tug-towed_ship.pdf

THE MANOEUVRING CHARACTERISTICS ON

TUG-TOWED SHIP SYSTEMS

Takashi Kishimoto ∗ Katsuro Kijima ∗∗

∗ Graduate School of Kyushu University, Fukuoka, JAPAN

∗∗ Kyushu University, Fukuoka, JAPAN

Abstract: Ships disabled from marine disasters are generally towed by tug-boat.

Concerning safe towing operations, we examined the course stability of the tug and

towed ship taking into account some factors such as the length of towing ropes,

the location of towing points and the condition of the disabled ship. By using of

the numerical simulations, we estimated manoeuvring performance of the ships, and

examined how those factors would aﬀect the course stability for tug-towed ship

systems.

Keywords: Tug-boat, Towed ship, Course stability, Fuzzy inference

1. INTRODUCTION

addition to applying towing factors. Third, we

considered fuzzy inference thought to resemble

human decision making process, and applyed it to

rudder steering control for the tug-boat in numer-

ical towing simulations. Finally, we examined the

calculated results to develop an eﬀective rudder

control system in towing operations.

Recently, marine disasters which cause serious

environmental pollution have been occuring fre-

quently. Ships disabled from marine disasters

must be removed as soon as possible from sea

route in the interest of navigational safety. Gener-

ally, disabled ships are towed by tugboats. Issues

concerning tug-towed ship systems are factors

such as the length of towing ropes, the location

of towing points and the condition of the disabled

ships. Up to the present time, these important fac-

tors have been entrusted to the knowledge and the

experience of towing operators, and under their

supervision, many accidents have occured because

there isn’t a uniform method to tow disabled

ships, towing operaters are forced to use their

own method, creating inconsistancy and errors in

methodology. Therefore, it is necessary that we

develop a uniform principle using a theoretical

approach, to ensure safe towing operations.

2. MANOEUVRING EQUATIONS

Assuming that the ship’s motions being in a hor-

izontal plane and that roll, pitch and heave mo-

tions are negligibly small, we can accept that ship

motions mainly consits of surge, sway and yaw

motions. Fig.1 shows the coordinate systems for

formulation of the tug and towed ship’s motions.

o 0 −

x 2 y 2 show

coordinate systems ﬁxed on the centre of gravity

of each ship. The terms with subscripts “1” and

“2” express “tug-boat” and “towed ship”. The

two ships are connected with a towing rope that

is assumed to be rigid. Furthermore, x f and x a

represent the location of the connection points of

the towing rope on the towed ship and on the

tug-boat from the centre of gravity of each ship.

The rope’s angle in relation to the tug-boat is

x 1 y 1 and G 2 −

First, we analyzed manoeuvring motions of the

tug-boat and the towed ship based on the mea-

sured hydrodynamic forces derived from the cap-

tive model tests. Second, we estimated the course

stability of the tug-towed ship systems besed on

the results found from manoeuvring motions in

x 0 y 0 shows a coordinate system ﬁxed on the

earth, where as G 1 −

X 2 = X H 2 + X T 2

Y 2 = Y H 2 + Y T 2

N 2 = N H 2 + N T 2

(3)

Fig. 1. Coordinate systems

In the equations (2)(3), the terms with subscript“ H ”

expresses the hydrodynamic force acting on the

hull. The term with subscript “ P ” indicates thrust

produced by the tug’s propeller. The subscript

“ R ” symbolizes rudder, and the “ T ” indicates

the towing rope. Regarding the towed ship, we

assumed that only hydrodyanamic forces were

acting and towing line tension acted on the ship’s

hull. The method of the expression for these terms

are the same as in reference (Kijima et al. , 2000).

expressed as ε 1 , and the rope’s angle in relation

to the towed ship is expressed as ε 2 .

The equations of the motion for tug ( i = 1) and

towed ship ( i = 2) can be written in following

form.

For the estimation of the course stability of tug-

towed ship systems, we paid close attention to

the sway and yaw motions of ships thought to

be most sensitive to course stability. First, if we

assume that the velocity of the ships U 1 are U 2

are equivalent and that changes in the heading

angle ψ 1 and ψ 2 , the drift angle β 1 and β 2 and the

towing angle ε 1 and ε 2 are all small, we can apply

Routh-Hurwitz discriminance for course stability.

Then, the following diﬀerential equations can be

obtained by the linearization of the equation (1).

( m i + m xi ) L i

U i

cos β i −

β i sin β i

+( m i

+ m yi

) r i

sin β i = X i

U i

( m i + m yi ) L i

−

U i

sin β i + β i cos β i

(1)

ψ ψ 2

β β 2

ε 1

ψ ψ 2

β β 2

ε 1

k 11 k 12 ···

k 17

. . .

) L i

U i

+( m i + m xi ) r i cos β i = Y i

2 U i

L i

= N i

k 21

(4)

. . .

