Embed Size (px)
Citation preview
Manoeuvrability model for a
Pure Car and Truck Carrier
D AN I EL ZA CH R IS SO N
d a n i e l z a @ k th . s e
0 7 3 - 0 2 1 9 2 8 2
Master Thesis
Ver. 1.0
KTH Centre for Naval Architecture
January 2011
2
ABSTRACT
This is a master thesis conducted during the autumn and winter 2010-2011 at KTH Centre for Naval Architecture in collaboration with Wallenius Marine AB. Traditionally the hull lines of typical Pure Car and Truck Carriers have been optimized for minimum resistance when going on a straight path and for maximum cargo capacity. This has resulted in vessels with slender underwater body, very high vertical centre of gravity and large flares in the waterlines of the aft body to provide form stability. Dynamic behaviour, such as manoeuvrability, has not been in main focus while designing the hulls. To create a tool for assessing the manoeuvrability, a model describing the motions in four degrees of freedom of a vessel have been developed. The equations of motion in surge, sway, yaw and roll are set up and solved numerically in Matlab. The code has been validated against available benchmark results and calibrated using trial data from a number of vessels from the Wallenius fleet. Good compliance to trial results is achieved for the initial part of a turn but some problems occur in the later part. Both trials and simulations indicate on very good turning and yaw checking abilities among the investigated vessels but also a tendency of dynamic instability. Happy reading!
3
ACKNOWLEDGEMENTS First of all I would like to thank Wallenius Marine for giving me the opportunity to perform this master thesis. A special thank goes to my supervisor Carl-Johan Söder for all support and help during the project. I would also like to thank the rest of the staff at the technical department for the nice working environment and the crews of M/V Otello, M/V Aida and M/V Faust for moving in zig-zag and in circles in the middle of the ocean providing me with invaluable data. Thanks also to Jakob Kuttenkeuler at KTH Centre for Naval Architecture for the inspiration and for pointing me in the right direction. Finally I would like to thank Kalle Garme at KTH Centre for Naval Architecture and my course mates Marcus Johansson, Paul Nielsen and Carl Hedgren for the good cooperation within the “Master thesis group”. Stockholm January 2011 Daniel Zachrisson
4
CONTENTS Nomenclature ................................................................................................................................................................ 5
1 Introduction ................................................................................................................................................................ 8
1.1 Background ......................................................................................................................................................... 8
1.2 Objective .............................................................................................................................................................. 8
1.3 Method ................................................................................................................................................................. 9
1.4 Studied vessels .................................................................................................................................................... 9
2 Modelling ...................................................................................................................................................................10
2.1 Surge, sway and yaw motion ...........................................................................................................................10
2.1.1 Coordinate systems ..................................................................................................................................10
2.1.2 Equations of motion ................................................................................................................................10
2.1.3 Non-dimensional variables ......................................................................................................................11
2.1.4 External forces ..........................................................................................................................................12
2.2 Roll motion........................................................................................................................................................19
2.2.1 Coordinate system ....................................................................................................................................19
2.2.2 Equation of motion ..................................................................................................................................19
3 Implementation ........................................................................................................................................................20
4 Validation ..................................................................................................................................................................21
5 Full scale trials ...........................................................................................................................................................23
5.1 Trial manoeuvres ..............................................................................................................................................23
5.1.1 Zig-zag test 10°/10° .................................................................................................................................24
5.1.2 Turning circle test 15° ..............................................................................................................................24
5.2 M/V Otello results ...........................................................................................................................................24
5.3 M/V Aida results ..............................................................................................................................................26
5.4 M/V Faust results ............................................................................................................................................27
5.5 Comments .........................................................................................................................................................28
6 Calibration .................................................................................................................................................................29
6.1 Propeller thrust and torque .............................................................................................................................29
6.2 Hull forces .........................................................................................................................................................29
6.3 Rudder force .....................................................................................................................................................32
6.4 Validity for another ship .................................................................................................................................32
7 Applications ..............................................................................................................................................................34
8 Conclusions ...............................................................................................................................................................35
9 References .................................................................................................................................................................37
Appendix 1 – Hydrodynamic coefficients
Appendix 2 – Rudder curves
Appendix 3 – Esso Osaka
Appendix 4 – Trial manoeuvres
Appendix 5 – Simulation results
5
NOMENCLATURE Latin letters:
a44 Added roll moment of inertia
AF Fin area
aH Ratio of additional lateral rudder force
AR Rudder area
ARF Fin effective aspect ratio
ARR Rudder aspect ratio
B Beam
b44 Roll damping coefficient
c44 Static roll restoring coefficient
CB Block coefficient
CD Rudder drag coefficient
CD0 Fin zero-lift drag coefficient
CDF Fin drag coefficient
CDi Fin induced drag coefficient
CL Rudder lift coefficient
CLF Fin lift coefficient
ClF Fin 2-D lift coefficient
CN Rudder normal force coefficient
CR Constant for expressing the difference of inflow speed for port and starboard rudder
CT Total resistance coefficient
CtP Propeller thrust correction factor
d Mean draft
da Draft at aft perpendicular
df Draft at fore perpendicular
DP Fin drag
