Vertical motions of ships with bolbous bows

August 1971

LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

VERTICAL MOTIONS OF SHIPS WITH BULBOUS BOWS

by

N. Yourkov

Report No. 320

"VIRTICAL MOTIONS OF SHIPS WITH BULBOUS BOWS", by

N.

Yourkov.:

Suwary.

Ship motions and hydrodynamic coeffioients wore calculated for ths models of ships with two values of block ooeffioient and different formo of bulbous bow.

Tha oomputed resulta of ship motions for two modela were oompared with the results of the experiment, which was

madi

in the Delft Shipbuilding Laboratory.

Engineer, Leningrad Shipbuilding University, visitor of the Shipbuilding Laboratory, Delft.

Io. jntredustien.

It van proved that for higher epeeds, where the wave making reeistanoe accounte for an important part of

the total

reeistance experienoed by a

ohip, a oorrectly conetruoted bulb oan reduce the still water reeietance °considerably. Lindblad (1), Inui (2) and others

W.

(4) showed that by adopting large bulb-areas great reduotion oan be obteined in the speed range Fh m 0.24 0.28.

In last years several publioations appeared comerning the influense

of the bulbous bou on

the Ship motions in wavee. Idllon and Lewis

(5)

eade an experiment with four models of paseenger linero with bulb sise 0%, 40%1 50% and 15.5% in emooth water and in wawa. In their experimental-they found that a vide variation in bulb.oise has a rather small effeot on the ship motions and reeistance in wavee. They stated that a choice of a large bulb oould be done on the basio of cala waiter resietanoe.

Doust (6) in his experiment° with trawlers found that the speed-loss in wave@ ie lose for the bulbouo bow form for Pn>0.22, below - the @peed

l000

is larger than for the oonventional form. Depending on the wave-ship length retio and epeed the motione of the tWawler with bulboue bow in reaular hood waves are larger or lees than for a ship without a bulb.

Tekesews (7) inveetigated the performanoe of the destroyer modal with-out bulb and with 26% bulb. In his

reosarch he came to

the oonolusion that the large belboue bow can decrease the ship motioni, but it ocaserna only pitch anplitudes, beoause no data for heave are given in Takesawale _paper. The thrust inoreaoe in wavee of the hull with large bulbous bow was

elightly bigger than that of the ordinary hull due to the reduotion of the propuloivo offioienoy in waves, whioh was eaused by the dot:resale of the meen immereion of the propeller, and due to larger resietance increase in

VOVOQ0 The total EHP in irregular waves seemed to be lose _{or nearly equal} that of the oonventional hull, exoept for the case of the very high ueao. Gerritoma and Beukelman (8) oempared the performanoee, _{with regard to} setione and propuleien in longitudinal irregular waves, of a CB

a

0.65 porieo Sixty hull and its modification with

10

_{bulb and sorrespondingly} medified forebody. It vas shown that the bulbous bow has a mailer pitching motion but an increased heaving motion in camparieon _{eith the parent model.} The differenoe appeared to be not larae, and it was oonoluded that the ship motions in longittdinal wavee were not muoh influenced by the bulbous bow.

The same was stated for the wetness characteristics, for there was no strong indioation that the hull with bulbous bow had better qualities than the parent model. As to the propulsive performance in waves it was

shown that the power increase was larger for the ship form with the bulbous bow; the sane for the inoreaoe of torque and revolutions. Beeed on the

average weather oonditions the difference in propulsive performance be-tween the two ship formo yes estimated to be small. A

oonclusion was made

that for that coneidered particular case the bulbous bow did not have raperior qualities in a seaway.

Vahab

(9)

investigated the behaviour of a fast cargo liner (CB L 0.62)

with a conventional and with a bulbous bow (17.2%) in a seaway. He found that in regular waves the added resistance due to the wavs was higher for the ship with a bulb than for the ship with a ()conventional bowoespeeially when the waves were longer than the ship's length. The pitching motion was slightly reduced by fitting a bulb, the heaving motion and the relative motion beteeen the ship and the wave aurface were beth reduced in rafter short waves and increased by the bulb in long waves.

ftperiments in irregular seas ahowed that the opeed increase due te the bulb with (=latent power was smaller in adverse weather than in smooth water. The advantage of the bulb vas expected to vanish in bad weather. The prebability of shipping green water and slamming vas small fer both bow oonfiguratione in ma states corresponding te wind force* unaer Beaufort 8.

In extremely badaveatherivBeaufort

8 and bigher,the bulb sawed an -imemeeeed liability to clamming.

Van Lammeren and Pangalila (10) made experiments with models of a 24,000 DWT bulkoarrier (CB 0.764) with cenventional and bulbeue bow

_(9%

in full load oonditien). They perceived that in leaded condition applioation of & bulb had hardly any effect on power both in still water and in waves. In ballast *audition a gain in speed was obtained by bulb fer mpoods above 13 knots. Bending moments were net affected adversely by the _{bulbous bew.} Relative motion of the bow was decteased nOtiseably by the bulb for the

ship in fallead.cenditiem; in ballaat condition there _{was no differenee.} Pitehing motions were practically the _{same for the models with and without} bulbous bow.

