Simulation of the steering - and manoeuvring characteristics of a second generation ship

t

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT

LEEGHWATERSTRAAT 5, DELFT

*

SIMULATION OF THE STEERING

-

AND

MANOEUVRING CHARACTERISTICS OF

A SECOND GENERATION CONTAINER SHIP

(DE SIMULATIE VAN DE STUUR- EN MANOEUVREER EIGENSCHAPPEN

VAN EEN CONTAINERSCHIP VAN DE TWEEDE GENERATIE)

by

G. M. A. BRUMMER

Ir. C. B. VAN DE VOORDE

Ir. W. R. VAN WUK

(Institute TNO for Mechanical Constructions)

Ir. C. C. GLANSDORP

(Shipbuilding Laboratory of the Deift University of Technology)

Na het in opdracht geven van een schecpstype dat aanzienhijk verschilde vergelekcn met de schepen waarop deervaring van de nautische staf van dc betrellende rcderjj berusite, werd de be-hoelie gevoeld van te voren informatie te hebben over de speci-fieke stuureigenschappcn, dus voordat het schip in dienst zou worden gesteld. Het betreffende containerschip van de 2e genera-tie werd besteld door de Koninklijke Nediloyd bij descheepswerf van "Van der Giessen"; het behoort tot een serie van vier zuster-schepen.

Een belangrijk verschil tussen het gedrag van dit schip en de gemiddelde stuur- en mafloeuvreereigenschappen waarmede gezagvoerders en stuurlieden bekend waren, wordt veroorzaakt door het grole windopperviak van het containerschip.

Een mathematisch model van bet manocuvreergedrag van dit schip, het t.s.s. "Abel Tasman", werd gezamcnhijk ontworpen door het lnstituut TNO voor Werktuigkundige Constructies en heI Laboratorium voor Scheepsbouwkùnde van dc Technische Hogeschool Deift. Dit mathematisch model waarop.desimulatie berust, bestaat uit de bewegingsvergelijkingen van het schip in het horizontale vlak; de hydrodynamische coefficienten werden experimented verkregen uit oscillatic proeven met cen schaal-model. Een speciale techniek werd toegepast om de invloed van 'de wind te bepaleh, waarbij van een hydrodynamisch model

gebrUik werd gemaakt.

Destijds werd juist destuur- en manoeuvreersimulator inDelft in gebruik genomen en het mathematisch model werd op dc hier-mede verbonden analoge computer geimplementeerd. Een check na koppeling van bet 'model met het visuele beeld, ultgevoerd door' de nautischedeskundigen van de betreffende rederjj verliep gunstig. Het bleek dat het gedrag van de combinatie schip-roerganger, onder zehs vrij extreme condities van wind en stroom als zeer reed werd ervarcn.

In overleg met' nautische deskundigen werd een trainings-programma opgesteld, waarin voor een periode van 5 dagen een verscheidenheid van manoeuvres werd opgcnomen. Ervaring opgedaan door vele trainingsgroepen van 5 à 6 man, heeft aan-getoond dat na eerste kennismaking en confrontatie met de mogehijkheden, zeer positief werd gereageerd waärbij met zeer grole gedegenheid en ernst gebruik werd gemaakt van de ter beschikking staande facihiteiten.

Volgens mondelinge overdracht, aflcomstig van dc nautische staf van de "Abel Tasman", kan men de conclusie trekken, dal het manoeuvreergdrag in werkehijkheid goed overeenstemt met de stuureigenschappen, die in het mathematische model voor de simulator zijn ingevoerd. Dit zal nicttemin nader onderzocht moeten worden. Pogingen orn aan boord metingen te verrichten tijdens enkele standaard manoeuvresslaagden aanvankelijk niet door ongunstige omstandighedcn. Kort geleden echter werden met succes metingen uitgevoerd; de resultaten hiervan zullen in de nabije toekomst worden gerapporteerd.

NEDERLANDS SCHEEPSSTUDIECENTRUM mo

After ordering a type olship, differing considerably from existing vessels on which the experience of the nautical staff of theship-ping company involved was based, the need was felt for informa-tion on the particular mànoeuvring characteristics beforeputting the ship into service. The vessel concerned, a second generation container ship, was ordered by the Royal Nedhloyd Lines at the shipyard of "Van der Giessen"; she belongs to a series of four sisterships.

