Towards a design tool for ship manoeuvreability

9 FEB.

_i8

ARCHIE

1. INTRODUCTION

Although the ability of ships to manoeuvre and

to stop in

a satisfactory manner

is

important for

their safe operation,

it

is only

in recent years

that

efforts

are

being

made

towards

imposing

mandatory

requirements

that

will

quantify

and

control

snip

manoeuvreability

from

the

design

stage.

The 'J.S. Administration started work first

towards the setting of controls on the rnanoeuvring

qualities of ships using U.S. ports.

uoting from

reference (1):

"The standards being developed are

designed

to

provide

a means

for

_rating

controllability under restricted water conditions

where

collisions,

rarnings

and

groundings

are

likely to occur".

Following the U.S.

initiative,

the 1MO Sub-Committee on Ship Design and Equipment

is now contemplating similar action and has set up

a

working

group

which

recently

produced

draft

guidelines on the manoeuvring qualities that ought

to be considered in ship design (2).

Quoting from

this document:

All ships should have manoeuvring

qualities

which

permit

them

to

keep

course,

to

turn, to check turns, to operate at acceptably low

be

consciously

evaluated

during

the

design

process."

The imposition of any such standards assumes that

the

appropriate

theoretical

methods

for

the

evaluation of

a design will be available, and for

this reason research efforts for the prediction of

a ship's rnanoeuvreability qualities are presently

greatly

encouraged.

Demands

for

realistic

mathematical models of ship handling behaviour are

also

made

from

the

increasing

numbers

of

Ship

Handling

Simulators

used

for

the

training

of

mariners

and

pilots,

for

ergonomic

studies

in

bridge design, for investigations of circumstances

leading to collisions, etc.

JvcAì-

M c

4

U

-o 4

-

-j a () ïc1

Lf

et

Lab.

y.

Scheepsbouwkunde

Technische Hogeschooi

Delfi

TOWARDS A DESIGN TOOL FOR SHIP MANOEUVREABILITY

N.E. Mikelis and K.V. Taylor

To describe

a

ship's motion,

use

is

made or

rigid body dynamics.

From Newton's laws the force

and the moment acting on the ship are equal to the

rates of chanme of momentum and

angular momentum

respectively.

In general these equations describe

motions in the six degrees of freedom (4).

It

is

customary however in cnanoeuvning studies, to reduce

the problem by considering only the motions in tne

horizontal plane, i.e. surge (X force, U velocity),

sway (Y, y) and yaw (N, r).

In most cases this is

a justifiable assumption, although there are some

ship

types,

e.g.

Roll

on-Roll

off

ships,

that

develop

a

considerable heel when turning at

hiah

soeed.

For such cases the roll

equation must be

coupled

with

the

horizontal

plane emuations,

as

demonstrated by Hirano and Takashina (5).

sceeds and to stop,

all

in

a satisfactory manner.

Since most manoeuvring mualities are inherent

in

2.

EOUATIONS OF MOTION

the design of the hull

and machinery they should

Observations

on model

exDeriments

and on

full

scale operations show that when a ship moves from

deep

to

shallow

water

or

into

a

canal,

its

handling

behaviour chanoes

noticeably,

and

since

such changes are often unexpected by the mariner,

they increase the risk of collision or grounding.

However,

although

the

need

for

accurate

predictions of rnanoeuvreability in

all

topoioaies

cannot

be

overemphasised,

most

current

work

relates

to

the

deep

water

condition,

mainly

because of the difficulty to obtain the necessary

coefficients

for

the

mathematical

models

of

shallow or restricted waters.

This

paper

briefly

reviews

the

existing

manoeuvring theories and the methods employed to

obtain the hydrodvnamic coefficients used in these

theories.

A simplified model

developed

and used

at

Lloyd's

Register

illustrates

simulations

of

deep water manoeuvres of

the tanker

Esso Osaka,

which are

also

compared

to

published

(3)

full

scale

measurements

for

the

same

ship.

The

agreement in these comparisons is shown to be very

reasonable.

