The effect of drift angle on side thruster performance

ARCHIEF

The Effect of Drift Angle on Side

Thruster Performance

Katsuro KIJIMA 54

..

_2i 'J u 52 8 Reprinted from TRANSACTIONS OF

THE WEST-JAPAN SOCIETY OF

NAVAL ARCHITECTS No. 54 AUGUST 1977

Lab.

_{y. Scheepsbotjw0}

Technische

_flogeschool

DeIft

oc

* Faculty of Engineering, Kyushu University

( 52 5

ìG

54 .179

The Effect of Drift Angie Qn Side.

Thruster Performance

Katsuro KIJIMA* member

Sununary

The decreasing side thruster effectiveness at non-zero ship speeds is a well known phenomenon. The author, in previous paper, also has discussed _{on this} matter theoretically and experimentally. And we have understood the effect _of ship speed on side thruster performance was, significant factor in ship manoeuvra-bility operating thruster. And, it should be noted that the tendency for the

thrus-ter effectiveness to increase with increasing speed afthrus-ter reaching a minimum at, a certain ship speed was confirmed experimentally. It will be considered that the flow field of reduced pressure region will exist in the intermediate _{range of hull}

and the circumference of the jet flow, therefore, the lateral force _{generated by}

the thruster will decrease in some degree because the jet of fluid

directed

normal into a mainstream of fluid _{will. be,, bent into the direction of a} maiñ-stream. 'Accordingly, it seems that the bow thruster is an effective, steering aid when backing, and the thruster should be located as forward as possible or under

the bottom of keel.

Simultaneously for a ship required the dynamic positioning a tidal current

becomes.a serious problem. On this problem, it _{is necessary to make clear the} relation between side thtuster performance and drift angle of hull. _Therefore, this paper dealt with the effect 'of drift angle on side thrUster performance the-oretiçally and experimentally. And the following conclusions may be reached.

There is no greatly effect of drift angle for the. lateral force actingon a hull generated by the side thruster as compared with the effect of ship speed.

For the moment acting on a hull, there isalmost no effect of drift angle.

For the analyses of ship motion operating side thruster, we shall be

necessary to consider both the influence of ship speed and drift angle of hull as significant fäctor.

Nomenclature

U '=ship speed

U, =jet velocity

O _{=local angle of inclination of the jet path measured from the horizontal} r,r0 =local and exit radii of the jet tube

C, _{sectional drag coefficient of the jet tube}

8 =drift angle of hull and, flat plate

E _{=entrainment rate per .unit Ieñgth of the jet tube}

$,E2,E=coefficient of entrainment function E

C =circumference of the jet tube x _{coordinate defined in Fig. '1}

180

d,d0 =2r and 2?' respectively

k =aspect ratio of flat plate

L =chord length of flat plate

1. Introduction

The decreasing side thruster effectiveness at non-zero ship speeds is a well known phe-nomenon which is due to suction fields acting on the hull, induced by the deflected jet. Al-most of the previously published information has dealt with model test results with headway on the ship. The author, in previous paper1, also has discussed on this matter theoretically and experimentally. As the results of the investigation, we had come to a decision that the decreasing side thruster effectiveness with increasing of ship speed was affected greatly by the deflection and diffusion of the jet exhausting from thruster outlet. We may consider on

this matter such as that lateral thrust generated by the thruster will decrease in some

de-gree, since the jet of fluid directed ñormally into a mainstream of fluid will be bent into the direction of the mainstream, simultaneously because the flow field of reduced pressure region

will exist in the intermediate range of the hull and the circumference of the jet

flow. From the theoretical results, in previous paper, that the lateral force decreased rapidly with increase of ship speed, and recovered slightly with more than some speed, i.e. the tendency

for the effectiveness to increase with increasing speed after reaching a minimum at a

cer-tain ship speed was confirmed, we may conclude that the exterior of the jet tube would just come in touch with surface of the hull at the minimum point of the decreasing lateral thrus-ter effectiveness. Then this means the suction fields cease to exist.

