ESSO OSAKA Tanker manoeuvrability investigations in deep and shallow water, using PMM

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"ESSO OSAKA" TANKER MANOEUVRABILITY INVESTIGATIONS IN DEEP AND SHALLOW WATER, USING PMM

* * _** *

p. Bogdanov, P.Vassilev, M.Lefte-ova, E.Milanov

ABSTRACT

Results of the experimental investigation of the effects of finite water depth on the hydrodynamic forces and moments acting on ship model moving in the hori-zontal plane are presented. The structure of the mathematical model used is

verified after the multiple linear regression and dispersion analysis methods. Comparison between the full scale and predicted ship manoeuvrability charac-teristics are made. This work is carried out at BSHC, Varna, Bulgaria with the help of PMM.

INTRODUCTION

It is universally acnowledged that the problems of ship manoeuvrability predic-tions in different condipredic-tions are in the center of the general problem related to ship's navigational safety.

The increased ship dimensions call the necessity of accounting for water depth in many harbours and water restrictions. The significance of carrying out research work in this area was confirmed by the XVI ITTC (Leningrad 1981). The programme of

the Manoeuvrability Corinittee contains "Esso Osaka" tanker model tests for investi-gating the water depth influence and composition of experimental data gathered from different tanks with the full scale trials results of the Exxon Int.Company

(9). Analogous are the recommendations given by the XVII ITTC (Goteborg 1984).

EXPERIMENTAL INVESTIGATION OF KEEL CLEARANCE INFLUENCE ON HYDRODYNAMIC FORCES

AND MOMENTS ACTING ON "ESSO OSAKA" TANKER MODEL 2.1. Experimental Equipment and Ship Model

The experimental investigation of water depth influence _{on the tanker model} hydro-dynamics, is carried out in the BSHC shallow and deep water tanks. The main tank dimensions are the following: length 200 m; breadth _{- 16 m; depth of the shallow} water tank - from O to 1.5 m; depth of the deep water tank - 6.5 m.

The Planar Motion Mechanism (PMM) allows carrying out of static and dynamic tests (sway and yaw forced motions) of the model in the horizontal plane. It is

instal-*)

Bulgarian Ship Hydrodynamics Centre, Varna, Bulgaria **)

Shipbuilding Centre, Higher Institute of Mechanical and Electrical Engineering, Varna, Bulgaria

led on console platforms at the rear end of the towing carriages. The shallow water tank platform (Fig.1) is vertically mobile and can be fixed at the neces-sary level above w ter with the help of hydraulic system,while the deep water tank platform is fixed. In this case the height of PMM positioning is regulated by means of special spacers.

The model is given forçed lateral and angular oscillations using automated elect-romechanical system. The period of oscillations varies from 5 to 50 sec. The maximum amplitude of the lateral motions is 1 m, and of the angular + 34°. The power of the system generating forced oscillations allows to test models of up to 90 kN waterdisplacement. During the experiments, inductive transducers with range of measured forces O 1000 N are used.

Data are taken directly from PMM and stored on magnetic disc using minicomputers PDP 11/lo and 11/34 located on the towing carriages.

The "Esso Osaka" tanker model is manufactured at X _{40 scale and principal} geometric model characteristics are presented in Table 1.

Table i

Principal Geometric Characteristics of "Esso Osaka" Tanker Model

2.2. Test Conditions

The choice of model test conditions is predetermined _{by the program of the full} scale trials conducted. Model hydrodynamic _{characteristics are investigated at}

Characteristics Dimensions Length between perpendiculars, m 8.125

Breadth, m _1.325

Draught at fore, m 0.545

Draught at aft, m 0.545

Mass, kg _487.570

Block coefficient, CB _0.831

Midship block coefficient, Cm 0.998 Prismatic coefficient, Cp 0.830

Centre of buoyancy, XB _0.258

four .Ç. ratios (h - water depth, T - draught); 1.2; 1.5; 2.0 and 11.9; The

ad-vance speed of model corresponds to the average full scale trails' speed (7.2 knots and is: V1 = 0.5848 rn/sec (En = 0.0655). The model is tested also at speed

V2 = 0.2848 m/sec, corresponding to ship's speed at manoeuvres 'stop" - 3.5 knots = 0.0319). In this case the experiments are carried out after model propeller reversing. All experiments are conducted with fully equipped hull.

The revolutions of screw propeller model at all relative depths are determined accounting for the difference between its frictional resistance and the full scale ship resistance.

