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Omitting the effects that are less important in
manoeuvring,themodelcanbepresentedasasetof
infinitesimal equations whose results show the
change in the speed of the ship with respect to the
bottomofthebasin (ʹv
g
ʹ)forthreelevels offreedom.
The basis for the math model of manoeuvring
movements of a vessel applied (infinitesimal
equations of movement and the structure of
functional dependences of each external interaction)
was presented in detail among others in [Artyszuk,
2005] and are in line with the current state
of
knowledgeinthisfield.
z
c
y
g
y
c
x
g
x
z
z
yz
c
xz
g
x
g
y
xz
c
ymz
g
ym
g
x
Mvvvvmm
dt
d
mJ
Fvmmvmm
dt
dv
mm
Fvmcmvmcm
dt
dv
mm
)(
112266
22111122
22112211
(1)
z
g
EW
g
NS
d
d
v
d
dy
v
d
dx
,,
00
(2)
g
y
g
x
g
EW
g
NS
v
v
v
v
cossin
sincos
(3)
where:
v
x
g
,vy
g
,z– Longitudinal, cross and tangential
velocity
x
0,y0,– Positioncoordinatesandvessel’scourse
M– Vessel’sdisplacement(weight)
M
11,m22,m66– Added weights (resulting from
movementinidealliquid)
c
m– Empirical coefficient taking into account
viscosityeffects
F
x,Fy,Mz – External interferences(total longitudinal
and cross forces, and the tangential moment) which
can be spread into the following for the modelled
two‐propeller ship (with two conventional rudders)
withadoublesternthruster:
2
1
2
2
1
2
1
2
1
2
2
1
2
1
2
2
1
2
1
i
zLTizWVzA
i
zRi
i
zPizHz
i
yLTiyWVyA
i
yRi
i
yPiyHy
xWVxA
i
xRi
i
xPixHx
MMMMMMM
FFFFFFF
FFFFFF
(4)
Theindexesstandfor:
H– Hull,
P – Propeller,
R – Sternrudder,
A – Wind,
WV2– Irregular wave (2nd class forces, so‐called
driftforces),
LT – Thruster.
All the above components of the generalized
external forces are basically a function of the ship’s
speedwith
respecttothewater(ʹv
w
ʹ):
z
w
y
w
xzz
z
w
y
w
xyy
z
w
y
w
xxx
vvMM
vvFF
vvFF
,,
,,
,,
(5)
c
y
g
y
w
y
c
x
g
x
w
x
vvvvvv ,
(6)
c
c
c
c
c
y
c
x
v
v
v
v
sin
cos
cossin
sincos
(7)
where:
c
v
andcarethespeedandgeographicaldirection
oftheseacurrent
2.3 Verificationofdatausedforsimulationsinthe
SMARTprogram
Tooptimisethemodel,originalsoftwarebasedonthe
MS Excel 2000 spreadsheet and the mode of
accelerated time of the above‐mentioned SMART
program were used, with the
visualization of the
convergenceofpredictionstotheactualdataplaying
animportantroleinit.Thecorrectfunctioningofthe
predictioncodeofthemodelappliedwasconfirmed
by several years of research during classes in ship
manoeuvringforstudentsattheMaritimeUniversity
inSzczecinandresearchstudiesof
anacademicteam
of sea traffic engineers, among others [Gucma L,
2005].
The hydrodynamic coefficients of each force and
moment were also initially determined according to
literature data published after hull (surface and
underwater parts) model research. In case of gross
disproportion, the appropriate extrapolation of
researchresultstotechnical
andoperationconditions
ofthemodelvesselwasused.
The results of the verification of the ship model
studied were conducted based on the manoeuvring
characteristics commonly adopted for verification:
speed, braking and acceleration, circulation and
standard test confirmed that the model of the
optimisationprogramcreatedwascorrect.Trialswere
conductedunderzeroconditionsandondeepwaters,
andadditionallycirculationtestswereconducted on
shallowwaters.
2.4 Modelinterface
TheinterfaceofthemodelispresentedinFigure3.It
is the so‐calledʺsingle taskʺ model (aimed for
designing waterways) with a perspective 2D
visualization(bird’s eye view)
of the electronic map
type. It contains information on the location of the
post,bathymetryofthebasin,informationonthestate
of the ship, hydrometeorological conditions and
control elements for steering. The model is
implementedinthe Delphi™environment using the
Object Pascal language and in the Visual C™
environment
usingtheC++language.