Motion Prediction
By:
Masayoshi Hirano*, Junshi Takashina**, Masahiro Fukushirna* and Shuko Moriya**
This paper presents q computer program system for the ship maneuvering motion prediction which makes it Pos-sible to simulate with accüracy varioùs kinds of ship maneuvering morion as governed or affected by rudder, main engine and thruster operations under various environmental conditions subject ro wind wave and current actions not only in qn open water area but also in a restricted water area. This computer program system is so designed as to en-able designers to obtain versatile simulation results only by inputting minimum necessary data such asprincrpalpartic ulars of ship hull, rudder and propeller, all of which are easily available in ordinary cases. Its validity has beeñ ex-amined and verified through comparative analyses of computed results with reference to results of full-scale trials or model experiments.
In this paper, system outline comes first, and its predictión method follo ws. The results of the comparative anal-yses are presented to show the effectiveness of the prediction method together with its applicability to a wide range of the ship maneuvering motion. Lastly, some examplès of actual application of this computer program system are introduced.
1. Introduction
According to the demand fòr economical and efficient
maritime transportation, various kinds of ships have been produced, such as container carriers,
roll-on/roll-off ships, LNG carriers, pure car carriers and lárge-sized
oil tankers Through the diversification in ship types or
the growth in ship size, as mentioned above, the
maneu-verability of ships has been receiving a great deal of attention because of the navigation safety problem in
ports. and on waterways.
FOr a ship designer, careful examination on the ship maneuverability is needed at the preliminary design
stage. Moreover, at the time of ship completion, rna
neuvering informations such as the maneuvering booklet
and the wheelhouse poster should be provided for each ship, as is recommended by 1MO (formerly IMCO)' and required by Panama Canal Regulations2.
Exten-sive efforts to improve the contents of those maneuver-ing informations are òurrently bemaneuver-ing made by 1MO. In addition to the ship design area, in the area of port
design, it has become necessary to perform maneuvering
safety studies of ships which are expected to enter the port to be planned.
For these kinds of needs, empirical methods such as design diagrams of the ship maneuverability based on accumulate4 data of existing ships are insufficient be-* Ship Peiformance Research Sect., Akishirna Laboratory,
Ship and Ocean Projoet Hq..
-Dynamics and Control Research Sect., Akishima Laboratory, Ship and Ocean Project Hq.
cause of their limited applicability; In order to flexibly
meet the needs mentioned above, the simulation
calcula-tion technique may be considered to be the most useful
and powerful tool.
In this context, in Mitsui Engineering and Shipbuild-ing Co Ltd, extensive studies have been made on the ship maneuvering simulation. Major emphasis was
placed on development of a practical calculation method
for a wide range of the ship maneuvering motion,
namely, for various kinds of the ship maneuvering motion
under various environmental conditions. A mathemat-ical model for the fUndamental maneuvering motion in calm and deep water was developed first"4, in which basic input data necessary for simulation calcúlations are the principal particulars of ship hull, propeller and rudder which are usually known at the preliminary
design stage. In this mathematical model, newly
de-veloped estimate formulae5 ° are fully utilized together
with data base for estimation of hydrodynamic fOrce coefficients, with which motion calculations of the ship maneuvering can be made with high accuracy. Then
applicability of this mathematical model was extended
to the wide range of the ship maneuvering motion, name
ly, such maneuvering motions as under external forces of wind, wave and current in shallow water. Thus a highly sophisticated mathematical model of the ship maneuvering motion for practical use was developed". Based on the products obtained and accumulathd through the above mentioned studies, an attempt was
made to develop a computer program system- for
the computer program system, çareful attention was paid to the following points.
To be a system with a wide range of applicability,
which can flexibly meet various kinds of needs for
pre-diction of the ship maneuvering motion.
To be a system which can easily be utilized even
by such a designer as has no specialized knowledge on
the ship maneuverability.
To be a system with high reliability and accuracy.
Consequently, a highly advanced computer program system for prediction of the ship maneuvering motion
was successfully developed.
This paper presents the outline of the computer
pro-gram system and its application. System description is
madé first, and the mathematical model of the ship maneuvering motion is described next Then validity
of the prediction method is shown by comparing com-puted results with results of full-scale trials or model
experiments. Lastly, some results of applibation studies
on the system are presénted together with typical
com-puter output examples.
2. System description 2.1 Features of system
The computer program system, in which simulation calculations of the ship maneuvering motion are made by solving motion equations numerically at every
mo-ment, has the following features and functions.
(I) Equations of the ship maneuvering motion are the coupled motiOn equations of surge, sway, yaw, roll and propeller revolìjtion. Namely, in addition to the horizontal motions (surge, sway and yaw), the motions
of roll and propeller revolution in the ship maneuvering can also be predicted.
For nine typical ship maneuvers such as turning,
Z-maneuver and spiral maneuver, standard rudder operating patterns are provided in the computer pro-gram system together with subroutines of prediction
result analysis. Motion calculations and its analysis for each rudder operating pattern can easily be made
by giving a simple command.
Maneuvering motions with main engine
opera-tion, for such main engines as slow- and medium-speed
diesels, steam turbines and electric propulsion units,
can be predicted. By combining this main engine opera-tion with the above menopera-tioned rudder operating pattern, variOus maneuvering simulations can be made.
Hydrodynamic force coefficients necessaty for simulation calculations can be estimated with estimate formulae or data base stored in the system by knowing
values of only fundamental factors sUch, as the principal
particulars of ship hull, propeller and rudder. Conse-quently, by inputting minimum necessary data such .as those mentioned above, versatile simulation results for a wide range of the ship maneuvering motion can be
obtained.