A prime difference between the behaviour of this ship and the average steering- and manoeuvring characteristics captains and nautical officers were familiar with, is caused by the very large wind' exposed area of the containership.

A mathematical model of the manoeuvring behaviour of this specific ship, the t.s.s. "Abel Tasman", has been developed jointly by the Institute TNO for Mechanical Constructions and the Shipbuilding Laboratory of the Dehft University of Tech-nology, also taking into account information about steering-and propulsion plant. This mathematical model on which the simulation was based, consists of the equations of motion of the ship in the horizontal plane; the hydrodynarnic coefficients vcrc experimentally obtained from planar motion tests with a geo-metrically scale model. A special technique, applying a hydro-dynamic scale model, was used to determine the effect of wind.

At the same time the steering- and manoeuvring simulatorat Delft was put into service and the mathematical model was implemented on the connected analog computer. After this simulation the mathematical model was coupled with the visual display. A check was carriedout by well experienced members of the nautical staff of the shipping company. The outcome of this evaluation appeared to be very favourable. The behaviour of the combination ship and helmsman even under rather extreme conditions of wind and current was judged as reasonable.

In co-operation with the nautical experts a set-up for a training and familiarization programme with a duration of five days was composed for a group consisting of five or six nautical officers. Experience gained by quite a number of training groups has shown that after first cognition and confrontation with' all the possibilities a very positive attitude was demonstrated. With a high degree of seriousness, use has been made of the disposed facilities.

According to verbal reports of the nautical staff of the "Abel Tasman", one may draw the conclusion that the manoeuvring behaviour on true scale is in good agreement with the steering characteristics which were put into the mathematical model serving the simulator. Nevertheless this has to be checked in a careful way. Attempsto carried out measurementsaboard during some standard manoeuvres failed initialy because of unfavour-able circumstances. However, recently these measurements suc-ceeded; the results will be published In the near future.

List of symbols

. 6

Summary

₉

I

Introduction

.

...

₉

2

Mathematical model

_lo

3

_{Determination of the coefficients of the mathematical model f the}

,,Äbel Tasman" class

₁₄

4

_{Someresultsofsimulatedship manoeuvres}

_...

. 16

5

_{Description of the ship manoeuvring simulator in use for training and}

famiIiarization

26

References

. . .. _{. 27}

Appendix I

Derivation of the equations for the hül! contribution to the forces and

moment exerted on the ship ...29

Appendix II

Model tests with a planar motion mechanism for the determinatiôn of

the hydrodynamic coefficients

.

..

_31.

Appendix Ill

. .

coefficients in the equations of motion

propeller disk area

expanded blade area,

blade area ratio

moulded ship's breadth

block coefficient'

drag coefficient of rudder

lift coefficient of rudder

propeller torque. coefficients

propeller thrust coefficients

wind force and' moment coefficients

diameter of propeller

drag force of rudder

delivered' horse power at propeller

polar mass iñertia moment of propulsion machinery

polar mass inertia moment of ship about vertical' axis through c.g.

length' óf ship 'between perpendiculars

lift force of rudder

total yawing moment exerted on ship

contribution to yawing moment of underwater ship without propeller and without rudder

contribution .to yawing moment of propeller

contribution to yawing moment 'of rudder'

contribution to yawing moment of superstructure due' to wind

pitch of propeller at blade tip

pitch ratio'

shaft torque' at turbine

shaft friction loss

shaft torque at propeller

number of revolutions per minute of propeller

rudder area

reference wind area

ship's draught

propeller thrust

ship's 'speed relative 'to' water absolute current speed absolute wind speed

relative wind speed

speed of water relative' to rudder

intake velocity of water into propeller

total force exerted on ship along x-and y-axis respectively

contributions to X and Y of underwater ship without propeller and without

rudder

contributions to X and Y of propeller

contributions to X and Y of rudder

contribution to X 'and Y of superstructure due to wind

mean geometric rudder chord

speed increase in propeller race

-centre of graviti of ship

rudder height

A1 through A5

B1 through B8

C1 through C8

A0 A E/AO

B

Cß CD CL I-' I-"

'Q,

Q

Cr,C.

CXjd, C

_Id'

CNWIfld

D

:3 DR

DHP

'p

¡z

L(= L,,)

LR'

N

NhUJI Nprop Nrudder

N1fld

P

P/D'

QT QF

QP.

RPM

SR S1

T

U

uc

Uw LÇr Us'. VA

x'Y

XhUIl, Yhull -Xprop* Yprop

X

rudder, íuddcr

Xfld, Ywind

C Ca c.g.