Ochi (11) made model experimente te _{determine the effect ef a bulbous} bow en ship's slamming. The experimente _{were condueted on two models .the}

From the resulte of his experiments he made eenclusiens that the mariner had less resistance than the mariner without bulb, both in still water and

in waves, bow acceleration for the mariner was lees than that for the modi-fied ene, however, the pitohing and heaving motions for the mariner were

larger than those for the medIfied-:mar¡ner. Slammingkmeeleratien far the:nariner was a little leas at comparatively low speed but became larger than for the

modified mariner at high speed.

Van Mater (12) made an experimental investigation of the behaviour in oalm water and in waves of a

model

equipped with en extremely large bow and sternr bulbs. It was found that suoh a ship had advantages related to the remietanoe in calm water and in waves in oomparison with oonventional dhips. Pitohing motions in head %levee were odbutantially less for high

epeeds, heaving

motions were larger, especially in long wavem.

Smith (13) and Smith and Salvesen (14) made an investigation the main objectine of whieh wae to prove the validity of the Korvin-Kroukeveky strip theory fer high

speed destroyer hulls with large bulbs. It was stated-(i3)

that for ahipa_with bulbous forma the usual Lewis-1mm station representation, whioh was wed in most strip theory ship motion computer programo would give resulte, which differed from those obtained from strip theoriee utilising a mere accurate olooe-fit ship section representation, and for thio reaaon s, new eleeefit method was developed and used in that work. The heave and piteh amplitudes end their phase angles were computed for twe bull

femme,

the Davidson A destroyer and ths Frieeland olaso frigate.

_{The,"Davideen A"}

had larger heave amplitudes than the "Friesland" for the entire wave-length range; the pitoh, on the ether hand, was increased by the bulb in the long wave range: and decreased in the Short wave range, the heave and tha

phsees were reduced by the effect of the bulb by as mueh as about 70 degrees The oomputatione show that the bulbs in general have ti offset of

increasing heave while decreasing pitch, but most experiments with _destroyers with large sonar domes did net show this large difference _{as indioated by} the strip theory. Fer this reason in (14) it vas decided te test carefully the "Davidson A", by investigating _{different testing techniques and the effect} of nerraineerity and to compare _{experimental resulta with oomputations.}

During the experiment it was found that heave _{staff technique, which} praotically universally has be en adopted for _{measuring pitch and heave in} head waves, could seriously affeot the _{measurements.}

L.

Helio with lar bulbs have coneiderably larger heave response than the regular forms. Finatly froaerunning tests were performed in regular sees with the model self propelled and remotely ¡steered. The investigation of non-linear effect ahowed a decrease in the nonedimensional heave amplitude with en increase OS the wave height. The piteh responses were found to be

affeoted similailrby the wave height, ehile the pitch and heave phases were not influenood by the melange in wave heieht. The final experimental

rooults were oompared with computed reoulte obtained from (15), where the program vas written aocerdineeeo the Gerritsma-Beukelman version of the Koevin-Ktoukoveky strip theory (15) and each ehip **cation was repreuented accuretely by the oleee-fit mapping promodure. The comparison Showed eoed adreement between computed remit° and free-running experimental resulto.

Seukelman (16) experimentally determined tha coefficients of equations of ship motion's and yaw foroos 8nd momonto for the model of the Devideon A deotreyer. The meacured reclaim were compared with the remits

e

compute..

tions bane& on two emodeeet of ¡strip theory and on a "rational,' strip

theory

fer slender

bodies. It was Shown that in moot SWIGS experimentally determined eoeffioiente better agreed with commuted resultmeaccerding to (15). The

ealculated chip metione according to differemt veraione

wore rather near,

but At we pointed out, that in the limit OWNQ of infinite long

UMW

the nemediceselenal motion applitueee

Z0g7a alai Clefts ehould

tend,te the value 1 and the lime glee for heave and pit& ahould

reepeete0WAead

to 0 and 90 neereeo. But thie tendency le only eerreet for the action reoulta according

to veroion (15) and appeaws te grow more importa:mat for

higher apeeds.

In the preoent paper there are preeented resulte of eyotematio eale

etlatiene, whish eere oarried out for model,. with twievulueo e block

oceffieient with eenventionel and bulbous booc.It isothown thatimlbouo

bow .119.E!

_{influence on the ship motions fer modele with 0E111 bleak}

oceffieient than for models with higher velum of block ooeffieient.

The

aaleulated values ef the ooeffieiento of equetion° ef chip motions =O.

presented._ Finelly,the caloulated reeelts for twe models

are oompared

II Models.

It is known, that in the present moment bulbous bows are used for different types of commeroial ships, starting from high*speed oarge liner with rather small values ef block ooeffioient (CB' 0.60) te huge **per tankers with high values of block coefficient (C3^.--- 0.80)0 In these inves-tigations it was decided to determine the influenoe of bulbous bows an

motions of ships with different valuem of block coefficient. Por this reason two groups of models were oonsidered - one on the basis of Sixty Series model with OB = 0.65 (5 models), the other en the basis of Sixty Series model with

CB .

0.75 (5

models . In each group the oomparieon is made between the model with oonventional bow and two modifications, each with an added oylindrical bulb of 10% and 20% of the middle cross section. Cylindrical bulbs are based en a sphere located in front of the ship, while the centre of the sphere is always in the longitudinal plane of symmetry of the ship on the P.P., and the lowest point of the otters is on the base line.