Maneuvering motions with LTU (lateral-thrust unit) operation can be predicted, in which the hydro-dynamic interference between LTU and ship hull is
2
taken into consideration.
Maneuvering motions iñ shallow water area can
be predicted, in which the shallow water effects on
hydro-dynamic forces can be estimated by inputting only the water depth value. In addition, maneuvering motions in narrow water channel can be predicted by
ôonsider-ing the bank effects on hydrodynamic forces.
Maneuvering motions under disturbed circum-stances such as in wind, waves and current can be pre-dicted, in which external forces can be estimated with data base.
Performance of the autopilot can be evaluated by
computing the course keeping motion steered by the autopilot nder irregular external forces, to which arbitrary shape of the spectrum can be given in the system.
Maneuvering motions of ships with
multi-propel-1er and multi-rudder system can be predicted by con-sidering arrangement of the propeller-rudder system. Many kinds of drawing functions by the use of a plotter are provided in the system, and by giving a simple command, motion trajectories and time histories
of motion variables can easily be drawn.
(1 1) Through dialog with computer terminal with
the graphic display function, actual ship manéuvers in ports and on waterways can be simulated by giving orders of operation of rudder, main engine, LTU, tug
etc. interactively. This computer program system can
be utilized as a handy-type ship maneuvering simulator. 2.2 System configuration
The computer program system consists of three major
stages, namely, the initialization stage, the calculation stage and the output stage as shown in Fig 1.
At the initialization stage, data input is made first. Based on the input data, coefficients necessary for the mañeüvering simulation, including hydrodynamic force coefficients such as hull resistance coefficients, self-propulsion factors, propeller open-water characteristics,
hull force derivatives and rudder force coefficients, are estimated by utilizing estimate formulae or data base stored in the computer program system. Initial value
setting for the simulation execution is made at this stage.
At the calculation stage, first, commands for opera-tion of rudder, main engine etc. are ordered according to the data initiálized at the first stage. Then hydro-dynamic forces and external forces acting on a ship at
every mOment are calculated based on the mathematical model describe1 in the next chapter. Setting these forces in the equations of the ship maneuvering motion, motion
variables such as ship velocity, propeller rpm etc. at
every moment are calculated by solving the motion
equa-tions numerically by the use of a numerical integration technique such as the Runge-Kutta method or the Euler
method. The simulation calculation Is completed by repeating the above mentioned procedure as many
times as necessary.
At the output stage, simulation results are analyzed according to simulation purposes. Both simulation
a C Data Input Principal Particulars Simulation Parameters Estimation
I-lull Force Derivatives Propéller Open-water
Charac-teristics etc.
Ordèr Commañds Rudder Angle Propeller RPM
Thruster (LTU) Pitch
Shallow Water Effects
Hull Force Correction Rudder Force Correction
Ship Forces Hull Forces Rudder Forces Propeller Forces Engine Torque o LTU Forces No
o.
4, LTU Diüibuíc External Forces Wind Forces - Wave Drifting Forces«L, 4 Current Effects Numerical Integration Accelerations Velocities Positions Interactive Output Used Pata Time Histories Trajectories Analyzed Result Stop Simi1atio'ñ End Yes
Fig. i Flow Diagram of System
I-i:
Data CardGraphic D isp lay Device Hard Copy Printer PIòttr
of printer output. Drawing of simulation results (motion trajectories and time histOries of motion variables) With
a plotter is made if ordered.
After completion of the output stage, the next simùla-tion run is made, according to the order, by returning to. the initialization or the calculation stage and by repeating
the same procedure as the above. 3. Mthematical model
3.1 Equations of motion
The mathematical model of the ship maneuvering motion in the computer program system is described based on the cóüpled motion equations of surge, sway, yaw, roll and propeller revolution, which enable the horizontal motions (surge, sway and yaw) to be calcu-lated, with consideration of coupling effects due to changes in roll and propeller revolütion. By reference to the ship-fixed coordinate system G-xyz, shown in Fig 2, the Newton s equations of the ship maneuvering
motion can be written in the following form.
X0
Fig. 2 Coordinate System
m(ùvr)=XH+XP+XR±XT+XW
+Xwv+XB+XF m(i'+ur)=Yfl+YP+YR+YT+YW ±Ywv+YB+YF=Nff+NP+NR+NT+Nw ...(1)
±NWV+NB±NFJk
=Kfl±Kp+KR±KT+Kw+Kwv+Ka+KF
2ni7,ñ =QE+QPwhere the terms with subscripts H, P, R, T, W, WV, B and F represent the hull forces, the propeller forces, the rudder forces, the LTU (lateral-thrust unit) forces, the wind forces, the wave drifting forces, the bank effect forces and other forcing functions such as forces due to tug, mooriñg line etc respectively, and QE represents
the main engine torque.
The current forces are not included in Eq. (1) because
Eq. (1) is written for the motion relative to the water,
and the current effect's 'on the ship maneuvering motion
can be calculated through the process in which the ship speed relative to the water is converted to that relative
to' the space.
z
No
3.2 Hull forces
The hydrodynamic forces actingon ship hull due to ship motion can generally be expressed as polynomials
of motion variables together with hydrodynamic
deriva-tives. The standard formulatiins of the hull forces used
in the system are as follows.
