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11. AnAnalysis of the Manoeuvrability of a Ship AssociatedUnder Steeragewith Unusual Characteristics
Seizo MoToRA', Mlamber Matao TAKAGi*', Mlamber Akihisa KoKuMAi**, IVtfember
Hiroharu KATo', Member and Takeo KoyAMA', Mbnfber(FVem LS.N,A. faPan, Vel. 12S, Dec. 1970)

Summary
In this paper, thedeal withauthors

theofmanoeuvrability

a

ship

which

was

reported

Result ofto have shown
yawingrudderangle;
at smallthat the ship responds
spiral test has also shownquite capriciously
rudderangle,
andanychangeofdirectionofturnwithout
i.e.the ship sometimes
swltched
havingwassuperposed.
The
authors,about
90
seconds
mostof cases,periodical yawing ofby separahydrodynarnic forces caused
these phenomena
te be inducedby unsteadyiss]medrunningmodel
investigations
using
a
free
experimentaltion of the boundary layer, conductedonanirnagealso
been
conducted
Flowline observations
have
as well
as a restrainedmodel.
ahydrodynamic
the authors proposedin a windtunnel. Analysing results obtained,
model
explanationof this unusual
behavior of the ship that it must be caused by a combinationof yawingandanabruptchangeofhydrodynamicof periodic change
yawing moment
anmomentandrudder

1. Introduction

Recently,in keeping withrapid

enlarge-

supposedtoof tanker size, phenomena
have
be due to separationof boundary Iayer

Se calledinstability
phenomena

propelling perthose designatedas so called
abnorrnal
phenomena in manoeuvrability2),3)
arethose phenomena,
Especially,the abin manoeuvrability
apnormalphenomena
recently,
only
in
model
ships
till
quite
pearedregardingandresistanceformancei)andand

did notin ships,

occur

relationof modeltremelydithcult.

In casephenomena

*
'*

and

ship

accordingly
was

made

corex-

large tankers, the abnormalinmanoeuvrability

in such form that course
withinimproved remarkably

mainlywasofautomatic

control.

large angular velocity of turning,has beenandhydrodynamical explanation
attempted
but they are not yet explained
not

ment

appeared.

undermotiondriftangle bas{s.

the

on

excessivevery

perfectly.
On the other hand, not only in largeships,
but also in fishing boats and other small
in manoeuvrability
ships,
the abnormalityof boundary
supposed
to be due to separationdifferent
layer has been found in somewhat
form, As one of them, ithas been reportedb
respondedthat a fishing boat sometimes
tosmall
rudderandindefinitely
capriciously
angle,

that yawing

rudderangle

the random

response

occurredthoughkept constant,to smallandrudder

the
that
angle

by attaching
improved remarkably
horizontal fin a littlein front of stern

appearedwasstabilityofbossing.

range

was

Being informed by trial result 'that the
took place in a cement
similarphenomena

Engineering Faculty of Tokyo University
Research Institute, Hitachi Shipbuildingand
EngineeringCo., Ltd.

carrier
examinetothe authors attemped
hydrodynamically the mechanisrn

recently,

171

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Hiroharu KATo and Takeo

Seizo MoToRA, Matao TAKAGI, Akihisa KoKuMAI,

172
tq cause

the

and

model

experiment

it. Asthe result,- Course Angle-- Helm Angle. ±[tD!nsMs.
'-NJ -'-'-'OO /L-.JnL'..ulthroughmeasurestophenomenaabnormalcounterqualitatively
seemedto be attained.
in wayherein, andTherefore it is justreported
explanation

s"r

50'

reasonable

comments

ofinvestigators

areconcerned

Fig. 2.2 Record of

by suggestmg
oneattemptwhen

theproblemsofthis sorting each

2.1 Manoeuyrability
pilot in actionofauto-pilot

and

was

rudderanglesused

Block diagrams of

Fig. 2.3

aut"

adjustment
the period

addition,

theofregardlessauto-pilot

systembelow about 30 even by chang-

the amplitude

2. Phenomena in ships
the timecoursearethe problems m the form of
to explain
the phenomena.

at

RudderAdjust 2
O'
Weather

RateAdjust 7

invited.

Of course,

KOYAMA

of

the

In

auto-pilot.

90 seconds
Fig. 2.2
angle.

about

wasrudderfor heading and.
part
Firstly,the phenomena taking place in a
of
the
ship.
motivate
directly rudder angle
ship are described,whichof
In order to investigatecharacteristics
tb lodge the problems. Principalparticulars
auto-pilot
controlsystemwiththeautomaticin Table 2.1,and herof the ship are shownin a blockdiagram ofof this ship as shown
body plan is given in Fig. 2.1.
periodically itscourse
knowledge in the past, it Fig.2.3, by changing
From common
to right
forautomatic
steering
settingknobthat course
has been dithcultto supposetherudderandtheand leftduring sailing,
keeping properties with auto-pilot pose operameasured,
heading angle at the time weretype and rudder
tional problems for such
responseoftheclosedloop
andfrequencyofarea
as this ship, but periodical yawing
of
which
is
difference
determined,input
wasduring straightlarge amplitude occurredsetting
courseandactual one andbetweenadvancewiththe auto-pilot in fullyloaded
course,An example
of
is
the
actualoutputit wasimpossiblete reduce
condition, and2.4,
andis shown
in Fig.
the measurement
Table 2,1 principal dimensions
standard
input was given by operating thecoursesetting knob periodically like trapeby a broken line inzoidalwaves
as shown
the figure,insteadof sinusoidal one. Analyshowsof recordsato equivalent
As amplitudeof thelinearizationmethod.
50
set course 30 andtrapezoidal wave-likein
rebut
difference(oneside) were taken,siscarried

was

sults

of

the

out

accordinganalysiswashardly observed

disThus, without
the cases.
andthe both cases, gain
criminating
phase
difference are plotted with respect frequency
that toin Fig. 2.5. It may be consideredischangethe set course
periodically equiforce acts
to that periodicalexternalvalentmargininthis caseon the ships,
and phase

betweenFig. 2.1 Body plan

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An Analysis of the Manoeuvrabilityof a Ship Asseciated with

Unusual Characteristics Under Steerage 173

Y-:g$.E

g

-i

40i

Iff14ecr

1
2.4 Records of frequency responsetest

bytrapezoidal

input

Y,(deglsec)

lo -Fig.

l.o

o

o

RudderAdjust27o69l(e05oofoo
o
co

-

tx
q

i

Fig, 2.5 Frequency

respon$eofloop transfer

function
about 50e as seen
ing that the automaticwasFig.2.6 Result of spiralfrom Fig. 2.5, showcontrol

systemwasin Fig.2.6. In this test, steady

test

turning anwhile
the rud-gular velocity was measttred,
As shown
der angle was kept constant.
angle,
ofsmall
rudderFig. 2.7, in casestable.