Two modifioations of Sixty Series with CB . 0.65 have the afterbedy of the original model and 10% and 20% bulbous bow with correspondingly ehanged forebody acoerding to (1).

In table 1 the main particulars of the modele are given, their body plena are given in figure 1.

III Calculations.

In the present moment several versions of the strip theory or of the slender body theory are used in different ship-motion computer programs. These are: Gerritsma _{Beukelman version of the Korvin-Eroukoveky strip}

theory (13), versions of Vugts (17), Blagowetsjenskij (18) and Netsvetaev (19) and a "rational" strip theory for

_{slender ships by}

_{Ogilvie and Tuck}

(20), the later is used in Me

Prank aleio-fitohipi-ototian

_{0029ater program (21).} It was not the taek of present work to _{inveetigate different versions of}

theory, so keeping in mind

the

_{results obtained in (14) and (16), it vas} decided to use for the present calculation

_the

_{standard ship-motion} com-puter program of the Delft _{Shipbuilding Laboratory (13), (13) and (16),} a000rding to the first mentioned version.

In this proven the coefficients of _{the equations of motion are for} heave (a

+V

+ bi + oz d - e E.?

9

=

F

pitch (A +

ky?,07)ij

_{+B(.9+CO-DS-ES-Gz .14T}

and having the following form

f

m

b Ntcbt - v

Lar

dal'

dx

2(/ g

lywdx

f

m tloix +

_'N'

_{dx - --v-2- Lai-, fix}

We2 L

_uj

_{e2 L uxf}

e =

_IN'xdx

- 2v ifmidn - ?:dg-/1- =ix

= 2e g y war dIr

' L

A = J mix2dx +

IN'Edz

-

_idm1

e2

Le2 L

xdx

co

B = JrNv1t2dx - 2v

fm'adn

v x2d.x L dx

e

ga 2 P g

fy2dz

L

fasmix

Nixdx _{dm zdx} L G = 2? g isfyttzdx

the wave foroe

¡Ea _-kT cos)(

,

)dx

°

we" EFt. =

_g

_Y sin 00E, ₊

sin

(kx)dz 1.0

_fm'o-kT

a t's _(kx)dx oeo 2 sin dm'% -kT*

y

art

e

the wave moment

M m-dmi

-kT

_a

e,

con

s

s

£M5

qg

fye

-kT

c

_in

os

(kx)dx .1

W4N,

cb...r)xe

L

s

L

*

)(

-kT

oos(kz)dx

sin

ein (

2 kx)di +

W

m'Ite

cos

_L o

1

/. L,

where T

*

. - r in kJ.

j ye

kz

de)

7

411

and T sectional draught.

In (14)

and

_{(16) it was shown that for ships with a transom stern} it is neoessary to take into account ther ending terms, this is _{the added} mass and damping oeefficiont for the atern cross &lotion. In the oase of

ships with a bulbous bow it is neoessary to take into acoount the added mass and

damping

_{coefficients of the cross section on the forward}

perpen-dioular. So in our ease the coefficiente of the equations of motion are a .

Jrieds

b dirE'dx vm2o

. 2Çg

fyiddx d

[Wads

+ JrNidx -

23-m20

to

2 L

_We2

./11'sdx -

v Jrm'ds

vm20 x"20

2fg

lywzds

Av2

fm,x2dx

+ _)(N'ads

_+1j5

_IM'dx

m20 20 Cd 2 L

We2

2

INIx2dx

vm 20

x'

20 C = 2i) g Lfy.ar2dx vi

a

_fm'xdx

L

a

f11,3cdx

+ v

_{irmidx - vm20 x 20}

L L

a

25)g

4wxds

L

The two dimensional added mass and damping of the oross sections vare

reoeived

by using Ursell's (22) solution _{for a circular cylinder} oscilla-ting at the free surface. itatthis reason the oonformal transformation of the cross emotion to the unit circle was used.

This methode-using a three coefficient or Lewis-form transformation are usefull for cross sections of oonventional ships (Tasai (23), Grim (24) ) but fail for motions with extreme chapee. In this ciao* it is necoaaary to extend the Lewis form tranaformation to a multi-coefficient transformation as given by Smith (13) or de Jong (25), or to use the olote-fitleethod,dayeloped by

Frank

(21)., in our case it was decided to use the tranaformational method whieh is given in (25).

This method allows to receive up to 19 transformational coofficients depending on the form of the cross section and on the given accuracy.

Only in extreme cases (with 20% bulb) where the above mentioned method felled, the (13) method is used, which gives up to 61 transfor-mational ooefficients.

IV Analysis of the calculated resulte.

Tho calculated ship motion amplitudes, phase angles, wave forces and momento, the coefficients of the equations ofmotion for different modele are given in a non-dimensional form as follows:

for heave for pitch

Zos/Da..

_K

4.

A

+ -2

S'Vr

6

VT_

çqv

qVLVir-cl

qvt_

çvL

E

e

vVC

qVV(317-Fa.

M

a

KAIA,

Ç'3IL

whore ku .

_éywdx

_{and IL .}

_fyw

_z2dx.