X= mù+(m+ Xvr)1'T ±
X(ZA)Y= mi'mur
Y7'r'+ Yvivi'V'"I + Yviri'v'Ir'I +
Yriri'r'r']
NH=
+AÇ'ip'+Nvvr'v'2r'±N,rr'v'r'2
+ rIrilInI +
k' I'v'IçoI+ Nr.pi 'r'ço]KH= JN(p)
W.GZ(ço)YH.zHThe data necessary for calculation of the hull forces such as hull resistance, added inertia terms and hydro-dynamic derivatives can be estimated by making use of subroutines in the computer program system. The hull resistance is calculated as a sum of the frictionaÏ resist-ance of the Schoenherr's mean line and the residual resistance based on a number of accumulated tank test results.. The added inertia terms can be estimated with estimate charts such as those proposed by Motora". The hydrodynamic derivatives of the lateral force YH and the yaw moment Nfl can be estimated by knowing
the principal dimensions of ship hull according to moue
and one of the authors"". The estimate formulae for the linear derivatives with inclûsion of effects of trim r
are given iñ the following forni.
YV'=[alk±f(CBB/L)](l +b,r') = a2k(l + b2r')
N'=aik(l+b3r')
Nr'=(a4k±a,k2)(l+b4r')
wherek=2d/L,
r'=r/d
(4)
and a1, a, ..., b,, b,, ... are the constants. The estimate
formulae for the nonlinear derivatives are given as functions of Cß and k but in which no trim effects are
considered.
As regards thç shallow water effects on the added
inertia terms and the hydrodynamic derivatives, estima-tion is made by applying correcestima-tion factors, as funcestima-tions
of the ratio of ship draft to water depth, to each co-efficient in deep water'".
3.3 Propeller forces
The propeller thrust X, and the propeller torque Q
are calculated with the following formulae.
Xp (1 Ip) ._1_p[ {u(1 w)}' ± (O. 72TnD)2]D2 CT(Op)
(5)
( 3)
4
Q= 2irJh_p[{u(l w)}2
+ (O.71TnDP)2J_DP3CQ(OP) whereO=tan'{u(l &)/(O.7imD)}
(6)
Estimations of the propeller openwater chaiacteristics C and CQ are made based on results of the systematic open-water tests by Yazaki' ' and the open-water tests with Wageningen BScrew series over the whole region of propeller operatiOn'". The thrust deduction coeffi-cient i and the effective propeller wake fraction w are
treated as functions of ship motion and propeller
operat-ing condition. The lateral force Y and the yaw moment N due to propeller action, which becomes important in the stopping motion with propeller reversing, are wntten in the following form according to Fujino et
al.'".
Y,, = pn'D4 Yp*
N =pn2D5N*
The coefficients Y* are N* are given as functions of
u/nP, which have zero välue except for the seòond
quad-rant (namely u>O, n<O)
3.4 Rudder forces
The rudder forces including the hydrodynamic forces induced on ship hull by rudder deflection are written in
the following form.
XR=FNsin
R= (1±aH)FVcos
NR = (xR +aHxHR)FNcos &= (1 +aH)xRFVcos KR= (ZR ± qHZHR)FNCOs& (l+aH)ZRFNcos
(8)
In Eq (8), the lateral force induced on ship hull is de-scribed in the form of aflF cos . The rudder normal
force FN can be written in the following-form with
concepts of the effective rudder inflow speed VR and the effective rudder inflow angle aR.
FN=±p[6.13A/(Á±2.25)]ARVR2 sincR
(9)
The following mathematical model is adopted for VR and aR in the computer program system.10
R+8OyßR
( )The term g(s) given as a function of the propeller slip ratio, s, represents the effect of propeller slip-stream on
V. The term Y/iR represents the effective drift angle at rudder position in consideration of the flow-rectifying effects due to both ship hull and propeller.
As regards the rudder forces in shallow water, the mathematical model given in Eqs. (8) through (10) can basically be used, but some corrections of the shallow water effects are needed for several coefficients such as the hull/rudder interaction coefficient a,1, the effective
rudder wake fraction w and the flow-rectifying
coeffi-cient y.
3.5 LTU forces
The hydrodynamic forces acting on ship hull by LTU operatión are given with the nominal thrust in bollard pull condition T0 and the coefficients of Xi', Y' and N' which represent the interference effects due to hull! thruster interaction
XT=Xr'(V', ßT).ToI
'T= YT'(VT', ß).T0N=N'(V', ßr).xrTo
K =
Z7Where X2', Y' and N' are given as functions of the ratio of ship speed to jet veloòity of LTU,, Vg.', and the
geometric incident angle of flow to LTU, ß, both
defined as
ß =ßx'r'
VT' = [{u2+ (v+xr)2} /( To/pAD)]'2
} ...(12)
In the case of a tunnel thruster, it is well known that the interaction between jet from LTU and main flow past ship hull gives significant effects on the resulting forces acting on ship hull'4, In calculation of the LU fOrces for a tunnel thruster, therefore, experimental data of X2', Y' and N' fòr both bow and stern thrusters are fully utilized'".
3.6 Wind forces
The wind forces are calculated by the following equa-tions.
V - V 'uf?
\ A 1/ 2w V"w)PA F W
Y= Ywl(/3w).pA4sVw2N= N'(ß) .
5L vw2 K = K'(ß). -_pA(As2/L)Vw2The wind force coefficients Xv', Y, N' and K' are
functions of the angle of the relative wind direction ß. In the case of no available wind force data for thesubject ship, the wind force coefficients can be estimated
with the method proposed by Isherwood'6 or with data on a similar ship which can be selected from data base
of about 40 types of ships stored in the computer
program system'7.3.7 Wave drifting forces
The wave drifting forces of regular waves are
calcu-lated as follows.