To provide the complete set of model hydrodynamic characteristics, the fol-lowing modes of motion are realized (Fig. 2):

Steady Motion Tests

Mode A - static drift angle and speec tests; Mode B - static rudder angle and speed tests;

Unsteady Motion Tests

Mode C - pure swaying tests;

Mode D - yaw and drift angle tests;

1'lode E - sway and yaw tests; Mode F - surge tests.

Node E tests are chosen due to the following considerations:

To fuller reproauce the combined hydrodynarnic effects _{when moving at drift} angle 13 (lateral speed y) and angular speed r;

To investigate and substantiate the structural _{form of the equation terms,} accounting this interaction phenomena.

The procedure of conducting this model _{tests, as well as the way of obtaining}

the hydrodynaîiiic characteristics _{are discussed in (3).}

The choice of forced oscillations' period is _{determined by the requirement that} measured forces be independent of frequency. The _{circular frequency chosen, is} w = 0.3768

_sec1

_{when corresponding to the period and frequency}

of forced oscillations: T = 16.666 sec and f = 0.06Hz _{and is smaller than}

the _{minimum resonance circular frequency of the}

standing waves in the tanks at the relative depths considered.

2.3. Experimental Results

Some results of the experimental investigation _{of water depth influence on the} hydrodyriamic forces and moments acting _{on the "Esso Osaka" tanker model, are} graphically presented in Figs. 312. The _{symbols and indices of the kinematic}

parameters are in compliance with the standard symbols and co-ordinate systems recommended by the X ITTC.

The hydrodynamic forces X,Y and moment N measured at steady tests are reduced to non-dimensional coefficients in the following manner:

C X,Y Cn

N

(1)

X,/

_{1/2pU Lpp l/2pU Lpp}

In sway mode, the non-dimensional coefficients and are obtained lx,y,fl lx,y,fl

after processing the time series of the forces along their first Fourier's harmonic components.

X,Y,N (t) = A coswt B sinwt

lx,y,n lx,y,n

-

; 61n

A1,

_1q 1x,y Bi 1/2pU Lpp 1/2pU Lpp where:

Aix,y,n - cosine component of the measured force or moment (out-components), Bixyn - sine component (in-components).

At the forced yaw oscillations, the non-dimensional coefficients are obtained after processing of measured forces and moment in the form:

X, Y, N(t) = A1 sirìwt + B cosit x,y,n lx,y,n where:

Aix,y,n - sine component (out-components), - cosine component (in-components).

Index i is omitted further in the text.

The analysis of experimental data shows that reduction of water depth leads to con-siderable chnge of almost all hydrodynamic forces and moment, acting on model.

The analysis of the dependences of the lateral force coefficient Cy and moment Cn as a function of the drift angle (Fig. 3 and 4) shows that when reducing the relative depth, the force strongly increases and at = 1.2 and angle 3 = 100 it is about 5 times bigger than that in deep water, as simultaneously, its non-linearity also increases. The influence of the shallow water on the moment is also strongly formulated (Fig. 4), but here the reverse tendency can be detected, towards reduction of its non-linearity with reduction of the water depth.

Figs. 5 and 6 present the dependences of the lateral force and moment coeffici-ents acting on hull, from the rudder angle 5R Their change with reduction of

(2)

5.

keel clearance is more slightly manifested.

At that, the increase of force is bigger than that for moment, which leads to the shifting of the point of force application far away ahead the midship.

The shallow water effect on the damping force and moment is considerable (Figs. 7 and 8). Accounting for the presence of centrifugal component in the measured hydrodynamic force it can be deduced that damping strongly increases in smaller depth/draught ratios. The non-linear character of the hydrodynamic dependences

is heightened, which for the force is stronger manifested

The reduction of the relative water depth leads to increase of added mass in transverse direction (Fig. 9) and added mass moment of inertia (Fig. 10). The shallow water effect on added mass

iS

remarkably greater, than that on added mass moment of inertia.

Analysing the non-dimensional force coefficients related to the combined hydro-dynamic effects (Figs. 11 and 12), we can conclude that at the traditional com-bination of yaw rate of turn and drift angle (lateral force): r'<O, 13<0 Cv'> 0) for left turns the force varies much stronger whereas minor variations are obta-ined for positive 13 (y' > 0).