In general, the thruster effectiveness will be decreased by about 50% at a shipspeed of 3-5 knots in lateral force. Minimum performance is observed at a speed of about 5-6 knots for thrustters of medium jet velocities. As an example of the improvement on the decreasing

these effects, we have known an anti-suction tunnel has been proposed by J. E BRIX,2

con-nects opposite fields of detrimental pressure on the hull aft of the lateral thruster tunnel. This anti suction tunnel will be an effective method to remove the detrimental suction fields. On the other hand, especially for a ship required the dynamic positioning such as the ca-ble layer ship, or supplying offshore rigs in tidal current and then carrying out emergency turns within an estuary, tidal current becomes a serious problem. These ships in most cases control to keep her position or direction by means of side thruster. Therefore in most cases of critical manoeuvring problem, the conventional side thruster cannot fulfil the nautical

re-quirements. In here, to deal with the ship motion generated by the side thruster theoreti-cally, it is necessary to make clear the relation between the thruster performance and drift

angle of hull, in addition to the effect of ship speed on the thruster performance. And also, it is much useful for the analyses of ship motion operating side thruster if we can know these relations.

A number of people have experimentally investigated the influence of ship speed on side

thruster performance and the flow fields in the vicinity of the jet exhausting from side thruster as being informationed by M. S. CHISLETT. However, there have been very

lit-tle theoretical work published to date for the interference effects between drift angle and

hydrodynamic forces generated by the side thruster.

In this paper, after making some assumptions by using P.T. WOOLER4 method, the equations

of motion determining the growth and displacement of the jet exhausting from side thruster are solved numerically. Then, the hydrodynamic forces generated by thruster acting on ship

The Effect of Drift Angle on Side Thruster Performance

_isi

are estimated by the lifting surface theory. _{And it is made clear the relation between} hy-drodynamjc force generated by the thruster and drift angle.

2. _{Mathematical Model of the Jet Exhausting from SideThruster}

To keep the ship's position and direction into _{tidal current, it must be made clear the}

interference effects between the flow field _{about hull and the jet exhausting from tunnel of} the side thruster, especialy drift angle _{and thruster performance. Thus it is necessary to} make clear, firstly, the relation between drift _{angle and the path of jet center line, or the} jet diffusion and jet velocity exhausting from side thruster tunnel.

The development of a turbulent jet in _{a cross-flow is not amenable to exact treatment} because it is actually flud-fluid interaction involving a chaotic turbulent process. Difficulties come above all from the existence of a mixing layer between the _{jet and external} non-tur-bulent flow where the flow structure is extreamly complex. Thus it is very difficult to make clear exactly these problems theoretically. _{In these problems, a great deal of interest has} been take in connection with the problem of aerodynamic interference with fan-wing VTOL or STOL aircraft.

Appling here P. T. WOOLER method which was referred in previous paper,1' a simplified mathematical model of the jet exhausting from side thruster _{is considered. It is known,} en-trainment may be regarded as the inflow of

_{water at the edge of a jet, then the effect of}

this inflow on the external flow field can be represented _{by the potential field of sinks} dis-tributed within the jet, the total strength of which equals _{to the local entrainment rate.}

The following assumptions which _{are analogous to the case of H. ENDOS' method are} here used

the jet from side thruster tunnel is confined in _{a stream tube of a circular}

cross-sec-tion,

the jet velocity within the jet tube is uniform,

entrainment is represented by the suction of the _{external flow through this} inter-face, and

the rate of diffusion and curvature of the jet tube are both small.

H. ENDO cleared the mechanics of the jet mixing_{and that of the vortex formation} un-der above assumptions in the field of these flows.

As the same method that WOOLER. if the sink _{represented the suction of the external}

flow for the jet tube, and entrainment

_{rate per unit length of the jet tube as the total}

strength of sinks is denoted by E, we can now write, using the coordinate system defined in Fig. 1, the equation of motion about unit length ds of the jet tube as follows

prr2Uj -v!- = EU sin 89+CdprU2 sin O

(i)

=EUcos O (2)

_--(p,rr2U,)= ₍₃₎

where Oß=Ofl

The first term and second term on the right hand side in equation (1) represent

vely. Then the qùation (1) i-eptesents the balance of the normal 'force per unit length of the jet tube, and the equations (2)-(3) reprèsent respectively the one of momentum flow and continuity.

As we have already known. H. ENDO formualted this'entrainment function E by the

terms of the part of entrainment due to axial velocity shear and due- to the vortex motion *hiòh is proportional to the characteristiC velocity of inflow induced by the rear vorticies.