I

_{distance between cg. and point at 50 percent of ë}

m

ship's mass

n

number of revolUtions per second of propeller

r

rate otchange of heading

t

_{yaw angular acceleration (t = dr/df)}

thrust deduction factor

component of U, álöñg x-axis

u, ú

_{component of U along x-axis,, û = du/dt}

u, û

_{component of U along y-axis, û = du/dt}

Uwr,,Vwr

components of 1J, along x- and y-axis

w

wake fraction

xo,yo,.zQ

co-ordinate axes of an earth fixed axissystem; positive z0-axis pointing vertically downward

absolute speed of ship along.x0-, y0-axis

io,,,.

relative wind speed along x0-, y0-axis

x,y,z

coordinateaxes of a bodyaxis system (principal:axes of ship); positivez-axis pointing vertically

downward, positive x-axis pointing towards ship's bow

fi.

drift angle,; positive for negative u; tanß= v/u

fi,,.

direction of relative wind speed; angle between the positive x-axis and relative wind vector;

positive going clockwise starting from positive x-axis

y

reduced frequency y

wu/g

(5 .

geometric rudder angle relative to x-axis; positive tòwards port

effective rudderangle (angle of attack)

(5,,

_{direction of U, relative to x-axis: tan (5,, = (u!r)/u,,}

density of water

density of air

characteristic propeller flow parameter

half the phase angle between the displacements of fore and ift strut (plan'ir motion mechanism)

course angle;:angle between positive x0-axis and positive x-axis; positive going clockwise

starting from positive x0-axis

rate of change of heading(= r)

i/it

_{direction of absolute current speed in x0}

_{Yo axis system}

diréction of ábsolute wind speed in x0y0 axis system

SIMULATION OF THE STEERING- AND MANOEUVRING CHARACTERISTICS

OF A SECOND GENERATION CONTAINER

_SHIP

by

G. M. A BRUMMER, Ir. C. B. van de VOORDE,

Ir. W. R. van W1JK and Ir. C. C. GLANSDOR:p

Summary

The steering and manoeuvring characteristics of a second generation containership of the "Abel Tasman" class are simulated.

The underlying mathematical model, describing the motions

_{of the ship in the horizontal plane, is given Results are presented}

oI.simulated ship manoeuvres.

A brief description is presented of the manoeuvring simulator

_{as a mean for training and familiarization of the future masters}

and officers of this- ship and her sister ships.

-i

introduction

The continuous growth in speed and size of surface

- ships has stimulated the quest for the manoeuvring

.ualities of a ship, while still in its design stage. It has

also become important that captains and officers

can

familiarize themselves with the ship long before the

maiden trip. These possibilities can be realized by

a

ship manoeuvring simulator developed following the

successful application of the "Flight Simulator" in the

field of aircraft engineering.

The ship manoeuvring simulator offers the

opportu-nity of real time manoeuvring of ships by

a human

operator. The facility can further be used for the

development of instruments, for studies of the human

behaviour and various nautical problems and for the

design of automatic pilots and: harbour entries.

The establishment of ship steering and manoeuvring

qualities is based on the solution of a mathematical

model, comprising a set of equations, describing the

motion of the ship and its rudder and engine control.

'he next step in accomplishing the manoeuvring

simulator has been to make the ship's motion as a

response to any change in rudder and/or engine control

setting perceptible on navigation instruments and

visible with respect to environment.

Generally the limitations of the simulator in

simula-ting real conditions are determined by the

mathemati-cal model, containing the-motion equations of the ship.

The coefficients of these equations, given with respect

to moving or Eulerian axes, have to be determined for

the ship concerned. Up to now -little information is

available about the equations of motion añd the -values

of their coefficients for a containership when rudder

settings and at the same time engine control settings

are applied and when the influences of current and

wind are present.

In the underlying report the forces añd moment on

the ship have been split up into contributions of the

naked ship's hull (without propeller, without rudder),

ofthe propeller, ofthe rudder and of thesuperstructure

due to wind.

