Some studies of the course stability of towed ships systems

(1)

ABSTRACT

As we have discussed in this Journal (Nos. 42,43,44 and 46,the course stability

for a towed ship system is influenced by the parameters: a) number of towed ships, b) fore- and aft-towing points, C) towing ropes' lengths, e) means of steering, f) course stability criterion of a ship g) radius of gyration, and h) resistance of towed ship. The effects for these parameters are as follows:

The larger.the number of towed ships, the poorer the course stability, is, and while stable towing of one towed ship is possible by adopting a suitable towing point and the tow rope length, it becomes impossible to tow more than two ships without steering.

The effect of aft-towing point is small, and in the case of forward towing point, it is better to place it away from the towed ships' center of gravity.

A longer towope ?LJvJ.des more stable towing than shorter towropes.

The course stability of a towed ship system increases with the increase of a ship's course stability criterion, and this effect becomes smaller for two and more towed ships.

By means of steering, the course stability increases remarkably.

The course stability of same sized towed ship is better than the large towed ship in the case of the same parameters of each ship.

When the radius of gyration in-creases, the course stability grows worse, even for one towed ship and when the radius of gyration ìs greater than O.50L, it is

impossible to have stable towing without steering.

As the resistance of the towed ship increases, w

ebair

tabie lowing of the towed ship system

SOME STUDIES OF THE COURSE STABILITY OF TOWED SHIPS SYSTEMS1

BY S. INOUE 2 K. KIJIMA2 M. MURAKAM42 K. SAKATA S. LIN 2 -20-TECHNISCHE

_UNIVffi&r

Ñchtef

Mekejweg 2, 28

_{co D&ft}

Tel.:

When an unstable ship like a barge is towed, its course stability is very poor (described in d )and to obtain stable

towing for towed ships such s barges, the course stability of the barge itself should be improved by utilizing skegs. In this paper, towing experiments for a siigle barge and tugboat and oblique test of the barge for the conditions shown in table

2, have been performed and the results are as follows:

1) When the skeg is filled to the barge, because of the increment of Y' and

the decrement of N', course stability of the towed ship system improves very much, so that when the high lift skegs like the slotted flap skeg and the slotted flap with rotor skeg are fitted to the barge, it is not difficult for us to imagine that the course stability of this system improves.

2) For the towing test of towed ships system, due to the effect of towed

cize. (see Ref. .1,2,3,4), it is not suitable to test in towing tanks with

narrow breadth. In other words, it is neces-sary that they be towed by a tugboat in

a wide surface area performance facility. TRANSLATION'4

1. Introduction

The authors have up to now made nu-merous theoretical studies concerning the towing of towed vessels. The course

stabi-1TRANSACTIONS OF THE WEST-JAPAN SOCIETY OF NAVAL ARCHITECTS, No. 50, August 1975,

pp. 65-74

2Department of Naval Architecture, Faculty of Engineering, Kyushu University.

3Matsukura Kaigi Co., Ltd.

4Prepared by R. Latorre, Department of Naval Architecture and Marine Engineering Tiniverstt.y of Michigan.

(2)

lityof a towed vessel, is determined by as-suming the towing rope as a weightless string which only transmits the tension force. If

the towed vessel can be considered stable with the above assumption, then it not

neces-sary to be concerned with the mass and elas-ticity of the towrope influencing the course stability.

_{El], (2], [3],}

(41.

When unstable vessels such as barges are considered as a towed ship system, their course stability performance is extremely poor. _{This paper discusses the course}

stability of a towed barge with skegs fitted to both sides of the stern in order to

improve its course stability performance. This is examined by towing experiments as well as oblique towing tests which _are presented with a discussion of the towing ship-towed vessel system experiments.

II. FACTORS INFLUENCING THE COURSE STABILITY

In the t.wing problem, the following factors are influential:

a) number of towed vessels, b) size of towing vessel and towed vessels, c) _length of the towing rope, d) location of towing point (forward and aft), e) the quality of each vessel's eoursestability performance,

f) the size of the radius of gyration with respect to the center of gravity of each vessel, g) the increase and decrease of the tension force which can be said to represent the increase and decrease of vessel's resistance, and h) steering. In (a) wheir the number of vessels increase the towing becomes unstable (l],[21. In

(b) when the towed vessel becomes larger, the course stability becomes poorer as

shown in Fig.2.