To facilitate the expression of hydrostatic and

hydrodynamic forces, a system of body axes is

employed (Cxy on fig. 1) that is fixed on the ship

and is moving relative to the inertial axes

0X0Y0 with velocity equal to the

ships

velocities, U, y and r. The

ships centre

of

gravity G is at a distance xG from the origin

C.

ifl

most experimental studies the origin is

located amidships and the same convention is

(dopted here.

o

Yo

X' X

Figure 1 Co-ordinate System

From rigid body dynamics the equations of motion

(see reference (4) for example) are:

Surge: rn (_vr_xGr2)=XHULL+XpROp+XEXT

Sway : m(i + Ur + x6)

HULLEXT

(i)

Yaw :

The terms on the right of eq. (1) represent forces

and moments due to hydrodynamic reactions on the

ships

hull (including rudder), due to the

propeller and due to the external disturbances.

The ships mass is m, its moment of inertia about

G is I and a dot over a symbol represents time

derivative.

The external forces and moment can be set to

represent a variety of actions, such as the effect

of wind, of current, the effect of suction experienced by a ship near a canal wall or when

overtaking another ship, the use of bowthrusters

Y ('i, v) Y (O, O) +

h

3 +

Yv + '-- Yv2 +

- y y + vvv .2 1 .3

Y.v

+ r

V

+...

VV 3. vvv (2)

Here a subscriot denotes the Dartial derivative

with respect to the subscripted variable when the

remaining variables are at the equilibrium position. Also a term like Y(O, O) would be zero

as it represents the force in the y direction in

the absence of a perturbation.

Because the hydrodynamic derivatives are constants for a given ship form and constant topology (water

depth, presence of canal walls, etc.), it follows

that the resulting equations of motion yield a

quasi- steady motion, i.e. one which is affected

only by the instantaneous values of its position,

velocity and acceleration parameters. An

alternative formulation exists that accounts of

fluid memory i.e. of the effect of the motion's

history on itself. This theory results in a set

of integro-differential equations linking frequency and time domains. For an application of

this approach and a comprehensive list of

references see Frank et al (7). As, however it

has been shown experimentally by Fujino (8) and by Scragg (9) that fluid memory effects are negligible for normal ship manoeuvres, the

classical equations remain widely used, and are

further discussed below.

etc. M3K and van der Bend (6) briefly discuss

these effects, which are ignored in the present

study. Equation (1) is sometimes found in the

literature expressed in terms of drift angle_f (

-tariv/U -v/U). Also it is often found in its

linearised form, i.e. excludinq oroducts of the

small perturbation terms y and r.

2.1 Hydrodynamic modelling

The hydrodynamic reactions on the hull XHULL, _HULL' NHULL can be expressed in a

variety of ways, accounting and neglecting of

different effects, and thus leading to a number of manoeuvring theories. The classical manoeuvrinq equations express the hydrodynamic reactions as

functions of all the motion parameters (U, U, y

etc.), these being treated as if they were independent variables. These functions are then

approximated by a Taylor expansion of

perturbations around the equilibrium steady forward motion (4). For example, a function of

two variables, say ' and y, would be approximated

2.2 Expressions for forces on a ships hull.

Consider an oblique towing experiment modelling the idealised situation of a ship

drifting in a steady state straight (but oblique) motion. All the perturbation terms except y are zero and thus the infinite sum on the second line

of equation (2) can be used to fit the experimental curve of Y and thus to determine the hydrodynamic coefficients

Y,

etc. In

practice the infinite series is truncated so that

it will usually contain one or two terms (linear

and non-linear model respectively). The linear term is the slope of the experimental curve at the

origin v0. Since the Y(v) curve is antisymmetric

about its origin, while the even order terms are

syrmnetric, then a non-linear model of Y(v) would

include in addition to the linear term either the

third order term or an even order antisymnietric

term like YV)V)v vI, the choice being determined

by the practice followed in different research establishments.

The functional expression of hull forces and

moment when all the perturbation motion parameters are present is of the form:

( Xu

) ( X

HULL = C Y ) (U,v,r,U,v,r,x,y,.f,S, ) (3) ( ) ( N )

From equation (3) it appears that even if only the linear terms were included, there would still be a

large number of coefficients to be determined. However, from physical reasoning, as also

explained in reference (4) it is deduced that a

number of these terms are identically zero. For

example: hydrodynamic derivatives with respect to position or orientation (e.g. _X<, Y,, etc.) are all zero in the open water condition since there

can be no hydrodynamic forces exerted on a ship

due to its position or orientation. This is not the case for the ship in a canal . Here a suction force and a bow to the centreline" moment are

applied by the fluid when the ship proceeds off

the canals centreline. Also, because of the port

and starboard symmetry of ships, terms like

etc. are zero, since a symmetric motion, i.e.

u or Ù, does not introduce an antisymmetric reaction. Furthermore, an antisymmetric motion (y,

r, , o,...) produces forces in the X direction

(Xv,Xr

etc.)that are symmetric about the

origin, y or r O, and thus the slope at the

origin (i.e. coefficient X

. etc.) is

zero. Finally the rudder rate effect is usually

ignored.

