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
arebeing
madetowards
imposing
mandatory
requirements
that
will
quantify
andcontrol
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 meansfor
rating
controllability under restricted water conditions
wherecollisions,
rarnings
andgroundings
arelikely 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
aworking
groupwhich
recently
produceddraft
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
themto
keepcourse,
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
methodsfor
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.
Demandsfor
realistic
mathematical models of ship handling behaviour are
also
madefrom
the
increasing
numbersof
Ship
Handling
Simulators
usedfor
the
training
of
mariners
andpilots,
for
ergonomic
studies
inbridge design, for investigations of circumstances
leading to collisions, etc.
JvcAì-
M c
4
U-o 4
-
-j a () ïc1
Lf
etLab.
y.
Scheepsbouwkunde
Technische Hogeschooi
Delfi
TOWARDS A DESIGN TOOL FOR SHIP MANOEUVREABILITY
N.E. Mikelis and K.V. Taylor
To describe
aship's motion,
useis
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
aconsiderable heel when turning at
hiah
soeed.
For such cases the roll
equation must be
coupled
with
the
horizontal
plane emuations,
asdemonstrated by Hirano and Takashina (5).
sceeds and to stop,
all
in
a satisfactory manner.
Since most manoeuvring mualities are inherent
in
2.
EOUATIONS OF MOTIONthe design of the hull
and machinery they should
Observations
on modelexDeriments
and onfull
scale operations show that when a ship moves from
deep
to
shallow
water
or
into
acanal,
its
handling
behaviour chanoes
noticeably,
andsince
such changes are often unexpected by the mariner,
they increase the risk of collision or grounding.
However,although
the
needfor
accurate
predictions of rnanoeuvreability in
all
topoioaies
cannot
beoveremphasised,
mostcurrent
workrelates
to
the
deepwater
condition,
mainly
because of the difficulty to obtain the necessary
coefficients
for
the
mathematical
modelsof
shallow or restricted waters.
This
paperbriefly
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
comparedto
published
(3)
full
scale
measurementsfor
the
sameship.
Theagreement 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
ofgravity G is at a distance xG from the origin
C.
ifl
most experimental studies the origin islocated 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 thepropeller 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 .3Y.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 anglef (
-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. Inpractice 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
) ( XHULL = 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 theorigin, 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-(mxU 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-Nrrl
Cr
G r y y rr - (N r+Nv)vrN
rrv vvr dThese 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
islost 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 than1.5).
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 fullscale 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 1,520
10 1.5 2.0 HT 2 5 Y 20 15 1,80 I .50 120 V, pL' 0.90 0,60 0 302
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 canthus be used for conventional hull forms.
A
three-dimensional
finite
element
modelof
potential flow around the Esso Osaka provided the
acceleration
coefficients
(for
deep andshallow
waters).
Fioure
5 showsthe
outline
of
fluid
finite elements bordering the tanker.
In
the
absenceof
anypropulsion
data,
the
resistance and thrust relation was approximated by
the
term X(U0_U)
in
eq.
(8)
and a fewtrial
anderror
runs
provided
the
value
of
the
coefficient
Xwhich produced the expected final
speed
drop.
Fromsubsequent
comparisons
it
appears remarkable that this simple model predicts
the forward speed drop so well
in every stage of
the manoeuvre.
Figs.
6 and 7show comparison
for
a 35 degreerudder to port turn, with an
initial speed of 7.7
knots.
All
the
computed and measuredmotion
parameters
in Fig.
6,with the only exception of
sway velocity,
arein very good
agreement.
The computedcurve
of
sway velocity
(at
the
ships
centre of gravity)
showsthe expected behaviour,
whereby a steady state value is reached after the
initial
disturbance.
Onthe
other
handthe
measured sway
velocity
(andthus
drift
angle)
shows
an oscillation, which interestingly appears
to have a period equal
to the time it takes the
ship the complete
afull
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
beenproperly corrected for
the effect of current
asclaimed in reference (3).
In Fig.
6 are also plotted results for the rate of
turn
in
the
first
700 secsof
the
manoeuvre,obtained
from
simulations
that
employedparametrically
derived
acceleration
coefficients
from
reference
(25).
Althouqh
the
numerical
values
of
these
coefficients
differed
significantly
from
the
computedpotential
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 adot 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 Parametricr L/u
O
-
-0,33
x0,20
-.---
0,20
-- 0,33
7-8
-6
-4
-2
0 2 4 6 8 (degrees)v(ktsl
5T.
¿:V
...
0 200 400 600 800 10001200140016001800 t sec) 200 400 600 800 10001200140016001800 O 0 -100 -200-300
-400
- 500 103r0 secFigure 6
Esso Osaka:Motion parameters during
turning circle in deep water
(rudder
350to port, U0
7.7 knots)
Figure 7
Esso Osaka:Path during turning
circle manoeuvre in deep water
(rudder =
350to port, U0 = 7.7 knots)
500 400 300 r sec 20O _.
0,3
1000.2
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 pathPuolished 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 sec4 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
aspiral
mannerinconsistent
with
asteady state turn,
probably due
to
aninadequate
U )kts)10-.
Simulationcorrection method for the effect of current.
9-
- Full scale measurement
8 7 6 5 U k s) 4 3 8 Simulation7 -
- Full scale measurement
- xSimulation (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 10001200140016001800tisec)
A
y (ml
-200
-400
-600
-800
-1000 -1200
200 400 xI ml 600 800 1000 1200Figures 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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