In (C) when the towrope becomes longer the course stability improves, but it is not desirable for it to become too long from the viewpoint of turning performance and navigation.

In (d) it is better if the forward towing point extends a distance ahead of the bow. An example of this is the generally used bridle system. Also, it will be best to locate the center of gravity behind the towing point.

In (c) the course stability performance of each vessel can be described by:

A = YN - (mfY').N'

(where Y'...Ye.. . are called the static and

rotary derivatives respectively which can be experimentally as well as theoretically determjned When ¿ is large the vessel's course stability performance is good, and when MO the vessel becomes course unstable, Fitting skeg

r-us-

1..irye

increase in

-21-the value 9f A. The skeg derivatives are de-noted by L8 and

Lr The derivatives of the

vessel with skegs are denoted by a bar-The following relations are obtained when

the skegs are fitted in the stern: = Y + L8'

iß' N8'- b'L8'

r''

Y+

Ñ N '+ b'L'

r r r

Here be is the ratio of the distance between the skeg's center of pressure and the vessel's center of gravity to the length of the ship. It is possible to write:

L'

b'L'

r B

Basically the derivatives LB' and Lr'are associated with the lift L generated by the skegs which causes a corresponding increase in A and an improvement in the course stability performance. Consequently skegs which cause increases in LB' or high lift may be preferable. With a larger value of A, it becomes possible to use shorter towrope lengths and to locate the towing point closer to the vessel's center of gravity.

In (f) when the radius of gyration becomes larger, the vessel becomes course unstable. An example is shown in Figs. 3 and 4.

In (g) the increase of resistance causes an improvement of course stability. Con-sequently, not only from this point of view, but also from a large improvement in A (discussed in (e)) it is reconunended to fit skegs.

In (h) when the vessel is steered in pro-portion to its course, its course stability is extremely good,and there is a remarkable improvement in the course stability of the towing boat itself.

III. _{EQUATION OF MOTION FOR N NUMBER OF}

TOWED BARGES FITTED WITH BRIDLES Fig.l shows the i-1 to i+l towed vessels of a towed barge system. Here we consider the equilibrium conditions

for forces by making use of the notation used in previous four articles (1], [2],

[3] , [4]

From Fig.l it can be seen that: Cosc1

B/2i,

_gmbh

=

2m1'm In the case when c< iT/2

- from

(3)

T ' cos(!. _{- ait) +} T .'.cosCt a li 2 2i ) Forces in y direction:

= T' cos e,

_i

2. T ' cos (T e ) = T ' sine = T .' e. (2) ii i. ii i ii T1 sin (- - a1.) +

+ Tsin (. - a .) = T'

Moment around the z. axis:

2i. i.

i

2.

Now assuming that is very small it is possible to make the approximation:

T.'f.

T 'f

coses, 1 sin e3, Cj and

_0li

a2

- _L L],

+ 1 2i e.

Then from (2) the following expression is written: T1 _{+ T2!} Ti,' f 2j (2) T1! - T2.' T.'

X=X_1_a_1_

_- +

Consequently the external force and moment, hich are exerted by the towrope segment

of the vessel with Bridle, are expressed as follows:

The external force in the y direction:

f f +f cos

T2' cose

2i T (T1 -T2 )

resultin:'

2i

2L.

_B. X

_{= x0-'E}

_{k-lkkk =}

= (T.'

e.)

= T.'e.

k1

B 2t i i

- r

(ak_jk_1+fkk+k.

Moment ajuuiid

the

.

exis:

+ °k

i

li i. T B. T2. =

(ak_lekl+(fk+k)ek

2Li

(3) = (T1

-T2)

(f .+f .) T.'f. = T."

i

12. 2i > i T

i

where it is assumed that (f .+f .}> f.

li 2i i.

> 1

Next the case when

Cj

-

a1.

will be considered. From the character-istics of the towrope T2 must be equal to zero and consideratiOn is again given to the equilibrium

of

fuzces:

f.

T.'B.

f.

,

i

Tr

li.

i. 2i T1.

- cos (. - e) +

2L. 1. 3. '(f .,+f .) T.'f.