3. PREDICT1UN 0F "ESSO OSAKA" TANKER MANOEUVRING CHARACTERISTICS

3.1. Mathematical jvjodel

The derivation of mathematical description of ship motion in deep and shallow water conditions is made using the multiple linear regression and dispersion analysis methods.

Accounting for the fact that when solving this problem, samples from the general experimental set of data are used, and the estimations obtained for the coef-ficients as well as for the whole mathematical model are with degree of relia-bility whichshould be validated, then the process of mathematical model developmer has the following stages:

- choice of mathematical model structure; - estimation of its coefficients;

- obtaining the statistical characteristics of the coefficients and analysis of the modtl.

The derivation of the mathematical model is made on the basis of the following assumptions (7),(6),(3):

- the nature of dependences of the hydrodynamic forces and moments on the kine-matic parameters in each test modes, allow that they be presented as 3rd order polynomials.

- taking into account the physical picture of the flow, the longitudinal forces are even function of the kinematic parameters y', r' and while the lateral forces and moments - odd functions.

- the dependence of the longitudinal force on ship propulsion ratio is assumed quadratic, and that of the longitudinal force and moment - linear.

Accounting the stated so far, the specification of the mathematical model is made, on the basis of analysis on the following dependences of the

non-dimen-sional coefficients of the hydrodynamic forces and moments of the kinematic motion parameters.

Mode A tests:

y',' +Y'.fl +Y'.v'fl +Y'

Iv'jv' +Y'vIIH.VV'lfl +Y',.v'fl2 +

Y' 1.v'3 = Cy; v'v'v Mode B tests: + Y'

Y.ÔR

+ Y'n.n +

RnR

+

'R!RV

RIRnRR!

+ + +

RR5RR3

= Cy; Mode D tests:

(m'+Y'ri).r' +YH rI'''

+Y'rrtri.r'3 +Y',.f'

=Cy(t) (4)

Mode E tests:

(_m'+Y'r,).rl Y'i.v' +(-m'Y',)

+Y'.1.f'' +Y',

.vv'j +Y'rvI

.r'v

_{+Y'vi!rj.v'r'}

+Y'rir,.r'r' +Y',,1.v'3 +Y'riii.r'3 +

+Y',,,.r'2.v' =Cy(t)

Analogous in form are the dependences for the moments of yawing. The choice of adequate regression equation is made using the multiple correlation coefficient R and F - ratio (1),(2). For evaluation of the significance of coefficients, the

Student crierion is used (1) (2).

The results of the statistical analysis of experimental data for yawing moments obtained at mode A testing, are given in Table 2.

Four simulation models are considered, for which coefficients estimation are ob-tained, as well as the other characteristics necessary for statistical analysis STO - standard model error, t - coefficients' ratios, coefficients of multiple

correlation R and Fisher's ratio F. Also, the tabular values tî-for evaluation of coefficients' significance and FT-for evaluation of the significance of the model-included (i.e. for evaluation of R significance).

The obtained results allow to make the following analysis of the structure of the observed dependences.

Table 2

Mathematical Model No.

Coefficient Values ( 10e)

Model Statistical Characteristics

Nv Nvrì _{NVIVI Nvlvlrì} Nvnn Nvvv STD F _FT R t-i-1 _{-1645,2 262,8 516,9 -14,9 -427,2 7038,7 047.10k 1405,2 2,71 0,9992 2,056} t - ratios 0,71 0,68 0,47 0,48 0,47 1,23 2 -1667,5 85,3 489,1 -18,7 - - 0,49.101645,1 2,82 0,9989 2,056 t - ratios 5,01 0,56 4,09 .0,60 -3 _-1572,3 97,8 - -32,6 - 10005,2 O,50.10 1624,1 2,82 0,9990 2,056 t - ratios 4,84 0,52 - 0,56 - 4,2 4 -1680,0 435,0 364,0 - - - 0,52.10'115045,0 3,03 0,9987 2,056 t - ratios 52,2 6,5 _________ 11,8 - -

-4odel No.1 in which all linear, quadratic and the IIItd order functions are

included, has high coefficient of multiple correlation R. The equation terms con-siderably influence (F>FT) the output parameter (coefficient Cn) - In it however, all coefficients prove insignificant (t _< tx). This leads to the conclusion that the useful information is distributed comparatively equally over large number of coefficients, and for that reason, each one of them becomes insignificant. The attempts to optimize the mathematical description introducing the quadratic

(model No.2) or incomplete polynomial of IIItd order (model No.3), show that the coefficients of multiple correlation remain practically constant. As a whole the models are significant (F>FT), but some of their coefficients are again insignifi-cant.