2.2 Spiraltest
Results of spiral test forthe ship

are

shown

angularvelocity

did notsettleatintheconstant=1

4eq-

Fig.2.7

Typicalcourserecordof spiraltests

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Hiroharu

Matao TAKAGI, AkihisaKOKUMAI,174

Seizo MoTORA,

value,

but phenomenon

nearlytion (period;of90

Takeo KeYAMA

andfluctua-

periodicalseconds)

KATooccurrecl,

directionof the turning suddenly varied.
Black circles in Fig. 2.6 arefrom theaverageangularvelocityreadbroken linein Fig. 2.7 for the case of apThis figure
pearance of such phenomenon.
sometimes

andthat average

represents

good

at

small

city

stability

but

is

it

is un-

that turning angularvelo-rudderstable in a sense

courseangle,

fluctuates.(Whitecircles in Fig. 2.6ofvelocity
the case that the angularbut
settledatconstant
turning did not vary,
value.)
These phenornena seem to be similar
in modelto those that frequently appear

show

ships

of

fullshape.2),3)
in model3. Phenomenaship

3.1 Spiraltest of nakedAs

theinvestigate

to

means

hull
abnormalin ships and to look for counterto improve it,rnodel test isuseful
if itis reliable, Therefore first,spiral test
whether
the abwas
carriedout to examine
in
the
ships
are
occurred
normalphenomena

phenomena

Fig. 3.1 Result of spiraltestsmodel)(original

measureswith

reproducible

model

The model ship usedequipped
ef L..:::263cm,

ships.

is a wooden
withrnodelsteermgradio

to steer by le per pulse,
Vin=92cmfsec using storage
batteryon board as power source. Employed
applianceandcapable

can

water

run

area

at

was

basin of thethe seakeeping

angle.

Thoughthe variation

appears

randoma glance, at times distinctively
periodical
might
as seen in case of the ship
fluctuationitseemedtooccur
frequentlyatoccur,
andatofrudderangle
of le-30. An example
in Fig.
the periodical fluctuationis shown
and3.2. The period was about8seconds,
and
swing
was
about
O.40!sec,
the arnplitude
wasable
to be observed evenof the modelby carefull 1ooking.
small

above,
setting aside whetherwas
As mentioned
University of Tokyo, and condition
was
it
rnay
be
said
that
the
phenomena are truely
quite excellent because calm conditionin the ship, a view
roof.
However, sameas tho$e occurredguaranteed by covering
measurement
was
limitedto only one plot may be taken that fairlysimilar phenomena
by one test because the waterarea is naroccur also in the model.
row.
A method was adopted in which initial
angular velocity was
given by taking larger
rudderangle
than the one set for the test
deatsec

andinitially,

angle

was

velocity

andrudderrecorders

The

were

angle

prescribed

The angular

recoyered.

in the rnodel
resulttheafterwards

rudderrecorded

2

on

ship.

thus obtained

as shown

marks
3,1. Connection with arrow
figuremeans that the angular velocity
in spite of constantwithin therange

in Fig.
in thisvariedrudderO

5

Fig. 3.2

10

20

I5

Periodical change

25
of

iO

yaw

,se;

rate

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An Analysis of the Manoeuvrability of a Ship Associated with Unusual Characteristics Under Steerage175

3.2 Effect of finof

types

yarious

It has been knowni) hitherto that to attach
fins on both sides of stern is effective tosometo prevent such abtheory
However,anyphenomena.

extentnormalasa means

has not been establishedmechanism

effecton

position of the fins.In case of Fmone,
No. 1, the ship is typically unstab!e
and
it
may
is
not
unusual,but the property"gentlyofFinunstable".
The casebe said
No. 2 hardly differsfrom that of the naked
mounting

throughwhat

the finsappears.

offore spiral test was

Thereby attachingin Fig. 3,3,

conducted

types of the fins shown
into consideration.
taking tentative rneasures
The resu!ts are shownin Figs.3.4-3.6.
threeChange of characteristics
fin position waswithrespect

toEspeciallyin

eye-opening.

No. 2, unbelievable
cases of Fin No. 1 andindifference was caused by slight difference

B

A

AP

/f2

:/a

5"

1

Fig. 3.3 Arrangement of finsFig. 3.5 Spirar'tests(FinNo. 2)r5-1--- 4
]

i
1

l
1

.

