propulsion point of the model.

Propulsion and motion tests in regular

longitu-clinal head waves,

SY PLANS

Figure 1

These tests were carried out with a constant wave

height of --. Six wave lengths were used,

corre-sponding to A/L = 0.6, 0.8, 1.0, 1.2, 1.4 and 1.6.

Pitching and heaving motions, the phase angles with regard to the waves and the vertical accelerations at

0.15L from the forward perpendicular were deter-mined in the speed tange from Fn = 0.15 to Fn = 0.30. In addition, the mean values of model speed,

thrust and torque were measured at constant revolu-tionsof the propeller.

Finally a visual estimation was made of the ship-ment of water across the bow by using a high speed film camera.

TABLE 1. Model particulars

Series Sixty Modification

Length between

perpen-diculars

226 m 2.26

m

Length on the waterline 2.30

m 2.30

m

Breadth

0311 m

0.3 11 m Depth

0 194 m

0 194 m

Draught

0125 m

0.125 m

Volume of displacement 0.0570 m3 0.0570 m3 Block-coefficient 0. 650 0.65 0 Prismatic coefficient 0.661 0.66 1 Waterplane coefficient 0.746 0.733 Coefficient of midlength section 0 982 0.9 82

Half angle of entrance 9.1 ° 7.8 °

LCB aft. . 0.5'O % 0.44 %

Longitudinal radius of

inertia .0.2 5 0.25 Limp

Waterplane area 0.5 24 m2 0.515 m2

Moment of inertia of

wa-terplane area . 0.142 m4 0.134 m4

Centre of effort of

water-plane aft L8

2.65 % 3.38 %

Bulb area in percent of

midship area

0%

i'o % Propeller diameter . 8.73 cm 8.73 cm

Pitch ratio 1.10 1.10

20 'Yr 0 .000 ALo 0 05 0.4 .00 A.40 05 Oh 03 0/9 A 10.1 0 2.0.. 2.0 2.0 1.0 zo

I

.00 as Oh 0.3 0/g 0.1 Figure 2a

"a

20 0 2.0 10 A 0 .80 as a4 0.3 0/9 0i 20 1.0 20 to -0.0 Oh 0.3

7

1.0 Or/to14 -I I

--2y 1.6 I I _.. o_t _0_0 -I - I-- I I A41.2 2r/LO - --I - I I 0.1 0.3 0.1 0.2. 01 0.1 0.5_ I I 0.1 0.2 0.3 C 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 03

8

+1200

El

rz

-r

4. Test results

The results of the tests in still water and in regular

waves are given in the figures 2 and 3. Figure 2a

represents the dimensionless amplitudes of heave and

pitch as a function of speed and wave length, were:

OI)o pitch amplitude

a - maximum wave siope

z(, heave amplitude

-

o__o_

Figure 2b

PHASE ANGLES Er&IAND _Crz

wave amplitude

The phase angles (figure 2 a), and r,. (figure

2b) are defined in the following way:

=rcos Wet

wave elevation at the cross-section through the centre of gravity.

= '1/', cos (Wet + rO')

the pitching motion (bow up is positive).

z = z0 cos (wet +

r)

the heaving motion (positive upward). rrP Er2

The acceleration amplitude at 0.1 SL from the

forward perpendicular is given as , where g is the

acceleration due to gravity. The values for - are

valid for the wave 'height.

The natural periods' for heave and pitch

were

determined by decay-tests as a function of the model speed. There is a very small variation with speed and

this resultsin _{average values which are summarized} in Table 2.

TABLE 2.

Natural periods for heave and pitch

No bulb

10% bulb heave in seconds pitch 0.947 0.970

Resonance. conditions for heave and pitch are

indicated 'by i1 = 1 and' A = 1 (see figure 2a).

The wetness of the' bow region of the modelswas

studied with the aid of high speed films. Three

degrees of wetness were defined according 'to the

method used 'by Newton [10], namely:

very wet - green seas break across the deck at

any position along the forecastle.

wet -' height of wave formation at the bow

reaches' higher than the forecastle deck at any

position in its length, but without

_{green seas}

being shipped.

dry

_{- height of wae formation at the bow is}

below the level' of forecastle.

In Table 3 the three degrees of wetness are given as a function of speed and wave length.