Considerably better results are obtained with the choice of model No.4. The model has high coefficient of multiple correlation, it is adequate, and the assessment of the coefficients after Student's criterion confirm their significance (for all

coefficients t>tT).

In an anlogous way the form of particular mathematical expressions describing the hydrodynamic influence in the different test modes, is specified. Adequate regression dependences with significant coefficients are obtained. An exeption is the coeffi -cient N' , , . Its contribution is small (t<tT) at ct=O.05 and water depth ratio

.;=

1.2.v V

The final mathematical model , describing the hydrodynamic load in deep and shallow water, obtained as a result of statistical processing of the experimental data, has the following form:

Equation X:

(m'-X'ùi).ú' = X'0 +

X'.

X.2

+ X'vIviV'2

+ X',,.r'2 +

X'6.SR2

+

+ (_m'+X'vr).v'r' + X'V,v, .V'2 +

X6fl.6R2n

Equation Y:

(m-Y,).''-

= y' + +

Y'.v

_{+ (_m'+Y'ri).r'}

+

6RR

+

'v1V'

+

.v'!v'

+Y',,.r'r'

_6RRRIR

+Y,,,.v2r

+

+ Y1 , , ,.v'r'2 + Y' 6 n2

vrr

6R R (5) Equation N:

(I-N'i).- N'.,.

= N +

N'.

+ N'.'» + N',.r'

N'6 6R +

N'i.v'n

+

N'6.6Rn

+ _N'vi v' y' + N' 'r'' Ir'! + N' j

RI6RI +

N'

6R2

+ r N'vivir.v'2r' + N',iri.v'r'2

9

It would be interesting; to point out that the mathematical model obtained has a structure very similar to that commonly used "absolute square" model

(7),(8), and in this connection it is a confirmation of the widely applied "cross-flow" concept (6) with small Froude number values.

The values of the coefficients in the equations of motion (5) for depth draught ratios 1.2, 1.5, and 11.9 are given in Tables 3,4,5.

3.2. Results

The prediction of the manoeuvring characteristics of the tanker "Esso Osaka" is performed using the mathematical model (5) with the aid of the program package for ship handling prediction on the base of PMM test results (4). The geometric and kinematic characteristics of a large part of the manoeuvres carried out with the full scale ship are simulated. Part of the results are given below.

Conventional Turning Circles

The ship's turning characteristics for 35 degrees left rudder at the three draught ratios given in Figs. 13,14,15. The analysis shows good agreement between predicted characteristics and fuliscale data. Greater discrepancy occurs at the smallest h/T value with advance and transfer. It should be

remembered, however, that the fuliscale data are corrected for wind and waves disturbance.Besides, there are no data for ship hull mass distribution.

Zig - Zag manoeuvres

The results from zig-zag manoeuvre characteristics prediction at

R I= 20/20

for different water depths are shown in Figs. 16,17 and 18. For port entry type manoeuvres the first yaw angle overshoot varies from 9.7 degrees in deep water to 10.9 degrees in medium depth (h/T = 1.5), to 7.2 degrees in extremely

shallow water ( = 1,2).Corresponding full scale ship motion characteristics are respectively: 9.50,11.20, and 7.8°,which indicates a very good agreement.

Coasting Turns

Simulation results for the coasting turn to the right with 35 degrees rudder show that the ship turns at all relative depths. Initial turning is greatest at medium water depth and least in deep water. The full scale trial results confirm this, with the exception of medium depth at which the ship reverses

slightly toward the end. Açcelerating turns

The characteristics of this manoeuvre are investigated at relative depths

h = 1.5 and 1.2. In this case the discrepancies between simulation and

full-ale measurements are more essential. The predicted tactical diameter at

Table 3

Non - dimensional Coefficients in Equation X

= 0,0655

Relative Water Depth h/T

11,9 1,5 1,2 X't

*lO

92,2 131,5 141,0 X'v'r' 1264,5 1487,2 4990,6 X'r1r' 164,3 437,4 442,6 X'o -106,7 -136,0 -216,4 -22,2 -21,7 75,1 X' 128,9 158,3 141,3

XSRR

-54,0 -165,7 -180,0

XSRSRn

-20,0 -27,6 -67,0 Ri = 0,0319 X'o -99,0 -135,0 -204,0 X'r 138,0 90,0 34,0 X' -13,0 -30,0 -43,0 J