e Fin span efficiency factor
FN Rudder normal force
g Acceleration of gravity
g(s) Propeller influence on rudder inflow speed
GM Metacentric height
hF Fin span
hR Rudder span
I44 Roll moment of inertia
Izz Yaw moment of inertia
izz Added yaw moment of inertia
JP Propeller advance ratio
K Roll moment
6
KG Vertical centre of gravity
KQ Propeller torque coefficient
KT Propeller thrust coefficient
L Length between perpendiculars
LF Fin lift
m Ship mass
mx Added mass in surge
my Added mass in sway
n Propeller revolution rate
N Yaw moment
NF Fin yaw moment
NH Hull yaw moment
NR Rudder yaw moment
N'v, N'r, N'vvv, N'rrr, N'vvr, N'vrr Hull hydrodynamic yaw coefficients
P Propeller pitch
PD Delivered power
Q Propeller torque
r Rate of turn
r4 Roll radius of gyration
r6 Yaw radius of gyration
Rn Reynolds number
RT Total resistance
S Wetted surface
s Effects on rudder inflow speed due to the propeller rotation
tP0 Thrust deduction factor at straight forward motion
tP Thrust deduction factor
tR Coefficient for additional rudder drag
u Surge speed
U Real speed
UF Fin inflow speed
UR Rudder inflow speed
v Sway speed
vA Added sway speed at rudder location
wP Wake fraction at propeller location
wP0 Wake fraction at propeller location at straight forward motion
wR Wake fraction at rudder location
wR0 Wake fraction at rudder location at straight forward motion
X Surge force
X'0 Non-dimensional total resistance
XF Fin surge force
x'F Non-dimensional x-coordinate of the centre of lateral fin force
7
xG Distance from amidships to LCG (positive ahead)
XH Hull surge force
x'H Non-dimensional x-coordinate of the centre of additional lateral force
XP Propeller surge force
x'P Non-dimensional x-coordinate of propeller
XR Rudder surge force
x'R Non-dimensional x-coordinate of the centre of lateral rudder force
X'rr, X'vr, X'vv, X'vvvv Hull hydrodynamic surge coefficients
Y Sway force
YF Fin sway force
YH Hull sway force
YR Rudder sway force
Y'v, Y'r, Y'vvv, Y'rrr, Y'vvr, Y'vrr Hull hydrodynamic sway coefficients
zF z-coordinate of the centre of lateral fin force
zH z-coordinate of the centre of lateral hull force
zR z-coordinate of the centre of lateral rudder force
Greek letters:
F Fin effective angle of attack
R Rudder effective angle of attack
Drift angle
A Added drift angle at rudder location
F Drift angle at fin location
P Drift angle at propeller location
R Drift angle at rudder location
Flow straightening factor
Rudder angle
eq Equivalent linear roll damping
Effects on rudder inflow speed due to the distance between rudder and propeller
Kinematic viscosity of water
Density of water
Roll angle
8
1 INTRODUCTION The concept of manoeuvrability in general covers a ship’s ability to keep its course, to change its course and to change its speed. All of these abilities have a great importance in order to operate a ship in an efficient and safe way. The International Maritime Organization (IMO) identifies the following significant qualities for the evaluation of ship manoeuvring characteristics in their standards for ship manoeuvrability [1]:
Inherent dynamic stability
Course-keeping ability
Initial turning/course-changing ability
Yaw checking ability
Turning ability
Stopping ability A ship which is dynamically stable will when it is exposed to a small disturbance whilst moving on a straight course, soon settle on a new straight course without any corrective rudder. The course-keeping ability is a steered ship’s ability to follow a predetermined course without excessive oscillations of rudder or heading. An acceptable course-keeping ability can therefore be achieved even for a ship which is slightly dynamically instable. The initial turning ability describes the change of heading per distance sailed when initiating turn and the yaw checking ability is a measure of the ship’s response to counter-rudder when already in a turn. The turning ability is the ability to turn the ship at maximum design rudder angle, and is measured by the advance at 90° change of heading and the tactical diameter which is the transfer at 180° change of heading. The stopping ability measures how long it takes for the ship to stop with the engine at full astern.
1.1 BACKGROUND
Traditionally the hull lines of typical Pure Car and Truck Carriers (PCTC) have been optimized for minimum resistance when going on a straight path (i.e. in a towing tank) and for maximum cargo capacity. This has resulted in vessels with slender underwater body, very high vertical centre of gravity and large flares in the waterlines of the aft body to provide form stability. Dynamic behaviour, such as manoeuvrability, has not been in main focus while designing the hulls. In the requirements on newbuildings manoeuvrability is usually only briefly mentioned as “the ship should have good manoeuvrability” without specifying it closer. Even though manoeuvrability has been lower priority, it is an important issue for this type of vessel. For example powerful flap rudders with large lever to the centre of gravity in combination with low stability gives these vessels special characteristics while manoeuvring that puts high requirements on the auto pilot and the crew. In sharp turns for example, the force from the rudder causes the ships to heel and rudder movements have to be kept small to minimize induced resistance. Experience from operation of the vessels also shows that a very active steering is needed to keep the course, which may depend on dynamic instability. More knowledge about the dynamic stability, or instability, of the vessels is needed to determine its influence on the resistance, and if the resistance can be reduced by changing the course stability properties of the vessel.
1.2 OBJECTIVE
The aim of this master thesis project is to develop a manoeuvrability model calibrated for an example ship from the latest generation of Wallenius vessels. The model will describe the vessel’s movements in the surge, sway, yaw and roll degrees of freedom and will be a tool to assess the manoeuvring characteristics stated above by simulating different kind of manoeuvres.
9
1.3 METHOD
The used method is to set up and solve the vessel’s equations of motion in surge, sway, yaw and roll in the time domain. This is done using numerical methods implemented in Matlab. The hydrodynamic forces acting on the hull is initially predicted using hydrodynamic coefficient estimations based on the main particulars. Required data is, as much as possible, taken directly from documentation of the vessel, or if that is not possible from semi-empirical formulae and diagrams. Validation of the implementation is done by using a benchmark ship suggested by the 23rd International Towing Tank Conference (ITTC) in 2002. By running the program with the benchmark input data and then comparing the results with trial, model test and simulation results for the benchmark ship the validity of the implementation can be determined. To be able to calibrate the model, full scale trails are done with example vessels from the Wallenius fleet. Appropriate manoeuvres are performed and recorded, and then compared with the results from the simulations. The model is then modified to fit the example vessel.
1.4 STUDIED VESSELS
The vessels which in this thesis will be used as an example is the sisters M/V Aida and M/V Otello (see Figure 1), built in 2006 at Daewoo Shipbuilding & Marine Engineering (DSME) in Korea. They have a load capacity of 6700 car units each and main particulars according to Table 1.
Figure 1. M/V Otello outside Terneuzen, Netherlands [2].
Table 1. Main particulars [3].
Length, over all 199 m
Length, between perpendiculars 190.50 m
Beam 32.26 m
Draft, design 9.50 m
Draft, ballast 8.20 m
CB 0.56 -
10
2 MODELLING The ship’s motion is simulated by solving the ship’s equations of motion numerically in the time domain. For each time step all the external forces acting on the ship is calculated. The model has four degrees of freedom (DOF), including surge, sway, yaw and roll.
2.1 SURGE, SWAY AND YAW MOTION
There are several similar 3-DOF models described in the literature [4, 5, 6, 7]. The common factor of these models is that they are variants of the so called MMG-model concept developed by a Japanese research group, named Manoeuvring Mathematical Modelling Group (MMG), in the late 70’s and early 80’s [4]. The major difference between the models is how the equations of motion are expressed. In this thesis the different parts of the model are combined from the models described in the literature.
2.1.1 Coordinate systems
Two coordinate systems are introduced according to Figure 2. One global coordinate system defined by the x0- and y0-axis, and one local ship fixed coordinate system, with its origin at the ship’s centre of gravity, defined by the x- and y-axis. The local system does not follow the ship’s roll motions.
Figure 2. Coordinate systems [5].