The calculated ship motions and their phase angles for different modelo

are given in

figures 2 - 9, for Fn . .20 and Fn *30. Ftom theoe figures it is possible to see that the bulbous bow increases the heave amplitudes, practically in the whole range of waves. A greater bulb causes a stronger increase in heave amplitudes. For the models with a low block coefficsient the increase of heave amplitudes for oylindricial bulbs is practiomlly the same as in the oase of changed form. For the models with a high block

coefficient the tendenoy of the change of the heave amplitudes iø the same, but the differenoe between models with conventional bow and with bulbous bow beoame less. At the same time it _{tt3 interesting to note that the}

in-crease in heave amplitudes for all modele is _{practioally independent of the} speed, so with the increase of model's _{speed the relative increase of heave} amplitudes beoame lees.

The pitch amplitudes of the models _{with bulbous bow are, generally,} larger than of the models with _{conventional bows in long}

waves and less

in

short waves. Tho bigger bulb the greater difference in pitch amplitudes.

The wave length for whioh the modele with bulbous bow became euperior in piteh amplitudes depends on the model's speed; with the increase of speed the bulbous modela became superior in pitch

for.longer waves..At the same

timo it is showed, that

for the modols with e low

block eoeffioient the difference in pitch amplitudes is mere signifioant, than for the modela with a high block coefficient; this differenoe is very small in the ehole range of waves.

The pitoh and heave phase angles for all models are practioally not influenced by the bulbous bows. For the modela with a low block °coefficient it is possible to notioe, that the difference in phase angles between the modele with conventional and bulbous bows, is greater for pitch phase angles and less for heave phase angles, while the models with a high block coefficient practically show no difference.

Ile may oonolude that bulbous bows onuse Larger heave amplitudes, and inorease in pitoh amplitudes in long

WIWI

and decrease in

short waves,

the laot depends on the ship's

speed.

Tho

motions

of the dhip

with a low

block coefficient are more influenced by a bulbous bow than of the ship with a high block coeffieient. The phase anglos ate-net influeneed by the

form of the bow.

The ealculated ooefficienteef the equations of motions are given in the

slo-

26, as well as the wave forces and moments.

Concerning the coeffioiento of the motion oquatiens it is apparent that coefficients "a" and "A" are practically the oame for the models with

oonventional and bulbous bobo, their values are independent of the form of the bow; se, added mass and added moment of inertia of a ship are net influenoed,by the bulbous bow.

Coofficlients "b" and "B" for models with bulbous bew are smaller then

for the model's with conventional

bow, the difference is bigger at lew frequencies and deoreaseo with the inorease of frequency. The difference in oesffieient B in dependent en the speed and inoreases with the increase of opeed. For the modela with a high block coeffieient the difference in the ooefficiontseb" and "B" is smaller than for the models with a low block ooeffioient.

As te the arose coupling ooefficients "d", "D", "e" and "EP it is

poceible to eay that the differenoo in the ooeffieients "d" and "D" _{for models} with oenventional and bulboue beefs is very small, the coefficients "e" and "Ep are more sensitive for the form of the bow, but at the same time the difference in theee ooeffioients is practically independent of the _speed.

The comparison of the calculatd values of the wav exciting force and momenta shows that the bulboas bow practiOally don't influence them; a small difference ()mid be found only in thort yaws for the modele with a low block coefficient.

From the statements whioh were made Above it ie possible to conclude that the main differenoe in motions for ships with conventional and belbous boye is (mused by the difftrence in coefficients of the equations of motion "b", "B", "e" and nEr. As it was ehovn by the preliminary oaloulations thy magnitude of these ooeffioients (espeoially of the oross-ooupling coefficiente) to a high degree depends on the *mosey of determining the

sectional added mass and damping of the end cross sections, so the bulb orates seotions. And as this accuracy is mainly defined.by the 111001=4y of

the conformal transformation of these cross seotiens, this problem must be treated very carefully. From thio point of view it is difficult to mee with the statement made by Beak in (26), that even the poor repreoentation of bulb type sections by a Lewis form

doee

not influence the resulted ehip motions. Such a statement is possible only in the ease that the chip motion equatiena are solved without

taking

inte_account the end terms.

it-vas,4homa bp Ut9011 and Porter that wemisubmerged circular, elliptio and Lewio form cylinders give rise to non-sere forest] for heaving easillation at finite frequencies in deep water. Motora and Koyama (27) had meowed the heave exciting foroes on circular and elliptic oylinders,with vertical otrute in regular waves. Their resulte indicated the exciotenee of almost

vaniehing

minimum forces for some of their test modelo. They, oenjeotured that corresponding to these minimum exoiting forces on

the

teeted bulbous forme, the damping coefficients for the respective wave nueber muet be prac-tically sero. Frank ehowed in

(20 by

direct °amputation that far different

bulbous oylinders the damping vanish for soma wave numbers; this

wave number dependa an the geometry of the bulboue cylinder. Fromthe seme-obbsilatiens it could be seen that the added mass of such oylinders is also dependent on the geometrical form.

From this it might be possible to dray the conclueion that in special oases by wpattieularly eenstraeted,bulboue bau,r4 is peeeible-to reeeive a

certain ohange in ship motions in some range of waves and speedo. But this question needs; additional and thorough investigation.