The mathematical model of equation (3) should now appear of manageable size. References (4), (5)

and (10) to (14) provide examples of expansions of equation (3) used for simulations by different researchers. Differences occur in the choice of

the direct and cross-coupling

non-linear terms used. Nlandel (15) and Norrbin (15) assess the order of importance of the various

coefficients used, while moue et al (17) provide

graphs of 6 non-linear coefficients as functions of a simple ship form parameter. It must also be noted that mathematical and physical reasoning (4) exclude non-linear acceleration terms and

cross-coupling terms between velocities and

accelerations.

2.3 Propulsion and rudder forces.

The propulsion force along the x axis is given

by:

XPROP = (1-t) T (Ja) (4)

T is the thrust, which is a function of the speed coefficient J0 = (l-w)U/nD, t is the thrust deduction, w is the wake fraction and D, n are the propeller diameter and revolutions. The Dropulsion characteristics w, t, T along with the resistance

X(U), are determined for every ship design and apply to a straight course. The effect of

perturbation motions y and r on the propulsion characteristics may be modelled by the empirical

method proposed by MMG of the Manoeuvreability Sub-committee of the Japanese JITO and described

in (14).

In general, the lift and drag on the rudder are resolved along the body axes to oroduce the X,Y,N

forces and moment due the rudder action. As drag

is comparatively small, the effect of the rudder

can be expressed by a constant (slope of lift to

angle of attack curve) times the angle of attack,

times the flow velocity squared. The existence of

a perturbation motion and accelerated flow in the

propeller race result in both angle of attack and flow velocity being different to the rudder angle

and ships speed respectively. The Japanese MMG

grouo (14) have proposed an empirical method to

account for these effects given the propulsion

characteristics of the ship. In the absence of

such data for the simulations presented in this

paper and as a first stage of development, a much simpler model is used, i.e.

= c( O u + (l-e) u0)

(5)

The constant c accounts for the accelerated flow

in the propeller race, while B accounts for the

fact that although during the manoeuvre the ships

speed U can be considerable less than the initial

speed U0, the propeller however still works at

the initial RPM and thus delivers flow to the rudder at a speed between cU and cU . For the

o

simulations presented in this paoer the value of c used was 1.15 while was given values between 0.5

and 1.0. It should be noted that the turning

circle simulations are not particularly sensitive

to small changes of these constants.

A linear Taylor expansion of equation (3) produces

the rudder effect as and N while = O

by symmetry argument.

The rudder coefficients are functions of rudder

geometry. Means to obtain them are discussed in

reference (25).

2.4 Linear equations of motion.

(m-X -(m-Y. )vr-(mx-Y. Consider the equations of motion for a ship in

open deep or shallow waters, obtained from equation (1) along with a linear expansion of

equation ). It is assumed that no wind, current or other external force is acting.

(m_X)Û+X(U0_U)'0

=0 (6)

V

(Ic_Nir+(mx8U_Nr)r+(mxo_N)v_Nvv_NgS 0

The equations of motion for a ship in a canal

require the inclusion of terms from the expansion

of y and perturbations. In the above equations the resistance and propulsion terms have been Combined in the coefficient X. U0 and U are the initial and instantaneous speeds in the x

direction. All the coefficients are about the

origin C and must be obtained at the simulated water depth. Gill and Price (18) determined experimentally the effect of forward speed and

water depth on the coefficients and concluded that

for a tanker form, all the acceleration and the

sway velocity coefficients are highly dependent on water depth while the speed affects the acceleration coefficients and the dimensionless

N only in very shallow waters. The same

conclusion regarding acceleration coefficients is

reached numerically in reference (19). As

discussed by Fujino (20) the effect of shallow water on the rudder coefficients is small due to

the presence of two compensating effects: (a)

increased flow separation at the stern region

leading to diminishing effectiveness of the rudder, and (b) increased resistance in shallower

water which reduces the ships speed so that the

rudder works in a stronger slipstream thus

increasing its effectiveness. From the above considerations and from experimental evidence,

Fujino claims that water depth has little effect

on the rudder.