Xwv = X'Qt/L,
.1}'w= Y'(A!L,
=N'(À/L,
The wave drifting force coefficients X', Y/ and
N' are usually given as functions of the ratio of wave length to ship length À/L and the angle of the wavedirectiöñ In the case of no available data for the
subject ship, the computer program system automatically
provides the coefficients estimated from the results of
model experiments for several types of ships'8. 3.8 Bank effect forces
The bank effect forces acting on ship hull in narrow
water channel are calculated as follows.
= XB'(').
-LPLdV2 YB=NB
NB'(').
IpL2dV2KB = KB'(')
IpLd2
V2In this. equation, ' represents the off-centerline pàrame-ter given by
'=2/(WB)
(16)where i, is the distance betWeen the centerline Of channel and the center of gravity of the ship, and W is the width of channel. The force coefficients as functions of '
depend on water depth, channel width and sectional configuration of channeP9.
3.9 Main engine torqUe
The mathematical model of the main enginè torque QE depends on engine types, and Q is calculated according to its characteristics in each engine operating
condition. The main engine torque characteristics of the slow-speed diesel, which is the most popular main engine, are described as a typical example in the following.
In the case of the normal runningcondition, propeller
shaft rpm is automatically controlled to maintain a
con-stant value against varying loads. This results in the
main engine torque QE equal to the propeller torque Q
However, when Q exceeds the torque limit of main engine due to load increase, such as caused by the turning motion at a large nodder angle, the main engine is operated at the allowable màximum torque, which results in reduction of propeller shaft rpm.
In the case of the crash stop astern, sequential three stages of main engine operation are made, namely, the fuel-cutoff operatioñ, the propeller shaft braking and reversing operation driven by brake-air, and the
propel-1er shaft reversing operation fed with fuel. In the com-puter program system, three types of the main engine torque models corresponding to each stage are
em-ploye4 as follows.
First stage: Propeller shaft free-ròtating due to the fuel-cutoff operation from the issue of an order of the crash stop astern;
QE=QF(fl)
Second stage: Propeller shaft braking and reversing driven by brake-air from the time when shaft
100
50
rpm is decreased low enough to start brake-air
in-jection; V
QE=QA(1', te)
(3) Last stage: Propeller shaft reversing fed with
fuel from the time when reversing shaft rpm is increased
high enough to start fuel injection for the astern; QE = Q0(n,
t)
In the above, the torque characteristibs are given as functions of propeller shaft rpm, n, and time elapsed from the crash stop astern order,
t.
V4. Prediction results and validity
In order to confirm validity of the prediction method based on the mathematical model described in Chapter 3, it is of great importance to investigate the correlation between computed results and results of full-scale trials or model experiments for various types of mer-chant ships and for a Wide range of thé maneuvering
characteristics Some examples of comparisons between
computed results and measurements during full-scale
trials or model experiments are shown in the following. 4.1 Standard maneuvering motion in calm water
At the time of ship completion, full-scale trials for the
maneuverability such as turning tests and Z-thaneuver tests are conducted to obtain information on the
funda-mental characteristics of ship response to rudder.
In Figs. 3 and 4 the computed results of the turning
6 CONTAINER - 20 Prediction 5 0 Full-scale Trial 10 O
Fig. 3 Turning Trajectories (Container Carrier)
CONTAINER
Prediction
o Full -scale Trial
3- -- 4 t (thin)
Fig. 4 Time Histories of HeadingAngle,ShipSpeed and Number of PrOpeller Revolution in Turning Motion (Container Carrier)
motion with 350 rudder for a 1400 TEU contaiñen cari rier are shOwn in. comparison with the results of!
full-scale trials. Fig. 3 shows the turning trajéctories for both
port and starboard túrns, and Fig. 4 shows the time
histories of heading angle, ship speed and propeller rpm
for starboard turn. In Fig. 5 the results of the computed V
heading response in the 100/100 Z-maneuver fo'r the same container carrier are compared with the résults of full-scale trials. It
can be mentioned from these
figures that the computed résults
give satisfáctoryägreement with the fu1-scale measurements.
This kind of comparisons for various types an sizes of ships ranging from a general cargo boat of 10000 DWT class to a ULCC have already been presented by the authors4 Summarized results of these comprisons are given in Fig. 6 for the tactical diameter in the 35° turning circle and in Fig. 7 for the second yaw anlitude in the 100/100 I.maneuver. In both figures thd com-puted results are taken in abscissa and the fuU-scále trial results in ordinate. Satisfactory correlation be-tween the prediction and the full-scale trials can Ie seen
in both figures.
Fig. 5 1O°/10° Z-maneiiver Response (Container Carrier)
CONTAINER
-3
Prediction
Prediction
O FIl -scale Trial
C Containei G General Cargó R Ro/Ro B Bulk T Tanker k Dr/L
Fig. 6 Comparison of Tactical Diameter betweei Predic tiöns and Fullsöale Trials
-E I. -XC
Comparisons of the computed results of the steady turning performance with the full-scale trial results for
three different types of ships, namely, the container
car-rier mentioned above, a RO/RO (roll-on/roll-off) ship and a 270 000 DWT tanker, are shown in Fig. 8 The
computed results explain very well the characteristic
behavior of each ship in its steady turning performance.