..2
l

I:[

l-2

i

-6 .-4
PORT

l

,

iO
: .o
l .-1

-t

L-

Fig, 3.4 Spiraltests (FinNo, 1)

Fig. 3.6 Spiral tests CFinNo. 3)

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176

Seizo MOTORA, Matao TAKAGI, AkihisaKoKuMAI, Hiroharu KATo

KoyAMA

Takeo

andinstalledon the ship, and an
found for executing
a few
opportunity
wasrneasurementsonthe ship in order to inthe effect.
The results are devestigate
scribedbelow briefly.
the model

wasThough sharp
time of straightnotobserved,

angle

was

1.5e, andable

reductionofadvancewithyawingat theauto-pilot

wasdouble amplitude
to be restrained

obstacles

yawingofbelow about

actual naviagtion

agalnstRecord of course
to be eliminated.
during the auto-pilot was in operationis shown
in Fig. 4,1. Next, as for results ofseemedangle

in Figs. 4.2 and 4.3 it istest shownatthe case that fluctuation
phenomena

spiralnotsmall rudder
it remained

angle

completely,

vanished

andslightly, but range of the rudder
occurred,
in whichthe phenomena
very
narrow,andyariation
turned out to bevelocitycarne
to be considerof the angularConsequently, relation of theably small.
angle,

Fig. 3.7 Spiraltests (FinNo. 1 and

Fin No. 3)

seems
hullwithout fin,and the abnormality
to intensify
on the contrary.
The case of Fin No. 3 is within bounds oflimitedstability, and the abnormal
phenomena
but asymmetrywithreseemto weaken,
is remarkable.
Usually,spect
to ordinate
itis consideredthat the stern finsare useful for stabilization, accordingly
attainment
be notable.
Fig. 3.7
to such result may
shows
resultfor the case of joint
use of Fin
No. 1 and Fin No. 3. Although plots scatterin case of the rudder angle ofconsiderably
zero,
itmay be said that characteristic are
gentle in general.
Frem the experimental results stated above,it seems
to be dangerous to use Fin No. 1
becausein practice as tentative measure,largedifference
isproduced in characteristicsof the mounting
by slight change
position,though itseffect is of great interest.Thus
it wasdecided to installonly Fin No. 3

tentatively on

the actualf.-.rlmin-..-.J.
-N.

It

ReteAdlust7

Fig. 4.1

and
when

was

auto-pilot

rudderangles(shipwith

used

fins)
Ytfdeg/Sec)
LO

-

oO

geo
di}
o

1

･

loo

se

el

/

S

5eioe

co
o

L

Fig. 4.2 Spiraltests of ship

with

fins

ship.

4. Effectof finsin the ship

describedin the preceding
finsalmost similar to Fin No. 3forBy the reason
chapter,Fig. 4.3 Course records
with
fin)

of

spiraltests

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An Analysis of the Manoeuvrability of a Ship Associatedwith

trollthrough the auto-pilot[/K:.je:e'?a,1,
2

is-

g A.

i

s

OT'
o

loop･
(f) when

ifT

Igez

tests

the rriodel
property almost

velocity

in

shown

ship

the

showedtosimi!arlyt,rendtha.t the angularduring turnmg intensified
hull.
more than the naked(g) The fluctuationof angular velocity
when
Fin No. 3 was attached,almostvanished
variedvelocity(ship)

attached,ofhull but

the naked.

Iooz

Fin No.2wasstableabnormalangular,uf.//R.ae,2iR,'/Lf,iolc

manoeuvrability.

Fig. 4,4 Result of zig-zag
vs.

O

with

s
soz

e

"

,?vllg9.

O'

is:,2,g:illi,\nOi,if " C t?,X･g,6tr･;gyZ
2g

ili,

'02

angle

so forth.

and.gz),,XIYe,;n,.F.':IF,2･g,:･,iie,lta.'i:g,o,,Eh.:to,rudderUnder Steerage !77
Unusual Characteristics

Fig. 4.2 takes form quite close to the caseclose toof the spiral test cameand result
by the abof ordinary ship not accompanied .
ofmarginal
toextentthe case crf Fin No. 1,
companson
normalphenomena. In addition,
in regard to presenceof the stability.
of Z test results
fins is given in Fig. 4.4. Effectof the fins
5.2 Presentation of hypothetical model
angle, and mean
rudderappears
at smallIt has been well known from long agoi)t3)-

course5.

statibility

is reduced.

Analysisof the phenomena
the5.1 Summarization ofabnormalphenomena
kinematic models
In this sectien, severalof various
explanation
are presented, andin the previous chapters
phenomena stated
The abnormal
phenomena to
is attemped.
as follows, forare summarized
be explained

description:Ca) The rneasured values in spiral test of

convenienceofthe ship often scatter at small rudder angle,
hysteresis.
tendency of reverseand showis rathertheship
Moreover, they show thatarethe scattermg
pomts
stablewhen
averaged.

(b) Though rudder was fixed at small
inthe spiral test of ships, the angularangle
variedby period of about 90 seconds
velocity
during turning.
(c) Direction of the turning sometrmes
variesduring the spiral test of ship at srnall
rudderthat abnormal

righting

during motion

atstabilizes

theis generated

momentruddersmall

manoeuvrabilityofangle andships, asdescribed in this report, and it has been
separatton
presumed that three-dimensionaltoreferring
Hereupon, by
is the reason.
observation
regardingformer experiments
aroundaxisymonflow
of flow and studies
bodies5),the followingthree models
metrical
wereconsidered.

hav-

moment5.2.1 System with abnormal
ing the origin as itscenter

momentasthat abnorrnal
inadditionenhulls
in Fig. 5.1 acts
shown
Here, M is.theto usual fluid moment.

It is assumed

normalangle

moment,andP represents

mcommgto aft part of the hulls. Whentest wascarriedout
Mby fixingrudderFb-spiralangle

lBangle.

motiontakes placestraight
3"-5eduringby double amplitude
cannotwith
auto-pilot. This motion
advanceof rate confurtherby means
be restrained(d) PeriodicalyawingofFig. 5.1 Unusua!

rnoment

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Hiroharu KATo

Seizo MoToRA, Matao TAKAGI, Akihisa KoKuMAI,

178

came

of the spiraltest of the ship.
it
is
shown
in
the Appendix that
Next,
there is possibilitythat ships sailing by aprnake
zig-zagmotion,plication of auto-pilet
said

1!

bx

f3

r

B'

L

--e

VtiThaJt
Unusv]'NomenT

Mome"t
-･

test

9
1
ll

6

/l,VVithouTUnus

MorTEntMement
I/WithUnvsuo

Fig. 5.3 Spiraltest

asof suchin Fig. 5.3 wasshown

is represented

resultansymmetricalequation

of

ship

city

is turning resistance
f(di)

and

sys-

io

carriedsteadystate wasnot

D' and limitcycle
ever,

it isassumed

momentchangesout.