In the present moment it is poesible te aey that for transport shipo the bulbous bow leads to the increase of heave amplitudes, _{while pitoh,amplitudes}

in most cases are increased in long _{waves and decreased in}

_{short waves. But}

the last depende on the ship'e block ooefficient and

_with

_{its inorease the} different,e became leas,

V. EXperiment.

In order to check th possibility of the strip theory to predict the pitoh and heave amplitudes and their phase angles for hulls with a bulbous bow, an experiment was made in the Delft Shipbuilding Laboratory, with the ship models (CB . 0.65) with a oonventional bow and with

a 20%

cylindrioal bulb. The principal datas of these modela are given in

table 1. The modele were tested in the small towing tank in regular waves

;LA

.

0.6 - 1.6 with a constant wave height ofz.t. 1/50 L and a speed range of Fn . 0.20 - 0.30.

The results of the experiment are shomn in tha figures

27

-The results of the experiment show that the model with a bulbous bow practically in all wavee has smaller pitoh amplitudee than the model with a oonventional bow. The heave amplitudes are prectioally the same forhoth modele in the range of wavew which was inveetigated; only fer long waives the model with bulbous bow shows the trend for higher heave amplitudes than the model with the oonventional hew.

The heavy and piteh phase angles are practically the same for both models.

During the experiments the added wave resistance forleth modele wae measured4' it appears, that the model with the bulbous bow has higher added wave resietance than the modal with the conventional bow im:Ahe Mhole range of waves and speeds (figure 29).

The resulte of the experiment were compared with the calculated results. It was done for the model.with CB . 0.65 and 20% eYlindrical bulb, which was tested during investiaations, and for the model CB

a

0,65 with 10% bulb and changed forepart; in this case the experimental reeults were t8ken'frea.(8). The resulta are ehown in the

fifieree 50,-133.

From the eomparison it ie possible to see that experimental and

caloulated piteh amplitudes are in a rather good agreement; the same could be said.about heave and pitoh phase angles. For the heave amplitudes, it appears

that the

measured values are smaller than the calculated ones, especially in the resenanoe region. But as it was stated in (14) the

experimental heave amplitudes are'greatly influenced by-the applied test teehnitue. In our experiments,the model mas tested with a heave staff, whieh according to:(14) can deorease the heave amplitudes'beeause they are very sensitive for all extra frietiolvthat could ooeur in the-heave staff.

However reeont tests in the Shipbuilding Laboratory in Delft, the resulta of which would be published latera shows that non-linearity may be

the

main reason of the derivation between caleulated and measured heave tions.

It is possible te conolude, that

strip,theary

can predict

ship motions for hulls with bulbous bow with suffioient accuracy.

VI Conclueion.

From this investigation the following oenclusiens can be derived. Por a normal transport ship the bulbous tows cause an inorease of heave amplitudes practically in the whole wave range. This increase can be very significant and depende on the bulb sise - the bigger bulb the greater increase of heave. The pitoh amplitudes in most oases are decreased in

short waves and inoreased in long waves, but the difference in pitoh ampli-tudes is not so significant. The pitch and heave phase angles practically are not influenced by the bulbous bows.

The influence of the bulbous bows on the ship motions is greater for ships with low Vaiutsof the bleak coeffioient and rather small for !hips with a high block coefficient.

The comparison between the calculated and experimental resulta shows that the theory can quite accurately predict *he pitch and heave amplitudes and their phase anglas for hulla with different bulbs.

While uaing ship-cotion oomputer programs it in necessary to

_pay

m4oh attontion te oorreot cloae-fit representation of bulb sections, especially for those looated near the fore perpendioulibr. The accurately oaloulated eeotienal added masa and dapping for suoh cross sections will lead to

MOTV oorreot ship motions reeulfts.

At the same time babous bous can lead to the inorease of added resis-tance in waves in comparison with conventional ships.

Aoknowledgement.

The author is indebted te the staff of the Delft Shipbuilding Laboratory who gave him the possibility te,fulfil this work during his stay in the Netherlands.

The author wishes te thank:

Prof.ir. J.Gorritama, for allowing hits to carry out this investigation and for the oontinuous encouragement and stimulating discussions.

Mt. W. Beukeltan, for his constant help, uhieh allowed him to finiah this work in such a rather short period of time.

Mt. A. Versluis, for his assistance and belp in carrying out all the oomputer work.

The mtaff moMbers of the towing tank, for assisting him in tho experia4ntal part of the work.

Referenoes.

Lindblad, A.:"Experiments with Bulboua Bows."

Publication of the Swedish

State Shipbuilding

Ekperimantal Tank, 1944 Inui, T. s "Wave-making Resistanos of Shipa".

Transactions of the Society of Naval Arohiteots and Marine Engineors. 1962.

Takahei, T. and Inuit T.: "The Wave-oancelling Effects of Waveless Haab On the high speed Passenger Coaoter m.s. "Kurenai Maru".

Part III. Journal ef the Society of Naval Architects of Japan, 1961, Vol, 110.

Takesawa, S.: "A Study on the Large Bulboua Boy of a High Speed

Displace-ment Ship".

Part I. Journal of the Society of Naval Architects of Japan, 1961,

Vol. 110.

Dillon, E.S. and Lewis, E.V.: "Ships with

_{Bulbous Bous in Smooth Water}

and in Waves".

Transaotions of tho Sooiety of Naval Architects and Marine Engineers, 1955. Dount, D. J.: "Trawler Forms with

_{Bulbous Bows".}

Fishing Boats of the World : 2, London 1960.