It is found from Figs. 3 thrOugh 8 that the
computa-tions, in which the estimated hydrodynamic coeffi-cients based simply on the piincipal particulars of hull, propeller and rudder are utilized, can predict the funda-mental maneuvering characteristics of full-scale ships with sùfficient accuracy. More accurate predibtions will be expected by making use of the hydrodynamic coefficients obtained from a captive model test such as
PMM test. 30 (t E-. a 20 r a lb2 (dég) 40 10 r CONTAINER 1.0 IO 20 Prediction 0.5
0.5
1..0 RB C Container G General Cargo R Ro/Ro B Bulk T Tanker 30 40 çfr2(deg)Fig. 7 Comparison of 2nd-Yaw Amplitude in 10°/iO O maneuver between Predictions and Full-scale Trials
40 30 20 10
10 20 3040 40 30 20 10
i(deg)
RO/RO
In Figs. 9 and 10 the results of computed nondi-mensional steady rate of turn r' and steady roll angle ..p for a RO/RO ship model running at three different approach speeds are shown against a rudder angle 8
together with the results of model experiments20>. The computations with consideration of the coupling effects
of roll on the horizontal motions simulate well thè changes in the steady turning performance with
ap-proach speed, which are caused by the changes in roll. 4 2 Stoppmg motion
The sÑopping characteristics due to main engine
revers-ing are so important that stopprevers-ing tests are always re qúired during sea trial trip. Typical examples of the computed stopping motion are shown here together
with the full-scale trial results.
Computations are made for stopping motions at
RO/RO MODEL
40 30 20 10
0Fig. 9 Steady Tùrning Performance (RO/RO Ship Model)
10 20 30
40 40 30 20
8(deg)
- Prediction
0 Full Hscale Trial
TANKER
0.5
Fig. 8 Steady-Turning PerfOrmance for Three Different Types of Ships
1.0 10 20 30 40 ô(deg) 1.0 0.5
0.5
1.0
10 20 30 40 4(deg) 7 fredict ion 021 0.26 0 0.30 D 0.26.00t r 1.0 05RO/RO MODEL Vo=6Skn TANKER t'(kn)
-
nL Prediction O Full-sèàle Trial o Vni0.6ka -20 -zlo
20-Fig.10 R011 Angle at Steady Turning (RO/RO Ship
Model) TANKER aIL 15 Vo = 16. 5ko 10. a) 4 y/L
Fig. il MotiOn Trajectories iñ Stopping Motiòñ (27ô 000 DWT Tanker)
10 15 20
t(iiii,)
various approach speeds of the 270 000 DWT tanker on
which a slow-speed diesel engine is mounted The re-suits are shown in the form of motion trajectories and motion time histories in Figs. 11 and 12 respectively. It
can be found from these figures that the computed rsults
give satisfactory agreement with the full-scale trial
re-sults in all cases of approach speeds. f 4.3 Maneuvering lotion with LTU
Among variouS types of LTU, .a tunnel, thruster is the
most common for merchant ships The computed re-suits of the maneuvering motion with tunnel thrusters
RO/RO
P red ic t ioñ
FuII=scale Trial
5 6
t (rnit)
Fig 13 Heading Changes iñ Turning Motion with Bow Thruster (RO/RO Ship)
Fig. 14 irajectories Of Ïurnñg Mtion with Bow Thruster (Drilling Ship Modél)
DRILLING SHIP MODEL
x/L x/L
Fig. 12 Time Histories of Ship Speed and Tiavel Distance
along Path in Stopping Motion (270 000 DWT Fig 15 TrajectoriesofTurningMotionwithStern1Thruster
Tanker) . (Drilling Ship Model)
-F. Model Prediction .L21. A 0.26 0 030 D
40
-3O-20 10
0 10 203
40 Ô (deg) 10 - - Prediction 6 o Fnll-ocale Trial x/Lare compared here with the results of full-scale trials or
model experimeflts.
Fig 13 shows a comparison between the computation and the trial run of heading change during the turning motion with a bow thruster for the RO/RO ship. Thç computed results indicating that the bow thruster is less effective at an approach speed of 4 knots than at ero knots, gIve good approximation to the full-scale
añd Stern Thrùstérs (Drilling Ship Model)
8(deg) 30 20 Prediction gIL K=4 LNG MODEL 8 (deg) 30 20
-
io o ß(deg) 30 20 10 y/yo Prediction K=5 - go: trial results'5.Similar comparisons of the turniñg motion with a bow
thruster and with a stern thruster are shown iñ Figs. 14
LNG MODEL - 15 Modi Exp. y/L 90 1b,,. (deg) 180 90 180 1b0, (deg) Modcl Exp.
A2
-Fig. 16 Trajectories Of Lateral Shifting Motión with Bow Fig. 17 Turñing Trajectory in Steady Wind (LNG Carrier Model) 6(deg) 0 1w (deg) ß(deg) 30 y, y0 90 S1'iç (deg)
Fig. 18 Check Helms, Drift Angles and Speed Reduôtions in Steady Wind (LNG Carrier Model)
DRILLING SHIP MODEL
x/L x/L 90 1b (deg) 180 fi(deg) 30 K=4 20 o IO 90 Ø. (deg) 380 1.0-0.5 K'=6 - 90 t00. (deg) 180
and 15 respectively for a drilling ship model of 5 m long,
and in Fig. 16 for the lateral shifting motion with both bow and stern thrusters. In the predictions shown in these figures the hydrodynamic. data obtained from a captive model test are used. These figures indicate that the computation can simulate well such highly non-linear motions caused by thruster operation.
4.4 Maneuvering motion under external forces
Computed results of maneuvering motion under ex-ternal forces are compared here with model experimen
tal results for which external forces are clearly known.
