&

_20

The Influence of a Bulbous Bow on th. and

the ulenngu"nal Waves.gaB 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 sistership 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.

speed range up to 0.50. At high apa.d a 26% bulb appeared to

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 restBtancLTb. 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 [81Takezawe ['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 nsrlyequal to that of the conventional bull, except for var )tigb waveswtere the ER? of the bulbous, bow ship Li larger,

F4-In this paper the performance, with regard to motione and pro-

pulaion in longitudinal ir'regular waves, of a 0.65 Serieasixty hull, will be compared with the performanøe of a modificationof this hull which has a 10% bulb and a correspondingly Eodifidforebody. 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 inflenoeof 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 aLength on the waterline. 2.30 m 2.30 a

Breadth. 0.311 a O.311 iiDepth. 0.194 m 019k aDraught . - 0.125 a aVolume of displacement. o . 057Oa 0,O57m38leck.'øotftoisnt. O.6o 04650Prismatic cofficjent. 0.661

0

0.661

Waterplane coifticteztt. 004 746 0.733Coffioient of midlength section. 0.982 0.982Half angle of entrance,

409,' 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 a20.142 a4

0.515 a0.134 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. 8.73cmPitch ratio.xpañdød area ratio, 0.25 O.,25

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 infigur. 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 phaseangles 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 wavesare given in the figures 2 and 3. Figure aa represents the dimen-

sionlase amplitude, of heave and pitch as a function of speed andwave length, wh.re

tob alitj4e_CC maximum wave siope

bts ilitudV wave saplituO

Tha phase ang2ea 2P (figure 2a), and trz (figure 2b) aredefined in the following way:

P OO$)t wave levation at the oroee'.e.ctiothrough 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 porpendicu3er 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 bydicay-teata mu a function of the jiod.l speed. There is a very smallv*riation with speed and this results in average values whi'oh aresummarized in Table .

TABLE 2..

atqrai keriodu f .ave1 and ,pitchtjtee,cond.

Resonance condition. for heave a6 pitch are indtoated byI and Ap I (i.e figure a).

The wetness of the bow region of the models was studied withthe aid of high speed films. Three degrees of wetness were dafinedaccording to the ct.thod used by Newton 110), namely:

very wet green seas break across the teok at any positionalong the forecastle.wet - height of wave formation at th. bow resohei higher thanthe forecastle deck at any poeition in its length, but with-

dry - height of wave for*atton at tbe bow is below the eviIof f*reoaetle.

-7,.

heave itob

No bulb10% bulb

0.87, 0.947Q9O

C'

.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.iht4..

Od17xw*t

cx .ry wet.

The propulsive obarsoteriettos in still water arid in regularwav-ae tot both models are rihown in figur. 3. In this figure themean values for apud, thrust, torqu. arid revolutione are plotted.

oonstant propeller revolutions atthe self-propulsion point oS the odiI

Nobuib.

0.225 0.250 0.275

¶0% bulb.

Oi5O 0175 O200 0225 025O 0.275

1O1,2

1,6

0J

0 0 0x

xx

0x xx

xxx

xxx

xx *0

00

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.

whichk.

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/Lparticularly

of the bow

and phase

visible. Althoughno major

motion amplitudeswaves, defined

of the

comparison are

PAL

çfullj developed seas).

'uU scale values.

Beaufort

number,

Windspeed

*eters per secondSignificantwave height

meter.

Period of maz.energy of spectrum

3econdl.

Significant

range of periods

seconds.

56.

7

9.813.L,

14

a,i

'*.6

6.7.

7,710.511

2.8.-lo.6k10-lk.511..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/UCJ220 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 comparisonwith 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 thebulbous bow ha. bettar' qualities than th. parent mod.l.

'4tf the radiu. of inertia have the same valø forboth model., the naturat uidomatnty depend-on tha are&adth.*oment of insrtia of the watirplane on tb. on. band and on the

10

- 10 -

hydrodyn.iiiio mass and *oaent of inertia on the other band. Using thedata 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 powerestimation 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.

11 -

1he power increases for a IOO ft. ship were calculmt*d for thesee conditions given in 'abl. II. They us plotted on the basis ofship 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 instill water is assumed. An eatimati*n f th. still water power wasmade 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 forth 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

- 12 *

EflENCES.