Takosawa, S.: "A Study on the Large Bulbous Bou of a High Speed Displace-ment Ship".

Part II. Journal of the Sooisty of Naval Architects of Japan, 1962,

vol.

Gorritoma, J. and Beukelman, W.: "The Influence of a Bulbous Bow

on the

Motione and the Propuloion in Longitudinal Waves". I.S.P, 1963, Vol. 10, No. 105.

Wahab, R.: "Research on

Bulboun Bou Snipe".

Part I.B. Publioation of the Netherlands

_Research

_{Centre,T.N.O. for} Ship-building end Navigation, 1965, report N 765.

Van Lammoren, W.P.A.

_{and Pangalila F.V.A.: "Research on Bulbous Boy}

Ships".

Part II.B.

Publioation of the Netherlands Research Centre T.N.O. for

Shipbuilding and Navigation, 1965, report N 728.

Oohl, K.: "Model Experiments on the Effect of _{a Bulbous Bow on Ship} Slamming°.

David Taylor Model Basin, 1960, report 1360.

12. Van

_{Meter, P.R.: "Preliminary Eieluation of a Large-Bulb Ship for High}

Speed Operation in Smooth Vale* end in Rough Seas".

Smith, W.E.: "Computation of Pitch and Heave Motions for Arbitrary Ship Forms".

I.S.P. 1967, Vol. 14.

Smith, W.E. and Salveson, N.: "Comparison

of Ship-Motion Theory and Egperiment for Dmvideon A Destroyor Form".

Naval Ship

Research

_{and Development Center 1969; Technical Note 102.} Gorrittma, J. and Boukelman, W.: "Analysis of the Modified Strip Theory for the Caloulation of Ship Motions, and Wave Bonding Moments".

Nothorlande Ship Rosearch Centre, 1967, report N 965.

Boukolean, W.: "Pitoh and &love Charactoristies _{of a Destroyer".} I.S.P, 1970; Vol. 17, No. 192.

Vugta,

_{J.: "The Hydrodynamic Forces and Ship Motions in Waves".}

Dolft,.Utivetity Of Te4hno1ogy, Dissertaticn.

Somme

Tjan Tsanskij, _{Blagovetsjenskij, S.N. and Golodilin,}

A.N. Book: °Motions of Ships".

Publishing Off ice "Shipbuildire,

_1969,

_Loningrad.

Berodaj, _{Notevetasf, U.A. Book: "Ship Motions in Sea}

wavee". Publishing office "Shipbuilding", 1969, Leningrad.

Ogilvie, T.F. and Tuck, E0.: "A rational _{strip theory of ship Motions".} Part I. Department of Naval Arohiteoture _{and Marine Engineering ef tho} University of Michigan, 1969, N 013.

Frank; W. and Salveoen, Ls "The Frank Cloao-fit Ship Motion Cmputer Program".

Naval Ship Reeearoh and Development _{Center, 1970, report 3289.}

Ursell, F.s "On the

_{Heaving Motion of a Circular. Cylinder on the} Surfaeo of a Fluid".

Quarterly Journal of Mechanical _{and Appliod Mathematics, 1949, Vol.}

11,

Pt. 2.

Tonal, F.: "On the Damping Force and Added Mass of Ships Heaving and

Pitohine.

Report of Research Institute for _{Applied Mechanics, Kyushu University,}

1960.

Grim, O.: "A Method for a More Precise Computation of _{Hoaving and}

Pit-fishing

Motions, Both in Smooth Water _{and in Waves".} Third Syaposium on Naval _{Hydrodynamics, 1960.} do Jong, B.;

_{"Computation of the}

Hydrodynamic Coefficionto of _{°affiliating} Cylindors".

(

Book, Bait "A Computerised Prsoodurs for Prodiotien of Soakoaping

Porfornanoo".

Mapeashuaetta Institute of Technology, Dopartnent of Naval Architooture

and Marino Ingiboorinff 1969, ropert N 69-Z.

Nstoral,S. and germs, T.' "Oa UlarmAMOitation Pros Ship Peron".

Journal of Zoson iri, (Tho Ssoioty of Naval Arehitoats of Japan)

1965, Vol. 117.

Franht EI.. s "The gown Damping Cooffioionta of Bulbous Cylinder°, partially

tumormed in Deep %tor".

AsaiskUak.

abodeg

osoffioiemto ef the equations of motion

BCDEGJ

far hobo= and piteh

Ato

won ef watorplare

OB

bleak ooaffioient

wave torso

Pa

ammo fame amplitude

Pa

Proude nmmbor

a000leration of gravity

IL

longitudinal moment of inortia of vatorplons mom

2117X,

VIM

number

lonaitudinal radiva of inortia of the model

lane* between perpendiculars

wayo momant

Ma

ways smolt amplitude

m°

sestionel addod mass

g20'

motional added nose at tha bow

N'

¡motional damPing

draught of the modal

y

forward wed of the model

YV

half width of waterlina

'wave dieplecoment

sa

teams amplitude,

E.

phaao angle batman motions

ingtantanaous wave 0.ov-et/on

yaw applitude

pitoh -male

ea

_{piteh amplitude}

Tommy length

dencity of water

S7

'volume of dieplacement

LA..)