By neglecting the non-linear hydrodynamic terms,

it can be seen from eq. (5) that the Y and N

equations are uncoupled from the X one, imolvinq

that the equations cannot model the speed drop

observed in ghio manoeuvres. For some studies this is acceptable. Flowever, the aim of this paper

is to compare simulations with full scale measurements where a considerable speed drop was

observed (3). For this purpose it is suggested

here that use can be made of the ideal fluid model. Following Lamb (21) and Imlay (22) we

obtain:

(m-Y )+(mX)Ur+(mx0_Y. )=0 (7)

The above equations, describing the early stage of

the response following some initial disturbance,

are the complete ideal flow expressions for

motions in the horizontal plane and appear in terms of linear acceleration coefficients only,

which as discussed later can be evaluated theoretically. In this paper the surqe equations

from eq. (6) and (7) are combined to produce couoled equations with linear coefficients.

2.5 A simplified non-linear simulation model.

Earlier work (23) employing linear equations

of motion proved reasonably successful, provided

experimental data were available for the simulated

ship. In this paper however, effort is

concentrated on predictions using hydrodynamic

data that can be easily accessible to the

designer. 0f the various alternatives tested for

this purpose the combination of directly calculated acceleration coefficients end

parametrically derived linear and non linear

velocity coefficients proved most successful for

the deep water simulations. The available parametric expressions (17) provide coefficients for the Y and N equations only, so in order to arrive at equations that keep the three planar

motions coupled the surge equation is constructed

by combining the real and ideal fluid equations

(m-X')-(m-Y.)vr-(mx_{U y}

_Gr

Y.)r2+X(U_U)0

(in-Y. )+(mx -Y.)-Y v+(mU-Y )r-Y v(vI-Y v(r(

y G r y r vv vr -Y

_rlr=Y

(8) rr (I -N.)+(mx U-N )r+(mx8-N.)-N v-N

rrl

Cr

G r y y rr - (N r+N

v)vrN

rrv vvr d

These equations of motion can now be discretised

by a time finite difference scheme to produce the

three accelerations at time "n+l" in terms of the

velocities and rudder actions at time n. Then a

trapezoidal integration produces the velocities at time "n+l", and a transformation:

Ucos_vsiny ; UsirT$+vcos/, ; Rr (9)

followed by another integration, yields the ships

trajectory relative to the inertial frame

OXY.

The computer CPU time for these simulations is negligible and thus a mini computer could be used for much faster than real time runs.

3. EVALUATION OF HYORODYNAMIC COEFFICIENTS

Three different approaches are available for

the evaluation of the coefficients, namely; Experiment, parametric formulae and direct calculation. In the experiments use is made of a

captive scale model in (a) towing tank or circulating water channel with oblique tow and

with Planar Motion Mechanism tests and (b)

manoeuvring basin with Rotating Arm tests. More

recently free running model tests and System Identification techniques have been used for the

determination of manoeuvring coefficients. The

experimental methods are described in some detail

by Burcher(24) and by Gill(13). Alternatively, the transient testing proposed in (7) may be

employed. Although experiments are usually ari

accurate means of determining all the

coefficients, they are too expensive and time consuming for routine design work while the

problems of cost and time delay are magnified if

the effect of shallow or restricted waters is to

be examined.

For these reasons researchers (17), (25) have

accumulated published experimental data and have

fitted parametric equations expressing the

hydrodynamic coefficients as functions of ships

principal dimensions (L, B, T, C3). Although

this, in principle, is the most cost effective

method to obtain the coefficients, it is open to

the following criticisms:

the experimental data usually used originate

from various establishments with different

practices on the use of non linear terms and,

thus, show considerable scatter even for similar ships,

important information about

a ships form

is

lost when it is defined only by its principal

dimensions. Reanalysing the data to account for additional parameters is not simple, as

the necessary geometric information is not

always published, and

the formulae are of limited use for non conventional ship forms.

Clarke et al (25) also provide formulae to correct the deep water coeffiCients for the effect of

shallow water. However, as demonstrated in the discussion to this paper, these formulae are

inapplicable to very shallow water cases (ratios

of water depth

H to ships draught T

less than

1.5).