As regards the model experiments in wind, a
free-running model test with a 125000 m3 LNG carrier model
of 5 m long has been carried out by utilizing three
wind fans oñ the model deck controlled so as to generate required wind forces2 Fig. 17 shows the experimental turning trajectory in wind with wind-to-ship speed ratio'
RO/RO 'IODEL
lo
lo
- Prd,Oon
ModI E.p.
Fig. 19 Turning Trajectory in Regular Waves (RO/RO Ship Model)
RO/RO MODEL
of 4 at a rudder angle of 15° port, in comparisoi with
the computed turning trajectory. Fig. 18 shows
compari-Sons between the computed and experimental results of
the same model for the course keeping motion in uniform
wind, in which check helm , drift angle ß and speed
reduction V/ V0 are presented against wind direction
The comparisons are made for three different ratios of
wind speed to ship speed, namely, the ratios K=4, 5 or 6.
Examples of the tûrning mOtion in regular wayes for
the RO/RO ship model are presented in Figs. 19 and 20,
in which computed results are compared with
experi-mental results18. Fig. 19 shows the turning trajectory iñ
regular waves With wave-to-ship length ratioOf AIL = 05 and Wave height to wave length ratio of H/A=l/ 25 at a rudder angle of 15 port.
Fig. 20 sho's the
time histories of yaw rate r and roll angle (p during the turning motion shoWn in Fig. 19. lt should be noted that the computations shOWn in these figures are made in consideration of the wave drifting forces alOne, in which the oscillatory wave exciting forces are notcon-sidered.
It can be mentioned from Figs. 17 through 20 that the above compütations predict well the maneuvering
mo-tion under external forces as well.
4.5 Maneuvering motion in shallow watet
It is well known that the maneuvering trials of the 278 000 DWT tanker 'ESSO OSAKA' provided com-prehensive information about the shallow water effects
on the maneûvering motion of a fulhscale ship22.
Com-putations of the turning motion with 35° rudderinShal-low water for the ESSO OSAKA are made with respect
to three cases of wäter depth, namely, the Water depth to
ship draft ratio of 4.2, 1.5 and 1.2. Fig. 21 shows the computed results of the turning trajectories in compan-son with the füll-scale trial results. Satisfactory agree-ment between the computed and the full-scale1trial re suIts can be seen in this figüre, and what is more, the computed results explain very Well the shallow water effects on the turning motion.
50 100 t (s)
''Model Exp.
Prediction
20 çc(deg)
ò= 35
TUONINO NOTION
-C535.5 (DEC.)0 COnTaINER INVIO 559flI
rat
Fig. 22 Effect of Number of Rudders on Turning Trajec-tory (Twin ScrèwContàiner Carrier)
Prediction o Fullscale Trial
ò= 35
ylL
Fig. 21 Turning Trajectoriés in Shallow Water (ESSO OSAKA)
ZIO - ZOO 150N(UNEN
C S'OR - 5)0.5 CNEO.)
/
Fig. 23 Effect of Number of Rudders on lou/lou Z-maneuver Response (Twin Screw Container Carrier)
5. Application examples
In Chapter 4, computed results were compared with. results of full scale trials or model expenments It is clearly shown through this comparison that, by inputt-ing minimum necessary data such as the principal par-ticulars of ship hull, propeller and rudder which are usually known at the preliminary design stage, predic tion with fairly high accuracy for a wide range of the ship maneuvering motion òan be made with the com-puter program system mentioned in this paper. In the
following, some resUlts of application studies by the use of the system are presented.
At the preliminary design stage, the ship maneuver-ability is examined in many aspects. Through this ex-amination, design of rudder and other control devices such as LTU is made. Moreover, from a viewpoint of the ship maneuverability, improvement on stem
con-figuration etc is made if necessary The computer pro-gram system is extensively utilized for the above
men-tioned purposes in the preliminary ship design.
11
TANKER(ESSO OSAKA)
Deep Shallow (H/d=i .5) Shallow (H/d 1.2)
aIL
Twin Rudders
Figs 22 through 24 show some results obtained in
rud-der design fòr a container carrier with twin propellers, in which the maneuverability in both cases of twin and single rudder is examined and compared. The rudder design is made so that the sum of the twin rudder areas
( movable parts) is equal to the single rudder area
(mov-able part) It-can be seen from these figures that the maneuverability with twin propeller and twin rudder system is quite supetior to that with twin propeller and
single rudder system in all aspects.
In the preliminary design of a ship with large
super-structure, careful attention should be paid to its
maneu-verability under wind condition. Fig. 25 shows Òne
typical result obtained in a study on the maneuverability
of a PCC (pure car carrier), in which check helms to
keep straight course in the wind with wind-to-ship speed
ratio of4 are predicted in both cases of with and
with-out aid ofa bow thruster showing considerable
improve-ment by LTU. The rudder area and the LÏU capacity
required from a viewpoint of the ship maneuverability in
wind can reasonably be determined by performing this kind of prediction for appropriate cases of wind condi-tions as expected in actual ship operation.
Change in ship loading condition usually causes change in the maneuverability2 This change in the ship maneuverability becomes considerably large under
some circumstances, and it is one of the key points to .be
examined at the preliminary design stage. Moreover,
information on the maneuverability change due to varying loading condition should be included in the maneuvering booklet at the time of ship complétion2 because it is an important information also for ship
operaters. Figs. 26 through 28 show prediction results for three kinds of maneuvering motions of a 270 000 DWT tanker at two typical loading conditions, nathely the full load and the ballast cóndition. Definite change is not. seen in the turning motión at a large rudder
angle, but remarkable difference between the
maneuver-ability at those two loading conditions can be seen in
a range of small rudder angles.