attained

HEFG

was

con-

Fig, 5,4 Unusualwithmornent

respect

is symmetnc

whichto theoriginT VV

It shows
thatat the point

BA

9

formed. How-that sign of the abnormal
the phase point on XX'.
wasinterest
that
when
mean
value
It is ofvelocity
taken
for a part of the angular
at

ex-

p

e

with
respectto ¢ .
be nonlinear
and
the
solid
line
show
relaThe broken line
tion between ip
andipat zero rudder angle,
theand AA'BB' shows
progress by whichtest wasangle

motiontospiraltolvt

pt+f(di)=ne
sideredrespect

to the ruddercorresponding

approxlmatlon

wheremomentwithdriftangle
the abnormal
mornentas
In this model,whentheinshown
in Fig. 5.1 originates
angle
to stern is withina certain
comingin Fig. 5.4.
range,
andresult is as shown
momentis
Also at this time, the abnormal
by hysteresisphenomenon
to be accompaniedshownin the figure.
momentacts on ships,
When this abnormal
courseof which
isoriginally unstable, angularincreasesor decreases because of
velocity
angle,and thethe instabi!ity
at small rudder
limitcycle occurs on arrival at the points A
and B, thus the ships makeperiodicalmotion.
of transition beBut there exists possibility
the ships are subjected
tween A and B whenor wind.
When
to disturbancedue to wave
angle
is in.creased,and angular velorudder

obtainedby fo!lowingfirstorderab-moment.

throughin Fig.5.2. Fig. 5.2 shows

progress as shownphase plane, andtem

moment,abnomalby suchcaused

5.2.2 System having abnormal
originXJt
xLinvsvo]

Eig.5.2 Phase portrait at spiralnormalA'

xX

actionresultforming the lirpitcycle,

-sN

under

in Fig. 5.3,the gradient of ipto 6
anditresembles
toto be moderated,variation

x1'

Takeo KoyAMA

andFig. 5.5 Phase portrait withWhich

is symmetricunusualwithrespect

mornent

to theongln

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An Analysis of the Manoeuvrability
ceeds
not

Ship Associatedwith Unusual CharacteristicsUnder Steerage179

does

point, the limitcycle
any
more,
and the ships

separation
originate

at a

of a

turn

If stabilizavelocity.
definiteangularof stabilizing
by installation

tion is attained

do notfinsand others, abnormal
phenomena
motake place,even though the abnormal
rnent

originates.

5.2.3 System having origin
abnormalsymmetricalexperiodical

andmomentternal force
In this model, in order

let ships makeduring spiral test
fluctuation
angu!arvelocityof autoby
application
or straight advancetaken
into acpilot,periodical fluidforce is
momentcountin addition to the non-linear
momentin theabnormaldealt with as theisnotnecespreceding section. However, itin this case.
especiallysary to have hysteresis
andThe phenomena (a),(b)(c)can be exor

tosimilarly
plained easily with this model,
the section 5.2,2. Also itcan be explained
duringas wellthat yawing that appears
strightadvancereducedbywithadjustingauto-pilotbecannotthe auto-pilot,

which(1) System withabnormalhavmg

momentitscenterin the section 5.2.1,
reasonfor thecanexplainthis model(b)and (d).The phenomenon
phenornena (a),if it is assumed
canbeexplained,
also
Ce)
and
the abis
suppressedthat separation
by attaching Fin
tnoment vanishednormalto be supNo. 1. Effects of Fin No. 3 seemfineffect inandpression of the separation
Because of relative
positionusual
sense.
layer,Fin
Ne. 2
boundaryflow
outsidewithagainsteffectseems
not to have suppressing
the origin

In this case,

the

as

as shown

andit seems

almostsimilarseparation,

noeuvrability

hull. Thus, this model
well

the

can

mato show
to the naked

explainin general,phenomena
the phenomenon (c).

abnormalbut can(2) System having origin-symmetricalnotexplainnormalfairlyab-momentcase,hydroDifferent from the abovecanandis practical
dynarnicalexplanationandbe accepted easily with this mode!,

phenomenaabnormalvariousthat take placecanbe exin the spiral test of actualin the section
to be explained
However, as instability
5.2.2. Reason for the latteris described plained reasonably.
rudderangle
is assmall
in the vicinity ofbrieflyas follows.
beexsumed,the phenomenon(d)cannot
Namely, value of 90 seconds for this yawsystem
of motion
stabilization
for the conshortplained, whening period is considerably
taken
mto
account.
isfor 50Z by the use of auto-pilot
trol system in view of time constantabto
frequency
and it correspondsof 80 seconds,(3) System having origin-symmetrical
was

ship

unable,in which effect of external disturbance
Condisappearsor enlarges on the contrary.
reducetheit is hardly possible tosequently,
range

yawingapplyingbyadjustingrate

control

the auto-pilot,

exceptstrongly.

very

normalforce
Cornpared withmodel

cempatibility

actionofmodelsstatedexplain the phenomena

help consideringsomeexternal
periodical

the twothis model canto(a) (g)comparatively
above,

it cannot

5.3 Examination ofandmomenteasily. Especially,that it means

periodical external

forcefromsystemthat
three hypothetical outside ef loop of the control
straight
advanceduringperiod of fiuctuation
modelswere
presented to prove the abnorrnal
does not vary with change
frorn
with
auto-pilot
wereexamined
phenomena, and they
Also itmay be saidof rudderangle ratio.
the various
kinernaticalpoint of view whether
fact that the system
theby
to be suggested
describedin the section 5.1 canphenomenaAsmentioned

above,

wasdeterrnined
response
response
test of the
in
the
force
by external
if some kinematically adaptable
2.1, butinthesectiondescribed
model exists, it is investigated on the basis auto-pilot
in self-propelling
the limit cycle originatedof hydrodynamics further.
in which
thismodel,
Accordingly,
condition.
5,3.1 Examination based on kinematics