=T

13. 2i > i i li L. i. L i 2.

From comparing (3) and (4) it is clear that both relations are exactly the saine. On the other hand from geometric conditions:

(5)

Y. = Y. -a. O.

-Le.-(f .+f .+.)O.

i. i-1 i-1 i-1

1 3.

li

2i i.

i

are obtained. Differentiating (5) with respect to time t and assuming that

here X0,Y0 are the coordinates of the towing vessel, T ,T1, .. . are the values

obtained by dividing T1T1by 1/2pAU

where p is fluid density, A1=dL.

(L. vessel length, d1vessel draft), ¡J. vessel forward velocity.

Taking the forward velocity of the towing vessel as U results in:

k0=u0cos (001-B0) =U0

i (7)

(6) (4)

(4)

i0=U0sin(80+B0) = 130(004-B0) From (6) and (7): = U0 _a . T.' le. i

iii

B=6+ß

e.

-o ]. U0 (ak_1Ök_1+(fk+tk)Òk+kk) - (N8

N61)

_{[(ak_l+fkl+ £kl)}

k_l]

-1

k=l

Substituting (8) into equations (1) and (2) of [11, after rearranging results in the following equations of moiton for the ith towed barge:

L.

f. +L.

(1)2

i

₁₈

yi U. L

i

-

t-(N8'-N').E (k_lck_l)

= 0 +i__

r

_,

_.-m.+(k.

.i.i)

y _{' )L1+(f.+L.).} U L yi ]. i2 2 f5]. .(Y .' + .Y .'

il

. Bi i.

j

i. L.

+1

_{.'+(k. +l)Y} B il

'+T.+le.+m

1

J

1. y]. (8)

i .. IV INVESTIGATION OF COURSE STABILITh

PER-E((a,. l+fk+.ek)Ok_l) FORMANCE OF TOWED VESSELS BY TOWING

kÌ

_{VESSELS BY TOWING EXPERIMENTS}

i (y .'+Y ').

E

_{((ak_l+fk+.ek)ekl)} k=l L. - (Y

.'+

Y ')e " Bi Si. o - i+i 1+l _myi_ , , L..e.

-(Y.+Y. )8 +m.

Bi

Si

o

71

u2 i (Y .'+Y .') . Bi 6i

i

L. i

+ T1'c. -

T.+1'c+i+m.-..

E (Lklk1)

k=l + (y

kl

Bi S k-1 k-1 23-L.

n.(-)2

_iU1

e.

+:__

f

(N .'+(k.24)N6.')L. -ri.

(f.+ .f.).q

o

i i

Bi -N ')

J&j

, a i

- T.1

ç

-

(N8+ N1)c.

+ (N8.' -N _)e + (N8

_Ndi')ß

(10)

These relations are exactly the saine as equa-tions (5) and (6) of [11 when is taken as the length to the tip of the bridle and

e. is taken as the length of towrope from the tip of the birdie.

The quality of the towed vessel course stability performance changes with the 5ie of. the towing vessel and towed vessel as shown in Fig.2. However, it does not follow that the course stability of the towing ship-towed vessel system is equal to the towed vessel course stability perfor-mance when towed by the towing tank carriage.

Therefore, a towing ship - towed vessel system should be used when investigating

the course stability performance. (Here the towing ship-towed vessel system desig-nates the towing vessel and all towed

ves-sels.)

To investigate the course stability of the system a study was conducted by changing the towrope length and examining the path of the vessels.

Naturally, it is preferable to calcu-late the course stability performance using the towed vessel(s) and towing vessel's derivatives. However since the.cou,- sta-bility performance is qualitatively shown in Figs.2, 3, and 4, experiments were conducted to determine the

minimum

tow rope length namely the limit rf

th

_{"ourse stability}

(5)

in Table 1. The skegs were fitted in pairs. Two types of skegs were used:

the Mariner skeg with a symmetric air-foil section and the Deformed Skeg with a chambered air-foil section which are shown in Fig. 5.

Table 5

U = 0.367m/s,F5=O.O7423

In the experiments radio controlled steering was used. The towrope length was changed and the model ship's course stability performance was investigated by photographing the towing path whii the model moved forward. These results are shown in Figs. 7, 8, and 9 while a comparison for g=UL=2 is presented in Fig. 10. The results are:

Without the skegs the course stability performance is poor, so that whatever e is used, straight lind towing is not possible.