And- he has pointed out that a pair of counterrotating vorticiesfòrniing along the rear side

of a jet plays an important tole in the turbulent mixing of the jet.'

In this paper, this entrainment function E of mainstream fluid- intó unit'length of the jet

is assumed as follows, as the same thät P. T. WOOLER éxpresed V

-E -EUdsine

+PEI(Uj_Ucos6a)C V - (4)

-Vp 3 B _{1+E3Usinea/U,:} V

WOOLER' has explainèd this èxpression as follows. ' - ' V

A' fluid particle approaching thé jet and near the plane of symmetry will be more easily

en-trained by the jet than a pirticle that is moving away from the jet. The susceptibility of

the approaching particles to jet, entrainment is accounted for the first term on right hand side in equation (4) while the second term is taken under the consideration that particles moving away from 'the jet or to its side with momentum not directed towards the jet are

less tolerant to the jet entrainment.

V

Under the above assumptions, we can rewrite the equation (l)-(3) as follows

-dU_ cosO8U f15

dx' rr'U cos Os L 1+E., Sin 65/U,'

-. dr'

2Ucos

_lE

₊ ,rEi(Ucos O)

- ,(J2 cos Oa L ' 1+E3 sin O5/L1

dO tan O sin-O

+!CU0s Os)l

- CaSifl O

-irr'U2 1

-- IE3 Sin ea/U; J

irr'U cos 0 -.

-where dimensionless paraniçterS U=U1/U, r'=r/r0, x'=x/ are used.

We -see that preceding group of equations represents a - set of- differrential- equation to be

solved for U, r', O, represented the jet velocity, - local radius of the jet tube and local angle

of inclination of the jet path, respectively, as function of- x'. And it is necessary here to establish values fôr the parameter-S E.,, E,, E, and C. V

Firstly, it is necessary to determine the values of parameters E,E2, E,. We shall apply-a yematching.techi1ique by finding out-such a set of the constants as-would give the best agreement of calculated with measured paths and widths of jets in model ship which is

shown in Fig. 2, Table i and 2. In the measurement, the velocity of model ship is setted in

F=0.024. For the observation of the jet

flow exhausting from side thruster outlet, it is

made a clear distinction the jetflow.from an uniform flow by pouring a paint into the

thrus-ier inlet. Exactly, we have to investigate as coinciding numerical rsults with observed ones

in connection with paths and widths of the jet over all ship speeds, however, for convenience

Table 1- artiòulafs o( Model Ship

Table 2 Particulars of Thrtster Units

Tunnel Diameter (m) 0.0469 L» B d Cb (ni) (m) (ir') --/ 3. 000 0.553 0.123 0.479

Tunnel Axis about Base Line (m) Tunnel Axis from F. P. (m) Propeller Diameter (rn) No. of Blade 0.0555 0.3570 0.0460 4

Fig. 2 Bodj Plan and Plofile of Model Ship here the values of these coefficients are constructed at U1/U=12.8 only.

Secondly, also it it is necessary to estimate the value of C represents the sectional

drag coefficientj of the., jet tube directed normally into an unifórm stréam. We must éxactly

estimate the value of C of fluid tube into an uniform stream, however, this value in here is approximated,to that of the drag coefficient of a solid cylinder.

With these assumptions, numerical results of the jet center line, the rate of the jet dif-fusion and decreasing of the jet vèlocity are shown in from Fig. 3 to Fig. 8.

3. Calculation of lateral force acting on hull generated by sld& thruster

It is known the velocity field induced by the jet is determined by replacing the jét bya

sink-doublet distribution, then the

distribu-tion of sinks represents the entrainment

effect of the jet, and the doublet distribution

represents the blockage effect of the -jét.

In this paper, lateral force and moment

about midship actingon hull operating side thruster are obtained numerically by apply-ing the above mentioned method.

Side thruster: will be placed on the

lead-ing edge of the rectangular wlead-ing, asshown

in Fig. 9, after making the assumption which is applied the rectangular flat plate of

equi-valent small aspect ratio in place of the

hull. Then, the locus of the center line of jet exhausting from side thruster will be on

the plane containing x and z axis.

--Jet

CenterLine.-Fig 9 Coordinate System

Considering an element of the jet, length 8, centerèd at (X,O,Z), the sink 'strength per

(8) unit length in y direction will then be given by

mEE'T's 08+

-

pE2(UjUcos 88)ird l6s1+E3Usin 08/U, J

With the help of Fig. 1, we see that the z axis component of the induced velocity at a point P(x,O,O) due to a sink will be given as follows.