be explained
them, andwithout

any

contradiction

with

was

stablewhen

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180

Seizo MoToRA,

Matao

TAKAGI,

AkihisaKOKUMAI,

Hiroharu

KATo

and

Takeo

KOYAMAthe back side and abnermal moment
vanishes
when
angle
of incidence becomeslarge.
best.
Itisconsidered that hydrodynamical originof periodical external
force is that the cross
5.3.2 Hydrodynamical examinationof the
flow
model
to
hullsmakes
unsteady
fiowfieldsimilar
compatible
in twoAs describedin the preceding section, it to generation of Kirman vortexes
wasmade clear that the model given in 5.3.2 dimensionalflow. Considering thus, per'iodof the unsteadyflow fieldseerns to be calcuis most compatible
as a medel
for motion,
latedwith same Strouhalnumber
as the two
but it is necessarythat non-linear
righting
dimensional flow madeby taking effective
momentand periodical fluidforce originatemeanvelocityof the cross flow. Thus, period
withina certain
range
of incoming angle toin case of the ship canstern.
to generate the of about 90 seconds
Hereupon, mechanisrn
in terms of order of magnitude.
above
forces was examinedfrom hydro- be explained
In addition to the above explanation, in the
dynamical point of views.
above
model
assuming
the separationon theFirst,concerning the non-!inear righting
face side, flow against the cross flow is inmoment,
it ispresumed as followsaccording
but intensity
bodies by duced by the verical vortexes,
to researchon axi-syrnmetricisweakened
by theNonweiler5),Generallyspeaking, in case of of the vertical vortexes
inducedinducedvelocity,
andthevelocity
on
back
side
is
slenderbodies, pressure
becomes low, thus the verticalvortexes
higher than that on face side behind section
themselves develop again.
As the verticalof maximum
cross-section
when
angle
of
vortexes
andtheir induced velocity
affectincidence is small.
In consequence,crossmutuallycyclically
due
to
the
unsteadyflow
flow flowsbackward within boundary layer,field,the periodical fluidforeceseems to beandverticalvortexesthat induce fiowto stop
from
case
the cross flow originate. Different
generated.
of large angle
of incidence,these vortexes
Next, the effect of fins is discussed. As
streamaffect flow on the face side, rnake
for flow around not axi-symmetic
bodiessuch
fiow
wise
fiowseparate on face side, thus theas ships,
torsion of the stream-wise
flow isas a wholeseparates
three dirnensionally at
This
seems
to
be
relatedto thepresumed.
rearof the face side
anddischarges the generation of verticalvortexes
described
verticalvortexes.
At this time, pressure
to be atbefore. Fin No. 1 was supposed
difference
between the face side and the back effeetive position with respect to externalside
aft part of hullsis reduced
because of flow, so that the torsional flow was restrained.
induced velocity adverseto the cross flow, Furthermore, it can be consideredthat theanditseems that liftis generated,in comfinsstabilize the backward flowof cross flow
verticalvortexes.
in the boundary layer, and play role of preprison with cases without
In addition, the Iiftgives rise to stabilizing
venting
flow field
generation of the unsteady
momentaroundcenterof gravity.
mentioned
above.
It is presumed that posito play the role inIn the flow mentioned above, the genera- tion was not appropriatetion of vertical vortexes
andthe separation
caseof Fin No. 2. Reason why
Fin No. 3
periodical external force is added to nonlinear force,can explain the actual phenomenaofstream-wisetion of stream-wise

flow cooperate,(theseparaface
fiowon theside makes

form of hullsasymmetric,

andto ap-

acts

acts

effectively

seems

near

stern

was

well

of

the

separation

parenly increase effective angle of incidence prevented.
andthe verticalvortexes
As mentioned
grow up to acertainextent),

once

such

combinedmechan-ism is initiated.
Accordingly it is supposedthat the vortexes
arefullytowardpushedabove,

tobe that flow fieldstream-lined,stream-wise

a

and

the

flow waspoint at whichthefluidforcein this report isdifferent
from observation in the model test of a fullship isgenerationof periodicalexternal
force.
abnormal

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'

Under Steerage181
Unusual Characteristics

tAnAnalysisof the Manoeuvrabilityof a Ship Associatedwith

tunnel, static pressure
G6ttmgen type wmd
key point ishow strong the backward
measured.
a ship hullwas
aroundfiow of the cross flow on face side is. It distribution
andiscirculartunnelin Iongi- The outlet of the windseernsthat shape and itsvariation
withvelo1.5m in diameter,and maximumof frame lines m the vicmity
tudinal direction
has 28 holes fororigicity is 40m/sec. The model
the vertical vortexesof the site where
the static pressure, and the presmeasuring
natedaffect this problern.
inclined
multi-tube
withmeasuredsure wasofthe manometers
Posiexamination
or Betz'stype manometers.
6. Hydrodynamicalandaholes in the vicinity
in Fig.6.1.Fig. 6.2showstion of the measurement

modelsdeOn the hydrodynamical assumption
few
exscribed
in the preceding chapter, aand itsadequacy
periments were conducted,
wasinvestigated.

stern

of

isshown

distributionaroundthe ship hull.The figure6.2 (a)corresponds
hull and angle of into case of the nakedThecidence P=O",and (b)to that ofP=40.
white
6.1 Wind tunnel test
withpressure on port side is indicateddisof
staticside with black
Measurement
pressurecircles, and that on starboard
6.1.1
the two
betweendifference
tribution
circles. Pressurereinandof Lpp=1.2m
Putting an image model
corresponding
pointsis determinedthetpresented as AP in the figure6.2 (b).Inof the pressure

outline

lt/

case

Flo1

of

P=Oe, the pressures onboth port
in theandsides are equal,
thepressure on the face side
P=4e,
half
of the ship hull,and thatin front

andstarboard

case

of

rises

is higher in the rear half.
The pressure at 16 points in the vicmity
effect of finsis supposedof the stern, wherereadby Betz's typewasto be remarkable,of O.Olmm
Aq, andto accuracy
manometerson the back side

,4

:.p

Fig. 6.1

12

Position of,i/L}:u c, p,es;'ftprsc'e
pressure taps

in Fig. 6.3 was obtained.
The followingsare seen from this figure:(a) The effect of finswas mainlyproduced
result-v(Ega

on

as

shown

the backside,oncruiser stern

Ordinate-

the pressure

andthe face side did-1Fig.

le-around6.2(a) Pressure distribution
model

P=O`)
Cnaked,

ship

-

GqEga

u=]04

Nol

o

F/n
Fm

-No2
±

O1m/s

e

vary.