With the Mariner skeg when £>6L, straight line towing is possiblewhile with a shorter towrope length it is im possible.

With the Deformed skeg there is ade-quate stabi1ty for straight line towing when

Consequently although the deformed skeg has a slightly higher value of resistance

than the mariner skeg in forward motion, it enables course stable performance to be achieved with a short towrope. V EXPERIMENTAL STUDY FOR IMPROVING THE

COURSE STABILITY PERFORMANCE OF A SINGLE TOWED VESSEL.

One way to improve the course sta bility performance of the towing ship-towed vessel system is to improve the course stability performance of the individual vessels. Consequently the various improvements from the mariner, deformed, slotted flap and slotted flap with rotor skegs were investigated, Figs.

5,6, and 7, to determine the best skeg

type.

(1) Investigation Using Free Running

Models

It is known that when a model which was towed from a towing tank carriage

t c'rnstant qr.d ;i :sd Jt' ere'-

rUll.

.4

tests there is a reduction in the model's speed,and it has a slightly poorer course stability performance. To simply decide the relative characteristics of skegs free running model tests were used.

Figs. 11 to 14 present the paths of the free running models when the skegs are fitted to the barge. From Fig.lO, it is clear that without skegs,a straight line path does not occur and the stability per-formance is bad. It is also evident that the course stability performance improves when the mariner skegs or deformed skegs are fitted. The course stability performance with the deformed skegs is better than when the mariner skegs are fitted.

Fig.11 shows the results from using the slotted flap skeg. From this figure when n increases the stability performance

is improved. Thus when rp2O° a straight running is possible. However, when n>70°

'Ifl

:CUrF,!1d

i-he .t-bilify perfor-mance becomes poor. The model paths of the case when the slotted flap skegs with rotors are fitted are shown in Fig.l2. The turning rotor causes a high lift force. In addition, when n is increased, the stability becomes better so that even when n>70° good results are obtained. A comparison of slotted flaps skegs with and without rotor action is shown in Fig.

18. When ri is small the turning rotor

does not cause a large difference, but when n>70° its effect is clear. Therefore,

-...rtder tod that the turning rctor causes a large lift force and the c-;urse stability performance improves. From these experiments,it is therefore antici-pated the stability performance is improved by skegs in the following order:

Mariner skeg Slotted flap sieg

DfLIed skeg

Slotted f 1p skeg with rotors [best]

(2) Oblique Towing Experiments

To detemine the hydrodynamic forces in each case, the improvement

in

the course stability performance of the barge model was ir.'restigated by comparing the effects of the various kinds of skegs on the hull.

rr.i

was done by .blique towing ex-peri'..r's. These tests were made using the

carroe of the University of Kyushu's Faci... of Engineer.r Naval Architecture's ship motion basin. The skegs used in these tests are shown in Figs.5 and 6. For the case of the slotted flap skegs with rotors experiments were made by changing the revolutions n of the rotor as shown in Table 2. Tugboat Barge 0.800m 2.500m B 0.228m 0.600m d 0.027m 0.143m Dispi. 0.436kg 188.26kg CB 0.651 0.875

(6)

and N8'

The experimental results are shown in Figs. 15 to 25 and the corresponding Y3' and N8' values are shown respectively in Figs. 24 and 25. Table 3 summaiizer the values of X'. Y3' and N8' with no skegs, mariner skegs and deformed skegs. When the mariner skeg and deformed skeg are f itted.to the barge, there is not a very large difference in the values of Y in comparison wich the large differences in the values of N8' When the deformed skegs a is.-c1. '.':eir. ;.hei.e i .

able reduction in the N3' value and a large contribution to A. In addition, when the slotted flap skeg is fitted there

s a remarkable increase in the values .f Y wth increasing r

It

.s

dc....

of Iß' is negative when is ne

O,

as shown in Fig. 25, and stall nocurs

-n>10°. As FigS indicates as tneroto turns er.nrgy .s supplied preventing stall so a high lift force results. Although there is ar increase'

n Y3' wcr

both and n become larger in Fig.24, there is little noticeable difference n

the value of N3' in Fig.25.