2.1.2 Equations of motion
The equations of motion used are described in [6] and [7], and are chosen because of their simplicity. The equations in [5] mix dimensional and non-dimensional variables, which makes life harder than necessary from both a programming and understanding point of view. The equations of motion are described based on the ship’s centre of gravity. The external forces however, are described based on the mid-ship position what for the yaw equation has to include the lateral force and its lever to the centre of gravity.
x
y
zz zz G
m m u mvr X
m m v mur Y
I i r N x Y
(1)
where:
m, mx, my : mass of ship and added mass in x- and y-directions respectively
Izz, izz : moment of inertia and added moment of inertia around z-axis
u : longitudinal speed
v : transversal speed
r : rate of turn
11
xG: distance from amidships to LCG (positive ahead)
X, Y, N : external surge and sway forces, and yaw moment respectively
Assumptions of the added masses and added moment of inertia are, according to [8], made as follows:
5/3
2
2
2
3 2
2.79
5.11 0.16
2 /
41 0.2
24 /
B
x
By
Bzz
C LBdm
L
C Bm Ld
d L B
C Bi L d
d L B
(2)
where is the water density, CB the block coefficient, L the length between perpendiculars, B the width
and d the draft. In this thesis the draft used is the mean draft of the ship defined as
2
a fd dd
(3)
where da and df are the drafts at the aft and fore perpendicular respectively. The ships dry yaw moment of inertia can, according to [9], be calculated as
2
6zzI mr (4)
where r6 is the yaw radius of gyration, which for conventional merchant ship hull shapes can be approximated as 0.25L. Whether the hull shape of a PCTC could be considered as conventional may be questionable, but according to a SSPA report [10] on a larger 230 meter PCTC the yaw radius of gyration is 0.26L for that vessel, which supports the approximation.
2.1.3 Non-dimensional variables
Some expressions contain non-dimensional quantities, for which primed symbols are used. Non-dimensionalization of masses, forces and moments are made as follows [5]:
21, , , ,
2x y x ym m m m m m L d (5)
21, ,
2X Y X Y LdU (6)
2 21
2N N L dU (7)
where U is the real ship speed expressed as
2 2U u v (8)
The rate of turn is non-dimensionalized as
rL
rU
(9)
12
and the drift angle is calculated as
arcsinv
U
(10)
As can be seen, if small angle approximation is used the drift angle (in radians) correspond to the negative non-dimensional transversal speed. Lengths are non-dimensionalized by dividing them by the ship length.
2.1.4 External forces
The external forces in (1) can be divided into forces acting on the hull, the propeller the rudder and a possible fixed fin, denoted by the suffixes H, P, R and F respectively:
H P R F
H R F
H R F
X X X X X
Y Y Y Y
N N N N
(11)
Hull A ship hull is a very complex shape and it is a quite difficult task to make correct estimations of all the hydrodynamic forces and moments acting on it. The approach here is to express the hydrodynamics as functions of the ship’s rate of turn and transversal speed (or drift). Just as was the case with the equations of motion, the expressions for the hydrodynamics are slightly different depending on publication. The difference is which terms are included in the expressions. In this thesis the expressions from [7] are used, with some modifications:
0
3 2 2 3
3 2 2 3
H vr y
H v r x vvv vvr vrr rrr
H v r x vvv vvr vrr rrr
X X X m v r
Y Y v Y m r Y v Y v r Y v r Y r
N N v N m r N v N v r N v r N r
(12)
In the expression for the surge force some higher order terms are excluded since no proper way to estimate the coefficients for these have been found and because they have a rather small influence on the result. It should also be noticed that the surge force in the current coordinate system should have a negative sign. Otherwise the ship would have the rather exclusive quality to propel itself using its own resistance, which would be quite economic but not very realistic. (This negative sign is not included in any of the publications which the author has found, and must therefore in some way be implied since a positive surge force generated by the hull is obviously wrong.)
0X is the non-dimensional total resistance of the ship calculated as
0 20.5
TRX
L d U
(13)
where RT is the towing resistance which can be expressed as
20.5T TR C S U (14)
where CT is the total resistance coefficient and S is the wetted surface of the hull [11]. By combining these two equations the following expression is obtained:
0TC S
XL d
(15)
13
CT is obtained from model resistance tests performed by SSPA [13].
The vrX coefficient can, according to [14], be approximated between 0.25 ym (tankers, bulk carriers etc.)
and 0.40 ym (container vessels). In [12] the corresponding coefficient rX , which with equation (10) in
mind could be considered asvrX , is obtained as
1.66 1.50r B yX C m (16)
which for the example vessel would be 0.57 ym .
The hydrodynamic coefficients in the sway and yaw expressions are obtained using a set of semi-empirical equations described in [14], which can be seen in Appendix 1. A few of these equations are slightly changed in order to adapt the coefficients to the example vessel. This will be further treated in the calibration chapter. Propeller The example vessel has a five-bladed fixed pitch propeller with data according to Table 2.
Table 2. Propeller data [3].
Diameter, DP 6.6 m
Pitch ratio, (P/DP)0.7R 1.0174 -
The propeller is modelled as in [5] and the thrust force is expressed as
2 4 2
0
11 /
2P tP P P TX C t n D K LdU (17)
where DP is the propeller diameter, n the propeller rate of revolution and tP0 the thrust deduction factor at the propeller location in straight forward motion. The constant CtP is not defined in [5], but is in [12] set to one and neglected. It is in this thesis used to adjust the thrust so that the speed is constant when the ship moves straight forward without any disturbances acting on it. The thrust coefficient KT is interpolated, as a function of the propeller advance ratio JP, from the propeller open water characteristics [13]. This function can, together with the similar function for the torque coefficient KQ, be seen in Figure 3.
Figure 3. Propeller characteristics
14
The advance coefficient is expressed as
cos 1 /P P PJ U w nD (18)
where wP is the wake fraction coefficient at propeller location compensated for drift and turn according to
2
0 exp 4.0P P P
P P
w w
x r
(19)
where wP0 is the wake fraction coefficient at propeller location in straight forward motion and Px the non-
dimensional x-coordinate of the propeller, usually approximated as -0.5, i.e. half the ship length. The wake fraction and trust deduction factor can according to [11] be approximated as
0 0.05P Bw C (20)
and
0 00.6P Pt w (21)
but is for the example vessel also available from model tests [13]. The engine control system works to keep the engine running at a pre-set RPM. When the resistance increases, e.g. in a sharp turn, the propeller torque increases and thereby also the power needed to keep the desired RPM. The propulsion point though must be kept within the load range limits (marked by the thick blue line in Figure 4) in order not to overload the engine.
Figure 4. Load range limits of the engine.
To do this, the engine control system detects if the power outtake is too high and then gradually decreases the engine RPM until a propulsion point within the range is reached. This in modelled as described below. The torque coefficient KQ is determined, in the same manner as the thrust coefficient, from the propeller open water characteristics [13] (see Figure 3). The propeller torque is then determined [11] as
15
5 2
Q PQ K D n (22)
The delivered power may then be calculated according [11] to
2DP n Q (23)
If the delivered power is higher than the maximum allowed power for the current engine RPM (see Figure 4), RPM is decreased. Rudder The rudder of the example vessel is a so called flap rudder, from Becker Marine Systems, with a flap along its trailing edge which is extended gradually when the rudder angle is increased, as can be seen in Figure 5.
Figure 5. Principle sketch of a flap rudder
[http://nippon.zaidan.info/seikabutsu/2003/00574/images/375.gif].