N Lindblad, A.Expsrients with bulbous bow..Publication of the Swedish stats 8hipbuilding Experimental ThcGtsborg 19½k.

[a] Douat, DJ.Trawler forM with bulboue bowe.Tubing boats of tb. world 2.London 190.

['1 Xnui, T4Wave..asking resistance rf shipe.Transactione of the Society of Naval Architects and MarineEngineers.1962,

[i1 Takahet, T. and Xnui, T.The ways*oanuefljng .ff.cts of wavleee bulb on the high speedpassenger 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 speedpassenger coaster a.s. 'Kurenai Naria", Part XI - The full-sealseZp.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 displacementship, 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;hsandaveaaLTransection, of. The $peiety of Naval Architicte end MarineEngineers,

- 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*ntship, 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 inL.C.1. positio*.Transactions of the Society of Naval Architects and MenusEnginears.I 9.

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

SHIPBUILDING DEPARTMENT MEKELWEG 2, DELFT

*

THE INFLUENCE OF A BULBOUSBOW 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.1lunless 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

List of symbols 14

THE INFLUENCE OF A BULBOUSBOW ON THE MOTIONS AND THE PROPULSION

IN LONGITUDINAL WAVES*)

1. Introduction

With regard to thegeneral increase of speed ofnormal cargo ship, shipowners sometimes considerthe use of a bulbous bow to take advantage of thepossible reduction of wave resistance in still water.The bulbous bow is certainly not a new approachto the resistance problem of a ship. In fact, manypublications, which began to appear many yearsago, discuss the subject.

Well-known investigations on the merits of thebulbous bow were carried out by Taylor, Bragg,Eggert, Wigley, Weinblum and Others. A reviewpresenting some of their results in a suitable way fordesign work was given by Lindblad [1].

It was proved that for higher speeds - sayFit > 0.24 --- a correctly constructed bulb canreduce the still water resistance. The best results,however - according to Lindblad - will be obtain-ed in thespeed range from Fit = 0.30 to Fit = 0.42.Especially on oer-driven ships a good . result maybe expected from a bulbous bow.

The improvement will be partly due to the effectof the pressure reduction caused by .the bulb in theregion of the 'bow wave. Also the reduction of theangle of entrance of the waterlines, as comparedwith 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 totalresistance seldom exceeds 4 % when Fit < 0.30. Fora trawler with a 5 % bulb he found a 5 % to 7 %reduction in EHP in the speed range Fit = 0.27 toFit = 0.32 when compared with a correspondingconentional form. Due to an increased propulsiveefficiency the total reduction in power for this par-ticular model amounted from 10 % to 15 %

In the last few years Japanese investigators drewthe attention to the use of rather progressive bulbousbow 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 firstmodel is a parent form. of the Series Sixty and has a block coefficient C1 = .0.65. The other model has the sameafterbody 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 thatthe influence of the bulbous bow on the motions in longitudinal irregular waves is small. The increase in power, due tothe sea waves is largerfor the bulbous bow model.

is a ship form which has the same main particularsas model .nr. M 4240 of the DT.M.B. Sixty Series(GB = 0.60). A 20 % bulb is fitted and the EHPprediction for a 600 feet ship, using model testresults, showed that the design speed - Fit = 0.28 -an EHP reduction of the order of 22 % could beobtained in comparison with the Sixty Series model.The effect of large bulbs is clearly shown by photo-graphs or stereophotographs of the wave formationsof running ship models [3, 4]. A notable decreaseof surface elevation is obtained and in this respectJapanese 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 casehas a maximum cross-section which is 17 % of theship's main section. In comparison with a cOn-ventional sister ship which has a S % bulb, the"Kurenai Maru" needs 13 % less shaft-horsepowerat Fit = 0.33, thedesign speed [5]. Very large bulbson destroyer ship forms were investigated by Take-zawa [6] in .the speed range up to Fit = 0.50 Athigh speed a 26 % bulb appeared to give an optimumsolution and resulted in a 7 % EHP reduction

Some of the bulbous bow research concerned theinfluence of the bulb on the ship motions in waves.Dillon and Lewis [7] carried out wave model teststo investigate the influence of bulb size on shipmotions. Four models of a passenger liner weretested with bulb sizes 0, 4.%, 9 % and l3 %.This wide variation in bulb size was found to haverather a small effect on the ship motions and on theresistance in waves. It was concluded that the choiceof a fairly large bulb can be made on the basis ofcalm water resistance.