The propulsive characteristics in still water and

in regular waves for both models are shown in

figure 3. In this figure the mean values 'for speed, thrust, torque and revolutions are plotted. The tests were carried out with constant propeller revolutions

at _{the self-propulsion point of the model.}

0 0:1

MODEL WITHOUT BULB

_________ MODEL WITH BULB

120

0.3

0.875

I I- - I

I-05 0.6 0.7 09 09 10 1.1 12- 1.3 1.L

No bulb

MODEL WITHOUT BULB

0 - dry

MODEL WITH BULB

Figure 3

TABLE 3.

Wetness as a function of speed and wave length Wave height L

X -

wet-I . I

05 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

OF TORQUE,THRUST AND REVOLUTIONS.IN

xx = very wet 54 .as RE VO LUll ON S WAVES 10% bulb 9 0.150 0.I75 0.200 0.225 0.250 0.275 0.6 0 0 0 0 0 -0 0.8 0 0 0 0 0 0 1.0 x 0 0 0 0 0 1.2 x xx xx xx xx x 1.4 0 0 x xx xx x 1.6 0 0 0 0 0 x 0.150 0.175 - 0.200 0.225 0.250 0275 O6 0 0 0 0 0 . 0 0.8 0 0 0 0 0 0 1.0- 0 x 0 0 0 0 1.2 x xx xx

xx.

x x 1.4 0 0 x xx xx x 1.6 0 0 0 0 0 0 05 0.6 0.7 0.0 09 10 1.4-MEAN VALUES a? 05 09 10 1.1 1.2 1.3 U

10

5. Analysis of the results where: 5. 1. The motions in waves

Figure 2 shows that thç bolbous bow has some

influence on the pitching and heaving amplitudes.

For the speed range under consideration pitching is reduced in comparison with the original model

for wave length ratios varying from A/L

=

0.,8 to

2/L

=

1.4. In some cases the reduction is quite

substantial and attains values of the order of 25 _% to 30 _%. The heaving motion on the other hand is larger for the bulbous bow model.

The difference in bow motion is shown by the

acceleration amplitudes at 0.15L. For 2/L 1.2 a

reduction is found for the bulbdus bow form,

par-ticulrIy at 1/L

=

1. FOr larger waies there is a

slight increase of the bow motion. The result of the differences in motion amplitudes and phase angles

on wetness, as shown in Table 3 is hardly visible.

Although this wetness analysis is very qualitative in nature, no major differences between the two

models can be detected.

Finally the mean motion amplitudes of both mod-els in irregular longcrested head waves, defined by Neumann. spectra were compared. The main

partic-ulars of the full scale sea. conditions, which were

used for this comparison are listed in Table 4.

Z()

The dimensionless transfer functions - and

r

for heave nd pitch are given in figure 4. The

mean squared values for the heave and pitch ampli-tudes follow from the following relations:

f

Gr

(We) ()2 (We)

dWe

(we)

(oL

) (we). dw5

In these formulae 2 Gr corresponds to the

Neu-mann spectrum, viz:

4.8 e 2211J2w2

2 Grr _'Jo m2 sec.

=

circular frequency.

U

=

windspeed in meters per second g acceleration of gravity.

The means of the one-third highest values are

u3ed- to compare the motions of the two ship forms. They follow from:

i

=

2 and z0113 2 Vz02.

A ship length of 400 feet was chosen for the

full-scale comparison. In the figure 5 the significant

amplitudes for heave and pitch are given

as a

function of the ship speed and the significant wave

height. It

is shown that the bulbous bow has a

smaller pitching motion (0.2-0.4 degrees), but

heaving is increased in comparison with the parent

model (0.06-0.24 meters).

As the differences are not large, it may be

con-cluded that the .ship motions in longitudinal waves

are not very much influenced by the bulbous bow. The same holds for the wetness characteristics, as

is shown in Table 3. It is admitted that the wetness

analysis is of a qualitative nature, but there is no strong indication that the bulbous bow has better

qualities than the parent model.

As the mass and the radius of inertia have the.

same value for both models, the natural periods

mainly depend on the area and the moment of inertia

of the waterplane on the one hand and on the

-hydrodynamic mass and moment of inertia on the other hand. Using the data of the Tables 1 and 2 it is easily shown that the hydrodynamic mass and

moment of inertia have approximately the same

values for both models at their natural periods.