A flap rudder is very efficient and gives a 60-70% higher maximum lift than a conventional rudder of the same shape, size and area [15]. As a result of this a smaller rudder can be used, which in turn leads to a lower resistance in straight forward motion. The rudder dimensions are listed in Table 3.
Table 3. Rudder dimensions [13]
Area 34.1 m2
Aspect ratio 1.33 -
The method used for calculation the forces and moment generated by the rudder follows what is described in [5] if nothing else is stated.
1 sin
1 cos
cos
R R N
R H N
R R H H N
X t F
Y a F
N x a x F
(24)
where tR is the coefficient for additional drag, aH the ratio of additional lateral force, Rx the non-
dimensional x-coordinate of the centre of lateral force, Hx the non-dimensional x-coordinate of the
centre of additional lateral force, δ the rudder angle and NF the non-dimensional rudder normal force.
tR is approximated according to
1 0.28 0.55R Bt C . (25)
and the interaction coefficients aH and Hx are taken from the diagrams in Figure 6. For the example
vessel this means aH = 0.25 and Hx = -1.5.
16
Figure 6. Interaction coefficients [5].
The non-dimensional rudder normal force is expressed as
2R
N N R
AF C U
Ld
(26)
where AR is the rudder area, CN is the rudder normal force coefficient and RU is the non-dimensional
effective rudder inflow speed. The normal force coefficient is determined from the lift and drag curves of the rudder received from the manufacturer (see Appendix 2) as
cos sinN L R D RC C C (27)
where R is the effective angle of attack of the rudder. For a conventional rudder the normal force
coefficient could, according to [5], be approximated as
6.13
sin2.25
RN R
R
ARC
AR
(28)
where ARR is the rudder aspect ratio, if lift and drag curves are not available. The effective angle of attack is obtained by compensating the rudder angle for effects due to the drift and the propeller stream as
2
R R
R Rx r
(29)
where γ is the flow straightening factor and R is the drift angle at the rudder location. The flow
straightening factor is determined as
2
22.2 / 0.02 / 0.68B BC B L C B L (30)
The expression for the drift angle at the rudder location in (29), 2R Rx r , is somewhat confusing
because of the “2”. Consider it as the drift angle should be corrected with an additional term for the effect of the yaw rotation as
17
R A . (31)
Small angle approximation gives that the additional drift angle is equal to the negative additional non-dimensional transversal speed as
A A Rv x r . (32)
By inserting this into (31) the expression
R Rx r (33)
is obtained, which is the same as in (29) except for the “2” and perfectly corresponds to the expression for the drift at the propeller location in (19). Nevertheless this factor 2 is included in the expression in several publications [5, 12] for some, probably very good, reason which exceeds the authors understanding. The non-dimensional effective rudder inflow speed is determined as
22 1 1 ( )R R RU w C g s (34)
If this expression it can be observed that both effects due to the hull shape, described by the wake fraction wR, and the propeller, described by the term g(s), are taken into account. CR is an empirical constant for expressing the difference between port and starboard rudder which according to [12] could be set to 1.065 for port turn and 0.935 for starboard turn. What it should be for rudder amidships is not mentioned but should reasonably be 1. The wake fraction is calculated as
0
0
R PR
P
w ww
w (35)
where wR0 is the effective wake fraction at the rudder location in straight forward motion obtained using the relationship between (1-wR0) and (1-wP0), expressed as
20
0
1156.2 / 41.6 / 1.76
1
RB B
P
wC B L C B L
w
(36)
The effects due to the propeller are collected in the term g(s) expressed as
2
( ) 2 2 / 1g s s s s (37)
where symbolises effects due to the relationship between the propeller diameter and the rudder height,
effects due to the distance between the rudder and the propeller and s effects due to the propeller rotation. They are calculated as
/
1 / 1
1 1 cos /
P R
x P R
P
D h
k w w
s w U nP
(38)
where hR is the height of the rudder and P the propeller pitch and kx a factor depending of the distance between the propeller and the rudder which is set to 0.6.
18
Fixed fin None of the models includes a fixed fin but this is easy modelled, using classical wing theory as described in [16], as a lifting surface placed behind the propeller. The non-dimensional surge and sway forces and the yaw moment generated by the fin are calculated as
sin cos
cos sin
F F F F F
F F F F F
F F F
X L D
Y L D
N Y x
(39)
where F is the drift angle at the fin location and Fx is the non-dimensional x-coordinate of the fin. The
non-dimensional lift and drag forces of the fin are calculated similarly to the rudder normal force in (26) as
2
2
F
F
FF L F
FF D F
AL C U
Ld
AD C U
Ld
(40)
where AF is the fin area and FU the non-dimensional inflow speed, which in this case is assumed to be
the same as the rudder inflow speed calculated in (34). Due to rather small angles of attack the 2-dimensional lift coefficient is linearized as
Fl FC (41)
where αF is the angle of attack taken as the drift angle multiplied by the flow straightening factor.
F F (42)
The 3-dimensional lift coefficient is then calculated according to
21
F
F
l
L
F
CC
eAR
(43)
where e is the span efficiency factor (e ≈ 0.85) and ARF is the effective aspect ratio, which for a hull mounted fin is twice the geometric aspect ratio and calculated as
22 F
F
F
hAR
A (44)
where hF is the fin span and AF the fin area. The drag coefficient is divided into zero-lift drag and lift induced drag according to
0FD D DiC C C (45)
The zero-lift drag, referring to the rudder area, can according to Bertram [14] be estimated as
0 2
0.075
log 2D
n
CR
(46)
19
where Rn is the Reynolds number. Since the fin is located far aft at the hull, the Reynolds number is referred to the ship length instead of the fin chord and calculated as
n
ULR
(47)
where ν is the kinematic viscosity of water (ν ≈ 1.2∙10-6 m2/s). The lift induced drag is expressed as
2
FL
Di
CC
eAR (48)
2.2 ROLL MOTION
The ship’s motion in roll is modelled by formulating the roll equation with the hydrodynamic lateral forces as external forces.
2.2.1 Coordinate system
The heel angle and moment of the vessel are denoted as positive for a starboard heel, see Figure 7.
Figure 7. Coordinate system (vessel seen from the aft).
2.2.2 Equation of motion
The roll equation is formulated as
44 44 44 44a I b c K (49)
where a44 is the added water mass moment of inertia, I44 the ship moment of inertia in roll, b44 the roll
damping, c44 the roll restoring coefficient, the heel angle and K is the heeling moment which with the
given notation is expressed in terms of the lateral forces as
H H R R F FK Y z Y z Y z (50)
where zH, zR and zF are the z-coordinates of the centre of lateral force for the hull, rudder and fin forces respectively. The forces are taken from (12), (24) and (39) and re-dimensionalized according to (6). The levers to the centre of gravity are all assumed as
2
dz KG (51)
where KG is the distance from the keel to the vertical centre of gravity. The moment of inertia and the coefficients in (49) are according to [9] estimated as
G
K
z
y
φ
YR,F
Y
H
20
2
44 4
44 44
44
44 44 44 444eq
I mr
a I
c g m GM
b c I a
(52)
where r4 is the roll radius of gyration which can be estimated as 0.45B and eq is the equivalent linear
damping coefficient which is depending on the ship speed. Since no information about the roll damping of the Aida-class is available, estimation is done based on information about the longer vessels M/V Faust and M/V Elektra [10, 17]. The hull shape of M/V Faust is identical to the Aida-class except for the length. For simplicity the damping at about 15 knots is used for the whole speed interval, and this is estimated to 0.045.