. . . k 67

+ U i

L i

( I zzi

+ i zzi

r i

k 71 ···

k 76 k 77

The superscript “ ” refers to the nondimensional-

ized quantities, and its method is the same as in

reference (Kijima et al. , 1990).

where

If the real part of the eigen value of the matrix in

equation (4) are all negative, then we can conclude

that the tug-towed ship systems can hold their

courses steadily throughout manoeuvres.

L i : length of ships,

β i : drift angle of ships,

U i , r i : velocity and angular

velocity of ships,

m i : mass of ships,

m xi , m yi : x i , y i axis components of

added mass respectively,

I zzi , i zzi : moment of inertia and added

moment of inertia respectively

As for the expression of external forces and mo-

ment shown in the right hand side of equation (1),

external forces acting on tug and towed ship are

expressed below.

3. CONDITIONS FOR CALCULATION

The principal particulars of the tug-boat for calcu-

lation is shown in Table 1, and the towed ship for

calculation is shown in Table 2. As for the towed

ship, we considered 2 conditions pertaining to the

disabled ships as shown in Fig.2. In addition, the

hydrodyanmic forces acting on the towed ship’s

hull, that is, X H 2

, Y H 2

, N H 2

X 1

= X H 1

+ X P 1

+ X R 1

+ X T 1

In numerical calculations, we estimated the course

stability for tug-towed ship systems in bowward

towing motion and sternward towing motion.

+ Y T 1

N 1 = N H 1 + N R 1 + N T 1

= Y H 1

+ Y R 1

(2)

in the equation (3)

were measured by captive model tests, and the

results of the experiments are shown in reference

(Kijima et al. , 2000).

Y 1

Table 1 Principal dimensions of tug-boat

Length(m) 85.000

Breadth(m) 12.375

draft(m) 4.616

C b

Table 2 Principal dimensions of towed ship

Length(m) 325.000

Breadth(m) 53.000

draft(m) 22.050

C b

Fig. 3. Connection points of the towing rope

VWDEOH

XQVWDEOH

O /

Fig. 2. Conditions for the towed ship

(YHQ .HHO WULP

(a) Bowward towing

4. COURSE STABILITY

VWDEOH

Taking into account the length of the towing rope

and the location of the connection points as shown

in Fig.3, we examined how those factors would af-

fect the course stability of the tug-towed ship sys-

tems. Considering the actual towing operations,

we assumed the location of the connection point

on the tug-boat ( x a /L 1 ) to be 0.25.

The calculated results of the course stability in

bowward towing motion is shown in Fig.4(a).

Horizontal axis shows nondimensionalized length

of the towing rope (= /L 2 ), and vertical

axis shows nondimensionalized location of the

connection point of the towing rope x f

XQVWDEOH

O /

(YHQ .HHO

WULP

(b) Sternward towing

Fig. 4. Course stability of tug-towed ship systems

5. FUZZY INFERENCE FOR RUDDER

CONTROL

(= x f /L 2 ).

Each line in the ﬁgure indicates the border which

divides into stable and unstable regions. In the

case of the even keel condition, it can be thought

that putting the connection point of the towing

rope on about 1 . 0 L 2 from the centre of gravity of

the towed ship can stabilize the towing systems.

However, the stable region for trimmed condition

(

In the towing operations, it is important to hold a

constant course, in addtion to lessening towing an-

gle ε 1 as much as possible in order for the tug not

to capsize. It is believed that the steering for the

tug has a considerable eﬀect on the manoeuvring

motions for tug-towed ship systems. Therefore,

we applyed fuzzy inference for the steering and

considered the heading angle of the tug ψ 1 and the

towing angle ε 1 as the parameters for the rudder

control in the numerical towing simulations.

Fig.5(a) shows membership functions as to ψ 1

and ε 1 for antecedent part in fuzzy inference,

and Fig.5(b) shows it as to rudder angle δ for

consequent part. In these ﬁgures, K ψ and K ε

represent the rate of the rudder reaction to ψ 1

and ε 1 , when those values are small, that is, the

rudder angle alters sensitively with the changes

5 . 3% L ) only appears where x f /L 2 is large.

That is, it is necessary to put the connection point

of the towing rope as far oﬀas possible from the

towed ship for the safe towing operation.

Fig.4(b) shows the course stability in backward

towing motion. From this ﬁgure, we can conclude

that the towing sternward in both conditions can

be carried out safely by the attachment of the

towing rope to a point around the stern.

0.5717

0.8299

−

ε 1

Table 3 Rules of fuzzy inference

ψ 1

N ZO P

N PS NS NB

(a) Antecedent part

Fig. 6. Relative amplitude of sway motion

(b) Consequent part

Fig. 5. Membership functions for fuzzy inference

6. EXAMPLES OF TOWING SIMULATIONS

in ψ 1 and ε 1 .“ P ”, “ ZO ”, “ N ” in the ﬁgures

represent “Positive”, “Zero”, “Negative” respec-

tively, and rudder angle δ is deﬁned to be posi-

tive for a turn to starboard. For the consequent

part,“ PB ”, “ PS ”, “ ZO ”, “ NS ”, “ NB ” indicate

“Positive Big”, “Positive Small”, “Zero”, “Neg-

ative Small”, “Negative Big” respectively. Addi-

tionally, the rules of fuzzy inference for the rudder

control are shown in Table 3.