Noked

.

P:4e

near

not

No3Fin

t
:Lll

86

.a
Eg
-

OrdinaTeO-ola-2.5Fig,

}
'

'

-?

Ofdirore

kePressure

distribution around6.2(b)
model

ship<naked,B=4a)( t t"o ofFig, 6,3 Pressure distribution near

pfess

tops

stern

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Seizo MoToRA, Matao TAKAGI, Akihisa KeKuMAI, Hiroharu KATo

182(b) The pressurenear

the cruiser

sternin the order of Fin
No, 1>the naked hull=Fin No. 2>Fin No. 3.
Mean values of the pressure differencedP
at 8 pairs of the measurement
pomts aregiven below.
AqdP (naked)dP (Fin No. 1)=1.42mm Aq
dP (FinNo. 2):=1.12mm Aq
MP (FinNo. 3)=1.08rnm Aq
near the stern
As Iargepressure difference
moment,it canorunstablemeans
increase
be explainedthat instabilityof manoeuvrabilityis increasedby Fin No. 1, and that
Fi'nNo. 2 has no effect. However, rather
on

the

back

side

was

=1.17rnm

With No. 1 Fin fi=40back

Fig, 6.4(e)With' No, 2 Fin

Fig,

Takeo KoyAMA

forthe effect of
Fin No. 3. But the positionof pressure
contrary

comes

out

pointswasresultrneasurement

as

restricted,

and

must
be carried out
further measurement
the effect of fins comin detailto elucidate

pletely. Variation of the pressure could notof thebe measured
because of slow response
used.

rnanometer

6,1.2 Observation of limit stream lines
the ship hulllines around
Limit stream
mode!
described in
with
the
were
observed
the section
6.1.1,and elucidation of flow field
wasattemped.
The following method
wasstreamlines.
toobservethelimit
adoptedOil soot was rnixed in fluid paradin and thebackFig, 6.4(b)Originalp=40

Fig. 6,4(a) Original P==4D faceFig.6,4<c)andFig. 6.4(d) WithNo.

6.4(O XNrithNo. 3 Fin P=4e

P=4o6,4
Limtting

1 Fin S=4e

streamlineFig.near

stern

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Under Steerage183
Unusual Characteristics

An Analysis of the Manoeuvrability of a Ship Associatedwith
mixtureabout

painted on the hull. Windwas

35mfsec speed

than ten minutes.

was

of

magnitude

for more
directionof theable to be observedin Fig. 6.4.
applied

when

Then

seernsofbe about 1`-20
intorudder angle, andthe force rnay

it is converted
measurement
to be within

error

even

out.
Actest is carriedwhen
oblique run
limit stream lineswas
wasattempted,
run
test
tually, the oblique
by white Iine,as shownwas
not observed
fiuctuation40,
but remarkable
for
the
case
of
Every photograph isP=
and Figs. 6.4 (a)and(b) are for the face within accuracy of the measuring instrument.
tunnelPressure fluctuationin the windside and back sides of the naked hull reordinary
be detected with
spectively. Characteristic black part isfound test cannot
manometers,
and Betz's type manometersin the vicinity of the stern on the face side.
have deficiency
that fiuctuatmgpressure canthat velocity
It is shown
gradient near surThus, proof for action of
not be rneasured.
is easily
face is so small that separation
initiatedor takes place in this part. Such the periodical external force has not been
Therefore, in order to observe thewasreportedby NomotoS). On obtained.
separationvortexes
at the stern, aluminium
powder wasvertexes
arethe other hand, large verticalthe model
tank
and
in
a
towingscatteredgenerated on the back side, and itresultsofincidence.
The was towed at a certain angle
flow near hull surface.
in downward
As the result, new fact was discovered.
finsattached on the fullside has angle of
the abNamely in case of ships causing
incidence of 2-300 with respect to the flow.
The flow on the back side in case of installa- normal phenomena, though particularchange
in Fig. 6.4 (c), is not in the vicinity of the stern, waketion of Fin No. 1 isshownconsiderably
periodicallyin a zigand
it is seen that the downward flow due stretches
not
found
is restrainedby the zag line. This is a phenomenon
to the vertical vortexes
6.5and 6.6),and
ships(Figs.
fins. Figs. 6.4 (d),(e)and (f)are the photo- out in ordinary
when
Fin No. 1
wakedisppears
the zigzag
the finsof No.
graphs for cases of installing
Wave lengthof the zigzag wake
1, No, 2 and No. 3 taken from ship bottom. is attached.
of angle of incidence
isabout 5.5m regardlessIn every photograph, lower side corresponds
The
wave
length divided
and ship speed.
side is the backto the face side, and upperby the ship speed comes out to be 6 seconds,
changeApparently most remarkableside.
for meanderand value of about 8 seconds
onof the fins appears
due to installation
ship
described
in theing period of the model
below
the face side, and flow is acceleratedin
3 seems to be in good agreement
disappearsat down- chapter
the fins,and separationitshouldregardedoforder,
thereforein view
This effect is most remarkablestream.
to the abnormalthat it is closely relatedcomparingFin
the case of Fin No. 1, andNo. 2 and Fin No. 3 installedon the stern,
to be rather larger.
effect of Fin No. 3 seems
This factissirnilar to the result of manouvralll
3 and ofbilitytest stated in the chapter
2f2777/7T7/

great lnterest.

force

6.2 Periodical external

5, there is
probabilitythat periodical external forceactsmcasevortexes
due to initiationof unstableof

As mentioned

in theabnormalphenomena.