3 IMPLEMENTATION The model is implemented in Matlab with a structure as described in Figure 8. The direction of the arrows describes the flow of data between the different parts of the program.
main.m
ode45
EOM.m
hull.m propulsion.m rudder.m fin.m
steering.m
resistance.m propchar.m ruddercoeff.m
RPM.mShip data
load_limit.m
Figure 8. Program structure.
In the main program main.m initial conditions such as approach speed and rudder angle are set. Vessel specific data is imported from an input file and the engine speed which corresponds to the vessel approach speed is received from RPM.m. In main.m the time integration also takes place, solving the differential equations set up in EOM.m using the ode45 solver, and finally the visualization of the results.
21
The function steering.m simulates the helmsman and changes the rudder angle depending of what type of manoeuvre performed. There is also a version of the program which instead loads a vector of rudder angles for which the simulation is executed. The functions hull.m, propulsion.m, rudder.m and fin.m, which are called by EOM.m, return the forces and moments generated by hull, propeller, rudder and fin respectively. In turn these functions calls functions which return interpolated values of the vessel´s total resistance, propeller characteristics and the rudder normal force coefficient, i.e. resistance.m, propchar.m and rudder_coefficient.m. The function load_limit.m reduces the engine speed when the load becomes the large according to the limit shown in Figure 4.
4 VALIDATION To validate the model, simulations are done for the 278 000 DWT tanker Esso Osaka (see Figure 9 and Table 4) which by the 23rd ITTC was selected as a benchmark ship for comparison of various methods for predicting ship manoeuvrability [7]. Esso Osaka was launched in 1973 and was in 1977 involved in a comprehensive test series in the Gulf of Mexico. Several model tests, with models of various sizes, have also been done by different institutes.
Figure 9. Esso Osaka.
Table 4. Data for Esso Osaka [18,19]
Length, between perpendiculars 325 m
Beam 53 m
Draft 21.73 m
Displacement 319 400 tonnes
CB 0.83 -
LCG 10.3 m
Wetted surface 27671 m2
Total resistance coefficient 0.00306 -
Propeller diameter 9.10 m
Pitch ratio at 0.7R 0.715 -
Engine speed at 10 knots 51 RPM
Rudder chord 9.00 m
Rudder height 13.85 m
Rudder rate 3 deg/s
Simulations of a starboard circle with 35° rudder angle and a 10°/10° zigzag test are done and compared to the benchmark results from [7]. The hydrodynamic forces acting on the hull are calculated as
22
2 2 4
0
3 2 2 3
3 2 2 3
H vv vr y rr vvvv
H v r x vvv vvr vrr rrr
H v r x vvv vvr vrr rrr
X X X v X m v r X r X v
Y Y v Y m r Y v Y v r Y v r Y r
N N v N m r N v N v r N v r N r
(53)
where the hull derivatives are taken from the benchmark data set in [7], which can be seen in Appendix 3. The simulations are done without any torque limit, i.e. with constant engine speed, and with a conventional rudder. As can be seen in Figure 10 and Figure 11 the compliance between the simulated results and the trial results are good for the turning circle test and very good for the zigzag test.
Figure 10. Simulated (solid blue line) and trial (dots) turning trajectories.
Figure 11. Simulated (solid blue line) and trial (dots) time history of heading.
If one instead compare the simulated result for the turning circle to the model test and simulation results presented in [7] the compliance is slightly better, see Figure 12. Since the benchmark derivatives are produced by models tests, it is not very strange that the compliance to model tests is better than the compliance to full scale trials.
23
Figure 12. Simulated (solid blue line), model test (solid black line) and other simulated turning trajectories.
The same thing can be noticed when comparing the time histories of the drift angle, see Figure 13 and Figure 14. The simulation overestimates the drift angle at full scale trials, but has a very good compliance to the model tests.
Figure 13. Simulated (solid blue line) and trial (dots) time histories of drift angle.
Figure 14. Simulated (solid blue line), model test (solid black line) and other simulated time histories of drift angle.
Remaining comparisons can be found in Appendix 3.
5 FULL SCALE TRIALS In order to create a basis for the calibration, full scale trials have been performed by M/V Otello and M/V Aida. To make it possible to investigate how well the calibration for the example vessels works for a similar vessel of a different size, trials have also been performed by the larger M/V Faust.
5.1 TRIAL MANOEUVRES
The trial manoeuvres was decided in consideration to give as much information as possible but at the same time not to be very time consuming for the vessel to carry out. For diagrams of the manoeuvres and for definitions used, see Appendix 4. Zig-zag manoeuvres were done to investigate the yaw checking ability, and also the initial turning ability when entering the manoeuvre. Turning circle manoeuvres were performed to investigate the turning ability. Both manoeuvres were ended by a pull-out manoeuvre to investigate the inherent dynamic stability. In order not to cause too much heel (because of the safety of the cargo) and not to decrease the speed out of the valid range the rudder deflections were kept quite moderate. The following test procedures were sent to the vessel.
24
5.1.1 Zig-zag test 10°/10°
The test is performed at cruise speed and initiated to both starboard and port according to the following
procedure:
1. The ship is brought to a steady course and speed.
2. The rudder is ordered to 10° starboard/port.
3. When the heading has changed by 10° off the base course the rudder in shifted to 10°
port/starboard.
4. When the heading is 10° off the base course the rudder is reversed as before.
5. The procedure is repeated until the ship heading has passed the base course three times.
6. When passing the base course the third time the test is ended by a pull-out manoeuvre (rudder is
returned to the midship position and kept there until a steady turning rate is obtained)
5.1.2 Turning circle test 15°
The test is performed at cruise speed and made to both starboard and port according to the following
procedure:
1. The ship is brought to a steady course and speed.
2. Rudder is ordered to 15° starboard/port. Rudder and engine controls are kept constant during
the turn.
3. The turn continues until 360° change of heading has been completed.
4. The turn is ended by a pull-out manoeuvre (rudder is returned to the midship position and kept
there until a steady turning rate is obtained)
5.2 M/V OTELLO RESULTS
The manoeuvres were performed on 10 November 2010, west of the Northern Mariana Islands in the Philippine Sea. The wind was 7 m/s from north-east and waves 1 m high. The vessel was in ballast condition with an aft trim (see Table 5).