Table 4

Non - dimensional Coefficients in Equation Y

11

Fn= 0,0655

Relative Water Depth h/T

11,9 1,5 1,2

y''

_{-1694,0 -3513,3 -7456,2} YIf' -87,9 -130,0 -150,0 Y'v' -2090,0 -3275,0 -8972,0 -330,4 -294,0 0,0 Y'v'

v'I

-1507,0 -19000,0 -47923,0

Y'r'

816,4 982,4 1343,8

y'r'Ir'I

169,4 224,9 1302,2 Y'v'r'r' 6700,9 10673,4 47580,8 Y'r'v'v' 0,0 0,0 -5237,9

YOR

310,0 330,0 444,0 210,0 210,0 _210,0 135,0 60,0 0,0

YRIÖR

-340,0 -220,0 0,0 Y'o 2,0 4,0 6,0 2,0 4,0 6,0 rn 1843,8 1843,8 1843,8

Table 5

Non - dimensional Coefficients in Equation N

i

= 0,0655

Relative Water Depth hiT

11,9 1,5 1,2 N'cr' *10e -28,2 6,6 6,6 N'f' -90,6 -90,6 -130,0 N'y' -910,0 -1680,0 -3100,0 90,0 135,0 613,5 452,0 364,0 0,0 N'r' -338,5 -347,9 -376,3 N'r'jr -179,4 -315,9 -635,2 N'v'r'r' -3000,5 -5847,6 -18991,0 N'r'v'v' 0,0 0,0 2618,7 N'GR -155,0 -160,0 -222,0 N'SRn -105,0 -100,0 -101,6 -67,0 -30,0 0,0

N'RR

170,0 110,0 0,0 N'o -1,0 -2,0 -3,0 -1,0 -2,0 -3,0

scale effect related to discrepancies between model and full scale ship propeller operation conditions.

Stopping manoeuvres

Simulation results are obtained for stopping from slow speed with 35 degrees right rudder.The comparison between predicted characteristics and full scale trial results shows a good agreement, except lateral daviations of the ship's CG, which have a positive sign. The fulisize measurements show that the deviations at medium and shallow water are negative.

Spiral Test

Simulation results at all depth/draught ratios are shown in Figure 19.Predicted turning rates versus rudder angle results agree very well with full scale

measurements at medium and shallow water. Results of full scale spiral test in deep water show that the ESSO OSAKA is marginally dynamically stable; i.e. no definite "loop". The predictions indicate that in this case the ship is unstable and has a narrow loop with a dimensionless height at about 0.15. 4. Conclusions

The possibility for prediction of the marioeuvring characteristics of the

tanker "Esso Osaka" by PMM model tests results is investigated. The full scale ship trial data are used for comparison. As a result of the investigations the following conclusions can be drawn;

- the decrease in water depth leads to significant changes in a large part of hydrodynamic forces and moments;

- the ship's temporary characteristics during its manoeuvring predicted

with the aid of the synthesized mathematical model agree very well with full scale measurements;

- more significant differences are observed with respect to the values of some geometric elements of ship turning circle paths ( advance and transfer

at

4

= 1.2 ). Again it should be pointed out that the large part of the differences between predicted and full scalecharacteristics of nonlinear motion in its unsteady phase are due to the absence of accurate data for ship inertia characteristics. This is confirmed by the fact that the corre-spondance between stationary motion parameters is very good;

- a certain non-correspondence is observed with respect to predicted ship directional stability in deep water ( it is analysed on the basis of the

initial sector of the spiral curve ). The predictions indicate extent of the instability, whereas the full scale data show that a ship is marginally stable;

- the predicted characteristics of accelerating turns show ship reaction less stronger than that obtained during full scale measurements.

Literature

Boianov E., Vouchkov I. "Statistical Methods for Modelling and Opti-mization of Multiplefactors Systems",Ìechnika, Sofia, 1973.

Draper N. "Applied Regression Analysis Statistics". Moscow, 1973, ( in Russian).

Lefterova M. "Experimental Planning for PMM - Tests' XIII SMSSH, BSHC, Varna, 1984.

Milanov E. "Development and Adoption of a System for Ship Handling Prediction after PMM Model Test Results", Dr Thesis, Leningrad, 1983 ( in

Russian ).