A detailed analysis of the differences in motion

amplitudes can oniy be made by using forced oscilla-tion technique and by measuring the exciting forces and moments, in waves. Such an elaborate analysis

was not undertaken, since the overall effect of the

bulb on the motions appeared to be small.

TABLE 4,.

Sea state particulars (fully developed seas)

Full scale values

5 9.8 2.1 7.7

2.8-106

6 13.4 4.6 10.5

4.0-145

7 I 5.4 6.7 12.!

4.7 16.7

Beaufort number Windspeed meters per second

- Significant wave height meter Period of max. energy of spectrum seconds Significant range of periods seconds

1.20 1.00 0.80 _, 0.60

4k

0.40 0 20 -0. 0. 0

.vc

L

WITHOUT BULB PITCH 5. 6 0 1 2

3

4 We

DIMENSIONLESS TRANSFER FUNCTIONS FOR HEAVE AND PITCH Figure 4 F,..2SO Fn 225 Fn.200 Fn .175 Fn.1SO HEAVE AMPLITUDE 400ft. SHIP H vs __-rn WITH BULB WITHOUT BULB 1 1 WITH BULB WITHOUT BULB PITCH AMPLITUDE 8 600ft. SHIP 3 7

w6

a, 4, 5 4, 01 E 2 4-0 4.6 'I, 0 3-2 :H,2i rs 1-0 0 10 11 12 13 14 15 16 17 18 10 11 12 17 14 15 16 17 18 V5 KNOTS KNOTS

SIGNIFICANT AMPLITUDES OF PITCH AND HEAVE

12

5. 2 The propulsive performance in waves

A power estimation in longitudinal longcrested

head waves was made for both models, in which the method given in reference [8], was used In principle the resistance increase due to the seaway is a func-tion of the mofunc-tion amplitudes and the phases of the

motions with regard to the waves. Each of these

quantities is influenced by the bulbous bow, as can be seen in the figures 2a and 2b, and some influence in waves could be expected.

The performance in regular wa'es is the basis

for the power estimation in irregular waves Figure 6

gives the dimensionless transfer functions of the

mean increase of thrust, power, torque and revolu-tions, viz: T. PT

-

_{grB2/L gr2B2/L.V} K gr2B2/L.D and: 17rD3 V - gr2B2/L II -0.

MODEL WITHOUT BULB

The mean increase of power Pr

in a particular

wave spectrum Gr follows from:

Pr

= 2 5

Gr r (We) (w0) d w

where r is the wave amplitude. Similar expressions

are valid for thrust-, torque- and revolutions

in-crease.

The power increases for a 400 ft. ship were

caku-lated for the sea conditions given in Table 4. They are plotted on the basis of ship speed in figure 7.

It is shown that the power incrçase js larger for the

ship forin with the bulbous bow. A similar picture holds for the increase of torque and revolutions.

There is a relative small difference in thrust increase. For speeds smaller than Fn 0.20 the bulbous bow

is slightly better but for higher speeds the thrust

increase is higher than for the parent model. For

speeds higher than Fu = 0.24 the bulbous bow model

needs about 3 % less power in still water than the

parent model; below this speed the parent model is slightly better.

For the present purpose, viz, the comparison of

the power in waves, these differences are neglected and an equal performance in still water is assumed.

TRANSFER FUNCTIONS FOR THRUST.TORQUE REVOLUTIONS AND POWER INCREASE IN WAVES

--a 1000 15- 8-0 INCREASE OF POWER 400ft. SHIP H5.7 ESTIMATION OF POWER 400tt. SHIP H,,sO.1RR

MEAN INCREASE OF POWER IN A NEUMANN HEAD SEA

Figure 7

An estimation of the still water power was made by

using the data in [11]. By adding the power

in-creases in waves a comparison of the total power could be made for both models, see figure 8. It is

shown that the bulbous bow ship needs more power to maintain a certain speed.

In terms of speed loss, assuming for instance a

constant maximum power of 6O0 hp, the extra

WITH BULB WITHOUT BULB WITH BULB WITHOUT BULB I TRIAL I SERVICE

speed loss in 2.1 meter waves is negligible, in 4.6

meter waves the speed loss is about 0.3 knots larger

for the bulbous bow and in 6.7 meter waves the difference is about0.6 knots.