-The hydrodynamic forcesand moment on-the naked

ship's hull have been assumed to be proportional to

the square of the instantaneous velocity component

along the longitudinal body axis (being also the

velocity used for nondimensionalization). The

coeffi-cients-of the forces and moment on the ship's hull only,

were determined by means of model tests with a planar

motion mechanism. The contributions of the propeller

and rudder weré calculated and finally the wind forces

and moment on the superstructure were determined

by towing tests. The experiments were conducted

at

the Shipbuilding Laboratory of the University of

Technology, Delft. Though effects of waves

and-con-fined waters can be introduced, in this case only calm

and unrestricted water has been considered.

-The manoeuvres determined using the described

mathematical model will be compared in the

near

future with full scale results of a ship of the "Abel

Tasman" class.

The steering- and manoeuvring characteristics of

ships of the "Abel Tasman" class were simulated at

the simulator óf the Institute TNO for Mechanical

Construct-ions, Delft. The simulator has been used for

training and familiarization of future captains and

officers of the "Abel Tasman" and her sister ships.

The simulator consists apart from an analog

com-puter, of a mock-up of the interior of a ship's

wheel-house with a- forward view through a window onto a

display screen showing either an open sea, harbour

or

coastal view. The forepàrt of the ship also being

projected, one -has a realistic appreciation of ship,

surroundings and of the ship's relative motion. Bridge

equipment includes all the usual instruments.

advanced, experimental one, described in ref.

[1 11.

The new one incorporates a larger angle o view from

the bridge, a complete bridge outfit and an extension:

of the mathematical model' and of the computer

capa-city, enabling thé simulation of more realistic ship

manoeuvres.

2

Mathematical model

2.1 Co-ordinate syslerns

The ship path is referred to an earth fixed right-hand

orthogonal coordinate system 'O, x0, Yo,

Za..

The ship

motion is described relative to a ship fixed orthogonal

co-ordinate' system,. cg., x, y, z. The origin of'this axis

system coincides with the centre of gravity of the ship.

The positive directions of the principal axes are

indi-cated in the sketch.

2.2 Kinenia tic relations/zips

The kinematic relations are:

= ticos4ivsini+UcosIl

S'o

= u'siìi4i±.vcos,lt+ Usin'/I

(1)

= i.

2.3

Equations of.nzolion

The equations of motiön .relathe to the moving or

2BC(û - ru

+ X0

l'course angle

+y0

Fig. i. Co-ordinaie systems and dëfiñition of positive directions of ship's motion, wind and' current.

Eulerián axes are, the ship. being considered as a rigid

body, for the three degrees of freedom, which are

relevant for martoeuvring:

m(ùrv)

Y = m(ò+ ru)'

(2)

N = I,/

The forces and the moment exerted on the ship can be

split up into contribütions of the ship's hull (without

propeller, without rudder) of the propeller, of the

rudder and of 'the superstructure due to wind.

Hence:

nz(ttrv) = X = XhuIl+Xprop+Xrudder+Xwind

zn(v + ru)'

Y =

huIl +Ypf0p ± rudder +

Yj0d (3)

Jr

=. N - NhUII + Nprop ± Nrudder + NIfld.

Division of all terms. of the first two equations by

LT and those of the last equation by

L2T yields

with

m = QCBL.B.T.; I = ,ui

and

¡;

=

(4)

-'huII Xprop

+

Xrdder X,,,,mi

QLT

ÜLT

LT

LT

(2BCB

(2 BC8

+

Yprop

+

+

(5)

feLT

QLT

jQLT

LT

NhU,I

+

+

Nruddcr

+

NWIfld +QL2T QL2T QL2T +QL2T

2.4

Hull contribution to the forces and moment

exerted on the ship

The forces and moment exerted on the ship's hull

(without propeller, without rudder) due to its motion

are expressed as (for the derivation, see appendix I):

= A1LÛ +A2u2+.A3v2+A4L2r2+A5Lvr

Yhull

B1 Li) + B2L2t+ B3uv+B4v3/u + B5Lur +

QLT

+ B6L3r3/u + B7Lv2r/u+ B8L2vr2/u

(6)

NhUII

= C1L2i+C2Lû+ C3uv+ C4v3/u + C5Lur+

QL2 T

+ C6L3r3/u + CLv2r/u + C8L2vr2/u

Coupling effects of roll, pitch and heave motións into

the horizontal motion have been neglected.