The third approach is the use of direct calculation. It has long been established (4) that potential flow ought to provide accurate predictions of acceleration coefióients, since the fluid flow around an accelerating body is

dominated by inertia effects. This has been demonstrated in references (19) and (26) by

satisfactory comparisons between three-dimensional potential flow analysis and experimental measurements for 2 ships in deep, shallow and

restricted waters. Figures 2 and 3 demonstrate

this agreement between computed and measured (20)

acceleration coefficients for the tanker Tokyo

Maru and for a Mariner type ship in deep and in

shallow waters.

The calculation of velocity coefficients however poses a flore difficult problem as in this case the

fluid actions are dominated by lifting and

separation effects. Furthermore, the separation

in the aft region of the ship increases as the

water depth reduces. Fujirio (20) reports efforts

to calculate velocity coefficients using low

aspect ratio wing theory and also the method of

images to model shallow water and canal walls.

The results of this work show qualitative agreement with experimental measurements for three velocity coefficients but fail to predict the shallow water effect ori the coefficient N

y

Poor correlation is also shown between theory and

experiments for the canal wall effects. It is

expected however that more accurate predictions can be made by a three-dimensional numerical model of rotational and separated flow. Work is now irr

-Y, 3 X 10 r pL 45,0 30 Q 15.0 10 25 3 20 0 5.0 1.10 0.5 0.30 10

-

cl,---Esperiments (12 knots full scale) O-- Experiments 7 knots full scale)

S _Computations

HIT

HIT

Figure 2 Computed and measured acceleration coefficients for the tanker Tokyo-Maru

in shallow and deep waters

HT

Figure 3 Computed and measured acceleration coefficients for a Mariner type ship in

shallow and deep waters

2 5VVDe3p

progress at Lloyd's Register towards this goal.

In the mean time use can be made of the computed

acceleration coefficients. This has the benefit

of reducing considerably the number of experimental

tests and avoiding the use of the Planar Motion Mechanism. Alternatively, linear and non linear velocity coefficients for deep water can be

obtained, for the initial desian of conventional

ship forms, from the parametric plots and

expressions by

moue et

al (17). This latter approach is used in the next section.

4. SIMULATIONS OF MANOEUVRES IN DEEP WATER

A variety of manoeuvres are used to assess a

ships handling behaviour, as discussed in (2),

(15) and (24). Two manoeuvres are simulated here,

for the 278000 dwt tanker Esso Osaka for which

extensive full scale rnanoeuvring tests were carried out in deeP and shallow waters (3). Namely, the turning circle where the rudder is

fixed at a given angle and the zig-zag manoeuvre

where the rudder is turned to say 20 degrees,

until the ship's heading reaches a certain value,

say 20 degrees (20/20 test), then the rudder is

turned to -20 degrees until

the ships

heading reaches -20 degrees and so ort. The published full

scale measurements incorporate corrections to

allow for the presence of current, which is

assumed to come from a constant direction. However records (3) of current measurements during

the Esso Osaka trials show a considerable variation in the speed and direction of current in

both horizontal and vertical planes. The

approximation of unidirectional current appears to have introduced some errors in the published corrected measurements. For this reason further

comparisons are 2lanned in the near future using

model experimental data, free from these uncertainties.

A set of simulations employing parametric linear

velocity coefficients From each of references (17)

and (25) did not reproduce the manoeuvres of Esso Osaka with any realism. By trial and error it was found that the value

f

r had to be doubled

before obtaining a reasonable turning circle.

However, the parametric non linear velocity coefficients from reference (17) cured this

problem. To test these expressions the predicted

Y force and N moment have been compared with published measurements from Rotating Arm experiments. A typical comparison is shown on

figure 4 for a B.S.R.A. form (27). It should be

noted that the auadrants of practical interest are

those where the drift angle and rate of turn are

of the same sign. It therefore apoears that,

u

'A

t'li

--

Experiments

- 0'

Experiments Computations 112 knots (7 knots fu)) 1. ful) scam' sca I el 1,5 2.0 2.5 TV Deep 1,5

20

10 1.5 2.0 HT 2 5 Y 20 15 1,80 I .50 120 V, pL' 0.90 0,60 0 30

2

Figure 4

Measured and parametrically derived

dimensionless sway force and yaw moment against

drift angle and dimensionless yaw rate for a

B.S.R.A. form

Figure 5

Outline of fluid finite elements

bordering the tanker Esso Osaka

following such random comparisons, the parametric

coefficients

are

reasonably

successful,

and can

thus be used for conventional hull forms.