It is quite certain, however, that the ship will

reduce power in 6.7 m head waves and therefore

this condition may not be significant for the..com-parison. Also the various assumptions which have

been made for this analysis may be questionable

in such rather extreme conditions (significant wave height/ship leiigth

₌

Based on average weather conditions the

differ-ence in propulsive performance between the two ship forms will be very small. All that can be said

for this particular case is that the bulbous bow

does not have superior qualities in a seaway. This

result may seem surprising because of the smaller pitching motions which were found for the bulbous

bow model. It has to be remarked, however, that the change on the phase of the motions can result

in a reduction of the propulsive efficiency. Such a

reduction was found by Takezawa [9]. This could

be a possible explanation for the larger power in-crease of the bulbous bow ship.

References

I. Lindblad, A.: Experiments with bulbous bows. Publication of the Swedish State Shipbuilding Experimental Tank, Goteborg

1944.

Doust, D. Jr Trawler forms with bulbous bows. Fishing boats

of the world: 2. London 1960.

Inui, T.: Wave-making resistance of ships. Transactions of the Society of Naval Architects and Marine Engineers. 1962. Takahei, T. and .T. Inui: The waveLcancelling effects of

wave-less bulb on the high speed passenger coaster ms. 'Kurenai

Maru", Part Ill - Photogrammetrical observations of ship waves. Journal of the Society of Naval Architects of

Japan, Vol. 110, 196!.

S. Shigcrntsu, M. and K. Kai: The cancelling effects of wave-less bulb on the high speed passenger coaster ms. 'Kurenai

Maru", Part II - The full-scale experiment. Journal of the

Society of Naval Architects of Japan, Vol. 110, 1961.

Takezawa, S.: A study on the large bulbous bowof a high speed

dis-placement ship, Part I - Resistance in still water. Journal of the.Society of Naval Architects of Japan, Vol. 110, 1961. Dillon, E. S. and E. V. Lewis: Ships wih bulbous bows irs smooth water and in waves. Transactions of the Society of Naval

Architects and Engineers. 19SS.

Gerritsma, J;, J. J. van den Bosch and W. Beukelman: Propulsion in regular and irregular waves. International Shipbuilding

Progress, 1961.

Takezawa, S.: A study on the large bulbous bow of a high speed displacement ship, Part II - Performance in waves. Journal of the Society of Naval Architects of Japan, VoIr liii, 1962. Newton, R. N.: 'Wetness related to freeboard and flare

Trans-actions of tlse Institution of Naval Architects, 1959

13

12 13 iS 15 16 17 18 19 20

V .09015

II. Todd, F. H. and P. C. Pien: Series 60 - The effect upon

resist-ESTIMATION OF TOTAL POWER IN WAVES _{ance and power of variation in L.C.B. position. Transactions}

of the Society of Naval Architects and Marine Engineers,

- Figure_s . 1956.

8 9 10 11

I

II

10 11 12 13 1!. 15 16 17 18

14

List of symbols

maxilnum wave slope.

= tuning factor fOr pitch.

tuning factor for heave.

= phase angle between wave and pitch.

phase angle between wave and heave

= phase angle between pitch and heave.

= wave length.

density of water. pitch angle. pitch amplitude.

= significant pitch amplitude. = circular frequency.

= circular frequency of encounter..

a = acceleration amplitude.

B breadth of ship or model.

C11 = block-coefficient.

propeller diameter. EHP effective horsepower.

Gr r (0)) = wave spectrum

g acceleration due to gravity.

H'/3 = significant wave height. a er,p 19 2 L LCD ii P

0

T V vs z zo tn zo1/3 Fn 'Zr Pr Q, Tr Pr xl

length between perpendiculars.

= centre of buoyancy..

propeller revolutions per second.

= power.

torque. wave amplitude.

= thrust.

= model' speed.

= ship speed.

= heave.

= heave amplitude.

significant heave amplitude.

V _{= Froude number.} /gL = increase of revolutions. increase of pOwer. = increase of torque

= increase of thrust.

-= dimensionless increase of revolutions. = dimensionless incrèàse of power.

= dimensionlessincrease of torque.

PUBLICATIONS OF THE NETHERLANDS RESEARCH CENTRE T.N.O. FOR SHIPBUILDING AND NAVIGATION

Reports

No. I S The determination of the natural frequencies of ship vibrations (Dutch). By prof. ir H. E. Jaeger. May 1950.