Substitution of equations (6) into (5) yields

Ai)Lù=

A2u2+A3v2+A4L2r2+

+ (A 5L+ 2BC8)vr +

±

rap

+

X;udder

+

XWIfld

QLT

QLT

QLT

Bz)Lt) = B2L2,+B3uv+B4v3fu+

2BC8)33/

+ B;Lv2r/u+ B8L2vr2/t, +

+

'prop

+

1Çuddcr

+

Ywjnd

+QLT

+QLT

+QLT

C1)L2t = C2LO+C3uv+C4v3/u+

+C5Lur± C6L3r3/u+

± C7Lv2r/u + C8L2vr2/u +

+

Nprop

+

Nrudder

+

NWlfld +QL2T

-QL2T.

QL2T

The coefficients A, B and C are relatedto the so-called

hydrodynamic derivatives (see appendix I).

(7)

2.5

Propeller con tributiön to the forces and izzonient

exerted on the s/zip

The propeller thrust and torque are written as

T =CTQD2[VA+(nD)2j

= CQQD3[V+(nD)2]

It is assumed that C. and CQ are known as a functión

of the propeller flow parameter

nD

a -

(ref. [9])

(9)

,JV+(nD)2

Now the propeller contribution to the X-force can be

calculated, assuming the wake fraction and the thrust

deduction factor are known, according'to:

X1,,,,,, (1

t)CrQD2[u2(1

w)2+(nD)2]

-,

+QLT

QLT

=2(1 OCT

:[(l

w)2u2+(nD)2]

(10)

with

nD

C,.= C.(o')

and a =

'/(1 w)2u2+(nD)2

The effect of propeller action in creating a side force

and moment is neglected i.e.

Yprop and

Nprop

are

assumed to be zero.

2.6

Rudder contribution to the forces and moment

exerted on the s/zip

The velocity along the x-axis in the slipstream of the

propeller at the position of the rudder amounts to

U5, VA

+

Ca, in whiôh the sign of the speed increase

C0

is directly related to the sign of the thrust (Cr).

The application of momentum theory yields for the

thrust

T= QD2(VA++Ca)Ca,

from which

VA+Ca

=

+

2 T D2

or

u,=

V4±co=(1_w)u.j1

+CT

lt is thought reasonable to assume u5, being zero for

8 1

l+CT

₂₀

ir

1a

(8)

2BC8(O +ru)

2i2BC8Lt

-f

yir

tan

₌

Usr

The flow field at the position of the rudder is not only

With

determined by Usr, but also by the sideslip velocity u

and the yawing velocity Ir (I being the distance be-

sin'&,

y r

and cosö=

-f-tween the centre of gravity and the 50 per cent chord

' S'

pint of the mean geometric rudder length).

the rudder forces and moment exerted on. the ship.

The total oncoming speed relative to the rudder

become becomes

Usr =

(12)

-rt;r

_{J(b - ir)2 ± u,,{CL(v._L ir) ±C0u5,]}

(The effect of slipstream rotation on both magnitude

_,,

_s

and direction of the speed relative to the rudder is

= L' rJ(v_ir)2+u,[CLusr_ C0(vlr]

(b)

neg1ected

It is assumed that effects on the upper and

lower part .of the rudder will cancel each other).

. Nrudder _1'rudder

4QL2T

L{QLT

ttsr

v-t r

¿r

Fig. 2. Relativespeeds wi hrespect to rudder.

The direction of the oncoming flow is determined by

LR

Fig. 3. Frees on thdrijdder.

These forces become 'along the x- and y-axis

Xruddcr = LR Sifl5U'DRcO5SV

Çudder = +LRcos$VD.Rsin5V

Nrudder = - I Yuijcr

The coefficients CL and C0 have.to be known as

func-tions of the angle

5e for the rudder configuration.

concerned'.

23

Wind contribution io I/le forces and moment

exerted on 1/le s/up

The components of the relative wind velocity in the

x0y0 axis system are given by

(13)

xo,,,.= Uwcosl/iw±o

5'0, =..0 sin i/i.j'

(16)

The .directión of the relative ,wind vector is given by

tanß

=

(19)

fl

is defined as the angle between the positive x-axis

and the relative wind vector: positive going clockwise

starting from the positive x-axis.

The wind färces and moment are written as

XWi,ld

= Cx1+Q,U,S,

1'wind = CyId+QIU.rSw

NWfld

=

CN5I4j-Q,UWS,L

For a rudder deflection of +ô (to.wards port) the

effective ,angleof attack becomes

. ₍ and

are given by equations (I))

Those in the xy axis system are given by

(14)

The lift and drag force on the rudder are vrtten as

=

(

= owin±ow,cos

LR = CLU2,SR

DR

CDQUSR

The resultant relative wind velocity is equal to

Hence XWjfld

-c

_{QU2 S}

4-QLT -

XwInd

wrLf

Çind

-

Li

u2

+QLT'

Ywlnd

WYf

nd _ç, 01 +QL2 T

- 'Nwind

O

LT

The coefficients CxWjfld, CYWIfld'and CNWIfld have to be

known as functions of the angle ß.