2rEz(Ucos 08) 1 Z' sec 0 2iIfr' _{dx' (9)}

ws

=

_-1[, sin 08+ E3 sin08/U1JZ'2+(X'x')2 Z'2+(X'x')2+(dr')2

Where dimensionless parameters U=U,/U, r'=r/r0, X', x', z'=X, z, z/, d=d0/d are used. From the geometry, if the strength of the doublet distribution is given by

27 rL& SinO8, (10)

we see that the Z axis component of the induced velocity at the P(x,0,0) due to doublet will be

i 3,r tan O8dv'2

= i) [(X'x')1+Z'2] 5/2

_-1 (((x'X')2Z'2) sin 208+2(x'X')Z' cos 208] dx'

2,rdy'2 3C(x'X')sin 08+Z' cos 0)2 ldX' (11

41r [(XI_x)2+ZI] L (X'x')2+Z'2 J

Then the Z axis component of the total induced velocity at the P(x,0,0) due to sink and doublet will be

W1 1 rE, sin O8+?!:z:T;_c0s OB) 1 Z' sec 08 2d0'r'

4,r J_1L 1+E3 sin 08/Ui] Z'2+(X'x')2 [Z'2+(X'x')2+(do'r')2]

dx'

i

r" 32v tan O8dr'2

5/2 [(x'X')2Z'2) sin 208+2(x'X')Z' cos 20e] dx'

1 _(" 2ird2r'2 3((x_X')sinOa+Z'cosO8)1dX., [(X'x')2+Z'2]312L (X'z')2+Z'2 J

(12)

On the other hand, when a flat plate wing with small aspect ratio, with chord length L and span length b, is inclined at the angle of attack fi with respect to the free stream

velo-city U, W. BOLLAY8 have obtained theoretically the normal force on a rectangular flat plate wing by introducing the idear of the system of horse-shoe vortices. In that case, it is shown that an equivalent vortex system replacing the wing consists of a distribution of bound vor-tices which is assumed constant along the span and variable intensity along the chord, and

at the ends of span each bound vortex is assumed to leave as a straight trailing vortex at

some angle to the wing. In the case of calculation at the velocity field due to the jet of a side thruster, it is a matter of course that we must be considered a distribution of vortices

which intensity vary along both the chord and span, however, this paper used his method in order to simplify the calculation.

Then, the Z axis component of the induced velocity at a point P(x,0,0) due to bound

vortices and a pair of trailing vortices, as the vortex strength

r(f)

at x=e, is given as follows.

b ILIZ

(f)r

₊

-

i_{_LIZ} L (xC) i/(x_C)2+(b/2)2 (xE)2 Sifl2 (fi/2)+(b/2)2 (xC) COSI (fi/2)

+

_{[(e)2 j2 (ß/2)+(b/2)2)}

_{/(x_C)2+(b/2)2]} (13)

(13). WB =

--;;--J- r(e') 2 _{2 cos (f12)} 2(x'f') cos° (f/2) ide'

+

_{(yf/)2 jni (fl/2)+k2)o/(x/_f/)2+kzJ}

As the boundary condition here, being assumed that also the induced velocity _{at the wing}

surface due to the jet flow exhausting from side thruster is follows

_{to that due to the}

dis-tribution of vortices as above mentioned assumptions, we can write as follows,

WJWB (15)

Then, in order to get the pressure distribution over the wing, it is necessary to solve this

integral equation for r(f'). In this paper, we shall restrict ourselves to finding the total

force alone. _{This makes it necessary to satisfy the integral equation only in the mean. We} assume some reasonable distribution for the vorticity over the chord such _as

=

Ua(f')}/ j;

where a(f') represents an arbitrary function with respect to f'.

We get then,

k _f

a(f') /1f'

K(x', e')de'

=

2r J

'e'V

i-pe'

where K(x', f') represents a kernel function of eq. (14).