Fina1lyt is

anticipated that the course stability performance is increased by skegs ir. the

following order:

Marinee Skeq, Slott.d f p skeg Deformed skeg Slott-d f ;keg

w4t,

r r

Table 2

The skegs shown in Fig.5 were fitted to both sides of the bottom of the barge stern.

They form the three-component, force measure-ments at midships, the hydrodynamic forces

in the x and y axis and the moment around the z axis were measured tc obtain

Table 3

25-only a small effec-.

IV CONCLUSION

From the previous results the following conclusions were obtained.

The major effects of the skegs on the course stability performance are to in-crease L3 and to decrease N8 , ah well

as _{caüsing a slight increase in resistance.}

Consequently, it is conceivable that the stability performance becomes good when a high lift skeg such as the slotted flap skeg is used.

In straight line towing ..n the towing tank where the towed vessels are towed from the carriage, che effective towing vessel becomes extremely big and the towed vessel extremely small. As Figs. 2 and 3 indicate this represênts a situation different from the actual one. _Thereforeto investi-gate the 'course stability performance of the towing ship-towed vessel system, it

is necessary to conduct the experiments using a towed vessel system in an installa-tion with a large unrestricted water

sur-face.

The authors express their sincere thanks to Messrs. Nagiri, Yamada, and Yamamoto fcr their cooperation in experi-ments.

REFERENCES

i

moue,

ci.. and et-al., "The Course Stability of Towed Boats," Journai of the Societ', of Naval Architects of West-Japan, Nc 42, July, 1971 pp.11-25

[In Japanese]

2) T.nrme., nd T,.im

"Th

Course Stàb..jj.y of Towea Boats(continued)," Journal of the Society of Naval Archi-tects ,f West Japan, No.43, March 1972, pp. 35-44 [In Japanese]

moue,

and Lim S., "The Course Stabili.1 of Towed Boats-When the Mass of the 'fc'. ope is Considered," Journcl of - 'eSocicy of Naval Architects of

We- Japan No.44. august- 1972, pp.

29-14

(In Jpanse

In..te, S. and Ljitt S. "The Course StabLlity of Towed Boats-Effect of the Towzig Points and Restricted Water-," Journal of the Society cf Naval Archi-tects of West Japan, No.46, August 1973 pl5-31. [In Japanese]

Winifred R. Jacbs, "Estimation of Stibility Derivatives and Indi;es of Various Ship Forms and Comparison with Experimental. Results," Davidson

boratc-y, D.D.C. September 1.964

o.7-U.

e n 0° 5° 10° 20° 30° 500 70° o o o o C O O O 800 3 0

0

0 2000 o o o o o o o Without skeg - Mariner skeg Deformed skeg X' 0.04316 0.04711 0.05409 Y3' 0.3124 0.3210 0.3672 N' 0.1428 0.0937 0.0607

(7)

3.0

2.5

2.0

1.5

LO

0.5

0

1.0

2.0

3.0 FIG. 2 Notation: q = p = f/L

6) Lim, S., "On the Steady Turning of Towed Ship System," Journal of the Society of Naval Architects of Japan Vol.137, June 1975, pp177-185.

(In Japanese) English Version pub-lished in Selected papers from the-Journal of Society of Naval Architects of Japan Vol. 14, 1976 pp. 43-55.

ONE TOWED SHIP WITH TUGBOAT

=O.00671, r=O,C =L/L,K=O.24L

A

=0.00671

S

---- A..=-0.00758

- --- -.:

&= 0.06494

-26

7)

moue,

s.

ad et.al.

"Some Considera-tions on Tanker Model-Ship's Emergent Steering Avoidance," Journal of the Society of Naval Architects of West-Japan, No.44, August 1972, pp.83-94.

[In Japanesel

TRANSLATOR'S NOTE: The Interested reader can obtain a summary of

El] [2] ,

[3] , (4] in:

moue, S., and Lim, S., "The Manoeuverability of Towed Ships System," PROCEEDINGS

14th International Towing Tank Conference, Vol. 2, Ottawa, Canada, 1975. pp. 571-580.

0.5

I

-'

« =1

¡

ONE TOWED SHIP WITH

TUGBOAT

PI

_{=0.00671. r =0. C = LulL}

¡

K =O.35L

3.0-

e

-

A 0.00671

S

_{----A, =-0.00758}

=2

.