'2.8

Turbine control simulation

For the calculation of the turbine torque Q a method

as described by Gòodwin et al. [I] was used, which

states that

Qr = QT.

(Percj:eam){(a

+1) a :1 } (21)

in which a is a constant differing for the ahead and

astern operation. The shaft friction loss QF is assumed

to vary with RPM squared.

QF

= Q,,,,,.

n22 max

is taken to amount to 4% of the maximum

propeller torque.

The propeller torque is taken from eqUation (8)

Q,, = C.oD3[u2(l w)2+(nD)2]

(23)

in which CQ is known as a function ot the flow

par-ameter

nD

(ref. [9])

j[u(1 w)]2+(nD)2

Hence

2irI!'

= QTQPQF

(24)

The torques and the polar inertia moment of the

rotating parts of the propulsion machinery, inclüding

added inertia are all related to the number of

revolu-tions of the propeller., By means of the telegraph a

percentage steam is adjusted, assuming that always

enough steam is available. A servo system sets the

steam valve at the, required value. lt is assumed that

the servo system can be described by

(25)

arcq)

(20) a

(22)

with c limited to a' certain value, in which

= instantaneously measured value of percentage

steam

req = required percentage steam

= time constant

2.9

Steering gear simulation

A simplified sketch of a rudder control system isgiven

in fig. 4 A servo valve controls the oil flow to the

hydraulic cylinders of the steering gear. The required

valve opening kreq

is proportional to 'the difference

between the required, rudder angle 5req .as prescribed

by the position of the steering wheel and the rudder

angle

instantaneously measured. As soon as this

difference exceeds a certain value, krgq

becomes'maxi-mum (100% opening).

o..,steeriog wheeL O rudder ungle

Fig. 4. Schematic diagram' of à rudder control system.

lt is assumed that the servo system can be'described by

k

=

kreq

k)

where k is limited to a certain value, and in which

k

= Instantaneous percentageof servo valve òpening

kreq = required percentage of valve opening

Tk = time constant

Now 5= constant times k, constant depending on the

capacity of the oil pump. Hence the maximum rudder

rate (which is supposed to be known) occurs, if the

servo valve is fully open (k = 100%).

Hence'

max loo.

The maximum value of the rudder angle is considered

to be known.

QF changes sign if n changes sign;

Qp='Qpmon

'tma,c

cylinder

3

Determination of the coefficients of the mathematical model of the "Abel Tasman" class

3.1

Principal s/lip data

The principal characteristics of ship and propeller are summarized

in the following table:

L=2lOm

B=30.5m

Tattat station O = 11.20 m Tfor%vard at station 20 = 10.04 m Tn3eanat station 10= 10.62 m Displacement volume 41,936 m3 Block coefficient C 0.617 Radius of gyration

about the z-axis 15-O.254L

Centre of gravity forward of station O lOI. 16 rn

Reference wind area S = 3401.6 m2

335m

Fig. 5. Sketch of rudder.

12

Determination of /,ydrodynamic coefficients

The values of the A, B and C coefficients of equations

(7) (in section 2) have to be established for the ship

concerned. The following assumptions were made.

principal data of ship considered

Type: fixed blades

DiameterD = 7.00 m

Pitch ratio at blade tip P/D = 0.935 m Blade area ratio AE/Ao = 0.78 Number of blades z = 5 Designed to absorb 32,450 DHP

(at RPM 110)

Machinery: StalLavaI steam turbine installation

Total polar inertia moment of all rotating parts (including the added inertia

moment = 25 per cent. of propeller inertia moment): l= 1,001,297 kgnt4 (refèrred to propeller RPM) Horn 4.06m 0.93m 4.11 m

The added mass term

A1 = -0.1-in'

012BC8

= -0:01792.

The coefficients A3 = A4 = A5 = 0.

The resistance coefficient A2 is fäund from towing

tank

test results (corrected

for trial condition):

A2 = 0:00914.