°Uvular fragile-nay

Table 1.

MODEL

DIMENSIONS AND PARTICULARS.

Model designation

and condition

Series

60

I modifi-cation II modifi-cation

Series 60

plus

cylindrical

bulb

Series 60

plus

cylindrical

bulb

Series

60

Series

60

plus

cylindrical

bulb

Series

60

plus

cylindrical

bulb 1

Displacement

56.970

56.970

56.970

57.300

58.020

_75.300

75.660

_76.210

Length between

perpendiculars

2.26

2.26

2.26

2.26

_2.26

_2.26

_2.26

_2.26

3

Breadth

0.311

0.311

0.311

0.311

0.311

0.335

0.335

_0.335

4 Draught

0.125

_0.125

_0.125

_0.125

_0.125

_0.134

_0.134

_0.134

5

Block coefficient

0.65

0.65

0.65

_0.75

6

Midship section

coefficient

0.982

0.982

_0.982

_0.982

_0.982

_0.990

_0.990

_0.990

7

Prismatic coefficient

_0.661

_0.661

_0.661

_0.661

_0.661

_0.758

_0.758

_0.758

8

Naterplane coefficient

0.746

_0.733

_0.728

_0.746

_0.746

_0.827

_0.827

_0.827

9

Half angle of entrance

9.1

7.8

7.0

_9.1

_9.1

_22.5

_22.5

_22.5

10

Centre of effort of

waterplane

-0.060

-0.076

_-0.077

-0.060

-0.060

-0.016

-0.016

-0.016

11

Centre of buoyancy

-0.0113

-0.0099

-0.0026

-0.0048

_0.0060

_0.0299

_0.0347

_0.0419

12

Longitudinal radius

of inertia

_0.25LBp

_0.25LBp

_0.25LBp

_0.25LBp

_0.25LBp

_0.25LBp

_0.25LBp

_0.25LEip

13

Bulb area in percent

Fig.1: BODY PLANS

1 MODIFICATION 10% BULB 1 SERIES SIXT Y C_e I MODIF !CATION 20% BULB

2.4

2A

0.8

0.4

O 1.6

1.2

e

0.8

Oh

CB

= 0.65

_{V =const}

10% bulb

without bulb

20 Vo

bulb

Fig 2

Heave and pitch amplitudes for Fn = 0.20.

12

2.4

11

12

ea/Ka

0.8

0.4

O

0.2

CB

=0.65

0.4

0.6

0.8

IrT7

111111111.

V =const.

without

bulb

10% bulb

1.0

Fig 3

Heave and pitch amplitudes for Fn = 0.30.

-40

80

s-cn

a

1

120

Ezc 160

Ee

200

240

280

320

CB

=0.65

V

= Const.

.\ 777

0

0.2

0.4

0.6

0.8

1.0

1.2

without bulb

10% bulb

20% bulb

E4

160

Elac

200

240

280

320

CB=0.65

V=

Const.

l\FTX7 -31111w

Fig 5

Heave and pitch phases for Fn = 0.30.

-40

a,'"

80

012

-a

120

1.0 1.2

0

0.2

0.4

0.6

0.8

2.4

2.0

$1.66

0.8

0.4

o

1.6

0.4

CB= 0.65

+ cylindrical

bulb

without bulb

10%

bulb

20% bulb

0.2

0.4

0.6

0.8

1.0

1.2

0.-7)7

2.4

2.0

Za/

1.2

0.8

0.4

O

1.6

0.4

O

CB =0

65 + cylindrical bulb

without bulb

10%

bulb

1.2

0.2

0.4

0.6

0.8

1.0

\i/175:7

2.4

2.0

1.6

Za/,

/

_1.2

0.8

0.4

O

1.6

1.2

ea/

/K

Ea

0.8

0.4

Fig 8

_Heave

CB=

0.75 + cylindrical

bulb

without bulb

----

10 % bulb

20% bulb

and pitch amplitudes for Fn = 0.15.

0.2

0.4

0.6

0.8

1.0

1.2

2.4

2.0

16

0.4

08

0.4

Fig 9

CB

=

0.75 +cylindrical bulb

without

bulb

10% bulb

20% bulb

0.2

0.4

0.6

0.8

1.0

\/757

---1111111w

Heave and pitch amplitudes for Fn = 0.25.

1.2

Za

1.

a

25

2.0

05

without bulb

----

10% bulb

20% bulb

O 1

₃

₄

W

1\r7-1/T

CB

= 0.65

_{V= const}

O

2

3

w 1.VW

5

Fig 10

_{Coefficients of added mass "a" and damping}

?lb?,

2.5 11

CB

_{0.65 +cylindrical bulb}

2.5

2.0

1.5

1.0

without bulb

10

%

bulb

0.5

20% bulb

Fig 11

Coefficients of added mass "a" and damping "b" for Fn = 0.20.

5

1

2

3

₅

o

3

₄

Lig

25

2.0

05

10 % bulb

20% bulb

O

F g 12

3

w\g-Tg'

4

CB=

_{035 + cylindrical bulb}

f

Coefficients of added mass "a" and damping "b" for Fn = 0.20.