No. 2 Confidential report, not published. July 1950.

No. 3 S Practical possibilities of constructional applications of aluminiuni alloys to ship construction. By prof. ir 11. L. Jaeger. March 1951.

No 4 S Corrugation of bottom shell platilg in ships with all-welded or partially welded bottoms (Dutch) By prof. ir H. E. Jaeger a,,iI ir 11. A. Verbce/,. November. 1951.

No. 5 S Standard-recommendations for measured mile and endurance trials of sea-going ships (Dutch)1 By prof. ir J. W. Bo,iebakker, Jr ir W. J. Muller and ir E. J. Diehl. February 1952.

No. 6 S ome tests on stayed and unstayed masts and a comparison of experimental results and calculated stresses

(Dutch).

By ir A. Verduin and ir B. Bur.g/gracf. June 1:9.52. No 7 M Cylinder wear in marine diesel engines (Dutch).

By ir H. Visser. December 1952.

No. 8 M Analysis and testing of lubricating oils (Dutch).

By ir R. N. M. A. Malolazix and ir I. G. Suzit. July 1953..

No. 9 S Stability experiments on models of Dutch and French standardized lifeboats.

By prof. ir i-I. E. Jaeger, prof. ir J. W. Bonebakiter and J. Pereboo;n, in collaboration with A. Audige. October 1952.

No. 10 S On collecting ship service performance data and their analysis. By Prof.. ir J. W. Bonebaklzer. January 19.53.

No. 11 M The use of three-phase current for auxiliary purposes (Dutch). By ir J. C. G. van Wijk. May 1953.

No 12 M Noise and noise abatement in marine engine rooms (Dutch). By "Technisch-Pbysiscbe Diensi T.N.O. - T.H." April 1953.

No. 13 M Investigation of cylinder wear in diesel engines by means of laboratory machines (Dutch). By ir H. Visser. December 1954.

No. 14 M The purification of heavy fuel oil for diesel engines (Dutch). By A. iiren,cr. August 1953.

No. 15 S Investigation of the stress distribution in corrugated bulkheads with vertical troughs.

By prof ir II £ Jaeger, :r B Burgbgraef and 1 van der Ham September 1954

No. 16 M Analysis and testing of lubricating oils II (Dutch).

By ir K. N. M. A. Malotaux and drs 1. B. Zabel. March 1956.

No. 17 M The application of new physical methods in tne examination of lubricating oils. By ir K. N. M. A. Malotauv and dr F. vu;: Zeggeren. March 1957.

No. 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 applied on board of these ships and their influence on the generating capacity (Dutch).

By ir J. C. G. van V7ijk. February 1957

No. 19 M Crankcase explosions (Dutch).

By. ir J. H. Minkhorst. April 1957.

No. 20 S An analysis of the application of aluminium alloys in ships' structures.

Suggestions about the riveting between steel and aluminium alloy ships' structures.

By prof. ir H. E. Jaeger. January 1955.

No. 21 S On stress calculations in helicoidal shells and propeller blades.

By dr ir J. W Cohen. July 195.5.

No. 22 S Some notes on the calculation of pitching and heaving in longitudinal waves. By ir J. Gerritsmna. December 1955.

No. 23 S Second series, of stability experiments on models of lifeboats.

'By ir B. Bnrghgraef1 September 1956.

No. 24 M Outside corrosion of and slagforrnation on tubes in oil-fired boilers (Dutch).

By dr W1 J Taut. April 1957.

No. 25 S _{Experimental determination of damping, added mass and added mass moment of inertia of a shipmodel.}

By ir 1. Gcrritsma. October 1957.

No. 26 M Noise measurements and noise reduction in ships.

By ir G. J. van Os and B. van. Steenbrugge. May 1957.

No. 27 S Initial metacentric height of small _{seagoing ships and the inaccuracy and unreliability of calculated}

curves of righting levers.

-By prof. ir J. W. Bonebalzker. December 1957.

No. 28 M Influence of piston temperature on piston fouling and piston-ringwear in diesel engines using residual fuels

By ir. H. Visser, June 1959.