Table 5. Loading condition
Draft, fwd 7.4 m
Draft, aft 8.4 m
Displacement 26 536 tonnes
GM 3.34 m
LCG -4.7 m
The zig-zag test was carried out with an initial speed of 17.3 knots and the results can be seen in Figure 15 and Table 6.
25
Figure 15. Otello zig-zag 10°/10°.
Table 6. Results of Otello zig-zag test.
Trial IMO criteria
1st overshoot angle 8.5 15.7 deg
2nd overshoot angle 10.3 33.6 deg
Distance to turn 10 deg 1.1 2.5 ship lengths
Turning circle tests were carried out with both starboard and port rudder. The starboard turn had an initial speed of 15 knots and the port turn 15.7 knots. The turning trajectories can be seen in Figure 16 and the advances and tactical diameters are listed in Table 7.
Figure 16. Otello turning circle 15°.
Table 7. Results of Otello turning circle test.
Port Starboard
Advance 3.0 Ship lengths 3.1 Ship lengths
Tactical diameter 3.9 Ship lengths 4.1 Ship lengths
Both turns were ended by a pull-out manoeuvre for which the time histories of the rate of turn can be seen in Figure 17.
26
Figure 17. Otello pull-out manoeuvre.
5.3 M/V AIDA RESULTS With Aida a zig-zag test was performed on 29 December 2010, between the Australian east coast and the Salomon Islands in the Coral Sea. The wind was 5 m/s from north and waves 0.5 m high. The vessel was in ballast condition on even keel (see Table 8).
Table 8. Loading condition
Draft, fwd 8.3 m
Draft, aft 8.3 m
Displacement 27 824 tonnes
GM 2.91 m
LCG -3.1 m
The test was carried out with an initial speed of 20.3 knots and the results can be seen in Figure 18 and Table 9.
Figure 18. Aida zig-zag 10°/10°.
Table 9. Results of Aida zig-zag test
Trial IMO criteria
1st overshoot angle 9.9 14.1 deg
2nd overshoot angle 11.9 31.2 deg
27
Distance to turn 10 deg 1.3 2.5 ship lengths
Another test sequence with rapid rudder actions was performed on 20 March 2010, in the middle of the Mediterranean right between Malta and Crete, with the vessel in fully loaded condition according to Table 10.
Table 10. Loading condition
Draft, fwd 9.5 m
Draft, aft 9.5 m
Displacement 33 791 tonnes
GM 1.26 m
LCG -4.3 m
Rapid rudder actions were made to both starboard and port and with rudder angles of 10, 15 and 20 degrees as can be seen in Figure 19.
Figure 19. Aida rapid rudder actions.
5.4 M/V FAUST RESULTS
Zig-zag tests have also been performed by the 30 meters longer M/V Faust, on 7 January 2011 in the Mediterranean between Italy and Sardinia. The vessel had a loading condition according to Table 11.
Table 11. Loading condition
Draft, fwd 8.8 m
Draft, aft 8.8 m
Displacement 38 254 tonnes
GM 1.86 m
LCG -4.0 m
The tests were initiated to both starboard and port with initial speeds of 13.8 and 13.7 knots respectively and the results can be seen in Figure 20.
28
Figure 20. Faust zig-zag 10°/10°.
Table 12. Results of Faust zig-zag tests.
Starboard Port
Trial IMO criteria Trial IMO criteria
1st overshoot angle 5.6 20 6.2 20 deg
2nd overshoot angle 9.3 40 8.9 40 deg
Distance to turn 10 deg 1.2 2.5 1.1 2.5 ship lengths
Both tests were ended by a pull-out manoeuvre for which the time histories of the rate of turn can be seen in Figure 21.
Figure 21. Faust pull-out manoeuvre.
5.5 COMMENTS
The recommendations for environmental conditions stated by IMO [1] says that the water should be more than 4 times deeper than the mean draft, the wind should not exceed Beaufort 5 (8.0–10.7 m/s), the waves should not exceed sea state 4 (1.25 –2.5 m) and the current should be uniform. The water deep criterion was fulfilled for all the tests and the wind and wave criterions were fulfilled for the zig-zag and turning circle tests performed by M/V Otello and M/V Aida. The wind and sea state at the remaining occasions is unfortunately not known, which is also the case regarding the current conditions at all occasions. Some inaccuracy exists in the handling of the rudder, especially for M/V Faust where the rudder angles are closer to 12° than the intended 10°. The zig-zag test by M/V Aida is also ended with a rudder angle of 5°, but since this is after the second overshoot it has less importance.
29
The manoeuvrability criteria stated by IMO are intended for fully loaded draft and even keel, which is not the case for any of the zig-zag or turning circle tests performed. The initial speed of the M/V Faust tests were also lower than intended for the criteria. It may nevertheless be of interest to relate the results to the criteria for an indication. As can be noticed both the first and second overshoots of the zig-zag tests are well within the limits which indicates on a very good yaw checking ability. The same applies to the initial turning ability indicated by the distance to turn 10° with 10° rudder. Even the criteria for turning ability, with an advance not exceeding 4.5 ship lengths and a tactical diameter not exceeding 5 ship lengths, are fulfilled although they are intended for a rudder angle of 35° and not 15° as in the tests performed. From the pull-out manoeuvres done by M/V Otello and M/V Faust it can be read out that the ships are not dynamically stable since the rate of turn does not decrease all the way down to zero when the rudder is returned to amidships.
6 CALIBRATION In this chapter it is described how the model is calibrated to fit the example vessels. All simulation results with the final settings can be found in Appendix 5.
6.1 PROPELLER THRUST AND TORQUE
If both the propeller thrust and the ship resistance are perfectly modelled the speed should be constant when the ship is simulated as going on a straight path. There are however a few sources to errors which means that that is not the case. Both the thrust coefficient and the propeller RPM are taken from interpolated curves, which furthermore describes a propeller which is slightly different from the one used on the example vessels. This in compensated by tuning in the coefficient CtP in equation (17) so that the speed is constant. The same errors occur for the propeller torque which affects the calculation of the delivered power in equation (25). Just as for the thrust this is compensated for by multiplying the expression with a coefficient. In this case it is tuned to the delivered power for different speeds according to [13].
6.2 HULL FORCES
As already mentioned it is difficult to model the hydrodynamic forces acting on the hull in a good way, and particularly to make proper assessments of the hydrodynamic coefficients which are used to calculate the forces. The most reliable way is of course to derive the coefficients using model tests for the hull in question, as is the case for the benchmark coefficients for Esso Osaka, but this cannot always be done for different reasons. Instead semi-empirical methods based on regression of a larger amount of test results for other ships. Two examples of these methods are those described by Kijima [5] and Lee [14], of which the later after evaluation is determined to be most suitable for this thesis. However, the regression is based on a population of ships not shown in the source but probably including all types from tankers and bulk carriers to container vessels. Since a PCTC is a quite unconventional ship it turns out that the coefficients obtained from [14] needs to be modified to better fit the example vessel. In Figure 22 and Figure 23 the simulation results, using the unmodified coefficient, for the zig-zag tests performed by M/V Otello and M/V Aida are shown. As can be seen the compliance with the trial results is rather bad. Using an iterative procedure the coefficients are tuned to better describe the manoeuvring characteristics of the example vessels.