1

4

w

1V7.1;--7

25

2D-1.5

0.5

=0.20

without bulb

10%

bulb

20%

bulb

1

2

3

4

CB =0.65

const

O

2

3

w

w

1..VW

CB

=0.65

V= const

o

2

3

4

o

2

3

4

5

w

1\f=k-7

-Mow

w

1/7/ 7

2.5

2.0

0.5

without

bulb

10% bulb

20% bulb

Fig 15

CB= 065

_{+cylindrical bulb}

0125

0.100

0.075

Q-0050

0.025

U.N17i7

-21111

for Fn = 0.20. W

Coefficients of added mass moment of inertia Ati and damping moment IIBII

1

2

3

₄

_O

Fig 16

3

₄

WW1

Coefficients of added mass moment of inertia

2

₅

CB= 0.75

_{+ cylindrical bulb}

ITA

0125

0100

0.075

0.050

0.025

and damping moment BIT

2

3

4

(DOW-7

----sm.

for Fn = 0.20.

o

Fig 17

CB::

0.65

2

3

4

w\FA-7

Mass coupling coefficients "d" and "D" for Fn = 0.20.

01.75

0.50

-G25

V const

075

0.50

1

025

17113-CL

0

025

without

bulb

10% bulb

20% bulb

O

Fig 18

CB

=0.65 + cylindrical bulb

5

for F

= 0.20.

0.75-a50

025

0.25

I I

2

3

4

ItDIT

2

3

4

UNI:7(i7

Fig 19

2

3

Mass coupling coefficients

4

11d11

_{and "D" for Fn = 0.20.}

CI3

_{= 0.75 + cylindrical bulb}

0.75

0.50

1

3

--awe-0.50

Q25

c.

Q25

0.50

Fig 20

Coupling

without

bulb

10% bulb

20% bulb

-1 1

3

4

075-7

coefficients for damping IT

CB

=0.65

V =const.

025

0.50

025

0.50

and "E" for Fn = 0.20.

1

3

4

0.50

Q25

0

r>

025

0.50

without bulb

10 % bulb

20% bulb

o

Fig 21

Coupling

3

(1)074-1-7

coefficients for

4

---1111m

damping "e" and 111E11

CB =1165

_{V =const}

050

0.25

Q50

for Fn = 0.30.

2

3

4

W

5

Q50

050

without bulb

10% bulb

20% bulb

1

2

3

4

w FL.7g-7

CB =0.65

+ cylindrical bulb

0.50

11

0.25

050

O 1

3

w

IVRT

050

025

Fig 23

without bulb

10 % bulb

20% bulb

CB= 0.75 +cylindrical bulb

11

050

0.25

-050

4

w

1/W/

Coupling coefficients for damping "e" and "E" for Fn = 0.20.

1

2

co\frAi-7

-0.25

Fig 24

CB

= 0.65

_{V =const}

5

1

2

3

4

w

L17

Wave exciting forces and moments for Fn = 0.20.

5

2

3

4

1.1) 075

ro

050

0.25

without

bulb

10%

bulb

20 % bulb

CB 0.65 + cylindrical bulb

1

2

3

w0,71-g-7

Fig 25

_{Wave exciting forces and moments for Fn = 0.20.}

1.25

1.00 ro

075

ro

M 050

025

O

1.25

1.00

L.

₅

1

2

3

wVLig

1.25

1.00

,51 075

cr) L1-111

0.50

025

Fig 26

10%

bulb

without

bulb

20%

bulb

1

2

UART7

Wave exciting forces and moments

_{for Fn = 0.20.}

CB= 0.75 + cylindrical bulb

1.1)

075

cn

ro

X

050

0.25

O

3

4

\ 1/-7

_--31111

--5

2.4

2.0

Za

1.6

ka

1.2

0.8

0.4

Oh O

CB =0.65

--- 20% cylindrical

butt)

without bulb

0.2

0.4

0.6

0.8

1.0

1.2

280

320

CB= 0.65

0.8

1.0

1.2

without bulb

20 %

_cylindrical

_bulb

Fig 28

Experimental heave and pitch phases for Fn = 0.25.

\(177;177

0.2

0.4

0.6

-4.0

cn U)

f

80

120

160

J.-J1

o

s...A

200

N

240

2.5

2.0

2.5

2.0

Fn = 025

CB

=0.65

without bulb

20 % cylindrical bulb

Fn =0.20

0.2

0.4

_0.6

_0.8

_{1.0 1.2}

VE-7

24

2.0

0.8

0.4

O

--

experiment

calculations

1.2

CB

= 0.65

const

10% bulb

Fig 30

0.2

0.4

0.6

0.8

1.0

VT..77

-40

80

41)

120

f

160

240

280

calculations

--- experiment

320

CB=0.65

V =const

10% bulb

VET'

0.2

0.4

0.6

0.8

1.0

1.2

2.4

2.0

1.6

Za4a

12

0.8

0.4

o

1.6

0.4 O

CB

=0.65 + 20 % cylindrical

bulb

calculations

experiment

1.2

1.0

0.2

0.4

0.6

0.8

---mm.

Fig 32

Heave and pitch amplitudes for Fn = 0.25.

-40

80

Lfl L-13)

120

160

-240--280

calculations

320--CB= 0.65

+ 20 % cylindrical bulb

-- experiment

VTIT

-Mom

0.2

0.4

0.6

0.8

1.0

1.2

Fig 33

_{Heave and pitch phases for Fn = 0.25.}