No._29_M _{The-influence-of-liystercsisontheyalue of the modulus 0f rigidity of steel.}

4o.. 30 S An expedmental analysis of shipmotions in longitudinal regular waves. By Jr. I. Gerri/snia. Dcçcmber 1:958.

No. 31 M Model tests concerning damping coefficients and the increase in the moments of inertia due to entrained

water on ship's propellers.

By N. I. Visser. October 1959.

No. 32 S The effect of a keel on the rolling characteristics of a ship.

By ir. J. Gerri/sn:a. July 195-9.

No. 33 M The application of new physical methods in the examination of lubricating oils. (Continuation of report No. 17 M.)

By ir. R. N. M. A. Malotaux and dr -P. van Zeggeren. November 1959k

No. 34 S Acoustical principles in .ship design.

By ir. f. H. Janssen, Octobc 1959. .. No. 35 S Shipmotions in longitudiial waves;

By Jr. I. Gerrilsina, February 1-960.

No 36 S Experimental determination of bending moments for three models of different fullness in regular waves By ir. J. Ch. de. Does. April 1960.

No. 37 M Propeller excited vibratory forces in the shaft of a single screw tanker. By dr.. Jr. I. 'D. van Manen and ir. R. Wereldsma. June 1960.

No. 38 S Beamknees and other bracketed connections

By prof. ir. H. E. Jaegqr and ir. J. J. W. Nibbering. January 196-1.

No. 40 S On the longitudinal reduction factor for the adthd mass of vibrating ships with rectangular cross-section. By ir. W'. P. A. Joosen and dr. J. A. Sparenberg. April 1961.

No. 41 S Stresses in flat propeller blade models determined by the moire-method.

By ir. F. K. Ligtenberg. May 1962.

No 42 5 Application of modern digital computers in naval-architecture. By Jr H. J. Zunderdorp. June 1962.

No. 43 C Raft trials and ships' trials with some underwater paint systems. By drs P. de Wolf and A. M. van Londen. July 1962.

No. 44 S Some acoustical properties of ships with.respect to noise control. Part I.

By Jr. J. H. Janssen. August 1962.

No. 45 S Some acoustical properties of ships with respect to noise control. Part IL.

By Jr. J. H. Janssen. August 1962.

No. 46 C An investigation into the influence of the method of application on the behaviour of anti-corrosive paint

systems in seawater.

By A M. van Londeni. August 162.

No 47 C Results of in inquiry into the condition of ships hulls in telation to fouling and coiiosion

By Jr. H. C. Ekama, A. M. van Londen and drs. P. de Wolf. December 1962.

No. 48 C Investigations into the use of the wheel-abrator for removing rust and millscale from .shipbuilding steel (Dutch). (Interim report)-.

- By ir. J. Re-rn-melts and L. D. B.. van den Bnrg. December 1962.

No. 49 S Distribution of damping and added mass along the length of a shipmodel. By prof. ir. J. Gerritsma and W. Benkel-man. March 1963.

Co-ui- in unicalions

No. I M Report ois the use of hcavy fuel oil in the tanker "Auricula" of the Anglo-Saxon -Petroleum Company

(Dutch). August 1950

No. 2 S Ship speeds over the measured mile (Dutch-). By ir W. H. C. 'E. Rösiuigh. February 19-51.

No. 3 S On -voyage logs of sea-going ships and their analysis (Dutch).

By prof Jr 1. W Bonebak/ze, and Jr J. Grrritsrna. November 1952

No. 4 S Analysis of model experiments, trial and service performance data of a single-screw tanker. By prof. Jr I. W. Boncba/Jtcr. October 1954.

No. S S Determination of the dimensions of panels subjected to water pressure only or to a combination of water pressure and edge comprcssion.-(Dutch).

By prof. ir H. E. Jaeger. November 1954.

No 6 S ( Approximative calculation of the effect of free surfaces on transverse stability (Dutch)

By ft L P. I-lerfst. April 19S6.

No. 7 S On the calculation of stresses in a stayed mast..

By ir B. Burghgraef. August .1916. -

-No 8 S Simply supported rectangular plites subjected to the combined action of a unifo mly distributed literal load and compressive forces in the middle plane.

- By ir. B. Bnrghgraef. February 1958.

No. 9 -C - Review of the investigations into the-prevention of corrosion and fouling of ships' hulls (Dutch).

By ir. H. C. Ekuina. October 1962