However, this integral cannot be exactly calculated by any of the conventional method. Now

then, after writing _{=cos8, and f'=cosO, we assume the representation as follows, using}

Sugai71 method ; X!

a(f')'K(x', f') = a(O')K(C, O')

2 041 ¡+1

= Lpa(0)K(8, O)ECg COSqO cos qO'

gO whe re çCp, eq = 1/2 for p, q = O, 1H-1 Cg = 1 for p, q 4 0, 1+1 And we get, k 1 I _{/1+cosû' cosq8'.sínOdO,}

-2ir(j+1)o

ep.a(Op)K(O, 8p)E LgcosqOpgo

_{1coso' cos Ocos 8'}

k ¡41

[1+cosolFi

-

_{2(1+1) p-o}E Lpa(O,)K(O, E e0'COSqO.sin O+Lo]

p_o

Then letting

01+1

C [1+cos _{E ea.cosqo.s1nqe+eo]}

°iTL sinO

g-o

we can rewrite as follows

clt'+

1

4(1+1)

c

e _{f 1(_-1)P+s 1+cos O}

+ i

TÏ1. 2 cosOcosO5 2 J

The Effect of Drift Angle on Side Thruster Performance 185

-i

(x'_f')V(x/_f)2fk2

(x'f)° j2 (ß/2)+k°

Cs

Cp.

2(1+1)

We can transform the above integral equation into .thealgebraical expression such as

w,=--Ea(ep)K(O5, O,)C

After getting the solution of a(8,,, we can easily rewrite as follows,

'l+coso' 2 ¡+1

r(O') y'

_{1c0' ¡+1}

e,Ua(8p) EE5 cos qO. cos qe'

and for the normal force to the wing,

¡+1

E e,a(O,)(1+cos O,)

.1-t-i D-s

for the moment about center of area.

N' epa(epX1+2 cos e,+cos 2e,) - (21)

where Y' = i( fiLbU2). N'

=

N/(. L2bU2).

4. Experimental Investigation

To compare with the above mentioned the theoretical results, the experimental

investiga-tion for model ship was carried out. The lateral force and moment acting on hull generated by the bow thruster was measured with respect to drift anglé wheñ thé ship had some drift angle fi. The model ship shown in Table 1 and 2was used and those forces were measured by oblique towing test. In that case, to investigate the interference effect of the flow field

for ship hull and jet exhausting from tunnel of side thruster, lateral forces were measured

in three cases, i.e. for without fin being conventional condition, for with fin of length 2cm and 5cm on the front edge of the tì.innel exit of the model ship such as shown in Fig. 2-1. respectively. And these results were shown in Fig. 10 and 11.

Fig. 2-1 Thruster Outlet with Fin

In addition, the author has mentioned in previous paper that the most significant factor in influence of ship speed on side thruster performance would be the rate of deflection and diffusion of the jet tube exhausting from thruster tunnel. In connection with this problem,

the lateral force acting on hull with fin on froút part of thruster tunnel was measured also with respect to ship speed. These results are shown in Fig. 14 and 15, where are represented as the comparison with the lateral force (Y(V)) or the moment about midship (Ñ(U)) at ship

The Effect of Drift Angie on Side Thruster Performance 187

speed U and the Y(0) or H(0) at ship speed zero, respectively. 5. TheoretIcal and Experimental Results

The final set of the parameters determined by the method in previous section is as fol-lows,

E1=0.40. E2=O.5024, E3=8.0, Cd=l.BO

By using these parameters in the integration, the curvature of jet path, the ratio of diffusion

in jet flow and reduction in jet velocity are estimated numerically such as shown in from

Fig. 3 to Fig. 8 for the coefficient of UI/U (=3.2, 4.59, 6.40, 12.8)

as the ratio of the jet

velocity (U,) at the tunnel exit in thruster to ship speed (V). respectively.

We see that the rate of deflection of jet center line will reduced with increasing of the

values of UI/U or e.

But the ratio of radius of jet tube into uniform stream to that of

thruster tunnel does not almost change with respect to drift angle fi, and also that of deduc-tion in jet velocity is the same.

To be here noticeable, this calculation was carried out to estimate the jet flow

ex-hausting from side thruster into uniform flow in case of without hull, however, it must be

considered exactly the interference effect of the jet flow.

On the other hand, the results measured the lateral force and moment acting on a hull

with respect to drift angle will be shown in Fig. 10 and li.