By the use of the optimum values of K ψ and K ε ,

we examined manoeuvring motions of the tug-

towed ship systems that are given the following

intial disturbances.

ψ 1 (0) = 10 . 0( deg. )

ε 1 (0) = 10 . 0( deg. )

(8)

For safe towing operations, we estimated the op-

timum values of K ψ and K ε by repeating the

numerical simulations in which we assumed that

the initial towing speeds U 1 and U 2 were 5 . 0 knots

and considered the following conditions as initial

disturbances.

Fig.7(a) shows the variation of S with K ψ and K ε

in the case of the rope length being 1 . 0 L 2 , the

connection point x f being 0 . 5 L 2 and the towed

ship being in even keel condition when being

towed bowward. The value of S varies with K ψ

and K ε and appears to be at minimum where

the values of K ψ and K ε are 16 . 351 and 8 . 283

respectively. Fig.7(b) shows the calculated results

of the numerical towing simulation in which tra-

jectories of the ships and changes in heading angle

ψ 1 and ψ 2 , rudder angle δ and towing angle ε 1

are described. In this case, the tug-towed ship

systems are considered to be unstable from Fig.4.

Therefore, trajectories of the ships ﬂuctuate exag-

geratedly, and we can assume that it is necessary

to steer with a large rudder angle in order to hold

a constant course.

ψ 1 (0) = 5 . 0( deg. )

ε 1 (0) = 5 . 0( deg. )

(5)

Taking into account of the changes in the rudder

angle and relative amplitude of sway motion of

the towed ship “ A S ” that is shown in Fig.6, we

applyed the following equation and deﬁned it as a

parameter to ﬁnd the optimum values of K ψ and

K ε .

t 1

Fig.8 shows the calculated results in the case of

the rope length being 1 . 0 L 2 , the connection

point x f being 1 . 0 L 2 and the towed ship being in

even keel condition when being towed bowward.

In this situation, the tug-towed ship systems are

considered to be stable. The minimum point of

S appears when the values of K ψ and K ε are

25 . 451 and 28 . 348. ψ 1 and ψ 2 ﬂuctuating within

about 6.0(deg.), the towed ship follows the tug

with smaller angle of ε 1 and δ when compared

to previous case. Therefore, in order to have a

safe towing operation, it is important for the tug-

towed ship systems to be stable.

S =

δ ( t )

A S ( t ) /L 2 |

dt (6)

where, t 1 is expressed as a following form.

t 1 = 3 . 0 L 2

U 1

(7)

Then, we examined the manoeuvring motion of

the ships for a short period of time while the

ships moved forward by 3 . 0 L 2 , and picked out

the optimum combination of K ψ and K ε that

minimized the value of S .

ZO PS ZO NS

P PB PS NS

0.2

(a) Variation of S with K ψ and K ε

\ /

7XJ ERDW 7RZHG VKLS

[ /

ψ ψ GHJ

δ ε GHJ

[ /

δ ε GHJ

[ /

(b) Trajectories of ships and

changes in ψ 1 , ψ 2 , δ and ε 1

(b) Trajectories of ships and

changes in ψ 1 , ψ 2 , δ and ε 1

Fig. 7. Results of numerical towing simulation ;

Even keel, Bowward towing, =1 . 0, x f =

0 . 5 (unstable)

Fig. 8. Results of numerical towing simulation ;

Even keel, Bowward towing, =1 . 0, x f =

1 . 0 (stable)

Fig.9 shows the results of the calculation in the

case of the rope length being 1 . 3 L 2 , the con-

nection point x f being 1 . 5 L 2 and the towed ship

being towed bowward in

Therefore, we can assume that towing sternward

can stabilize the tug-towed ship systems when the

towed ship is trimmed by the bow.

5 . 3% L 2 trimmed con-

dition. It is considered to be unstable in this ex-

ample. The minimum point of S appears when the

values of K ψ and K ε are 10 . 700 and 8 . 995. When

the towed ship follows the tug, it shows a large yaw

motion throughout manoeuvres. Consequently, we

should avoid bowward towing especially for ships

with large trim angle by the bow.

−

7. CONCLUDING REMARKS

In this paper, we estimated the course stability

of the tug-towed ship systems, and applyed the

fuzzy inference to consider the steering for the

tug in order to hold a steady course in towing

operations.

Fig.10 shows the results of the calculation in

the case of the rope length being 1 . 0 L 2 , the

connection point x f being 1 . 0 L 2 and the towed

ship being towed sternward in

5 . 3% L 2 trimmed

condition. In this case, the tug-towed ship systems

can be considered to be stable. The value of S

appears to be at minimum where the values of

K ψ and K ε are 26 . 667 and 28 . 348 respectively. In

this case, both ships remain on a constant course,

−

As for the tug-towed ship systems considered to

be stable, we concluded that the ships can remain

on a constant course without large sway and yaw

motions using current steering.

As for the tug-towed ship systems considered to

be unstable, the ships are able to hold their course

while applying the present steering, however the

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