In FÏ. 29 prediction
resUlts on the lO°/l0° Z-maneuver response of a container carrier are shownfor a case of the GM-valué change due to loading
condition change. It can be understood from this figure that the course keeping ability may be deteriorated as the GM-value is decreased in_connection with the rolleffects On the. horizontal motions. In Figs. 22, 23, 26
and 27 typical output examples using the drawing func
tion of the computer prpgram system are presentëd In the above, application examples by the use of the batch process System are. presented. A study on the ship maneuvering safety
in a certain port the
de-signed ship will enter is sometimes required at the preliminary design stage. For this kind of needs, the interactive simulation technique may be thought most desirable and useful, because rudder operating pat-terns are standardized in the maneuvering simulation with the batch process system and its applicability islimited. Thus the computer program system has a
12 Fig. 25 = 35_ Check Helms 10 20 30 40 (deg) - Ta ja Ruudders Siagle Ruudder
Fig. 24 Effect of Number of. Rudders on Steady Tdrning Performance (Twin Screw Container Carrier)
Without Bow Thruster
With Bow Thruster( T07.5tons)
With Bow Thruster( To=15.Otons)
a- -a-. 'a
/1'
180 90. i5iv (deg)in Steady Wind (Pure Câr Óarrier)
TURPIINC RollaN
T 535.0 (DEC.T I
Fig. 26 Effect of Loading Conditiòn on Turning Trajecto-ry (270 000 DWT Tanker) CONTAINER (Tuai, Sërauvs) 1.0 FCC d(deg)
40-TANKER
10 20 30 40
ô (dog)
Fig. 28 Effect of Loading Condition on Steady Turniñg Performance (270 000 DWT Tanker)
function with which actual ship maneuvers in ports and on waterways can be simulated, through dialog with computer terminal With the graphic display function, by giviñg orders for operation of rudder, mäin engine,
LTU, tug etc. interactively.
Some results of the interactive simulation by the use of the fùnction are presented in Figs. 30 through 32, in which otrtput results on the graphic display are shown.
Fig 30 shows a simulation result obtained in the
maneu-vering safety study for a VLCC in a certain Port "A".
In this study, the ship is operated according to an
operat-ing procedure prepared in advance by well experienced ship masters, and the operational safety in entering
20
ZIO - ZOO 0OOEUVR
1 510.0 - 510.0 (DEC.) 1
Fig. 27 Effect of Loading Condition on 100/loe Z-maneuver Response (270 000 DWT Tankér)
CONTAINER
b(dég)
30
GM=co(wjthout Heei)
GM =0 . 6m
1011015G S0IIGUUCR III PORT. 'A 01CC I
Fig. 30 SimulatiOn df Entering Maneuvòr (VLCC) mm)
13
Fig. 29 Efféct of GM on 100/100 Z-maneuver Response (Container Carrier)
14
ENTERING MANEUVER IN PORT 'R
LEAVING MANEUVER IM PORT 'C' FERRY BOATI
Fig. 31 Simulation of Entering Maneuver (Large-Sized BulkCarrier)
Fig. 32 Simulation of Leaving Maneuver (Ferry Boat)
maneuvers from port entrance to berth front under external forces of wind, wave and current is examined
inccrniiection with ship approach speed at port entrance.
Fig. 31 shows a simulation result for a large-sized bulk carrier in a certain Port "B". Because such a large ship has never entered the port which has very shallow water area, extensive studies on entering and leaving maneuvers in this port under external forces of wind and current are performed in view of the maneuvering
safety.
In Fig. 32 a simulation result for leaving
maneuvers of a ferry boat from a narrow port area of a certain Port "C". This ship has a bow thruster and twin prcpelIer and twin rudder system, and the operationál
safety in leaving maneuvers by fully utilizing propeller,
rudder and LTU are examined.
In output results on the graphic display, as shown in Figs. 30 through 32, motion trajectory is drawn on the left half while time histories of motion variables such as ship velocity, propeller rpm etc. at certain time inter-vals are displayed on the right half. In this way, the cOmputer program system can be utilized as a
handy-type ship maneuvering simulator which can flexibly meet -I
.1
such various kinds of needs as mentioned in Chapter 1, although the simulator is not a real-time one, and ac-cordingly, the human factor in man-machine system can not be taken into consideration24.
6. ConclUding remarks
Development of the computer program system of this paper started about six years ago. Since then ex-tensive efforts to improve the system have been made by validating its prediction accuracy through compari-sons of computed results with results of full-scale trials or model 'experiments, and also by adding new func-tions. with which applicability of the system
an be
extended. Consequently, a highly advanced con puter program system for prediction of a wide range of the
ship maneuvering motion with high accuracy has been
successfully developed. This system is now iitilized
extensively in the ship design area and other applibations
as well in Mitsui Engineering and Shipbuilding Co.,
Ltd. I
Lastly the authors wish to express their sincere grati-tude to Dr. Y. Yamanouchi, formerly the director of Akishima Laborator.y, for his kind encouragernènt and
suggestions in developing the computer program system
of this paper.
References
1MO: Recommendation on Information to be Inluded in the Maneuvering BoOklets, Resolution, A.209 (VII) adopted on 12 October (1971).