-,6 =

I -I

2.5

20

1.5

1.0

40

L where: 2. f U I I 5.0

0

1.0 2.0 3.0 4.0 5.0

Towed Vessel Length. FIG. 3

Length of towing rope between vessels.

(8)

pp

3.0

2.5

2.0

1.5

1.0

0.5 ONE TOWED SHIP WITH TUGBOAT

4 :0.00671, r =0,K =Radius of

Gyrat ion

=0.00671

=0.00343

,

=-0.00758

(

U

FIG. 4

(Notation as in Figs. 2 and 3)

-ONE TOWED BARGE WITH TUGBOAT

PATH OF

BARGE

D E FOR M E D

SKEGS

k: 0.50 L

K :0.24L- 0.

PATH OF

TUG BOAT

FIG. 7

ONE TOWED BARGE WITH TUGBOAT

Yf

q>i.O

X

-27-ONE TOWED BARGE WITH TUGBOAT

MARINER

vf q =2.0

SKEGS

_{q =6.0}

PATH OF

BARGE

ONE TOWED

S KEG S

WITHOUT

V

MARINER

---DEFORMED

PATH OF O

BARGE

FIG. 5

PATH OF

TUGBOAT

FIG. 10

PATH OF

O

_{PAH OF}

X

BARGE

TUGBOAT

FIG. 9

PATH OF

X

TUG BOAT

FIG. 8

BARGE WITH TUGBOAT

q = 2.0

3.0

40

5.0 Ej 1.0 2.0

vf

WITHOUT

q = 2.0

SKEGS

- . - q = 6.0

(9)

0.30

0.20

Y,

0.10 FIG. 11

WITHOUT SKEG MARINER SKEGS DERO SKEGS

SKEG

WITHOUT

MARINER

----DEFORMED

---SLOTTED FLAP

(q =0°)

°

_10°

FIG. 16

150

_20o

-28-XI f

0.015

0.010

0.0 05

FIG. 13

(.3_O rpm 800

SLOTTED FLAP SKEGS

WITH ROTORS

SLOTTED FLAP SKEGS

WITH ROTORS

W=

0rpm

w=800rpm

_.w2OOO rpm

20°

40°

600

8Ö

FIG 15

SKEGS

MARINER

WITHOUT

'

DEFORMED

SLOTTED FLAP

10°

15°

20°

o

(10)

0.30 SLOTTED FLAP SKEGS

WITH ROTORS w=Orpm

0.10 N'

I

0.015

0.010

0.005 o

0.005

0.30

VI I

0.20

10 0°

0.015 0.0 0

0.005 N'i.

O

-0.005

-0.0

10-50 ₁₀₀

15°

20°

0.015

0.010 70°

0.00 5 00

N'f0

-0.005

SLOTTED FLAP SKEGS

WITH ROTORS WOrpm

SLOTTED FLAP SKEGS

WITH ROTORS W=800rp

q. 70° I I

N f

0.15

,.-10°

15°

jo°

_0.10

SLOTTED FLAP SKEGS

WITH ROTORS W800

rpm

FIG

0.30

90

O Y'

io:

'0

0.20

0.1 0

50:

1.50

Y, 1.00

0.50 ri = 70°

_50°

SLOTTED FLAP SKEGS

_{/ 30°}

WITH ROTORS

w =2000rpm

SLOTTED FLAP SKEGS

WITH ROTORS

W

= 2000rpmO.._

5° 10° I I I

r1 = 70°

FIG. 23

SLOTTED FLAP SKEGS

WITH ROTORS

0rpm

-I--.,

----w

800 rpm

---w

=

_.-'r--.

0 Ti 10°

20° 30° 40° 50° 60° 70° 80°

FIG. 24

SLOTTED FLAP SKEGS

WITH ROTORS

-w=

0rpm

-W

_{800 rpm}

---W =2000 rpm

Iv

_flAc

I-t

-30°

_20°

_40°

_60°

_80°.J.!...

00

S

q=70"

_o

0..05 PTG. 25 2

-0.10

-29-10° I

5°

10°

'5°

20°

FIG. 20

10°

FIG. 22

15°