A

three-dimensional

finite

element

model

of

potential flow around the Esso Osaka provided the

acceleration

coefficients

(for

deep and

shallow

waters).

Fioure

5 shows

the

outline

of

fluid

finite elements bordering the tanker.

In

the

absence

of

any

propulsion

data,

the

resistance and thrust relation was approximated by

the

_{term X(U0_U)}

in

eq.

(8)

and a few

trial

and

error

runs

provided

the

value

of

the

coefficient

X

which produced the expected final

speed

drop.

From

subsequent

comparisons

it

appears remarkable that this simple model predicts

the forward speed drop so well

in every stage of

the manoeuvre.

Figs.

6 and 7

show comparison

for

a 35 degree

rudder to port turn, with an

initial speed of 7.7

knots.

All

the

computed and measured

motion

parameters

in Fig.

6,

with the only exception of

sway velocity,

are

in very good

agreement.

The computed

curve

of

sway velocity

(at

the

ships

centre of gravity)

shows

the expected behaviour,

whereby a steady state value is reached after the

initial

disturbance.

On

the

other

hand

the

measured sway

velocity

(and

thus

drift

angle)

shows

an oscillation, which interestingly appears

to have a period equal

to the time it takes the

ship the complete

a

full

turn.

The almost zero

value

it reaches at 1300 secs

is contrary to the

way ships turn, and thus it

is suggested that the

experimental

_{plot for sway velocity has}

not

been

properly corrected for

the effect of current

as

claimed in reference (3).

In Fig.

_{6 are also plotted results for the rate of}

turn

in

the

first

700 secs

of

the

manoeuvre,

obtained

from

simulations

that

employed

parametrically

derived

acceleration

coefficients

from

reference

(25).

Althouqh

the

numerical

values

of

these

coefficients

differed

significantly

from

the

computed

potential

flow

ones, their effect on the predicted motion is not

large.

The simulated path of the ships centre of gravity

for the 35 degree turn to Port IS depicted on Fig.

7 as a

dot every 20 seconds, while the recorded

path of

the centre

of

gravity

at

the

trial

is

shown by a continuous line.

_{Also shown on Fig. 7}

is the time in seconds to reach 90,

180,

270, and

360 degrees of turn for the trial and simulation.

The agreement appears to be very reasonable up to

270 degrees of turn.

After that the experimental

Experiment Parametric

r L/u

O

-

-0,33

x

0,20

-.---

0,20

-- 0,33

7

-8

-6

-4

-2

0 2 4 6 8 (degrees)

v(ktsl

5

T.

¿:V

...

0 200 400 600 800 10001200140016001800 t sec) 200 400 600 800 10001200140016001800 O 0 -100 -200

-300

-400

- 500 103r0 sec

Figure 6

Esso Osaka:

Motion parameters during

turning circle in deep water

(rudder

350

to port, U0

7.7 knots)

Figure 7

Esso Osaka:

Path during turning

circle manoeuvre in deep water

(rudder =

350

to port, U0 = 7.7 knots)

500 400 300 r sec 20O _.

0,3

100

0.2

0, 1 O O 200 400 600 800 10001200140016001800 ti sec)

Figure 8

Esso Osaka:

Motion parameters during

turning circle in deep water

(rudder = 350 to starboard, U0 = 10.0 knots)

y Im)

1200 1000 800 600 400 200 O

Figure 9

Esso Osaka:

Path during turnina

Circle manoeuvre in deep water

(rudder = 350 to starboard, U

= 1fl.O knots)

O 200 400 600

x)m)

800 1000 1200 Simulated path

Puolished experimental turning circle Path obtained by integration of experimental velocities and heading

e»..

.1

1060 sec

....

1480 14

/"O8O sec'

II Ii

1510 sec 660 sec 340 sec

4 sec

u

330 sec t)) E xperiment J S imulation

titre (sec)

90 262 258

180 512 515

270 820 829

360 1150 1155

path

drifts

increasingly

to

the

right

of

the

figure

in

a

spiral

manner

inconsistent

with

a

steady state turn,

probably due

to

an

inadequate

U )kts)

10-.

Simulation

correction method for the effect of current.