30
Figure 22. Otello unmodified zig-zag 10°/10°.
Figure 23. Aida unmodified zig-zag 10°/10°.
When trying to simulate the turning circle tests using the unmodified coefficients the model cannot even handle the simulation. The reason for this appears to be that the drift increases way too much during the turn. By comparing the benchmark coefficients for Esso Osaka to the coefficients calculated according to
[14] for the same vessel (see Appendix 3), it can be seen that the coefficient vvvY is large and negative in its
benchmark value and large and positive in its calculated value. Since the coefficient affects the sway forces acting on the hull, it also affects the drift. By changing the sign of the calculated coefficient, the turning trajectories in Figure 24 are obtained for M/V Otello. The zig-zag results are only minor affected.
Figure 24. Otello unmodified turning circle 15°
(the small marks shows advance and tactical diameter).
Continuing the iterative procedure it is found out that the coefficient vN , which describes the yaw
moment depending on transversal speed, has a big influence on the turning ability. By multiplying the expression with a factor of 3.2 the compliance with the trial results becomes much better, especially for the zig-zag tests as can be seen in Figure 25 and Figure 26.
31
Figure 25. Otello modified zig-zag 10°/10°.
Figure 26.Aida modified zig-zag 10°/10°.
A comparison is also made for a 20°/20° zig-zag test performed by M/V Otello at ballast draft (8.2 m even keel) at her delivery sea trial. The initial speed was 21 knots. As can be seen in Figure 27 the compliance between simulations and trial results is fully acceptable even here.
Figure 27. Otello modified zig-zag 20°/20°.
The compliance is better also for the turning circle tests in Figure 28, but in the later part of the turn the difference is still quite big. If one looks ate the predictions of advance and tactical diameter though, the compliance is rather good.
Figure 28. Otello modified turning circle 15°.
The prediction of the drift angle is only good in the first 50 seconds of the turn, after which it becomes very poor (see Figure 29 and Figure 30). This problem does not affect the zig-zag prediction since a turn
32
never goes that far in that case, but for the turning circle it becomes a problem, which most likely is a major reason for the bad prediction in the later part of the turning trajectories.
Figure 29. Starboard drift.
Figure 30. Port drift.
Although the prediction in the later part of the turn is rather bad, these settings are accepted at this state on the grounds that the initial part of the turn is the most relevant and that further investigations to correct it goes out of the time frame of this project.
6.3 RUDDER FORCE
Another essential thing to estimate correct is the rudder force. To investigate this, the ship’s roll motion is observed. When initiating a turn the ship first heels inwards the turn, due to the rudder force, before the hydrodynamic and inertial forces acting on the hull takes over and causes the ship to heel outwards the turn. By looking at the first peak in the time history of roll motion, the compliance of the rudder force estimation thereby can be determined. To do this the 20 degree rudder actions from Figure 19 are used and the roll behaviour can be seen in Figure 31 and Figure 32.
Figure 31. Heel at starboard rudder.
Figure 32. Heel at port rudder.
Because the first peak correspond almost perfect for both starboard and port rudder the estimation of the rudder force can be considered as correct.
6.4 VALIDITY FOR ANOTHER SHIP
It is of course desirable that the model is valid for not just the example vessels, but also other vessels in the Wallenius fleet. To get an indication of this, simulations are done for the larger M/V Faust, which as earlier mentioned has an identical hull shape except for the length. Using the hull coefficients modified for M/V Otello and M/V Aida the zig-zag characteristics in Figure 33 and Figure 34 are obtained. For the manoeuvre initiated to starboard rudder angles of 12° are used to better match the rudder angles from the trial.
33
Figure 33. Faust starboard zig-zag 10°/12°.
Figure 34. Faust port zig-zag 10°/10°.
Since it turns a bit to slow in the simulations the rudder force is investigated in the same way as earlier, looking at the first rudder action in the one of the zig-zag tests. As can be seen in Figure 35 the rudder force seems to be a bit too small and the lift coefficient is thereby increased by 30%. After this change the some increase of the first peak appears as can be seen in Figure 36.
Figure 35. Heel at starboard rudder (CL unmodified).
Figure 36. Heel at starboard rudder (CL modified).
This change of the rudder force makes the zig-zag results, shown in Figure 37 and Figure 38, much better.
Figure 37. Faust starboard zig-zag 10°/12° (CL modified).
Figure 38. Faust port zig-zag 10°/10° (CL modified).
34
7 APPLICATIONS As already clear it is possible to simulate zig-zag and turning circle manoeuvres using the developed code. Of course the code can be used for more than this, and in this chapter some simple examples are explained. The feature where the model is fed with a vector containing a series of rudder angles both gives the opportunity to perform a simulation with a series of “real” rudder angles registered on the actual vessel or with a series of produced rudder angles for a certain manoeuvre sequence. Such a sequence is the so called spiral manoeuvre from which the dynamic stability can be studied. The steady state rate of turn is registered for a number of rudder angles and presented in a plot as described in Appendix 4. The loop height is a measure of the dynamic instability of the ship and according to [20] a guideline should be to have a loop height not exceeding 0.1-0.2 deg/s. The simulated results for the example vessel indicates a loop height of 0.8 deg/s at ballast draft and 1.3 deg/s at design draft as can be seen in Figure 39. It should be noticed that the results within the instability loop not are shown in the figure. The problems with the prediction of the later part of the turn should be remembered when interpreting the results.
Figure 39. Spiral manoeuvre.
One way to analyse the course-keeping ability is a so called Very Small Zig Zag (VSZZ) which quite closely approximates the behaviour of a ship steered to maintain a straight course [1]. This is performed by setting the maximum yaw angle to 0° and the maximum rudder angle to 5° in a zig-zag manoeuvre, see Figure 40.
Figure 40. VSZZ at ballast condition.
35
The model can also be used to investigate how the manoeuvrability is affected if a fixed fin is added. Figure 41 and Figure 42 shows how the zig-zag and turning circle results are changed if a 10 m2 fin is added at the aft of the ship.
Figure 41. Zig-zag 10°/10°, 20 knots, ballast draft
Figure 42. Turning circle 20°, 20 knots, ballast draft
At a turn in 20 knots with 20° rudder one can also see how the power limiter sets in and decreases the RPM (see Figure 43)
Figure 43. RPM decrease in a 20° turn.