The B and C coefficients were determined by means

of tests with a planar motion mechanim on a model

toa scale of 1:64. Here theresults of these tests will be

given. For a description of the test program and

evaluation of results reference is made to appendix 11.

Type: semi-balance rudder with Horn Chord at root 6.400 m

Chord at tip 3.350 m

geometric mean chord ë = 4.875 m Taper ratio 0.52

Height rudder /q = 9.100 m Total rudder area S -44.4 m2 Aspect ratio hR/C = 1.87

Hinge axis at 36.7% Profile thickness 23% Horn dimensions see fig. 5

3.3

-Calcùlation of propeller and rudder contribution

For the wake fraction and the thrust deduction factor

were taken the values u'=0.25 and t =0.175. Under

the conditions of running ahead, while RPM is being

reduced,, it is thought realistic to set the thrust

deduc-tion factor at zero as soon as the thrust has become

negative. From available results of towing tank tests

- --. -:

.4.

coefficient value x IO' coefficient value X IO'

2BC8/L-Bl

+

339.24

¡'z-Ci

± 22.14 82

-

12.74 C,

-

9.33 B,

-

l982

C, -117.61 B4 -2,1-95.60 C1 0.00

ß5-28C,j/L

- -l3447

C,

- 39.60

¡J,

-

6798 C,

- 11.74

B, 000 C; -420.33 B,

- 35982

C, 0.00

Fig. 6. The propeller thrust coefficient versus flow parameter a

Fig. 7. The propeller torque coefficient versus flow parameter a.

the thrust and torque coefficient are .known for the

value of the flow parameter

in the self-propulsion

condition at maximum power.

These values agree with those for the B5-75 propeller

with pitch ratio 1.0 of which the available propeller

characteristics (figures 6 and 7) are used for the other

propeller loading conditions. Now the propeller

con-tribution to the X-force as a fûnction of the speed u

and propeller RPM can be calculated with the aid of

equation (IO) in section 2.

For the calculation of the rudder contribution to

the forces and moment exerted on the ship the lift and

drag coefficient of the ruddèr have to be known These

coefficients CL and CD are dependent on ôe, and

as a

consequence of the fixed Horn-part. Little data for this

type of rudder are available. According to ref. [2J it

is to be expected, that the maximum lift coefficient

amounting to 0.67 will occur at an angle of attack

of 23°.

Graphs8 and 9 show the estimated curves for the

lift and drag coefficient as a function of the effective

rudder angle. In particular the complete guess of the

curve in the stall region because of lack of

experi-mental data is felt as a severe shortcoming.

Experi-.0.7

Fig. 8. Rudder lift force coefficient on a base of effective rudder angle. .12 CD

.08

+04

o

-1

-90

0

.90

_.180 - _{6e6-Öv(degrees)}

N

tÌ s

40

80 120 160 be O -öv(degrees) Tp.C1PD2{u2(1_i4i).n2tf} e . i _J

/

Vu1'i42.DP

1

*04

u'O

n.cO e +02

u>0

n>

/

-Q8

-04

0

.04

.08

A CL4°/6

____

T

_;02

1--¡

\\\

QPrC0PD3{ua(i_4j)2. n2D'} nD

₀₈

.0

1jU(_2

_D C0

u>0

n<0

.o

004

.

u>0

n0

-08

-04

0

:004

0.4

08

Fig. 9. Rudder drag force coefficient on a base of effective rudder angle.

-01

-0.3

'if

ments (e.g. wind tunnel tests) would be highly

re-commendable. The rudder contribution to the forces

as a function of u and n can becalculated according to

equations (Il) aiid.(15).

032 0.21. 0.16 '0.08

C-to

-008 -0.16 -0.21. -0.32 C 1.0 0.8 0.6 'y.-.-0.1. 0.2 012 0.08

Fg. IO. Longitudinal wind force coefficient ona base of relative wind direction.

20 ¿0 60 80 100 120

_ (d.gr)

Fig. Il.

Transverse wind forcc coefficient on a base of relative wind direction.

Fig. 12. Yawing wind moment wind direction.

160

) 100 120

coefficient on a base of relative

:'.

3.4

Results

of

lowing tesis for the determination

of

the

wind forces on tile superstructure

For

the calculation, according to equations (i) and.

(16) through (20) of the wind contribution to the forces

and moment exerted on the ship, the coefficients

CXW,fld, C.,, and

have to be known as a func-'

tion of the angle fJ. These were determined by means

of towing tests on a model' of the superstructure to a

scale of 1: 150. The results of these tests are shown in

figures 10, II añd î2 For a description of the tests

reference is made to appendix 111.

