Directional stability of towed ship

17 SEP. 1982

ARÇHIEF

DIRECTIONAL STABILITY OF TOWED SHIP

)(cos

) ( sin J3 .cos f3. ) + fli1r1cos f31 = L . Û

12

1.

y

'

i

i

lab. y. Sheepsbouwkund

Technische Hogeschool

Deift

In the problem of towing ships, the important thing _{is the directional}

stability of tug-towed ships system. _{The. stability will be affected by the}

size of tugboat and towed ships, the length of tow-line ànd _{the attaching}

point of tow-line to the ship, etc.,. _{This ñote presents the cQmputed}

results on relation between the directional stability _{of one towed ship and}

the length of tow-line.

EQUATIONS OF MOTION FOR TUG-TOWED SHIPS SYSTEM

Linear motion with a small perturbation from a original course is here considered, and the following assumptions has been _made.

Froude number of the towed ship is sufficiently _{so small that}

free surface effects can be ignored, .and towing line is always

taut.

Wake effects between tugboat and towed ship are also ignored.

(3)Çj's

elasticitÒf

The equations of motion about ith ship for _{tug-towed ships system based on}

these assumptions may be given as follows,

where the suffix i represents that i = O and i 1 .for tugboat and for one towed ship respectively if the system consist of _{one tugboat and one towed}

ship. ( c.f. Fig.l )

Let the distance between center of gravity and the fore-towing point of ith towed ship be f1 , and it to the aft-towing point of tugboat be _{a1_1}

so we. can get the following equations;

(2)

cYi =

+ Y1i + T(

Ni - N.Ç31

- N1r

-According to the équations (1) , (2) and

= + Ej , we get two differential equations of motion for towed ship as function of

₉

For the directional stability analysis _{, we can find the eigen value 7 for} the differential equations of motion by replacing e1= Aiet and = Bjet.

[31 CONPTJTED RESULTS

This note deals with the directional stability for one towed ship being towed by one tugboat.1 The main particulars of towed ship (VLCC) and tugboat used here for computation-are showinTäIe. 1.

The computed results when the tugboat is keeping a straight course are

shown in from Fig.2 to Fig.5- , where the value of a representing the towing o

point of tugboat is zero. In these figures, the non-dimensional parameters p and q ( p = f /L , q = 21/L1 ) represent the distance between attaching

point of towing line and cénter of gravity in towed ship and the length of

towing line respectively. In this case, stable région of the directional stability for towed ship will be decided by the condition, p)Np/Yp , and by the solution of the eigen value _{for the differential equations of motion.}

From these results, we can see that the stable region will be extended _n

full load or in trini by stern.conditions, _{but the stability of towed ship in}

ballast and trim by bow conditions will be much poor.

Fig.6".-8 provide the results for when towing and towed ships are

identical VLCC as shown in Table 1, and when towing point is located on after

perpendicular (A.P.) which a0 = L0/2 . In this case, the stable region is

ecreased comparing with the results in when tugboat is smaller than towed ship and when simultaneously a0 _{= Q}

[4] COÑCLUDING REM RXS

Directional stability of the tug-towed ships systn is affected by the

parameters such as fore and aft aingpoin of towing

towing I1ie, number of tugboat and towed ship, directional stability criterion

of a ship and size of tugboat and towed ships.

From the computed results and refering some papers''2'3, the following

remarks may be given.

(i) _{The stability of tug-towed ships system improves together with the} increment of the directional stability criterion of a ship

Generally, a long towing line provides stable towing, but the maxmutnlength will be imited by some conditions.

The directional stability of towed ship will be much stable in full

load and in trim by stern conditions.

By means of steering of towed ships, the stability of tug-towed ships

system improves remarkably.

REFERENCE

S.Inoue and et al.

" The Course Stability of Towed Boats "

Jour. of the Society of Nàval Architects of West Japan,

no. 42 , 1971.

S.Inoue and S.T.Lirn 't

Turn±ng the Tug-Towed Ships System due to the Steering of the Last Towed Ship and the New Course Keeping Test "

Trans. of West-Japan Society of Naval Architécts, no.51, 1976.

S.T.Lim

" Research on the Nanoeuvrability of Tug-Towed Ships Systems "

Doctor's Thesis in Kyushu University, 1976.

NOMENCLATURE (,.

L1 length of ith ship

1.y've1ocity

drift angle of ith ship r1 : angular velocity of ith ship

added mass of ship in x and y directions respectively

ni : added moment of inertia of mass of ship

C1 ,

Ni : external force and moment acting on ship in x,y direction

and around z axis respectively

linear derivative of hydrodynamic force acting on ship

Npi Nri : linear derivative of moment acting on ship

NR : rudder force and moment in tugboat

T1 : tension to ith towing line

Main Particulars of Towed Ship and Tugboat

Table i

/

4

-Towed Ship (VLCC)

Tugboat

Lpp

3100m

Lpp

B

_B

80m

d

d

23m

1.0 1.5 1.0 0.5 0 UNSTABLE lt

Full Load and Eveñ Keel Cond.

(TABtE

\Ballaatìand Even Keel Cond.

:5.0 V 10.0

b-q

Fig.) _{Directional stability of towed ship in ballast and} even keel conditions.

5.0 _lO.Oz

Fjg.2 _{Dreciona1 stability of towed ship in full load}

Ballast and T by Stern Cond.

Ballast and Trim by BOW Cond.

UNSTABLE.

-5.0 _10.0

Fig.5 _{Directional stability of towed ship in ballast}

and trim by bow ( - 1% L1) conditions.

6

q

o _{5.0 10.0}

q

Fig.4 _{Directional stability of towed ship}

in ballast and trim by stern ( 1% L1) conditions.

p20

Full Load and Even Keel Cond.

p 2.0 1.0 1.0 STABLE 1.0 UNSTABLE 10 20 40 50

Fig.6 _{Directional stability of towed}

ship in full q

load and even keel conditions _{when L0 = L1.}

UNSTABLE

Ballast and Even Keel Cond. STABLE

STABLE

O 10 20 ₃₀

40 50

Fig.7 _{Directional stability of towed}

ship in bállast

and even keel condition when _{t0 L1.}

Ballast and Trim by Stern _{( l%L1) Cond.}

0 _{10 20 30}

40 50

Fig.8 _{Directional stability of towed ship in}

Ballast

and trim by stern ( 1% L1) condition _{when L0 L1.}