8 CONCLUSIONS A manoeuvrability model describing the motion of a PCTC in surge, sway, yaw and roll has been developed. It shows good compliance both to benchmark results and to trial results from different Wallenius vessels and has the capability to simulate different kind of manoeuvres which can be used to assess the manoeuvre characteristics of a vessel. By that, the project can be considered as successful. Due to the structure of the code it is easy to expand the model with additional features such as influence from wind, current and waves. By adding different kind of autopilot functions the course keeping can be further investigated as well as the possibility of roll damping by the rudder. Something that needs further investigation is the hydrodynamic coefficients describing the hull forces. By doing that it should be possible to achieve better predictions even in the later part of a turn, which would expand the utility of the model even more.
36
Further calibration of the model would benefit from more full scale trials. Especially, more turning circle manoeuvres should be done to obtain a reliable base for the calibration. Since the trials in this thesis are performed mainly at ballast draft, both turning circle and zig-zag manoeuvres should also, if possible, be performed by vessels in a fully loaded condition to be able to adapt the model to different loading conditions. The same is of course also desirable for different speeds. As a final conclusion all the investigated vessels shows very good turning and yaw checking abilities but also a tendency of dynamic instability, both from full scale trials and simulations. Hopefully the further use of the model developed in this thesis can show if benefits could be achieved by changeling the dynamic behaviour of the vessels.
37
9 REFERENCES 1. IMO MSC/Circ.1053, Explanatory notes to the standards for ship manoeuvrability, 16 December 2002 2. Seyler J., http://www.faktaomfartyg.se/otello_2006_b_3.htm, Online 2 November 2010 3. DSME, Daewoo Shipbuilding & Marine Engineering Co.,Ltd, Trim & Stability Booklet, H.NO
4443, 2006 4. Yoshimura Y., Mathematical Model for Manoeuvring Ship Motion (MMG Model), Workshop on
Mathematical Models for Operations involving Ship-Ship Interaction, Tokyo, 2005 5. Kijima K. et al. , On a prediction method of ship manoeuvring characteristics, MARSIM ´93 proceedings,
pp. 285-294 6. Hasegawa K. et al., A study on improving the course-keeping ability of a pure car carrier in windy conditions,
Journal of Marine Science and Technology 11:76-87, 2006 7. The Specialist Committee on Esso Osaka, Final Report and Recommendations to the 23rd ITTC, Proceedings
of the 23rd ITTC – Volume II, 2002 8. Hooft J.P., Pieffer J.B.M., Manoeuvrability of Frigates in Waves, Marine Technology, Vol. 25, 1988 9. Rosén A., Introduktion till fartygs sjöegenskaper, KTH Centre for Naval Architecture, Stockholm,
2009 (In Swedish) 10. Jacobsson S., Rask I., DSME 7900 units PCTC Seakeeping model tests, SSPA report no. 2008 4871-2 11. Garme K., Fartygs motstånd och effektbehov, KTH Centre for Naval Architecture, Stockholm, 2008
(In Swedish) 12. Ishiguro T., Tanaka S., Yoshimura Y., A study on the accuracy of the recent prediction technique of ship’s
maneuverability at early design stage, MARSIM ´96 proceedings, pp. 547-561 13. Liljenberg H., 6700 Units PCTC, DSME newb. H4442/43 for Wallenius Lines, Model Tests with final
propeller and rudder, SSPA report no. 2004 3483-8 14. Lee T. et al, On an Empirical Prediction of Hydrodynamic Coefficients for Modern Ship Hulls, Proceedings
of MARSIM ´03, Vol. III, August, 2003 15. Bertram V., Practical Ship Hydrodynamics, Butterworth-Heinemann, 2000 16. Kuttenkeuler J., Segling så funkar det, KTH Centre for Naval Architecture, Stockholm, 2009 (In
Swedish) 17. Huss M., Roll damping study, Technical report for NB 4457, WM-MH-09-004, Wallenius Marine,
Stockholm, 2009 18. McTaggart K., Simulation of Hydrodynamic Forces and Motions for a Freely Maneuvering Ship in a Seaway,
Defence Research and Development Canada, 2005 19. Simonsen C., Rudder, propeller and hull interaction by RANS, Technical University of Denmark,
Department of Naval Architecture and Offshore Engineering, 2000 20. Norrbin N. H., Fartygs manövrering och manöverbarhetskriteria (med girprovsanalys), SSPA, 1989 (In
Swedish)
38
APPENDIX 1 – HYDRODYNAMIC COEFFICIENTS
/
0.145 2.25 0.2
0.282 0.1 0.0086 0.004
1.281 0.031
0.029 0.004
0.6
v SR
r SR B L
vvv
Brrr
vvr
d d dY
L L L
d dY m
L L
d dY
L L
C BdY
L L
dY
L
28 0.066
0.4 0.007
0.222 0.1 0.00484
0.0424 0.03 0.004 0.00027
0.188 0.01
0.
B
B
vrr
v SR
r SR C
vvv
rrr
C B
L
d dY
L L
d dN
L L
d dN
L L
d dN
L L
dN
L
/
3
07
014 0.002
0.178 0.037
0.158 0.005
0.18 ( / )
0.18
1.12 0.735
28.7 0.54
B
B
B
B
B
Bvvr
vrr
C B
C
C
B L
SR RSR
SR
C
SR
PR
PS
C B
L
C BdN
L L
d dN
L L
P C
P
B L
P S
P
dP
L
PL
BS
B
BPS : Half breadth at the height of propeller shaft in 2.0 station BP07 : Half breadth at the height of 70% of propeller radius in 2.0 station
39
APPENDIX 2 – RUDDER CURVES
40
41
APPENDIX 3 – ESSO OSAKA Hydrodynamic coefficients:
Benchmark Estimation
X'vv -0.00329 -
X'vvvv 0.277875 -
X'rr 3.4e-5 -
X'vr+my' 0.183616 0.1874
Y'v -0.3831 -0.3453
Y'r-mx' 0.082145 -0.1852
Y'vvv -1.05375 1.7446
Y'vvr 0.59837 0.2881
Y'vrr -0.25589 0.5047
Y'rrr -0.01119 -9.3991e-4
N'v -0.14716 -0.1247
N'r -0.04836 -0.0442
N'vvv 0.053257 0.0384
N'vvr -0.29699 -0.1919
N'vrr 0.023637 0.0832
N'rrr -0.01835 -0.0015
Simulation compared to trials: Simulation compared to free run model test and
other simulations:
42
Simulation compared to trials:
43
APPENDIX 4 – TRIAL MANOEUVRES Pictures are taken from the IMO Explanatory notes to the standards for ship manoeuvrability [1] Zig-zag manoeuvre:
Turning circle:
44
Pull-out manoeuvre:
Spiral manoeuvre:
Dynamically stable Dynamically unstable
45
APPENDIX 5 – SIMULATION RESULTS Otello zig-zag 17.3 knots: Aida zig-zag 20.3 knots:
46
Otello starboard turn 15.0 knots: Otello port turn 15.7 knots:
47
48
Faust zig-zag starboard 13.8 knots: Faust zig-zag port 13.7 knots:
49