3.5

Turbine, control si,nulation

The maximum power ahead at the turbine amounts to

32,450 HP (at the propeller) + 4% (shaft losses)= 33,748

HP at RPM = 110 ("at = 1.83/sec).

Hence

Q1-,,,..-ahead amounts to 2,137,403 N.m.

The maximum power astern at the propeller shaft

amounts to 15,800 HP at RPM =66. Hence Qr,,,,,

astern = 1,711,690 N.m. (this includes the friction

losses at the reduced' RPM = 66).

Equation (21) states:

Qr

Q

(Perc steam) {(a

± 1)

a

}

'For the constant

a

is taken

a =

I

in the ahead and

a =

0.5 in the astern condition [il).

The shaft friction loss QF is given by equation '(22).

Q p = QF,..,,. 2

= 24,329,12 N.m.

The propeller torque Q, as a function of the speed u

and propeller RPM can be calculated with the aid of

equation (23) and' of CQ = CQ(a) as given in figure 7.

With the foregoing the equation of motion for the

turbine shaft, eq.

(24) -

2zrl dn/dl

QT - Q - Q can

be solved.

The time constant in' the servo system (eq. 25) is set

at 5.0' seconds; d is limited to IO per cent. per second.

4.6

Rùdder

control si,nulatio,i

The maximum rudder angle amounts to 35 degrees to

either -board and the maximum rudder rate amounts

'to 2.32°/sec; kreq = l/4.5(6reqt5), 5 in degrees.

The timê constant in the servo system (eq. 26) is set

at 0.2 seconds; k is limited to 33 per cent. per second.

4 Some results of simulated ship manoeuvres

4. 1 Standard ship manoeuvres

Dieudonn

spiral manoeuvres, zig-zag, and turning

11.0 160 180 120 3.. (d.r.) 80 100 £0 60 20

circle trials were simulated for three initial ahead

speeds of the containership viz. 8, 12 and 22 knots.

Some results are presented in figures 13 through l7

The results of the spiral manàeuvres show that the

ship is course stable for all three speeds.

As shown by the results of the turning circle tests,

in which no significant speed dependence is found, the

smallest diameter to be attained with hard rudder

applied, amóùnts to about 600 metres, yielding

a value

of about three for the diameter-ship's length ratio.

This value is considered as to be sufficient, according

to the ship's handling quality criteria, given by Gertler

and Gover tef. [12], and based upon the analysis of

many manoeuvring data collected during standard

manoeuvres.

The results of the three 20/20 degrees zig-zag trials

show that the ship is rather sluggish in response to

helm, based on a comparison of the time to reach.

execute with the vàlues of the nomograph as presented

by Gertler and Gover. During one period of the zig-zag

manoeuvre the containership travels about 10-il ship

lengths asan average for the three initial speeds This

indicates a normal behaviour in view of the fact that a

normal average of 12 hasbeen found.

4.2

Turning circlès wit/i wind influence

The following brief exposé is intended as an example

of how manoeuvres conducted on the manoeuvring

to starboard

40°,

30°,

0.4

t 08

'12

1.2 o) t, Q) OB t) o' C a u b.4 t) o L

simulator can assist

the

practical shiphandler by

supplying him with useful information which cañ be

available for closer study and ready at hand on the

bridge. This example is by no means meant as a

thorough study of the subject, but may suffice to

indicate possible applications.

As the turning circle of a ship comprises often as a

whole, or even more often as a part, an important part

of the manoeuvres executed by shiphandlërs,

a case

of the influence of wind on the turning circle of the

ship was examined. Of main interest to him is the

resulting path of the ship in first instance. Speed loss

during the turn and the occurring drift speed will also

have his attention.

The following data apply:

Initial conditions

Ship speed:

8 knots

True wind speed: 12 m/sec, Beaufort scale 6

Rudderangle:

350 _{to Port.} 200 rudder

to port.-.

30° 40° angle

approach speed:

8 knots

Fig. 13. Rate of change of heading versus rudder angle for predicted spiral manoeuvre.

12 knots

22 knots

condition true wind at initial

direction course, Wind

I

no wind

11 _Ww 00 _{from astern}

111 'Pw = 1800 _{head on}

Iv

'I'w = 900 _{on Port beam}

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