Denoting the lateral force

acting on a hull non-operating side thruster by Y(L), and the composed force with the lift force acting on hull indipendently and the reaction force due to thruster operating by

Y(L,R). we assume simply the lateral force generated by side thruster as follows

Y(L,R)Y(L)=Y(R)

And now, we shall consider the lateràl force due to side thruster denoted by Y(R) as the

comparison with the lateral fcrce Y(fi) at drift angle fi and Y(0) at zero drift angle. This

result is shown iii Fig. 12.

Under the same assumption, the result for the yawing moment is shown in Fig. 13.

In Fig. 12, we can see that the lateral force has a tendency to be increasing slightly for

positive fi. and to be decreasing for negative. fi. This means, the deflection of jet ceñter line is small when the direction of jet flow exhausting from side thruster is the same one to

the uniform stream. And also in the region òf negative fi, it may be supposed these ten-dency reasonable from that the jet flow is opposite direction to the uniform stream.

We shall see the theoretical results agree almost with the experimental values in-this

figure, that the value of Y(fi)/Y(0) has a tendency to be increasing slightly with fi. and there

is almost no effect of U,/U for Y(fi)/Y(0) in small drift angle. From the comparison with the theoretical results and experimental values,, we shall be able to approximate in the

region of small drift angle than about 10 degrees as follows, Y(fi)/Y(0) 1.0+0.7fi2(U,/U)

Also then Fig. 13 shows the moment about midship generated by side thruster as function of drift angle. It may be considered that there is no effect in regard to this moment. There-fòre, it does not matter in practical application even though the following approximation_for

N(fi)/N(0) is used. ,

N(fi) IN(0) 1.0 .

the front edge of the thruster tunneL outlet in hydrodynamic forces acting on hull.

The author, in previous paper, has investigated theoretically on the problem that the

side thruster effectiveness at non-zero ship speed were decreasing. From the numerical

re-sults, we understood that the deflection and diffusion of the jet exhausting from thruster outlet were the most significant factor on this matter. This problem is here investigated experimentally. As shown in Fig. 14, the lateral force acting on a hull generated by thruster

will decrease rapidly with increase of ship speed. However, the rate of this decrease for

the ship with fin of 5cm length will be slightly small comparing with ship withou tfin. It can be considered that the deflection of jet flow is forced to decrease because of the fin setted on the front of thruster tunnel outlet. And this also shows that the rate of decrease

of lateral force when backing is small as compared with ship without fin. It seems therefore, the deflection or difusion of the jet flow have significant effects on side thruster performance.

In regard to the moment as shown in Fig. 15, it seems there is almost no effect of forward

speed. These mean that the center of pressure move to forward with increase of ship speed from the initial point when ship stopping.

As describing in previous paper, the existence of reduced pressure region which existsin the intermediate range of the hull and circumferenceof the jet tube will be significant

fac-tor on that performance.

Finally, as mentioned also D. E. R1DLEY7, it can be concluded that the bow thtucter is

an effective steering aid when backing. And the thruster should be located as forward as

possible, not only for the purpose of miximizing the yawing moment arm, but also to

mini-mize the hull area exposed to the deflected jet when going astern.

To summarize our interpretation of these results, we can explain that there is no greaf-ly effect of drift angle in regard to the lateral force and moment generated by thruster, the

lateral force only increase slightly with increase of e. Accordingly, it can be considered the effect of ship speed is very significant than that of drift angle on side thruster performance.

6. Conclusion

A ship required the performance to keep the constant direction or location agáiflst the tidal current, such as the cable layer ship, has to control the ship's heading with the aid of

side thruster etc, when a conventional rudder is of greatly reduced effectiveness. Various

ways has been considered to use the side thruster effectively. We also are necessary to find

out the relation between the thruster performance and ship speed or drift angle to make clear the ship motion theoretically. In connection with the problems on ship design for

using side thruster effectively, or the problems on the characteristic of ship motion by means of the auto-pilot, it will be mainly investigated theoretically and experimentally the relation between drift angle and thruster prformance in this paper. In addition, it will be also inve-stigated experimentally the effect of ship speed on side thruster performance.

The following conclusions are reached in the preceding.

There is no greatly effect of drift angle for the lateral force acting on a hull

gene-rated by side thruster in small drift angle. But, in the region of drift angle more

than 10 degrees, we shall have to consider also the effect of drift angle on side

thruster performance.

For the moment, there is almost no effect of drift angle. Ship speed affects the most on side thruster performance.

ship speed.