9-

_{- Full scale measurement}

8 7 6 5 U k s) 4 3 8 Simulation

7 -

_{- Full scale measurement}

- x

Simulation (all coefficents

o 200 400 600 800 1000120014001&OO1BOO t) sec) parametrically) 0 200 400 600 800 10001200140016001800

3-O y ( kts) 200 400 600 800 10001200140016001800

tisec)

A

_{y (ml}

-200

-400

-600

-800

-1000 -1200

200 400 xI ml 600 800 1000 1200

Figures 3 and 9 compare the simulated and measured

turning circle at 10 knots with the rudder at 35

degrees to starboard. It is seen from Figure 8

that the agreement for the motion parameters is

excellent, with the usual exception of the sway

velocity where the measured curve shows again an

oscillatory behaviour with a period corresponding roughly to a complete turn. Figure 9 Shows the

simulated path at 20 second intervals and also two different curves for the measured circle. 0f

these, the dashed curve is obtained directly from

the report of the triai (3) and is supposed to

have been corrected for current effects. No

correlation could be obtained between this and the simulated curve however. Also, the published curve is dissimilar to the expected turning circle

path (e.g. compare initial stages of measured turns in figs. 7 and 9) and it was therefore

checked for consistency with the published motion

parameters by an appropriate integration and

transformation of the U,v and time histories from Fig 8. The result is shown in Figure 9 as a

continuous curve, which demonstrates a close agreement with the theoretical simulation.

It is of interest to note that a very similar turning diameter was obtained from the two manoeuvres in Figs. 7 and 9, which confirms expectations for turning at low speeds.

U Ikts) Simulation

8 Full scale measurement

7 6 0 200 400 600 800 10001200140016001800 tISec) 50 20'-10 O -lo -20 -30 r °/sec 0.2-0, 1 O -0,1 -0,2 U ) ktsl 8- 7- 6- 5-4 O 40 30 20 10 O -10 -20 -30 r c'sec y lktsl 1,0-0,5 200 500 -1,0-200 00 500 Simulation

- Full scale measurement

8001000 120014001600 1800 t( sed

8001000 . ". 1800

1500

100 400 800 1000 1400 17001900

Figure 11 Esso Osaka: 200/200 zig zag

test in deep water (lie = 7.8 knots)

Figures lO and li show comparisons for a 10/10 and

a 20720 zip zag test respectively. The agreement

between full _{scale measurement and simulation in}

both tests is satisfactory and now a much better correlation is demonstrated between the sway

velocity time histories. The reason for this better agreement, compared to that in the turning circles, may be attributed to the lesser effect of current on a zig zag manoeuvre where the averaoe

ships heading remains constant.

A further set of simulations was carried out using

the complete set of ideal flow equations (7) with

computed acceleration coefficients. Good agreement between the ideal and the real fluid

models was recorded for the initial staqe of the

manoeuvre, i.e. when accelerations dominate the motion. Although this may be of no direct interest in ship handling simulations, it could be

of value in ship design, since the chanqe in

heading occuring in the time to travel one ship

lenoth provtdes a measure of the ship's turning ability.

5. CONCLUSIONS

The mathematical models used for simulations

of ship handling in deep, shallow and restricted

400 600 L1300 1600

200 800 1000 1900

Figure 10 Esso Osaka: lO°/10° zig zag test in deep water (U0 = 7.5 knots)

waters nave been aiscussed. Also, a simple model has provided simulations of manoeuvres of a tanker

in deep water and comparisons of these with full

scale measurements.

The manoeuvring work carried out at Lloyds

Register of Shipping is aiming to arrive at a

method for accurate predictions of ship handling

at the design stage. Such a method should not

rely on data from model experiments, and with these targets in mind the following conclusions are reached:

The acceleration hydrodynamic coefficients can be

safely calculated from the ships lines for all

water depth cases.

The non linear parametric expressions used for

the deep water velocity hydrodynamic coefficients

appear to be acceptable for the preliminary design of conventional hull forms.

The theoretical prediction of velocity coefficients is to be encouraged as the longer term solution to provide the remaining necessary data for modelling

manoeuvring behaviour of any marine structure in

deep or shallow waters.

The mathematical model adopted here relied on

empirical constants to account for rudder effectiveness and for the thrust-resistance relation. This simplification is unnecessary and

as the propulsion characteristics are known from

the ships initial design stage these should be

incorporated in the simulation model.

ACKNOWLEDGEMENT

The authors wish to express their appreciation to

Lloyd's Register of Shipping for the permission to prepare and present this paper. Gratitude is also expressed to Dr I.W. Dand of N.M.I. Ltd, U.K. for

fruitful discussions and comments on simulation models and velocity hydrodynamic coefficients.

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