The trawler model tests by Doust [2] indicatedthat the speed loss in waves is less for the bulbousbow form for Fit> 0.22. Below this speed the speedloss is larger than that of the conventional form.Depending on wave length ratio and speed thç

5

motions of the trawler in regular head waves arelarger or less than for the ship without a bulb.

A useful approach in judging the performance inwaves can be made by using regular wave test resultsfor the prediction of significant motion amplitudesand the.mean increase of resistance, thrust and powerin irregular waves [8].

Takezawa [9] used a similar method to investigatcthe performance of the destroyer model already men-tioned with a 26 % bulb. Neumann spectra wereused to define the sea state. In comparison with thecopventional form there is a fairly large reductionof the significant pitch amplitude,, both in moderateand in high seas. No data on heave are given inTakezawa's paper. A reduction of the significantbow acceleration is only attained at high speed andshort waves. The thrust increase in waves is sligthlylarger than for the conventional hull and this isdue to a larger resistance increase in waves and dueto a reduction of the propulsive efficiency in waveswhich, following Takezawa, is caused by a decreascof the mean immersion of the propeller.

The total EHP in irregular waves is slightly lessor nearly equal to that of the conventional hull,except for very high waves where the EHP of thebulbous bow ship is larger.

In this paper the performance, with regard tomotions and propulsion in longitudinal irregularwaves, of a C,1 = 0.65 Series Sixty hull will becompared with the performance of a modificationof this hull which has a 10 % bulb and a correspond-ingly modified forebody. The construction of thebulb form has been done according to the data in[1].

From the foregoing it will be clear that for theusual service-speed Fn = 0.24 of a C8 = 0.65 hulla conventional bulbous bow will only give a smallimprovement in the still water resistance. The recentJapanese approach to new bulb form was not knownto 'the authors when the modified Sixty Series hullform was designed, The main object of this paper,however,.is to study the influence of the bulbon theperformance 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 shipmodels are given. A body plan for each of the twohull forms is given in figure 1. Both models weremade of polyester, reinforced with glass fibre.

Test programme

The following tests were carried out with bothship models:

A progressive propUlsion test in still water at theself-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 withregard to the waves and the vertical accelerations at0.15L 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 speedfilm 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 mBreadth 0311 m 0.3 11 mDepth 0 194 m 0 194 mDraught 0125 m 0.125 mVolume of displacement 0.0570 m3 0.0570 m3Block-coefficient 0. 650 0.65 0Prismatic coefficient 0.661 0.66 1Waterplane coefficient 0.746 0.733Coefficient of midlength

section 0 982 0.9 82Half angle of entrance 9.1 ° 7.8 °

LCB aft. . 0.5'O % 0.44 %Longitudinal radius of

inertia .0.2 5 0.25 LimpWaterplane area 0.5 24 m2 0.515 m2Moment of inertia of wa-

terplane area . 0.142 m4 0.134 m4Centre 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 cmPitch ratio 1.10 1.10Expanded area ratio 0.525 0.52 5

20

'Yr

0

.000

ALo

0

05

0.4

.00

A.40

05

Oh

03

0/9

A10.1

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/to 14

-

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 I0.1 0.2 0.3

C 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 03

MOTION AMPLITUDES AND PHASE LAGS(HEAVE AFTER PITCH)

8

+1200

Elrz

-r

4. Test results

The results of the tests in still water and in regularwaves are given in the figures 2 and 3. Figure 2arepresents the dimensionless amplitudes of heave andpitch as a function of speed and wave length, were:

OI)o pitch amplitudea - 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,. (figure2b) are defined in the following way:

=rcos Wetwave elevation at the cross-section throughthe 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 weredetermined by decay-tests as a function of the modelspeed. There is a very small variation with speed andthis resultsin average values which are summarizedin Table 2.

TABLE 2.

Natural periods for heave and pitch

No bulb10% bulb

heave

in seconds

pitch

0.9470.970

Resonance. conditions for heave and pitch areindicated 'by i1 = 1 and' A = 1 (see figure 2a).