Acknowledgment

This work has been carried out as part of the research with aid of the Ministry of

Edu-cation of Japan (No. 165101).

The calculation has been carried out on FACOM 230-75 of the computer center of Kyushu University. The author wishes to express his sincere gratitude to Mr. Y. NAKIRI who made

his effort for the accomplishment of the experimental program Reference

K. KIJIMA and S. ¡NOUE ; "Influence of Forward Speed on the Manoeuvrability of

Ship with a Side Thruster". Trans. of The West-Japan Society of Naval Architects, No. 51, March 1976.

J. E. BRIX and O. BUSSEMAKER "Lateral Thruster with Anti-Suction Tunnels". ist

North American Tug Convention Organized by Ship & Boat International.

M. S. CHISLETT and O. BJORHEDEN ; "Influence of Ship Speed on the Effectiveness of a Lateral Thrust Unit". _{Hydro-Og Aerodynamic Laboratrium, Report No. Hy-8,1966.}

P. T. WOOLER, G. H. BURGHART and J. T. GALLAGHER "Preñure Distribution _on

a Rectangular Wing with a Jet Exhausting Normally into an Airstream". J. of Aircraft,

vol. 4, 1967.

H. ENDO ; "A Working Hypothesis for Predicting and Inducèd Velocity of

a Jet

Ex-hausting at a Large Angle into a Uniform Cross Flow". Trans. of The Japan _Society for Aeronautical and Space Science, vol. 17, 1974.

W. BOLLAY "A Non Linear Wing Theory and its Application to Rectangular Wing

of Small Aspect Ratio". Z.A.M.M., 1939.

K. Sugai ; "A Linear Approximation for the Lifting Surface with Low Aspect _Ratio". The Society of Naval Architects of Japan, vol. 117, 1965.

D. E. RIDLEY ; "Observations on the Effect of Vessel Speed _{on Bow Thruster}

Perfor-mance". S.N.A.M.E., 1970.

190 30

e---

:-20

.-.-ß. 8 12 16 20 24 28 32 6 40

Fig. 3 Theoretical Result of the Jèt

CenterLine

-0 4 8 12 16 20 24 28 32 36- 40 5e.

Fig. 5 Theoretical Result of the Jet

Center Line

54

Fig. 7 Theoretical Result of the Jet

Width 30 Vd. L%59 _{e____} 20

/Z

IO 30 10 12 Io

t'

6

\

4 '/d.

Fig. 4 Theoretical Result of the Jet

- Center Line

-0 4 8 - 12 16 20 24 28 32 3 40

Fig. 6 Theoretical Result of the Jet Center Line

0 ¿ 8 12 16 20 24 28 32 36 ¿0 X/d.

Fig. 8 Theoretical Result of the Jet

Velocity

-10

Fig.

0.05 Y

The Effect of Drift Angle o Side Thruster Performance 191

-0.10

-e- WITHOUT FIN 0rpm.

-)+- WITHOUT FIN 3000rpm.

-- WITH FIN(R.-L.)3000r.pm.

2cm

-t-WITH FIN(RL)300Orp.m.

5cm 10 Measured Lateral Fe acting ön

Ship as Function of Drift Angle

-l0

Fig. 11 Measured Yàwing Moment acting

on ship as Function of Drift Angle

N

03

0.02 0.01 --0.04 -ü05 _{WITHOUT FIN 0rpm.} -*- WITHOUT FIN 3000rpm. -0.06-WITH FIN(R-L.)3000r.p.m. --W!TH FIN(R-L.)300Ôr.pjn. 5cm )CAL 0 _EXP.(u459) -10 -5 0 5 10 15 20 _{_ - O} 5 10 15 20 13

Fig. 1 T e R lation between L Fig. Te Relation between Yawhug

enerated by Side Thr-

J1L.'.

_{generated by Side}

o

-0.6 - O.2 0 0.2 04 0.6 OB

U/j1

Fig. 14 Lateral Fo eaíFúnction of Ship

Speed

Y(o)

-e- WITHOUT FIN -.* WITH FIN2cm(R-L.) G-WITH FIN5an(R.-L.) D

.-Ncu No ft-c £ A5 £5 -0.8 -0.6 -0.4 -02 0 0.2 0.4 0.6 0.8 U/U1

Fig. 15 Yawing Moment as Function of