When

with
initiate
fluctuation
periodstatedinthechapters
seconds,
attributed

Y/7/1/

chapter

cause
of

about

2 and

to such periodical external

to
90

3, is
force,

Fig. 6.5 Comparison(upperside

withunusual

of

1

of

wakes

and
of figure)moment

usual
ship

ship

affectecl(lowerside)

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184

Seizo MoToRA,

Matao

TAKAGI, AkihisaKoKuMAI, Hiroharu KATO and

Takeo KoyAMA

vortexesonthe face side and theflow than due to Karmtin vortexes
amongthose discussedin the chapter
5. Thisconsideration
is supportedby the factsthat
the zigzag
wakedescribedin the preceding
sectionis remarkableon the face side, andthe period is independent of angle
of in'
cidence,
Furthermore, the finsmounted onvertical
cross

8E

xv"p

=.9uy'w'tu,s)os,

suitable position seems

to rectify thisopposite

fiow and to have capability
flow field.
Fig. 6.6 Unusual

phenomena.
In viewof theabove,is should

wakeexperirnentsbementionedthat

considered

someperiodical external foree acts as a part of
the abnormal
throughthe vorphenomena
texes andso forth, since abnermal
wake
originatesin the model run obliquely undersomerestramt.

ofstabilizing

7. Conclusien
As forthe ship which showed
the abnormalofmanoeuvrability
listedin thephenomena
section
in
the
ship
and
rnodelexperi5,1
canments, it was found that the phenomena
be explainedin outline from kinematic pointof view
by assuming
the followinghydrodynamical model. In addition it was confirmedthat this model can be accountedforhydrodynamically through model
basin
test and wind tunnel experiment.
First, as for the assumed
model,
the folalso

6.3 Examination

Presuming cross flow of the naked hull
form observationof the limitstreamlines lowings are concluded.
(1) This ship is originally course-unstable
near the stern described in the section 6.1,
it comes
to be as shownin Fig. 6.7. it is unless there isabnormal flow such as separalike the flow aroundaxi-symrnetricbodies tion.
(2) Though the abnormal fluidforcedoes
previously stated in the section 5,3.2. Whenrange
not initiatewithinof quite small drift
fins are attached,
the vortexes
stretchtng
angle
abnormalflow is generated suddenly
verticallyto the fiow is suppressed,
and
the
in
the
vicinityofstern when
the driftangle
effect is large on the back side especially,
accordinglyofpressure at upstream
the finsturns out to rise.
Also as forperiodical fluidforce,itismore
probable that the periodicalfluidforce iscausedinteraction of the fiow due to thestatic

'

Y:CK

Fi[E

momentlimit,consequently
in directionof decreasing

momentis generated. The counter-moment

exceedsa certain

counter-

unstableis origin-symmetricwithrespect
to the drift
It is considered that the abnormal
flow is the verticalvortexes
causedby crossflow and separationon the face sideby the vortexes.
of the(3) Owing to growth and vanishingabnormalflow,perioclicalmoment
is caused.
angle.

,induced

LFti.1,J:.[.

Fig. 6,7 Assurned pattern of Vertical Vortex
andCross Flowis about le as co'nverEed intoandthe period is bout 90

Themagnituerudderangle,

seconds

in the ship.

Useing the above
model,
canbe explained
phenomena(4) Because of the coursetheasabnormalfollows.

instability,the

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An Analysisof the Maneouvrability of a Ship Associated with Unusual Characteristics
Under Steerage185

lines,thoroughly that effect of thefins appears
remarkably
on the face side, on
hardlya certain
angularvelocity
because of the the other hand, pressure variationisrnore
abnormal
momentof (2)and
the ship begins
occursenthe face side, andremarkableon the back side.
steady turning but yawing takes place atthat
Furthermore, it cannot be explained
period of about 90 seconds due to the periodical moment
mentionedin (3).In addition,
despite longitudinal
positionand vertical posidirectionof the turnning is varied by slight tion of Fin No. 1 and No. 2 do not differ
disturbance,and steady turning is started
much,there iseye-opening
differencein their
ship cannot advancestraight,
andstarts toturn.
Though the turning was stabilized atof stream

to affect
the opposite
side, aceffect. This seems
probably very
the ship yaws while turning. This local change
in shapeof the ship Iargely
but these are prooccurs
in case of rudder angle
separation
phenomenon,
phenomenonof 1-20 as well.
When the course is conblems to be elucidated
hereafter.
sideredin terms of averaged fluctuation, At the end of this report, the authors offer
courseof the ship comesto be stable. (See their cordial thanks to ProfessorNomoto ofata stability point on

cordingof (a),(b)and (c)of 5.1.)
moPeriodofthe(5)
periodical abnormal
ment
is about 90 seconds,
andis too short
to be suppressedby auto-pilot, and limitcycleof nearly
same
Acperiod is originated.
cordingly,
it is expectedthat period of'thelimit cycle hardly varies even whenrate ofrudderangleof the auto-pilot
is changed,

Osaka University for his useful discussion
andfrom initialstageof the present study,
Zosen
to Kinkai Yusen Co. Ltd., Setoda
Co.
Ltd. and Tokyo Keiki Seizoshofor lending
forcarrying
understanding
andconvenienceout the ship test.
The authors express deep sence of gratitude
to Mr. Wataru Koderayama of Osaka UniverHikino of Technical Reand rate control is not so effective, and thesesity, Mr. Masami
factsagree well with actuality.
searchLaboratory of Hitachi Zosen, and(6) Horizontalfinsof type No,1attached members of Takano Laboratoryof Aeronautito stern as shown in the section 3.2, suppress
calEngineering Division, High Speed
the
of
the
verticalvortexeson
Lavoratory and Seakeeping
Mechanics
generationback side, and stabilizes those on the face Laboratory of Marine Engineering Divisionside. Consequently,limitdriftangle to causeof the University ef Tokyo fer their cothe abnormal
momentis increased,and the operation given at the time of the ship test

the explanation

ship

recovers

propertyoforiginal"gentle

and

model

experirnent.