The wetness of the' bow region of the models wasstudied with the aid of high speed films. Threedegrees of wetness were defined according 'to themethod used 'by Newton [10], namely:

very wet - green seas break across the deck atany position along the forecastle.

wet -' height of wave formation at the bowreaches' higher than the forecastle deck at anyposition in its length, but without green seasbeing shipped.dry - height of wae formation at the bow isbelow the level' of forecastle.

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

The propulsive characteristics in still water andin regular waves for both models are shown infigure 3. In this figure the mean values 'for speed,thrust, torque and revolutions are plotted. The testswere carried out with constant propeller revolutionsat the self-propulsion point of the model.

0 0:1MODEL WITHOUT BULB

_________ MODEL WITH BULB120

0.3

0.8750.8 82

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 x1.4 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 someinfluence on the pitching and heaving amplitudes.For the speed range under consideration pitchingis reduced in comparison with the original modelfor wave length ratios varying from A/L = 0.,8 to2/L = 1.4. In some cases the reduction is quitesubstantial and attains values of the order of 25 %to 30 %. The heaving motion on the other hand islarger for the bulbous bow model.

The difference in bow motion is shown by theacceleration amplitudes at 0.15L. For 2/L 1.2 areduction is found for the bulbdus bow form, par-ticulrIy at 1/L = 1. FOr larger waies there is aslight increase of the bow motion. The result of thedifferences in motion amplitudes and phase angleson wetness, as shown in Table 3 is hardly visible.Although this wetness analysis is very qualitativein nature, no major differences between the twomodels can be detected.

Finally the mean motion amplitudes of both mod-els in irregular longcrested head waves, defined byNeumann. spectra were compared. The main partic-ulars of the full scale sea. conditions, which wereused 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) d We

(we)(oL

) (we). dw5

In these formulae 2 Gr corresponds to the Neu-mann spectrum, viz:

4.8 e 2211J2w2

2 Gr r 'Jom2 sec.

= circular frequency.

U = windspeed in meters per second

g acceleration of gravity.

The means of the one-third highest values areu3ed- 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 thefull-scale comparison. In the figure 5 the significantamplitudes for heave and pitch are given as a

function of the ship speed and the significant waveheight. It is shown that the bulbous bow has asmaller pitching motion (0.2-0.4 degrees), butheaving is increased in comparison with the parentmodel (0.06-0.24 meters).

As the differences are not large, it may be con-cluded that the .ship motions in longitudinal wavesare not very much influenced by the bulbous bow.The same holds for the wetness characteristics, asis shown in Table 3. It is admitted that the wetnessanalysis is of a qualitative nature, but there is nostrong indication that the bulbous bow has betterqualities than the parent model.

As the mass and the radius of inertia have the.same value for both models, the natural periodsmainly depend on the area and the moment of inertiaof the waterplane on the one hand and on the-hydrodynamic mass and moment of inertia on theother hand. Using the data of the Tables 1 and 2 itis easily shown that the hydrodynamic mass andmoment of inertia have approximately the samevalues for both models at their natural periods.

A detailed analysis of the differences in motionamplitudes can oniy be made by using forced oscilla-tion technique and by measuring the exciting forcesand moments, in waves. Such an elaborate analysiswas not undertaken, since the overall effect of thebulb 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 2.8-1066 13.4 4.6 10.5 4.0-1457 I 5.4 6.7 12.! 4.7 16.7

Beaufortnumber

Windspeedmeters per second

- Significant waveheightmeter

Period of max.energy of spectrum

seconds

Significant range ofperiodsseconds

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,..2SOFn 225

Fn.200Fn .175

Fn.1SO

HEAVE AMPLITUDE400ft. SHIP

Hvs __-

rn

WITH BULB

WITHOUT BULB

1 1

WITH BULB

WITHOUT BULB

PITCH AMPLITUDE

8600ft. SHIP

3

7

w6a,4,

5

4,01

E2

4-

0 4.6 'I, 03-

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

Figure

12

5. 2 The propulsive performance in waves

A power estimation in longitudinal longcrestedhead waves was made for both models, in which themethod given in reference [8], was used In principlethe resistance increase due to the seaway is a func-tion of the motion amplitudes and the phases of themotions with regard to the waves. Each of thesequantities is influenced by the bulbous bow, as canbe seen in the figures 2a and 2b, and some influencein waves could be expected.