Seber J.I.F. "Linear Regression Analysis" Moscow, 1980 C in Russian ).

Sobolev G. "Ship Handling and Shipping Automation' Leningrad, 1976,

C in Russian )

Abkovitz LA. "Lectures on Ship Hydrodynamics - Steering and

Manoeuvr-ability" HyA Pubi. Hy-5, 1964.

AltmannR.J., Goodman A. "Description and Operation of Large - Amplitude Horizontal PMM", Hydronautics Inc. Technical Manual 8099-1, 1982.

Manoeuvring Trials of the 27800 DWT Esso Osaka in Shallow and Deep Waters, Report Number EII4TM.79, Exxon International Company, January, 1979.

)IUL AM MO119S 8L

UI

tapON VNVSO OSS3

O

SOj WWd

1.

V

X

FIG. 2

À3ASIC MODES OF Pi1M

_TESTS

lip

_,p

O.-- h/T

1.2

t.-- h/T = 1.5

x

h/T=2.O

h/T=

LATERAL FORCE COEFFICIENT VERSUS DRIFT ANGLE,

F

= 0.0637

O--- h/I

1.2

k--- h/T

1.5

D---- h/T

-30 -20 -10

FIGI 6

YAWING MOMENT COEFFICIENT

VERSUS RUDDER ANGLE,

F

= 0.0637

-0.001

6[deg]

2b 30 10 20 30

FIG, 5

LATERAL FORCE COEFFICIENT

-0.003

_{VERSUS RUDDER ANGLE,}

Fn = 0.0637

-0.4

FIG, 7

SIN-COMPONENT OF LATERAL FORCE VERSUS r,

F

= 0.0637

-0.3 -0.2 -0.1

-e--- h/T= 1.2

2I h/Trn 1.5

x

h/T=2.0

=

FIG, 8

SIN-COMPONENT OF YAWING MOMENT VERSUS r1

F

= 0.0637

0.002

I

-i

-0.6

VERSUS

F

= 0,0637

FIG. 10

C0S-00MP0NENT

OF

YAWING MOMENT

VERSUS

j.', F

= 0.0637

-0.3 -0.2 -0.1 -0.01 -0.02

-O--- h/T = 1.2

h/T 1.5 -0fl3

-ir--X

hIT= 2.0

-D--- h/T

-0.04

FIG. 9

SIN-COMPONENT OF LATERAL FORCE

10

SIN-COMPONENT OF LATERAL FORCE VERSUS

FIG. 12

COS-COMPONENT OF LATERAL FORCE VERSUS

t

AMT\ l

-PATH DURING 35 - DEGREES

_PoRT

_TURNING1

' V

= 7.7 KN

Ç\j , J '1

Y0[km}

fltTi

*

TRIAL

PREDICTION

/ *

-:

-.

X0

{kml

t

t

FIc.

1b

SPEED REDUCTION DURING 35

- DEGREES PORT TURNING)

= W)

VS = 7.7 KN

*

TRIAL

a

PREDICTION

* a I a a P a a

if:t7i. Iii Vi

2F1I7). 17'1

t[secl

a

I

P i7H VU7 ;; 17ì IJi Iii

!jÍ fJii7

r

[deg/sec]

,

t[sec]

I _t 7ll7c

LjÌt.Vit7i

\lc

\

I i

B(LVIVÌ

I

12

kUL

I I i 1

____

l[tl1,fl1

I

2U

A

f

L t *

TRIAL

PREDICTION

-4 'i

qi

[deg]

E)

zj

FIG. 13d

COURSE CHANGE DURING 35 - DEGREES PORT TURN INGJ

= ,

V

= 77 KN

V. íc1

t[sec]

( j

I Vi

I i f -s *

TRIAL

PREDICTION

p

Ç\J

X0

[km]

*

TRIAL

PREDICTION

w

Y

_{1km]__-1}

i .

-1.2

I

\-4-»,,/

i I i -.

(3)

FIG. 114

SPEED REDUCTION DURING 35-DEGREES PORT TURNING,

= 1.5, V

= 6.8 KN

*

TRIAL

PREDICTION

-p , p p

j

17! 1juli t::! Iii. V

i

7IVi

i

(Ji

Ì(/tI

I

Ç\J

r

[deg/sec]

s

t[sec]

TLlJ11

i

\

t

¡ V1 J E VU?)

12L

J [11f?)

i

,[11 VU?)