instability".
(Seethe explanation of (e).)
Longitudinal
and vertical positionof the(7)
References
finsisdelicate,and effect of Fin No, 2 a little 1) K. WATANABE:
behind and below Fin.No. 1 isnearly same as
Self-Propulsion Test of Full Ship Form Models'',that of the naked
hullor rather promotes
J.S.N.A.,Japan Vol. 126,1969 (inJapanese)
the abnormality.
(Seethe explanation(f).) 2) JapanShip Research Association Rep. of SR 98
1961, March (inJapanese)(8) Fin No. 3 attached to stern center
3)
K. NoMoTo:
Scale Effect on Maplane acts to broaden a littlethe limit of
noeuvrabilities
of
Ships
with
Blunt Bodies",
moment.
In conoriginating
the abnormal
1966
11th
ITTC,
Tokyo,
Oct.,
sequence,
despitethe center plane fin with
4) T. KoyAMA:
JTTC Tech. Note, 1965, Octobereffect only was
installed,theusual stabilizing(Unpublished)
ship
became more unstable than the naked
theoretical
study
of
the
5) T. NoNwEILER:
course'`UnstablePhenomenoninthe"Unusual``Ahull. (Seethe explanation

As mentioned

rnade
unknown

above,

of(g).)

explanation

can

be

to someextent,yet there are many
points. Especiallyin observation

layer fiow and side force on inclined
bodies'', Rep. Coll,Aero, Cranfield 115.

boundary
slender

orB,Thwaites:``IncompressibleAerodynamics;'

Oxford, 1960'

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186

Matao TAKAGI, Akihisa KOKUMAI, Hiroharu KATo

Seizo MoTORA,

\] \I

)

･. K:P

Appendix
the limitcycle

Examination concernmg

of

M,==

1. Equation ofdi.. AZf+di.(i+gKi ¢auto-pilot ship

a

bB-cC

th

,

KOYAMA

Takeo

and

M

b
bB-cC

=

motion(A-5)
Below, assuming

withconformity'

considera-

linearity,
Mis assumed assinusoidal
function.
By putting right hand side of (A-5)as Ms
function F
anddenoting phase of arbitrarytion of equivalent

by

argF,

:
'g

By denoting the abnormalof motion
for ships

andmoment(A-1)

In order\i)2.amp.
)2+(
(A-7)

that

the

periodical solution,

where

as

MT'O

A4k=V(

amp.

l

crp+bp+cip=d6

is expressed

the amplitude

by M,

are

Adi+Bip+CP=Dti+M

=:.

(A-6)

Coordi"atesequations'l.r,a,tom-tan-iMcY:,ill.)-:il.i',g."=Fig. A.1

aM

have a com'
' K

must

£Ie,gS.gi::g,e":,o,f.s..
yi,:aKm,e.p,h,aA=n(Lv)2,

B=cM.(r{;'),

C=-C.p,. .T.(il?,ip,

D=C.,

(A-2)

b==Cyp,a--mv(r:l;N),

d=Crb

c==-(mx-CF.)(r:l;-),Eliminating P from the two equations1),the followingrelation is obtained.

of

(A-

produce the limitcycle, as there exists nonlinear damping term.
Presentobject of interestisto obtain necessary
condition
for producing the limitcycle
1+KKI
in case of>o. Ifitis assumed that
T

･

where

a･

bB-,c
7li,n, 7le

and

M+

b
M (A-3)bB-cC

K are given usually.

hold in order

(A-g)

that

ME

.
3. Relationbetween diandPshonldcomponent

hasasameQ.

as(A-9)deof phases of dian P ismade

Before consideringofin equation(A-2).At this time,
approxlmacarriyingout first
order system
are resulted.
tion, the followingexpression(A-8)

the followingrelation-ll->a+ti>-gthe lirnit
2. Necessary
J ,cyclethat auto-pilot
It is assumed
given by
-6==K,ip+K, ¢(A4)
condition

M:= arg ip+o"arg

T,7h¢ +(T, + Tb)Q+e=K6+Klleb+(A-5) hasequationMk

the equation

finitely,
relationclear.
By putting

ip=eocos tot
r>E>-T
P:=l3Dcos(wt+e),

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An Analysis of the ManoeuvrabilityofaShip Associatedwith

Under Steerage187
Unusual Characteristics

K2daw-wbc+bKidca

cose=

P!f2
ato2e+aa,2Kid+Khdb

SME=(A-10)

Plf2

plX2Kb

Po= K2(a!w2+b2)+2abKiw2+(ae)2c+aw2Kid+K?db)
P-mJ(K2datu-a,bc+bKidw)2

Phase characteristics

C.

by value

control!edarethe equationsof(A-10)

holds,pQssibilityof the limitcycle
From

4. Phase offorce

external(a) Case of origination

above

we

consideration

exists.

know thatwhenright-of abnorrnal

in relation to di･
ing moment
When hysteresisis taken into account,phase lag of ai is expected
Accordingly.

ap--O,
ora.large,ahnF>Ci.

,(g).ab>O).
(A-11)

6=-a"+n

hold,

the

and

statisfied.

(A-9)

d

equationHence thethelimit

cycle,

when

even

limitcycle trends to generate. We can also
is not able
see in Fig.A.2 that the situation
under
the said
to be improved by Ki-large
conditions.

momentabnormalat the phase oforiginatedbecannotc-large,

ipcannotproducethe hysteresisissff..c1x'

taken into account.

(b) Case ofmornent

rightmgoforiginationinrelation

the abnormal
to P

As there exists phase delay of afi when
the hysteresisis considered,o"=e-crp

holds,and
n-a>-Emto

into(A-9)

andsubstituting

account,

whenrrx-a>E>--a+afi

taking2(A-12)

K:Larger

IfiiKiSmaller

'

±n

f!1/

-7

-m

-

.-.F-X-I

c

Em=-tanmiAitiL-is .
i.It&n'T?MIVktyUp)'
Fig. A.2easafunction of

coefucientofC

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