The performance in regular wa'es is the basisfor the power estimation in irregular waves Figure 6gives the dimensionless transfer functions of themean increase of thrust, power, torque and revolu-tions, viz:

T. PT-grB2/L gr2B2/L.V

Kgr2B2/L.D

and:

17r D3 V- gr2B2/L

II -

0.

MODEL WITHOUT BULB

The mean increase of power Pr in a particularwave spectrum Gr follows from:

Pr = 2 5 Gr r (We) (w0) d w

where r is the wave amplitude. Similar expressionsare 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. Theyare plotted on the basis of ship speed in figure 7.It is shown that the power incrçase js larger for theship forin with the bulbous bow. A similar pictureholds 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 bowis slightly better but for higher speeds the thrustincrease is higher than for the parent model. Forspeeds higher than Fu = 0.24 the bulbous bow modelneeds about 3 % less power in still water than theparent model; below this speed the parent model isslightly better.

For the present purpose, viz, the comparison ofthe power in waves, these differences are neglectedand an equal performance in still water is assumed.

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

Figure 6 -- -

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 byusing the data in [11]. By adding the power in-creases in waves a comparison of the total powercould be made for both models, see figure 8. It isshown that the bulbous bow ship needs more powerto maintain a certain speed.

In terms of speed loss, assuming for instance aconstant 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 4.6meter waves the speed loss is about 0.3 knots largerfor the bulbous bow and in 6.7 meter waves thedifference is about 0.6 knots.

It is quite certain, however, that the ship willreduce power in 6.7 m head waves and thereforethis condition may not be significant for the..com-parison. Also the various assumptions which havebeen made for this analysis may be questionablein such rather extreme conditions (significant wave

height/ship leiigth =Based on average weather conditions the differ-

ence in propulsive performance between the twoship forms will be very small. All that can be saidfor this particular case is that the bulbous bowdoes not have superior qualities in a seaway. Thisresult may seem surprising because of the smallerpitching motions which were found for the bulbousbow model. It has to be remarked, however, thatthe change on the phase of the motions can resultin a reduction of the propulsive efficiency. Such areduction was found by Takezawa [9]. This couldbe a possible explanation for the larger power in-crease of the bulbous bow ship.

References

I. Lindblad, A.: Experiments with bulbous bows. Publication of theSwedish State Shipbuilding Experimental Tank, Goteborg1944.

Doust, D. Jr Trawler forms with bulbous bows. Fishing boatsof the world: 2. London 1960.

Inui, T.: Wave-making resistance of ships. Transactions of theSociety 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. 'KurenaiMaru", Part Ill - Photogrammetrical observations ofship waves. Journal of the Society of Naval Architects ofJapan, Vol. 110, 196!.

S. Shigcrntsu, M. and K. Kai: The wave-cancelling effects of wave-less bulb on the high speed passenger coaster ms. 'KurenaiMaru", Part II - The full-scale experiment. Journal of theSociety 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. Journalof the.Society of Naval Architects of Japan, Vol. 110, 1961.

Dillon, E. S. and E. V. Lewis: Ships wih bulbous bows irs smoothwater and in waves. Transactions of the Society of NavalArchitects and Engineers. 19SS.

Gerritsma, J;, J. J. van den Bosch and W. Beukelman: Propulsionin regular and irregular waves. International ShipbuildingProgress, 1961.

Takezawa, S.: A study on the large bulbous bow of a high speeddisplacement ship, Part II - Performance in waves. Journalof 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 .09015II. 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. Transactionsof the Society of Naval Architects and Marine Engineers,

- Figure_s . 1956.

8 9 10 11

I II10 11 12 13 1!. 15 16 17 18

'V9 KNOTS

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 spectrumg acceleration due to gravity.

H '/3 = significant wave height.

a

er,p

19

2

L

LCD

ii

P

0

TV

vszzotn

zo 1/3

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.= dimensionless increase of thrust.

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 purposesespecially with regard to fault protection with a survey of winch drives recently applied on boardof these ships and their influence on the generating capacity (Dutch).

By ir J. C. G. van V7ijk. February 1957No. 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 calculatedcurves of righting levers. -

By prof. ir J. W. Bonebalzker. December 1957.No. 28 M Influence of piston temperature on piston fouling and piston-ring wear 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.

By ir. A. Hope and ir. A. M. Hens, December 1959.

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 entrainedwater 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 wavesBy 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 connectionsBy 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 paintsystems 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 waterpressure 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 literalload 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

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