Maneuvering Characteristics, Data Required, Codé of Fed-eral Regulations, 35 Panama Canal, Par. 103, 4.la (1977). M. Hirano : A Practical Calculation Method of Ship Ma
. neuvering Motion at Initial Design Stage, Naval
Architec-turc and Ocean Engineering, 19 (1981), p. 80 (pußlished by the Society of Naval Architects of Japan), or Journal of the Society of Naval Architects of Japan, 147 (1980), p. 144 (in Japanese).
S. Inoue, et al,: A Practical Calculation Method of Ship Maneuvering Motion, mt. Shipbuilding Progress, 28, 325
(1981), p. 207.
S. moue, et al.: Hydrodynamic Derivatives on Ship Ma-neuvering, mt. Shipbuilding Progress, 28, 321 (198l), p. 112. S. moue, et al.: The Hydrodynamic Derivatives on Ship Maneuverability in Even Keel Condition, The Non-linear Terms of Lateral Force and Moment Acting on Ship Hull in the Case of Maneuvering, Trans. of the West-Japan Society of Naval Architects, 57(1979), p. 13, (in Jãpanese) 58(1979), p. 153 (in Japanese).
M. Hirano, et al.: Maneuvering MotiOn Prediction by Computer in Ship Design, IFIPIIFAC Fourth mt. Confer-ence (ICCAS 82) (1982), p. 329.
S. Motora: On the Measurement of Added Mass ándAdded
Moment of Inertia for Ship Motions (Part 1»2 and 3), Journal of the. Society of Naval Architects of Japan, IQS (1959), p. 83 (in Japanese), 106 (1960), p. 59 (in Japanese), 106 (1960), p. 63 (in Japanese).
M. Fujino: Maneuverability in Restricted Waters: State of the Art, University of Michigan, Report No.184 (1976). M. Hirano, et al.: An Experimental Study on Maneuvering Hydrodynaniic Forces iñ Shallow Water, Trans. of the West-Japan Society of Naval Architects, 69 (1985), p. Ï01.
il)
A. Yazaki: The Design of AU-Type Ship Screw Propellers, Monthly Reports of Transportation Technical Retearch Institute, 11, 7 (1961) (in Jäpanese).12) W. P. A. van Lammeren, et al.: The Wageningen B-Screw Series, Trans. SNAME, 77 (1969), p. 269.
M. Fujino, et al.: On the Maneuverability of Ship While Stopping by Adverse Rotation of Propeller, Journal of the Kansai Society of Naval Architects, 169 (1978), P. 57 (in Japanese), 173 (1979), p. 45 (in Japanese).
M. S. Chislett, et al.: influence of Ship Speed on the Effec-tiveness of a Lateral-Thrust Unit, Hydro- and Aerodynamic LabOratory, Report No. Hy-8 (1966).
M. Hirano, et al.: A Study on Motion Characteristics of Roll-on Roll-off Vessels (The Second Report: Maneuver-ability), Mitsui Technical Review, 108 (1980), p. 16 (in
Japa-ñese).
R. M. Isherwood: Wind Resistance of Merchañt Ships, Trans. RINA, 115 (1973), p.327.
C. Aage: Wind Coefficients for Niñe Ship Models, Hydro-and Aerodynamic Laboratory, Report No. À-3 (1971).
M Hirano, et al.: Ship Turniñg Trajectory in Regular Waves, Trans. of the West-Japan Society of Naval Architects;
60 (1980), p. 17
K. E. Schoenherr: Däta for Estimating Bank Suction Effects in, Restricted Water and on Merchant Ship Hull, DTMB,
1461 (1960).
M. Hiraño, et al.: A Calculation of Ship 'Turning Motion Taking Coupling Effect Due to Heel into Consideration, Träns. of the West-Japan Society of Naval Architects, 59
(1980), p. 71.
M. Hirano, et al.: Ship Maneuverability in Wind (ist Report: Experimental Study with Wind Force Simulating Device), Journal of the Society of Naval Architects of Japan,
155 (1984),.p. 129 (in Japanese).
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(1979), P. 251.
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Appendix Nomeflclatuie
AD=duct sectionál area of LTU
A F = projected front area above waterline A11=ru1der area
A=projected side area above water line B= breadth of ship Cß=block coefficient D= propeller dIameter d draft of ship H=water depth H = wave height
I, 1=moment of inertia of ship with'respect to
x' and z-axes respectively
= moment of rotary iñertia of
propeller-shaft-ing system
J, J= added moment of inertia of ship with
re-spect to x and z-axes rere-spectively
J= added moment of rotary inertia of propeller
L = length of ship (between perpendiculars)
m=mass of ship
m, m= added mass of ship in x and y-axes direction respectively
n=number of propeller revolution p=rol1 rate
r=yaw rate
r'=dimensionless yaw rate (rUy)
U=ship speed in space= current speed
U= absolute wind speed
u=ship speed in x-axis direction V=ship speed (=(ü2+v2)"2) V = relative wind speed
v=ship speed in y-axis direction
v'=dimensionless ship speed in y-axis direction (=v/V)
W=displacement of ship
xR=x-coordinate of point on which rudder force R acts
x=x-coordinate of LTU position
zH=z-coordrnate of point on which lateral force
Y11 acts.
zR=z-coordinate of point on which rudder force YR acts
z=z-coordinate of point on which LTU force
Yacts
ß=drift angle (=sin' y')
ß= angle of relative wind direction8= rudder angle
A=wave amplitude (=H/2) A=aspect ratio of rudder À=wave length p=density of water pA=density of air r=trim quantity
çroll angle
Lr=headiñg anglefr=angle of absolUte winddirection
Lr1,.=angIe of wave directjon