2

- p p p *

TRIAL

PREDICTION

-I

i

fdeg]

- -H

FIG, 1L

COURSE CHANGE DURING 35-DEGREES PORT TURNING,

= 1.5, VS =

6,8 KN

t[sec]

(i

.

L r j 1(1 i i r

I

V' V: r f Vi Vi

2

-J

*

TRIAL

PREDICTION

I 1G.

15a

PATH DURING 35-DEGREES PORT TURNING,

= 1.2, V

= 7 KN

X0

[km]

*

TRIAL

PREDICTION

--*

N

-it

t

FIG.

15b

SPEED REDUCTION DURING

35-DEGREES PORT TURNING,

= 1,2,

vs = 7 KN

1. .

'.LJ1

i

v.

4

,' V V . V

-

_t[sec}

*

TRIAL

PREDICTION

p p e I I '1 I 'I

! A.

1Tt

E)

Ç\J

E)

[deg/sec]

35-DEGREES PORT TURNING,

_{= 1,2, vs = 7}

_KN

t [sec]

Ti I 1/i Jj LL I-;. VI Vi I _I 'i .. VI VI _1.

---r

I I (Û (fiVI

i {

i

I I Vi VI (Ti _{2 C} a

*

TRIAL

---PREDICTION

FIG. 15d

COURSE CHANGE DURING 35-DEGREES PORT TURNING,

= 1.2, vs = 7 KN

t[sec]

viVI

I

lkt

_.___-'__ b b

2

*

TRIAL

PREDICTION

1

4i

[deg]

_(.

(deg]

Ç\J

3

3

3

FIG,

16a

_{COURSE CHANGE OF 20-20 ZIG-ZAG MANOEUVRE,}

₌

°°

VS =

' KN

-A

I

A * $ 4 ) A A A

-1LH.

ft

i 1(1ì i

11(1

i a

12[1L[ÌWI

i

i

A i

2

*

TRIAL

PREDICTION

A s A

r

[deg ¡sec]

FIG. 16b

YAW RATE CHANGE OF 20-20 ZIG-ZAG MANOEUVRE1

₌ V

= 7.3 KN

4

lì

lí

y I 4/

I

b * b 2J1l

18

/

/

f i p

t,

íli I

\

I

\

4 I j X I

î

4 k * I i I

U

b V1TJ b z

2

t

*

TRIAL

PREDICTION

\

I

b

I,

tO

b

f.

r

FIG.

17a

COURSE CHANGE OF 20-20 ZIG-LAG MANOEUVRE,

_{= 1,5, vs = 7.3}

KN J'

/

\

\

/

/

/

V

H.

(ft

1

/

/

l. V«

t [sec]

*

TRIAL

PREDICTION

\.

,/

r

[deg /sec]

tf)

çr

FIG. 17b

YAE RATE CHANGE OF 2U-20 ZIG-ZAG MANOEUVRE,

_{p = 15}

=

7.3

KN y

/

/

/

/

N

i

\

. 1 i

i.

N

I

I

/

7

4 :i.

/

i

i

i '

t

'

j

1/

'l

/

p

[sec]

*

TRIAL

---PREDICTION

u

I,

G

9.Jz

[deg]

G

G

u

G

ç\J

G

FIGS

COURSE CHANGE OF 20-20 ZIG-ZAG MANOEUVRE,

G

G

G

u

G

G

G

a

G

G

G

u

G

L1LJ

A

p -

-t[sec]

-I 4 a i p I r i

L

p

-

---PREDICTION

*

TRIAL

p

G

G

a

G

G

a

FIG, 18b

YAW RATE CHANGE OF 20-20 ZIG-ZAG MANOEUVRE,

= 1,2, V

= 7.3 KN

I

a

I.

¡

I

I.

I.

\

"-t[sec]

-iI

\

\

i

II

I

fi

J

I.

-'

I

il

J I

l2J1IVJLTÌ

I

I I

2

-

---

*

TRIAL

PREDICTION

G

r

a

[deg ¡sec]

t

_G

Ç'sJ a

G

a

FIG. 1Y

SPIRAL CURVE FOR DIFFERENT DEPTH CONDITIONS

((i(U

Q

¿

¿

SR

TRIAL

h/T=oo

a U

[deg]

n

--2V1

I I VIVI n A -a-

_dl

,[1I[1J

I

2fl..

I IÛLU

A

O

_oh/T=co

¿

=

1.5

=.2

I

PREDICTION